Helmholtz monolayer

A mmiolayer of ionic species can be adsorbed at the interface with a solid substrate (a Helmholtz monolayer), Fig. 10.10a. A diffuse layer of ions of the opposite sign with density p(z) provides the overall electrical neutrality. This mechanism is not specific for liquid crystals, it takes place in the isotropic liquids as well. However, in liquid crystals the surface field E = 47cPs rf can interact with the director and change orientation of the latter. Qualitatively, the ionic polarization can be estimated as Psurf = where n is the number of charges q and is a characteristic (Debye) length for the charge distribution. 

In experiment, surface ionic layers can be studied using the measurements of the electrokinetic effect, that is, the appearance of the potential difference in the plane of the interface when a liquid crystal flows along a solid substrate [26, 27]. The effect is due to a shift of the diffused layer with respect to the Helmholtz monolayer. The magnitude and sign of the effect is very sensitive to small amounts of impmrities (down to 10 by weight). 

The surface potential-area curves vs. pH (see Figures 5, 7, 9, and 11) can be treated, as a first approximation only, by the Helmholtz formula for a partially charged weak acid monolayer (5, 10, 20) ... 

Figure 2.13 illustrates what is currently a widely accepted model of the electrode-solution interphase. This model has evolved from simpler models, which first considered the interphase as a simple capacitor (Helmholtz), then as a Boltzmann distribution of ions (Gouy-Chapman). The electrode is covered by a sheath of oriented solvent molecules (water molecules are illustrated). Adsorbed anions or molecules, A, contact the electrode directly and are not fully solvated. The plane that passes through the center of these molecules is called the inner Helmholtz plane (IHP). Such molecules or ions are said to be specifically adsorbed or contact adsorbed. The molecules in the next layer carry their primary (hydration) shell and are separated from the electrode by the monolayer of oriented solvent (water) molecules adsorbed on the electrode. The plane passing through the center of these solvated molecules or ions is referred to as the outer Helmholtz plane (OHP). Beyond the compact layer defined by the OHP is a Boltzmann distribution of ions determined by electrostatic interaction between the ions and the potential at the OHP and the random jostling of ions and... 

Frequently, e.g. in the case of alkane thiol monolayers, the electrode is modified with a low-dielectric-constant layer. Film formation causes the Helmholtz layer to change from a mixture of ions and solvent with a high dielectric constant to an ion-free, often organic, layer with a low dielectric constant. The interfacial capacitance... 

A thermodynamic treatment is first suggested on the basis of which one can explain the inclined phase transition that occurs in monolayers of insoluble surfactants. By minimizing the Helmholtz free energy of the monolayer, the equilibrium radius and the equilibrium area fraction of the LC islands are obtained as functions of the average molecular surface area A. The mixing entropy provides a negligible effect on... 

For the chemical potentials the situation is different. For the surfactant the chemical potential in the monolayer p is not defined by that in the subphase because of the absence of transport. Nevertheless, this quantity is well-defined as the molar Helmholtz energy needed to add more surfactant to the layer ... 

A variety of authors have paid attention to the question of how the charging of a monolayer affects the (Helmholtz or Gibbs) energy, and hence the interfacial pressure. (See for instance refs. ) Thermod3mamics can help to answer some of the basic questions that have given rise to unnecessary confusion in the literature. 

Over a long period of time experimental results on amphiphilic monolayers were limited to surface pressure-area ( r-A) isotherms only. As described in sections 3.3 and 4, from tc[A) Isotherms, measured under various conditions, it is possible to obtain 2D-compressibilities, dilation moduli, thermal expansivities, and several thermodynamic characteristics, like the Gibbs and Helmholtz energy, the energy cmd entropy per unit area. In addition, from breaks in the r(A) curves phase transitions can in principle be localized. All this information has a phenomenological nature. For Instance, notions as common as liquid-expanded or liquid-condensed cannot be given a molecular Interpretation. To penetrate further into understanding monolayers at the molecular level a variety of additional experimental techniques is now available. We will discuss these in this section. 

