EPA-600/1-77-045
September 1977
Environmental Health Effects Research Series
HIGH SENSITIVITY FOURIER TRANSFORM NMR
Intermolecular Interactions Between
Environmental Toxic Substances
and Biological Macromolecules
Health Effects Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL HEALTH EFFECTS RE-
SEARCH series. This series describes projects and studies relating to the toler-
ances of man for unhealthful substances or conditions. This work is generally
assessed from a medical viewpoint, including physiological or psychological
studies. In addition to toxicology and other medical specialities, study areas in-
clude biojnedical instrumentation and health research techniques utilizing ani-
mals — but always with intended application to human health measures.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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x/
EPA-600/1-77-045
September 1977
HIGH SENSITIVITY FOURIER TRANSFORM NMR
Intermolecular Interactions Between
Environmental Toxic Substances and Biological Macromolecules
George C. Levy
Department of Chemistry
The Florida State University
Tallahassee, Florida, 32306
Grant 803095
Project Officer
Nancy K. Wilson
Environmental Toxicology Division
Health Effects Research Laboratory
Research Triangle Park, North Carolina, 27711
U.S. ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
HEALTH EFFECTS RESEARCH LABORATORY
RESEARCH TRIANGLE PARK, N.C. 27711
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DISCLAIMER
This report has been reviewed by the Health Effects Research
Laboratory, U.S. Environmental Protection Agency, and approved
for publication. Approval does not signify that the contents
necessarity reflect the views and policies of the U.S. Environ-
mental Protection Agency, nor does mention of trade names or
commercial products constitute endorsement or recommendation
for use.. ,
(ii)
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FOREWORD
The many benefits of our modern, developing, industrial
society are accompanied by certain hazards. Careful assessment
of the relative risk of existing and new man-made environmental
hazards is necessary for the establishment of sound regulatory
policy. These regulations serve to enhance the quality of our
environment in order to promote the public health and welfare
and the productive capacity of our Nation's population.
The Health Effects Research Laboratory, Research Triangle
Park conducts a coordinated environmental health research~pvogram
in toxicology, epidemiology, and clinical studies using human
volunteer subjects. These studies address problems in air pollu-
tion, non-ionizing radiation, environmental carcinogenesis and
the toxicology of pesticides as well as other chemical pollutants.
The Laboratory develops and revises air quality criteria docu- .
ments on pollutants for which national ambient air quality
standards exist or are proposed, provides the data for registra-
tion of new pesticides or proposed suspension of those already
in use, conducts research on hazardous and toxic materials, and
is preparing the health basis for non-ionizing radiation standards.
Direct support to the regulatory function of the Agency is provided
in the form of expert testimony and preparation of affiddvits as
well as expert advice to the Administrator to assure the adequacy
of health care and surveillance of persons having sufferedimmi-
nent and substantial endangerment of their health.
This report represents a research effort to extend and
improve analytical methodology for the examination of interac-
tions of organic pesticides and other toxic substances in environ-
mental systems. The results of several studies of the basic.
molecular phenomena underlying the toxic effects of these sub-
stances are included in the report.
~
. j
hn . K~, M.D.
Director,
Health Effects Research Laboratory
(iii)
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ABSTRACT
This project explored the feasibility of developing new
techniques for evaluation of the effects of environmental toxic
materials on complex biopolymer systems using high sensitivity
Fourier transform nuclear magnetic resonance (nmr) spectroscopy.
Commercial instrumentation available in 1974-75 did not possess
adequate sensitivity, and thus one goal of this project was to
increase spectral sensitivity, especially for 13C and other
nuclides having low magnetogyric ratios. Initially, modifica-
tions to an existing Bruker HX-270 spectrometer prov~ded moderate
improvements in sensitivity for 13C and a substantial sensitivity
increase for 15N observation. During the second (last) year of
this grant, a new instrument design was initiated. While the
latter nmr spectrometer was not completed during the period of
this grant, it was clear that the limits of 13C, 15N, and metal
nuclide sensitivity could be extended by at least an order of
magnitude over that available on typical spectrometers. Improve-
ments were also made in ~echniques required to obtain spin-relax-
ation and other nmr data.
Several studies were begun to elucidate the nature of chloro-
phenol interactions in liquids, and when incorporated into lecithin
bilayer membrane models. In the latter case pentachlor9phenol was
observed to bind to the C-2, C-3 carbon region of the fatty acid
alkyl chains, increasing the mobility of these chain fragments
considerably. Evaluation of chlorophenol interactions in solution
showed the presence of both inter and intra-molecular hydrogen
bonding, when chlorines were substituted ortho to the hydroxyl
groups.
Variable frequency 13C spin lattice relaxation time (Tl)
measurements were used to probe cooperativity of molecular chain
dyaamics in some simple molecules and in two complex synthetic
polymers. A new theoretical modification involving a non-exponen-
tial autocorrelation function a~d also allowing for multiple
independent internal rotations, allowed effective analysis of a
large experimental data "set. Application of this new approach to
the study of correlated or cooperative motional dynamics in
complicated biosystems is underway. It is hoped that new insight
will be obtained into the organization of biopolymers and possible
disruptions of this organization by interaction with toxic materials.
A short project demonstrated that high field 13C nmr spectros-
copy can be used to analyze complex mixtures of polychlorinated
(iv)
-------
biphenyls rapidly without prior separation. Analyses so obtained
are not directly competitive with separation analysis techniques.
However, they do serve well for screening and semi-quantitative
identification.
This report was submitted in fulfillment of Grant No. 803095
by the Florida State University under the sponsorship of the U.S.
Environmental Protection Agency. This report covers the period
Oct. 2, 1974 to Oct. 1, 1976 and work was completed April 30, 1977.
(v)
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CONTENTS
Disclaimer. . . . . . . . . . . . . . ." . . . . . . . . . .
Foreword .........................
Abstract. . . . . . . . . . . . . . . . . . . . . . . . .
Co n t en t s .........................
List of Abbreviations and Symbols. . . . . . . . . . . . .
Acknowledgement. . . . . . . . . . . . . . . . . . . . . .
Introduction. .. . . . . . . . . . . . . . . . . . . . . . .
A. NMR SENSITIVITY IMPROVEMENT AND DESIGN OF MORE. . . .
EFFICIENT Tl EXPERIMENTS. . . . . . . . . . . . . . .
AI. Improvements of Bruker HX~270 High Field.. . . . .
Spectrome.ter ." . . . . . . . . . . . . . . . . . .
A2. Seminole Project. . . . . . . . . . . . . . . . .
A3. Time Saving in 13C Spin-Lattice Relaxation
Measurements by Inversion-Recovery. A Fast
Inversion-Recovery FT NMR Pulse Scheme. . . . . .
A4. Optimal Use of a Non-Linear Three Parameter
Fitting Procedure for Analyzing Inversion-
Recovery Measurements of Spin-Lattice.
Relaxation Times. . . . . . . . . . . . 13' . . .
A5. Use of a Modified DEFT Pulse Sequence in C
NMR: Dynamic Range Improvement for Relaxation.
Experiments and Dynamic NMR Measurements at
~ High Resolution. . . . . . . . . . . . . . . . .
B. INTERMOLECULAR INTERACTIONS. . . . . . ... . . . . .
Bl. Chlorophenol Effects on Model Membranes: ESR Study
B2. Chlorophenol Effects on Model Membranes: 13C
NMR Study. . . . . . . ... . . . . . . . . . . ..
B3~ Variable Field NMR Experiments on Model Membranes
B4. Variable Field 13C Tl Studies of Complex Systems
C. INTERACTIONS OF CHLORINATED PHENOLS: HYDROGEN BONDING
D. ANALYSIS OF POLYCHLORINATED BIPHENYLS BY CARBON-13
NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY . . . . . . .
E. CHAIN MOLECULAR DYNAMffCSIN COMPLEX MOLECULES. . . . .
CONCLUSIONS. . . . . . . . . .. . . . . . . . . . . . .
( vi)
ii
iii
iv
vi
vii
lX
1
2
2
5
8
12
17
30
30
32
35
36
38
39
44
83
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ABBREVIATIONS
LIST OF ABBREVIATIONS AND SYMBOLS
cal
CMR
Cr(acac)3
DCP
DEFT
DNMR
DPL
EPR
ESR
FID - -
FIRFT
FT
glc
IRFT
NOE
NTCFT
PBMA
PCB
PCP
PHMA
ppm
PSFT
quad
rf
S:N
SRFT
SEMINOLE
TCP
WLL
-- calories
-- carbon-13 Nuclear Magnetic Resonance
-- trisacetylacetonatochromium
-- dichlorophenol
-- "Driven Equilibrium Fourier Transform"
-- Dynamic nmr
-- Dipalmitoyl Phosphatidyl choline
-- Electron Paramagnetic Resonance
-- Electron Spin Resonance
--:Free Induction Decay
-- Fast Inversion Recovery Fourier Transform Pulse
Sequence
-- Fourier transform
-- gas-liquid chromatography
-- Inversion-recovery Fourier Transform Pulse Sequence
-- Nuclear Overhauser Effect
-- a software package for the Nicolet 1080 minicomputer
series
-- Poly(n-butyl methacrylate)
-- polychlorinated biphenyl
-- pentachlorophenol
-- PolyCn-hexyl methacrylate)
-- parts per million
-- progressive saturation Fourier Transform pulse
sequence
-- quadrature
-- Radio Frequency
-- Signal to Noise
-- Saturation-recovery Fourier Transf0rm pulse sequence
-- Sensitivity Enhanced Modular Instrument for Nuclei
of Low Enrichment
-- tetra chlorophenol
-- collectively the motional dynamics theories of
Wallach, Levine & London
C v i i)
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SYMBOLS
Da,...Di
Do
Ea
y
G
G(TC)
h
Ho
Ji(w)
JH-H
A
-+- -+-
MA' MB' MA' MB
Mz
Mtr Mtr
A' B
11
NTI
p
S
T
S
CD
T
TO' Tc
TD
Tg, Tint
Tmax
TI
TIe
TIp
T2
W
WA' wB
-- rotational diffusion constants
-- isotopic rotational diffusion
-- energy of activation
-- gyromagneticratio
-- Gauss
-- probability density function
-- Planck's constant
constant
-- the laboratory magnetic field
-- spectral density functions
-- Spin-Spin Coupling constant (IH-IH)
-- chemical exchanged rate
-- magnetizations
-- magnetization in the (z) longitudinal direction
-- transverse magnetic components
-- 11 = NOEF = NOE-I NOE-factor
-- total # of protons attached to the carbon times
the Tl-:~f that carbon
-- characteristic distribution width (log-X2
distribution
-- amplitude of a line after some waiting time T
-- amplitude of a line at thermal equilibrium
-- waiting time between pulses
-- correlation time for molecular tumbling
-- correlation time of conformation transitions
-- correlation time for internal rotation
-- longest T
Spin Lattice Relaxation Time
-- electron-induced spin-lattice relaxation
-- spin lattice relaxation time in the rotating
frame
-- spin-spin relaxation time
-- frequency in rad sec-l
-- Larmor frequencies of nucleus
A and B
(viii)
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ACKNOWLEDGMENTS
The author acknowledges the work of Drs~ E. Edlund, T. Holak,
1. R. Peat, J. Kowalewskl., D. Axelson, and J. Hochmann, as well
as Ms. Mary Pat Cordes, Mr. James M. Hewitt, and Mr. Robert Schwartz.
The author is particularly grateful to Dr. Nancy K. Wilson and the
staff of the Health Effects Research Laboratory for their help and
encouragement.
(.ix).
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INTRODUCTION
The various techniques of Fourier transform (FT) nuclear
magnetic resonance (nmr) spectroscopyl which have been developed
in recent years, have become a powerful analytical tool for the
elucidation of structure and chemistry in complex molecular
systems. Possible applications2 to environmentally significant
problems have expanded at a rate proportional to improvements in
nmr methodology and instrumentation. .
The objectives of this research project were twofold. The
first set of objectives sought to extend nmr spectroscopy sensi-
tivity limits in order to make this technique more emenable to
studies of complicated biosystems. The second set of objectives
included initiation of a group of studies of environmental toxic
materials and their chemical interactions with biosystBms. Inclu-
ded in this work was evaluation of the interactions of chlorinated
hydrocarbon, chlorophenol pesticides, .and toxic heavy metals with
phospholipid model cell membrane systems. In addition, studies
of biological conformations were initiated for several peptide
hormone systems (in collaboration with the National Research
Council of Canada, Drs. I. C. P. Smith and R. Deslauriers).
While several of the initial objectives of this 2-year pro-
ject were not fully realized, several unforeseen major develop-
ments occurred. These included:
(1) Initial design and construction stages of a new ultra-
high sensitivity FT nmr spectrometer system, designed to extend
present day sensitivitl limits for environmentally significant
studies of 13C, 15N, 3 P, and other nuclides under conditions
approaching natural environmental sampling.
(2) NMR Studies of the chemically unique and biologically
significant nitrogen nucleus 15N at its natural isotopic abundance.
This work has set boundary conditions for future applications.
Included was development of 15N nmr spin-labeling techniques which
may become capable of resolving questions of biopolymer-toxin
interactions for a class of toxins including several heavy metals
(e.g., Mn, Cu, Fe, and lanthanide and actinide metals, etc.) as
well as stable organic free radicals.
(3) The demonstration in our laboratory that 13C Tl
obtained at more than one magnetic field can be a unique
sensitive prob~,of transient higher structure in complex
data
and
molecular
(l)Shaw, "Fourier Transform N.M.R. Spectroscopy", Elsevier (New
York) 1976.
(2)R. Haque and F. J. Biros, eds. "Mass Spectrometpy!:gnd NMR Spec-
troscopy in Pesticide Chemistry", Plenum (New York) 1974.
1
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systems. Initial experiments indicate promise for application to
studies of interrupted biofunction induced by toxin chemical
interactions.
A.
NMR SENSITIVITY IMPROVEMENT AND DESIGN OF MORE EFFICIENT
!l EXPERIMENTS
_Al. Improvements of Bruker HX-270 High Field Spectrometer.
. 13
When our Bruker HX-270 spectrometer was installed we had C
and 15N sensitivity which was only 25%-30% better than that avail-
able on a 1973 stock Varian XL-IOO spectrometer. Combining the
various methods discussed immediately below, we have been able to
obtain a factor of >3 improvement in 13C and 15N sensitivity.
It is important to note that these improvements are stated
in terms of signal-to-noise (S:N), the decrease in time require-
mentis a factor of 10 for 13C and over 50 for 15N. Thus we have
been able to perform experiments that are impractical on typical
FT nmr systems. One application for our improved. sensi tivi ty is
the 13C Tl study of model membranes (Section B) underway. Another
application is the use of 15N nmr for spin-labeling experiments.
Here we are beginning to take advantage of the chemical specificity
of nitrogen to probe interactions of paramagnetic toxic heavy
metals with biological molecules.
13C ...
Table 1 summarizes the sensltlvlty of our Bruker HX-270
as developments were added.
TABLE 1.
FSU BRUKER HX-270 CHRONOLOGY
decoupler
quadrature detection
larger sample probes
larger sample probes
RESULTING S:Na
75CIOmm tubes)
90CIOmm tubes)
120(10mm tubes)b
225(13mm tubes)C
~300(15mm tubes)d
YEAR
1973
1974
1975
1975
1976
IMPROVEMENT
a
Standard test 50% ethyl
window ,ca. O. 8 Hz line
b2ml required;
c3.5ml required;
d 5 . Oml required.
benzene, single 90° pulse, 15kHz spectral
broadening applied;
2
-------
The actual S:N numbers in Table 1 are not relevant. The
HX-270 spectrometer does not achieve the best results on a narrow
,line spectrum such as that for ethyl benzene, due to decoupler
and lineshape limitations that have never been fully analyzed.
A sample which we use for evaluation of sensitivity is 1.OM sucrose
in H20/D20. ~ typical single pulse spectrum of 1.OM sucrose is
given in Figure 1. The observed S:N is 25:1.
F. 2 h . 1 15N ...
19ure sows a typlca sensltlvlty check.
shown was obtained with' a single 90° pulse.
The spectrum
FIGURE 1.
13C Sensitivity of the FSU HX-270 (15 mm sample).
27.36MHz (63.4kG)
NATURAL ABUNDANCE 15N NMR
90% FORMAMIDE, SINGLE PULSE
(15mm TUBE, QUAD DETECTION)
S:N ~ 40:1 (MARCH, 1976)
(70: 1 SHOWfl)
2kHz SPECTRAL WIDTH
1kHz SHOWN
FIGURE 2.
15N Sensitivity of the HX-270, 15 mm sample.
3
-------
Figure 3 shows that 15N Tl's can be determined efficiently
on our HX~270 spectrometer. This entire Tl and nuclear over-
house effect (NOE) experiment (shown for a neat sample in a 13mm
tube) was run in less than 1 hour. This experiment simultaneously
measures Tl's and NOE's. (In section A3 we will show further
efficiency improvements in 15N Tl measurements).
One final 15N spectrum is shown below (Figure 4). This is a
natural abundance coupled spectrum of formamide.
DYNAMIC NOE T1 MEASUREMENT
15N (NATURAL ABUNDANCE) ETHANOLAMINE, 27.4MHz
11.J............ ':2 1.6 2.0 2.5 3.0 3.5 4.0 5.0 60 '300'
000. 01 04 08 1111111- .
"-
FIGURE 3.
DynamicNOE Tl and NOE Measurement:
neat ethanolamine.
15N, 27. 4 MHz,
RJRMAMCE: !i5N NATIJRAI.. A8UN().1,\tEl ABC X SPECm..M
127.4 MHz. 36 PULse:si GATED 0Ct:0..PI.Ni
""'
.-J
!-...)
'J".-142 Hz
. '.c'B8Hz
'''---92Hz
FIGURE 4.
15
UndecoupledN Spectrum of Formamide, 36 scans,
gated decoupling.
4
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A2. Seminole Prdject.
In our EPA proposal we planned to up-date and optimize our
HFX-90 spectrometer. For several reasons we decided to abandon
that course. The HFX-90 magnet and console are now 11 years old
and are showing signs of wear with respect to reliability.
Furthermore, we realized that our narrow gap 21kG magnet
would never be sufficient for sensitivity improvements beyond
15mm sample tubes. Thus, after modifying the HFX-90 as much as.
possible J{..t;o include quadrature detection), we embarked on design and
construction of an entirely new spectrometer, names tne SEMINOLE
[Sensitivity Enhanced Modular Instrument fo~ Nuci~i Of Low Enrich-
ment]. The SEMINOLE .will be a large sample,-intermediate field
superconducting solenoid-based spectrometer, designed to observe
any nuclide having a magnetogyric ratio below that of 205Tl.
The SEMINOLE spectrometer will be ideally suited for a number
of environmental studies where large samples are available:
13C 1. f . d,. 1
1. Ana YS1S 0 organlc compoun s ln natura and processed
drinking waters. .
2. Speciation of phosphorus in interstitial and
3. Examination of interactions of environmenl~l
systems using 13C, metal nuclei nmr, and N
(with enrichment).
other waters.
toxins with bio-
spectroscopy
Other applications of course are possible.
given in Section B.
Some examples are
Progress on the SEMINOLE has been fairly good over the past
six months.
We are currently operating with 20, 25, and 30mm sample tubes
at a field of 21kG (22.63MHz for 13C). The final operating field
for the SEMINOLE will be 35kG, corresponding to 150MHz for IH. We
will initiate operation at 35kG in early May 1977.*
Some early 21kG test spectra for the SEMINOLE are shown below.
The line-shape and resolution of the initial solenoid, while
adequate for 25mm operation, was inadequate with 30mm sample tubes.
The result was lower sensitivity than expected. Using our own
22.6MHz preamplifier and temporary 2MHz i.f. quad detection
receiver we maintained 13C sensitivity of ca. 150:1 on 50% ethyl
benzene versus 300 to 500:1 as would be deSIrable prior to probe
re-design.
