Mark-Houwink constant

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

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). 

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). 

Mark-Houwink constants for PEG, PEO, and PSC are summarized in Table 20.4. These were measured in either an aqueous mobile phase of 0.10 N NaNOi or a mobile phase of 20% acetonitrile in aqueous 0.10 N NaNOi (which also exhibits universal calibration behavior). The values for a fall within... 

TABLE 20.4 Mark-Houwink Constants for PEG, PEO, and PSC from SEC/Viscometry Using TSK-PW Columns... 

This equation appears to have a number of names, of which the Mark-Houwink equation is the most widely used. In order to use it, the constants K and a must be known. They are independent of the value of M in most cases but they vary with solvent, polymer, and temperature of the system. They are also influenced by the detailed distribution of molecular masses, so that in principle the polydispersity of the unknown polymer should be the same as that of the specimens employed in the calibration step that was used to obtain the Mark-Houwink constants originally. In practice this point is rarely observed polydispersities are rarely evaluated for polymers assigned values of relative molar mass on the basis of viscosity measurements. Representative values of K and a are given in Table 6.4, from which it will be seen that values of K vary widely, while a usually falls in the range 0.6-0.8 in good solvents at the 0 temperature, a = 0.5. 

Table 6.4 Typical values of Mark-Houwink constants (from J. Brandup and E. H. Immergut, Polymer Handbook , 2nd Edn., Wiley, New York, 1975)...

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. 

Relationships between dilute solution viscosity and MW have been determined for many hyperbranched systems and the Mark-Houwink constant typically varies between 0.5 and 0.2, depending on the DB. In contrast, the exponent is typically in the region of 0.6-0.8 for linear homopolymers in a good solvent with a random coil conformation. The contraction factors [84], g=< g >branched/ <-Rg >iinear. =[ l]branched/[ l]iinear. are another Way of cxprcssing the compact structure of branched polymers. Experimentally, g is computed from the intrinsic viscosity ratio at constant MW. The contraction factor can be expressed as the averaged value over the MWD or as a continuous fraction of MW. 

D. SEC Measurement of Mark-Houwink Constants Using Only Polydispersed Standards. If the SEC-MW calibration curve of the polymer-solvent system is known in addition to the [n] calibration, the Mark-Houwink constants of the polymer-solvent system are... 

The validity of a practical method of direct viscosity calculation from size exclusion chromatographic analysis is demonstrated. The method is convenient to use and is not limited by the availability of narrow MWD standards. It is possible to accurately measure polymer Mark-Houwink constants using the suggested broad standard SEC-[n] and SEC-MW calibration procedure. 

K and a are the Mark-Houwink constants for the linear homologue in the same solvent and at the same temperature as the SEC measurements. The constants b and c are to be determined. If there is no LCB below a certain molecular weight M., the c in equation (3) can be replaced with... 

For the copolymerization work, GPC 1 and GPC 2 (Table I) were used, Mark Houwink constants are shown in Table II. 

There are three imknowns, K, a and. One might question the availability of Mark-Houwink constants for the polymer in the open literature. Mark-Houwink constants in the literature differ widely for the same polymer and it is difficult to decide on the correct pair to employ. Another problem which can arise is that the universal molecular weight calibration curve may not apply exactly for the polymer in question. The use of the true Mark-Houwink constants would therefore introduce an error in the molecular weight calibration. Calibration with a broad MWD standard should eliminate this error. The Mark Houwink constants obtained in the calibration would in this instance be effective rather than true values. 

K and a = Mark-Houwink constants (which reflect polymer/solvent interactions)... 

---