Variation of solution viscosity

Figure 4. Variation of solution viscosity as a function of BCB-2 prepolymer in xylene.

The viscosity of the dilute solutions of PBI in FA and DMAc containing LiBr or LiCl has been studied by Kojima et al. [44, 45], Shogbon et al. [46], and Lin et al. [36]. The variations of solution viscosity as a function of PBI concentration under a fixed salt stabilizer (i.e., LiBr or LiCl) concentration and as a function of stabilizer concentration under a fixed PBI concentration have been reported. The solution viscosity strongly depends on the molar ratio of the salt and PBI repeat unit (i.e., [LiBr]/[BI] or [LiCl]/ [BI], where [BI] is the concentration of the PBI repeat unit). 

Figure 1. Variations of the viscosity of a tetraethoxysilane solution as a function of time. (Reproduced with permission from Ref. 1. Copyright 1984 Plenum Press.)...

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

F ure 4.20 Variation of intrinsic viscosity of aqueous protein solutions with axial ratio and extent of solvation. Reprinted, by permission, from P. Hiemenz, Polymer Chemistry, p. 598. Copyright 1984 by Marcel Dekker, Inc. 

Figure 3. Variation of reduced viscosity with concentration at 40°C for solutions exposed to irradiation doses of , 0 ...

The role of the sample introduction system is to convert a sample into a form that can be effectively vaporized into free atoms and ions in the ICP. A peristaltic pump is typically used to deliver a constant flow or sample solution (independent of variations in solution viscosity) to the nebulizer. Several different kinds of nebulizers are available to generate the sample aerosol, and several different spray chamber designs have been used to modify the aerosol before it enters the ICP Gases can be directly introduced into the plasma, for example, after hydride generation. Solids can be introduced by using electrothermal vaporization or laser ablation. 

Viscosity measurements have been widely used as a method for determining molecular weights on account of the ease with which they can be carried out. Although the method is simple it is not absolute and requires calibration. The characteristic quantity used in these measurements is the specific viscosity (ri.v) defined by Staudinger as n,r = (77 — vo)/vo where 77, 770 are the viscosities of solution and solvent respectively. For concentrations of solute of less than 1 g. per 100 ml., the variation of specific viscosity with concentration C, can usually be expressed by an equation of the form... 

Schmitz et al. [89] also reported on the influence of solids on kEa in stirred tanks. Although they applied only one type of solid (glass beads of 88 and 320 pm average diameter) in aqueous solutions, their study is of particular interest because of the wide range in variation of liquid viscosity applied by adding carboxy methylcellulose and by investigating the scale-up aspects by measuring both in a 20 cm and a 45 cm diameter stirred tank. As Schmitz et al. [89] also point out, their result. 

FIG. 16.30 (left) Variation of the viscosity of PpBA in dimethylacetamide/lithium chloride solutions with polymer concentration for various molecular weights expressed as intrinsic viscosities (in mVkg) ... 

Fig. 62.—The variation of specific viscosity (tjs) with composition of mixtures of 0.5% aq. solutions of gelatin and dispersed starch. (By permission from Lipatov and Lipatov.988)...

The intrinsic viscosity [r ] is defined in the above equation as a limit at zero concentration. The rj/t o ratios which are actually measured are at finite concentrations, and there are a variety of ways to estimate [rj] from these data. The variation in solution viscosity (p) with increasing concentration can beexpres.sedasa power series in c. The equations usually used are the Huggins equation [8] ... 

Figure 5.7 shows the temperature dependence of the viscosity of water-methanol and water-acetonitrile mixtures in the entire composition range [132]. The existence of a viscosity maximum for a methanol concentration close to 45% is conspicuous. For water-acetonitrile, there is also a viscosity maximtun, but it is less pronounced and takes place at a lower organic solvent concentration ( 20%). We also show in Figure 5.8 the variation of the viscosity of various aqueous solutions with their composition [135]. 

