SC IEN CE

United States

Environmental Protection

Agency

Determination of Sorption 

Parameters for 36 VOC/Material 

Combinations

FINAL REPORT

Office of Research and Development

National Homeland Security Research Center
ii

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October 2007 EPA 600/R-07/035-R1

Determination of Sorption Parameters 

for 36 VOC/Material 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 Crain1, 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, VA USA

Office of Research and Development

National Homeland Security Research Center, Decontamination and Consequence Management Division
iv

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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.
vi

The Charles Edward Via, Jr. Department of Civil and 

Environmental Engineering

John Little, Ph.D., P.E.

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

	 	 	 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 massflow controller. The diffusion vial emission rate is determined by measuring the mass of the vial before and after 

the experiment using a mechanical balance.
vii

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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.
viii

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ix

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 Test 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., 2001b; 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 Crain, 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 (σ = 0.01 mm; n= 5). The mean 

thickness of the carpet backing (fibers shaved off) was 1.23 

mm (σ = 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 Sample Size Description

Unpainted Gypsum 

Board

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. 

The nominal 1⁄2-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 1.27 cm.

The mortar was prepared using screened ovendried 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) × 2.66 cm 

(width) × 0.0175 cm (thickness).

Polyurethane Foam The polyurethane foam sample tested had 

dimensions of 1.39 cm (radius) × 4.70 cm 

(length).

A flexible polyether-type, open cell polyurethane 

foam was purchased from Airtex (Cokato, MN). 

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.


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 (SF6) 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.

Test Materials Chemicals Test Method

Unpainted gypsum board Base case + ethylbenzene + SF6 Dual-volume chamber

Painted gypsum board Base case + ethylbenzene + SF6 Dual-volume chamber

PVC-backed carpet Base case + ethylbenzene + SF6 Dual-volume chamber

Mortar Base case + ethylbenzene + SF6 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 #

Molecular Weight 

(g/mol) Boiling Point (°C)

Vapor pressure 

(mm Hg) at 20 °C

n-Butanol* 71-36-3 74.1 118 4.4

Hexanal* 66-25-1 100.2 128–131 10

Ethylbenzene 100-41-4 106.2 136 7

Decane* 124-18-5 142.3 173–174 2.7

Undecane* 1120-21-4 156.3 196 1 (33 °C)

Dodecane* 112-40-3 170.3 216 0.3

Tetradecane 629-59-4 198.4 252 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 1⁄4" SwagelokTM 

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.


Figure 2-. Schematic of experimental dual-volume diffusion chamber.

Bolt

Mixing fan Injection/sample port

Top chamber

Substrate

Bottom chamber

Flange

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) (b) (c)

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. A10-μL volume of prediluted SF6

 was drawn from a TedlarTM bag, using a gastight 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 gastight syringes inserted through TeflonTM-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.
 

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. A volume 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 gastight syringe. Sorbent tubes were actually large-volume gas 

chromatograph glass injection inserts packed with 100 mg of 

TenaxTM-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.


Figure 2-. Digital images of microbalance test system: (a) whole test system, 

(b) microbalance system, (c) diffusion cell.

(a) (b) (c)

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 μg) 

dynamic micro-balance (Model D200-02, Cahn) 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. (2001b) 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 I.D. 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.

Chemicals Emission Rate (μg/min)

VF PUF

n-Butanol 217.5 194.1

Hexanal 186.0 –

Decane 42.9 43.0

Undecane 15.9 21.6

Dodecane 6.9 10.2

Tetradecane 5.1 8.3


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3. 

Data Analysis

3. 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 sorbedphase 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 Cair:

(3-1)

air

s

C

K =

where,

K = equilibrium partition coefficient 

 [(mg/m3

material)/(mg/m3air)] or 

 (m3

air/m3material),

Cs = sorbed concentration of test chemical 

 (mg /m3

material), and

Cair = concentration in air at equilibrium 

 (mg/m3

air).

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, Cair

reflects the average of test chemical concentrations in top an

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:

d 

C

 

solid

T bebairtetair isamp

s V

mVCVCm

C

−−− ∑ =

,, ,, ,

 (3-2)

where,

mT = total mass of test chemical injected into the system 

 (mg),

msamp,i= mass of test chemical removed from system 

 during i

 (3-3)

(3-4)

where,

Mt = mass sorbed to the material at time t (mg),

M∞ = mass sorbed to the material at equilibrium as 

 determined experimentally (mg),

α = ratio of volume of the air chamber to the 

 material (-),

qn

 = non-zero positive roots of the mathematical 

 expression: tan qn = - α qn.

l = thickness of the material (m)

t = time (hr), 

De = effective diffusion coefficient through material 

 (m2/hr), and 

T = 2

l

e (-).

tD
10

An alternate solution to Equation 3-3 for 

small values of T is given by Equation 3-5:

 (3-5)

Equation 3-4 is obtained from Equation 3-5 by substituting 

the asymptotic expansion for 

when is large.

For carpet, a total normalized, squared residual between 

predicted and observed mass sorbed fractions was defined as:

(3-6)

where,

R = total normalized squared residual (-), and

i = 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 (Fick’s first 

law) into the gypsum board and mass gain to the bottom 

chamber by diffusive flux (Fick’s first law) passing out the 

bottom of the gypsum board. Fick’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 

and bottom chamber air. The effective diffusion coefficient 

was chosen to minimize the total residual as defined by: 

∑= 













 − =

n

i air erimental

air erimental air predicted

C

C C

R

1

2

, exp

, exp , (3-8)

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: 

 

(3-8)

where,

Ψ = ratio of diffusion coefficients in air for a test 

chemical and SF6 (-),

Dvoc = molecular diffusion coefficient of VOC (test 

chemical) in air (m2/hr),

DSF6 = molecular diffusion coefficient of SF6 in air 

(m2/hr),

De

,

voc = effective diffusion coefficient of VOC in material 

pores (m2/hr),

De,

SF6 = effective diffusion coefficient of SF6 in material 

pores (m2/hr),

Ωvoc = collision integral for VOC (-),

ΩSF6 = collision integral for SF6 (-),

Ωvoc = characteristic length of VOC molecule interacting 

with air molecules (m), and

σSF6 = characteristic length of SF6 molecule interacting 

with air molecules (m).
11

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.

