Article pubs.acs.org/IECR
Decontamination of VX from Silicone: Characterization of Multicomponent Diffusion Effects Mark J. Varady,† Thomas P. Pearl,† Shawn M. Stevenson,‡ and Brent A. Mantooth*,‡ †
OptiMetrics, Inc., a DCS Company, 100 Walter Ward Boulevard, Suite 100, Abingdon, Maryland 21009, United States U.S. Army Edgewood Chemical Biological Center, 5183 Blackhawk Road, Aberdeen Proving Ground, Maryland 21010-5424, United States
‡
S Supporting Information *
ABSTRACT: A continuum model of the transport and reaction processes occurring during decontamination of the chemical warfare agent (CWA) [2-(diisopropylamino)ethyl]-O-ethyl methylphosphonothioate (VX) absorbed in a silicone elastomer using solutions of sodium hydroxide in water, methanol, and mixtures thereof is presented. This model is based on the Maxwell-Stefan formulation of multicomponent diffusion along with the FloryHuggins model of thermodynamic equilibrium in the polymer. It was found that, as methanol from the decontaminant absorbs into the silicone, the diffusivity of VX increases, accelerating its flux from the polymer phase to the decontaminant liquid phase. This composition dependence of the diffusivity was accurately described by the Vignes equation. Although the decontamination kinetics were slower for the methanol-based decontaminant in a well-stirred liquid-phase reactor, the overall performance was superior compared to the aqueous-based decontaminant due to the enhanced extraction rate from the polymer. These findings highlight the need to consider extraction dynamics on equal footing with reaction kinetics when formulating decontaminants intended for use on absorbing polymer materials.
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INTRODUCTION Decontamination of chemical warfare agents (CWAs, or “agent”) in the liquid phase where the agent is directly accessible by the decontaminant in solution has been wellstudied.1,2 For example, several methods have been investigated to decontaminate the persistent nerve agent [2(diisopropylamino)ethyl]-O-ethyl methylphosphonothioate (VX) including oxidative chemistries,3,4 perhydrolysis,5,6 vaporized hydrogen peroxide,7 and household cleaners.8 These studies have primarily considered liquid-phase reaction rate and byproduct composition as the key performance metrics for decontaminants. However, in actual contamination events, the agent can be absorbed into the bulk of exposed materials, diminishing the accessibility of the agent by the decontaminant and thus decontamination efficacy. Further, decontamination of the agent retained by the material is paramount because it is human exposure to insufficiently decontaminated material that can produce toxicological responses. Recognizing this, several studies have treated the infiltration of agents into porous materials such as sand9,10 and concrete.11−13 Absorption can also occur in nonporous polymers via diffusive transport, a process that is well-understood for myriad chemicals over a wide range of polymers,14 including thin film coatings.15 This work focused on the processes of (1) absorption of a sessile droplet of liquid-phase agent into a polymer and (2) subsequent decontamination of the polymer by application of a © 2016 American Chemical Society
liquid-phase solution as illustrated in Figure 1. When chemical agent is absorbed in a polymer and decontamination is carried out by application of a liquid-phase solution on the polymer surface, species from the decontaminant liquid can be absorbed by the polymer and multicomponent diffusion results. At the continuum scale, the most physically consistent mathematical description of species transport in this situation is provided by the Maxwell-Stefan (M-S) equations.16−18 The appeal of using the M-S model is that the diffusivity tensor, D̵ ij, that provides the proportionality between driving force (i.e., gradient of chemical potentials) and species fluxes is symmetric (D̵ ij = D̵ ji) and positive definite, independent of reference frame, and has a clear physical meaning, being directly relatable to pairwise intermolecular interactions between species i and j in the mixture.16 When the decontamination process is carried out in the absence of any external driving forces, chemical potential gradients solely drive species transport. The Flory-Huggins (FH) model,19,20 or modifications of it to appropriately account for composition dependence of polymer−liquid and liquid− liquid interaction parameters,21,22 can be used to relate chemical potentials of species to composition within the Received: Revised: Accepted: Published: 3139
December 17, 2015 February 28, 2016 February 29, 2016 February 29, 2016 DOI: 10.1021/acs.iecr.5b04826 Ind. Eng. Chem. Res. 2016, 55, 3139−3149
