Enthalpy of mixing for polymer solutions based on Gibbs excess function limit of hard spheres mixtures

Enthalpy of mixing of polymer with solvent has been evaluated by the new polymer/solvent theory proposed by the authors in a previous article. The new theory was based on the excess Gibbs function limit of hard sphere mixtures with infinite size difference. The calculated enthalpy of mixing for polymer/solvent mixtures by the new theory, agreed with experimental data with good accuracy and indicated that the theory is capable to produce the enthalpy of mixing in the whole concentration range of polymer compared with Flory–Huggins theory. Also the calculations provided information on the studied polymer chains and the molecular interaction effects which were consistent with the properties of polymers and solvents used in the mixtures.     

A new theory for polymer/solvent mixtures based on hard-sphere limit

Based on hard-sphere limit of binary mixtures with different molecular size of components a theory has been developed for calculating activities of solvents in polymer/solvent mixtures. The theory considers various chain configurations for polymer molecules, varying from extended chain to the coiled chain. According to this theory the activity of solvent can be calculated from molecular weights (MWs) and densities as the only input data. The only adjustable parameter in the calculations, is the hard-sphere diameter of polymer, which provides useful criteria for the judgement on the chain configuration of polymer.The activity calculations have been performed for seven binary mixtures of polymer/solvent and compared with experimental data at various temperatures and for a varying range of MWs of polymers.The solvents in the mixtures were both of polar and nonpolar natures. The activity calculations for the same systems were performed by the well-known Flory-Huggins theory. Comparing the results of calculations with those of Flory-Huggins theory indicates that, the proposed theory is able to predict the activities of the solvent with good accuracy.The radius of gyration, excluded volume and interaction parameter for polymer chain have been calculated using the parameter obtained in the new theory. The calculated interaction parameter in the new theory, is interpreted in terms of attraction, repulsion and interchange energy of polymer and solvent in the mixture.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Solvent size effect on the depletion layer of a polymer solution near an interface

By varying polymer concentration phi0p and Flory-Huggins parameter chi, the effect of solvent size on the depletion interaction between polymer coils and a hard wall was investigated by the real-space version of self-consistent field theory (SCFT). The depletion profiles and depletion thickness indicated that the depletion effect is strong in less good solvent with large molecular volume. Through the analysis of the respective free energies of polymer coils and solvent molecules, we found that the increment in the translation entropy of the solvent is the key to strengthening the depletion interaction. On the basis of the SCFT results, we define a solvent with volume about one to six times that of the polymer segment as a "middle-sized solvent". The density oscillations previously studied by Van der Gucht et al. and Maassen et al. were also observed in our simulation, and the addition of middle-sized solvent will magnify the amplitude of the oscillations. The solvent-size-dependent depletion interaction may be an explanation for the reduced entanglement and promoted crystallization behavior of polymer coils prepared from the solution with middle-sized solvent.     

Solvent response of mixed polymer brushes

We have performed classical density functional theory calculations to study the behavior of mixed polymer brushes tethered to a planar surface. We assume no lateral segregation of the polymer at the grafting density studied and consider an implicit solvent. For a binary mixture of short and long athermal polymer chains, the short chain is compressed while the long chain is stretched compared with corresponding pure polymer chains at the same grafting density, which is consistent with simulation. This results from configurational entropy effects. Furthermore, we add a mean-field interaction for each polymer brush to simulate their different response towards a solvent. The long chain is forced to dislike the solvent more than the short chain. Through the interplay between the solvent effects and configurational entropy effects, a switch of the polymer brush surface (or outer) layer is found with increasing chain length of the long chain. The transition chain length (long chain) increases with increasing the solvent selectivity, and decreases with increasing the grafting density of the long chain. These results can provide guidance for the design of smart materials based on mixed polymer brushes.     

Volume Phase Transition of Polymer Networks in Polymeric Solvents

A strong concentration dependence of the solvent–polymer interaction parameter χ is known to be a requirement for the first‐order volume phase transition in uncharged polymer networks in solvents. Another possibility for the observation of phase transition in nonpolar networks is to increase the number of lattice sizes occupied by a solvent molecule. This possibility has been indicated earlier and is worked out in detail in this paper. Using the theory of swelling equilibrium, we examine the polymer network systems immersed in a polymer melt. The critical conditions for the phase transition in both uncharged and ionic networks are described.     

