Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

CO2/离子液体体系热力学性质的分子动力学模拟

超临界CO2和离子液体(ILs)是两种绿色溶剂. 离子液体可以溶解超临界CO2, 而超临界CO2不能溶解离子液体. 由此设计构成的CO2/IL二元系统, 同时具备了超临界CO2和离子液体的许多优点: 既可以降低离子液体的粘度, 还便于相分离, 是新型的耦合绿色溶剂. 其物理化学性质对于设计反应、分离等过程非常重要. 因此, 本文以CO2/IL二元系统为研究对象, 通过选择合适的分子力场和系综, 运用分子动力学(MD)模拟方法研究了CO2/[bmim][PF6]、CO2/[bmim][NO3]等体系的热力学性质. 结果表明, CO2对ILs膨胀度的影响非常小, 当CO2摩尔分数为0.5时, ILs膨胀仅为15%. CO2/ILs的扩散系数远小于CO2膨胀甲醇、乙醇溶液的扩散系数. 随着CO2含量的增加, ILs的扩散系数提高, 粘度显著下降, 表明CO2能有效地改善ILs扩散性, 减小其粘度. 因此CO2可用以改善离子液体溶剂体系的传递特性, 增强反应分离过程在其中的进行.     

Origin and influence of water‐induced chain relaxation phenomena in chitosan biopolymers

Chain dynamics, probed by dielectric spectroscopy, provide a route to further understanding of the molecular interactions induced by hydration, degree of crosslinking, and microstructural changes occurring on swelling of biopolymers such as chitosan, which is becoming a focus for biomedical engineering and therapeutic delivery. The basis of the β‐wet relaxation peak is established as segmental chain relaxation between chitosan water bridges and related to its hysteresis induced by microstructural changes during wetting and dewetting cycles. Linear expansion probes the hysteresis arising from bridging water interactions during the hydration–dehydration paths which is also shown in the resultant ionic conductivity. β‐wet relaxation and ionic conductivity exhibit identical hysteresis behavior with both degrees of chemical crosslinking and water contents. X‐ray diffraction shows that the degree of crosslinking and hydration also influences the degree of disorder of the polymer chains changing both the crystalline phase fraction and lattice dimensions. These molecular interactions provide power law behavior between β‐wet relaxation dynamics and ionic mobility over five orders of magnitude for all degrees of chemical crosslinking and water bridging which is independent of the significant hysteresis in these properties indicative of scaling behavior within the noncrystalline gel phase. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

The Soret effect in dilute polymer solutions: influence of chain length, chain stiffness, and solvent quality

Thermal diffusion in dilute polymer solutions is studied by reverse nonequilibrium molecular dynamics. The polymers are represented by a generic bead-spring model. The influence of the solvent quality on the Soret coefficient is investigated. At constant temperature and monomer fraction, a better solvent quality causes a higher affinity for the polymer to the cold region. This may even go to thermal-diffusion-induced phase separation. The sign of the Soret coefficient changes in a symmetric nonideal binary Lennard-Jones solution when the solvent quality switches from good to poor. The known independence of the thermal diffusion coefficients of the molecular weight is reproduced for three groups of polymers with different chain stiffnesses. The thermal diffusion coefficients reach constant values at chain lengths of around two to three times the persistence length. Moreover, rigid polymers have higher Soret coefficients and thermal diffusion coefficients than more flexible polymers.     

Transport properties of solid polymer electrolytes prepared from oligomeric fluorosulfonimide lithium salts dissolved in high molecular weight poly(ethylene oxide)

Transport properties such as ionic conductivity, lithium transference number, and apparent salt diffusion coefficient are reported for solid polymer electrolytes (SPEs) prepared using several oligomeric bis[(perfluoroalkyl)sulfonyl]imide (fluorosulfonimide) lithium salts dissolved in high molecular weight poly(ethylene oxide) (PEO). The salt series consists of polyanions in which two discrete fluorosulfonimide anions are linked together by [(perfluorobutylene)disulfonyl]imide linker chains. The restricted diffusion technique was used to measure the apparent salt diffusion coefficients in SPEs, and cationic transference numbers were determined using both potentiostatic polarization and electrochemical impedance spectroscopy methods. A general trend of diminished salt diffusion coefficient with increasing anion size was observed and is opposite to the trend observed in ionic conductivity. This unexpected finding is rationalized in terms of the cumulative effects of charge carrier concentration, anion mobility, ion pairing, host plasticization by the anions, and salt phase segregation on the conductivity.     

