Hindrance to free rotation

Hindrances to free rotation of a steric or any other nature may of course restrict the values which the rotation angles 0 may assume. 

If the preceding analysis of hydrodynamic effects of the polymer molecule is valid, K should be a constant independent both of the polymer molecular weight and of the solvent. It may, however, vary somewhat with the temperature inasmuch as the unperturbed molecular extension rl/M may change with temperature, for it will be recalled that rl is modified by hindrances to free rotation the effects of which will, in general, be temperature-dependent. Equations (26), (27), and (10) will be shown to suffice for the general treatment of intrinsic viscosities. 

Note The steric factor reflects the effect of hindrance to free rotation. 

In Figure 2.14, it is implied that the terminal carbon atom can occupy any position on the rim of the cone that is, there is assumed to be perfectly free rotation around the penultimate carbon-carbon bond. This is equivalent to saying that all values of , the angle that describes the rotation (see Fig. 2.14), are equally probable. Any hindrance to free rotation will block certain configurations, expanding the coil dimensions still further. 

The possibility of optical isomerism arising from restricted rotation (atropisomerism) about the 2,2 -bond in 3-substituted 2-(2-naphthyl)-benzo[6]thiophenes has been recognized by Lamberton and McGrail.54 Schuetz and Ciporin164 have interpreted the UV spectra of six 3-aryl-benzo[6]thiophenes according to a theory of steric hindrance to free rotation about the pivot bond of the two aromatic rings, but the results are now invalid, since some of the 3-arylbenzo[6]thiophenes used in this study have been shown to be the corresponding 2-isomers (see Section IV, C). No attempt appears to have been made to resolve compounds of this type. 

Van t Hoff postulated free rotation round a single bond in order to explain the lack of cis and Irons isomers in molecules of the type of di-chlorethane. In the light of the quantum mechanical theory of the chemical bond, the free rotation is explained by the axial symmetiy of the a bond between the two carbon atoms. Thus the a bond is not in itself a hindrance to free rotation, but as the rotation occurs the relative configurations of the atoms will be changed, so that the distances between the non-bonded atoms and consequently their energies of interaction will alter. 

Introduction.—Most theoretical v> ork on the relation between intermolecular forces and the thermodynamic properties of liquids and liquid mixtures has been limited to potential fields which are independent of the orientation of the particles. This condition, however, is only strictly satisfied by monoatomic substances. For a great many molecular substances directional intermolecular forces are likely to be important and will have a significant effect on the thermodynamic properties of liquids both because of the additional cohesive energy and because of the loss of entropy associated with hindrance to free rotation. Although many of the observed properties of liquids have been attributed to directional forces in a qualitative manner, there has been little in the way of general quantitative theory. 

In conclusion to this section, we note that the statistical mean dipole moment of the molecule, as well as its mean displacement, should be proportional to the square root of the degree of polymerization. Hindrance to free rotation tends to decrease the mean statistical dipole moment and to increase the mean statistical displacement. Since hindrance to rotation must disappear at sufficiently high temperatures, the mean dipole moment of the isolated molecule should increase with temperature whilst the mean displacement should be a decreasing function of temperature. 

Let v0 be the energy associated with the hindrance to free rotation of eleme. i, element 0 being fixed. This energy should be very nearly independent of molecular weight. The total energy barrier characterizing the rotation of element 1 in solution is (AHq +v0), where AH0 is the activation energy necessary to permit a completely free unit to rotate from one equilibrium position to another. 

Space models of these alcohols shows immediately how important must be the steric influences on the association processes. One can see how difficult it is for molecules such as pentamethylethanol to form linear hydro-gen-bonded chains of the Zachariasen type. The alkyl groups of alternate molecules can be seen to be close together if no bending occurs in the hydrogen bond chain, and when alkyl substitution occurs in the a position, there is certain to be some hindrance to free rotation around the —C—O— bond. Accordingly, from the lack of a multimer band in the infrared spectrum and the linearity of the curve of NMR chemical shift vs. concentration out to 0.35M we can presume that only dimers are formed initially in pentamethylethanol, with possibly cyclic multimers at higher concentrations. 

Solution K is a constant that is essentially independent of the molecular weight of the polymer and the character of the solvent medium, as amply demonstrated by the above data. However, K shows a decrease with increasing temperature. From Equation 12.72, K is proportional to the factor t JM. We recall that the unperturbed root-mean-square end-to-end distance (r ) is expanded invariably to greater dimensions relative to completely free rotation as a result of the effects of hindrances to free rotation. As the temperature is increased, the tendency to completely free rotation is enhanced as the effects of these hindrances are diminished. Consequently, K also decreases. 

Note that for some properties, such as melting temperature, both the chemical structure and the long chain nature of polymers play important roles. As will be seen later, the stiffness and flexibility characteristics of polymers are largely determined by the degree of hindrance to free rotation about single bonds in the backbone chain. 

In view of the preceding analysis, should be a constant independent of both polymer molecular weight and solvent. To some extent, it may, however, vary with temperature, considering that the unperturbed dimension is modi ed by hindrances to free rotation whose effects are,... 

But the change in the rate of the reaction can be due simply to a change in the environment of the reactants (change in dielectric constant, hindrance to free rotation of atoms, etc.), without which the homogeneous process does not take place. 

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