Surface phase ideal

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

As we shall have occasion to note in dealing with solutions, the composition of the surface phase is very different from that of the bulk liquid. When a liquid interface is newly formed the system is unstable until the surface phase has acquired its correct excess or deficit of solute by diffusion from or into the bulk of the solution. This process of diffusion is by no means instantaneous and, as has been observed in discussing the drop weight method, several minutes may elapse before equilibrium is established. In the ripple method the surfece is not renewed instantaneously but may be regarded as undergoing a series of expansions and contractions, thus we should anticipate that the value of the surface tension of a solution determined by this method would lie between those determined by the static and an ideal dynamic method respectively. 

The various regions on the isotherm are determined by the lateral interaction between the surfactant molecules within the surface phase. In the dilute, gaseous state, the molecules can be considered to be negligible in size and non-interacting. Under these conditions the isotherms obey an ideal, two-dimensional gas equation of the form nA = kT. As the pressure is increased, a point is reached (at about 8 nm for myris-... 

Finally, assuming y = Y aad ideal mixing of the two surfactants in the surface phase, i.e. x 2 Equation 17 reduces to the following expression for the composition in the surface ... 

The statistical thermodynamic approach to the derivation of an adsorption isotherm goes as follows. First, suitable partition functions describing the bulk and surface phases are devised. The bulk phase is usually assumed to be that of an ideal gas. From the surface phase, the equation of state of the two-dimensional matter may be determined if desired, although this quantity ceases to be essential. The relationships just given are used to evaluate the chemical potential of the adsorbate in both the bulk and the surface. Equating the surface and bulk chemical potentials provides the equilibrium isotherm. 

Equation (3) has the same form as one of Gibbs s fundamental equations for a homogeneous phase, and owing to this formal similarity the term surface phase is often used. It must be remembered, however, that the surface phase is not physically of the same definiteness as an ordinary phase, with a precise location in space neither do the quantities c , if, mf refer to the total amounts of energy, entropy, or material components present in the surface region as it exists physioally they are surface excesses , or the amounts by which the actual system exceeds the idealized system in these quantities. Care must be taken not to confuse the exact mathematical expression, surface phase , with the physical concept of the surface layer or surface film. 

In the case of gel permeation or size-exclusion HPLC (HP-SEC), selectivity arises from differential migration of the biomolecules as they permeate by diffusion from the bulk mobile phase to within the pore chambers of the stationary phase. Ideally, the stationary phase in HP-SEC has been so prepared that the surface itself has no chemical interaction with the biosolutes, with the extent of retardation simply mediated by the physical nature of the pores, their connectivity, and their tortuosity. In this regard, HP-SEC contrasts with the other modes of HPLC, where the surfaces of the stationary phase have been deliberately modified by chemical procedures by (usually) low molecular weight compounds to enable selective retardation of the biosolutes by adsorptive processes. Ideally, the surface of an interactive HPLC sorbent enables separation to occur by only one retention process, i.e., the stationary phase functions as a monomodal sorbent. In practice with porous materials, this is rarely achieved with the consequence that most adsorption HPLC sorbents exhibit multimodal characteristics. The retention behavior and selectivity of the chromatographic system will thus depend on the nature and magnitude of the complex interplay of intermolecular forces... 

We derived this before, see [1.3.9.6 and 7. The configurational integral requires the computation of the potential energy of the system for all configurations of the system, that is for all x, y, z positions of all molecules (numbered 1, 2,. .. N) in a volume V. Equations [2.9.5 and 6] are exact for three-dimensional systems of monatomic fluids, be they ideal or non-ideal. Now we apply them to a surface phase and introduce approximations compatible with the energy-entropy de-coupling. 

The total (global) activity coefficient f j (i=l,2) reflects the non-ideality of the surface phase caused by differences in molecular interactions and the non-ideality of this phase generated by the adsorbent heterogeneity. According to our earlier considerations [16,17] this coefficient is expressed as follows ... 

For inner sphere complexes with the entire charge at the surface plane Uxi x = Zx and the Boltzmann factor becomes simply exp(—ZxFV s/RT). For outer sphere complexes nx = 0 and both activities are determined by ipd only. Assuming that, except for the electrostatic interactions, the surface phase behaves ideal, the ratios of the surface group activities in Eqs. (46), (51) and (52) can be replaced by ratios of site fractions, 6x = SX/Nj where is the total density of surface sites ... 

