Diffusion-solubility mechanism

The ideas of Overton are reflected in the classical solubility-diffusion model for transmembrane transport. In this model [125,126], the cell membrane and other membranes within the cell are considered as homogeneous phases with sharp boundaries. Transport phenomena are described by Fick s first law of diffusion, or, in the case of ion transport and a finite membrane potential, by the Nernst-Planck equation (see Chapter 3 of this volume). The driving force of the flux is the gradient of the (electro)chemical potential across the membrane. In the absence of electric fields, the chemical potential gradient is reduced to a concentration gradient. Since the membrane is assumed to be homogeneous, the 

Meanwhile, computational methods have reached a level of sophistication that makes them an important complement to experimental work. These methods take into account the inhomogeneities of the bilayer, and present molecular details contrary to the continuum models like the classical solubility-diffusion model. The first solutes for which permeation through (polymeric) membranes was described using MD simulations were small molecules like methane and helium [128]. Soon after this, the passage of biologically more interesting molecules like water and protons [129,130] and sodium and chloride ions [131] over lipid membranes was considered. We will come back to this later in this section. 

---

Because of its apolar interior, the lipid bilayer is a barrier to diffusional equilibration of solutes between the two aqueous compartments that it separates. The ability of most small solute molecules (50 < molecular weight < 300) to cross the bilayer is directly proportional to their ability to partition into hexadecane or olive oil from an aqueous solution (58), which is an observation first made by Overton (59) and is often referred to as Overton s Law. Permeation of lipid bilayers by small polar molecules and ions seems to occur via one or a combination of both of two mechanisms depending on the nature of the permeants and the nature of the bilayers. First, a solubility-diffusion mechanism treats the bilayer as a slab of liquid hydrocarbon sandwiched between two bulk aqueous compartments. The permeant must partition into the bilayer slab from one of the aqueous compartments, diffuse across it, and leave by dissolving into the second aqueous compartment. In this case, the permeability coefficient, P, is given by ... 

S. Paula, A.G. Volkov, and D.W. Deamer. Permeation of halide anions through phospholipid bilayers occurs by the solubility-diffusion mechanism. Biophys. J., 74 (1998) 319-... 

A thorough discussion of the mechanisms of absorption is provided in Chapter 4. Water-soluble vitamins (B2, B12, and C) and other nutrients (e.g., monosaccharides, amino acids) are absorbed by specialized mechanisms. With the exception of a number of antimetabolites used in cancer chemotherapy, L-dopa, and certain antibiotics (e.g., aminopenicillins, aminoceph-alosporins), virtually all drugs are absorbed in humans by a passive diffusion mechanism. Passive diffusion indicates that the transfer of a compound from an aqueous phase through a membrane may be described by physicochemical laws and by the properties of the membrane. The membrane itself is passive in that it does not partake in the transfer process but acts as a simple barrier to diffusion. The driving force for diffusion across the membrane is the concentration gradient (more correctly, the activity gradient) of the compound across that membrane. This mechanism of... 

If the pore-mechanism applies, the rate of permeation should be related to the probability at which pores of sufficient size and depth appear in the bilayer. The correlation is given by the semi-empirical model of Hamilton and Kaler [150], which predicts a much stronger dependence on the thickness d of the membrane than the solubility-diffusion model (proportional to exp(-d) instead of the 1 Id dependence given in equation (14)). This has been confirmed for potassium by experiments with bilayers composed of lipids with different hydrocarbon chain lengths [148], The sensitivity to the solute size, however, is in the model of Hamilton and Kaler much less pronounced than in the solubility-diffusion model. 

In dense membranes, no pore space is available for diffusion. Transport in these membranes is achieved by the solution diffusion mechanism. Gases are to a certain extent soluble in the membrane matrix and dissolve. Due to a concentration gradient the dissolved species diffuses through the matrix. Due to differences in solubility and diffusivity of gases in the membrane, separation occurs. The selectivities of these separations can be very high, but the permeability is typically quite low, in comparison to that in porous membranes, primarily due to the low values of diffusion coefficients in the solid membrane phase. 

