The unperturbed dimensions

Rotational isomeric state theory predicts the dimensions of polymer chains in 0-solvents, i.e. the unperturbed dimensions r J, where the subscript 0 denotes that the bonds are considered to be volumeless lines in space. As stated previously, these can be expressed as 

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Flory s viscosity theory also furnishes confirmation of the w temperature as that in which a=V.2, and it permits the determination of the unperturbed dimensions of the Polymer chain. Even if a Q solvent is not available, several extrapolation techniques can be used for the estimating the unperturbed dimensions from viscosity data in good solvents. The simplest of these techniques seems to be that of Stockmayer. 

As explained earlier (Sect. 1.3.1), macromolecules in a low-molecular-weight solvent prefer a coiled chain conformation (random coil). Under special conditions (theta state) the macromolecule finds itself in a force-free state and its coil assumes the unpertubed dimensions. This is also exactly the case for polymers in an amorphous melt or in the glassy state their segments cannot decide whether neighboring chain segments (which replace all the solvent molecules in the bulk phase) belong to its own chain or to another macromolecule (having an identical constitution, of course). Therefore, here too, it assumes the unperturbed ) dimensions. 

With the exception of the report by Pannell (45), published data on the behaviour of branched polymers in GPC support the generalisation (46,47) that the so-called hydrodynamic volume, M[ ], is a valid parameter for the correlation of GPC retention volumes, for polymers differing in either chemical nature or branching or both. The question of the most suitable correlation parameter for linear polymers has been studied in some detail by Dawkins and co-workers (48), who compared M[rj] with the unperturbed dimensions, e.g. , but experimental accuracy was insufficient to distinguish between them (49). 

For POM, a matrix algorithm for the statistical mechanical treatment of an unperturbed -A-B-A-B- polymer chain with energy correlation between first-neighboring skeletal rotations is described. The results of the unperturbed dimensions are in satisfactory agreement with experimental data. In addition, if the same energy data are used, the results are rather close to those obtained by the RIS scheme usually adopted. The RIS scheme is shown to be also adequate for the calculation of the average intramolecular conformational energy, if the torsional oscillation about skeletal bonds is taken into account in the harmonic approximation. 

The conformational energies of the lower members of POM, 2,4-dioxapentane and 2,4,6-trioxaheptane are estimated by the empirical force field method. The gauche states of the Internal rotation around the skeletal C—0 bonds are successfully predicted to be of lower energies in both molecules. In order to calculate the unperturbed dimension and dipole moment of POM, RIS approximations are made by using the results obtained from the force field calculations on 2,4,6-trioxaheptane. Although these parameters are significantly different from those estimated earlier, they reproduce the observed values fairly well. 

The lack of any strong conformational preference is the origin of the relatively small value of the unperturbed dimensions and of the insensitivity of both the unperturbed dimensions and dipole moments to changes in temperature. 

Evidence of only a low barrier to inversion in Si—O—Si sequences could be important with regard to the interpretation of the statistical properties of silicone polymers. The effects are estimated for the temperature coefficients of the unperturbed dimensions, dipole moments, and the optical anisotropy for PDMS. 

The mean-square dipole moments of POE and POMg are determined from dielectric constant measurements on dilute solutions in benzene. The values obtained are in good agreement with those predicted using the RIS models for these chains. In addition, the unperturbed dimensions of POMg are calculated as a function of molecular weight using the RIS theory. 

The epimerization equilibria for the diastereomers of 2,4,6,8-tetramethylnonane and 2,4,6,8,10-pentamethylundecane are determined and the results are interpreted in terms of a RIS model. The results yield correct values for the optical activity and are consistent with conformational energies calculated from experimental values of the unperturbed dimensions of PP. 

The unperturbed dimensions and their temperature coefficients are evaluated for poly n-pentene-1), poly(n-butene-l), and PS with the RIS model. The calculated values of the unperturbed dimensions for atactic and isotactic chains are in good agreement with the experimental data. The measured temperature coefficients, however, are described satisfactorily by the model for atactic polypentene and polybutene only. 

Conformational energies as function of rotational angles over two consecutive skeletal bonds for both meso and racemic diads of poly(Af-vinyl-2-pyrrolidone) are computed. The results of these calculations are used to formulate a statistical model that was then employed to calculate the unperturbed dimensions of this polymer. The conformational energies are sensitive to the Coutombic interactions, which are governed by the dielectric constant of the solvent, and to the size of the solvent molecules. Consequently, the calculated values of the polymeric chain dimensions are strongly dependent on the nature of the solvent, as it was experimentally found before. 

Conformational energies associated with PTP chains are calculated by using semiempirical potential energy functions. Reliability of these functions is tested against the known values of conformational energies of various simple alkyl sulfides. The magnitude of the gauche sulfur effect is estimated from the RIS analysis of the experimental values of the unperturbed dimension, dipole moment, and their temperature coefficients observed for atactic samples of PTP. 

