Disentanglement and reptation during dissolution of rubbery polymers

The dissolution mechanism of rubbery polymers was analyzed by dividing the penetrant concentration field into three regimes that delineate three distinctly different transport processes. The solvent penetration into the rubbery polymer was assumed to be Fickian. The mode of mobility of the polymer chains was shown to undergo a change at a critical penetrant concentration expressed as a change in the diffusion coefficient of the polymer. It was assumed that beyond the critical penetrant concentration, reptation was the dominant mode of diffusion. Molecular arguments were invoked to derive expressions for the radius of gyration, the plateau modulus, and the reptation time, thus leading to an expression for the reptation diffusivity. The disentanglement rate was defined as the ratio between the radius of gyration of the polymer and the reptation time. Transport in the second penetrant concentration regime was modeled to occur in a diffusion boundary layer adjacent to the polymer-solvent interface, where a Smoluchowski type diffusion equation was obtained. The model equations were numerically solved using a fully implicit finite difference technique. The results of the simulation were analyzed to ascertain the effect of the polymer molecular weight and its diffusivity on the dissolution process. The results show that the dissolution can be either disentanglement or diffusion controlled depending on the polymer molecular weight and the thickness of the diffusion boundary layer. © 1996 John Wiley & Sons, Inc.     

Relaxation by reptation and tube enlargement: A model for polydisperse polymers

Modern theories of the dynamics of concentrated polymeric liquids have not yet accounted for the effects of polydispersity to a sufficient extent. In order to approach quantitatively the problem of polydispersity, a model is proposed here which is based on the concept that the “tube” of constraints around a chain enlarges as the relaxation proceeds. Predictions of linear viscoelasticity obtained with this model compare favorably with experimental results on homopolymeric blends reported in the literature. However, the theory is limited to the case of very long chains and it embodies an arbitrary, if plausible, closure assumption in the self-consistency scheme. Thus, quantitative agreement remains incomplete.     

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     

Multifractal model of gas diffusion in polymers

A probabilistic (multifractal) model of gas diffusion in polymer membranes is proposed. This model has a simple and clear physical meaning and provides fairly accurate predictions of the diffusivities of various gases. For the latter purpose, a minimum set of structural characteristics is required.     

Phase and structural transformations in melts, solutions, and blends of crystallizing polymers under deformation

Experimental results concerning the effect of shear deformation on phase and structural transitions in melts, solutions, and blends of crystallizing polymers are generalized and analyzed. The mechanism responsible for the influence of deformation on the melting (crystallization) temperature, on the structure of the polymers, and on the position of liquidus curves of their solutions and blends depending on the shear rate, molecular mass, and concentration of components is considered.     

Influence of local chain dynamics on diffusion of gases in polymers as determined by pulsed field gradient NMR

Diffusion of gases in polymers below the glass transition temperature, T_g, is strongly modulated by local chain dynamics. For this reason, an analysis of pulsed field gradient (PFG) nuclear magnetic resonance (NMR) diffusion measurements considering the viscoelastic behavior of polymers is proposed. Carbon‐13 PFG NMR measurements of [¹³C]O₂ diffusion in polymer films at 298 K are performed. Data obtained in polymers with T_g above (polycarbonate) and below (polyethylene) the temperature set for diffusion measurements are analyzed with a stretched exponential. The results show that the distribution of diffusion coefficients in amorphous phases below T_g is wider than that above it. Moreover, from a PFG NMR perspective, full randomization of the dynamic processes in polymers below T_g requires long diffusion times, which suggests fluctuations of local chain density on a macroscopic scale may occur. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 231–235, 2010     

Theoretical models for diffusion in glassy polymers

A model is derived which incorporates and unifies many of the diverse observations occurring in diffusion in glassy polymers. This unification is made possible by explicitly formulating the common property of a glassy polymer in all its various modes, namely the finite relaxation time due to its slow response to changing conditions. The application and use of the model in various situations is discussed.     