(*)
After set-up of a replacement magnet by Bruker.
SEMINOLE magnet, while performing reasonably well,
ifications. . 5
The initial
had not met spec-
-------
Figure 5 shows a single pulse spectrum for CS2 with 0.4Hz
resolution in a 30mm sample tube. Spinning sidebands are 3-6%
generally.
Figure 6 shows a30mm sample of dioxane with 3 watts of wide-
band lH decoupling. The resulting resolution of 0.8Hz with only
2% spinning sidebands is rather difficult to achieve on our
current magnet.
CS2
O.4Hz
RESOLUTION
30mm TUBE
FIGURE 5.
30 mm Sample of CS2 showing resolution of 0.4 Hz.
DIOXANE (75%)
1 PULSE
O.8Hz RESOLUTION
2'1 SSB
30nm TUBE
FIGURE 6.
30 mm Sample of dioxane showing 0.8 Hz resolution.
6
-------
One outstanding feature of the SEMINOLE is its HI rf homo-
geneity for intermediate and large sized samples. Figure 7 shows
an excellent signal for a 15mm x 15mm cylindrical sample. In 30mm
samples we are still able to achieve ratios of >10:1 for 90° versus
180° pulses. This contrasts with ~3 or 4:1 for only a 10mm sample
in a Bruker HX-270 spectrometer."
" 1- X 15nm sample
RF HOMOGENEITY TEST
75% DIOXANE
1 PULSE
NO DECOUPLING
2Hz LINEBROADENING
30mm TUBE
900 "
180°
~~it~,~~
I. ".
FIGURE 7. Rf Homogeneity Test.
90° and 180° pulse response from
a 15 mm 415 mm cylindrical sample.
FIGURE 8. Single 90° pulse on
75% dioxane, undecoupled, 30 mm
sample. .
One other SEMINOLE test spectrum is shown in Figure 8. This
is a single pulse coupled (no NOE) spectrum of 75% dioxane. The
sensitivity here is not poor but we feel that we can do consider-
ably better with improvements now underway in the preamplifier
and probe. The new solenoid and operation at 35kG should give an
improvement a factor of ca. 3 in signal-to-noise for small mole-
cules.
In considering the design of the SEMINOLE we are attempting
to partially circumvent two limitations. of the highest sensitivity
spectrometer developed to date, the Bruker WH-180:
7
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1.
Decreased lH decoupling
l80MHz
High field spin-lattice
biopolymer studies.
efficiency for large samples at
2.
relaxation disadvantages for
The somewhat lower final operating field of the SEMINOLE (relative
to the WH-180) should prove to be a good compromise for biopolymer
work while retaining most of the inherent sensitivity of high field
operation. We are constructing an especially powerful lH decoupler
(80 watts, up to 20gauss for iarge sample tubes)
A3. Time Saving in llC Spin~Lattice Relaxation Measurements
by Tnver.sion-Recovery.. A Fast TnVer.sion-Rec.oVery FT NMR
Pulse Scheme.
Measurements of spin-lattice relaxation times in multiline
NMR spectra are often achieved by the inversion-recovery method
combined with Fourier transform (IRFT).3 This method is based on
the well-known pulse sequence: [1800-T-900(FID)-T]. T is a time
set to 5(Tl)max' where (Tl)max is the longest spin-~attice relax-
ation time to be measured. The free induction decays (FID's) are
stored and then Fourier transformed leading to a spectrum which
has partially relaxed for a time, T. If we call S1 the amplitude
of a line in such a spectrum and Soo the correspondlng amplitude
at thermal equilibrium, the relaxation time Tl can be deduced from
the following equation: .
S = S [1 - 2 exp(-T/T1)].
T 00
(1)
The applicability of this method is limited by the duration
of the experiment which depends on the number of Bcans, n, and on
the waiting time, T. This difficulty is particularly severe for
low sensitivity nuclei wuch as l3C (or l5N) because these nuclei
may have long relaxation times and because extensive time aver-
aging may be required even to obtain a single spectrum. The
problem becomes less acute with methods based on 90° pulse
sequences which do not utilize a long waiting time (so-called
saturation-recovery sequences, SRFT). These sequences can be
obtained using a burst of 90° pulses4 or by field inhomogeneity
gradients. 5 A similar result to eliminate magnetization [cause
. saturation] is more simply obtained by progressive saturation (PSFT);
(3)R. L. Vold, J. S. Waugh, M. P. Klein, and D. E. Phelps, J. Chem.
rh)'s.,~, 3831 (1968). .
4 - .
J. L. Markley, W. H. Horsley, and M. P. Klein, J. Chem. Phys.,
~, 3604 (1971).
(5)G. G. McDonald d J S L h. J J M R 9
an . . eig, r., . agn. esonance,_,
358, (1973).
8
-------
as proposed by Freeman and Hill.6,7 These authors showed that
sequences of the type: [90-(FID)-TJn lead to spectra obeying
Eq. ( 2 ) .
ST = Soo[l - exp(-T/T1J.
(2)
However these three rapid methods entail a loss of dynamic
range (or sensitivity) of 50% with respect to inversion recovery.
Furthermore, they require minor instrumental adaptations. The
PSFT method is also not appropriate for short relaxation time~
because data acquisition and resolution requirements place a
lower limit on T.
We wish to show here that inversion-recovery with an arbitrary
short waiting time is comparable to the SRFT and PSFT methods in
speed, and that such a sequence gives optimum dynamic range with
respect to experimental time for each individual resonance line.
(For a se~of Tl spectra, dynamic range is essentially equivalent
-to sensitivity6,7,B). Furthermore, this new sequence does not
share many of the disadvantage~_of theSRFT and PSFT sequences.
In this case we observe three "short" Tl's and one "lopg" Tl.
The FIRFT sequence gains an advantage over the SRFT and IRFT
methods when there is a range of Tl's to be determined, including
Tl's ~ 10 sec. When all Tl's to be determined in a spectrum are
very long and approximately equal, then the FIRFT and SRFT sequence
are comparable in efficiency.
COMPARISON
80%
TABLE 2.
OF IRFT AND FIRFT EXPERIMENTS.
(w/v) PHENOL IN D20a
Tl(seconds)b
CARBON IRFTc FIRFTd
C-l 29.5 28.8
C-2 4.2 4.2
C-3 4.1 4.0
C-4 3.1 3.0
(6 )R.
(7)R.
2, 82
"(8)G.
Freeman and H. D. W. Hill, J. Chern. Phys., 54, 3367 (1971).
Freeman, H. D. W. Hill and R. Kaptein, J. Magn. Resonance,
(1972).
C. Levy and I. R. Peat, J. Magn. Resonance, 18, 500 (1975).
9
-------
aTl'S determined at 67.9MHz and 40°C; sample not degassed.
bThe accuracy of these Tl's is !5% (2 standard deviations).
c(T-1800-T-900)5: T=5 sec; T values, 0.05, 0.5 1.0, 1.5, 2.0,
3.0, 4.0, 5.0, 10.0,20.0, 30.0, 40.0, 160.0~
d(T-1800-T-900)5: T=160 sec; same T values.
2.5,
We called this method9 fast inversion recovery (FIRFT) by
contrast to standard inversion recovery (IRFT). The sequence
utilizes a waiting time T much smaller than 5(Tl)max but suffi-
cient to allow the decay of transverse magnetizatlon before the
next 180° pulse. This is actually achieved in a short time for
carbon-13 measurements with broad-band proton irradiation. The.
successive FID's have amplitudes equal to:
~C".[l
00
- 2 exp(-T/Tl)]; Soo[l - (2 - El) exp(-T/Tl)];...;
Soo[l - (2 - El)exP(-T/Tl)]' where El = exp(-T/Tl).
The accumulated signal S is consequently related to:
T
(3)
S :a S [1 - a exp(-T/Tl)]
T 00
(4)
with
a =(2 - EIO[(n - l)/n)].
(5)
If n is large or if the first FID is deleted S reduces to:
T
ST = Soo[l - (2 - El) exp(-T/Tl)]
(6)
and the usual logarithmic plot* allows the determination of Tl:
In(S - S )/S ) = In a - T/TI. (7)
00 T 00
T values are chosen exactly as in a conventional IRFT experiment.
Of course, the measur~ment of S requires that one spectrum be
obtained where T is ~5(Ti)max.00 If exponential fits are used, even
this requirement is ~aived.lsee section A4).
Note from Eq. (6) that instead of a dynamic range of 2 as in
the standard IRFT sequence, the FIRFT sequence has a dynamic range
of (2 - El)' where El
-------
of the experiment is optimized for each resonance line since El
is very small when the waiting period, T,is longer than or
comparable to TI. When T«Tl' El approaches 1 and the dynamic
range is reducea to that of the SRFT and PSFT methods.
Thus the dynamic range will vary from a little over 1 (for
very long Tl's) to exactly 2 (for very short Tl's) for different
nuclei during a single experiment, whose total experimental time
can be up to an order of magnitude shorter than with the standard
IRFT sequence. The exact time saved depends on the discretionary
value of T in both cases (e.g., 3 to 5 times Tl in IRFT; 1 to ca.
10 sec in FIRFT) and on the number of scans, S1nce the IRFT does
not discard the first FID.
Figure 9 and Table 2 show the results of conventional IRFT
and FIRFT experiments on a solution of 80% (w/v) phenol inD20.
The factor of 7 in time savings for the FIRFT experiment (see.
Table 2) is,of course,partly offset by the increase in dynamic
range of the IRFT experiment. (Note that for the protonated
carbons the FIRFT dynamic range is nearly as large as in the con-
ventional IRFT experiment). Also, in the IRFT scheme a reduction
in the waiting time, T, to 4(Tl) would lower theFIRFT time
. max
advantage by ca. 20%.
(a) FWT DPENMENT
c-I
meta
ortIIo
ilia cONVOfTl()NAL IRFT EXPERIMENT
- .-
),.,
..--
- - _0 -.-..... ----
-
FIGURE 9. Comparison of IRFT and FIRFT pulse sequences for a
sample of phenol in D20. 11
-------
Optimal Useofa::-.NO'n:-::LinearThree Parameter Fitting
Procedure for Analyzing Inversion-Recovery Measurements
. of Spin-Lattice Relaxation Times.
In recent years the methodology for accurate measurements of
nuclear spin-lattice relaxation times (Tl's) has occupied the at-
tention of many authors. In particular, choices of pulse se~ ~~.~~
quencelV,ll, delay timesll,9 and data reduction methods12-14 have
been discussed extensively.
A4.
In an earlier communication from this laboratory~ we advo-
cated use of the inversion-recovery method with a short waiting
time, T, between pulse sequences (fast inversion-recovery, FIRFT).
This method has the advantage of speed while also retaining the
advantage of maximum available or optimized dynamic range. As
has been pointed out12-14, the determination of Tl's can further
be shortened by omitting the time consuming measurement of the
equilibrium magnetization corresponding to t > 5Tl in the (1800-
T-99°-T)~ s~quence. In order to obtain this additional ti~e
sav1ng, 1t 1S, however, necessary to replace the usual sem1-
logarithmic plot method of data reduction by a non-linear least
squares fitting procedure. For an ideal experimental case, the
signal intensities may be fitted to a two-parameter expression:
SeT) = A[1-2(1-exp(-T/T1»]exp(-T/T1)
(8)
'where A is the equilibrium magnetization and T is the waiting
time between the 180~T-9~ sequences. Use of equation (8) has the
disadvantage of being highly sensitive to systematic errors such
as misadjusted pulse angles, frequency offset between the carrier
frequency, the resonance line positions and rf inhomogeneity.
Sass and Ziessow14 have recently suggested that a more flexible
expression to which the measured signal intensities can be fitted
should contain three parameters\ it should be of the type:
SeT) = A + B exp(-T/T1)
(9)
where A, Band Tl are adjustable parameters. This procedure does
not overparameterize the data. In fact, the usual method using
semi-logarithmic piots contains three "independent" parameters:
(10) .
G. C. Levy and I. R. Peat, J. Magn. Resonance, 18, 500 (1975)
and references therein. .
(11) ..
R. K. Harr1s and R. H. Newman, J. Magn. Resonance, ~,449 (1976).
(12)D. L. DeFontaine,D. K. Ross and B. Ternai, J. Magn~ReSonance,
18, 276 (1975).
TI3) .
T. K~ Keipert and D. W. Marquardt, J. Magn. Resonance, ~,
lel (1976). .
(14)M. Sass and D. Ziess6w, J.
Magn. Resonance ,25, 263 (1977).
12
-------
(1) the equilibrium magnetization (which is fixed and in general
rather accurately determined), (2) the slope and (3) the intercept
of the best straight line. Deviations from experimental ideality
in semilogarithmic plots show up first in the intercept of the
line. Since Tl is calculated from the slope of this line and not
the intercept, Tl is relatively insensitive to pulse and mild
frequency offset defects in IRFTIO and FIRFT9 experiments. Sass
and Ziessow14 have shown that the non-linear three parameter fit
procedure is capable of producing reliable data in cases of mis-
adjusted pulses and for large frequency offsets.
In this discussion we present a simple and empirical attempt
to find the minimal acceptable value for the longest T(T ) used
in FIRFT experiments. We also discuss some additional r~~~fications
of the use of exponenti~l fitting procedures for Tl determination.
The results of three experiments using different waiting times,
T, are presented in Table 3. The error limits quoted in the table
are standard deviations. 15 The most important feature of these
results is the great increase of the uncertainty (measured by
large standard" deviations) for T of order of T or less. This
decreased"accuracy is only to am!~or extent due to a small number
of experimental points, as can be seen in the comparison of two
sets of data using 8 T'S covering different ranges (calculations
2 and 8, Table 3.) (It is important to realize that the 8 calcu-
lations were performed on the same 3 experimental data sets.)
Rather, the loss of accuracy is due to the fact that excluding
longer T'S makes the function of eq. 9 less well-defined, greatly
increasing the correlation between parameters. This is illus-
trated in Figure 10, for the cases of T=l.S sec and eight experi-
mental points covering a "small" and "large" range of T'S (calcu-
lations 2 and 8). The figure presents the variance (sum of
squared errors divided by number of degrees of freedom) corres-
ponding to adjustment of parameters A and B, eq. 9 at fixed Tl
versus these Tl values. The sharpness of the minimum is a sig-
nificant measure of accuracy: the Tl range corresponding to a
doubling of the minimum variance may be used as a realistic esti-
mate of possible calculated TI error limits. For the case of the
large T value range, calculatlon 2, the limits are about !2.S%.
For calculation 8, including T values only up to ~ 0.8 Tl' gives
an error limit exceeding !lO%. Figure 1 shows that calculation 8
gives a Tl that is too low and furthermore well outside of the
error limlts for calculation 2. On this basis only, it appears
necessary to use T values covering a range up to at least 1.5 or
2 Tl for accurate determination of Tl's. Inclusion of such T'S
is also motivated by dynamic range and signal-to-noise considera-
tions, since the peak intensities may be rather attenuated for
(lS)As calculated according to standard practice; see for example
W. E. Deming, "Statistical Adjustment of Data," John Wiley & Sons
(New York) 1943.
13
-------
short T values in the FIRFT experiment (when the ratio !/Tl is
small) .
A few other comments might be made concerning the calcula-
tions shown in Table 3:
1. For these experiments, no significant increase in accu-
racy was noted with larger numbers of T values. Only the range
of T values covered affected the precision and accuracy of the
Tl calculation.
2. As long as one or more"long' T values were included in the
data set, there was no significant loss in accuracy for the three
experimental values of T. Since the time T is required to obtain
each T value, it is far-more efficient to use a shorter T aRa,_10ne
or two long T values as in experiment 3 calculation 2, than to
utilize long T values as in experiment 1 (approaching a normal
IRFT experlment). Note however that for experiments where signal-
to-noise ratios are low and Tl's are long, the use of a short T
will negate the use of short T values since the signals will then
be below the noise level. In this case, well spaced T values
starting at a low value and including several T'S of the order of
the estimated Tl will produce optimum results.
3. Use of the exponential fit for determination of Tl cir-
cumvents a systematic problem inherent in semi-logarithmic plots,
that is, biased error limits.~O
The data shown in Table 3 and Figure 10 have been obtained
using the general least-squares program GENLSS16 on an off-line
CDC6400 computer. For routine purposes, when elaborate statis-
tical analysis is not necessary, the least squares fitting may
also be performed using on-line minicomputers. This procedure
. greatly reduces the effort needed for evaluation of the Tl data
and it is being extensively used in this laboratory. We are
utilizing a modified version of the NTCFT software package,
available for Nicolet 1080 series minicomputers.
Unmodified NTCFTsoftward currently contains a two parameter
exponential fit Tl calculation using eq. 8 that works only under
near-~deal experimental conditions. Our 3-parameter fit calcula-
tionl was successfully used for a large number of experiments
including cases where mis-set pulse angles and large frequency
offsets were intentionally introduced~ In all cases the 3-param-
"eter fit calculated on the Nicolet computer was equivalent or
superior to semi-logarithmic data treatment. Our current on-line
(16).
D. F. DeTar, "Computer Programs for Chemlstry," Vol. IV,
Academic Press (New York), 1972.
(17). '.
Avallable from the authors and recently added to the product
line by Nicolet Technology.
14
-------
3-parameter fit, however, is not extremely time efficient.
Typical Tl calculations require 1-3 min. but can take consid-
erably longer if the data set is poor (e.g., low signal-to-noise
and poor choice of T values).
TABLE 3.
PROTON Tl's OF 2% ACETONE SOLUTION IN CDC13.a
Characteristics of T
Values Used in the
Fitting Procedure
Number
T (sec) of T' S
max
Calculated Tl (sec)
Calculation
Experiment 3
W = 1. 5 sec
1
2
3
4
5
6
7
8
17
17
11
8
7
6
5
4
18
8
17
16
14
12
10
8
Experiment 1
W = 17 sec
Experiment 2
W = 6 sec
5.25:!:.06
5.2l:t.03
5.42:!:.08
5. 23:!:.07
5.27:!:.08
5.21:Lll
5.1l:t.16
5.07:t.27
5.35i.05
5.33:!:.05
5.40i.07
5.39:!:.10
5.25i.12
5.25:!:.12
5.45i.19
5.32i.31
aAt 270 MHz and 30°C; solution not degassed.
5.2l:!:.05
5.19:!:.06
5.23:!:.07
5.14i.09
5.0H.ll
4.92i.15
4.74i.17
4.99i.24
15
-------
80
. T mox=17sec
-
~
~
f 60
-
:a
~
c
-
>
N
b
cu
~ 20
.;:
~
4.6
4.8
5.0 5.2
Tr (see)
5.45.6
5.8
Figure 10. The variance corresponding to least-squares adjust-
ment of A and Busing eq. (2) as a function or a fixed Tl. Eight
experimental points have been used, the TIS were the same as in
calculations 2 (<:) and 8 (.). (See Table 3). .' .
16
-------
AS.
Use of a Modified DEFT Pulse Sequence in 13C NMR:
Dynamic Range Imrovern:ent for Relaxation Ex eriments
and Dynamlc N R easurements at 19h Resolutlon.
Introduction
A refocusing three pulse sequence, "Driven Equilibrium
Fourier Transform" (DEFT), was introduced in 196918. The sta~ad
application for DEFT was signal enhancement in situations where
nuclear spin-lattice relaxation times (Tl's) were too long to
allow rapid repetition of scans in normal FT nmr spectroscopy.
As a result of experimental ~ifficulties~9 the DEFT sequence has
not been widely applied to high resolution nmr spectroscopy. We
describe here an application of a variation20 of the DEFT (90°-
T-1800-T-900-T)n pulse scheme which is useful, not for signal
enhancement but for effective suppression of single or multiple
large solvent lines in nmr spectra, even-during Tl determinations.