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chemical potential, and molar flux of species i, and V̅ r is a reference molar volume, which is taken here to be the molar volume of the most mobile (in this case, also the smallest) molecule in the multicomponent mixture.27 Also, the relation between concentration and volume fraction, ci = ϕi/V̅ i, was used to express the corresponding equation in Fornasiero et al.27 in terms of only volume fraction and molar fluxes. The F-H equations relate the activity of each species i in the polymer, ai, to the volume fractions of all species. Attention here was restricted to the case where a maximum of two penetrant chemicals were absorbed in the polymer and the twocomponent F-H model accounting for composition dependence of all interaction parameters was employed:28 ⎛ ⎛ V̅ ⎞ V̅ ⎞ ln a1 = ln ϕ1 + ⎜1 − 1 ⎟ϕ2 + ⎜⎜1 − 1 ⎟⎟ϕp V2̅ ⎠ Vp̅ ⎠ ⎝ ⎝ + (χ12 ϕ2 + χ1p ϕp)(1 − ϕ1) − χ2p − ϕ1ϕp 2
+ ϕ2ϕp(ϕ1 + ϕp) +
Vi̅ RT
j
⎝ Vr̅ D̵ ij
−
Vi̅ ϕj Ni ⎞ ⎟ Vr̅ D̵ ij ⎟⎠
∂ϕ1
− ϕ1ϕ2 2
∂χ12 ∂ϕ2
(2)
∂χ2p ∂ϕ2
− ϕ2ϕp 2
∂χ2p ∂ϕp
−
V2̅ 2 ∂χ12 ϕ ϕ V1̅ 1 2 ∂ϕ1
∂χ V2̅ ϕ1ϕ2(ϕ1 + ϕp) 12 V1̅ ∂ϕ2
where the subscripts 1 and 2 refer to the penetrant species, the subscript p refers to the polymer, χip is the interaction parameter between species i and the polymer, and χij is the interaction parameter between the two penetrant species (χij = χji). The size of the penetrants (VX, methanol, and water) considered in this work are at least a factor of 100 smaller than the size of the polymer chains in silicone so that the ratio of penetrant molar volume,V̅ i, to polymer molar volume, V̅ p, was approximated as zero for all cases studied in this work. Using the familiar definition of chemical potential, μi = μ0i + RTlnai, with the F-H equations providing the values for ai, the chemical potential can be inserted into eq 1, giving a system of two vector equations for the penetrant species fluxes in terms of their volume fractions. In all cases, it was assumed that the polymer was stationary (Np = 0). Using the fluxes from the M-S equations in the generalized transport equation,
MODEL DEVELOPMENT General Transport Model. The M-S equations relate the molar fluxes of species in the polymer to the gradients in species chemical potentials (driving forces), where the formulation is written in terms of volume fraction rather than the traditional mole fraction, following the work of Heintz and Stephan,26 Fornasiero et al.,27 and Ribeiro et al.23 ⎛ Vj̅ ϕ Nj i
∂χ12
⎞ ⎛ V̅ V̅ + ⎜ 2 χ12 ϕ1 + χ2p ϕp⎟(1 − ϕ2) − χ1p 2 ϕ1ϕp V1̅ ⎠ ⎝ V1̅ ∂χ1p ∂χ1p V̅ V̅ − 2 ϕ1ϕp(ϕ1 + ϕp) − 2 ϕ1ϕp 2 V1̅ V1̅ ∂ϕ2 ∂ϕp
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∑ ⎜⎜
∂χ2p V1̅ 2 ∂χ2p V̅ − 1 ϕ2ϕp 2 ϕ2 ϕp V2̅ V2̅ ∂ϕ2 ∂ϕp
⎛ ⎛ V̅ ⎞ V̅ ⎞ ln a 2 = ln ϕ2 + ⎜1 − 2 ⎟ϕ1 + ⎜⎜1 − 2 ⎟⎟ϕp V1̅ ⎠ Vp̅ ⎠ ⎝ ⎝
polymer. For example, the combination of the F-H equations with the M-S diffusion model has been used to quantitatively study separation of multiple species using polymer membranes.23−25 A similar modeling approach was employed here to study the decontamination of VX absorbed in a silicone elastomer using sodium hydroxide (reactive component) in solution with water, methanol, or mixtures thereof (solvent components). Sodium hydroxide was chosen as the reactive component since it is a single-species decontaminant that has known reactivity with VX in solution.1 Methanol was chosen as the solvent additive to the decontaminant because it readily diffuses into silicone but exhibits a low equilibrium uptake so that the polymer remains relatively unaffected during the decontamination process. Experiments were specifically designed to determine model parameters with minimal fitting of data to provide a model capable of predicting the dynamics of the decontamination process. Particular emphasis was placed on characterizing the composition dependence of the M-S diffusivity of VX in silicone as a result of absorption of the decontaminant solvent and how the decontamination dynamics are influenced.
=
∂ϕp
−
+ ϕ1ϕ2(ϕ2 + ϕp)
Figure 1. Schematic of relevant processes occurring during (a) contamination and (b) decontamination of an absorbing polymer.
ϕi ∇T , P μi
∂χ1p
∂χ1p V1̅ ϕ2ϕp − ϕ1ϕ2ϕp V2̅ ∂ϕ2
(1)
1 ∂ϕi + ∇·Ni = rip Vi̅ ∂t
where the subscripts T and P denote differentiation at constant temperature and pressure, ϕi, μi, and Ni are the volume fraction, 3140
(3) DOI: 10.1021/acs.iecr.5b04826 Ind. Eng. Chem. Res. 2016, 55, 3139−3149
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separate experiments for validation. The specific experiments performed and rationale are discussed in this paragraph with the name of the particular experiment called out in parentheses, and the following sections describe each of these experiments in further detail. The experiments include immersion of polymer in solvent to determine the diffusivity and equilibrium volume fraction of the solvent in the polymer (Solvent Uptake). For VX experiments, it was not practical to perform equivalent immersion experiments. Instead, a small droplet of VX was allowed to reside on the surface of a silicone sample for varying times (VX Contamination). The amount absorbed as a function of residence time was determined by extraction of the contaminated silicone sample in 2-propanol for 24 h (VX Absorption versus Contamination Time). Extraction process characterization demonstrated that 90% of the VX was recovered from the silicone with such a treatment. In another experiment, placing the contaminated silicone sample in a sealed container for varying times allowed the