Staudinger’s equation

At about the same time, Staudinger derived his well known "law of viscosity". His work was formulated in 1929 and published in 1930 (34, 35). Also based on the Einstein relationship, Staudinger s equation was a direct relationship between the specific viscosity and the polymer molecular weight. 

The first probable values for the molecular size of the native pectins from apple and sugar beet were obtained by Schneider and co-workers.71 These workers prepared the nitro- and acetyl-derivatives in order to avoid the anomalous behavior due to charge effects which occurred using the unsubstituted polysaccharides. From osmotic and viscometric measurements on the nitrate, values for the molecular weight of 30,000-100,000 were found, the constant Km in Staudinger s equation being 6(10)-4. Viscometric measurements indicated that there was little difference in size between the two derivatives. 

K. H. Meyer and v. d. Wyk Tables 85 and 86 give some important results. From them it is evident that Staudinger s equation... 

The experimental material which has been drawn on for proving this relation in the field of hemi- and eu-colloidal substances is very extensive the particle weights measured osmotically by various authors have been compared with those calculated from equation (105) and it has been found in this field also that Staudinger s equation is certainly of considerable importance in the approximate estimation of molecular weights, although it cannot be considered being an exact law. 

Deviation from Staudinger s equation occurs for molecular weights above 10,000, and a modified equation has been introduced ... 

In the following four years Mark successively reported on the viscosity and molecular weight of cellulose (40), Staudinger s Law (41), high polymer solutions (42), and the effect of viscosity on polymerization rates (43). Confident of his findings, he proposed (at the same time as R. Houwink) the general viscosity equation now known as the Mark-Houwink Equation (44, 45). 

Ultrasonic waves also bring about a reduction in the viscosity of nitrocellulose. The effect is more marked the higher the initial viscosity, and thus the longer the nitrocellulose chains (Sollner [93] Schmidt and Rommel [94]). For instance, nitrocellulose with a molecular weight of 123,000, estimated by means of Staudinger s viscosity equation, subjected in solution form to the action of ultrasonic waves suffered a degradation to a molecular weight of 70,000-80,000. 

The equation (28) is in conformity with Staudinger s viscosity rule according to which... 

This rule was found experimentally by Signer. It is completely analogous to Staudinger s viscosity rule and is subject to the same restrictions (compare the preceding section). The two equations (31) and (28) may be combined to give... 

The relation with Staudinger s constant in equation (17) is represented by M = lOmKm Wg- WoMKrn... 

Mn obtained from osmotic pressure determinations, we derive a value of in equation (16) which is too large. Many of the viscosity constants given in Staudinger s earlier work have thus been revoked in his later papers. Similarly, the value of tg 20 in experiments on the extinction angle will always be smaller than that found in a uniform sample with the same weight average. A reliable check can only be performed in sharply fractionated samples, or in samples where the distribution of molecular weight is known. 

On the basis of the assumption that linear macromolecules can also exist as clusters, Hermann Mark (1895-1992, editor s note) co-operated with the Dutch physical chemist Roelof Houwink (1899-1987, editor s note) in Vienna to continue tanpirical development of Staudinger s viscosity equation (Mark-Houwink equation). [...] The corrections/addi-tions to Staudinger s viscosity law made by Mark and Houwink proved to be correct, but they were still being rejected by Staudinger in the 1950s. ([19], p. 410)... 

Hultin (77) has derived an expression for the enzymic depolymerization of hyaluronic acid based on Staudinger s (182) equation relating specific viscosity and molecular weight. This equation permits the calculation of a microunit for enzymic activity. The formula was applied to data published by Madinaveitia and Quibell (112) and Swyer and Emmens (183). The values obtained showed fairly good agreement for the higher substrate concentrations. 

These reactions, first described by Staudinger, have received little attention. A more recent investigation shows that the C -S bond of the thiones regioselectively adds across the C—C bond of the ketenes (equation 11) to form 2-thietanones (p-thiolactones). Primary adducts have been isolated only in a few cases. Most often they spontaneously decompose to yield an ene and COS (equation 12). 

Viscosity tj) is calculated using the Staudinger equation, whereas surface tension (y), density (p), and contact angle (0) are measured. The droplet s velocity (i and in-flight diameter (do) are calculated irom the stroboscopic images. From these values, the Reynolds (Re), Weber (We), and Z-numbets were calculated. 

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