Simha

Simha equation), where a/b is the length/diameter ratio of these cigarshaped particles. Doty et al.t measure the intrinsic viscosity of poly(7-benzyl glutamate) in a chloroform-formamide solution and obtained (approximately) the following results ... 

Use the Simha equation and these data to criticize or defend the following proposition These polymer molecules behave like rods whose diameter is 16 A and whose length is 1.5 A per repeat unit. The molecule apparently exists in fully extended form in this solvent rather than as random coils. 

The spherical geometry assumed in the Stokes and Einstein derivations gives the highly symmetrical boundary conditions favored by theoreticians. For ellipsoids of revolution having an axial ratio a/b, friction factors have been derived by F. Perrin, and the coefficient of the first-order term in Eq. (9.9) has been derived by Simha. In both cases the calculated quantities increase as the axial ratio increases above unity. For spheres, a/b = 1. 

In the last section we noted that Simha and others have derived theoretical expressions for q pl(p for rigid ellipsoids of revolution. Solving the equation of motion for this case is even more involved than for spherical particles, so we simply present the final result. Several comments are necessary to appreciate these results ... 

Based on these ideas, the intrinsic viscosity (in 0 concentration units) has been evaluated for ellipsoids of revolution. Figure 9.3 shows [77] versus a/b for oblate and prolate ellipsoids according to the Simha theory. Note that the intrinsic viscosity of serum albumin from Example 9.1-3.7(1.34) = 4.96 in volume fraction units-is also consistent with, say, a nonsolvated oblate ellipsoid of axial ratio about 5. 

Figure 9.3 Intrinsic viscosity according to the Simha theory in terms of the axial ratio for prolate and oblate ellipsoids of revolution.

Using 1.32 g cm as the density of the polymer, estimate the axial ratio for these molecules, using Simha s equation ... 

R. Simha, "Degradation of Polymers," in Polymerisation andPoljcondensation Processes, No. 34, Advances in Chemistrj Series, American Chemical Society, Washington, D.C., 1962, p. 157. 

Where Ua-b is a molecular shape (Simha 1940) parameter known as viscosity increment and... 

The viscosity increment Ua-b is referred to as a universal shape fimction or Simha number (table 4) it can be directly related to the shape of a particle independent of volume. For its experimental measurement it does however require measurement of Usp, v, 5, po, as well as of course [rj]. 

Simha, R. The Influence of Brownian Movement on the Viscosity of Solutions. J. Phys. Chem. 44, (1940) 25-34. 

The viscosity increment was determined as v = B v = 172.7 ( 2 5 for spheres) where B is the viscosity coefficient characteristic of a given solue-solvent pair, and amounts to (9.91 0.24)xl0" ff/ A g" for PGA in aqueous solution. is the partial specific volume of the macromolecular component equal to [Pg.612]

Simha [53] made the first attempts to model the transition from a dilute to a concentrated solution. He assumed that in the range from lscaling laws a theory has been developed which allows for the prediction of the influence of Mw c and the solvent power on the screening length [54,55]. This theory is founded on the presumption that above a critical concentration, c, the coils overlap and interpenetrate. Furthermore it is assumed that in a thermody-... 

Professor Mark s story is told in three chapters by the Editor and four reminiscences by Rudolf Brill (whose association with Mark dates back to 1922), Hans Mark (his son), Linus Pauling, and Maurice Morton. The history of polymer science is given in separate chapters by the Editor, Robert Simha (who has worked with Professor Mark in two countries), and Carl Speed Marvel. One chapter by Charles Carraher gives an up to the minute report on the status of polymer education. The remainder of the book is a collection of reviews and previews of specific, timely topics in polymer science. Despite the diversity of topics, each area covered has contributions from Herman Mark. 

Guth, and R. Simha physical chemists F. Eirich, P. Gross,... 

I first approached my theoretition friend and co-worker of many years, R. Simha, for statistical-mechanical assistance, and we obtained further the cooperation of H. Frisch, then just completing his Ph.D. at the Polytechnic Institute. The model we evolved was that of a macromolecule in solution colliding first with one of its segnents with a solvent-solid interface, becoming adsorbed when a complicated set of energetics becomes negative. 

Most important, however, was the discovery by Simha et al. [152, 153], de Gennes [4] and des Cloizeaux [154] that the overlap concentration is a suitable parameter for the formulation of universal laws by which semi-dilute solutions can be described. Semi-dilute solutions have already many similarities to polymers in the melt. Their understanding has to be considered as the first essential step for an interpretation of materials properties in terms of molecular parameters. Here now the necessity of the dilute solution properties becomes evident. These molecular solution parameters are not universal, but they allow a definition of the overlap concentration, and with this a universal picture of behavior can be designed. This approach was very successful in the field of linear macromolecules. The following outline will demonstrate the utility of this approach also for branched polymers in the semi-dilute regime. 

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