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Predicting the Effects of Composition, Molecular Size and Shape, Plasticization, and Swelling on the Diffusion of Aromatic Additives in Block Copolymers Dustin W. Janes,*,† Vaishnavi Chandrasekar,‡ Steven E. Woolford,‡ and Kyle B. Ludwig‡ †

Joris Helleputteplein 5, 3000 Leuven, Belgium Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, Maryland 20993, United States

‡

S Supporting Information *

ABSTRACT: The rate of diffusion of small molecules within polymer matrices is important in an enormous scope of practical scenarios. However, it is challenging to perform direct measurements of each system of interest under realistic conditions. Free volume theories have proven capable of predicting diffusion coefficients in polymers but often require large amounts of physical constants as input. Therefore, we adapted a version of the Vrentas−Duda free volume theory of diffusion such that the necessary parameters may be obtained from a limited set of diffusion data collected at the temperature of interest using commercially available and automated sorption equipment. This approach correlates the size and shape of molecules to their trace diffusion coefficient, D, such that D of very large, solid diffusants can be predicted based on properties measured for condensable vapor diffusants. Our analysis was based on the volume-averaged transport properties of polyaromatic color additives within segmentally arranged poly(ether-block-amide) (PEBAX) block copolymer matrices. At very high polyamide content the considerable plasticization effects due to absorbed water can be accommodated by increasing the available hole free volume as a function of water content. Alternatively, if the release rate of additives is measured for very high polyether content and degree of swelling, the release rate in the unswollen elastomer may be anticipated using the tortuosity model of Mackie and Meares. Agreement of these physical models to new experimental data provides a scientific basis for accurately predicting the in vivo leaching of aromatic additives from medical device polymers using accelerated and/or simplified in vitro methodologies.

1. INTRODUCTION The rates at which molecules and/or ions1 diffuse through polymer matrices is critically important to technological applications in membrane separations,2,3 barrier films,4 solidstate battery electrolytes,5,6 and drug delivery,7 among others. While it is usually possible to experimentally measure transport coefficients of interest, such as the diffusion coefficient (D), partition coefficient (K), and solubility (S), it is challenging to develop and apply methodology across the full scope of possible materials and temperatures. Highly specialized and bespoke techniques are often employed to conduct these experiments within realistic time scales.8−12 As a result, strong practical and financial motivations exist to supplement data with computations and/or physical theory to predict D on a general basis and rapidly guide material design.13,14 To this end we describe here four main strategies for predicting D in block copolymers based on physical theories. The methods were applied to PEBAX block copolymers, which are composed of segmentally arranged polyether soft blocks and polyamide hard blocks, due to their prevalence as drug or fragrance release media and as medical device materials.15 Leaching of additives from polymer matrices is a common safety concern in environmental, medical, and packaging © XXXX American Chemical Society

applications. We are specifically interested in placing a meaningful upper bound on exposure to potentially harmful additives that could take place during patient contact with medical device polymers.16 Since D of additives within polymers may be extremely low, scientifically valid predictions of patient exposure can provide a convincing rationale for device biocompatibility when combined with a toxicological risk assessment16 and lessen the need for costly animal studies to address these concerns. To provide a basis for making these assessments, we examined a wide range of diffusant masses (ca. 50−550 Da) and polyether contents (0−84 mol %) via gravimetric and spectroscopic sorption techniques. Our aim is to critically evaluate the ability of available physical models to predict D, and, by extension, leaching, for device-relevant polymers and additives. We focused here on aromatic additives because they are often used as antioxidants, plasticizers, initiators, and color additives in polymers. First, we show that volume-averaged transport properties of a single diffusant in block copolymer Received: April 2, 2017 Revised: July 6, 2017

A

DOI: 10.1021/acs.macromol.7b00690 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules matrices can be predicted as a function of polymer composition using knowledge of D and K for the constitutive homopolymers. This was accomplished using the effective medium theory of Sax and Ottino, upon specification of a lattice parameter related to the microstructure of the heterogeneous material. Second, the effect of diffusant size and shape was accounted for using an adaptation of the free volume theory of Vrentas and Duda that correlated D of relatively small solvent molecules to predict D of much larger additives.17 Our use of a curated set of small probe molecules to characterize a polymer’s internal hole free volume in the solid state evaluates material properties much more rapidly than aggregating literature data, which could take years to accumulate for a given material.18 The free volume approach is broadly applicable to other solid polymers used in medical devices such as polystyrene, polyethylene, or polypropylene, among others, which are not plasticized by ambient water.17,19−22 The structure−property relationships defined in this study for polyaromatic additives, as a function of molar mass, can power assessments within polymer matrices beyond the specific additives tested here. Third, we show that the presence of trace amounts of water plasticize polyamides and significantly increase D beyond what one would anticipate from simple, pure-component mixing arguments. Of course, water is an important potential plasticizer to consider in biomedical applications. Fortunately, this effect can be accounted for by linearly increasing the hole free volume with water content in the ternary free volume equation. Other semipolar polymers such as polycarbonate or poly(ethylene terephthalate) could also be plasticized by water; in addition, plasticizers are often intentionally added to polymers such as poly(vinyl chloride) to modify their properties. Therefore, our technique of accounting for plasticization in polyamides is useful and could be applied to other important materials, even for different polymers and plasticizers. Finally, to validate our ability to predict leaching rates using experimental and/or predicted D, leaching experiments were performed on PEBAX 4033 tubing that was compounded with quinizarin blue by a commercial manufacturer of catheter tubing. In practice, solvents are often employed that accelerate extraction by significantly swelling the polymer.23 The release profiles that result may be greatly exaggerated and not be directly suitable for use in risk assessments. For example, the leaching rate of the color additive quinizarin blue is at least 4 orders of magnitude faster from toluene-swollen PEBAX 4033 than it is from water-swollen PEBAX 4033. To show that it is possible to correlate the solvent-accelerated leaching rate to a physiologically relevant value, we demonstrate here that the simple tortuosity model of Mackie and Meares provides excellent agreement to our data set.24−26 This approach should be applicable to other elastomers used in medical devices, such as silicone rubber or soft polyurethanes, for example.

Figure 1. Generalized chemical structure of 33 series PEBAX block copolymers.

