On the Pace–Datyner theory of diffusion of small molecules through polymers (original) (raw)

Transition-State Theory Model for the Diffusion Coefficients of Small Penetrants in Glassy Polymers

Macromolecules, 1997

Previous molecular dynamics simulations have shown that the diffusion of a penetrant in a glassy polymer involves occasional jumps between cavities through the opening of a "neck", and thus, because this is a rare event, the diffusion coefficient can be estimated using transition-state theory. We treat this process as a unimolecular rearrangement and develop semiempirical means of estimating the activation energy, frequency factor and jump length. The activation energy is obtained by treating the polymer as a continuous solid and calculating the energy required to expand a neck in that continuum. The model for the frequency factor uses the result from simulations that the distribution of frequencies of the modes in the transition is very similar to that distribution for the reactant state. The frequency factor is estimated by considering only the motion of the penetrant. These motions are treated as harmonic oscillators. The jump length is obtained from simple geometric considerations of the polymer chain. The parameters are readily evaluated from bulk properties of the polymer such as the isothermal compressibility. The model reproduces experimental trends semiquantitatively and could be used to interpolate and extrapolate experimental diffusion data.

Multicomponent Diffusion of Penetrant Mixtures in Rubbery Polymers: A Molecular Dynamics Study

Bulletin of the American Physical Society, 2016

Chemical Biological Center-The importance of understanding transport of chemical species across liquid-solid boundaries is of particular interest in the decontamination of harmful chemicals absorbed within polymeric materials. To characterize processes associated with liquid-phase extraction of absorbed species from polymers, it is necessary to determine an appropriate physical description of species transport in multicomponent systems. The Maxwell-Stefan (M-S) formulation is a rigorous description of mass transport in multicomponent solutions, in which, mutual diffusivities determine the degree of relative motion between interacting molecules in response to a chemical potential gradient. The work presented focuses on the determination of M-S diffusivities from molecular dynamics (MD) simulations of nerve agent O-ethyl S-[2(diisopropylamino)ethyl] methylphosphonothioate (VX), water, and methanol mixtures within a poly(dimethylsiloxane) matrix. We investigate the composition dependence of M-S diffusivities and compare the results to values predicted using empirical relations for binary and ternary mixtures. Finally, we highlight the pertinent differences in molecular mechanisms associated with species transport and employ non-equilibrium MD to probe transport across the mixture-polymer interface.

Diffusion of small-molecule penetrants in semicrystalline polymers

Progress in Polymer Science, 1996

This paper is a review of the kinetics of diffusion of small-molecule penetrants in semi-crystalline polymers. The variations in diffusion impedance resulting from variations in morphology and segmental mobility in the amorphous component are highlighted. Deviations from Fickian diffusion appearing in many systems are discussed, as well as the effect of morphology, crystal orientation and chain orientation on the diffusivity.

Diffusion of small-molecule penetrants in polyethylene: free volume and morphology

Polymer, 1996

Based on desorption and permeation measurements, the diffusivity and solubility of n-hexane and oxygen have been obtained for a wide range of linear and branched polyethylenes (PEs) with crystallinities between o 3 6 l 40 and 97 Vo and mass-average molar masses between 10 and 10 g mol-. The morphology and contents of crystal core (CC), crystal-core-like lnterfaclal (Icc), liquid-like interfacial (Ih) and liquid (L) components • " 13 n were assessed by transmission electron microscopy, Raman spectroscopy, C cross-polarizatio / magic-angle spinning nuclear magnetic resonance spectroscopy, differential scanning calorimetry, density measurements and small-angle light scattering. The penetrant solubility in the non-crystalline phases increased with increasing concentration of chain ends and chain branches. This effect was masked at certain crystallinities by the constraining effect of the crystallites. The diffusivity selectivity of oxygen over n-hexane increased strongly with increasing crystallinity and decreasing non-crystalline layer thickness, demonstrating that the crystal-induced constraint on the non-crystalline chains more efficiently retards the diffusion of larger molecules. The fractional free volume of the non-crystalline components decreased strongly with increasing crystallinity in the low-crystallinity range (<60%), above which it remained practically constant. The latter is because the constraining effect of the crystals is compensated for by the plasticizing effect of the chain ends, which leads to a constant free volume in this crystallinity range. A model, based on the Cohen-Turnbull-Fujita (CTF) model, considering the polymers to consist of four components, CC, Icc, Ir and L, was applied to the diffusivity data. The branched PEs and the majority of the linear PEs could be described by the modified CTF model. However, the lowest-molar-mass linear PEs exhibited a considerably larger interfacial free volume than the other samples. Real-time Raman spectroscopy on CC14-swollen samples showed that the changes in the CC and Icc contents during sorption were only small.

