United States
Environmental Protection
Agency
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October 2007 EPA 600/R-07/035-R1
Determination of Sorption Parameters
for 36 VOC/M ate rial Combinations
Final Report
Submitted to:
Dr. Zhishi Guo
U.S. Environmental Protection Agency
Office of Research & Development
National Risk Management Research Laboratory
Air Pollution Prevention & Control Division
Indoor Environment Management Branch
Submitted by:
Richard L. Corsi1, Neil Grain1, John Fardal1, John Little2, and Ying Xu2
1: Center for Energy & Environmental Resources, The University of Texas, Austin, Texas USA
2: Department of Civil and Environmental Engineering, Virginia Polytechnic Institute
and State University, Blacksburg, VAUSA
Office of Research and Development
National Homeland Security Research Center, Decontamination and Consequence Management Division
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NOTE: This report was revised in October 2007. The following letter explains the reason for
the revision. The previous version of this report has been removed from the NHSRC web site.
This version should be used.
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IVirginiaTech
The Charles Edward Via, Jr. Department of Civil and
Environmental Engineering
College of Engineering John Little, Ph.D., RE.
418 Durham Hall
Blacksburg, Virginia 24061-0246
Phone: (540) 231 8737 Fax: (540) 231 7916 E-mail: jcl@vt.edu
MEMORANDUM
To: Dr. Zhishi Guo
U.S. Environmental Protection Agency
Office of Research & Development
National Risk Management Research Laboratory
Air Pollution Prevention & Control Division
Indoor Environment Management Branch
From: Dr. John Little i<(< '
Professor
Environmental and Water Resources Engineering Program
Department of Civil and Environmental Engineering
Virginia Tech
Date: 1 October, 2007
Subject: Balance Malfunction Affecting Partition Coefficient Measurement
Measuring the material/air partition coefficient (K) for a VOC in a building material requires exposing a material
sample to a gas stream containing a known concentration of target VOC. The mass of the sample is recorded
as the VOC partitions to the surface and then diffuses into the material until the sample reaches gravimetric
equilibrium. The equilibrium concentration of VOC in the material is calculated by dividing the sample mass gain
by the sample volume. K is the ratio of material-phase VOC concentration to gas-phase VOC concentration.
The VOC laden gas stream is produced using a VICI Dynacalibrator. The Dynacalibrator contains a vial containing
the target VOC. A clean gas stream is passed through the diffusion cell at a known flowrate. VOC is emitted
from the diffusion vial at a constant rate into the gas stream. The gas-phase VOC concentration is calculated by
dividing the VOC mass emission rate by the gas flowrate. The gas stream flowrate is controlled using a mass-
flow controller. The diffusion vial emission rate is determined by measuring the mass of the vial before and after
the experiment using a mechanical balance.
Invent the Future
VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY
An equal opportunity, affirmative action institution
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The problem with the initial K measurements was the result of a malfunction in a mechanical balance. One of the
balance rings in the mechanical balance became dislodged from a support hook. This condition allowed the user
to accurately zero the balance, but produced an erroneous reading when the diffusion vial was placed on the
balance. The erroneous diffusion vial mass obtained from the mechanical balance produced errors in gas-phase
VOC concentration calculations.
The mechanical balance was repaired and the K measurements were satisfactorily repeated. A revised report
was produced. To eliminate the possibility of similar malfunctions occurring in the future the mechanical balance
operation procedures have been modified. The revised procedures require that after zeroing the balance a
calibration weight be used to confirm accurate balance operation before each use.
Invent the Future
VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY
An equal opportunity, affirmative action institution
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Table of Contents
1. Introduction 1
1.1 Problem Statement 1
1.2 Purpose of Study 1
1.3 Scope of Study and Division of Responsibilities 1
2. Experimental Methodologies 3
2.1 lest Materials 3
2.2 Test Chemicals 4
2.3 Dual-Volume Diffusion Chamber Experiments 4
2.4 Dynamic Microbalance Experiments 7
3. Data Analysis 9
3.1 Dual-Volume Diffusion Chamber Experiments 9
3.2 Dynamic Microbalance Experiments 11
4. Results 17
5. Discussion and Summary 19
5.1 Gypsum Board (Unpainted and Painted) 19
5.2 Carpet 19
5.3 Vinyl Flooring 20
5.4 Polyurethane Foam 20
5.5 Mortar 20
5.6 Summary 20
6. References 21
Appendix A - Quality Assurance Metrics 23
Appendix B - Finite Difference Equations and Program to Calculate De for Gypsum Board 31
Appendix C - Results for Mortar Experiments 47
Appendix D - Results for VF and PUF 49
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1.
Introduction
1.1 Problem Statement
Sorptive interactions between gaseous pollutants and
materials can be beneficial in terms of lowering pollutant
concentrations and, thus, human exposure to those pollutants
in buildings. However, the sorption process also leads to
contamination of indoor materials and prolonged desorption
of pollutants from materials. Scenarios for which sorptive
interactions affect indoor air quality range from routine
activities in buildings, e.g., use of cleaners or fragrances in
homes to cigarette smoking in bars, to infrequent and extreme
events, e.g., chemical spills in laboratories or terrorist
releases of chemical warfare agents. A critical need in
modeling indoor air quality during either routine or extreme
events is the ability to model sorptive interactions between
gaseous pollutants and indoor materials. However, the
existing database is sparse with respect to model parameters
for a wide range of chemicals and indoor materials. We
address that need in this study through the use of seven
chemicals with a wide range of physico-chemical properties
and six different test materials that are commonly found in
buildings.
1.2 Purpose of Study
The purpose of this study is to provide data to the United
States Environmental Protection Agency (USEPA) for the
evaluation of mathematical models that are best suited for
analysis of the fate of chemical warfare agents (CWAs) and
toxic industrial chemicals (TICs) that could be employed
during acts of terror on buildings.
1.3 Scope of Study and Division of Responsibilities
This study involved 36 combinations of test chemicals
and materials. Material/air partition coefficients (K) and
effective diffusion coefficients (De) were determined for
30 of those combinations; values of K and De could not be
determined for mortar. These parameters were determined for
use in models that predict chemical migration into and out
of materials based on an equilibrium partitioning between
air and the exterior surfaces of the material, and effective
diffusion within the material. Examples of such models
include those developed by Little et al., 1994; Cox et al.,
2002; Zhao et al., 2002; Xu and Zhang, 2003; Kumar and
Little, 2003; Deng and Kim, 2004; and Lee et al., 2005).
Procedures to determine the key model parameters for
these mechanistic models (including K and De) have been
described by Haghighat and Zhang, 1999; Bodalal et al.,
1999; Cox et al., 2001a; Cox et al., 200Ib; Blondeau et al.,
2003; Zhang and Niu, 2003; Zhao et al., 2004; and Li and
Niu, 2005.
Two bench-top laboratory systems were employed to conduct
the study. Twenty-four chemical/material combinations
were tested at the University of Texas at Austin (UT) using
a dual-volume diffusion chamber. Twelve chemical/material
combinations were tested at Virginia Tech (VT) using a
dynamic microbalance system. The experimental methods
and data analysis procedures are described separately for
each of these approaches in Chapters 2 and 3, respectively.
Results are combined in Chapter 4 and summarized in
Chapter 5. A discussion of quality assurance metrics is
included in Appendix A.
Project team responsibilities were divided between staff
at UT (dual-volume diffusion chamber experiments) and
staff at VT (dynamic microbalance experiments). Staff at
UT included Dr. Richard L. Corsi, Dr. Neil Grain, and John
Fardal. Staff at VT included Dr. John Little and Ying Xu. It is
noted that the VT Ph.D. student who was originally intended
to work on the project (Huali Yuan) graduated earlier than
expected. As a result, a new VT Ph.D. student (Ying Xu) was
trained in the microbalance procedure and was the primary
person responsible for collecting the experimental sorption/
desorption data.
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2.
Experimental Methodologies
2.1 Test Materials
This project involved experiments to quantify the sorptive
interactions between six materials and seven test chemicals.
The test materials were unpainted gypsum board, painted
gypsum board, PVC-backed carpet, mortar, vinyl flooring,
and polyurethane foam. A summary of test materials is
presented in Table 2-1. All test specimens were provided to
either UT or VT by the USEPA with two exceptions. Mortar
specimens were generated at UT. Polyurethane foam samples
were secured by VT. Unpainted gypsum board was marketed
as 1/2" (1.27 cm) thickness wallboard, which was confirmed
by direct measurement. Painted gypsum board was slightly
(less than 0.005 cm) thicker than unpainted gypsum board.
Carpet specimens were characterized by closed-loop nylon
fibers attached to a PVC backing. The mean thickness of
the carpet (backing and fibers) as measured using a Vernier
caliper was 3.40 mm (o = 0.01 mm; n= 5). The mean
thickness of the carpet backing (fibers shaved off) was 1.23
mm (o = 0.12 mm; n = 5). A common lot of each test material
was used throughout the experimental program to ensure
consistency.
Table 2-1. Summary of test materials.
Material
Unpainted Gypsum
Board
Jample Size
Unpainted gypsum board was cut into 26 cm
diameter circles using a Roto-Zip spiral saw.
The measured thickness of the unpainted
gypsum board was 1.27 cm.
description
The nominal '/2-inch gypsum board was
manufactured by National Gypsum Company,
Charlotte, NC 28211. The material was purchased
on 8/9/04 from Home Depot in the Raleigh, NC
area.
Painted Gypsum Board
Painted gypsum board was cut into 26 cm
diameter circles using a Roto-Zip spiral saw.
The measured thickness of the painted gypsum
board was 1.27 cm.
Same as above but painted by US EPA with
Classic 99 Flat Interior Latex Paint manufactured
by Sherwin Williams.
Type: Base color: 6405-10178
Color: Dover White
Color Code: A27W51 SW6385
The paint was purchased in the Raleigh, NC area
on 4/7/04.
Vinyl Carpet
Vinyl Carpet was cut into 26 cm diameter
circles using a template and a utility knife.
The mean thickness of the carpet (backing and
fibers) was determined to be 3.40 mm. The
mean thickness of the carpet backing (fibers
shaved off) was 1.23 mm.
The vinyl carpet was manufactured by Surfaces.
The product description was given as Type: ST103
Stratos/830 Gray item #97937, outdoor marine
carpet. The carpet was purchased 11/04 from
Lowe's in the Raleigh, NC area.
Mortar
Mortar specimens were cast in plywood molds
to a diameter of 26 cm and a nominal thickness
of 1.27cm.
The mortar was prepared using screened oven-
dried 3/4-in. siliceous river gravel, oven-dried
ASTM C 33 siliceous sand, Type I/II cement, and
tap water. Prior to testing, the mortar specimens
were cured for 28 days in a room at 70 °F and
100% relative humidity (RH).
Vinyl Flooring
The vinyl flooring sample tested had
dimensions of 3.78 cm (length) X 2.66 cm
(width) X 0.0175 cm (thickness).
Polyurethane Foam
The polyurethane foam sample tested had
dimensions of 1.39 cm (radius) X 4.70 cm
(length).
A flexible polyether-type, open cell polyurethane
foam was purchased from Airtex (Cokato, MM).
The bulk density was measured to be 0.022 g/cm3
at 21 °C and an RH of 21%, and bulk porosity of
97.6%. This commercial product is widely used
in pillows, beds, sofa pads, and cushions in both
homes and offices.
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2.2 Test Chemicals
Seven different organic test chemicals were used in this
study: ethylbenzene, n-butanol, hexanal, decane, undecane,
dodecane, and tetradecane. The first six were employed by
UT, using a dual-volume diffusion chamber. The latter six
were employed by VT, using a dynamic microbalance. Thus,
five test chemicals comprised a "base case" that was used for
testing with each method. Sulfur hexafluoride (SF ) was also
used for four of the six test materials. Sulfur hexafluoride
is an effective inert tracer, i.e., it does not adsorb to test
materials and can be used to determine actual diffusion
coefficients through materials in the absence of sorption
processes. Materials, corresponding chemicals, and test
methods are listed in Table 2-2. Several relevant properties of
test chemicals are listed in Table 2-3.
Table 2-2. Test materials, chemicals, and methods.
Unpainted gypsum board
Base case + ethylbenzene + SF
Dual-volume chamber
Painted gypsum board
Base case + ethylbenzene + SF,
Dual-volume chamber
PVC-backed carpet
Base case + ethylbenzene + SF,
Dual-volume chamber
Mortar
Base case + ethylbenzene + SF
Dual-volume chamber
Vinyl flooring
Base case + tetradecane
Microbalance
Polyurethane foam
Base case + tetradecane
Microbalance
Note: Base-case: n-butanol, hexanal, decane, undecane, dodecane
Table 2-3. Some relevant properties of test chemicals.
Chemical CAS #
n-Butanol*
Hexanal*
Ethylbenzene
Decane*
Undecane*
Dodecane*
Tetradecane
71-36-3
66-25-1
100-41-4
124-18-5
1120-21-4
112-40-3
629-59-4
^^ffl
74.1
100.2
106.2
142.3
156.3
170.3
198.4
1 »iu HI IBM rfo I iiBMCHB
118
128-131
136
173-174
196
216
252
Vapor pressure
(mm Hg) at 20 °C
4.4
10
7
2.7
1 (33 °C)
0.3
1 (76 °C)
Note: Boiling point and vapor pressure values based on Verschueren (1996).
* = base-case chemical
2.3 Dual-Volume Diffusion Chamber Experiments
2.3.1 Experimental System
Two separate dual-volume experimental chamber assemblies
were used for this study and were operated in parallel. A
diagram of the dual-volume chamber assemblies is provided
as Figure 2-1. Digital images of the system are provided
in Figure 2-2. Each chamber assembly was constructed
of electro-polished stainless steel to minimize nonspecific
sorption. The assemblies were comprised of two sections,
corresponding to the top and bottom chambers. Each section
had a nominal volume of 8.5 liters, with a slight reduction
in the top chamber when a test material was placed in the
system.
The test material was seated atop a neoprene gasket on a lip
around the perimeter of the bottom section of the chamber.
Another neoprene gasket was placed on the top lip of the test
material. The top section of the chamber slid over the bottom
section across an o-ring with 4/1000 of an inch tolerance and
compressed the material specimen around its perimeter. The
o-ring was seated in a groove around the perimeter of the
bottom section of the chamber. An external flange was bolted
around the system perimeter to secure the seal around the
material specimen. The diameter of the exposed surface of
the material was 26 cm.
