Viscosity of a Solution

2 Viscosity of a Solution Now we learn how to express the concentration dependence of the viscosity in solutions. When the concentration c, expressed in g/L, is sufficiently low, the viscosity rj of the solution is not much different from the viscosity tJs of the pure solvent. The ratio of rj to rj is called the relative viscosity. Although the ratio is dimensionless, it is customary to use the symbol for the relative viscosity. When c is low. 

The dimension of [17] is (concentration) . As we will learn in Section 3.3.3, how [17] of the polymer solution depends on the molecular weight of the polymer gives a hint on the conformation of the polymer. The second-order coefficient can be positive or negative. 

Sometimes, the specific viscosity rjsp, defined as rjsp = 17 — 1, is used  

The reciprocal of the intrinsic viscosity is often used to represent the overlap concentration of a given polymer c = I/Itj] (Eq. 1.110). It means that we can expect the polymer solution at c to be about twice as viscous as the pure solvent. 

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Viscosity additives are aliphatic polymers of high molecular weight whose main chain is flexible. It is known that in a poor solvent, interactions between the elements making up the polymer chain are stronger than interactions between the solvent and the chain (Quivoron, 1978), to the point that the polymer chain adopts a ball of yarn configuration. The macromolecules in this configuration occupy a small volume. The viscosity of a solution being related to the volume occupied by the solute, the effect of polymers on the viscosity in a poor solvent will be small. 

The intrinsic viscosity of a solution of particles shaped like ellipsoids of revolution is given by the expression... 

The viscosity of a solution of microbial exopolysaccharide must, therefore, be defined as a function of the shear rate (see Figure 7.7). 

In a study of the viscosity of a solution of suspension of spherical particles (colloids), suggested that the specific viscosity rjsp is related to a shape factor Ua-b in the following way ... 

In this work, we propose a method based on different combined semi-empirical laws to predict the evolution of the viscosity of a solution of acrylamide - acrylic acid copolymer. In fact, it appears... 

The viscosity of the solution is significantly increased when macromolecules are dissolved in a solvent. The specific viscosity of a solution t sp=(ri-r o)lr o expected to increase proportionally to the concentration c. The reduced viscosity rjgp/c still increases with increasing concentration. The data, however, can be extrapolated to zero concentration and results in the intrinsic viscosity, or the viscosity number [77], sometimes also called the Staudinger index... 

Albert Einstein derived a simple equation for the viscosity of a solution of spherical particles, and from this result it is obvious that if we could make the polymer in small colloidal-sized balls, then the solution would be much less viscous. Also, if we could use surfactants to stabilize (e.g. by charging) the polymer particles in water, then there would be no need for organic solvents. Both these conditions are neatly obtained in the emulsion polymerization process, which is schematically explained in Figure 5.3. A polymer latex is produced by this process and can contain up to 50% polymer in the form of 0.1-0.5 im size spherical particles in water. A typical starting composition is ... 

Figure 6. Viscosity of a solution containing SrSt and the terminated dead poly-S at various values fr = SrS ]/total poly-S) but at constant weight concentration of total polystyrene (whether as SrSt or dead poly-S). The dashed line corresponds to a mixture of living strontium polystyrene ([SrS.,] = 4.3 X 1

Polymers are macromolecules composed of specific repeating units. The properties of the polymer, such as viscosity of a solution, elasticity, and solid strength, are determined by the number of repeating units, or monomers, and ultimately the radius of the polymer. The properties of a polymer can be predicted based upon theoretical calculations (Flory 1953). The diversity and predictability of properties are the reason that polymers are so useful in controlled drug delivery. Careful choice of the polymer leads to dosage forms that can deliver an active agent with reproducibility and... 

Absorption is an unavoidable consequence of passing ultrasonic waves through matter. In particular, to reach the cavitation zone in a solution, large-amplitude ultrasound must pass through the solution. Generally, the higher is the viscosity of a solution, the higher is the ultrasonic absorption. There is an additional loss associated with finely divided particles, known as... 

The viscosity of a solution also depends on the concentration the higher the concentration, the higher the viscosity. In order to make the measurement independent of concentration, a new viscometric parameter is used which is called intrinsic viscosity, [17]. This number is... 

A further complication of determination of the viscosity of a macromol-ecular solution is that the viscosity depends on the concentration of macromolecules. Newton developed a formula for predicting the viscosity of a solution of macromolecules and solvent q, knowing the solvent viscosity r, shape factor for the macromolecule v, and the volume fraction of macromolecules 9. Newton s law of viscosity is given in Equation (4.2) and provides a relationship among viscosity, shape factor, and volume fraction of polymer. 

The viscosity of a solution of a given polymer will be dependent upon the concentration of the polymer in that solution. Viscosity depends also upon molar mass. Higher molar mass means greater chain entanglement and therefore higher viscosity. Thinking about this in reverse, we can use viscosity as a method to determine the molar mass of a polymer sample. 

