Agent-to-Simulant Relationships for Vapor Emission from Absorbing


Sep 1, 2017 - Mark J. Varady†, Thomas P. Pearl‡, Stefan A. Bringuier‡, Joseph P. Myers†, and Brent A. Mantooth†. † Edgewood Chemical Biolo...
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Agent-to-Simulant Relationships for Vapor Emission from Absorbing Materials Mark J. Varady,† Thomas P. Pearl,‡ Stefan A. Bringuier,‡ Joseph P. Myers,† and Brent A. Mantooth*,† †

Edgewood Chemical Biological Center, U.S. Army, 5183 Blackhawk Road, Aberdeen Proving Ground, Maryland 21010-5424, United States ‡ DCS Corporation, 100 Walter Ward Boulevard, Suite 100, Abingdon, Maryland 21009, United States S Supporting Information *

ABSTRACT: When using a simulant to predict the behavior of a chemical warfare agent (CWA), it is not always possible to sufficiently match all relevant properties, and the use of an agent-to-simulant relationship is required. The objective of the agent-to-simulant relationship developed here is to enable the prediction of vapor emission rate of a CWA from a polymer given an experimental measurement of the vapor emission rate of a simulant from the polymer. Vapor emission experiments for the CWA sulfur mustard (HD) and the simulants methyl salicylate (MeS) and 2-chloroethyl ethyl sulfide (CEES) absorbed in the polymers silicone and polydimethylsiloxane (PDMS) were carried out to verify the theoretical predictions. It was found that the agent-to-simulant relationship holds if the initial dimensionless concentration distributions and Biot numbers in the polymer are similar for the agent and simulant. The mathematical agent-to-simulant relationship also provides guidance on the critical properties to match in simulant selection.



INTRODUCTION Due to the significant hazards involved in experimentation with chemical warfare agents (CWAs), or agents, it is useful to have less toxic simulant chemicals that mimic the agent properties of interest for the specific experiment. In cases where the simulant matches all of the relevant agent properties, the experimental data acquired for the simulant can be directly substituted for those of the agent. For example, determining the efficacy of a decontaminant using a simulant requires the agent and simulant to have similar chemical functionality and, thus, reactivity with the decontaminant.1−3 Similar logic is followed when using simulants for the development of CWA sensors that depend on the interaction of particular functional groups on the agent with the sensor.4−6 Simulants have also been used to assess the permeation of agent through skin7 and through polymer films8 and the environmental fate of agents.9 Transport of agent absorbed in materials must account for agent−material interactions, and other studies have looked at how materials behave as sinks for agents and simulants.10 Note that the choice of simulant depends on the process under study, which determines the critical agent properties. Finding a simulant that adequately represents the properties of the agent while satisfying toxicity requirements is not always practical. When there are significant discrepancies between the agent and simulant properties, a mathematical transform is necessary that can be applied to the simulant experimental results to obtain the corresponding results for the agent. This transform is also known as an agent-to-simulant relationship © XXXX American Chemical Society

and can be a function of the agent and simulant properties and the experimental conditions. For example, considering the evaporation of a liquid droplet from an impermeable surface, the ratio of the downwind concentrations of the agent and simulant is equal to the corresponding ratio of the vapor pressures.11 Of particular interest in this work is vapor emission of agent absorbed in a polymer, which is of practical interest due to the widespread use of polymers in both civilian and military infrastructure, including in protective coatings (i.e., paints).12,13 The slow release of agent vapor from the polymer into the surrounding environment presents inhalation hazards, and it is important to accurately predict emission rate to assess risk to individuals in the vicinity of contaminated materials. For vapor emission of agents and simulants that are absorbed in nonporous polymers, the situation is more complicated than the analogous situation for impermeable materials11 due to the additional processes of solution and diffusion of the chemical in the polymer. The corresponding solubility and diffusivity values depend on the chemical structure of both the penetrating chemical (i.e., agent or simulant) and the polymer, and experimental values are not widely available. Thus, finding a simulant that exactly matches these properties of an agent is Received: Revised: Accepted: Published: A