A second, and unrelated, application to be described, involves
measurement of dynamic nmr (DNMR) parameters, i.e., chemical
exchange rates.
The first application, peak suppression, can be easily per-
formed on typical commercial spectrometers. Required rf homo-
geneity and other. stringent experimental conditions limitappli-
. cability of this sequence for DNMR studies.
In reference 20 a significant simplification of the lH-spec-
trum of a large paramagnetic protein was achieved through the.
application of the "Modified DEFT" pulse-sequence [900-T-1800-T-
90° data acquisition]. The modification derives from the fact
that the data are acquired after the final 90°-pulse, and not
during the waiting period between pulses, as in the usual DEFT-
technique. For every resonance having Tl>T, the longitudinal
magnetization M4, built up during the first waiting period ~, is
approximately T/T1' The 180° pulse inverts M , and then during
the second period T-Mz is eliminated tosecona order in (T/T1).
The signal resulting after the final 90°-pulse is then roughly
proportional to (T/T1)2, which supplies effective suppression for.
resonances where T/Tl is less than ca. 0.13. Resonances having
Tl~T or Tl
-------
fections (c.f. r~ference 20). The principal advantage of this
technique is the possibility of measuring Tl's of fast relaxing
lines by the variation of T .over an appropriate range and fitting
of the resultant signals to equation 10, at the same time suppres-
sinQcill slowly relaxing lines (even-if-those lines have quite
?iflerent Tl's). The degree of suppression achievable, ~ 102,
1S less ~han that obtainable by other peak-peak suppress10n
methods. 1-22 However, the other methods cannot extend peak
suppression over a reagonable range of T values, nor do they
" operate for multiple lines having significantly different Tlts.
-The present method deals with the dynamic range problem encountered
commonly in lH nrnr, or in l3C-Tl measurements when dilute solu-
tions are utilized and the solvent contains carbon.
Experimental
The measurements were performed on our spectrometer SEMINOLE"
based on a wide bore superconducting solenoid, and currently
operating at the l3C frequency of 22.63 MHz. Quadrature-detec-
tion at an i.f. of 2.05 MHz was used for these experiments. Pulse
timing was obtained with a Nicolet 293 universal controller. The
probe uses a single 4 turn Helmholtz-coil (diameter 35mm, height
35mm). All spectra were recorded with broadband proton decoupling.
The temperature was controlled with an input thermocouple-regula-
ted temperature controller. For the peak suppression experiment
a30mm spinning tube (height of sample, 50rnril) was used. It con-
tained 0.4M of commercial reagent'grade cholesteryl chloride in
cyclGhexane (10% cyclohexane-d12)'
With the 30mm tube the solvent line is ~lOO times stronger
than the individual steroid resonances (Figure 11). The strong
(effectively, ~50M) solvent signal in this large sample exceeds
the linear"range of the receiver giving rise to the baseline
artifacts (see Figures lla and l2a). For chemical exchange appli-
cations of the modified DEFT sequence, experimental requirements
are far more stringent than for peak suppression experiments.
The DNMR experiments in principle differ from the peak suppres-
sion experiments only by using T spacings in the 1-25 msec range
(of the same order as the chemical exchange lifetime). In fact,
r.f. homogeneity and other instrumental requirements for the DNMR
experiment described below are only marginally met with our spec-
trometer, such that a smaller l5mm sample, a very narrow spectral
window, and a specific choice of T were required to achieve a 1%
null for the non-exchanging acetyl methyl carbon (see the discus-
sion below.) Deviations from this choice of T, use of a larger
(21) .
A. G. Redf1eld, S. D. Kunz, and E. K. Ralph, J~ Magn.
19, 114 (1975); J. P. Jesson, P. Meakin, and G. Kneissen,
rnem.Soc., 95, 618 (1973).
( 2 2 ) S L P tt d B D S k "J' 'Ch
. . a an . . yes, . ern.
F. W. Benz, J. Feeney, G. C. K. Roberts,
(1972)
Resonance,
J. Am.
Phys. ,56, 3182 (1972).
J. Magn:-Resonance, ~, 114
18
-------
sample or larger spectral offset, or inclusion of sample spinning
individually resolted in DEFT "null" signals of 5 to >10% for the
acetyl methyl carbon.
T, Determination Using the Modified DEFT Sequence
In the steroid sample, Tlfor cyclohexane is about 15 sec;
Tl'S of the steroid lines range from 0.4 to 5 sec. This differ-
ence enabled us to achieve a Tl measurement on nearly all carbons
of the steroid with simultaneous suppression of the solvent line
by the Modified DEFT sequence. Calculation of Tl values from the
data using equation (10) was performed with the general least
squares program GENLSS.~6
As can be seen in Figures llc and 12b, the solvent resonance
can be suppressed effectively 'with the Modified DEFT-sequence for
T-values of abo~t 1 sec, in agreement with the theoretical predic-
tion of -(TIlT). For shorter T'S, however, which become comparable
with T2 of the solvent-line, the suppression factor is lower,
typically ca. 20, due to imperfect nulling of the residual trans-
verse magnetization by the final 90° pulse, (using a 30mm spinning
tube with corresponding limited r.f. homogeneity). We plan to
circumvent this problem by the use of a homospoil pulse.
Table 4 contains resulting Tl values for six selected reson-
ances of the steroid. In those cases where standard inversion-
recovery Tl data were obtainable (lines well separated from the,
solvent resonance), there was good agreement between the modified
DEFT and IRFT determined Tl's. ' .
TABLE 4. Tl VALUES FOR SELECTED CARBONS OF CHOLESTERYL CHLORIDEa
b c
Tl(sec) ,
Inversion-
Recovery
Carbon
b d
Tl(sec) ,
Modified DEFT
(unresolved)
o .53
o .63
o .87
1. 84
o .94
o .90
(J .53
o .64
o .85
1.88
o .90
o .93
11
7,8
3
27
9
6
(a) 0.4M in cyclohexane (10% d12-cyclohexane), 41°C, 22.63MHz;
(b) Estimated accuracy :t5-10%; (c) Calculated from S' (T)=S oo[l-a'
exp(-T/Tl)] using a three parameter non-linear least squares fit;
(d) calculated ,from eq. 1, same method as in (c).
19
-------
O.4M CHOLESTERYL CHLORIDE
(in cyclohexane,cyclohexane -d12 ':::::::::
32 scans, 4 K Hz spectrum
I. a)NFT
I.j Vertical
,~If¥ ~c;~e
zero
quod image
b) NFT
XI
C-5
. TI16sec
c) MOD. DEFT
X 64
(T = 1.6sec)
13 .
FIGURE 11. 22.63 MHz C NMR Spectra of 0.4 M cholesteryl chloride
in cyclohexane (10% cyclohex~ne d 2)' 30mm sampl~, 41°C: (a) a~d
(b) Normal FT .spectrum, vertlcal ~cale expanded ln (a); (c) modl- 0
fied DEFT spectrum. For both cases 32 scans were accumulated, with
a pulse sequence interval of 80 sec. For the modified DEFT spectrum
Twas 1.6 sec. The spectral width in each case is 4kHz. Base-
line rise in Figure Ie results from HO.innomogerieity and not from
the DEFT experiment.
20
-------
O.4M Cholesteryl
Chloride
n cyclohexane, cycl~~2 . . (~fully relaxed)
32 Scans. cyclohexane
. 4 KHz spectral width solvent line
400 Hz shown
a)NFT
b) DEFT
FIGURE 12. Spectral expansion of the data in Figures lla and llc.
400 Hz spectral width shown. (Use of 80 sec pulse interval
emp1;asizes. the cy-clQh~xane.-d12 r:sonances ~n. Figu~e l?a). . Har-
mon1C and other Dase11ne d1stort10ns are v1s1ble 1n F1gure 12a.'
'2il
-------
Use of the modified DEFT scheme for Tldeterminations offers
many practical advantages. In particular, the stringent experi-
mental requirements necessary to the use of the normal DEFT
technique are loosened. Nevertheless, it is possible to realize
such conditions (mainly a good rf homogeneity) using small, non-
spinning samples in our large receiver coil. This allows a rela-
tively precise alignment of the nuclear magnetization with HO
through the final 90° pulse of the DEFT-sequence and thus an effec-
tive zeroing of the transverse magnetization.* This stimulated.
our interest in a possible application of DEFT in Dynamic NMR
(DNMR) at high resolution, based on the fact that the chemical
exchanging resonances will not have their transverse components
zeroed, due to exchange-induced dephasing during the two waiting
periods, 1'.
Chemical Exchange
Let us consider nuclei undergoing a chemical exchange between
2 equally populated sites A and B with the rate A (i.e., the life-
time in each si!e is A-l). Figure 13a shows the behavior of the
magnetizations MAaria MB (corresponding to Larmor frequencies
ooA 6/2 and
usually defined in lineshape studie~. .
exchange for A > 6
A < 6/2, as lt is
22
-------
MOOIFIEO OEFT PULSE SEOUENCE
CHEMICAL EXCHANGE APPLICATION
.1
'(
90.
FID
90.
1:
180.
,.,.-t4-.+ .~ -}_.~~-+ +.
(81 w.tw. .,t~ +' . i t J_/' ~ +'
aT' T a .a T -~~:- a -Jj\1- a
FIGURE 13. Behavior in the rotating frame of macroscopic nuclear
magnetizations in a chemically exchanging 2 site system during the
modified DEFT pulse sequence. MA and MB and projections in the
xy-plane of magnetizations correspo~ding to the respective spin-
populations of both s~tes A and B; tll is the applied rf field;.
the pol~rizing field HO has the direction~. The circular fre-
quency of the rotating frams is arbitrarily set to wA + wB.
2
(Shortening of MA and MB due t~ the spin-spin re~q~ation time is-
neIlected); (a) Slow exchange 0.<6), T is chosen smaller than
6-. Dashed arrows represent MA and MB in the non-exchanging case
().=O), (b) Fast exchange ().>o), T is chosen greater than ).-1.
23
-------
The modifi~d Bloch-~quations (11) for the transverse magne-
tic components M tr and MBtr (which are, as usual, represented by
complex numbers ~A' MB) predict the expression (12Y for the decay
recorded after a DEFT sequence.
dMA = (io-A) MA +. A MB
dt .
dMB -
dt -(-io+A) MB + A MA
(11)
- - .~~2~
FID = MA + MB = 2 2
(O-A )~
exp [(~A+io)tJ-exp [(~A-io)tJ
exp [-2ATJ (l-cos 2T/02_A2)
(12)
The ratio between the peak height difference for the
ing opposite peaks (=2SDEFT) and the height SECHO of
(obtained in this sequence by omitting the final 90°
then. given by:
two result-
the Hahn echo
pulse) is .
2SDEFT 2A
SECHO = ~ (l-cos 20T)
if second order terms ~(T2/02) are neglected. For A/o close to 1,
the relation between 2SDEFT and A is no longer simple as in (12).
(13)
+In the case of a "fast exchange" (A>O), the movement of MA
and MB during the DEFT-sequence is shown in Figure 13b. The
free precession during the fi~st T-period has the same Larmor
frequency wA + wB for MA and MB' the two being split apart with
2 ...
and angle (o/A), which represents a compromise between their
divergent (difference between wA and wE) and convergent (exchange
process) tendencies. Such a configuration is established from an
arbitrary initial situation within a time -A-I, esp~cially after
the 180° pulse (which re~erses the order of'MA and ~.' so that
they -have to cross e~ch o!her afterwards) and after ~he final '90°
pulse (which leaves MA = MB)' so that the total magnetization has
to build up afterwards, starting from zero. The actual FID,
recorded after DEFT for the "fast exchange" case is given by (14):
02A
FID = MA(t) + MB(t) = 2(A2-02)%
exp[2T('A2_cSt-A~] +
exp [-2T('A2_02+A~~
. .
exp (-{'A2-02*A)tJ
- 2 exp [-2ATJ
exp [(/A2_02_A)tJ -
(i4)
24
-------
It consists of a "slow" and a "fast" exponential term which have
opposite signs and cancel each other for t=O. The Fourier trans-
form (phased as in the normal FT experiment) will then be a sum
of a narrow positive and a broa~ negative line. The broad compon-
ent disappears quickly as (02/1: ) with rising temperature. The
ratio bet~R8n the height of the positive signal, SDEFT, and the
height S of the Hahn echo is given by (15):
SDEFT 02
SECHO - 4A2
2 exp [-2A1:]
2 2 2 2
exp [21:(A -0 ~A)] + exp [-21:(A -0 +A)] -
(15)
if only the leading second order-term (-02/A2) is retained. From
the A2 denominator in (15), it is clear that SDEFT decreases in
slow exchange. On the other hand, the information provided is of
more value since A and 0 can in principle be determined from (15)
for any given temperature, although the lineshape gives merely
their combination, (02/1:). -'
For the DNMR experiment, in order to achieve the necessary
.rr. homogeneity, a sample of a small volume (as compared to the
volume of the receiver coil) had to be used (15mm tube, height of
the sample, 23mm) and the spinning of the sample had to be exclu-
ded. This still allowed operation at sufficiently high resolution.
As a test system for the new technique, we chose the internal
hindered rotation in N,N-dimethylacetamide, which we used as a
neat liquid (reagent grade, not purified further).
Figure 14a demonstrates the ability of the DEFT sequence to
null the transverse magnetization of the acetyl methyl carbon,
which is not influenced by the process of internal rotation. The
residual signal is on level of -+% of that observed in a normal
FT spectrum. This quality of signal suppression could, however,
be reached only over a very narrow spectral window (-100 Hz)
close to the carrier frequency (due to finite power and non-
rectangular shape of the applied pulses; a width of 100 ~sec was
needed for a 1800 pulse). The investigated N-methyl resonances
were then placed in the middae of this r~ge. For each temperature,
DEFT and Hahn echo spectra were recorded under identical condi-
tions.
25
-------
(o)
55Hz
t------4
lem
~
(b)
S ECHO
- ------
~}S~FT
FIGURE 14. (a) The suppression of the acetyl carbon resonance of
N,N-dimethylacetamide in the modified DEFT-sequence. On the top
is the normal FT spectrum, on the bottom is 'the spectrum recorded
by the modified DEFT-sequence with T=4 msec. Temperature 730C
(5 Hz artificial line-broadening applied). (b) Resonances of
N-methyl carbons recorded as a- Hahn-echo, i.e., with the sequence
90o-T-180o-T-FID (top) and with the modified DEFT-sequence, i.e.,
90o-T-180o-T-900-FID (bottom). The bottom-spectrum is 90° out of
phase, T=4 msec in both cases, Temperature 69.5°C (5 Hz arti-
ficial line-broadening applied).
26
-------
Figure 15 shows the temperature dependence of the signal
shape resulting from the application of the DEFT-sequence, which
confirms the qualitative theoretical predictions. Table 5 summar-
izes the results for temperatures far. enough removed from coales-
cense, so that the simple relations (13) and (15) hold. A crude
estimate of activation energy from the obtained rates yields
Ea=18.8!0.5 kcal mol-I, in agreement with the val~e of 19.0 ! 0.1
kcal mol-I, found from lineshape-analysi~ of the H spectra.23
We feel that optimization of our instrumental facilities should
precede a systematic quantitative study and thus we limited our.-
selves in this case to a demonstration of the feasibility of this
kind of analysis.
(0) 55°C
+
(b) 65°C
Cc) 8~ Cd) IOloe
~
FIGURE 15. The temperature dependence of N-methyl carbons in
N,N-dimethylacetamide recorded with the modified DEFT sequence.
(a) 55°C, (b) 65°C, (c) 82.5°C, (d) 101°C. (a) and (b) are 90°
out of phase. T=4 msec. (5 Hz artificial line broadening applied).
(23)T. Drakenberg, K. 1. Dahlqvist, and S. Forsen, J.Phy.s. Chern.,
~, 2178 (1972).
27
-------
TABLE 5.
EXCHANGE RATES OF INTERNAL HINDERED ROTATION IN N,N-
DIMETHYLACETAMIDE FOR DIFFERENT TEMPERATURESa
2. ~EFT ~EFT c
Temperature (oC)b fCHO -fCHO X-l(msec)
55 0.108 85.6
65.5 0.247 34.7
69.5 0.293 28.5
73 0.415 18.7
101 0.061 2.4
(~) ~eas~red with t~e _modified DEFT pulse sequence.
All measurements are made on the N-methyl ca~b9J:t ti'
r-e.son'anc'es; (b) Temperatures :!:1°C; (c) "fast e.xchan~
region".. . -- '.' .
SlimIIiary
The basic requirements for DNMR application of this tech-
nique are good rf homogeneity, accurate pulse timing and good
pulse shape. This makes its use on current commercial instru-
ments (where these conditions are generally far from being met)
highly difficult. We suggest here, nevertheless, some prospective
applications in areas where modified DEFT advantages can compen-
sate for experimental difficulties encountered with other known
methods. One of th~se p~rticular features is the f~e~li*~t~d
identification of resonances undergoing exchange, as opposed to
those that aren't. This can be helpful for analysis of complex
spectra. Slowly exchanging resonances can be assigned to each
other from their symmetrical periodic dependence on T (equation
13). The chemical shift differences 26 can then be determined
from (13~,se~en if only one line is resolved. From (13) or (15),
6 and A can be determined independently for each temperature and
therefore, no assumptions have to be made about the temperature
dependence of these parameters, as in lineshape analysis. Also
loosened are requirements of temperature stability of (T2*)-1,
purity of the sample, etc. All of these may be useful in situa-
tions where for example, the dependence A(T) is of a complex
nature and cannot be described with a single ~E or when the range
of temperature variation is limited, as in manyabiological systems.
(In this last case, it is often' hard to tell from analysis of the
lineshape whether a rate process is actually taking place!)
Further, it should be pointed out, that the sensitivity of the
method does not become reduced in many cases where other methods
become insensitive because exchange makes a comparatively small
28
-------
contribution to the relevant total rate of magnetization decay
(i.e., to (T2*)-1 for linesh~pe analysis, to' (Tl)-l for satura-
tion transfer,24 to (TZ)-l for echo-train measurements with
variable pulse separatlon25 and to (TlP)-l for experiments in
the rotating frame). For lH studies we anticipate that the modi-
fied DEFT DNMR methods will not be affected by the presence of
homonuclear couplings (provided that the coupling constants are
s.maller than the chemical shift difference).* The presence of
unresolved homo-nuclear co~plings presented a serious complica-
tion in the lineshape for H studies of hindered internal rota-
tion indimethylformamide (DMF).26 .
*
This holds for both intramolecular and intermolecular exchange.
(24)
S. Forsen and R. A. Hoffman, J. Chern. Phys., 39, 2892 (1963).
(25) ==
A. Allerhand, and H. S. Gutowsky, J. Chern. Phys., 41, 2115(1964).
(26) .-
C. Deverell, R. E. Morgan, R. E. Mnd J. H. Strange, Mol. Phys.,
:18, 553 (1970).
29
-------
B.
INTERMOLECULAR INTERACTIONS
B1.
Chloro~henol Effects on Model Membranes: ESR Study
(C 11 . to b I 'C P. Smith,'et. al.>
o a ora lon y ..'.
The basic work from which arose the idea for a study of the
effect of a series of chlorinate9 phenols on model membrane
systems was that of Vermaet.al.L7 In that paper Verma reported
observing, for certain uncouplers of oxidative phosphorylation,
a disordering effect on the degree of order or organization of
phospholipids in hydrated multibilayers. Verma monitored these
effects on the phospholipids by using the cholestane spin probe
(CSL) incorporated into the multibilayers. 'One of the uncouplers
studied was pentachlorophenol (PCP). He found that at PCP concen-
trations of 2xlO-5M in hydrating buffer, the multibilayers of egg
lecithin-cholesterol (2:1 mole ratio) were maximally disordered
at the pH corresponding to the pK of the PCP. This disordering
effect was intensified when the multibilayers were composed only
of egg lecithin, and it was maximal at a pH different from that
of PCP's pK. The series of experiments suffered from a reliance
on having to note and interpret a very small change in the CSL's
EPR spectrum. This special parameter is not only sensitive to the
effects of the PCP on multibilayer, but also depends on the
experimenter's ability to make the films (it is difficult to
obtain near identical films). Despite these problems, Verma felt
he was observing a real disordering effect of PCP on m~ltibilayers.
