Immersion, free energy

A number of methods have been described in earlier sections whereby the surface free energy or total energy could be estimated. Generally, it was necessary to assume that the surface area was known by some other means conversely, if some estimate of the specific thermodynamic quantity is available, the application may be reversed to give a surface area determination. This is true if the heat of solution of a powder (Section VII-5B), its heat of immersion (Section X-3A), or its solubility increase (Section X-2) are known. 

The structure of hydrogels that do not contain ionic moieties can be analyzed by the Flory Rehner theory (Flory and Rehner 1943a). This combination of thermodynamic and elasticity theories states that a cross-linked polymer gel which is immersed in a fluid and allowed to reach equilibrium with its surroundings is subject only to two opposing forces, the thermodynamic force of mixing and the retractive force of the polymer chains. At equilibrium, these two forces are equal. Equation (1) describes the physical situation in terms of the Gibbs free energy. 

Even single metals, however, are subject to aqueous corrosion by essentially the same electrochemical process as for bimetallic corrosion. The metal surface is virtually never completely uniform even if there is no preexisting oxide film, there will be lattice defects (Chapter 5), local concentrations of impurities, and, often, stress-induced imperfections or cracks, any of which could create a local region of abnormally high (or low) free energy that could serve as an anodic (or cathodic) spot. This electrochemical differentiation of the surface means that local galvanic corrosion cells will develop when the metal is immersed in water, especially aerated water. 

The subject of interest is a gel swollen by solvent. Let F be the Gibbs free energy change after mixing of solvent and an initially unstrained polymer network [1]. When the gel is isotropic and is immersed in a pure solvent with a fixed pressure Po, F is a thermodynamic potential dependent on the temperature T, the pressure p inside the gel, and the solvent particle number Ns inside the gel. It satisfies... 

Fint is the free energy of non-Coulomb interactions of monomer units. Finl can be expressed, for example, in terms of the Flory-Huggins lattice theory [21]. In the general case, when network is immersed in solvent which includes 1 different components some of which can be polymeric with the degree of polymerization Pi(Pi 1, i = L 2,... k), Fim in the Flory-Huggins theory has the following form [21-22] ... 

The practical characteristic of a dyestuff is that when a textile is immersed in a solution containing a dye. the dye preferentially adsorbs onto and diffuses into the texiile. The thermodynamic equations defining this process have been reviewed in detail. The driving force for this adsorption process is the difference in chemical potential between the dye In the solution phase and the dye in the fiber phase. In practice it is only necessary to consider changes in chemical potential and to understand that the driving force is the reduction in free energy associated with the dye molecule moving from one phase to the other, as the molecule always moves to the siate of lowest chemical potential. 

Christopher J. Cramer and their co-workers during the last decade [61,100, 55, 56], In SMx, terms responsible for cavity foimation. dispersion, solvent structure and local field polarization are present [51,57], The solvation energy is obtained via the usual approximation that the solute, treated at the quantum mechanical level, is immersed in an isotropic polarizable continuum representing the solvent. Therefore the standard free energy of the solute in solution can be expressed as ... 

In immersional wetting, the solid, which is not originally in contact with the liquid, is immersed completely in the liquid. The area of liquid-gas interface, therefore, remains unchanged. The free energy change for immersion of a solid in a liquid is given by... 

Free energy, enthalpy and entropy of immersion are related by... 

The force can also be calculated starting from an expression for the free energy. The free energy (F) of a colloidal system composed of two charged parallel plates immersed in an electrolyte solution containing charged particles is composed of three contributions electrical (Ft.ie), entropic (Fent), and chemical (Fche).25 26... 

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