Houwink

R. Houwink and G. Salomon, eds.. Adhesion and Adhesives, Elsevier, New York, 1965. J. Israelachvili, Intermolecular Surface Forces, 2nd ed.. Academic, San Diego, CA, 1992. 

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

The viscosity average molecular weight is not an absolute value, but a relative molecular weight based on prior calibration with known molecular weights for the same polymer-solvent-temperature conditions. The parameter a depends on all three of these it is called the Mark-Houwink exponent, and tables of experimental values are available for different systems. 

At 25°C, the Mark-Houwink exponent for poly(methyl methacrylate) has the value 0.69 in acetone and 0.83 in chloroform. Calculate (retaining more significant figures than strictly warranted) the value of that would be obtained for a sample with the following molecular weight distribution if the sample were studied by viscometry in each of these solvents ... 

This relationship with a = 1 was first proposed by Staudinger, but in this more general form it is known as the Mark-Houwink equation. The constants k and a are called the Mark-Houwink coefficients for a system. The numerical values of these constants depend on both the nature of the polymer and the nature of the solvent, as well as the temperature. Extensive tabulations of k and a are available Table 9.2 shows a few examples. Note that the units of k are the same as those of [r ], and hence literature values of k can show the same diversity of units as C2, the polymer concentration. 

Table 9.3 lists the intrinsic viscosity for a number of poly(caprolactam) samples of different molecular weight. The M values listed are number average figures based on both end group analysis and osmotic pressure experiments. Tlie values of [r ] were measured in w-cresol at 25°C. In the following example we consider the evaluation of the Mark-Houwink coefficients from these data. 

Table 9.2 Values for the Mark-Houwink Coefficients for a Selection of Polymer-Solvent Systems at the Temperatures Noted...

Evaluate the Mark-Houwink coefficients for poly (caprolactam) in w-cresol at 25°C from the data in Table 9.3. 

By taking the logarithm of both sides of Eq. (9.34), the Mark-Houwink equation is transformed into the equation of a straight line ... 

Since viscometer drainage times are typically on the order of a few hundred seconds, intrinsic viscosity experiments provide a rapid method for evaluating the molecular weight of a polymer. A limitation of the method is that the Mark-Houwink coefficients must be established for the particular system under consideration by calibration with samples of known molecular weight. The speed with which intrinsic viscosity determinations can be made offsets the need for prior calibration, especially when a particular polymer is going to be characterized routinely by this method. 

It is apparent from an examination of Table 9.2 that the Mark-Houwink a coefficients fall roughly in the range 0.5-1.0. We conclude this section with some qualitative ideas about the origin of these two limiting values for a. We consider a polymer molecule consisting of n repeat units, and two different representations of its interaction with solvent. 

Equations (9.42) and (9.46) reveal that the range of a values in the Mark-Houwink equation is traceable to differences in the permeability of the coil to the flow streamlines. It is apparent that the extremes of the nondraining and free-draining polymer molecule bracket the range of intermediate permeabilities for the coil. In the next section we examine how these ideas can be refined still further. 

Our primary objective in undertaking this examination of the coil expansion factor was to see whether the molecular weight dependence of a could account for the fact that the Mark-Houwink a coefficient is generally greater than 0.5 for T 0. More precisely, it is generally observed that 0.5 < a < 0.8. This objective is met by combining Eqs. (9.55) and (9.68) ... 

For conditions of intermediate solvent goodness, a shows a dependence on M which is intermediate between the limits described in items (1) and (2) with the corresponding intermediate values for the Mark-Houwink a coefficient. 

Suspension- and emulsion-polymerized PVDF exhibit dissimilar behavior in solutions. The suspension resin type is readily soluble in many solvents even in good solvents, solutions of the emulsion resin type contain fractions of microgel, which contain more head-to-head chain defects than the soluble fraction of the resin (116). Concentrated solutions (15 wt %) and melt rheology of various PVDF types also display different behavior (132). The Mark-Houwink relation (rj = KM°-) for PVDF in A/-methylpyrrohdinone (NMP) containing 0.1 molar LiBr at 85°C, for the suspension (115) and emulsion... 

Molecular Weight. The molecular weight of polypropylene is typically determined by viscosity measurements. The intrinsic viscosity [Tj] of the polymer in solution is related to the molecular weight, Af, by the Matk-Houwink equation ... 

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

Table 3. Mark-Houwink Constants for PET in Various Solvents at 25°C...

Fig. 3. Solution viscosity vs concentration for ethylene oxide polymers (10). The molecular weight of the polymer is indicated on each curve. The dependence of the intrinsic viscosity [Tj] on molecular weight M for these polymers can be expressed by the Mark-Houwink relationship ...

Table 2. Mark-Houwink Constants for Poly(ethylene oxide)...

Intrinsic viscosity is often used to characterize tetrahydrofuran polymers. Intrinsic viscosities in a variety of solvents and Mark-Houwink constants for the equation [rj] = Khave been deterrnined for a wide variety of solvents (39—45),where [Tj] is the intrinsic viscosity, M is molecular weight, and K and a are constants many of the constants have been summarized and tabulated (6). 

Universal SEC calibration reflects differences in the excluded volume of polymer molecules with identical molecular weight caused by varying coil conformation, coil geometry, and interactive propenies. Intrinsic viscosity, in the notation of Staudinger/ Mark/Houwink power law ([77]=fC.M ), summarizes these phenom-... 

FIGURE 16.10 Intial dextran calibration ( ) and resultingnb/Icbglucan calibration ( )forthe Sepha-cryl S-SOO/S-1000 (60 + 9S X 1.6 cm) system achieved from broad standard calibration with Dextran T-SOO and universal calibration, respectively Staudinger/Mark/Houwink constants (dextran Ksu = 0.0978 ml Mg . Osw = O.SO nb/lcb amylose = pullulan K pi. = 0.0268 ml M g . = 0.6S). 

Molecular weight calibration from a monomer to several million daltons can be carried out by a variety of techniques. Because narrow standards of p(methyl methacrylate) (pMMA) are available, these are often used. Narrow standards of p(styrene) (pSty) are also available and can be used. Using the Mark-Houwink-Sakurada equation and the parameters for pSty and pMMA, a system calibrated with pSty can give pMMA-equivalent values, and vice versa. 

The relationship between molecular weight, M, and intrinsic viscosity, [tjJ, of a polymer is given by the widely used Mark-Houwink expression... 

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