Effect of polymer architecture on self‐diffusion of LC polymers

Two LC side‐group poly(methacrylates) were synthesized, and their melt dynamics were compared with each other and a third, main‐chain side‐group combined LC polymer. A new route was developed for the synthesis of the poly(methacrylate) polymers which readily converts relatively inexpensive perdeuteromethyl methacrylate to other methacrylate monomers. Self‐diffusion data was obtained through the use of forward recoil spectrometry, while modulus and viscosity data were measured using rotational rheometers in oscillatory shear. Diffusion coefficients and complex viscosity were compared to previous experiments on liquid crystal polymers of similar architecture to determine the effect of side‐group interdigitation and chain packing on center of mass movement. The decyl terminated LC side‐group polymer possessed an interdigitated smectic phase and a sharp discontinuity in the self‐diffusion behavior at the clearing transition. In contrast, the self‐diffusion behavior of the methyl terminated LC side‐group polymer, which possessed head‐to‐head side‐group packing, was seemingly unaffected by the smectic–nematic and nematic–isotropic phase transitions. The self‐diffusion coefficients of both polymers were relatively insensitive to the apparent glass transition. The presence of moderately fast sub‐T_g chain motion was supported by rheological measurements that provided further evidence of considerable molecular motion below T_g. The complex phase behavior of the combined main‐chain side‐group polymer heavily influenced both the self‐diffusion and rheological behavior. Differences between the self‐diffusion and viscosity data of the main‐chain side‐group polymer could be interpreted in terms of the defect structure. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 405–414, 1999     

Study of the self‐diffusion of poly(ethylene glycol)s in poly(vinyl alcohol) aqueous systems

We have measured the self‐diffusion coefficients of a series of oligo‐ and poly(ethylene glycol)s with molecular weights ranging from 150 to 10,000, in aqueous solutions and gels of poly(vinyl alcohol) (PVA), using the pulsed‐gradient spin‐echo NMR techniques. The PVA concentrations varied from 0 to 0.38 g/mL which ranged from dilute solutions to polymer gels. Effects of the diffusant size and polymer concentration on the self‐diffusion coefficients have been investigated. The temperature dependence of the self‐diffusion coefficients has also been studied for poly(ethylene glycol)s with molecular weights of 600 and 2,000. Several theoretical models based on different physical concepts are used to fit the experimental data. The suitability of these models in the interpretation of the self‐diffusion data is discussed. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2396–2403, 1999     

Calculation of diffusion coefficients for carbon dioxide + solute system near the critical conditions by non-equilibrium molecular dynamics simulation

A non-equilibrium molecular dynamics simulation was adopted to calculate the diffusion coefficients for a pseudo-binary system of carbon dioxide and for a carbon dioxide + solute system at 308.2 and 318.2 K. The calculated results were compared with the self- and tracer diffusion coefficients calculated by an equilibrium molecular dynamics simulation. The simulated results for the pseudo-binary system of carbon dioxide by the non-equilibrium molecular dynamics simulation are in good agreement with the results of self diffusion coefficients for pure carbon dioxide by the equilibrium molecular dynamics simulation. The simulated results of mutual diffusion coefficients for the carbon dioxide + solute system by the non-equilibrium molecular dynamics simulation are slightly lower than the results of the tracer diffusion coefficients by the equilibrium molecular dynamics simulation. The anomalous behavior of diffusion coefficients near the critical concentration was represented by the results of the non-equilibrium molecular dynamics simulation.     

Phase behaviors of polymer solutions using molecular simulation technique

Phase behaviors of polymer solutions are estimated using a combination of thermodynamic models and molecular simulation technique. In general, many parameters of binary systems are determined by fitting a thermodynamic model with experimental data. In this study, we obtained all parameters using molecular simulation. To take the specific interaction into account, we assume that it only occurs between a solvent molecule and a specific group. Our results show that the theoretical treatment accounting for the specific interaction gives more accurate predictions than those without consideration of specific interaction. Also, our approach describes the phase equilibria of various polymer solutions over the entire concentration remarkably well.     

