Diffusion thermodynamic membrane

Nonequilibrium thermodynamics provides a second approach to combined convection and diffusion problems. The Kedem-Katchalsky equations, originally developed to describe combined convection and diffusion in membranes, form the basis of this approach [6,7] ... 

The insertion of proteins into intracellular membranes has incising effects upon the kinetic and thermodynamic properties of the corresponding biological interactions. Although diffusion in membranes is approx. 100-fold slower than in aqueous solution the probability for two molecules to meet... 

The starting point for the mathematical description of diffusion in membranes is the proposition, solidly based in thermodynamics, that the driving forces of pressure, temperature, concentration, and electrical potential are interrelated and that the overall driving force producing movement of a permeant is the gradient in its chemical potential. Thus, the flux,. /,(g/cm2 s), of a component, i, is... 

Diffusion across membranes is an alternative route to separations where transport rates can enhance thermodynamic differences. In most cases, membrane diffusion depends on the permeability, which is the product of a diffusion coefficient and a partition coefficient, often called a solubility. Such membranes, coated onto porous support to provide mechanical strength, may be used as hollow fibers or in spiral-wound modules to increase the area per volume and hence increase the flux per volume. 

Reverse osmosis models can be divided into three types irreversible thermodynamics models, such as Kedem-Katchalsky and Spiegler-Kedem models nonporous or homogeneous membrane models, such as the solution—diffusion (SD), solution—diffusion—imperfection, and extended solution—diffusion models and pore models, such as the finely porous, preferential sorption—capillary flow, and surface force—pore flow models. Charged RO membrane theories can be used to describe nanofiltration membranes, which are often negatively charged. Models such as Dorman exclusion and the... 

Membra.ne Diffusiona.1 Systems. Membrane diffusional systems are not as simple to formulate as matrix systems, but they offer much more precisely controlled and uniform dmg release. In membrane-controlled dmg deUvery, the dmg reservoir is intimately surrounded by a polymeric membrane that controls the dmg release rate. Dmg release is governed by the thermodynamic energy derived from the concentration gradient between the saturated dmg solution in the system s reservoir and the lower concentration in the receptor. The dmg moves toward the lower concentration at a nearly constant rate determined by the concentration gradient and diffusivity in the membrane (33). 

From a thermodynamic and kinetic perspective, there are only three types of membrane transport processes passive diffusion, faeilitated diffusion, and active transport. To be thoroughly appreciated, membrane transport phenomena must be considered in terms of thermodynamics. Some of the important kinetic considerations also will be discussed. 

Passive diffusion is the simplest transport process. In passive diffusion, the transported species moves across the membrane in the thermodynamically favored direction without the help of any specific transport system/molecule. For an uncharged molecule, passive diffusion is an entropic process, in which movement of molecules across the membrane proceeds until the concentration of the substance on both sides of the membrane is the same. For an uncharged molecule, the free energy difference between side 1 and side 2 of a membrane (Figure 10.1) is given by... 

The general theoretical treatment of ion-selective membranes assumes a homogeneous membrane phase and thermodynamic equilibrium at the phase boundaries. Obvious deviations from a Nemstian behavior are explained by an additional diffusion potential inside the membrane. However, allowing stationary state conditions in which the thermodynamic equilibrium is not established some hitherto difficult to explain facts (e.g., super-Nemstian slope, dependence of the selectivity of ion-transport upon the availability of co-ions, etc.) can be understood more easily. 

Figure 10.5 shows the basic concept of the particle-level MR that gives (i) selective addition of reactants to the reaction zone and (ii) selective removal of products from the reaction zone. In the first case, if the diffusivity of one reactant (A) is much higher than that of the other components (B), the reactant (A) selectively diffuses into a catalyst particle through a membrane. Undesired reactions or the adsorption of poisons on the catalysts can be prevented. In the second case, the reaction has a hmited yield or is selectivity controlled by thermodynamics. The selective removal of the desired product from the catalyst particle gives enhancement of selectivity when the diffusivity of one product (R) is much greater than that of the other products (S). 

Before we describe the chemistry of the compartments involved, note that like prokaryotes, a number of oxidative enzymes are found in the cytoplasm but they do not release damaging chemicals (see Section 6.10). We also observed that such kinds of kinetic compartments are not enclosed by physical limitations such as membranes. We have also mentioned that increased size itself makes for kinetic compartments if diffusion is restricted. In this section, we see many additional advantages of eukaryotes from those given in Section 7.4. How deceptive it can be to use just the DNA, the all-embracing proteome, metabolome or metallome in discussing evolution without the recognition of the thermodynamic importance of compartments and their concentrations These data could be useful both here and in simpler studies of single-compartment bacteria even in the analysis of species but not much information is available. 

The only potential that varies significantly is the phase boundary potential at the membrane/sample interface EPB-. This potential arises from an unequal equilibrium distribution of ions between the aqueous sample and organic membrane phases. The phase transfer equilibrium reaction at the interface is very rapid relative to the diffusion of ions across the aqueous sample and organic membrane phases. A separation of charge occurs at the interface where the ions partition between the two phases, which results in a buildup of potential at the sample/mem-brane interface that can be described thermodynamically in terms of the electrochemical potential. At interfacial equilibrium, the electrochemical potentials in the two phases are equal. The phase boundary potential is a result of an equilibrium distribution of ions between phases. The phase boundary potentials can be described by the following equation ... 

