Relative viscosity concentration

Figure 11 shows the relative-viscosity-concentration behavior for a variety of hard-sphere suspensions of uniform-size glass beads. Even though the particle size was varied substantially (0.1 to 440 xm), the relative viscosity is independent of the particle size. However, when the particle diameter was small ( 1 fJLm), the relative viscosity was calculated at high shear rates, so that the effect of Brownian motion was negligible. Figure 8 shows that becomes independent of the particle size at high shear stress (or shear rate). 

Figure 2. Relative viscosity-concentration plots in toluene. Key A. nonneutralized a,o)-dicarboxylic PBD ( Mn = 4,600) , Mg salt of a,o)-dicarboxylic PBD, 25 °C Mg salt of a,oi-dicarboxylic PBD, 80 °C.

Figure 6 depicts the effect of volume fraction of solids on the relative viscosity for 40 lb HPG/1000 gal fluid at 100 s-1 and at test temperatures of 26.7, 43.3, and 60 °C (23). A Newtonian relative viscosity-concentration curve based on Thomas (24) and Maron and Pierce (25) correlations are shown for comparison. 

Figure 2. Relative viscosity-concentration plots in toluene at 25 C for poly 06-methylstyrene (Mn 6,000) end -capped with ( ) Mg carboxylate, (A) Mg sulfonate and ( ) dimethyl benzyl ammonium chloride.

Figure 5. Temperature effect on the relative viscosity- concentration plot for 0,0)-Mg dicarboxylato PBD (Hycar CTB) in toluene.

Figure 3.35. Calculated decrease in viscosity of a sol of very small discrete particles owing to particle growth relative viscosity Concentration of SiOi g per 100 ml 15 B, 6.34 C,...

Rheology. Flow properties of latices are important during processing and in many latex appHcations such as dipped goods, paint, inks (qv), and fabric coatings. For dilute, nonionic latices, the relative latex viscosity is a power—law expansion of the particle volume fraction. The terms in the expansion account for flow around the particles and particle—particle interactions. For ionic latices, electrostatic contributions to the flow around the diffuse double layer and enhanced particle—particle interactions must be considered (92). A relative viscosity relationship for concentrated latices was first presented in 1972 (93). A review of empirical relative viscosity models is available (92). In practice, latex viscosity measurements are carried out with rotational viscometers (see Rpleologicalmeasurement). 

The viscosity ratio or relative viscosity, Tj p is the ratio of the viscosity of the polymer solution to the viscosity of the pure solvent. In capillary viscometer measurements, the relative viscosity (dimensionless) is the ratio of the flow time for the solution t to the flow time for the solvent /q (Table 2). The specific (sp) viscosity (dimensionless) is also defined in Table 2, as is the viscosity number or reduced (red) viscosity, which has the units of cubic meters per kilogram (m /kg) or deciUters per gram (dL/g). The logarithmic viscosity number or inherent (inh) viscosity likewise has the units m /kg or dL/g. For Tj g and Tj p, the concentration of polymer, is expressed in convenient units, traditionally g/100 cm but kg/m in SI units. The viscosity number and logarithmic viscosity number vary with concentration, but each can be extrapolated (Fig. 9) to zero concentration to give the limiting viscosity number (intrinsic viscosity) (Table 2). 

Viscosity—Concentration Relationship for Dilute Dispersions. The viscosities of dilute dispersions have received considerable theoretical and experimental treatment, partly because of the similarity between polymer solutions and small particle dispersions at low concentration. Nondeformable spherical particles are usually assumed in the cases of molecules and particles. The key viscosity quantity for dispersions is the relative viscosity or viscosity ratio,... 

The relative viscosity of a dilute dispersion of rigid spherical particles is given by = 1 + ft0, where a is equal to [Tj], the limiting viscosity number (intrinsic viscosity) in terms of volume concentration, and ( ) is the volume fraction. Einstein has shown that, provided that the particle concentration is low enough and certain other conditions are met, [77] = 2.5, and the viscosity equation is then = 1 + 2.50. This expression is usually called the Einstein equation. 

The deviation from the Einstein equation at higher concentrations is represented in Figure 13, which is typical of many systems (88,89). The relative viscosity tends to infinity as the concentration approaches the limiting volume fraction of close packing ( ) (0 = - 0.7). Equation 10 has been modified (90,91) to take this into account, and the expression for becomes (eq. 11) ... 

Antioxidants are used to retard the reaction of organic materials with atmospheric oxygen. Such reaction can cause degradation of the mechanical, aesthetic, and electrical properties of polymers loss of flavor and development of rancidity ia foods and an iacrease ia the viscosity, acidity, and formation of iasolubles ia lubricants. The need for antioxidants depends upon the chemical composition of the substrate and the conditions of exposure. Relatively high concentrations of antioxidants are used to stabilize polymers such as natural mbber and polyunsaturated oils. Saturated polymers have greater oxidative stabiUty and require relatively low concentrations of stabilizers. Specialized antioxidants which have been commercialized meet the needs of the iadustry by extending the useflil Hves of the many substrates produced under anticipated conditions of exposure. The sales of antioxidants ia the United States were approximately 730 million ia 1990 (1,2). 