degradation of VX to be quantified (VX Degradation in Silicone). The VX absorption and degradation experiments were used to fit the VX diffusivity and degradation rate constant in silicone. Separate experiments in which the quantity of VX extracted into a solvent (e.g., water) as a function of time were used to assess model predictions (Time Resolved Extraction of VX). Global second order liquid-phase reaction rates of VX with NaOH in water and methanol solvents were characterized in a well-stirred reactor (Liquid-Phase Reaction). Lastly, to validate the model, the full decontamination system was characterized by contaminating the polymer and performing decontamination using the NaOH/solvent solutions and measuring the quantity of VX remaining after the decontamination process (Decontamination). Solvent Uptake. In order to assess the extent of solvent absorption into silicone, an uncontaminated, dry silicone elastomer disc (2.54 cm diameter, 0.32 cm thick, density 1.2 g/cm3, Goodfellow, Silicone Elastomer MQ/VMQ/PMQ/ PVMQ, part number SI303300) was weighed using an analytical balance (Mettler Toledo AX205 DeltaRange), placed in a bath of solvent (pure water, pure methanol, or a methanol/ water mixture) for a fixed time, patted dry, and weighed again. This process was repeated several times to obtain the dynamics of solvent absorption into the silicone. The mass of absorbed solvent at equilibrium was obtained in a separate experiment by leaving a 1.88 cm silicone disc in a solvent bath for at least 7 days, measuring the mass multiple times to ensure equilibrium had been achieved. VX Contamination. Caution: The following should only be performed by trained personnel using applicable safety procedures! Contaminating silicone involved depositing a 2 μL droplet of VX (1.008 g/mL) onto the center of a silicone elastomer disc (substrate, same material, and geometry as described above) sitting in a 60 mm × 15 mm polystyrene Petri dish. The VX droplet was applied using a manual positive displacement pipet (Eppendorf Repeater Plus). The VX used in this study was high purity, 89.0% VX by mass. Materials were contaminated for a fixed time (contamination time) under temperature and humidity controlled conditions (20 °C, 50% RH) and subsequently rinsed with deionized water to remove residual agent liquid on the surface prior to decontamination or extraction steps. Top-down images of the VX droplet were taken at the beginning and end of the contamination time to obtain the wetted area of the droplet, which was used in the numerical simulations. Further details related to materials
the spatiotemporal evolution of each species in the polymer can be solved, where rip is the rate of production of species i in the polymer due to chemical reaction. Absorption of Pure Liquids. When the polymer is exposed to a liquid where only a single species absorbs into the bulk and χip is independent of composition, eqs 1, 2, and 3 combine to give: ∂ϕi ∂t
= ∇·[D̵ ip(1 − 2χip ϕi)∇ϕi] + rip
(4)
At the liquid−polymer interface, under conditions of thermodynamic equilibrium, the activities for species i in the liquid and polymer phases were equated to provide a boundary condition for eq 4: ln(γixi) = ln ϕi + (1 − ϕi) + χip (1 − ϕi)2
(5)
where γi is the activity coefficient and xi is the mole fraction of species i in the liquid (both unity for a pure liquid). Liquid-Phase Extraction of Species from Polymer. When a polymer containing absorbed species (i.e., agent) is brought into contact with a liquid, as would be the case upon application of a decontaminant solution, species from the decontaminant (i.e., solvent) can absorb into the polymer and the full multicomponent formulation must be used. In general, the transport equations for both the contaminant and solvent in the polymer can not be written in explicit form as done in eq 4, and eqs 1, 2, and 3 must be solved simultaneously. Additionally, transport in the adjacent liquid phase must be accounted for. Here, it was assumed that the contaminant species remained sufficiently dilute in the liquid throughout the extraction process so that (a) Fick’s law with constant diffusivity could be accurately used and (b) the concentration of solvent did not appreciably change. The model results were checked for all cases studied here to ensure that the assumptions hold. Since the solvent concentration did not change in the liquid phase, only the transport of contaminant was solved:
∂Cil = Dil ∇2 Cil + ril ∂t
(6)
where Cil is the contaminant concentration, Dil is the Fick diffusivity, and ril is the rate of contaminant production in the liquid phase, l. Thermodynamic equilibrium and mass conservation at the liquid−polymer interface couple the transport equations in each phase. The F-H equations, eqs 2, at the interface were applied for both the contaminant and solvent in a similar manner as done in eq 5, equating polymerphase and liquid-phase activities of each species. Mass conservation for the contaminant required equality of the fluxes in the polymer and liquid at the interface, n ·Ni = n ·Dil ∇Cil
(7)
where n is the unit normal vector at the liquid−polymer interface.