Solvent diffusion in amorphous glassy polymers

In this article, a mathematical model is proposed for predicting solvent self‐diffusion coefficients in amorphous glassy polymers based on free volume theory. The basis of this new model involves consideration of the plasticization effects induced by small molecular solvents to correctly estimate the hole‐free volume variation above and below the glass‐transition temperature. Solvent mutual‐diffusion coefficients are calculated using free volume parameters determined as in the original theory. Only one parameter, which can be predicted by thermodynamic theory, is introduced to express the plasticization effect. Thus, this model permits the prediction of diffusion coefficients without adjustable parameters. Comparison of the values calculated by this new model with the present experimental data, including benzene, toluene, ethyl benzene, methyl acetate, and methyl ethyl ketone (MEK) in polystyrene (PS) and poly(methyl methacrylate) (PMMA), has been performed, and the results show good agreement between the predicted and measured values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 846–856, 2000     

Prediction of solvent diffusion coefficient in amorphous polymers based on an equation‐of‐state

This study develops a modified free‐volume model to predict solvent diffusion coefficients in amorphous polymers by combining the Vrentas–Duda model with the Simha–Somcynsky (S‐S) equation‐of‐state (EOS), and all the original parameters can be used in the modified model. The free volume of the polymer is estimated from the S‐S EOS together with the Williams‐Landel‐Ferry fractional free volume, and the complex process of determining polymer free‐volume parameters in the Vrentas–Duda model and measuring polymer viscoelasticity can be avoided. Moreover, the modified model includes the influence of not only temperature but also pressure on solvent diffusivity. Three common polymers and four solvents are employed to demonstrate the predictions of the modified model. The calculation results are generally consistent with the experimental values. It is reasonable to expect that the modified free‐volume model will become a useful tool in polymer process development. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1000–1009, 2006     

Computer‐Aided Estimation of Diffusion Coefficients in Non‐Solvent/Polymer Systems

A novel method for estimating the mutual and self‐diffusion coefficients of a non‐solvent/polymer system is proposed in this work. The idea is to study the evaporation process from non‐solvent/solvent/polymer systems as a one‐dimensional numerical experiment and to use polymer solution weight versus time data to fit the unknown parameters of the diffusion‐coefficient correlations based on free‐volume theory. For this purpose, the evaporation process is modeled as a coupled heat‐ and mass‐transfer problem with a moving boundary, and the Galerkin finite‐element method is used to solve simultaneously the non‐linear governing equations. This method is successfully applied to the estimation of water–cellulose acetate diffusion coefficients and is valid over the whole range of temperatures and concentrations for practical applications in membrane technology. Additionally, there is a detailed discussion on if water affects the morphology of the final cellulosic membrane by studying the concentration profiles of the constituents of the casting solution.     

Effect of side‐chain length on the electrospinning of perfluorosulfonic acid ionomers

The effect of the side‐chain length (short side chain and long side chain, SSC and LSC, respectively) of perfluorosulfonic acid (PFSA) ionomers on the properties of nanofibers obtained by electrospinning ionomer dispersions in high dielectric constant liquids has been investigated with a view to obtaining electrospun webs as components of fuel cell membranes. Ranges of experimental conditions for electrospinning LSC and SSC PFSAs have been explored, with a scoping of solvents, carrier polymer and PFSA ionomer concentrations, and carrier polymer molecular weight. Under optimal conditions, the electrospun mats derived from SSC and from LSC PFSA show distinct fiber dimensions that arise from the different chain lengths of the respective ionomers. Enhanced interchain interactions in SSC PFSA with low equivalent weight compared to LSC PFSA result in a considerably lower average fiber diameter and a markedly narrower fiber size distribution. The proton conductivity of nanofiber mats of SSC and LSC PFSA with equivalent weights of 830 and 900 g mol^?1, respectively, are 102 and 58 mS cm^?1 at 80°C and 95% relative humidity. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Self‐diffusion of styrene, 2,2′‐azobisisobutyronitrile,and polystyrene in bulk polymerization by pulsed‐gradient spin‐echo nuclear magnetic resonance spectroscopy