Chemical Collision Integral 

(-)

Characteristic 

Length (Å)

n-Butanol 1.174 4.627

Hexanal 1.180 4.923

Ethylbenzene 1.185 4.922

Decane 1.207 5.467

Undecane 1.219 5.580

Dodecane 1.230 5.687

Sulfur hexafluoride 1.048 4.374

The parameter Mr includes the molecular weight of air and 

chemical i (VOC or SF6) in accordance with Equation 3-9:

 

iair

air i

ir MM

MM

M

+ , = (3-9)

where,

Mair = molecular weight of air = 29 g/mol, and

Mi = 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 SF6 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., 2001b). For a particular 

VOC, the sorption equilibrium was described using a 

partition coefficient:

air

s

C

C K = (3-10)

where,

K = equilibrium partition coefficient

 ([mg/m3

material]/[mg/m3air]) or (m3air/m3material),

Cs = sorbed concentration of test chemical 

 (mg /m3

material), and

Cair = concentration in air at equilibrium (mg/m3

air).

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 Cair was calculated from:

air = E C

Q

 (3-11)

where,

E = constant emission rate of VOC generated by the 

 diffusion cell (mg/s), and

Q = air flow rate through the system (m3/s).
12

Figure 3-. Sulfur hexafluoride concentration profiles for unpainted gypsum board in the top chamber (a) and bottom 

chamber (b) of the dual-volume diffusion chamber.

(a)

(b)

	S F 6	an d 	Gyp su m 	B o ard 	T o p 	C h am b er

0

5

10

15

20

25

0 20 40 60 80 100 120 140 160

T im e 	(m in )

Concentration	(ppB)

S F 6	an d 	Gyp su m 	B o ard 	B o tto m 	C h am b er

0

2

4

6

8

10

12

0 50 100 150 200

T im e 	(m in )

Concentration	(ppB)
13

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. 

(a)

(b)

U n d ecan e	an d 	Gyp su m 	B o ard 	T o p 	C h am b er

0

10

20

30

40

50

60

70

80

90

0 500 1000 1500 2000 2500 3000

T im e 	(m in )

Concentration	(mg/m3)

U n d ecan e	an d 	Gyp su m 	B o ard 	B o tto m 	C h am b er

0

0.5

1

1.5

2

2.5

3

0 500 1000 1500 2000 2500 3000

T im e 	(m in )

Concentration	(mg/m3)
14

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):

2 2

2 2 2

0

8 (2 1) 1 exp (2 1) 4

t e

n

M D n t

M n L

p

p

∞

∞ =

− +  = − ⋅   +   ∑ 

(3-12)

where,

Mt = total mass of a VOC that has entered or left the slab 

in time t (g),

M∞ = 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):

( ) M

M a

D t t

n

e n

∞ n=

∞

= − × − 1 ∑ 4

2 2

2

0 α

exp α (3-13) 

where, 

the αn values are the positive roots of J0 (aαn) = 0, 

a = radius of the cylinder, and

J0 = 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.

Tim e(hrs)

0 10 20 30 40

Mass(mg)

185.54

185.56

185.58

185.60

185.62

185.64

185.66

185.68

185.70

185.72

raw 

m odel	
15

Figure 3-. Dodecane sorption/desorption profiles for polyurethane foam with fitted diffusion model.

Tim e(hrs)

0 2 4 6 8 10 12

Mass(mg)

97.32

97.34

97.36

97.38

97.40

97.42

97.44

97.46

97.48

R aw 

m odel	
16

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17

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).*

Test Chemical

K 

(mg/m3)

solid/(mg/m3)air De

 (m2/hr)

n-Butanol 920 2.2 × 10-5

Hexanal 590 1.9 × 10-5

Ethylbenzene 100 3.4 × 10-5

Decane 230 1.7 × 10-5

Undecane 1,640 3.8 × 10-5

Dodecane 4,160 4.6 × 10-7

Sulfur hexafluoride — 7.8 ×10-4

* Analysis by dual-volume chamber.

Table 4-2. Equilibrium partition and diffusion coefficients (Gypsum Board - Painted).*

Test Chemical

K 

(mg/m3)

solid/(mg/m3)air De

 (m2/hr)

n-Butanol 720 7.8 × 10-6

Hexanal 350 1.4 × 10-5

Ethylbenzene 38 3.4 × 10-5

Decane 130 1.3 × 10-5

Undecane 270 9 × 10-6

Dodecane 1,130 3.1 × 10-6

Sulfur hexafluoride — 1.6 × 10-3

* Analysis by dual-volume chamber.

Table 4-3. Equilibrium partition and diffusion coefficients (Carpet, PVC-backed).*

Test Chemical

K 

(mg/m3)solid/(mg/m3)

air De

 (m2/hr)

n-Butanol 710 / 180 2.4 × 10-11 / 3.3 × 10-10

Hexanal 1090 / 280 1.9 × 10-11 / 4.4 × 10-10

Ethylbenzene 2,600 / 660 2.3 × 10-12 / 3.6 × 10-11

Decane 5,730 / 2,070 1.9 × 10-10 / 1.4 × 10-9

Undecane 8,600 / 2,200 1.3 × 10-10 / 1.7 × 10-9

Dodecane 72,300 / 18,400 2.7 × 10-12 / 4.4 × 10-11

Sulfur hexafluoride — —

* Analysis by dual-volume chamber. 

 Values for De based on thickness of carpet backing (left of /) and on thickness of backing + fibers (right of /).
18

Table 4-4. Equilibrium partition and diffusion coefficients (Vinyl Flooring).*

Test Chemical

K

(mg/m3)solid/(mg/m3)air De

 (m2/hr)

n-Butanol 1,100 2.7 × 10-09

Hexanal 46,000 2.0 × 10-09

Decane 6,000 1.8 × 10-09

Undecane 17,000 2.0 × 10-09

Dodecane 47,000 6.9 × 10-10

Tetradecane 110,000 4.2 × 10-10

* Analysis by microbalance.

