Houwink Parameters

The Mark-Houwink parameters for the acrylates of interest in this thesis, have been determined by Penzel and Goetz [14] and more recently by Hutchinson and coworkers [15, 16]. The former group based their results on measurements of relatively broad molecular weight samples (obtained by fractionation with methanol), while the latter groups used a triple detector SEC set-up. Table 4.1 shows the Mark-Houwink coefficients for the acrylates (and styrene) obtained by these two groups. The differences between the two data sets become apparent when, for instance, the hydrodynamic volume, HV, defined by [7, 8, 17]  

The only question that now remains is which data should be selected for the third monomer, ethyl acrylate At first sight, three different options seem to be available  

For the same reasons outlined above, the EA data of Hutchinson and coworkers could be preferred over the data by Penzel and Goetz. However, as explained previously, this implies a rather peculiar tendency in the hydrodynamic volume of a homologous series of acrylates. 

A third possibility is an interpolation of the available data. The basic assumption in this interpolation is that the tendency in hydrodynamic volume of the three acrylates in the data of Penzel and Goetz is a reasonable one. This then opens the possibility to estimate improved Mark-Houwink coefficients for EA that fit well in the already made selection of the Mark-Houwink parameters for MA and BA. If this interpolation is made on the basis of hydrodynamic volumes, then the following condition could be used for this purpose  

Unfortunately, the data structure of the hydrodynamic volume of the different polymers does not allow such a precise linear relation (though the deviations are rather small) and therefore the interpolation will be replaced by a somewhat simpler approach  

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Table 8. Mark-Houwink Parameters for Polyolefin Solutions ...

Table 3 shows the classical values calculating for Mark-Houwink parameters, a and k for temperature. These studies on M-H parameters are usually carried out at a given temperature, obtaining a consistent result but in a very limited range of temperature (for gelatin Pouradier Venet 1954 and Bohidar 1998 Monkos for serum proteins 1996, 1997, 1999, 2000, 2004 and 2005). This value shows a clear functionality between these parameters and temperature. 

Table 3. Data obtained of intrinsic viscosity and Marck-Houwink parameters of gelatin B at different temperatures.

The Mark-Houwink parameters are influenced by temperature. The numerical value of a indicates that gelatin acquire a shape of a rod-like in aqueous solution with temperature increases and k demonstrates that under water their value increases with temperature. 

The unusual feature of the programs is the automatic processing based on sample class. The operator provides the relevant parameters to the system of programs using the program SETUP, which contains several fill-in-the-form screens. These parameters Include the "class" of the specimen and the required automatic processing, as described below, and other pertinent information such as Mark-Houwink parameters, vial number, injection number, and documentation of the experimental conditions under which the chromatogram is to be measured. 

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

Star-branched butyl rubber, 4 437-438 copolymers, 4 445-446 Starch(es), 4 703-704, 20 452-453 as blood substitute, 4 111-112 cationic, 18 114-115 in cereal grains, 26 271-274 in cocoa shell from roasted beans, 6 357t compression effects in centrifuges, 5 513 depolymerization, 4 712 in ethanol fermentation, 10 534—535 etherified, 20 563 as a flocculant, 11 627 high-amylose, 26 288 Mark-Houwink parameters for, 20 558t modified and unmodified, 12 52-53 in paper manufacture, 18 122-123 performance criteria in cosmetic use, 7 860t... 

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. 

Table I indicates good agreement between the molecular weight distribution statistics obtained by coupled GPC/Viscometer method and the nominal values for t BS 706. The discrepancy between the Mark-Houwink parameters obtained here and the reported values for polystyrene standard ( ) in THF at 25°C (i.e., a = 0,706 and k = 1.60 x 10 ) may in part be due to the uncertainty involved in the determination of the dead volume between DRI and viscometer detectors. Our simulation studies over a range of dead volume values (0 to 120u)l) showed that a and k are quite sensitive to the dead volume between the detectors. Larger dead volume results in smaller o and larger k values. This is a direct result of a clockwise rotation of log [q] vs. log M(v) curve (Figure 12) which occurs when the dead volume correction is applied in quantitative analysis. The effect on the molecular weight statistics, however, appeared to...

Other possible reasons for the discrepancy in the Mark-Houwink parameters may be due to the band spreading effects and inadequate signal-to-noise quality at the tails of the viscometer chromatogram. These subjects will be the topic of our future investigations in this area. 

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... 

Gruendling T, Junkers T, Gullhaus M, Bamer-Kowolllk C (2010) Mark-Houwink parameters for the universal calibration of acrylate, methacrylate and vinyl-acetate polymers determined by online size-exclusion chromatography-mass-spectroscopy. Macromol Chem Phys 211 520-528... 

We can thus obtain [q] for a slice of the chromatogram as narrow as we wish, or for the whole polymer. The only information required independently of our SEC system is the molecular weights of our calibration standards. This represents a significant advance over the previous situation in which [q] had either to be determined in a separate experiment or through use of the Mark-Houwink parameters, K and a, if available from the literature. 

The intrinsic viscos.ity plot for po 1 ys tyr enec a distinct creak at about 10,000 daltonsi. Above this value the Merk-Houwink parameters a --. 718, K = 1.28 X 10 -6. ... 

K, a = Mark-Houwink parameters Kg = K value at theta condition... 

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. 

Polystyrene. Table 3 shows the results obtained for three broad MWD polystyrene samples. The agreement for M and M values obtained from SEC/Viscometry analysis and the nominaY values supplied by the vendors is excellent. In addition the Mark-Houwink parameters, K and a values also are in excellent agreement with each other as well as with literature values.(28,39) This shows the consistency of the analysis method and the technique for determining the dead volume between detectors. The lower M value for the NBS 706 sample is due to the low molecular weight tail associated with the sample. 

Polyvinyl Chloride. The results obtained for a polyvinyl chloride sample are listed in Table 5. It is seen that the measured molecular weight statistics are in reasonable agreement with the nominal values. The Mark-Houwink parameters K and a obtained from the linear plot of log [nl vs. log M are in good agreement with one group of literature values (41-43) while the a value is lower than that of another group. (3,44-46)... 

Gamma radiation can be used with macroscopic amounts of polymer. This is particularly welcome when polymers are not compatible with the GPC technique. Larger samples can be characterized by viscosity changes, usually measured in dilute solutions. All that is needed is a suitable solvent. If the Mark-Houwink parameters are known, it is possible to calculate viscosity-average molecular weight, Mv, from dilute solution viscosities. However, even the raw viscosity-concentration data in terms of the reduced viscosity may be enough to indicate the sensitivity of a given polymer in qualitative terms. The reduced viscosity at concentrations c is isp/c where t]sp — (solution viscosity — solvent viscosity)/solvent viscosity. 

If the Mark-Houwink parameters are known or can be established for a polymer standard that is soluble in TFE as well as for the polymer of interest, the molecular weight calibration curve for the polymer of interest,... 

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