Viscosity, dilute solution flexible chains

Diffusion and sedimentation measurements on dilute solutions of flexible chain molecules could be used to determine the molecular extension or the expansion factor a. However, the same information may be obtained with greater precision and with far less labor from viscosity measurements alone. For anisometric particles such as are common among proteins, on the other hand, sedimentation velocity measurements used in conjunction with the intrinsic viscosity may yield important information on the effective particle size and shape. ... 

In Table 1 we present the Zp values determined in THF and two different THE/DME mixtures. These values, on the order of 1 rm, are comparable to those reported by Discher and coworkers [38,70] and by Bates and coworkers [71,72] for PEO-PI cylindrical micelles with a core diameter of 20 nm in water. Here PEG denotes poly(ethylene oxide). Bates and coworkers deduced their values of Zp from small-angle neutron scattering experiments, whereas Discher and coworkers determined the Zp values using fluorescence microscopy. The fact that the Zp values that we determined from viscometry are comparable to those of the PEO-PI cyUndrical micelles with similar core diameters again suggests the validity of the YFY theory in treating the nanofiber viscosity data. This study demonstrates that block copolymer nanofibers have dilute solution properties similar to those of semi-flexible polymer chains. 

The worm like chain model has been applied to interpret data on intrinsic viscosity"l2, light scattering" 3... in dilute solutions. These measurements can be used to fix approximately the value of q for a given polymer system, although the solvent often affects the numerical value due to excluded volume interactions, A connection to the flexibility introduced in the lattice model has been given" 4,... 

The zero shear viscosity of flexible linear polymers varies experimentally with and theoretically with [20]. Due to the highly restricted rotational diffusion, the viscosity of TLCPs is much more sensitive to the molecular weight than that of ordinary thermoplastics as discussed in section 3. Doi and Edwards predicted that the viscosity of rod-like polymers in semi-dilute solutions scales with A/ [see Equation (12)] [2]. Such a high power dependence of viscosity on the molecular weight has been experimentally observed both for lyotropic LCPs [14,15] and for TLCPs [16-18]. The experimental values of the exponent range from 4 to 7 depending on the chemical structure, the chain stiffness, and the domain or defect structure of the liquid crystalline solution or melt. The anisotropicity of the liquid seems to have little effect on the exponent. A slightly smaller exponent for the nematic phase than for the isotropic phase (6 in the nematic phase versus 6.5 in the isotropic... 

The behaviour of diluted solutions is related to the relation between the viscosity and the chain characteristics (structure, configuration, conformation, etc). Usually, the polymer solutions are treated as two-phase systems, consisting from mechanical elements, the macromolecules, immersed into a continuous media, the solvent. For long time, it was considered that the solvent acts to the polymer macromolecules in the same manner in which a fluid exerts forces about a small particle suspended in it. However, the extension of this model to the polymer solution is not adequate since, the ratio between the dimensions of macromolecules and those of solvent molecules essentially differs by that between the dimensions of a solid immersed particle and solvent molecules. On the other side, the flexible macromolecules, randomly coiled, can not be assimilated with the solid particles and therefore the typical relations applied to solid suspensions in liquids can not be used in this case. 

The classical method to determine and a of a given polymer is as follows. First, prepare fractions of different molecular weights either by synthesis or by fractionation. Next, make dilute solutions of different concentrations for each fraction. Measure the viscosity of each solution, plot the reduced viscosity as a function of polymer concentration, and estimate [17] for each fraction. Plot [17] as a function of the molecular weight in a double logarithmic scale. This method has been extensively used to characterize polymer samples because the exponent a provides a measure of the chain rigidity. Values of a are listed in Table 3.2 for some typical shapes and conformations of the polymer. The value of a is around 0.7-0.8 for flexible chains in the good solvent and exceeds 1 for rigid chains. In the theta solvent, the flexible chain has a = 0.5. 

If the shear rate is higher than the time for the first normal mode, the chain does not have time to respond to the applied perturbation, and only the higher modes are able to be activated. In other words, at times which are shorter than Tj the first normal mode is frozen out and hence cannot contribute to the observed viscosity. Further increase in the rate of shear will progressively remove further modes until the viscosity falls to a value which corresponds to that of the solvent. This simple description, with minor modifications, describes the behaviour of most polymer molecules in dilute solution. Because in solution the backbone motions are effectively liberated, so that the chains are fuUy flexible, the description of the viscosity of dilute polymer solutions is essentially independent of the chemical nature of the molecules. The modes are purely defined by the end to end length of the polymer chains and hence by the molar mass of the polymer. 

As with flexible chains, most studies of conformational behavior of stiff chains have involved light scattering and intrinsic viscosity studies of dilute polymer solutions. Excluded volume effects are of much diminished significance for stififer chains, so measured persistence lengths usually show only a mild dependence on the nature of the solvent. In fact, Norisuye and Fujita [72] have shown that excluded volume effects become measurable only when chains are very long (L 100 q). Thus, the choice of solvent is normally of less importance in studying the conformation of stiff chains than it is for flexible ones. Temperature, however, frequently has a pronounced impact on the value of q for stiff chain polymers [73]. 

However, viscometric measurements of dilute polymer solutions in a steady flow are inadequate for this purpose although, as already indicated, viscosity is related to molecular rotation. This has been demonstrated by Zimm s theory ). Zimm considered the kinetics of the motion and deformation of a kinetically flexible polymer chain in a weak mechanical field with harmonic velocity gradient g at frequency v. It has been found that under steady and weak flow conditions... 

Measurements of the steady shear viscosity in the Newtonian or linear regime yields valuable information on molecular interactions. The molecular weight (Mw) and polymer concentration (C) dependence of the zero-shear viscosity, rjo, of cellulose solutions, exhibits two distinct regions. The dilute regime shows a linear increase of zero-shear viscosity with respect to CMw In the semi-dilute region, the CM is no longer linearly proportional to r o-It is well established for linear, flexible polymer chains that rjo is proportional to [13]. This proportionality for cellulose in the NH3/NH4SCN... 

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