Membrane permeability phase equilibrium

We have already defined Dalton s pressures and the partial pressures. There is still one more pressure of a gas in a gas mixture that must be considered. This is the equilibrium pressure, and was first discussed by Gibbs [15]. The equilibrium pressure of a component is the pressure exerted by the pure component when it is in equilibrium with a gas mixture through a rigid, diathermic membrane that is permeable only to that component. The temperature of the pure phase and that of the gas mixture must be the same, but the pressure of the two phases will be different. We may conceive of two phases at the same temperature separated by such a membrane, one phase being the pure fcth component and the other the gas mixture. The condition of equilibrium is that the chemical potential of the fcth component must be identical in each phase. If P is the equilibrium pressure, then by Equation (7.69)... 

Editor s note The resin matrix serves as a membrane permeable to difiiisible components. At equilibrium their chemical potentials are equal in separate phases. The fact that one or more species are observable in only the gel phase suggests that these species are immobilized by their interaction with the charged surface of the organic gel matrix. 

Let us consider a solution (denoted by a single prime) separated from the pure solvent (denoted by a double prime) by a membrane which is permeable only to the solvent. A membrane of this kind is called a semi-permeable membrane. The chemical equilibrium eventually established between the phases is called osmotic equilibrium. 

This section considers the Donnan equilibrium which is established by the equilibrium distribution of a simple electrolyte between an aqueous protein-electrolyte mixture and an aqueous solution of the same simple electrolyte, when the two phases are separated by a semipermeable membrane. A difference in osmotic pressure is estabhshed across the membrane permeable to all other species but proteins. This difference is measurable and provides important information about the protein-protein interaction in solution [37, 109-112, 116]. The principal goal of the theory is to explain how factors such as protein concentration, pH, protein aggregation, salt concentration and its composition, influence the osmotic pressure. At the moment this goal seems to be too ambitious these systems are often complicated mixtures of highly concentrated electrolytes and protein molecules, and the principal forces are not easy to identify [117]. 

Sousa et al [5.76, 5.77] modeled a CMR utilizing a dense catalytic polymeric membrane for an equilibrium limited elementary gas phase reaction of the type ttaA +abB acC +adD. The model considers well-stirred retentate and permeate sides, isothermal operation, Fickian transport across the membrane with constant diffusivities, and a linear sorption equilibrium between the bulk and membrane phases. The conversion enhancement over the thermodynamic equilibrium value corresponding to equimolar feed conditions is studied for three different cases An > 0, An = 0, and An < 0, where An = (ac + ad) -(aa + ab). Souza et al [5.76, 5.77] conclude that the conversion can be significantly enhanced, when the diffusion coefficients of the products are higher than those of the reactants and/or the sorption coefficients are lower, the degree of enhancement affected strongly by An and the Thiele modulus. They report that performance of a dense polymeric membrane CMR depends on both the sorption and diffusion coefficients but in a different way, so the study of such a reactor should not be based on overall component permeabilities. 

We shall consider a homogeneous gas phase of r components and r -f 1 degrees of freedom (x,. . . , Xr-i,p,T). In order to compute the chemical potential of component i in the mixture, the notion of the partial pressure of component i will be introduced. The partial pressure of component i in the mixture, is defined as the pressure exerted by pure i in equilibrium with the mixture through a membrane permeable to i alone. 

In the vinyl-chloride process, because of the significant differences in the volatilities of the three principal chemical species, distillation, absorption, and stripping are prime candidates for the separators, especially at the high production rates specified. For other processes, liquid-liquid extraction, enhanced distillation, adsorption, and membrane separators might become more attractive, in which case the design team would need to assemble data that describe the effect of solvents on species phase equilibrium, species adsorption isotherms, and the permeabilities of the species through various membranes. 

In many technical applications, liquids with different concentrations are separated by so-called semipermeable membranes, this means membranes which are permeable only for the solvent but not for the dissolved species. Phase equilibrium between these two liquids can only be achieved by diffusion of the solvent through this membrane. This happens in a way that the solvent is transported from the solution with the lower solute concentration to the solution with the higher concentration. This phenomenon is called osmosis. 