Solubility and diffusion of water in acetal polymers

The rate of water sorption at 25°C. has been determined for a number of polyacetal films differing in structure, density, and orientation induced by extrusion. The equilibrium water uptake was found to be a linear function of density only; no other effect of structure or orientation was detectable. The extrapolated density for zero sorption was 1.51 g./cc., not far from the theoretical crystalline density. The diffusivity of water in unoriented films rose with decreasing density; for linear copolymer, the trend was parallel to that of the area under the dynamic mechanical loss peak associated with long-range chain motions in the disordered regions (β-transition). Less pronounced effects of molecular weight and long chain branching on diffusivity were also noted. Films crystallized while an extruded melt was still oriented showed considerable increases in water diffusivity, but no significant changes in the apparent activation energies of permeation (about 6.6 kcal./mole) or diffusion (about 11.5 kcal./mole). On annealing these films, the diffusivity remained almost constant while the sorption coefficient and retraction on remelting decreased.     

Quantitative analysis of gaseous diffusion in glassy polymers

The current theoretical treatment of diffusion of gases in glassy polymers is based on the “dual sorption” model, but also includes certain other important assumptions, at least some of which cannot be fully justified a priori. They require experimental validation, which, however, is not possible by the procedures used or proposed so far. Methods suitable for this purpose are discussed here.     

Temperature dependence of exciton diffusion in conjugated polymers

The temperature dependence of the exciton dynamics in a conjugated polymer is studied using time-resolved spectroscopy. Photoluminescence decays were measured in heterostructured samples containing a sharp polymer-fullerene interface, which acts as an exciton quenching wall. Using a 1D diffusion model, the exciton diffusion length and diffusion coefficient were extracted in the temperature range of 4-293 K. The exciton dynamics reveal two temperature regimes: in the range of 4-150 K, the exciton diffusion length (coefficient) of approximately 3 nm (approximately 1.5 x 10 (-4) cm2/s) is nearly temperature independent. Increasing the temperature up to 293 K leads to a gradual growth up to 4.5 nm (approximately 3.2 x 10 (-4) cm2/ s). This demonstrates that exciton diffusion in conjugated polymers is governed by two processes: an initial downhill migration toward lower energy states in the inhomogenously broadened density of states, followed by temperature activated hopping. The latter process is switched off below 150 K.     

The rate of solvent diffusion in amorphous polymers

The present work is a contribution to our understanding of one aspect of the diffusion process, the diffusion rate. It attempts to show that all diffusion theories must satisfy the following: 1) the rate of diffusion at the initial stages of the process must be finite 2) the rate of diffusion must have square root time dependence at longer diffusion distances. Deviations of experimental data from these rules usually result from experimental inaccuracies. Whereas Fickian approach satisfies the second but not the first rule and Case II sorption the opposite, their combination satisfies neither. Two alternative explanations, which provide a very good correlation with the experimental data, are suggested: Limited diffusion rate and sorption kinetics.     

Water vapor sorption and diffusion in glassy polymers

By establishing relationships between polymer structure and gas permeation behavior, significant advances have been made in designing materials for membrane separation of gas mixtures. However, the situation is not so well understood when water vapor is one of the components since water molecules may interact with the polymer (plasticization) or each other (clustering) in ways that complicate the structure-property relationships. In addition, accurate measurement of water sorption, diffusion, and permeation is more complicated than for gases because of the unique hydrogen bonding capability of water, e.g., its tendency to strongly adsorb on high-energy surfaces and high heat of vaporization. A progress report on a broad program to understand water sorption and diffusion in glassy polymers that may be of interest for membrane applications is outlined; specific strategies include studies of structurally related polymers and miscible blends of hydrophobic/hydrophilic polymer pairs.     

