Rotational isomeric model

The observed low Tg s of most polyphosphazenes are consistent with the low barrier to internal rotation predicted for them and indicate the potential these polymers have for elastomeric applications, Theoretical calculations, based on rotational isomeric models assuming localized it bonding, predict the lowest ( 100 cal per mol of repeating unit) known polymer barrier to rotation for the skeletal bonds of polydifluorophosphazene,... 

For random coils, is directly proportional to the contour length. If n is the number of main chain atoms in the chain, = an. The parameter a is relatively insensitive to environment (21), and has been calculated for a number of polymers from strictly intramolecular considerations using the rotational isomeric model (22). The root-mean-square distance of segments from the center of gravity of the coil is called the radius of gyration S. The quantity S3 is an approximate measure of the pervaded volume of the coil. For Gaussian coils,... 

Necklace models represent the chain as a connected sequence ctf segments, preserving in some sense the correlation between the spatial relationships among segments and their positions along the chain contour. Simplified versions laid the basis for the kinetic theory of rubber elasticity and were used to evaluate configurational entropy in concentrated polymer solutions. A refined version, the rotational isomeric model, is used to calculate the equilibrium configurational... 

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

Guenza M, Freed KF (1996) Extended rotational isomeric model for describing the long time dynamics of polymers. J Chem Phys 105(9) 3823-3837 Hansen JP, McDonald JR (1986) Theory of simple liquids, 2nd edn. Academic Press, London... 

Flgare 20 Graphs of dielectric saturation correlation factors, (i) B Z) calculated from formula (304) for the rotational isomerism model with Z = U/kT Oi) R Z) calculate from formula (307) for internal rotation, with Z = UJkT. In ather case an invasion in sign of is found to occur very rapUily with... 

NMR chemical shift prediction by quantum chemical calculation and the 7-gauche effect method has become a useful approach for stereochemical assignment of vinyl polymers. Recently C NMR assignments based on 7-effect and the rotational isomeric model were demonstrated successfully for a series of polyolefins, poly(l-pentene) to poly(l-octene).188... 

The effect of temperature on unperturbed dimensions although straightforward in principle, has proved to be difficult to evaluate experimentally. Based on the rotational isomeric model, one would expect a negative temperature coefficient since as the thermal energy increases the relative populations of the g+ and g states increases over the trans and consequently (Fg)1 2 and therefore Kg should decrease. However, evaluation of the temperature coefficients for stereoregular polymers have resulted in inconsistencies43,44,4S. These inconsistencies have been attributed in part to different techniques used to obtain the temperature coefficient, d In [Pg.6]

The experimental data and mathematical models derived for the isolated polymer chain and for the size distribution of polymer chains in the aggregate have been the basis for describing many polymer properties in rubbers and thermoplastics. Early work in this area concentrated on simplified models that were amenable to the calculation devices then available. With the advent of high-speed computers and the consequent reduction in computational labor, the more exact rotational isomeric model has been developed and fruitfully applied to many polymer problems. 

Guttman, C. M. and DiMarzio, E. A. (1982) Rotational isomeric modeling of the polyethylene-like polymer between two plates connection to the Gambler s Ruin ... 

Thus the use of an equivalent gaussian link chain, which appeared artificial in the case of the freely hinged chain, is quite acceptable for the freely rotating chain, the chain with hindered internal rotation, or the rotational isomeric model. In these cases there is no pretense of reality of the equivalent links, so they need not be given fixed lengths /eit- This equivalent chain is therefore a summary of the chainlike character of flexible polymer chains, and its simplicity enables the investigation of those properties of polymer systems which are solely dependent on the flexible chainlike nature of the polymer molecules. It is then only natural to attempt to formulate simple models which are characteristic of stiff... 

Detailed atomic positions in polymer helical conformations can he determined using the rotational isomeric model developed (1). It helps to obtain a... 

If it is assumed that the chain is flexible, that is that the barrier between conformational states is sufficiently low that rapid interchange can occur, then the time averaged shape of the polymer will be described by the distribution between the available conformations. This allows a statistical mechanical analysis, called the rotational isomeric model. This indicates that the population of the gauche states causes the chain to adopt a random quasi-spherical shape and not the often pictured zigzag extended aU trans form. The analysis allows calculation of two fundamental parameters the radius of gyration, which is the size of the polymer molecule if it were to undergo free internal rotation, and the related end-to-end distance. These quantities define the shape of the isolated polymer... 

The success of the rotational isomeric model lies in predicting the time averaged shape and size of polymer molecules in dilute solution. However, we have to look further to find the way in which the molecule moves between the various states that are averaged in the model. 

The problem can be further simplified taking Into account only a discrete number of rotational states (which are chosen in general to be coincident with conformational potential energy minima), in the calculation of the partition function. This is the rotational isomeric model, first proposed by Volkenstein and principally de-velopped by Flory and his school. 

In the case of isotactic polystyrene or of polyacrylates, other effects must be taken into account. In particular, together with the conformations TG and G T, for a piece of chain of the kind (40), also conformations near to TT planar are available. Without discussing the more complicated rotational isomeric model which result, it is interesting to explain why conformations near to the TT planar are possible for polystyrene and more unlikely for a polymer such as polypropylene. 

Finally we want to point out that an application of the rotational isomeric model to a polymer is the evaluation of the portion of the entropy of melting, which depends on the conformational freedom which the chains acquire in the melt. The conformational contribution to the difference in entropy may be evaluated, again by standard methods of statistical mechanics, as ... 

A good account of rotational isomeric model is given in ... 

The distribution of TG, GT, TT and GG pairs is in accordance with the distribution provided by the rotational isomeric model, as applied to isolated molecules (1) ... 

As the rotational isomeric model is used, all the conformations of a lipid can be generated to produce the distribution function and other quantities of statistical mechanics. After the parameters were fitted to the experiment NMR order parameters, experimental values were accurately calculated, e.g., the transition temperature for the gel to liquid crystalline phase transition and the bilayer thickness. f... 

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