(tetramethylene glycol) (PTMO) subunits.27 The microphaseseparated hard nylon-12/adipic acid domains represent physical junctions that solidify and reinforce the rubbery PTMO domains. The mol % PTMO in these polymers was previously characterized by nuclear magnetic resonance spectroscopy by Sheth et al.27 and was shown to decrease linearly with Shore D hardness ≥35 D (see Figure S2). Therefore, the composition of PEBAX 5533 and 7233 was obtained via interpolation. All gases used in this work were purchased from Roberts Oxygen. Toluene, benzophenone (BP), butylated hydroxytoluene (BHT), and manganese(II) phthalocyanine (MnPC) were purchased from SigmaAldrich. Acetone was purchased from Fisher Scientific. Methyl benzoate (MB) and quinizarin blue (QB, CAS: 81-48-1) were purchased from TCI America. Solvent Orange 60 (SO60, CAS: 692569-5) and Pigment Red 2 (PR2, CAS: 6041-94-7) were purchased from AK Scientific, Inc. (Union City, CA). Phosphate buffered saline (PBS) powder was purchased from Sigma-Aldrich (P5368) and diluted to 0.1 M by deionized water. The resulting solution was stored at 4 °C. Saturated aqueous solutions of solid additives were made by adding an excess amount of solid additive to a PBS solution. 20 wt % Pluronic F87 surfactant (BASF) was included for the SO60, QB, PR2, and MnPC solutions. Sorption experiments in these solutions were started after they were stored at 55 °C for at least 24 h, cooled at 4 °C for at least 8 h, and finally equilibrated at 37 °C for at least 48 h. Gas and Solvent Vapor Sorption Intervals. Diffusion (D) and partition (K) coefficients of acetone, toluene, methyl benzoate, noctane, and n-decane in polymer samples were obtained via sorption interval methodology performed using a quartz spring microbalance (TGA-HP50, TA Instruments). Electrostatic charge on tared samples was neutralized prior to loading using an antistatic gun. Samples were dried at 75 °C for 90 min under vacuum or dry N2 purge. The activity of diffusant surrounding the sample was subjected to a step change, and the subsequent change in sample mass was continuously recorded until it reached a steady equilibrium value. The instrument was operated as a flow-through sorption apparatus at atmospheric pressure using ultrahigh purity N2 as a carrier gas. Vapor saturated by solvent at 25 °C was diluted by dry N2 prior to being flowed over the sample. Saturated partial pressures of solvent vapors were obtained from Antoine’s coefficients.28 Relative flow rates of saturated and dry solvent vapor streams are controlled by electronic mass flow controllers connected to the instrument software. The activity of gas or solvent vapor is the ratio of diffusant partial pressure in the sample chamber, p1, to that of its saturated maximum at the sample chamber temperature, p1°. The step change in diffusant activity was controlled such that the weight fraction of diffusant in the film, ω1, did not increase or decrease more than 0.01, so that the diffusion coefficient was constant over the interval.8 Water conditioning was performed by soaking samples in deionized water at 37 °C for at least 1 day. The vapor sorption experiment could be performed at 51% relative humidity by placing water in both the vapor saturator containing volatile solvent and the vapor saturator through which dry N2 was passed. These bubblers are held at 25 °C. A normalized mass uptake, M̃ (t) during each sorption interval was calculated based on the sample mass at time t, m(t):

2. EXPERIMENTAL SECTION Materials. Catheter tubing (127 μm wall thickness) made from PEBAX 3533, 4033, 5533, 6333, and 7233, and nylon-12 was purchased from Apollo Medical Extrusion Technologies, Inc. (Sandy, UT). A separate set of PEBAX 4033 tubing samples were compounded with quinizarin blue (QB) by Compounding Solutions LLC and extruded by Apollo Medical Extrusion Technologies, Inc.; those catheters contained 0.14 wt % QB (see Figure S1). As depicted in Figure 1, the grades of PEBAX used here are segmentally arranged block copolymers containing nylon-12, adipic acid, and poly-

M̃ (t ) = B

m(t ) − m(t0) m(t∞) − m(t0)

(1) DOI: 10.1021/acs.macromol.7b00690 Macromolecules XXXX, XXX, XXX−XXX

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Macromolecules where t0 designates the start time of the sorption interval and t∞ represents a long time at which the sample mass has equilibrated. The diffusion of gases, solvents, and additives into polymers are in many cases well-described by Fick’s second law of diffusion. Solutions to Fick’s second law using boundary and initial conditions valid for sorption intervals into films are

determined by ultraviolet/visible light absorption spectroscopy (UV/ vis, Agilent 8453). The absorbance value at the characteristic peak absorbance wavelength, A(λmax), was subtracted by the baseline absorbance at a long wavelength at which the chromophore does not absorb light, AB. A(λmax) − AB was subtracted by an analogous background value acquired from a sample which did not contain any chromophore. Because absorbance is linearly proportional to concentration, provided A(λmax) < 2, sample concentration was determined by comparison to calibration absorbances found from solutions of known concentration. For BP (λmax = 341 nm, DMF) and BHT (λmax = 277 nm, DMF) a quartz cuvette was used, and for SO60 (λmax = 445 nm, DMF), QB (λmax = 587 nm, DMF), PR2 (λmax = 493 nm, 1-butanol), and MnPC (λmax = 708 nm, 1-butanol), glass cuvettes were used. Solid Sorption Experiments. The diffusion coefficient (D) and solubility (S) of the solid additives BP, BHT, SO60, QB, PR2, and MnPC were obtained by soaking sections of PEBAX 4033 tubing in saturated aqueous dispersions of those additives. BP and BHT experiments were conducted in PBS buffer, while the color additive experiments were performed in PBS buffer containing 20 wt % Pluronic F87. The addition of nonionic surfactant solubilizes these additives, which are otherwise insoluble in aqueous solution. At various times sections of tubing were removed from solution, and the concentration of color additive was determined by UV/vis adsorption spectroscopy. The tubing was dissolved in 1-butanol,30 1−3 mg/mL (tubing/solvent) for PR2 and MnPC experiments at 80 °C for 15 min. The dye was removed from tubing for all other solid additives by soaking in 80 °C DMF, 1 mg/mL (tubing/solvent) for 15 min. The mathematics in eqs 2 and 3 are also valid when the symbols indicating mass are replaced by analogous concentration terms. The normalized concentration is represented by

