Vrentas-Duda Free-volume Research Articles

Extreme dependence of dynamics on concentration in highly crowded polyelectrolyte solutions.

Charge-carrying species, such as polyelectrolytes, are vital to natural and synthetic processes that rely on their dynamic behavior. Through single-particle tracking techniques, the diffusivity of individual polyelectrolyte chains and overall system viscosity are determined for concentrated polylysine solutions. These studies show scaling dependences of D ~ c-6.1 and η ~ c7.2, much stronger than theoretical predictions, drawing the applicability of power law fits into question. Similar trends are observed in concentrated solutions prepared at various pH and counterion conditions. These hindered system dynamics appear universal to polyelectrolyte systems and are attributed to the large effective excluded volumes of polyelectrolyte chains inducing glassy dynamics. The framework of the Vrentas-Duda free-volume theory is used to compare polyelectrolyte and neutral systems. Supported by this theory, excluding counterion mass from total polymer mass results in all environmental conditions collapsing onto a common trendline. These results are applicable to crowded biological systems, such as intracellular environments where protein mobility is strongly inhibited.

Predicting Gaseous Solute Diffusion in Viscous Multivalent Ionic Liquid Solvents.

Calculating solute diffusion in dense, viscous solvents can be particularly challenging in molecular dynamics simulations due to the long time scales involved. Here, a new scaling approach is developed for predicting solute diffusion based on analyses of CO2 and SO2 diffusion in two different multivalent ionic liquid solvents. Various scaling approaches are initially evaluated, including single and separate thermostats for the solute and solvent, as well as the application of the Arrhenius relationship and the Speedy-Angell power law. A very strong logarithmic correlation is established between the solvent-accessible surface area and solute diffusion. This relationship, reflecting Danckwerts' surface renewal theory and the Vrentas-Duda free volume model, presents a valuable method for estimating diffusion behavior from short simulation trajectories at elevated temperatures. The approach may be beneficial for enhancing predictive modeling in similar challenging systems and should be more broadly evaluated.

Characterizing the free volume of ultrahigh molecular weight polyethylene to predict diffusion coefficients in orthopedic liners.

Liners used in orthopedic devices are often made from ultrahigh molecular weight polyethylene (UHMWPE). A general predictive capability for transport coefficients of small molecules in UHMWPE does not exist, making it difficult to assess properties associated with leaching or uptake of small molecules. To address this gap, we describe here how a form of the Vrentas-Duda free volume model can be used to predict upper-bound diffusion coefficients (D) of arbitrary molecules within UHMWPE on the basis of their size and shape. Within this framework, the free-volume microstructure of UHMWPE is defined by analysis of a curated set of model diffusants. We determined an upper limit on D for vitamin E, a common antioxidant added to UHMWPE, to be 7.1 × 10-12 cm2 s-1 . This means that a liner that contains 0.1 wt% or less Vitamin E and has <120 cm2 patient contacting surface area would elute <100 µg/day of vitamin E. Additionally, the model predicts that squalene and cholesterol-two pro-oxidizing biological compounds-do not penetrate over 820 µm into UHMWPE liners over the course of 5 years because their D is ≤7.1 × 10-12 cm2 s-1 . © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 106B: 2393-2402, 2018.

Predicting the Effects of Composition, Molecular Size and Shape, Plasticization, and Swelling on the Diffusion of Aromatic Additives in Block Copolymers

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(...

Decoupling energetic modifications to diffusion from free volume in polymer/nanoparticle composites.

Diffusion coefficients of small molecules in a model composite of spherical nanoparticles and polymer with attractive interfacial interactions are reduced from that in the pure polymer, to a degree far below the level expected from geometric tortuosity arguments. We determine whether such dramatic reductions are due to modifications to the matrix polymer free volume near the nanoparticle surface, or alternatively are due to energetic attractions between the diffusants and nanoparticle surface. We performed ethyl acetate sorption experiments within the vicinity of the polymer glass transition (Tg ≤ T ≤ Tg + 25 K) for a model polymer/nanoparticle composite, silica-filled poly(methyl acrylate). By application of the Vrentas-Duda free volume theory of diffusion we have decoupled the energetic effects from those related to free-volume and segmental dynamics. While the latter is unaffected by addition of nanoparticles, the energy needed for the ethyl acetate diffusant to overcome neighboring attractive forces doubles after adding 40 vol% nanoparticles with a diameter of 14 nm. This is qualitatively consistent with hydrogen bonding interactions between the silica surface and ethyl acetate slowing its rate of diffusion. On the other hand for benzene, which does not hydrogen bond to the silica surface, diffusion coefficients that can be explained by tortuosity effects were obtained. This work provides quantitative evidence that the diffusant-filler energetic interactions and geometric blocking effects can be fully responsible for the substantially reduced diffusivity commonly observed in polymer/nanoparticle composite systems.

