Diffusion of small molecules

The diffusion of small molecules in polymers can be described using Pick s first and second laws. In a onedimensional situation, the flux J(c, x) as a function of the concentration c and the position x is given by... 

Frisch FI L and Stern S A 1983 Diffusion of small molecules in polymers Crit. Rev. Solid State Mater. Sc/. 11 123... 

Brown, W Stilbs, P Lindstrom, T, Self-Diffusion of Small Molecules in Cellulose Gels using FT-Pulsed Field Gradient NMR, Journal of Applied Polymer Science 29, 823,1984. Brownstein, KR Tarr, CE, Importance of Classical Diffusion in NMR Studies of Water in Biological Cells, Physical Review A 19, 2446, 1979. 

Solid-state NMR methods have been much used to study the characteristics of the network chains themselves, particularly with regard to orientations [265], molecular motions [266], and their effects on the diffusion of small molecules [267], Aspects related to the structures of the networks include the degree of cross-linking [268,269], the distributions of cross-links [270] and stresses [271], and topologies [272,273]. Another example is the use of NMR to clarify some issues in the areas of aging and phase separation [274],... 

Cation Size. In their early studies, Hlnsberg (1) and Arcus (3) found that dissolution rates of resists decreased as the size of the cation of the base Increased. Our results support their conclusion. In Figure 5, the dissolution rates of a PMPS(10X)/p-N02-PHMP film 1n different alkali solutions clearly show a decreasing trend with increasing cation size. In fact, the rate 1s Inversely proportional to the cross-sectional area of the unhydrated cation (Figure 6). It is known 1n the diffusion of small molecules 1n polymers, the diffusion constant is Inversely related to the size of the molecule (IS). The observed dependence of dissolution rate on cation size 1s therefore suggestive of cation diffusion as a crucial step. It is... 

The papers of Mallon and Ray [98, 123] can be regarded as the state of the art in understanding and modelling solid-state polycondensation. They assumed that chain ends, catalysts and by-products exist solely in the amorphous phase of the polymer. Because of the very low mobility of functional groups in the crystalline phase, the chemical reactions are modelled as occurring only in the amorphous phase. Additionally, the diffusion of by-products is hindered by the presence of crystallites. The diffusivity of small molecules was assumed to be proportional to the amorphous fraction. Figure 2.32 shows the diffusion coefficients for the diffusion of EG and water in solid PET. 

Beta-lactam antibiotics must pass through the outer layer of the cell in order to get the desired PBP to the surface of the membrane. In Gram-positive bacteria, the cell membrane is the only layer covering the cytoplasmic membrane. In a few types of this bacteria, there is a polysaccharide capsule on the outer side of the cell membrane. However, not one of the described structures can serve as a barrier for the diffusion of small molecules such as beta-lactams. Therefore, the idea that the cause of possible resistance is the inability of beta-lactam antibiotics to get the desired PBP is not likely to be a possible mechanism of resistance for Gram-positive bacteria. 

It is relatively easier for a small neutral molecule (such as Fie or H2) to move through a liquid or solid structure, than for a large molecule (such as Xe). Hence, the activation energy for diffusion of small molecules is small and the diffusion coefficient is large. 

The jamming effect, i.e., the slowing down of the longitudinal diffusion of a polymer chain by the head-on collision with other chains, can be treated by a model similar to that proposed by Cohen and Turnbull [112] for self diffusion of small molecules in a fluid. This model assumes that if at least one surrounding polymer chain exists within the critical hole ahead of a test chain, both collide, and this prevents the test chain from diffusing longitudinally. With this assumption, we express the longitudinal diffusion coefficient Dp of the test chain as... 

The derived X-ray data indicate that the solvent-salt region in the crystals is in part not crystalline, and this is consistent with fast diffusion of small molecules into the crystals. 

The technical term for this is hydrodynamic focusing, flow of a sample stream within the center core of a sheath stream is called coaxial flow. The exact diameter of that central sample core within the sheath stream is related to, among other things, the rate at which the sample is injected into the sheath stream a 100 pm sheath stream may, depending on sample injection velocity, have a core width of perhaps 5-20 pm (Fig. 3.4). Because hydrodynamic focusing tends to confine the cell sample to this central core, there is little mixing of sample with sheath fluid (but diffusion of small molecules will occur). The reason that this type of coaxial sample flow suits flow cytometry... 

Berens, A. R. (1989). Solubility and diffusion of small molecules in PVC. Journal of Vinyl... 

Escherichia coli cells (BL21) were entrapped in hydrogel micropatches. The cells were found to remain viable in the patches. Furthermore, diffusion of small molecules through the polymer (with 1-10 nm pores) to the cells allows cell reactions to be studied. For example, the fluorescent dye BCECF-AM diffused to the cells and the dye was converted to BCECF by intracellular enzymes present only in live cells [1053]. 

In this chapter, subsequent to an introduction to devolatilization equipment, we review the thermodynamics of polymer solution equilibrium, which determines the maximum amount of volatiles that can be separated under a given set of processing conditions the phenomena associated with diffusion and diffusivity of small molecules in polymeric melts, which affects the rate of mass transfer the phenomena and mechanisms involving devolatilization and their modeling and the detailed and complex morphologies within the growing bubbles created during devolatilization of melts. 

Yet in spite of all the evidence just presented, it is not impossible that at very low volatile levels the Latinen-type model may have some validity, but this likelihood appears to be small because foaming was observed at volatile concentrations as low as 50 ppm. Moreover, the likelihood further diminishes due to the fact that, as shown in Section 8.5, the diffusivity of small molecules in polymeric melts may drop by orders of magnitude, with dropping concentrations at these levels. 

Larry Duda and Jim Vrentas were the first to systematically study the diffusion of small molecules in molten polymers, formulate a free volume-based theoretical model, and elucidate the sharp dependence of the diffusion coefficient on temperature and concentration.2 Figure 8.8 shows diffusivities of toluene in polystyrene as a function of concentration and temperature. The values were computed using the Vrentas and Duda (17) free volume model and, as shown, coincide well with available data. 

Various dynamic processes have been investigated using computer simulations of phospholipids. These include the dynamics of the alkyl chain movement of the phospholipid, the structure of water at the interface, diffusion of small molecules, interactions of phospholipids with water, dmgs, peptides, and proteins, and the effect of unsaturation or the presence of cholesterol on the phospholipid conformation. 

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