Diffusion in polymer–solvent systems. III. Construction of Deborah number diagrams

A method is presented for anticipating condition under which anomalous diffusion effects can be expected for amorphous polymer–solvent systems. The diffusion process is characterized by a dimensionless group called the diffusion Deborah number, and a method for calculating this dimensionless number is presented. Deborah number diagrams are constructed for the unsteady diffusion of ethylbenzene and polystyrene in thin films, and observed diffusion phenomena are discussed on the basis of these diagrams.     

The entropy of inhomogeneous polymer–solvent systems

The entropy of inhomogeneous polymer solutions has been evaluated using a lattice model. Previous models for polymer solutions considered only the enthalpic contributions, and a more complete expression for the free energy is obtained by adding the entropic term. The resulting expression is used to predict the characteristics of spinodal decomposition of polymer solutions and the interfacial tension between demixed polymer solutions. There is general improvement in the agreement between theory and experiment when the entropic effects are included.     

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.     

Evaluation of free-volume theories for solvent self-diffusion in polymer–solvent systems

An evaluation of free-volume theories for solvent self-diffusion is carried out using recent comprehensive data sets for penetrant self-diffusion in polymer solutions. Different theories are compared, and free-volume theories in the prediction of penetrant self-diffusion coefficients in glassy polymer systems is also evaluated. © 1993 John Wiley & Sons, Inc.     

Free energy of an inhomogeneous polymer–polymer–solvent system. II

A complete expression for the enthalpy of mixing of inhomogeneous polymer–polymer–solvent systems applicable for small as well as large concentration fluctuations has been developed. This is used to express the free energy of inhomogeneous polymer–polymer–solvent systems in an extended form of the Landau-Ginzburg functional. The gradient energy parameters obtained here are consistent with the published results. The free energy functional has been applied to develop a generalized continuity equation for spinodal decomposition in polymer–polymer systems. A linearized version of this continuity equation has been used to study the effect of the gradient terms on the dominant wavelength during spinodal decomposition.     

Evaluation of theories for diffusion in polymer–solvent systems

A method is proposed for examining differences in the predictive capabilities of three versions of the free-volume theory of polymer—solvent diffusion using only a small amount of diffusivity data. The utility of the method is illustrated using a limited diffusivity data set for the methanol-poly(vinyl acetate) system.     

Free-volume theories for self-diffusion in polymer–solvent systems. II. Predictive capabilities

The predictive and correlative capabilities of two recent versions of the free-volume theory for self-diffusion in polymer–solvent systems are examined by comparisons with experimental data. Neither the Vrentas–Duda free-volume theory nor the Paul version generally provides satisfactory predictions for the temperature and concentration variations of solvent self-diffusion coefficients. However, the Vrentas–Duda theory does provide good correlations of solvent self-diffusion data, and, furthermore, this theory can provide good predictions if a small amount of solvent self-diffusion data is used to help estimate the parameters of the theory. New diffusivity and equilibrium data were collected for the toluene-PVAc system to provide a broader database for evaluation of the self-diffusion theories.     

Free-volume theories for self-diffusion in polymer–solvent systems. I. Conceptual differences in theories

Conceptual differences in two recent versions of the free-volume theory for self-diffusion in polymer–solvent systems are identified and discussed. The validity of the assumptions of these two theories is tested using experimental data. In all cases, the experimental evidence favors the Vrentas–Duda free-volume theory over the Paul version of this theory.     

Diffusion behavior in polymer–clay nanocomposites

This paper reviews our previous studies on the diffusion behavior in polymers clay nanocomposites. A geometric model for predicting the effective diffusivity through this type of systems as a function of clay sheets orientation, volume fraction, polymer clay interaction, and aspect ratio is proposed. Model predictions are compared to the effective diffusivity generated using random walk simulations as well as with predictions obtained from already existing theoretical models. Fair agreement is found between the model prediction and the results of numerical simulations. With respect to the already existing theoretical models, the present mathematical derivation seems more adequate to describe diffusion behavior in conventional nanocomposites systems (i.e. when fillers present very low values of volume to surface ratio). Experimental diffusion tests are discussed and interpreted with the aid of the proposed model. In addition to the aspect ratio and clay concentration, the polymer clay interactions as well as the sheets orientation are the factors controlling the barrier properties of polymer‐layered silicate nanocomposites. Good agreement was found in the case of samples containing exfoliated clay, whereas the model fails in the case of micro‐composites, in which the inorganic lamellae are agglomerated in clusters. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 265–274, 2006     

Diffusion in polymer–solvent systems. II. A predictive theory for the dependence of diffusion coefficients on temperature,concentration, and molecular weight

A new free-volume theory is combined with the thermodynamic theory of Flory and the entanglement theory of Bueche to provide a means of predicting the temperature, concentration, and molecular weight dependence of mutual-diffusion coefficients in amorphous polymer–solvent systems. The predictions of the theory are compared with actual data for the ethylbenzene–polystyrene system.     