This is, of course, the historically famous Staudinger equation. It is well known that the intrinsic viscosity of a solution of completely free draining Gaussian chains [Kuhn (153) Huggins (128 ) Kramers (14V) and Debye (87)] also follows a Staudinger law ... 

Estimate the viscosity of a solution of polystyrene (p = 1050 kg/m3) in diethyl phthalate under the following conditions ... 

The intrinsic viscosity is a measure of the ability of a polymer to enhance the viscosity of a solution. It is related to the molecular weight of the polymer by the Mark-Houwink equation ... 

Asphaltene content bears directly on the physical properties of the liquid product. Viscosity is of particular interest because of the importance of this parameter to operation of liquefaction plants and as a measure of the extent of liquefaction. The correlation between asphaltene content and the viscosity of the liquid has been a subject of a number of investigations (23-27). The logarithm of the viscosity ratio, In 7j/rj0 (where i and y0 are the viscosities of the solution and solvent, respectively) was found to be a linear function of concentration when asphaltene was redissolved in the pentane-soluble oil isolated from a coal-derived liquid (24). The slopes of these lines, termed the logarithmic viscosity numbers, are a measure of the contribution to the viscosity of a solution attributable to asphaltene. By comparison of logarithmic viscosity numbers of asphaltenes and their acidic and basic subfractions, it was determined that intermolecular association, which is especially strong between the acid and base subfractions, is responsible for a significant portion of the viscosity of these solutions. 

Molecular weights are not often measured directly for control of production of polymers because other product properties are more convenient experimentally or are thought to be more directly related to various end uses. Solution and melt viscosities are examples of the latter properties. Poly(vinyl chloride) (PVC) production is controlled aceording to the viscosity of a solution of arbitrary concentration relative to that of the pure solvent. Polyolefin polymers are made to specific values of a melt flow parameter called melt index, whereas rubber is characterized by its Mooney viscosity, which is a different measure related more or less to melt viscosity. These parameters are obviously of some practical utility, or they would not be used so extensively. They are unfortunately specific to particular polymers and are of little or no use in bringing experience with one polymer to bear on problems associated with another. 

Solution viscosities for a particular polymer and solvent are plotted in the form (rj — j o)/(cr o) against c where rj is the viscosity of a solution of polymer with concentration c g cm and /o is the solvent viscosity. The plot is a straight line with an intercept of 1.50 cm g and a slope of 0.9 cm g. Give the magnitude and units of Huggins s constant for this polymer-solvent pair. 

Mixtures of the polygalacturonases or of the pectinesterases were also ineffectual. Only the combined action of at least one of the polygalacturonase fractions with one of the pectinesterase fractions was effective in clarification. Purified endopolygalacturonase alone could decrease the viscosity of a solution of citrus pectin (64% esterification), but it was completely ineffectual when apple pectin was used [90% esterified (iS6)]. 

The -maxima and minima on viscosity-composition curves are reminiscent of those on vapour pressure-composition curves of binary, mixtures. 5 The vapour pressures and viscosities are equal at some temperatures, say T and To, and T and To respectively. Then To/T—To7T =C(T —T), where C is a constant. A plot of TojT—To IT against T—T gives a straight line in many cases, both for vapour pressure and viscosity in other cases, the vapour pressure shows a minimum and the viscosity a maximum, and the vapour pressure a maximum and the viscosity a minimum. Prasad, 6 from the relation with vapour pressure deduced the equation rj =rjjrio= +ac, where c=conc. of non-electrolyte. The theoretical value of a is 0 00652 the observed values were glucose 0 44, fructose 0 44, sucrose 0 78, independent of temperature. According to Errera, the curves depend on the electric dipolarity of the liquids if both are nonpolar, the curve is concave to the composition axis whilst if both are polar, it is convex. Wolkowa found that the viscosity of a solution is approximately proportional to its heat of dilution. There seems to be no relation between the viscosity and surface tension of a mixture of acetic acid and water (cf. salt solutions, 13.VIII E). Mixtures of isomorphous substances obey an approximately linear relation. 

Like other physical properties, the viscosity of a solution niay have a complicated variation with composition, due to the possibility of H bonds among the solute and solvent molecules. See, for example, Madsen (1314), and Staveley and Taylor (1939). 

The intrinsic viscosity of a solution of molecules described by a kinetically rigid chain necklace that can adopt any conformation (from the straight rod to the spherically symmetrical bead distribution) is given by > 2)... 

Solutions may also be sterilized by autoclaving, although this process can decrease the viscosity of a solution/ The change in viscosity after autoclaving is related to solution pH. Solutions at pH less than 4 had viscosities reduced by more than 20% subsequent to autoclaving. ... 

Viscosity (dynamic) the viscosity of a solution of polyvinyl acetate phthalate methanol (1 1) is 5000 mPas. In metha-nol/dichloromethane systems, viscosity increases as the concentration of methanol in the system increases. 

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