Entropy surface pressure

Salts of fatty acids are classic objects of LB technique. Being placed at the air/water interface, these molecules arrange themselves in such a way that its hydrophilic part (COOH) penetrates water due to its electrostatic interactions with water molecnles, which can be considered electric dipoles. The hydrophobic part (aliphatic chain) orients itself to air, because it cannot penetrate water for entropy reasons. Therefore, if a few molecnles of snch type were placed at the water surface, they would form a two-dimensional system at the air/water interface. A compression isotherm of the stearic acid monolayer is presented in Figure 1. This curve shows the dependence of surface pressure upon area per molecnle, obtained at constant temperature. Usually, this dependence is called a rr-A isotherm. 

Since surface pressure is a free energy term, the energies and entropies of first-order phase transitions in the monolayer state may be calculated from the temperature dependence of the ir-A curve using the two-dimensional analog of the Clausius-Clapeyron equation (59), where AH is the molar enthalpy change at temperature T and AA is the net change in molar area ... 

In these expressions k is the rate constant, p and E are the entropy term and the energy of activation respectively for breaking the chemical bonds Z is the collision rate. It will be noted that the first and third of the additional factors for interfacial reaction, i.e. the surface pressure II and the film cohesion have been included in the accessibility function tj). This is defined as the relative accessibility of the potentially reactive groups in the film it is unity at high areas when II 0 and when the cohesion also becomes negligible. 

Membrane equilibria give rise to a pressure difference between the two phases. For three-dimensional systems this is the osmotic pressure 77, for two-dimensional systems it is the surface pressure, n. For osmosis the driving force is the fact that the chemical potential of the water is lower on the side containing the molecules that cannot pass the membrane. As a result, water is imbibed and this process continues until the water transport has resulted in a pressure compensating n. The driving force is primarily entropical and stems from the mixing entropy the osmotic pressure follows from see [1.2.12.15],... 

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. 

It is of interest to estimate the thermodynamic functions of siuface layers of different composition. Since a binary system is considered, it is possible to make thermodynamic calculations for mixtures of different concentrations at different temperatures (Fig. 2.27). This was done using the equation that connects the surface pressure with the change in entropy and enthalpy of the surface layers [232] ... 

P = surface pressure, presenting the difference between surface tension of the solvent and solution (mN/m) dP/dT = rate of change of the surface layer entropy [c d/(mol de )]... 

There is an advantage in using the constant surface pressure standard state since it yields molar properties (enthalpies and entropies of adsorption) analogous to those associated with phase changes evaluated from the Clapeyron equation [80]. The use of the standard state with constant surface concentration provides differential quantities for the enthalpy and entropy changes which are not directly comparable with those calculated using the methods of statistical thermodynamics. The values of AS calculated by these two standard states differ only by the gas constant, B, and are readily interconverted. 

The work of adsorption is determined from Eq. (1) by using the Hnear section of the surface pressure curve as a function of the bulk concentration of the surfactant (the surface pressure does not exceed 3mN/M). The values obtained for the work of adsorption are usually compared with the values obtained for certain fractional surface coverages. Thus, it becomes possible to estimate the change in the free energy as a function of the molecular interaction in the monolayer. (The relation between the values of the work of adsorption determined from different isotherms is discussed in Refs. [37-39]). The adsorption entropy and enthalpy are determined from the temperature dependence of the work of adsorption [36-39]. 

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