Determination of thermodynamic parameters of polymer–solvent systems from sedimentation–diffusion equilibrium in the ultracentrifuge

Sedimentation equilibrium in the ultracentrifuge means that there is such a distribution of molecular species throughout the cell, that the centrifugal forces are balanced by differences in the activities. This provides a method for determination of the activities and the chemical potentials in polymer solutions which, in principle, is very simple and reliable. A complication is caused by polydispersity of the dissolved polymer. If one assumes that the interaction parameter depends on concentration and temperature, but not on molecular weight, it is possible to determine the chemical potential of polymer and solvent from the ultracentrifugal data. Experiments have been carried out on the systems polystyrene–toluene and polystyrene–cyclohexane at different temperatures and in the concentration range 0–80 wt-%. The results are expressed in the data for the chemical potential of the solvent, the number average chemical potential of the polymer and the interaction parameter χ.     

Velocity‐correlation analysis in polymer–solvent mixtures

The subject of this article is the combined interpretation of intradiffusion and mutual‐diffusion data for polymer–solvent mixtures in terms of integrals over velocity self‐correlation functions and velocity cross‐correlation functions. The combination of mutual‐diffusion, intradiffusion, and activity data allows the evaluation of velocity‐correlation coefficients (VCCs) and distinct‐diffusion coefficients in systems containing one monodisperse solute. This study is the first attempt to extend these approaches to polymers that are polydisperse solutes. Because of the polydispersity, this correlation analysis may become critical for polymers. Its application to polydisperse samples requires the reduction of intradiffusion and mutual‐diffusion coefficients to the same average. After such a reduction, the VCCs and distinct‐diffusion coefficients are evaluated for a homologous series of poly(ethylene glycol)s (PEGs). Attractive PEG–PEG interactions depend on the chain length and concentration of PEG. In this analysis, network formation in PEG–water systems appears to be a smooth process. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 43–51, 2002     

Conformational energy contribution to the heat of solution in polymer–solvent systems. Part I. Theory

The conformational energy contribution (ΔU_conf) to the heat of solution in polymer-solvent systems is presented and discussed in connection with chain conformational properties. In particular, ΔU_conf has been discussed in terms of various possible mechanisms of coil deformation.     

Conformational energy contribution to the heat of solution in polymer–solvent systems. Part II. Experimental results

Heats of solution (ΔH_exp) in solvents of increasing thermodynamic power have been measured for four polymers: polystyrene (PS), poly(vinyl acetate) (PVAc), polyisobutylene (PIB) and polydimethylsiloxane (PDMS). After subtraction from ΔH_exp of an interaction term (calculated by the Hildebrand treatment based on solubility parameters) and the excess volume term, the quantity remaining is interpreted as the conformational energy contribution (ΔU_conf) to the heat of solution. ΔU_conf appears to correlate well with some basic conformational properties of the chain, such as the sign of the temperature coefficient of unperturbed dimensions derived from solution properties, and shows a monotonic behavior with α, the expansion coefficient of the polymer coil in the final solution. Numerical values of ΔU_conf, at least for those cases in which polymer solubility parameters are known with some certainty, are much larger than those evaluated from rubber elasticity experiments (through the experimentally accessible value of the energy component of the force of retraction im simple elongation).     

Phase equilibria in polymer–liquid–liquid systems

The phase equilibria in polymer–liquid 1–liquid 2 ternary systems have been calculated on the basis of the Flory-Huggins theory of polymer solutions. A new approximation method based on the “cluster” concept has been introduced for mixed solvents comprising a solvent and a nonsolvent. This concept has been verified with polystyrene–solvent–methanol systems.     

Principal component analysis of polymer–solvent and filler–solvent interactions by inverse gas chromatography

Polymers (polyethylene, polyurethane), silica and modified silicas (modified with: N-2-aminoethyl-3-aminopropyltrimethoxysilane, 3-aminopropyltriethoxysilane, 3-merkaptopropyltrimethoxysilane, triethoxyoctylsilane) were examined by inverse gas chromatography at four different temperatures: 363, 383, 393 and 403 K. The modifiers of silica were applied at five different concentrations. Small amounts of the following test solutes were injected to achieve the infinite dilution conditions: pentane, hexane, heptane, octane, nonane, dichloromethane, chloroform, carbon tetrachloride, and 1,2-dichloroethane.

