Temperature dependence of tracer diffusion coefficients in polystyrene

The temperature dependence of the tracer diffusion coefficient D* of long deuterated polystyrene (d-PS) chains of molecular weight M>Mc, where Mc is the critical molecular weight for entanglement, diffusing into highly entangled PS matrices, each of molecular weight P = 2×107, is studied using forward recoil spectrometry. It is found that the temperature dependence of D*/T, reflected primarily in the monomeric friction coefficient, is accurately described by a Vogel equation. The constants that are used to fit these results are independent of M and are the same as those used to fit the temperature dependence of the zero shear rate viscosity of polystyrene.

Effect of the Reference Chain Dimensions in the Molecular Theory of Viscoelastic Behavior of Polymer Networks

Mooney's version of the molecular theory of polymer networks has been generalized to the case when the external strain applied in the isotropic state is different from that at network formation. As in the theory of equilibrium behavior of the polymer networks, this generalization allows inclusion in the viscoelastic functions of effects connected with the temperature dependence of internal energy of the chains and with the strain effect of the solvent. From viscoelastic functions thus generalized, it is possible to derive a relation for calculation of the monomeric friction coefficient. It also suggests the possibility of superposing data obtained at various temperatures, degrees of swelling, and condition of network formation.

Dynamic Mechanical Properties of Cross-Linked Rubbers. II. Effects of Crosslink Spacing and Initial Molecular Weight in Polybutadiene

The complex shear compliances of eight samples of polybutadiene crosslinked by cumyl peroxide and four samples crosslinked by sulfur have been measured over a frequency range from 0.2 to 2 cps at temperatures from − 6 to 45° C by a torsion pendulum. On four of the samples, measurements were extended by the Fitzgerald transducer from 45 to 600 cps at temperatures from − 71 to 55°. The vulcanizates had been prepared from polymers of two different molecular weights (180,000 and 510,000) with sharp molecular weight distribution; the physical crosslink density ranged from 0.57 to 2.68×10−4 mole/cm3, and the chemical crosslink density calculated following Kraus ranged from 0.22 to 1.49×10−4 mole/cm3. The mechanical data were all reduced to T0=298° K by shift factors calculated from the equation log aT=−3.64(T−T0)/(186.5+T−T0). In the transition zone of frequencies, the viscoelastic functions of the cumyl peroxide vulcanizates were closely similar, except for a shift toward lower frequencies with increasing crosslinking, corresponding to a small but unexpected increase in the monomeric friction coefficient. Cross-linking by sulfur caused a somewhat larger shift toward lower frequencies at a comparable crosslink density. In the rubbery zone, the sample with least cross-linking exhibited a substantial secondary loss mechanism at very low frequencies. The low-frequency losses are evident in all the samples, but their magnitude falls rapidly with increasing crosslink density as previously found for natural rubber. It also falls somewhat with increasing initial molecular weight, indicating a contribution from network strands with loose ends. The possible relation of the low-frequency losses to trapped entanglements is discussed.