Given this then, a series of chlorinated phenols were pro-
posed for a new study using the spinllabel ESR technique just as
in Verma's study. To date the experiments have largely been of a
preliminary nature involving only three ~ompounds of the series:
phenol, 2,3,5-trichlorophenol and 2,3,5;6..tetrachlorophenol. Two
model systems ha~e b~enused to prepare the multibilayers; egg
lecithin-cholesterol (2:1 mole ratio), and decholesterolized
brain lipid. The spin probe has been CSL in all cases, and the
buffer (pH 2 to 12). The three phenol-like compounds have been
made up at .each pH to 4xlO-5M and thus all reported observations
and effects are due to the perturbing effects of the compounds at
this physiologically reasonable concentration.
The effects of these compounds on the multibilayers have not
been pronounced as Verma interpreted PCP to exert. When eg~
lecithin-cholesterol multibilayers were hydrated with 4xlO- M
phenol at integral pH values between 2 and 12, no disordering
effect was observed in the spectra. Even when the hydrating
buffers contained 2xlO-5M phenol, the disordering effect, if the
data can truly be interpreted as such" would be very small (less
than 10% in terms. of the parameter measured, which may not be
-.
(27) .
. S. P. Verma, H. Schnelder and 1. C. P. Smith, Archives Biochem.
and Biophys.,: T54, 400 (1973).'.
30
-------
above experimental error). While it appears that no disordering
effect is made manifest by the phenol, these experiments should
be repeated since they were performed while im the process of
learning good film making technique, and also because no re-
equilibration/experiments were attempted with these films.
The most extensively studied system has been the egg
lecithin-cholesterol multibilayers; first hydrated with buffered
4XIO-SM2,3,S,6-tetrachlorophenol, and then re-equilibrated with
the appropriate pH buffer. The results here have been contra-
dictory: one time "indicating increased order after re-equili-
brat ion with buffer (i.e., a disordering effect by the chloro-
phenol with an effect maximal near the pK of the compound), and
the other time a very small disordering effect being observed
equally at all pH's. When the films were hydrated in the reverse
order (with buffer and then re~equilibrated with buffer plus the
chlorophenol), the effect was essentially zero since some pH's
showed small negative changes while others showed small positive
ones. ~
In like manner, when egg lecithin-cholesterol films were
hydrated first with 4x10-SM 2,3,S-trichlorophenol buffers and
then re-equilibrated with buffers, a small disordering effect for
the chlorophenol was noted over all pH's. This disordering
effect of the trichlorophenol needs to be validified with more
experiments just as in the case of the tetrachlorophenol compound.
Only one system seems to have given definite positive proof
for t~e disordering effect of 2,3,S,6-tetrachlorophenol at
4x10- M, pH 6.00. This system is mUltibilayer films composed of
de-choIesterolized brain lipid containing an added 8 gm% choles-
terol. With this cholesterol content the brain lipid has just
passed through its gel-liquid crystal phase transition, and is in
the liquid crystal phase. Since it is right at the transition
point, the system is very responsive to disordering effects back
to the gel. This is in fact what one observes by monitoring
films labelled with CSL and hydrated with the chlorophenol. When
the mUltibilayers are hydrated with buffer first and a spectrum
recorded, and then re-equilibrated with buffer containing 4x10-SM
2,3, S ,6-tetrachlorophenol for 3-7 days, "interpretable' spectral: ":.e
d~fferences~"areeob~ained. Using the method of Neal et.al.* one
obtains molecular order parameters for the CSL in the two hydra-
tion cases. After a 3 day re-equilibration with the tetrachloro-
phenol buffer, the order parameter aecreased 23% from the original
order parameter obtained after buffer hydration. After 7 days,
the order parameter for the same film was 28% less than the start-
ing value. While-the careful control film and pH correction were
lacking in arriving at these decreases in the order parameter, the
disordering effect of thetetrachlorophenol is still regarded
*
Pre-publication procedure, expected to be published in Molecular
Pharmacology.
31
-------
as real.
These results have implications fC1r future experiments which
may lead to improved quality results. Certainly the time scale in
which chlorophenols are allowed to exert their effects should be
increased. Secondly, the low cholesterol brain lipid system may
be a better system than the egg-lecithin cholesterol one for.
observing the effect of the compounds. In progress also are
some experiments using multilamellar dispersions. These should
be valuable in manifesting c~lorophenol effects since the two
dispersions tried to date have given some promising results which
may be interpretable with some amended experimental procedures.
B2.
Chlorophenol Effects on Model Membranes:
l3C NMR Study
Simultaneously with the new ESR work on chlorophenol lncor-
poration into model membranes, a supportive l3C nmr study was
begun.
There are two main disadvantages to the nmr techniques;
(1) The membrane models are imperfect (vesicle bilayers); (2) A
high concentration of "membrane" component is required.
Offsetting these disadvantages is the fact that 13C nmr
methods are capable of giving us a more detailed look at the
ac'EU~JL process of. Clisrupti6h bf tne memBrane nioCle:L sysTem.
Using 13C spin-lattice relaxation times (Tl's) we are able to
evaluate the form of .the effect of the chlorinated phenols on the
model membranes. The potential information obtainable from the
nmr data is more detailed than that available from the ESR experi-
ments. However, it should be pointed out that the overall order
parameter (ESR data) is generally more sensitive to membrane
structure than is the mobility of the lipid alkyl chains (as
measured by 13C Tl's).
Preli~in~r~ 6?9 ~z13C Tl.da~a on 5 sonicatedd~spersions
of synthetlcd~~dlpalml toyl lecl thln (DPL) are shown ln Table 6.
In these experiments we are able to observe the internal and
overall mobility of the lecithin bilayers with added 3,5-dichloro-
phenol (DCP), 2,3,5,S-tetrachlorophenol (TCP), pentachlorophenol
(PCP) (2 concentrations), and without incorporation of any foreign
compounds.
The data in Table 6 are preliminary. However, they already
indicate one important and somewhat unexpected result of penta-
chlorophenol incorporation into the bilayer structure.
l3C relaxation data (Tl's and/or T2's) for individual carbons
in DPL bilayers indicate the general degree of mobility of the
long alkyl chains in the hydrophobic portion (of the bilayers).
They also give insight into the overall motional freedom of the
DPL molecules, using the relatively anchored group resonance C-2
32
-------
as the monitor.
TABLE 6.
13C RELAXATION DATA IN MODEL 'MEMBRANE SYSTEMS
INCORPORATING CHLORINATED PHENOLS
13' b
C Tl{sec)
SOLUTIONa C-2 G-3 C-4to C-14 C-15 C-16
G-T3
DPL .55 ..75 -0.95 2.2 3.8,. 6.6
DPL, O. OIM PCP .46 .55 -0.72 2.7 2.5. 5.9
DPL, 0.04M DCP .44 .55 -0.82 1.1 :. 2.8 ~ 5.0
DPL, O.04M PCP 1.5 1.6 -1. 0 2.3 ~ 2.9 5.6
DPL, O.04M TCP 0.8. 0.5 -1.0 2.5 2.5 4.6
aDPL - synthetic dipalmitoyl lecithin, (0.3M), PCP - pentachloro-
phenol, DCP - 3,5-dichlorophenol; TCP - i,3,5,6-tetrachlorophenol;
bat 63° and 67.9 MHz; Accuracy, !15% (estimated).
o
ff2 3.. 13 1.. 15 16
CH2- 0- CCH2CH2 (CH2) lOCH2CH2CH3
I ~2 3.. 13 1.. 15 16
CH-0-CCH2CH2 (CH2) 10CH2CH2CH3
I eo + yH 3
CH 2 bp- OCH 2 CH 2N- CH 3
~ I .
CH3
FIGURE 16.
Dipalmitoyl Lecithin (Phosphatidyl Choline)
In the micellar DPL solutions containing
no definitely significant trends were noted.
the hydrophobic inner portion of the bilayers
segmental motion. Unfortunately, the present
not sufficiently accurate nor reproducible to
bility.
O.OIM PCP or O.04DCP,
It is possible that
has somewhat reduced
preliminary data are
confirm this }possi-
On the other hand, one surprising fact emerges from these
first experiments. The l3C TI'~ for C-2 and C-3 in the DPL solu-
tion containing O.04M PCP clearly show a substantial loosening up
of the polar end of the alkyl chains. Interestingly, the polar
. head groups themselves do not show significant increased mobility
33
-------
except at one carbon (see Table 7); just the -C-2 and C-3 (plus
presumably the unresolved C-4 and C-5) methylene groups undergo
increased motion. Thelengtheriing of Tl by a fa6tor of 53 (~s for
C-2 and C-3) corresponds to an increase in motion by a factor of
3 to -9~ ~~B~n~ipg on w1)~G~ tp~qr:::ticg.l ~8<;iel iQ qhosen.*
Our first experiment with 2,3,5,6-tetrachlorophenol is incon-
clusive. However, it appears the TCP may be affecting the bilayer
structure significantly. .
Table 7 summarizes 13C Tl data for the same solutions, but
in this case listing the polar head groups. As stated above,
the glycerol residue mobility does not appear to be affected by
PCP incorporation. The preliminary data do indicate that the
choline OCH2. group may be experiencing increased motion with PCP
incorporation. This apparent result is being verified currently.
While we might now propose a model showing pentachlorophenol
to incorporate within a specific area of the bilayer structure we
feel that such a model would be premature.
A much stronger case for any model will undoubtedly arise
from intended variable field l3C Tl measurements on DPL and egg
lecithin bilayers, incorporating PCP, TCP, and other materials.
TABLE 7.
13C T DATA FOR tTHEGLYCEROL AND .-POLAR ;H£AD GROUP
RE SrlfuE S - -.
13 a
C Tl(sec)
SOLUTION +NMe3 glycer chollne
-OCH
2
DPL 1. 24 0.16 0.55
DPL, O.OlM PCP 1. 32 0.13 0.67
DPL, 0:"04M DCP 1.18 0.17 0.66
DPL, 0.04M PCP 1.25 0.16 0.35
DPL, 0.04 TCP 1.15 n.m. n.m.
choline.
~NCH
2
0.73
0.75
0.8
0.83
n.m.
aAt 67.9 MHz and 63°; Accuracy i 15-25% (estimated).
'*
See for example:
G. C. Levy,J. Am. Chern. Soc. ,95, 6117 (1973).
34
-------
B3.
Variable Field NMR Experiments on Model Membranes.
As a result of research finished or underway in our labora-
tory (see section's B4 and E) we can now proi ectsignificantnew
information to be derived from multi-field 3CTI measurements
on DPL and other model membranebilayers, incorporating chloro-
phenols and other materials. .
This summary forms an initial informal disclosure of this
anticipated expari~ion of scope.
It has been noted above that both ESR spin-labeling measure-
ments27 and 2H nmr measurements28 can be useful for ch~~acteri-
zation of the order parameter in bilayer structures. C Tl
measurements on the other hand have not elucidated higher order
in membrane models. The main advantage of 13C nmr measurements
has been their ability to probe the various structural parts of
the molecular system. This is in contrast to the overall nature
of the spin-labeling experiments. Deuterium nmr experiments
using specific isotope labeling can give increased information.
However, those experiments require large experimental efforts and
may be impractical for extended pesticide incorporation studies.
In the-limited 2H work reported, the order parameters were appre-
ciably lower than as obtained from ESR spin-label measurements.
This ambiguity is thought t6result from spin-label perturbations
or from differences of nmr and esr method sensitivities to short-
lived deformations of the bilayer structure.28
"b f" 13C T b . "
The varla Ie leld 1 measurements eglnnlng now may
prove to be a sensitive new probe into membrane structure since
they probe molecular motion at each carbon site and also since the
cooperativity of the chain motions will be probed. Thus, a param-
eter bridging and com~lementing previously available data will be
developed. Previous. 3C Tl studies of model membranes have been
conducted at one magnetic field, and thus this extra information
was not obtainable. Computer programs are under development in
this laboratory to interpret the variable field data in terms of
physically realistic models. .
(28)H. H. Mantsch, H. Saito and I. C. P. Smith, in a
Prog.in NMRSpectr6sc., J. W. Emsley, J. Feeney and
Sutcliffe, eds., (Pergamon Press}, in press.
35
review in
L. H.
-------
B4.
Variable Field 13C T, Studies of complex Systems
Two projects near completion in our laboratory are ~xamining
the. effect of mag~etic field on 13C Tl measur~ments. In one.
proJect (see Sectlon E) we are extendlng prevlous models of
complex chain 'molecular motions in polymers. In the second pro-
ject we are probing cooperative long time-scale motional compon-
ents.for the carbons of relatively small associated molecules,
such as alcohols, glycols, carboxylic a~ids, etc.
In these cases we are confirming anticipated magnetic field
dependencies for carbons undergoing insufficient motion to be in
the "extreme narrowing" limit. 'But,m:oreim:portantly, we are
learning that in many cases cooperative long time-scale motional
components may strongly influence molecular dynamics for carbon
. groups apparently reorienting rapidly enough to be'well within the
nmr motional narrowing limit (to <10-12secY).
In 1,2-decanediol the strongly associated glycol function
results in a large dggcee of observed segmental motion. This is
clearly seen in the increasing Tl values for carbons successively
removed from the hydroxyl groups. This observation of segmental
motion is not unexpected, since the situation is quite close to
that observed for I-decanol in 1971 by Doddrell_and Allerhand.29
. New information may be derived from the fact that all 10
carbons of 1,2-decanediol exhibit a significant dependence on
magnetic field, despite the fact that according to its observed
Tl even the motionally restricted C-2 CH carbon does not signifi-
cantly violate the condition of "extreme spectral narrowing". 30,31
At 67.9 MHz, dipolar Tl's (CH) of less than ~400 msec (corres-
ponding to TC >lO-lOsec) increasingly deviate from Tl's obtained
at lower field. The large dependence of these Tl's on the experi-
mental Larmor frequency can be explained if the molecular dynamics
is not explainable in terms of one, two, or three discrete effecQ
tive correlation times. Instead it is necessary to invoke a
distribution of correlation times, with some motional components
that are relative slow. The interesting point here, is observa-
tion of a large field dependence not only for the C-l and C-2
carbons, but for all of the carbons of the pendant carbon alkyl
chain. . -
(29)D. Doddrell and A. Allerhand,J. Am. Chern. Soc., 93, 1558(1971).
(30)A.Abragam, "The Principles of Nuclear Magnetism," Oxford
Press (Oxf6rd) 1961, p. 299 ff.
(31)J. R. Lyerla and G. C. Levy, in Topics inCarbon-13 NMR
Spec-t-ros'c-oPY,: 1, - 88 (1974).
36
-------
TABLE 8.
13C SPIN-LATTICE RELAXATION TIMES FOR 1,2-DECANEDIOL AND SEVERAL
SIMILAR MOLECULES.
a Ft;equency
Compound Temp (oC) MHz C-l
1,2-decane- 54 22.6 0.26 0.41 0.30 0.36
diol 54 67.9 0.5 0.80 0.60 0.75
d 37 0.7 0.7 0.7
I-decanol 22.6 ---
37 67.9 0.6 0.6 0.7 ---
n-eicosane 49 22.6 6.0 4.0 2.8
49 67.9 5.9 4.3 3
13 c
C Tl (sec)
C-2
C-3
C-4
C-5
C-6
C-7
C-8
C-9
C-IO
---
--
--
--
--:- "'0.5
--- "'0.9
--- 0.95 1.5
--- 1. 8 2. 7
3.4
5.3
--- "'1. 0
--- "'1. 0
--- 1. 5
--- 1. 4
2.4
2.3
3.9
3.8
1.4
1.4
a
Samples neat;
bTemperature !2°, measured directly before and after data collection;
cMaximum probably error !5-15%. Decanediol data, average of two runs:
reproducibility was !3% except for C-3 and C-IO (at 22.6 MHz);
d 1"
Pre 1m1nary data, !10-15%.
Metcalfe, Levine, and co-workers have developed a theory
which predicts that 5 CH2 - CH2 bonds are sufficient to decouple
the m~~i~~ of a straight chain CH2, group from a site of restric~
tion.' The two field 13CTI daTa for the "pendant" eight
carbon chain of 1,2-decanediol indicate that the published theory
is not valid at least for this molecular system.
We are currently investigatin! theoretical models for chairi
segmental motion, using two field 3C relaxation data from solu-
tions of poly-en-butyl) and poly-(n-hexyl) methacrylates. The
polymer main and side chain Tl's cover a wide range of values,
some apparently'within the region of extreme spectral narrowing.
A significant field dependence was noted for all carbon T 's 'and
in addition, a complex behavior ~as observed for the 13C tlH] NOE's.
While this theoretical work is not yet completed, it does indicate
that when long time-scale motions are mixed with faster motional
components (resulting in a distribution), TI's will be strongly
frequency dependent over a wide range of efrective correlation
times (T) including the region of ~xtreme spectral narrowing.
(32) .
Y. K. Levlne,
P. Partington and
( 33) K' L ' .
Y. ., eVlne,
,:~, 497 (1973).
N. J. M., Birdsall,
G.C.K. Roberts, J.
P. Partington, and
37
A. G.
Chem.',
G. C.
Lee, J. C. Metcalfe,
Phys.,~, 2890 (1974).
K. Roberts, MoT.Phys.,
-------
Our calculations show that even a small contribution from long
time-.scale motions will affect. TI' s significantly, but will affect
NOE's considerably less (see section E for details).
Thus, all of the TI field dependences for 1,2-decanediol can
be explained with a model of cooperative segmental motions super-
imposed on a slow overall molecular reorientation. The slower
motions are incompletely decoupled from the segmental motions of
the chain carbons, including the C-IO CH3 group.
In order to validate the unexpected experimental results
obtained here, variable field TI's were obtained on the alkane
n-eicosane (Table 8). No field dependence was noted for this
non-associated molecule. .
In another experiment l-decanol was examined (see Table 8).
The preliminary data do not show an unequivocal field dependence
for this alcohol. If the final numbers show an insignificant
field dependence, then this will indicate that segmental motion,
as observed in this simple alcohol, is not strongly cooperative
as in the diol. Furth~r experiments are underway to investigate
the effects of structure, solvent, and temperature on cooperativity
of molecular motion.
C.
INTERACTIONS OF CHLORINATED PHENOLS:
HYDROGEN BONDING
As an initial step to the understanding of chlorophenol
intermolecular interactions, we undertook a study of self asso-
ciation of three dichlorophenols and model compounds. That study
gave us insight into the differences resulting from ortho versus
meta or para halogen substitution. The initial disclosure of our
results has been published in the Journal of Physical qhe_mis~_~y
"'-'--79'(21): 2325-2326. 1975: [A more. complete man-used.pt- i~ - in. .... ---------
--'p-repa-ra tion ; it "should-'b-e- r-e-a'-dy-- for "submission for pub lica t ion_-
in fall 1977].
38
-------
D.
ANALY.STS OFPOLYCHLORINATEDBTPHENY.LS BY CARBON-13 NUCLEAR
MAGNETIC RESONANCE SPECTROSCOPY.
Aroclors, which are mixtures of polychlorinated biph~nyls,
have been used extensively as insecticide ~ynergists34 in the
United States (a synergist is a compound which enhances the
relativity of another' compound to which it is added). Although
the use of Aroclors in the United States is currently highly
restricted, they are still being used in large quantities in other
countries. In spite of the current restrictions on their use in
the United States, Aroclors continue to enter our environment
today. These materials have high toxicity.35 It is desirable to
develop a quick method for the analysis of these complex mixtures.
