Interface internal energy

Fig. 14.9. Interface internal energy eint plotted versus temp>erature T at Pc = Pm = 1 atm ( ), and its temperature derivative at constant interface strain and constant S3fstem volume, demt/dT) f ( ). Reprinted from [30] with wiitten permission from Elsevier...

Ebox = total calculated energy inside the box drawn around the interface. This should be the Gibbs free energy. An approximation to it would be the internal energy atT=OK. 

Insulation see also lagging 554 Intelligent transmitters 240,241,242 Intensity of turbulence 701 Interface evaporation 484 Interfacial turbulence 618 Internal energy 27,44... 

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. 

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 ... 

T, may become positive or negative, depending on the particular interface in question. Other surface excess properties, such as the surface internal energy and surface entropy, are defined similarly ... 

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. 

The change in internal energy for the two phases adjacent to the interface is now... 

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... 

Let us consider a process in a system with two phases, a and / , which are divided by an interface we could, for instance, do work on that system. As a consequence the state quantities like the internal energy, the entropy, etc. change. How do they change and how can we describe this mathematically In contrast to the usual bulk thermodynamics we have to take the interface into account. 

The TdS terms stands for the change in internal energy, which is caused by an entropy change, e.g. a heat flow. The p dNi terms consider the energy change caused by a change in the composition. Both PdV terms correspond to the volume-work of the two phases. Since the interface is infinitely thin it cannot perform volume work. 

The Gibbs treatment of molecules at interfaces starts from the excess internal energy Es and excess entropy Ss at the interface of a two-component system, with n moles of component 1 at the surface of area A, nf moles of component 2 at the surface, and an interfacial surface tension IT ... 

We consider a system of N electrons separated from the surroundings by a wall that allows work to be performed on the surroundings and heat to be exchanged. In addition, electrons may enter or leave the system through the wall (i.e., through an interface). Thus, the system is open with respect to electrons. The change in the internal energy, U, is accounted for by the so-called central law of thermodynamics ... 

T absolute temperature R molar ideal gas constant Cp mean molar heat capacity area of surface or interface T thickness of interfacial layer Q heat (extensive) q heat per mole of adsorbate U internal energy H enthalpy S entropy G Gibbs free energy y surface tension... 

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. 

Since our concern is primarily with interface energy transfer rather than with the energy associated with the dividing surface, we normally neglect all interfacial effects and write the jump internal energy balance (3.99) as ... 

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