Table 4-5. Equilibrium partition and diffusion coefficients (Polyurethane Foam).*

Test Chemical

K

(mg/m3)

solid/(mg/m3)air De

 (m2/hr)

n-Butanol 110 3.0 × 10-05

Hexanal —

Decane 72 2.2 × 10-06

Undecane 490 1.1 × 10-05

Dodecane 1,400 7.7 × 10-06

Tetradecane 5,400 5.4 × 10-07

* 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 Ψ 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 De for gypsum board in the absence of sorption.

Test Chemical

Ψ

Eq. 3-7

Unpainted 

De (m2/hr)

Unpainted 

[sorption/

no sorption]

Painted GB 

De (m2/hr)

Painted 

[sorption/

no sorption]

SF6* 1 7.8 × 10-4 — 1.6 × 10-3 —

n-Butanol 0.856 6.7 × 10-4 0.033 1.4 × 10-3 0.0056

Hexanal 0.725 5.7 × 10-4 0.033 1.2 ×10-3 0.012

Ethylbenzene 0.718 5.6 ×10-4 0.061 1.1 ×10-3 0.031

Decane 0.557 4.3 ×10-4 0.040 8.9 × 10-4 0.015

Undecane 0.525 4.1 × 10-4 0.093 8.4 × 10-4 0.011

Dodecane 0.498 3.9 ×10-4 0.0012 8.0 ×10-4 0.0039

* measured value.
19

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 m2/hr) 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-1,3-

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 
20

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 PVC-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)solid/(mg/m3)air. This indicates that VF has a 

similar sorption capacity to carpet. The effective diffusion 

coefficients for VF range between 2.7 × 10-9 and 4.2 ×

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/m3)

solid/(mg/m3

)

air. This indicates that PUF 

has a similar sorption capacity to gypsum board. The 

effective diffusion coefficients for PUF range between 3.0 

× 10-5 and 5.4 × 10-7 m2/hr 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 μg. 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 μg 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-1,3-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.
21

6.

References

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Measuring Concentrations of Volatile Organic Compounds 

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Partition and Diffusion Coefficients for Volatile Organic 

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22

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23

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.
24

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% 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 lowvolume (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 “bakeout” 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 μg 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) × 2.66 cm (width) × 0.0175 cm (thickness). The 

polyurethane foam’s dimension was 1.39 cm (radius) ×

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 
25

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 Crain 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 gastight 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 Crain prior to usage.

VT: There are no samples to be preserved using the microbalance 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 gastight 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. Crain or Dr. Corsi. 

Response – Material specimens were wrapped in aluminum 

foil as described above. Dr. Neil Crain 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. Crain’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.
26

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. Crain to Dr. Corsi on an approximate biweekly basis. Electronic copies are maintained by both Dr. 

Crain 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 USEPA TO-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-1.

Table A-1. Emission rates from diffusion vials.

Chemicals Emission Rate 

(μg/min)

VF PUF

n-Butanol 217.5 194.1

Hexanal 186.0 -

Decane 42.9 43.0

Undecane 15.9 21.6

Dodecane 6.9 10.2

Tetradecane 5.1 8.3

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 
27

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 μg. 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 μg. 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 
28

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:

 (A-1) % , ,

, ,

difference X

C C

C C

air air

air air

= = × −

+

2 ×100 1 2

1 2

where, 

Cair,

1

 and Cair,

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).

Chemical

Mean % 

difference (X)

Standard 

Deviation (%)

n-Butanol 7.8 4.2

Hexanal 6.0 4.7

Ethylbenzene 3.0 2.1

Decane 5.5 2.1

Undecane 7.3 3.0

Dodecane 4.9 1.9

SF6 0.98 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).
29

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.
30

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31

Appendix B

Finite Difference Equations and Program to 

Calculate D

e

 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”: 

(B-1) 

where,

Cair,

t = chemical concentration in the air of the top

 chamber at time step n (mg/m3

air),

C1,

s = sorbed-phase concentration at the midpoint

of the top (first) layer of gypsum board 

 (mg/m3

material),

De = effective diffusion coefficient (m2/hr),

A = exposed surface area of material adjacent to air in 

 each chamber (m2),

 ∆t = time interval of the time steps used in the 

 numerical solution (hr),

 ∆x = thickness of each slice of material as used in the 

 numerical calculation (m),

Vtop = volume of the top chamber (m3), and

Keq = equilibrium partition coefficient (m3

air/m3material).

The concentration at the mid-point of the first layer (C1,

s

above) was predicted as:

 

[ ]

2

,2

1

,1 2 , 1

,1 3 1

2

x

tD

C C

x

tD C

C e

n

s

n

topsurface

n e

s n

s

∆

∆

+

+

∆

∆

+

=

+

+

 (B-2)

where, 

1

,

n+ C topsurface = concentration on the top surface of the 

material (mg/m3

material): .

All other variables are as defined previously. 

Interior Gypsum Board

Fick’s second law was used to develop a finite difference 

solution for diffusion through the gypsum board. The sorbedphase concentration of a test chemical in all “i” layers of 

gypsum board, other than the top and bottom layers, was 

predicted as:

2

,1

1

, 2 ,1 1

, 2 1

x

tD

CC

x

C

C e

n

si

n

si

n e

si n

si

∆

∆

+

+

∆

+

= +

+

− + (B-3)

[ ] D ∆t

where,

Δx = 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:

[ ]

2

,

1

, 2 ,1 1

, 3 1

2

x

tD

C C

x

tD C

C e

n

botsurface

n

sfinal

n e

sfinal n

sfinal

∆

∆

+

+

∆

∆

+

=

+

− +

 

(B-4)

n C ,botsurface = concentration on the bottom surface of the 

 material (mg/m3

material): 

,

Cair,

b

n

 = chemical concentration in air of bottom chamber 

 at time n (mg/m3

air).