A mathematical model for stress-driven diffusion in polymers

A model for case II diffusion into polymers is presented. The addition of stress terms to the Fickian flux is used to produce the characteristics progressive front. The stress in turn obeys a concentration-dependent evolution equation. The model equations are analyzed in the limit of small diffusivity for the problem of penetration into a semiinfinite medium. Provided that the coefficient functions obey two monotonicity conditions, the solvent concentration profile is shown to have a steep front that progresses into the medium. The formulas governing the progression of the front are developed. After the front decays away, the long time behavior of the solution is shown to be a similarity solution as in Fickian diffusion. Two techniques for approximating the solvent concentration and the front position are presented. The first approximation method is a series expansion; formulas are given for the initial speed and deceleration of the front. The second approximation method uses a portion of the long time similarity solution to represent the short time solution behind the front.     

Continuous fractionation of polymers in solution by thermal diffusion

The possibility of carrying out continuous fractionation of polymers by the thermodiffusion method was investigated. From the working space of a plate-type column, fractions of polymer were continuously withdrawn simultaneously with filling of the column with fresh solution from a storage vessel. After equilibrium had been established, the distributions of molecular weights of the fractions were determined by a modified Baker and Williams method. In the same apparatus, and at constant temperature and concentration, fractionation, which may be characterized by a limiting viscosity number, is dependent on the total rate of withdrawal and on the ratios of amounts of polymer withdrawn in various places on the column.     

Segmental mobility model for diffusion of gases in polymers

Diffusion of small molecules in polymers is described quantitatively in terms of segmental mobility processes. The diffusion coefficient depends on a diffusive jump length, which is characteristic of the polymer, and a jump frequency, which is equated to the segmental mobility rate. The presence of a particular solute increases mobility of the surrounding polymer segments by a predictable amount, which is related to the partial molar volume of the solute. The theory is fit to experimental diffusion data, and partial molar volumes are calculated from the fitting parameters. Good agreement with experimental partial molar volumes is obtained.     

On the diffusion of gases in partially crystalline polymers

The diffusion of gases through partially crystalline polymers is studied. The effective diffusion coefficient D^eff is obtained as the result of the averaged superposition of two fundamental mechanisms, namely, diffusion through the crystallites is considered to be zero, and diffusion through the rubbery fraction of the polymer obeys a Fujita-like free-volume theory. The predicted D^eff is compared with experimental data of Kreituss and Frisch. The behavior of the diffusion coefficient in terms of concentration and crystalline fraction is satisfactorily explained through the model.     

Adhesion of high polymers. I. Influence of diffusion,adsorption, and physical state on polymer adhesion

It is possible to identify three distinct types of polymer adhesion on the basis of the physical state of adhesive and adherend: (1) rubbery polymer–rubbery polymer (R–R adhesion); (2) rubbery polymer–glassy polymer (R–G adhesion); (3) rubbery polymer–nonpolymer (R–S adhesion). Limitations of the diffusion and adsorption theories and their conflicting results are discussed within the framework of the proposed classification. By defining the physical state of the polymer as an adhesive or as an adherend, it is possible to eliminate many of the discrepancies commonly noted in attempted application of the diffusion and adsorption theories. As predicted by the Bueche-Cashin-Debye equation, the diffusion of a polymer into another should be greatly reduced as it changes from the rubbery to the glassy state. For this reason, diffusion, which depends to a great extent on the physical state of the polymer, is actually a limited, selective process. Assuming a 10¹³ poise bulk viscosity at glass temperature, self-diffusion constants of forty polymers were calculated to be 10^?21cm.²/sec. or 10^?5A.²/sec. This slow rate of diffusion is unmeasurable and insignificant. Adsorption, which is less dependent on the physical state of the polymer, is more frequently encountered.     

Formulation of the coupled cluster theory with localized orbitals in correlation calculations on polymers

It is shown that in the framework of coupled cluster theory both the correlation energy per unit cell and quasi-particle band structures of polymers can be computed directly from matrix elements of the excitation operator and the two-electron integrals calculated in localized orbital basis. Further, it is described how to thake advantage of the localized nature of the orbitals applied. Ab initio test calculations on a finite model system similar to the Pariser–Parr–Pople Hamiltonian are presented.