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.     

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.     

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.     

On the determination of molecular weight distributions from sedimentation–diffusion equilibrium data at a single rotor speed

The problem of inferring molecular weight distributions from concentration gradient data taken at sedimentation-diffusion equilibrium for a single rotor speed is ill posed: significantly different distributions correspond to concentration gradients which differ so slightly that they cannot be distinguished by the experiment. It is this intrinsic property of the problem which accounts for the lack of success of the several schemes proposed for its solution. Integral equation theory is applied to show explicitly just what can be inferred with bounded error. Several methods for recovering this information are discussed and applied to example problems.     

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.     

Interchain electron donor–acceptor complexes. Determination of equilibrium constant and thermodynamic parameters in the solid state

The interpolymeric electron donor–acceptor (EDA) complex of donor poly[(N-ethylcarbazol-3-yl)methyl methacrylate] (PHMCM-2) with acceptor poly-(2-[(3,5-dinitrobenzoyl)oxy]ethyl methacrylate) (PDNBM-2) presents a single glass transition temperature and a decomplexation endotherm on differential scanning calorimetric (DSC) thermograms. This system is considered a “polymer blend model” which exhibits a lower critical solution temperature (LCST). Phase separation of this blend is kinetically controlled and positive deviations of the glass transition temperatures from weight average values suggest that it behaves as a thermally reversible crosslinked network. Calorimetric methods to determine the heats of mixing of small molecule complexes in solution were adapted for this solid state blend to estimate the equilibrium constant (K_eq) and other thermodynamic parameters. Applying a computer iterative procedure and assuming 1 : 1 stoichiometry, a least-squares fit was found for several different donor molecular weights with three different high molecular weight acceptors. At moderate molecular weights, K_eq rises to represent saturation fractions near unity as found in biological systems. K_eq decreases for higher molecular weights, possibly due to trapped chain entanglements. These results are supported by a composition-independent, “horizontal line” phase diagram, thus resembling the completely complexed/denaturation process in DNA.     

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.     

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     

Solvent diffusion in amorphous polymers: Polystyrene–solvent systems

The inverse gas chromatography (IGC) technique was used to obtain the partition and diffusion coefficients of solvents in polystyrene over a wide range of temperatures. Infinite dilution experiments were performed with three solvents: toluene, benzene, and hexane. Finite concentration data were measured for the polystyrene–toluene system at various concentrations from 110 to 180 °C. For the finite concentration region, the modified capillary column model used by Tihminlioglu and Danner (J Chromatogr A 1999, 845, 93–101) was used to calculate diffusion and thermodynamic data. Finite concentration thermodynamic data were also calculated with the retention theory approach and compared with the capillary column model. The experimental IGC results are in good agreement with data from other experimental techniques. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1965–1974, 2000     

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.     

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.     

Radical equilibrium studies; the thermodynamic parameters of n-propyl

A novel method for the investigation of the thermodynamic properties of free radicals is described. It involves the establishment of an equilibrium of the form where R₁ and R₂ are free radicals, and the measurement of the recombination products of R₁ and R₂. The method is applied to the case where R₁ is n-propyl, R₂ is methyl, and the olefin is ethene, using the thermal decomposition of azomethane (a source of methyl) in the presence of ethene in the temperature range of 581–649°K. Using the best available thermodynamic parameters for methyl, it is concluded that those for n-propyl are in need of adjustment. We recommend the values ΔH_f°(300°K) = 22.6 ± 1 kcal/mol and S₃₀₀° = 67.4 ± 3 cal/mol · K together with either the heat capacity data of O'Neal and Benson or the essentially identical data derivable from the results of Purnell and Quinn.     

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.     

Determination of volatile components of systems not in thermodynamic equilibrium

A review is given of the literature on the analysis of complex mixtures of organic compounds and a procedure proposed for the separation and identification of the components of such mixtures. Retention data obtained with several chromatographic columns are combined with information from mass and Fourier-transform infrared spectra and identifications made with the aid of a computer.     

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     

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.     

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.     

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.     

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).