The self‐diffusion of styrene, polystyrene, and 2,2′‐azobisisobutyronitrile has been determined in the bulk polymerization of styrene with pulsed‐gradient spin‐echo nuclear magnetic resonance at 25 °C. Data on small molecules are discussed with respect to recent diffusion models. They can fit self‐diffusion coefficient data of small molecules in dilute or semidilute polymer solutions; in concentrated solutions, however, there is a breakdown. A semiempirical model based on scaling laws is used to describe the self‐diffusion of styrene and 2,2′‐azobisisobutyronitrile over the whole range of concentrations studied. The dependence of the polystyrene self‐diffusion coefficient on the polymer concentration is described with a stretched exponential function, D = D₀ exp(?αc^ν), where α depends on the molecular weight of the polymer and ν depends on the kind of solvent. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1605–1614, 2003     

Polymer solubility in mixed solvents

Modeling results indicate that polymer chains in mixtures of a good with a bad solvent exhibit preferential adsorption of the good solvent. That phenomenon is found to be strongly dependent on molecular weight and it increases with a decrease in chain length. These results have important consequences on polymer solubility. Thus, a low molecular weight chain in a solvent mixture behaves as if it were dissolved in the pure good solvent component, whereas the solubility of a longer chain is controlled by the average mixture composition. As a result, quenching a polydisperse system below the cloud point may induce molecular weight segregation between the two phases: the longer chains, which precipitate out first, tend to populate the polymer rich phase whereas the shorter chains, having greater solubility, remain in the solvent phase. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2782–2787, 1999     

Water‐mediated transport in ion‐containing polymers

Water‐mediated ion conduction enables high conductivity in hydrated polymer membranes commonly used in electrochemical devices. Understanding the coupling of the absorbed water with the polymer matrix and the dynamics of water inside the polymer network across the full range of length scales in the membrane is important for unraveling the structure–property relationships in these materials. By considering the water behavior in ion‐containing polymers, next‐generation fuel cell membranes are being designed that exceed the conductivity of the state‐of‐the‐art materials and have optimized conductivity and permeability that may be useful in other types of devices such as redox flow batteries. Water–polymer associations can be exploited to tune the transport and mechanical property tradeoffs in these polymers. Measurements of water motion provide important criteria for assessing the factors that control the performance of these types of materials. This review article discusses current understanding of water behavior in ion‐containing polymers and the relationship between water motion and ion and molecular transport. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Salt Responsive Morphologies of ssDNA‐Based Triblock Polyelectrolytes in Semi‐Dilute Regime: Effect of Volume Fractions and Polyelectrolyte Length

A comprehensive study is reported on the effect of salt concentration, polyelectrolyte block length, and polymer concentration on the morphology and structural properties of nanoaggregates self‐assembled from BAB single‐strand DNA (ssDNA) triblock polynucleotides in which A represents polyelectrolyte blocks and B represents hydrophobic neutral blocks. A morphological phase diagram above the gelation point is developed as a function of solvent ionic strength and polyelectrolyte block length utilizing an implicit solvent ionic strength method for dissipative particle dynamics simulations. As the solvent ionic strength increases, the self‐assembled DNA network structures shrinks considerably, leading to a morphological transition from a micellar network to worm‐like or hamburger‐shape aggregates. This study provides insight into the network morphology and its changes by calculating the aggregation number, number of hydrophobic cores, and percentage of bridge chains in the network. The simulation results are corroborated through cryogenic transmission electron microscopy on the example of the self‐assembly of ssDNA triblocks.     

