Compressibility of polymers

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. 

One of them assumes the possibility of a compression of polymer coils at average concentrations down to the dimensions less than in the -solvent. The alternative is based on the existence of the wide distribution of macromolecule dimensions in any time.It is rather natural to assume an increase of the probability of intramolecular reaction with an increase of the dimensions of the macromolecule.. e. more extended conformations go to the gel-fraction and more coiled remain in the sol. With the increase of solution concentration the distances between coils are diminished and the critical dimensions, necessary for a transition into the gel are decreased too. This process will be accompanied by a decrease of the average dimensions of molecules in sol. 

Bioadhesive tablets can be made by the compression of polymers or can consist of a matrix base or bilayers, with an impermeable backing layer covering the layer with the drug and the mucoadhesion polymer. Examples of these systems are discussed below. 

Probably the most direct and, in principle, the most powerful method for determining the distance dependence of steric interactions is the compression of polymer chains attached to macroscopic objects as they undergo close approach. The most successful method to-date has unquestionably been the crossed mica cylinders technique. This was originated by Tabor and coworkers (Tabor and Winterton, 1969 Israelachvili and Tabor, 1972) and improved by Israelachvili and Adams (1976 1978). In the hands of Pashley and Israelachvili (1981), it has been successfully exploited to test the predictions of the Deqaguin-Landau-Verwey-Overbeek (DLVO) theory of electrostatic stabilization. It is also likely in the future to prove to be the most sensitive method for testing the predictions of theories for the distance dependence of steric interactions. 

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). 

Consider the phase diagram for a binary polymer-solvent mixture in which the solvent is roughly the size of one monomer unit (segment). Starting from a one phase mixture, a decrease in temperature can lead to separation into polymer-rich and polymer-lean phases at the upper critical solution temperature (UCST) phase boundary. In general a polymer solution also phase separates as temperature is increased to the lower critical solution temperature (LCST) phase boundary [40]. In near critical and supercritical fluids, the driving force for phase separation at the LCST phase boundary is the difference in the compressibility of polymer and solvent, which becomes large... 

The rest of the paper consists of two sepaurate Sections, respectively on the compression of polymer networks amd on polymer-mediated adhesion. The two may be read independently of each other. We sketch the mathematical derivations, which au e given more fully in refs.[12, 13], and try to emphasize the most significauit physicaJ results. 

Sheng, Y, Briscoe, B. (., Mating, R., Rovea, M. J., 2004. Compression of polymer bound alumina agglomerates at the micro deformation scale. Powder Technol. 140 228-239. 

Plastics are prepared by the melting, molding, extruding, or the compression of polymers. The word polymer implies a molecule consisting of a long chain of units of smaller molecules or monomers. Thus, the polymer is also called a macromolecule. Such large molecules exist in nature and common examples of these are cellulose, rubber, cotton, silk, wool, starch, and keratin. 

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. 

By combining the above relationships, the isothermal compressibility of polymers at Til can be calculated from the intrinsic molecular volume Vj, . However, the value of P at is necessary to estimate the light scattering loss in the glassy state, p increases linearly with T from to Tjj. It is interesting that the values of (1/ at between and Tn for many amorphous polymers are... 

Bulk Compressibility of Polymers at Fabricating Temperatures," with Shiro Matsuoka, S.P.E. JouAnaZ Feb. 1957. 

Figure 11 Variation of the adiabitic compressibility of polymer solutions with frequency...

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. 

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