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METHODS Multiple experimental methods were implemented to characterize or verify model parameters, with the corresponding experiments numerically simulated in COMSOL v5.1.29 The general approach was to experimentally interrogate transport and/or reaction in the liquid and polymer materials independently to determine model parameters. The resulting model parameters were used to generate model predictions for 3141
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points and placed in 5 mL of IPA, diluting the solution by a factor of 500 to quench the reaction. Analysis indicated that diluting these samples by at least a factor of 100 quenched the reaction such that less than 5% degradation was observed over 7 days. The dilute samples were analyzed by LC/MS/MS. Decontamination. Decontaminant solutions consisted of 1000 mM NaOH (active component) (NaOH: Amresco, ACS grade pellets) dissolved in deionized water or methanol (solvent component) (CH3OH: Sigma-Aldrich, Chromasolv Plus for HPLC grade) of varying volumetric ratios. Contaminated silicone samples were fully immersed in 8 mL of the decontaminant solution for 30 min. After decontamination, the sample was rinsed with deionized water and the decontaminant solution was collected for subsequent chemical analysis. Numerical Simulations. Simulations were performed for solvent uptake, VX absorption and degradation in silicone, liquid-phase extraction of VX from silicone, and reactive decontamination of VX from silicone. The solvent uptake simulations were fit to experimental solvent mass uptake versus time with the diffusivity of the solvent in silicone as the fit parameter. The solvent uptake simulations were implemented in a 1D geometry since all faces of the silicone were exposed to solvent and the thickness to diameter ratio of the silicone disc was greater than 10. The remainder of the simulations were implemented in a 2D-axisymmetric geometry due to the symmetry created by the VX droplet during the contamination process. VX absorption and degradation simulations were simultaneously fit to the corresponding experimental data with the VX diffusivity and degradation rate constant as the fit parameters. Fitting was performed using the LevenbergMarquardt nonlinear least-squares technique as implemented in MATLAB’s nlinfit function to minimize the value of the chi square, χ2, measure of error,
handling and sample preparation have been published elsewhere.30 Chemical Analysis. Samples were analyzed by LC/MS/MS (Agilent 1200/1290 series LC and Applied Biosystems API5000/5500 triple-quadrupole mass spectrometer equipped with a TurboV ion source) after dilution and the addition of an internal standard (D5VX) to quantify the mass of VX and its primary phosphorus containing reaction byproducts ethyl methylphosphonic acid (EMPA) and ethyl methylphosphonothioic acid (EA2192). The liquid chromatography was performed using a mobile phase consisting of 5 mM ammonium acetate and 0.1% formic acid, where mobile phase A (MPA) was 95% water/5% 2-propanol and mobile phase B (MPB) was 5% water/95% 2-propanol. Chromatography was performed using an isocratic flow configuration (50% MPA/ 50% MPB) using an Agilent Technologies Zorbax SB-C18, Rapid Resolution 4.6 × 75 mm, 3.5 μm particle size column (part # 866953-902). VX was analyzed using the electrospray ionization (ESI) multiple reaction method (MRM) ion transition of 268.1−128.0; EMPA was analyzed using MRM transitions 123.0−94.8, and EA2192 involved MRM transitions 240.1−128.0. VX Absorption Versus Contamination Time. Contamination times (i.e., time liquid contaminant was left on the silicone surface before treatment with the rinse process) of 5, 60, and 240 min were used, and the contaminated silicone disc was then placed in 20 mL of 2-propanol for 24 h to extract the absorbed VX. Chemical analysis was subsequently performed on the 2-propanol/VX mixture to determine the amount of VX absorbed in the silicone disc as a function of the contamination time. VX Degradation in Silicone. Experimental results from VX absorption measurements indicated that VX degraded as a function of time when absorbed in silicone, and experiments were performed to quantify the degradation rate. After a contamination time of 60 min, a silicone disc was placed in a sealed container for periods of 1, 10, 60, 240, and 1440 min before being placed in 20 mL of 2-propanol for 24 h to extract the absorbed VX. Chemical analysis was subsequently performed on the 2-propanol/VX mixture to determine the amount of VX absorbed in the silicone disc as a function of the time after contamination. This allowed the degradation rate of VX in the silicone disc to be determined and determination of the primary reaction pathway based on the ratio of byproducts. Time Resolved Extraction of VX. After contamination times of 5, 60, or 240 min, a silicone disc was placed in a jar containing 40 mL of pure water or pure methanol. Ten samples of 1 mL volume were taken on a predefined sampling schedule over a total period of 200 min, where the liquid was stirred to homogenize the solution before taking each sample. Chemical analysis was performed on the samples to determine the total quantity of VX extracted at each time on the sampling schedule. Liquid-Phase Reaction. To obtain kinetic data for the reaction between VX and hydroxide dissolved in different water/methanol mixtures, time-resolved measurements of VX consumption and reaction byproducts formation in the liquidphase were recorded. Reaction product concentrations were evaluated at a hydroxide solution concentration of 100 mM in water/methanol mixtures of varying volumetric ratios. Glass vials were filled with 4.9 mL of a NaOH solution and then dosed with 100 μL of a dilute VX solution (250 mM in methanol). The liquid was stirred to keep the reacting species well-mixed. Samples (10 μL) were taken at predetermined time
⎛ y (ti) − y (ti , β) ⎞2 exp mod ⎟ χ = ∑ ⎜⎜ ⎟ σ i ⎝ ⎠ i 2
(8)
where yexp(ti) and ymod(ti, β) are the experimental and model responses at time ti, respectively, β is the vector of fit parameters, and σi is the standard deviation of the experimental response at time ti. Simulations of liquid-phase extraction and reactive decontamination of VX from silicone were compared to corresponding experimental results for model validation. When fitting of model parameters was performed, COMSOL’s LiveLink for MATLAB capability was used to interface with MATLAB’s optimization toolbox. Further details of the simulations described herein are available in the Supporting Information.
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RESULTS AND DISCUSSION Determination of Interaction Parameter and Diffusivity for Solvents. The equilibrium gravimetric uptake data of pure water, pure methanol, and water/methanol mixtures was converted to volume fraction using mass fractions with the following formula: ϕi =
ωi /ρi ωi /ρi + ωp /ρp
(9)
where ωi and ρi are the mass fraction and mass density of species i, respectively. Eq 5 was then used to compute the values of the interaction parameter for water, χwp, and 3142
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Industrial & Engineering Chemistry Research methanol, χmp, at room temperature, T = 293 K. Hildebrand solubility parameters for water,31 δw = 47.9 MPa0.5, methanol,31 δm = 29.7 MPa0.5, and silicone,32 δp ∼ 19 MPa0.5, were also used to compute approximate interaction parameters according to the following equation for comparison: χip =
Vi̅ (δi − δp)2 RT
transport of VX and was unimportant for the predictive decontamination model. Determination of Interaction Parameter, Diffusivity, and Degradation Rate Constant of VX. Equilibrium gravimetric uptake could not be achieved for VX on the silicone samples used in this work due to its high toxicity. Instead, the VX−silicone interaction parameter was computed from solubility parameters. The Hildebrand solubility parameter for VX was computed from its enthalpy of vaporization,33 ΔHvap, VX = 80.32 kJ/mol, and the following equation,31
(10)
Table 1 below summarizes the equilibrium uptake data and interaction parameters computed from eqs 5 and 10 with the Table 1. Equilibrium Uptake Data for Pure Water, Pure Methanol, and a 70/30 v/v Methanol/Water Mixture in Silicone with Corresponding Interaction Parametersa solvent water methanol 70/30 v/v methanol/water mixture
mass uptake (mg)
ωi
ϕi
χip exp.
