Polyethylene rotational isomerism

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

Grime, D., and I. M. Ward The assignment of infrared absorptions and rotational isomerism in polyethylene terephthalate and related compounds. Trans. Faraday Soc. 54, 959—971 (1958). 

In Eq. (25) the first term represents the contribution to the entropy from rotational isomerism without regard to lattice interferences, and 0.86 R the decrease in entropy due to packing on the lattice . The values of A SD calculated by difference were found to lie between 1.7 and 2.0 cal deg-1 mole-1 for polyethylene, polyoxymethylene and polytetrafluoro-ethylene. According to this theory when E equals zero,/equals Vs instead of V3 as one would expect if pentane interference did not occur. Assuming that A SD is compensated for by 0.86 R, values of A SR computed from the first term on the right hand side of Eq. (25) agreed farily well with the observed values of (A S,)v. 

An interesting application of the molecular dynamics technique on single chains is found in the work of Mattice et al. One paper by these authors is cited here because it is relevant to both RIS and DRIS studies and deals with the isomerization kinetics of alkane chains. The authors have computed the trajectories for linear polyethylene chains of sizes C,o to Cioo- The simulation was fully atomistic, with bond lengths, bond angles, and rotational states all being variable. Analysis of the results shows that for very short times, correlations between rotational isomeric transitions at bonds i and i 2 exist, which is something a Brownian dynamics simulation had shown earlier. 

More sophisticated approaches to the evaluation of wfr) exist. Some of them are the technique based on the Yoon-Flory expansion, variations of the Gaussian approximation, and an implementation of the Koyama distribution. Freely jointed chains and rotational isomeric chains have also been used as models of chains. Research is actively pursued on the subject of formulating more realistic closure relationships. In considering the choice of an intramolecular structure factor, a paper by McCoy et al. on model polyethylene melts will be useful. 

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... 

In the liquid state the C—C bonds transform from one rotational isomeric state to another, and the lifetime of a rotational isomer is about 10 s. For the polyethylene chain the potential energy A of the gauche isomers is about 2kJmol higher than that of the trans isomers. The relative numbers n(g ) and n t) of bonds in the isomeric states can be calculated using... 

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 ... 

There are also numerous examples where the RIS models have more substantial differences, because they use statistical weight matrices of different dimensions. Several examples are presented in Table 3.6. An obvious origin of the differences in dimension of the U s is a difference in the number of rotational isomeric states assigned to individual bonds. Thus polyethylene has been described with RIS models that assign three [14], five [14], or seven [155] states to each internal braid. An increase in u should lead to a more accurate model, because it permits the incorporation of more detail into the calculation. Of course, it also introduces more parameters into the model, with the added burden on the user of assigning values to these parameters. The most popular RIS models for polyethylene use u = 3 because... 

Mark, J. E. Curro, J. G., A Non-Gaussian Theory of Rubberlike Elasticity Based on Rotational Isomeric State Simulations of Network Chain Configurations. I. Polyethylene and Polydimethylsiloxane Short-Chain Unimodal Networks. J. Chem. Phys. 1983, 79, 5705-5709. 

Fig. 4. A Kratky plot for a 1001 site rotational isomeric state polyethylene chain. The circles are from a Monte Carlo simulation [31] and the curve is the corresponding result using the approximate procedure described in the text. L is the carbon-carbon bond length...

The rotational isomeric state model can be used to rationalize the temperature-dependence of conformation-dependent properties, through the dependence of the statistical weights on temperature. How strong is the temperature dependence of the dimensions of the chains in a polyethylene melt, assuming that we remain above the temperature at which crystallization occurs Calculations of r )o from equations (2), (4), and (6), assuming that the only temperature dependence is from the Boltzmann factors a = expi-E /kT) and co = exp(-EJkT), yields 9 In (r )o/9 T = -0.001 deg. ... 

Rotational isomerism arises because of the alternative conformations of a molecule that can result from the possibility of hindered rotation about the many single bonds in the structure. Spectroscopic techniques [4] developed in small molecules have been extended to polymers, and as an example we illustrate (Figure 1.7) the alternative trans and gauche conformations in the glycol residue of polyethylene... 

Fig. 1.28. Comparisons among the rotational isomeric (RIS) radial distribution functions at 413 K for polyethylene (o) and PDMS ( ) chains having n — 20 skeletal bonds, and the Gaussian approximation ( — ) to the distribution for PDMS [45]. The RIS curves represent cubic-spline fits to the discrete Monte Carlo data, for 80 000 chains, and each curve is normalized with respect to an area of unity (with / being the skeletal bond length).

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