Mark-Houwink equations poly

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 ... 

It is of some interest that the mechanical treatment of poly(vinyI chloride) under conditions of high shear stress in the melt, in a Brabender Plastograph, was found to increase the degree of LCB, as estimated from deviations from the Mark-Houwink equation 204). This is presumably due to chain scission under the influence of the shear stress followed by attack of the radicals produced on other polymer chains, and subsequent recombination reactions. 

In fact, for random-coil conformations, b in Equation 41 is explicitly related to the exponent in the Mark-Houwink equation by 3b = a 1. In this way values of M may be determined directly from measurements of D° provided KD and b are known. Although both these parameters could in principle be calculated from a detailed knowledge of the geometry of the solute, it is usual to regard them as experimentally determinable parameters. A similar relationship has also been found to hold true for the polypeptide poly(y-benzyl L-glutamate) (PBLG) dissolved both in 1,2-dichloroethane and in dichloroacetic acid. These results are shown in Figures 6 and 7, respectively. 

When a value of r = 0.78 is used, the data points for MSM copolymers (shown as crosses) coincide with the curve for polystyrene. According to Equation 4, r may be calculated from the coefficient K for homopolymers. When applied to the data on polystyrene and poly (methyl methacrylate) (3), a value of 0.72 is obtained, in good agreement with the above value of 0.78. The slight difference is probably the result of the polydispersity in the copolymers since the Mark-Houwink equation requires monodispersed polymers. 

Intrinsic Viscosity - Molecular Weight Relationship. A rod-like polymer has a large a value in the Mark-Houwink equation (Eq. 25). Such an example is poly(y-benzyl L-glutamate)... 

Chiu FC, Ung MH (2007) Thermal properties rmd phase morphology of melt-mixed poly (trimethylene terephthalate)/polycarbonate blends-mixing time effect. Polym Test 26 338-350 Chuah HH (2004) Effect of process variables on bulk development of air-textured poly (trimethylene terephthalate) bulk continuous filament. J Appl Polym Sci 92 1011-1017 Chuah HH, Lin VD, Soni U (2001) PTT molecular weight and Mark-Houwink equation. Polymer 42 7137-7139... 

Figure 5.1 Dependence of the K value of the Mark-Houwink equation on vinyl content (a) for polybutadiene, and on styrene content (b) for poly(styrene-butadiene) copolymers having 28% vinyl content [16], O, calibration samples cisUrans ratio is about 0.8.

SEC of tightly cross-linked poly(styrene-divinylbenzene) microgels with molecular masses in the range 10 -10 was measured in DMF containing 7 g L LiBr at 80°C [27]. Molecular mass data obtained using the universal calibration curve was in satisfactory agreement with results obtained by other techniques. The Mark-Houwink equation was as follows ... 

Allen, Booth, and Jones (96) investigated the intrinsic viscosity-molecular weight behavior of amorphous and crystalline fractions, as well as whole polymers of poly(propylene oxide), and found that their combined behavior could be described by the following Mark-Houwink equations. 

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. 

The concept of a unique hydrodynamic volume for all rodlike polymers was derived from examination of the Mark-Houwink constants, K and a, of the equation [rj ] = KMa. Macromolecules with values of a greater than unity are commonly accepted to be stiff or rigid rods. However, it was also found that such molecules (even for values of a less than unity) obey a relation illustrated by close concordance with the curve in Fig. lb (13) flexible, branched or otherwise irregular polymers, on the other hand, show dispersion around the upper part of the curve. The straight line curve in Fig. lb implies that the constants K and a are not independent parameters for the regular macromolecules to which they apply. Poly (a- and polyQJ-phenylethyl isocyanide) fall on this line the former has a value of a > 1 while the latter has a value a < 1 (14) both polymers give linear concentration dependence of reduced specific viscosity for fractionated samples... 

