Configurational statistics of vinyl polymer chains

Abstract

The primary chiral elements of a vinyl polymer chain CHS(CRR'CH2)ZH, in which R' ^R, are the skeletal bonds rather than the substituted carbons as conventional terminology implies. The conformation in relation to any specified stereochemical configuration may be treated with full generality in terms of the chiralities of skeletal bonds. Statistical weight matrices are formulated in a parallel manner for both mono-(R' = H) and disubs tituted chains, with emphasis on the latter. As an indirect consequence of the copious second-order interactions (involving groups separated by four bonds) when the sizes of both R and R' are commensurate with or larger than CH3, interactions of higher order (involving groups separated by as many as eight bonds) are not averted by interactions of second order, as is the case when R' = H. Significant interactions of longer range in disubstituted chains may introduce interdependence between consecutive pairs of skeletal bonds, the relevant pairs being the two that adjoin each substituted carbon. The complications thus arising are easily managed by resort to statistical weight matrices (of orders 7 X 7 for three states per bond) that relate the combined state of one such bond pair to that of the neighboring pair. Previous methods are adapted to the formulation of generator matrices suitable for calculation of configuration-dependent properties on the basis of these pair-pair statistical weight matrices. Simplifications for symmetric chains are introduced.The spatial configurations of monosubstituted vinyl polymer chains, CH3[CHRCH2]IH, are greatly restricted by steric interactions if, as is usual, the substituent R is comparable to or greater than CH3 in size.12 The predominant interactions are those involving pairs of groups from the set CH2, CH, and R that are separated by four bonds. The distance between the centers of two groups thus related depends on the angles of rotation about the central pair of the sequence of four bonds; see Figure 1 with R' = H. Hence, following Birshtein and Ptitsyn,s we refer to these as interactions of second order.1 2 The mutual orientation of the two groups depends, of course, on the rotations about the two outer, or pendant, bonds of the set of four. In particular, for groups like CH2 and CH3 the mutual disposition of the peripheral hydrogen atoms, which are the atoms most directly involved in the interaction, depends on these rotations. To an approximation that is often adequate, groups such as these may be treated as spherical domains. Rotations about the outer two bonds of the sequence (1) P.

Temperature Dependence of Polypropylene Configurations

“…According to the dihedral distribution of Figure calculated in this work, the three state model seems a reasonable scheme. By the fundamental paper of Flory et al, the internal rotation characteristic of vinyl polymers can be expressed in terms of the three statistical weigh matrices: for the first of the two bonds connecting two consecutive asymmetric carbon atoms, and for the second bond of the meso and racemic bond dyad, respectively. Both the row and column is indexed by the isomeric states t , g and , respectively.…”

“…According to the dihedral distribution of Figure 3 calculated in this work, the three state model seems a reasonable scheme. By the fundamental paper of Flory et al, [51,52] the internal rotation characteristic of vinyl polymers can be expressed in terms of the three statistical weigh matrices:…”

Simple Trends in NMR Spectra of Vinyl Polymers: The 1H NMR Spectrum of Poly(propylene)

“…Sketches of the three conformations expected for rotation on an enantiotopic bond of a vinyl polymer. The enantiotopic bond shown is named d, [30] (-) [31] or pro-S according to different nomenclatures. [19] Different nomenclatures of the conformers are also reported.…”

On the Microstructural Analysis of (Pseudo)Copolymers

“…[7] For long polymers, the formerly different methines become prochiral, which implies that one should no longer adopt the 0/1 labeling. Nevertheless the two sides of the chain starting from each methine can still be distinguished as +/-, [8] pro(R)/pro(S) [9] or d/l, [10] and thus adjacent methines have two distinguishable arrangements, indicated in terms of the well-known m/r dyadic nomenclature, [6,11] which originate from the facing of groups of same (++ or --, r dyad) or opposite (-+ or +-, m dyad) prochirality.…”