Surface dipole correlations

Recognition that a further correlation contribution exists, due to two-dimensional permanent dipole (zwitterionic) head-group fluctuations confined to a surface accounts for the discrepancy in equilibrium lamellar spacings [31,32]. 

Elegant force measurements have been made between adsorbed monolayers of die protein cytochrome-c, and insulin on mica, immersed in water [26]. Hydration forces here play no role. If the full armoury of theoretical predictions is invoked, the complicated force curves measured all seem to fall into place. It is possible, indeed probable that with real biological membranes that contain up to 50% proteins, the hydration forces that prevent fusion of pure phospholipid membranes do not always operate. 

On the other hand, with acetate as coxmter-ion, the forces are an order of magnitude larger, the fit to theory is perfect, with no free parameters [46]. There are no bound coimter-ions. The Poisson-Boltzmann theory here can be shown to provide an upper bound to the magnitude of the double-layer interaction. If the more refined theory [23-25] is used, the predicted result is somewhat less than the measured curve, less still if there exists any real ionbinding. (How much of a difference exists depends on the presumed hydrated 

Specific coimter-ion effects are critical to biological function, in determining forces between individual sub-units of macromolecules and in the consequent shapes they take up. How much these effects can be attributed to physics and how much to specific chemistry can only be revealed by a reanalysis of all data in the light of the new theories of molecular forces. Until that reanalysis is done, present experimental inferences on binding surface potential and charge remain phenomenological curve fitting. 

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This correlation has been explained in terms of two effects (1) the surface energies of the two metals involved and (2) the formation of a surface dipole potential. 

Without the external field, the Stockmayer fluid near the wall exhibits symmetric density oscillations that die out as they reach the middle of the film. Near the surface, the fluid dipoles are oriented parallel to the walls. Upon turning on the electric field, the density profile of the Stockmayer fluid exhibits pronounced oscillations throughout the film. The amplitude of these oscillations increases with increasing field strength until a saturation point is reached at which all the fluid dipoles are oriented parallel to the field (perpendicular to the walls). The density profile remains symmetric. The dipole-dipole correlation function and its transverse [] and longitudinal [] com-... 

On the other hand, in the absence of surface dipoles, the correlation between the water dipoles induced by a surface charge is expected to increase the repulsion as compared to the DLVO theory. This is due to the tendency of the water dipoles to orient in the same direction the adjacent water dipoles, thus increasing the decay length of the polarization. 

In order to explain the interactions between silica surfaces, the polarization model is adapted to poorly-organized surfaces. To account for the disorder induced in water by the rough surfaces of silica, the dipole correlation length Am, which is the main parameter of the polarization model, is allowed to decrease from Am=14.9A obtained for water perfectly organized in ice-like layers in the vicinity of a surface to smaller values. For Am=4A, good agreement with experiment is obtained for reasonable values of the parameters involved (such as surface dipole and charge densities) [7.9],... 

The second difficulty can be removed if one assumes that in the vicinity of an interface the water is organized in icelike layers. The electrical interactions between the water dipoles of successive layers lead indeed to an oscillatory behavior of the polarization [35], If the surface is not perfectly flat, of if the water is not perfectly organized in water layers, the statistical average smooth out the polarization oscillations [35], The latter results have been also supported by molecular dynamics simulation, in which the surface dipoles were allowed to move [36], Let us now examine in detail how the correlation between neighboring dipoles occurs. 

It should be emphasized that the assumption of an icelike structure of water in the vicinity of the surface is only an approximation used to calculate the dipole correlation length A, (Eq. (TO)). In feet, if the water would be organized in perfect ice-like layers parallel to the planar surface, the model would predict an oscillatory behaviour of the polarization in the vicinity of the surface [35],... 

The polarization model is extended to account for the ion-ion and ion-surface interactions, not included in the mean field electrical potential. The role of the disorder on the dipole correlation length A, is modeled through an empirical relation, and it is shown that the polarization model reduces to the traditional Poisson Boltzmann formalism (modified to account for additional interactions) when X, becomes sufficiently small. 

Eqs. (5b) (5c) (5d) (5e). The constitutive equation of the polarization model contains only one unknown parameter, namely A, which expresses the correlation between neighboring dipoles. However, in order to solve the system of equations, both the surface charge density a (or the surface potential ip(z —d)) as well as the polarization of water near the surface have to be known. The latter can be related, in a microscopic model that will be examined in the next section, to the surface dipoles. In the limit A,—>0, the polarization model reduces to the Poisson— Boltzmann approach, and the two boundary conditions become dependent on each other, because in this case... 

If no microscopic model is available to calculate the dipole correlation length, one might consider A, as a phenomenological parameter of the polarization model. However, before investigating the applicability of the polarization model to the interactions between silica surfaces, a more microscopic representation is used in the next section to obtain an expression for and to derive a relation between the surface dipoles and the polarization of water near the interface. 

Since we are interested only in the dipole correlation along the z directions (it is assumed that t//(z) and m(z) do not depend on the x and y coordinates in the plane of the surface because of this planar symmetry the x and y components of m (z) vanish), the component of the field along the z direction has the form ... 

Polarity may also be healed by the removal of a certain percentage of atoms in the outer layers. When the vacancies order, most of the time, this leads to surface reconstructions. The surface concentrations compatible with a vanishing max roscopic dipole moment can be correctly estimated within a fully ionic picture. Low energy configurations are expected to be insulating, and indeed, on non-polar oxide surfaces, a correlation has been found between the stability of a surface orientation and the surface gap value [58,59]. 

Beyond this, the inclusion of the competition for surface sites of different competing species (e.g. H vs. Na" ") gives rise to the further problem of surface charge regulation [22, 27-30], with a concomitant appearance of a so-called "secondary hydration force". Surface localised dipole-dipole correlations give rise to a further force [31, 32], and much of what was confused falls into place. These developments represent a first conceptual step forward on the way to a more complete and necessary stage of... 

For multilamellar liposomes, the hydration forces should balance the predicted longer range attractive van der Waals forces, to give an equilibrium lamellar phase spacing of about 30A in water. They do not, but once surface dipole-dipole correlations are taken into account [31, 32], theory and experiment do agree. 

In the second model (and in the case that ex e2), the pressure between surfaces arises from dipole correlations and dielectric images. Asymptotically the pressure is... 

In the case of a polymer-coated metal substrate in a humid air atmosphere (for simplificity, only the situation of a polymer that is not highly oriented and has rather a small dipole potential is considered), a situation for the correlation of the corrosion potential with the Volta potential difference A R° f measured here (outer polymer surface and the probe as reference) could be derived analogously to the situation of an electrolyte-covered metal substrate (Eq. (10) with xpoI the surface dipole potential of the polymeric phase, which should be constant for a given polymer and a given gas phase as long as the polymer surface is stable). 

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