Bottom Chamber

The change in concentration in the bottom chamber was 

determined based on a mass balance and Fick’s first law for 

estimating flux into the chamber from the lower side of the 

gypsum board. A finite difference approximation led to:

 (B-5)

where,

Vbot = volume of the bottom chamber (m3).

All other variables are as defined previously.
32

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 tTTime1,tTTime2,tTTime3,tTTime4,tTTime5,tTTime6,tTTime7,tTTime8,tTTim

e9,tTTime10;

private JTextField tBTime11,tBTime12,tBTime13,tBTime14, tBTime15;

private JTextField tBTime1,tBTime2,tBTime3,tBTime4,tBTime5,tBTime6,tBTime7,tBTime8,tBTim

e9,tBTime10;

private JTextField tTTime11,tTTime12,tTTime13,tTTime14, tTTime15;

private JTextField tTConc1,tTConc2,tTConc3,tTConc4,tTConc5,tTConc6,tTConc7,tTConc8,tTCon

c9,tTConc10;

private JTextField tTConc11,tTConc12,tTConc13,tTConc14, tTConc15;

private JTextField tBConc1,tBConc2,tBConc3,tBConc4,tBConc5,tBConc6,tBConc7,tBConc8,tBCon

c9,tBConc10;

private JTextField tBConc11,tBConc12,tBConc13,tBConc14, tBConc15,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;
33

public DiffusionSolver() {

 super( “Diffusion Solver” );

 c = getContentPane();

 gbGrid = new GridBagLayout();

 c.setLayout(gbGrid);

 gbConstraints = new GridBagConstraints();

 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];

 tTTime1 = new JTextField();

 tTTime2 = new JTextField();

 tTTime3 = new JTextField();

 tTTime4 = new JTextField();

 tTTime5 = new JTextField();

 tTTime6 = new JTextField();

 tTTime7 = new JTextField();

 tTTime8 = new JTextField();

 tTTime9 = new JTextField();
34

 tTTime10 = new JTextField();

 tTTime11 = new JTextField();

 tTTime12 = new JTextField();

 tTTime13 = new JTextField();

 tTTime14 = new JTextField();

 tTTime15 = new JTextField();

 tTConc1 = new JTextField();

 tTConc2 = new JTextField();

 tTConc3 = new JTextField();

 tTConc4 = new JTextField();

 tTConc5 = new JTextField();

 tTConc6 = new JTextField();

 tTConc7 = new JTextField();

 tTConc8 = new JTextField();

 tTConc9 = new JTextField();

 tTConc10 = new JTextField();

 tTConc11 = new JTextField();

 tTConc12 = new JTextField();

 tTConc13 = new JTextField();

 tTConc14 = new JTextField();

 tTConc15 = new JTextField();

 tBTime1 = new JTextField();

 tBTime2 = new JTextField();

 tBTime3 = new JTextField();

 tBTime4 = new JTextField();

 tBTime5 = new JTextField();

 tBTime6 = new JTextField();

 tBTime7 = new JTextField();

 tBTime8 = new JTextField();

 tBTime9 = new JTextField();

 tBTime10 = new JTextField();

 tBTime11 = new JTextField();

 tBTime12 = new JTextField();

 tBTime13 = new JTextField();

 tBTime14 = new JTextField();

 tBTime15 = new JTextField();

 tBConc1 = new JTextField();

 tBConc2 = new JTextField();

 tBConc3 = new JTextField();

 tBConc4 = new JTextField();

 tBConc5 = new JTextField();

 tBConc6 = new JTextField();
35

 tBConc7 = new JTextField();

 tBConc8 = new JTextField();

 tBConc9 = new JTextField();

 tBConc10 = new JTextField();

 tBConc11 = new JTextField();

 tBConc12 = new JTextField();

 tBConc13 = new JTextField();

 tBConc14 = new JTextField();

 tBConc15 = new JTextField();

 tD=new JTextField();

 tKeq=new JTextField();

 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 Conc”,SwingConstants.RIGHT),5,1,1,1);

 addComponent(new JLabel(“Bottom Chamber Time”,SwingConstants.RIGHT),5,2,1,1);

 addComponent(new JLabel(“Bottom Chamber Conc”,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=1;

 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(tTTime1,6,0,1,1);
36

 addComponent(tTTime2,7,0,1,1);

 addComponent(tTTime3,8,0,1,1);

 addComponent(tTTime4,9,0,1,1);

 addComponent(tTTime5,10,0,1,1);

 addComponent(tTTime6,11,0,1,1);

 addComponent(tTTime7,12,0,1,1);

 addComponent(tTTime8,13,0,1,1);

 addComponent(tTTime9,14,0,1,1);

 addComponent(tTTime10,15,0,1,1);

 addComponent(tTTime11,16,0,1,1);

 addComponent(tTTime12,17,0,1,1);

 addComponent(tTTime13,18,0,1,1);

 addComponent(tTTime14,19,0,1,1);

 addComponent(tTTime15,20,0,1,1);

 addComponent(tTConc1,6,1,1,1);