∞ ⎛ Dp(t − t0) ⎞1/2 ⎡ ⎢π −1/2 + 2 ∑ (− 1)n ⎟ M̃ (t ) = 2⎜⎜ ⎟ ⎢ S2 ⎝ ⎠ ⎣ n=1

⎤ ⎥ ierfc Dp(t − t0) ⎥⎦ nS

(2a)

and

⎛ − D (2n + 1)2 π 2(t − t ) ⎞ 8 0 ⎜ p ⎟ exp ⎜ ⎟ 2 2 2 (2n + 1) π 4S ⎝ ⎠ n=0 (2b) which converge rapidly at short (t → t0) and long (t → t∞) times, respectively. In eq 2, S represents half the dry film thickness (when diffusion occurs on both side of the film) and Dp represents the polymer material coordinate diffusion coefficient. Dp may be related to the binary mutual diffusion coefficient D12 by the relation D12 = Dpϕ2−2, where ϕ2 is the volume fraction of polymer in the swollen film.29 Asymptotic solutions to eq 2 can be found by excluding the summation in the right of eq 2a and using only the first term in the summation on the right of eq 2b. Therefore, a simplification of eq 2a valid for M̃ (t) < 0.6 is ∞

M̃ (t ) = 1 −

∑

2 M̃ (t → t0) = S

Dp(t − t0) π

C̃(t ) =

(3a)

and a simplification of eq 2b valid for M̃ (t) > 0.4 is ⎛ − D π 2(t − t ) ⎞ 8 p 0 ⎟ M̃ (t → t∞) = 1 − 2 exp⎜⎜ ⎟ π 4S2 ⎝ ⎠

(5)

Therefore, D = Dp was determined by regression of eq 3a to the experimental data where C̃ (t) ≤ 0.6, and the uncertainty in D corresponds to the 95% confidence interval of the regression. The solubility of the additive in the polymer is given by S = C(t∞) − C(t0). Leaching Experiments. Small sections of PEBAX 4033 tubing containing 0.14 wt % QB, prepared by compounding and extrusion in a commercial catheter tubing prototyping facilities, were immersed in extraction solvents at 37 °C while agitated in a plate shaker at 130 rpm. Tubing samples were removed at various times, rinsed with distilled water, and analyzed for QB concentration by UV/vis spectroscopy. Based on how C̃ was defined, eq 2 also describes leaching of additives that are initially dissolved homogeneously in the polymer matrix. Therefore, exposure profiles were predicted from eq 2 with C(t∞) = 0. The mass of QB released from the tubing, M, was calculated from

(3b)

Dp and t0 were varied in a nonlinear regression of eqs 3a and 3b to appropriate portions of experimental data. When Dp(ω1) was found via eq 3a, it was attributed to the ω1 at M̃ = 0, and when Dp(ω1) was found via eq 3b, it was attributed to the ω1 at M̃ = 1. In the trace limit of diffusant, Dp represents a tracer diffusivity, D. In instances where Dp was found at various ω1, D was found by linearly extrapolating ln[Dp(ω1)] to ω1 = 0, e.g., ln[Dp(ω1 → 0)] = ln D, and the uncertainty calculated based on the 95% confidence limits of the linear regression. In other cases where only one sorption interval was performed for ω1 < 0.01, D ≈ Dp , and the uncertainty represents the average 95% confidence limits found from the regression of eq 3 to the data. The partition coefficient K was found by calculating the ratio of diffusant concentration in the film, in units mol cm−3, to that in the surrounding atmosphere. The relation that results is

K=

C(t ) − C(t0) C(t∞) − C(t0)

M = (C(t0) − C(t ))(1 − C(t ))−1mtubing

(6)

where mtubing is the total initial tubing mass, and concentration is expressed in terms of QB mass per total tubing mass.

RTω1ρ1ρ2 M1p1 [ω1ρ1 + (1 − ω1)ρ1]

3. FREE VOLUME THEORY OF VRENTAS AND DUDA The effects of temperature and composition on the binary mutual diffusion coefficient D12 in polymer/solvent mixtures can be predicted by the free volume theory of Vrentas and Duda. Their original working relationship21 was

(4)

where R is the gas constant, T the absolute temperature, ρ1 the condensed-phase mass density of diffusant, ρ2 the polymer’s mass density, and M1 the diffusant molecular weight. Note that Henry’s law implies that K is invariant with ω1 and that this behavior is usually observed for polymer/solvent systems above the glass transition.8 Therefore, the reported K represents a mean K(ω1). If K has been determined at relatively low vapor pressures, it is possible to make a crude estimation of diffusant solubility, S, by setting p1 to its saturated value and solving for ω1 ≈ S. Equation 4 is developed under ideal vapor/liquid equilibrium assumptions and is not applicable to the data collected under humid conditions. UV/Vis Spectroscopy. The concentrations of solid additives in N,N-dimethylformamide (DMF) or 1-butanol solutions were

⎡ −E ⎤ D12 = D0 exp⎢ (1 − ϕ1)2 (1 − 2χϕ1) ⎣ RT ⎦⎥ ⎡ −ω V̂ * − ξ (1 − ω )V̂ * ⎤ 12 1 2 ⎥ × exp⎢ 1 1 ̂ γ −1 ⎢⎣ ⎥⎦ VFH

(7a)

where V̂ FH represents the mixture’s specific “hole” free volume: C

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Macromolecules ̂ /γ = VFH

̂ VFH1 V̂ ω1 + FH2 (1 − ω1) γ γ

⎡ −E ⎤ a = D0 exp⎢ ⎣ RT ⎦⎥

(7b)

The weight and volume fractions of diffusant in the film are ω1 and ϕ1, respectively. Estimations of the specific volume at 0 K of the diffusant and polymeric repeat unit provide values of V̂ *1 and V̂ 2*, respectively.31 For metal atoms and water we utilized van der Waals volumes, which were multiplied by 1.3, and Avogadro’s number to estimate their molar volumes at 0 K.32 γ is an overlap factor between 0 and 1. V̂ FH is clearly a composition-proportional combination of diffusant hole free volume, V̂ FH1, and polymer free volume, V̂ FH2. When the diffusant and polymer are both liquids,

̂ VFH1 γ

and

̂ VFH2 γ

and ̂ )−1 b = γ(M 2VFH2

can be

(8)