One example has been given by Rakshit et al. ) who used [3.4.17] to obtain the Helmholtz energy for monolayers of CjjCOOH. CigCOOH, Cj COOH and C gCOOH, substituted fatty acids and unsaturated acids. The integration was car ried out from (almost) infinite area to r =. the equilibrium spreading pressure. 

For the implied infinitesimal changes of y with T the factor RTF remains constant. Generally, however, the derivative dy/dT also depends on T. From (4.3.22) S° will eventually be obtained as a function of x and T. As, for each T, F is accessible as a function of x, it is also possible to derive the surface excess entropy as a function of the monolayer composition. Accurate data are, as before, a prerequisite. From S the surface excess enthalpy = TS is obtainable. Alternatively, one can differentiate y /T with respect to the temperature, obtaining the enthalpy directly using the appropriate Gibbs-Helmholtz relation. 

Functionals are functions of functions. In this Volume we met functionals in van der Waals theory for the interfacial tension (sec. 2.5a) and in the mean field theory for the surface pressure of polymeric monolayers (sec. 3.4e). In these two cases equations were derived in which the excess interfacial Helmholtz energy had to be minimized as a function of a density distribution across the interface and of the spatial derivative of this profile [density Junctionals). The technique of finding the function that minimizes the Helmholtz energy is called variational calculus, or calculus of variations. 

Fig. 8 Design of an interfacial stress rheometer. Here a magnetized rod is subjected to an oscillatory force generated by the Helmholtz coils. The motion of the rod is detected using a microscope and photodiode array. Differences between the applied force and resulting phase and magnitude of the displacement give information on the viscoelastic properties of the monolayer. Both the storage modulus G and the loss modulus G" can be determined [2,21] (reproduced with permission from the American Chemical Society)...

If the monolayer and its associated double layer occupy a separate phase which lies between two homogeneous bulk phases, then for constant temperature, volume, and total number densities of species in this phase, the total differential Helmholtz free energy for a planar interfacial region is given by (20) ... 

The Helmholtz surface free-energy change due to the formation of a monolayer is the difference between the Helmholtz free energy of the pure solvent surface and that of the solution surface (ymonola) er = FS- Ps0). The Helmholtz free energy at the surface was defined... 

Equation (427) shows that when no monolayer is present over the water surface ( > = 0), there is only pure water and we may write, = yAs- Then, the Helmholtz surface free energy due to the presence of a monolayer may be given as... 

The first term in Eq. (10) is just the GC capacity at the pzc the second term is independent of the ionic concentration, and can be identified with the Helmholtz capacity. However, in this model the Helmholtz capacity is not caused by a single monolayer of solvent with special properties, like in the Stern model, but results from an extended boundary layer. It depends on the dielectric properties of the solvent and on the diameters of the particles. Since A. C e, the influence of the ions on the capacity is predicted to be small. This is in line with the experimental... 

Ions can be adsorbed specifically if the main contribution to their interaction with the interface (ions, dipoles) is caused by non-coulombic short-range forces. Specific adsorption caimot be explained using only the theory of diffuse double layer. Specifically adsorbed ions penetrate to the compact layer and form a compact or loose monolayer. The surface passing through the centers of specifically adsorbed ions is usually called the inner Helmholtz plane. If several kinds of specifically adsorbed ions... 

The double layer in the case of specific adsorption In the case of specifically adsorbed ions it is assumed that they penetrate into the inner layer and may (but not necessarily) come in contact with the metal surface. They are usually assumed to form a partial or complete monolayer. The locus of the electrical centers of this layer of specifically adsorbed ions is the inner Helmholtz plane (IHP) assumed to be at a distance x from the metal surface. In certain cases the amount of charge of the ions specifically adsorbed in the IH P (n ) is higher than the charge on the metal phase... 

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