Single molecule diffusion in polymeric systems

2019

By submitting this thesis electronically, I declare that the entirety of the work contained therein is my own, original work, that I am the sole author thereof (save to the extent explicitly otherwise stated), that reproduction and publication thereof by Stellenbosch University will not infringe any third party rights and that I have not previously in its entirety or in part submitted it for obtaining any qualification.

Diffusion of small penetrant molecules in polybutadienes

Molecular Physics, 2011

The diffusion coefficient D in the dilute limit for three different penetrants-oxygen, water, and methanol-in three different conformations of polybutadiene (all cis-1,4, all trans-1,4, and a random copolymer containing 50% trans-1,4, 40% cis-1,4, and 10% vinyl-1,2 repeat units) has been computed using molecular dynamics simulations for temperatures in the range T = 300-400 K. Simulations runs of 25 and 50 ns made for each of the 45 combinations of penetrant, conformation, and temperature studied. Over this temperature range the density of the all-cis-1,4 conformation is higher than that of the all-trans-1,4 and random copolymer conformations, which are approximately equal. For all three conformations, D for oxygen and water are comparable and larger than that of methanol. However for a given penetrant, strong differences were observed in the rate of increase of D for the three conformations. We find that the activation barriers for the three penetrants are generally between 20 and 30 kJ/mol, in agreement with experimental results. The magnitude of the activation energy is directly proportional to the size, rather than the mass, of the penetrant molecule.

Rate type equations for the diffusion in polymers: Thermodynamic constraints

AIChE Journal, 1993

ABSTRACT Conditions imposed by the second law of thermodynamics on viscoelastic rate type constitutive equations for the diffusive mass flux are considered. The analysis of three different rate type models proposed in the literature points out that presently physically unrealistic predictions are possible in desorption processes. The thermodynamic analysis of such models, based on the entropy inequality and on the stability requirement of the equilibrium states, leads to precise relationships among relaxation times, diffusion coefficients, and entropy equations of state. In particular, the analysis shows that relaxation times and diffusion coefficients cannot be simply constant numbers. When the thermodynamic constraints imposed on the constitutive equations are introduced, the models do not show physically unrealistic behaviors any more; Fickian diffusion close to the pure penetrant or pure polymer regions is also recovered. Finally, it is shown that the stability requirement for the equilibrium states may introduce very rigid requirements for the model feasibility, well beyond what appears explicitly from the kinetic equations alone.

Estimating diffusion coefficients for small molecules in polymers and polymer solutions

Polymer, 2001

The diffusion coefficient for small molecules (solvent or monomer) through polymer solutions in the vicinity of the glass transition are known to change by as much as six orders of magnitude with only a small change in polymer concentration. Experimental measurements are difficult in this region and consequently there are data for only a limited number of systems. A rather simple method to estimate these diffusion coefficients for the rubbery, glass transition, and glassy regions as a function of polymer concentration and application temperature is presented. While the method is empirical in nature, it is based on carefully executed experimental studies, sound scaling laws, and agrees extremely well with free volume theories in the rubbery region. The method only requires a knowledge of the pure polymer glass transition temperature in order to estimate the diffusivity of molecules like styrenic and acrylic monomers (molecular weight of approximately 100 g/mol) at any polymer concentration and for temperatures above and below the polymer glass point. ᭧