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These rates, however, did not approach the inflation rates of the 1920 s in spite of the new devaluation of the mark and the division and destruction of the country During the 1950 s, West German short rates declined irregularly at a time when short rates were rising in America and England, although West German bond yields were far above American bond yields After 1960, the West German government and Bundesbank, the central bank, adopted a very dynamic interest-rate policy to cope with twin and conflicting objectives: to prevent a rapid rise in the international value of the mark and to control the rate of inflation The official discount rate was moved frequently and substantially up and down: 3% low, 71 2% high Short-term rates averaged below 4% in the 1960 s, about 6% in the 1970 s, and somewhat over 6% in the 1980 s.

Thus the practical aspect of a polymerization requires one to carry out the process to obtain a compromise molecular weight a molecular weight suf ciently high to obtain the required strength for a particular application without overly sacri cing other properties Synthesizing the highest possible molecular weight is not necessarily the objective of a typical polymerization Instead, one often aims to obtain a high but speci ed, compromise molecular weight The utility of a polymerization is greatly reduced unless the process can be carried out to yield the speci ed molecular weight The control of molecular weight is essential for the practical application of a polymerization process When one speaks of the molecular weight of a polymer, one means something quite different from that which applies to small-sized compounds Polymers differ from the smallsized compounds in that they are polydisperse or heterogeneous in molecular weight.

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Even if a polymer is synthesized free from contaminants and impurities, it is still not a pure substance in the usually accepted sense Polymers, in their purest form, are mixtures of molecules of different molecular weight The reason for the polydispersity of polymers lies in the statistical variations present in the polymerization processes When one discusses the molecular weight of a polymer, one is actually involved with its average molecular weight Both the average molecular weight and the exact distribution of different molecular weights within a polymer are required in order to fully characterize it The control of molecular weight and molecular weight distribution (MWD) is often used to obtain and improve certain desired physical properties in a polymer product Various methods based on solution properties are used to determine the average molecular weight of a polymer sample.

d bent the nail into a general question mark shape, the head of the nail at the bottom. Clamping the nail in a vise, head up, I went at it with a large file. My aim was to turn the head into a small triangle shape, a shape that would fit the equilateral triangular recess in the odd screws holding my next bending project closed. After about 20 minutes of filing, removing the nail to test the fit, and filing again, I finally ended up with a tool that should remove these weird screws. Holding the hook of the question mark as a handle, I placed the filed nail head into a screw s triangular hole. Good fit. Feeling quite confident, I turned the new tool to loosen the oddball fastener and promptly stripped the nail head into a nice cylinder as it slipped around and around in the stubborn screw. Knowing that I could have just gone out and bought a set of security drivers with assorted unusual heads would have been nice. Knowing that some security screws unscrew clockwise would have been even nicer.

These West German rates were usually lower and more stable from year to year than short rates in most other nations German bond yields averaged above the German short rates quoted almost all the time since the 1850 s An exception was the inflation years of 1922 1923, when there were spectacular short rates The differential widened in the 1930 s and 1940 s It narrowed somewhat in the 1950 s and 1960 s but remained very wide, at about 300 basis points In the 1970 s and 1980 s the differential narrowed further as short rates increased more than long rates did The German money market recovered from the effects of two disastrous wars and two inflations more rapidly than did the German investment market for long-term bonds In the 1970 s and 1980 s, West Germany s relative financial stability completed the recovery of the long-term market.

These include methods based on colligative properties, light scattering, and viscosity [Heimenz, 1984; Morawetz, 1975; Slade, 1998; Sperling, 2001] The various methods do not yield the same average molecular weight Different average molecular weights are obtained because the properties being measured are biased differently toward the different-sized polymer molecules in a polymer sample Some methods are biased toward the larger-sized polymer molecules, while other methods are biased toward the smaller-sized molecules The result is that the average molecular weights obtained are correspondingly biased toward the larger- or smaller-sized molecules The following average molecular weights are determined: 1 The number-average molecular weight M n is determined by experimental methods that count the number of polymer molecules in a sample of the polymer.

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