June 6, 2017 August 8, 2017 September 1, 2017 September 1, 2017 DOI: 10.1021/acs.iecr.7b02323 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research extremely difficult. Additional practical constraints such as the toxicity, commercial availability, and cost of the chemical factor into simulant choice. Considering all criteria, it is likely that an agent-to-simulant relationship would be required to translate experimental data gathered with the simulant to predict agent emission rate from a polymer. This work considers the absorption of agent uniformly covering the surface of a polymer and the subsequent vapor emission of the agent from the polymer, enabling a onedimensional analysis. The objective is to develop an agent-tosimulant relationship to predict the vapor flux of a CWA from a polymer given a corresponding experimental measurement of the vapor flux of a simulant from the polymer. The mathematical form of the vapor emission rate is developed in terms of the relevant properties and experimental conditions. A dimensionless analysis of the governing equations yields criteria under which the agent-to-simulant relationship holds and the corresponding mathematical transforms are derived. The developed agent-to-simulant relationship also provides insight into the critical properties to consider in simulant selection and thus provides a valuable tool for this purpose. However, rational simulant selection based on the developed criteria is not the focus of this work, and the agent-to-simulant relationship developed here is applied to data from vapor emission experiments performed for the CWA sulfur mustard (HD) and two of its traditional simulants, methyl salicylate (MeS) and 2-chloroethyl ethyl sulfide (CEES), emitting from the polymers silicone and polydimethylsiloxane (PDMS). CEES has been used as a reactive simulant for HD,14−18 while MeS has been used as a simulant for vapor exposure to HD.19

Figure 1. Schematic of (a) agent/simulant sorption into a polymer and (b) a subsequent vapor emission process from a permeable polymeric material and governing equations considered in this work.

t̃ =



∂ 2c ̃ ∂cĩ = 2i , ∂t ̃ ∂z ̃

(1)

where is the concentration distribution of species i in the polymer resulting from the sorption process. During the emission process, the vapor flux, n″i , is

z=0

, cĩ =

ci cisat

(3)

cĩ(z ̃, t ̃ = 0) = cĩ0(z)̃

(4)

ni″L ∂c ̃ = Bicĩ(z ̃ = 0) = − i ∂z ̃ Dicisat

z ̃= 0

(5)

where the mass transfer Biot number, Bi, has been defined as

c0i (z)

⎛ pvap ⎞ ∂c ci(z = 0) − ci∞⎟⎟ = −Di i ni″ = hm⎜⎜ sati ∂z ⎝ ci RT ⎠

z L

The dimensionless vapor flux can then be expressed as nĩ ″ =

ci(z , t = 0) = ci0(z)

z̃ =

which yields the following for the dimensionless diffusion equation and initial condition:

METHODS AND MATERIALS Development of Agent-to-Simulant Relationship. Consider the sorption of a chemical species, i, into a polymer for a specified time, tsorp, followed by vapor emission from the polymer as illustrated in Figure 1. The vapor emission process is described by the 1D diffusion equation with the following initial condition: ∂ci ∂ ⎛ ∂ci ⎞ ⎜Di ⎟ , = ∂t ∂z ⎝ ∂z ⎠

Dt , L2

Bi =

hmLpivap DicisatRT

(6)

The Biot number is a dimensionless number that represents the ratio of the transport resistance in the polymer to the transport resistance in the air.20 This dimensionless quantity appears in many heat and mass transfer problems such as electronics cooling23,24 and drying of foods.25,26 From eq 5, if Bi and the initial dimensionless concentration profiles of the agent and simulant are equal, then the dimensionless vapor fluxes will be equal. The initial dimensionless concentration profiles are equivalent when the dimensionless sorption times are equal, and this condition can be used to define a relationship between the dimensional sorption times of the agent and simulant:

