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The common condensation polymers and the reactions by which they are formed are shown in Table 1-1. It should be noted from Table 1-1 that for many of the condensation polymers there are different combinations of reactants that can be employed for their synthesis. Thus polyamides can be synthesized by the reactions of diamines with diacids or diacyl chlorides and by the self-condensation of amino acids. Similarly, polyesters can be synthesized from diols by esteri cation with diacids or ester interchange with diesters. Some naturally occurring polymers such as cellulose, starch, wool, and silk are classi ed as condensation polymers, since one can postulate their synthesis from certain hypothetical reactants by the elimination of water. Thus cellulose can be thought of as the polyether formed by the dehydration of glucose. Carothers included such polymers by de ning condensation polymers as those in which the formula of the repeating unit lacks certain atoms that are present in the monomer(s) from which it is formed or to which it may be degraded. In this



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In the next section we review the canonical quantization method. This is one of the finest "wines" in physics. To help even newcomers appreciate it fully, we establish the connection with the more familiar elementary quantum mechanics formalism by using canonical quantization to derive the SchrOdinger equation description of a nonrelativistic particle from classical mechanics. In Section 2.2 we explain why it is only the radiation field, rather than the total field, that is quantized. In Section 2.3 we review cavities. Rather than just presenting a formal calculation of cavity modes (such a calculation is done in Appendix A), we discuss the idea of a cavity or resonator and the physics it involves. We start with an elementary introduction to the phenomenon of resonance. Then we go on to show how the features we associate with resonators emerge when an oscillating field is confined spatially. The actual quantization is done in Section 2.4 for a perfect cavity (2.4.1) and for free space (2.4.2). In Section 2.5 we discuss an amazing effect of the free field that can be regarded as a direct consequence of the quantum nature of light and of its vacuum having zero-point energy: the Casimir force. In this free tasting all the wines are quite traditional. If, as I do, you like to sample some of the alternative wines, make sure not to miss 3. If nothing else, that free tasting of alternative wines will at least change forever the way you think about the Dirac equation for the electron.





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pressure as a 1-molal solution of a polymer of molecular weight 103 or a 1-molal solution of a small molecule such as hexane. M n is de ned as the total weight w of all the molecules in a polymer sample divided by the total number of moles present. Thus the number-average molecular weight is

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Dirac remarked once [158] that there was a time during the development of quantum mechanics when even the average physicist could do outstanding work. According to him, this happened because of his discovery of a rule for going from classical to quantum mechanics. Then people could play a little game, where they could take the various classical models of dynamical systems and transform them into the new quantum mechanics. This game, called canonical quantization, is what we review here. One of the most striking features of quantum mechanics is that it requires an algebra that differs from the one we are used to from classical physics: an algebra where dynamical variables in general do not commute. So the main hurdle someone faces when trying to construct a quantum version of a classical theory is how to generalize the classical theory to include noncommutability. Dirac realized that Hamilton's formulation of classical mechanics is in a form that makes adoption of noncommutability extremely easy. He noticed that the Poisson brackets,4 in terms of which Hamilton's formulation becomes simpler, have the same algebra as that of the commutators of quantum mechanics. So he saw that he could obtain the quantum equations for vir-

P w Nx Mx Mn P P Nx Nx 1-15

4If you are not familiar with Poisson brackets. have a look at the recommended reading at the end of the chapter. Even if you are already familiar with Poissonian brackets. the historical accounts might be worth reading.

where the summations are over all the different sizes of polymer molecules from x 1 to x 1 and Nx is the number of moles whose weight is M x . Equation 1-15 can also be written as

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