Both chambers of the experimental system contained a small
fan used to promote mixing. The top section contained three
injection/sample ports, which contained V*" Swagelok™
fittings with silicon-lined septa for syringe injection/
sampling. The bottom section contained two ports of similar
design. Both chamber assemblies were previously leak tested
using sulfur hexafluoride.
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Figure 2-1. Schematic of experimental dual-volume diffusion chamber.
Mixing fan
\
Injection/sample port
Bolt
Y,
Top chamber
Flange
Substrate
Bottom chamber
Figure 2-2. Digital images of experimental dual-volume chamber system: (a) fully-assembled,
(b) view into bottom chamber with mixing fan visible, (c) bottom half with gypsum board seated
(o-rings visible around circumference).
(a)
2.3.2 Experimental Procedure for SF6
The experimental chamber was cleaned prior to starting
any experiment. The cleaning procedure involved several
steps. First, the chamber was disassembled and cleaned with
methanol. Following the methanol cleaning, the chamber
was reassembled and placed in an electric oven for 12 to 18
hours. An electric controller was used to maintain the oven
temperature at 115 °C. Following heat treatment in the oven,
the chamber was removed and allowed to cool before being
disassembled. Finally, the chamber was again cleaned with
methanol.
Once the chamber had been cleaned, the test material was
sealed in the chamber and allowed to "rest" for at least
four hours before background samples were collected from
both the top and bottom chambers. AlO-jjuL volume of pre-
diluted SF6 was drawn from a Tedlar™ bag, using a gas-
tight syringe, and injected into the top chamber through a
septum on the injection port. An initial sample was collected
approximately one minute after injecting the SF6. Samples
were collected from the top and bottom chambers using gas-
tight syringes inserted through Teflon™-lined septa into side
sampling ports. Sample volumes of 25 mL were collected
and immediately direct injected into a GC/ECD calibrated for
analysis of SF6 (Lagus Applied Technology, Inc. - Autotrac).
For tests involving gypsum board, subsequent samples were
collected over two to three hours until the SF6 concentrations
in the top and bottom chambers were approximately equal.
The tests conducted using mortar, however, lasted for more
than two months and were terminated before equilibrium
conditions were achieved. The effective diffusion coefficient
for SF6 could not be determined for carpet specimens due
to the rapid migration of SF6 through the specimens. All
dual-volume chamber experiments were completed at a
temperature of 24 ± 2 °C and relative humidity between 30
and 50 percent.
2.3.3 Experimental Procedure for Organic Test
Chemicals
Experiments with organic test chemicals involved the
same pre-cleaning procedure described above for the SF6
experiments. Background samples were also collected from
each chamber before the test chemical was introduced into
the top chamber.
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To initiate experiments, the selected organic compound
was added to a 2-L glass bottle fitted with a septum. The
compound was allowed to reach an equilibrium condition,
i.e., creating a saturated headspace. Avolume of between
50 and 600 mL of headspace gas was drawn from the bottle,
using a gas-tight syringe, and injected into the top chamber
of an experimental system; greater volumes were injected
for compounds with lower vapor pressure. A purge valve
was left open during injections into the top chamber so as
to avoid over-pressurization of the system, and was closed
immediately after injection.
Following the injection of the test compound, samples
were sequentially withdrawn from both the top and bottom
chambers at time intervals approximately 2 to 24 hours apart.
Samples were collected from the top and bottom chambers
until the system reached an equilibrium condition, i.e., the
concentrations of the test chemical in the top and bottom
chambers were approximately equal and constant. The
first sample was collected approximately 30 seconds after
the test compound was introduced to the top chamber. The
time required to achieve system steady state for the tests
with gypsum board and carpet ranged from several hours
to several days. However, experiments with mortar did not
achieve a steady-state condition over a period of more than
two months.
All samples were collected by withdrawing 25 to 100 mL
of chamber air through a sorbent tube connected to a gas-
tight syringe. Sorbent tubes were actually large-volume gas
chromatograph glass injection inserts packed with 100 mg of
Tenax™-TA (80/100 mesh), allowing for zero-path thermal
desorption of samples (see section 2.3.4).
Experiments involving mortar were conducted using a
mixture of all six organic compounds. This change was
made in an attempt to allow the test compounds to come to
system steady state over an extended experimental period.
The sample collection and analytical procedures used to test
the mortar sample were the same as those used to test the
gypsum board and carpet samples, although a steady-state
condition was not achieved for experiments involving mortar,
even after two months of sampling.
2.3.4 Analytical Methods
Samples were thermally desorbed using a programmable
injector and large-volume injection port (ATAS Optic 2),
with subsequent analysis using GC/FID (Hewlett-Packard
6890 GC; RTX 502.2 50 m mega-bore column with 0.53
mm i.d.) with a 1:1 split ratio. All analyses were completed
using a ramped oven temperature from 60 to 280 °C. The
oven temperature ramp rate was fixed at 30 °C/min. The
initial injector temperature for all experiments was fixed
at 60 °C. The injector temperature ramped to 280 °C in the
first minute. A detector temperature of 300 °C was used
for all samples. Calibration standards were generated by
spiking sorbent tubes with known volumes of the organic test
chemical dissolved in methanol, followed by purging of the
tube with helium for 20 minutes at 25 mL/min. Seven-point
external calibration curves were generated, with a minimum
correlation coefficient (R2) of over 0.99 for all experiments.
Figure 2-3. Schematic of the microbalance test system.
Constant Temperature Enclosure
To
Exhaust
Hood
Temperature
Transducer (RTD)
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Figure 2-4. Digital images of microbalance test system: (a) whole test system,
(b) microbalance system, (c) diffusion cell.
2.4 Dynamic Microbalance Experiments
Dynamic microbalance experiments were completed in
the Air Quality Laboratory of the Department of Civil and
Environmental Engineering at Virginia Tech. Measurements
were conducted using a high-resolution (0.1 to 0.5 (jug)
dynamic micro-balance (Model D200-02, Calm) equipped
with a PC-based data-acquisition system (DAQ) as shown in
Figure 2-3. This procedure was described in detail by Cox et
al. (200 Ib) but is briefly reviewed here. Digital images of the
system are provided in Figure 2-4.
The microbalance was placed on a marble balance stand that
damped out vibrations. An enclosure was erected around
the microbalance and covered with foil-faced polyethylene
insulation to minimize potential signal fluctuations due
to thermal variation or electromagnetic radiation. The
temperature in the microbalance enclosure was controlled to
within 25.6 ± 0.3 °C, using a constant temperature circulator
(Isotemp, 1028D, Fisher Scientific) connected to a heat
exchanger within the enclosure. The sample chamber was
constructed of borosilicate glass. A glass frit was installed
at the inlet end of the sample chamber to improve gas flow
distribution.
For sorption tests, a gas concentration of a specific VOC
was generated, using a constant temperature diffusion cell
(Dynacalibrator Model 190, VICI Metronics, Inc.) modified
as needed by substituting a stainless steel/glass flow path.
For desorption tests, clean, dry air was supplied from gas
cylinders (Medical Air USP, UN1002, Air Products). The
flow path was constructed of 3.2-mm ID. 304 stainless steel
and Teflon tubing with stainless steel fittings. Mass flow
controllers (MFC, Model FC-280S, Tylan-General) were
used to control the air flow rates.
The material sample was suspended on the microbalance
in the sample chamber. Samples were pre-conditioned in a
separate chamber that was flushed with clean, dry air. This
substantially reduced the time it took for the sample to reach
equilibrium once it was placed on the microbalance prior
to the start of the sorption/desorption experiment. After it
was put in the microbalance, the sample mass was allowed
to stabilize by passing clean, dry air through the sample
chamber until equilibrium was obtained. An air stream
containing a constant and known VOC concentration was
then passed through the sample chamber. The air flow rate for
the entire series of experiments was 0.334 actual L/min. VOC
sample mass gain over time was monitored until equilibrium
was reached. Influent air was then switched to clean air and
the desorption process was monitored until equilibrium was
reestablished. The airflow rate was relatively slow, and did
not significantly influence the sample weighing procedure.
For example, toward the end of the preconditioning period,
turning off the air flow rate did not result in a noticeable
change in microbalance response. A wider tube than supplied
by the manufacturer was used to reduce the air velocity and a
glass frit was introduced at the chamber entrance to ensure a
uniform air velocity profile across the diameter of the sample
chamber.
The diffusion vial with liquid VOC was weighed four
times before sorption, after sorption, and after desorption.
The emission rates were determined from the difference in
the average mass of the diffusion vial divided by the time
between the two measurements. The final emission rate
was taken as the mean of the two emission rate values. The
measured emission rates are shown in Table 2-4.
Table 2-4. Diffusion vial emission rates.
n-Butanol
Hexanal
Decane
Undecane
Dodecane
Tetradecane
Emission Rate (ug/min)
VF
217.5
186.0
42.9
15.9
6.9
5.1
PUF
194.1
-
43.0
21.6
10.2
8.3
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3.
Data Analysis
3.1 Dual-Volume Diffusion Chamber Experiments
3.1.1 Determination of Equilibrium Partition
Coefficients for Test Chemicals
The equilibrium partition coefficient (K) is a
measure of the sorption capacity of a material for a specific
chemical. Throughout this study we have assumed a linear
sorption relationship between test chemical concentrations in
air and on a material at equilibrium. As such, the equilibrium
partition coefficient was calculated as the ratio of the sorbed-
phase concentration (solid- or material-phase concentration)
to that in the air adjacent to the material at a condition of
equilibrium and was assumed constant for all values of C^:
K =
where,
K
(3-1)
equilibrium partition coefficient
[(mg/m3matenal)/(mg/m3 J] or
(m3 . /m3 . ,),
v air material7 '
sorbed concentration of test chemical
C^ = concentration in air at equilibrium
(mg/rtfj.
The concentration in air should be the same in the top and
bottom chamber sections at equilibrium. In fact, small
(emphasized) differences existed in the top and bottom
chamber air concentrations at equilibrium. As such, C^
reflects the average of test chemical concentrations in top and
bottom chamber air.
The mass of chemical sorbed to the test material at
equilibrium was determined as the difference between mass
added (minus mass removed in test samples) and the mass
contained in the air of each chamber. Adsorption of test
chemicals to stainless-steel chamber walls was assumed to
be negligible. The chemical concentration associated with
the material (sorbed-phase concentration) was determined in
accordance with Equation 3-2:
(3-2)
V.
solid
where,
m, =
m =
total mass of test chemical injected into the system
(mg),
mass of test chemical removed from system
V
air,t,e
during 1th sample (mg),
volumes of top and bottom chambers,
respectively (m3),
volume of material (m3),
concentration of test chemical in top chamber air
at equilibrium condition (mg/m3), and
concentration of test chemical in bottom
chamber air at equilibrium condition (mg/m3).
3.1.2 Determination of Effective Diffusion Coefficients
for Test Chemicals
Carpet. For experiments involving carpet, the test chemical
concentrations in the top and bottom chambers rapidly
reached equal values and then gradually decreased in both
chambers for a prolonged period of time. The following
equations from Crank (1975) were employed to determine
effective diffusion coefficients:
M,
M.
(3-3)
M.
^- = (l + ffMl-
a
(3-4)
where,
Mt = mass sorbed to the material at time t (mg),
Mra = mass sorbed to the material at equilibrium as
determined experimentally (mg),
a = ratio of volume of the air chamber to the
material (-),
qn = non-zero positive roots of the mathematical
expression: tan qn = - a qn.
/ = thickness of the material (m)
t = time (hr),
De = effective diffusion coefficient through material
(mVhr), and
Dt
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An alternate solution to Equation 3-3 for
small values of T is given by Equation 3-5:
and bottom chamber air. The effective diffusion coefficient
was chosen to minimize the total residual as denned by:
M
M
(3-5)
" C - C
~~1 air, experimental air, predict
, predicted
Equation 3-4 is obtained from Equation 3-5 by substituting
the asymptotic expansion for
( T \ ( T V'2 T
exp —- er/q —- when — is large.
\a' ) ' \a* ) a-
For carpet, a total normalized, squared residual between
predicted and observed mass sorbed fractions was denned as:
M
M,
M,
/M,
(3-6)
where,
R
i
total normalized squared residual (-), and
counter for each of n values of Mt (-).
The effective diffusion coefficient was selected as the value
that minimized the total residual R.
Gypsum board. In the case of gypsum board (unpainted
and painted), the initial concentrations in the top and
bottom chambers were not equal and changed with time. An
analytical solution could not be derived or found for these
conditions. A finite difference approximation was therefore
used to predict chemical diffusion through the gypsum board,
from the top chamber to the bottom chamber. Mass balances
were completed on the top and bottom chambers, with mass
loss from the top chamber due to diffusive flux (Pick's first
law) into the gypsum board and mass gain to the bottom
chamber by diffusive flux (Pick's first law) passing out the
bottom of the gypsum board. Pick's second law was applied
to predict chemical diffusion through the gypsum board (a
minimum of 10 layers/nodes was used for discretization of
the gypsum board). Equilibrium conditions were assumed
between chamber air and the exposed outer surfaces of the
gypsum board. Although gypsum board is porous, it was
treated as a solid slab for consistency with the models used
for other materials in this study. Resulting finite difference
expressions solved for concentration are presented in
Appendix B.
A residual analysis similar to that described above for carpet
was completed, with the exception of the normalized residual
involving measured and predicted concentrations in top
c
(3-8)
air, exp erimental
All variables are as described previously (the concentrations
in Equation 3-7 include those in both the top and bottom
chambers). Due to the large number of calculations required
to find a minimum residual, a program was written using
the Java programming language to facilitate timely results.
The source code for that program is included in Appendix B,
along with the key equations used in the numerical solution.
In addition to determining effective diffusion coefficients
for test chemicals and materials, i.e., that do not separate
the effects of sorption and diffusion, effective diffusion
coefficients (separated from the effects of sorption) were also
estimated for unpainted and painted gypsum board and each
test chemical. Effective diffusion coefficients were estimated
through the use of sulfur hexafluoride (SF6), an inert chemical
not affected by sorption processes in gypsum board, and
theoretical relationships between SF6 and each organic test
chemical. Specifically, the ratio of diffusion coefficients in
air for a test chemical and SF6 should be equal to the ratio of
effective diffusion coefficients through a porous test material,
e.g., gypsum board, and can be described by Equation 3-8:
D.
