Viscosity behavior

In order to study the solution behavior of dendrimer-like star-branched polymers, the intrinsic 

Since the molecular weight of dendrimer-like star-branched polymers can be made to vary widely by a change in the branched architecture, it is possible to compare the viscosity values between themselves, each in the same generation (Hirao et al, 2009b). The [t/]dendrimer-iike 

Generation Type Mw (kg/mol) [rj] (miyg) ] dendrimer-like [ llinear 

Very surprisingly, the [ )]dendrimer-iike values of the four 3G polymers were close to each other (between 32.2 and 35.2 mL/g), although their values varied considerably from 2.95 x 10 to 9.39 X 10 g/mol. For instance, the (A-A4-Ai6)4 polymer was almost equal in [t ] value to the (A-A2-A4)4 polymer, while the former was three times higher in value than the latter. A similar trend was also observed among the 4G polymers. The [t]] value of the (A-A4-Ai6-A4d)4 polymer was the same as that of the (A-A2-A4-Ag)4 polymer, having only one-sixth the value 

In regular-type star-branched polymers, the branching factor, g value, defined as [ /]dendrimer-iike/[bilinear. IS an important factor in examining the volume extended in solution by the nmnber of arm segments. The g value correlates with the number of arm segments and decreases 

Chitosan, being a polycationic material having pKa value 6.3, requires acidic pH is for its dissolution [4]. The conformational arrangements of polyelectrolyte chains, mainly responsible for viscosity behavior, are influenced by various factors such as pH, concentration of polyelectrolyte, molecular weight, nature of counter 

Incorporation of sodium acetate has been found to drop the viscosity of chitosan solution (Fig. 19.16) [50]. The effect of electrolyte was observed to be more pronounced on high-molecular-weight chitosan, CHT-MC. With decrease in molecular weight of chitosan, the amount of sodium acetate required to attain a minimal viscosity was decreased. The decrease in viscosity with increase in electrolyte concentration can be attributed to the shielding effect 

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Lubricants. Petroleum lubricants continue to be the mainstay for automotive, industrial, and process lubricants. Synthetic oils are used extensively in industry and for jet engines they, of course, are made from hydrocarbons. Since the viscosity index (a measure of the viscosity behavior of a lubricant with change in temperature) of lube oil fractions from different cmdes may vary from +140 to as low as —300, additional refining steps are needed. To improve the viscosity index (VI), lube oil fractions are subjected to solvent extraction, solvent dewaxing, solvent deasphalting, and hydrogenation. Furthermore, automotive lube oils typically contain about 12—14% additives. These additives maybe oxidation inhibitors to prevent formation of gum and varnish, corrosion inhibitors, or detergent dispersants, and viscosity index improvers. The United States consumption of lubricants is shown in Table 7. 

For a Hquid under shear the rate of deformation or shear rate is a function of the shearing stress. The original exposition of this relationship is Newton s law, which states that the ratio of the stress to the shear rate is a constant, ie, the viscosity. Under Newton s law, viscosity is independent of shear rate. This is tme for ideal or Newtonian Hquids, but the viscosities of many Hquids, particularly a number of those of interest to industry, are not independent of shear rate. These non-Newtonian Hquids may be classified according to their viscosity behavior as a function of shear rate. Many exhibit shear thinning, whereas others give shear thickening. Some Hquids at rest appear to behave like soHds until the shear stress exceeds a certain value, called the yield stress, after which they flow readily. 

The Williamson equation is useful for modeling shear-thinning fluids over a wide range of shear rates (15). It makes provision for limiting low and high shear Newtonian viscosity behavior (eq. 3), where T is the absolute value of the shear stress and is the shear stress at which the viscosity is the mean of the viscosity limits TIq and, ie, at r = -H... 

The microphase separation of an amphiphilic polyelectrolyte is clearly reflected in the viscosity behavior of its aqueous solution. As a representative example, Fig. 5 shows the reduced viscosities of ASt-x with different styrene (St) content plotted against the polymer concentration in salt-free aqueous solution [29], The AMPS homopolymer and its copolymers with low St content exhibit negative slopes, which is the typical behavior of polyelectrolytes in the concentration range shown in Fig. 5. With increasing St content, however, the slope systematically decreases and eventually turns to be slightly positive, while reduced viscosity itself markedly decreases. These data indicate that, with increasing St content, the... 

Filler orientation is not the only consequence of geometric effects in strained systems with an anisodiametric filler. The appearance of normal stresses has been named as another such phenomenon [169,171,185] which, like the abnormal viscosity behavior of suspensions, may not be due to the elasticity of system components. 