In recent years, the use of carbon-13 nuclear magnetic
resonance has become significant for identification of organic
compounds and also for quantitative analysis of simple mlxtures.36
The recent growth of applications for 13C nmr followed major
instrumental advances in the early 1970's. The advantages of 13C
spectroscopic techniques include ultrahigh resolving power with a
chemical shift range of over 200 ppm, compared with -10 ppm for
proton chemical shifts. 13C spectrometers operating at high
magnetic fields have particularly high resolving power, especially
when utilizing broadband proton decoupling techniques that make
it possible for 13C resonances to be (generally) observed as
. sharp singlets. One major drawback for 13C nmr methods of chemical
analysis is the relatively low sensitivity (in the sense of required'
sample size) for this technique, when compared with optical spec-
troscopies, and 13C nmr is far less sensitive than IH nmr. Never~
theless, the increased information available from nmr spectros-
copies and 13C spectra in particular, allows these techniques to
be advantageous in some instances.
Problems are known to exist in "quantitative" 13C analysis.
A major problem: arises from 'the need for relatively long delays
between time-averaged acquisitions of spectra. These relatively
long delays (sometimes >1 min.) are caused by the need to allow
complete relaxation of each nuclear spin (13C nucleus) between data
acquisitions. It is necessary to wait at least 3-4 times the
(34)0. T.Sanders, R. L. Zepp, and R.. L. Kirkpatrick, Bull Environ.
Contam. Toxicol.' 12,394 (1974); (b) N. S. Fisher, E. J. Carpenter,
R. C . Remsen, and-C-. F . Wurster , Microb. Ecol., 1, 39 (19.74) ; (c)
S. Innami, H. Tojo, Y. Utsuyi, A. Nakamuia, and ~. Naguyama,
. Eiyogaku Zasehi,~, 58 (1974).
( 35 )H. Berge, Nat~wis's Rundsch,2 7, 447 (1974).
~369;G. C. Levy and G. L. Nels.on, "Carbon-13 Nuclear Magnetic Reson-
ance for Organic Chemists," 1972; J. B. Stothers, "Carbon-13 NMR
Spectroscopy," 1912; E. Breitmaier, "13C NMR Spectroscopy," 1974.
39
-------
spin-lattice relaxation time (Tl)37 to allow this complete relax-
ation. This waiting period can be circumvented using commer-
cially available paramagnetic relaxation reagents such as (Tris)
acetylacetonatochromiuin III (Cr(acac)3) which shortens spin-
lattice relaxation times for carbons not having efficient relax-
ation pathways. 38 Once the spin-lattice relaxation time has
been decreased to <0.3 sec, it is then possible to greatly expe-
di te~da:ta.':,acquisi tion. Use of these relaxation reagent's also
helps to overcome another problem. As a result of the complete
proton decoupling used to obtain singlet resonances in 13C spectra,
there is normally a perturbation of spectral peak intensities
attributable to the nuclear Overfiauser effect. NOE's may affect
different carbons to a varying extent thus peak intensities may
be misleading. The relaxation reagents, under proper conditions,38
can effectively suppress the nuclear Overhauser effect for all
carbons. "
The spin-lattice relaxation times for several individual
polychl~9inated biphenyls have been reported previously by
Wilson. These Tl's were observed to be 2-5 seconds for C-H
,carbons. The carbons not having directly bonded hydrogens have
Tl's which were considerably longer, as expected. Cr(acac)3
added at a concentration near 3 x la-2M decreases these Tl's to
under 0.5 seconds. Thus the, time required for the experiment is
decreased, and NOEls can be effectively suppressed for all non-
proton bearing carbons (C-Cl and C-l carbons).
A major method for study of Aroclors is gas-liquid chromatog-
raphy (g.l.c.). This method, although accurate, can be time'
consuming since samples are often of insufficient purity for,
directg.l.c. analysis. Although direct 13C nmr analysis is not
as versatile for analysis of chlorinated biphenyl mixtures, in
some cases it can provide useful information very rapidly. Unlike
g.l.c., 13C spectra on large samples can be obtained in seconds
or minutes and sample preparation may only require dissolution in
a solvent. Many materials which might prove disastrous to g.l.c.
experiments can be easily handled.' One major advantage, of course,
for g.l.c. is the very small amount of sample required for analysis.
In all Aroclor systems examined in this study, sufficient samples
were available. Figure 17 shows the spectrum of Aroclor 1221
o~tained without t~e use of Cr(acac)3; Figure 18 shows the result
wlth added relaxatlon reagent. '
(37)J. R. Lyerla and G. C. Levy, "Topics in Carbon-13 NMR Spec-
troscopy," Vol;:r'a.~'g.ie';',Levy, Editor, 1974, Chapter 3.
(38)G. C. Levy and Ulf Edlund,J. Am.Chem. Soc. ,97, 4482 (1975)
and references cited within. -
(39)N. K. Wilson;J. Arri.' Chern. Soc., ~, 3573 (1975).
40
-------
FIGURE 17.
FIGURE 18.
rC-H Region,
,-- C -I Region
C-CI
r Region-,
I
140PIIIII
135ppm
130".
67.9 MHz 13C NMR Spectrum of Aroclor 1221 (Aromatic
region shown). No paramagnetic relaxation reagent
added; 300 scans, 8 sec scan interval.
c;-" CeIt8I
I.....,
.!.
140-
.!.
1"-
.!.
~
. 13
67.9 MHz C NMR Spectrum of Aroclor 1221 (Aromatic
region shown). 3 x 10-2M relaxation reagent
(Cr(acac)3) added; 300 scans, 1 sec scan interval.
41
-------
FIGURE 19.
67.9 MHz 13C NMR Spectrum of Aroclor 1232, chlorine
content 32%. 3 x la-2M relaxation reagent added.
300 scans, 1 sec scan lnterval.
TABLE 9.°
COMPOSITION AROCLOR 1221
Chlorine Substitution Mole % G.C. 40
Nil .~ 10% +
2 ~ 17% +
3 < 3% +
4 - 17% +
-
2, 2' :S 11% +
3, 3' < 3% +
4, 4' - . 5% +
-
2, 6 undetectable
3, 4 20%a +
2, 4, 2' 4 ' undetectable
,
2, 5, 2', 5' < 3%
2, 6, 2', 6' undetectable
3, 4, 3', 4' undetectable
3, 5, 3', 5' < 3%
2, 3, 5, 6 undetectable
42
-------
The spectra in Figures 17 and 18 illustrate the dramatic
changes upon the addition of Cr(acac)3' The carbons normally
having long Tl's and lower NOE's (C-CI and C-l carbons) are more
easily observed with the relaxation reagent. 13C chemical shifts
for each of the individual isomers composing an Aroclor mixture
had been previously determined by Wilson,39 and with this infor-
mation available, assignments for the Aroclors were greatly facil-
itated. The high magnetic field employed (63 kGauss) to obtain
the spectra enhanced peak identification by increasing the reso-
lution over normal (14-23 kGauss) field 13C NMR spectrometers.'
To make assignments of peaks more straightforward, isomers con-
taining more than four chlorines were not considered (the mixture
is known to contain on an average 1.2 chlorines/molecules). The
relative intensities of the assigned peaks were then assumed to
be proportional to the particular isomer concentration in the
mixtures. For the above procedure to be valid the relaxation
time with Cr(acac)3 present must be short «0.5 sec) and also the
NOE's must be equivalently suppressed. The 13C Tl's for all
carbons in a representative Aroclor were measured in the presence
of 3 x 10-2M Cr(acac)2; the measured value was 0.4 seconds. This
is sufficiently short to fill both requirements.
13C analysis of Aroclor 1221 is given in Table 9. Quite
good agreement with g.l.c. analysis40 can be noted. As one check
, on the quantitative accuracy', "a total chlorine analysis was obtained
from the spectra using relative peak intensities. The total
chlorine content from this method (1.4 atoms per molecule) does
not agree quantitatively with the stated Aroclor chlorine content
(1.2 atoms per molecule).41
Direct analysis of heavily chlorinated mixtures of PCB's is
far more difficult since there are a larger number of compounds
present and it is very difficult to assign peaks by manual ~e
methods. 42 Figure 19 shows the partially interpreted spectrum
of Aroclor 1232 (32% chlorine). Future computer analysis of
similar spectra should extend analysis to at least 50% and
possibly higher total chlorine content. '
(40)G. Webb andA. C. McCall, J. of A.O.A.C., 55, 746 (1972).
(41)However, the semi-quantitative agreement is gratifying since
this type of determination, using both C-Cl and C-H carbon
resonances, is not expected to be as accurate as isomer deter-
mination which'uses resonance lines arising from similar type
carbons.
(42) .
Even the Avoclor 1232 sample analysis proved difficult.
43
-------
E.
CHAIN MOLECULAR DYNAME,CS IN COMPLEX MOLECULES
As equipment and relaxation measurement techniques have
become more spPhisticated and sensitive in the last few years~3~
the amount of molecular dynamics information which can be obtained
by nmr has increased greatly.44-47 As these experiments become
more accurate, the possibility of elucidation of more subtle'
molecular dynamic processes is also enhanced. These additional
consequences of the development of the field result in other
problems, namely, the analysis of any relaxation data presupposes
that an adequate model has been chosen. The generally accepted
approximation of a single correlation time characterizing the
exponential decay of the autocorrelation function has been the
preferred choice for most analyses.48-55
( 4 3 )¥'\ -- S" P . d. 1 R t 1 )
-lJ.r.-.-"''Hoult, peclallst, erlO lca - epor, s, vo . 5 (Chern. Soc. .
(44)R. L. Somorjai and R. DeslauE~ers, J. Am. Chern. Soc., ~,
6460 (1976).
(45)K. Levine, P. Partington, G. C. K. Roberts, N. J. M. Birdsall,
A. G. Lee and J. C. Metcalfe, FEBS Letters, 23, 203 (1972).
(462K. Levine and N. J. M. Birdsall, A. G. Lee and J. C. Metcalfe,
Biochemistry, 11, 1415 (1972). '
(47)D. Robinso~ N. J. M. Birdsall, A. G. Lee and J. C. Metcalfe,
Biochemistry, 11, 2903 (1972).
(48)A. Abragam-:-"The Principles of Nuclear Magnetism", Oxford
University Press, London, Chapter 8.
(49) ,
T. C. Farrar and E. D. Becker, "Pulse and Fourier Transform
NMR", Academic Press; New York, 1971.
(50)D. Doddrell, V. Glushko and A. Allerhand, J. Chern. Phys., ~,
3683 (1972).
(51) .
J. GranJean and P. Laszlo, Mol. Phys., 30, 413 (1975).
(52) " =
A. Allerhand and R. A. Komoroski, J. Am. Chern. Soc., ~,
8228 (1973).
(53) . '
H. Salto, H. H. Mantsch and I. C. P. Smith, J. Am. Chern. Soc.,
~,SfiSB (1973).
TI4)M. C. Fedarko,J. Magn. Resonance,g, 30 (1973).
(55) G. C. Levy, Accounts' Chern. 'Resonanc;:- ~, 161 (1973).
44
-------
Recent theoretical advances56-65 have allowed for the interpre-
tation of more complex molecular motions, but extensive variable
temperature and variable frequency experiments have not been
available to properly test each 'model. Such testing should in
theory encompass measurement of all three accessible parameters:
the spin-lattice relaxation time, Tl' the spin-spin relaxati0n
time, T2' and the nuclear Overhauser enhancement, NOE.
We report here the results of an investigation of two poly-
mers, poly(n-butyl methacrylate) and poly(n-hexyl methacrylate)
at a number of temperatures and at two widely different magnetic
fields. The inadequacies of the available models will be discussed
and suggestions for improvement of the present theories will be
proposed.
Experimental
Poly(n-butyl methacrylate) (PBMA) was obtained from Poly-
science, Inc. as a high molecular weight material. Solutions
were made without further purification using toluene-d8 and
benzene-d6 as solvents. Poly(n-hexyl methacrylate) (PHMA) was
purchased as a toluene solution (25wt%) from the Aldrich Chemical
Company. All samples were sealed in nmr tubes but not degassed.
50% PHMA samples were prepared by solute concentration at -?-Qg
under a N2 gas stream. ~
Natural abund~nce 13C spectra were obtained using Bruker
HX-270 and HFX-90 spectrometers operating for 13C at 67.9 MHz
and 22.6 MHz, respectively. Free induction decays were accumu-
lated using Nicolet 1080 series computers and Fourier transformed
to yield 4096 data points in the frequency domain spectra. .
(56)S.
J. Am.
(57)D.
Proc. ,
T"58"T
D. E. Woessner, J. Chern. Phys., ~, 1 (1962).
(59) . --
D. Wallach, J. Chern. Phys., ~, 5258 (1967).
~~O)y. K. Levine, P. Partington,-;nd G. C. K. Roberts, Mol. Phys.,
2.5.~ 497::' (1913).:'c, ."
~l)y. K. Levine, N. J. M. Birdsall, A. G. Lee, J. C. Metcalf~.~"'-
P. Partington, and G.C.K. Roberts, J. Chern. Phys., ~, 2890 (1974).
(62)R. E. London and J. Avitabile, J. Chern. Phys., 65, 2443 (1968).
(63) . =
W. T. Huntress, Jr., J. Chern. Phys., 48, 3524 (1968).
(64) ==
L. G. Werbelow and D. M. Grant, J. Chern. Phys., 63 544 (1975).
(65)L. G. Werbelow and D. M. Grant,J. Chern. Phys., 63, 4742 (1975).
Berger, F. R. Kreissel, D. M. Grant and J. D. Roberts,
Chern. Soc., ~, 1805 (1975).
E. Woessner and B. S. Snowden, Jr., Adv.. Mol. Relaxation
1, 181 (1972).
45
-------
Quadrature detection was employed for all Tl experiments and some
of the NOE determinations.
Tl measurements were performed using the ~T-1800-"[-900)n
Fast Inversion Recovery pulse sequence, FIRFT. 6 Intensities
obtained from the FIRFT spectra were used to calculate relaxation
times using the expression In(Soo-ST)=T/Tl where S is the equi-
librium amplitude of the fully relaxed peak and S~ is the ampli-
tude of the peak at some pulse delay time T. The estimated error
in Tl is approximately 10%, but repetitive measurements indicated
that the reproducibility was much better.
Nuclear Overhause, enhancements, NOE values, were determined
with gated decoupling6 generally using single phase detection.
Experiments were set up to take two sets of spectra: two were
acquired with constant wideband decoupling and two others using
interrupted decoupling. The pulse interval equalled or exceeded
ten times the longest Tl involved. NOE values were determined.
from the average of the two data sets and are considered accurate
to within f15%-20%.
The temperature was controlled with a Bruker B-STIOO heating
unit. The sample temperature was measured using a thermometer
placed in an equivalent sample tube containing an equivalent
volume of benzene of toluene solvent, under identical decoupling
conditions. Decoupling power was kept low to prevent sample
heating during gated decoupling NOE measurements (-3-4 watts).
All theoretical calculations were performed on a CDC 6400
computer with programs written in FORTRAN IV.
Theory
For two.nonequivalent spin-l/2 nuclei the spin-lattice
relaxation time48,49 (Tt) and the nuclear Overhauser enhancement
factor (NOEF) may bewrltten in terms of the spectral density.
functions, J. (w), as:
1
1 2 2 2 -6
Tl = 0.1 N Yc YH ~ r . [Jo(wH-wc) + 3Jl(wc) + 6J2(wH + wc)]
(15)
and
NOEF (NOE-l)=n=3.976
[Jo(~
6JA(WH + W ) - J (wH - w) ~
L . C 0 C
- W c) + 3 J 1 ( W c) + 6 J 2 ( wH + W c )
(16)
(66) .
However, these experlments were normal IRFT measurements for
all but the longest Tl carbons.
(67)R. K. Harris and R. H. Newman, Ibid., l:!:., 449 (1976).
46
-------
where N is the number of directly attached hydrogens (for 13C_lH
dipolar relaxation), Yc and YH are the magnetogyric ratios of
carbon and hydrogen respectively, and r is the carbon-hydrogen
internuclear distance. ' ,
If the autocorrelation function can be described48 by an
exponential characterized by a single correlation time, T :
c
TC
J"(w) =
J. 1 + W2T 2
c
(17)
F d. "b. f 1" " 68-74 ( h .
or a lstrJ. utlon 0 corre atlon tlmes mat ematlcally
indistinguishable from a non-exponential autocorrelation function)
one can introduce a mUlti~licative factor known as the probability
destiny function, G(T ),6 and equation (17) becomes
c
J" (w)
1
= I: 1
G(T )T
C c
+ 2 2
. W T
C
, dT
C
(18)
Vlhere
JOO G(T )dT = 1
c c
o
(19)
Of h "bl d" ;b . f "68-74 h
t e many pOSSl e lstrl utlon unctlons only t e
spectral densities for three (Cole-Cole, Monnerie diamond lattice'
and log_X2)69-71 and their derivatives will be given. ,
Each distribution yields quantitatively similar results when
applied to a common data set es~ecially if the experimental data
are obtained at a single field.71 Under these circumstances,
choosing the model which best describes polymeric dynamics is
somewhat arbitrary. The pros and cons of these three functions
will be briefly discussed below. It is important, however, to
(68)ta) T. M. Connor, Trans. Faraday Soc., 60, 1574 (1964);
(b) J. Mikayke, J. Polymer Science, ~ 477=f1958).
(6'9')K. S. Cole and R. H. Cole, J. Ch;;. Phys., ~, 341 (1944).
(70)J. Schaefer, Macromolecules, 6, 882 (1973).
(71) =
F. Heatley and A. Begum, Polymer, 16, 399 (1976).
(72) '" ==
R. M. Fuoss and H. G. Klrkwood, J. Am. Chern. Soc..,
(73) '" '
D. W. Davldson and R. H. Cole, J. Chern. Phys., ~,
(1950); :19.;:.,1484U1951).
(74)F. Noack, NMR Ba's'ic'Prihc.ahd Progress, ~, 1971.
g, 385(1941).
1417
47
-------
examine the general consequences of adopting this type of model
for the behavior of the backbone carbon molecular dynamics.
Many of the trends experimentally determined for the, side chain
carbons are intimately linked to the model chosen for the back-
bone carbons.
Use of a distribution results in the prediction of frequency-
dependent relaxation times over a very wide range of correla-
tion times, including those within the so-called extreme 9frrowing
region predicted from a single correlation time model.68- Thus,
very long relaxation times can be field dependent. Measurements
made (and conclusions drawn) in such cases may be quite mis-
leading if only one magnetic field is used. NOE's also exhibit
more complex behavior relative to that from single correlation
time models. A decrease in the NOE can be observed at shorter
correlation times, while an increase in the NOE is obtained at
longer correlation times depending on the width of the distribu-
tion.70-71 Therefore, carbons exhibiting long, but still fre-
quency dependent Tl's may have unexpectedly low NOE's. Conversely,
carbons with very long correlation times may have abnormally high
NOE's. It should be noted that, as in the single correlation
time model, a given NOE is associated with only one correlation
time. ' ,
The position of the Tl minimum for a given carbon as a
function of motion (temperature) is also affected by the width
or the distribution of c'orrelation times especially for broader
distributions (as in the log-X2 model).70 In addition, the curves
for Tl and NOE as a function of correlation times become more
shallow as the width of the distribution increases. This is
illustrated in Figures 20 and 21 for the log-X2 distribution. As
a result (for a constant distribution width) the observed temp-
erature dependence of the TI's and NOE's may be small, particu-
larly for very broad distriDutions. For cases in which the
distribution width varies with temperature, the derivation of a
'simple' activation energy for the polymer becomes impossible.75
The spectral densities for the simple distribution functions
are as follows:
'c 'I ' 'C' I' D' t 'b t' 69-71
o e~ 0 e 1S r1 u lon
The spectral density function is given by:
( ) - 1 [ COS[(1-y)w/2] , J ( )
Ji 00 - 200 cosh(ylnooT) + sln[(1-y)w/2] 20
where y is the width parameter and may take on any value in the
range 0 to 1.0. In the limit y=l the expression for Tl (and NOE)
reduces to essentially the single correlation time model. The
( 75 ) R M D 1 d 'J" 'C'h'" ,
. ac ona , . em. PhYs.,~, 345 (1962).
