Entropic Barrier Idea

One of the inherent properties of an isolated polymer chain is its ability to assume a large number of conformations Rf. As a result, the chain entropy k laj f-,k is the Boltzmann constant) can be high and its free energy F is given by 

It is important to recognize that the role of conformational entropy of polymer chains in various biological processes cannot be treated as only a minor factor. Since the temperature T is essentially fixed for a given physiological system and because only rather minor variations are permitted in E for a fixed T, the only way the free energy landscape can be dramatically modified must 

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Polymer crystallization theory is a mature area, and there are several review articles available that present and discuss the different theories in great detail (eg, 103,104). Having said that, over the last 5 years or so there has been a flurry of new interest becanse of the increase in computational power, which has the potential to decisively enter the debate in some areas. In the following the underlying themes of the two principle theories of polymer crystallization, secondary nucleation theory and rough-surface or entropic barrier theory, are outlined. The results of more recent simulations are then briefly discussed, in which the constraints of the above theories, introduced to provide analytical solutions, have been relaxed. Finally, some of the more fundamentally different ideas that have recently appeared are discussed. 

We have introduced in Section 1.4 the idea of entropic barriers for polymer translocation through nanopores, primarily based on intuitive arguments (Figure 1.8). The relevance and the extent of contfibutions from entropic barriers are generally hard to discern based only on experimental data, as contributions from many control variables need to be separately assessed in interpreting the data. In this context, computer simulations, particularly with the use of toy models, have helped to identify the key molecular mechanisms of polymer translocation. 

Extreme cases were reactions of the least stabilized, most reactive carbene (Y = CF3, X = Br) with the more reactive alkene (CH3)2C=C(CH3)2, and the most stabilized, least reactive carbene (Y = CH3O, X = F) with the less reactive alkene (1-hexene). The rate constants, as measured by LFP, were 1.7 x 10 and 5.0 X lO M s, respectively, spanning an interval of 34,000. In agreement with Houk s ideas,the reactions were entropy dominated (A5 —22 to —29e.u.). The AG barriers were 5.0 kcal/mol for the faster reaction and 11 kcal/ mol for the slower reaction, mainly because of entropic contributions the AH components were only —1.6 and +2.5 kcal/mol, respectively. Despite the dominance of entropy in these reactive carbene addition reactions, a kind of de facto enthalpic control operates. The entropies of activation are all very similar, so that in any comparison of the reactivities of alkene pairs (i.e., ferei)> the rate constant ratios reflect differences in AA//t, which ultimately appear in AAG. Thus, car-benic philicity, which is the pattern created by carbenic reactivity, behaves in accord with our qualitative ideas about structure-reactivity relations, as modulated by substiment effects in both the carbene and alkene partners of the addition reactions. " Finally, volumes of activation were measured for the additions of CgHsCCl to (CH3)2C=C(CH3)2 and frani-pentene in both methylcyclohexane and acetonitrile. The measured absolute rate constants increased with increasing pressure Ayf ranged from —10 to —18 cm /mol and were independent of solvent. These results were consistent with an early, and not very polar transition state for the addition reaction. 

In our view, Rehbinder s doctrine on the structure-mechanical barrier had been proposed much earher than the idea of steric stabilization. The latter, related (at least, initially) to the conformational statistics of hydrophilic tails and loops, presents only the entropic part of elastidty and is not responsible for the mechanical strength. 

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