The thermodynamic approach does not make explicit the effects of concentration at the membrane. A good deal of the analysis of concentration polarisation given for ultrafiltration also applies to reverse osmosis. The control of the boundary layer is just as important. The main effects of concentration polarisation in this case are, however, a reduced value of solvent permeation rate as a result of an increased osmotic pressure at the membrane surface given in equation 8.37, and a decrease in solute rejection given in equation 8.38. In many applications it is usual to pretreat feeds in order to remove colloidal material before reverse osmosis. The components which must then be retained by reverse osmosis have higher diffusion coefficients than those encountered in ultrafiltration. Hence, the polarisation modulus given in equation 8.14 is lower, and the concentration of solutes at the membrane seldom results in the formation of a gel. For the case of turbulent flow the Dittus-Boelter correlation may be used, as was the case for ultrafiltration giving a polarisation modulus of ... 

Even when using LDPE and PP, the diffusive losses of most nonpolar solvents may be unacceptably large for A designs that exceeded 1 cm . This is especially true at higher exposure temperatures because both solute diffusion and polymer free volume increase with temperature (Comyn, 1985). Even when solvent losses were not excessive, uptake of HOCs by membrane-enclosed solvents appeared to become curvilinear well before thermodynamic equilibrium was approached. This phenomenon is likely due to the outward flux of sampler solvent with elevated HOC levels (relative to water), which appears to facilitate residue... 

The simplest practicable approach considers the membrane as a continuous, nonporous phase in which water of hydration is dissolved.In such a scenario, which is based on concentrated solution theory, the sole thermodynamic variable for specifying the local state of the membrane is the water activity the relevant mechanism of water back-transport is diffusion in an activity gradient. However, pure diffusion models provide an incomplete description of the membrane response to changing external operation conditions, as explained in Section 6.6.2. They cannot predict the net water flux across a saturated membrane that results from applying a difference in total gas pressures between cathodic and anodic gas compartments. 

Buccal dosage forms can be of the reservoir or the matrix type. Formulations of the reservoir type are surrounded by a polymeric membrane, which controls the release rate. Reservoir systems present a constant release profile provided (1) that the polymeric membrane is rate limiting, and (2) that an excess amoimt of drug is present in the reservoir. Condition (1) may be achieved with a thicker membrane (i.e., rate controlling) and lower diffusivity in which case the rate of drug release is directly proportional to the polymer solubility and membrane diffusivity, and inversely proportional to membrane thickness. Condition (2) may be achieved, if the intrinsic thermodynamic activity of the drug is very low and the device has a thick hydrodynamic diffusion layer. In this case the release rate of the drug is directly proportional to solution solubility and solution diffusivity, and inversely proportional to the thickness of the hydrodynamic diffusion layer. 

Facilitated diffusion within organisms takes place when carriers or proteins residing within membranes—ion channels, for instance—organize the movement of ions from one location to another. This diffusion type is a kinetic, not thermodynamic, effect in which a for the transfer is lowered and the rate of diffusion is accelerated. Facilitated diffusion channels organize ion movements in both directions, and the process can be inhibited both competitively and noncompetitively. It is known that most cells maintain open channels for K+ most of the time and closed channels for other ions. Potassium-ion-dependent enzymes include NaVK+ ATPases (to be discussed in Section 5.4.1), pyruvate kinases, and dioldehydratases (not to be discussed further). 

For single-component gas permeation through a microporous membrane, the flux (J) can be described by Eq. (10.1), where p is the density of the membrane, ris the thermodynamic correction factor which describes the equilibrium relationship between the concentration in the membrane and partial pressure of the permeating gas (adsorption isotherm), q is the concentration of the permeating species in zeolite and x is the position in the permeating direction in the membrane. Dc is the diffusivity corrected for the interaction between the transporting species and the membrane and is described by Eq. (10.2), where Ed is the diffusion activation energy, R is the ideal gas constant and T is the absolute temperature. 

Novel unit operations currently being developed are membrane reactors where both reaction and separation occur simultaneously. Through selective product removal a shift of the conversion beyond thermodynamic equilibrium is possible. The membrane itself can serve in different capacities including (i) a permselective diffusion barrier, (ii) a non-reactive reactant distributor and (iii) as both a catalyst and permselective membrane [44]. 

When it comes to the equilibration of water concentration gradients, the relevant transport coefficient is the chemical diffusion coefficient, Dwp. This parameter is related to the self-diffusion coefficient by the thermodynamic factor (see above) if the elementary transport mechanism is assumed to be the same. The hydration isotherm (see Figure 8) directly provides the driving force for chemical water diffusion. Under fuel-cell conditions, i.e., high degrees of hydration, the concentration of water in the membrane may change with only a small variation of the chemical potential of water. In the two-phase region (i.e., water contents of >14 water molecules... 

This chapter is based on the thermodynamic theory of membrane potentials and kinetic effects will be considered only in relation to diffusion potentials in the membrane. The ISE membrane in the presence of an interferent can be thought of as analogous to a corroding electrode [46a] at which chemically different charge transfer reactions proceed [15, 16]. Then the characteristics of the ISE potentials can be obtained using polarization curves for electrolysis at the boundary between two immiscible electrolyte solutions [44[Pg.35]

Figure 19.3 schematically describes in more detail the transport phenomena occurring during pervaporation. First, solutes partition into the membrane material according to the thermodynamic equilibrium at the liquid-membrane interface (Fig. 19.3a), followed by diffusion across the membrane material owing to the concentration gradient (Fig. 19.3b). A vacuum or carrier gas stream promotes then continuous desorption of the molecules reaching the permeate side of the membrane (Fig. 19.3c), maintaining in this way a concentration gradient across the membrane and hence a continuous transmembrane flux of compounds.

---