Gilbert F. Lee

Loss factor height and width limits for polymer relaxations

Polymer relaxations at the glass transition are often used in damping applications. Questions arise whether there is any limit to the height and width of the damping peak that can be achieved. A related question is whether there are any limits on the combination of these two properties that are achievable. This later question arises because of the experimental observation that the height of the peak is inversely related to the width of the peak. In this paper, these questions are addressed using various analytical models of polymer behavior. Starting with the single relaxation time model and progressing to the Cole–Cole model, the Davidson–Cole model, and finally the Havriliak–Negami (HN) model, height and width predictions are obtained. It is found that the HN model predicts a band of physically possible height and width combinations when using reasonable values of the model parameters. High peaks are narrow and broad peaks are low. For a loss factor peak height of 2, the half‐width must be less than 3 d...

Polyurethane networks with controlled architecture of dangling chains

Network formation from A x + B y precursors (A + B → A - B) with functionality and molecular weight distributions is described by the statistical theory of branching processes. Network formation is described in terms of sol and gel fractions, dangling chains, elastically active network chains (EANC), elastically active crosslinks, free chain ends and branch points partitioned between sol and gel. Various definitions of an EANC are considered. The general relations are applied to a special case of A1 + A2 + A3/B2 system. It is show how the size and weight fractions of dangling chains can be varied indepently by varying the functionality or molecular weight distributions. This is demonstrated experimentally analyzing corresponding polyetherurethane networks prepared from mixtures of polyoxypropylene polyols. The width of the main transition region correlates with the fraction of material in dangling chains. The dependence of the equilibrium shear modulus on the concentration of EANCs indicates much weaker intermolecular interactions for networks with many short dangling chains compared with systems having few longer dangling chains.

DYNAMIC PROPERTIES OF POLYUREA 1000

The shock response of the viscoelastic polymer material polyurea 1000 has been investigated. Sabots carrying Al or Cu metal disks were launched into target assemblies containing the polyurea material. The target consisted of a thin metal disk on the impact side, a 6.5‐mm‐thick polyurea disk, and a thick metal backup disk. 50‐Ω manganin gauges were epoxied between the metal/polymer and polymer/metal interfaces to measure the interface stresses and shock transit time. Measured longitudinal stresses ranged from 6 to 43 kbar. The measured shock velocity‐particle velocity relationship was linear over this stress range. Maximum volume compression was about 30% for the initial shock wave. Several reshock waves were also measured for each experiment.

A method for modeling polymer viscoelastic data and the temperature shift function

Dynamic viscoelastic polymer data is traditionally time-temperature shifted to obtain a temperature shift function (TSF) and then fitted to various analytical models. The process of obtaining the TSF can introduce considerable procedural or operator bias. Nevertheless the Havriliak and Negami (HN) model using the TSF methodology can generally describe polymers that are rheologically simple. In this paper the “wicket” plot is utilized as an important tool in analyzing data, as it is completely independent of time-temperature shifting (TTS). Using the wicket plot the data is fit to the HN equation to determine the four material HN constants independent of TTS. Having obtained the complete spectra of dynamic properties the specific relaxation time (frequency) at each temperature is obtained by matching the HN curve to the experimental data at that temperature thus determining the TSF. The procedure is illustrated by analyzing computer-generated data with random error in modulus and loss and finally real data...

Dynamic mechanical relaxation in some polyurethanes

Abstract Dynamic mechanical measurements of complex shear modulus versus frequency and temperature were made on a series of polyurethanes of varying soft-segment molecular weight. The time-temperature shifted data (master curves) mapped out the soft-segment glass transition. Shift factor curves were fitted to the Williams-Landel-Ferry (WLF) equation to obtain shift constants. The fractional free volume and coefficient of thermal expansion at the glass transition, determined from the shift constants, decrease as the molecular weight increases. Master curves were fitted to the modified Havriliak-Negami equation and the fitting parameters related to molecular structure. The limiting low-frequency modulus is dependent on the soft-segment molecular weight and percent crystallinity, but the limiting high-frequency modulus is about the same for all these polymers. The average relaxation time decreases with increasing soft-segment molecular weight and is correlated with glass transition temperature.