χip comp.
0.52 21.8 4.78
5.2 × 10−4 2.1 × 10−2 4.7 × 10−3
6.3 × 10−4 3.3 × 10−2 7.1 × 10−3
6.38 2.64 3.45
6.17 1.92 N/A
δVX =
ΔHvap , VX − RT VVX ̅
(11) 31
A group contribution method was used to compute the molar volume of VX, V̅ VX = 265 cm3/mol (see Supporting Information for details), yielding δVX = 17.1 MPa0.5. To obtain a more accurate value for the Hildebrand solubility parameter for the particular silicone used here, eq 10 was used with the experimentally determined interaction parameters of water and methanol presented in Table 1. The average of the two values obtained using the water and methanol interaction parameters was taken, yielding δp = 17.8 MPa0.5. Using eq 10 with the solubility parameters for VX and silicone, it was found that χVXp = 1.28. From the VX degradation in silicone experiments (Figure 3b), it was found that the amount of VX decreased by ∼65% over 24 h producing EMPA and EA2192 in about a 20:1 molar ratio. It was assumed that the chemical reaction was first order in VX, so that, in eq 4, rip = kipϕi. The model parameters D̵ VXp and kVXp were simultaneously fit using the data from the VX absorption versus contamination time experiments (Figure 3a) and VX degradation in silicone experiments. In these simulations, care was taken to implement the correct boundary condition for the volume fraction of VX since there were impurities (89% pure by mass when deposited). In the deposited liquid, the molar ratio of EMPA to VX was ∼15−20%, whereas after a 30 s contamination time, the molar ratio of EMPA to VX absorbed in the silicone was 1 min. The model overpredicts the extraction rate for the 240 min contamination time, which was expected on the basis of the overprediction of absorbed VX mass during contamination as seen in Figure 3a. Prediction of VX Extraction into Pure Methanol. Eqs 1, 2, and 3 were used to predict the extraction of VX into methanol (methanol sorption was not neglected due to its appreciable uptake in silicone at equilibrium) with composition independent interaction parameters. Eq 14 was used to find the activity coefficient of VX in methanol.
⎛ V̅ ⎞ ln γVXxVX , sat = ln ϕVX , sat + ⎜1 − VX ⎟ϕm , sat + ϕp Vm̅ ⎠ ⎝ + (χVXm ϕm , sat + χVXp ϕp)(1 − ϕVX , sat ) − χmp
VVX ̅ ϕ ϕ Vm̅ m , sat p (14)
As previously, χVXp and ϕVX,sat were taken as 1.28 and 0.18, respectively. For methanol, the values were taken from Table 1 as χmp = 2.64 and ϕm,sat = 3.3 × 10−2. This assumes that the saturated volume fractions are the same for the multicomponent and pure component cases. An estimate of χVXm = 2.65 was furnished from eq 10 using the solubility parameters of VX and methanol and the molar volume of methanol. Methanol and VX are miscible, so that at saturation there are equal parts methanol and VX by volume. The corresponding mole fraction of VX, xVX,sat = 0.13, yields γVX = 13.0. The lower value for the activity coefficient compared with water is congruous with the higher solubility of VX in methanol. Using the Wilke-Chang equation35 to compute the diffusivity of VX in methanol yields DVXl = 9.9 × 10−10 m2/s. The M-S diffusivity between methanol and VX absorbed in silicone, D̵ VXm, was approximated with the same value. Comparing the predicted time evolution of extracted VX mass to the corresponding experimental result for a 60 min contamination 3144
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a critical role in determining the corresponding change in mobility of VX. The influence of the composition dependence of interaction parameters was investigated by a parametric study in which the linear functional forms χVXp = 1.28 + αϕm and χVXm = 2.65 + βϕm were assumed, similar to what was done by Yang and Lue.28 The values of both α and β were independently varied between −30 and 30, with corresponding variations in χVXp of 0.3−2.3 and χVXm of 1.6−3.6. Figure 6 shows the VX extracted mass versus time for each of these parameter combinations. The composition dependence of χVXp resulted in about a 10% variation in the VX extraction rate. However, it is unlikely that the value of χVXp would approach zero or negative values, which it appears would be required to reconcile model predictions with experimental observations. The influence of variations in χVXm had a negligible effect on VX extraction rate, as evidenced by all curves lying on top of each other in Figure 6b. Thus, composition dependence of the interaction parameter was dismissed, and attention was focused on composition dependence of the diffusivities. The composition dependence of M-S diffusivities in nonideal multicomponent systems has been studied primarily using empirical relations. The Vignes model, originally developed for binary systems,36 has been extended to ternary systems37 and has even been employed to study transport of two species, i and j, in a polymer, p:24
time shows that the amount extracted after 200 min is underpredicted by ∼25%, as shown in Figure 5.
Figure 5. Comparison of model predicted (lines) and experimental (circles) extracted VX mass from silicone into methanol for a 60 min contamination time for composition independent interaction parameters. Error bars represent the range of the experimental results.