The retention times for these test solutes were determined and Flory–Huggins parameters were calculated. Values of these physico-chemical parameters characterizing the examined materials were arranged in a matrix form: in the rows the supports and modifiers were enumerated at different temperatures whereas the columns contained the test solutes. The input matrix was subject to principal component analysis after standardization. Three principal components explain more than 93% of the total variance in the data. Four test solutes (hexane, heptane, chloroform and carbon tetrachloride) carry very similar information. Therefore, it is justified to eliminate any three of them from the series of test solutes. Modifiers, supports and various temperatures were classified and different groups were observed according to the dominant interactions. Type of modifier, its content, and temperature can change and shift the properties from the dominant clusters to the neighboring clusters. Unambiguous separation was observed in cases of silica modified with 5 and 10 parts of triethoxyoctylsilane at all examined temperatures.     

Diffusion study of a polymer–diluent system using the optical mass transport method

Thermotropic polymers and low-molecular-weight mesogens share many common textural features. This circumstance is exploited to determine diffusion coefficents in a system consisting of a cholesteric polymer and a low-molecular-weight nematogen using the recently developed optical mass transport method. The self-diffusion coefficient and its concentration dependence were determined by using a distance–time approach, whereas the time dependence of the mutual diffusion coefficient was evaluated by a conventional concentration–distance analysis of the diffusion profile. Comparison with literature data indicates satisfactory agreement. The coefficient of the scaling law relating the self-diffusion coefficient and concentration is in accord with the value predicted by de Gennes for semidilute polymer solutions.     

Effect of composition on the width of the calorimetric glass transition in polymer–solvent and solvent–solvent mixtures

The calorimetric glass‐transition temperature (T_g) and transition width were measured over the full composition range for solvent–solvent mixtures of o‐terphenyl with tricresyl phosphate and with dibutyl phthalate and for polymer–solvent mixtures of polystyrene with three dialkyl phthalates. T_g shifted smoothly to higher temperatures with the addition of the component with the higher T_g for both sets of solvent–solvent mixtures. The superposition of the differential scanning calorimetry traces showed almost no composition dependence for the width of the transition region. In contrast, the composition dependence of T_g in polymer–solvent mixtures was different at high and low polymer concentrations, and two distinct T_g's were observed at intermediate compositions. These results were interpreted in terms of the local length scale and associated local composition variations affecting T_g. The possible implications of these results for the dynamics of miscible polymer blends were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1155–1163, 2004     

Investigation of polymer–solvent interactions in poly(styrene sulfonate) thin films

The swelling behavior of acid form poly(styrene sulfonate) (PSS‐H) thin films were investigated using in situ spectroscopic ellipsometry (SE) to probe the polymer–solvent interactions of ion‐containing polymers under interfacial confinement. The interaction parameter (χ), related to the polymer and solvent solubility parameters in the Flory–Huggins theory, describes the polymer‐solvent compatibility. In situ SE was used to measure the degree of polymer swelling in various solvent vapor environments, to determine χ for the solvent‐PSS‐H system. The calculated solubility parameter of 40–44 MPa^1/2 for PSS‐H was determined through measured χ values in water, methanol, and formamide environments at a solvent vapor activity of 0.95. Flory–Huggins theory was applied to describe the thickness‐dependent swelling of PSS‐H and to quantify the water‐PSS‐H interactions. Confinement had a significant influence on polymer swelling at low water vapor activities expressed as an increased χ between the water and polymer with decreasing film thickness. As the volume fraction of water approached ～0.3, the measured χ value was ～0.65, indicating the water interacted with the polymer in a similar manner, regardless of thicknesses. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1365–1372     

Metastable liquid–liquid and solid–liquid phase boundaries in polymer–solvent–nonsolvent systems

In general liquid–liquid demixing processes are responsible for the porous morphology of membranes obtained by immersion precipitation. For rapidly crystallizing polymers, solid–liquid demixing processes also generate porous morphologies. In this study, the interference of both phase transitions has been analyzed theoretically using the Flory–Huggins theory for ternary polymer solutions. It is demonstrated that four main thermodynamic and kinetic parameters are important for the structure formation in solution: the thermodynamic driving force for crystallization, the ratio of the molar volumes of the solvent and the nonsolvent, the polymer–solvent interaction parameter, and the rate of crystallization of the polymer compared to the rate of solvent-nonsolvent exchange. An analysis of the relevance of each of these parameters for the membrane morphology is presented. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 763–770, 1997