Bueche

Based on this equation, one can make a Debye-Bueche plot by plotting [i (q)] versus q and detemiine the slope and the intercept of the curve. The correlation length thus can be calculated as [21]... 

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

Figure 2.13 Model of several orders of coupling through entanglements according to Bueche theory.

If this approach is to have any success, the weighting factors Cj must also decrease with increasing i to avoid a catastrophic increase in viscosity due to the proposed web of entanglements. We shall not detail the entire derivation of these C values as developed by Bueche but shall only note the following points ... 

Bueche was able to incorporate these ideas into a quantitative theory, the mathematical details of which need not concern us. The result is complex, but simplifies when applied to polymers of very large molecular weight. In this limit the Bueche theory predicts... 

Equation (2.61) predicts a 3.5-power dependence of viscosity on molecular weight, amazingly close to the observed 3.4-power dependence. In this respect the model is a success. Unfortunately, there are other mechanical properties of highly entangled molecules in which the agreement between the Bueche theory and experiment are less satisfactory. Since we have not established the basis for these other criteria, we shall not go into specific details. It is informative to recognize that Eq. (2.61) contains many of the same factors as Eq. (2.56), the Debye expression for viscosity, which we symbolize t . If we factor the Bueche expression so as to separate the Debye terms, we obtain... 

Bueche, F., Physical Properties of Polymers, Interscience, New York, 1962. 

Next let us consider the differences in molecular architecture between polymers which exclusively display viscous flow and those which display a purely elastic response. To attribute the entire effect to molecular structure we assume the polymers are compared at the same temperature. Crosslinking between different chains is the structural feature responsible for elastic response in polymer samples. If the crosslinking is totally effective, we can regard the entire sample as one giant molecule, since the entire volume is permeated by a continuous network of chains. This result was anticipated in the discussion of the Bueche theory for chain entanglements in the last chapter, when we observed that viscosity would be infinite with entanglements if there were no slippage between chains. 

We refer to this model as the bead-spring model and to its theoretical development as the Rouse theory, although Rouse, Bueche, and Zimm have all been associated with its development. 

Hollomon s ethos, combined with his ferocious energy and determination, and his sustained determination to recruit only the best researchers to join his group, over the next 15 years led to a sequence of remarkable innovations related to materials, including man-made diamond, high-quality thermal insulation, a vacuum circuit-breaker, products based on etched particle tracks in irradiated solids, polycarbonate plastic and, particularly, the Lucalox alumina envelope for a metal-vapour lamp. (Of course many managers besides Hollomon were involved.) A brilliant, detailed account of these innovations and the arrangements that made them possible was later written by Guy Suits and his successor as director, Arthur Bueche (Suits and Bueche 1967). Some of these specific episodes will feature later in this book, but it helps to reinforce the points made here about Hollomon s coneeption of broad research on materials if I point out that the invention of translucent alumina tubes for lamps was... 

Suits and Bueche conclude their case-histories with a superb analysis of the sources, tactics and uses of applied research, and make the comment The case histories just summarised show, first of all, the futility of trying to label various elements of the research and development process as basic , applied or development . Given almost any definition of these terms, one can find variations or exceptions among the examples. ... 

Suits, C.G. and Bueche, A.M. (1967) in Applied Science and Technological Progress A Report to the Committee on Science and Astronautics, US House of Representatives, by the National Academy of Sciences (US Government Printing Office, Washington, DC) p. 297. 

Burke, and also Suits and Bueche (1967), tell the history of the evolution of pore-free, and hence translucent, polycrystalline alumina, dating from the decision by Herbert Hollomon at GE (see Section 1.1.2) in 1954 to enlarge GE s research effort on ceramics. In 1955, R.L. Coble Joined the GE Research Center from MIT and... 

One of the most successful attempts to include the effects of temperature in a relatively simple expression similar to the one above, has been made by Zhurkov and Bueche using an equation of the form... 

The same effect happens inside a random flight chain where the close proximity of the polymer segments offers mutual screening from the bulk flow field. The idea of a chain being non-drained was first considered by Debye Bueche who introduced the concept of a shielding length defined as [46] ... 

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