Diffusivity in polymeric systems

JL Duda. Molecular diffusion in polymeric systems. Pure Appl Chem 57 1681-1690, 1985. 

J. M. Zielinski and J. L. Duda, Solvent Diffusion in Polymeric Systems, in Polymer Devolatilization, R. J. Albalak, Ed., Marcel Decker, New York, 1996. 

The first attempts in the direction of simulating theoretically at an atomistic level the diffusion of simple gas molecules in a polymer matrix were made more than two decades ago (100). But, the systematic development of ab initio computer simulations of penetrant diffusion in polymeric systems dates only from the late 80 s (101-104). At the beginning of the 90 s it was achieved to simulate some qualitative aspects such as the diffusion mechanism, temperature, and pressure dependence of diffusion coefficients (105-109). The polymers chosen for investigation mainly fell into two categories either they were easily described (model elastomers or polyethylene) or they were known to have, for simple permanent gases like H2, 02, N2, H20 or CH4,... 

Vibrational spectroscopy is perhaps the most frequently used technique for the study of diffusion in polymeric systems because it provides a rapid way to quantitatively describe this phenomenon. The two areas of this type of research include the diffusion of small molecules into polymers and polymer-polymer interdiffusion. The easiest and most commonly used technique for this purpose is ATR. In this experiment, a polymer film is placed in contact with an ATR crystal, and the diffusing species is placed on top of the polymer. As diffusion progresses, the diffusing species moves closer to the ATR crystal and shows up in the spectrum obtained as an increase in the diffusant specific spectral band. This spectral change can be used to determine the diffusion coefficient of the system with the appropriate diffusion equation. This technique is limited to IR because of the optics and sample geometry required. 

Freeman, B. D. (1992). Mutual diffusion in polymeric systems. In S. L. Aggarwal and S. Russo (Eds.), Comprehensive Polymer Science First Supplement. Pergamorr, New Yrrrk p. 167. Freeman, B. D. (1999). Basis of permeabihty/selectivity tradeoff relations in polymeric gas separation membranes. Macromolecules 32, 375. 

Table 1 summarizes several of the experimental methods discussed in this chapter. A need exists for new or revised methods for transport experimentation, particularly for therapeutic proteins or peptides in polymeric systems. An important criterion for the new or revised methods includes in situ sampling using micro techniques which simultaneously sample, separate, and analyze the sample. For example, capillary zone electrophoresis provides a micro technique with high separation resolution and the potential to measure the mobilities and diffusion coefficients of the diffusant in the presence of a polymer. Combining the separation and analytical components adds considerable power and versatility to the method. In addition, up-to-date separation instrumentation is computer-driven, so that methods development is optimized, data are acquired according to a predetermined program, and data analysis is facilitated. 

The extent of hydration or solvation of a molecule also has a profound effect on the transport of the substance. The apparent solubility of the drug in both aqueous and nonaqueous media may be influenced by the absence or presence of moisture. Diffusion of drugs in polymeric systems may also be influenced by the hydration of the polymers and hydration of the membrane through which transport is occurring for example, skin hydration may enhance the diffusion of drug molecules significantly. 

To summarize, the hydration status of the drug molecule and other components of a pharmaceutical formulation can affect mass transport. Solubility of drug crystals in an aqueous or nonaqueous solvent may depend on the presence or absence of moisture associated with the drug. Hydration may also determine the hydrodynamic radii of molecules. This may affect the frictional resistance and therefore the diffusion coefficient of the drug molecules. Diffusion of drugs in polymeric systems may also be influenced by the percent hydration of the polymers. This is especially tme for hydrogel polymers. Finally, hydration of... 

The main focus of the following considerations is on catalysis using inorganic materials. Similar considerations come into play for catalysis with molecular compounds as catalytic components of course, issues related to diffusion in porous systems are not applicable there as molecular catalysts, unless bound or attached to a solid material or contained in a polymeric entity, lack a porous system which could restrict mass transport to the active center. It is evident that the basic considerations for mass transport-related phenomena are also valid for liquid and liquid-gas-phase catalysis with inorganic materials. 

Thermal diffusion, also known as the Ludwig-Soret effect [1, 2], is the occurrence of mass transport driven by a temperature gradient in a multicomponent system. While the effect has been known since the last century, the investigation of the Ludwig-Soret effect in polymeric systems dates back to only the middle of this century, where Debye and Bueche employed a Clusius-Dickel thermogravi-tational column for polymer fractionation [3]. Langhammer [4] and recently Ecenarro [5, 6] utilized the same experimental technique, in which separation results from the interplay between thermal diffusion and convection. This results in a rather complicated experimental situation, which has been analyzed in detail by Tyrrell [7]. 