Coupled concentration-dependent diffusivities of ethanol/water mixtures through a polymeric membrane: Effect on pervaporative flux and diffusivity profiles

The partial pervaporative (PV) fluxes of ethanol/water mixtures in polydimethylsiloxane (PDMS) were predicted using Fick's first law and modified Maxwell–Stefan equation. The sorption levels were predicted using UNIQUAV-HB and the experimental solvent diffusion coefficients of the mixtures were expressed in terms of their sorption concentrations according to Long's model. Both permeant diffusion coefficients were found to vary with the ethanol concentration alone. The predicted partial fluxes and the PV separation factor agreed well with the experimental data by integrating Fick's law over the ethanol concentration. The modified Maxwell–Stefan equation was employed to estimate the partial fluxes by taking into account both permeant concentration gradients. The modified Maxwell–Stefan equation rendered similar partial permeant flux and ethanol-over-water separation factor as in Fick's law. The agreement between the predicted PV performance and the experimental data indicates that the unsteady-state permeant diffusion coefficients reflect the diffusion behavior in the steady-state PV operation. The concentration and diffusivity profiles for the permeants in the PDMS were illustrated along the trans-membrane direction. These diffusivity profiles can be explained using the Vrentas–Duda free volume theory.

Interval Sorption of Alkyl Acetates and Benzenes in Poly(methyl acrylate)

We describe a simple, low-cost, gas flow vapor sorption/desorption apparatus that enables “interval” or “differential” experiments on supported polymer films, with control of small step changes in diffusant weight fraction, ω1, to intervals as small as 0.1%. The apparatus permits accurate determination of the binary mutual diffusion coefficient D12(ω1) for ω1 up to at least 3% for “condensable” organic species that typically exhibit very sharp increases in D12 with the diffusant’s weight fraction. We report results for two homologous series of diffusants, n-alkyl acetates and alkyl benzenes, in monodisperse poly(methyl acrylate) (PMA). The Vrentas–Duda free volume theory adequately accounts for the strong concentration dependence of D12 seen in all cases. Nearly constant values of the jump-unit size ratio, ξ, for the homologous set of n-alkyl acetates in the range ξ = 0.61–0.67 closely match those reported previously. For the alkyl benzenes, ξ for benzene (ξ = 0.78 ± 0.04) was higher than those for the larger homologues toluene, ethylbenzene, and cumene (ξ = 0.58–0.60). The ξ values for both homologous series are well-predicted by a free volume based estimate for eccentric diffusants, which jump as a single unit in a mixture whose components contribute different amounts of free volume per jump unit, according to their geometries.

Solubility and diffusivity of solvents and nonsolvents in poly(methyl methacrylate co butyl methacrylate)

In this study, thermodynamic properties, namely retention volume, infinitely dilute weight fraction activity coefficient, Flory–Huggins interaction parameter, solubility parameter of the polymer, partition coefficient and diffusion coefficients of the various solvents in poly(methyl methacrylate co butyl methacrylate) (PMMA co BMA) at infinite dilution of the solvent have been determined by inverse gas chromatography (IGC). In this technique, a small amount of the solvent was injected into the capillary column and its retention time was measured and used to calculate several polymer–solvent interaction parameters which are mentioned above. The solvents used in this study were methanol, ethanol, propanol, butanol, methyl acetate, ethyl acetate, propyl acetate, dichloromethane, trichloromethane, acetone, methyl methacrylate, butyl methacrylate for PMMA co BMA. The thermodynamic results, obtained from the experiments, indicated that trichloromethane and dichloromethane were the most suitable solvents among all the solvents studied for PMMA co BMA. The partition ( K) and diffusion coefficients ( D p) of various solvents at infinite dilution of the solvent were calculated by using the model developed by Pawlisch et al. [C.A. Pawlisch, A. Macris, R.L. Laurence, Solute diffusion in polymers.1. The use of capillary column inverse gas chromatography, Macromolecules 20 (1987) 1564–1578]. The optimum K and D p values that best fit the data were found and the model predicted experimental data very well. Vrentas–Duda free volume theory was used to correlate the diffusion data and to investigate the effect of solvent size on diffusion process. The theory has shown to correlate diffusion data above the glass transition temperature very well for the PMMA-co-BMA–solvent system.

Prediction of mutual-diffusion coefficients in polymer solutions using a simple activity coefficient model

Using a simple activity coefficient model in conjunction with the Vrentas–Duda free-volume (FV) theory, the diffusion behavior of small molecular solvents between and amongst polymer chains is then predicted for several polymer/solvent systems over a wide range of concentrations. The estimations are comparable with experimental data for some systems. For diffusion over- and under-predicted systems, a pre-exponential factor D 0 can be adjusted to improve the predictions. It is found that the entropic-FV model is a suitable alternative to the Flory–Huggins equation for predicting mutual-diffusion coefficients in polymeric solutions. To understand the impact of the model on the prediction thoroughly a sensitivity analysis is done for free-volume. The influence of the free-volume of solvent is the opposite of that of the polymer.