(2)

where hm is the convective mass transfer coefficient, pvap is the i vapor pressure, csat is the saturation concentration in the i polymer, and Di is the diffusivity in the polymer. The concentration of species in the air, c∞ i , is assumed to be zero for all cases considered in this work. Here, the value of hm is estimated using the correlation arising from the Blasius solution for laminar flow over a flat plate,20 and further details are given in the Supporting Information. All modeled vapor fluxes and emission rates presented in this work are a result of solving eqs 1 and 2 numerically using the Crank-Nicolson finite difference method.21,22 The problem can be made dimensionless by defining the following variables

sorp ̃sorp = tag̃sorp → tsim = t sim

Dag Lsim 2 sorp tag Dsim Lag 2

(7)

where the thickness of the polymer can, in general, be different for the agent and simulant experiments. B

DOI: 10.1021/acs.iecr.7b02323 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research ̃ = tsorp ̃ are satisfied, a When the conditions Bisim = Biag and tsorp sim ag relatively simple relationship between simulant and agent flux can be constructed. In this case, the dimensionless agent flux equals the dimensionless simulant flux, ñ″sim = ñ″ag, which can be written in terms of the dimensional fluxes as (see eq 5) ″ = nag

Dag Cagsat Lsim ″ nsim sat Lag DsimCsim

(8)

This provides the desired relationship of agent flux in terms of simulant flux. The time scales of the emission processes are not the same if the agent and simulant diffusivities are different. ̃ = tag̃ , However, the dimensionless times are equivalent, tsim providing the following relationship between the dimensional emission times for the agent, tag, and the simulant, tsim: tag =

2 Dsim Lag tsim Dag Lsim 2

(9)

In other words, eqs 8 and 9 provide the agent-to-simulant relationship to give the agent vapor flux given the simulant vapor flux. Since the time is scaled by the ratio of simulant and agent diffusivities, the time over which the agent-to-simulant relationship holds could be greater or less than the experimental vapor emission time for the simulant depending on the value of this ratio. For example, if the simulant diffusivity is a half the agent diffusivity, then the simulant experiment must be run for twice as long as the desired valid time range of the agent-to-simulant relationship. Corrections to Dimensionless Simulant Flux for Biag ≠ sorp ̃ ̃ Bisim and tsorp sim ≠ tag . In the general case where Biag ≠ Bisim and sorp sorp ̃ ≠ tag̃ , the transformation of simulant vapor emission data tsim to predict agent vapor emission is not obvious. However, in certain cases, corrections can be applied to make the dimensionless simulant vapor flux nearly equal to the dimensionless agent vapor flux, and the agent-to-simulant ̃ relationship of eqs 8 and 9 becomes more accurate. When tsorp sim sorp ̃ and tag ≪ 1, the concentration profile is reasonably approximated by the diffusion equation in a semi-infinite medium.20 For all of the experiments conducted in this work, these criteria are satisfied, as will be shown in the Results and Discussion section. Under these conditions, the dimensionless total amount of species absorbed by the polymer, ñsorp, is obtained by integrating the expression for concentration as a function of depth in a semi-infinite solid as given in20 n ̃sorp = 1 + 2

Figure 2. (a) Dimensionless vapor fluxes of simulant with Bisim = 0.1, ̃ = 0.2 (red line). (b) ̃ = 0.1 (blue line) and agent with Biag = 0.1, tsorp tsorp sim ag Ratio of simulant and agent dimensionless fluxes (black line) and ratio of simulant and agent dimensionless absorbed mass predicted by solution to diffusion equation in a semi-infinite domain (black dashed line).

̃ = tsorp ̃ , a suitable correction factor is When Bisim ≠ Biag and tsorp sim ag not as obvious since the ratio of simulant to agent dimensionless vapor flux is not constant as seen for two hypothetical cases shown in Figure 3. Focusing on Figure 3a, the initial ratio of simulant to agent dimensionless vapor flux is equal to Bisim/Biag (see eq 5). As agent species is depleted from the polymer, the agent dimensionless flux decreases at a faster rate relative to the simulant dimensionless flux and the flux ratio changes. This suggests scaling the dimensionless emission time for the simulant by the ratio Bisim/Biag in addition to scaling the dimensionless simulant flux by Biag/Bisim to recover the dimensionless agent flux: Biag Bi corr ̃ = sim tsim ̃ , nsim ″̃ corr = ″̃ nsim t sim Biag Bisim (12)

