Staudinger equation, viscosity-molecular weight

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. 

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). 

Staudinger showed that the intrinsic viscosity or LVN of a solution ([tj]) is related to the molecular weight of the polymer. The present form of this relationship was developed by Mark-Houwink (and is known as the Mark Houwink equation), in which the proportionality constant K is characteristic of the polymer and solvent, and the exponential a is a function of the shape of the polymer in a solution. For theta solvents, the value of a is 0.5. This value, which is actually a measure of the interaction of the solvent and polymer, increases as the coil expands, and the value is between 1.8 and 2.0 for rigid polymer chains extended to their full contour length and zero for spheres. When a is 1.0, the Mark Houwink equation (3.26) becomes the Staudinger viscosity equation. 

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. 

Viscosity measurements have been widely used as a method for determining molecular weights on account of the ease with which they can be carried out. Although the method is simple it is not absolute and requires calibration. The characteristic quantity used in these measurements is the specific viscosity (ri.v) defined by Staudinger as n,r = (77 — vo)/vo where 77, 770 are the viscosities of solution and solvent respectively. For concentrations of solute of less than 1 g. per 100 ml., the variation of specific viscosity with concentration C, can usually be expressed by an equation of the form... 

Staudinger has developed an empirical equation relating the viscosity of a polymer in dilute solution to its molecular weight ... 

Here ),p, the specific viscosity, is equal to the relative viscosity minus one. Staudinger designates C as the concentration of the solution in basal moles or the number of moles of the polymeric repeating unit per liter thus, for a starch acetate, it is the number of grams per liter divided by 288. K , is a constant particular to a definite series of homologues measured in a definite solvent, and M is the molecular weight. Ordinarily, this equation is employed for viscosity values extrapolated to zero concentration. Although the relationship is by no means exact " ... 

For calculation of molecular weights from intrinsic viscosities we used the Staudinger equation (35). On account of the high molecular weights of emulsion polymers we exceeded the range for which the constants were determined to a considerable amount. 

Ghosh and Schnitzer (1980b) calculated molecular weights from viscosity measurements using the Staudinger equation ... 

Routinely, molecular weights of polymers are conveniently estimated from intrinsic viscosity measurements using the Staudinger (also known as the Mark-Houwink-Sakurada) equation... 

In a great many papers published since 1930, Staudinger has tried to establish that the specific viscosity increase due to long-chain molecules in dilute solutions is proportional to their molecular weight and conforms to the equation ... 

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. 

As shown in Figure 2, we found a strong concentration dependence of the reduced viscosity even at low concentrations, which in contrast to the findings with the low molecular a-PMMA samples is not linear. It is worthwhile to note that the order with respect to solvent power is obviously the same as found with the other a-PMMA samples. Calculation of the viscometric molecular weight in toluene and chloroform, based on the Staudinger-Mark-Houwink TSMH)-equation is in very good agreement with the My, -value determined by GPC. Values for the constants K and a are taken from the literature. ... 

Viscosity is a measure of the friction (resistance to mechanical movement) of a fluid. In the case of liquids, the viscosity of a solution is different from the pure solvent and is dependent on the nature and concentration of the solute. The following Staudinger equation (Tanford 1961 Clapp, Emerson, and Olness 1990 Stevenson 1994) allows to estimate molecular weights ... 

The viscosity of a solution increases with the molecular weight of the solute. By making measurements on solutions of low concentrations, Staudinger derived the following empirical equation ... 

Mark-Houwink Equation Staudinger (1932) suggested that the molecular weight M of polymers is proportional to the reduced viscosity ... 

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. 

The Mark-Houwink-Staudinger (MHS) equation provides a relationship between the intrinsic viscosity (Equation 8.12b) and the (average) molecular weight (M) of (synthetic) polymers ... 

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