Thermodynamic parameters for the mixing of dimyristoyl lecithin (DML) and dioleoyl lecithin (DOL) with cholesterol (CHOL) in monolayers at the air-water interface were obtained by using equilibrium surface vapor pressures irv, a method first proposed by Adam and Jessop. Typically, irv was measured where the condensed film is in equilibrium with surface vapor (V < 0.1 0.001 dyne/cm) at 24.5°C this exceeded the transition temperature of gel liquid crystal for both DOL and DML. Surface solutions of DOL-CHOL and DML-CHOL are completely miscible over the entire range of mole fractions at these low surface pressures, but positive deviations from ideal solution behavior were observed. Activity coefficients of the components in the condensed surface solutions were greater than 1. The results indicate that at some elevated surface pressure, phase separation may occur. In studies of equilibrium spreading pressures with saturated aqueous solutions of DML, DOL, and CHOL only the phospholipid is present in the surface film. Thus at intermediate surface pressures, under equilibrium conditions (40 > tt > 0.1 dyne/cm), surface phase separation must occur. 

The dependence of the ttv values on the composition of the vapor and condensed states for DML-CHOL, DOL-CHOL, and DOL-DML mixtures is shown in Figure 6. The upper curve is the surface vapor pressure as a function of the mole fraction of the liquid-expanded film the lower curve is for the dependence of irv on the composition of the gaseous phase. Ideal mixing behavior is given by the linear dotted line which joins the 7ry° points for each of the pure compounds. In all cases there was complete miscibility of the components as represented by the continuous function of 7rv with x. In the cholesterol mixtures positive deviations from Raoult s law are observed for the mixture of lecithins, ideal mixing is observed. These results confirm those obtained with lipid mixtures—i.e., cholesterol mixed with liquid-expanded lipid films forms rion-ideal mixtures with positive deviations for mixtures of lipids which are in the same monolayer state, as in the case of the liquid-expanded DOL-DML mixtures, ideal mixing results (8). 

Figure 6. irv-x surface phase diagrams for lipid mixtures on water, pH 5.8 at 24.5°C. Dotted line represents ideal mixing. 

In the present study on the stepped Pt(100) clean surface the ideal "hex" phase with its large unit cell has not been observed so far by field ion microscopy. LEED studies of the Pt[4(100)x(lll)]and Pt[9(100)x(111)] (ref.10) surfaces, however, give evidence for a reconstruction modulated by the steps. 

This Datareview has described the known surface phases which exist on both a- and P-SiC. Surface treatments by annealing in UHV, by ion bombardment and by laser irradiation are not suitable to prepare SiC surfaces for further study. Chemical reduction of surface oxides is the preferred route to surface preparation, particularly using a Si flux at temperatures < 1000°C. A distinction is drawn between ideal surfaces prepared in UHV and practical ones where substrates are chemically treated or ion bombarded prior to metallisation. Processes occurring during deposition of the first few monolayers of metal and subsequent treatments are discussed in terms of chemical and physical properties. A total of 15 metal-SiC combinations are reviewed and discussed in terms of silicide and carbide formation. 

An ideal surface phase may be characterized by the criteria fi — 1 and Af = A°. It is obvious that these conditions imply that the surface phase is both uniform and ideal in the ordinary sense and in addition that t is a constant. From Eqs. (69) and (71), we may deduce that for an ideal binary system the following inequality always holds if yj > yl... 

Under actual conditions of reforming, several species are chemisorbed on the Pt/Al203 surface and they influence the overall dynamics(l-6). Significant adsorbate-adsorbate interactions can be present and they affect the sorption and reaction rates and equilibrium (6-11) markedly, especially for bi-molecular reactions. These also can have pronounced consequences in surface dynamics(7-16). While their roles in surface phase transformations have been demonstrated, using ideal single crystal surfaces(12,13), their consequences in surface dynamics are much less understood.(l,12-14)... 

Under ideal conditions, a thermodynamic equilibrium will be reached when the chemical potential of the solute i is equal at the membrane surface and the feed phase adjacent to it. The sorption of these solutes at the membrane surface creates a solute concentration gradient across the membrane, resulting in a diffusive net flux of solute across the membrane polymer (Fig. 3.6-lOB). In vapor permea-tion/pervaporation, any solute that has diffused toward the membrane downstream surface is ideally instantaneously desorbed and subsequently removed from the downstream side of the membrane (Fig. 3.6-lOC). This can be achieved either by applying a vacuum (vacuum vapor permeation/pervaporation), or by passing an inert gas over the membrane downstream surface (sweeping-gas vapor permea-... 

The geometric stmcture is used conventionally for identification of a particular metal/semiconductor surface phase. The surface structures are usually labeled in accordance with their periodicity with respect to the underlying semiconductor crystal plane. Two methods for the description of the two-dimensional lattices are used conventionally. The first one was proposed by Park and Madden [68P] and it consists in the determination of the matrix which establishes a hnk between the basic translation vectors of the surface under consideration and those of the ideal (unreconstructed) substrate sirrface. That is, if a and b are the basic translation vectors of the substrate lattice, while and As are the basic translation vectors of the surface phase, than they can be linked by the equations... 

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