Entropic strain

Fig. 8.18 Compression stress-strain curves of nearly glassy PET (crystalline content 9%) for seven temperatures reaching Tg, showing strong yield phenomena and strain-softening effects that decrease with increasing temperature, having a relatively temperature-independent entropic strain-hardening contribution (from Zaroulis and Boyce (1997) courtesy of Elsevier).

As shown by Senden et al. [121], conventional material models that incorporate entropic strain hardening give a qualitatively incorrect prediction of the Bauschinger effect. This can be illustrated by investigating the effects of cyclic loading. For a two-arm model such as that of Haward and Thackray, when loaded in tension and then unloaded, during unloading the... 

The entropic hypothesis seems at first sight to gain strong support from experiments with model compounds of the type listed in Table 9.1. These compounds show a huge rate acceleration when the number of degrees of freedom (i.e., rotation around different bonds) is restricted. Such model compounds have been used repeatedly in attempts to estimate entropic effects in enzyme catalysis. Unfortunately, the information from the available model compounds is not directly transferable to the relevant enzymatic reaction since the observed changes in rate constant reflect interrelated factors (e.g., strain and entropy), which cannot be separated in a unique way by simple experiments. Apparently, model compounds do provide very useful means for verification and calibration of reaction-potential surfaces... 

For convenience the averaged 0AS-data are tabulated (Table 19) together with the corresponding entropic components of the EM. The latter are the ideal EM-values predicted for a cyclisation reaction for which the strain is unimportant for all of the terms of the series. They can be read directly from the right-hand ordinate in Fig. 23. 

Each submolecule will experience a frictional drag with the solvent represented by the frictional coefficient /0. This drag is related to the frictional coefficient of the monomer unit (0- If there are x monomer units per link then the frictional coefficient of a link is x(0- If we aPply a step strain to the polymer chain it will deform and its entropy will fall. In order to attain its equilibrium conformation and maximum entropy the chain will rearrange itself by diffusion. The instantaneous elastic response can be thought of as being due to an entropic spring . The drag on each submolecule can be treated in terms of the motion of the N+ 1 ends of the submolecules. We can think of these as beads linked... 

Direct step-step interaction terms in the step energy ( direct interactions are entropic repulsion, strain terms, electronic structure effects etc.) do influence the step fluctuations, and they also drive the spreading of step trains, wires and bumps. Nevertheless, it is instructive to first ignore these direcf step-step repulsion, as is done in... 

Side reactions that occur with intramolecular cycloaddition, such as linear oligomerization or dimerization of the nitrile oxide, are not very common when shorter chain lengths n < 1) are used due to the entropically favored intramolecular process. A rather unusual result in this regard involves the formation of a fused cyclooctane instead of the less-strained six-membered ring (also fused) in the cycloaddition of the nitrile oxide derived from p-naphthoquinone (Scheme 6.43). This result is consistent with the effect of electron-withdrawal in the enedione part, leading to increased reactivity (247), and also reflects the known sluggishness of cyclohexenes towards nitrile oxides (cf. Section 6.2.1.2). 

Analysis of the activation parameters for the different encapsulated substrates reveals that the source of catalysis is more complex than simply a reduction of the entropy of activation, since different effects are observed for substrates 26,27,30. While the rate acceleration for the encapsulated 26 was exclusively due to lowering the entropic barrier, for 27 and 30 a decrease in the enthalpic barrier for rearrangement is observed in addition. It is possible that, for 27 and 30 binding into the narrow confines of the metal-ligand assembly induces some strain on the bound molecules, thereby raising their ground-state energies compared to those of the unbound... 

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