Mark-Houwink-Sakurada equation constants

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. 

The constant a in the Mark-Houwink-Sakurada equation can take values between 0.5 and 0.8, depending of the... 

Equation (9-151) is known as the modified Staudinger equation (originally with Or, = 1) or as the Kuhn-Mark-Houwink-Sakurada equation. It was originally found empirically. K and Qrj are empirical constants obtained by calibration (see also Sections 9.9.7 and 9.9.8 and Figure 9-26). In certain special cases, Qr, can also be theoretically calculated (see Table 9-7). 

What is the Mark-Houwink-Sakurada equation Can you suggest a way to determine constants K and a experimentally for a given polymer ... 

The logarithms of intrinsic viscosities of fractionated samples are plotted against log or log Mn. The constants a and K of the Mark-Houwink-Sakurada equation are the intercept and the slope, respectively, of that plot. Except for the lower molecular weight samples, the plots are linear for linear polymers. Many values of K and a for different linear polymers can be found in the literature [66]. 

Mark-Houwink equation n. Also referred to as Kuhn-Mark-Houwink-Sakurada equation allows prediction of the viscosity average molecular weight M for a specific polymer in a dilute solution of solvent by [77] = KM, where K is a constant for the respective material and a is a branching coefficient K and a (sometimes a ) can be determined by a plot of log [77] versus logM" and the slope is a and intercept on the Y-axis is K. Kamide K, Dobashi T (2000) Physical chemistry of polymer solutions. Elsevier, New York. Mark JE (ed) (1996) Physical properties of polymers handbook. Springer-Verlag, New York. Ehas HG (1977) Macromolecules, vols 1-2. Plenum Press, New York. 

Constant of the Kuhn-Mark-Houwink-Sakurada equation ([q]-M-equation)... 

On the other hand, using molecular weights measured by GPC, the constants of the Mark-Houwink-Sakurada equation for poly(3-hexylthiophene) were determined in tetrahydrofiiran at 25°C [78] ... 

Kasaai M.R. 2007. Calculation of Mark-Houwink-Sakurada (MHS) equation viscometric constants for chitosan in any solvent-temperature system using experimental reported viscometric constants data. Carbohydrate Polymers 68, 477-488. 

Viscosity molecular weight is calculated using the Mark-Houwink-Sakurada (MHS) equation of [rj] = Km Mv, where 7] is intrinsic viscosity, Mv is viscosity molecular weight, a is the MHS exponential factor (material and system-specific, between 0.9 and 1.0 for metal complex-based solvents), and Km is a constant. Moiecuiar weight distributions resuit from GPC experiments. 

Also, according to Mark-Houwink-Sakurada (MHS) equation (3.183) with the assumption that the constants K and a are independent of molecular weight, one can write... 

The Mark-Houwink-Sakurada (MHS) equation (eqn (5.5)) offers a convenient means of determining the molecular weight of a polymer which is soluble in a solvent. It has been experimentally confirmed that the parameters Km and a in the MHS equation are constant over a wide range of molecular weights under the constraints of zero shear rate at given temperature for a... 

The exponential factors of Kuhn-Mark-Houwink-Sakurada(KMHS) equation for kraft lignin (KL) are 0.11, 0.13, and 0.23 in dimethylformamide (DMF) at 45.2°C, in DMF at 77.7°C, and in 0.5N sodium hydroxide at 30.2°C, respectively [16]. The fact that KMHS exponential factors of KL in DMF are small indicates that the molecular mass of lignin scarcely affects the reduced viscosity. This suggests that the lignin molecules in DMF have a compact spherical structure and approach the limit of an Einstein sphere, a constant-density sphere. The above results had also been reported by the research group of Goring [4]. 

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