What was not accounted for in the model results presented in Figure 5 was the possibility that absorption of methanol increased the flux of VX, NVX. In reference to the M-S equations, eq 1, this can result from an increase in the chemical potential gradient and/or an increase in the M-S diffusivities, D̵ VXp and D̵ VXm. In other words, a composition dependence of the interaction parameters and/or diffusivities could account for the experimentally observed extraction rate. Transport plasticization due solely to an increase in free volume was ruled out in this case because (a) the equilibrium volume fraction of methanol was only ∼0.03, which was much smaller than the value of ∼0.18 for VX, and (b) contamination experiments in which the silicone was pretreated in methanol for 60 min prior to depositing the VX droplet showed about a 35% decrease in the mass uptake of VX over a 60 min contamination time (the details of these experiments are provided in the Supporting Information). If methanol increased the free volume available for diffusion, then the pretreated sample would have absorbed more VX. Thus, it is likely that the nature of the chemical interactions between VX, methanol, and silicone and how they change as a function of composition play
x → 1 xp
D̵ ip = (D̵ ipxi → 1)xi (D̵ ipp
x → 1 xj
) (D̵ ipj
)
(15)
The vast majority of work on estimating such diffusivities in multicomponent systems has been performed for liquid-phase systems. The validity of extending this model to systems where the polymer is the primary component by mass is certainly not clear, but eq 15 was used here with the recognition that more work needs to be done to fundamentally understand composition dependence of diffusivities in bulk polymer solutions. The diffusivities of VX and methanol in silicone are written as, x →1
xm → 1 xm 0 1 − xm xVX → 1 xVX p D̵ VXp = (D̵ VXp ) (D̵ VXp )xp (D̵ VXp ) ≈ (D̵ VXp ) xm → 1 xm (D̵ VXp )
(16)
Figure 6. Comparison of model predicted (lines) and experimental (circles) extracted VX mass from silicone into methanol for a 60 min contamination time accounting for methanol absorption with linear dependences of interaction parameters on methanol volume fraction. Error bars represent the range of the experimental results. 3145
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Industrial & Engineering Chemistry Research xm → 1 xm xp → 1 xp xVX → 1 xVX 0 1 − xVX D̵ mp = (D̵ mp ) (D̵ mp ) (D̵ mp ) ≈ (D̵ mp ) xVX → 1 xVX (D̵ mp )
ϕVX = (17)
where the first two terms in each expression have been combined and are approximated by the average diffusivities 0 determined by fitting the absorption of VX and methanol, D̵ VXp 0 −11 2 −10 2 = 2.86 × 10 m /s and D̵ m,p = 1.5 × 10 m /s. The values of m→1 D̵ xVXp , the diffusivity between VX and silicone both dilute in methanol, and D̵ xmpVX→1, the diffusivity between methanol and silicone both dilute in VX, are more difficult to obtain. Significant effort has been made to express this ternary diffusivity in terms of easier to obtain binary diffusivities. Several empirical models have been put forth,37−40 and those listed in Table 2 were used in this model and compared on the
ϕM =
model
equation
Kooijman and Taylor (KT)
38
Krishna and van Baten,39 based on Vignes (VKB) Krishna and van Baten,39 based on Darken (DKB) Rehfeldt and Stichlmair40 (RS)
x →1 D̵ ipj
x →1
D̵ ipj
x →1
D̵ ipj
x →1
D̵ ipj
x →1
D̵ ipj
=
x →1 D̵ ipp D̵ ipxi → 1
=
D̵ ij j
x →1
x →1
D̵ pjj
(
)(D̵ pjxj→ 1)xp/ (xi + xp)
x →1 x / x +x i i p
= (D̵ ij j
=
)
xp xi x →1 x →1 (D̵ ij j ) + (D̵ pjj ) xi + xp xi + xp x →1
= (D̵ ij j
x →1
D̵ pjj
x →1
D̵ ipp
xVX VVX ̅
xmVm̅ + xmVm̅ + xpVp̅
(18)
Figure 7a shows that, for the RS model, varying V̅ p by a factor of 2 impacts the prediction of extracted VX mass by only a few percent. Similar variations with V̅ pwere observed for the other ternary diffusivity models but are not shown here. Figure 7b shows that using the RS model for the ternary diffusivity term in the Vignes equation results in the best match to experimental observations over most of the extraction period. The WK model significantly underpredicts, while the KT, VKB, and DKB models significantly overpredict the extraction rate. Considering that the RS model is essentially a mixture of the WK and KT models, the results are not surprising. It is conceded that the use of the RS is an empirical model and was used in the decontamination model because it provided the closest match to experimental results. Since it was concluded that water absorption was negligible, the model for VX extraction that was applied to the pure methanol case can also be applied when the extraction liquid is a mixture of water and methanol. The mole fraction of methanol can be computed from the known mixture composition, and corresponding activity coefficient of methanol can be computed from an appropriate model, for example, the van Laar model.44 The solubility of VX in the water/methanol mixture, xVX,sat, must also be known to find the activity coefficient of VX, γVX, in the liquid mixture from eq 14. Explicit results for the time-resolved extraction of VX using a mixture are not shown here, but the corresponding results for a reactive decontamination are discussed in the next section. Prediction of Decontaminant Performance. Liquidphase reaction with sodium hydroxide was incorporated into the models for extraction assuming second-order kinetics so that, in eq 6, rVXl = kVXlcVXcNaOH. The rate constants for NaOH solutions in pure water, pure methanol, and a 70/30 v/v methanol/water mixture were determined to be 6.0 × 10−6, 2.1 × 10−6, and 3.8 × 10−6 m3/mol/s, respectively, by fitting to experimental data from a well-stirred liquid-phase reactor (see Supporting Information for more details). Using these values of the rate constants along with the other model parameters as
Table 2. Summary of Models Used to Estimate Ternary Diffusivity in the Vignes Model of Multicomponent Diffusivity with Composition Dependence Wesselingh and Krishna37 (WK)
xVX VVX ̅ , xVX VVX ̅ + xmVm̅ + xpVp̅
D̵ ipxi → 1)1/4
basis of how well the experimentally observed VX extraction rate was predicted. The use of mole fractions requires knowledge of the molar volume of the polymer, as shown in eq 18, which converts volume fractions to mole fractions. However, since the exact value of the molar volume of the silicone used in this work was not known, the range 15 000− 30 000 cm3/mol was used on the basis of published values41−43 to determine the sensitivity of the results to this variation.
