Observable modulus

Molecular orientation and the testing direction strongly influence the observed modulus of a polymer sample. Fibers are typically highly oriented and exhibit much higher modulus values than non-oriented samples prepared from the same polymer. In the case of films, we typically observe anisotropy a film exhibits a range of modulus values depending upon the testing direction. 

Paul Weisz suggested in a lucid note published in 1973 that cells, and indeed even entire organisms, have evolved in a way that maintains unity effectiveness factor [24]. That is, the size of the catalytic assembly is increased in nature as the overall rate at which that assembly operates decreases, and the relationship between characteristic dimension and activity can be well approximated by the observable modulus criterion for reaction limitation. It is possible that Weisz s arguments may fail under process conditions, and internal gradients within a compartment or cell may be important. However, at present it appears that the most important transport limitations and activities in cells are those that operate across cellular membranes. Therefore, to understand and to manipulate key transport activities in cells, it is essential that biochemical engineers understand these membrane transport processes and the factors influencing their operation. A brief outline of some of the important systems and their implications in cell function and biotechnology follows. 

Figure 23. Relative selectivity A. 2,i of a Type II reaction (first and zero order) plotted against the observable modulus

When constructing a master curve, one arbitrarily picks a reference temperature, T0. (Instead of T0, many authors choose to use Tr to signify the reference temperature.) The modulus at any time t, which one would observe at the temperature T0 in terms of the experimentally observed modulus values at different temperatures T, is therefore given as... 

Although the reinforcement by aromatic polyamides was remarkable, the composites prepared by these researchers were not molecular. As mentioned above, the molecules were coagulated into microfibrils of 15 un. 30 nm in thickness. Using the Halpin-Tsai equation modified by Nielsen (1975) and the modulus values of Ei = 0.91 GPa and E2 = 182 GPa for nylon 6 and PPTA as well as the observed modulus of the composites, the calculated L/D ratio was 15 for low molecular weight PPTA and 25 for high molecular... 

Figure 3.6.C-I Effectiveness factor plot in terms of observable modulus. 

Lee and Luss also presented results for the maximum surface-to-interior temperature difference. Recall from Eq. 3.6.C-4 that the observable modulus can also be written in terms of the usual modulus and effectiveness factor ... 

Figure 7.4 Effectiveness factor as a function of the Weisz (observable) modulus ( nd also the Thiele modulus ).

Figure 20.2 Effectiveness factor vs. the observable modulus (f> for immobilized enzyme catalysts with Michaelis-Menten intrinsic kinetics (/ = [i4]j,/AfM) (Bailey and Ollis, 1986)...

The per chain modulus of this pol3nner is about equal to that of diamond in the [110] direction. A polyethylene fiber with the same per chain mechanical properties would have an ultimate tensile strength in excess of one million psi. The theoretical modulus calculated for a defect free polydiacetylene chain using a spectroscopic force field is within 10% of the observed modulus. This contrasts with the case for conventional polymers, where the bulk tensile modulus is typically much less than 50% of the theoretical (spectroscopic) modulus. 

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