48
-------
TI
(msec)
100
10
II
10 '
9
-log t
8
7.
6
FIGURE 20.
Spin-lattice relaxation time, Tl' as a function of
correlation time, T and distribution width, p, for
the log-X2 distribution (22.6 MHz).
NOEF
2.0
0.4
0.8
II
10
9
-log t
8
7
6
FIGURE 21.
Nuclear Overhauser enhancement factor, NOEF, as a
function of correlation time and distribution width
for the log-X2 distribution (22.6 MHz).
49
-------
Cole-Cole distribution is a symmetrical distribution.
Monnerie Diamond Lattice Mode171
The spectral density function is given by:
J.(I.\)) =
1
~( )1/2
LOLD (LO - LD) LO
( )2 + 2 2 2 2TD
L - LD I.\) L Ld
00.
['1+
I.\) 2 T 2) 1/ 2 +
o
1 + 1.\)2L 2
o
1 ] 1/ 2
(~ \1/2
2LD)
I.\)LOLD
L - L
o D
t 22 1/2 ~1/2
(1 + I.\) L) - 1
o
1 + 1.\)2L 2
o
-J
(21)
where L is the correlation time characterizing molecular tumbling
motionsoand LD is characteristic of conformation transitions since
the model involves conformational jumps of a polymer chain on a
diamong lattice. For LD/L greater than 10 this model also reduces
to the single correlation ~ime results.
L 2 D" . "b " 70,71
og-X lstrl utlon
The spectral density function is given by:
J.(I.\))
1
IOO L H(s)(exPbs-l)
= .'2 2 2 ds
o (b-l){l + I.\) :r [(exPbs-l)/(b-l)2 }
(22)
where
H(s) = 1 (ps)p-le-psp
npr
(23)
in (23) is the width parameter and f(p) (which is a normalization
factor) is the value of the gamma function for the value p.
Due to the use of a logarithmic scale the variable :8 is
defined by:
:s = logb[l + (b-l) LC/T"J
(24)
The average correlation time is given by L and the logarithmic
base is described by the parameter b (usually take to be 1,000).
For p greater than 100 this model reduces to the single correla-
tion time model. Note that this is an asymmetrical distribution
with gr,ster weighting of the correlation times for longer L
values.
Log-X2 Distribution Including 'Simple' Internal Rotation71
The first modification to be made involves inclusion of
internal rotation in the equations of the log-X2 distribution in
antic~pation that such a correction may better describe the motion
50
-------
of the side-chains. The internal motion is incorporated under
the following assumptions: (1) only one extra degree of freedome
is involved and (2) the carbon in question is assumed to experience
a three-fold barrier to rotation. In addition, it can be assumed
that the motion of the substituent is either dependent on or
independent of the motion of the backbone. For this reason the
spectral densities are given in two parts.
1.
Dependent Internal Rotation
The spectral density function is given by:
foo [
1 2 2
Ji(w) = . b H(s) ~(1-3cos a)
T(~
1 + w2:r2(bS-l)2
b-l
3(sin22a + sin4a)
bS-l)2
b-l
ds
(25)
where
K = Tg/Tc
(26)
and
where K is a constant, T is the correlation time for internal
rotation and a is the an~le between the CH vector and the rota-
tion axis.
Inde~endent Internal Rotation71
For lndependent internal rotation the spectral density
functci.on is.
2.
foo [ G s )
1 2 2- b -1
J i (w) = 0 H ( s ) ~( 1- 3 co s a )T j):T""" .
1 + w2:r2(bS-l) 2
j I b-l.
- s
T T(b -1) . 2 T T (bS-l) 2 d
g (1 + W g ) s
~(bS-l) + "g(b-l) (~(bS-l) + "g(b-l~ J
+ 3(sin22a+ sin4a)
(27)
Log-X2 Distribution Including.Multiple Internal Rotations
The final change involves incorporating multiple internal
rotations into the dynamics of the sidechain carbons while main-
taining the distribution of correlation times for the backbone
carbons.
51
-------
The theory beh~nd derivation of the spectral density func-
tions for the multiple internal rotations has been described in
previous papers60-62 and only the essential equations relevant
to the present discussion will be given here.
. The spectral density functions for internal rotation alone
are given by:60-62 .
Ji(W) = f .ldab(Ba)12Idbc(Bb)12...ldni(Bn)12Idio(Bi)12
a,b,...,l .
T
1 + W2T2
(28)
where
T = (6D
o
+ a2D
+ b2D
. b
+ ... +
i2D.)-1
1
(29)
and D is the overall (isotropic) rotational diffusion constant
for tHe molecule, D_, Db' ... D. are the rotational diffusion
constants for-the cgrbon-carbon~onds in the alkyl chain; and the
dlj are the reduced second order Wigner rotation matrices. The
angles ,Ba, -B-b' ... are the angles between the final axis of
rotation and the qipole-dipole vector between the coupled nuclei
under investigation. .
London and Avitabile70 have shown that the problem may be
considerably simplified, the resulting spectral densities being
given by: .
J.(W) = L B bBb ...Bh.B. T
1 , b . a c 1 10 1 + ,.\2... 2
a, ,...,1 w .
(30)
where the B matrix elements are geometric factors describing the
alkyl chain (their values can be found in reference 62).
Rather -than refer to these papers individually the above
theory 8f Tultiple inte~nal rotations developed by Wallach,59
Levine6 ,6 and London6 will be referred to collectively as the
WLL theory.
We propose that the present theory is unsatisfactory for
describing the frequency dependent dynamic parameters (Tl' NOE)
of the sidechain carbons attached to "macromolecules" whose over-
all molecular motion must be described by a distribution of
correlation times. The extensive data obtained will allow a
rigorous comparison of these theories to be made.
We have, therefore, extended the present WLL theory to the
situation in which the presence of a distribution of correlation
52
-------
times is required for the backbone carbons. This is accom~lished
by applying the probability density function for the log-X distri-
bution (equation 22) to the spectral density of (equatlon 28).
Of the possible choices of distributions upon which one could
expand the model for sidechain dynamics, the 10g-X2 distribution
mode170 was chosen. All the models suffer fro~ various defi-
ciencies, however. The Cole-Cole69,7l is a symmetrical distribu-
tion while the asymmetrical 10g-X2 model weights the longer corre-
lation times to be expected in polymeric systems. It should be
noted that there is no particular advantage in using the asymme-
tric log-X2 distribution for descriptions of syste~s characterized
by relatively narrow distributions. It can be shown that the X2
distribution can be approximated very closely by a normal (i.e.,
symmetric) distribution for cases in which the number of degrees
of freedom is approximately 45 or greater. The most serious
deficiency of the Monnerre diamond lattice model is the erratic
temperature dependence of TD/T for comparable polymers and the
physical basis of the model ha~ been questioned.7l The 10g-X2
model suffers from the presence of the parameter b which must be
judiciously chosen so that a wide range of data can be examined
bya change in width parameter, p, only. The model breaks down
for cases in which p
-------
paint mare to. the canclusian that these lang range 'caaperative'
matians have eluded detectian. This emphasizes' the need far
multi-frequency Tl and NOE measurements far the accurate inter-
pretatian af dynamics in palymeric and other camplex malecular
systems.
Recently, Yasukawa et al.77 have simulated the randam matians
af an n-hexyl chain baund to.' a macramalecule (paly(n-hexyl-4-vinyl
pyridinium bramide)) by Mante Carla methads. Different madels
were tested accarding to. the transitian prababilities chasen far
the canfarmatianal intercanversians. They faund that the spectral
density functians far the main chain agreed well with the canven-
tianal spectral density appraximatian [2T/(1+w2Tc2)J but that the
functians far the hexyl chain cauld nat be represented by the same
expressian.
While a satisfactary fit to. the experimental Tl values was
abtained, no. mentian was made af the predictive value af the
theary as applied to. the NOE's ar changes in frequency.
NuIIiericalResults
Figure 22 illustrate$ the trends exhibited far the variaus
carbans af an alkyl chain which is described by equal internal
ratatianal diffusian canstants (Di=l.O x lOll sec-l) abaut each
band, the chain being attached to. a macramalecule (defined as
carban zero.) with an isatrapic carrelatian time af 1.0 x 10-10sec.
~hen the o~erall molecul~r carrelatian t~me (Tm 1) is langer
than the carrelatian time far internal ratatian, thearelaxatian
times increase dramatically alang the chain (subject, af caurse,
to. the D. 's being canstant alang the chain). Hawever, the rela-
tive NTlldifferences far these carbans are attenuated cansider-
ably by the presence af a distributian af carrelatian times far
the backbane carbans, until finally far a braad distributian
(e.g., p=8), the NT1's change very little aver the length af the
chain. The same effect accurs when the internal ratatianal
diffusian canstant is slawer than the averall matian.78 The
presence af a distributian can be distinguished fram the latter
situatian fram the frequency dependence af the TI's as well as
fram certain trends in the NOEF's, as discussed ln the fallawing
paz<>agraphs.
There is anly a slight frequency dependence far the Tl's near
the end af the chain with a narraw distribitian (p=50); that
dependence increases cansiderably far' braader distributians and
is present even far the end methyls af lang chains far the braad
distributians. As the trends indicate, the frequency dependence
(78)R. Deslauriers and R. L. Samarjai,J. Am. Chern. Sac., ~,
1931 (1976).
54
-------
FIGURE 22.
10.
-
o
~ 9
..=-
Z 7
21
19
17
SPIN-lATICE RElAXATION TIMES FOR
SIDECHAIN CARBONS A FUNCTION OF
DISTRIBUTION WIDTH
( Di (j = 1,4) = 1.0 It 10"set'1 )
67.90 MHz -
22.63 MHz ----
15
II
5
..
..
..
..
,
,
"
,.... pa20
,
,..
,,"
...'
., ",.
...'
,
.-----':'---e- ----
. 3
1
...------- --8
- paS
.2
CARBON NUMBER
3
4
Spin-Lattice Relaxation Times for Sidechain Carbons
A Function of Distribution Width
55
-------
disappears entirely for sidechain carbons attached to a backbone
whose motion can be described by a single correlation time model.
The presence of the distribution lowers TIts for the sidechain
carbons relative to the values calculated for the single correla-
tion time model for identical diffusion constants. Also apparent
is the fact that a change in the width of the distribution can
induce a large change in the TIts.
Figure 23 illustrates the effects on the nuclear Overhauser
enhancement factor, NOEF, assuming the parameters given in
Figure 22.
FIGURE 23.
1.0
LL .
lJJ
o
Z
. '-
2.0
.--- -----.
------ P=50
..--
...---'-
....-- .
1.5
p=50
--~
-e--- --
---- p=20
.--- .
--
--
.----
p=20
NUCLEAR OVERHAUSER ENHANCEMENT
FACTORS FOR SIDECHAIN CARBONS AS
A FUNCTION OF DISTRIBUTION WIDTH
O.
Di(j=I,4)= Ix 109 see', Tmol= l'OxIO,osec
67.90
MHz-
22.63
MHz ------
0.0
I 2
CARBON NUMBER
Nuclear Overhauser Enhancement Factors For Sidechain
Carbons As A Function of Distribution Width
56
\,J
-------
The NOEF's range from 1.2 to 1.5 for C-l under the given
conditions at both fields and increase for the remaining carbons
in the chain. For p=50, however, the NOEF is substantlal and
might be considered maximized within experimental error (depending
on the accuracy of the experiment). For very broad distributions
the NOEF value is quite low, even for C-4 with a value of approx-
imately 1.4. In general, for most distribution widths, there is
only a slight frequency dependence of the NOEF.
The other common situation is depicted by Figures 24 and 25.
The rotational diffusion constants along the chain have been
reduced by two orders of magnitude so that the internal motion is
now comparable to the overall or polymer backbone segmental
molecular motion. As has been noted and as shown in Figure 24,
there is only a small gradation in the relaxation times along the
.51
SPIN- LATTICE RELAXATION TIMES OF SIDECHAIN
CARBONS AS A FUNCTION OF DISTRIBUTION WIDTH
9 -10
Di(j-I,4)=I.OxI0. Tmol= 1.0 x 10 see
~
67.90
MHz-
22.63
MHz ----
~3
.39
.2
p=20 ,,0
. ,
,"
,
. ,
,
, .
,p' p=so
,
,
,,"
,
,
,,0,,,
"
,
,
"
,
d"
~.o
, ~'
...~
~~ ~ ,0~;.20
--
..._.0--
--
~--
.35
-
u
G)
~ .31
t=
Z
.27
.19
.15
2 3
CARBON NUMBER
FIGURE 24.
Spin-lattice relaxation times of sidechain carbons as
a function of distribution width. All diffusion con-
stants are equal along the chain with a value of Di=
1 x 109 sec...;I for 67.905 MHz (-) and 22.635 MHz'
(----). Backbone (carbons) isotropic correlation time
. 1 10-10
1S . x sec. 57
-------
FIGURE 25.
2.0
u..
UJ
o 1.0
Z
0.5
O.
NUCLEAR OVERHAUSERENHANCEMENT FACTORS
FOR SIDECHAIN CARBONS AS A FUNCTION OF
DISTRIBUTION WIDTH
1 - -10
Di 0" 1,4)" 1.01(10' see' , Tmol" 1.0xi0 see
67.90 MHz -
22.63 MHz -----
2 .
CARBON NUMBER
NuclearOverhauser enhancement factors for side chain
carbons as a function of distribution width. .
Conditions the same as for Fig. 24.
58
...
-------
FIGURE 26.
-
u
.
.
E 100
.=
T. VI. T at two fields
for P .100 and P.8.
1000
67. 9MHz j .
}""
"
'..
10
10-10
10-9
10-8
T (sec)
Spin-lattice relaxation time versus correlation time
for distribution widths of p = 8(----) and p =
100(----) for 67.905 MHz and 22.635 MHz.
59
D
-------
sidechain. When
molecular motion
along the chain.
quency dependence
distribution.
internal motions are much slower than the overall
there would be virtually no change in the Tl's
In relative terms there is a substantial fre-
which, as expected, increases for the broader
When T. ~ < T 1 the Tl's experience a greater frequency
dependence tR~n fo~o~he case T. t < T 1.
ln mo
The effects of these parameters on the NOEF's are substantial.
The motion results in a larger frequency dependence compared with
Di=l.O x 109 and p=20 the C-4 carbon NOEF is 1.2-1.4 at the two
flelds, whereas, forD.=l.O x lOll sec-l a much broader distribu-
tion (p=S) was requirea to attain comparable NOEF values. The
effect of the distribution w~dth is enhanced also. Changing from
p=20 to p=50 for D.=l.O x 10 sec-l results in an NOEF 6harige of
0.35 - 0.4. Thes~me change in p when D.=l.O x lOll sec-1 affects
the NOEF for C-4by.!-c:mly 1. O. 1
Two Fields
71
Heatley and Begum noted that the model parameters should
be dependent on the nmr parameters if they are to be calculated
with accuracy. The areas which are least sensitive, in general
(but not always) are the region of the Tl maximum and the long
correlation time region for the NOEF. In these cases the experi-
mental.data (within the limits imposed also by experimental
accuracy) are, therefore, reproduced by a number of different model
parameters. This ambiguity is alleviated by the use of two fields
as widely separated as possible. Three (or more magnetic field
strengths) would be even more advantageous. Figure 26 illustrates
that a simple frequency measurement of Tl can lead to the predic-
tion that any distribution width (up to and including the possi-
bility that no distribution exists) will reproduce the experi-
mental Tl for certain correlation times. The unequivocal state-
ment tha~ a distribution of correlation times is not required for
data obtained at only one frequency can now be seen to be an
extremely misleading supposition. .
Examination of the Tl data presented in Tables 10-13 reveals
several characteristic trends. The TI's for the sidechain carbons
generally increase as a function of dlstance from the backbone.
. This is not unexpected, since the same behavior is observed in
smaller molecular systems having aliphatic chains effectiv~ly.
anchored at one end because of the presence of a relatively
immobile functional group or because of ionic or bonding in4sr6l 79 so
actions between the molecule and its immediate environment. ' , ,
(79)D. Doddrell and A. Allerhand,J. Am. Chern. Soc., 93. ;558
(1971).
60
-------
I~ the.absence, of such a situation,NTl values gen~rally i~crease
wlth dlstance from thB center of mass.61,80-82 Slnce motlonal
restriction is greater for the carbon'positions closer to the
restricting group, correlation times describing these positions
should be longer than for carbons removed from the site of
restriction. The motions along the aliphatic sidechains of PBMA
and PHMA are predominantly characterized by apparent correlation
times to the left of the T minimum. Note, however, that the Tl
values for C-3 sometimes s~ow a slight decrease with respect to
the Tl values for C-l and C-3 at lower temperatures and at the
higher field strength.
The most surprising fact is that there is a consistently
large field dependence associated with the Tl's of the sidechain
carbons. Simple theory 48-49 predicts that ~he dipolar T of any
carbon is independent of the magnetic field strength if t~e corre-
lation time describing its motion is within the extreme narrowing
region [(wC+wH)2Tc2«lJ. ,
With the exception of C-l, for each sidechain carbon an
increase in temperature results in an increase in Tl' The C-l Tl
values remain relatively static over the wide temperature range
studies (-100°) and give evidence for shallow Tl minimum (particu-
larly for PBMA).
As the temperature is increased, the backbone methylene
carbon in PBMA shows a definite Tl minimum at each magnetic
field, while Tl for the main chain CH2 carbon of PHMA monotoni-
cally increases over the same range. This difference may orig-
inate from the fact that, for comparable temperatures, PHMA is
further above its glass transition temperature83 and hence has
relatively more freedom, of motion. . '
The minima observed for PBMA (50% w/w toluene-d ), shown in
Table 10, also prove interesting. The backbone CH2' ~lminimum is
found at ca. 56°C at 22.6 MHz but at ca. 77°C at 67.~ MHz. This
is consistent with the fact that the ~minimum for the 67.9 MHz
magnetic field strength occurs at a sh6rter correlation time than
for the 22.6 MHz field strength. This implies that a greater
temperature would be required at higher field strengths to observe
the Tl minimum. The same trend is observed for the quaternary
backbone carbon of PBMA.
(81)N.J.M. Birdsall, A~G. Lee~ Y.K.Levine, J.C. Metcalfe,
P. Partington and G.C.K. Roberts, J.e.s. Chem.Comm. 757 (1973).
(82)C. Chachaty, Z. Wolkowski, F. Pirious and.G. Lukacs, Chern.
Comm. 951 (1973). ' -
T831"S. S.,Rogers and L. Mandelkern, J. Chern. Phys. ,61, 985 (1957);
J. D. Ferry, "Viscoelastic Properties of Polymers", WIley, New
York, 1961. '
61
-------
TABLE 10. 13C SPIN-LATTICE RELAXATION TIMES OF POLY(BUTYL
METHACRYLATE) IN 50%(WIW) SOLUTION IN TOLUENE-De.
. .,.
Tl . (see)a
Temp.