D
M,
where,
D
D, =
^
fl
fl
(3-8)
ratio of diffusion coefficients in air for a test
chemical and SF6 (-),
molecular diffusion coefficient of VOC (test
chemical) in air (mVhr),
molecular diffusion coefficient of SF6 in air
(mVhr),
effective diffusion coefficient of VOC in material
pores (nrYhr),
effective diffusion coefficient of SF6 in material
pores (mVhr),
collision integral for VOC (-),
collision integral for SF6 (-),
characteristic length of VOC molecule interacting
with air molecules (m), and
characteristic length of SF6 molecule interacting
with air molecules (m).
-------
Methods for estimating the collision integral and
characteristic lengths of interaction can be determined based
on Tucker and Nelken (1990). Resulting values are listed in
Table 3-1.
Table 3-1. Collision integrals and characteristic lengths
for select test chemicals.
n-Butanol
Hexanal
Ethylbenzene
Decane
Undecane
Dodecane
Sulfur hexafluoride
ion Integral Characteristic
Length (A)
1.174
1.180
1.185
1.207
1.219
1.230
1.048
4.627
4.923
4.922
5.467
5.580
5.687
4.374
The parameter Mr includes the molecular weight of air and
chemical i (VOC or SF6) in accordance with Equation 3-9:
M.
where,
M
air
M
M M
(3-9)
molecular weight of air = 29 g/mol, and
molecular weight of i (VOC or SF6)
(g/mol).
This approach allows a comparison between effective
diffusion coefficients that were determined from experiments
and that do not separate the effects of sorption with those that
should occur in the absence of sorption. For example, if the
former is similar to the latter, then sorption plays only a small
role in retarding chemical migration through a material such
as gypsum board. In contrast, a large difference indicates a
substantial effect of sorption in terms of retarding migration
through a material. The diffusion coefficient of SF6 in air
can also be normalized by its effective diffusion coefficient
through a material to determine a tortuosity factor that
reflects the average increased diffusion path length through a
material.
Example concentration-time profiles are shown in Figures
3-1 and 3-2 for sulfur hexafluoride and undecane diffusion
through unpainted gypsum board. In each case, the
convergence of concentrations in top and bottom chambers is
obvious, as is the fact that equilibrium is reached much faster
for SF, than for undecane.
3.2 Dynamic Microbalance Experiments
3.2.1 Determination of Equilibrium Partition
Coefficients for Test Chemicals
Using the sorption and desorption data recorded by the
microbalance, the equilibrium and kinetic parameters, K and
De, were determined (Cox et al., 200 Ib). For a particular
VOC, the sorption equilibrium was described using a
partition coefficient:
K =
where,
K
(3-10)
equilibrium partition coefficient
(|mg/m3 t ,1/lmg/m3 1) or (m3 /m3 t ,),
VL G material-1 L G airj/ v air material"
sorbed concentration of test chemical
(mg/m3materM),and
concentration in air at equilibrium (mg/m3^).
For a linear relationship, a higher K value represents a
higher sorption capacity for a specific VOC. The equilibrium
concentration in the material phase was obtained from the
difference between the initial and equilibrium weight of the
sample specimen, whereas Cmr was calculated from:
c .=
air Q
(3-11)
where,
E
Q
constant emission rate of VOC generated by the
diffusion cell (mg/s), and
air flow rate through the system (m3/s).
-------
Figure 3-1. Sulfur hexafluoride concentration profiles for unpainted gypsum board in the top chamber (a) and bottom
chamber (b) of the dual-volume diffusion chamber.
SF6 and Gypsum Board Top Chamber
20
£f
S- -IR -
3, 10
c
o
1 1n_
c 10
o>
o
c
o
0 c .
* +
• • • . .
0 i i i i i i
0 20 40 60 80 100 120 140 160
Time (m in)
(a)
SFGand Gypsum Board Bottom Chamber
•m - *
t
i R
~ 6
S
S 4-
O
»
•
+
•
•
+
•
*
0 50 100 150 200
Time (m in)
(b)
-------
Figure 3-2. Undecane concentration profiles for unpainted gypsum board in the top chamber (a) and bottom
chamber (b) of the dual-volume diffusion chamber.
Undecane and Gypsum Board Top Chamber
90 H
fO
£ oO
•&
C
o Art
-.3 4U
£
§
o 20
o
1 0
[
•
»
****
» »
iii
0 500 1000 1500 2000 2500 3000
Time (min)
(a)
Concentration (mg/m3)
O — ^ K>
Undecane and Gypsum Board Bottom Chamber
• •
••
•
•
•
•
U ill
0 500 1000 1500 2000 2500 3000
Time (min)
(b)
-------
3.2.2 Determination of Effective Diffusion Coefficients
for Test Chemicals
The effective diffusion coefficient, De, was determined
by fitting a diffusion model to the experimental sorption
and desorption data. For the vinyl flooring samples,
which conform to the geometry of a thin slab, under the
experimental conditions, the rate of change in mass due to
Fickian diffusion is given by Crank (1976):
=1-I:
ML
M.
where,
Mt = total mass of a VOC that has entered or left the slab
in time t (g),
MCO = corresponding quantity after equilibrium has been
reached (g),
2L = thickness of the material sample (m), and
De = effective diffusion coefficient (m2/s).
The counter n is varied from zero to a large number until the
sum of terms converges.
For the polyurethane foam samples, which conform to the
geometry of a cylinder, the rate of change in mass due to
Fickian diffusion is given by Crank (1976):
where,
the «n values are the positive roots of Jg (a«n) = 0,
a = radius of the cylinder, and
Jn = Bessel function of the first kind of zero order.
Figures 3-3 and 3-4 show example microbalance sorption/
desorption data for vinyl flooring (VF) and polyurethane
foam (PUF), respectively. In both cases, the compound
being absorbed and desorbed is dodecane. All the other data
sets for both VF and PUF are provided in Appendix B. The
appropriate models (Equations 3-12 or 3-13) were fitted to
the data using MS EXCEL.
Figure 3-3. Dodecane sorption/desorption profiles for vinyl flooring with fitted diffusion model.
40
-------
Figure 3-4. Dodecane sorption/desorption profiles for polyurethane foam with fitted diffusion model.
97.48
97.46
97.44
97.42
97.40
97.38
97.36
97.34
97.32
4 6
Time(hrs)
10
-------
-------
4.
Results
Equilibrium partition coefficients (K) and effective diffusion
coefficients (De) are presented in Tables 4-1 through 4-5.
These parameters were not determined for mortar due to
the length of time required for chemicals to diffuse through
mortar specimens. However, several observations related to
mortar experiments are included in Section 5.
Table 4-1. Equilibrium partition and diffusion coefficients (Gypsum Board - Unpainted).*
it Chemical
n-Butanol
Hexanal
Ethylbenzene
Decane
Undecane
Dodecane
Sulfur hexafluoride
920
590
100
230
1,640
4,160
2.2 x 10-5
1.9 x 10-5
3.4 x 10-5
1.7 x 10-5
x lO'5
7.8
* Analysis by dual-volume chamber.
Table 4-2. Equilibrium partition and diffusion coefficients (Gypsum Board - Painted)."
"st Chemical
n-Butanol
Hexanal
Ethylbenzene
Decane
Undecane
Dodecane
Sulfur hexafluoride
/(mg/m3)
720
350
130
270
1,130
D (m2/hr)
7.8 x 10-6
1.4 x 10-5
3.4 x 10-5
1.3 x 10--
3.1 x 10-f
1.6
* Analysis by dual-volume chamber.
Table 4-3. Equilibrium partition and diffusion coefficients (Carpet, PVC-backed).*
Test Chemical
n-Butanol
Hexanal
Ethylbenzene
Decane
Undecane
Dodecane
Sulfur hexafluoride
/(mg/m3)
710 / 180
1090 / 280
2,600 / 660
5,730 / 2,070
8,600 / 2,200
72,300 / 18,400
2.4 x 10-11 / 3.3 x 10-1'
1.9 x 10-11 / 4.4 x 10-1'
2.3 x 10-12 / 3.6 x 10-'
1.9 x IQ-10 / 1.4 x
1.3 x IQ-10 / 1.7
2.7 x IQ-12 / 4.4 x 10-'
* Analysis by dual-volume chamber.
Values forD based on thickness of carpet backing (left of/) and on thickness of backing + fibers (right of/).
-------
Table 4-4. Equilibrium partition and diffusion coefficients (Vinyl Flooring).*
Test Chemical
n-Butanol
(mg/m3) /(mg/m3)
1,100
D (m2/nr)
2.7 x 10-(
Hexanal
46,000
2.0 x 10-(
Decane
6,000
1.8 x lo-(
Undecane
17,000
2.0 x lo-(
Dodecane
47,000
6.9 x 10-'
Tetradecane
110,000
4.2 x 10-'
* Analysis by microbalance.
Table 4-5. Equilibrium partition and diffusion coefficients (Polyurethane Foam)."
n-Butanol
(mg/m3) /(mg/m3)
110
3.0 x 10-(
Hexanal
Decane
72
2.2 x 10-(
Undecane
490
1.1 x lo-(
Dodecane
1,400
7.7 x 10-(
Tetradecane
5,400
5.4 x 10-(
* Analysis by microbalance.
Equation 3-8 was used in conjunction with De for sulfur
hexafluoride to predict effective diffusion coefficients for
organic test chemicals in the absence of sorption. Results are
presented in Table 4-6. The multiplier ^P was determined as
described in Section 3 (Equation 3-8). Effective diffusion
coefficients in the absence of sorption are shown for both
unpainted and painted gypsum board. The ratio of measured
effective diffusion coefficients (with sorption) to those
predicted for the case of no sorption are listed for each
chemical and both types of gypsum board.
Table 4-6. Predicted D for gypsum board in the absence of sorption.
1.6 x io-3
Painted
sorption/
o sorption]
n-Butanol
0.856
6.7 x 10-'
0.033
1.4
0.0056
Hexanal
0.725
5.7 x 10-'
0.033
1.2
0.012
Ethylbenzene
0.718
5.6
0.061
1.1
0.031
Decane
0.557
4.3
0.040
8.9
0.015
Undecane
0.525
4.1 x 10-'
0.093
8.4
0.011
Dodecane
0.498
.9
0.0012
8.0
0.0039
measured value.
-------
5.
Discussion and Summary
5.1 Gypsum Board (Unpainted and Painted)
For gypsum board (both unpainted and painted) the
equilibrium partition coefficients for n-butanol and hexanal
were both greater than for ethylbenzene, presumably due to
polar-polar interactions between the oxygenated compounds
and calcium sulfate in gypsum board. The equilibrium
partition coefficients for the three n-alkane compounds
increased in a predictable order, from highest to lowest vapor
pressure (decane to dodecane).
The effective diffusion coefficients through gypsum board
were of comparable magnitude for all organic test compounds
other than dodecane, which had a significantly lower
effective diffusion coefficient than other test chemicals. For
painted gypsum board, the effective diffusion coefficients for
the n-alkane series decreased with increasing carbon number
(decreasing vapor pressure), and was inversely proportional
to the equilibrium partition coefficient. For unpainted
gypsum board, the effective diffusion coefficients for decane
and undecane were reversed from what was expected based
on carbon number and K value; the difference in De may be
due simply to experimental error and uncertainties in the
parameter estimation method (Section 3 and Appendix B).
The large effective diffusion coefficients for sulfur
hexafluoride, an inert tracer compound, relative to organic
test chemicals underscores the significant effects of sorption
processes on chemical migration through gypsum board.
When De for SF6 are translated to organic test chemicals
(Table 4-6), the ratio of chemical-specific De for the
case of sorption to the case of no sorption was between
approximately 0.09 and 0.0011, i.e., a 91 percent to 98.9
percent reduction in De caused by sorption. The effective
diffusion coefficients for SF6 can also be used to estimate
tortuosity factors for gypsum board. Using an SF6 diffusion
coefficient in free air of 0.073 cm2/s (= 0.026 mVhr) at near
room temperature (Ward and Williams, 1997) and dividing
this value by the effective diffusion coefficients determined
in this study (Table 4-6) yields tortuosity factors of 16 and
33, i.e., diffusion path lengths through material of 16 and 33
times the actual thickness of painted and unpainted gypsum
board, respectively.
The results for unpainted and painted gypsum board are
largely counter-intuitive when compared against one another.
It seems logical that the paint film would increase the
equilibrium partition coefficient, since diffusion through the
gypsum board is required to achieve equilibrium and the
paint provides a second sorptive medium for test chemicals.
However, the equilibrium partition coefficients for each
chemical were greater for unpainted than for painted
gypsum board. It would also seem logical that a paint film
would reduce the migration rate through gypsum board by
providing an additional layer of resistance to diffusion. This
was true for four of the six chemicals; De was identical in
each case for ethylbenzene and greater for painted gypsum
board than unpainted gypsum board for dodecane. However,
the effective diffusion coefficient for sulfur hexafluoride
was observed to be a factor of two greater for painted than
unpainted gypsum board.
The reasons for some counter-intuitive effects for De and
gypsum board may have been due to differences in the extent
of chemical sorption inside the gypsum board caused by
components of the paint wicking into the gypsum board or
diffusing into the gypsum board and consuming sorption
sites. This could have lead to the higher partition coefficients
of unpainted versus painted gypsum board, i.e., there were
greater sorption capacities for test chemicals inside the
gypsum board that had not already been challenged by paint
components such as ethylene glycol and 2,2,4-trimethyl-l,3-
pentanediol monoisobutyrate. This would also account for
lower De for unpainted gypsum board, since the additional
sorption would slow the diffusive migration of test chemicals
through the gypsum board.
5.2 Carpet
For both K and De, two values are presented (/) in Table
4-3. The first (left of /) corresponds to parameter estimation
based on an assumption that all partition and diffusion
occurs in/through the backing material; only the volume and
thickness of the PVC backing was used in calculations. The
second (right of /) corresponds to parameter estimation based
on use of the entire carpet (backing and fibers); the volume
and thickness of the entire carpet was used in calculations.