M1V1̂ *

which we seek to correlate to diffusant size. In practice, D0 and E do not need to be defined rigorously for every diffusant. One previous examination of D0 and E did not find these terms to possess any discernible relationship to diffusant size; furthermore, the prefactor D01 = D0 exp[−E(RT)−1] was the same order of magnitude for six hydrophobic, organic solvents sized 58 Da > M1 > 138 Da.19 Therefore, D01 does not appear to be strongly related to diffusant size and may be regarded to be fairly constant across a set of molecules possessing similar polarity. The denominator of the rightmost exponential in eq 8 is related to the polymer’s free volume, not the diffusant size. Conversely, the numerator of the rightmost exponential term in eq 8 has a clear relationship with diffusant size: for symmetric diffusants which diffuse as a single jump unit, the product ξ12V̂ 2* increases linearly with the molar volume of diffusant at 0 K, meaning ξ12V̂ *2 ∼ M1V̂ *1 .35 Diffusants such as water vapor and gases (O2, N2, CH4, etc.) are so much smaller than polymeric jumping units (M1V̂ 1* ≪ M2V̂ 2*) that they are effectively symmetric as well. The jump unit ratio for diffusants satisfying the above physical criteria is defined as ξL = M1V̂ *1 (M2V̂ *2 )−1. For some polymers such as PEBAX the WLF parameters cannot be obtained from liquid viscosity data at the temperature of interest because they retain a solid form due to physical junctions or chemical cross-links. In that case it is justified to correlate D(M1V̂ 1*) by two fitted parameters representative of the volume-average properties, a and b, to yield the form of D = a exp[−bM1V1̂ *]

(9c)

Thus, b is a grouping of explicit physical constants related to the polymer’s hole free volume, temperature, and jump unit molecular weight. Note that eq 9 suggests a plot of D(M1V̂ 1*) on logarithmic axes is shaped concave down and that the degree of concavity is increased for polymers possessing slower dynamics (increased b, e.g., higher Tg2). Therefore, eq 9 qualitatively agrees with and provides a fundamental basis for the shape of historically aggregated log[D(M1V̂ 1*)] data, in which natural rubber (Tg2 = −70 °C) is much flatter than that obtained in poly(vinyl chloride) (Tg2 = 80 °C).36 However, many diffusant molecules are not symmetric, and eq 9 is not fully applicable. For example, a linear hexane molecule will diffuse much faster through a given polymer than any branched or cyclic isomer, even though all may possess similar M1V̂ *1 .37 To address this discrepancy, Vrentas and coworkers17 proposed incorporating shape effects into their theory which appropriately accounted for observed D12 of asymmetric diffusants, as defined by a geometric aspect ratio P (P ≥ 1). The geometric aspect ratio can be calculated using publicly available 3-D conformer models of diffusant molecules.38 P is the ratio of the two major principal axes of the rectangle that encloses the molecule.17 This revision accurately represented the diffusion properties of linear alkanes such as ndecane, providing substantial evidence that even relatively long and flexible solvent molecules diffuse as a single unit. The most important addition was providing a general definition of ξ12

defined explicitly by the Williams−Landel−Ferry (WLF) parameters.19,21 ξ12 is the ratio of critical molar volume needed for a diffusive “jump” of diffusant relative to that of the polymer, and χ is the Flory−Huggins interaction parameter for the diffusant−polymer pair. D0 is a pre-exponential factor, and E is the critical energy needed for a diffusant to overcome neighboring attractive forces. Note that E represents an energetic correction to hard-sphere interactions assumed in the underlying Cohen−Turnbull theory,33 not an “activation energy of diffusion”. Typically, exact values of D0, E, and ξ are found via regression to D12(ω1,T) data.34 We seek to simplify eq 7 so that less physical constants or adjustable parameters are needed to power the free volume theory. In the vanishing limit of diffusant, eq 7 reduces to a tracer diffusivity ⎡ − ξ V̂ * ⎤ ⎡ −E ⎤ ⎢ 12 2 ⎥ D = D12(ω1 → 0) = D0 exp⎢ exp ⎣ RT ⎦⎥ ̂ γ −1 ⎥⎦ ⎢⎣ VFH2

(9b)

ξ12 = 1+

M 2V2̂ * M V̂ * 1 1

M 2V2̂ *

(1 − P1 )

(10a)

which is based on the concept of asymmetric molecules adding a greater portion of free volume to the mixture than an equivalently large symmetric molecule. Incorporating this into eq 8, we obtain ⎡ * ⎢ −bM1V1̂ D = a exp⎢ 1 ⎣ 1 + ξL 1 − P

(

)

⎤ ⎥ ⎥ ⎦

(10b)

Zielinski and Duda proposed an empirical relationship of M2V̂ *2 = 0.6224Tg2 (K) − 86.95 for poly(styrene), poly(methyl methacrylate), and poly(vinyl acetate) melts.39 It implies that higher polymer glass transition temperatures, Tg2, are associated with higher critical volumes of polymer segments that facilitate diffusion. However, since the PEBAX polymers we are interested in possess Tg2 much below these polymers, we consider c = (M2V̂ *2 )−1 to be another unknown, yielding ⎡ −bM1V1̂ * ⎢ D = a exp⎢ ̂* ⎣ 1 + cM1V1 1 −

(

1 P

)

⎤ ⎥ ⎥ ⎦

(11)

Using eq 11 and D(M1V̂ *1 ,P) data, one may determine best-fit a, b, and c−1 parameters for a representative set of diffusants. At this point the polymer material would be completely characterized at the temperature of interest, and D(M1V̂ 1*,P)

(9a)

where D

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Macromolecules may be predicted for other diffusants. We note here that previous works also seek to predict D(M1V̂ *1 ) and other pertinent transport coefficients.17,32,40−43 The presence of adsorbed water may significantly plasticize some polymers like nylon-12 by disrupting hydrogen bonding.44 In this case it is appropriate to consider the ternary free volume equation, simplified in the limit of low additive content45 ⎡ ω ξ V̂ * + (1 − ω )ξ V̂ * ⎤ 3 12 2 ⎥ D = a exp⎢ − 3 13 3 ̂ ⎢⎣ ⎥⎦ VFH/γ

(12)

Figure 2. Unprocessed quartz spring microbalance sorption interval data for methyl benzoate diffusing into PEBAX 4033 tubing at 37 °C. The number above each interval represents the solvent vapor activity, and the value below each interval represents the binary mutual diffusion coefficient found by applying eq 3b to the data.

where V̂ 3* is the specific volume of water at 0 K. The jump unit ratio of diffusant to water is M1V1̂ *

ξ13 = 1+

M3V3̂ * M V̂ * 1 1

M3V3̂ *

(1 − P1 )

(13)

Because of the specific and localized hydrogen bonding interactions between water and amide linkages, the hole free volume of the mixture may differ from that anticipated by pure component properties (e.g., eq 7b). When the weight fraction of absorbed water, ω3, is relatively low, we consider that the free volume in the wet polymer increases linearly46 relative to the dry polymer with respect to ω3 by slope ϵ, yielding ̂ ≈ VFH2 ̂ (1 + ϵω3) VFH

(14)

Figure 3. Tracer diffusion coefficients and mean partition coefficients of toluene at 37 °C in a homologous series of PEBAX copolymer and nylon-12 tubing samples. Unfilled points were acquired under 51% relative humidity, and filled points were acquired in the absence of water. The dashed line represents eq 16 with fitted constants z = 12, DPTMO = 9.1 × 10−8 cm2 s−1, and KPTMO = 2400.

