Probable configuration

To calculate the most probable configuration, we start with equation (10.15) and take the logarithm of both sides to get... 

The molecular models upon which the theoretical intensity curves of Fig. 4 are based have. been chosen to distinguish between the three most probable configurations of fluorine nitrate. The... 

The probable configuration of isosucrose was systematically discussed by Georg,who thought that the yield was much greater when the beta anomer, rather than the equilibrium mixture or the alpha anomer, of 2,3,4,6-tetraacetyl-D-glucose was used in the condensation. Analogy with tetraacetyl-D-fructopyranosyl chloride, which yielded the acetylated... 

Figure 13. Schematic showing the probable configuration of atomic steps surrounding the (001) terrace at a saddle point of a 2-D grating on Si(OOl). Note that if the surrounding steps are mono-atomic they are all of the same type and will prefer to be all of the low energy type(SA) if the saddle point moves up or down by one step unit the surrounding steps will all be of the high energy type. This is believed to be the basic reason for the preference in type of saddle point terrace.

Imagine the liquid to be divided into microscopic cells as shown in Fig. 22. The volume of a cell must be chosen carefully to have a particular, special value, described later. A cell is small enough so that occasionally it may be empty. At other times one or many molecules may occupy the cell. Consider all possible configurations of all the molecules in all the cells. The most probable configuration will exist for a large mass for a long time. In this respect the most probable distribution is a description of the steady-state condition. The problem is to calculate the most likely distribution. Once this is known, the rate of formation of any density in a cell can be calculated. 

W2 is then proportional to the probability of electron 1 being found at position x1 and electron 2 at xz. The significant points to be noted are (1) that if = x2 the wave function vanishes so that the configuration has zero probability and (2) that there are two equivalent most probable configurations in which the electrons are in different halves of the wire. These two configurations differ only in the numbering of the electrons and are otherwise indistinguishable. 

Figure 2. Probable configuration of a secondary crosslink in a PVC-PVAc melt...

However, as shown in Figure la, the approximation of the thickness of the brush by the length of the most probable configuration is in many cases arbitrary, since configurations that end up at different distances can contribute notably to the brush thickness. In addition, the derivation of eq 14 implies that the random walk can be described by a Gaussian extended from z = 0 to z = oo,... 

The thickness of the grafted polyelectrolyte brush can be described roughly by the length of the most probable configuration, which is provided by the solution of... 

In Figure 5, the length of the most probable configuration is plotted as a function of the reservoir length L for... 

Each of the rare-earth atoms has the xenon core, but the probable configurations of the valence electrons vary as tabulated below. From the list, decide which two of these metals would have the most stable +2 valence states and which two would have the most stable +4 states (ail have stable +3 states). 

In any reversible process, the free-energy difference between two states is independent of the path. Since the compression step, with accompanying displacement of segments, can be carried out reversibly, we can use this procedure to evaluate the free energy difference between a protein molecule in its most probable configuration at a given equilibrium interfacial pressure, IIe, and the molecule in its... 

The force balance between the attractive force (entropy term) and the repulsive one (potential term) is attained at the most probable configuration corresponding to the minimum of the free energy, A. To find the solution, differentiating Eq. (18) with respect to r, and putting dAldr = 0, we have... 

At temperatures above 435°C CuCl has a disordered wurtzite structure, and a mass spectrometric study shows that CU3CI3 molecules are the predominant species in the saturated vapour at 450°C. The probable configuration of the trimer is an essentially planar 6-ring, but the detailed structure was difficult to establish with certainty. A later mass spectrometric study of the vapour in equilibrium with solid CuCl (280-430°C) indicated comparable concentrations of CU3CI3 and CU4CI4 molecules and a smaller concentration of CU5CI5 molecules. ... 

For xA l, the component A may be referred to as the solvent and B as the solute. For any pair of species a/ , we can pick up two specific particles (one of species a and the other of species / ) and refer to these particles as a dimer. From the first row of figure 2.17, we see that the most probable configurations of the dimers occur either when the separation is aaig or when they are solvent separated, i.e., when the distances are R aaig + no AA, where n = 1, 2, 3, for the second, third, and fourth peaks. Note that because of the approximate nature of the computations, the curves gAB (R) and gBA (R) may come out a little different however, theoretically they should be identical and in our computation they are nearly identical and may not be distinguished on the scale of figure 2.16. 

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