The equilibrium partition coefficients for carpet increased
with increasing molecular weight; the trend for the n-alkane
series was increasing partition coefficient with increasing
carbon number or decreasing vapor pressure. The effective
diffusion coefficients decreased with increasing carbon
number (increasing K and decreasing vapor pressure) for the
n-alkane series. A similar trend was observed for the other
three chemicals if treated in isolation from the n-alkanes;
effective diffusion coefficients decreased with increasing
K and molecular weight. Effective diffusion coefficients
for sulfur hexafluoride could not be determined for carpet
because of the rapid transport through the carpet specimen
and rapid approach to equal SF6 concentrations in each of
the dual-volume chambers. Initial mixing of organic test
chemicals was also rapid through the carpet (quickly reaching
equal concentrations in top and bottom chamber) but was
followed by a period of very slow decline in concentration of
test chemicals as they diffused into the carpet system.
With the exception of n-butanol, the K values for carpet,
particularly in the case of carpet backing only, were greater
than those for gypsum board. This indicates that carpet has a
-------
greater sorption capacity than gypsum board, although there
is typically a greater area of gypsum board than carpet in
most buildings. However, the effective diffusion coefficients
for P VC-backed carpet are orders of magnitude lower than
for gypsum board. As such, while the sorption capacity for
carpet is high, diffusion into the carpet may preclude an
approach to equilibrium, especially during transient source
events, i.e., capacity is high but the actual extent of sorption
may be much lower than capacity.
5.3 Vinyl Flooring
The K values for vinyl flooring (VF) range from 1,100 to
110,000 (mg/m3)soHd/(mg/m3)m. This indicates that VF has a
similar sorption capacity to carpet. The effective diffusion
coefficients for VF range between 2.7 X 10~9 and 4.2 X
10'10 m2/hr and are also similar to those for carpet. While the
sorption capacity for VF is high, diffusion into the VF is slow
and may preclude equilibrium being established during rapid
transient source events.
5.4 Polyurethane Foam
The K values for polyurethane foam (PUF) range from 72
to 5,400 (mg/m\m/(mg/rn?)^. This indicates that PUF
has a similar sorption capacity to gypsum board. The
effective diffusion coefficients for PUF range between 3.0
X 10'5 and 5.4 X 10'7 mVhr and are also similar to those
for gypsum board. While the sorption capacity for PUF
is low, diffusion into the PUF is rapid and may mean that
equilibrium is established during rapid transient source
events. Two experiments were conducted for hexanal in PUF,
but both yielded unusual results (as shown in Appendix D).
It appeared that the hexanal reacted with the PUF in some
way. This one set of results (hexanal/PUF) was therefore
abandoned.
5.5 Mortar
Experiments involving mortar did not approach equilibrium
conditions over a two-month period. Only small amounts of
sulfur hexafluoride were observed in the bottom chamber
over this period. Of the organic test chemicals, only a small
amount of ethylbenzene was observed in the bottom chamber
after two months. Hexanal was rapidly removed from the top
chamber, to undetectable levels, but never appeared in the
bottom chamber. None of the other four test chemicals were
observed in the bottom chamber after two months. As such,
it was impossible to determine either K or De for mortar and
any of the test chemicals.
An interesting observation is that for all test chemicals, there
was a relatively rapid reduction in chemical concentrations
within the first 30 or 50 hours of an experiment, followed
by a very slow decay in concentration within the top
chamber. These two stages of decay are evident in the plots
provided in Appendix C. It is conceivable that the first stage
corresponds to a relatively rapid adsorption of test chemicals
to the exterior surface of the mortar and the second stage
corresponds to a much slower diffusion process into the pores
of the mortar. The fact that test chemicals never appeared in
the bottom chamber suggests that substantial sorption occurs
in the pores of the mortar during the slow diffusion stage.
5.6 Summary
Two different methods were used in this study, dual-volume
diffusion chamber and dynamic microbalance, to determine
equilibrium partition coefficients (K) and effective diffusion
coefficients (De) through common building materials. The
goal was to provide these parameters for use in models to
predict the sorptive interactions between contaminants such
as chemical warfare agents (CWA) and indoor materials.
Attempts were made to determine these parameters for
36 chemical/material combinations. These attempts were
successful for 30 of the combinations; parameters could not
be determined for mortar due to the extended period required
for chemical diffusion through the mortar specimens.
Results indicate that diffusion within gypsum board
(unpainted and painted) and polyurethane foam is much
more rapid than through mortar, PVC-backed carpet, or
vinyl flooring. This is important in so much as it suggests
that even though the latter materials may have high sorption
capacities, equilibrium conditions may not be approached
for transient source events for which diffusion into these
materials is limited. This result underscores the need for
models that can predict both the diffusive and adsorptive
behavior of materials, i.e., as opposed to simply assuming an
instantaneous equilibrium condition.
Generally, the results demonstrate that the dual-volume
chamber method is better suited to measure the sorption
properties of the more volatile VOCs, whereas the
microbalance method is better suited to measure the sorption
properties of the less volatile VOCs. The effective mass
resolution of the microbalance is ~1 (jug. To accurately
determine both K and De using the microbalance method,
the K value has to be sufficiently large to allow an overall
mass increase that is ~20 (jug or more. This mass increase is
related to the imposed gas-phase VOC concentration and the
magnitude of K. Thus, for a given gas-phase concentration,
the higher the K value, the larger the overall mass increase,
the more reliably the parameters can be determined.
As described in Section 5.1, the results for unpainted and
painted gypsum board are somewhat counter-intuitive. We
believe that the internal properties of painted gypsum board
may be significantly modified relative to unpainted gypsum
board by paint component (glycol, glycol ethers, and 2,2,4-
trimethyl-l,3-pentanediol monoisobutyrate) consumption of
available sorption sites.
The authors hope that this study provides meaningful
parameters that will facilitate the USEPA's needs with respect
to modeling sorptive interactions between CWA and other
contaminants with materials in buildings.
-------
6.
References
Blondeau, P., Tiffonet, A. L., Damian, A., Amiri, O.
and Molina, J. L. (2003), Assessment of Contaminant
Diffusivities in Building Materials. Indoor Air, Vol. 13,
pp. 302-310.
Bodalal, A., Zhang, J. S. and Plett, E. G. (1999), A Method
for Measuring Internal Diffusion and Equilibrium Partition
Coefficients of Volatile Organic Compounds for Building
Materials. Building and Environment, Vol. 35, No. 2,
pp. 101-110.
Cox, S. S., Hodgson, A. T. and Little, J. C. (2001a),
Measuring Concentrations of Volatile Organic Compounds
in Vinyl Flooring. Journal of the Air & Waste Management
Association, Vol. 51, pp. 1195-1201.
Cox, S. S., Little, J. C. and Hodgson, A. T. (2002), Predicting
the Emission Rate of Volatile Organic Compounds from
Vinyl Flooring. Environmental Science & Technology,
Vol. 36, pp. 709-714.
Cox S. S., Zhao D. and Little J. C. (200Ib), Measuring
Partition and Diffusion Coefficients for Volatile Organic
Compounds in Vinyl Flooring. Atmospheric Environment,
Vol. 35, pp. 3823-3830.
Crank, J. (1975), The Mathematics of Diffusion, 2nd Edition.
Oxford University Press, New York.
Deng, B. and Kim, C. N. (2004), An Analytical Model for
VOC Emissions from Dry Building Materials. Atmospheric
Environment, Vol. 38, pp. 1173-1180.
Haghighat, F. and Zhang, Y. (1999), Modelling of Emission
of Volatile Organic Compounds from Building Materials -
Estimation of Gas-Phase Mass Transfer Coefficient. Building
and Environment, Vol. 34, pp. 377-389.
Kumar, D. and Little, J. C. (2003), A Single-Layer Model to
Predict the Source/Sink Behavior of Diffusion-Controlled
Building Materials, Environmental Science & Technology,
Vol. 37, pp. 3821-3827.
Lee, C. S., Haghighat, F. and Ghaly, W. S. (2005), A Study on
VOC Source and Sink Behavior in Porous Building Materials
- Analytical Model Development and Assessment. Indoor
Air, Vol. 15, pp. 183-196.
Li, F. and Niu, J. L. (2005), Simultaneous Estimation of
VOCs Diffusion and Partition Coefficients in Building
Materials via Inverse Analysis. Building and Environment,
Vo. 40, No. 10, pp. 1366-1374.
Little, J. C., Hodgson, A. T. and Gadgil, A. J. (1994),
Modeling Emissions of Volatile Organic Compounds from
New Carpets. Atmospheric Environment, Vol. 28, pp.
227-234.
Tucker, W.A., and Nelken, L.H. (1990), Diffusion
Coefficients in Air and Water. Chapter 17 in Handbook
of Chemical Property Estimation Methods. Lyman, W.H.,
Reehl, W.F., Rosenblatt, D.H., eds., Washington, D.C.,
American Chemical Society.
United States Environmental Protection Agency (1999),
Compendium of Methods for the Determination of Toxic
Organic Compounds in Ambient Air - Compendium
Method TO-17 - Determination of Volatile Organic
Compounds in Ambient Air Using Active Sampling Onto
Sorbent Tubes. Second Edition. Center for Environmental
Research Information, Office of Research and Development,
Cincinnati, Ohio.
Verschueren K. (1996), Handbook of Environmental Data on
Organic Chemicals, 3rd Edition, Van Nostrand Reinhold.
Ward, D.B., and Williams, C.V (1997), Verification of the
Integrity of Barriers Using Gas Diffusion. Sandia National
Laboratories report - SAND97-1425.
Xu, Y. and Zhang, Y. (2003), An Improved Mass Transfer
Based Model for Analyzing VOC Emissions from Building
Materials. Atmospheric Environment, Vol. 37, pp. 2497-
2505.
Yang, X., Chen, Q., Zhang, J. S., An, Y, Zeng, J. and Shaw,
C. Y. (2001), A Mass Transfer Model for Simulating VOC
Sorption on Building Material. Atmospheric Environment,
Vol. 35, pp. 1291-1299.
Zhang, L. Z. and Niu, J. L. (2003), Laminar Fluid Flow and
Mass Transfer in a Standard Field and Laboratory Emission
Cell. International Journal of Heat and Mass Transfer,
Vol. 46, pp. 91-100.
Zhao, D. Y, Little, J. C. and Cox, S. S. (2004),
Characterizing Polyurethane Foam as a Sink for or Source of
VOCs in Indoor Air, Journal of Environmental Engineering,
ASCE, Vol. 130, pp. 983-989.
Zhao, D. Y, Little, J. C. and Hodgson, A. T. (2002),
Modeling the Reversible, Diffusive Sink Effect in Response
to Transient Contaminant Sources, Indoor Air, Vol. 12,
pp. 184-190.
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-------
Appendix A
Quality Assurance Metrics
This appendix includes relevant excerpts from the initial
quality assurance project plan (QAPP). The text of some
sections was removed for brevity and the reader is referred
to the original QAPP for text. The original QAPP section
numbers are used for cross-referencing. Below each
section we have provided a brief response related to quality
assurance metrics. UT refers to use of the dual-volume
diffusion chamber at the University of Texas. VT refers to the
dynamic microbalance used by Virginia Tech.
2.0. SAMPLING
2.1 Sampling Points
UT: Sampling points were as described in the QAPP.
VT: Sampling points were as described in the QAPP.
2.2 Sampling Frequency
UT: A minimum of five (5) samples will be collected from
both chambers (top and bottom) for each experiment, for a
minimum of 10 samples to be analyzed. The time interval
between samples will depend on the material/chemical
combination, which will affect the time to reach an
equilibrium condition in the experimental system. This time
interval may be as low as 20 minutes or less for a highly
porous material, to tens of hours for a relatively nonporous
material.
Response - We exceeded the QAPP requirements for all tests
— more than five samples were collected from both top and
bottom chambers.
VT: The sample mass gain or loss over time will be
monitored every five minutes during the sorption/desorption
process.
Response - Although we exceeded the QAPP requirements
for all tests — more than one measurement every five
minutes, fewer data were plotted for purposes of clarity.
2.3 Expected Measurements
UT: The goal of the experimental program is to determine
the equilibrium partition coefficient and effective diffusion
coefficient for each combination of test chemical and
material. This will require several types of measurements.
Air samples will be used to determine test chemical
concentrations in the top and bottom volumes of the chamber
apparatus depicted in Figure 2-1. Optimal methods for
determining the effective diffusion coefficient for each test
material may differ by material. As such, for some or all of
the materials tested, material density and porosity will be
measured. Alternately, for some or all of the test materials,
sulfur hexafluoride (SF6) diffusion through test materials will
be determined, and gaseous SF6 samples will be collected in
top and bottom volumes of the experimental chamber system.
Response - Air samples were collected and used to determine
test chemical concentrations in top and bottom chambers.
Porosity and bulk density were not determined. Porosity was
not required for the specific model to be employed based on
this study. The original intent for determining bulk density
was to determine the solid-phase concentration. However,
this was not needed in Equation 3-2. Sulfur hexafluoride
injections and analyses in top and bottom chambers were
completed for all test materials, not just some.
VT: Several types of measurements will be required in the
experiment. The dimensions of the material sample will
be carefully measured. In addition, the emission rate of
VOC generated by the diffusion cell will be gravimetrically
obtained by weighing the diffusion cell before and after the
run.
Response - No changes to original QAPP.
2.4 Site-Specific Factors That May Affect Sampling
Procedures
UT: We do not anticipate any major factors that will
affect sampling procedures at UT. It is always possible that
instrumentation requires repair or troubleshooting, but such
events can not be anticipated.
As described above, the actual method for determining
effective diffusion coefficients for each chemical/material
combination will need to be determined. Two methods are
available to the research team as described in Section 5.1.
One method requires determination of material porosity. Our
experience is that this is difficult with some materials due to
interstitial voids that can not be effectively wetted, leading
to underestimates for gas-phase porosity. For other materials,
submergence in water to determine porosity can lead to
material breakdown. As such, we will employ a method
based on diffusion of SF6, a non-adsorbing tracer, with
theoretical adjustment to test chemicals. This method does
not require analysis of material porosity to determine De.
Response - See item 2.3 above. Sulfur hexafluoride
measurements were made and were employed to estimate
theoretical effective diffusion coefficients for test chemicals
in the absence of sorption. However, this analysis was done
only for the unpainted and painted gypsum board specimens,
since transport of sulfur hexafluoride was too rapid across
carpet specimens and the mortar experiments far exceeded
the time constraints of this study.