Combining eqs 12−14, it can be shown that ⎡ ⎛ ⎢ − bM V̂ * ⎜ 1 1 ⎢ ⎜ D = a exp ⎢ 1 + ϵω3 ⎜ 1 + ⎢⎣ ⎝

M

ω3 M2

3

M1V1̂ * M3V3̂ *

(1 − P1 )

1 − ω3 + 1 + cM1V1̂ * 1 −

(

1 P

)

⎞⎤ ⎟⎥ ⎟⎥ ⎟⎥ ⎠⎥⎦

(15)

Therefore, using a, b, and c values obtained by prior analysis of a dry film, the effect of water can be accounted for by a single additional unknown, ϵ. Diffusivity data acquired under humid conditions, i.e., nonzero ω3, allow determination of ϵ.

be expected, the samples with the highest PTMO contents, PEBAX 3533 and 4033, have the highest D. The D of toluene in PEBAX 3533 tubing is roughly a factor of 540 higher than that in neat nylon-12 tubing. K is generally higher for higher PTMO contents. Toluene may partition more into PEBAX 3533 and 4033 than the other polymers due to PTMO having lower crystallinity27 than nylon-12 and/or possibly a greater affinity for toluene. Because medical device polymers are often utilized in a water-saturated environment, we also measured D in waterconditioned PEBAX 4033, 7233, and nylon-12 tubing in a 51% relative humidity environment. The D values are up to a factor 2.2× higher in the humid samples, confirming that the presence of water can significantly plasticize polymers with high polyamide contents. The D of toluene in PEBAX 4033 is invariant with water content. Since the 33 series of PEBAX block copolymers are microstructured, biphasic materials, the effective medium theory (EMT) of Sax and Ottino is highly applicable to correlate the effects of composition on transport coefficients.47 Their result provides the volume-averaged K and D of PEBAX using model inputs of pure phase properties and specification of a lattice parameter z. For the 33 series of PEBAX block copolymers the volume fraction of soft PTMO block defines the system properties, ϕPTMO, which was estimated based on the molar composition and pure component mass densities of PTMO, adipic acid, and nylon-12. The resulting relations for D(ϕPTMO) and K(ϕPTMO) are

4. RESULTS AND DISCUSSION Gas and Solvent Vapor Sorption Intervals. Sorption intervals were performed on polymer samples using a quartz spring microbalance. Analysis of that data by the methods described above provided D and K values for acetone, toluene, n-octane, n-decane, and methyl benzoate as diffusant molecules. A representative set of raw sorption interval data for methyl benzoate diffusing into PEBAX 4033 tubing is shown in Figure 2. Each sorption interval begins with a step increase in the solvent vapor activity flowed over the sample, resulting in a slow mass increase prior to reaching equilibrium. From each interval a diffusion coefficient was extracted, which increases very slightly with each subsequent interval. This effect is due to solvent plasticizing the polymer and accelerating molecular motion as it is introduced. However, this plasticization effect is relatively weak in PEBAX 4033 because the experimental temperature, 37 °C, is far above the glass transition temperature of the soft PTMO block, ≈−80 °C.13 D and K were measured for toluene diffusing into the 33 series PEBAX block copolymer tubing samples as well as nylon12 tubing, and the results are shown in Figure 3. These samples represent a homologous set in which the ratio of soft PTMO block to hard nylon-12 blocks are varied systematically. As can E

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Macromolecules

Figure 4. Diffusion coefficients of acetone (1), toluene (2), methyl benzoate (3), n-octane (4), and n-decane (5), in different grades of catheter tubing. The solid line represents eq 11 with the listed physical constants and P = 1.4; the dashed line uses P = 0.0212M1V̂ *1 + 1 to represent the trend observed for n-alkanes.

⎡ D(ϕPTMO) = DPTMOX ′−1⎢Y + ⎣

Y2 +

⎤ 2 X ′X ″ ⎥ ⎦ z−2

⎛ ⎞−1 1 − X′ × ⎜1 + ϕPTMO⎟ ⎝ ⎠ X′

of a heterogeneous material containing at least two distinct free volume microstructures, while eq 11 is strictly applicable to homopolymers. This discrepancy is not important for characterizing PEBAX 4033 because it is composed mainly of the soft PTMO block, which dominates diffusion, and we obtain precise values of b and c−1 relevant to PTMO. PEBAX 4033 is effectively homogeneous from a free volume perspective. Conversely, the hard nylon-12 block is the primary constituent of PEBAX 7233, creating marked heterogeneity in its segmental dynamics and free volume, which are not directly captured by our development of eq 11. Previous analyses of diffusion in block copolymers by forced Rayleigh scattering experiments have obtained transport coefficients within the microphase-separated, pure homopolymer domains,9 while our analysis of sorption data yields a volume-averaged diffusivity for the total copolymer. For this reason the uncertainty in c−1 found via regression to PEBAX 7233 data was relatively high. We used a conservative value of c−1 based on the lower limit of the 95% confidence interval, ensuring D is not underpredicted. The c−1 for nylon-12 was set by presuming it to be linearly proportional to ϕPTMO. We return here to the diffusion data collected in a humid environment, which showed that the D of toluene in polymers with high polyamide content was doubled at 51% relative humidity. Note that the glass transition temperature of nylon12, 40 °C, is very near the temperature of measurement, 37 °C, so D is extremely sensitive to small changes in water uptake.20,49 This pronounced plasticization effect is due in part to the strong ability of water to disrupt hydrogen bonding between polyamide linkages.50 The effect of water uptake on diffusion, as shown in Figure 5, was rationalized using eq 15 and a single fitted parameter, ε = 7, which provided agreement to the data for both PEBAX 7233 and nylon-12 tubing. According to our measurements at 37 °C, dry nylon-12 has a hole free volume of γ−1V̂ FH2 = 0.074 cm3 g−1, and the corresponding literature value for water is γ−1V̂ FH3 = 0.344 cm3 g−1.19 Relative to dry nylon-12, the value of ϵω3 indicates that hole free volume increases about 17% for samples held in 51% relative humidity, which is 2.2× greater than is anticipated from pure component properties and eq 7b. Solid Sorption Experiments. Sorption experiments of solid additives into PEBAX 4033 tubing were performed in saturated solutions of butylated hydroxytoluene (BHT), benzophenone (BP), solvent orange 60 (SO60), quinizarin blue (QB), pigment red 2 (PR2), and manganese(II) phthalocyanine (MnPC) in PBS buffer. These additives were chosen because they represent a homologous series of increasing molar mass and also are broadly representative of

