Persistence length model

The anisotropy of the coil has been calculated for other models of the macromolecule. Expressions for the anisotropy coefficient are known in the case where the macromolecule has been represented schematically by a continuous thread (the persistence length model) (Gotlib 1964 Zgaevskii and Pokrovskii 1970) and also in the case where the microstructure of the macromolecules has been specified. In the latter case, the anisotropy coefficient of the macromolecule is expressed in terms of the bond polarisabilities and other microcharacteristics of the macromolecule (Flory 1969). 

The persistence length model therefore describes the whole spectrum from the more rodlike oligomers (small j) to the well-developed coils (large y). However, the model ignores the finite thickness of the chain, and so it only holds strictly for unperturbed coils. The error due to the finite thickness may be neglected when the persistence length is much greater than the chain thickness. 

Geometrical and flexibility data pertaining to the same polymers are also given in Table 1, namely the persistence length and the average chain-to-chain interaxial distance D. The first five polymers in Table 1 have D values smaller than 6 A, unlike all the following polymers (i.e., no. 6 to 19 in Table 1, Class II). This is a consequence of the relatively bulky substituents carried by Class II polymer chains. For some of the polymers in Table 1 the C0o and P literature values are widely scattered or unavailable. In those cases lower-limit values of P from experimentally determined geometrical parameters, are predicted from our model by suitable interpolation and reported within parentheses. 

It is considered that, if ideal, optically active poly(alkyl(aryl)silane) homopolymer and copolymer systems could be obtained which had stiffer main-chain structures with longer persistence lengths, it should be possible to clarify the relationship between the gabs value and the chiral molar composition. The magnitude of the chirality of the polyisocyanates allowed precise correlations with the cooperativity models.18q In the theory of the cooperative helical order in polyisocyanates, the polymers are characterized by the chiral order parameter M, which is the fraction of the main chain twisting in one helical sense minus the fraction of the main chain twisting in the opposing sense. This order parameter is equal to the optical activity normalized by the value for an entirely one-handed helical polymer. The theory predicts... 

Recently a very detailed study on the single chain dynamic structure factor of short chain PIB (M =3870) melts was undertaken with the aim to identify the leading effects limiting the applicability of the Rouse model toward short length scales [217]. This study was later followed by experiments on PDMS (M =6460), a polymer that has very low rotational barriers [219]. Finally, in order to access directly the intrachain relaxation mechanism experiments comparing PDMS and PIB in solution were also carried out [186]. The structural parameters for both chains were virtually identical, Rg=19.2 (21.3 A). Also their characteristic ratios C =6.73 (6.19) are very similar, i.e. the polymers have nearly equal contour length L and identical persistence lengths, thus their conformation are the same. The rotational barriers on the other hand are 3-3.5 kcal/mol for PIB and about 0.1 kcal/mol for PDMS. We first describe in some detail the study on the PIB melt compared with the PDMS melt and then discuss the results. 

For coarse-grained models of linear biopolymers—such as DNA or chromatin— two types of interactions play a role. The connectivity of the chain implies stretching, bending, and torsional potentials, which exist only between directly adjacent subunits and are harmonic for small deviations from equilibrium. As mentioned above, these potentials can be directly derived from the experimentally known persistence length or by directly measuring bulk elastic properties of the chain. 

The analysis described above is useful for modelling colligative properties but does not address polyelectrolyte conformations. Polyelectrolyte conformations in dilute solution have been calculated using the worm-like chain model [103,104], Here, the polymer conformation is characterized by a persistence length (a measure of the local chain stiffness) [96]. One consequence of the... 

A theoretical approach is applied to elucidate the molecular conformations, associated flexibility, and dynamics of polylp-hydroxybenzoic acid) esters, pHB. Properties such as the radius of gyration and persistence length which are characteristic for the stiffness of a macromolecule are calculated on the basis of two different theoretical methods (a) Molecular dynamics and (b) the RIS model augmented by the more recent scheme for the matrix computations. The analysis of the results obtained by the latter method reflects a strong dependence on the choice of the structural parameters of the system. 

A theoretical analysis of the possible conformations of polylp-phenylene terephthalate) (PPTA) and polylp-phenylene isophthalate) (PPIA) is performed on the basis of molecular mechanics and molecular dynamics trajectories. The dependence of the persistence length on the fluctuations of the torsional angle around the ester bond is discussed for PPTA in the frame of the RIS model. Realistic parameters like bond length and bond angles are provided by computer simulations using MD. 

The procedure used for testing the ideal Donnan theory is applicable to any model that decouples ionic effects from network elasticity and polymer/solvent interactions. Thus we require that nnet depend only on EWF and not C. While this assumption may seem natural, several models which include ionic effects do not make this assumption. For example, the state of ionization of a polymer chain in the gel and the ionic environment may affect the chain s persistence length, which in turn alters the network elasticity [26]. Similarly, a multivalent counterion can alter network elasticity by creating transient crosslinks. 

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