Robert F. Landel’s research while affiliated with California Institute of Technology and other places

Stress relaxation measurements on SBR were carried out at temperatures from −5 to +60° C and at initial strains of up to 550%. The effects of strain and time were found to be factorable, so that the isochronal stress-strain curve may be written as a modified Hooke's law with a time-dependent modulus: S=E(t)eƒ(α), where ƒ(α) is an appropriate function of the strain. By defining a strain-reduced stress S*=S/∫(α), i.e., a strain-reduced modulus E*(t)=E(t)ƒ(α), it can be shown that Ferry's method of reduced variables may be extended to large deformations. An appropriate strain function was obtained from the empirical Martin-Roth-Stiehler equation as ƒ(α)=α⁻² exp A(α−α⁻¹) with A=0.40. Although it cannot yet be certain that A is truly a constant and the same for all elastomers, this equation has the advantage of being valid right out to the breaking strain.

The mechanical properties of rubberlike composite propellants and similar filled elastomers are determined largely by the volume fraction of filler, the visco-elastic properties of the binder, and the interactions between the binder and filler particles. The ratio of the quasi-equilibrium modulus of the composite to that for the unfilled elastomer increases with the volume fraction of the filler, apparently according to an equation of the form proposed by Eilers and Van Dyck. However, the same ratio for the dynamic storage modulus decreases as the frequency is increased or the temperature is decreased. The time-dependent tensile properties can be characterized by stress-strain curves measured at different strain rates and temperatures. Both the small deformation and ultimate properties can be represented by master curves, which are functions only of the experimental time scale, along with a temperature function which is a near-universal function of the glass temperature. Propellants under constant loads initially exhibit creep which is qualitatively similar to that of unfilled elastomers, but subsequently dewetting of the filler particles may begin and this causes the deformation to increase exponentially with time. A discussion is given of the use of Poisson's ratio, defined in terms of Hencky strain and measured as a function of extension, to indicate the initiation of dewetting and the subsequent volume increase.

Stress relaxation measurements on SBR were carried out at temperatures from -5 to +60°C and at initial strains of up to 550%. The effects of strain and time were found to be factorable, so that the isochronal stress‐strain curve may be written as a modified Hooke's law with a time dependent modulus: S = E(t)ef(α), where f(α) is an appropriate function of the strain. By defining a strain‐reduced stress S^* = S / f(α), i.e., a strain‐reduced modulus E^*(t) = E(t)f(α), it can be shown that Ferry's method of reduced variables may be extended to large deformations. An appropriate strain function was obtained from the empirical Martin‐Roth‐Stiehler equation [Trans. Inst. Rubber Ind. 32, 189 (1956)] as f(α) = α^-2 expA (α-α^-1) with A =0.40. Although it cannot yet be certain that A is truly a constant and the same for all elastomers, this equation has the advantage of being valid right out to the breaking strain.

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Viscosities of solutions of six fractions of cellulose tributylate in 1,2,3-trichloropropane have been measured over a wide range of concentrations up to a weight fraction of 0.41 and at several different temperatures between −5° and 50°C. The apparent activation energy for viscous flow was a single function of the product of concentration in grams per cubic centimeter (c) and molecular weight (M) over the range of cM from 0 to 20,000, and in this range it increased by about 5 kcal., but at higher concentrations comparatively little. At 25°C., the relative viscosity was a single function of c5M3.4, and at high values of this argument was directly proportional to it. The results of these and measurements on other polymers are discussed in relation to the average number of entanglement points per molecule in Bueche's sense. The average molecular weight between entanglement points in cellulose tributylate, extrapolated to the undiluted state, is estimated as about 10,000. It is concluded that the monomeric friction coefficient for translation of a polymer segment is proportional to the solvent viscosity and to the 1.6 power of the polymer concentration.

