Molecular discrepancies

In polymer theories, the length of a segment (molecular unit) a is the natural unit of the length scale at the molecular level, but experimentally measured quantities Q do not feel this molecular discrepancy. Hence mathematical expressions of the macroscopic quantity Q have to be well-defined in the limit a —> 0. Regarding the problem of the molecular coil excluded volume, this limit should be treated as a rejection with the consideration of the interactions of a segment with itself (self-excluded volume). 

Under 0 conditions occurring near room temperature, [r ] = 0.83 dl g for a polystyrene sample of molecular weight 10. f Use this information to evaluate tg and for polystyrene under these conditions. For polystyrene in ethylcyclohexane, 0 = 70°C and the corresponding calculation shows that (tQ /M) = 0.071 nm. Based on these two calculated results, criticize or defend the following proposition The discrepancy in calculated (rQ /M) values must arise from the uncertainty in T>, since this ratio should be a constant for polystyrene, independent of the nature of the solvent. 

The reaction center is built up from four polypeptide chains, three of which are called L, M, and H because they were thought to have light, medium, and heavy molecular masses as deduced from their electrophoretic mobility on SDS-PAGE. Subsequent amino acid sequence determinations showed, however, that the H chain is in fact the smallest with 258 amino acids, followed by the L chain with 273 amino acids. The M chain is the largest polypeptide with 323 amino acids. This discrepancy between apparent relative masses and real molecular weights illustrates the uncertainty in deducing molecular masses of membrane-bound proteins from their mobility in electrophoretic gels. 

This discrepancy between experiment and theory (and many others) can be explained in terms of an alternative model of covalent bonding, the molecular orbital (MO) approach. Molecular orbital theory treats bonds in terms of orbitals characteristic of the molecule as a whole. To apply this approach, we carry out three basic operations. 

The nature of the termination reaction in MMA polymerization has been investigated by a number of groups using a wide range of techniques (Tabic 5.5), There is general agreement that there is substantial disproportionation. However, there is considerable discrepancy in the precise values of k tk. In some cases the difference has been attributed to variations in the way molecular weight data are interpreted or to the failure to allow for other modes of termination under the polymerization conditions (chain transfer, primary radical termination).154 In other eases the reasons for the discrepancies are less clear. MALDI-TOF mass... 

Many solvents and additives have measurable transfer constants (Table 6.5). The accuracy of much of the transfer constant data in the literature is questionable with values for a given system often spanning an order of magnitude. In some cases the discrepancies may be real and reflect differences in experimental conditions. In other cases they are less dear and may be due to difficulties in molecular weight measurements or other problems. 

Finally we would like to draw attention to low molecular weight results and their analysis on the basis of surface nucleation theory. The theory was originally developed for infinitely long chains and cannot easily be applied to extended or once-folded chain crystallization. Therefore any discrepancies in this area would not be surprising and would not discredit the theory at higher molecular weights. 

If we assume that the same discrepancy between theory and experiment in M-M enters in M +-M, we can estimate the vibrational relaxation times for the molecular ions. Table II shows the estimated vibrational relaxation times r+ at various temperatures. The values are shorter than those for the neutrals by factors given in Figure 4. 

Comparisons of relative rate constants obtained with Mv s of the total polymer and M s of the HMWF for the same samples show similar trends negligible transfer and termination control of molecular weights for the f-BuCl/Et2AlCl/MeCl system in the —40° to —60 °C range and also for the f-BuBr/Et2AlCl/MeCl at —50 °C (Table 7). For the samples prepared with the f-BuCl/Et AlCl system Mayo plots based on Mv s show zero intercept while that based on Mn s of the HMWF shows a small but finite intercept, z., ktr/kp = 1.91 x 10-5 and 2.14 x 10-s at —50° and -60 °C. Similarly, for the samples prepared with the t-BuBr/Et2AlCl system the Mayo plot based on Mn s of HMWF shows zero intercept while the Mayo plot based on Mv s show a very small intercept, ie., ktr/kp = 5.0 x 10-s at —50 °C. The reasons for this small discrepancy are not known. 

Hartree-Fock (HF), molecular orbital theory satisfies most of the criteria, but qualitative failures and quantitative discrepancies with experiment often render it useless. Methods that systematically account for electron correlation, employed in pursuit of more accurate predictions, often lack a consistent, interpretive apparatus. Among these methods, electron propagator theory [1] is distinguished by its retention of many conceptual advantages that facilitate interpretation of molecular structure and spectra [2, 3, 4, 5, 6, 7, 8, 9]. 

Naphthalene undergoes electrophihc substitutions at the a rather than p position. The Hueckel molecular orbital calculations show that all the carbons have the same jt electron density 1.0. This is not in agreement with the theory of organic reactions based on the Coulombic interaction that electrophilic attack occurs on the most negatively charged atom. Fukui [7] proposed the frontier orbital theory for the discrepancy between the theory and the experimental observation. The importance of... 

Table II shows that for SRM 706 good agreementis obtained between SEC/LALLS and conventional SEC sample My, and Rp values when the band-spreading correction was used. However, the NBS 706 polydispersity index (Ry/Rp) given by the supplier (ca. 2.1) does not agree with that 1.°) found here using the SEC/LALLS and conventional SEC techniques. Insensitivity of the LALLS detector to a small amount of low molecular weight material may account for a larger sample R however, this is not supported by the conventional SEC data. The reason for the discrepancy remains unclear.

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