Smoothed Potential Cell Model

This corresponds to a heat of vaporization (per particle) of 0.678 ze. As this value of the heat of vaporization seems to be in agreement with experimental data (cf. Fig. 7.2.3) we shall use this relation to obtain information about the value of e when other more direct values are lacking. 

The complexity of the excess functions in mixtures make an analytical discussion highly desirable. For this purpose the Lennard-Jones and Devonshire model is unfortunately not suitable because of the complicated form of the mean potential w(r). It is possible, however, to develop a simplified version of the cdl model valid in a restricted range of density. For hig densities, as in the solid state, we may use a harmonic potential approximation (cf. Fig. 7.1.2). We shall develop this approximation in more detail in the next paragraph. On the other hand, for the range of densities corresponding to the liquid state we may use the smoothed potential model (Prigogine and Mathot [1952]) (cf. Fig. 7.1.2). This is however an oversimplification and the conclusions have to be used with some caution. 

The smoothed potential model is based on the following assumption r farding )(r) (cf. 7.1.10 7.1.11) 

The choice of the upper limit (a — a) is rather arbitrary. In so far as we are interested in excess properties of solutions, we could as well take (a — r)/2. The difference in these limits contributes only a constant term to the free energy and disappears in the excess functions (cf., however, Ch. XVIII for the quantum case). As in the Lennard-Jones and Devonshire model, we shall use (7.1.23) for the lattice energy of our system. The cell partition function W is clearly of the same form as for hard spheres (cf. 7.1.11) and depends only on the density. It may be written in the form 

At vanishing external pressure the equation of state (7.3.6) becomes 

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Fig. 7.3.1 compares the equation of state deduced from the smoothed potential cell model with that deduced from the exact Lennard-Jones model. Especially in the region between 20 > ze >15 the orders of magnitude are the same. 

Model 149. 4. Smoothed Potential Cell Model 151. 5. Intermolecular Forces and Excess Functions 153. 

In the smoothed potential cell model the cell partition function depends only on the density and is the same as for pure liquids (7.3,2)... 

Fig. 4.1. Cellular model illustrating cell types in vascular wall involved in vasorelaxation induced by SERMs. Putative targets of SERMs are indicated within cyan tags. SERMs directly affect L-type VDCC, BK fil subunit in smooth muscle cells, and ER in endothelial cells. L-type VDCC L-type voltage-dependent calcium channel BK calcium-activated large conductance K+ channel PKG protein kinase G eNOS endothelial nitric oxide synthase GC soluble guanylate cyclase cGMP cyclic GM P V electrochemical membrane potential ER estrogen receptor. See text for further details...

In the smooth muscle cell, CD is incorporated into the thin filaments in the "contractile domain" of the cell (Furst et al., 1986 North et al., 1994a). Ultrastruc-tural studies presented in Chapter 4 (this volume) have shown that CD is located in the thin filament in an extended form beside TM along the axis of the actin double helix. The model (Fig. 2) places CD in potential contact with actin and TM throughout its length and allows a possible end-to-end interaction. These structural arrangements form the basis of caldesmon function in the thin filament. 

Bormulae (8.2.7) and (8.2.8) are much simplified if the cell partition functions depend only on the density or more generally if the ratio aI aa (and WbI bb) is temperature independent. This simplifying feature is realized in both the smoothed potential and the harmonic oscillator cell models (cf. Ch. VII, 3, 4). 

BB-SFG, we have investigated CO adsorption on smooth polycrystaHine and singlecrystal electrodes that could be considered model surfaces to those apphed in fuel cell research and development. Representative data are shown in Fig. 12.16 the Pt nanoparticles were about 7 nm of Pt black, and were immobilized on a smooth Au disk. The electrolyte was CO-saturated 0.1 M H2SO4, and the potential was scanned from 0.19 V up to 0.64 V at 1 mV/s. The BB-SFG spectra (Fig. 12.16a) at about 2085 cm at 0.19 V correspond to atop CO [Arenz et al., 2005], with a Stark tuning slope of about 24 cm / V (Fig. 12.16b). Note that the Stark slope is lower than that obtained with Pt(l 11) (Fig. 12.9), for reasons to be further investigated. The shoulder near 2120 cm is associated with CO adsorbed on the Au sites [Bhzanac et al., 2004], and the broad background (seen clearly at 0.64 V) is from nomesonant SFG. The data shown in Figs. 12.4, 12.1 la, and 12.16 represent a hnk between smooth and nanostructure catalyst surfaces, and will be of use in our further studies of fuel cell catalysts in the BB-SFG IR perspective. 

Schematic representation of the mesenchymal and endothelial cascade of differentiation in a murine model (mice) and in humans (hum). All mesenchymal and endothelial cells are negative for the antigen CD45. Based on this, the dynamics of surface antigen expression along development of different mature cells derived from the mesenchymal and endothelial systems can be observed. Rounded arrows indicate selfrenewal potential. Smooth, thinner arrows indicate directions of cellular differentiation, and dotted arrows indicate possible hierarchies, but yet to be proved experimentally. The question marks indicate lack of data on the pathway or on cellular identity. The identification of CDs (clusters of differentiation) and other antigen cell markers can be found in the list of abbreviations LT-HSC, long-term hematopoietic stem cell EC, endothelial cell PDMPC, placental-derived mesenchymal progenitor cell MSC, mesenchymal stem cell MAPC, mesenchymal adult progenitor cell.

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