VT: Aside from regular maintenance, we do not anticipate
any special site-specific factors that will affect sampling
procedures at VT. We have already used the microbalance
quite extensively in conducting these types of measurements
(for example, see Cox et al., 2001 and Zhao et al., 2004).
Response - No changes to original QAPP.
-------
2.5 Site Preparation Needs
UT: There are no site preparation requirements at UT.
VT: There are no site preparation requirements at VT.
2.6 Sampling Procedures and Maintenance
Requirements
UT: Air samples for determination of test chemical
concentrations will be collected using adsorbent tubes
outfitted with personal sampling pumps. Sample collection
rates will range from 25 to 50 mL per minute. Ultimate
sample sizes will depend on the vapor pressure of the
test chemical and its mass concentration in chamber air.
All personal sampling pumps used for this work will be
calibrated every 10 samples.
The personal sampling pumps used for these experiments
are SKC Pocket Pump 210-1000 series. These units have a
manufacturer provided "accuracy variance between LCD
reading and actual flow rate (after calibration) of +/- 5%."
The personal sample pumps are calibrated daily using a
Gillian Bubble Flow Meter.
If used, sulfur hexafluoride samples will be collected in
gas-tight syringes. SGE gas-tight syringes will be used for
this work. The manufacturer states these syringes have an
"accuracy and reproducibility of +1-1% of volume."
Response - We did not use the personal sampling pumps
described above as they were found to be prone to flow faults
and had to be shipped frequently back to the manufacturer
for maintenance. Instead, we attached gas-tight syringes to
the back end of adsorbent tubes and collected samples by
drawing known volumes of air through the sorbent tubes
using syringes. We believe that this method is more accurate
than the use of sample pumps, particularly for relatively low-
volume (e.g., 50 mL) sampling. Gas-tight syringes were used
for both test chemical sample collection (through sorbent
tubes) and direct sampling of sulfur hexafluoride
VT: The mass gain/loss of the material sample will be
recorded by the PC-based data-acquisition system. The
ultimate number of data points will depend on the time
required for the test chemicals to reach equilibrium during
either sorption or desorption.
Response - For vinyl flooring, there was a constant emission
of some substance (we believe it to be a vinyl plasticizer)
that did not abate after several weeks in the microbalance. To
remove this, we subjected the vinyl flooring to a short "bake-
out" period. For polyurethane foam, there were no changes to
the original QAPP
2.7 Compositing/Splitting of Samples
UT: Compositing/splitting of air samples for test chemicals
or SF6 is not required for this project. The actual material
specimens used for experiments will be cut into smaller
pieces for analysis of material density and porosity, where
required. Material properties will be evaluated based on one
specimen from a specific batch of a material that will be
used for all analyses with that material and after use of the
specimen in the test chamber. One exception might be mortar,
since each specimen would be formed separately.
Response - See Section 2.3 above. Thickness measurements
were made of gypsum board, carpet, and carpet backing
using Vernier calipers. Thickness measurements were not
made for mortar, since the lack of diffusion through the
mortar precluded any attempts at parameter estimation.
VT: Sample compositing/splitting is not required for this
project.
Response - No QAPP modifications.
2.8 Sample Quantity Requirements
UT: The air sample volume for test chemicals (volume
pulled through adsorbent tubes) will depend on the vapor
pressure of the test chemical being tested and its anticipated
concentration in chamber air. Based on previous experience,
we expect sample volumes to be on the order of 100 mL or
less.
When employed, SF6 samples will be collected in gas-tight
syringes with volumes less than or equal to 1 mL.
When material properties are determined, a minimum of
three replicate analyses will be completed to determine mean
bulk density and porosity, and spread around the mean.
Response - To sample for organic test chemicals, the sample
volumes varied between 25 mL and 100 mL, depending on
the concentration in the chamber, e.g., lower volumes were
required initially in the top chamber, since concentrations
were at a maximum. For accurate measurements of SF6
a volume of 25 mL was required, i.e., greater than the
1 mL specified in the QAPP. This was due to using a lower
concentration SF6 source that was available to us for this
project, i.e., relative to what we had originally planned. For
material properties (thickness), five instead of three samples
were collected to determine a mean and standard deviation
(see Section 2.1 of main report).
VT: The mass gain for test chemicals will depend on the
vapor pressure of the chemical being tested, its concentration
in the microbalance chamber air and the volume of the test
material. Based on previous experience, we expect mass gain
to be at least 200 ug for the most volatile compound tested.
For vinyl flooring, the sample specimens are chosen to be
roughly 1 cm wide by 4 cm long by 0.03 cm thick.
Response - A Vernier caliper was used to measure the length
and width of vinyl flooring, and the length and radius of the
polyurethane foam. A screw micrometer was used to measure
the thickness of the vinyl flooring. Each measurement
was repeated four times and the average was used as the
final value. The vinyl flooring had a dimension of 3.78 cm
(length) X 2.66 cm (width) X 0.0175 cm (thickness). The
polyurethane foam's dimension was 1.39 cm (radius) X
4.70 cm (length).
2.9 Containers Used for Sample Collection, Transport,
and Storage
UT: All air samples for target chemicals will be collected
onto Tenax TA 80/100 mesh packed into glass tubes. The
glass tubes are actually large volume injection liners that
allow for zero-path thermal desorption directly onto a GC
-------
column (to minimize analyte losses in the transfer lines of
conventional thermal desorption systems). Samples will be
analyzed as collected (within 15 minutes of collection in the
case of two samples drawn simultaneously). Samples will not
be transported or stored.
When employed, SF6 samples will be collected in gas-tight
syringes. They will be analyzed immediately. As such, there
will be no transport or storage issues associated with samples
that contain SF6.
Test materials will be maintained in plastic bags in a secure
office environment prior to testing.
Response - Air samples (organic test chemicals and SF6)
were collected and analyzed as described above. Test
materials were not maintained in plastic bags, but rather were
wrapped in aluminum foil and maintained in the office of Dr.
Neil Grain prior to usage.
The GC method used for this study required 21 minutes to
complete. Simultaneously collected samples were analyzed
within 30 minutes of collection.
To provide the data required to the model the diffusion of
organic chemicals through the vinyl carpet required eight
to ten samples be collected in the first 30 minutes of the
experiment. These additional sample tubes were stored in
color-coded stainless steel tubes until they could be analyzed.
These samples were analyzed within four hours of collection.
VT: The VT method employs a micro-balance for
gravimetric analysis. Measurements are made directly by
mass changes. Air sample collection, transport, and storage
are not required. Test materials will be stored in aluminum
foil in a refrigerator prior to testing.
Response - No changes to original QAPP.
2.10 Sample Preservation Methods
UT: Air samples (adsorbent tubes for test chemicals and gas-
tight syringes for SF6) will be analyzed as collected. As such,
preservation methods are not required. Test materials will
be maintained in plastic bags in a secure office environment
prior to testing.
Response - Air samples were analyzed as described above.
Test materials were not maintained in plastic bags, but rather
were wrapped in aluminum foil and maintained in the office
of Dr. Neil Grain prior to usage.
VT: There are no samples to be preserved using the micro-
balance method. Test materials will be stored in aluminum
foil in a refrigerator prior to testing.
Response - No changes to original QAPP.
2.11 Requirements for Shipping of Samples
UT: Air samples (adsorbent tubes for test chemicals and
gas-tight syringes for SF6) will be analyzed as collected. No
air samples will be shipped. The USEPA may provide some
of the test materials to UT. These material samples will be
mailed directly to the point of contact noted in Section 1 of
this document.
Response - The USEPA shipped three of the four test
materials (carpet, unpainted, painted gypsum board) to the
University of Texas for testing. Mortar specimens were
developed by the Materials Engineering group within the
Department of Civil, Architectural, and Environmental
Engineering at the University of Texas.
VT: No air samples will be shipped. The USEPA will provide
some of the test materials to VT. These material samples will
be tightly packed within aluminum foil and mailed directly to
the point of contact noted in Section 1 of this document.
Response - No changes to original QAPP.
2.12 Holding Time Requirements
UT: Air samples (adsorbent tubes for test chemicals and gas-
tight syringes for SF6) will be analyzed as collected. As such,
there are no holding time requirements for air samples. Test
materials will be maintained in a secure office environment
as described above. There should be no specific holding
requirements for test materials.
Response - No changes to original QAPP.
VT: There are no holding time requirements for the VT
analysis method. Test materials will be stored in a refrigerator
as described above.
Response - No changes to original QAPP.
2.13 Sample Tracking and Chain of Custody
UT: Air samples (adsorbent tubes for test chemicals and
gas-tight syringes for SF6) will be analyzed as collected by
laboratory personnel. The same individual who collects an
air sample will prepare the sample for direct analysis. Test
materials will be maintained in plastic bags in a secure office
environment prior to testing. The contents of the bags will be
marked on the exterior of each bag with a notice not to move
or open without the permission of Dr. Grain or Dr. Corsi.
Response - Material specimens were wrapped in aluminum
foil as described above. Dr. Neil Grain was the only staff
member to handle material specimens throughout this entire
study.
VT: Test materials will be stored in a refrigerator prior
to testing. The contents of the bags will be marked on the
exterior of each bag with a notice not to move or open
without the permission of Dr. Little.
Response - No changes to original QAPP.
2.14 Information Recording and Maintenance by
Field Personnel
UT: A dedicated laboratory notebook will be maintained
for this experimental effort. Sample records will be noted
on a sample record sheet, and sheets for each experiment
will be maintained in a three-ringed binder stored after each
experiment in Dr. Grain's office. The sample record sheet will
be transcribed to an EXCEL spreadsheet each day that a set
of samples is analyzed. The EXCEL file will be backed up to
electronic media on a weekly basis and also sent to Dr. Corsi
for separate storage every two weeks or sooner.
-------
Response - Results of all GC/FID analyses were printed
as hard copies and maintained in a three-ringed binder. All
sample records were transcribed to an EXCEL spreadsheet
and sent from Dr. Grain to Dr. Corsi on an approximate bi-
weekly basis. Electronic copies are maintained by both Dr.
Grain and Dr. Corsi.
VT: A dedicated laboratory notebook will be maintained
for the entire experimental effort. The data record sheet for
each experimental run will be transcribed to an EXCEL
spreadsheet. The EXCEL file will be backed up to electronic
media and also sent to Dr. Little for separate storage after
each sorption/desorption cycle.
Response - No changes to protocol.
3.0 TESTING AND MEASUREMENT PROTOCOLS
3.1 Specific Analytical Methods
UT: Air sample measurements for test chemicals will be
completed using a modified version of USEPATO-17,
"Determination of Volatile Organic Compounds in Ambient
Air Using Active Sampling onto Sorbent Tubes." Tenax-TA
will be the primary adsorbent used in this study. However, a
different adsorbent may be substituted as needed, depending
on the specific test chemicals that are employed. A GC/FID
with zero-path length thermal desorption will be employed
for sample analysis. The mass of the test chemical will be
measured by comparison with an external calibration curve
for that chemical. The gaseous concentration of the test
chemical will be calculated as mass collected divided by
volume of air sample.
If employed, SF6 samples will be analyzed by direct injection
from a gas-tight syringe to a GC/ECD tuned specifically for
analysis of SF6.
For material specimens in which material properties are
evaluated, gravimetric and volume displacement methods
will be used to determine these properties. Specifically,
material specimens will be weighed to determine mass
of the bulk specimen. The volume of the specimen will
be determined by use of precision calipers or initial
displacement of water upon submergence (for relatively
impermeable materials). Bulk density will be determined
as the ratio of specimen mass to volume. Porosity will
be determined by submergence of a material for a period
sufficient to achieve complete saturation. The difference
between bulk volume (measured as described above)
and volume displacement at complete saturation will be
normalized by bulk volume to determine material porosity.
Response - Air samples were analyzed as described above
for both organic test chemicals and sulfur hexafluoride. As
described above, other than material thickness the material
properties were not measured or needed for this study.
VT: Specifically, the diffusion vial with VOC will be
weighed. The emission rate generated by the diffusion cell
will be determined from the difference in mass of diffusion
cell divided by the time between the two measurements.
Response - The diffusion vial with liquid VOC was
weighed four times before sorption, after sorption, and after
desorption. The emission rates were determined from the
difference in the average mass of the diffusion vial divided
by the time between the two measurements. The final
emission rate was taken as the mean of the two emission rate
values. The measured emission rates are shown in Table A-l.
Table A-l. Emission rates from diffusion vials.
Chemicals
Emission Rate
n-Butanol
Hexanal
Decane
Undecane
Dodecane
Tetradecane
VF
217.5
186.0
42.9
15.9
6.9
5.1
PUF
194.1
43.0
21.6
10.2
3.2 Modifications to EPA-Approved or Other Validated
Analytical Methods
UT: Some of the test chemicals (e.g., decane and dodecane)
are not specifically listed for analysis using USEPA Method
TO-17. However, they will be analyzed using the procedures
outlined in EPA TO-17.
Response - No changes to protocol.
VT: No modifications required.
Response - No modifications required.
4.0 QA/QC CHECKS AND PROTOCOLS
4.1 Analytical System Calibration and Checks
UT: Prior to experiments involving a specific test chemical,
a five-point calibration curve will be developed and will span
the anticipated range of experimental concentrations. The
R2 value for each calibration curve will be greater than or
equal to 0.97. If the criterion R2 is not achieved, individual
calibration points will be repeated until the criterion R2 is
achieved. The calibration of the GC/FID system will be
confirmed using a mid-point standard injection every 12
samples or 24 hours, whichever comes first. The criterion for
mid-point check will be ± 15 percent of the calibration curve.
If this criterion is not satisfied, the mid-point check will be
repeated. If the criterion is not met the second time, a new
calibration curve will be generated for the target chemical.
Response - We exceeded the calibration curve requirement,
completing seven-point instead of five-point external
calibrations. The R2 values always exceeded 0.994 (greater
than the QAPP requirement of 0.97). Mid-point checks
were completed as described above on a daily basis during
experiments. The mid-point check of ± 15 percent was
violated only once (for ethylbenzene) and was corrected as
described above.
VT: A minimum of three replicates will be completed for
determination of emission rate generated by the diffusion
cell. This gravimetrically determined emission rate is used
-------
to calculate the gas-phase concentration passing through the
microbalance chamber.