Solvent activity changes and phase separation during crosslinking of coating films

Changes in solvent activity and thermodynamic stability of a system undergoing crosslinking in the presence of a solvent are modeled by combination of branching theory with thermodynamics of polymer solutions and swelling of a crosslinked polymer. The system is considered as a quasiternary one in which the solvent, polydisperse soluble polymer (sol) and crosslinked network, respectively, represent the components. Crosslinking brings about growth of polymer structures but also changes in polymer-solvent interactions. The results are compared with onset of phase separation and changes in evaporation rates from films formed from a hydroxy-functional star oligomer and triisocyanate.     

Impact of solvent quality on nanoparticle dispersion in semidilute and concentrated polymer solutions

We investigated how solvent quality affects the stability of polymer-grafted nanoparticles in semidilute and concentrated polymer solutions, which extends our previous studies on these types of dispersions in good solvents [Langmuir 2008, 24, 5260-5269]. As discussed in the current article, dynamic light scattering (DLS) was used to quantify the diffusion of polydimethylsiloxane-grafted silica nanoparticles, or PDMS-g-silica, in bromocyclohexane as well as in PDMS/bromocyclohexane solutions. We established that bromocyclohexane is a theta solvent for PDMS by varying the temperature of the solutions with PDMS-g-silica nanoparticles and detecting their aggregation at a theta temperature of T(Θ) = 19.6 °C. Using this temperature as a benchmark for the transition between good and bad solvent conditions, further stability tests were carried out in semidilute and concentrated polymer solutions of PDMS in bromocyclohexane at T = 10-60 °C. Irrespective of temperature, i.e., solvent quality, we found that the nanoparticles dispersed uniformly when molecular weight of the graft polymer was greater than that of the free polymer. However, when the free polymer molecular weight was greater than that of the graft polymer, the nanoparticles aggregated. Visual studies were also used to confirm the correspondence between nanoparticle stability and graft and free polymer molecular weights in a wide range of marginally poor solvents with PDMS. Further, the correspondence between nanoparticle stability and instability with graft and free polymer molecular weight and solvent quality was also supported with self-consistent mean-field calculations. Thus, by relating experiment and theory, our results indicate that nanoparticle stability in semidilute and concentrated polymer solutions is governed by interactions between the graft and free polymers under conditions of variable solvency.     

Thermodynamic properties of some concentrated polymer solutions

Solubilities of several solvents were measured in four molten polymers by using an isobaric vapor-pressure apparatus. Solvent concentration ranged from 0.5 to 15 wt-%. The systems polyisoprene–benzene and polyisobutylene–benzene were studied at 80.0°C; polyisobutylene–cyclohexane was studied at 100.0°C; ethylene–vinyl acetate copolymer (EVA)–cyclohexane, EVA–isooctane, and poly(vinyl acetate)–isooctane were studied at 110.0°C. Of six polymer–solvent systems studied, all except poly(vinyl acetate)–isooctane appear to exhibit hysteresis in a single sorption–desorption cycle starting with dry polymer. The desorption curves of solvent activity plotted versus solvent weight fraction show an inflection point, suggesting localized adsorption of solvent molecules. Experimental data were analyzed with a theory which takes into account adsorption of solvent by polymer in addition to differences in free volumes and intermolecular forces. The theory gives a semiquantitative representation of the experimental data.     

高分子动力学的单链模型

高分子单链模型是高分子稀溶液理论研究的基本模型.对其进行深入地分析,不仅有助于解决高分子稀溶液体系中溶液黏度和分子链扩散等基本问题,而且能够增进人们对高分子链结构与溶液性质间关联性的理解.虽然基于经典连续性介质力学的流体动力学理论可以定性,甚至半定量地获得稀溶液的一些重要性质,但是,随着科学技术的发展,人们从分子水平上建立了许多描述高分子稀溶液性质的模型和理论,期望能够定量地描述高分子稀溶液的性质.本文以高分子稀溶液中3个典型的单链模型为例(包括:不含流体力学相互作用的Rouse模型、含二体流体力学相互作用的Zimm模型和含多体流体力学相互作用的部分穿透球模型),综述高分子稀溶液的重要性质,并详细地给出其动力学方程的推导过程及其重要的研究进展.特别是,对于Rouse模型,本文还将其预言结果拓展到了短链高分子流体体系;此外,还介绍了这一领域的关键科学问题、发展前景和研究方向.     