⎛ ⎛ 1 ⎞ t ̃sorp ⎡ 1 ⎞⎤ ⎢1 − exp⎜− ⎟⎥ − erf⎜ ⎟ sorp π ⎢⎣ ⎝ 2 t ̃ ⎠⎥⎦ ⎝ 2 t ̃sorp ⎠ (10)

̃ tsorp sim

̃ tsorp ag

When ≠ and Biag = Bisim, the dimensionless vapor fluxes of agent and simulant differ by a constant factor except at early emission times. This constant factor is approximately equal to sorp ñsorp sim /ñag , as illustrated in Figure 2 for the hypothetical case of ̃ = 0.1, and tsorp ̃ = 0.2. Additional illustrative Bisim = Biag = 0.1, tsorp sim ag cases are summarized in the Supporting Information. Multiplying the dimensionless simulant vapor flux by the sorp ratio ñasorp g /ñsim provides a correction that improves the performance of the agent-to-simulant relationship, as will be subsequently shown in the Results and Discussion section: ″̃ corr nsim

=

nag̃sorp nsim ̃ sorp

″̃ nsim

The green dashed lines in Figure 3 show the result of applying both the time and flux scaling of eq 12 to the simulant dimensionless flux. For the case of Bi ≪ 1 (Figure 3a), the correction reproduces the dimensionless flux of the agent within 30% for t ̃ < 0.5 and within 5% for t ̃ > 0.5. For the case of Bi ∼ 1 (Figure 3b), the correction is within 30% for t ̃ < 2 and becomes less accurate for larger values of t.̃ However, the correction still brings the dimensionless simulant and agent fluxes in closer proximity. Applying the corrections of eqs 11

(11) C

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After the prescribed tsorp, the residual liquid agent or simulant was rinsed from the surface with deionized water and then placed in a chamber with a 32.5 cm3 gas volume. A controlled laminar flow rate of 300 sccm of dry air was passed over the polymer surface which was used to measure the offgassing rate; details for the experimental apparatus are provided in the Supporting Information. In this setup, the sweep gas is diverted to a solid-sorbent tube (CAMSCO, silico-steel coated 0.25 in diameter, 3.5 in length, packed with Tenax TA sorbent) at specified emission times, ti, and for specified durations, Δti, throughout the experiment. The tubes are analyzed by a Markes Unity Thermal desorption system into an Agilent 6890 gas chromatograph with an Agilent 5975 Inert Mass Selective Detector (MSD) to determine the total mass emitted from the polymer for each interval, mi. The method can detect a range of 50−2000 ng of analyte.28 The emission rate at time ti is calculated by ṁ i = mi/Δti. After the 48 h emission period, the material was placed in 20 mL of isopropyl alcohol (IPA) for simulants; chloroform was used for samples contaminated with HD, for 24 h to extract the residual absorbed agent or simulant in the polymer. The mass of the agent or simulant, mRES, in solution after the extraction process was determined using an Agilent 1200 liquid chromatograph with an Applied Biosystems API5000 triple quadrupole mass spectrometer for simulants; HD samples extracted with chloroform were analyzed with an Agilent 6890 GC with 5975 MSD.28 The procedure was repeated for four replicates for each agent−polymer and simulant−polymer combination. Estimation of Transport Parameters. The inverse parameter estimation methodology employed for obtaining the values of csat i and Di from the experimental vapor emission rate has been described in detail elsewhere.29−33 Briefly, initial guess values of csat i and Di are used in one-dimensional finite difference models of the absorption and vapor emission processes to produce a model-predicted vapor emission rate. The emission rate predicted by the model, ṁ mod i , was computed from the molar flux of eq 2 by multiplying by the constant material area of 0.32 cm2 (based on the material diameter of 0.25 in., A = πd2/4) and the molecular mass of the chemical involved. The difference between the model-predicted and experimentally measured emission rate curves was quantified using the chi-squared metric:

Figure 3. Comparison of simulant (blue) and agent (red) ̃ = 0.01 and different Bi, (a) ̃ = tsorp dimensionless vapor fluxes for tsorp sim ag Bisim = 0.1 and Biag = 0.2 and (b) Bisim = 1 and Biag = 2. Also shown for each case are the results of correcting the simulant dimensionless time scale and vapor flux by the ratio of simulant and agent Bi (green dashed lines) using eq 12.

and 12 to the dimensionless simulant flux can be thought of as a preconditioning operation prior to application of the agent-tosimulant relationship of eqs 8 and 9 to increase its accuracy. Experimental Study of Vapor Emission of HD and Simulants from Polymers. Caution: The following should only be performed by trained personnel using applicable safety procedures! In these experiments, 10 μL of liquid HD or simulant was deposited by a calibrated positive displacement pipet on either silicone (Goodfellow, Silicone Elastomer MQ/ VMQ/PMQ/PVMQ, part number SI303300) or polydimethylsiloxane (PDMS, Dow Corning Sylgard 184). The 10 μL volume ensured that at least 90% of the polymer surface was covered so that the absorption process could be approximated as one-dimensional, and this was confirmed by top-down imaging of the droplet covering the polymer surface. Silicone material was punched from a larger stock into a 0.25 in. diameter × 0.125 in. thick sample and press-fit in a 0.245 in. diameter hole in an aluminum disc with dimensions of 2 in. diameter and 0.125 in. thick. The two-part PDMS was mixed according to the manufacturer instructions and poured into a 0.25 in. diameter, 0.1 in. deep cavity milled in an aluminum disc and allowed to cure under vacuum overnight at ambient temperature. The liquid droplet resided on the surface of the polymer under temperature and humidity controlled conditions (20 °C, 50% RH) for variable tsorp of 5, 60, or 240 min for the simulants and for 15, 30, or 45 min for HD. Different simulant sorption times were selected to assess the possibility of the diffusivity being a function of agent/simulant concentration in the material, while the range of sorption times for HD were ̃ and tsorp ̃ based on preliminary data. chosen to try to match tsorp sim ag Because the preliminary data was not accurate in all cases, there ̃ and tsorp ̃ , which are addressed were discrepancies between tsorp sim ag later. Further details related to materials handling and sample preparation have been published elsewhere.27

χ2 =

⎡ [ṁ exp(t ) − ṁ mod(t , c sat , D )]2 ⎤ [mexp − m mod(c sat , D )]2 i i i i i i RES i i ⎥ + RES ⎥⎦ σi 2 σRES 2 ⎣

∑ ⎢⎢ i

(13)

where ṁ i is the emission rate at time ti, the superscripts exp and mod denote whether the data is the observed experimental value or the model-predicted value, respectively, σi2 is the variance of all experimental vapor emission rate observations at time ti, and σRES2 is the variance of all experimental residual mass observations. Correctly weighting the emission rate and residual mass data is nontrivial, and without further investigation, we took the first-order approach of weighting the two pieces of data equally. Inclusion of the residual mass in the χ2 error metric offers a secondary measurable quantity to minimize the likelihood of a nonunique solution and improve the ability to correctly estimate the chemical-material parameters. New values of csat i and Di are computed on the basis of the gradient of χ2 with respect to the parameters, and the iterative process is repeated until the value of χ2 is minimized. To accomplish this, the Levenberg-Marquardt nonlinear least-squares regression (nlinfit) and constrained D

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Figure 4. Optimal fits of experimental vapor emission rate for methyl salicylate from (a) silicone with tsorp = 60 min and (b) PDMS with tsorp = 5 min. The corresponding optimal values of csat i and Di are shown along with experimentally measured and model predicted values of the residual mass after vapor emission; data variance for mRES represents one standard deviation.