Response - The diffusion vial with VOC was weighed four
times before sorption, after sorption, and after desorption.
4.2 Determination of Method Detection Limits
UT: Method detection limits for air samples containing test
chemicals will be determined as per Section 14.2 of EPA
Method TO-17 (United States Environmental Protection
Agency, 1999), i.e., by making seven replicate measurements
of a concentration of the compound of interest for the lowest
calibration concentration, computing the standard deviation
and multiplying by 3.14 (the Student's t value for 99 percent
confidence for seven values).
The method detection limit for SF6 using existing
instrumentation at UT is approximately 50 parts per trillion
by volume. If SF6 is employed, we will maintain minimum
concentrations at least three times greater than the method
detection limit.
Response - Minimum detection limits on GC/FID area counts
were determined as described above and were extremely
low (area counts of 8.6 for undecane to 73 for hexanal).
Importantly, these minimum detection limits were generally
two or more orders of magnitude lower than minimum
area counts in samples. Sulfur hexafluoride concentrations
in experimental samples were generally at least 10 x
greater than the 50 ppt MDL (always exceeding the QAPP
requirement of 3 x MDL).
VT: The experimental limit for the microbalance
measurements is about 100 (jug. If the overall mass gain is
lower than this, the signal to noise ratio becomes too large to
obtain very good results.
Response - Some of the experimental runs for PUF had an
overall mass gain of only about 40 (jug. However, as shown in
the raw data provided in Appendix D, the microbalance was
working well and the signal to noise ratio was well below this
level.
4.3 Background Sampling / Experimental Blanks
UT: All experimental samples will be collected from
existing dual chamber systems located at the University of
Texas at Austin. Background air samples will be collected
from the laboratory prior to sealing the experimental
chambers. Experimental blanks will be collected from the
sealed experimental chambers prior to the introduction of
the experimental VOCs. If the background concentration for
the VOC of interest is more than 5 percent of the expected
experimental concentration, the chamber will be re-cleaned.
If the background chemical concentration arises from the
material sealed in the chamber (e.g. plywood) the background
chemical concentration will be subtracted from the measured
experimental concentration.
Response - Background (laboratory) and experimental blank
air samples were collected prior to each experiment and
test chemicals never exceeded 5 percent of experimental
concentrations (in most cases were not identifiable at all).
VT: Before use, the sample materials will be pre-conditioned
for several weeks in a special chamber and then again within
the microbalance for at least 24 hours prior to commencing
the sorption/desorption run.
Response - No changes to original QAPP.
4.4 Laboratory Sample Blanks
UT: Laboratory sample blanks will be injected every 10
samples or 24 hours, whichever comes first. The laboratory
blank will be accepted if the measured concentration is less
than 5 percent of the measured experimental concentration.
If the laboratory sample is more than 5 percent of the
experimental concentration, measurements will be stopped
until the background level can be brought below 5 percent of
the measured experimental concentration.
Response - Laboratory sample blanks were injected every 24
hours during the experiments. Sample blanks never exceeded
5 percent of experimental concentrations.
VT: Before starting the experiment, the sample materials
will be conditioned in clean air in the microbalance for at
least 24 hours to get a stable data baseline.
Response - No changes to original QAPP.
4.5 Sample Breakthrough Analysis
UT: Triplicate analyses of breakthrough will be conducted
for each test chemical at the maximum expected
concentration in the chamber system. For each analysis,
two adsorbent tubes will be connected in series and a
standard sample volume pumped though the adsorbent
tube. If any of the triplicate samples contain a test chemical
mass in the breakthrough tube that exceeds 10 percent of
the primary (first) tube, or if the triplicate average mass in
the breakthrough tube is greater than or equal to 5 percent
of the primary tube, two tubes in series will be employed
and analyzed for each sample. Results of the breakthrough
analysis will be reported in the final quality assurance
summary for this project.
Response - Triplicate analysis of breakthrough was
completed at the maximum possible concentration of each
test chemical (saturated headspace samples) at collection
volumes consistent with those used during experiments.
No mass (of any test chemical) was ever observed on the
breakthrough tube, i.e., even under extreme conditions the
first tube captured all test chemical mass.
VT: Thermal breakthrough analysis is not relevant to the VT
microbalance method.
Response - Thermal breakthrough analysis is not relevant to
the VT microbalance method.
4.6 Sequential Thermal Desorption Analysis
UT: For each test chemical, each primary tube (the first of
two tubes in series) used for breakthrough analyses (see
Section 4.5 above) will be thermally-desorbed twice in
sequence. Thus, three thermal desorption analyses will be
completed for each test chemical. This will allow analysis
-------
for any residual test chemical mass on Tenax-TA following
the standard thermal desorption process, and possible
adjustments to the thermal desorption temperature program.
If the mass of test chemical observed during the second
desorption analysis exceeds 10 percent for any one sample
or if the mean exceeds 5 percent for all three samples, the
thermal desorption program will be adjusted and this process
will be repeated until the mean mass associated with the
second desorption is less than or equal to 5 percent of the first
desorption. Residual mass will be reported in the final quality
assurance summary for this project.
Response - We observed complete thermal desorption
from the first tube used in breakthrough analyses for each
test chemical, i.e., there was no observable test chemical
mass upon the second thermal desorption of the tube. No
adjustments were necessary.
VT: Thermal desorption is not relevant to the VT
microbalance method.
Response - Thermal desorption is not relevant to the VT
microbalance method.
4.7 Sample Duplicates
UT: One air sample (for test chemical) duplicate
measurement will be made for each material/chemical
combination. Sample duplicate analyses will be reported in
the final quality assurance summary for this project.
As described above, when material properties are determined,
a minimum of three replicate analyses will be completed.
Response - Four duplicate samples were collected for each
test chemical over the course of all experiments. The relative
difference in duplicate samples was determined as follows:
n/ J-£f v <-i
% difference = X = 2x
where,
C -C
air'1
alr'2
i f\r\
x 1 00
(A-l)
'^2 = Gaseous concentrations of duplicate air
sample collected in series at equilibrium
(mg/m3).
The mean and standard deviation of differences in duplicate
sample concentrations (X) are presented in Table A-2. The
mean differences in duplicate samples were all less than
8 percent. The only duplicate samples that varied by greater
than 10 percent were butanol for painted gypsum board
(13.8%), hexanal for carpet (12.3 percent), and undecane
for mortar (10.2 percent). Over one-half (13 of 24) of the
duplicate measurements (X values) varied by less than
5 percent.
Table A-2. Results of duplicate sample analyses for test
chemicals (n = 4 samples).
n-Butanol
Hexanal
Ethylbenzene
Decane
Undecane
Dodecane
SF,
lean %
"rence (X)
Standard
Deviation (%)
6.0
3.0
5.5
7.3
4.9
0.98
4.2
4.7
2.1
2.1
3.0
1.9
0.15
VT: Sample duplicates are not relevant to the VT
microbalance method.
Response - Sample duplicates are not relevant to the VT
microbalance method.
4.8 Experimental Replicates
UT: At least one chemical/material combination experiment
will be completed in triplicate to characterize general
repeatability of experiments. Time permitting, additional
experiments will also be completed in duplicate or triplicate.
Response - Prolonged experiments involving mortar put
the project team behind schedule. As such project time
constraints precluded doing a replicate experiment.
VT: At least one chemical/material combination experiment
will be completed in triplicate to characterize general
repeatability of experiments. Time permitting, additional
experiments will also be completed in duplicate or triplicate.
Response - One chemical/material combination experiment
was completed in duplicate for both types of material (VF
and PUF) using dodecane as the common test compound. The
difference between the two measurements for VF was within
5 percent for K and 7 percent for De. For PUF the difference
was within 8 percent for K and 3 percent for De. These results
demonstrate quite reasonable reproducibility for the entire
experimental measurement procedure.
4.9 Cleaning of Experimental System
UT: The experimental system will be disassembled, and
heat treated (cleaned by desorption) in a drying oven for a
minimum of 24 hours at a temperature greater than
115 °C following each experiment. If experimental blanks
fail to meet the QA criterion (see Section 4.3), the heat
treatment procedure will be repeated, possibly using a longer
conditioning time or oven temperature. The process will be
repeated until the blank criterion is achieved.
Response - A heating time of 12 hours (less than QAPP
plan of 24 hours) at 125 °C (greater than QAPP 115 °C)
was employed to expedite system cleaning. This protocol
was found to effectively clean the experimental system (see
Section 4.3 of this appendix).
-------
VT: Clean air will be passed through the microbalance
chamber for at least 24hr for cleaning.
Response - No changes to original QAPP.
4.10 Reporting of QA/QC results
UT: A summary of QA/QC results will be reported in an
appendix of the final report.
Response - The summary is provided in this appendix.
VT: A summary of QA/QC results will be reported in an
appendix of the final report.
Response - The summary is provided in this appendix.
-------
-------
Appendix B
Finite Difference Equations and Program to
Calculate D for Gypsum Board
Top Chamber
The change in concentration in the top chamber was
determined based on a mass balance on the top chamber and
diffusive flux into the gypsum board for each time step "n":
C " + C
*- air.I T *- l.s
C,
n-t-I
1 +
2KD.AM
(B-l)
where,
C^,t = chemical concentration in the air of the top
chamber at time step n (mg/m3^),
Cj,s = sorbed-phase concentration at the midpoint
of the top (first) layer of gypsum board
(mg/m3 t ,),
v G material"
De = effective diffusion coefficient (mVhr),
A = exposed surface area of material adjacent to air in
each chamber (m2),
A/ = time interval of the time steps used in the
numerical solution (hr),
Ax = thickness of each slice of material as used in the
numerical calculation (m),
Vtop = volume of the top chamber (m3), and
K = equilibrium partition coefficient (m3 /m3 t ,).
eq A A v air matenar
The concentration at the mid-point of the first layer (Cps
above) was predicted as:
» AA/r n+1 „-!
^l,s A 2 t surface,top ^ ^ 2,s J
(B-2)
where,
^-surface top " = concentration on the top surface of the
material (mg/m3matenal): Csm.JaCiJJ<>!!"+ = KCairJ"+ .
Interior Gypsum Board
Pick's second law was used to develop a finite difference
solution for diffusion through the gypsum board. The sorbed-
phase concentration of a test chemical in all "i" layers of
gypsum board, other than the top and bottom layers, was
predicted as:
(B-3)
Ax2
where,
Ax = thickness of gypsum board layer i (m).
All other variables are as described previously.
The sorbed-phase concentration in the bottom, or final, layer
of material was predicted as:
f "-U e f)(^ "+1 4- f "I
^ final,s ~l 7 2^ L final-l,s ' ^ surface,hot J
/-t n+1 _ AX
final,s ~ T.D \t
surface bo
Ax2 (B-4)
= concentration on the bottom surface of the
material (mg/m3matenal):
C " = KC "
surface. bot air .h ,
C ,,n = chemical concentration in air of bottom chamber
air'b
at time n (mg/m3^).
Bottom Chamber
The change in concentration in the bottom chamber was
determined based on a mass balance and Pick's first law for
estimating flux into the chamber from the lower side of the
gypsum board. A finite difference approximation led to:
r " + r
*- air.h T *- final. .1
c.AF
H-fl
(B-5)
,
1 +
2KD
where,
Vbot = volume of the bottom chamber (m3).
All other variables are as defined previously.
All other variables are as defined previously.
-------
Java Program
Source code for program used to calculate De
for painted and unpainted gypsum board:
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
public class DiffusionSolver extends JFrame implements ActionListener {
private JButton done;
private String sThickness;
private String sArea;
private String sVolTop;
private String sVolBot;
private String sWeight;
private String sCTopEq;
private String sCBotEq;
private String sDeltaT;
private String sLayers;
private double [] [] aTopTimeAndConc, aBotTimeAndConc, aMaterialTimeAndConc;
private double [] aPredictedTopConc, aPredictedBottomConc;
private JTextField tThickness, tArea, tVolTop, tVolBot, tWeight, tCTopEq, tCBotEq,
tDeltaT, tLayers;
private JTextField tTTimel,tTTime2,tTTime3,tTTime4,tTTimeS,tTTime6,tTTime?,tTTimeS,tTTim
e9,tTTimelO;
private JTextField tBTimell,tBTime!2,tBTime!3,tBTime!4, tBTimelB;
private JTextField tBTimel,tBTime2,tBTime3,tBTime4,tBTimeB,tBTime6,tBTime?,tBTimeS,tBTim
e9,tBTimelO;
private JTextField tTTimell,tTTime!2,tTTime!3,tTTime!4, tTTimelB;
private JTextField tTConcl,tTConc2,tTConc3,tTConc4,tTConcB,tTConc6,tTConc?,tTConcS,tTCon
c9,tTConc10;
private JTextField tTConcll,tTConc!2,tTConc!3,tTConc!4, tTConclB;
private JTextField tBConcl,tBConc2,tBConc3,tBConc4,tBConcB,tBConc6,tBConc?,tBConcS,tBCon
c9,tBConclO;
private JTextField tBConcll,tBConc!2,tBConc!3,tBConc!4, tBConclB,tD,tKeq,tSampledMass;
private int iTopSize,iBotSize;
private double dThickness, dArea, dVolTop, dVolBot, dWeight, dCTopEq, dCBotEq, dDeltaT,
dLayers, dD, dKeq, dResidual,dSampledMass,dBestResidual;
private Container c;
private GridBagLayout gbGrid;
private GridBagConstraints gbConstraints;
-------
public DiffusionSolver() {
super( "Diffusion Solver" );
c = getContentPane();
gbGrid = new GridBagLayout();
c.setLayout(gbGrid);
gbConstraints = new GridBagConstraintsi
done=new JButton("Find D") ;
sThickness = new String("Thickness");
sArea = new String("Area");
sVolTop = new String("VolTop");
sVolBot = new String("VolBot");
sWeight = new String("Weight");
sCTopEq = new String("CTopEq");
sCBotEq = new String("CBotEq");
sDeltaT = new String("Delta T");
sLayers = new String("Layers");
tThickness = new JTextField(".0125");
tArea = new JTextField(".06742");
tVolTop = new JTextField(".008665");
tVolBot = new JTextField(".008665");
tWeight = new JTextField("548");
tCTopEq = new JTextField();
tCBotEq = new JTextField();
tDeltaT = new JTextField(".1");
tLayers = new JTextField("10");
tSampledMass = new JTextField();
aTopTimeAndConc = new double [2][15];
aBotTimeAndConc = new double [2][15];
tTTimel = new JTextField();
tTTime2 = new JTextField();
tTTime3 = new JTextField();
tTTime4 = new JTextField();
tTTimeS = new JTextField();
tTTime6 = new JTextField();
tTTime? = new JTextField();
tTTimeS = new JTextField();
tTTime9 = new JTextField();
-------
tTTimelO = new JTextField(!
