Gibbs interfacial energy

Let the radius of a latex particle swollen to equilibrium be r. If dr is the increase in radius caused by the imbibition of dn, moles of monomer, the cMie-sponding increase in interfacial area is Snrdr, causing an increase in the Gibbs interfacial energy of the particle AGj = Sjrrdry, where y is the interfacial tension. The increase in the volume of the particle is... 

The monomer concentration can remain constant for two reasons. First, a steady state can exist in which consumption of monomer by polymerization is directly compensated by subsequent diffusion of free monomer into the latex particle. The monomer concentration is then always lower than the saturation concentration at equilibrium. Second, the monomer concentration in the latex particles will be constant when the Gibbs interfacial energy A Gy and swelling A Gq cancel, so that the Gibbs energy of the monomer in equilibrium will be zero ... 

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].

In order to evaluate which of these scenarios leads to the most stable interfacial structure, we have to analyze the relation between the chemical potentials of both reservoirs and the overall energy. Therefore, we begin with the Gibbs free energy of the interface. 

In cases where the interfacial energy is dependent on orientation, the equilibrium condition (6.41) does not hold [19]. Some grain boundaries will then represent higher Gibbs energies than others, and if kinetics allow for reorientation, certain grain boundaries will become dominant. However, in most cases the kinetics of... 

Molecules in the surface or interfacial region are subject to attractive forces from adjacent molecules, which result in an attraction into the bulk phase. The attraction tends to reduce the number of molecules in the surface region (increase in inter-molecular distance). Hence work must be done to bring molecules from the interior to the interface. The minimum work required to create a differential increment in surface dA is ydA, where A is the interfacial area and y is the surface tension or interfacial tension. One also refers to y as the interfacial Gibbs free energy for the condition of constant temperature, T, pression, P, and composition (n = number of moles)... 

In Chapter 4.2 we introduced the interfacial (surface) tension (equivalent to surface or interfacial energy) as the minimum work required to create a differential increment in surface area. The interfacial energy, equally applicable to solids and liquids, was referred to as the interfacial Gibbs free energy (at constant temperature, pressure and composition) (n refers to the composition other than the surfactant under consideration). 

Gibbs concept of an (infinitely thin) dividing surface lends itself to the determination of interfacial energies, in accordance with the regular solution model which takes into account the bonds of nearest neighbors only. If species A and B are randomly distributed in phases a and (i, it follows from merely counting bonds that... 

The partial derivative of the Gibbs free energy per unit area at constant temperature and pressure is defined as the interfacial coefficient of the free energy or the interfacial tension (y), a key concept in surface and interface science ... 

Key Concepts of Interfacial Properties in Food Chemistry Equation D3.5.12 G = U + PV - TS = yA + p,/j, i Equation D3.5.13 where H is the enthalpy, F the Helmholtz free energy, and G the Gibbs free energy. These basic equations can be used to derive explicit expressions for these quantities as they apply... 

Free surface energy, interfacial enthalpy and Gibbs surface energy... 

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]

Here, R is the radius of the droplets and 7 is the liquid-liquid interfacial tension (see Section 13.5 and Table 13.2). The amount of AGem is equal to the Gibbs free energy gained upon demulsification. 

Surfactants form semiflexible elastic films at interfaces. In general, the Gibbs free energy of a surfactant film depends on its curvature. Here we are not talking about the indirect effect of the Laplace pressure but a real mechanical effect. In fact, the interfacial tension of most microemulsions is very small so that the Laplace pressure is low. Since the curvature plays such an important role, it is useful to introduce two parameters, the principal curvatures... 

Thus surface or interfacial tension can also reflect the change in Gibbs free energy per area, consistent with the idea that area expansion requires energy. 

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.

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