Diffusion mobile carrier

All of the transport systems examined thus far are relatively large proteins. Several small molecule toxins produced by microorganisms facilitate ion transport across membranes. Due to their relative simplicity, these molecules, the lonophore antibiotics, represent paradigms of the mobile carrier and pore or charmel models for membrane transport. Mobile carriers are molecules that form complexes with particular ions and diffuse freely across a lipid membrane (Figure 10.38). Pores or channels, on the other hand, adopt a fixed orientation in a membrane, creating a hole that permits the transmembrane movement of ions. These pores or channels may be formed from monomeric or (more often) multimeric structures in the membrane. 

Ionophores and other mobile carriers. Facilitated diffusion of a molecule or ion is sometimes accomplished by binding to a mobile carrier. An example is the diffusion of a complex of K+ with the... 

Since biological membranes act as barriers for hydrophilic and large molecules, a mobile carrier molecule, due to increased mobility of the substrate-carrier complex, may increase the transport of a substrate. Facilitated transport may be described by the jumping mechanism for a fast reaction between the carrier and substrate. Consider a schematic of facilitated transport shown in Figure 9.8. If the transport of substance-carrier across the membrane is not fast enough, then the conventional diffusion-reaction system of Eq. (9.180) is described by... 

Most transporters are proteins. Small proteins can bind some substance on one side of a membrane, diffuse across the membrane, and then release that substance on the other side. Such mobile carriers may bind a single substance, or they may bind two different substances, like the proton-solute symporter portrayed in Figure 3-l4a. Candidates for transport by a proton symporter in plants include inorganic ions such as Cl- and metabolites such as sugars and amino acids. Many substances apparently move in pores or channels, which can be membrane-spanning proteins. Some channels can have a series of binding sites, where the molecule or molecules transported go from site to site through the membrane (Fig. 3-l4b). As another... 

The depth of this diffuse part depends predominantly on the concentration of mobile carriers in each phase, in a metal the concentration of mobile electrons is so high that practically all the charges behave like surface charges. In the electrolyte solution the situation is similar only at very high electrolyte concentrations, hi dilute solutions, part of the potential difference occurs in a region of 10 - 100 X in the solution phase. 

In most semiconductors the concentration of mobile carriers (electrons or holes) is very low. Therefore a diffuse part of the double layer can extend into the interior of a semiconductor electrode (2) (this point is discussed in more detail by... 

In most cases an external electric field is applied across the material with the result that the mobile carrier distribution will experience drift in the field toward a new position. Even in the absence of an applied field, the nonuniform distribution of the mobile charge carriers created will lead to their relocation due to diffusion. Although the free carriers are generated where the optical intensity is high, their recombination with counterions (in the case of hole transport these are anions) may occur anywhere in the medium. This includes recombination where the intensity is low, resulting in the separation of the charge distributions. Subsequent optical excitation is unlikely in these darker regions. We know that the counterions exist in... 

It should be mentioned here, that the capacity of the space charge layer in an intrinsic semiconductor looks very similar to that of the diffuse Gouy layer in the electrolyte (compare with Eq. 5.8). This is very reasonable because the Gouy layer is also a kind of space charge layer with ions instead of electrons as mobile carriers. Q was actually derived by the same procedure as given here for Csc- Similarly as in the case of Cn and C(j, the space charge capacity Cjc and the Helmholtz capacity Ch can be treated as capacitors circuited in scries. We have then... 

Facilitated or carrier-mediated transport is a coupled transport process that combines a (chemical) coupling reaction with a diffusion process. The solute has first to react with the carrier to fonn a solute-carrier complex, which then diffuses through the membrane to finally release the solute at the permeate side. The overall process can be considered as a passive transport since the solute molecule is transported from a high to a low chemical potential. In the case of polymeric membranes the carrier can be chemically or physically bound to the solid matrix (Jixed carrier system), whereby the solute hops from one site to the other. Mobile carrier molecules have been incorporated in liquid membranes, which consist of a solid polymer matrix (support) and a liquid phase containing the carrier [2, 8], see Fig. 7.1. The state of the art of supported liquid membranes for gas separations will be discussed in detail in this chapter. 

In carrier facilitated gas transport through liquid immobilized membranes, the overall process can be considered as a passive transport since the solute molecule is transported from a high to a low chemical potential. At the high-pressure feed side, the gas molecule that has to be selectively transported complexes with the carrier molecule diffuses along with the mobile carrier through the liquid membrane phase and desorbs at the low-pressure permeate side of the membrane [2, 4]. 

Mass transfer rates attainable In menbrane separation devices, such as gas permeators or dlalyzers, can be limited by solute transport through the menbrane. The addition Into the menbrane of a mobile carrier species, which reacts rapidly and reversibly with the solute of Interest, can Increase the membrane s solute permeability and selectivity by carrier-facilitated transport. Mass separation is analyzed for the case of fully developed, one-dimensional, laminar flow of a Newtonian fluid in a parallel-plate separation device with reactive menbranes. The effect of the diffusion and reaction parameters on the separation is investigated. The advantage of using a carrier-facilitated membrane process is shown to depend on the wall Sherwood number, tfrien the wall Sherwood nunber Is below ten, the presence of a carrier-facilitated membrane system is desirable to Improve solute separation. 

In many cases of practical interest, the membrane s mass transfer resistance is significant, i.e., the wall Sherwood number is small, leading to relatively low mass transfer rates of the solute. The diffusive flux of the permeate through the membrane can be increased by introducing a carrier species into the membrane. The augmentation of the flux of a solute by a mobile carrier species, which reacts reversibly with the solute, is known as carrier-facilitated transport (25). The use of carrier-facilitated transport in industrial membrane separation processes is of considerable interest because of the increased mass transfer rates for the solute of interest and the improved selectivity over other solutes (26). 

Since then, a number of papers have been published on this type of membrane [93-96]. Along with the use of ion exchange membranes as supports, yet another approach to overcome the previously mentioned limitations was developed by introducing carriers directly into polymer membranes [60,97,98]. These FSC membranes have carriers covalently bonded to the polymer backbone hence, the carriers have restricted mobility but are favorable when stability is considered. It is obvious that the diffusivity (and thus permeability) in an FSC membrane is lower than that of a mobile carrier membrane. The diffusivity of a swollen FSC membrane should however show diffusivities between that of a mobile and a fixed carrier. 

The charge carrier mobility (p) of a material is defined as the ratio between the drift velocity of the charge carrier (v) induced by the electric field and the amplitude of the applied electric field (F) (p = v/F). In general, carrier mobility is dictated by the diffusion coefficient (D) since the charge transport follows a diffusive mechanism. Carrier mobility is related to the diffusion coefficient via the Nemst-Ejnstein equation ... 

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