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where A and B are the two different types of functional groups. The characteristics of these two polymerization reactions are very similar. The successful synthesis of high polymers (i.e., polymer of suf ciently high molecular weight to be useful from the practical viewpoint) using any step polymerization reaction generally is more dif cult than the corresponding small molecule reaction, since high polymers can be achieved only at very high conversions (>98 99%). A conversion of 90%, which would be considered excellent for the synthesis of ethyl acetate or methyl benzamide, is a disaster for the synthesis of the corresponding polyester or polyamide. The need for very high conversions to synthesize high polymer places several stringent requirements on any reaction to be used for polymerization a favorable equilibrium and the absence of cyclization and other side reactions. These stringent requirements are met by a relatively small fraction of the reactions familiar to and used by chemists to synthesize small molecules. An additional requirement for achieving high molecular weights is the need for the A and B functional groups to be be present at very close to stoichiometric amounts.



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But there are also radio photons So why is it that quantum noise is not a problem for mdio, where the classical wave description seems to work very well The answer is that the amount of quantum noise depends on how much energy a photon carries As this energy is proportional to the frequency, radio photons carry much less energy than do light photons So a mdio coherent state can already be regarded as a classical wave at much lower intensities than it would be possible to regard a light coherent state as a classical wave In fact, at room temperature, for radio, 1iw is much smaller than kT (Le, the Boltzmann constant times the absolute temperature), showing that thermal noise is much more of an issue for radio than is quantum noise For light, the situation is inverted (ie, 1iw kT).

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Light can still be used for communication, indeed, it is actually already being used in many fiber optic telephone and data networks For these engineering applications, it can basically be regarded as a very noisy high-frequency classical radio wave There is, however, a way to take more out of light: a way to reduce the quantum noise effectively so that we are able to do with it the same things that we can do with low-noise mdio waves This section is about this way of effectively reducing quantum noise There are applications for this not only in communications, where it increases the channel capacity, but also in optical measurements, where it increases the precision The idea is that for radio communications and many interferometric measurements, one does not use the entire complex wave amplitude, only its real or its imaginary part (or any arbitrary quadrature, see Section 424).

The evidence for this mechanism is based on mass spectroscopy of the gas-phase radiolysis of isobutylene, which may not be applicable to the typical liquid-phase polymerization system. Initiation in condensed systems may follow the same course as electroinitiation coupling of radical cations to form dicarbocations.

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For a single mode, these are Hermitian opemtors proportional to what we call quadmtures of d, (456) and (457) respectively So all that we have to do is to decrease the noise (Le, the variance) in the required quadrature As the uncertainty relation involves the product of the variances in each of two complementary quadratures Gust as q and p in Section 24), reducing the variance of only one of them will not violate quantum mechanics, because the variance in the other quadrature is free to increase In the next subsection we introduce quantum states with such a reduced noise in one of the quadratures In Section 422 we discuss a way of generating these states Then in Section 423, we present a nice way of visualizing them Finally, in Section 424, we discuss how they can be measured..

Cationic polymerization initiated by ionizing radiation is markedly different from other cationic polymerizations in that the propagating species is a free ion remote from a counterion. Overall electrical neutrality is maintained by electrons trapped by the monomer.

For a single mode, we can define dimensionless position (4.58)

The initiator ion pair (consisting of the carbocation and its negative counterion) produced in the initiation step (Eq. 5-4) proceeds to propagate by successive additions of monomer molecules

(4.60)

H CH2C(CH3)2 + (BF3OH) + (CH3)2C CH2 n H CH2C(CH3)2

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