So far the results have been shown in which the metal alkoxide solutions are reacted in the open system. It has been shown that the metal alkoxide solutions reacted in the closed container never show the spinnability even when the starting solutions are characterized by the low acid content and low water content (4). It has been also shown from the measurements of viscosity behavior that the solution remains Newtonian in the open system, while the solution exhibits structural viscosity (shear-thinning) in the closed system. 

Viscosity Behavior. The polymeric nature of triorganotin fluorides dissolved in nonpolar solvents is outlined in the introduction. As a result of the transient polymer formation, these solutions exhibit nonlinear concentration vs. viscosity curves. 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

Figure 3-7 Some examples of structural viscosity behavior.

Ludwig s (2001) review discusses water clusters and water cluster models. One of the water clusters discussed by Ludwig is the icosahedral cluster developed by Chaplin (1999). A fluctuating network of water molecules, with local icosahedral symmetry, was proposed by Chaplin (1999) it contains, when complete, 280 fully hydrogen-bonded water molecules. This structure allows explanation of a number of the anomalous properties of water, including its temperature-density and pressure-viscosity behaviors, the radial distribution pattern, the change in water properties on supercooling, and the solvation properties of ions, hydrophobic molecules, carbohydrates, and macromolecules (Chaplin, 1999, 2001, 2004). 

Nelson and Conrad29 have recently confirmed the viscosity behavior observed by Davidson26 and Nickerson and Habrle27 and have drawn a similar conclusion, namely, that after the rapid destruction of about 2 % of the intercrystalline network, hydrolysis occurs mainly on lateral crystallite surfaces. They also show that the apparent degree of crystallinity is reduced by fine grinding of cotton fibers. 

Table 6. Dependence of viscosity behavior on packing factor.

A unified understanding of the viscosity behavior is lacking at present and subject of detailed discussions [17, 18]. The same statement holds for the diffusion that is important in our context, since the diffusion of oxygen into the molecular films is harmful for many photophysical and photochemical processes. However, it has been shown that in the viscous regime, the typical Stokes-Einstein relation between diffusion constant and viscosity is not valid and has to be replaced by an expression like... 

Tj max increases [19] linearly with M. An increase in the salt concentration moves Umax toward higher c so that c ax c, and it drastically lowers the value of Analogous to the viscosity behavior, the dynamic storage and loss moduli also show [22] a peak with c. The unusual behavior at low c where the reduced viscosity increases with dilution in the polyelectrolyte concentration range between and c, along with the occurrence of a peak in the reduced viscosity versus c, has remained as one of the most perplexing properties of polyelectrolytes over many decades. 

The viscosity of some polymers at constant temperature is essentially Newtonian over a wide shear rate range. At low enough shear rates all polymers approach a Newtonian response that is, the shear stress is essentially proportional to the shear rate, and the linear slope is the viscosity. Generally, the deviation of the viscosity response to a pseudoplastic is a function of molecular weight, molecular weight distribution, polymer structure, and temperature. A model was developed by Adams and Campbell [18] that predicts the non-Newtonian shear viscosity behavior for linear polymers using four parameters. The Adams-Campbell model is as follows ... 

While it can be expected that a number of physical properties of hyperbranched and dendritic macromolecules will be similar, it should not be assumed that all properties found for dendrimers will apply to hyperbranched macromolecules. This difference has clearly been observed in a number of different areas. As would be expected for a material intermediate between dendrimers and linear polymers, the reactivity of the chain ends is lower for hyperbranched macromolecules than for dendrimers [125]. Dendritic macromolecules would therefore possess a clear advantage in processes, which require maximum chain end reactivity such as novel catalysts. A dramatic difference is also observed when the intrinsic viscosity behavior of hyperbranched macromolecules is compared with regular dendrimers. While dendrimers are found to be the only materials that do not obey the Mark-Houwink-Sakurada relationship, hyperbranched macromolecules are found to follow this relationship, albeit with extremely low a values when compared to linear and branched polymers [126]. 

With the least polar solvent, 9 1 MIBK/MEOH, aggregation dominates the viscosity behavior. This solvent is of intermediate quality, between pure MeOH and the 1 1 mixture. Still, the viscosity is greatest using the 9 1 mix at all temperatures, by up to a factor of four. The effect of temperature on the aggregation in the 9 1 MIBK/MeOH solution is so large that the fmj versus 1/T curve becomes significantly nonlinear. An apparent E determined when... 

The viscosity behavior described so far is valid only for uncharged polymers. If polyelectrolytes are analyzed, a quite different viscosity behavior may be found in polar solvents (e.g., polymeric acids in water). The q p/c values at first fall off with decreasing concentration as for uncharged polymers but then climb steeply again and may drop down later again (see Fig. 2.16). Addition of salt to the solution of polyelectrolytes (e.g., 1% and 5% sodium chloride in aqueous solution) restores, step by step, the normal behavior (see Fig. 2.16, curves b and c). 

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