Internal Energy of the Interface

The internal energy of the interface can be calculated in our MC simulations according to (14.10), with the aid of the position of the Gibbs dividing surface, zdiv (see Fig. 14.3). The results are shown in Fig. 14.9 ( ). The interface energy increases steadily from 0.30 J/m at 380 K to 0.335 J/m at the melting temperature (T — 410K), and remains approximately constant above. 

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The contributions of the two phases and of the interface are derived as follows. Let ua and vP be the internal energies per unit volume of the two phases. The internal energies ua and vP are determined from the homogeneous bulk regions of the two phases. Close to the interface they might be different. Still, we take the contribution of the volume phases to the total energy of the system as uaVa + vPV. The internal energy of the interface is... 

Measurements of the interlamellar domain and interface, as presented here, develop their full strength when put in a wider context and combined with the material properties of the adjoining phases, e.g. the effect of the internal energy of the interface on the heat capacity of the semicrystalUne material. 

Let us consider Equation 18.84 again for the interface between the two phases shown in Figure 18.4. In this equation, dS is the excess entropy due to the presence of the interface, dV is the volume of the interface, and dn represents the excess moles of species I within the interface. For a constant composition, we get the internal energy of the interface by integrating Equation 18.84. The result is shown in Equation 18.89. 

The instability of these chiral monolayers may be a reflection of the relative stabilities of their bulk crystalline forms. When deposited on a clean water surface at 25°C, neither the racemic nor enantiomeric crystals of the tryptophan, tyrosine, or alanine methyl ester surfactants generate a detectable surface pressure, indicating that the most energetically favorable situation for the interfacial/crystal system is one in which the internal energy of the bulk crystal is lower than that of the film at the air-water interface. Only the racemic form of JV-stearoylserine methyl ester has a detectable equilibrium spreading pressure (2.6 0.3dyncm 1). Conversely, neither of its enantiomeric forms will spread spontaneously from the crystal at this temperature. 

Postsource reactions are governed by a number of factors such as the internal energy of the ions, the time between exit of ions from the source to mass analysis, and the pressure of the mass analyzer. Since there is no ideal mass analyzer [2], a range of analyzers are commercially available which have been interfaced with most of the common ionization methods. Each mass analyzer has unique properties which can influence the actual mass spectrum observed. 

Guidelli, R. A reply to the question of whether the internal energy of sohd interfaces can be of anon-homogeneous nature. J. Electroanal. Chem. 472(2), 174-177 (1999)... 

Since is the internal energy of an interface, an interface must exist between two bulk phases, for a finite value of interfaeial tension. The consequence of Eq. (82) is that a stable interface requires a positive value of interfaeial tension, implying that energy must be increased if the interfa-... 

The equations of motion for a fluid whose internal energy is a function only of density, entropy and their spatial derivatives are able to explain motions through non-isothermal liquid-vapour interfaces. Molecular and statistical models which take the local state of molecules into consideration lead to such an internal energy of the fluid... 

The internal energy associated with the interface is the difference between the internal energy of the system and that of the a and (3 phases, as determined by the position of the Gibbs dividing surface,... 

Random interface models for ternary systems share the feature with the Widom model and the one-order-parameter Ginzburg-Landau theory (19) that the density of amphiphiles is not allowed to fluctuate independently, but is entirely determined by the distribution of oil and water. However, in contrast to the Ginzburg-Landau approach, they concentrate on the amphiphilic sheets. Self-assembly of amphiphiles into monolayers of given optimal density is premised, and the free energy of the system is reduced to effective free energies of its internal interfaces. In the same spirit, random interface models for binary systems postulate self-assembly into bilayers and intro-... 

Surface-active agents may be added during the processing of films (internal addition) or by surface treatment of the film (external addition). These tend to reduce the surface energy of the film/water droplet interface promoting a continuous film of water thus enhancing transparency. Examples include hydrophilic surfactants, such as sorbitol or glycerol fatty acid mono- or di-esters. 

The simplest way to treat an interface is to consider it as a phase with a very small but finite thickness in contact with two homogeneous phases (see Fig. 16.1). The thickness must be so large that it comprises the region where the concentrations of the species differ from their bulk values. It turns out that it does not matter, if a somewhat larger thickness is chosen. For simplicity we assume that the surfaces of the interface are flat. Equation (16.1) is for a bulk phase and does not contain the contribution of the surfaces to the internal energy. To apply it to an interface we must add an extra term. In the case of a liquid-liquid interface (such as that between mercury and an aqueous solution), this is given by 7 cL4, where 7 is the interfacial tension - an easily measurable quantity - and A the surface area. The fundamental equation (16.1) then takes on the form ... 

The exact position of the geometrical surface can be changed. When the location of the geometrical surface X is changed while the form or topography is left unaltered, the internal energy, entropy and excess moles of the interface vary. The thermodynamics of the interface thus depend on the location of the geometrical surface X. Still, eq. (6.13) will always be fulfilled. 

TABLE 11 Summary of Methods for Measuring the Surface Stress T, the Surface Tension y. the Internal Surface Energies of the Solid Surface i/ or of the Solid-Liquid Interface. and Changes in Surface Stress AT... 

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