As explained in Chapter 5, the transport mechanism in dense crystalline materials is generally made up of incessant displacements of mobile atoms because of the so-called vacancy or interstitial mechanisms. In this sense, the solution-diffusion mechanism is the most commonly used physical model to describe gas transport through dense membranes. The solution-diffusion separation mechanism is based on both solubility and mobility of one species in an effective solid barrier [23-25], This mechanism can be described as follows first, a gas molecule is adsorbed, and in some cases dissociated, on the surface of one side of the membrane, it then dissolves in the membrane material, and thereafter diffuses through the membrane. Finally, in some cases it is associated and desorbs, and in other cases, it only desorbs on the other side of the membrane. For example, for hydrogen transport through a dense metal such as Pd, the H2 molecule has to split up after adsorption, and, thereafter, recombine after diffusing through the membrane on the other side (see Section 5.6.1). 

Many computational studies of the permeation of small gas molecules through polymers have appeared, which were designed to analyze, on an atomic scale, diffusion mechanisms or to calculate the diffusion coefficient and the solubility parameters. Most of these studies have dealt with flexible polymer chains of relatively simple structure such as polyethylene, polypropylene, and poly-(isobutylene) [49,50,51,52,53], There are, however, a few reports on polymers consisting of stiff chains. For example, Mooney and MacElroy [54] studied the diffusion of small molecules in semicrystalline aromatic polymers and Cuthbert et al. [55] have calculated the Henry s law constant for a number of small molecules in polystyrene and studied the effect of box size on the calculated Henry s law constants. Most of these reports are limited to the calculation of solubility coefficients at a single temperature and in the zero-pressure limit. However, there are few reports on the calculation of solubilities at higher pressures, for example the reports by de Pablo et al. [56] on the calculation of solubilities of alkanes in polyethylene, by Abu-Shargh [53] on the calculation of solubility of propene in polypropylene, and by Lim et al. [47] on the sorption of methane and carbon dioxide in amorphous polyetherimide. In the former two cases, the authors have used Gibbs ensemble Monte Carlo method [41,57] to do the calculations, and in the latter case, the authors have used an equation-of-state method to describe the gas phase. 

Liquid water on one side of a silicone contact lens permeates through the lens by a solution-diffusion mechanism and evaporates on the other side quickly according to the permeability of water, whereas the solubility of water in silicone polymer is low [1]. The high water vapor permeability was speculated to be one of the reasons causing the suction cup effect that makes the lens stationary on one spot and tenaciously stick to the cornea this may damage the corneal epithelium and result in other complications. However, the high permeability per se cannot be the reason for the suction cup effect if the exterior surface is covered by the tear film, i.e., if there is no driving force for water permeation. 

The passive permeability of lipid membranes is another fluidity related parameter. In general, two mechanisms of membrane permeability can operate in the membrane (8). For many nonpolar molecules, the predominant permeation pathway is solubility-diffusion, which is a combination of partitioning and diffusion across the bilayer, both of which depend on lipid fluidity. In a few cases, such as permeation of positively charged ions through thin bilayers, an alternative pathway prevails (9, 10). It is permeation through transient pores produced in the bilayer by thermal fluctuations. This mechanism, in general, correlates with membrane fluidity. However, for model membranes undergoing the main phase transition, permeation caused by this mechanism exhibits a clear maximum near the phase transition point (11). 

Since a monolayer of material is completely sputtered in a matter of seconds in a typical FAB ion source, it is essential that the sample surface be continuously regenerated during prolonged examination. This is done naturally by diffusion of the sample to the surface of the solution. It is therefore essential that the sample have some solubility in the low-volatility solvent, to provide the diffusion mechanism and also to act as a reservoir of material. Ionic groups that render compounds involatile, thus ruling out conventional methods of ionization, are also those groups that frequently lead to solubility in polar solvents, and to the associated surfactant properties that facilitate good sample preparation for FAB ionization. It follows that the detection of solvent substrate peaks in a FAB mass spectrum implies that optimal sample preparation has not been achieved. 

The operation, since 1945, of nuclear reactors has made available radioisotopes of most elements. The isotopes are useful in a variety of chemical investigations, including those concerned with solubility, diffusion, reaction mechanism and structure. They have given rise to new analytical techniques, such as isotopic dilution and radioactivation analysis. In industry also, they have a wide and rapidly expanding application. All this is made possible by the ease with which small quantities of the nuclides can be detected, often remotely, and quantitatively determined by commercially available and easily operated equipment. 

Transport through nonporous membranes follows the solution-diffusion mechanism, and separation is achieved either by differences in solubility or diffusivity. Therefore,... 

---