Membrane permeability is defined as the product of the solubility and diffusivity of a compound in the selective membrane layer (f, - = S,D,). Note the selectivity offered by the membrane is independent of the phase equifibrium of the system, such as the vapor—liquid equilibrium (VLB) behavior. 

Section 12.2.2 sketched a derivation of the conditions needed for equilibrium in a two-phase system in which a membrane permeable only to solvent separates a solution from pure solvent. We can generalize the results for any system with two liquid phases separated by a semipermeable membrane in an equilibrium state, both phases must have the same... 

Computer simulations of both equilibrium and dynamic properties of small solutes indicate that the solubility-diffusion model is not an accurate approximation to the behavior of small, neutral solutes in membranes. This conclusion is supported experimentally [57]. Clearly, packing and ordering effects, as well as electrostatic solute-solvent interactions need to be included. One extreme example are changes in membrane permeability near the gel-liquid crystalline phase transition temperature [56]. Another example is unassisted ion transport across membranes, discussed in the following section. 

Example 14.5 In Figure 14.3, phase 1 is seawater and phase 2 is freshwater, both at 40°F. The two phases are separated by a membrane permeable to water but not to salts. If they are at equilibrium, what is the pressure difference between them ... 

Since lipophilic molecules have affinity for both the membrane lipid and the serum proteins, membrane retention is expected to decrease, by the extent of the relative lipophilicities of the drug molecules in membrane lipid versus serum proteins, and by the relative amounts of the two competitive-binding phases [see Eqs. (7.41)-(7.43)]. Generally, the serum proteins cannot extract all of the sample molecules from the phospholipid membrane phase at equilibrium. Thus, to measure permeability under sink conditions, it is still necessary to characterize the extent of membrane retention. Generally, this has been sidestepped in the reported literature. 

As we indicated in Chapter 13, the requirement that all phases be at the same pressure at equilibrium does not apply in all situations, and in particular, it does not apply to two phases of different composition separated by a rigid membrane. If the membrane is permeable to only one component, we can show that the pressure on the two phases must be different if equilibrium is maintained at a. fixed temperature. 

Donnan equilibrium phys chem The particular eq ul 11 bri u m set up when two coexisting phases are subject to the restriction that one or more of the ionic components cannot pass from one phase into the other commonly, this restriction is caused by a membrane which is permeable to the solvent and small ions but impermeable to colloidal ions or charged particles of colloidal size. Also known as Gibbs-Donnan equilibrium. dO-non e-kwo lib-re-om ... 

At least two different techniques are available to compress an emulsion at a given osmotic pressure H. One technique consists of introducing the emulsion into a semipermeable dialysis bag and to immerse it into a large reservoir filled with a stressing polymer solution. This latter sets the osmotic pressure H. The permeability of the dialysis membrane is such that only solvent molecules from the continuous phase and surfactant are exchanged across the membrane until the osmotic pressure in the emulsion becomes equal to that of the reservoir. The dialysis bag is then removed and the droplet volume fraction at equilibrium is measured. 

The final colligative property, osmotic pressure,24-29 is different from the others and is illustrated in Figure 2.2. In the case of vapor-pressure lowering and boiling-point elevation, a natural boundary separates the liquid and gas phases that are in equilibrium. A similar boundary exists between the solid and liquid phases in equilibrium with each other in melting-point-depression measurements. However, to establish a similar equilibrium between a solution and the pure solvent requires their separation by a semi-permeable membrane, as illustrated in the figure. Such membranes, typically cellulosic, permit transport of solvent but not solute. Furthermore, the flow of solvent is from the solvent compartment into the solution compartment. The simplest explanation of this is the increased entropy or disorder that accompanies the mixing of the transported solvent molecules with the polymer on the solution side of the membrane. Flow of liquid up the capillary on the left causes the solution to be at a hydrostatic pressure... 

---