Molecular weight Mark-Houwink-Sakurada

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. 

To perform this analysis, we first prepare a dilute solution of polymer with an accurately known concentration. We then inject an aliquot of this solution into a viscometer that is maintained at a precisely controlled temperature, typically well above room temperature. We calculate the solution s viscosity from the time that it takes a given volume of the solution to flow through a capillary. Replicate measurements are made for several different concentrations, from which the viscosity at infinite dilution is obtained by extrapolation. We calculate the viscosity average molecular weight from the Mark-Houwink-Sakurada equation (Eq. 5.5). 

The viscosity average molecular weight is determined through the use of the Mark-Houwink-Sakurada equation [3] using solution viscosity ... 

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. 

The Mark-Houwink-Sakurada constants for PMMA resin are o = 0.73 and K = 1. X 10 Table 3.3 contains solvent viscosity versus concentration data. Find the intrinsic viscosity using both the specific and relative viscosities and the viscosity average molecular weight. 

Next, a plot is made for the terms and n(ri )/c as a function of c as was shown in Fig. 3.7. Extrapolation of the functions to a concentration of zero provides the intrinsic viscosity of 0.565 dl/g, as shown in Eig. 3.8. Using Mark-Houwink-Sakurada Eq. 3.22, the viscosity average molecular weight is calculated at 221,000 kg/kg-mole. 

Mark-Houwink-Sakurada constant Mass transfer coefficient around gel Fractional reduction in diffusivity within gel pores resulting from frictional effects Solute distribution coefficient Solvent viscosity nth central moment Peak skewness nth leading moment Viscosity average molecular weight Number of theoretical plates Dimensionless number... 

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 ... 

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],... 

The molecular weight dependence of fr ] can be expressed by the semi-empirical Mark-Houwink-Sakurada (MHS) equation,... 

B. Assume that the GPC curve of Polymer A is that of a polydisperse linear poly-chloroprene with Mark-Houwink-Sakurada constants in THF at 30°C of K = 4.18 x 10 5 dl/g and a - 0.83. Calculate the weight and number molecular weight averages, the polydispersity and the intrinsic viscosity of this polychloroprene. 

We take the Mark-Houwink-Sakurada equation (Eq. 3-44) as given. We assume also that the same values of K and a will apply to all species in a polymer mixture dissolved in a given solvent. Consider a whole polymer to be made up of a series of I monodisperse macromolecules each with concentration (weight/volume) c, and molecular weight A/,. From the definition of [r ] in Eq. (3-37),... 

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 ... 

Viscosity measurements alone cannot be directly used in the Mark-Houwink-Sakurada equation to relate absolute viscosity and polymer molecular weight, since additional unknowns, K and a must be determined. Therefore, viscometry does not yield absolute molecular weight values it rather gives only a relative measure of polymer s molecular weight. Viscosity measurements based on the principle of mechanical shearing are also employed, most commonly with concentrated polymer solutions or undiluted polymer these methods, however, are more applicable to flow properties of polymers, not molecular weight determinations. 

Molecular weight is related to [r/] by the Mark-Houwink-Sakurada equation given as... 

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. 

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

The classical method for determining K and a values of the Mark-Houwink-Sakurada (MHS) equation involves fractionation of a whole polymer into subspecies, or fractions, with narrow molecular weight distributions. An average molecular weight can be determined on each such fraction, by osmometry (M ) or light scattering (My,), and, if the fractions are narrow... 

HEMA, MMA, and MAA or DMAEMA (66, 67). Polymer molecular weight control was attempted by adjustment of initiator concentrator through the presumed inverse square root relationship between initiator level and kinetic chain length, (63) and this was reflected in measured intrinsic viscosities. Comparisons across a series are made difficult by changing Mark-Houwink-Sakurada coefficients. However direct comparisons may be made between polymers of similar composition, for example lc, 2c, and 3c, to show an expected increase in hydrodynamic volume from series 1 through series 3. 

Dilute Solution Properties. The rheology of dilute polymer solutions has been used extensively to gain insight into the structure and conformation of polymers in solution (11). The intrinsic viscosity provides a measure of the molecular weight of a polymer through a relationship such as the Mark-Houwink-Sakurada equation. Earlier studies of polyacrylamide (PAM) systems and details of the complexity of the characterization of high-molecular-weight water-soluble systems can be found in references 9, 13, and 14. 

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

---