Infinite dilution diffusion coefficients of n-hexane, n-heptane and n-octane in polyisobutylene by inverse gas chromatographic measurements

Based on the Hadj-Romdhane–Danner model of the chromatographic process, the infinite dilution diffusion coefficients of n-hexane, n-heptane, n-octane and toluene in polyisobutylene (PIB) have been measured at temperatures in the range of 323.2–373.2 K by inverse gas chromatography (IGC). The measured infinite dilution diffusion coefficients for the toluene/PIB system were compared with the diffusivity data at finite concentration determined previously from NMR experimental method by using the Vrentas–Duda free volume theory. The good agreements indicate the IGC method studied in this work is reliable. Moreover, the correlations of the experimental data with the free volume equation were preformed. The correlated results show that the free volume theory is a quite good description of the relationship between the observed solvent diffusion coefficient and temperature.

A diffusion model of the pervaporation separation of ethylene glycol-water mixtures through crosslinked poly(vinyl alcohol) membrane

The pervaporation separation of ethylene glycol-water mixtures was carried out over the full range of compositions at temperatures varying from 60 to 80°C, using chemically crosslinked PVA dense membrane which had been developed in our laboratory. A new thermodynamic diffusion coefficient equation is derived based on the modified Vigne equation. Combining Lee-Thodos equations, Wilke-Chang equations, Vrentas-Duda's free volume theory, diffusion equations and swelling equilibrium equations, the permeation fluxes of individual components in ethylene glycol-water mixture through crosslinked poly(vinyl alcohol) (PVA) dense membrane have been calculated and showed to be in agreement with the experimental values.

Finite concentration inverse gas chromatography: Diffusion and partition measurements

Inverse gas chromatography (IGC) is a very fast, accurate, and reliable technique to measure diffusion coefficients. This technique however, has been limited to measurements in the infinite dilution region, i.e., in the region of negligible amount of solvent in the polymer. We have extended the scope of inverse gas chromatography to measure diffusion coefficients at finite concentrations of the solvent. This involves doping the carrier gas with a solvent of interest to achieve finite concentrations of solvent in the carrier gas and hence in the polymer. The carrier gas is passed through a saturator maintained at constant temperature to achieve this purpose. Diffusion coefficients for polyvinyl acetate–toluene, and polystyrene–toluene systems were determined at finite concentrations. The results were compared with the traditional gravimetric sorption and piezoelectric sorption measurements reported in the literature. The data are in excellent agreement with the values reported, correlate well with the Vrentas–Duda free volume theory, and can also be predicted from infinitely dilute data using the free volume theory. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1279–1290, 1997

Finite concentration inverse gas chromatography: Diffusion and partition measurements

Inverse gas chromatography (IGC) is a very fast, accurate, and reliable technique to measure diffusion coefficients. This technique however, has been limited to measurements in the infinite dilution region, i.e., in the region of negligible amount of solvent in the polymer. We have extended the scope of inverse gas chromatography to measure diffusion coefficients at finite concentrations of the solvent. This involves doping the carrier gas with a solvent of interest to achieve finite concentrations of solvent in the carrier gas and hence in the polymer. The carrier gas is passed through a saturator maintained at constant temperature to achieve this purpose. Diffusion coefficients for polyvinyl acetate–toluene, and polystyrene–toluene systems were determined at finite concentrations. The results were compared with the traditional gravimetric sorption and piezoelectric sorption measurements reported in the literature. The data are in excellent agreement with the values reported, correlate well with the Vrentas–Duda free volume theory, and can also be predicted from infinitely dilute data using the free volume theory. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1279–1290, 1997

Predicting ability of free-volume theory for solvent self-diffusion coefficients in rubbers

The effect of solvent size on the diffusion process is studied for various solvents with natural rubber and polybutadiene in terms of the free-volume theory. The importance of energy effects on the diffusion of penetrants in rubbers is examined. The critical molar volume of the polymer jumping unit is correlated with its glass transition temperature over the range 172 K to 305 K. The correlation shows a linear relationship between these two properties and can be used to predict one of the most sensitive free-volume parameters. Using this parameter in conjunction with the Vrentas-Duda free-volume theory, solvent self-diffusion coefficients in rubbers are then predicted over wide ranges of concentration and temperature. For all the systems, the predictions are comparable with experimental data. © 1996 John Wiley & Sons, Inc.

