Permeability coefficient solubility-diffusion limit

As described above, some solutes such as gases can enter the cell by diffusing down an electrochemical gradient across the membrane and do not require metabolic energy. The simple passive diffusion of a solute across the membrane is limited by the thermal agitation of that specific molecule, by the concentration gradient across the membrane, and by the solubility of that solute (the permeability coefficient. Figure 41—6) in the hydrophobic core of the membrane bilayer. Solubility is... 

Thus, in the simplest limiting case of a membrane-permeant system, one in which Henry s law and Pick s laws are observed, the coefficients of permeability P, solubility 5, and diffusion D are related as follows P = D x 5. 

The separation of a mixture of molecules A and B is characterized by the selectivity or ideal separation factor a/b = P(A)/P(B), i.e. the ratio of permeability of the molecule A over the permeability of the molecule B. According to Equation (5.5), it is possible to make separations by diffusivity selectivity D(A)/D(B) or solubility selectivity S(A)/S(B) [25,26]. This formalism is known in membrane science as the solution-diffusion mechanism. Since the limiting stage of the mass transfer is overcoming of the diffusion energy barrier, this mechanism implies the activated diffusion. Becanse of this, the temperature dependences of the diffusion coefficients and permeability coefficients are described by the Arrhenins equations. 

The dependence of permeability, diffusion, and solubility coefficients on penetrant gas pressure (or concentration in polymers) is very different at temperatures above and below the glass transition temperature, Tg, of the polymers, i.e., for mbbery and glassy polymers, respectively. Thus, when the polymers are in the rubbery state the pressure dependence of these coefficients depends, in turn, on the gas solubility in polymers. For example, as mentioned in Section 61.2.4, if the penetrant gases are very sparsely soluble and do not significantly plasticize the polymers, the permeability coefficients as well as the diffusion and solubility coefficients are independent of penetrant pressure. This is the case for supercritical gases with very low critical temperatures (compared to ambient temperature), such as the helium-group gases, Ha, Oa, Na, CH4, etc., whose concentration in rubbery polymers is within the Heruy s law limit even at elevated pressures. 

Capillaries in the Brain (the Blood-Brain Barrier). Capillaries in the brain are less permeable than capillaries in other tissues. This limited permeability, which is frequently called the blood-brain barrier, is essential for brain function. Reduced permeation provides a buffer that maintains a constant brain extracellular environment, even at times when blood chemistry is changing. The basis for this lower permeability is the relative paucity of pores in the brain endothelium. Therefore, molecules that move from blood to brain must diffuse through the endothelial cell membranes. As expected from this observation, the permeability of brain capillaries depends on the size and lipid solubility of the solute. In general, molecules that are larger than several hundred in molecular weight do not permeate into the brain. Empirical relationships between cerebrovascular permeability and the oil / water partition coefficient have been developed [26] (see Figure 5.27) ... 

When the permeability, diffusion, and solubility coefficients are functions of pressure their experimental values are mean values (P,D, and S) for the pressures applied at the membrane interfaces, cf., eqs. (61.6-61.8). Equations (61.12-61.14) are applic able als o to P, D, and 5 over a limited range of temperatures. The activation energies Ep and Ed commonly decrease with increasing pressure. 

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