R. N. Work

Dielectric relaxation spectrum of undiluted poly(4‐chlorostyrene), T≳Tg

Dielectric relaxation characteristics of undiluted, atactic poly(4‐chlorostyrene), P4CS, have been determined at temperatures 406 K⩽T⩽446 K from measurements made at frequencies 0.2 Hz⩽f⩽0.2 MHz. After effects of electrical conductivity are subtracted, it is found that the normalized complex dielectric constant K*=K′−i K″ can be represented quantitatively by the Havriliak–Negami (H–N) equation K*=[1+(iωτ0)1‐α]−β, 0⩽α, β⩽1, except for a small, high frequency tail that appears in measurements made near the glass transition temperature, Tg. The parameter β is nearly constant, and α depends linearly on log τ0, where τ0 is a characteristic relaxation time. The parameters α and β extrapolate through values obtained from published data from P4CS solutions, and extrapolation to α=0 yields a value of τ0 which compares favorably with a published value for crankshaft motions of an equivalent isolated chain segment. These observations suggest that β may characterize effects of chain connectivity and α may describe ef...

Theory of Relaxation Phenomena in Polymers. I. Rotational Motion of Side Elements around the Backbone

Dielectric relaxation in polymers is investigated by means of an extension of Glaubers dynamical theory of the Ising model. The theory is applied to a linear chain of rotators with arbitrary interactions between neighbors, and the frequency dependence of the complex electric susceptibility is found to be simply expressed in terms of the Fourier—Laplace transform of a correlation function. The latter is related to the extent of correlated motion of nearby segments. If the correlation function contains a time dependence of the form (1/τ1) exp(—t/τ1), where τ1 is the time constant for the establishment of the equilibrium correlation function, then both the effective dielectric relaxation time and the effective dipole moment of the dipolar rotators are frequency dependent. A time dependence of this form may introduce asymmetry or even a bimodal structure into the dielectric loss spectrum. The temperature dependence of the spectrum is discussed within the framework of the theory, and application is made to me...

Brillouin and ultrasonic study of the temperature dependence of the elastic constants in NaCN

Abstract The temperature dependence of the elastic constants of NaCN has been studied by propagation of ultrasonic waves at 15 MHz and by Brillouin scattering at 3 GHz over the temperature range from 287K to 355K. c 44 is observed to soften linearly with temperature as the order-disorder phase transition at 284K is approached from above. The other elastic constants also soften, except for c 12 which stiffens. Considerable dispersion is seen in the values of c 44 obtained ultrasonically and by Brillouin scattering. Measurements of the temperature dependence of the density are also reported.

Angular correlations in linear copolymers from the compositional dependence of their dipole moments. III. Experimental: Poly(4‐chlorostyrene, 4‐methylstyrene) copolymers

The complex dielectric constants e*=e′−je″ of members of a set of ten poly(4‐chlorostyrene, 4‐methylstyrene) copolymers, P(4CS,4MS), that spans the whole composition range and includes the homopolymers P4CS and P4MS, have been measured at temperatures ranging from about 450 °K downwardly to their glass transition temperatures at about 390 °K. The compositional dependence of the effective dipole moment per structural unit μ2e, as determined from these measurements is analyzed by methods developed in Papers I and II of this series, but as modified for applications to copolymers having nearly random ordering of sequences of chemical types of structural units. The analysis presupposes knowledge of the compositional dependence of the condtional probabilities Pαβ that a structural unit of type β immediately follows one of type α, where α,β=0,1. The analysis is done with the help of a series expansion of the compositional dependence of μ2e, the terms of which are linearly independent functions of composition wit...

Angular correlations in linear copolymers from the compositional dependence of their dipole moments. I. Random copolymerization

A theory is developed, without recourse to a detailed model, for evaluating certain linear combinations of the average cosines of the angles between dipole moments of pairs of structural units that are closely spaced along the chain contour. Measurements of the compositional dependence of the effective dipole moment per structural unit together with a knowledge of the compositional dependence of the probabilities for various types of sequences of structural units provide the required information. The theory offers a possibility for testing the validity of certain restrictive assumptions that are implicit in earlier treatments of the problem. Additionally, the theory provides a basis for determining unequivocally from experimental measurements whether angular correlations exist among the structural units that contribute to the orientational part of the polarization and whether the angular correlation parameters, if they exist, depend on the types of structural units involved.

Angular correlations in linear copolymers from the compositional dependence of their dipole moments. II. Markovian typal sequences

An earlier treatment of the problem of extracting configurational information from experimental determinations of the compositional dependence of the dipole moments of copolymers containing random sequences is extended to include the case wherein typal correlations arise from pair dependent probabilities for the occurrence of the structural units in the copolymer. If the typal correlations are sufficiently strong, it is possible to evaluate certain, meaningful, linear combinations of terms containing the average cosines of the angles between the dipole moments of nearby pairs of structural units, as well as the angular correlation length M, measured by the number of structural units beyond which the average cosines are negligible. Conditions are given in order to be able to separate and evaluate the average cosines belonging to individual pairs of structural units.

Temperature coefficient of the dipole moment of undiluted poly(4‐chlorostyrene), T≳Tg

Temperature coefficients of the dipole moments of undiluted poly (4−chlorostyrene) are reported. (AIP)

Temperature coefficient of the dipole moment of poly(4‐chlorostyrene, 4‐methylstyrene) copolymers in benzene solutions

Mean square values of the dipole moments of poly(4‐chlorostyrene) and copolymers of poly(4‐chlorostyrene, 4‐methylstyrene) have been determined at up to five different temperatures. There is a significant positive temperature coefficient of the mean square dipole moment. Curves of the dipole moments and of the slopes, normalized to unity at P4CS, have essentially the same shapes. The copolymers in benzene solutions lead to values of the mean square dipole moments that are about 20% larger than measurements in p‐xylene.

Dielectric relaxation in undiluted poly (4‐chlorostyrene). II. Characteristics of the high frequency tail

The shape of the principal dielectric relaxation process that occurs just above the glass transition temperature Tg in well annealed, atactic, undiluted poly (4‐chlorostyrene) exhibits a small tail at the high frequency end of the spectrum of relaxation times. This high frequency tail (HFT) has been characterized at temperatures varying from 351 to 413 K by using the Havriliak–Negami equation. The glass transition temperature Tg of P4CS is about 400 K. It is suggested that the HFT is distinct from the β relaxation process which occurs in polystyrene at temperatures just below Tg; and that the HFT is experimental evidence of the existence of localized, fast conformational changes. This fast process is presumed to be slowed and broadened by interactions with the surroundings.

Angular correlation in linear copolymers from the compositional dependence of their dipole moments. VI. Time dependent correlations in poly(4‐chlorostyrene, 4‐methylstyrene) copolymers

The compositional dependence of the shape of the map in the complex plane of the dielectric constant of undiluted poly(4‐chlorostyrene, 4‐methylstyrene) copolymers, P(4CS,4MS), has been investigated at temperatures above the glass transition. The copolymer method, which was developed for the study of equilibrium dipole–dipole angular correlations, has been adapted to include time dependence for this investigation. Results are given in terms of differences of the shapes of contributions of 000, 010, 011, and 111 sequences, where 0 and 1 represent 4MS and 4CS units, respectively. The short range (next neighbor) of the compositional dependence of the relaxation characteristics relative to the longer range already established for the equilibrium angular correlations suggests that the latter represent averages over rotational states of backbone bonds that are undergoing fast and nearly independent transitions from one state to another.