Solid-liquid interface, Gibbs energy

Table VI. Gibbs Energies of Solid-Liquid Interfaces, ergs/sq. cm., 25°C.

The cosine cannot exceed one. Then we might ask What happens, if 7s — 7sl — 7l > 0 or 7S - 7Si is higher than 7// Does this not violate Young s equation No, it does not because in thermodynamic equilibrium 7s — Ysl — 1l can never become positive. This is easy to see. If we could create a situation with 7s > 7SL + 7l, then the Gibbs free energy of the system could decrease by forming a continuous liquid film on the solid surface. Vapor would condense onto the solid until such a film is formed and the free solid surface would be replaced to a solid-liquid interface plus a liquid surface. 

Any flexible polymer adsorbing to a solid/liquid interface must (1) be transported from the solution towards the surface, (2) establish a sufficient number of attachment points, and (3) change its conformation to achieve the state of lowest Gibbs energy, by accommodating to the geometrical properties of the substrate [1]. 

If we deform the liquid surface slightly so that the area of the solid-liquid interface increases by dA i, then the Gibbs energy change is... 

Thus, if (7 is positive, (dG/dA i) is negative, and the Gibbs energy will decrease as the solid-liquid interface enlarges the liquid will spread spontaneously. If = 0, the configuration is stable (in equilibrium) with respect to variations in the area of the solid-liquid interface. If is negative, the liquid will contract and decrease spontaneously. Combining Eqs. (18.21) and (18.22) we get... 

Fig. 1. Gibbs free energy curves with respect to composition near a solid—liquid interface (schematically). C, and Cj points correspond to an equilibrium state at the interface, and chemical potentials of components in the phases (tangents to the curves at these points) are equal. Deviation of the actual liquid composition (C,) at the interface temperature T, ftom the equilibrium concentration C, generates a tendency to restore the equilibrium (C — Ci, C2) or a driving force (AG,) for nucleation.

Recently, Angioletti-Uberti et al. [24, 25] have used a novel approach based on MTD to calculate Ysi at the melting temperature Tm- Since the chemical potentials lx P,T)(P denotes the pressure) of the solid and liquid bulk phases coincide at Tm, the Gibbs free energy G (P, 7] ) of a system containing a solid-liquid interface can be written as ... 

The fact that a liquid can be supercooled is best understood qualitatively in the framework of classical nucleation theory (CNT) (see e.g. Ref. [3]). According to CNT the free energy of a spherical nucleus that forms in a supersaturated solution contains two terms. The first term accounts for the fact that the solid phase is more stable than the liquid. This term is negative and proportional to the volume of the nucleus. The second term is a surface term. It describes the free energy needed to create a solid/liquid interface. This term is positive and proportional to the surface area of the nucleus. The (Gibbs) free energy of a spherical nucleus of radius R has the following form ... 

Fig. 10. Standard Gibbs energy profile along the axis of an ion transfer across the liquid-liquid interface in the absence (1) and presence (2) of an additional potential barrier at the interface. The broken line represents the contribution of the long-range electrostatic forces the solid line corresponds to the sum of the long- and short-range contributions X2 Helmholtz planes in the aqueous and the organic solvent phases.

Further, A5, Gb and Gi denote thermal conductivities and temperature gradients in the liquid and solid, and D the solute diffusivity in the liquid. m = dTjdCoo and k are volumetric latent heat of fusion, liquidus slope and interfacial distribution coefficient. G o is the concentration far from the interface and F = Tmlsi/Ly the Gibbs-Thompson parameter based on the solid liquid interfacial energy 7 / and melting temperature Tm is the solidification velocity and uj = 27t/A the wave number of a perturbation. 

The applicability of eq. (11.22) to a successful description of adsorption from a solution was established by Langmuir himself, when he compared his adsorption isotherm to the Gibbs equation and ended up with the Szyszkowski equation as a result. The transition from localized to non-localized adsorption (which can be viewed as the transition from fixed adsorption sites to moving ones) does not, therefore, change general trends in the adsorption in the cases described. One should also keep in mind that the liquid interface is more uniform in terms of energy than the solid interface, which contains active sites with different interaction potentials.4 The latter is probably the reason why... 

Evidently if S > 0 then k>+1. Were S>0 so that > o-, + a, this would imply that the solid-gas interface would immediately coat itself with a layer of the liquid phase and replace the supposedly higher free energy per unit area of direct solid-gas contact, cr g, by the supposedly lower sum of the free energies per unit area of solid-liquid and liquid-gas contacts, cr i + cr, thereby lowering the free energy of the system. However, in thermodynamic equilibrium this cannot be realized (Gibbs 1906, Rowlinson Widom 1982). Therefore, for a spreading film in thermodynamic equilibrium k = +1 S = 0), and locally there is a state of mechanical equilibrium at the contact line between the three phases. 

Call the phases a and p they could be any combination of solid, liquid, or gas. Although the interface between two phases is open to mass and energy transfers, the entire system here is closed. Since T and P are fixed for the entire system, the NPT criterion for equilibrium (7.1.40) applies that is, the system s total Gibbs energy will be a minimum at equilibrium,... 

Before approaching the problem of dynamics of contact line, we shall briefly review the equilibrium properties of gas-liquid interfaces and their dependence on the proximity to solid surfaces. We shall consider the simplest one-component system a liquid in equilibrium with its vapor. Thermodynamic equilibrium in a two-phase system implies equilibrium of the interphase boundary, which tends to minimize its area. The thermodynamic quantity that expresses additional energy carried by the interface is surface tension, defined as the derivative of the Helmholtz or Gibbs free energy with respect to interfacial area E ... 

Gibbs s approach to the determination of a is valid for any interface liquid/gas (L/G), liquid/ liquid (L1/L2), solid/gas (S/G), solid/liquid (S/L), or solid/solid (S1/S2). The methods are used to either measure or indirectly estimate the interfacial free energy, which may vary significantly depending on the type of interface [3,5]. 

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