Mark-Houwink characteristics

The analysis of the main properties of aqueous solutions of polyacrylamide and copolymers of acrylamide has been reviewed [4,5]. The main characteristics of aqueous solutions of polyacrylamide is viscosity. The viscosity of aqueous solutions increases with concentration and molecular weight of polyacrylamide and decreases with increasing temperature. The relationship between the intrinsic viscosity [q]) in cmVg and the molecular weight for polyacrylamide follows the Mark-Houwink equations ... 

Staudinger realized that for macromolecules [77] depends characteristically on the molar mass which can be expressed by the Kuhn-Mark-Houwink-Sakurada (KMHS) relationship... 

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. 

Solution characteristics of the polymer have been studied particularly in dimethylformamide that was made 0.1 V in anhydrous lithium bromide to suppress an apparent polyelectrolyte effect occasionally observed [16]. In this system the Mark-Houwink relation for the intrinsic viscosity at 90°C was found to be... 

The coefficients and a are characteristic for each combination of polymer, solvent and temperature and are known as the Mark-Houwink constants. If we have these constants for the polymers under the conditions of interest, we can... 

CV. The intrinsic viscosity [ri] and can be obtained directly from the viscosity distribution, outlined earlier, in connection witli Equation (3). Now, a Mark-Houwink exponent [Equation (6)] can be approximated. The ratio n can then be estimated from the viscosity distribution when the molecular weight distribution is set equal to either a log normal or the even more widely applicable generalized exponential distribution. The parameters characteristic of either assumed molecular weight distribution are easily fit from the moments of viscosity distribution. Once this is done, all average molecular weights can be estimated in principle. Because of analytical uncertainties in the high-molecular-weight tails of the distributions of most synthetic polymers, however, it is wise to confine these estimates to... 

Solution Characteristics of Poiymers. The molar mass characterization techniques often provide additional information on the nature of the polymer species in solution. In most cases, the solutions used are sufficiently dilute so that the properties being measured are those of the isolated molecule. At infinite dilution the size of the polymer coil is dictated by both inter- and intramolecular interactions, the nature of the solvent used, and the temperature. In a viscosity or GPC/SEC experiment the properties being observed can be related to the hydro-dynamic volume of the poljmier coil. This hydrodynamic volume is the effective volume which the poljmier occupies in solution. The hydrodynamic volume is implicit in the Mark-Houwink relationship, which describes the value of the limiting infinitely dilute increment to the viscosity—the intrinsic viscosity [ j] to the molar... 

Dilute solution characteristics show the expected trends arising firom the variation in composition for poly(sytrene-a>-methyl methacrylate), but in poly (acrylonitrile-co-methyl methacrylate) the Mark—Houwink exponent v is greater than 0.8 for compositions rich in acrylonitrile and results indicate a highly... 

Table 1 Mark-Houwink parameters, unperturbed dimensions, characteristic and steric parameters for flexible polymers... 

The grouping in the parenthesis of Equation 10.10 can be related to the characteristic ratio and is nearly independent of the polymer molecular weight the dependence of intrinsic viscosity on solvent quality is therefore proportional to the product aM. In theta solvents, a is unity (the intrinsic viscosity scales with and in good solvents a is proportional to (the intrinsic viscosity scales with M ). Comparison with Equation 10.1 suggests that the Mark-Houwink parameter should lie in the range 0.5 expansion factor if theta conditions for the polymer solution are known. 

The molecular characterization of PLA depends on the accurate knowledge of its fundamental properties. These include such parameters as Mark-Houwink constants that relate intrinsic viscosity to molecular weights, theta-condition front factors (K ) used to calculate single chain properties, and characteristic ratios (Coo) that give an indication of the bonding structure of polymers. 

Table 2. Constants of Mark-Houwink equation (K,a) constant Kq and characteristic ratio Coo (eq. (4)]... 

Table 4. Values of v, the exponent in the Houwink-Mark-Sakurada relation, and characteristic ratio 0/(Mj ) for polypeptides in helix-breaking solvents...

This fact was also reported in earlier studies [4, 5]. Dioxane lignins, as well as other lignin polymers except for lignosulfonates, are characterised by rather low intrinsic viscosities and exponential coefficients in the Mark-Kuhn-Houwink equations (note that b, is always smaller than b ). The lower limit of b is 0.1, whereas the upper limit is 0.3. As demonstrated by the data on translational diffusion, for most polymers, the values of the exponent lie in a rather narrow range = 0.38 0.05, that is, the characteristics of translational friction of the macromolecule are almost independent of the lignin source and the solvent used. 

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] ... 

The characteristic viscosity [qjg can be estimated either directly from experiment, or from Equation (16.1) under the condition that b = 0.5, which is valid at the point, if the constant in this equation is known. To test the relationship (16.11), we used the data of Pavlov and co-workers [4] for the polysaccharide rhodexman, for which the Mark-Kuhn-Houwink equation has the form ... 

As it is known, the same polymer, produced by equilibrium and nonequilibrium, differs by its characteristics, in particular, has different exponents a in Mark-Kuhn-Houwink equation [53], The values a and are linked between themselves by the Eq. (4). For polyarylate on the basis of phenolphthaleine the values D = 1.96 (equilibrium polycondensation) and Dj.=1.80 (nonequilibrium polycondensation) were obtained, that corresponds to p=0.0185 and 0.039. Thus, polycondensation mode change from equilibrium up to nonequilibrium (interfacial) one results to p increase approximately twice. Approximately the same relation is valid at polycondensation mode change for other polyary lates of different chemical structure. 

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