Surface excess internal energy

In an exactly similar manner, the respective surface excess internal energy Ex and entropy Sx can be defined by the following mathematical relationships (Chattoraj and Birdi, 1984 Birdi, 1989) ... 

Note that since the surface excess enthalpy, Ha, is defined as U°+pVa, Ha = U°. Similarly, the differential surface excess enthalpy, h°, equals the differential surface excess internal energy, u°. 

The surface excess internal energy U") is defined as the difference between the total internal energy of the system and the internal energies of the solid and gas phase ... 

The effects of the variation of temperature on the surface tension and surface excess internal energy can be predicted from surface thermodynamics. At constant pressure (dP = 0) with varying temperature, Equation (206) can be written as... 

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 ... 

Quite apart from thermolysis occurring before fragmentation, the temperature of the ion source may have a marked effect on the appearance of a mass spectrum. Comparison of mass spectra obtained with hot and cooled ion-sources and of spectra obtained by photon impact or field ionization show by the increased amount of fragmentation that a molecular ion possesses a greater excess of internal energy when formed in a hot, electron-impact source. Possible origins of this excess internal energy are collision with or radiation from surfaces. Some effects of hot and cold ion sources are discussed. 

U, S, and Nf are, respectively, excess internal energy, entropy, and number of molecules ascribed to the film surfaces... 

Experimental evidence obtained from the literature and from current research has been cited to demonstrate that densification processes are responsive to at least five independent experimental variables, temperature, remnant porosity, remnant surface area, applied stress, and the concentration of non-thermodynamic defects, which represent annealable excess internal energy. An empirical model for densification kinetics incorporating these variables has been proposed which provides for nonlinear dependences of densification rate upon porosity and total stress. The proposed relationship is com-... 

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. 

Gibbs postulated the fundamental equation for the surface excess of internal energy as [10,11]... 

In TIRF protein adsorption experiments, it is desirable to correlate the intensity of excited fluorescence with excess protein concentration at the interface. Such an adsorbed layer is often in equilibrium with bulk-nonadsorbed protein molecules which are also situated inside the evanescent volume and thus contributing to the overall fluorescence. Various calibration schemes were proposed, using external nonadsorbing standards40,154 , internal standard in a form of protein solution together with a type of evanescent energy distribution calculation 154), and independent calibration of protein surface excess 155). Once the collected fluorescence intensity is correlated with the amount of adsorbed protein, TIRF can be applied in the study of various interactions between surface and protein. 

For pure liquids the description becomes much simpler. We start by asking, how is the surface tension related to the surface excess quantities, in particular to the internal surface energy and the surface entropy ... 

The differential energy of adsorption can also be regarded as the change of internal energy of the complete adsorption system, produced by the adsorption of an infinitesimal surface excess amount dn°, when temperature, volume and surface area are held constant (and assuming the adsorbent to be inert and that its internal energy is not changed). Thus,... 

The above equations are all based on the internal energy. Similar equations can be written with the enthalpy since the surface excess enthalpy and energy are identical in the Gibbs representation when 1 =0 (Harkins and Boyd, 1942). Therefore the various energies of immersion defined by Equations (5.6)—(5.8) are all virtually equal to the corresponding enthalpies of immersion, i.e. (A inmH°, AimmHr and Ah 1), thus ... 

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