(OC) C-l C-2 C-3 C-4 C-CH C"'CHZ C-CR
3 4
-5 0.27 0.20 0.35 0.93 00053 2.7
6 0.35 0.23 0.39 1.0 00057 0.21 2.3
21 0.35 0.37 0.73 1.7 0.062 0.17 203
46 0.33 0.57 1,,2 2.4 0.081 0.12 1.8
55 0.33 0069 1.5 2.9 0011 0.098 1.7
75 0.28 0.79 1,,5 3.4 0.15 00085 1.5
80 0.29 0.90 2.5 3.8 0.14 0.086 1.4
93 0.31 0.95 207 4.0 0.18 00093 103
98 0.32 1.1 2.8 4.3 0.18 00094 1~5
111 0.35 1.4 3.4 6.2 0.26 0.11 1.6
a 67.9 MHz
Performed at
Tl a
(see)
Temp.
(OC) C-l C-2 C-3 C-4 C-CH C-CH2 C-CR
3 4
10 0.13 0.20 0045 1.1 0.025 0.69
22 0.11 0.25 0.52 1.3 0.030 0.034 0.64
37 0.093. 0.27 0.70 1.5 0,,033 0.031 0.56
49 0.094 0.33 0.89 107 0.048 0.031 0.54
66 0.085 0.37 0095 1.8 0.059 00030 0.49
83 0.10 0.45 1.1 2.1 00079 0.035 0.53
105 0.15 0067 1.4 2.8 0.13 .0.043 0.70
a at 22.6 MHz
Performed
62
-------
TABLE 11. 13C SPIN-LATTICE RELAXATION TIMES OF POLY(HEXYL
METHACRYLATE) IN 50%(W/W) SO LUTION IN TOLUEN E..D a.
. . . . . . . . . .
. ~.".....
a
T1 .(see)
Temp.
(0 C) C-1 C-2 C-3 C-4 C-5 C-6 C-CH C-CH C-CR
3 2 4
3 0.32 0.21 0.30 0.57 0.81 105 00069 0.32 2.9
34 0.30 0.30 0.55 1.1 1.7 2.6 0.068 0.13. 1.8
49 0.31 0.47 0.85 1.6 2.4 3.7 0.092 0.11 1.6
63 0.31 0.54 1.1 2.1 3.2 4.6 0.10 0.097 1.6
83 0.30 0.65 104 2.3 3.7 5.3 0.12 0.090 1.5
100 0.31 0.81 1.8 2.9 5.1 7.1 0022 0.093 1.4
a Performed at 67.9 MHz
a
Tl (see)
Temp.
( 0 C) C-l C-2 C-3 C-4 C-5 C-6 C-CH C-CH C-CR
2 3 4
17 0.12 0.14 0.26 0.47 0.75 1.6 0.Q24. ----- 0.63
43 0.11 0.24 0.47 0.90 1.5 2.3 0.037 0.035 0.54
64 0.10 0.28 0.63 1.1 201 3.3 0.057 0.029 0.40
74 00 098 0.36 0.83 1.5. 2.5 4.2 0.073 0.028 0.46
89 0.10 0.38 0.95 1.7 3.0 4.8 O. 086 0.031 0.47
102 0.13 0.52 1.0 1.8 3.3 5.1 0.14 0.042 0.58
a 22.6 MHz
Performed at
63
-------
TABLE 12. 13C SPIN~LATTICE RELAXATION TIMES OFPOLY(BUTYL
METHACRYLATE) IN 50%(W/W) SOLUTION IN BENZENE-DS
a
Tl (see) .
Temp. C CH c
( 0C) C-l C-2 C-3 C-4 C-CH C-CR
3 - 2 4
10 0.41 0 .30 0.51 1.2 00065 2.5
22 0039 0.38 0.67 1.7 0 ,,069 0.19 2.3
31 0.46 0.51 1..0 2.3 00076 0.17 2.4
40 0.41 0053 101 :L.4 00078 0.13 2.1
50 0.26. 0.65 1.4 207 0.088 0.11 1.9
a At 67.9 MHz, estimated maximum error:!: 10% typical error <: 5%
(see text)
b
Temperature:!: 2°C
c
At low temperature, unable to calculate Tldue to peak
broadening
TABLE 13. 13C SPIN-LATTICE RELAXATION TIMES OF POLY(HEXYL
METHACRYLATE) ln 20%(W/W) SOLUTION IN TOLUENE-D8
Tl .a
(see)
Temp.
(oC) C-l C-2 C-3 C-4 C-5 C-6 C-CH C-CH2 C-CR
3 4
16 0.26 0~27 0.54 0.87 1.4 2.1 0.049 0.084 1.6
22 0.25 0.28 0.55 1.0 1.5 2.4 00057 0.079 103
35 0.24 0.35 0.67 1.2 2.0 2.8 0.060 0.063 1.2
65 0.30 0.60 1.4 2.4 3.6 4.3 0.099 0.067 1.2
91 0.37 0.92 2.0 4.2 5.0 6.8 0.18 0.081 1.5
a Performed at 67.9 MHz
64
-------
A minimum is observed for PHMA (50% w/w in toluene-dS) at
22.6 MHz, as can be seen from the data in Table 11. Observation
of a minimum at the higher field strength, requires temperatures
unattainable in toluene-dS' A more dilute solution of PHMA (20%
w/w in toluene-dS) does exhibit a minimum at approximately 50°C.
Table 14 contains the nuclear Overhauser enhancement factors
for PBMA. At low temperatures, the NOEF's for the sidechain carbons
become equal near the theoretical maximum value of 2. AS,the
temperature is increased, the NOEF for C-l decreases cons~derably
(by a factor of ca. 5) while the C-2 and C-4 NOEF values decrease
much less (by a factor of ca. 2). The NOEF difference between
C-l and C-2 increases as the temperature increases while the C-2
and C-4 difference remains relatively constant. The backbone
methylene NOEF also decreases somewhat with temperature. At 101°C
it reaches an NOEF which is comparable to that observed for C-l
sidechain~ The backbone methyl substituent NOEF increases with
temperat#~~ by a factor of 2 over the range 14°-101°C.
The situation is somewhat different for the low field data.
The C-l NOEF increases with temperature while the C-2 and C-4
NOEF values remain relatively constant over the temperature range,
but at lower than the maximum permissible value. At high temp-
eratures, the NOEF's for the sidechain carbons tend to equalize.
A small increase in NOEF with temperature is noted for both the
backbone carbons.
C-CH3
The trends exhibited by the methyl group directly attached
to the backbone can be reproduced by a model which incorporates
dependent internal rotation of the substituent attached to a
backbone whose overall molecular motion must be described by a
distribution of correlation times.
Figure 27 illustrates that the T and NOEF should increase
with increasing temperature for the c~lculated backbone correla-
tion times for the various temperatures studied.
Previous studies on related methyl groups have pointedly
illustrated the varied behavior of these substituents. The
correlation time of the methyl group in poly(propylene oxide) was
found to be independent of the average correlation time of the
backbone while the methyl in poly(isobutylene) exhibits an internal
correlation time which is proportional to the backbone correlation
time. This is similar to the situation for poly(methyl meth-
acrylate) .
65
-------
2.0 -
67.9MHz -
D=I.OX Io'°sec-I
1.5
1L.
W
o
Z
I
I
NUCLEAR OVERHAUSER ENHANCEMENT \ I
FACTORS FOR SYSTEM UNDERGOING \. I
MULTIPLE INTERNAL ROTATIONS AS A \ I
FUNCTION OF THE (ISOTROPIC) \ /
CORRELATION TIME FOR BACKBONE \ I
MOTION \ /
\ I
22.6 MHz---- \ /
D=!.OX 10,osec-1 \ ,
\ ,
\ I
, ,
,~'"
1.0
10-11
1010
T (see)
10-9
10-8
107
FIGURE 27. Nuclear
enhancement factors
undergoing multiple
rotations.
Overhauser
for a system
internal
65a
-------
TABLE 14.
NUCLEAR OVERHAUSER ENHANCEMENTS FOR POLY(BUTYL
METHACRYLATE) IN 50% (W/W) SOLUTION IN TOLUENE-DS
a b
. NOEF .
Temp. C-3c
(0 C) C-l C-2 C-4 C-CH. C-CH C-CR
3 . . . . .2. . .4
-5 2.0 1.9 2.0 0.51
.14 1.4 1.7 1.8 0.71 0.67 0.47
34 0.81 1.6 1.6 0.83 0.56 0.61
42 1.1. 1.6 1.5 1.2 0.43 0.66
52 0.80 1.4 1.5 1.2 0.44 0.50
64 0.61 1.3 104 1.3 0.44 0.59
80 0.54 1.3 1.3 1.3 0.43 0.56
101 .0.42 0.98 1.3 104 0.36 0.59
?i At 67.9 MHz, estimated maX1.mum error :t 10%
b NOE = NOEF + 1, therefore NOEF = 1.988
max
NOEFa
Temp. C-3 c C-CHb
( 0C ) C-1 C-2 C-4 C-CH2 C-CR4
.3
11 0.47 1.5 1.6 . 0.99 0.89
. 21 0. 54 1.7 1.7 0 .30 0.88
31 0.23 1.0 --- 1.2 0.91 0.30 0.22
50 0. 69 1.2 1~6 1.8 0 .40 0.68
63 0.79 1.9 1.3 1.3 0.71 0.75
81 0.9 1.1 1.4 1.8 0.66 1.3
104 1.1 1.3 1.4 1.4 0 .59 1.1
. ..
a Performed at 22.6 MHz
b NOEF at 21°C absent due to apparent large error, (NOEF = 2.21)
~NOEFts not determined, overlap with solvent resonances prevents
~peak integration. .
,.
66
-------
TABLE 15. NUCLEAR OVERHAUSER ENHANCEMENT FACTORS FOR POLYJHEXYL
METHACRYLATE) IN 50%(w/w) SOLUTION IN TOLUENE-D8
Temp(OC) 61.'.9 WIz
C-l C~2 C-3 C-4 . .C_-_5 C-6 C-CH C-CH C-CR'I
- 1.9-4 1:66 1758 1..50 1.6'2 0':6"13 """""""'2
3 2.06 -- 1.15
17 1.73 1.83 1.62 1.60 1.51 1.6'6 0.79 0.70 0.81
35 1.21 1.63 1.68 1.64 1.63 1.71 1.09 0.62 0.47
50 1.04 1.57 1.71 1.75 1.75 1.73 1.12 0.27 0.58
66 1.88 1.56 1.80 1.79 1.85 . 1.94 1.57 0.42 0.64
100 1.79 1.52 1..83 1.89 .1.91 1.98 1.76 0.51 0.72
Temp(OC) 22.6 MHz
C-l C-2 C-3 C-4 C~::> C-6 C-CH3 C-CH C-CR11
0.64 1.6-7 ............... 1.59 - 1.98 0 . 412
17 1.83 1.91 0.91 0.51
44 0.95 1.60 1.72 1.72 1..71 1.80 1.-6 0.33 0.88
66 1.06 1.46 1.28 1.22 1.12 1.31 1.53 0.52 0.58
76 0.87 1.30 1.44 1.32 1.52 1.39, 1.04 0.67 0.68
90 0.91 1.07 1.06 1.43 1.15 1.44 1.11 0.-1 .0.81
103 1.09 1.25 1.31 1.46 1.19 1.15 1.65 0.52 0.76
67
-------
C-l Carbons
No attempt was made to fit all data exactly by systematically
varying the p parameter, the diffusion .constants or the average
correlation times by very small increments. The purpose of the
present analysis is the determination of the relative importance
of the distribution of correlation times for the backbone carbons
with respect to the multiple internal rotations about the C-C
bonds. It should suffice to choose parameters which encompass
the extremes of measured Tl and NOE values and hence the extremes
of temperature. Numerous parameters have been varied to illus-
trate their effects and to elucidate whether the trends in the
experimental data are satisfactorily reproduced.
. Data for the C-l carbons in both polymers indicate an insen-
sitivity to change in temperature at both fields. In addition
there is a great similarity in the magnitude and frequency depend-
ence of the Tl values when comparing PBMA with PHMA. Considering
the changes in correlation times and distribution widths asso-
ciated with an approximate change in temperature of 100°C the
question becomes one of whether the theory can reasonably predict
this behavior.
Table 17 summarizes the numerical results for the C-l carbon
with a set of parameters (T, p) chosen from the experimental
results for ~wo widely different temperatures. Therefore, the
average correlation times span two orders of magnitude with the
shorter correlation times (5 x 10-9 sec) being associated with
the narrower distribution parameters (p=50 and p=20) while.the
long correlation time is associated with the broad distribution
width (p=8, b=lOOO in all cases).
For a large range in distribution widths and correlation
times the calculated T1's at a given field are relatively constant,
even allowing for a moaerate increase in the internal rotational
diffusion constant (Dl) with increasing temperature.
The observed Tl's differ in value by a factor of two to three
at the two magnetic field strengths; a trend which can be repro-
duced with the parameters of Table 17.
The nuclear Overhauser enhancement factors are calculated to
be in the range 1.0-1.3 for the given parameters, but inspection
of the data reveals that a much wider range of values are observed,
as evidenced by the extreme values obtained at the highest and
lowest temperatures for both polymers. While the calculated NOEF's
are within experimental error of the observed (fO.3n) for most. of
the intermediate temperatu~es, the deviations from calculated values
at the highest and lowest temperatures are definitely outside of
experimental error. ..
68
-------
Figure 27 illustrates the fact that for short correlation
times (high temperatures) the NOEF at 22.6 MHz is. greater than
the NOEF at. 67.9 MHz. This is the situation one predicts (and
observes) for a system which can be described by a single corre-
lation time or a simple distribution of correlation times. How-
ever, the more complex behavior observed in the present case can
be attributed to the effect of internal rotation superimposed
upon the overall molecular motion. Note that as the correlation
times increase (as the temperature decreases) the difference
between the two magnetic field strengths becomes smaller.
Finally, for corr~lation times long~r tha~ _2.0 x 10-9sec the
NOEF at 67.9 MHz becomes greater by a substantial amount; the
differences diminishing again for very long correlation times.
The experimental data verify this behavior qualitatively.
The NOEF for PBMA at 67.9 MHz and -5°C is at its maximum value
(2.0n). As the temperature is increased the trend reverses until
at -IOOoC the NOEF at 22.6 MHz is greater than that at 67.9 MHz.
Theoretically, the presence of the distribution equalizes the
NOEF's but the effects of the internal rotation tend to negate
this. The net result is that the present theoretical modifica-
tion emphasizes the effect of the distribution in a manner contrary
to observation at the lowest temperatures. .
Anisotropy in the backbone motions can introduce an addi-
tional angular factor in the calculations. It has been shown
that changing the angle between the first bond and the molecular
Z axis (assuming the symmetric rotor model) can affect the relax-
ation times considerably as a function of the anisotropy. This
possibility has not been included in the present calculations and
may partially obviate the discrepancies, particularly for C-I
since the effects of anisotropic motion are calculated to be
greatest at this chain position.
For a constant diffusion coefficient the WLL theory predicts
that the TI's will increase as the temperature decreases (within
the calculated range of correlation times for PBMA and PHMA).
While this is not in fact the case, it should be noted that such
an insensitivity to temperature may result from the WLL theory
provided that the diffusion constants decrease enough to offset
the increase due to the longer backbone correlation times.
C-2 Carbons
For similar temperatures the C~2 carbon TI's of PBMA are
larger than the corresponding. values of PHMA. This is consistent
with the greater motional freedom associated with a shorter chain
which lessens the effects of inter- and intra-molecular inter-
actions due to chain entanglements. However, the glass transi-
tion temperature of PHMA should be lower than that of PBMA so that
. direct and absolute comparison of the polymers at similar tempera-
69
-------
tures is not free of ambiguity as to the origin of the dynamic
differences.
The frequency dependence of the T 's for C-2 is not as great
on the "average as. that observed for C-! but is still of consider-
able magnit~de and outside experimental error. Inspection of
Table 9 in conjunction with Tables 10 and 3 reveals that the
distribution-modified internal rotation theory is able to predict
the frequency dependent behavior. ~
The NOEF's (Tables 14 and 15) do not follow the trends that
were so obvious for C-l. They tend to average -1.5 i 0.3~
(except for the temperature extremes at 67.9 MHz). Table 18
therefore would indicate that the distribution is relatively
broad (p<20) and further shows that an increase in p values
(i.e., approaching the WLL theory) will result in predicted NOEF's
which are consis~ently larger than the observed values (~hil~ also
predicting a small or negligible frequency dependence contrary to
observation). .
Under certain circumstances, the C-2 carbon Tl's of PBMA and
PHMA are less than the T '8 of C-l and C-3 at the same tempera-
ture. The effect is gre~test for low temperatures and the higher
magnetic field strength. Even for 67.9 MHz the effect disappears
for temperatures above 20-40oC.
Doddrell et ale have shown that increasing the rate of inter-
nal rotation can result in a decrease in Tl if motion of the
backbone carbons satisfies the condition w2T2»1 in conjunction
~ith the condition W2T2eff -1 for the sidechain carbon whose Tl
1S shortened. .
The latter condition is not necessary for observation of the
phenomenon. Even for w2T2eff«1 the effect may occur. Levine,
et al.60,61 have proposed the following explanation.
The transformation along the chain decreases the effective
correlation time of the slow motion, leading to an increase in
the spectral density at high frequencies. . For carbon 2 this
increase is greater than the concomitant decrease in spectral
density due to the internal rotations. This results in a net
increase in spectral density at high frequencies andoa reduction
in Tl values.
It was noted that the effect is very sensitive to the Larmor
frequ~ncies involved. Thus (at 24kG) the effect was seen for
lH... H relaxation but not for 13C_1H relaxation. This is consis-
tent with the fact that the C-2 Tl's only decrease relative to C-l
for the higher field (higher Larmor frequencies) and only at cer-
tain temperatures (for which the condition w2 T2»1 is satisfied).
70
-------
C-3 Carbons
Not until one reaches C-3 (see Tables 19 and 20) do the
greatest differences in theories become apparent. The WLL theory
predicts that a virtually maximum NOEF should be observed for the
correlation times spanned by the backbone carbons. In fact, a
consistently reproducible NOEF which is less than the maximum
value is observed for PHMA. While data ar.e not available for C-3
of PBMA, interpolation from the C-2 and C-4 NOEF's confirm the
trends of PHMA. It is not reasonable to expect that the C-3
NOEF's of PBMA could vary greatly from the average values of the
C-2 and C-4 NOEF's since the values for theSe latter carbons are
, generally so close over the entire temperature range studied.
The frequency dependence of the C-3 Tl's is again considerable
for both polymers. Even for p values of 50, one predicts that
the frequency dependence is quite small; vanishing for the single
correlation time (WLL) theory. The low and intermediate tempera-
ture data is reproduced quite reasonably by inclusion of the
distribution effects, particularly for PHMA. The frequency depend-
ence of the T 's for PBMA at high temperatures «90°C) cannot be
reproduced with a reasonable set of parameters, the backbone dis-
tribution is too narrow to accomodate the observed differences.
C-4 Carbons
PBMA
The C-4 carbon of PBMA is (Tables 21 and 22) methyl group
and, therefore, direct comparison with the C-4 carbon of PHMA is
not possible in the manner chosen for carbons C-l through C-3.
Table 21 specifically illustrates the calculated methyl values for
C-4 carbon with the given parameters, hence the corresponding Tl's
of Table 10 for PBMA can be compared directly. "
The low temperature (less than -50°C) frequency dependence of
the Tl's (see Table 22) is reasonably predicted by the present
theory, i. e., the T 1 's vary by approximately 20% with the change
in frequency from 2z.6 MHz to 67.9 MHz. At high temperatures the
frequency dependenceincre~ses in relative magnitude and cannot be
quantitatively predicted by this or any other theory presently
known.
The implication is that the terminal methyl has ,associated
with it some very long correlation times. The gradual evolution
of the frequency dependence under our present theore,tical assump-
tions does not le~d to the observed facts. Obviously, factors as
yet unaccounted for contribute significantly to the dynamic
behavior of the terminal methyl group.
