Model rotational-isomer

Rapoport N.Ya., Mostovaya E.M., Zaikov G.E. (1986)."SimuIation of Polychromatic Kinetics of the Propagation step of the Chain Oxidation Reaction in Strained Polypropylene Basing on the Rotational Isomers Model" Vysokomolek. Soedin. 28 A. Nq 8. PP.1620 -1628. (In Russian)... 

FIG. 2 The most common simplified models of polymer chains freely-jointed chain (a), bead-spring chain (b), rotational isomer model (c), and the typical torsional potential V [Pg.8]

A very common approximation goes by the name of rotational isomeric state model (RIS). With such a model it is assumed that the molecular population is placed exclusively in a few energy minima, always according to the Boltzmann distribution. The conformations corresponding to the minima are called conformers, or rotational isomers, and are indicated by one or more letters (G, T) for butane three conformers are considered (G, T, G ), for pentane five (TT, G T, TG, G G, G G ). A more detailed examination of pentane reveals the existence of two further wells (fl, = 65 , 2 = 260° and 0, = 100°, 02 = 295°), sometimes indicated by G G and G G , respectively, close to the forbidden G G" conformation, but with a much tower energy (157, 158). 

The model parameters are varied systematically within reasonable limits to fit the experimental results. The minimum positions of the rotational bond angles probably do not deviate more than 5° from planar trans and from symetrically staggered gauche, respectively. Entropy contributions to the free energies of the rotational isomers are discussed with respect to the influence on the temperature coefficient. 

Dipole moments and Kerr constants of dibenzoates of several diols are measured at 298 K. Theoretical analysis is performed with standard methods of the RIS model. Comparison of theory with experiment indicates that is almost insensitive to the conformational energies, particularly for m > 3. Kerr constants are much more sensitive to the conformational energies. Good agreement between theoretical and experimental values of both dipole moments and Kerr constants of all these compounds Is achieved by adjustement of the optical parameters and the position of the rotational isomers. 

If interactions of an electrostatic nature have some effect on the relative stability of trans and gauche rotational isomers, it seems reasonable to expect an effect of solvent, though perhaps small, on the factor a. Such effects on the conformations of small molecules are well known [see Mizushima (14,188) and Wada (259)]. The relatively high value of a for poly(methyl methacrylate), as discussed in paragraph (iv) above, may be due to electrostatic interactions, and it is therefore appropriate to search for a solvent effect here. No such effect was found by Marchal and Lapp (175) in their measurements of the apparent dipole moment of the polymer in various solvents as compared with that of the model monomeric compound, methyl isobutyrate. They concluded that to within experimental error (about 3%) the unperturbed dimensions were independent of the solvent. More recently a very small solvent effect on the dipole moment of the isotactic polymer has been reported by Salovey (223a). 

The conformations of several N-acyl-L-prolines were studied by CD and nmr (Nishihara et a/., 1975), and it was found that JV-acetyl-L-proline has two rotational isomers (S-trans and S-cis) about the amide bond. The two rotamers show CD Cotton effects of opposite sign associated with the n-7C transition of the amide moiety. The chiroptical properties of L-proline conformational isomers were examined on a theoretical model, and spectra-structure correlations were proposed for the anionic and cationic forms of L-proline in solution (Madison and Schellman, 1970b Richardson and Ferber, 1977). 

What matters, however, for ensuring that the states are essentially discrete, is that the energy barrier between the two states is about five times thermal energies at room temperature, so that most of the time the molecule will simply perform small oscillations around a discrete tram or gauche state. The various conformations of a molecule are often called rotational isomers and the model of a polymer chain introduced by Flory in which the chain is imagined to take up only discrete conformational states is called the rotational isomeric-state approximation. 

Interestingly, there was a sort of over-reaction among researchers now many people consider worm like chain model either more realistic or just real — while in fact many polymers (e.g., proteins) should be described by other models, with rotational isomers etc. 

The success of worm-like chain model for dsDNA made this model and formula (7.42) fashionable among the scientists (somewhat surprising fact of life is that there is such thing as fashion in science ) nowadays formula (7.42) is often used to fit the data for which it is not at all the most appropriate. We sincerely hope that Langevin formula (7.41) and its underlying freely-jointed model, as well as rotational isomers and other models will soon regain their rights and will be used where appropriate. 

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