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Equations 3-13 through 3-19 constitute the detailed mechanism of a free-radical-initiated chain polymerization. The chain nature of the process resides in the propagation step (Eq. 3-15) in which large numbers of monomer molecules are converted to polymer for each initiating radical produced in the rst step (Eq. 3-14). In order to obtain a kinetic expression for the rate of polymerization, it is necessary to assume that kp and kt are independent of the size of the radical. This assumption is inherent in the notation used in Eqs. 3-15 through 3-18. It is exactly the same assumption the equal-reactivity assumption that was employed in deriving the kinetics of step polymerization. Very small radicals are more reactive than propagating radicals, but this effect is not important because the effect of size vanishes at the dimer or trimer size [Gridnev and Ittel, 1996; Kerr, 1973]. There are limitations to the equal-reactivity assumption with respect to the sizes of propagating radicals, and this is discussed in Secs. 3-10 and 3-11b.

3-180

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anada provides very little autonomous interest-rate history. In the nineteenth century, there was little or no organized bond market in Canada. The country was then being developed by foreign capital, chiefly English. A period of very rapid growth from 1900 until World War I was also financed largely by the influx of some $2.5 billion of foreign capital, over half of it from London. After 1914, Canada turned briefly to New York to help finance war requirements. When the United States entered the war in 1917, Canada was for the first time forced to rely on her own financial resources. (538) Canada s war effort was large. She supplied some 640,000 troops for World War I, which cost her $1.5 billion. The Victory Loan campaigns at 5% and 51 2% led to the development of a domestic bond market. In the drive of October 1918, more than 1 million people subscribed $700 million. Before this time, Dominion of Canada bonds were largely sterling obligations, and their rates belong to the history of the English market rather than to that of the Canadian market. Although there was a local market for Canadian provincial obligations before World War I and a local market for Dominion obligations after World War I, both markets were very limited until World War II. A Canadian money market was an even later development. The Bank of Canada was not organized until 1935. It was not until the 1950 s that a modern money market based on a day-to-day credit was organized. Canada, which achieved a large measure of political independence in 1867, when the British North America Act created the Dominion, was late in achieving financial independence. No doubt the enormous opportunities

3-181

Theoretical considerations indicate that kc would be very large, about 8 109 L mol 1 s 1 , in low-viscosity media (such as bulk monomer) for the reaction between two radicals. The rate constants for reactions of small radicals (e.g., methyl, ethyl, propyl) are close to this value (being about 2 109 L mol s 1 ) [Ingold, 1973]. Experimentally determined kt values for radical polymerizations, however, are considerably lower, usually by two orders of magnitude or more (see Table 3-11). Thus diffusion is the rate-determining process for termination, kc ) k4 , and one obtains

Pressed (contacts are closed)

Rt k1 k3 M 2 k2 k3 3-182

afforded for profitable investment in Canada so far exceeded the local savings of a small population that dependence on foreign capital seemed natural and inevitable. The lack of an early Canadian interest-rate history is no doubt due to the same conditions that deprived the American colonies of much of an interest-rate history. The land was primitive, but the people were not. They brought with them the sophisticated financial techniques of modern Europe and employed them as rapidly as their financial resources would permit. In the meantime, they financed in London and New York. When local Canadian markets and rates of interest finally emerged, they provided no novelties. The credit forms were the familiar ones of Europe and America. The range of interest rates, similar to that of the other countries studied, tended to be moderately higher than interest rates in the United States. Canada has been accorded a separate chapter here, not because her interest rate history has been novel or important, but because her markets are now rapidly achieving independence and importance. Before the organization of the Dominion, Canadian sterling obligations sold at high yields in the London market. In 1860 Canada Consolidated Sterling 5s were floated in London, to yield 5.12%, which was 191 basis points more than the prevailing yield on British consols. A few years later British Columbia and Vancouver Island brought out sterling 5s. After 1867, the obligations of the new Dominion commanded lower yields. Quotation on a sterling issue of Canada 5s due in 1903, and not guaranteed by the government of the United Kingdom, provided market yields as follows, at annual high prices: (539)

by assuming steady-state concentrations of both XXXVIII and XXXIX. Two limiting cases of termination arise. For the case of slow translational diffusion, k3 ) k2 , and

Rt k1 M 2 3-183

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