Diffusion processes in polymers

Methods for enhancing diffusion processes in polymer electrodes... 

However in the packaging sector the large majority of the diffusion processes in polymers imply penetrants with a relative molecular weight ranging between 100 and 1200 daltons and have often quite complex structures. From experiments one knows that these diffusion processes are characterized by D ranging from 10 9 to 10"l2cm2/s or even lower levels (see Appendix I). In (98) it was stated that, to study with MD techniques polymer penetrant systems in which the D are that small, is certainly out of reach for several generations of supercomputers to come. 

On the other hand, based on the rapid progress which was recorded in the last decade in the atomistic simulation of diffusion processes in polymers one may be confident that these computational methods will be one day able to cope with the prob-... 

Despite the large number of analytical solutions available for the diffusion equation, their usefulness is restricted to simple geometries and constant diffusion coefficients. The boundary conditions, which can be analytically handled, are equally simple. However, there are many cases of practical interest where the simplifying assumptions introduced when deriving analytical solutions are unacceptable. For example, the diffusion process in polymer systems is sometimes characterized by markedly concentration-dependent diffusion coefficients, which make any analytical result inapplicable. Moreover, the analytical solutions being generally expressed in the form of infinite series, their numerical evaluation is no trivial task. That is, the simplicity of the adopted models is not necessarily reflected by an equivalent simplicity of evaluation. 

Any treatment of diffusion processes in polymers must include estimates of the "internal viscosity", of the solid polymer... 

Any treatment of diffusion processes in polymers must include estimates of the internal viscosity -qin, of the solid polymer matrix. For example, for recombination of active free radicals which occur at every collision, one can write the rate expression in the form... 

KRY Krykin, M.A., Bondar, V.I., Kukharsky, Yu.M., and Tarasov, A.V., Gas sorption and diffusion processes in polymer matrices at high pressures, J. Polym. Sci. Part B Polym. Phys., 35, 1339, 1997. 

Diffusion. Diffusion processes in polymers have been extensively studied by simulation since about 1990. Not only is diffusion one of the more accessible transport properties to compute, it is also a property of considerable practical importance for barrier polsrmers and separation membranes. 

Pick s first and second laws were developed to describe the diffusion process in polymers. Fickian or case I transport is obtained when the local rate of change in the concentration of a diffusing species is controlled by the rate of diffusion of the penetrant. For most purposes, diffusion in rubbery polymers typically follows Fickian law. This is because these rubbery polymers adjust very rapidly to the presence of a penetrant. Polymer segments in their glassy states are relatively immobile, and do not respond rapidly to changes in their conditions. These glassy polymers often exhibit anomalous or non-Fickian transport. When the anomalies are due to an extremely slow diffusion rate as compared to the rate of polymer relaxation, the non-Fickian behaviour is called case II transport. Case II sorption is characterized by a discontinuous boundary between the outer layers of the polymer that are at sorption equilibrium with the penetrant, and the inner layers which are unrelaxed and unswollen. 

TIK Tikhomirova, N.S., Malinksii, Yu.M., and Karpov, V.L., Studies on diffusion processes in polymers. I. Diffusion of monoatomic gases through polymer films of different stractures... 

One of the most common rubber adhesives are the contact adhesives. These adhesives are bonded by a diffusion process in which the adhesive is applied to both surfaces to be joined. To achieve optimum diffusion of polymer chains, two requirements are necessary (1) a high wettability of the adhesive by the smooth or rough substrate surfaces (2) adequate viscosity (in general rheological properties) of the adhesive to penetrate into the voids and roughness of the substrate surfaces. Both requirements can be easily achieved in liquid adhesives. Once the adhesive solution is applied on the surface of the substrate, spontaneous or forced evaporation of the solvent or water must be produced to obtain a dry adhesive film. In most cases, the dry-contact adhesive film contains residual solvent (about 5-10 wt%), which usually acts as a plasticizer. The time necessary... 

Equations (37) and (38), along with Eqs. (29) and (30), define the electrochemical oxidation process of a conducting polymer film controlled by conformational relaxation and diffusion processes in the polymeric structure. It must be remarked that if the initial potential is more anodic than Es, then the term depending on the cathodic overpotential vanishes and the oxidation process becomes only diffusion controlled. So the most usual oxidation processes studied in conducting polymers, which are controlled by diffusion of counter-ions in the polymer, can be considered as a particular case of a more general model of oxidation under conformational relaxation control. The addition of relaxation and diffusion components provides a complete description of the shapes of chronocoulograms and chronoamperograms in any experimental condition ... 