RIS theory is used to study the unperturbed dimensions of PMPS chains as a function of their stereochemical structure. The required conformational energies are obtained from semi-empirical, interatomic potential energy functions and from known results on PDMS. 

Matrix calculations are carried out for theoretical calculation of the unperturbed dimensions of e/ s-1,4-polybutadiene which takes into account the particular nature of the energy barriers to the rotation around single C—C bonds adjacent to the double bonds. 

The Flory-Williams RIS models describing the conformational characteristics of polyesters and polyamides are combined to calculate the dimensions of the alternating polyesteramide PEA. Excellent agreement is found with experimental values of the unperturbed dimensions. New determinations of molecular dipole moments are reported for dimethyl-frans-1,4-cyclohexanedicarboxylate and for trans-1,4-cyclohexanedlol diacetate. 

Values of the dipole moment ratio of PNS are obtained from dielectric measurements. From thermoelastic experiments, performed on polymer networks, the temperature coefficient of the unperturbed dimensions is determined. Analysis of these results using the RIS model is performed leading to the parameters given above. 

Values of the mean-square dipole moment of PNA are determined from measurements of dielectric constants and refractive indices of the polymer in benzene. The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions are critically interpreted using the RIS model. Good agreement between theory and experiment is obtained by assuming that the gauche states about C(CH3)2— CH2 bonds have an energy 2.5 kJ mol-1 lower than the alternative trans states. 

Values of the mean-square dipole moment, , of PDEI are determined as a function of temperature. The value of the dipole moment ratio is 0.697 at 303 K. Trifunctional model networks are prepared. From thermoelastic experiments performed on the networks over a temperature range 293 - 353 K, it is found that the value of the temperature coefficient of the unperturbed dimensions amounts to 1.05 0.17 K-1. The dipole moments and the temperature coefficients of both the dipole moments and the unperturbed dimensions are critically interpreted in terms of the RIS model, and are found to be in a reasonable agreement. 

RiS theory is applied to investigate chain configuration of POLA. Independent conformations for each repeat monomer unit of the chain are assumed in the calculations of the unperturbed dimensions. Rotations about the oxygen-phenytene-carbon bonds are considered to be free with twofold symmetric potentials. The trans and cis conformations of the carbonyl-phenylene-carbon and the indan-carbonyl residues are assumed to have equal probability. The bond vectors for this model lie in a plane because every torsion angle is 0D or 180°. 

The dipole moment ratio and the temperature coefficient of both the dipole moment and the unperturbed dimensions of the polyesters PDA and PDS are measured. The experimental value of dlln 0) / d Tshows an anomalous dependence on the elongation ratio of the networks at which the thermoelastic measurements are performed. Although the rotational states scheme gives a fairly good account of the polarity of the chains, it fails in reproducing the experimental values of d (In 0) / d T, the causes of this disagreement are discussed. 

The unperturbed dimensions and characteristic ratios of PTMPS chains are calculated using the RIS approximation. The low experimental value of the characteristic ratio reported for this polymer is successfully Interpreted by these computations. The stiffening effect expected from introduction of thep-phenylene group into the chain backbone is apparently offset by its reducing the repulsive Interactions that would otherwise occur among the atoms or groups before and after it eiong the chain. 

Using an Ising model for rotational isomeric states the unperturbed dimensions, 0 / nl2, are evaluated for copolymers of propylene and pentene-1. Chemical composition, tacticity, and sequence length distribution are varied. It is found that only for atactic copolymers 0 I n 2 depends linear on the chemical composition. Deviations from linearity cannot be attributed... 

RIS theory is used to predict values of the optical-configuration parameter Aa for ethylene - propylene copolymers as a function of chemical composition, chemical sequence distribution, and stereochemical structure of the propylene sequences. The calculations are based on information available for ethylene and propylene homopolymers, and on the model used to interpret the unperturbed dimensions of these copolymers. Values of Aa are generally found to decrease significantly with increase in the fraction of propene units, but to be relatively insensitive to chemical sequence distribution and stereochemical structure. Geometries and conformational energies are the same as those used for the interpretation of the unperturbed dimensions of these chains. The conformational energies used are E(q) = 0, EM 2.09, and E a>) = 0.37 kJ mol-1. 

Reduction of the unperturbed dimensions of the main chain is calculated when ethyl groups are attached to a polyethylene backbone. Values of most of the paramters are taken from the well-known RIS model for unperturbed polyethylene (Abe, A. Jernlgan, R. L. Flory, P, J, J, Am. Chem. Soc. 1966, 88, 631) the bond angle is 112°, gauche states are located at 60° trans 180°l. First- and second-order interactions are weighted by using o 0.43 and m 0.034 (for 300 K). An additional statistical weight, denoted by t, is required at each bond to an atom that constitutes a trifunctional branch point (Flory, P, J, Sundararajan, P. R. DeBolt, L. C. J. Am. Chem. Soc. 1974, 96, 50151. Calculations are performed with t = 0 and t = [Pg.410]

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