Relaxation Master Curves Research Articles

Effect of polydispersity in polystyrene on stress relaxation

AbstractStress relaxation master curves are presented for twenty‐three polystyrene samples whose weight‐average molecular weights Mw varied from 20,800 to 310,000 and whose heterogeneity indices varied from 1.0 to 15.92. The maximum relaxation times τm, the associated partial modulus Em, and the flow viscosity η were determined for these samples at 115°C. It is shown that at 115°C. the relation log τm (minutes) = −15.10 + 3.4 Mw is obeyed. It is also shown that the quantity αB = τmEm/η correlates with the heterogeneity index of the sample. It is concluded that stress relaxation studies can be used to obtain weight‐average molecular weights and also to provide a qualitative measure of the heterogeneity index.

Stress Relaxation of Thermo-Reversible Gels. Polyvinyl Alcohol–Congo Red–Water System

Abstract Stress relaxation curves were obtained for the gels of the polyvinyl alcohol-conga red-water system in the temperature range, 15∼60°C, by means of a chainomatic relaxometer. The molecular weight of polyvinyl alcohol was 8.5×104, and gels of 15.0 and 17.5% were used, where the concentration of congo red was adjusted to be 1/10 of that of polyvinyl alcohol. Master relaxation curves were obtained for each concentration over the range, 10−2∼109hr, and relaxation spectra were calculated by the second order approximation. The following results were obtained. 1) The logaT vs. T relation gives a single curve for two concentrations, and does not obey the equation of WLF form, Also it has characteristics similar to that of agar-agar gels. 2) The apparent activation energy is kept constant to be 42 kcal. below about 43°C, and above this temperature it sharply increases with temperature. 3) The reduction on concentration to a single composite relaxation curve seems to be possible in rough approximation.

Stress Relaxation of Non-electrolytic Thermo-reversible Gels Concentration Dependence of Distribution Function of Relaxation Times. Polyvinyl Alcohol-Glycerin-Water Gels

Abstract From a stress relaxation experiment by means of a chainomatic balance relaxometer the stress relaxation curves were obtained for the gel of polyvinyl alcohol-glycerin-water system, which was taken as an example of non-electrolytic thermoreversible gel. Gels of 8.3%, 9.9% and 12.1% were used. The temperature of the samples was changed between about 2°C and 75°C. Master relaxation curves were obtained for each concentration over the range of time, 10−4∼105 hours, using the time temperature superposition principle. According to Alfrey’s approximation, relaxation spectra were calculated. The following results were obtained. 1) The master relaxation curves exhibit a fairly complicated nature on concentration dependence. 2) The logar vs. T–Ts relation obeys approximately the formula by Williams, Landel and Ferry in the range of T–Ts, −40∼0°C, but outside the range deviates fairly from it. 3) The apparent activation energy is 60 kcal./mole, which is nearly kept constant over the temperature- and concentrationrange in the present work. 4) The shift of the relaxation spectrum due to the change of concentration is not uniform over the region of box type. The maximum point in that region shifts upwards and to the longer-time side with increase of concentration.

Diffusion‐controlled stress relaxation in polymers. II. Stress relaxation in swollen polymers

AbstractStress relaxation in the systems PVAc (polyvinyl acetate)‐water, PVAc‐methanol, PMA (polymethyl acrylate)‐water, and PMA‐methanol was measured at several temperatures above the glass‐transition points of the pure polymers in ranges of sufficiently low concentrations of diluents. It was found that the time‐concentration superposition principle as proposed by Ferry is applied successfully to these data to obtain master relaxation curves of the pure polymers at fixed temperatures. The master relaxation curves so obtained at different temperatures were further superposed with each other by horizontal shift along the log time axis, in agreement with the time‐temperature superposition principle. The concentration shift factor ac as a function of diluent concentration C at fixed temperature was well interpreted in terms of the modified Doolittle's free volume equation for the viscosity of supercooled systems on the assumption that the fractional free volume of the system increases linearly with C. The proportionality coefficient, β, of this linear relation provides a measure of the plasticizing effect of a given diluent on a given polymer. It was found that β is practically independent of temperature at sufficiently small C and is larger for water than for methanol in both polymers studied. On the basis of Doolittle's viscosity equation modified to account for the concentration effect, it is shown that the glass‐transition temperature Tg of a given polymer‐diluent pair decreases with C in a linear fashion in the range of small C. The value of β can also be calculated from the slope of this linear relation. Values of β determined in terms of this procedure from literature data on a variety of polymer‐diluent pairs are given in a tabular form. For a given polymer the β values generally become smaller as the size of diluent molecule is increased, but no unique relation can be obtained between the two quantities. Equilibrium sorption and integral sorption processes were studied on the four pairs of polymer and diluent mentioned above, not only to obtain data needed for analyzing the present stress‐relaxation data but also to find information which will serve a study described in Part III of this series which is concerned with diffusion‐controlled stress‐relaxation in amorphous linear polymers. Some correlation (though not definite) appears to exist between the diffusion coefficient D (at zero concentration) and the plasticizing parameter β for a given polymer. This may be expected because both D and β are quantities depending on the frequency at which polymer segments jump cooperatively in the presence of a low molecular weight diluent.

Stress-relaxation behavior of polyvinyl acetate films

Extensive stress-relaxation data were obtained on twelve samples of polyvinyl acetate (including 8 fractionated, 2 roughly fractionated, and 2 unfractionated) over a wide range of temperature from 10° to 130°C. By making use of the time-temperature superposition principle they were combined to form a composite master relaxation curve for each of the samples, where all data were reduced to 75°C. chosen as the reference temperature. The master relaxation curves so obtained all cover the range from glassy consistency to rubbery flow as a function of time. From these, the relaxation distribution functions were calculated using the second approximation method proposed by Ferry, and compared with that derived by Williams and Ferry from dynamic mechanical measurements on an unfractionated sample of polyvinyl acetate. It was found that in the transition region where the comparison could be made, both results agreed quite satisfactorily, except in its upper terminal zone encompassing the glassy state. The real and imaginary parts of the complex dynamic modulus and the mechanical loss tangent were computed as functions of frequency for one sample from its relaxation spectrum using the well-known equations in the theory of linear viscoelasticity. These predicted properties were found to agree fairly well with Williams-Ferry's experimental data in the transition region, again except in its portion near the glassy consistency. From these results, the validity of the time-temperature super-position principle in the high-modulus portion of the transition region was suspected, in line with a similar conclusion drawn by Tobolsky and Catsiff from their stress-relaxation study on polyisobutylene. Steady-flow viscosities were calculated for all the samples studied from their relaxation spectra and found to increase with 3.4 powers of viscosity-average molecular weight, in agreement with the recent results on many other polymers. The shift factor which represents the temperature dependence of viscoelastic behavior was obtained over the temperature range studied and found to be practically independent of molecular weight. The shape of the shift factor curve thus obtained is quite similar to those for many other linear high polymers and agrees closely with that derived by Williams and Ferry for an unfractionated polyvinyl acetate sample from dynamic measurements in the range 50°–90°C. The apparent activation energy for mechanical relaxation calculated from the shift factor data increases sharply with decreasing temperature and passes through a maximum at 29°C. This behavior is also entirely the same as those observed for other polymers. The temperature at which the apparent activation energy for mechanical relaxation appeared may be compared favorably with the second-order transition temperature determined dilatometrically on undiluted polyvinyl acetate. Under the assumptions that the relaxation spectrum for a homogeneous (with respect to molecular weight) polymer in the rubbery region is represented by the so-called box-type function and that interactions between polymer molecules of different chain lengths are negligible, an equation was derived which represents the relaxation spectrum of a given heterogeneous polymer as the sum of relaxation spectra for its component polymers multiplied by its weight distribution of molecular weights. This equation was applied to the relaxation data for one unfractionated sample whose weight distribution of molecular weight had been determined using the successive fractional extraction method. It was found that the molecular weight distribution so derived from mechanical relaxation data is surprisingly close to the one from fractionation data except in the region of low molecular weights.

MECHANICAL BEHAVIOR OF WOOL FIBERS

Relaxation curves of wool fiber streched 10-25 per cent in aqueous media and phenol solution have been firstly determined. A conditioning temperature of 50°C was chosen, being as high as can be used without chemically damaging the wool fiber. Conditioning for half an hour at this temperature between measurements resulted in reproducible relaxation curves, as long as the period of extention of the fiber did not exceed 30 per cent.An apparatus used is constructed with the magnetostriction constructed for measuring the relaxation of stretched fiber. The output from the strain meter is applied to inkwriting oscillograph from the start for 10 seconds and after this time range value of valve voltmeter was measured.From the relaxation curves the reciprocal absolute temperatures corresponding to each test and the time required to attain the stress of 3.5×105g/cm2_??_4.75×105g/cm2 are obtained. The points for each specified stress are seen to lie in straight line. From the slope of these lines, the energies of activation for relaxation process in water are found from each deformation (15, 20 and 25 per cent) to be approximately 10Kcal, 20Kcal and 25_??_30 Kcal.The amount of breaking of hydrogen bonds depends on the concentration of phenol solution and temperature. With increasing temperature and concentration of phenol solution the rate of the stress relaxation becomes smaller than under the wet condition. Supplementary measurements of relaxation at various humidity were perfomed during 1/10sec_??_3000sec appling the former method. The each relaxation curve may be shifted log time scale and master relaxation curve may be constructed.