Intrinsic viscosity Mark-Houwink parameter

The Mark-Houwink parameters allow to relate the intrinsic viscosity [q] with the viscometric average molecular weight Mv through the relation ... 

A continuous capillary viscosity detector has been developed for use in High Performance Gel Permeation Chromatography (HPGPC). This detector has been used in conjunction with a concentration detector (DRI) to provide information on the absolute molecular weight, Mark-Houwink parameters and bulk intrinsic viscosity of polymers down to a molecular weight of about 4000. The detector was tested and used with a Waters Associates Model 150 C ALC/GPC. The combined GPC/Viscometer instrumentation was automated by means of a micro/mini-computer system which permits data acquisition/reduction for each analysis. 

The use of a continuous GPC viscosity detector in conjunction with a DRI detector permits the quantitative determination of absolute molecular weight distribution in polymers. Furthermore, from this combination one can obtain Mark-Houwink parameters and the bulk intrinsic viscosity of a given polymer with a GPC calibration curve based only on polystyrene standards. Coupling these two detectors with ultraviolet and infrared detectors then will permit the concurrent determination of polymer composition as a function of molecular weight and... 

Dead Volume. The dead volume difference between the viscometer and DRI must be accounted for. Otherwise systematic errors in Mark-Houwink parameters K and u can occur. In the previous paper (16), a method developed by Lesec and co-workers (38) based on injecting a known amount of a very high molecular weight polystyrene standard onto low porosity columns was used. From the viscometer and DRI chromatograms, the apparent intrinsic viscosity [h] was plotted against retention volume V. A series of [n] vs. V plots are then constructed assuming a range of dead volume, AV. 

If the Mark-Houwink parameters are unknown and there is insufficient data available for their direct generation, molecular weight calibration curves can be generated by (a) an empirical technique based upon the determination of the intrinsic viscosity of each polymer fraction obtained by the GPC syphon counter or (b) using at least two out of three experimental observables, number- and weight-average molecular weights Mn, Mw, and [77] to fit mathematically for effective values of e and K. 

If the determination of the intrinsic viscosity of each polymer fraction obtained from the GPC syphon counter is infeasible, use can be made of [77], Mn, Mw, and the GPC trace of the whole polymer sample for the determination of the Mark-Houwink parameters. Provder and co-workers (I, 2) have derived expressions for Mn, Mw, and [77] in terms of c, K, and Z which are summarized below ... 

The GPC analysis of block copolymers is handicapped by the difficulty in obtaining a calibration curve. A method has recently been suggested to circumvent this difficulty by using the calibration curves of homopolymers. This method has been extended so that the calibration curves of block copolymers of various compositions can be constructed from the calibration curve of one-component homopolymers and Mark-Houwink parameters. The intrinsic viscosity data on styrene-butadiene and styrene-methyl methacrylate block polymers were used for verification. The average molecular weight determined by this method is in excellent agreement with osmometry data while the molecular weight distribution is considerably narrower than what is implied by the polydispersity index calculated from the GPC curve in the customary manner. 

GPC with an on-line viscometer can be used instead of a LALLS detector to analyze branched polymers. In this case the intrinsic viscosity is measured so that the Mark-Houwink parameters are not needed. It is complementary to the LALLS instrument in intrinsic viscosities. 

FIGURE 6.11 Viscosity parameters of solutions of carboxymcthyl cellulose (Na salt) at various ionic strengths (molar). Mark-Houwink parameters K (ml/g) and a, and intrinsic viscosity [>y]0(ml/g) for a molar mass of 106Da. (From results by W. Brown and D. Henley. Makromol. Chemie 79 (1964) 68.)... 

To explore the influence of hydrophobe structure and content, a reference PAM was prepared that had a weight-average molecular weight of 3 X 10 g/mol and an intrinsic viscosity of 7.3 dL/g (Table I). These values agreed with the Mark-Houwink parameters found for PAMs synthesized by other techniques (13). With data obtained from a large variety of PAM samples studied in water at 25 C, Kulicke et al. (13) proposed the following relationship ... 

Determine the Mark-Houwink parameters. For the same samples, intrinsic viscosities in toluene are greater than in cyclohexane. Comment on the different solvent quality. 

Note that the intrinsic viscosity-molecular weight data for the corresponding linear polymer are required to calculate g. Ideally this should be determined from a linear sample analyzed by SEC-viscometry. Alternatively, literature values for the Mark-Houwink parameters for the linear polymer may be used. If neither of these data are available, the least branched sample or a secondary linear standard can be used as the control. Table 2 lists selected references on the use of SEC-viscometry for branching studies. 

Cellulose and Cellulose Derivatives. The solubilization of cellulose to determine its molecular weight is delicate one of the most powerful solvents is cupriethylenediamine for which the Mark-Houwink parameters relating the intrinsic viscosity to the molecular weight ([ j] = KM" ) have been determined (see Table 4). Some authors previously prepared cellulose derivatives (nitrocellulose or cellulose tricarbanilate) to determine the molecular weight and molecular weight distribution, assuming no polsrmer degradation (72-83,91,92). 

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. 

Listed below are values of the intrinsic viscosity as a function of the degree of polymerization for solutions of hydrophobieaUy modified (hydro-xyethyl) cellulose in 0.1% sodium oleate [32]. Determine the Mark-Houwink parameters. 

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. 

Benoit and co-workers [18] proposed that the hydrodynamic volume, Vr which is proportional to the product of [17] and M, where [17] is the intrinsic viscosity of the polymer in the SEC eluent, may be used as the universal calibration parameter (Fig. 18.3). For linear polymers, interpretation in terms of molecular weight is straightforward. If the Mark-Houwink-Sakurada constants K and a are known, log [t7]M can be written log M1+ + log K, and VT can be directly related to M. The size-average molecular weight, Mz, is defined by this process ... 

Molar mass of polymers can be deduced from intrinsic viscosity measurement through a Mark-Houwink cahbration curve. This approach can be apphed to supramolecular polymers if Mark-Houwink and Huggins parameters are known [191]. However, finding a suitable covalent model to estimate these coefficients is a difficult task. 

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