Concentration and molecular weight

Concentration and Molecular Weight Effects. The viscosity of aqueous solutions of poly(ethylene oxide) depends on the concentration of the polymer solute, the molecular weight, the solution temperature, concentration of dissolved inorganic salts, and the shear rate. Viscosity increases with concentration and this dependence becomes more pronounced with increasing molecular weight. This combined effect is shown in Figure 3, in which solution viscosity is presented as a function of concentration for various molecular weight polymers. 

Experimental values of X have been tabulated for a number of polymer-solvent systems (4,12). Unfortunately, they often turn out to be concentration and molecular weight dependent, reducing their practical utility. The Flory-Huggins theory quahtatively predicts several phenomena observed in solutions of polymers, including molecular weight effects, but it rarely provides a good quantitative fit of data. Considerable work has been done subsequentiy to modify and improve the theory (15,16). 

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 ... 

Detailed studies on radiation chemistry of PEO have been performed [74-77]. Upon y-irradiation, the gel-dose drops abruptly along with an increase in the concentration and molecular weight of the polymer, thus reaching values of 0.15-0.25 Mrad in the range of practical interest [75]. Oxygen is a strong inhibitor and when it is carefully removed from the solution, crosslinking of PEO occurs at doses as low as 0.01 Mrad [76]. 

The solution viscosity is a function of the polymer concentration and molecular weight, and can be determined by the Mil Iyer and Leonard method [j 2]. 

The Non-Newtonian behaviour, i.e. the decrease of the viscosity as a function of the shear rate, becomes increasingly important when the polymer concentration and molecular weight... 

Rymden, R. Stilbs, P. (1985b). Concentration and molecular weight dependence of counterion self-diffusion in aqueous poly(acrylic acid) solutions. Journal of Physical Chemistry, 89, 3502-5. 

As will be demonstrated later, LS can be quantified by an experimental quantity termed the excess Rayleigh ratio between solution and solvent, R, which is related to the concentration and molecular weight of solute by the following expression... 

It is possible for chiral mesogens to produce essentially achiral mesophases. For instance, in certain ranges of concentration and molecular weight, DNA will form an achiral line hexatic phase. A curious recent observation is of the formation of chiral mesophases from achiral mesogens. Specifically, bent-core molecules (sometimes called banana LCs) have been shown to form liquid crystal phases that are chiral. In any particular sample, various domains will have opposite handedness, but within any given domain, strong chiral ordering will be present. 

Mineral segregation in industry relies heavily on the selective adsorption of macromolecules onto the surfaces of those minerals that have particular industrial applications. This selectivity is governed mainly by the surface chemistry of the mineral and the type of polymer used as a flocculant. " Effectiveness of flocculation depends upon the charge, concentration and molecular weight of the polymer, and also the pH and salt concentration of the clay suspension. The bonding between the anionic flocculant polyacrylamide (PAM) and clay mineral surfaces has been effectively reviewed recently by Hocking et al and the reader is referred to this should they require an in-depth literature review. For more information on general colloidal chemistry of clay suspensions the reader is referred to the review of Luckham and Rossi." ... 

For a polydisperse polymer, experimental measurements of M for the chromatogram at high Tr may not be accurate. When average molecular weights are computed from the distribution w(M) derived fromdata obtained with concentration and molecular weight detectors, the value of Mw is likely to be more valuable than M , which could be substantially in error [25,26]. 

The zero-shear viscosity r 0 has been measured for isotropic solutions of various liquid-crystalline polymers over wide ranges of polymer concentration and molecular weight [70,128,132-139]. This quantity is convenient for studying the stiff-chain dynamics in concentrated solution, because its measurement is relatively easy and it is less sensitive to the molecular weight distribution (see below). Here we deal with four stiff-chain polymers well characterized molecu-larly schizophyllan (a triple-helical polysaccharide), xanthan (double-helical ionic polysaccharide), PBLG, and poly (p-phenylene terephthalamide) (PPTA Kevlar). The wormlike chain parameters of these polymers are listed in Tables... 

Simha and Zakin (126), Onogi et al (127), and Comet (128) develop overlap criteria of the same form but with different numerical coefficients. Accordingly, flow properties which depend on concentration and molecular weight principally through their effects on coil overlap should correlate through the Simha parameter c[ /], or cM , in which a is the Mark-Houwink viscosity exponent (0.5 < a < 0.8). If coil shrinkage, caused by the loss of excluded volume in good... 

Fig, 5.3. Viscosity at various concentrations and molecular weights in the low to moderate concentration range. Polystyrene-decalin and polymethyl methacrylate-xylene are theta or near-theta systems the remainder are good solvent systems (121,177). Note that the c[i/] reduction is somewhat better in theta solvents, and that the Martin equation [Eq. (5.9)], which would give a straight line in the figure, is a somewhat better representation for... 

The plateau region appears when the molecular weight exceeds Mc [(Mc)soln. for solutions], and is taken to be a direct indication of chain entanglement. Indeed the presence of a plateau may be a more reliable criterion than r 0 vs M behavior, especially in solutions of moderate concentration where viscosity may exhibit quite complex concentration and molecular weight behavior. It is postulated that when M greatly exceeds Mc, a temporary network structure exists due to rope-like interlooping of the chains. Rubber-like response to rapid deformations is obtained because the strands between coupling points can adjust rapidly, while considerably more time is required for entire molecules to slip around one another s contours and allow flow or the completion of stress relaxation. 

The usual concentration and molecular weight dependence of the structural variables thus combine to give... 

Figure 8.14 shows the result of combining the correlations of /30 (Fig. 8.13) and JeR (Fig. 5.18). The product (30Jcr is remarkably independent of concentration and molecular weight from infinite dilution all the way to the undiluted melt state and shows no substantial variation from one polymer to another. For the particular definition of critical reduced shear rate y0 used here, the experimental result for narrow distribution linear chains can be expressed as...

Fig. 8.16. Superimposed plots of y(y)M0 and J(y)/J° as functions of shear rate for poly( -methyl styrene) solutions (199). Curve A is for data at low concentrations and molecular weights curve B is for data at high concentrations and molecular weights. Data have been shifted along the shear rate axis to produre superposition. [Reproduced from Macromolecules 5,791 (1972).]...

Holmes, L. A., Ferry, J.D. Dependence of the steady-state compliance on concentration and molecular weight in polymer solutions. J. Polymer ScL Pt C 23,291-299 (1968). 

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