Theory rotational isomeric state

N 077 "Unperturbed Dimensions of Crosslinked Histones Evaluated Using Random-Flight Statistics and Rotational Isomeric State Theory"... 

Extremely detailed models for unperturbed flexible linear homopolymers can be constructed using rotational isomeric state theory.[14,20 In the limit as n — °°, these detailed models yield... 

A valuable reference on the subject of single chains is the work by Flory, described in his book Statistical Mechanics of Chain Molecules. A new book on the subject is of interest. The reader may also wish to study the 1974 paper by Flory in Macromolecules, which serves as an excellent introduction to the rotational isomeric state theory.Another classic book is Hopfinger s Conformational Properties of Macromolecules... 

P. J. Flory, Macromolecules, 7, 381 (1974). Foundations of Rotational Isomeric State Theory and General Methods for Generating Configurational Averages. 

Yoon and Flory > have compared the experimental data of Gawrisch et al. to the scattering of unperturbed chains calculated on the basis of the rotational isomeric state theory. They found good agreement up to the highest values of the scattering vector corresponding to distances of approximately one chain diameter... 

There are two broad classes of dihedral space models for studying and building flexible chain molecules. The first, known as Rotational Isomeric State Theory (RIS) [25], was developed to study industrial polymers. The second, known as Chain Buildup (CB) [26], was... 

From consideration of molecular models and the geometric requirements for excimer formation, we have concluded that the trans, trans meso rotational dyad is the predominant EPS in the aryl vinyl polymers. [5,22] The identification of the EPS trap with a particular rotational dyad state was a critical factor because it opened the way to utilize the powerful rotational isomeric state theory of Flory [23] to calculate the EPS population for the isolated PS chains. This trap population is relatively small in polystyrene. 

While we have thus been able to correlate certain conformation-related properties with connectivity indices, we have not been able to do so for many other conformation-related properties. For example, the very complex nature of the stress-optic coefficient defies a simple treatment. Such complicated conformation-related properties are still best predicted via more sophisticated calculations [6-9], such as those using rotational isomeric state theory. 

The use of more sophisticated calculations based on rotational isomeric state theory [9,10] allows calculation of CM(T), but this capability still does not enable us to predict Tg accurately since CJTg) cannot be calculated without having some idea of what Tg should be before the calculation. Despite this limitation, Equation 6.18 and the general theoretical framework which led to its development hold out the hope that further extensions of this approach or similar methods may be able to allow accurate predictions of the effects of tacticity on Tg in the future. 

The valence angle model, though more realistic than the freely jointed model, still underestimates the true dimensions of polymer molecules, because it ignores restrictions upon bond rotation arising from short-range steric interactions. Such restrictions are, however, more difficult to quantify theoretically. A simpler procedure is to assume that the conformations of each sequence of three backbone bonds are restricted to the rotational isomeric states that correspond to the potential energy minima such as those shown for n-butane in Fig. 2.3. For the simplest case of polyethylene and for vinylidene-type polymers, the application of the rotational isomeric state theory yields the following equation... 

Flory (1969 1971 1974) has developed the rotational isomeric state theory for predicting the conformation of polymer molecules. This incorporates the interdependence of the bond rotational potentials. This theory is fully explained in Flory s comprehensive monograph (Flory, 1969) and only the barest details will be mentioned here. 

The rotational isomeric state theory is essentially a matrix procedure that, in princi e, allows all of the myriad of conformations accessible to a polymer molecule to be appropriately averaged. The end-to-end length r is simply the sum of the individual bond vectors I,... 

Rotational isomeric state theory predicts the dimensions of polymer chains in 0-solvents, i.e. the unperturbed dimensions J, where the subscript 0 denotes that the bonds are considered to be volumeless lines in space. As stated previously, these can be expressed as... 

At present the only rigorous way of treating isolated polymer molecules at an interface is by a combination of rotational isomeric state theory and Monte Carlo procedures. Some results for tails have been published by Feigin and Napper (1979) and Mattice and Napper (1981). These strictly apply only in a... 

Cyclization studies have also been carried out on the chemical copolymers poly(ethylene, dimethylsiloxane) and poly(styrene, dimethylsilox-ane). Numerous intramolecular interactions need to be taken into account in a chemical copolymer. Consequently, the results on the copolymers have been given only a preliminary interpretation in terms of rotational isomeric state theory. Cyclization calculations have also been carried out for poly(dihydrogensiloxane) [-SiH O-], but at present there are no experimental data available for comparison with theory. 

The conformational properties of a chain are reflected in dilute solution properties, and in particular its characteristic ratio. Coo which was defined in Chapter 1. The characteristic ratio can be detennined experimentally by straightforward methods, or calculated theoretically using rotational isomeric state theory.(219) The characteristic ratios of a large number of polymers have been determined and it is... 

From Tables 6.1, 6.2 and 6.3. (2) Average between virgin sample and melt crystallized. (3) From Eq. (6.2). (4) Phenyl ring taken as single bond. (5) Calculated from rotational isomeric state theory. (6) Estimate. 

Mattice and co-workers (144) investigated this problem using rotational isomeric state theory. The characteristic ratios and components of the persistence... 

From the few examples that have been described, it should be apparent that, as a general mle, the chain stmcture influences the melting temperature through its conformational properties and thus the entropy of fusion. In fact, by utilizing rotational isomeric state theory, a quantitative correlation between the entropies of fusion at constant volume and the chain conformations of the many polymers can be made [11, 13]. 

P. J. Flory, Foundations of rotational isomeric state theory and general methods far generating configurational averages. Macromolecules 7(3), 381-392 (1974). 

---