Figure 7. (a) Influence of V̅ p variation on predicted time evolution of VX extracted mass from silicone for a 60 min contamination time using the RS model for calculating D̵ xipj→1. (b) Comparison of models used for calculating D̵ xipj→1 at fixed V̅ p = 25 000 cm3/mol. Error bars represent the range of the experimental results. 3146
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Industrial & Engineering Chemistry Research summarized in Table 3 enabled prediction of the decontamination dynamics. Table 3. Summary of Model Parameters Used in Decontamination Simulations liquid phase model parameter xm,l [−] D̵ VXl [m2/s] γVX [−] γm [−] xVX,sat [−] kVXl [m3/mol/s] model
water
methanol
70/30 v/v methanol/water mixture
0 5.2 × 10−10 346 N/A 0.0029 6.0 × 10−6
1 9.9 × 10−10 13 1 0.13 2.1 × 10−6
0.51 7.6 × 10−10 10.9 1.13 0.10 3.8 × 10−6
parameter
χVXp [−] χmp [−] χVXm [−] kVXp [1/s] D̵ 0VXp [m2/s] xm→1 D̵ VXp [m2/s] D̵ 0mp [m2/s] x →1 D̵ mpVX [m2/s]
Figure 8. Comparison of model predicted and experimentally observed VX mass in both polymer and liquid phases after a 30 min decontamination with solutions of 1000 mM NaOH in pure water (blue), pure methanol (red), and a 70/30 v/v methanol/water mixture (green).
polymer phase 1.28 2.64 2.65 9.71 2.86 6.63 1.50 7.92
× × × × ×
10−6 10−11 10−11 10−10 10−11
solvent depends on the decontamination time. The model predictions in Figure 9b show that the 70/30 v/v methanol/ water solvent performs best for times of less than about 30 min, whereas the pure methanol solvent performs best for longer times. A practical consideration for decontaminant formulation design is the safety of transporting and using volatile solvents, and the results here suggest that optimization of solvent composition is possible to simultaneously improve decontamination performance and minimize safety risks.
The quantity of VX remaining in both the polymer and liquid phases was experimentally determined after a 60 min contamination time with five 2 μL droplets followed by a 30 min decontamination step with 1000 mM solutions of NaOH in the pure solvents and the 70/30 v/v methanol/water mixture. Five droplets were used in this case to ensure a sufficient amount of VX and byproducts to detect in the liquid phase after the decontamination process. In the experiments, the droplets were spaced out sufficiently so there was no interaction between droplets and the corresponding model prediction for a single droplet was multiplied by five to obtain the prediction for the overall system. Byproduct analysis showed that, over the 30 min decontamination time, the reaction of VX in silicone was negligible compared to that in the liquid-phase and that byproducts measured in the polymer were observed in the absence of decontaminant solution (due to VX degradation in silicone). Therefore, neither transport nor reactivity of NaOH in silicone are considered in the model (see Supporting Information for more details and results of this analysis). The experimental results for VX mass remaining are plotted in Figure 8 along with corresponding model predictions, which show that the model accurately predicts the VX mass in the liquid phase but overpredicts the VX mass remaining in silicone by about 40%. However, the model correctly predicts the dif ference in the VX mass remaining in the silicone between the three decontaminant solutions. Although the model predictions were only compared to experimental results for a single decontamination time, the fact that the model predicts the correct trends across different decontaminant formulations provides confidence in using the model at different decontamination times. Figure 9a shows that the trends of faster VX extraction from silicone and slower disappearance of VX in the liquid-phase for solutions of increasing methanol content hold across the entire range of decontamination times from 0 to 60 min. The overall decontamination performance depends on the net effect of these two mechanisms, and the choice of best decontaminant
■
CONCLUSIONS A comprehensive model for the decontamination of CWA absorbed in a polymer was formulated on the basis of the Maxwell-Stefan model of multicomponent diffusion and the Flory-Huggins equations for thermodynamic equilibrium in the polymer. The model was applied to study the specific case of the CWA VX absorbed in silicone and decontaminated using sodium hydroxide in solutions of water, methanol, and mixtures thereof. The values of the interaction parameters and M-S diffusivities in the model were fit using pure component uptake data only. This enabled accurate prediction of extraction rates of VX from silicone into pure water. Extraction into pure methanol and methanol/water mixtures occurred with simultaneous absorption of methanol into the silicone, which altered the VX diffusivity. It was found that accounting for the composition dependence of the diffusivities of VX and methanol using the Vignes equation along with Rehfeldt and Stichlmair’s model for the ternary diffusivity accurately predicted the extraction rate of VX from silicone into pure methanol. The prediction of relative performance between the decontaminants using different solvents matched experimental observations. A primary highlight of this work is the observation that decontaminants containing methanol in the solvent outperformed the aqueous-based decontaminant despite its lower reactivity in a well-stirred liquid-phase reactor. This underscores the need to broaden the scope of decontaminant development efforts beyond maximizing reaction rate (as has been the focus in the past) and to consider components that can enhance the transport rate of absorbed CWA to increase extraction rate. The addition of components such as methanol to a decontaminant solution should also consider compatibility with the polymer(s) to be treated, striking the right balance between sufficient 3147
