Malcolm L. Williams’s research while affiliated with University of Wisconsin–Madison and other places

The real (J′) and imaginary (J″) components of the complex compliance have been measured between 24 and 2400 cycles/sec. in the temperature range from 75° to 155°C. for two fractions of polyethyl methacrylate of weight-average molecular weights 1.73 × 106 and 0.164 × 106. The data were practically identical for the two fractions except that J″ was slightly higher at the highest temperatures and lowest frequencies for the lower fraction. The method of reduced variables did not give superposed curves for J′ and J″ over the entire temperature range. However, the data could be analyzed in terms of two additive mechanisms; for the α mechanism, J′ and J″ superposed with reduction factors aT whose temperature dependence followed an equation of the WLF form, and for the β mechanism they also superposed with reduction factors aTβ whose temperature dependence corresponded to a constant activation energy of 31 kcal. The coefficients of the WLF equation, reduced to the glass transition temperature, were similar in magnitude to those observed in other polymers. Relaxation and retardation spectra have been calculated for both mechanisms. Those for the α mechanism, attributed to the usual chain backbone motions, resemble in form those for other disubstituted vinyl chains; the friction coefficient per monomer unit in backbone motion has been calculated from the extended Rouse theory. The spectra for the β mechanism, attributed to side chain motions, are relatively broad. The relative locations of the two mechanisms on the time scale change rapidly with temperature.

The real and imaginary components of the complex compliance have been measured between 30 and 3000 cycles/sec. in the temperature range 25° to 89°C. for a sample of polymethyl acrylate of weight-average molecular weight 2.2 × 106. Results at all temperatures and frequencies superpose by the method of reduced variables to give the components at 25°C. over 7.5 decades of frequency, corresponding to the transition from rubberlike to glasslike consistency as a function of frequency at this temperature. Relaxation and retardation distribution functions have been calculated, and the friction coefficient per monomer unit has been estimated from an extension of the Rouse theory. The temperature dependence of the relaxation processes agrees with that derived from dielectric measurements, and it has been analyzed in terms of the free volume and its thermal expansion coefficient.

Data for dielectric constant (ε′) and dielectric loss (ε″) of polyvinyl acetal (by Funt and Sutherland) and of polyvinyl acetate, polyvinyl chloroacetate and polymethyl acrylate (by Mead and Fuoss) have been treated by the method of reduced variables. The normalized variables (ε′ - ε∞)/(ε0 - ε∞) and ε″/(ε0 - ε∞), where ε0 and ε∞ are the limiting low and high frequency values of ε′, superpose at various frequencies and temperatures to form composite curves when the frequency scale is reduced by a temperature-dependent factor bT. From bT the apparent activation energy for dielectric relaxation is obtained and found to be strongly temperature dependent. From the composite reduced plots, the distribution function of electrical relaxation times is calculated over a wide range of time scale for the 4 polymers; the values from ε′ and from ε″ are in good agreement. The relation of this analysis to the more customary plots of ε′ and ε″ against temperature is discussed.

The Rouse theory for viscoelastic properties of very dilute solutions is modified for application to undiluted linear polymers. With the effective segment mobility expressed in terms of steady‐flow viscosity, the theory is applied to polymers of rather low molecular weight essentially without further change. In high molecular weight polymers, it is assumed that for modes of motion with relaxation times above a critical value the effective segment mobility drops abruptly, in accordance with the effect of entanglement coupling on steadyflow viscosity as described by Bueche. Properties in both the transition region between glasslike and rubberlike consistency and the rubberlike or plateau region are predicted semiquantitatively with no arbitrary parameters. In an alternative application to the transition region, the average effective friction coefficient per monomer unit can be calculated for both linear and lightly cross‐linked systems.

The real and imaginary components of the complex compliance have been measured between 30 and 4500 cycles per second in the temperature range −11°C. to 40°C. for a 50% (by volume) solution of polyvinyl acetate in tri-m-cresyl phosphate. Results at all temperatures and frequencies superpose by the method of reduced variables to give the components at 25°C. over 7.5 decades of frequency, corresponding to the transition from rubberlike to glasslike consistency at this temperature. Values of the steady-flow viscosity have been measured between 0° and 41°C. and found to give nearly the same temperature reduction factors as found empirically from the dynamic measurements. Relaxation and retardation distribution functions have been calculated. By reducing these data to a common temperature for both plasticized and undiluted polymer, it is concluded that the presence of 50% diluent reduces the monomeric friction coefficient by a factor of 107. By reducing the data to a hypothetical reference state of unit density and unit steady-flow viscosity and combining them with previous data on solutions of the same polymer in 1,2,3-trichloropropane, the distribution function of mechanical relaxation times can be obtained at 25°C. over 13.5 decades of time. The distribution function is found to be similar in shape and location on the time scale to that obtained for polystyrene in decalin previously studied in this laboratory.

The contributions of the slowest relaxation mechanisms to time-dependent mechanical behavior in concentrated polymer solutions can be derived from dynamic viscosity, stress relaxation, or (according to a recent theory of DeWitt) apparent viscosity in non-Newtonian flow. The results of such measurements are compared for four samples of polyisobutylene, one of polystyrene, and one of polyvinyl acetate. They are in close agreement with one exception. For samples not too heterogeneous with respect to molecular weight, the time-dependent behavior at the slow end of the time scale can be approximately predicted by a modification of the theory of Rouse, the only quantities needed being the molecular weight and steady flow viscosity. The elastic compliance of a linear polymer in steady-state flow is dominated by the slow relaxation mechanisms; according to the modified Rouse theory, it is J = (2/5)Mz + 1Mz/MwcRT, where c is concentration in g./cc. and the other symbols have their usual significance.

The real and imaginary components of the complex compliance have been measured between 30 and 5100 cycles/sec. at nine temperatures between 50°C. and 90°C. on an unfractionated sample of polyvinyl acetate (Mn = 140,000, Mw = 420,000). The results superpose by the method of reduced variables to give composite curves covering the transition from rubberlike to glasslike consistency as a function of frequency at 75°C. From these, the reduced curves for the real and imaginary parts of the complex shear modulus, and the real part of the complex viscosity, have been calculated. Earlier data of Mead and Fuoss on dielectric dispersion and dielectric loss of polyvinyl acetate have been reduced to 75°C. in the same manner, and the mechanical and electrical reduction factors are found to be identical. The apparent activation energy for mechanical and electrical relaxation increases sharply with decreasing temperature, as observed for other polymers. Distribution functions of mechanical relaxation and retardation times, and of electrical relaxation times, have been calculated from both real and imaginary components of modulus, compliance, and dielectric constant, respectively. The results of the approximation formulas of Williams and Ferry and of Schwarzl and Staverman are found to be closely similar. The electrical relaxation spectrum is somewhat flatter, and lies at shorter times, than the mechanical retardation spectrum.