One is reminded at this point of the results of Levine76 which
predicted that a strong correlation in the motions of pairs of
C-H vectors on adjacent atoms may be possible. Thus, the C-4
71
-------
carbon of PBMA could
carbon and acquiring
such as an increased
sion coefficients.
be considered as interacting with the C-3
characteristics indicative of the C-3 carbon
frequency dependence for comparable diffu-
The origin of the unusual Tl's of these polymers for C-4 is
not reflected in any precipitous changes in nuclear Overhauser
enhancement factors at this position~ The experimental values
are still less than maximum as predicted by distribution widths
less than or equal to about p=20. .
C- Sand C-6Carhons'(PHMAorily)
The NOEF's for C-S are predicted from the relatively broad
distri~ution width. associated with ~he backbone 7arb~n Tl'~.. ~s
noted ln the numerlcal results sectlon;the relatlve lnsensltlvlty
of the NOEF's for broad distributions is predicted to extend quite
-a distance from carbon 0 for reasonable diffusion coefficients.
The same can be said for the C-6 carbons. Despite NTl values of
the order of 20.0 seconds, the NOEF's are generally less than
maximum. .
The low temperature C-S results shown in Table 23 are in
accord with theoretical predictions, particularly for temperatures
less than SOoC.
Cross Correlation Effects
Cross correlation effects (even under proton decoupled condi-
tions) should be most evident for methylene (or methyl) carbons
undergoing anisotropic reorientation with correlation times that
are 6f the order of w -6D where D is the diffusion constant
for overall motion ofCthe golecule gnd w is the Larmor frequency
of carbon. London et al. have shown that, except for C-l, the
effects are-insignificant for internal diffusion constants, Di,
equal to i09 sec-l but became more important for Di=lOlO sec-l
and lOll sec-l and an internal rotational diffusion constant (Di)
of -1010 sec-l.
The cross correlation effects are attenuated as the carbon
under consideration becomes more remote from the site of substi-
tution on the main chain. .
Examination of the data in Table 16 shows that the range
D =-106 - 108sec-l for the backbone diffusion constant is covered
b~ the temperature changes.
This is precisely the most sensitive region for detection of
cross correlation effects. In addition the rotational diffusion
constants are of the order of 1010 - lOll sec-l. The predicted
deviation due to cross dorrelation effects neglecting the effects
of a distribution of correlation times, in the NOEF for C-l and
72
-------
C-2 under these conditions is approximately 0.2-0.5 units.
data show no evidence for these effects.
The
Surnrriary and ConcTusions
1. Invocation of a distribution of correlation times for the
backbone carbons of PHMA and PBMA yields a satisfactory fit of
the experimental data at two fields and a variety of temperatures.
2. The single correlation time approximation may be inadequate
for describing not only the dynamic behavior of polymer backbone
carbons but also the alkyl (or related) sidechain substituents.
3. Carbons which are, strictly speaking, eight bonds removed
from the backbone exhibit frequency dependent relaxation times and
less than maximum nuclear Overhauser enhancement factors. We
have preliminary data on a related polymer, poly-(n-octyl acrylate),
which ind~cates that ten bonds are required in these polymers be-
fore relatively temperature independent NOEF's are observed.
4. Multiple internal rotation effects alone cannot account
for the observed nmr parameters.
5. The distribution of correlation times for the backbone
carbons is effective in altering the dynamic parameters of the
sidechaincarbons, inducing frequency dependent Tl behavior.
6. The inability to fit the high temperature spin-lattlce
relaxation times for the termlnal ~PHMA, PBMA) and penultimate
carbons (PHMA) indicates that the present theoretical modifica-
tions are insufficient in some respect. The assumptions of
independent bond rotations and/or stochastic diffusion may be one
source of the discrepancy.
7. Alkyl chain dynamics in various environments,. as measured
by nmr, require qUlte different motional models. One model should
not evell be expected to uniquely determine the nmr parameters in
different polymers.
8. Unlike data for the n-alkanes, the relaxation data for
these polymers cannot be interpreted by the model in which the
diffusion constants for internal rotation are the same for all
bonds. The data is better explained in terms of a slower diffu-
sion constant for the first bond and slightly increasing diffu-
sion constants for the remaining carbons. The data for the
terminal methyl, however, does require that a large increase in
internal rotation about the final bond be invoked. .
Studies of hydrocarbon chains in dipaiffiitoyl lecithin bi-
layers provide an interesting comparison in that the motions of
the chain near the terminal methyl are identical with those of
the corresponding n-alkane carbons and in qualitative agreement
73
-------
with the present calculated diffusion constants. The most signif-
icant observation is that the motions of the C-C bonds near the
glycerol bridge of the lipids are an order of magnit~de slower
than those of the .remaining chain carbons. .
It is possible that the slow motions required to fit the
observed data may be oscillatory in nature rather than involving
a full rotation. .Under these circumstances, the correlation time
is the product of the true correlation time "and a factor describ-
ing the amplitude of the oscillatory motion. Unfortunately, it is
not possible to distinguish an increase in the true rotational
diffusion constant from an increase in the amplitude of oscilla-
tion along the chain. .
74
-------
TABLE 16.
CORRELATION TIMES, WIDTH PARAMETERS, AND SPECTRAL
QUANTITIES FQR PBMA IN TOLUENE -dB AS A FUNCTION OF
TEMPERATURE AND THE LOG-X2 DISTRIBUTION MODEL
Te::;p. 22.7 MHz T Cl09sed p
i~. ~C &7.9 MHz c
T1 (cal.) T1(obs.) NOEF(ca1.) :\OEF(obs.) T1 (cal.) T1(obs.) NOEF( ca1.) NOEF(obs.)
100 0.19 0.19 1. 37 1. 3& .059 .079 1. 59 1. 59 7.1 20
80 0.17 0.17 1. 43 1. 43 .051 .0&9 1. &7 1. && 5.0 20
50 0.22 0.22 1. 41 1.44 .059 .063 1. 59 1.40 11 12
40 0.25 0.25 1. 45 1. 43 .068 .062 1. 61 16 8
35 0.27 1. 56 .0&2 1. 30 .22 <8
20 0.34 1. 63 .067 1. 30 .130 <8
a
All the observed values are for the methylene backbone carbon
(C-CH). All Tlvalues are in sees. and are equal to 2X the
actual or predicted value for this carbon (otherwise known as
the NT 1 or the Tl expected had there only been one proton
presen'L.)
75
-------
TAB LE 17.
CALCULATED METHYLENE SPIN-LATTICE RELAXATION TIMES AND
NUCLEAR OVERHAUSER ENHANCEMENT FACTORS FOR THE C-1
CARBON
67 0 9 MHz
22.6 MHz
Distribution Wid~ha
T 1 (sec)
NOEF(ll)
T1 (sec)
NOEF(ll)
P=8
(T=1.3X10-7sec)
D1-102
D =300
1
P=20
(-r=500X10-9sec)
0.24
0.34
1.1
1.1
0012
0.16
101
101 .
D1=102
D1=300
P=50
(T"= 5 0 0~nO-9sec)
0.26
103
Uo14
103
0040
103
0021
102
D1=102
D1=3.0
0029
1..3
0015
1.2
0046
1.2
0.21
100
aLog~X2 distribution assumed; all Di's are given in units of 1010
sec,.,I
76
-------
TABLE 180
CALCULATED METHYLENE SPIN-LATTICE RELAXATION TIMES AND
NUCLEAR OVERHAUSER ENHANCEMENT FACTORS FOR THE C-2
CARBON
67 . 911Hz
Distribution Widtha
II (see) .
P=8
(T"=l. 3X10-7 see)
Dl=1.2, D2=3.0
D1=1.2, D2=5.0
D1=1.2, D2=10.0
P=20
(T"=v.OX10-9see)
0.36
0.41
0.48
D1=1.2,
D1=1.2,
D1 =1. 2 ,
D2=3.0
D2=5.0
D2=10.0
0.52
0.62
0.75
P=50
- -9
(.T=5.0X10 see)
D1=1.2,
D1=1.2,
D1-1.2,
D1=1.2,
D2=1. 0
D2=3.0
D2=5.0
D2=10.0
0.51
0.78
0.92
1.13
NOEF(n)
!l(see)
22.6 MHz
Experimental
Temperature (OC)t
1.2
0.20
NOEF(n)
PBMA PHMA
1.2
1.3
0.22
0.26
--
1.3
34
1.6
0.37
1.3
1.3
21
43
1.6
1.6
0.44
0.53
1.6
46
63
1.8
1.8
0.40
0.60
0.69
1.6
1.6
55
83
1.7
1.7
0.81
100
1.7
1.6
1.6
1.5
98
given in units of 1010
a 2
Log-X distribution assumed; all Di's are
sec-l
blisted diflusion coefficients reproduce observed data for the
stated experimental temperatures
77
-------
TABLE 19.
CALCULATED METHYLENE SPIN-LATTICE RELAXATION TIMES AND
NUCLEAR OVERHAUSER ENHANCEMENT FACTORS FOR THE C-3
CARBON
67.9 MHz 22.6 MHz Experimental (oC)b
Temperature
Distribution Widtha !l(see) NOEF( Tj) !l(see) NOEF(Tj) ~ ~
P=8
(T'=1. 3XIO-7 see)
Dl =1. 2, D2=5.0, D3=5.0 0.59 1.3 0.34 1.4 34
Dl=1.2, D2=5.0, D3=7.0 0.63 1.3 0.37 1..4
Dl=1.2, D2=5.0, D3=lO.0 0.69 1.3 0.40 1.4 21 43
P=20
(T'=5.0X10-9see)
Dl = 1. 2, D2=5.0, D3=5.0 1.18 1.7 0.96 1.8 46 63
Dl =1. 2, D2=5.0, D3=7.0 1. 30 1.7 1.08 1.8 83
D1=1.2, D2=5.0, D3=10.0 1.47 1.7 1.21 1.8 55
P=50
(T-5,OX10-9see)
D1=1.2, D2=5.0, D3=5.0 . 2.20 1.9 2.00 1.9
Dl=1.2, D2=5.0, D3=7.0 2.47 1.9 2.24 1.8
D1 =1.2, D2=5.0, D3=10.0 - 2.80 1.9 2.51 1.8 98
a 2
Log:!
sec.
bLo
lsted
stated
distribution assumed; all Di's are given in units of 1010
diffusion coefficients reproduce observed data for the
experimental temperatures.
78
-------
TABLE 20.
CALCULATED METHYLENE SPIN-LATTICE RELAXATION TIMES AND
NUCLEAR OVERHAUSER ENHANCEMENT FACTORS FOR THE C-3
CARBON
Experimental (oC)b
67.9 MHz 22.6 MHz Temperature
Dis1:ribution Widtha !l (see) NOEF(n) !l(sec) NOEF( 11 ) PBMA
P=8
(t=1. 3XlO-7 sec)
Dl=1.2. D2-D3=10.0 0.78 1.4 0.46 1.4 21
Dl=1.2. D2=10.0. D3=30.0 1. 03 1.4 0.62 1.4 37
Dl=1.2. D2=10.0, D3=70.0 1. 30 1.4 0.79 1.4 46
P=20
(t=5.0XlO-9sec)
Dl=1.2. D2=D3=10.0 1.80 1.8 1.49 1.8
Dl=1.2, D2=10.0, D3=30.0 2.61 1.7 2.13 1.8
D,=1.2. D2=10.0, D3=70.0 3.39 1.7 2.70 1.7
...
P=50
(t=5.0XlO-9sec)
D1=1.2. D2=D3=10.0 3.49 1.9 3.06 1.8
D1=1.2. D2=10.0, D3=30.0 5.00 1.8 4.18 1.7
Dl =1. 2, D2=10.0, D3=70.0 6.24 1.8 5.00 1.7
a 2
Log-X
see-I.
bListed
stated
distribution assumed; all Di's are given in units of 1010
diffusion coefficients reproduce observed data for the
experimental temperatures.
79
-------
TABLE 21.
CALCULATED METHYLENE SPIN-LATTICE RELAXATION TIMES AND
NUCLEAR OVERHAUSER ENHANCEMENT FACTORS FOR THE C-4
CARBON . .
67.9 MHz
22.6 MHz
Experimental
Temperature (oC)b
Distribution Widtha
:Il(see)
NOEF(Tj)
:II (see)
NOEF(Tj)
PHMA
P=8
(T=1.3XIO-7see)
Dl=1.2, D2=D3=D4=D5=S.0
Dl=1.2, D2=5.0, D3=7.0,
D4=10.0
0.74
1.4
0.44
1.4
.1.4
1.4 34
0.87
1.4
0.53
Dl=1.2, D2=5.0, D3=10.0
.D4=30.0
P=20
(r = 5 . 0 Xl 0 - 9 )
1.18
1.4
0.73
Dl=1.2,
Dl=1.2,
D4=30.0
Dl=1.2, D2=5.0, D3=10.0,
D2=D3=D4=5.0
D2=5.0, D3=7.0,
1. 74 1.8 1.51 1.9 49
2.28 1.8 2.01 1.9
3.58 1.8 3.1!.} 1.9
D4=30.0
P=50
(T-5.0XlO-9see)
Dl=1.2, D2=D3=D4=5.0
Dl=1.2, D2=5.0, D3=7.0,
D4=10.0
D1=1.2, D2=5.0, D3=10.0
3.64 ~ 2.0 3.56 2.0
4.95 2.0 4.82 2.0
7.98 2.0 7.68 2.0
D =30.0
1+
aLOg:i2
sec.
bL'
lsted
stated
distribution assumed; all Di's are given in units of 1010
diffusion coefficients reproduce observed data for the
experimental temperatures.
80
-------
TABLE 22.
CALCULATED METHYL SPIN-LATTICE RELAXATION TIMES AND
NUCLEAR OVERHAUSER ENHANCEMENT FACTORS FOR THE C-4
CARBON
, .
22.6 MHz
Experimental b
Temperature (OC)
,
67.9 Mliz
Distribution Widtha
!l(sec)
NOEF(T)
!l(sec)
NOEF(T)
PBMA
p=8
- -7
(T=1. 3xlO sec)
Dl=1.2, D2=5.0, D3=10~0,
D4=30.o0
Dl=1.2, D2=10.0, P3=10.0,
D4=30.0
p=20
(T"=5.0xlO-9sec)
0.79
1.4
0.49
1.4
0.84
1.4
0.53
1.5
Dl=1.2, D2=5.0, D3=10.O, 2.39 1.8 2.13 1.9 66
D4=30.0
Dl=1.2, D2=10.0, D3=10.0, 2.69 1.8 2.42 1.9 83
D4=30.0
p=.50 -9
(T=5x10 sec)
D1=1.2, D2=5.0, D3=10.0, 5.32 2.0 5.12 .' 1.9
D4=30.0
D1=1.2, D2=10.0, D3=10.0, 6.11 2.0 5.86 1.9
D4=30.0
a 2
Log:!
sec.
bListed
stated
distribution assumed; all Di's are given in units of 1010
9iffusion coefficients reproduce observed data for the
experimental temperatures.
81
-------
TABLE 23.
CALCULATED METHYLENE SPIN~LATTICE RELAXATION TIMES AND
NUCLEAR OVERHAUSER ENHANCEMENT FACTORS FOR THE C-5
CARBON .
67.9 MHz
22.6 MHz
Distributiori Widtha
!l(sec)
NOET(ll)
. Tl(sec)
NOEF(n)
p=8
- -7
(T=1. 3xl0 sec)
Dl=D2=D3=D4=D5=1.0
Dl=D2=D3=1.0, D4=4.0,
D5=7.0
Dl=D2=D3=D4=DS=10.9
p=20
- -9
(T=5.0xl0 sec)
0.43 1.3 0.25 1.4
0.68 1.3 0.46 1.4
1.43 1.4 0.91 1.5
Dl=D2=D3=D4=D5=1.0
Dl=D2=D3=1.0, D4=4.0,
D 5 = 7 .0, "
Dl=D2=D3=D4=D5=10.0
0.74 1.7 0.60 1.8
1.50 1.8 1.29 1.9
fi'
5.25 1.9 4.88 1.9
aL 2 d. . b .
. og-X lstrl utlon assumed; all Di' s are given inuni ts of
1010 sec-l.
. 82
-------
CONCLUSIONS
13 15 . f . h h
C and N Fourler trans orm nmr spectroscoples ave sown
their potential as powerful probes of tqxic environmental chem-
icals. These two related spectroscopic techniques can perform
chemical structure elucidation and, moreover, they can be used to
probe physico-chemical interactions between environmental contam-
inants and model bio-systems (i.e., lipid bilayers). For some
important environmental studies spectrometer sensitivity must be
extended past the state-of-the-art; this is particularly true for
15N work at natural (0.36%) iso~opic abundance.
A number of general nmr techniques were developed for this
project. They include improved methods for performing quantita-
tive nmr analysis, relaxation experiments, and 15N detection.
A semi-quantitative analysis was demonstrated for polychlorinated
biphenyl mixtures not requiring prior separation of individual
species.
The joint use of 21.3 and 63.4kGauss magnetic fields to
determine 13C relaxation data allowed a new analysis of complex
motions of alkyl chains in various molecular systems, including
model membrane systems. This work should allow future detailed
analysis of the disruption of membrane function~when chemical
contaminants are incorporated into bilayer structures..
83
-------
TECHNICAL REPORT DATA
(Please read InUrlictiolls on the reverse before completing)
1. REPORT NO. 12. 3. RECIPIENT'S ACCESSION-NO.
EPA-600/1-77-045
4. TITLE AND SUBTITLE 5. REPORT DATE
HIGH SENSITIVITY FOURIER TRANSFORM NMR. Intermolecular September 1977
Interactions Between Environmental Toxic Substances and 6. PERFORMING ORGANIZATION CODE
BJological Macromolecules
7. AUTHOR(S) 8. PERFORMING ORGANIZATION REPORT NO.
George C. Levy
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT NO.
Department of Chemistry lEA615
The Florida State University 11. CONTRACT/GRANT NO.
Tallahassee, FL 32306 803095
.
12. SPONSORING AGENCY NAME AND ADDRESS 13. TYPE OF REPORT AND PERIOD COVERED
Health Effects Research Laboratory RTP, NC
Office of Research and Development 14. SPONSORi"NG AGENCY CODE
U.S. Environmental protection Agency
Research Triangle Park, N.C. 27711 EPA 600/11
15. SUPPLEMENTARY NOTES
16. ABSTRACT
This project explored the feasibility of developing new techniques for evaluation of
the effects of envirQnmental toxic materials on complex biopolymer systems using high
s.ens i.ttvity Fourier transform nucl ear magneti c resonance (nmr). spectroscopy. Commerc i a 1
tnstrumentation available in 1974-75 did not possess adequate sensitivity, and thus
Qnegoal of this project was to increase spectral sensitivity, especially for the 13C
and oth~r nuclides having lowmagnetogyricratios. Initially, modifications to an
T~isting Bruker HX-270 spectrometer provided moderate improvement in sensitivity for
C and substantial sensitivity increase for 15N observation. During the second
(last) year of this grant, a new instrument design was initiated. Several studies
were begun to elucidate the nature of chlorophenol interactions in liqUidSj and when
incorporated into lecithin bilayer membrane models. Variable frequency 1 C spin
lattice relaxation tirne tTl) measurements were used to probe cooperativity of moleculal
chai.n dynamics in some simple molecules and in two complex synthetic polymers. A new
theoretical modification involving a non-exponential autocorrelation function and also
allowing for rnultiple independent , internal rotations, allowed effective analysis of
a large experiment~lset." ..
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS b.IDENTIFIERS/OPEN ENDED TERMS C. COSATI Field/Group
Fourier analysis 06 B, T
Fouri.er transforrni;itton
Nuclear magnetic res.Qnance
toxici..t.y .
bi..ornathernatics
biomedical measurement
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