Theory of polymer fractionation efficiency

The theory of the equilibrium distribution of a mixture of different size species of a polymer between two liquid phases is reviewed and used as a basis for the calculation of the dependence of fractionation efficiency on overall concentration, interaction coefficient (hence, choice of solvent and temperature), average molecular weight, and the spread of the molecular weight distribution in the polymer. The special case of a single type of polymer in a single solvent, for which the polymer–solvent interaction coefficient is independent of concentration, is dealt with quantitatively. The ultimate aim is to make it possible to determine systematically the optimum solvent (or mixture of solvents), temperature, and overall concentration for fractionation of a given type of polymer, having a given average molecular weight and molecular weight distribution, considering practical limitations, e. g., the total volume which can conveniently be handled and the time required to achieve a sufficiently close approach to equilibrium.     

Investigating the Dynamic Viscoelasticity of Single Polymer Chains using Atomic Force Microscopy

In single‐molecule force spectroscopy (SMFS), many studies have focused on the elasticity and conformation of polymer chains, but little attention has been devoted to the dynamic properties of single polymer chains. In this study, we measured the energy dissipation and elastic properties of single polystyrene (PS) chains in toluene, methanol, and N,N‐dimethylformamide using a homemade piezo‐control and data acquisition system externally coupled to a commercial atomic force microscope (AFM), which provided more accurate information regarding the dynamic properties of the PS chains. We quantitatively measured the chain length‐dependent changes in the stiffness and viscosity of a single chain using a phenomenological model consistent with the theory of viscoelasticity for polymer chains in dilute solution. The effective viscosity of a polymer chain can be determined using the Kirkwood model, which is independent of the intrinsic viscosity of the solvent and dependent on the interaction between the polymer and solvent. The results indicated that the viscosity of a single PS chain is dominated by the interaction between the polymer and solvent. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1736–1743     

A dynamic density functional theory for particles in a flowing solvent

We present a dynamic density functional theory (dDFT) which takes into account the advection of the particles by a flowing solvent. For potential flows, we can use the same closure as in the absence of solvent flow. The structure of the resulting advected dDFT suggests that it could be used for nonpotential flows as well. We apply this dDFT to Brownian particles (e.g., polymer coils) in a solvent flowing around a spherical obstacle (e.g., a colloid) and compare the results with direct simulations of the underlying Brownian dynamics. Although numerical limitations do not allow for an accurate quantitative check of the advected dDFT both show the same qualitative features. In contrast to previous works which neglected the deformation of the flow by the obstacle, we find that the bow wave in the density distribution of particles in front of the obstacle as well as the wake behind it are reduced dramatically. As a consequence, the friction force exerted by the (polymer) particles on the colloid can be reduced drastically.     

Diffusion in polymer—solvent systems. I. Reexamination of the free-volume theory

The free-volume theory describing diffusion in polymer–solvent systems is reexamined. Calculation of the specific free volume for such systems is discussed, and equations are presented for the determination of the self-diffusion coefficients of the polymer and the solvent. Conditions under which the mutual diffusion coefficient can be deduced solely from free-volume considerations are clarified, and a more general version of the free-volume diffusion theory proposed by Fujita is presented. The further restrictions needed for the theory of Fujita are discussed, and it is concluded that these additional restrictions are responsible for failures of the Fujita theory.     

Towards a modellisation of the solvation energy in multi-component solvents. The interesting case of a charged solute imbedded in a polymer-containing electrolyte solution

In this paper we propose a mean-field theory to calculate the solvation free energy of a charged solute imbedded in a complex multi-component solvent. We considered a solvent made up of a mixture of small (electrolyte solution) and large (polymer) components. The presence of macromolecules ensures reduced mixing entropy among the different solvent components, an effect due to polymer connectivity. The reduced entropy favours strong preferential distribution of a particular solvent even in the presence of weak preferential solute–solvent interactions. In addition, two energy terms must be considered: (a) the interaction between the solute electrostatic potential and the electrolyte solution and (b) the formation of a polymer–solute interface. Because of the different dielectric permittivity of the solvent components, the electrolyte and polymer distribution functions are strongly coupled: ions, indeed, are more solvated in regions of higher local dielectric permittivity arising from the inhomogeneous mixing of solvent and polymer. We combined together the different energy terms in the framework of the de Gennes free energy functional for polymer solutions along with a generalised Poisson–Boltzmann equation developed for inhomogeneous dielectric media. Moreover, the preferential electrolyte solvation in regions of greater polarity was considered by an extension of the Born equation. Setting the polymer dielectric permittivity smaller than the solvent one and making null the specific polymer–solute interactions, we calculated enhanced electrolyte concentration and reduced polymer concentration near the solute surface on raising the solute surface charge density. The theory shows also the breakdown of the widely used separation between electrostatic and surface tension-dependent contributions to solvation energy when non-ideal mixed solvents are considered. In fact, according to the model, the surface tension of such mixed solvents strongly depends on the solute surface charge density: at high potentials the interfacial tension may increase rather than decrease on raising the polymer volume fraction. The theoretical results have been compared with experimental data on polymer+electrolyte solution surface tension and with solubility data of colloidal particles. The comparison evidences the complex behaviour of multi-component solvents going well beyond the trivial weighted average of the dielectric permittivity and surface tension of the isolated chemical components. Deviations from the simple behaviour predicted by an average picture of multi-component solvents could be understood by developing more sophisticated, but still simple, approaches like that proposed in this paper.Contribution to the Jacopo Tomasi Honorary Issue. This paper is dedicated to Jacopo Tomasi. I learned much of the difficult art of transforming complex problems into simple models after reading his early works on solvation energy.     

