Entropy loss, orientational

Clearly, proximity and orientation play a role in enzyme catalysis, but there is a problem with each of the above comparisons. In both cases, it is impossible to separate true proximity and orientation effects from the effects of entropy loss when molecules are brought together (described the Section 16.4). The actual rate accelerations afforded by proximity and orientation effects in Figures 16.14 and 16.15, respectively, are much smaller than the values given in these figures. Simple theories based on probability and nearest-neighbor models, for example, predict that proximity effects may actually provide rate increases of only 5- to 10-fold. For any real case of enzymatic catalysis, it is nonetheless important to remember that proximity and orientation effects are significant. 

The orientation dependent parameter p defined by Eq. (11) becomes unity in the isotropic state, and decreases as the polymers are uniaxially oriented. Therefore, it follows from Eqs. (9) and (10) that the wormlike hard spherocylinder system has a smaller translational entropy loss from the ideal solution in the liquid crystal state than in the isotropic state. This difference drives the system to form a liquid crystal phase. However, in order to determine the equilibrium orientation of the system, the orientation dependence of Sor has to be formulated, and this is done in Sect. 2.3. 

When a wormlike spherocylinder is in the liquid crystal phase, its tangent vector a at each contour point should align more or less to the preference direction of the phase specified by the director n. This alignment induces the orientational entropy decrease — Sor from the entropy in the isotropic state. Since the orientation of the tangent vector stretches the wormlike spherocylinder, — Sor includes a conformational entropy loss of the spherocylinder. 

Since the free energy of the chain is given by - kBT In Z, the orientational entropy loss - Sor can be written... 

If we neglect the distortion of the segment distribution in the fuzzy cylinder by the shear flow, we can apply Doi s stress expression, Eq. (61), to fuzzy cylinder systems as it stands. The neglect of the distortion may be justified when the shear-rate is low. Equation (61) expresses the contribution of the end-over-end rotation of the chain to asegment distribution is not distorted, the orientational entropy term Sor in the static free energy expression contains only the orientational entropy loss of the entire chain, but not the conformational entropy loss cf. Sect. 2.3. 

The Widom-Wheeler model of water-oil-and amphiphile systems consists of only two kinds of variables, a water-like variable and an oil-like one. A water molecule consists of two water-like variables an oil molecule, of two oil-like variables and an amphiphile, of one of each. This guarantees that all amphiphiles are located at oil/water interfaces and are oriented correctly. In contrast, in the three-component model [12], there are three kinds of variables representing the three components, with the consequence that the amphiphiles may or may not be found at oil/water interfaces, depending on the relative energy gain to do so versus the entropy loss. 

It appears from these studies that the picture of an iceberg around the solute in hydroxylic solvents is overdrawn. The shell of tangentially oriented molecules is only a monolayer, and though these molecules are restricted in their radial motion (giving rise to the entropy loss), they are not strongly ordered within the monolayer. 

Not only must the OH be near the hydrogen, but the hydrogen mu.st be oriented anti to the chlorine atom. When the two reacting molecules collide, if the OH should be near the chlorine atom or near R or R, no reaction can take place. In order for a reaction to occur, the molecules must surrender the freedom they normally have to assume many possible arrangements in space and adopt only that one that leads to reaction. Thus, a considerable loss in entropy is involved, that is, A5, is negative. 

As we shall see in Chapter 17, with some molecules elimination is also possible if the hydrogen is oriented syn, instead of anti, to the chlorine atom. Of course, this orientation also requires a considerable loss of entropy. 

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