Table 1. Summary of Average Optimal Fit Transport Parameters, Relative Errors of Fit, and Bi for All Simulants and HD in Both Silicone and PDMS chem

pvap (Pa)

hm (m/s)

polymer

L (m)

3 csat i (mol/m )

MeS

13.3

0.00672

silicone PDMS silicone PDMS silicone PDMS

0.0032 0.0016 0.0032 0.0016 0.0032 0.0016

588 436 1400 1210 287 228

CEES HD

320 9.2

0.00734 0.00662

minimization (fmincon) functions available in MATLAB 2015b34 were utilized, and in each case, the two functions yielded the same values of the parameter. Both of the optimization routines operated on the base-10 log transform of csat i and Di because (1) this provides an effective scaling of the parameters and (2) it avoids the possibility of nonphysical negative parameter guesses. In a few select cases, multiple initial guesses were used by employing the particle swarm method available in MATLAB, and in each case, the values of the optimum parameters were nearly identical to those found via the other methods.

|| δṁ || =

Di (m2/s) 3.18 2.76 3.34 3.43 5.70 1.58

1 N

∑ i

× × × × × ×

10−10 10−10 10−10 10−10 10−10 10−10

|ṁ iexp − ṁ imod | ṁ iexp

Bi

∥δṁ ∥

0.62 0.49 6.54 3.71 0.48 1.11

0.078 0.216 0.070 0.156 0.108 0.120

(14)

where the sum is over the total of N experimental time points. The value of δṁ is less than 0.22 for all cases. A more detailed table showing the fit parameters and their 95% confidence intervals for each value of tsorp is given in the Supporting Information along with the additional cases of 2-chloroethyl phenyl sulfide (CEPS) in silicone and PDMS. Also shown in the Supporting Information are plots of the model parameters sorp csat for each chemical−material pair. i and Di as a function of t It is seen that the parameters do not change much with tsorp for all chemicals in silicone, but MeS shows a decrease in Di with tsorp, indicating a possible composition dependence. Although care should be taken in applying the agent-to-simulant relationships in cases of composition dependence, the averages of the parameter values were assumed to adequately describe MeS transport in PDMS and we proceeded with application of the agent-to-simulant relationship in this case. Application of Agent-to-Simulant Relationship. The accuracy of the agent-to-simulant relationship depends on the ̃ . Since relative values of the agent and simulant Bi and tsorp experiments were performed for multiple tsorp, an analysis was performed to determine which pairs of HD and simulant ̃ . The results are experiments provide the closest values of tsorp summarized in Table 2 with only the closest simulant−agent ̃ are less than one, so tsorp pairs shown. Note that all values of tsorp the criteria presented for the corrections to the dimensionless simulant flux embodied in eqs 11 and 12 are satisfied.



RESULTS AND DISCUSSION Fit of Model Parameters to Experimental Data. Figure 4 shows examples of optimum fits to the experimental data for the vapor emission of MeS from silicone and PDMS and the corresponding values of the optimum parameters. For the example fits, there is a discrepancy of 33% and 82% between the model-predicted and experimentally observed mRES after the emission process for MeS in silicone and PDMS, respectively. Since the primary objective of this work was to correctly predict the emission rate, this was regarded as acceptable. Table 1 shows the average of the optimal fit parameters over all values of tsorp along with other properties required for computation of Bi for each chemical/polymer combination. The values of Bi presented in Table 1 are computed from the average values of csat i and Di. A mean relative error, δṁ , between model and experimental emission rate over the entire emission period was also computed, and the average of this over all values of tsorp is also shown: E