Molecular dynamics study of the methanol effect on the membrane morphology of perfluorosulfonic ionomers

The membranes of a perfluorosulfonic acid polymer swollen in 10-80 wt % methanol solution were investigated to elucidate the methanol effect on their morphologies, such as size of the solvent cluster, solvent location, and polymer structure, by using isothermal-isobaric molecular dynamics simulations. In higher methanol concentrations, we found less-spherical solvent aggregation and a more spread polymer structure because of the ampholytic nature of methanol. The partial radial distribution functions between solvent oxygen and fluorocarbons, which are composed of the main chain, clearly show that methanol is located closer to the polymer matrix than water. On the other hand, water is preferentially located in the vicinity of an acidic headgroup, SO(3)(-), compared with methanol, although both have similar attractive interaction energies to the acidic group. Furthermore, we discussed solvent dynamics and hydrogen bonding between sulfonic oxygen and solvent O-H groups.     

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.     

Morphology development of main‐chain liquid crystalline polymer fibers during solvent evaporation

A nonequilibrium thermodynamic approach has been developed for describing the emergence of fiber morphologies from a liquid crystalline polymer solution undergoing solvent evaporation, including fibrillar structures, concentric rings, and spiral structures. We utilized Matsuyama–Kato free energy for main‐chain liquid crystalline polymer (MCLCP) solutions, which is an extension of Maier–Saupe theory for nematic ordering and incorporates a chain‐stiffening, combined with Flory‐Huggins free energy of mixing. Temporal evolution of the concentration and nematic order parameters pertaining to the above free energy density of liquid crystalline polymer solution was simulated in the context of time‐dependent Ginzburg–Landau theory coupled with the solvent evaporation rate equation under the quasi‐steady state assumption. The emerged morphological patterns are discussed in relation to the phase diagram of the MCLCP solution and the rate of solvent evaporation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 429–435, 2007     

Sorption phenomena of organic solvents in polymers: Part I

In this work we use the vapor-sorption equilibrium data to show the degree of solvent upturn in each solvent-polymer system. For this purpose, 23 isothermal data sets for four polymer + solvent binaries, one block copolymer + solvent binary and for the corresponding polymer pairs have been used in the temperature range of 25-70 °C. Solvents studied are benzene, carbon tetrachloride, chloroform and pentane. Homopolymers studied are polyisobutylene, poly(ε-caprolactone), poly(ethylene oxide), n-heptadecane, polystyrene, poly(vinyl chloride), poly(vinyl methyl ether), and n-tetracosane.According to these data sets, solvent weight fraction in the polymer is plotted against solvent-vapor activity that is calculated assuming an ideal gas phase of pure solvent vapor neglecting the vapor pressure of the polymer. We use the Flory-Huggins theory to obtain dimensionless interaction parameter, χ. Also the Zimm-Lundberg clustering theory and non-ideality thermodynamic factor, Γ are used to interpret the equilibrium data.     

Diffusion of large penetrant molecules in amorphous polymers

A new version of the free-volume theory of diffusion is modified to describe self-diffusion phenomena in polymer + solvent systems for solvents which do not move as single units. The free-volume equations are used to interpret data which appear to illustrate that some large solvent molecules do indeed move in a segmentwise manner. The dependence of the effective activation energy for diffusion on solvent size is examined, and the importance of energy effects on the diffusion process is considered.