 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(tTConc8,13,1,1,1);

 addComponent(tTConc9,14,1,1,1);

 addComponent(tTConc10,15,1,1,1);

 addComponent(tTConc11,16,1,1,1);

 addComponent(tTConc12,17,1,1,1);

 addComponent(tTConc13,18,1,1,1);

 addComponent(tTConc14,19,1,1,1);

 addComponent(tTConc15,20,1,1,1);

 addComponent(tBTime1,6,2,1,1);

 addComponent(tBTime2,7,2,1,1);

 addComponent(tBTime3,8,2,1,1);

 addComponent(tBTime4,9,2,1,1);

 addComponent(tBTime5,10,2,1,1);

 addComponent(tBTime6,11,2,1,1);

 addComponent(tBTime7,12,2,1,1);

 addComponent(tBTime8,13,2,1,1);

 addComponent(tBTime9,14,2,1,1);

 addComponent(tBTime10,15,2,1,1);

 addComponent(tBTime11,16,2,1,1);

 addComponent(tBTime12,17,2,1,1);

 addComponent(tBTime13,18,2,1,1);

 addComponent(tBTime14,19,2,1,1);

 addComponent(tBTime15,20,2,1,1);

 addComponent(tBConc1,6,3,1,1);
37

 addComponent(tBConc2,7,3,1,1);

 addComponent(tBConc3,8,3,1,1);

 addComponent(tBConc4,9,3,1,1);

 addComponent(tBConc5,10,3,1,1);

 addComponent(tBConc6,11,3,1,1);

 addComponent(tBConc7,12,3,1,1);

 addComponent(tBConc8,13,3,1,1);

 addComponent(tBConc9,14,3,1,1);

 addComponent(tBConc10,15,3,1,1);

 addComponent(tBConc11,16,3,1,1);

 addComponent(tBConc12,17,3,1,1);

 addComponent(tBConc13,18,3,1,1);

 addComponent(tBConc14,19,3,1,1);

 addComponent(tBConc15,20,3,1,1);

 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();

 startIterations();

 printResults();

 }

public void getData() { 

 if(tThickness.getDocument().getLength()>0) 

 dThickness = Double.parseDouble(tThickness.getText());

 if(tArea.getDocument().getLength()>0)

 dArea = Double.parseDouble(tArea.getText());
38

 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(tTTime1.getDocument().getLength()>0)

 aTopTimeAndConc[0][0] = Double.parseDouble(tTTime1.getText());

 if(tTTime2.getDocument().getLength()>0)

 aTopTimeAndConc[0][1] = Double.parseDouble(tTTime2.getText());

 if(tTTime3.getDocument().getLength()>0)

 aTopTimeAndConc[0][2] = Double.parseDouble(tTTime3.getText());

 if(tTTime4.getDocument().getLength()>0)

 aTopTimeAndConc[0][3] = Double.parseDouble(tTTime4.getText());

 if(tTTime5.getDocument().getLength()>0)

 aTopTimeAndConc[0][4] = Double.parseDouble(tTTime5.getText());

 if(tTTime6.getDocument().getLength()>0)

 aTopTimeAndConc[0][5] = Double.parseDouble(tTTime6.getText());

 if(tTTime7.getDocument().getLength()>0)

 aTopTimeAndConc[0][6] = Double.parseDouble(tTTime7.getText());

 if(tTTime8.getDocument().getLength()>0)

 aTopTimeAndConc[0][7] = Double.parseDouble(tTTime8.getText());

 if(tTTime9.getDocument().getLength()>0)

 aTopTimeAndConc[0][8] = Double.parseDouble(tTTime9.getText());

 if(tTTime10.getDocument().getLength()>0)

 aTopTimeAndConc[0][9] = Double.parseDouble(tTTime10.getText());

 if(tTTime11.getDocument().getLength()>0)

 aTopTimeAndConc[0][10] = Double.parseDouble(tTTime11.getText());

 if(tTTime12.getDocument().getLength()>0)

 aTopTimeAndConc[0][11] = Double.parseDouble(tTTime12.getText());

 if(tTTime13.getDocument().getLength()>0)

 aTopTimeAndConc[0][12] = Double.parseDouble(tTTime13.getText());

 if(tTTime14.getDocument().getLength()>0)

 aTopTimeAndConc[0][13] = Double.parseDouble(tTTime14.getText());
39

 if(tTTime15.getDocument().getLength()>0)

 aTopTimeAndConc[0][14] = Double.parseDouble(tTTime15.getText());

 if(tTConc1.getDocument().getLength()>0)

 aTopTimeAndConc[1][0] = Double.parseDouble(tTConc1.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(tTConc5.getDocument().getLength()>0)

 aTopTimeAndConc[1][4] = Double.parseDouble(tTConc5.getText());

 if(tTConc6.getDocument().getLength()>0)

 aTopTimeAndConc[1][5] = Double.parseDouble(tTConc6.getText());

 if(tTConc7.getDocument().getLength()>0)

 aTopTimeAndConc[1][6] = Double.parseDouble(tTConc7.getText());

 if(tTConc8.getDocument().getLength()>0)

 aTopTimeAndConc[1][7] = Double.parseDouble(tTConc8.getText());

 if(tTConc9.getDocument().getLength()>0)

 aTopTimeAndConc[1][8] = Double.parseDouble(tTConc9.getText());

 if(tTConc10.getDocument().getLength()>0)

 aTopTimeAndConc[1][9] = Double.parseDouble(tTConc10.getText());

 if(tTConc11.getDocument().getLength()>0)

 aTopTimeAndConc[1][10] = Double.parseDouble(tTConc11.getText());

 if(tTConc12.getDocument().getLength()>0)

 aTopTimeAndConc[1][11] = Double.parseDouble(tTConc12.getText());

 if(tTConc13.getDocument().getLength()>0)

 aTopTimeAndConc[1][12] = Double.parseDouble(tTConc13.getText());

 if(tTConc14.getDocument().getLength()>0)

 aTopTimeAndConc[1][13] = Double.parseDouble(tTConc14.getText());

 if(tTConc15.getDocument().getLength()>0)

 aTopTimeAndConc[1][14] = Double.parseDouble(tTConc15.getText());

 if(tBTime1.getDocument().getLength()>0)

 aBotTimeAndConc[0][0] = Double.parseDouble(tBTime1.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(tBTime5.getDocument().getLength()>0)

 aBotTimeAndConc[0][4] = Double.parseDouble(tBTime5.getText());

 if(tBTime6.getDocument().getLength()>0)
40

 aBotTimeAndConc[0][5] = Double.parseDouble(tBTime6.getText());

 if(tBTime7.getDocument().getLength()>0)

 aBotTimeAndConc[0][6] = Double.parseDouble(tBTime7.getText());