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For the case of MeS in silicone (Figure 5a), Bisim and Biag are ̃ and tsorp ̃ (tsorp ̃ /tsorp ̃ relatively close (Bisim/Biag = 1.29), as are tsorp sim ag sim ag = 1.12), and the agent-to-simulant relationship closely matches the experimental agent emission rate as expected. Employing the correction in this case slightly improves the performance of the agent-to-simulant relationship. For the case of MeS in PDMS, there are larger discrepancies between Bisim and Biag ̃ and tsorp ̃ (tsorp ̃ /tsorp ̃ = 0.58) (Figure (Bisim/Biag = 0.44) and tsorp sim ag sim ag 5b), and the agent-to-simulant relationship without correction results in significant error. Applying the correction of eqs 11 and 12 results in a much improved performance of the agentto-simulant relationship. For CEES in silicone (Figure 5c), Bi is an order of magnitude ̃ values greater than that for HD (Bisim/Biag = 13.5) while the tsorp ̃ = 1.17). Due to the ̃ /tsorp for CEES and HD are similar (tsorp sim ag large discrepancy between Bisim and Biag, the agent-to-simulant relationship poorly approximates the HD emission rate except at very early times. Application of the correction to the dimensionless simulant vapor flux causes the agent-to-simulant relationship to apply only for emission times greater than 500 min. Using the correction appears to produce the correct slope of the HD emission rate, but due to the large discrepancy in Bi, the absolute value of the agent-to-simulant relationship

Table 2. Optimal Pairs of Available Simulant and Agent Experiments That Minimize Discrepancy in Dimensionless ̃ )a Sorption Times (tsorp simulant

polymer

tsorp sim (min)

̃ tsorp sim

optimal tsorp ag (min)

closest tsorp ag (min)

closest/ optimal

MeS

silicone PDMS silicone PDMS

60 5 60 60

0.114 0.032 0.119 0.04

33.5 8.7 35.1 10.8

30 15 30 15

0.89 1.72 0.85 1.37

CEES a

Discrepancy is shown as the ratio of the closest available agent sorption time to the computed optimal agent sorption time for each particular simulant−polymer combination.

The agent-to-simulant relationship given by eqs 8 and 9 was applied to the experimental simulant vapor emission rates for the sorption times listed in Table 2 for each chemical−polymer pair. This was compared to the corresponding experimental vapor emission rate of HD for the agent sorption time given in Table 2, and the results are presented in Figure 5. Also shown is the result of the agent-to-simulant relationship with the additional corrections of eqs 11 and 12 applied to the dimensionless simulant flux.

Figure 5. Experimental vapor emission rates of HD (red squares) and simulants (blue circles) from silicone (top row, panels a and c) and PDMS (bottom row, panels b and d). The agent-to-simulant relationship applied to the experimental simulant data (eqs 8 and 9) is shown by the solid lines. The agent-to-simulant relationship with the correction applied to the dimensionless simulant flux (eqs 11 and 12) is shown by the dashed lines. Error bars on the experimental values represent the range of four replicates. F

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proceed with confidence in using this simulant to predict agent vapor flux under other experimental conditions. It is recognized that the need to perform laboratory experiments to obtain parameters can be daunting when considering the vast number of chemical−material combinations of interest. Unfortunately, this is the only reliable method to obtain the transport properties needed for the agent-to-simulant relationship. Estimation methods such as QSPR may eventually enable the rapid estimation of these properties with sufficient accuracy to reduce the need for more costly experimentation. When attempting to use a simulant to predict agent vapor emission from an object consisting of many materials (e.g., vehicles or buildings), the situation becomes more complicated. Objects such as vehicles consist of many different component material types, both soft, polymer-based (e.g., paint coating, weather sealant) and hard, impermeable (e.g., glass, metals) materials. For the multiple polymer-based materials, it seems impractical to find a simulant that satisfies Bisim = Biag in all of the polymers. Emission due to residual liquid on the impermeable material further complicates matters, and the observed concentration downwind of the object is the result of emission from all of the component materials. One strategy would be to identify a suitable simulant for each component material and perform a separate experiment for each of the simulants in which it is selectively applied to the corresponding material on the overall object and the vapor emission rate for that simulant measured. By synthesizing the results of all the experiments, the overall vapor emission rate of agent from the object could be estimated by applying the agent-to-simulant relationship to the results of each simulant experiment. One should also note that application of a simulant in an applied test would most likely result in sessile droplets on the surface of the object being tested, and the 1D analysis presented here would have to be extended to account for differences in wetting characteristics between the agent and simulant on the material(s) of interest. However, the agent-tosimulant relationship developed here can be used as a launching point for investigation of other effects, such as differences in agent and simulant droplet spreading on the polymer surface.

