Intrinsic viscosity Houwink-Mark-Sakurada relation

Houwink-Mark-Sakurada Relation for Intrinsic Viscosity... 

The 3.4 power law for melt viscosity, eq 5.1, is of surprising generality, well compared to the Houwink-Mark-Sakurada relation for intrinsic viscosity. Thus its derivation by molecular theory has been one of the central themes in polymer physics since it was proposed in 1951 by Fox tind Flory [63]. Despite many efforts no real success has as yet been achieved. The reader is advised to consult Graessley s review [64] in 1974 concerning the earlier theories. 

According to the Mark-Houwink-Sakurada equation, the intrinsic viscosity [jj] might be related to the molecular weight (M) of a linear pol3mier ... 

The Mark-Houwink-Sakurada equation relates tire intrinsic viscosity to tire polymer weight ... 

The specific viscosity )jsp of a dilute solution of spheres is directly related to their hydrodynamic volume VV Nl denotes Avogadro s number. Typically the intrinsic viscosity [tj] follows a scaling law, the so-called Mark-Houwink-Sakurada equation ... 

Intrinsic viscosity is related to the relative viscosity via a logarithmic function and to the specific viscosity by a simple algebraic relationship. Both of these functions can be plotted on the same graph, and when the data are extrapolated to zero concentration they both should predict the same intrinsic viscosity. The specific viscosity function has a positive slope and the relative viscosity function has a negative slope, as shown in Fig. 3.7. The molecular weight of the polymer can be determined from the intrinsic viscosity, the intercept of either function, using the Mark-Houwink-Sakurada equation. 

An appropriate formalism for Mark-Houwink-Sakurada (M-H-S) equations for copolymers and higher multispecies polymers has been developed, with specific equations for copolymers and terpolymers created by addition across single double bonds in the respective monomers. These relate intrinsic viscosity to both polymer MW and composition. Experimentally determined intrinsic viscosities were obtained for poly(styrene-acrylonitrile) in three solvents, DMF, THF, and MEK, and for poly(styrene-maleic anhydride-methyl methacrylate) in MEK as a function of MW and composition, where SEC/LALLS was used for MW characterization. Results demonstrate both the validity of the generalized equations for these systems and the limitations of the specific (numerical) expressions in particular solvents. 

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 ... 

Several authors have published the method for determining molar masses of DADMAC polymers, primarily in connection with practical applications [1]. In Table 11 intrinsic viscosity-molar mass relations of PDADMAC are summarized in the form of the Mark-Kuhn-Houwink-Sakurada (MKHS) relationship. The relatively high exponent of the relationships is attributed to the greater chain stiffness in comparison with vinyl backbones. One has to look quite skeptically at the values from reference [59] given its deviation from the remainder of the published data. 

The relation between number molecular weight, Mn and intrinsic viscosity, [t ], for poly(penLachlorophenyI methacrylate) (PPCIPh) can be represented by the Mark - Houwink - Sakurada equation [44],... 

A viscometric detector together with a concentration detector can provide information on molar masses of macromolecules emerging from the FFF system [76,134,142-144] using the Mark-Houwink-Kuhn-Sakurada coefficients. If these coefficients are not available, an intrinsic viscosity distribution can still be determined without calibration. Detailed features of this distribution are unique to a given polymer sample, and are not affected by changes in experimental conditions [145]. In fact, since the intrinsic viscosity distribution is more directly related to end-use properties, its measurement is preferred in certain applications. 

Intrinsic viscosity is the most useful of the various viscosity expressions because it can be related to molecular weight by the Mark-Houwink-Sakurada equation ... 

Even without the use of a UC curve (one must be generated for each series of measurements), measurement of [t7o] is believed by some to yield an intrinsic viscosity-weighted molar mass [2]. Most importantly, there is a historic interest in the relation of [t ] to molar mass and/or size. Indeed, the study and explanation of UC has occupied the theorists for some time and, accordingly, there are various formulations describing such relationships [2]. For linear polymers, the most popular empirical relationship between [77] and molar mass is the Mark-Houwink-Sakurada (MHS) equation... 

The Mark-Houwink-Sakurada (MHS) relation relates the intrinsic viscosity [t ] to the average molecular weight (MW) in the following form ... 

Intrinsic viscosity [t]] of a polymer solution is related to its viscosity average molecular weight by the Mark-Houwink-Sakurada relationship ... 

The intrinsic viscosity contains the information on the conformation and molecular motion of each individual polymer chain. It depends on the molecular weight in the power law (the Mark-Houwink-Sakurada relation)... 

REPORTED VALUES OF THE MARK-HOUWINK-SAKURADA PARAMETERS RELATING INTRINSIC VISCOSITY TO MOLECULAR WEIGHT FOR PHB... 

Much of the above discussion indicates that, to study excluded volume effects, an accurate determination of unperturbed dimensions is required. For this, a common procedure is to extrapolate intrinsic viscosity of known molecular weight samples to zero molecular weight. Several extrapolations have been used, notably the Stockmayer-Fixman plot. Dondos and Benoit have now introduced a modified version of this, which appears to be linear over a wider range of molecular weights. It introduces a parameter D, which is shown to be linearly related to the exponent of the Mark-Houwink-Sakurada equation. 

In Table II, the large variations in the parameters for the Mark-Houwink-Sakurada equation [Eq. (I)] relating intrinsic viscosity [/y] to molecular weight M (AT and a are parameters which have to be determined for each polymer-solvent system). 

Figure 12-16 shows plots of the intrinsic viscosity [ ] versus the reaction time, r/%, for four water contents, r. [ j] increases with increasing reaction time. Figure 12-17 shows plots of iog[r]] versus log Mn for the fom solutions. It is known that the Mark-Houwink-Sakurada relation holds for [ ] and Mn (Badgley, 1949 Tsuchida, 1975). 

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