 if(tBTime8.getDocument().getLength()>0)

 aBotTimeAndConc[0][7] = Double.parseDouble(tBTime8.getText());

 if(tBTime9.getDocument().getLength()>0)

 aBotTimeAndConc[0][8] = Double.parseDouble(tBTime9.getText());

 if(tBTime10.getDocument().getLength()>0)

 aBotTimeAndConc[0][9] = Double.parseDouble(tBTime10.getText());

 if(tBTime11.getDocument().getLength()>0)

 aBotTimeAndConc[0][10] = Double.parseDouble(tBTime11.getText());

 if(tBTime12.getDocument().getLength()>0)

 aBotTimeAndConc[0][11] = Double.parseDouble(tBTime12.getText());

 if(tBTime13.getDocument().getLength()>0)

 aBotTimeAndConc[0][12] = Double.parseDouble(tBTime13.getText());

 if(tBTime14.getDocument().getLength()>0)

 aBotTimeAndConc[0][13] = Double.parseDouble(tBTime14.getText());

 if(tBTime15.getDocument().getLength()>0)

 aBotTimeAndConc[0][14] = Double.parseDouble(tBTime15.getText());

 if(tBConc1.getDocument().getLength()>0)

 aBotTimeAndConc[1][0] = Double.parseDouble(tBConc1.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(tBConc5.getDocument().getLength()>0)

 aBotTimeAndConc[1][4] = Double.parseDouble(tBConc5.getText());

 if(tBConc6.getDocument().getLength()>0)

 aBotTimeAndConc[1][5] = Double.parseDouble(tBConc6.getText());

 if(tBConc7.getDocument().getLength()>0)

 aBotTimeAndConc[1][6] = Double.parseDouble(tBConc7.getText());

 if(tBConc8.getDocument().getLength()>0)

 aBotTimeAndConc[1][7] = Double.parseDouble(tBConc8.getText());

 if(tBConc9.getDocument().getLength()>0)

 aBotTimeAndConc[1][8] = Double.parseDouble(tBConc9.getText());

 if(tBConc10.getDocument().getLength()>0)

 aBotTimeAndConc[1][9] = Double.parseDouble(tBConc10.getText());

 if(tBConc11.getDocument().getLength()>0)

 aBotTimeAndConc[1][10] = Double.parseDouble(tBConc11.getText());

 if(tBConc12.getDocument().getLength()>0)

 aBotTimeAndConc[1][11] = Double.parseDouble(tBConc12.getText());

 if(tBConc13.getDocument().getLength()>0)
41

 aBotTimeAndConc[1][12] = Double.parseDouble(tBConc13.getText());

 if(tBConc14.getDocument().getLength()>0)

 aBotTimeAndConc[1][13] = Double.parseDouble(tBConc14.getText());

 if(tBConc15.getDocument().getLength()>0)

 aBotTimeAndConc[1][14] = Double.parseDouble(tBConc15.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 startIterations() {

 int i,j;

 double dCurrentD, dBestD, dIncrement;

 double [] aDValues = new double[10];

 dCurrentD=.000000001;

 dIncrement=.0000000001;

 dBestD=1;

 dBestResidual=10000;

 while(dCurrentD<.00000001) {

 dD=dCurrentD;

 calculateChamberConcentrations();

 calculateResidual();

//System.out.println(“dCurrentD: “+dCurrentD);

 if(dResidual<dBestResidual) {

 dBestD=dCurrentD;

 dBestResidual=dResidual;

 } 

 dCurrentD+=dIncrement;

 }

 dCurrentD=.00000001;

 dIncrement=.000000001;

 while(dCurrentD<.0000001) {

 dD=dCurrentD;

 calculateChamberConcentrations();

 calculateResidual();

//System.out.println(“dCurrentD: “+dCurrentD);

 if(dResidual<dBestResidual) {

 dBestD=dCurrentD;

 dBestResidual=dResidual;

 } 
42

 dCurrentD+=dIncrement;

 }

 dCurrentD=.0000001;

 dIncrement=.00000001;

 while(dCurrentD<.000001) {

 dD=dCurrentD;

 calculateChamberConcentrations();

 calculateResidual();

//System.out.println(“dCurrentD: “+dCurrentD);

 if(dResidual<dBestResidual) {

 dBestD=dCurrentD;

 dBestResidual=dResidual;

 } 

 dCurrentD+=dIncrement;

 }

 dCurrentD=.000001;

 dIncrement=.0000001;

 while(dCurrentD<.00001) {

 dD=dCurrentD;

 calculateChamberConcentrations();

 calculateResidual();

//System.out.println(“dCurrentD: “+dCurrentD);

 if(dResidual<dBestResidual) {

 dBestD=dCurrentD;

 dBestResidual=dResidual;

 } 

 dCurrentD+=dIncrement;

 }

 dCurrentD=.00001;

 dIncrement=.000001;

 while(dCurrentD<.0001) {

 dD=dCurrentD;

 calculateChamberConcentrations();

 calculateResidual();

//System.out.println(“dCurrentD: “+dCurrentD);

 if(dResidual<dBestResidual) {

 dBestD=dCurrentD;

 dBestResidual=dResidual;

 } 

 dCurrentD+=dIncrement;

 }
43

 dCurrentD=.0001;

 dIncrement=.00001;

 while(dCurrentD<.001) {

 dD=dCurrentD;

 calculateChamberConcentrations();

 calculateResidual();

//System.out.println(“dCurrentD: “+dCurrentD);

 if(dResidual<dBestResidual) {

 dBestD=dCurrentD;

 dBestResidual=dResidual;

 } 

 dCurrentD+=dIncrement;

 }

 dD=dBestD*60/.000001;

 tD.setText(Double.toString(dD));

 }

 

public void calculateResidual() {

 int i,iTimeStep;

 double dExpTime, dExpConc, dPredictedConc;

 dResidual=0.0;

 for(i=1;i<iTopSize;i++) {

 dExpTime=aTopTimeAndConc[0][i];

 dExpConc=aTopTimeAndConc[1][i];

 dPredictedConc=aPredictedTopConc[(int)(dExpTime/dDeltaT)];

 dResidual+= Math.pow((dExpConc-dPredictedConc)/dExpConc,2.0);