prediction is more than a factor of 3 different from the experimental HD emission rate. For CEES in PDMS (Figure ̃ are significantly different from those for 5d), both Bi and tsorp ̃ /tsorp ̃ = 0.72). In this case, the agentHD (Bisim/Biag = 3.71, tsorp sim ag to-simulant relationship without the correction does a poor job of predicting the HD emission rate. Applying the correction to the dimensionless simulant vapor flux shifts the range of applicability of the agent-to-simulant relationship to vapor emission times greater than 500 min. However, in this case, the agent-to-simulant relationship prediction passes through the error bars of the experimental HD emission rate. The application of the agent-to-simulant relationship for the additional cases of CEPS in silicone and PDMS is given in the Supporting Information. It is noted here that the vapor emission behavior of CEPS in both polymers is markedly different from HD and the other simulants and that the 95% confidence interval on the fit parameters for CEPS is much larger. This suggests that the constant diffusivity model employed here is not sufficiently accurate to capture the transport behavior of CEPS in either polymer. ̃ close Overall, it is evident that having the simulant Bi and tsorp to that of the agent gives the best performance of the agent-tosimulant relationship, as predicted. Also, it is clear that applying the additional correction to the simulant flux improves the performance of the agent-to-simulant relationship. Thus, the results for this particular case study indicate that the agent-tosimulant relationship developed here is a promising tool for ̃ criteria predicting agent vapor emission rate. The Bi and tsorp also provide guidance for proper simulant selection if the relevant properties are known. On the basis of chemical structure, it is counterintuitive that MeS performs best as a simulant for HD while CEES performs worst. A satisfactory explanation with respect to chemical structure is beyond the scope of this paper. The agent-tõ simulant relationship developed here is valid when Bi and tsorp are similar for the agent and simulant, which is the case for MeS and HD (and not the case for CEES and HD). These dimensionless quantities are based on phenomenological properties (csat i and Di) that are not directly linked to chemical structure. Techniques for linking these properties to chemical structure, such as quantitative structure−property relationships (QSPR) or molecular dynamics simulations, may be used to explore this further. Practical Considerations. The application of the agent-tosimulant relationship (eqs 8 and 9) and the correction to dimensionless simulant vapor flux data (eqs 11 and 12) illustrate the importance in choosing a simulant that matches the Biot number of the agent as closely as possible. Biot number matching requires accurate values of both the agent and simulant properties, particularly csat and D. However, because these values are not available for many chemicals or materials of practical interest, it seems necessary to perform parameter estimation experiments under laboratory conditions to determine the relevant properties of candidate simulants in the materials of interest to identify the most appropriate simulant. A list of candidate simulants can be compiled rationally by using available data such as solubility parameters (to roughly match saturation concentration in the polymer for agent and simulant), molecular volume and shape (to roughly match diffusivity in the polymer for agent and simulant), and other simulant criteria such as toxicity and cost. Once the scoping experiments have been completed and simulants that adequately match the agent Bi have been identified, one can



ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b02323. Correlation used for convective mass transfer coefficient, schematic of experimental apparatus, additional cases related to Figure 2, the parameter estimates for all sorption times, plots of parameters vs all sorption times, and the application of the agent-to-simulant relationship for the additional simulant CEPS (PDF)



AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] ORCID

Brent A. Mantooth: 0000-0001-6838-1741 Notes

The authors declare no competing financial interest. Technical reports cited in this manuscript are publicly available through http://www.dtic.mil/. G

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ACKNOWLEDGMENTS The authors thank Jerry Glasow, Michael Roberts, and Eric Lowenstein at the Defense Threat Reduction Agency (DTRA) for funding this work under program CB3062, Nick Sapienza and Michael Bergman of Leidos for laboratory support, and Jill Ruth of Leidos and David Gehring of ECBC for sample analysis. The contributions from T.P.P. and S.A.B. were performed under contract at the Edgewood Chemical Biological Center.



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DOI: 10.1021/acs.iecr.7b02323 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX