Edwin R. Fitzgerald

The Relaxation Distribution Function of Polyisobutylene in the Transition from Rubber‐Like to Glass‐Like Behavior

The steady flow viscosity of a sample of polyisobutylene of viscosity‐average molecular weight 1.35 million, distributed by the National Bureau of Standards, has been measured from 15° to 100°C. Its logarithm is a linear function of 1/T2. Application of the method of reduced variables to dynamic mechanical data from −45° to 100°, previously reported for this polyisobutylene, yields composite curves reduced to 25°C for the real and imaginary parts of the complex compliance and complex shear modulus; the real part of the complex dynamic viscosity; and the mechanical loss tangent. The latter exhibits a broad and peculiarly asymmetric maximum. The reduced time scale extends from 1 to 10−9 sec. The reduction factors aT obtained in this way are slightly higher than those derived either from the viscosity or from stress relaxation measurements of Tobolsky and associates. The distribution functions of relaxation and retardation times have been calculated by second approximation methods and their detailed shapes a...

Dynamic Mechanical Properties of Polyisobutylene

Values of complex shear compliance (and rigidity) have been obtained for a sample of polyisobutylene of viscosity‐average molecular weight 1.35×106 at 22 temperatures from −45 to 100°C and at about 20 frequencies from 30 to 5000 cps. Measurements were made by means of the transducer method of Fitzgerald and Ferry with a precision of ±2 percent and are estimated to be accurate to within ±3 percent as evidenced by agreement obtained between 7 different samples of widely varying dimensions. Values of the real part of the complex shear compliance J′ vary from 3.1×10−7 cm2/dyne at 99.9°C to 1.0×10−10 cm2/dyne at −44.6°C. The frequency dependence of the loss tangent J″/J′ indicates the presence of a low, broad maximum of 1.7 at −10 to −5°C and a second, smaller maximum at lower temperatures. This second maximum is also evident in a plot of J″/J′ at a fixed frequency against temperature. The wide temperature and frequency ranges of the measurements have provided an essentially complete experimental description o...

Method for determining the dynamic mechanical behavior of gels and solids at audio-frequencies; comparison of mechanical and electrical properties

A method is described for measurements of complex shear modulus or compliance on samples ranging from soft gels to stiff solids at −50 to +150°C. over the frequency range 25 to 5000 cycles/sec. By a proper choice of sample dimensions a precision of ±2% is obtained for values of compliance varying from about 10−5 to 10−10 cm.2/dyne although a single sample cannot be measured with this precision over the entire frequency-temperature range. Results are given for a sample of polyisobutylene from the National Bureau of Standards at 25.0°C., for a polyvinyl chloride-dimethylthianthrene gel (10% polymer by volume) at ten temperatures between −25 and 25°C., arid for polyvinyl chloride plasticized with dimethylthianthrene (40% polymer by volume) at ten temperatures between 5 and 60°C. Comparison of the dynamic mechanical results with measurements of complex dielectric constant previously reported for the polyvinyl chloride-dimethylthianthrene compositions shows that the dielectric constant and compliance give roughly the same type of temperature-frequency dispersion. While the frequency of maximum electrical loss tangent (ϵ″/ϵ′) and that of maximum mechanical loss tangent (J″/J′) are not the same at a given temperature, these maxima do appear to shift the same amount with temperature. Thus for each concentration the slopes of curves obtained by plotting the logarithm of the frequency of maximum loss tangent against the reciprocal of the absolute temperature are identical for the electrical and mechanical cases. This indicates that the activation energies for electrical and mechanical responses are the same. The maximum loss tangent for the mechanical case is much larger than the electrical maximum for both the 10 and 40% polyvinyl chloride concentrations.

Mechanical and electrical relaxation distribution functions of two compositions of polyvinyl chloride and dimethylthianthrene

Abstract Dynamic mechanical and electrical data on two compositions of polyvinyl chloride and dimethylthianthrene, containing 10% and 40% polymer by volume, covering a wide range of frequencies and temperatures, have been treated by the method of reduced variables. The reduced real part of the complex compliance and the reduced mechanical loss tangent fall on single composite curves when the frequency scale is reduced by a temperature-dependent factor a T . The reduced real part of the dielectric constant and the reduced electrical loss tangent fall on single composite curves when the frequency scale is reduced by a temperature-dependent factor b T . The factors a T and b T are identical, but the mechanical and electrical composite curves are very different. The apparent activation energy for mechanical and electrical relaxation increases rapidly with decreasing temperature, and the values for the 10% polymer composition are not far from those for the apparent activation energy for viscous flow of the solvent. The frequency-dependent properties have been expressed as distribution functions of mechanical relaxation and retardation times and of electrical relaxation times. The mechanical relaxation distribution for the 10% composition is sharper and lies at shorter times than that for the 40% composition. The latter is similar in shape to distributions in the transition range between soft and glassy consistency for several other widely different polymer systems. The maximum in the mechanical retardation distribution is, for each composition, at a much longer time than the maximum in the electrical relaxation distribution, and the mechanical curves are much steeper on the short-time side of the maximum. It is concluded that the mechanical properties are strongly influenced by a distribution of effective chain lengths.

Mechanical Properties of Substances of High Molecular Weight. X. The Relaxation Distribution Function in Polyisobutylene and Its Solutions

Previous twin transducer measurements of the dynamic rigidity and viscosity of a polyisobutylene sample of viscosity‐average molecular weight 1.2 million have been extended over a wider temperature range, and previous wave propagation data on solutions of this polymer in xylene have been extended by transducer measurements at lower concentrations. Values of the relaxation distribution function are derived from all these data and are compared with values obtained from stress relaxation measurements on solutions of the same polymer in Decalin, as well as stress relaxation data of Andrews and Tobolsky on solid polyisobutylene and dynamic measurements on butyl rubber from several sources. When reduced to a common reference state at 25°C by the assumption that all relaxation processes depend identically on temperature, the data for solid polyisobutylene provide a picture of the distribution function over eleven cycles of logarithmic time. It appears to have a plateau from 0.1 to 104 sec with a sharp rise at sh...

Temperature Dependence of Dynamic Properties of Elastomers. Relaxation Distributions

Abstract By the use of reduced variables, the temperature dependence and frequency dependence of dynamic mechanical properties of rubberlike materials can be interrelated without any arbitrary assumptions about the functional form of either The definitions of the reduced variables are based on some simple assumptions regarding the nature of relaxation processes. The real part of the reduced dynamic rigidity, plotted against the reduced frequency, gives a single composite curve for data over wide ranges of frequency and temperature; this is true also for the imaginary part of the rigidity or the dynamic viscosity. The real and imaginary parts of the rigidity, although independent measurements, are interrelated through the distribution function of relaxation times, and this relation provides a check on experimental results. First and second approximation methods of calculating the distribution function from dynamic data are given. The use of the distribution function to predict various types of time-depende...

Measurements of Mechanical Properties of Polyisobutylene at Audiofrequencies by a Twin Transducer

Apparatus has been developed for measuring the dynamic viscosity and rigidity of soft rubber‐like solids in small oscillating deformations. A plate rigidly attached between two identical coils in two permanent magnets shears a pair of disk‐shaped samples when a driving current is passed through one coil. The open circuit voltage from the other coil is compared in amplitude and phase with the driving current by a method in which all measurements are in the form of settings of a potential divider. The apparatus has two advantages over the more familiar resonance devices: (a) the amplitudes of motion, which need not be measured directly, are extremely small, thus minimizing any non‐linear effects, or temperature change due to heat dissipation; (b) a continuous range of frequencies, spaced as closely as desired, is available without adjusting masses. The dynamic rigidity and viscosity of two samples of polyisobutylene, of molecular weights 1.2 and 0.47 million, have been measured at 15, 25, and 35°C at freque...

Dielectric properties of the system polyvinyl chloride-dimethylthianthrene

Abstract A method is described for determining the dielectric behavior of liquids, gels, and solids at frequencies from 15 to 15,000 cycles/sec., and over a temperature range from −100 to +150°C. Included in the range of sample types are those of a gelatinous nature obtained by dissolving small amounts of polymer in plasticizer. The variation of complex dielectric constant with frequency and temperature for polyvinyl chloride (PVC) combined with dimethylthianthrene (DMT) is given for 0, 10, 20, 40, 60, 80, and 100% PVC by volume, and the apparent activation energy for dipole rotation is determined as a function of the pure plasticizer and low polymer concentrations indicates that a polar plasticized polymer. In view of the data presented here, and that cited for PVC plasticized with di-2-ethylhexylphthalate and tricresyl phosphate, it is concluded that the dielectric dispersion observed in a polar polymer combined with a polar plasticizer is a result of dipole rotation of the plasticizer molecule together with dipole rotation of chain segments of the polymer . The relative importance of each type of rotation will depend on the relative concentrations of polymer and plasticizer and the magnitude of their permanent dipole moments. Dipole-dipole coupling between plasticizer and polymer may also play a part in determining the dielectric dispersion in plasticized polymers.

Dynamic Mechanical Properties of a Carbon Black-Loaded Butyl Rubber Vulcanizate and a Carbon Black-Loaded Polyisobutylene

Abstract The dynamic mechanical properties of rubbers loaded with carbon black have been the subject of many investigations because of their importance in the performance of products, especially the energy dissipation, skid resistance, and other properties of vehicle tires. However, the important variables of frequency and temperature in oscillating deformations have usually been explored in fragmentary fashion. In particular, the degree to which these variables can be treated with frequency-temperature superposition appears to differ considerably depending on the type of compound investigated. In many cases, data have been insufficient to establish whether the essential criterion for superposition, namely, the same temperature dependence for all relaxation mechanisms, is satisfied. For this purpose, extensive measurements over wide ranges of closely spaced frequencies and temperatures are required. Such data are needed, in any case, to determine the responses of elements of a vehicle tire over the ranges...

Response of Carbon Black-in-Oil to Low-Amplitude Dynamic Stress at Audiofrequencies

Abstract The results reported here demonstrate the feasibility of investigating the dynamic mechanical properties of carbon black-agglomeration networks over wide ranges of temperature and frequency by measurements on carbon black mixed with oil. From the data displayed in Figures 3, 4, 5, and 6, it is evident that the general levels of audiofrequency elastic compliance and modulus, J′ and G′, change more than two orders of magnitude as the temperature is varied between − 12.2 and 50.6°C; the general levels of loss compliance and loss modulus, J″ and G″, change almost as much. A comparison of measurements at 25.2°C made at the beginning and after the conclusion of the measurements at various temperatures (Figure 7) shows little change except for an increase in low frequency values of J″ which are tentatively ascribed to water absorption due to condensation within the sealed measurement apparatus at low temperatures. From this close agreement of before and after compliance values, it is concluded that the ...