(16a)

and K (ϕPTMO) = KPTMOϕPTMO + K nylon‐12(1 − ϕPTMO) (16b)

where Y=

z ϕ 2 PTMO

z − 1 + X ′X ″⎡⎣ 2 (1 − ϕPTMO) − 1⎤⎦

(16c)

z−2

and X′ =

K nylon‐12 KPTMO

and

X″ =

Dnylon‐12 DPTMO

(16d)

Equation 16 represents the data in Figure 3 quite well with fitted parameter inputs of z = 12 ± 0.4, DPTMO = (9.1 ± 0.2) × 10−8 cm2 s−1, and KPTMO = 2400 ± 400. z = 12 is a constant that can be used to predict D of any diffusant in the 33 series of PEBAX provided input of D and K for the pure homopolymers PTMO and nylon-12. For release applications, a desired permeability DK of a given drug, fragrance, or pesticide could be obtained by tailoring the PEBAX composition via monomer feed ratio or blending strategies. Since z arises from the microstructural morphology of PEBAX, the same lattice parameter may also be appropriate for closely related segmented block copolymers such as polyether polyurethanes. Diffusion coefficients of volatile solvents in PEBAX 4033, 7233, and nylon-12 are shown in Figure 4 as a function of M1V̂ *1 . These data sets provide a basis for obtaining the polymer free volume constants a, b, and c−1 by regression. As can be anticipated by eq 11, increasing molar volume of diffusant decreases D, with a weaker dependence on M1V̂ 1* for asymmetric diffusants such as n-alkanes than more symmetric diffusants like acetone and toluene. PEBAX 7233 and nylon-12 possess a smaller prefactor a = D01 than PEBAX 4033. This difference arises from the higher crystallinity of the former polymers, which act as impermeable, microscopic barriers to diffusion.27 The c−1 = M2V̂ 2* being greater for PEBAX 7233 than 4033 means a greater volume of polymer segments is involved in each diffusive “jump”. This is consistent with its compositionweighted average Tg2 being higher.48 We note that the free volume parameters described in Figure 4 are average properties F

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Figure 5. Effect of water uptake on the D of toluene in two polyamides at 37 °C. Data points represent that collected in the dry (filled) and 51% relative humidity (unfilled) environments. The solid line represents the predictions of eq 15, extended out to the equilibrium water uptake at unit activity, as anticipated from Flory−Huggins solution theory.8,19 The solid line as depicted has already accounted for the presence of impermeable crystalline regions in these materials by using water concentration terms relevant to the amorphous fraction in eq 15. The method of Sudgen31 predicts V̂ *2 = 0.932 cm3 mol−1 for nylon-12, V̂ 2* = 0.923 cm3 mol−1 for PEBAX 7233, and M2 = (cV̂ 2*)−1.

many major parent structures (hindered phenol, anthroquinone, azo-, phthalocyanine51) to which many polymer additives belong. The solutions of SO60, QB, PR2, and MnPC included 20 wt % Pluronic F87 as a nonionic surfactant to solubilize the color additives without changing pH.16 A representative photograph of PEBAX 4033 tubing after various soaking times in the color additive solutions is shown in Figure 6. The uptake of color additive in the tubing is gradual, suggestive of a diffusion-controlled process, and appears faster for the smaller molecular weight color additives, SO60 and QB. While not shown in Figure 6, the tubing soaked in saturated solutions of BP and BHT was visually white and fuzzy after storage, evident of these additives blooming to the surface and recrystallizing once removed from solution. The additives were then extracted from the tubing, and the absorbance spectra of the resulting solutions were measured by UV/vis spectroscopy. Representative data for the PR2 samples are shown in Figure 7. The solutions possess absorption maxima at a characteristic wavelength of the specific additive, which increases with soak time prior to equilibrating at long soak times. The absorption maximum of each sample was related to the concentration of additive by comparison to linear calibration curves of known concentration. The concentration, C, of solid additives in PEBAX 4033 tubing after various soak times is shown in Figure 8 as a function of reduced time, S −1√t. All data except BHT are linear through the origin prior to equilibrating. For BHT, the C(t0) = 3.8 wt % implied by the ordinate intercept is suggestive of this hydrophobic additive quickly absorbing to the tubing surface from aqueous solution; otherwise, its uptake kinetics were Fickian. D was found for each data set by regression of eq 3a within the range of C(t0) ≤ C ≤ 0.6S. We observe that D and S decrease strongly with increasing molecular weight; the data for S are plotted in Figure S3. S is especially high for the two lowest molecular weight additives, BP and BHT. Since the sorption experiment was done over an excessively large interval (S ≫ 1 wt %), the PEBAX tubing may plasticize through the course of measurement, such that the reported D does not strictly represent a trace value. In contrast, the larger molecular size and planar, polyaromatic structures of the color additives contribute to reduce their solubility in PEBAX below 1 wt %, and the reported D represents a trace value.

Figure 6. (a) Chemical structures of color additives and (b) photograph of PEBAX 4033 tubing after various soaking times in saturated aqueous solutions of color additives at 37 °C.

Figure 7. Representative UV/vis absorption spectra for dissolved PEBAX 4033 tubing after various soaking times in saturated aqueous solutions of Pigment Red 2 at 37 °C. The raw data were vertically offset to correct for small variances in the baseline absorption.