An estimation of the multiphase viscosity is a preliminary necessity for convenient particle processing. For particle-doped liquids the classical Einstein equation [20] relates the relative viscosity to the concentration of the solid phase ... 

For scaly fillers the increase of relative viscosity with filler concentration is not as pronounced as in case of fibrous fillers [177,178]. Owing to filler orientation, the flow curves for systems with different concentrations of a fibrous and a scaly filler may merge together at high shear rates [181]. In composites with a dispersed filler the decrease of the effective viscosity of the melt with increasing strain rate is much weaker. 

Aliphatic PAs dissolve well in m-cresol, formic acid (85-90%), and concentrated sulfuric acid (96-98%). Industry usually determines the relative viscosity ((/rd) of a 1% solution in concentrated sulfuric acid. The inherent viscosity (r/inh) is... 

As the concentration is increased, the viscosity of the solution generally increases, although not linearly, and may eventually undergo a sudden decrease. This is due to changes in the internal geometry of the surfactant molecules. At relatively low concentrations the alcohol ether sulfate solution consists of spheri-... 

Interactions with xanthan were investigated for some GAX fractions of wheat bran [109]. Whereas, for lowly substituted GaMs a synergy in viscosity was observed at low total polymer concentrations, yielding a maximum of the relative viscosity at nearly equal proportions of both polysaccharides [124], the xanthan/xylan mixtures at the same experimental conditions showed no synergy. The observed decrease in the relative viscosity values upon addition of the xylan indicates that a certain interaction with xanthan takes place, but that it leads to a contraction in the hydrodynamic volume. The authors suggested that structural and conformational differences between GaM and GAX might be the reason for this observation. 

Single-point equations suppose that kn, kK and kss are constants and that kn + kK = 0.5, as is indicated by the combination of equations Huggins and Kraemer. They all include the values for relative viscosity, increment of viscosity and concentration. For example, Solomon-Ciuta (1962) proposes ... 

Calculations. For determination of the intrinsic viscosity [ti] the prepared pectins were solved in an 0.1 M phosphate buffer with pH 6.0. The relative viscosity was determined by a glass. Ubbelhode viscometer at 25 0.1 °C. The flow time of solvent (L) was 81.8 seconds. At least six pectin solutions with different concentrations were measured in a way that their flow times (ts) comply the order 1.2to[Pg.528]

Viscosity measurements of the extracted polysaccharides cross-linked at increasing concentrations showed a clear increase in relative viscosity, when the cross-linking reaction took place at concentrations higher than 0.5 % (Fig. 4). At a concentration higher than 1.5 % a gel was formed. 

Figure 4. Relative viscosity at increasing polysaccharide concentration in the second autoclave extract before (blank) and after cross-linking.

In practice it is customary to measure the relative viscosity at two or more concentrations so chosen as to give relative viscosities in the range from about 1.10 to 1.50. Either tjsp/c or (In nr)/c (or both) is extrapolated graphically to c = 0. 

Exciplexes are complexes of the excited fluorophore molecule (which can be electron donor or acceptor) with the solvent molecule. Like many bimolecular processes, the formation of excimers and exciplexes are diffusion controlled processes. The fluorescence of these complexes is detected at relatively high concentrations of excited species, so a sufficient number of contacts should occur during the excited state lifetime and, hence, the characteristics of the dual emission depend strongly on the temperature and viscosity of solvents. A well-known example of exciplex is an excited state complex of anthracene and /V,/V-diethylaniline resulting from the transfer of an electron from an amine molecule to an excited anthracene. Molecules of anthracene in toluene fluoresce at 400 nm with contour having vibronic structure. An addition to the same solution of diethylaniline reveals quenching of anthracene accompanied by appearance of a broad, structureless fluorescence band of the exciplex near 500 nm (Fig. 2 )... 

The formation of excimers and exciplexes are diffusion-controlled processes. The photophysical effects are thus detected at relatively high concentrations of the species so that a sufficient number of collisions can occur during the excited-state lifetime. Temperature and viscosity are of course important parameters. 

In both of these equations c is the polymer concentration in g/dl. The Kraemer function is based on the relative viscosity, which is a ratio of the solution viscosity [r ) and the viscosity of the pure solvent The Huggins function uses the specific viscosity, ri p, which is defined in terms of the relative viscosity as follows ... 

Intrinsic viscosity is related to the relative viscosity via a logarithmic function and to the specific viscosity by a simple algebraic relationship. Both of these functions can be plotted on the same graph, and when the data are extrapolated to zero concentration they both should predict the same intrinsic viscosity. The specific viscosity function has a positive slope and the relative viscosity function has a negative slope, as shown in Fig. 3.7. The molecular weight of the polymer can be determined from the intrinsic viscosity, the intercept of either function, using the Mark-Houwink-Sakurada equation. 

The Mark-Houwink-Sakurada constants for PMMA resin are o = 0.73 and K = 1. X 10 Table 3.3 contains solvent viscosity versus concentration data. Find the intrinsic viscosity using both the specific and relative viscosities and the viscosity average molecular weight. 

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