Curved membrane systems

In biological systems, one often observes membrane structures with nonzero spontaneous curvatures, e.g. in mitochondria. This type of bilayer structure is also essential in various transport related processes such as endo- and exocy-tosis (see Chapter 8 of this volume). These curved membrane systems may be stabilised by protein aggregation in the bilayer, or may be the result of the fact that biological membranes are constantly kept off-equilibrium by lipid transport and/or by (active) transport processes across the bilayer. These interesting... 

Curve 1 in Fig. 5 gives an example of the oscillation of membrane current observed with the liquid membrane system as in Eq. (3) by applying a constant AFwi-w2 of —0.48 V and measuring the time course of the current through the LM, /wi-w2- The cell used was the same as that used for the measurement of the potential oscillation, except a tetraphenyl-arsonium ion selective electrode [26,27], TPhAsE, was employed as a reference electrode in LM of NB ... 

In Fig. 4.10, the DDPV curves corresponding to a membrane system with two polarizable interfaces (solid lines) and also to a system with a single polarizable interface (dashed lines), obtained for two values of the pulse amplitude AE, are shown. The current A/DDPV has been plotted in all the cases versus the... 

For comparison of the SWV responses provided for systems of one and two polarized interfaces, Fig. 7.23 shows the/sw — E curves corresponding to the direct and to the reverse scans (solid line and empty circles, respectively) for both kinds of membrane systems, calculated for sw = 50 mV by using Eq. (7.44). The peaks obtained when two polarized interfaces are considered are shifted 8 mV with respect to those obtained for a system with a single polarized one, which implies that the half-wave potential for the system with two polarized interfaces can be easily determined from the peak potential by... 

In both types of membrane systems, the current-potential curves corresponding to the first and second scans must be mirror images, which indicates that the ion transfer processes taking place at both the outer and inner interfaces are reversible. Thus, CSWV can be used as an excellent tool for analyzing the reversibility of charge transfer processes. 

Regarding the influence of the target ion concentration on the SWV curves, the major difference found between systems with one or two polarized interfaces is that this variable causes a shift of the peak potentials toward more anodic values through an increase of E 2 in the latter case (see Eqs. (7.41)—(7.43)), whereas only an increase in the peak current is observed for systems with one polarized interface [36]. Therefore, SWV is a very good analytical tool for the determination of ion concentrations in both kinds of membrane systems. 

Ralf Kuriyel (Millipore Corporation) addressed some of the issues related to the use of Dean vortices, formed during the flow of fluids in curved conduits, to enhance the performance of cross-flow filters by increasing the back transport of solutes. Results were presented on coiled hollow fibers with a varying radius of curvature, fiber diameter, and solution viscosity, to characterize the relationship between the back transport of solutes and hydrodynamic parameters. A performance parameter relating back transport to the Dean number and shear rate was derived, and a simple scaling methodology was developed in terms of the performance parameter. The use of Dean vortices may result in membrane systems with less fouling and improved performance. 

Brewster ME, Chung KY, and Belfort G, Dean vortices with wall flux in a curved channel membrane system, 1. A new approach to membrane module design, J. Membr. Sci. 1993 81 127-137. 

Chung, K.-Y. Edelstein, W.A. Li, X. Belfort, G. Dean vortices in a curved channel membrane system. 5. Three dimensional magnetic resonance imaging and numerical analysis of the velocity field in a curved impermeable tube. AIChE J. 1993, 39, 1592-1602. 

A large variety of totally artificial membranes accessible by synkinesis have structures unknown to biological systems. One may, for example, prepare membranes as thin as 2 nm containing photoactive groups in various positions, and they may show a totally unsymmetrical distribution of two different head-groups on both surfaces of a curved membrane (see Sec. 2.5.3). Natural membranes, on the other hand, are incredibly functional. They perform the complex energy conversion and reproduction processes of life with unsurpassed efficiency and reliability. 

Equation (3) indicates that the membrane potential in the presence of sufficient electrolytes in Wl, W2, and M is primarily determined by the potential differences at two interfaces in the membrane system that depend on ion-transfer reactions at the interfaces. Taking into account the relationship in Eq. (3) and the electroneutrality in the membrane phase, the final rise in curve 1 (Fig. 3) is attributable to the simultaneous transfers of the same amounts of TPhB from M to Wl and of TPenA from M to W2 [6,7]. Similarly, the final descent in curve 1 is attributable to the simultaneous transfers of the same amounts of TPenA from M to Wl and of TPhB from M to W2. 

The voltammogram shown as curve 1 in Fig. 4 was recorded with the cell of Fig. 2(b). The voltammogram was very similar to that for perpendicular transport (curve 1 in Fig. 3), indicating that the voltammogram was realized mainly by the composite of two interfacial ion-transfer reactions, i.e., reactions at the W1 M interface of sites A and B. In other words, this result demonstrated that parallel transport of type I (Wl-M-Wl transport) could be realized when a potential difference was applied between two sites in one aqueous phase of a membrane system. 

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