Predicting ability of free‐volume theory for solvent self‐diffusion coefficients in rubbers

The effect of solvent size on the diffusion process is studied for various solvents with natural rubber and polybutadiene in terms of the free-volume theory. The importance of energy effects on the diffusion of penetrants in rubbers is examined. The critical molar volume of the polymer jumping unit is correlated with its glass transition temperature over the range 172 K to 305 K. The correlation shows a linear relationship between these two properties and can be used to predict one of the most sensitive free-volume parameters. Using this parameter in conjunction with the Vrentas-Duda free-volume theory, solvent self-diffusion coefficients in rubbers are then predicted over wide ranges of concentration and temperature. For all the systems, the predictions are comparable with experimental data. © 1996 John Wiley & Sons, Inc.

Diffusion of Solvents in Polybutadiene Rubber Using Capillary Column Inverse Gas Chromatography

Abstract The capillary column inverse gas chromatography (CCIGC) method at infinite dilution of solvent was used to measure the diffusion and partition coefficients of cyclohexane, toluene, n-heptane, chloroform and methyl ethyl ketone in polybutadiene (BR, 95% cis). Experiments were performed over a temperature range of 0 to 70°C. Chromatographic data analysis was carried out in terms of the elution model described by Pawlisch and coworkers. Attempts to conduct experiments at temperatures below 0°C yielded erroneous results. At these low temperatures the high activity of the solvent causes the system to be far from the linear portion of the absorption isotherm or in some cases results in condensation in the capillary column. The Vrentas-Duda free-volume diffusion model was used to interpret and correlate the diffusion data obtained at infinite dilution of the solvent.

Diffusion of organic solvents in isobutylene-based polymers

Diffusion behavior of several organic solvents in polyisobutylene (PIB) and in poly(p-methylstyrene-co-iso-butylene) (PMS-BR) with different monomer ratios has been studied. The experiments have been conducted over a temperature range of 50 to 100°C using a conventional gravimetric Sorption technique. The PMS-BR copolymers contained 2, 7, and 15 weight percent p-methylstyrene, respectively. Although employing temperatures were far above the glass transition temperatures of polymers, the diffusion coefficients are correlated well with the Vrentas-Duda free-volume theory. For all the solvents, the PIB shows the highest diffusivity while the copolymer with the 15% p-methylstyrene gives the lowest value. This behavior can be explained by the amount of fractional free-volume present in a system.

Use of Solvent Free-Volume Parameters from13C Relaxation to Study Polymer/Solvent Diffusion Behavior

Variable temperature 13 C nuclear magnetic resonance (NMR) spin-lattice (T 1 ) relaxation studies were carried out using pure ethylbenzene, tetrahydrofuran, and methanol samples. Single correlation times, determined from an isotropic rotational diffusion model, were correlated successfully using the free-volume equation. The solvent free-volume parameters estimated in this study were comparable with those determined from viscosity measurements. The solvent free-volume parameters estimated in this study were then used to correlate and predict diffusion behavior of polymer/solvent systems. The results were comparable with those using the parameters from viscometry when the Vrentas-Duda free-volume diffusion model was used.

1,3,5-triisopropylbenzene diffusion in polystyrene solutions

Self-diffusion coefficients of 1,3,5-triisopropylbenzene (TIB) in binary solutions with polystyrene and ternary mixtures comprised of TIB, toluene, and polystyrene have been measured by static gradient nuclear magnetic resonance (SG-NMR) techniques. These data, as well as mutual-diffusion coefficient data measured by capillary column inverse gas chromatography (CCIGC), have been analyzed here with the Vrentas-Duda free-volume diffusion model. Although both binary and ternary diffusion coefficient data can be accurately correlated with the model, the results contradict those of an earlier investigation, which suggested that TIB diffuses as a single unit in polystyrene solutions. The new data suggest that either: 1) TIB diffuses by piece-wise displacements in polystyrene solutions, or 2) a diffusive activation energy ceiling value has been reached. The implications of both possibilities are discussed in the context of established free-volume principles. © 1996 John Wiley & Sons, Inc.

1,3,5‐triisopropylbenzene diffusion in polystyrene solutions

Self-diffusion coefficients of 1,3,5-triisopropylbenzene (TIB) in binary solutions with polystyrene and ternary mixtures comprised of TIB, toluene, and polystyrene have been measured by static gradient nuclear magnetic resonance (SG-NMR) techniques. These data, as well as mutual-diffusion coefficient data measured by capillary column inverse gas chromatography (CCIGC), have been analyzed here with the Vrentas-Duda free-volume diffusion model. Although both binary and ternary diffusion coefficient data can be accurately correlated with the model, the results contradict those of an earlier investigation, which suggested that TIB diffuses as a single unit in polystyrene solutions. The new data suggest that either: 1) TIB diffuses by piece-wise displacements in polystyrene solutions, or 2) a diffusive activation energy ceiling value has been reached. The implications of both possibilities are discussed in the context of established free-volume principles. © 1996 John Wiley & Sons, Inc.