The complex shear compliance of a polyurethane elastomer has been measured in the transition region from rubbery to glasslike properties with a Fitzgerald transducer. Values for the real and imaginary components of the complex shear compliance J′ and J″ are reported over a frequency range of 45 to 6000 cycles/sec, and a temperature range of −16 to 39°C. Composite curves of J′ and J″ reduced to a standard temperature were obtained by the method of reduced variables. The temperature shift factors followed the WLF equation. The data do not extend to high enough reduced frequencies to approach the glassy compliance, but at low frequencies the dynamic compliance is essentially equal to the equilibrium rubbery value. The loss tangent passes through an extremely broad maximum with increasing frequency. The shape of the retardation distribution function resembles that of polyisobutylene; however, the value of the ratio of the maximum in the retardation distribution function to the equilibrium compliance is not the same for the two polymers. The value for the polyurethane agrees instead with that previously found for cellulose tributyrate and polyvinyl chloride gels (which are crosslinked by crystallization). For several decades at the long time end of the transition zone the relaxation distribution function has the slope of prescribed by the Rouse theory, as does a 20.4% cellulose tributyrate gel. At shorter times the experimental curve rises more steeply than predicted by theory, just as do the corresponding curves for vinyl polymers. However, the total deviation from the linear theoretical curve is small and the overall shape of the relaxation distribution function for the polyurethane more nearly resembles that found for disubstituted than for monosubstituted vinyls.

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.

Analysis of the temperature dependence of viscoelastic and dielectric relaxation processes in several individual polymers by the equation of Williams, Landel, and Ferry provides values of the fractional free volume at the glass transition temperature and its thermal expansion coefficient which are rather similar in different systems and of reasonable magnitude, with one exception (poly-n-butyl methacrylate). The friction coefficient per monomer unit at Tg, derived from viscoelastic data, varies from 103 to 106 dyn-sec/cm; it is believed to depend on the magnitude of intermolecular forces as well as the disposition of local free volume in the packing of chain segments, which will be affected by detailed geometry even though the average fractional free volume at Tg is apparently not much affected. The friction coefficient of a foreign molecule of comparable size to a chain monomer unit, derived from diffusion measurements, is similar in magnitude to that of a chain unit for polyisobutylene 96° above Tg; but is very much smaller than that of chain unit for polyvinyl acetate only 12° above Tg. The temperature dependences of these quantities are similarly related. It is suggested that a foreign molecule is provided with local excess free volume which is relatively unimportant when the average free volume is considerable (well above Tg) but greatly reduces the friction coefficient when the average free volume is small (near Tg).

The real and imaginary components of the complex compliance, J′ and J″, have been measured between 30 and 4500 cycles/sec. for three gelatinous compositions of cellulose tributyrate (Mη = 300,000) and dimethyl phthalate containing 20.4, 42.6 and 57.5% polymer. The temperature range was from 25 to -52°. Data for the 20.4% gel were combined by the method of reduced variables to give composite curves of J′ and J″ reduced to a standard temperature. Data for the 42.6% gel were similarly combined above -25° and separately below -25°; near -25° there was a change in properties attributable to a structural modification, probably increased crystallinity. Data for the 57.5% gel could not be combined by reduced variables, since there were progressive changes with decreasing temperature, attributable also to increases in crystallinity. Where reduced variables were applicable, the temperature shift factors followed a recently proposed equation of Williams, Landel and Ferry. The equilibrium rigidity approached at low frequencies at 25° was proportional to the 2.8 power of polymer concentration. The loss tangent passed through a maximum with increasing frequency; with increasing concentration (at constant temperature) this maximum became lower and broader and shifted to lower frequencies. The retardation distribution functions exhibited maxima whose heights were directly proportional to the equilibrium compliances. Increased crystallinity evidently depresses the retardation distribution, especially at long times; depresses J″; and depresses J′ somewhat less, at the same time flattening the slope of the latter. The relaxation distribution function of the 20.4% gel followed the slope prescribed by the Rouse theory remarkably well. The more concentrated gels showed somewhat flatter slopes in a region where vinyl polymer systems show steeper slopes than that predicted by the Rouse theory.

Dynamic mechanical properties of concentrated solutions of three fractions of cellulose tributyrate in 1,2,3-trichloropropane have been studied by the wave propagation and single transducer methods. Concentration ranges were about 5 to 25% for fractions H (Mη = 300,000) and R2b (152,000), and 28 to 45% for fraction L (55,000). H was also studied by stress relaxation at 25.6%. The real parts of the complex dynamic rigidity and viscosity, reduced to unit concentration and viscosity at 25° by the usual method of reduced variables, superposed for each fraction at all temperatures (-5 to 35°) and concentrations. The relaxation distribution functions calculated from dynamic rigidity, dynamic viscosity and stress relaxation were in good agreement for each fraction. Each relaxation spectrum consisted of a horizontal plateau with a terminal zone at long times very close to the location predicted by the Rouse theory. The plateaus were flatter and longer than those observed for solutions of vinyl polymers of comparable molecular weight, indicating that the tendency to mechanical coupling of neighboring molecules is much stronger in the case of the cellulose ester.