The phase separation in polymeric systems is determined by thermodynamic and kinetic parameters, such as the chemical potentials and diffusivities of the individual components and the Gibb s free energy of mixing of the entire system. Identification and description of the phase separation process is the key to understanding the membrane formation mechanism, a necessity for optimizing membrane properties and structures. 

Further possibilities are opened up for investigation of fluoropolymers by two-dimensional methods. Thus, solid-state F COSY can be used to study potential spin exchange (see Ref. 17 for a nonpolymeric example), which may arise from chemical exchange (rare in polymeric systems, but conceivable for internal rotation of C—CF3 groups in asymmetric environments) or from spin diffusion. 

In contrast to all of these studies related to more polymerized melts, the status of water diffusion in basaltic systems remains unchanged since the review of Watson... 

The kinetic aspects of immobilized enzymes are rather complicated. A typical situation is when the enzyme is immobilized within some polymeric material, which may be cut into slices and immersed in a suitably buffered solution of the substrate. This is the type of situation that occurs in a biological system, an example being a muscle (in which the enzyme myosin is immobilized) surrounded by a solution of the substrate ATP. For reaction to occur, the substrate has to diffuse through the polymeric material in order to reach the enzyme. Reaction then occurs and the products must diffuse out into the free solution. Since diffusion in polymeric materia occurs more slowly than in water, there is now a greater possibility of diffusion control (see p. 403) the overall rate of reaction may depend to some extent on the rates with which these diffusion processes occur. 

Because of the relatively slow rates of radical diffusion in polymer matrices, it seems likely that the probability of secondary recombination will depend very much on the separation achieved while the particles are moving apart with the original excess kinetic energy imparted in the primary dissociation step. This, in turn, should depend on the energy of the exciting photon. There is some evidence for this, even in small molecules in solution. For example, Slivinskas and Guillet (16) report a one-hundied-fold increase in the relative yields of Norrish type I radical products from simple aliphatic ketones, when the reaction is initiated by y-rays rather than ultraviolet light (Table 5). Similar increases were observed in polymeric systems such as in ethylene-CO copolymers (17). 

It follows that diffusion control is more frequently operative in polymeric systems than that in ordinary solution reactions, because and k are more likely to be comparable due to the low D values [9-16], If the election exchange reaction occurs between ionic species (charged polymer sites), the coulombic forces may reduce or enhance both the probability of the ions encoimtering each other and the rate of electron transfer. For the activation-controlled case, kg can be obtained as follows [17] ... 

There are several other experimental methods for determining diffusion coefficients for proteins in polymeric systems, such as interference microscopy and NMR spectroscopy. For a discussion of these methods, the reader is referred to Crank and Park (1968). 

The 1/(1 - CO a) term is commonly referred to as the frame of reference term. For many cases of importance in polymeric systems such as in gas permeation, coa is relatively small, and the 1/(1 - >a) factor can safely be neglected so that the flux relative to fixed coordinates is equal to the flux relative to moving coordinates. Even for intermediate concentrations (0.1 < coa < 0.5), this factor may often be of second-order importance compared to difficulties in accurately determining the mutual diffusion coefficient due to strong concentration dependencies. However, not accounting for the factor 1/(1 — coa) can lead to very significant errors in flux calculations in highly swollen systems (eg, 90-95% solvent), even if the mutual diffusion coefficient is accurately determined (6). 

The experimental results of this Section show that optically generated phonons can be used to study the transient broadening of the optical line shape of a single absorber. In principle, the dependence on the phonon frequency can be studied in such an experiment. In the same experiment the time-resolved dynamics of phonon diffusion and phonon decay in polymeric systems can be investigated via the dephasing mechanism of the optical probe. 

Usually, nanoparticles in polymeric systems, are supposed to increase the barrier properties of such materials. One of the most important effects of clays on the polymer matrix properties is the dramatic improvement of the barrier properties of polymers, since clay sheets are namrally impermeable. The extent of the improvement in the barrier properties depends on the degree of tortuosity created by the nanoparticles layers, and the manner by which diffusion of molecules through the polymer film occurs. The ratio of the actual distance to molecule diffusion to the shortest distance to diffusion (polymer film thickness) determines the tortuous factor. This is done by creating a maze or tortuous path that will ordinarily slow down or retard the progress of gas molecules through the polymeric matrix. 

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