Gibbs free energy surface

The excess energy associated with an interface is formally defined in terms of a surface energy. This may be expressed in terms either of Gibbs, G, or Helmholtz, A, free energies. In order to circumvent difficulties associated with the unavoidably arbitrary position of the surface plane, the surface energy is defined as the surface excess [7,8], i.e the excess (per unit area) of the property concerned consequent upon the presence of the surface. Thus Gibbs surface free energy is defined by... 

Here y is the surface or interfacial tension, G is the Gibbs surface free energy, A is a unit surface area, and i is a component forming the interface. 

In defining surface thermodynamic functions, the difficulty over the absence of a unique surface plane is circumvented by defining these functions in terms of surface excess— total minus bulk value of the property concerned [46,47]. Thus the Gibbs surface free energy is defined as... 

Now, the surface energy, more strictly the Gibbs surface free energy G , is the excess free energy of the system associated with the surface (per unit area), and so is defined as... 

The energy to produce a surface at a given temperature and pressure is the Gibbs surface free energy, G. The Gibbs surface free energy will be different for different facets of a crystal and is thus the key to determining the equilibrium crystal shape... 

Frasch process A process for mining sulfur that uses superheated water to melt the sulfur and compressed air to force it to the surface, free energy See Gibbs free energy. free expansion Expansion against zero opposing pressure. 

The Gibbs free energy G and the chemical potentials include contributions from the internal energy, vibrational free energy, and configurational entropy. Since most relevant stmctures will have a low surface free energy, we obtain from (5.4) that... 

Adsorption is accompanied by a loss of surface free energy. Free energy change is related to enthalpy, AH, and entropy, AS, changes by the Gibbs equation ... 

As in so many other fundamental aspects of the thermodynamics of surfaces, we are indebted to Gibbs 6) for pointing out that for solids the surface tension (7) and surface free energy (F ) are not equivalent quantities. Nevertheless, as Shuttleworth (7) mentions in an excellent review, the two terms have been (8) and still are (9) confused. The relationship between the quantities is... 

Equation (46), one form of the Gibbs equation, is an important result because it supplies the connection between the surface excess of solute and the surface tension of an interface. For systems in which y can be determined, this measurement provides a method for evaluating the surface excess. It might be noted that the finite time required to establish equilibrium adsorption is why dynamic methods (e.g., drop detachment) are not favored for the determination of 7 for solutions. At solid interfaces, 7 is not directly measurable however, if the amount of adsorbed material can be determined, this may be related to the reduction of surface free energy through Equation (46). To understand and apply this equation, therefore, it is imperative that the significance of r2 be appreciated. 

For a pure liquid the Gibbs dividing plane is conveniently positioned so that the surface excess is zero. Then the surface tension is equal to the surface free energy and the interfacial Gibbs free energy f[Pg.40]

From thermodynamics, the lowering of surface free energy due to surfactant adsorption is given by the Gibbs adsorption equation for a binary, isothermal system containing excess electrolyte ... 

Starting from this consideration, Rayner et al. [52] analyzed the spontaneous-transformation-based (STB) droplet-formation mechanism from the point of view of the surface Gibbs free energy with the help of the Surface Evolver code. Rayner et al. estimated the difference of surface free energy of the droplet before ( i) and after (E2)... 

From a thermodynamic point of view, protein adsorption at a surface depends on the Gibb s free energy of adsorption (AGads) ... 

The influence of surface free energy on solubility can be determined from straightforward thermodynamic considerations. The solubility of a solid can be calculated from the standard Gibbs free energy of reaction according to the relation ... 

The lamellar habit adopted by crystalline polymers adds surface terms to the specific Gibbs function (chemical potential), most importantly the fold surface free energy, ae, which contributes 2ae/Xg for a lamella of thickness k and crystalline density q. In consequence melting points are lowered from T, for infinite thickness, to Tm according to the Hoffman-Weeks equation... 

Another notation that emphasizes the fact that the surface free energy at a given temperature is identical with the excess Gibbs free energy, GE, can... 

In Eq. (83), all terms are either known or measurable, except the quantity of interest . Moreover, it should be noted that Eq. (83) is very interesting since it takes into account a small adsorbate, i.e., —CH2— group, whose surface area and surface free energy are slightly affected by temperature. This means that the variations in area and surface entropy of an adsorbed —CH2— group are negligible with temperature. Therefore, it is possible to determine the surface enthalpy derived from the Gibbs-Helmholtz equation... 

There is also an interesting relation between AG and the surface free energy, y, defined by Gibbs [cf. Equations 514 and 675 of (6) ]. 

Surface tensions can also be used to predict the behavior of multicomponent solid systems. Unlike single-component systems, the surface tension is no longer equal to the surface free energy G, but is related to the different component concentrations at the smface by the Gibbs equation ... 

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