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 considered effect is very similar to the received one at the comparison of polyarylates, S5mthesized by equilibrium and nonequilibrium (interphase) polycondensation [5], So, for polyarylate F-2, received by the first from the indicated methods, estimation according to the Eq. (4), gives D=. ll and by the second one—D=. 55. This distinction was explained by the polyarylates structure distinction, received by the indicated above methods. Hard conditions of equilibrium poly condensation (high temperature, large process duration) can cause the appearance of branched reaction products owing to lacton cycle rupture in phenolphthaleine residues then the exponent in Mark-Kuhn-Houwink equation should be reduced, since its value is less for a branched polymer, than for a linear one [5], If it is like that, then Devalue should be increased respectively according to the Eq. (4). 

Thus, the fractal analysis methods were used above for treatment of comb-like poly(sodiumoxi) methylsylseskvioxanes behavior in solution. It has been shown that the intrinsic viscosity reduction at transition from a linear analog to a branched one is due to the sole factor, namely, to a macromolecule connectivity degree enhancement, characterized by spectral dimension. This conclusion is confirmed by a good correspondence of the experimental and calculated according to Mark-Kuhn-Houwink equation fiactal variant intrinsic viscosity values. It has been shown that qualitative transition of the stmcture of branched polymer macromolecular coil from a good solvent to 0-solvent can be reached by a solvent change. 

In the above equation the R group designates the particular acrylate. Ethyl, iso-propyl, and / -butyl acrylates were produced yielding the polymers poly(ethyl acrylate)-di (PEA-di), poly(wo-propyl acrylate)-di (PIPA-di) and poly(n-butyl acrylate)-di. For PIPA the viscosity average molecular mass was measured to be 98,000 daltons.(5) The molecular masses of the other polymers were not estimated directly because their Mark-Houwink coefficients were not known, but they had similar intrinsic viscosities. At these molecular weights, we expect the relaxation times to be independent of molecular mass.(i)... 

Actually, the Mark-Houwink-Sakurada equation applies only to narrow molecular weight distribution polymers. For low molecular weight poly disperse polymers this equation is useful, because the deviations due to chain entanglement are still negligible. On the other hand, chain entanglement in high molecular weight polydisperse polymers affects viscosity and this equation does not really apply. 

Kuhn-Mark-Houwink-Sakurada equation Dimension factor of steric hindrance Length, capillary length Persistence length Low-density poly(ethylene)... 

On the other hand, using molecular weights measured by GPC, the constants of the Mark-Houwink-Sakurada equation for poly(3-hexylthiophene) were determined in tetrahydrofiiran at 25°C [78] ... 

The second calibration curve (deduced from universal calibration, figure 3) presented in this section can appear as illogical, being based on a closed loops reasoning. However, its only objective is to provide a calibration procedure indqjendent of the stability of polysilane standards. This is achieved by the pseudo-Mark-Houwink relationship (equation 5). This latta equation gives also the possibility to everyone to calibrate a GPC for poly(methylphenyl)silane on the basis of PS standards only. 

This way, assuming, as above, a similar Grc separation of PS and PSi, equations (1), (2) and (4) can be used to provide a more precise Mark-Houwink viscosity plot for poly(methylphenyl)silane. The results of that analysis for 35 "slices" are reported in fig. 4. It is observed that two different linear Ma -Houwink relationships can be written depending on range (equation (6) and (7))... 

Equation (6164) is known as the Mark-Houwink-Sakurada relation . It generally holds very well, as is also exemplified by the data obtained for two different solutions of poly(isobutylene) presented in Fig. 6.17. 

The solution viscosities of Poly 10a and Poly 10b were extremely low, and the [rj]s were in the range of 0.019-0.025 dLg The a value in the Mark-Houwink-Sakurada equation was 0.105. This small value was consistent with a highly branched... 

The three-dimensional property was characterized based on a viscosity study. The [rj] value increased with the increasing M sls value and the a value of the Mark-Houwink-Sakurada equation was found to be 0.29, which was obtained from the slope of the logarithmic plots of [rj] versus Mw,sls- H is well known that the a value is less than 0.5 for the various hyperbranched polymers, so that Poly 13 had a spherical shape in solution (Jikei and Kakimoto, 2001). 

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