tTTimell = new JTextField(!
tTTime!2 = new JTextField(!
tTTime!3 = new JTextField(!
tTTime!4 = new JTextField(!
tTTimelB = new JTextField(!
tTConcl = new JTextField() ,
tTConc2 = new JTextField(),
tTConc3 = new JTextField(),
tTConc4 = new JTextField(),
tTConcB = new JTextField(),
tTConc6 = new JTextField(),
tTConc? = new JTextField(),
tTConcS = new JTextField(),
tTConc9 = new JTextField(),
tTConc10 = new JTextField(}
tTConc11 = new JTextField(}
tTConc!2 = new JTextField(!
tTConc!3 = new JTextField(}
tTConc!4 = new JTextField(}
tTConc15 = new JTextField(!
tBTimel = new JTextField(),
tBTime2 = new JTextField(),
tBTime3 = new JTextField(),
tBTime4 = new JTextField(),
tBTimeS = new JTextField(),
tBTime6 = new JTextField(),
tBTime? = new JTextField(),
tBTimeS = new JTextField(),
tBTime9 = new JTextField(),
tBTimelO = new JTextField(}
tBTimell = new JTextField(}
tBTime!2 = new JTextField(}
tBTime!3 = new JTextField(}
tBTime!4 = new JTextField(}
tBTimelB = new JTextField(}
tBConcl = new JTextField()
tBConc2 = new JTextField()
tBConc3 = new JTextField()
tBConc4 = new JTextField()
tBConcB = new JTextField()
tBConc6 = new JTextField()
-------
tBConc? = new JTextFieldO;
tBConcS = new JTextFieldO;
tBConc9 = new JTextFieldO;
tBConclO = new JTextFieldO
tBConcll = new JTextFieldO
tBConc!2 = new JTextFieldO
tBConc!3 = new JTextFieldO
tBConc!4 = new JTextFieldO
tBConclB = new JTextFieldO
tD=new JTextFieldO;
tKeq=new JTextFieldO;
addComponent(done,21,0,1,1) ;
addComponent(new JLabel(sThickness,SwingConstants.RIGHT),0,0,1,1);
addComponent(new JLabel(sArea,SwingConstants.RIGHT),1,0,1,1);
addComponent(new JLabel(sVolTop,SwingConstants.RIGHT) ,2,0,1,1) ;
addComponent(new JLabel(sVolBot,SwingConstants.RIGHT),3,0,1,1);
addComponent(new JLabel(sWeight,SwingConstants.RIGHT),4,0,1,1);
addComponent(new JLabel(sCTopEq,SwingConstants.RIGHT) ,0,2,1,1) ;
addComponent(new JLabel(sCBotEq,SwingConstants.RIGHT),1,2,1,1);
addComponent(new JLabel(sDeltaT,SwingConstants.RIGHT),2,2,1,1);
addComponent(new JLabel(sLayers,SwingConstants.RIGHT) ,3,2,1,1) ;
addComponent(new JLabel("Sampled Mass",SwingConstants.RIGHT),4,2,1,1);
addComponent(new JLabel("Top Chamber Time",SwingConstants.RIGHT),5,0,1,1);
addComponent(new JLabel("Top Chamber Cone",SwingConstants.RIGHT),5,1,1,1);
addComponent(new JLabel("Bottom Chamber Time",SwingConstants.RIGHT),5,2,1,1)
addComponent(new JLabel("Bottom Chamber Cone",SwingConstants.RIGHT),5,3,1,1)
addComponent(new JLabel("D (*10*-6 m*2/hr)",SwingConstants.RIGHT),21,2,1,1);
addComponent(new JLabel("Keq",SwingConstants.RIGHT),21,3,1,1);
gbConstraints.fill = GridBagConstraints.HORIZONTAL;
gbConstraints.weightx=l;
addComponent(tThickness,0,1,1,1) ;
addComponent(tArea,1,1,1,1) ;
addComponent(tVolTop ,2,1,1,1) ;
addComponent(tVolBot, 3 , 1, 1, 1) ;
addComponent(tWeight,4,1,1,1) ;
addComponent(tCTopEq, 0,3,1,1) ;
addComponent(tCBotEq, 1,3,1,1) ;
addComponent(tDeltaT, 2,3,1,1) ;
addComponent(tLayers, 3,3,1,1) ;
addComponent(tSampledMass,4,3,1,1) ;
addComponent(tTTimel, 6,0,1,1) ;
-------
addComponent(tTTime2,7,0,1,1) ;
addComponent(tTTime3,8,0,1,1) ;
addComponent(tTTime4,9,0,1,1) ;
addComponent(tTTimeB,10,0,1,1) ;
addComponent(tTTime6,11,0,1,1) ;
addComponent(tTTime?,12,0,1,1);
addComponent(tTTimeS,13,0,1,1);
addComponent(tTTime9,14, 0, 1, 1) ;
addComponent(tTTimelO, 15, 0,1,1)
addComponent(tTTimell,16,0,1,1)
addComponent(tTTime!2 ,17,0,1,1)
addComponent(tTTime!3 ,18,0,1,1)
addComponent(tTTime!4,19,0,1,1)
addComponent(tTTimelB, 20,0,1,1)
addComponent(tTConcl ,6,1,1,1) ;
addComponent(tTConc2,7,1,1,1) ;
addComponent(tTConc3,8,1,1,1) ;
addComponent(tTConc4 ,9,1,1,1) ;
addComponent(tTConc5,10,1,1,1) ;
addComponent(tTConc6,11,1,1,1) ;
addComponent(tTConc7,12,1,1,1) ;
addComponent(tTConcS,13,1,1,1) ;
addComponent(tTConc9,14,1,1,1);
addComponent(t TConc10,15,1,1,1)
addComponent(t TConc11, 16,1,1,1)
addComponent(tTConcl2 ,17,1,1,1)
addComponent(tTConcl3,18,1,1,1)
addComponent(tTConcl4 ,19,1,1,1)
addComponent(t TConc15, 20,1,1,1)
addComponent(tBTimel,6,2,1,1) ;
addComponent(tBTime2,7,2,1,1) ;
addComponent(tBTime3,8,2,1,1) ;
addComponent(tBTime4,9,2,1,1) ;
addComponent(tBTimeB,10,2,1,1) ;
addComponent(tBTime6,11,2,1,1) ;
addComponent(tBTime7,12,2,1,1);
addComponent(tBTimeS,13, 2, 1, 1) ;
addComponent(tBTime9,14,2,1,1);
addComponent(tBTimelO,15,2 ,1,1)
addComponent(tBTimell, 16 , 2 ,1,1)
addComponent(tBTime!2,17,2,1,1)
addComponent(tBTime!3,18,2,1,1)
addComponent(tBTime!4 ,19,2,1,1)
addComponent(tBTimelB,20,2,1,1)
addComponent(tBConcl,6,3,1,1) ;
-------
addComponent (tBConc2, 7,3,1,1) ;
addComponent (tBConc3, 8,3,1,1) ;
addComponent (tBConc4, 9,3,1,1) ;
addComponent (tBConcB, 10, 3 , 1, 1) ;
addComponent (tBConc6, 11, 3 , 1, 1) ;
addComponent (tBConc?, 12 , 3 , 1, 1) ;
addComponent (tBConcS, 13 , 3 , 1, 1) ;
addComponent (tBConc9, 14 , 3 , 1, 1) ;
addComponent (tBConclO, 15,3,1,1)
addComponent (tBConcll, 16,3,1,1)
addComponent (tBConc 12 ,17,3,1,1)
addComponent (tBConc 13 ,18,3,1,1)
addComponent (tBConc 14 ,19,3,1,1)
addComponent (tBConclB, 20,3,1,1)
addComponent (tD, 22, 2, 1,1) ;
addComponent ( tKeq ,22,3,1,1) ;
done . addActionListener (this) ;
setSize (680,680) ;
show ( ) ;
private void addComponent (Component component, int row, int column, int width, int
height) {
gbConstraints . gridx=column;
gbConstraints .gridy=row;
gbConstraints .gridwidth=width;
gbConstraints .gridheight=height ;
gbGrid. setConstraints (component , gbConstraints) ;
c . add ( component ) ;
public void actionPerformed (ActionEvent e) {
getData ( ) ;
initializeValues ( ) ;
calculateKeq ( ) ;
startlterations () ;
printResults ( ) ;
public void getData () {
if (t Thickness .get Document ( ) .get Length ( ) >0)
dThickness = Double .parseDouble (tThickness .getText
if (tArea.getDocument ( ) .get Length ( ) >0)
dArea = Double .parseDouble (tArea. getText ());
-------
if(tVolTop.getDocument().getLength()>0)
dVolTop = Double.parseDouble(tVolTop.getText());
if(tVolBot.getDocument().getLength()>0)
dVolBot = Double.parseDouble(tVolBot.getText());
if(tWeight.getDocument().getLength()>0)
dWeight = Double.parseDouble(tWeight.getText());
if (tCTopEq.getDocument() .getLength()>0)
dCTopEq = Double.parseDouble(tCTopEq.getText());
if(tCBotEq.getDocument().getLength()>0)
dCBotEq = Double.parseDouble(tCBotEq.getText());
if(tDeltaT.getDocument().getLength()>0)
dDeltaT = Double.parseDouble(tDeltaT.getText());
if(tLayers.getDocument().getLength()>0)
dLayers = Double.parseDouble(tLayers.getText());
if(tSampledMass.getDocument().getLength()>0)
dSampledMass = Double.parseDouble(tSampledMass.getText());
if(tTTimel.getDocument().getLength()>0)
aTopTimeAndConc[0] [0] = Double.parseDouble(tTTimel.getText());
if(tTTime2.getDocument().getLength()>0)
aTopTimeAndConc[0] [1] = Double.parseDouble(tTTime2.getText());
if(tTTimeS.getDocument().getLength()>0)
aTopTimeAndConc[0] [2] = Double.parseDouble(tTTimeS.getText());
if(tTTime4.getDocument().getLength()>0)
aTopTimeAndConc[0] [3] = Double.parseDouble(tTTime4.getText());
if(tTTimeB.getDocument().getLength()>0)
aTopTimeAndConc[0] [4] = Double.parseDouble(tTTimeB.getText());
if(tTTime6.getDocument().getLength()>0)
aTopTimeAndConc[0] [5] = Double.parseDouble(tTTime6.getText());
if(tTTime?.getDocument().getLength()>0)
aTopTimeAndConc[0] [6] = Double.parseDouble(tTTime?.getText());
if(tTTimeS.getDocument().getLength()>0)
aTopTimeAndConc[0] [7] = Double.parseDouble(tTTimeS.getText());
if(tTTime9.getDocument().getLength()>0)
aTopTimeAndConc[0] [8] = Double.parseDouble(tTTime9.getText());
if(tTTimelO.getDocument().getLength()>0)
aTopTimeAndConc[0] [9] = Double.parseDouble(tTTimelO.getText())
if(tTTimell.getDocument().getLength()>0)
aTopTimeAndConc[0] [10] = Double.parseDouble(tTTimell.getText()
if(tTTimel2.getDocument().getLength()>0)
aTopTimeAndConc[0] [11] = Double.parseDouble(tTTime!2.getText()
if(tTTimel3.getDocument().getLength()>0)
aTopTimeAndConc[0] [12] = Double.parseDouble(tTTime!3.getText()
if(tTTimel4.getDocument().getLength()>0)
aTopTimeAndConc[0] [13] = Double.parseDouble(tTTime!4.getText()
-------
if(tTTimelS.getDocument().getLength()>0)
aTopTimeAndConc [0] [14] = Double.parseDouble(tTTimelB.getText())
if(tTConcl.getDocument().getLength()>0)
aTopTimeAndConc[1][0] = Double.parseDouble(tTConcl.getText());
if(tTConc2.getDocument().getLength()>0)
aTopTimeAndConc[1][1] = Double.parseDouble(tTConc2.getText());
if(tTConc3.getDocument().getLength()>0)
aTopTimeAndConc[1] [2] = Double.parseDouble(tTConc3.getText());
if(tTConc4.getDocument().getLength()>0)
aTopTimeAndConc[1][3] = Double.parseDouble(tTConc4.getText());
if(tTConcB.getDocument().getLength()>0)
aTopTimeAndConc[1][4] = Double.parseDouble(tTConcB.getText());
if(tTConc6.getDocument().getLength()>0)
aTopTimeAndConc [1] [B] = Double.parseDouble(tTConc6.getText());
if(tTConc?.getDocument().getLength()>0)
aTopTimeAndConc [1] [6] = Double.parseDouble(tTConc?.getText());
if(tTConc8.getDocument().getLength()>0)
aTopTimeAndConc[1][7] = Double.parseDouble(tTConcS.getText());
if(tTConc9.getDocument().getLength()>0)
aTopTimeAndConc[1][8] = Double.parseDouble(tTConc9.getText());
if(tTConc10.getDocument().getLength()>0)
aTopTimeAndConc[1] [9] = Double.parseDouble(tTConclO.getText());
if(tTConc11.getDocument().getLength()>0)
aTopTimeAndConc[1][10] = Double.parseDouble(tTConcll.getText())
if(tTConc12.getDocument().getLength()>0)
aTopTimeAndConc[1][11] = Double.parseDouble(tTConc!2.getText())
if(tTConc13.getDocument().getLength()>0)
aTopTimeAndConc[1] [12] = Double.parseDouble(tTConc!3.getText())
if(tTConc14.getDocument().getLength()>0)
aTopTimeAndConc [1] [13] = Double.parseDouble(tTConc!4.getText())
if(tTConcIB.getDocument().getLength()>0)
aTopTimeAndConc[1][14] = Double.parseDouble(tTConclB.getText())
if(tBTimel.getDocument().getLength()>0)
aBotTimeAndConc[0][0] = Double.parseDouble(tBTimel.getText());
if(tBTime2.getDocument().getLength()>0)
aBotTimeAndConc[0] [1] = Double.parseDouble(tBTime2.getText());
if(tBTime3.getDocument().getLength()>0)
aBotTimeAndConc[0][2] = Double.parseDouble(tBTime3.getText());
if(tBTime4.getDocument().getLength()>0)
aBotTimeAndConc[0][3] = Double.parseDouble(tBTime4.getText());
if(tBTimeS.getDocument().getLength()>0)
aBotTimeAndConc [0] [4] = Double.parseDouble(tBTimeS.getText());
if(tBTime6.getDocument().getLength()>0)
-------
aBotTimeAndConc[0] [5] = Double.parseDouble(tBTime6.getText());
if(tBTime?.getDocument().getLength()>0)
aBotTimeAndConc[0] [6] = Double.parseDouble(tBTime?.getText());
if(tBTimeS.getDocument().getLength()>0)
