Chain stiffness parameter

Earlier69 we obtained the following empirical equation relating Tg to the chain stiffness parameter ... 

Using Eqs. (25)-(28), one obtains for the lattice spacing Z, the chain stiffness parameter to and the number of segments y the expressions... 

According to Eq. (33), the chain stiffness parameter to decreases weakly with the chain length. Consequently, the polymer chain becomes slightly stiffer with increasing chain length, which is unreasonable. For this reason, an average of the values provided by Eq. (33) for the four PI chains employed was used. For the PI chains, Ms= 68 g/mol, lb = 5.07 A, p = 0.913 g/cm3 45 consequently Z=4.94 A and w=0.29 (calculated as the arithmetic average). All the parameters for PS and PI chains are listed in Table I, which also includes three polymer-solvent interaction parameters for reasons explained below. 

In the absence of a cooperative conformational transition, for many polysaccharide polyelectrolytes a linear dependence of [rj] upon I Ms observed, with the slope diminishing with the charge density associated to the polysaccharide chain (Figure 12.2.13). A theory has been presented for an estimation of the relative stiffness of the molecular chains by Smidsrod and Haug, which is based on the Fixman s theory and Mark-Houwink equation. The chain stiffness parameter is estimated from the normalized slope B of [r ] vs. the inverse square root of the ionic strength ... 

According to the Eq. 11.7 both and Coo provide a consistent prediction of the deformation behavior. It seems, however, that the entanglement density Vg can be considered as the primary parameter which controls the crazing behavior, whereas the chain stiffness parameter C o is predominant in controlling the shear yielding behavior. 

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... 

Monte-Carlo simulations are applied to estimate the characteristic ratios and p parameters from the RIS models for PE, POM, polybutadiene, and polyisoprene. Here the p parameter is defined as the ratio of the radius of gyration to the hydrodynamic radius. The p parameters of these real chains in the unperturbed state show only a slight dependence on the microconformation in the limit of large molecular weights and are found close to 1.504, which is the value for an idealized Gaussian chain. The estimated p parameters of the real chains appear to be correlated to the chain stiffness and increase with the characteristic ratios. 

Since the dilute solution theory is considered as the basis for the indicated treatment, it will receive considerable attention. Influences of several parameters as molecular weight, molecular weight distribution, thermodynamic and kinetic chain stiffness, intramolecular hydrodynamic inter-action, optical properties of the chain and solvent power will be considered. 

The chain stiffness expressed by the flex parameter F which, for a given chain of molar mass Me, is given by F = Me/Ne, where Ne is the number of elementary (undeformable) segments. F is essentially an increasing function of the content of aromatic nuclei, Ar. 

For many years, several authors have tried to explain and predict the yield stress of polymers (crosslinked or not), as a function of the experimental test parameters (T, e) and/or structural parameters (chain stiffness, crosslinking density). These models would be very useful to extrapolate yield stress values in different test conditions and to determine the ductile-brittle transition. 

In the elements p and r, the Heaviside functions vpr and vrp are included to avoid bond backfolding since a bond cannot be backward when the previous bond was forward and vice versa. In the supermatrix G, cj, characterizes a lateral bond in layer i, p, a forward bond starting from layer i, and r,- a backward bond starting from layer i. q,-, p,-, and r,-depend on three kinds of parameters. The parameters ah, a, 0, and to arise from local chain stiffness and bond arrangements, Pi from the intermolecular interactions and pLi, pzi from the nearest-neighbor bond correlations. 

In reality the interactions between polymer and solvent molecules, which determine the solution viscosity, are very complicated and dependent on a great number of parameters. The literature mentions the solubility parameters of polymer and solvent, polymer chain stiffness, free volume of the solution, etc. In principle, all these factors should be taken into account in predicting the viscosity of a polymer solution. However, the available experimental data are insufficient for this purpose. 

What about semiflexible polymers It is, in principle, possible to include the effect of the chain stiffness through the parameter y in (3.1). As shown... 

A great number of initiators and monomers are now available, allowing almost perfect control over most of the important parameters of LCPs main chain stiffness tacticity glass transition temperatures processabiUty from solution or melt mesogen density along the main chain combination with... 

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