Compressibility measurements, polymer

The compressibility of polymers is strongly nonlinear at pressures of a few GPa. In order to consider the nonlinearity of the piezoelectric effect at shock pressure, it is of interest to consider the piezoelectric polarization in terms of the volume compression as shown in Fig. 5.9. The pressure-versus-volume relation for PVDF is not accurately known, but the available data certainly provide a relative measure of changes in compressibility. When considered versus volume, the piezoelectric polarization is found to to be remarkably linear. Thus, large volume compression does not appear to introduce large nonlinearities. Such a behavior will need to be considered when the theory of piezoelectricity for the heterogeneous piezoelectric polymer is developed. 

Using Eq. (10), the measured average shift of -0.9 MHz/hPa and a solvent shift for a pentacene molecule in the center of Oj of -1745 cm (the So( Aig) —> Si( B2u) absorption of pentacene in a supersonic jet is at 18628 cm [38]), a compressibility K = 0.086 0.009 GPa is obtained. This value is about hdf of the compressibility of polymers (like polyethylene, polystyrene) at low temperatures. Sesselman et al. [34] measured a spectral shift for pentacene in polymethylmethacrylate (PMMA) of -0.33 + 0.02 cm /MPa ( —0.99 MHz/hPa) using holeburning. The mechanically measured, low temperature compressibility of PMMA is 1.5 times larger than the compressibility we calculated for p-terphenyl. This difference is approximately compensated by the different solvent shifts of pentacene in the two matrices, resulting in a similar pressure shift in Eq. (10). 

The stationary brushes are likely to interpenetrate each other. On similar PLL-g-PEG layers, a comparison of brush—brush and brush—hard-wall experiments revealed a significant overlap of the opposing brushes at the onset of measurable repulsion. On the basis of stochastic dynamics simulations, Neelov et al. predict that at low compressions the polymer brushes interpenetrate only in the outermost region next to the interface. At high compressions and zero shear rates, the polymer chains completely interpenetrate each other. However, a shear motion of the two brushes will result in a shear alignment of the chains and a reduced interpenetration of the brushes. 

In addition to the foregoing, mention should also be made of the pioneering work of Bridgman [19], who made rough compression measurements of a number of commercial plastics, and of Kovacs [20], who presented coefficients of thermal expansion for a number of polymers. 

Thermomechanical analysis has been used for softening measurements of polymers as well as the measurement of the amount of probe penetration into a polymer at a particular applied force as a function of temperature. This technique allows evaluation of T and the assessment of dimensional properties over the temperature range of use or under actual accelerated condition cycles (plots of temperature vs. compression (measure in mm)). The Fisher-Johns method has been applied for the determination of T . 

Although there have been several studies of compression of polymers at equi-librium, 2 measurements of volume creep are rather sparse. In the most extensive study on polystyrene by Goldbach and Rehage, normalized curves like Hg. 18-2 were obtained at 91.84", 92.77 , and 95.46 they were very similar in shape and their positions on the logarithmic time axis corresponded to a shift with temperature of d log t/dT = 0.38 d . (The reciprocal, dT/d log t = 2.6 deg, agrees well with the expectation from the WLF equation near Tg as expressed by equation 28 of Chapter 11.) The form of the distribution function of bulk retardation times, calculable from Fig. 18-2 by the methods of Chapter 4, is thus independent of teniperature within this range and the method of reduced variables is applicable. 

Adiabatic compressibility measurements have been performed on a number of polymer-solvent systems and have allowed indentification of specific interactions between polymer and solvent as in poly(ethylene oxide)-water or alcohol mixtures, effects of branching as in polyisobutene in hydrocarbon mixtures and helix-coil phenomena in polystyrene and polyether. ... 

Closely related to the issue of preferential curvature is the relation between curvature and interface width. The osmotic compressibility of polymer blends containing solvent enables the reduction of Laplace pressure by adjusting concentration differences between the two sides of the interface, but also by reduction of the interface tension by absorption of solvent at the interface. Curvature might have to be treated as a separate thermodynamic variable (besides interface area, [48]), which leads to the conclusion that measurements of the interface tension using different shapes of the interfaces or different ways of relaxation of the interface shape should be compared with each other with caution. 

Creep tests require careful temperature control. Typically, a specimen is loaded in tension or compression, usually at constant load, inside a furnace which is maintained at a constant temperature, T. The extension is measured as a function of time. Figure 17.4 shows a typical set of results from such a test. Metals, polymers and ceramics all show creep curves of this general shape. 

It has been shown [56] that if we measure the areas under the approach and retract curves of the force-distance plot we can get quantitative values of the resilience. Resilience is closely related to the ability of the polymer chain to rotate freely, and thus will be affected by rate and extent of deformation, as well as temperature. Different materials will respond differently to changes in these variables [46] hence, changing the conditions of testing will result in a change in absolute values of resilience and may even result in a change in ranking of the materials. Compared to more traditional methods of resilience measurement such as the rebound resiliometer or a tensUe/compression tester. 

FIGURE 1 Rate of polyanhydride degradation versus time. PCPP and SA copolymers were formulated into 1.4-cm-diameter disks 1 mm thick by compression molding, and placed into a 0.1 M pH 7.4 phosphate buffer solution at 37°C. The cumulative percentage of the polymer which degraded was measured by absorbance at 250 nm. 

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