Barrier height hindered rotation potential

From the Ti minimum, the correlation time for molecular motion at megahertz frequencies is obtained. The plot of log (tc) vs. 1/T for the DMS moiety in Fig. 17.31 shows a good linear relationship. The temperature dependence of the correlation time Tc usually obeys the Arrhenius form [39] as Tc = To exp(-AE/RT), where Tq is the prefactor, R is the gas constant and T is the absolute temperature. The activation energy AE, which is considered to correspond to the barrier height for the potential hindering rotation, can... 

But especially in cases where the hindered rotational potential is asymmetric (see Figure 1.1), the calculation of the partition function needs to take into account the different barrier heights and the according rotation angle as delimiter of the integral. 

Intramolecular excimer emission is also a valuable tool for the study of the dependence of the rate constant for a conformational transition kt on the properties of the solvent medium. This rate constant is related to the concept of the "internal viscosity" x] of a polymer chain which opposes the separation of the chain ends at a rate dh/dt in response to a force F so that dh/dt= F/ni Kuhn and Kuhn who originally introduced the concept s assumed that the internal viscosity was a function of the potential energy barriers characterizing hindered rotation around the bonds of the chain backbone it was, therefore, assumed to be an intrinsic property of the chain, independent of the solvent medium. More recently, it has been pointed out that the viscosity r of the medium must necessarily contribute to the resistance to conformational changes, so that Tii should be the sum of two contributions, one due to the height of the potential energy barriers, the other proportional to the viscosity of the solvent, i.e., rii= A+Bn. A similar reasoning would lead us to expect k to be of the form kt= kT/(A +B n) and studies of the dependence of... 

Fig. 55. The potential of hindered rotation of the CH3 group in nitromethane (CH3NO2) crystal, (a) calculated from INS data, Vi = 0.586 kcal/mol, V = 0.356 kcal/mol, S = 30°, and (b) calculated with the atom-atom potential method [Cavagnat and Pesquer 1986]. The barrier height is 0.768 kcal/mol.

Although these potential barriers are only of the order of a few thousand calories in most circumstances, there are a number of properties which are markedly influenced by them. Thus the heat capacity, entropy, and equilibrium constants contain an appreciable contribution from the hindered rotation. Since statistical mechanics combined with molecular structural data has provided such a highly successful method of calculating heat capacities and entropies for simpler molecules, it is natural to try to extend the method to molecules containing the possibility of hindered rotation. Much effort has been expended in this direction, with the result that a wide class of molecules can be dealt with, provided that the height of the potential barrier is known from empirical sources. A great many molecules of considerable industrial importance are included in this category, notably the simpler hydrocarbons. 

While the height of the potential barrier is about 3 kcal in normal paraffins, one only finds 2 kcal in the olefins for the rotation about the C—C bond, situated next to the C =C bond. There is completely free rotation about the C—C=C bond in toluene and xylene the rotation is also hindered but little 0.5 kcal. 

Nevertheless, there is no sharp boundary between the thermodynamics and kinetics of rotational-isomeric transitions in macromolecules. Thermodynamic characteristics that govern the ability of macromolecules to change their conformation are related to the total potential barrier height and thus to kinetic properties of macromolecules. Following Volkenshtein [101], the average cosine of the angle of hindered rotation, which determines the size of a statistical segment as a measure of thermodynamic flexibility of the chain, is equal to... 

The internal dynamics of the methyl group immensely complicates the spectroscopy of these molecules. Of course, this aspect of the problem also provides much of the spectroscopic interest. When the methyl hydrogens of acetaldehyde oscillate around the CC axis, they experience forces arising from the CHO frame of the molecule which vary sinusoidally. As a result, the potential function for internal rotation can be represented by a cosine function in which the crest to trough distance measures the height of the potential barrier. Since the energy barrier to methyl rotation is low in acetaldehyde, the internal motion is one of hindered internal rotation, rather than torsional oscillation. 

In a real polymer chain, rotation around backbone bonds is likely to be hindered by a potential energy barrier of height AEr. If AEr < RT, the population of the... 

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