Diffusion coefficients of volatile solvents and solid additives in PEBAX 4033 tubing are shown as a function of molecular weight in Figure 9. D monotonically decreases with M1, and the experimental values lie below an upper bound based on eq 11 and the trends for size and shape observed for n-alkanes. Data points representing predictions of eq 11 using calculated values of M1V̂ *1 and P generally lie atop or slightly above the experimental values with only two exceptions: BHT and MnPC. Therefore, the free volume methodology described near eq 11 shows promise in constructing meaningful and wellG

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Figure 8. Sorption experiments of solid diffusants into PEBAX 4033 tubing from saturated aqueous solutions held at 37 °C. The solid lines represent eq 2 using the appropriate values of D and C(t∞) − C(t0) = S.

Structure−Property Relationships for M1V̂ 1* and P of Polyaromatic Additives. In Figures 4 and 5 and the surrounding discussion we calculated free volume parameters for PEBAX 40D, PEBAX 72D, and nylon-12, valid for the dry or hydrated polymer at 37 °C. These can be used in conjunction with the free volume theory defined in eqs 11 and 15 to predict D on the basis of diffusant size and shape. It is required to measure D for a representative set of solvents containing symmetric and asymmetric examples.17 In our view, acetone, toluene, and cyclooctane are good examples of symmetric diffusants; n-octane and n-decane are good examples of asymmetric diffusants. The M1V̂ *1 and P of those solvents are defined explicitly in the Supporting Information (see Table S1). In Figure 9, D was predicted using diffusant shape factors that were calculated using publicly available 3-D conformer models. Since this step represents a roadblock for many experimentalists, we propose using observed structure− property relationships of M1V̂ 1* = 2.1195M0.807 and P = 1 0.0015M1V̂ 1* + 1.2429 to predict D of other additives which have similar overall polarity and compactness to the additives examined here (see Figures S5 and S6). As shown in Figure 9, these relationships enable excellent agreement of the model to the experimental data. However, in potential regulatory or riskassessment applications, conservative approaches are preferred over best-fit solutions. Therefore, as an alternative one may use an upper bound on P for these additives as defined by the 95% confidence limit on the linear regression in Figure S6, P = 0.0020M1V̂ 1* + 1.3466 (see Figure S7). Using this strategy, predictions of D on the basis of diffusant molar mass are shown in Figure 10 for dry and hydrated polymers. This demonstrates how our methodology can be transferred to other polymers. We used ω3 = 0.055 for PEBAX 7233 and ω3 = 0.065 for nylon-12 as inputs into eq 15. These values represent the water content in the amorphous fraction of polymer at unit activity (p1 = p°1 ), as predicted by Flory− Huggins theory. Therefore, the predictions of D made for hydrated polymer are valid for high water content scenarios, e.g., physiological implantation. The plasticization induced by water adsorption is predicted to significantly increase D,

Figure 9. Diffusion coefficients of acetone (1), toluene (2), methyl benzoate (3), BP (4), BHT (5), SO60 (6), QB (7), PR2 (8), and MnPC (9) at 37 °C in PEBAX 4033 tubing (●) alongside predictions made from eq 11 and P values from Table S1 (×). The dashed line uses M1V̂ *1 = 1.10M1 and P = 0.0212M1V̂ *1 + 1 as inputs to eq 11 to represent the trend observed for n-alkanes. The solid line represents eq and P = 0.0015M1V̂ *1 + 1.24 as color 11 with M1V̂ *1 = 2.12M0.81 1 additive structure−property relationships that enable agreement to the entire data set.

informed material property predictions using a limited set of measurements of volatile solvents as input. The D of BHT is underpredicted due to overestimation of M1V̂ 1* by the method of Sudgen,31,39 for which its M1V̂ 1* is even greater than that of SO60. If the M1V̂ *1 of BHT were determined by interpolating between the other diffusants as a function of M1, this outlier is resolved (see Figure S4). The D of MnPC is underpredicted by a factor of 4 × 104 due to the calculated value of P = 1.1 being much too small. The P calculation strategy of Vrentas and co-workers, originally validated for much smaller solvent molecules, calculates an aspect ratio based on its eccentricity along its major planes.17 This effectively ignores out-of-plane asymmetry and therefore may poorly represent very large molecules such as MnPC which happen to be symmetric along their two longest axes. Our results should motivate an improvement of how P is calculated that accounts for asymmetry in all three planes. In its absence, our experimental data suggest P = 2 as a conservative value for phthalocyanines, which would slightly overestimate D for MnPC (see Figure S4). H

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and accelerated aging methodologies52,53 to mimic the aqueous environment, salinity, and pH of the human body, although we and others note it does not contain the fats, proteins, and other biomolecules that are believed to also influence leaching and polymer degradation processes.50,51 At various times the tubing samples were removed and checked for QB concentration to determine how much QB was leached from them via a mass balance (eq 6). The leaching profiles for these solvents are shown in Figure 11a. Use of the nonpolar extraction solvent results in essentially instantaneous release of all extractable QB, while the polar extraction solvent does not result in any leaching, as was confirmed by HPLC analysis (see Figure S8). PBS solution is an inadequate extraction solvent because QB is insoluble in it; conversely, toluene and ethanol strongly swell the PEBAX 4033 polymer and therefore yield an exaggerated release profile that is not physiologically relevant. We argue that none of these extraction solvents directly provide meaningful information regarding the rate of color additive leaching that could occur in the human body and that improved extraction media and/or physical interpretation is necessary. To obtain a physiologically relevant leaching profile for QB into aqueous media, we look beyond the solvents suggested in ISO 10993-12 and utilize PBS solution containing 20 wt % Pluronic F87 as extraction media. That profile is shown in Figure 11b along with a regression to eq 3a using the dry tubing thickness. This regression yields an effective polymer materials coordinate diffusion coefficient, Deff, of 6.5 × 10−11 cm2 s−1. For our QB/PEBAX 4033 system, Deff = 0.36D, providing evidence that leaching predictions using eq 2 and D are not likely to underpredict the amount of additive released from medical device polymers. Note that processing effects can result in the extruded tubing containing incompletely dissolved QB, and therefore the inhomogeneous initial state would differ from that used to derive eqs 2 and 3. In that case the extraction profile may be slower than that predicted from diffusivities obtained from sorption measurements. Deff values were also determined using extraction solvents of varying polarity so that the effects of polymer swelling on leaching profiles could be investigated systematically. The volume fraction of the solvent in the tubing, ϕ3, was determined using bulk mass densities and gravimetric swelling experiments. Experimental Deff values were adjusted by the simple geometric factor

