Mark-Houwink relationships

Fig. 3. Solution viscosity vs concentration for ethylene oxide polymers (10). The molecular weight of the polymer is indicated on each curve. The dependence of the intrinsic viscosity [Tj] on molecular weight M for these polymers can be expressed by the Mark-Houwink relationship ...

The molecular weights were estimated by applying the Mark-Houwink relationship [r/ = KMa. The intrinsic viscosity [r/ was determined in m-cresol at 20°C. The values for K in the literature vary from 1.35 to 18.10 x 10-4 and the a values vary from 0.654 to 0.96 for polyamide-cresol systems. 

The relationship between g and gu can be found through use of the Mark-Houwink relationship. "The intrinsic viscosity of a linear polymer of the same molecular weight (M. ) as the branched polymer is... 

The rheological behaviour of polymeric solutions is strongly influenced by the conformation of the polymer. In principle one has to deal with three different conformations, namely (1) random coil polymers (2) semi-flexible rod-like macromolecules and (2) rigid rods. It is easily understood that the hydrody-namically effective volume increases in the sequence mentioned, i.e. molecules with an equal degree of polymerisation exhibit drastically larger viscosities in a rod-like conformation than as statistical coil molecules. An experimental parameter, easily determined, for the conformation of a polymer is the exponent a of the Mark-Houwink relationship [25,26]. In the case of coiled polymers a is between 0.5 and 0.9,semi-flexible rods exhibit values between 1 and 1.3, whereas for an ideal rod the intrinsic viscosity is found to be proportional to M2. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

Table 3. Mark-Houwink relationships for polystyrene in different solvents at 25 °C as com-... 

Also, a good correlation between Mw (light scattering) and intrinsic viscosity is observed for [Ph(Me)PN]n over the molecular weight range of the samples studied. Thus, the Mark-Houwink relationship, [rj] = K(AOa, yields values of K = 1.44x1 o 4 (with [rj] in dL/g) and a = 0.66. These data again indicate a well solvated, extended-chain structure of the polymer in THF. 

Markham and Benton model, 1 628 Mark-Houwink coefficients for cellulose, 20 558t for PBT, 20 64t for PET, 20 58 for PTT, 20 69t Mark-Houwink constants, for poly(ethylene oxide), 10 677t Mark-Houwink equation, 19 717, 839 Mark-Houwink relationship, 10 675 ... 

Flexible polymer chains expand with increasing solvent power of the medium, leading to an increase in [77] with increasing polymer solvation. For chains of a similar kind, varying in length (homologous series), the relationship between [77] and molecular weight, M, may be represented by the Mark-Houwink relationship [19-22],... 

In order to estimate g, it is necessary to measure [tj]b and MwB (or MnB). Also, a Mark-Houwink relationship of the linear polymer must be known for the conditions employed in the measurement of [tj]b. In general, if the log [77] versus log M relation is known for the linear species, the deviation from this relationship may be used to estimate the number of branches, provided certain assumptions can be made concerning the distribution of branches. 

Therefore, when dealing with polyelectrolytes, countless Mark-Houwink relationships must be established. This shows the increasing problems of simple molecular weight determinations on charged systems (for more details, see Kulicke. Horl (1985)). Thus, the molecular weight determination of polymer molecules or additives is an important fact in the drag reduction area. Molecules or particles which are effective have molecular weights above 105 g/mol (the polymer backbone chains should be linear, flexible, and unbranched). 

The dependence of the intrinsic viscosity [r ] on molecular weight M for these polymers can be expressed by the Mark-Houwink relationship ... 

In order to obtain molecular weight values from intrinsic viscosities it is necessary to use the calibration illustrated in Figure 2.9. It is based on the Mark-Houwink relationship, which is given by... 

Where the symbols used have the following meaning Mi = molar mass of the component molecules of kind i nj = number-fraction of the component molecules i Wj = weight-fraction of the component molecules i N = total number of moles of all kinds W = total weight of moles of all kinds a = exponent of the Mark-Houwink relationship relating intrinsic viscosity to molar mass. 

The intrinsic viscosity is a function of molar mass via the Mark-Houwink relationship, wherein K and a are coefficients for a given polymer in a given solvent at a given temperature. 

Fig. 17 Radiation of dilute PVME solutions. Top Effect of y-irradiation on Mw and viscosity [77] in comparison with the Kuhn-Mark-Houwink relationship (

Mark-Houwink Relations. The Mark-Houwink relationships obtained for pullulans and dextrans in 0.2 M NaNOa are as follows ... 

The GPC-viscometry with universal calibration provides the unique opportunity to measure the intrinsic viscosity as a function of molecular weight (viscosity law, log [17] (it versus log M) across the polymer distribution (curves 3 and 4 in Fig. 1). This dependence is an important source of information about the macromolecule architecture and conformations in a dilute solution. Thus, the Mark-Houwink equation usually describes this law for linear polymers log[i7] = ogK+ a log M (see the entry Mark-Houwink Relationship). The value of the exponent a is affected by the macromolecule conformations Flexible coils have the values between 0.5 and 0.8, the higher values are typical for stiff anisotropic ( rod -like) molecules, and much lower (even negative) values are associated with dense spherical conformations. 

Mark-Houwink relationships are also important for the application of the universal calibration procedure in GPC-SEC of polymer molecules, where the... 

---