Mark-Houwink calibration curve

D. SEC Measurement of Mark-Houwink Constants Using Only Polydispersed Standards. If the SEC-MW calibration curve of the polymer-solvent system is known in addition to the [n] calibration, the Mark-Houwink constants of the polymer-solvent system are... 

There are three imknowns, K, a and. One might question the availability of Mark-Houwink constants for the polymer in the open literature. Mark-Houwink constants in the literature differ widely for the same polymer and it is difficult to decide on the correct pair to employ. Another problem which can arise is that the universal molecular weight calibration curve may not apply exactly for the polymer in question. The use of the true Mark-Houwink constants would therefore introduce an error in the molecular weight calibration. Calibration with a broad MWD standard should eliminate this error. The Mark Houwink constants obtained in the calibration would in this instance be effective rather than true values. 

The molecular weight calibration curves obtained for PVC are shown plotted in Figure 3. Table III shows an investigation of the effect of the peak broadening parameter (a) assumed when a single broad MWD PVC standard is used. The corrections for imperfect resolution for PV2 and PVC with a a = 0.5 are now reduced to about k% for both standards. It is of interest to note that with a reduced correction for imperfect resolution the Mark-Houwink exponent obtained is closer to published literature values for PVC in THF (13). The use of the associated molecular weight calibration curve for PVC would reproduce the M j and M of the PVC standards with errors of about 15. ... 

Usually the function [Cn) M] (intrinsic viscosity times molecular weight) is used to represent hydrodynamic volume which is plotted versus elution volume. For such a plot the calibration curves of many polymers fall on the same line irrespective of polymer chemical type. Universal calibration methodology usually requires knowledge of Mark-Houwink constants for the polymer/ temperature/solvent system under study. 

From the primary calibration curve based on polystyrene standards and the Mark-Houwink constants for polystyrene (K,a) a universal calibration curve (Z vs. v), based on hydrodynamic volume is constructed. Z is calculated from... 

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... 

When the total polymer response, is known as a function of retention volume, the molecular weight distributlon can be obtained in the usual manner with the appropriate molecular weight calibration curve. The molecular weight calibration curve can be obtained (a) by using the Runyon (65) copolymer molecular weight scale approach, or (b) by using a hydrodynamic volume approach if the Mark-Houwink constants for the polymer of interest are known or can be determined, or (c) by using a hydrodynamic volume approach in conjunction with an on-line viscosity detector. 

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,... 

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. 

Both of these routes involve transforming the retention volume axis uThf to t>rFE via> the retention volume calibration curve and transforming the HDV axis for PMMA in tetrahydrofuran to that for PMMA in TFE by use of the Mark-Houwink parameters for PMMA in tetrahydrofuran and in TFE. 

Route 1 (a) Using the Mark-Houwink parameters of the PMMA test polymer in tetrahydrofuran, cthfia and thf A> construct the PMMA molecular weight calibration curve in tetrahydrofuran from the polystyrene HDV calibration curve by the use of Equation 2 where x is PMMA... 

Using the PMMA direct molecular weight calibration curve shown in Figure 4 and the Mark-Houwink parameters for PMMA in TFE shown in Equations 26 and 27, an HDV calibration curve can be constructed as described in the theory section. Then secondary molecular weight curves can be constructed for other polymers of interest by the methods discussed in the theory section as was done in Ref. 1, using the indirect PMMA molecular weight calibration curve. 

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. 

This is the case of parallel calibration curves discussed in the previous paper. Equation 4 shows that when the calibration curves are parallel, the equivalence ratio, r, is constant to the elution volume V. It varies with the latter when aA aB—i.e., the calibration curves are not parallel. For that case Equation 3 would have to be used. Equation 4 also shows that the equivalence ratio can be calculated from the Mark-Houwink parameters K and a. It offers a way to determine r in addition to obtaining it from the GPC calibration curves of homopolymers. 

The procedure to determine the molecular weight of a branched polymer is as follows. If for a certain GPC column the universal calibration curve is measured with the aid of a series of monodisperse linear polymers of known molecular weight, the next step is to determine the elution volume and the intrinsic viscosity of the unknown branched fraction. Then the product [rj]M corresponding to the mean elution volume of a branched fraction is read from the universal calibration curve this value divided by the determined intrinsic viscosity gives the molar mass of the fraction. At the same molar mass one can also calculate the intrinsic viscosity of the linear polymer by using the Mark-Houwink equation. 

If the Mark-Houwink coefficients are not available, a universal calibration curve is established using polystyrene calibration standards and the SEC-vis-cometer combination. The basic steps involved in the MMD analysis are summarized in Fig. 11. First, the universal calibration curve of the SEC separation system has to be established by using narrow molar mass standards as indicated by the top arrow pointing to the right. Once the universal calibration curve is established, the procedure can then be reversed, by going from right to left following the bottom arrow, to obtain the molar mass calibration curve of any unknown... 

The conversion of a calibration curve for one polymer (say, polystyrene, as in Fig. 3-10) to that for another polymer can be accomplished directly if the Mark-Houwink-Sakurada equations are known for both species in the GPC solvent. From Eq, (3-43), one can write... 

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. 

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