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Industrial & Engineering Chemistry Research
Figure 9. (a) Model prediction of VX mass in both polymer and liquid phases during decontamination with solutions of 1000 mM NaOH in pure water (blue), pure methanol (red), and a 70/30 v/v methanol/water mixture (green). (b) Corresponding model prediction of total VX mass in the system (liquid + polymer phases). (3) Yang, Y. C.; Szafraniec, L. L.; Beaudry, W. T.; Rohrbaugh, D. K. Oxidative Detoxification of Phosphonothiolates. J. Am. Chem. Soc. 1990, 112, 6621. (4) Cassagne, T.; Cristau, H. J.; Delmas, G.; Desgranges, M.; Lion, C.; Magnaud, G.; Torreilles, E.; Virieux, D. Destruction of Chemical Warfare Agents VX and Soman by Alpha-Nucleophiles as Oxidizing Agents. Heteroat. Chem. 2001, 12, 485. (5) Yang, Y.-C.; Szafraniec, L. L.; Beaudry, W. T.; Bunton, C. A. Perhydrolysis of Nerve Agent VX. J. Org. Chem. 1993, 58, 6964. (6) McAnoy, A. M.; Williams, J.; Paine, M. R. L.; Rogers, M. L.; Blanksby, S. J. Ion−Molecule Reactions of O,S-Dimethyl Methylphosphonothioate: Evidence for Intramolecular Sulfur Oxidation During VX Perhydrolysis. J. Org. Chem. 2009, 74, 9319. (7) Wagner, G. W.; Sorrick, D. C.; Procell, L. R.; Brickhouse, M. D.; Mcvey, I. F.; Schwartz, L. I. Decontamination of VX, GD, and HD on a Surface Using Modified Vaporized Hydrogen Peroxide. Langmuir 2007, 23, 1178. (8) Wagner, G. W. Decontamination of Chemical Warfare Agents Using Household Chemicals. Ind. Eng. Chem. Res. 2011, 50, 12285. (9) D’Onofrio, T. G.; Navaz, H. K.; Markicevic, B.; Mantooth, B. A.; Sumpter, K. B. Experimental and Numerical Study of Spread and Sorption of VX Sessile Droplets into Medium Grain-Size Sand. Langmuir 2010, 26, 3317. (10) Brevett, C. A. S.; Sumpter, K.; Pence, J.; Nickol, R. G.; King, B. E.; Giannaras, C. V.; Durst, H. D. Evaporation and Degradation of VX on Silica Sand. J. Phys. Chem. C 2009, 113, 6622. (11) Tang, H. R.; Cheng, Z. X.; Xu, M.; Huang, S. X.; Zhou, L. M. A Preliminary Study on Sorption, Diffusion and Degradation of Mustard (HD) in Cement. J. Hazard. Mater. 2006, 128, 227. (12) Wagner, G. W.; O’Connor, R. J.; Edwards, J. L.; Brevett, C. A. S. Effect of Drop Size on the Degradation of VX in Concrete. Langmuir 2004, 20, 7146. (13) Brevett, C. A. S.; Sumpter, K. B.; Wagner, G. W.; Rice, J. S. Degradation of the Blister Agent Sulfur Mustard, Bis-(2-Chloroethyl) Sulfide, on Concrete. J. Hazard. Mater. 2007, 140, 353. (14) Koros, W. J.; Madden, W. Transport Properties. In Encyclopedia of Polymer Science and Technology; Mark, H. F.; Kroschwitz, J. I., Eds.; John Wiley & Sons: Hoboken, NJ, 2004; Vol. 12, pp 291−381. (15) Cooley, K. A.; Pearl, T. P.; Varady, M. J.; Mantooth, B. A.; Willis, M. P. Direct Measurement of Chemical Distributions in Heterogeneous Coatings. ACS Appl. Mater. Interfaces 2014, 6, 16289. (16) Taylor, R.; Krishna, R. Multicomponent Mass Transfer, 1st ed.; John Wiley & Sons, Inc.: New York, NY, 1993. (17) Krishna, R.; Wesselingh, J. A. Review Article Number 50 - The Maxwell-Stefan Approach to Mass Transfer. Chem. Eng. Sci. 1997, 52, 861. (18) Whitaker, S. Derivation and Application of the Maxwell-Stefan Equations. Rev. Mex. Ing. Quim. 2009, 8, 213. (19) Flory, P. J. Thermodynamics of High Polymer Solutions. J. Chem. Phys. 1941, 9, 660.
interaction of the solvent with the polymer and ensuring that the polymer retains its functional properties. To this end, it is critical to gain a more fundamental understanding of composition dependent diffusion in polymers on the molecular scale. Specifically, this would involve a combined experimental and computational effort aimed at characterizing how intermolecular forces change with composition and to quantify the corresponding change in diffusivities.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.5b04826. Details of implementation of transport-reaction models in COMSOL, computation of molar volume of VX using a group contribution method, experimental results for VX contamination of silicone pretreated in methanol, liquid-phase reactor experiments, and comparison of VX reaction with hydroxide in liquid and polymer phases. (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Tel. +1 410.436.0967. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank Jerry Glasow, Eric Lowenstein, and Michael Roberts at the Defense Threat Reduction Agency (DTRA) for funding this work under program CB3062. The authors thank Janlyn Eikenberg, Janet Fouse, Stefanie Smallwood, Nicholas Sapienza, and Amanda Schenning for their support in performing the experiments and Michael Chesebrough for performing the chromatography analysis. The contributions from M.J.V. and T.P.P. were performed under contract at the Edgewood Chemical Biological Center.
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