Network structure dependence of volume and glass transition temperature

A series of polyurethanes was used to determine the molar contributions of chain ends (CE) and branch points (BP) to free volume and glass transition temperature Tg. The polyurethanes were copolymers of diphenylmethane diisocyanate and poly(propylene oxide) (PPO) with hydroxyl functionalities of one, two, and three. The equivalent weights of all the PPOs were equal, such that the chemical composition of the chain segments was essentially identical. Therefore, the only distinctions among polymers were differences in CE and BP concentration. Theory of branching processes computer simulations were used to determine the concentration of CE due to imperfect network formation. Other CE contributions were from the monofunctional PPO. Polymer volumes and Tgs were correlated to CE and BP concentrations, and the contributions of these species were determined from least squares fits. The molar volume and Tg contributions were then used to determine free volume thermal expansion coefficients. These values were compar...

Calculation of B/A for n-alkane liquids using the Tait equation

The B/A parameter of acoustic nonlinearity was calculated for a series of n-alkane liquids using the Tait PVT equation of state supplemented with specific heat data. The calculations of sound speed, sound speed derivatives, the two components of B/A, and the value of B/A itself were compared with experimental data taken from the literature and with earlier calculations using a different equation of state. In addition, a comparison of the results with Ballous rule (linear relation of B/A and reciprocal sound speed) was made. It is concluded that B/A can be calculated from the Tait equation of state with about the same accuracy as direct measurements of sound speed versus pressure and temperature, though the the temperature derivatives of the sound speed are calculated with much lower accuracy than pressure derivatives. The calculations made using the Tait equation are about the same accuracy as calculations made using our equation of state. Also, Ballous rule does not hold for these liquids.

THE EFFECT OF MECHANICAL DEFORMATION ON THE GLASS TRANSITION TEMPERATURE OF POLYUREA

The glass transition temperature (Tg) of a polyurea (Versathane P1000) is shown to be a function of mechanical strain and strain rate. For low strain rate (10−1/s), tensile testing, Tg values increase from −58 to −52 °C with strain. These results are interpreted as an increase in phase mixing. After annealing at 100 °C, the Tg decreases to a baseline value of −63 °C as an indication that the strain induced phase mixing is reversible. For one dimensional plate impact experiments, the Tg increases from −58 to −54 °C with strain. After annealing, the Tg value at the high strain level is about 4 °C higher than the baseline value. The impact may have caused some permanent change in the morphology. For a conical‐shaped steel impact experiment, Tg values also increase with strain from −58 to −50 °C. The Tg at the impact center after an annealing cycle is about 4 °C greater than the baseline value, indicating somewhat less than full reversal of the mixing.

Sound absorption height and width limits for polymer relaxations

An analysis was performed to relate the height and width of the peak in shear sound absorption per wavelength as a function of frequency for the glass transition of a polymer. For the single relaxation time model, the width is 1.14 decades only at small values of the ratio of relaxed to unrelaxed sound speed. For the larger values of sound-speed ratio observed in polymer glass transitions, the width increases as the height increases. For the Havriliak–Negami model, the width increases as the height decreases in a manner similar to that for the complex modulus, though in this case there is a cutoff below the absolute maximum. The curve can be described by the relation that height times width is 1.5 decades of frequency. These predictions are in good agreement with experimental data for 21 polyurethanes.

Resonance apparatus for damping measurements

The resonance apparatus was developed to characterize the damping properties of materials. The apparatus has been used extensively to determine Young’s modulus and loss factor of polymers in the kHz frequency range over a temperature range of -60 °C to 70 °C. However, very little work has been done in using the apparatus to characterize metallic materials. To demonstrate the limits of the instrument, measurements were made on a high damping material, an epoxy polymer, and a low damping material, aluminum. The loss factor for the epoxy polymer is 2.4, which is the highest value measured in this apparatus. The loss factor for the aluminum is 0.003, which is the lowest value measured in this apparatus. Based on the aluminum results, the accuracy and precision were found to be 2 pct for Young’s modulus. However, the accuracy and precision for loss factor were not as good as for the modulus.