Staudinger equation

This is, of course, the historically famous Staudinger equation. It is well known that the intrinsic viscosity of a solution of completely free draining Gaussian chains [Kuhn (153) Huggins (128 ) Kramers (14V) and Debye (87)] also follows a Staudinger law ... 

Fortunately, Staudinger found, in 1950, that for a series of samples of the same polymer in a given solvent and at a constant temperature, the intrinsic viscosity (or the viscosity number) is related to the molar mass of the polymer by the following equation, known as Mark-Houwink equation or Staudinger equation ... 

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 ... 

One often makes do with a viscosity measurement at a single concentration (usually 0.5%) to give what is called the inherent viscosity 17)0 = (lni7rei/c)c for this concentration. Fikentscher constants K are also used, particularly in the German literature, to characterize the classic polymers such as poly (styrene) and poly (vinyl chloride). [The K here is not to be confused with the K, defined by Equation (9-151), of the modified Staudinger equation.] K is evaluated from the relative viscosity at relatively high concentrations from tabular data and the equation... 

Equation (9-151) is known as the modified Staudinger equation (originally with Or, = 1) or as the Kuhn-Mark-Houwink-Sakurada equation. It was originally found empirically. K and Qrj are empirical constants obtained by calibration (see also Sections 9.9.7 and 9.9.8 and Figure 9-26). In certain special cases, Qr, can also be theoretically calculated (see Table 9-7). 

A comparison of the expressions giving the molar mass dependence of the intrinsic viscosity shows that the relationships can be generalized for all macromolecular types in the form of the modified Staudinger equation [77] = KM (see also Table 9-7). Both K and a, are usually unknown. For each polymer homologous series, therefore, the modified Staudinger equation must be empirically determined. To do this, the molar masses and intrinsic... 

In addition to this simple consideration, which appears to present only a rough idea of the conditions, there is an exhaustive discussion in progress on the Staudinger equation. 

Four degradation products at different stages of the decomposition process were secured. The corresponding average degrees of polymerization were 158, 100, 54, and 31, all estimated by the aid of the Staudinger equation from directly measured viscosities. 

In contrast, Mark maintained that macromolecules could assume many different conformations (shapes) and in collaboration with Guth and Kuhn, proposed a power form for the Staudinger equation i.e., qgp=KM . A similar equation was proposed simultaneously by Roelof Houvdhk and the above equation is now referred to as the Mark-Houwink viscosity equation. 

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 ... 

It can be seen to reduce to Af when a is unity. For accurate results with molecular weights greater than 10 the Staudinger equation must be further modified. 

Since standard viscosity measurements require a relatively large amount of materials, dynamic viscosities of each polymer solution were calculated using the Staudinger equation for the intrinsic viscosity ... 

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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