Surface area extension energy

Here, a is the radius of the non-deformed droplet, x(H) is the droplet shape function in the region ho/2 y x and F is force. Knowing the shape of the droplet surfaces [obtained from the solution of eqns. (10.43), (10.44) (10.46) and (10.47)], one may proceed to calculate the contributions to the interdroplet energy. Thus we obtain the surface area extension energy... 

Interaction Energy Contributions Due to the Interfacial Properties of the Individual Droplet—Surface Area Extension and Bending Energies... 

The first term on the right-hand side of eqn. (10.27) accounts for the surface area extension at constant interfacial tension, while the second is due to the possible increase in the interfacial tension along with the deformation. The surface extension energy could be expressed as a function of the film radius and for small deformations r/a < 1) reads ... 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

In this relationship. S is alkane solubility, A is the cavity surface area and a is the hydrophobic free energy per unit area. Extensive fitting of this equation [24] yields a value of 88 kJ mol A for the proportionality constant a. This value corresponds to an unfavourable free energy of about 3.6 kJ mol for the transfer of a CH2 group to aqueous solution. 

Our extension of the LIE approach to calculate free energies of hydration (AGhyd) incorporated a third term proportional to the solute s solvent-accessible surface area (SASA), as an index for cavity formation within the solvent.19,27 The latter term is needed for cases with positive AGhyd such as alkanes and additional improvement occurred when both a and P were allowed to vary. Equation 8 gives the corresponding LIE/SA equation for... 

As indicated in Chapter 2, the adsorbent surface is characterized by a surface tension y whose magnitude depends on the nature of the surrounding medium (liquid, gas or vacuum) with which the adsorbent is in equilibrium. The isothermal extension of the surface area A, with no other change in the thermodynamic state of the system of adsorption, results in an increase d F of the Helmholtz energy of the system. Thus, the surface tension, y, is defined as ... 

The term (dU/dA)TVn. was referred to as the total extension energy of the surface per unit increase of area by Einstein (1901). It is indeed the sum of the work, y, which must be supplied to extend the surface by one unit of area and the heat which must be supplied to carry out this extension reversibly and isothermally. 

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