Cell model justifications

A common further approximation assumes that the investigation of a small subvolume containing only one rod and its counterions will suffice to unveil much of the interesting physics. The main justification for this approach is that the subvolume has zero net charge. Moreover, the counterions will also efficiently screen higher order multipoles. Hence the interactions between two such subvolumes, which are neglected when focusing on just one rod, will be fairly weak. This approximation is called the cylindrical cell model, and it provides the framework for this study. 

Figure 1 and Tables I to IV describe the current model. Justification of parameter values have been given elsewhere (46-50). Almost all parameters were estimated from Independent measurements on exponentially growing cells or cell-free systems. Values for 112 and 113 (parameters associated with the ratio of envelope used for extension and cross-wall formation) were required to be positive but were otherwise considered adjustable. Values for adjusted within the range of 0 to... 

Justification of the Cell Model 131. 6 Multiple Ot cup , aons of Celb 136. 7 Hole... 

We shall first give a brief account of the cell model (or free-volume theory) for pure liquids- This model will be introduced here with a 3Binimum of details. Extensive discussions ms,y be found elsew here (e.g. Hirschfexder, Curtiss and Bird [1954], De Boer [1952]. Green [1952]. We shall introduce it in a semi-empirical v/ay ( 1-4) and then discuss its theoretical justification and some recent extensions. 

In the next paragraphs of this chapter we diall bri y discuss the justification of the cell model and some recrat extensions. 

Because this is similar to the dark J-V curves of conventional solar cells, it has led to suggestions that the current in DSSCs is controlled by a p-n electrical junction. This was used as one justification for modeling DSSCs as p-n junctions (Sec. V.D). However, such J-V data can be fit just as well to the Butler-Volmer equation, a mainstay of electrochemistry [48], as to the diode equation. The... 

To obtain coordinates for a three-dimensional model the two-dimensional (2D) projection was used to locate roughly the x, y coordinates of the caffeine molecule. The z coordinate of each atom in caffeine was calculated by assuming the planar molecule was positioned in the 1,2,2 plane. (The 1,2,2 was selected because it was the strongest reflection observed.) The orientation of pyrogallol was assumed to be as in I. (There was no justification for this assumption other than it appeared to give the least steric hindrance.) The z coordinates of pyrogallol were calculated by assuming it to be parallel to caffeine and unit cell above the plane of caffeine. The water molecule uncovered in the 2D projec-... 

The second approach (Allen and Martin 1982) to include coupling to the lattice is to assume that the hybridization matrix element Fkf between the conduction electrons and the 4f electrons varies as the volume varies. This form of coupling receives justification (Freeman et al. 1988) iiom band theoretic treatments of cerium and its compounds that show that the cell volume can decrease when the 4ficonduction-band l bridization increases, without significant associated change in f-count. One way to include this in the Anderson model is to assume that the volume dependence of Fkf is reflected in a dependence of the characteristic (Kondo) temperature Tk on V. In the Kondo limit, where the occupation number nf 1 does not vary with temperature. 

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