Polystyrene Mark-Houwink constants for

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 Mark-Houwink constants for polystyrene (Ki and < 1) in THF at 30 °C were measured in this laboratory to be 2.89 X 10"4 and 0.65, respectively, while those of cellulose nitrate were reported by Jenkins (4)... 

Two monodisperse polystyrenes are mixed in equal quantities by weight. One polymer has molecular weight of 39,000 and the other molecular weight of 292,000. What is the intrinsic viscosity of the blend in benzene at 25°C The Mark-Houwink constants for polystyrene/benzene are k = 9.18 X 10 dl/gandfl = 0.74. 

The Mark-Houwink constants for polystyrene in tetrahydrofuran at 25°C are K =6.82 x 10 - cmVg and <3=0.766. The intrinsic viscosity of poly(methyl methacrylate) in the same solvent is given by... 

The Mark-Houwink constants influence the accuracy of the universal calibration curve. The discrepancy between universal calibration curves for PS and P(VC-VAc) copolymers observed by Chen and Blanchard [15] may be due to misuse of the Mark-Houwink constants for polystyrene. These authors obtained the Mark-Houwink equation for P(VC-VAc) copolymers as... 

Mark-Houwink constants for both polystyrene and PMMA. 

Using these data together with the calculated values of [rj] for samples B and E, evaluate the constants of the Mark-Houwink equation for polystyrene in cyclohexane at 34 C. 

Ki, a2 = Mark-Houwink constants for polyethylene Ml = molecular weight of polystyrene M2 = molecular weight of polyethylene... 

This makes it possible to use standards of one polymer for characterization of another if the corresponding Mark-Houwink constants are known. For most known polymers, Mark-FIouwink constants are tabulated. For example, a polystyrene (PS)-based calibration could be used for characterization of polymethylmethacrylate (PMMA). 

The intrinsic viscosity behavior of polystyrene (PS) is very similar to that of linear PVAc. The following Mark-Houwink constants are often cited for PS in THF a = 0.706, K= 0.00016 (19,22). Therefore, PS and linear PVAc samples of the same molecular weight elute at nearly the same retention volume. Consequently, for certain PVAc products, the increased cost, complexity, and experimental uncertainty associated with analysis of SEC data by universal calibration may not be justified (26). 

The chromatograph is usually calibrated with polystyrene standards, although a limited range of other polymer standards is available (see Appendix 2). If standards are not available for the polymer of interest, and if the Mark-Houwink constants K and a are known, then the universal calibration procedure can be employed, making use of the following equation ... 

The Mark-Houwink constants K and a were determined for PEEK and polystyrene at 115°C in the phenol-TCB mixture (see Table 4.2). A typical chromatogram showed, in addition to the molecular distribution of the polymer, two solvent peaks, one positive and one negative. These occur beyond the permeation limit of the columns and did not interfere with the molecular mass distribution of the polymer. Narrow-distribution polystyrenes, PEEK samples characterized by light-scattering, and model low-molecular-mass compounds were used as molecular-mass standards. 

Estimate values for the Mark-Houwink constants using the following data for polystyrene samples in benzene ... 

Use these data to evaluate the constants in the Staudinger-Mark-Houwink equation. Are the values obtained consistent with the known facts that 35.4°C is the Flory (0) temperature for polystyrene in cyclohexane while benzene is a good solvent for polystyrene at 40°C. 

Universal Calibration In the conventional calibration (described above), there is a problem when a sample that is chemically different from the standards used to calibrate the column is analyzed. However, this is a common situation for instance, a polyethylene sample is run by GPC while the calibration curve is constructed with polystyrene standards. In this case, the MW obtained with the conventional calibration is a MW related to polystyrene, not to polyethylene. On the other hand, it is very expensive to constmct calibration curves of every polymer that is analyzed by GPC. In order to solve this problem, a universal calibration technique, based on the concept of hydrodynamic volume, is used. As mentioned before, the basic principle behind GPC/SEC is that macromolecules are separated on the basis of their hydrodynamic radius or volume. Therefore, in the universal calibration a relationship is made between the hydrodynamic volume and the retention (or, more properly, elution volume) volume, instead of the relationship between MW and elution volume used in the conventional calibration. The universal calibration theory assumes that two different macromolecules will have the same elution volume if they have the same hydrodynamic volume when they are in the same solvent and at the same temperature. Using this principle and the constants K and a from the Mark-Houwink-Sakurada equation (Eq. 17.18), it is possible to obtain the absolute MW of an unknown polymer. The universal calibration principle works well with linear polymers however, it is not applicable to branched polymers. 

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