Introduction The diffusion of small molecules in polymeric solids has been a subject in which relatively little interest has been shown by the polymer chemist, in contrast to its counterpart, i.e., the diffusion of macromolecules in dilute solutions. However, during the past ten years there has been a great accumulation of important data on this subject, both experimental and theoretical, and it has become apparent that in many cases diffusion in polymers exhibits features which cannot be expected from classical theories and that such departures are related to the molecular structure characteristic of polymeric solids and gels. Also there have been a number of important contributions to the procedures by which diffusion coefficients of given systems can be determined accurately from experiment. I t is impossible, and apparently beyond the author's ability, to t reat all these recent investigations in the limited space allowed. So, in this article, the author wishes to discuss some selected topics with which he has a relatively greater acquaintance but which he feels are of fundamental importance for understanding the current situation in this field of polymer research. Thus the present paper is a kind of personal note, rather than a balanced review of diverse aspects of recent diffusion studies.

Diffusion in polymer-diluent systems

Transport phenomena through polymeric systems

The viscosity of polymers and their concentrated solutions

Sisal nanowhiskers were used as novel reinforcement to obtain nanocomposites with polyvinyl acetate (PVAc) as matrix phase. They are seen as attractive materials due to the widespread availability and low cost of the sisal source material. Statistical analysis of the sisal whisker length and diameter resulted in average values of 250 nm and 4 nm, respectively, resulting in an average aspect ratio in the upper range of reported cellulose nanowhisker values. The high aspect ratio ensures percolation, with resulting mechanical improvements and thermal stability, at lower fiber loads. Water uptake and thermal behaviour of the sisal whisker–PAVc composites were studied. Whisker addition was found to stabilize the nanocomposites with no benefit seen when increasing the whisker content beyond the percolation threshold: For all whisker contents studied above percolation, the water uptake stays constant, and the Tg does not vary with whisker content at a given relative humidity. The water diffusion rate however increases due to water accumulation at the whisker–PVAc interface. Below whisker percolation, stabilization is only noticed at low relative humidity, whereas high humidity results in disruption of whisker–PVAc interactions. This work shows the potential of cellulose nanowhiskers to stabilize polar polymers even at high humidity conditions with minimal reinforcement addition.

Sisal cellulose whiskers reinforced polyvinyl acetate nanocomposites

Transport in non-porous polymeric membranes is based on the so-called ‘solution–diffusion’ concept [1,2]. This model, formulated in the 19th century, is grounded in the works of J. K. Mitchell [3], T. Graham [4] and S. von Wroblewski [5], who demonstrated that the presence of microscopic open pores or capillaries was not a prerequisite for mass transfer through polymeric films (or septa as they were referred to), such as natural rubber. First, Graham in 1829 [4], and then Mitchell in 1831 [3], noted that gases were capable of permeating through non-porous rubber films and that this process was related to gas dissolution and diffusion in the polymeric materials. The currently accepted interpretation of such experiments was given several decades later by Graham [4] (this and other articles from the early history of membrane science have been reproduced, in part, in a special issue of the Journal of Membrane Science) [6]. Because he did not find a monotonic correlation between the rates of transport and the known gas phase diffusion coefficients of the penetrant molecules, Graham concluded that the process of permeation comprised two stages: sorption of gas by the rubber ‘that must depend upon a kind of chemical affinity’ and diffusion of the sorbed gas molecules [4]. The sorbed gas, as he wrote, ‘comes to evaporate . . . . and reappears as gas on the other side of the membrane. Such evaporation is the same into vacuum and into another gas, being equally gas-diffusion in both circumstances’ [4]. Empirical observations of the pressure and thickness dependence of the steady-state gas permeation rate or flux, N, led von Wroblewski [5] to propose the following relation:

Transport of Gases and Vapors in Glassy and Rubbery Polymers

Concentration and temperature dependence of diffusion coefficients for systems polymethyl acrylate and n-alkyl acetates

An empirical viscosity vs concentration relation for concentrated polymer solutions is derived in terms of a simple free volume theory, and its applicability is tested with some available data for amorphous polymer+solvent systems. It is found that the derived relation fits well those data over the range of polymer concentrations so concentrated that interchain entanglements occur to form a weak network structure throughout the solution. In the region of relative low polymer concentrations, however, it shows deviation of a common feature from the experimental results. Two temperature‐dependent parameters are contained in the viscosity equation derived; one is characteristic of the polymer species and the other is dependent upon the particular combination of polymer and diluent. These parameters are evaluated from comparisons with experimental data, and their variations with temperature are discussed.

Interpretation of Viscosity Data for Concentrated Polymer Solutions

An approximate theory of the relaxation of stress in amorphous linear polymers accompanying sorption of a low molecular weight penetrant is worked out on the assumption that the relaxation time of each Maxwellian relaxation mechanism involved is changed in the presence of penetrant by a factor dependent on penetrant concentration. A method is derived from the theory which permits approximate evaluation of the integral diffusion coefficient D of the penetrant in the polymer from stress-relaxation data on swelling systems. The theory is checked on experimental data for the systems polymethyl acrylate-water and polymethyl acrylate-methanol at 40°C., and it is found that, for both systems studied, the values of D computed from mechanical data agree reasonably with those evaluated directly from usual sorption experiments. The theory described presents only a first attempt to the quantitative interpretation of the phenomenon discussed. Further improvement and modification of it is apparently desirable, in view of some drastic approximations incorporated in its mathematical development.

Diffusion‐controlled stress relaxation in polymers. III. Stress relaxation in a swelling polymer

A resinous composition excellent in processability and gas permeation resistance, which comprises (A) 30 to 98 % by weight of a crystalline polyolefin, (B) 2 to 70 % by weight of a saponified product of an ethylene-vinyl acetate copolymer having an ethylene content of 25 to 75 mole % and a degree of saponification of at least 93 %, and (C) 0.5 to 15 parts by weight, per 100 parts by weight of said polyolefin and ethylene-vinyl acetate copolymer saponified product, of a thermoplastic polymer containing a carbonyl group in the main or side chain thereof, and a molded structure formed therefrom, which has a specific multi-layer structure and a high gas permeation resistance.

Akira Kishimoto

Papers

Concentration and temperature dependence of diffusion coefficients for systems polymethyl acrylate and n-alkyl acetates

Interpretation of Viscosity Data for Concentrated Polymer Solutions

Diffusion‐controlled stress relaxation in polymers. III. Stress relaxation in a swelling polymer

Molded structures containing crystalling polyolefin saponified ethylene vinyl acetate copolymer and carbonyl containing copolymers

Successive differential absorptions of vapors by glassy polymers