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** Minimal Surfaces With Zero Curvature **

** Periodic zero potential surfaces **

** Potential-energy surfaces zero order **

** Surface tension and the potential of zero charge **

** Zero proton condition at the surface **

ordered molecular islands surrounded by disordered molecules are common in Langmuir layers, where even in zero surface pressure molecules self-organize at the air—water interface. The difference between the two systems is that in SAMs of trichlorosilanes the island is comprised of polymerized surfactants, and therefore the mobihty of individual molecules is restricted. This lack of mobihty is probably the principal reason why SAMs of alkyltrichlorosilanes are less ordered than, for example, fatty acids on AgO, or thiols on gold. The coupling of polymerization and surface anchoring is a primary source of the reproducibihty problems. Small differences in water content and in surface Si—OH group concentration may result in a significant difference in monolayer quahty. Alkyl silanes remain, however, ideal materials for surface modification and functionalization apphcations, eg, as adhesion promoters (166—168) and boundary lubricants (169—171). [Pg.538]

Bilayers have received even more attention. In the early studies, water has been replaced by a continuous medium as in the monolayer simulations [64-67]. Today s bilayers are usually fully hydrated , i.e., water is included exphcitly. Simulations have been done at constant volume [68-73] and at constant pressure or fixed surface tension [74-79]. In the latter case, the size of the simulation box automatically adjusts itself so as to optimize the area per molecule of the amphiphiles in the bilayer [33]. If the pressure tensor is chosen isotropic, bilayers with zero surface tension are obtained. Constant... [Pg.641]

When, after the attainment of zero surface concentration, a constant current density is maintained artificially from outside, the electrode potential will shift to a value such that a new electrochemical reaction involving other solution components can start (e.g., in aqueous solution, the evolution of hydrogen or oxygen). It follows from Eq. (11.9) that at a given concentration Cy the product is constant and is... [Pg.185]

The concentration asymptotically approaches the value Cq with increasing distance X (i.e., the reaction zone has no distinct boundary). Conventionally, thickness 5,. is defined just like the diffusion-layer thickness 5 [i.e., by the condition that Cq/5,. = (dcldx) o for zero surface concentration. Using Eq. (13.41), we find that... [Pg.232]

Besides surface reconstructions induced by heat treatment, potential-induced reconstruction has recently become a topic of interest in electrochemistry. It has been observed that at potentials negative with respect to the potential of zero surface charge, [Kolb, 1996, 2002 Dakkouri, 1997], the reconstructions found under UHV conditions are also stable in contact with an electrolyte. Although aU low index faces of Au and Pt undergo potential-induced reconstruction, it has been particularly well characterized for Au(lOO) (Fig. 5.5). [Pg.142]

FIG. 8 Inverse differential capacity at the zero surface charge vs. inverse capacity Cj of the diffuse double layer for the water-nitrobenzene (O) and water-1,2-dichloroethane (, ), interface. The diffuse layer capacity was evaluated by the GC ( ) or the MPB (0,)> theory. (From Ref. 22.)... [Pg.434]

Adsorbance of NaPSS, Ap. Hesselink (1, 2) derived a linear relationship between the amount of polyelectrolyte adsorbed in the plateau region on an adsorbent with zero surface charge and the square root of added salt concentration in bulk solution. [Pg.48]

Contrary to the accumulated knowledge on the static or quasi-static characteristics of thin lipid films at air/water interface, less attention has been paid to the dynamical or nonequilibrium behavior of the film. Studies on the dynamical characteristics of thin lipid films may be quite important, because the life phenomena are maintained under nonequilibrium conditions. According to the modern biochemistry [11,12], thin lipid membrane in living cells is not a rigid wall but a thermally fluctuating barrier with high fluidity. In the present section, we will show that thin lipid film exhibits the various interesting dynamical tc-A characteristics, such as the "overshoot hump", the "zero surface pressure", and the "flat plateau". [Pg.223]

Such a large overshoot hump, or zero surface pressure, was observed only for the subphase containing both CdCl2 and KHCO3. This result suggests that the stabilization effect of cadmium ion is enhanced in the presence of KHCO3 due to its buffering capacity of the subphase. [Pg.227]

Figure 6 shows the effects of compression rate on the ji-A curve for the PhDA2-8 thin film at air/water interface. Accompanied with the increase in the compression rate, the hump becomes more significant and the maximum surface pressure of the hump shifts toward the larger surface area. It is to be noted that the region with zero surface pressure appears only with appropriate compression rates of 3 - 7.5 (A2/molecule)/min as in (d), (e), and (f). [Pg.229]

As has been mentioned above, the 7t-A curves of the PhDA2-8 thin film show the existence of the zero pressure region after the formation of the overshoot hump. It is noteworthy that the remarkable overshoot hump and the subsequent zero surface pressure are observable only in a particular range of compression rates, suggesting that the inclusion of the effect of non-... [Pg.229]

Figure 7. Assumed structure for the bilayer formed at the zero surface pressure point (Z) in Figure 3. |

It is evident that the above simulation results can reproduce essentially all characteristic features such as "flat plateau", "zero surface pressure , and "overshoot hump observed in the actual it-A curves. These properties are characteristic examples of nonlinearity in the nonequilibrium state of a thin... [Pg.235]

Using symmetry arguments, the solution for diffusion with no flux at one end can be derived from these equations. Obviously, the concentration profile for zero surface concentration is symmetrical relative to X/2, which means that dC/dx is zero at that point the flux of diffusing substance through this point is zero. Other combinations of boundary conditions can be found in standard textbooks (Carslaw and Jaeger, 1959 Crank, 1976). [Pg.439]

Let us now calculate some solutions for short values of the time. For a sphere with homogeneous initial concentration and zero surface concentration, we replace On/a2 by z. From equation (8.6.11), the fraction Fsph left at z is... [Pg.474]

For a slab with homogeneous initial concentration and zero surface concentration, the dimensionless variable t/X2 is replaced by t. The fraction left at t, given by equation (8.5.16), is transformed as in the case of the sphere., 92 now appears in place of and is replaced by 94 through the first of the equations (8B.2). [Pg.475]

Laurie and Long59 studied the thermal decomposition of dimethyl cadmium in the absence of inhibitors. Rate coefficients were calculated on the basis of the undecomposed alkyl. A marked surface affect was noted. The homogeneous rate coefficient was obtained at 258 °C by studying the pyrolysis with various surface to volume ratios and extrapolating to zero surface. The mechanism proposed is... [Pg.216]

The dashed line in the complex in (4.21) and (4.22) indicates an outer-sphere (o.s.) surface complex, Kos stands for the outer-sphere complex formation constant and kads [M 1 s 1] refers to the intrinsic adsorption rate constant at zero surface charge (Wehrli et al., 1990). Kos can be calculated with the help of a relation from Gouy Chapman theory (Appendix Chapter 3). [Pg.99]

In this situation the CaC03 surface is characterized by zero surface charge (pH = pHpzc)... [Pg.304]

** Minimal Surfaces With Zero Curvature **

** Periodic zero potential surfaces **

** Potential-energy surfaces zero order **

** Surface tension and the potential of zero charge **

** Zero proton condition at the surface **

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