Interfacial free energy relationship

Considering a solid-liquid system, this relationship may be combined with the well-known Young s equation to eliminate the interfacial free energy. Hence,... 

Freitas, A. A., Quina, F.H., and Carroll, F.A. Eshmahon of water-organic interfacial tensions. A linear free energy relationship analysis of interfacial adhesion, J. Phys. Chem. B, 101 (38) 7488-7493, 1997. 

Fig. 14. Schematic illustration of a drop ofliquid spreading in contact with a solid surface, showing the relations between the relevant parameters the contact angle, 0 the solid/vapor interfacial free energy, Ysv the liquid/vapor interfacial free energy, yLV and the solid/liquid interfacial free energy, ySL. Young s equation describes the relationship between these parameters for a stationary drop at thermodynamic equilibrium [175]...

Before turning to the surface enthalpy we would like to derive an important relationship between the surface entropy and the temperature dependence of the surface tension. The Helmholtz interfacial free energy is a state function. Therefore we can use the Maxwell relations and obtain directly an important equation for the surface entropy ... 

Hono et al. [64, 65] confirmed that Cu in both amorphous Fev sSiia.sBgNbsCui and Fe89Zr7B3Cui alloys forms clusters prior to primary crystallization and the Cu clusters act as heterogeneous nucleation sites for bcc-Fe(Si) precipitates. They also confirmed orientation relationships between the Cu clusters and bcc-Fe crystals and concluded that the heterogeneous nucleation of the bcc-Fe phase is due to the lower interfacial free energy for nucleation [66]. 

This inverse relationship, for a constant interfacial free energy, between melting temperature and chain length contrasts markedly to the results obtained for molecular crystals. 

Let us assume at this point that the interfacial free energy, a, is the principal parameter responsible for the characterization of the interactions between the solid and the medium determined by their chemical composition. The following simplification allows one to obtain the relationship between the strength and the surface free energy of a solid body with a defect in the form of a microcrack. 

In the present paper, I wish to (i) review critically the literature pertaining to the relationship between the practical adhesion and thermodynamic adhesion, (ii) discuss various surface chemical criteria—Wa, interfacial free energy, penetration of the adhesive—and the conditions which optimize these criteria, (iii) test these criteria and conditions against the existing values of adhesive strengths, (iv) finally deduce the most important surface chemical criterion germane to the practical adhesion. 

The surface free energy has been typically determined experimentally by one of two methods from nucleation rates or by droplet experiments. In the first method, one assumes that classical nucleation theory is correct, which then gives a direct relationship between nucleation rates and the interfacial free energy of a flat, infinite surface. Given the large number of approximations that go into such a calculation, the values thus calculated should be viewed with suspicion. The second method, while direct and far more accurate than inversion... 

For generality Good and Girifalco set their relationship to 4> so that possessed a maximum value of unity and was defined in terms of molecular geometries and forces of interaction across adjacent phases [49]. Thus when expressed in terms of surface free energies for two phases a and b, the interfacial free energy between the phases, yab, is given by ... 

Fig. 25. Relationship between the measured interfacial strength and the (negative) Gibbs free energy of mixing, (-AG )o5, for glass beads treated with various silane coupling agents embedded in a PVB matrix. Error bars correspond to 95% mean confidence intervals. Redrawn from ref. [165].

It is useful to know, that for a given type of crystals (oxides, sulfates, carbonates), the interfacial mineral-aqueous solution free energy, y (or ycw), increases with decreasing solubility (Schindler, 1967). Nielsen (1986) cites the following empirical relationship... 

Figure 14. Characteristics of interfacial water in aqueous suspensions of A-300 sonicated (US) or treated in a ball-mill (MCA) at different concentration of silica (a) amounts of unfrozen water as a function of temperature at T < 273 K (b) relationship between the thickness of unfrozen water layer and temperature and changes in Gibbs free energy of interfacial water versus (c) pore radius, (d) pore volume, and (e) amounts of water unfrozen in these pores (f) interfacial Gibbs free energy as a function of silica concentration in suspensions differently treated.

A summary of the main relationships which are needed for the processing of immersion calorimetry is proposed hereafter. More details may be found in the recent literature about their derivation [3, 9, 10]. The wetting state of a liquid-vapor-sohd system depends on the value of the interfacial tensions y defined, for a given interface, as the free energy per unit area at constant volume and temperature ... 

An important principle from thermodynamics is the well-known Gibbs adsorption isotherm, which provides a relationship among the bulk-phase concentration c, the interfacial concentration T, and the interfacial tension (essentially the surface free energy per unit area) ... 

For a liquid that rests on a smooth surface with a finite contact angle, one can determine the relationship between the interfacial tensions at the different interfaces from consideration of the balance of surface forces at the line of contact of the three phases (solid, liquid, and gas). Remembering that the interfacial tension always exerts a pressure tangentially along the surface, the surface free-energy balance (a... 

FIGURE 38.13 Relationships between changes in the Gibbs free energy of the interfacial water in the frozen aqueous suspension of silicas of the first series and (a) amounts of unfrozen water (b) the volume and (c) the radius of pores filled by unfrozen water. 

A theoretical basis for different shapes of microemulsions (even for small W/O or O/W volume fractions) has been established on the basis of the relationship between shape and interfacial curvature [350,351]. It is reasonable to expect that the relevant properties of the surfactant film are represented by a bending elasticity with a spontaneous curvature, Co (as was demonstrated for binary systems). If the elastic modulii k, ksT, the fluctuations in curvature of the film are very small, and the entropy associated with them can be neglected. The actual morphology is the result of the competition between the tendency to minimize the bending free energy (which prefers spheres of optimal radius of curvature, = l/c ) and the necessity to use up all of the water, oil, and surfactant... 

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