Complex viscosity concentrated solutions

When equal amounts of solutions of poly(ethylene oxide) and poly(acryhc acid) ate mixed, a precipitate, which appears to be an association product of the two polymers, forms immediately. This association reaction is influenced by hydrogen-ion concentration. Below ca pH 4, the complex precipitates from solution. Above ca pH 12, precipitation also occurs, but probably only poly(ethylene oxide) precipitates. If solution viscosity is used as an indication of the degree of association, it appears that association becomes mote pronounced as the pH is reduced toward a lower limit of about four. The highest yield of insoluble complex usually occurs at an equimolar ratio of ether and carboxyl groups. Studies of the poly(ethylene oxide)—poly(methacryhc acid) complexes indicate a stoichiometric ratio of three monomeric units of ethylene oxide for each methacrylic acid unit. 

Towards the middle of 1929, Mark was clearly close to establishing a viscosity equation. He and H. Fikentscher published a somewhat complex relationship of viscosity, and molecular volume (33). It was based on the Einstein relationship of viscosity and solute concentration. 

Polyelectrolyte complexation in aqueous solution between PEI and PMAA has been studied through viscometry, conductometry, potentiometry, and IR spectroscopy [90]. Upon addition of increasing concentrations of PMAA to an aqueous PEI solution, viscosity dropped suddenly around a 1 to 4 ratio of PMAA to PEI because of the complexation and subsequent coiling of the complexed chains. Reduced viscosity then rose past this ratio indicating that the stoichiometry of the complex occurs in a 1 4 (PMAA groups PEI groups) formation. Conductance and titration experiments agreed with this theory. The... 

It has been observed that the concentrated solution viscosity decreases upon addition of TMEDA to solutions of poly(isoprenyl)lithium 93). This would be consistent with the process shown in Eq. (17) or (20) and not with Eqs, (18) or (19). The decrease in viscosity would be consistent with interaction of TMEDA to form an unassociated complex (Eq. (20)), but this does not seem to be in accord /with the stoichiometry observed by calorimetry. It is noteworthy that the break observed by calorimetry at R = 0.5 is consistent with the stoichiometric dependence of spectral, kinetic and microstructure effects 90). Again this shows that these kinetic effects are related to the stoichiometry of formation of base-organolithium adduct, i.e. that they are ground-state solvation effects. 

A mathematical expression relating forces and deformation motions in a material is known as a constitutive equation. However, the establishment of constitutive equations can be a rather difficult task in most cases. For example, the dependence of both the viscosity and the memory effects of polymer melts and concentrated solutions on the shear rate renders it difficult to establish constitute equations, even in the cases of simple geometries. A rigorous treatment of the flow of these materials requires the use of fluid mechanics theories related to the nonlinear behavior of complex materials. However, in this chapter we aim only to emphasize important qualitative aspects of the flow of polymer melts and solutions that, conventionally interpreted, may explain the nonlinear behavior of polymers for some types of flows. Numerous books are available in which the reader will find rigorous approaches, and the corresponding references, to the subject matter discussed here (1-16). 

Figure 9. The Complex Viscosity as a Function of the Detergent Concentration for Solutions of C F gCO NCCH ) at T - 20 C.

Figure 9.20 The effect of agent concentration in the organic phase on viscosity for solutions containing no uranium (uncomplexed agent) and solutions previously equilibrated with aqueous uranium solution (complexed agent).17 (Organic phase Alamine 336 dissolved in Aromatic 150).

The constant of proportionality in equation 2.10 is the viscosity of the liquid tf). Some fluids, such as water, olive oil and sucrose solutions obey this equation and are said to be Newtonian. Their viscosity does not depend on the velocity gradient, i.e. how fast the liquid is sheared - known as the shear rate, More complex fluids (e.g. solutions of polymers) have a viscosity that does depend on the shear rate. Such fluids are called non-Newtonian . Many complex fluids, for example tomato ketchup and ice cream mix, become less viscous when they are sheared and are described as shear-thinning . Tapping the bottom of the bottle applies shear to the ketchup, which becomes less viscous and flows more easily onto your plate. Other fluids, such as a concentrated solution of cornstarch or quicksand, become more viscous (i.e. they are shear-thickening ). Experiment 7 in Chapter 8 gives some examples of non-Newtonian fluids. A single viscosity is not sufficient to describe the flow properties of non-Newtonian liquids and if a viscosity is stated, the shear rate at which it was measured must also be given. 

Spin coating. A small amount of solution is dropped onto a spinning carrier. The thickness of the resulting film depends on the rotation speed, the evaporation rate of the solvent and the initial viscosity (concentration of polymer and metal complex) of the solution. 

Figure 12.1.5. Viscosity ofPMMA solutions indifferent Figure 12.1.6. Relative viscosity of block copolymers solvents vs. PMMA concentration. Basic solvents with and and without segments capable of forming tetrahydrofuran, THF, and dioxane, DXN neutral tolu- complexes vs. concentration. [Data from I C De Witte, ene, TOL and CCI4 acidic 1,2-dichloroethane, DCE, b G Bogdanov, E J Goethals, Macromol. Symp., 118, CHCI3, and dichloromethane, DCM. [Adapted, by per- 237-46 (1997).] mission, from M L Abel, M M Chehimi, Synthetic Metals, 66, No.3, 225-33 (1994).]...

These departures from simple relationships are representative of simple solutions. The relationships for viscosities of solution become even more complex if stronger interactions are included, such as the presence of different solvents, the presence of interacting groups within polymer, combinations of polymers, or the presence of electrostatic interactions between ionized structures within the same or different chains. Figure 12.1.5 gives one example of complex behavior of a polymer in solution. The viscosity of PMMA dissolved in different solvents depends on concentration but there is not one consistent relationship (Figure 12.1.5). Instead, three separate relationships exist each for basic, neutral, and acid solvents, respectively. This shows that solvent acid-base properties have a very strong influence on viscosity. 

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