Surface energy dependence

Accounting for the unusual r dependence of the surface tension c(r) oc modifies the standard result from Eq. (33) by a factor of. The reason is that the peculiar surface energy dependence F uTfiR) = 4nR a = AkgoR / o / calls for the following dependence of pressure on the curvature ... 

Epps TH, Delongchamp DM, Fasolka MJ, Fischer DA, Jablonski EL (2007) Substrate surface energy dependent morphology and dewetting in an ABC tiiblock copolymer film. Langmuir 23 3355-3362... 

There exists as we have noted a separate phase at the interface between a liquid and a gas. The magnitude of the vapour-liquid interfacial energy is markedly dependent on the composition of the liquid and although experimental data are somewhat scanty, the surface energy is also affected by the nature of the gas in contact with it. It is to be anticipated that at the interface between two immiscible liquids a similar new interfacial phase will come into existence possessing a definite surface energy dependent on the composition of the two homogeneous liquid phases. 

A similar calculation can be done for ionic crystals. In this case the Coulomb interaction is taken into account, in addition to the van der Waals attraction and the Pauli repulsion. Although the van der Waals attraction contributes little to the three-dimensional lattice energy, its contribution to the surface energy is significant and typically 20-30%. The calculated surface energy depends sensitively on the particular choice of the inter-atomic potential. 

The surface energy depends on the crystal faces exposed. For example, molecular dynamics simulations (Blonski and Garofalini 1993) give the different surface energies for various orientations of a- and y-alumina surfaces. However, for mineralogical and ceramic nanoparticles, it is difficult or impossible to control (or measure) which surfaces dominate, and usually only some sort of average (not rigorously defined in terms of... 

The relationship between the dispersion and non-dispersion components of the surface energy depends on the nature of the phases in contact. If one phase is polar (o">0), and the other one in non-polar (o"=0, and g2 then one can write that... 

The surface energy depends not only on the composition of the surface layer, but also on the compositions of the bulk phases. Bulk phases can be declared autonomous, while surface phases are non-autonomous. This distinction is the origin for dynamic surface tension, e.g. for liquid two component systems, as intensively studied in the classical monograph by Defay et al. (1966) and demonstrated in Fig. 2C.1. 

It is known that the surface energy depends not only on the composition of the surface layer, but also on that of the bulk phases [130]. To formulate the Gibbs law for the non-equilibrium chemical potential, additional so-called cross-chemical potentials (the partial derivatives of the surface free energy with respect to the component concentrations in the bulk phases) have been introduced. Rusanov and Prokhorov [131] derived the Gibbs equation and the expression for the free energy of the surface layer in terms of the ordinary chemical potentials by dividing the transition layer adjacent to the surface into n thin layers. For each layer an equilibrium state was assumed. The expression for surface energy was derived by the summation of the equilibrium equations over all these layers. Further, the expression for the additional contribution to the surface tension due to the non-equilibrium diffusion layer was derived in [48, 132]... 

Here the coefficients a and b characterize the surface-energy anisotropy and can be computed from the surface-energy dependence on the surface orientation. Naturally, the nonhnear operator Too i is invariant with respect to rotations by 7t/2, as well as any of the transformations x —s- —x, y — —y, x y, while Finis invariant with respect to rotations by 27t/3 as well as the transformation y —s- —y, b —b. The functions Wo 2,zih) are determined by the type of a wetting interaction model and can also differ for different orientations of the film surface. 

The Wulff plot draws a graph of y versus 0. This construction was developed to allow the equilibrium shape of crystals to be determined when the surface energy depends on crystallography. 

The surface energy depends on a crystal plane orientation. The experimental measurement of the surface energy for solids is extremely difficult. There are few data about values of y in the literature. 

In order to consider any mechanical or electro-optical effects for a liquid crystal layer placed between two solid substrates one must solve a problem of the distribution of the director over the layer with allowance for the boundary conditions. The standard variational procedure allows such calculations when the surface energy depends only on orientation of the director (angles 9 and 4> ) at both boundaries but not on their spatial derivatives. 

When the surface energy depends not only on the director itself but also on its spatial derivatives, ) so-called divergent elastic moduli... 

Eq 2.26 allows one to calcidate the dispersive component for a hquid having free surface energy dependent on dispersive and polar forces based on values obtained for hquid determined only by dispersive forces. For example, for hydrocarbons Yl = Yl > Slid then for water Yl = 0.0218 N/m. 

Leroux et al., showed that in the case of polyester (PET), the degree of increase in the surface energy depends on the textile fabric structure. Adhesion between silicon or fluorine compounds used to produce hydrophobic textile is very low on polyester fibers yielding a poor washing... 

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