aBotTimeAndConc[0] [7] = Double.parseDouble(tBTimeS.getText());
if(tBTime9.getDocument().getLength()>0)
aBotTimeAndConc[0] [8] = Double.parseDouble(tBTime9.getText());
if(tBTimelO.getDocument().getLength()>0)
aBotTimeAndConc[0] [9] = Double.parseDouble(tBTimelO.getText())
if(tBTimell.getDocument().getLength()>0)
aBotTimeAndConc[0] [10] = Double.parseDouble(tBTimell.getText()
if(tBTime!2.getDocument().getLength()>0)
aBotTimeAndConc[0] [11] = Double.parseDouble(tBTime!2.getText()
if(tBTime!3.getDocument().getLength()>0)
aBotTimeAndConc[0] [12] = Double.parseDouble(tBTime!3.getText()
if(tBTime!4.getDocument().getLength()>0)
aBotTimeAndConc[0] [13] = Double.parseDouble(tBTime!4.getText()
if(tBTimelS.getDocument().getLength()>0)
aBotTimeAndConc[0] [14] = Double.parseDouble(tBTimelB.getText()
if(tBConcl.getDocument().getLength()>0)
aBotTimeAndConc[1] [0] = Double.parseDouble(tBConcl.getText());
if(tBConc2.getDocument().getLength()>0)
aBotTimeAndConc[1] [1] = Double.parseDouble(tBConc2.getText());
if(tBConc3.getDocument().getLength()>0)
aBotTimeAndConc[1] [2] = Double.parseDouble(tBConc3.getText());
if(tBConc4.getDocument().getLength()>0)
aBotTimeAndConc[1] [3] = Double.parseDouble(tBConc4.getText());
if(tBConcB.getDocument().getLength()>0)
aBotTimeAndConc[1] [4] = Double.parseDouble(tBConcS.getText());
if(tBConc6.getDocument().getLength()>0)
aBotTimeAndConc[1] [B] = Double.parseDouble(tBConc6.getText());
if(tBConc?.getDocument().getLength()>0)
aBotTimeAndConc[1] [6] = Double.parseDouble(tBConc?.getText());
if(tBConcS.getDocument().getLength()>0)
aBotTimeAndConc[1] [7] = Double.parseDouble(tBConcS.getText());
if(tBConc9.getDocument().getLength()>0)
aBotTimeAndConc[1] [8] = Double.parseDouble(tBConc9.getText());
if (tBConclO.getDocument() .getLength()>0)
aBotTimeAndConc[1] [9] = Double.parseDouble(tBConclO.getText())
if(tBConcll.getDocument().getLength()>0)
aBotTimeAndConc[1] [10] = Double.parseDouble(tBConcll.getText()
if(tBConcl2.getDocument().getLength()>0)
aBotTimeAndConc[1] [11] = Double.parseDouble(tBConc!2.getText()
if(tBConcl3.getDocument().getLength()>0)
-------
aBotTimeAndConc [1] [12] = Double .parseDouble (tBConc!3 .getText ());
if (tBConc!4 .getDocument () .get Length () >0)
aBotTimeAndConc [1] [13] = Double .parseDouble (tBConc!4 .getText ());
if (tBConclB .getDocument () .get Length () >0)
aBotTimeAndConc [1] [14] = Double .parseDouble (tBConclB .getText ());
public void calculateKeq ( ) {
dKeq= (aPredictedTopConc [0] *dVolTop-dCTopEq*dVolTop-dCBotEq*dVolBot-dSampledMass)
(dArea*dThickness) / ( (dCTopEq+dCBotEq) /2 .0) ;
tKeq. setText (Double .toString (dKeq) ) ;
public void startlterations ( ) {
int i , j ;
double dCurrentD, dBestD, dlncrement;
double [] aDValues = new double [10] ;
dCurrentD= . 000000001;
dlncrement= . 0000000001;
dBestD=l;
dBestResidual=10000;
while (dCurrentD< . 00000001) {
dD=dCurrentD;
calculateChamberConcentrations (
calculateResidual () ;
//System. out .println ( "dCurrentD : "+dCurrentD) ;
if (dResidual
-------
dCurrentD+=d!ncrement;
dCurrentD=.0000001;
dlncrement=.00000001;
while(dCurrentD<.000001) {
dD=dCurrentD;
calculateChamberConcentrations()
calculateResidual();
//System.out.println("dCurrentD: "+dCurrentD);
if(dResidual
-------
dCurrentD=. 0001;
dlncrement= . 00001;
while (dCurrentD< . 001) {
dD=dCurrentD;
calculateChamberConcentrations (
calculateResidual () ;
//System. out .println ( "dCurrentD : "+dCurrentD) ;
if (dResidual
-------
while (aTopTimeAndConc [0] [i]!=0.0)
double dLongestTime;
dLongestTime=aTopTimeAndConc [0] [i
iTopSize=i-l;
1 = 0;
while (aBotTimeAndConc [0] [i]!=0.0)
iBotSize=i-l;
if (dLongestTime < aBotTimeAndConc [0] [i-1])
dLongestTime=aBotTimeAndConc [0] [i-1] ;
aMaterialTimeAndConc = new double [(int) (dLongestTime/dDeltaT) +1] [ (int ) dLayers]
//System. out .println ( "Time Steps: "+aMaterialTimeAndConc . length+" Layers:
"+aMaterialTimeAndConc [0] .length) ;
aPredictedTopConc = new double [ (int ) (dLongestTime/dDeltaT) +1] ;
aPredictedBottomConc = new double [(int) (dLongestTime/dDeltaT) +1] ;
for (i = 0; i< aMaterialTimeAndConc [0] . length; i
aMaterialTimeAndConc [0] [i] = 0.0;
aPredictedTopConc [0] =aTopTimeAndConc [1] [0] ;
aPredictedBottomConc [0] =0.0;
//System. out .println ( "Starting top chamber cone: "+aPredictedTopConc [0] ) ;
public void calculateChamberConcentrations() {
int j=0;
int 1 = 0;
for (1 = 1;i
-------
public void printResults ( ) {
dD=dD*. 000001/60;
calculateChamberConcentrations () ;
dD=dD*60/ .000001;
System. out .println ( "Top Chamber Predicted Final Cone: "+aPredictedTopConc [aPredictedTopConc .
length- 1] ) ;
System. out .println ( "Top Chamber Experimental Final Cone: "+aTopTimeAndConc [1] [iTopSize] ) ;
System. out .println ( "Bottom Chamber Predicted Final Cone: " + aPredictedBottomConc [aPredictedBotto
mConc . length- 1] ) ;
System. out .println ( "Bottom Chamber Experimental Final Cone: "+aBotTimeAndConc [1] [iBotSize] ) ;
System. out .println ( "Original Mass: "+aTopTimeAndConc [1] [0] *dVolTop) ;
double dFinalSorbedMass = 0.0;
int j ;
f or ( j =0 ; j < (int) dLayers; j++) {
dFinalSorbedMass+=aMaterialTimeAndConc [aMaterialTimeAndConc . length-
1] [j] *dThickness/dLayers*dArea;
System. out .println ( "C"+j+" : "+aMaterialTimeAndConc [aMaterialTimeAndConc . length- 1] [ j ] ) ;
}
double dFinalPredictedMass=aPredictedTopConc [aPredictedTopConc . length- 1] *dVolTop+
dFinalSorbedMass+aPredictedBottomConc [aPredictedBottomConc . length- 1] *dVolBot ;
System. out .println ( "Predicted Final Mass: "+dFinalPredictedMass) ;
System. out .println ( "Best residual: "+dBestResidual) ;
System. out .println ( "D : "+dD) ;
int i,iTimeStep;
double dExpTime, dExpConc, dPredictedConc;
for (i=l;i
-------
diff.addWindowListener(new WindowAdapter() {
public void windowClosing(WindowEvent e)
System.exit(0);
-------
Appendix C
Results for Mortar Experiments
The following plots show the relative concentration
parameter, -ln(C/Co) A/V, in the top chamber of the dual-
volume system versus time for five of six organic test
chemicals and mortar. Here, Co is the initial concentration
(time = 0) in the gas phase of the top chamber, C is the
chemical concentration in the gas phase of the top chamber
at a specific time, A is the area of the exposed surface of
mortar in the top chamber, and V is the air volume of the top
chamber.
Figure C-l. Relative concentration parameter versus time for mortar exposed to n-butanol.
0.6 -
0.5 -
I' °-4 "
3!
o
o
§. 0.3 -
C
0.2 -
01
0 J
C
n_butanol and Concrete
o ^__I-^— <— — *•*-; >
r * y = 9E-07x +0.4748
| R2= 0.6191
1 y = 0.0002X
I R2= 0.8661
I
10000 20000 30000 40000 50000 60000 70000 80000 90000
Tim e (m in)
Figure C-2. Relative concentration parameter versus time for mortar exposed to ethylbenzene.
Ethyl Benzene and Concrete
o
o
0.15
0.1
0.05
y = 1E-06x + 0.2582-
R2 = 0.812
1 y = 8E-05x
R2 = 0.8369
10000 20000 30000 40000 50000 60000 70000 80000 90000
Time (m in)
-------
Figure C-3. Relative concentration parameter versus time for concrete exposed to decane.
Decane and Concrete
y = O.OOOIx
R2 = 0.8093
10000 20000 30000 40000 50000 60000 70000 80000 90000
Time (m in)
Figure C-4. Relative concentration parameter versus time for mortar exposed to
undecane.
Undecane and Concrete
-E 0.3 -
S. 0.25
o
o
0.2 -
0.15 -
y = 1E-06x +0.3608"
R2 = 0.781
y = O.OOOIx
-R2 = 0.7835-
20000 40000 60000
Tim e (m in)
80000
100000
-------
Figure C-5. Relative concentration parameter versus time for motar exposed to dodecane.
Dodecane and Concrete
0 10000 20000 30000 40000 50000 60000 70000 80000 90000
Timefm in)
-------
-------
Appendix D
Results for VF and PUF
Figure D-l. Raw data and fitted diffusion model for sorption and desorption of hexanal in vinyl
flooring.
186.1
0)
C/5
C/5
CO
186.0 -
185.9 -
185.8 -
185.7 -
185.6 -
185.5
185.4
40
-------
QJ
C/5
C/5
Figure D-2. Raw data and fitted diffusion model for sorption and desorption of decane in
vinyl flooring.
185.46
Figure D-3. Raw data and fitted diffusion model for sorption and desorption of dodecane
(first replicate) in vinyl flooring.
C/5
CO
40
-------
fl)
CO
0)
C/5
C/5
CO
Figure D-4. Raw data and fitted diffusion model for sorption and desorption of dodecane
(second replicate) in vinyl flooring.
185.75 -
185.70 -
185.65 -
185.60 -
185.55
185.50
10 15 20
Time(hrs)
25
30
Figure D-5. Raw data and fitted diffusion model for sorption and desorption of undecane in
vinyl flooring.
10 15 20
Time(hrs)
25
-------
Figure D-6. Raw data and fitted diffusion model for sorption and desorption of butanol in
vinyl flooring.
185.46
0
10
15
20
Time(hrs)
Figure D-7. Raw data and fitted diffusion model for sorption and desorption of tetradecane
in vinyl flooring.
185.9
185.8 -
185.7 -
185.6 -
185.5 -
185.4
20
40 60 80
Time(hrs)
100
120
-------
0)
C/5
C/5
CO
QJ
C/5
C/5
Figure D-8. Raw data and fitted diffusion model for sorption and desorption of undecane in
polyurethane foam.
97.48
97.46 -
97.44 -
97.42 -
97.40 -
97.38 -
97.36 -
97.34 -
97.32
raw
model
0
10
12
Time(hrs)
Figure D-9. Raw data and fitted diffusion model for sorption and desorption of butanol in
polyurethane foam.
97
-------
QJ
c/5
C/5
Figure D-10. Raw data and fitted diffusion model for sorption and desorption of decane in
polyurethane foam.
97.52 -
97.50 -
97.48
10 15
Time(hrs)
20
25
Figure D-ll. Raw data and fitted diffusion model for sorption and desorption of dodecane
(first replicate) in polyurethane foam.
97.48
97.46 -
97.44 -
97.42 -
97.40 -
97.38 -
97.36 -
97.34 -
97.32
• Raw
— model
4 6
Time(hrs)
10
12
-------
C/5
C/5
CO
Figure D-12. Raw data and fitted diffusion model for sorption and desorption of dodecane
(second replicate) in polyurethane foam.
97.48
97.46 -
97.44 -
97.42 -
97.40 -
97.38 -
97.36 -
97.34 -
97.32
raw
model
0 2 4 6 8 10 12 14 16 18 20
Time(hrs)
Figure D-13. Raw data and fitted diffusion model for sorption and desorption of tetradecane
in polyurethane foam.
97.64
97.62 -
-------
Figure D-14. Raw data for sorption and desorption of hexanal (first replicate) in
polyurethane foam.
110.20.
ifl
110.15-
110.10-
110.05-
110.00-
109.95-
109.90-
109.85
0 10 20 30
Time (hrs)
40
50
60
Figure D-15. Raw data for sorption and desorption of hexanal (second replicate) in
polyurethane foam.
110.4-
110.3-
110.2-
110.1-
110.0-
0 10 20 30 40 50 60 70 80
Time (hrs)
-------
-------
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Agency
Office of Research and Development
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Cincinnati, OH 45268
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