Membrane solvents, relationship

A is defined here as permeate side - feed side. ) Assuming further that thermodynantic equilibrium is established at the membrane-solution boundaries, = a, where is the activity of solvent (moEm ) outside of the membrane. This relationship should be valid on both sides of the membrane. Because the osmotic pressure, Ft (Pa), is defined as... 

Traditional octanol-water distribuhon coefficients are shll widely used in quan-titahve structure-achvity relationship (QSAR) and in ADM E/PK studies. However, alternahve solvent systems have been proposed [80]. To cover the variabihty in biophysical characterishcs of different membrane types a set of four solvents has been suggested, somehmes called the critical quartet [81]. The 1,2-dichloroeth-ane-water system has been promoted as a good alternative to alkane-water due to its far better dissolution properties [82, 83], but may find little applicahon because of its carcinogenic properties. 

The octanol-water partition coefficient, Kow, is the most widely used descriptor of hydrophobicity in quantitative structure activity relationships (QSAR), which are used to describe sorption to organic matter, soil, and sediments [15], bioaccumulation [104], and toxicity [105 107J. Octanol is an amphiphilic bulk solvent with a molar volume of 0.12 dm3 mol when saturated with water. In the octanol-water system, octanol contains 2.3 mol dm 3 of water (one molecule of water per four molecules of octanol) and water is saturated with 4.5 x 10-3 mol dm 3 octanol. Octanol is more suitable than any other solvent system (for) mimicking biological membranes and organic matter properties, because it contains an aliphatic alkyl chain for pure van der Waals interactions plus the alcohol group, which can act as a hydrogen donor and acceptor. 

In case of solutions of high Molecular weight compounds, the selection of semi-permeable membrane is easier, because the solvent and the solute molecules are quite different in their size. The relationship between the Osmotic pressure of solution of a macromolecular compound and the Molecular weight is widely used for determination of Molecular weights and in the study of the interaction between the solvent and the solute molecules in the solution. 

S. E. Cross, W. J. Pugh, J. Hadgraft, and M. S. Roberts. Probing the effect of vehicles on topical delivery Understanding the basic relationship between solvent and solute penetration using silicone membranes. Pharm. Res. 18 999-1005 (2001). 

Relationship Between Nodular and Rejecting Layers. Nodular formation was conceived by Maler and Scheuerman (14) and was shown to exist in the skin structure of anisotropic cellulose acetate membranes by Schultz and Asunmaa ( ), who ion etched the skin to discover an assembly of close-packed, 188 A in diameter spheres. Resting (15) has identified this kind of micellar structure in dry cellulose ester reverse osmosis membranes, and Panar, et al. (16) has identified their existence in the polyamide derivatives. Our work has shown that nodules exist in most polymeric membranes cast into a nonsolvent bath, where gelation at the interface is caused by initial depletion of solvent, as shown in Case B, which follows restricted Inward contraction of the interfacial zone. This leads to a dispersed phase of micelles within a continuous phase (designated as "polymer-poor phase") composed of a mixture of solvents, coagulant, and a dissolved fraction of the polymer. The formation of such a skin is delineated in the scheme shown in Figure 11. 

In reverse osmosis both solvent and solute diffuse because of gradients in their chemical potentials. For the solvent there is no gradient of chemical potential at an osmotic pressure of x at applied pressures p greater than 7r, there is such a gradient that is proportional to the difference p — ir. To a first approximation, the gradient of the solute chemical potential is independent of p and depends on the difference between concentrations on opposite sides of the membrane. This leads to the result that the fraction of solute retained varies as [1 + const./(p — 7r)] 1. Verify that the following data for a reverse osmosis experiment with 0.1 M NaCl and a cellulose acetate membrane follow this relationship ... 

When solvent and solution are separated by a semipermeable membrane that permits solvent molecules to pass, an osmotic pressure is developed in the solution. This pressure, tt, is defined as the mechanical pressure that must be applied to the solution to prevent solvent molecules from diffusing into it. For water solutions the relationship between tt and the molal concentration m is given by the equation... 

Using the same terminology as before, except c, d is the donor solution and c ac the acceptor, various relationships may be obtained. For transfer from water, through a solvent-impregnated membrane, into water... 

How rapidly diffusion occurs is characterized by the diffusion coefficient D, a parameter that provides a measure of the mean of the squared displacement x of a molecule per unit time f. For diffusion in two dimensions such as a membrane, this is given by = 4Ht. The Saffman-Delbrtlck model of Brownian motion in biologic membranes describes the relationship between membrane viscosity, solvent viscosity, the radius R and height of the diffusing species, and D for both lateral and rotational diffusion of proteins in membranes (3, 4). This model predicts for example that for lateral diffusion, D should be relatively insensitive to the radius of the diffusing species, scaling with log (1/R). 

Extensive efforts have been made to develop quantitative structure/activity relationships (QSARs) that predict membrane transport (16, 17). Particularly extensive use has been made of log P (log solvent/water partition coefficient values) and the Hansch equation (Equation 14.3) ... 

For the case of pure solvent on the low pressure side of the membrane, the osmotic pressure relationship is... 

When a solution is separated from the pure solvent by a membrane that is permeable to the solvent but not to the solute, molecules of solvent migrate through the membrane into the solution compartment (Fig. 2 8a). The pressure that must be exerted to prevent the passage of solvent molecules is knoviin as the osmotic pressure (ir). The osmotic pressure of a solution depends on the concentration of solute and the temperature of the solution. The relationship (shown below) is identical to the PVT relationship of gases. 

The relationship between dye elimination coefficient and casting parameters is plotted in Figures 3 to 7. The curves given there show that, when the time of solvent evaporation (Fig. 5) and PS concentration in the casting solution (Fig. 7) increase, the separation factor also increases. On the other hand, increasing the temperature of the casting solution accounts for transitory deterioration of the separation properties of the membranes (Fig. 6). 

The relationship between separation properties and casting parameters depends on the membrane structure. According to the Bokhorst - Altena — Smolders theory of phase separation [ 8 ], when PS concentration in the casting solution is increased and the time of solvent evaporation is extended, pore diameter decreases, thus improving the selectivity of the membranes. However, the increase of temperature to a critical value accounts for the increase of pore diameter, which brings about a decrease of the separation factor value. Further increase in temperature brings about a rapid evaporation of the solvent to yield small pore diameter membranes characterized by better separation properties. 

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