Mark Houwink equation

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. 

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

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. 

The analysis of the main properties of aqueous solutions of polyacrylamide and copolymers of acrylamide has been reviewed [4,5]. The main characteristics of aqueous solutions of polyacrylamide is viscosity. The viscosity of aqueous solutions increases with concentration and molecular weight of polyacrylamide and decreases with increasing temperature. The relationship between the intrinsic viscosity [q]) in cmVg and the molecular weight for polyacrylamide follows the Mark-Houwink equations ... 

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. 

Studies of the hydrodynamic properties and unperturbed dimensions of fractionated PCL have shown that it is a flexible coil (54,55). The following Mark-Houwink equations have been reported ... 

If changes in the molecular weight distribution can be neglected, substitution of the Mark-Houwink equation into Eq. 7 leads to Eq. 8, where a is the Mark-Houwink exponent. 

Fig. 10. Dependence of the exponent a of Mark-Houwink equation on the 1,4-DVB content of the microgels formed in emulsion. The data points were calculated from the [x ] and Rvalues reported by Hoffmann ( ) [70] and by Bolle (A) [83].

Under the same reaction conditions macrogelation occurs later in the polymerization of 1,3-DVB. Moreover, the [r ] of the microgels from 1,3-DVB is much smaller than that from 1,4-DVB. The exponent a of Mark-Houwink equation for the 1,3-DVB polymers in toluene was found to be only 0.25 [250] and 0.29 [251 ] compared with 0.48 for 1,4-DVB polymers obtained under similar reaction conditions [230]. The delay of the gel point and the small hydro-dynamic volumes of 1,3-DVB microgels, compared with 1,4-DVB microgels also illustrate that the extent of cyclization is much higher in 1,3-DVB polymerization. 

Markham and Benton model, 1 628 Mark-Houwink coefficients for cellulose, 20 558t for PBT, 20 64t for PET, 20 58 for PTT, 20 69t Mark-Houwink constants, for poly(ethylene oxide), 10 677t Mark-Houwink equation, 19 717, 839 Mark-Houwink relationship, 10 675 ... 

In the following four years Mark successively reported on the viscosity and molecular weight of cellulose (40), Staudinger s Law (41), high polymer solutions (42), and the effect of viscosity on polymerization rates (43). Confident of his findings, he proposed (at the same time as R. Houwink) the general viscosity equation now known as the Mark-Houwink Equation (44, 45). 

Mark and Houwink were the first to formulate the equation in the power form and to demonstrate its validity by means of empirical values. In reality, the Mark-Houwink Equation is simply the Einstein viscosity equation, which assumed spheres, transferred to particles with size dependent particle density. 

The molecular weight is normally measured, for convenience sake, by solution viscosity and is often given as the intrinsic viscosity. There is a wide range of solutions used, with the average molecular weight related to the intrinsic viscosity by the Mark-Houwink equation ... 

As a norm, polyester molecular weights are reported by their intrinsic viscosities (IV), [r ]. The two are related by the Mark-Houwink equation, as follows ... 

Mark-Houwink equation phys chem The relationship between intrinsic viscosity and molecular weight for homogeneous linear polymers. mark hau.wigk l.kwa-zhan Markovnikoff s rule org chem in an addition reaction, the additive molecule RH adds as H and R, with the R going to the carbon atom with the lesser number of hydrogen atoms bonded to it. mar kov-ns.kofs, riil ... 

Viscosity Measurements. A Zimm-Couette type low shear viscometer was used. The intrinsic viscosities were estimated from single concentration viscosity measurements using the equations for the concentration dependence of the specific viscosity (5,6). The Mark-Houwink equation was used to determine My (5,6). 

Staudinger showed that the intrinsic viscosity or LVN of a solution ([tj]) is related to the molecular weight of the polymer. The present form of this relationship was developed by Mark-Houwink (and is known as the Mark Houwink equation), in which the proportionality constant K is characteristic of the polymer and solvent, and the exponential a is a function of the shape of the polymer in a solution. For theta solvents, the value of a is 0.5. This value, which is actually a measure of the interaction of the solvent and polymer, increases as the coil expands, and the value is between 1.8 and 2.0 for rigid polymer chains extended to their full contour length and zero for spheres. When a is 1.0, the Mark Houwink equation (3.26) becomes the Staudinger viscosity equation. 

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