Coverage variation

Tseng CW, Mangione CM, Brook RH, et al. 2007. Indenti-fying widely covered drugs and drug coverage variation among Medicare Part D formularies. JAMA 297 2596. 

Recent PEEM experiments revealed that the wavelike propagation of coverage variations across the Pt(100) surface during the CO oxidation are not restricted to the occurrence of autonomous oscillations or to local... 

Using the above-mentioned assumptions one can write the system of equations characterizing coverage variation for storage stage ... 

Figure 5. Coverage Variation CO added in 0.036cc pulses.

Equation (13) can be solved in closed form both for first- and second-order kinetics. In fact, defining the coverage variation... 

McCabe and Schmidt [275] have used a revised form of the Redhead equation, eqn. (116), including coverage variations of Ed, viz. 

If the coverage variations are significant, cd/RT> 1 but cd usually is small compared with Ed, then, at least approximately... 

Figfure 1. Coverage variation with assembly time derived from contact angle (CA) and grating coupler (GC) results, for two different concentrations of ODP inn-heptane/propan-2-ol(100/ 0.4 v/v). Error bars show standard deviations for repeated measurements. 

Thus from an adsorption isotherm and its temperature variation, one can calculate either the differential or the integral entropy of adsorption as a function of surface coverage. The former probably has the greater direct physical meaning, but the latter is the quantity usually first obtained in a statistical thermodynamic adsorption model. 

The rate of physical adsorption may be determined by the gas kinetic surface collision frequency as modified by the variation of sticking probability with surface coverage—as in the kinetic derivation of the Langmuir equation (Section XVII-3A)—and should then be very large unless the gas pressure is small. Alternatively, the rate may be governed by boundary layer diffusion, a slower process in general. Such aspects are mentioned in Ref. 146. 

It is not surprising, in view of the material of the preceding section, that the heat of chemisorption often varies from the degree of surface coverage. It is convenient to consider two types of explanation (actual systems involving some combination of the two). First, the surface may be heterogeneous, so that a site energy distribution is involved (Section XVII-14). As an example, the variation of the calorimetric differential heat of adsorption of H2 on ZnO is shown in Fig. 

As usual, things become more complicated when studied in detail. Note that for 0/W(l 10) 0 varies with 6 the situation is shown more fully in Fig. XVIII-15. The authors speculate that variations in Dq and E have to do with a p(2 x 1) structure at low oxygen coverage, with O atoms occupying alternate rows of W atoms, the empty rows becoming occupied above 0 = 0.5. The consequence is that O—O interactions shift from being mostly attractive to being in part repulsive. 

For other purposes, obtaining a measure of the adsorbate surface density directly from the experiment is desirable. From this perspective, we introduce a simple model for the variation of the surface nonlinear susceptibility with adsorbate coverage. An approximation that has been found suitable for many systems is... 

If we knew the variation m A as a fiinction of coverage 0, this would be the equation for the isothenn. Typically the energy for physical adsorption in the first layer, -A E, when adsorption is predominantly tlnongh van der Waals interactions, is of the order of lO/rJ where T is the temperature and /rthe Boltzmann constant, so that, according to equation (B1.26.6), the first layer condenses at a pressure given by PIPq. 10... 

An extensive coverage of the general pressure and temperature variation of thermal conductivity is given in the monograph by Vargaftik,... 

Other applications of REELM include monitoring variations like oxidation, segregation, and hydration in the surface chemistry of polycrystalline materials. Differences of 1 /10 of a monolayer in oxygen coverage due to variations in grain... 

For the equihbrium properties and for the kinetics under quasi-equilibrium conditions for the adsorbate, the transfer matrix technique is a convenient and accurate method to obtain not only the chemical potentials, as a function of coverage and temperature, but all other thermodynamic information, e.g., multiparticle correlators. We emphasize the economy of the computational effort required for the application of the technique. In particular, because it is based on an analytic method it does not suffer from the limitations of time and accuracy inherent in statistical methods such as Monte Carlo simulations. The task of variation of Hamiltonian parameters in the process of fitting a set of experimental data (thermodynamic and... 

In connection with the adsorption of organic molecules at the surface of an electrode it is possible to distinguish two types (a) adsorption of undissociated molecules and (b) adsorption of intermediates formed by dissociation of the original molecule. The variation of coverage of the surface of a... 

A very similar effect of the surface concentration on the conformation of adsorbed macromolecules was observed by Cohen Stuart et al. [25] who studied the diffusion of the polystyrene latex particles in aqueous solutions of PEO by photon-correlation spectroscopy. The thickness of the hydrodynamic layer 8 (nm) calculated from the loss of the particle diffusivity was low at low coverage but showed a steep increase as the adsorbed amount exceeded a certain threshold. Concretely, 8 increased from 40 to 170 nm when the surface concentration of PEO rose from 1.0 to 1.5 mg/m2. This character of the dependence is consistent with the calculations made by the authors [25] according to the theory developed by Scheutjens and Fleer [10,12] which predicts a similar variation of the hydrodynamic layer thickness of adsorbed polymer with coverage. The dominant contribution to this thickness comes from long tails which extend far into the solution. 

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