Effect of Concentration and Molecular Weight

At low solution concentrations. Equations 7.39 through 7.41 adequately describe the effect of concentration on polymer solution viscosity. In this same concentration range. Equations 7.42, 7.43, and 7.48 correctly describe the effect of polymer molecular weight on viscosity. These equations are inadequate, however, for predicting the viscosity of more concentrated polymer solutions. Several empirical expressions have been proposed in the literature for this purpose (see the work of Ott and Spurlin in Reference 51). An expression due to Lyons and Tobolsky [52] is particularly noteworthy  

This equation has been shown to reproduce the zero-shear viscosity of some polymers all the way from the dilute solution state to the melt. An equation of similar form has also been derived using free volume arguments [53,54], The constant b in Equation 7.49 may be either negative or positive, and at low solution concentrations, the constant k[ is the same as k in Equation 7.39. A simpler form, in which b is zero, was used earlier by Martin [51]  

This equation is popular for fitting solution viscosity data because it is a two-parameter equation, yet provides good quality fits at high solution concentrations 

In a melt of short chains. Equation 7.11 yields rj = rio = px Njs,ya% l6M. A more rigorous calculation that takes into account the time-dependent conformational changes that can occur in an isolated polymer chain (Rouse chain motion) [55,56] 

FIGURE 7.17 Logarithmic plots of viscosity ij versus weight-average degree of polymerization Z for six polymers. 1 poise = 0.1 Pa-s. (Data from Fox, T. G. et al., chap. 12 in F. R. Eirich, ed., Rheology, vol. 1, Academic Press, New York, 1956.) 

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Polarisation. In the event that e.e.m. takes place then the emission from the trap, excimer in the case of pure polymers, should be completely depolarised. Some time ago data was published on the emission of excimer for both polystyrene and poly(a-methyl styrene) indicating polarised emission (8) and therefore little e.e.m. More recently Phillips questioned the validity of the data and reported mesurements which suggest the excimer emission is depolarised (9 ). An experimental difference between the two sets of data is apparent - Phillips solutions were more dilute than these used in ref. 8. The range of concentrations has subsequently been extended with the results shown in Figure 1. A possible explanation for the effect of concentrations and molecular weights on the extent of polarisation of excimer emission is that the rate of rotational relaxation of this bulky entity becomes slower than the emission life-time as these two parameters increase. It is difficult to reconcile the concept of e.e.m. with polarised excimer emission. 

DoubUer, J. L., and Launay, B. (1976). Rheological properties of galactomannan in aqueous solutions Effect of concentration and molecular weight. Proc. Int. Congr. Rheol, 6th, pp. 532-533. 

Gupta RK, Nguyen DA, Sridhar T (1991) Extensional viscosity of dilute polystyrene solutions effect of concentration and molecular weight. Phys Fluid 12 1296-1318... 

Jones DM, Walters K, WilUams PR (1987) The Extensional Viscosity of Mobile Polymer Solutions. Rheol Acta 26 20-30 McKineley GH, Sridhar T (2002) Filament-Stretching Rheome-try of Complex Huids. Annu Rev Huid Mech 34 375-415 Li L, Larson RG, Sridhar T (2000) Brownian Dynamics Simulation of Dilute Polystyrene Solutions. J Rheol 4 291-322 Gupta RK, Nguyen DA, Sridhar T (1991) Extensional Viscosity of Dilute Polystyrene Solutions Effect of Concentration and Molecular Weight. Phys Huid 12 1296-1318... 

Wood, P.J. Beer, M.U. Butler, G. 2000. Evaluation of role of concentration and molecular weight of oat beta-glucan in determining effect of viscosity on plasma glucose and insulin following an oral glucose load. Br. J. Nutr. 84 19-23. 

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 investigations include the effect of (i) PVA molecular weight, particularly at higher concentrations which give different adsorption isotherms (ii) latex particle size over the range 190-llOOnm using a low-molecular-weight fully-hydrolyzed PVA (iii) electrolyte on bare and PVA-covered particles of different sizes. 

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." ... 

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... 

Figure 19.2. Diagram of osmotic behavior and the effect of solute concentration and molecular weight on osmotic pressure, (a) Osmotic-pressure behavior of solutions Ais the excess pressure on the solution required to stop flow of solvent through the semipermeable membrane, (b) Effects of solute concentration and molecular weight on osmotic pressure.

Figure 5. Effect of organic solvent concentration on the yield of copolymer and molecular weight of grafted chains in the pMMA-grafted dialdehydecellulose using a quartz lube. Conditions cellulose (C — 0, 29.8 mmol/100 g), 0.3 g H,0 + solvent, 10 mL MMA, 2 mL 50°C. Key to solvent O, CC/(, 1.5 h X, (CHs)t-CHCH%OH, 1.25 h A, HCON(CHs)t, 1 h <>, (CHs)2CO, 3 h.

Fig. 8. TEM studies of the effect of polydimethylsiloxane concentration and molecular weight on microphase development...

In addition to studying the effect of the stabilizer molecular weight on the MMA dispersion polymerization, the effect of the stabilizer concentration was also analyzed. The concentration of poly(FOA) stabilizer was systematically varied while the amount of MMA was held constant at 21 w/v % in CO2 (Table 2). It was found that as little as 0.24 wt. % (based on monomer) is needed to stabilize the polymerization and give spherical particles. Additionally, excess surfactant could be washed from the finished particle surface with CO2, resulting in... 

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