A generalized method to calculate diffusion rates in polydisperse systems. Further results on Rouse dynamics in the concentrated regime (original) (raw)
Related papers
Liquid−Liquid Limited-Supply Diffusion Studies in the Polystyrene−Poly(vinyl methyl ether) Pair
Macromolecules, 2004
Liquid-liquid diffusion at the interphase between poly(vinyl-methyl ether) (PVME) and polystyrene (PS) was experimentally studied using confocal Raman microspectroscopy. A combination of a specially designed experimental setup and a direct and precise quantification for the corrections to be applied to the Raman measurements allowed us to measure directly the PVME concentration along the diffusion path for a wide range of diffusion times. An already proposed and tested liquid-liquid diffusion model (based on liquid dynamics controlled by monomeric friction coefficients) was used to correlate and predict the detailed shape of the PVME concentration profiles and the diffusion rates as functions of diffusion time and temperature. The results obtained allowed us to discern among several approaches previously proposed in the literature to calculate monomeric friction coefficients in this system. Only the approach that considers independent monomeric friction coefficient values for PS and PVME (obtained from tracer diffusion measurements) gave good agreement between experimental results and model calculations. Calculations performed using literature data for a common monomeric friction coefficient for both PS and PVME (obtained from estimated blend viscosity data) do not agree with experimental measurements. The success of the model used for this work clearly ruled out the need for combinations of Fickean and Case II models used previously to describe PS-PVME polymer diffusion.
Polymer, 2002
Diffusion between a liquid polystyrene and a glassy poly(phenylene oxide) matrix is experimentally studied over a wide range of temperatures and diffusion times, using confocal Raman microspectroscopy. A specially designed experimental setup allows precise direct following of time evolution of the chemical composition profiles along the diffusion path. A direct and precise quantification is made for the experimental errors involved in two methods used for Raman measurements. An already proposed diffusion model is used to predict the time evolution of the advancing composition profiles along the diffusion path, and gives precise results. Experimental thermodynamic and kinetic data taken from literature are used for the model calculations, and excellent agreement with experimental results is obtained. Diffusion slow down is confirmed at the lowest diffusion temperature used, and probable causes are discussed.
Journal of Polymer Engineering, 2005
Attenuated Total Reflection (ATR) spectroscopy was used to study the interdiffusion mechanism at the interface of Polystyrene (PS) and Poly(vinyl methyl ether) (PVME), at temperatures above and below the glass transition temperature (T g) of PS, but in the miscible region. One molecular weight of PVME and 13 molecular weights of PS, both below and above the critical molecular weights of PS were used to investigate the effect of molecular weight on mutual diffusion process both below and above the critical molecular weight for entanglements of PS. To extract the diffusion coefficient from experimental data, we used the approach suggested by Jabbari and Pepas. Both Fickian and Case-II diffusion were necessary to fit the PVME concentration profile for the various molecular weights. The experimental results were also compared with the slow-mode and the fast mode theories2-3.
Diffusion Coefficient Matrix in Nonionic Polymer−Solvent Mixtures
Journal of Physical Chemistry B - J PHYS CHEM B, 2001
Recent predictive equations for evaluating the value of diffusion coefficients, developed for two hard spheresolvent systems, have been extended to n-hard-sphere-solvent systems. This model has been used to predict the diffusion behavior of nonionic polymer-solvent mixtures as a first-order function of volume fraction from the knowledge of the distribution function. Hence, the entire diffusion matrix for polydisperse systems, which include both main-and cross-term diffusion coefficients, has been built up for the first time. The main-terms diffusion coefficients D ii are mostly affected by the variation in viscosity. The magnitude of the cross-term diffusion coefficients D ij is strictly related to the abundance and diffusivity of solute i and to the molecular volume corresponding to solute j. The predicted diffusion coefficients have been used to calculate the apparent, average diffusion coefficients, which are compared with the experimental values measured by the Gouy interferometry method in the case of the poly(ethylene glycol) homologous series. The agreement between the calculated and experimental Gouy parameters is good. The cross-term diffusion coefficients are found to be significant in the calculation of the apparent diffusion coefficient for a polydisperse solute. Some comments on the study of ternary systems containing a polydisperse solute are done.
Diffusion in polymer-polymer mixtures
Journal of Polymer Science Part B: Polymer Physics, 1987
Two equations have recently been proposed to relate the mutual diffusion coefficient of a binary polymer-polymer mixture to the two tracer (self) diffusion
Journal of Polymer Science Part B: Polymer Physics, 1999
A comparison between various methods to determine diffusion coefficients of polymers in dilute solutions has been made. It is shown that Taylor dispersion analysis (TDA), dynamic light scattering (DLS), hydrodynamic chromatography (HDC), and size exclusion chromatography (SEC) can all be used to accurately determine diffusion coefficients when the polymer samples have low polydispersities. By the analysis of a series of practically representative styrene acrylonitrile copolymer (SAN) samples, it is shown that polydispersity of the samples and the presence of lowmolecular-mass material cause considerable differences between the methods. It was found that TDA is mostly disturbed by the presence of low-molecular-mass material, whereas DLS is more sensitive to the polydispersity of the polymer. With broad samples, DLS gives the Z-average diffusion coefficient. SEC can be used to obtain a diffusion coefficient distribution as well as an average diffusion coefficient of a polydisperse sample. Although, the same was expected for HDC, it was found that this method could only be successfully used for polymer samples having low polydispersities. Deviations between SEC, HDC, and TDA found for narrow samples were not related to the chemical composition of the samples.
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.
Self-diffusion of polydisperse linear polymers
Journal of Non-Crystalline Solids, 1991
Self-diffusion coefficients are measured at 145°C for model linear polymers by a method that uses SANS to follow homogenization of initially segregated layers of conventional and deuterated polymers. Monodisperse (Nw/N n <1.1) and polydisperse (Nw/Nn = 1.5) systems having the same weight average degree of polymerization N w were measured. Diffusion coefficients for the two systems are essentially identical, in accord with a simple model in which all chains diffuse by reptation.
Diffusion Coefficients of Additives in Polymers. I. Correlation with Geometric Parameters
Diffusion coefficients of a broad range of molecules with molecular weight ranging from 100 to 800 g/mol have been measured in polypropylene, by solid/solid contact methods (without liquid contact), at 40°C. The behaviors of the different molecules are compared to those of linear alkanes. The diffusion coefficients are correlated to parameters describing size, shape, and flexibility of the molecules. The concept of weighted fractionated volume is introduced using molecular modeling. It enables the classification of the molecules according to modes of molecule displacement (crawling, jumps, or dual mode).