FIGURE 11.14 Variation of the viscosity of solutions of partially chlorinated poly(l,4-phenylene-2, 6-naphthalamide) dissolved in a solvent mixture of hexamethylene phosphora-mide and iV-methylpyrrolidone containing 2.9% LiCl as a function of the solution concentration, showing the transition from isotropic to anisotropic solutions. (From Morgan, RW., Aromatic polyamides, CHEMTECH, 316, 1979. With permission of American Chemical Society, Washington, D.C.)... 

Solution. By Eq. (5.39), EcAn = Ey]s. Since the solution is dilute, the temperature variation of the viscosity of water can be used to predict the temperature dependency of D. According to Eqs. (5.33) and (5.38), semilogarithmic plots of m and D against l/T should have slopes which are equal but opposite in sign. Accordingly, in Fig. 5.5, the viscosity... 

The main aim of this study was to investigate the effects of the origin and amount of proteins on the aggregation of xanthan chains in solution by means of rheological measurements. Modifications of fermentation conditions led to variations of intrinsic viscosity, Huggins constant and pyruvate content of the xanthan produced. 

Laminar Flow Although heat-transfer coefficients for laminar flow are considerably smaller than for turbulent flow, it is sometimes necessary to accept lower heat transfer in order to reduce pumping costs. The heat-flow mechanism in purely laminar flow is conduction. The rate of heat flow between the walls of the conduit and the fluid flowing in it can be obtained analytically. But to obtain a solution it is necessary to know or assume the velocity distribution in the conduit. In fully developed laminar flow without heat transfer, the velocity distribution at any cross section has the shape of a parabola. The velocity profile in laminar flow usually becomes fully established much more rapidly than the temperature profile. Heat-transfer equations based on the assumption of a parabolic velocity distribution will therefore not introduce serious errors for viscous fluids flowing in long ducts, if they are modified to account for effects caused by the variation of the viscosity due to the temperature gradient. The equation below can be used to predict heat transfer in laminar flow. 

Fig. 125. Variation of the viscosity of 0.5% solutions in tricresol as a function of the duration of heating in air at 150 C. 1) Capron fiber 2) capron fiber with an addition of DNPDA (the additive was introduced by powdering).

Excepting the case of very low concentrations, in solution, the interactions between the polymer macromolecules determine the variation of reduced viscosity r Jc with polymer concentration. The characteristic value of the isolated macromolecule in solution is obtained by the extrapolation of to zero polymer concentration. In this case the following equations are valuable ... 

Figure 18.8 Variation of shear viscosity with weight per cent of NR at different shear rates (solution cast and melt mixed).

Figure 18.9 Variation of shear viscosity with shear stress of solution-cast blends.

A special variation of solution polymerization is precipitation polymerization. The only difference here is that the polymer becomes more and more Insoluble in the solvent as its molecular weight increases. The polymer precipitates from the solution and can be isolated by filtration. One interesting feature of precipitation polymerization is that the viscosity of the solution in the reactor remains almost constant. The production of polyacrylonitrile in water is an important example of this polymerization process. 

For surfactants with short-chain alkyl groups, Cg or Cio, the solution shows a gradual variation in properties with no phase separation. Figure 3.1 illustrates this, showing the variation of relative viscosity with micelle volume fraction for spherical micelles for a system of Ci2Es with an equal weight of solubilized decane [2]. The viscosity varies smoothly and approximately as predicted for a dispersion of spherical micelles. 

The polymer molecular weight is the most important factor determining the viscosity of melts. The scaling rule is tj In many cases a solution viscosity (for example, intrinsic viscosity, [ ]) is used as a measure for polymer molecular weight. Since for many flexible polymers [//] we can derive another scaling rule, of melt viscosity as a function of solution viscosity tj It is evident that a higher melt temperature will reduce melt viscosity, but only small variations in molecular weight can be compensated for by temperature adjustment. 

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