Nanoparticle arrangements in block copolymer particles with microphase‐separated structures

In this study, metal‐polymer particles with microphase‐separated structures were prepared by self‐organized precipitation, where a good solvent is evaporated from a solution that also contains block copolymer, Au NPs, and a poor solvent. Control of the microphase‐separated structure in composite particles consisting of Au NPs and block copolymer was accomplished by changing the Au NP size, the mix ratio, and the copolymerization ratio of the block copolymer. The morphology of the inner structures was changed from a lamellar phase to a spherical phase by increasing the Au NP concentration. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Transport coefficients of aqueous dodecyltrimethylammonium bromide solutions: comparison between experiments, analytical calculations and numerical simulations

We study dynamical properties of ionic species in aqueous solutions of dodecyltrimethylammonium bromide, for several concentrations below and above the critical micellar concentration (cmc). New experimental determinations of the electrical conductivity are given which are compared to results obtained from an analytical transport theory; transport coefficients of ions in these solutions above the cmc are also computed from Brownian dynamics simulations. Analytical calculations as well as the simulation treat the solution within the framework of the continuous solvent model. Above the cmc, three ionic species are considered: the monomer surfactant, the micelle and the counterion. The analytical transport theory describes the structural properties of the electrolyte solution within the mean spherical approximation and assumes that the dominant forces which determine the deviations of transport processes from the ideal behavior (i.e., without any interactions between ions) are hydrodynamic interactions and electrostatic relaxation forces. In the simulations, both direct interactions and hydrodynamic interactions between solutes are taken into account. The interaction potential is modeled by pairwise repulsive 1/r(12) interactions and Coulomb interactions. The input parameters of the simulation (radii and self-diffusion coefficients of ions at infinite dilution) are partially obtained from the analytical transport theory which fits the experimental determinations of the electrical conductivity. Both the electrical conductivity of the solution and the self-diffusion coefficients of each species computed from Brownian dynamics are compared to available experimental data. In every case, the influence of hydrodynamic interactions (HIs) on the transport coefficients is investigated. It is shown that HIs are crucial to obtain agreement with experiments. In particular, the self-diffusion coefficient of the micelle, which is the largest and most charged species in the present system, is enhanced when HIs are included whereas the diffusion coefficients of the monomer and the counterion are roughly not influenced by HIs.     

Phase separation in binary mixtures containing polymers: A quantitative comparison of single-chain-in-mean-field simulations and computer simulations of the corresponding multichain systems

We discuss a phenomenological, coarse-grained simulation scheme, single-chain-in-mean-field (SCMF) simulation, for investigating the kinetics of phase separation in dense polymer blends and mixtures of polymers and solvents. In the spirit of self-consistent-field calculations, we approximate the interacting multichain problem by that of a single chain in an external field, which, in turn, depends on the local densities of the components. To study the time evolution of the mixture, we perform an explicit Monte Carlo (MC) simulation of an ensemble of independent chains in the external field and periodically calculate the average densities and update the external field. Unlike dynamic self-consistent-field theory, these SCMF simulations do not assume that the chain conformations relax much more quickly than the density and incorporate the single-chain dynamics explicitly rather than via an Onsager coefficient. This allows us to study systems with large spatial inhomogeneities and dynamic asymmetries. To assess the accuracy and limitations of the simulation scheme, we compare the results of SCMF simulations using a discretized Edwards Hamiltonian with computer simulations of the corresponding multichain system for (1) the early stages of spinodal decomposition of a symmetric binary polymer blend in response to a quench from χN = 0.314 to χN = 5 (where χ is the Flory–Huggins parameter and N is the number of segments), for which the growth rate of composition fluctuations is compared with MC simulations of the bond fluctuation model and alternative dynamic self-consistent-field calculations, and (2) the evaporation of a solvent from a low-molecular-weight thin polymer film, for which a comparison is made with molecular dynamics (MD) simulations of a bead-necklace model with a monomeric solvent. In the latter case, the polymer conformations are extracted from MD simulations and modeled in the SCMF simulations by a discretized Edwards Hamiltonian augmented by a chain-bending potential. From the MD simulations of thin polymer films in equilibrium with its vapor, phase coexistence has been determined, and the second- and third-order virial coefficients in the SCMF simulations have been adjusted accordingly. Finally, MD simulations of bulk solutions of a polymer and a solvent over a range of compositions, as well as the pure solvent at various densities, have been performed to determine self-diffusion coefficients that enter the SCMF simulations in the form of density-dependent segmental mobilities. A comparison of the polymer and solvent profiles in a thin film as a function of time and the fraction of the solvent evaporating from a solvent-swollen film, as obtained from MD simulations and parameterized SCMF simulations, shows satisfactory agreement for this simple mapping procedure. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 934–958, 2005