Figure 10. Predicted upper-bound D of polyaromatic color additives in PEBAX 7233 and nylon-12 at 37 °C based on the free volume parameters defined in Figures 4 and 5 and the conservative structure− property relationship of P = 0.0020M1V̂ *1 + 1.3466 defined by the data in Figure 9. The solid lines represent dry polymer (eq 11), and the dashed line represents hydrated polymer (eq 15).

especially for high molar mass diffusants. For example, hydration is predicted to increase D by more than a factor of 100 for a 600 Da color additive in both matrices. This effect is so strong that in the hydrated state D in PEBAX 4033 is higher than in nylon-12 by only a factor of 220 at 600 Da. Leaching Experiments. Predictions of solute diffusivities in polymers are useful as inputs into advanced and generalizable risk assessment platforms which anticipate rates of exposure to chemicals that could leach from polymers into food, humans, the environment, or other scenarios of concern. However, some researchers may favor case-by-case evaluations which are powered by empirical and costly extraction experiments. In this section we will show the results of extraction experiments performed on a model system, with some conditions suggested by ISO 10993, an internationally recognized biocompatibility assessment standard.23 PEBAX 4033 was compounded with 0.14 wt % QB and extruded into catheter tubing (127 μm wall thickness) using equipment and practices highly representative of medical device fabrication. ISO 10993-12 specifies that the polarity of extraction media should be varied significantly, without providing unambiguous guidance on whether recommended solvents are compatible with a given polymer and yield physiologically representative results.23 Therefore, we initially utilized polar (0.1 M phosphate buffered saline solution), nonpolar (toluene), and midpolar (ethanol) solvents as extraction media (37 °C, 2 mg tubing/mL solvent) and changed the solvents often so that the extraction conditions represented as close to a “perfect sink” as was reasonably possible. PBS solution is used exceedingly often in extraction

Deff,123 = Deff (1 − ϕ3)−2

(17)

from which an effective diffusion coefficient in the ternary system is obtained, Deff,123, in order to account for the role of

Figure 11. (a, b) Representative leaching profiles and analysis of QB from PEBAX 4033 tubing into various extraction media at 37 °C. The solid line in (b) represents eq 2. (c) Effective diffusion coefficients obtained from leaching profiles using aqueous Pluronic solution (1), ethylene glycol (2), octamethyl trisiloxane (3), propylene carbonate (4), ethanol (5), hexane (6), and toluene (7) as extraction media. I

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history, may also influence the results and require consideration to provide clinically relevant assessments.

swelling and properly compare material properties across the data set.29 The Deff,123 values for various ϕ3 are shown in Figure 11c. Notably, increasing ϕ3 from 0.02 to 0.51 resulted in an increase in the Deff,123 by approximately 4 orders of magnitude. Provided QB is soluble in the extraction media, leaching is strongly correlated to the volumetric swelling of PEBAX 4033, not the absolute polarity of the extraction media. To correlate our data, we chose to utilize the simple tortuosity-based model of Mackie and Meares.1,24,25 Their model assumes solute diffusion is fast in the space occupied by extraction media but must take a longer diffusion pathway due to obstructions caused by the relatively immobile polymer chains. The corresponding model predictions were obtained using the relation Deff,123

⎛ ϕ ⎞2 3 ⎟⎟ = D13⎜⎜ ⎝ 2 − ϕ3 ⎠

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.7b00690. Figures S1−S8 and Table S1 (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (D.W.J.). ORCID

Dustin W. Janes: 0000-0003-2959-5856 Notes

(18)

The authors declare no competing financial interest.

■

Here, D13 = 4.2 × 10−6 cm2 s−1 is the trace diffusion coefficient of QB in a pure liquid, which we varied in a regression to provide excellent agreement to the entire data set. While our set of experiments were performed on a model additive/polymer pair, we anticipate the same trends would hold true for other leachables in a wide range of related rubbery polymers (T ≫ Tg), e.g., elastomeric polyurethanes, poly(dimethylsiloxane), poly(isoprene), etc. The quality of agreement provides evidence that leaching data from solvent-swollen polymer elastomers can be used to make physiologically relevant leaching assessments provided it is interpreted by appropriate physical theory as described above.

ACKNOWLEDGMENTS The findings and conclusions in this paper have not been formally disseminated by the Food and Drug Administration, are the views of the authors, and should not be construed to represent any agency determination or policy. The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services. This research was funded by the CDRH Critical Path program, DBCMS program funding, and was partially administered by the Oak Ridge Institute for Science and Education through an agreement between the U.S. Department of Energy and the U.S. Food and Drug Administration. The authors thank Chris Forrey, Laura Espinal, and Antonio Toledo for help with the quartz spring microbalance apparatus and Joseph Stephens, Matt Bills, Melissa Levasseur, Taylor Boissonneault, and Nathan Doyle for the catheter tubing samples. The authors also thank Samanthi Wickramasekara, Ji Guo, Jennifer Goode, and Brendan Casey for helpful conversations. The authors thank Dave Saylor for providing aspect ratio values for the diffusant molecules.

5. CONCLUSIONS We have demonstrated here that predicting the leaching rates of various additives in block copolymer thermoplastics can be greatly simplified by utilizing physical models that can account for polymer composition, diffusant size and shape, and degree of swelling. This allows for diffusivity data collected under accelerated conditions to replace relatively slow and burdensome direct measurements. For example, the diffusion coefficients of solvent vapor in a given polymer may be collected such that D for much larger additive molecules may be predicted. Furthermore, leaching in highly swollen polymer matrices may be used to predict leaching under physiologically relevant swelling conditions. The 33 series PEBAX copolymers possesses a wide range of transport properties due to its composition of fast-mobility polyether blocks and rigid polyamide blocks. Therefore, the success of our approaches in modeling its properties across full scope of experiments here means the same techniques could likely be applied to many other important polymers with the anticipation of excellent model-data agreement. Beyond just a repository of material characterization of a specific system, this study is intended to be foundational and instructive to investigators who wish to predict transport properties of arbitrary diffusants in polymers on a very general basis, all while making efficient use of their original experimental data. Free volume models have been highly successful at predicting D in polymer materials.17,19−22 Therefore, we feel confident that these approaches may be extended to other polymer materials used in medical devices, packaging, and other applications. Please note that other complicating factors, such as plasticization, swelling, processing methodology, and thermal

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DOI: 10.1021/acs.macromol.7b00690 Macromolecules XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.macromol.7b00690 Macromolecules XXXX, XXX, XXX−XXX