Polymerization continues in stage II, and monomer continues to be supplied to the particles by the droplets in the aqueous phase. These droplets disappear when about 30% of the monomers has been converted to polymers. Polymerization continues in stage III after about 60% conversion, but all monomers must now be supplied to the macroradicals by a diffusion process in the micelles. 

This paper will deal primarily with rapid transport derived from diffusion processes in aqueous solution. These processes may be observed in simple polymer, water systems following well-established thermodynamic principles. In particular, we shall discuss temaiy polymer-containing systems in which very rapid transport processes, associated with the formation of macroscopic structures in solution, occur. 

Polymer molecules in a solution undergo random thermal motions, which give rise to space and time fluctuations of the polymer concentration. If the concentration of the polymer solution is dilute enough, the interaction between individual polymer molecules is negligible. Then the random motions of the polymer can be described as a three dimensional random walk, which is characterized by the diffusion coefficient D. Light is scattered by the density fluctuations of the polymer solution. The propagation of phonons is overdamped in water and becomes a simple diffusion process. In the case of polymer networks, however, such a situation can never be attained because the interaction between chains (in... 

This classification should in principle be valid for both rubbery and glassy polymers. However, as will be shown in this section, until now more detailed and true microscopic" treatments have mainly been models for diffusion in rubbery polymers. An explanation for this may be the much more complex nature of the diffusion process in glassy polymers (9,13,32-34). 

The problem of diffusion modeling in polymers changes to some degree when one envisages to develop a really atomistic model, with trully predictive capabilities and without making any ad hoc assumption on the molecular behaviour and/or motions in the polymer penetrant system. In principle, a possibility to develop such diffusion modelings, is to simulate theoretically the process of penetrant diffusion in a polymer matrix by computer calculations. 

One of the unique characteristics of Th-FFF is that retention depends not only on the molar mass but also on the chemical composition of the polymer. This chemical differentiation is due to the dependence of the underlining thermal diffusion process on polymer (and solvent) composition [84]. This effect can likely be used to determine compositional distributions in copolymers and blends [111]. Figure 10 compares the resolving power of Th-FFF and SEC on two polymers of similar molecular weight but varying chemical composition. The polymers coelute in SEC because their sizes are similar whereas Th-FFF resolves the polymers because they differ in chemical composition. 

When considering the rates of chemical processes in polymers which require diffusion of reagents and products, it is necessary to estimate the internal viscosity q. to substitute in expressions such as Equations 6 and 7. We ave made estimates for q in solid polyethylene from luminescence quenching of naphthalene fluorescence in ethylene -OO copolymers [24]. (Table VII)... 

Gotlib, Yu. Ya., Svetlov, Yu. E. The theory of vibrational and rotational diffusive processes in diains of rotators and polymer chains. In collected articles Mekhanizmy relaksatsionnykh yavlenii v tverdykh telakh (Mechanisms of relaxation phenomena in solids), Moscow Nauka 1972 (pp- 215-219)... 

In the aq/polymer/org situation, the organic solvent typically penetrates the polymer causing it to swell considerably, and the situation is very similar to that of MMLLE. With a fixed composition of the membrane, the possibilities for chemical tuning (such as application of carriers) of the separation process are greatly reduced compared to SLM extraction or MMLLE. Also, as diffusion coefficients in polymers are lower than in liquids, the mass transfer is slower, leading to slower extractions. On the other hand, as the membrane is virtually insoluble, any combination of aqueous and organic liquids can be used, and the entire system becomes very stable. 

It was found meanwhile that nearly every slim unbranched polymer chain, such as poly(trimethylene oxide) [224], poly(l,3-dioxolane) [225], poly(tetramethylene oxide) [226], polyethylene imine) [227], poly(3-hydroxy propionate), poly (4-hydroxybutyrate) and poly(6-hydroxyhexanoate) [228,229], poly(butylene succinate) [229], polyadipates [230], nylon-6 [231], and even oligomers of polyethylene [232], form a-CD ICs with channel structures. In all of these cases, inclusion is a heterogeneous process, since the guest polymer and its CD complex are almost insoluble in water. Therefore, extensive sonication had to be applied to accelerate the diffusion process. The polymer was also dissolved in an organic solvent, e.g., nylon-6 in formic acid, and this solution was added to the solution of a-CD [231], Alternatively, a monomer, such as 11-aminoundecanoic acid, was included in a-CD and polymerized to nylon-11 by solid state polycondensation within the channels of the IC. Thus, the IC of nylon-11 was formed under conservation of the crystal packing [233-235],... 

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