Statistical argument for

The values of 3.3 to 3.6 obtained for the pK pp value to be assigned to the C-25 gel is close to the pK value of 3.31 (I = O.lCNaClO )) published for methoxyacetic acid [58], the weak carboxylic acid that most closely resembles the weak-acid functionality repeated in the cross-linked carboxymethyldextran. It can be concluded, on the basis of this observation, that Eq. (25) provides an adequate resolution of pKjn,. Indeed, the resemblance between pKjpp and pKjp, has led to the use of statistical arguments for the rationali2ation of the absence of nonideality in the a/(l - a) term. The pKjpp values for the highly swollen gel of C-50 at Cs = 0.01 mol dm, on the other hand, increases with increasing a. The extrapolated pK pp values of 3.3-3.6 at a = 0 are consistent with the values of 3.3-3.6 obtained for the C-25 gel over the a range studied. 

The statistical argument for tlie concerted cycloaddition reaction controlled by the Woodvvard-Hofi nann rules, which is summarized in tlie reaction scheme of Fig. 4.3, seems to be oversimplified. The actual picture may not be as simple as depicted in Fig. 4.3. The scheme in Fig. 4.3 does not take into account tlie stereoelectronic effects, which could influence the relative amounts of the tliree intermediates, and the rates of the nine decomposition reactions. Future, more reliable, experiments should provide more insight into this discussion. 

Finally, a statistical argument for the existence of multiple states of adsorbed molecules can be made. Chemical species are thought to exist in a series of states governed by a probability function that is related... 

In this section, we present statistical arguments for determining the size of polymer chains. Consider as an example a polyethylene chain... 

Gaussian plume models for continuous sources can be obtained from statistical arguments or can be derived by solving ... 

The detailed analysis of the way in which the overall and internal structure of PCNTs apparently arise is discussed elsewhere[20j. Here, we draw attention to some particularly interesting and unusual structures which occur in the body of the nanotubes. An expansion of the section of the central core which lies ca. 5 below the tip of the nanotube in Fig. 1 is shown in Fig. 2. Loop structures occur at points a-d and a -d in the walls in directly opposing pairs. This parallel behaviour must, on the basis of statistical arguments, be related and we interpret the patterns as evidence for a hemi-toroidal connection between the inner and outer adjacent concentric graphene tubes (i.e., turnovers similar to a rolled-over sock). That the loops, seen in the HRTEM, are evidence for very narrow single-walled closed-ended tubes trapped within the walls can be discounted, also on statistical grounds. 

For simple alkyl radicals, the product distribution appears to be predictable using statistical arguments. 

The excited state of a molecule can last for some time or there can be an immediate return to the ground state. One useful way to think of this phenomenon is as a time-dependent statistical one. Most people are familiar with the Gaussian distribution used in describing errors in measurement. There is no time dependence implied in that distribution. A time-dependent statistical argument is more related to If I wait long enough it will happen view of a process. Fluorescence decay is not the only chemically important, time-dependent process, of course. Other examples are chemical reactions and radioactive decay. 

It can also be shown with related statistical arguments that the enthalpy of mixing for a regular polymer-solvent solution is given by... 

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