Entropic considerations

The Arrhenius frequency factors [log(T/M V)] for addition of carbon centered radicals to the unsubstiUited terminus of monosubslituted or 1,1-disubstituted olefins cover a limited range (6.0-9.0), depend primarily on the steric demand of the attacking radical and are generally unaffected by remote alkene substituents. Typical values of log(T/M V) are ca 6.5 for tertiary polymeric (e.g. PMMA ), ca 7.0 for secondary polymeric (PS, PMA, and ca 7.5, 8.0 and 8.5 for small tertiary (e.g. /-C4H9 ), secondary (i-CiH ) and primary (CHj, CbHs ) radicals respectively (Section 4.5.4).4 For 1,2,2-trisubstituted alkenes the frequency factors arc about an order of magnitude lower.4 The trend in values is consistent with expectation based on Iheoretical calculations. 

Frequency factors arc often determined from data obtained within a narrow temperature window. For this reason, it has been recommended4 that when extrapolating rate constants less error might be introduced by adopting the standard values for frequency factors (above) than by using experimentally measured values. The standard values may also be used to estimate activation energies from rate constants measured at a single temperature. 

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For the united atom models of realistic polymers the wall PRISM theory predicts interesting structure near the surface [95]. For example, the side chains are found preferentially in the immediate vicinity of the surface and shield the backbone from the surface. This behavior is expected from entropic considerations. Computer simulations of these systems would be of considerable interest. 

The importance of entropic considerations in the formulation of a thermodynamic model for micelle formation in mixtures of ionic and nonionic surfactants has been demonstrated by the ability of the... 

Another limitation of the regular solution theory is the assumption diat is negligible. While this assumption may be valid for solutions in which all components (solute and solvent) are of similar sizes, it breaks down when the molar voinmes of the components are significantly different, i.e., in the case of high molecular weight (polymeric) solvents and low molecular weight solutes. For such cases, more rigorous models that include entropic considerations, such as... 

The intramolecular attack of an excited carbonyl on an alkene can occur to provide oxetane products, even in cases when the corresponding intermolecular reaction is imsuccessful. Thus the intramolecular reaction surely benefits from favorable entropic considerations. Jones and Carless have summarized the scope and utility of intramolecular Patemo-BUchi photocycloadditions. There is general agreement that successful implementation of an intramolecular reaction requires that the Norrish type II photoreactionsand other hydrogen abstraction processes be overcome. In addition, the intramolecular reaction provides access to polyoxygenated ring systems that can exhibit remarkable properties because of their strain. 

It must be re-emphaslzed at this point that the solubility parameter and Its use for quantifying physicochemical Interactions Is based on enthalplc considerations only entropic considerations are neglected. Consequently, while the Ideas outlined In this section provide a basis for membrane material selection (or at least for narrowing the number of possible choices), prediction of permeation and rejection remains elusive until the ability to predict effective transport corridor size 4 Is more firmly established. At that time the differences - 4, and ik, - i > can be used In conjunction with A and A for meiftrane Mterral... 

The distinctions between these two pure types may also be viewed from entropic considerations and the nature of the driving mode. The entropic change in an order-disorder phase transition is mainly configurational, and the driving mode is of diffusive (nonpropagating) nature. On the contrary, for a displacive phase transition, the entropy change is mainly vibrational, with an associated underdamped soft phonon. 

The lactam-bridged and hydrocarbon-stapled helices feature flexible crosslinks. Entropic considerations would suggest that rigid linkers might afford more stable helices. Two groups have recently studied the effect of linker flexibility on helix stability. Woolley and coworkers found that a rigid aromatic linker that matches the distance between the i and (+11 side-chains provides much greater stability... 

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