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Gelation was studied as a function of concentration and the results extrapolated to in nite concentration where intramolecular reactions would be expected to be nil The experimental pc value of 0:578 0:005 compared exceptionally well with the theoretial value of 0577 The value of pc calculated by the Carothers equation is 075 for this system In many reaction systems the difference between the observed pc values and those calculated from Eq 2-148 are at least partially ascribed to the failure of the assumption of equal reactivity of all functional groups of the same type An example is the glycerol-phthalic acid system previously mentioned The difference between the calculated and observed values of pc (0709 vs 0765) would be decreased, but not eliminated, if the calculation were corrected for the known lower reactivity of the secondary hydroxyl group of glycerol.

Parts Open It Up! Circuit at First Glance Step-by-Step Bending Choosing a Cool Control Layout Case Considerations Marking the Board Drilling Holes Painting Control Mounting Soldering Testing 277 278 278 279 279 279 280 280 280 280 280 281.

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It is dif cult to nd crosslinking systems that are ideal in that all functional groups are of equal reactivity and intramolecular cyclization is negligible The crosslinking of vinyl terminated poly(dimethylsiloxane) polymers with tri- and tetrafunctional silanes appears to be an exception Thus the calculated and experimental pc values were 0578 and 0583, respectively, for the tetrafunctional silane and 0708 and 0703, respectively, for the trifunctional silane (with r 0:999) [Valles and Macosko, 1979] Although both the Carothers and statistical approaches are used for the practical predication of gel points, the statistical approach is the more frequently employed The statistical method is preferred, since it theoretically gives the gel point for the largest-sized molecules in a size distribution From the practical viewpoint the use of the Carothers approach alone can be disastrous, since the Carothers approach always predicts a higher pc than observed.

Crosslinked polymer becomes intractable above pc ; the reaction must be stopped at an extent of reaction below pc before starting the technological step of fabricating the polymer into the shape of nal desired product (see Sec 2-12) Further, the statistical approach offers a greater possibility of adaption to various systems of reactants as well as the inclusion of corrections for the nonapplicability of the equal reactivity assumption and the occurrence of intramolecular reactions Equation 2-148 and its modi cations have been used extensively in the technology of crosslinked polymers..

Federal Funds rate, in the Eurodollar market To the extent that such key interest rates follow inflation rates, there is little difference between variable- or floating-rate financing and inflation indexing A NOTE ON CORPORATE BOND YIELD AVERAGES AND INDICES The prevailing market yields for the best bonds of well-defined types and terms are usually known within a narrow range each day by contemporary bond dealers and professional investors Nevertheless, the construction of a time series tracing the history of these market yields over long periods presents difficulties Economists sometimes ask the impossible: a series of yields or interest rates over long periods of time derived from instruments of substantially identical terms and quality that fulfill the same economic function in the same way in one decade as in another The.

The statistical approach has been applied to systems containing reactants with functional groups of unequal reactivity [Case, 1957; Macosko and Miller, 1976; Miller and Macosko, 1978; Miller et al., 1979]. In this section we will consider some of the results for such systems. Figure 2-15 shows a plot of M w vs. extent of reaction for the various values of s at r 1 for the system

Fig. 2-15 M w versus extent of reaction for polymerization of A3 with B B0 for different s values. After Miller and Macosko [1978] (by permission of American Chemical Society, Washington, DC).

objectives of some forms of economic analysis require just this uniformity In real life it often does not exist, even from year to year At the outset of this history, it was made clear that the security behind the rates quoted for various times or places could not always be uniform Such comparability over time as the principal series provide is derived from the attempt to compare rates on only the most highly regarded credits of their type at each time and place The lowest acceptable market yields at one point of time are compared with the lowest acceptable market yields at another point of time, provided that terms are similar and prices are not distorted by extraneous circumstances These prime rates are treated as comparable limits An important attempt was made by Frederick R.

Reassembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Musicality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

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