//System.out.println(“residual for top predicted: “+dPredictedConc+”, and experimental: 

“+dExpConc+”, Residual: “+dResidual);

 }

 for(i=0;i<iBotSize;i++) {

 dExpTime=aBotTimeAndConc[0][i];

 dExpConc=aBotTimeAndConc[1][i];

 dPredictedConc=aPredictedBottomConc[(int)(dExpTime/dDeltaT)];

 dResidual+= Math.pow((dExpConc-dPredictedConc)/dExpConc,2.0);

//System.out.println(“residual for bottom predicted: “+dPredictedConc+”, and experimental: 

“+dExpConc+”, Residual: “+dResidual);

 }

 }

public void initializeValues() {

 int i=0;
44

 while(aTopTimeAndConc[0][i]!=0.0) i++;

 double dLongestTime;

 dLongestTime=aTopTimeAndConc[0][i-1];

 iTopSize=i-1;

 i=0;

 while(aBotTimeAndConc[0][i]!=0.0) i++;

 iBotSize=i-1;

 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 conc: “+aPredictedTopConc[0]);

 }

public void calculateChamberConcentrations() {

 int j=0;

 int i=0;

 for(i=1;i<aMaterialTimeAndConc.length;i++) {

 aPredictedTopConc[i]=(aPredictedTopConc[i-1]+aMaterialTimeAndConc

[i-1][0]*2*dD*dArea*dDeltaT/(dVolTop*dThickness/dLayers))/(1+dKeq*2*dD*dArea*dDeltaT/

(dVolTop*dThickness/dLayers));

 aMaterialTimeAndConc[i][0]=(aMaterialTimeAndConc[i-1][0]+dD*dDeltaT/

Math.pow(dThickness/dLayers,2.0)*(2*aPredictedTopConc[i]*dKeq+aMaterialTimeAndConc[i1][1]))/(1+3*dD*dDeltaT/Math.pow(dThickness/dLayers,2.0));

 for(j=1;j<(int)aMaterialTimeAndConc[0].length-1;j++)

 aMaterialTimeAndConc[i][j]=(aMaterialTimeAndConc[i-1][j]+dD*dDeltaT/

Math.pow(dThickness/dLayers,2.0)*(aMaterialTimeAndConc[i][j-1]+aMaterialTimeAndConc[i1][j+1]))/(1+2*dD*dDeltaT/Math.pow(dThickness/dLayers,2.0));

 aMaterialTimeAndConc[i][j]=(aMaterialTimeAndConc[i-1][j]+dD*dDeltaT/Math.

pow(dThickness/dLayers,2.0)*(aMaterialTimeAndConc[i][j-1]+2*aPredictedBottomConc[i-1]*dKeq))/

(1+3*dD*dDeltaT/Math.pow(dThickness/dLayers,2.0));

 aPredictedBottomConc[i]=(aPredictedBottomConc[i1]+aMaterialTimeAndConc[i][j]*2*dD*dArea*dDeltaT/(dVolBot*dThickness/dLayers))/

(1+dKeq*2*dD*dArea*dDeltaT/(dVolBot*dThickness/dLayers));

 }
45

 }

public void printResults() {

 dD=dD*.000001/60;

 calculateChamberConcentrations();

 dD=dD*60/.000001;

System.out.println(“Top Chamber Predicted Final Conc: “+aPredictedTopConc[aPredictedTopConc.

length-1]);

System.out.println(“Top Chamber Experimental Final Conc: “+aTopTimeAndConc[1][iTopSize]);

System.out.println(“Bottom Chamber Predicted Final Conc: “+aPredictedBottomConc[aPredictedBotto

mConc.length-1]);

System.out.println(“Bottom Chamber Experimental Final Conc: “+aBotTimeAndConc[1][iBotSize]);

System.out.println(“Original Mass: “+aTopTimeAndConc[1][0]*dVolTop);

 double dFinalSorbedMass = 0.0;

 int j;

 for(j=0;j<(int)dLayers;j++) {

 dFinalSorbedMass+=aMaterialTimeAndConc[aMaterialTimeAndConc.length1][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=1;i<iTopSize;i++) {

 dExpTime=aTopTimeAndConc[0][i];

 dExpConc=aTopTimeAndConc[1][i];

 dPredictedConc=aPredictedTopConc[(int)(dExpTime/dDeltaT)];

System.out.println(“Predicted top conc: “+dPredictedConc+”, and experimental conc: “+dExpConc+” 

at time: “+dExpTime);

 }

 for(i=0;i<iBotSize;i++) {

 dExpTime=aBotTimeAndConc[0][i];

 dExpConc=aBotTimeAndConc[1][i];

 dPredictedConc=aPredictedBottomConc[(int)(dExpTime/dDeltaT)];

System.out.println(“Bottom predicted conc: “+dPredictedConc+”, and experimental conc: 

“+dExpConc);

 }

 }

public static void main(String args[]) {

 DiffusionSolver diff = new DiffusionSolver();
46

 diff.addWindowListener(new WindowAdapter() {

 public void windowClosing(WindowEvent e) {

 System.exit(0);

 }

 });

 }

}
47

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 dualvolume 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-. Relative concentration parameter versus time for mortar exposed to n-butanol.

n _b u tan o l	an d 	C o n cr e te

y = 0.0002x

R2

 = 0.8661

y = 9E-07x + 0.4748

R2

 = 0.6191

0

0.1

0.2

0.3

0.4

0.5

0.6

0 10000 20000 30000 40000 50000 60000 70000 80000 90000

T im e 	(m in )

-ln(C/Co)/(A/V)

Figure C-2. Relative concentration parameter versus time for mortar exposed to ethylbenzene.

