Mark-Kuhn-Houwink equations

Since the intrinsic viscosity depends not only on the size of the macromolecule but also on its shape, on the solvent, and on the temperature, there is no simple relationship for the direct calculation of molecular weights from viscosity measurements. However, the Mark-Houwink-Kuhn equation gives a general description of how the molecular weight can be calculated from the intrinsic viscosity ... 

Note 2 Kuhn and Sakurada have also made important contributions and their names are sometimes included, as, for example, in the Kuhn-Mark-Houwink-Sakurada 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). 

Mark-Houwink equation n. Also referred to as Kuhn-Mark-Houwink-Sakurada equation allows prediction of the viscosity average molecular weight M for a specific polymer in a dilute solution of solvent by [77] = KM, where K is a constant for the respective material and a is a branching coefficient K and a (sometimes a ) can be determined by a plot of log [77] versus logM" and the slope is a and intercept on the Y-axis is K. Kamide K, Dobashi T (2000) Physical chemistry of polymer solutions. Elsevier, New York. Mark JE (ed) (1996) Physical properties of polymers handbook. Springer-Verlag, New York. Ehas HG (1977) Macromolecules, vols 1-2. Plenum Press, New York. 

Kuhn-Mark-Houwink-Sakurada equation Dimension factor of steric hindrance Length, capillary length Persistence length Low-density poly(ethylene)... 

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. 

Kuhn-Mark-Houwink-Sakurada (KMHS) Equation.163... 

The thermodynamic quality of a solvent for a polymer can be also estimated from Kuhn-Mark-Houwink-Sakurada viscosity law (often called Mark-Houwink equation) ... 

Determination of D is the first step in studying macromolecular coils by fractal analysis. D is usually estimated by finding the exponents in the Mark-Kuhn-Houwink type equation, which relate the characteristic viscosity [r ], the translational diffusion coefficient Dq, or the rate sedimentation coefficient Sq) with the molecular weight (M) of polymers [3] ... 

P19.7 The empirical Mark-Kuhn-Houwink-Sakurada equation [19.25] is [ij] = KM . ... 

PI 9.35 The procedure is that described in Problem 19.7. The data are fitted to the Mark-Kuhn-Houwink-Sakurada equation. 

This can be done as follows. Using experimentally determined rjred values, [rj] can be calculated according to Shultze-Braschke empirical equation (Eq. (6) of Chapter 1) and then to determine the coefficient in Kuhn-Mark-Houwink equation according to the Eq. (58) of Chapter 1. Farther the value MM is determined according to the Eq. (57) of Chapter 1 and polymerization degree N is calculated as follows ... 

FIGURE 17 The comparison of experimental (1) and calculated according to the Eq. (38) of Chapter 2 at using different (2) and one (3) Kuhn-Mark-Houwink equations dependences of molecular weight MM on isopropanol contents cis in reactionary mixture for PHE synthesis. 

Let us note, that the dependences m(MM) with fractional exponent gother polymers as well. So, in work [4] the constants of Kuhn-Mark-Houwink equation for -solvent in case of the branched polyarylate D j and its linear analog have been adduced, that allows to calculate intrinsic viscosities [tj] 0 and [Tjjj g, accordingly, for arbitrary MM. Then, the value g can be estimated according to the relationship [4] ... 

Properties.—A polyimide from succcinic acid has been fractionated and Mark-Houwink equation parameters determined, Several studies have appeared devoted to the investigation of the flexibility of polyimide molecules. Theoretical and experimental data indicate that these polymers have rather a high flexibility. " The Kuhn segment has been reported to consist of 2.5 monomer units. Also used to examine polyesterimides have been ultrasonic velocity and Rao formulism. ... 

The exponential factors of Kuhn-Mark-Houwink-Sakurada(KMHS) equation for kraft lignin (KL) are 0.11, 0.13, and 0.23 in dimethylformamide (DMF) at 45.2°C, in DMF at 77.7°C, and in 0.5N sodium hydroxide at 30.2°C, respectively [16]. The fact that KMHS exponential factors of KL in DMF are small indicates that the molecular mass of lignin scarcely affects the reduced viscosity. This suggests that the lignin molecules in DMF have a compact spherical structure and approach the limit of an Einstein sphere, a constant-density sphere. The above results had also been reported by the research group of Goring [4]. 

Two of the early theorists that demolished the Staudinger Law were Kuhn and M.L. Huggins. Huggins derived a theoretical form that depends on the nature of the molecules in solution. This equation is now called the Mark-Houwink equation, but like many other historical artifacts, it traces its origin to Huggins. 

For linear polymers, lire intrinsic viscosity [ t) ] and the molecular weight M are generally found to obey the Mark-Kuhn-Houwink einperical equation... 

The experimental values MM for PHE were determined according to the Equation (12) and the constants K and a — according to the formulas (13) and (23), respectively. The values K and a, obtained by the indicated mode, are adduced in Table 3. It is necessary to note, that for the same polymer (PHE) different values of constants in Kuhn-Mark-Houwink were obtained, that is due to different structure of PHE macro-molecular coils, received at different T. 

Hence, the model of irreversible diffusion-limited aggregation allows correct quantitative description of rednced viscosity (or molecular weight MM) change with variation of reagents initial concentration c. At the condition of value D know ledge and polymer chemical constitution Kuhn-Mark-Houwink equation for it can be received theoretically, that allows to avoid laborious measurements. The relationship (41) predicts that value MM at the fixed t depends not only on c , but also on macro-molecular coil structure [60]. 

Since PHE, produced in different mixtures water-isopropanol, has different values D (i.e., different stmcture), then from the Equations (13) and (23) it follows, that for them values a and K will be different, that is the relation between [q] and A/Mfor the same polymer will be defined by different Kuhn-Mark-Houwink equations. Therefore, strictly speaking, polymer viscosity should be determined in the same solvent, in which it was synthesized. This rule is confirmed by a well known fact [25], that synthesized by different polycondensation modes polyarylates, having the same chemical... 

---