Eth yl	Be n z e n e 	a n d 	Co n cre te

y = 8E-05x

R2

 = 0.8369

y = 1E-06x + 0.2582

R2

 = 0.812

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 10000 20000 30000 40000 50000 60000 70000 80000 90000

T im e 	(m in )

-ln(C/Co)/(A/V)
48

Figure C-3. Relative concentration parameter versus time for concrete exposed to decane.

D e c a n e 	a n d 	C o n c re te

y = 0.0001x

R2

 = 0.8093

y = 1E-06x + 0.3194

R2

 = 0.7725

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 10000 20000 30000 40000 50000 60000 70000 80000 90000

T im e 	(m in )

-ln(C/Co)/(A/V)

Figure C-. Relative concentration parameter versus time for mortar exposed to 

undecane.

U n d e c a n e 	a n d 	C o n c re te

y = 0.0001x

R2

 = 0.7835

y = 1E-06x + 0.3608

R2

 = 0.781

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 20000 40000 60000 80000 100000

T im e 	(m in )

-ln(C/Co)/(A/V)	(m)
49

Figure C-. Relative concentration parameter versus time for motar exposed to dodecane.

D o d e c a n e 	a n d 	C o n c re te

y = 0 .0 0 0 1 x

R 2 = 0 .9 9 9 4

y = 2 E -0 6 x + 0 .3 9 5 7

R 2 = 0 .7 3 7 3

0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 0 6 0 0 0 0 7 0 0 0 0 8 0 0 0 0 9 0 0 0 0

T im e (m in )

-ln(C/Co)/(A/V)
50

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51

Appendix D

Results for VF and PUF

Figure D-. Raw data and fitted diffusion model for sorption and desorption of hexanal in vinyl 

flooring.

Tim e(hrs)

0 10 20 30 40

Mass(mg)

185.4

185.5

185.6

185.7

185.8

185.9

186.0

186.1

raw 

m odel	
52

Tim e(hrs)

0 5 10 15 20

Mass(mg)

185.46

185.48

185.50

185.52

185.54

185.56

185.58

185.60

185.62

raw 

m odel	

Figure D-2. Raw data and fitted diffusion model for sorption and desorption of decane in 

vinyl flooring.

Tim e(hrs)

0 10 20 30 40

Mass(mg)

185.54

185.56

185.58

185.60

185.62

185.64

185.66

185.68

185.70

185.72

raw 

m odel	

Figure D-3. Raw data and fitted diffusion model for sorption and desorption of dodecane 

(first replicate) in vinyl flooring.
53

Tim e(hrs)

0 5 10 15 20 25 30

Mass(mg)

185.50

185.55

185.60

185.65

185.70

185.75

raw 

m odel	

Figure D-. Raw data and fitted diffusion model for sorption and desorption of dodecane 

(second replicate) in vinyl flooring.

Tim e(hrs)

0 5 10 15 20 25

Mass(mg)

185.52

185.54

185.56

185.58

185.60

185.62

185.64

185.66

185.68

185.70 raw 

m odel	

Figure D-. Raw data and fitted diffusion model for sorption and desorption of undecane in 

vinyl flooring.
54

Tim e(hrs)

0 5 10 15 20

Mass(mg)

185.46

185.48

185.50

185.52

185.54

185.56

185.58

185.60

185.62

raw 

m odel	

Figure D-6. Raw data and fitted diffusion model for sorption and desorption of butanol in 

vinyl flooring.

Tim e(hrs)

0 20 40 60 80 100 120

185.4

185.5

185.6

185.7

185.8

185.9

raw 

m odel	

Figure D-. Raw data and fitted diffusion model for sorption and desorption of tetradecane 

in vinyl flooring.

Mass(mg)
55

Tim e(hrs)

0 2 4 6 8 10 12

Mass(mg)

97.32

97.34

97.36

97.38

97.40

97.42

97.44

97.46

97.48

raw 

m odel	

Figure D-. Raw data and fitted diffusion model for sorption and desorption of undecane in 

polyurethane foam.

Tim e(hrs)

0 1 2 3 4 5 6 7

Mass(mg)

97.45

97.50

97.55

97.60

97.65

97.70

97.75

97.80

97.85

raw 

m odel	

Figure D-. Raw data and fitted diffusion model for sorption and desorption of butanol in 

polyurethane foam.
56

Mass(mg)

Tim e(hrs)

0 5 10 15 20 25

Mass(mg)

97.48

97.50

97.52

97.54

97.56

97.58

raw 

m odel	

Figure D-0. Raw data and fitted diffusion model for sorption and desorption of decane in 

polyurethane foam.

Tim e(hrs)

0 2 4 6 8 10 12

97.32

97.34

97.36

97.38

97.40

97.42

97.44

97.46

97.48

R aw 

m odel	

Figure D-. Raw data and fitted diffusion model for sorption and desorption of dodecane 

(first replicate) in polyurethane foam.
57

Tim e(hrs)

0 2 4 6 8 10 12 14 16 18 20

97.32

97.34

97.36

97.38

97.40

97.42

97.44

97.46

97.48

raw 

m odel	

Figure D-2. Raw data and fitted diffusion model for sorption and desorption of dodecane 

(second replicate) in polyurethane foam.

Mass(mg)

Tim e(hrs)

0 10 20 30 40 50 60

Mass(mg)

97.48

97.50

97.52

97.54

97.56

97.58

97.60

97.62

97.64

raw 

m odel	

Figure D-3. Raw data and fitted diffusion model for sorption and desorption of tetradecane 

in polyurethane foam.
58

Figure D-. Raw data for sorption and desorption of hexanal (first replicate) in 

polyurethane foam.

0 10 20 30 40 50 60

109.85

109.90

109.95

110.00

110.05

110.10

110.15

110.20

Mass (mg)

Time (hrs)

raw data

Figure D-. Raw data for sorption and desorption of hexanal (second replicate) in 

polyurethane foam.

0 10 20 30 40 50 60 70 80

110.0

110.1

110.2

110.3

110.4

Mass (mg)

Time (hrs)

raw data
59

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