Viscosity-concentration plots

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.

It was assumed that the solutions were Newtonian at the shear rates in the capillary. This assumption was assessed with Couette viscometer measurements of these dilute solutions over a range of shear rates and was reasonable. Deviations were found for solutions at the higher concentrations, as indicated by negative departure from linearity of the reduced-viscosity-concentration plots these values were not used for intrinsic viscosity and Huggins constant determination. 

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 3. Effect of solvent on the reduced viscosity-concentration plots for a,cu -quaternary ammonium chloride-PMS at 25 C ( ) toluene, (A) THF, ( ) DMF and ( ) non-quaternized a,w -di tert-amino PMS in DMF.

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

Aqueous Solution Properties. Acrylamide copolymers containing even small quantities of surfomer units (i.e. < 0.5 mol %) also exhibit interesting solution properties. For example, below C the surfomer copolymers show lower intrinsic viscosities rj and elevated Huggins constants, (Table 3.1). As with the RAM polymers, below C the chains interact intramolecularly to collapse the coil, lowering [rj ] and raising the slope of the reduced viscosity concentration plot, i.e. /ch [1 ] ... 

In industrial production of acid-modified starches, a 40% slurry of normal com starch or waxy maize starch is acidified with hydrochloric or sulfuric acid at 25—55°C. Reaction time is controlled by measuring loss of viscosity and may vary from 6 to 24 hs. For product reproducibiUty, it is necessary to strictly control the type of starch, its concentration, the type of acid and its concentration, the temperature, and time of reaction. Viscosity is plotted versus time, and when the desired amount of thinning is attained the mixture is neutralized with soda ash or dilute sodium hydroxide. The acid-modified starch is then filtered and dried. If the starch is washed with a nonaqueous solvent (89), gelling time is reduced, but such drying is seldom used. Acid treatment may be used in conjunction with preparation of starch ethers (90), cationic starches, or cross-linked starches. Acid treatment of 34 different rice starches has been reported (91), as well as acidic hydrolysis of wheat and com starches followed by hydroxypropylation for the purpose of preparing thin-hoiling and nongelling adhesives (92). 

The most widely used molecular weight characterization method has been GPC, which separates compounds based on hydrodynamic volume. State-of-the-art GPC instruments are equipped with a concentration detector (e.g., differential refractometer, UV, and/or IR) in combination with viscosity or light scattering. A viscosity detector provides in-line solution viscosity data at each elution volume, which in combination with a concentration measurement can be converted to specific viscosity. Since the polymer concentration at each elution volume is quite dilute, the specific viscosity is considered a reasonable approximation for the dilute solution s intrinsic viscosity. The plot of log[r]]M versus elution volume (where [) ] is the intrinsic viscosity) provides a universal calibration curve from which absolute molecular weights of a variety of polymers can be obtained. Unfortunately, many reported analyses for phenolic oligomers and resins are simply based on polystyrene standards and only provide relative molecular weights instead of absolute numbers. 

In semi-dilute solutions, the Rouse theory fails to predict the relaxation time behaviour of the polymeric fluids. This fact is shown in Fig. 11 where the reduced viscosity is plotted against the product (y-AR). For correctly calculated values of A0 a satisfactory standardisation should be obtained independently of the molar mass and concentration of the sample. 

The viscosity of the oxidized polymer (VIII) was determined using DMF as a solvent. Chloroform was not a good solvent because it was too volatile and resulted in poor reproducibility. The reduced viscosities are plotted against polymer concentration (Figure 6). Polymer VIII behaved like a polyelectrolyte, the reduced viscosities increased sharply on dilution in a salt free solution. The addition of 0.01 M KBr did not completely suppress the loss of mobile ions however, at 0.03 M KBr addition a linear relationship between the reduced viscosities and concentration was established. 

Viscosity data are reported in Table I for a number of the polysaccharide derivatives in 5% LiCl/N,N-dimethylacetamide solutions. At low concentrations of polymers, an upward curvature in the DSp/c (reduced viscosity) vs c (concentration) plot was observed. Additionally, nonlinear increases in solvent viscosity were observed for increased lithium ion concentrations in the absence of polymer. Therefore, reduced viscosities at 0.25 dl/g are reported. 

Solvent viscosity vs, concentration plots for cellulose dissolved in TFA-CH2CI2 (70/30, v/v) do not exhibit a maximum (1I,S1) in contrast to the typicid behavior of polymer liquid crystal solutions. This same behavior is exhibited by other cellulose-solvent systems (52,fiQ). Conio et al. (59) si gest that due to the close proximity of the cholesteric mesophase to its solubility limit, it is only observed in a metastable condition. 

With each system the viscosity is shown to increase markedly with filler concentration. This relationship is particularly evident at very low shear rates and becomes even more pronounced when viscosity is plotted as a function of shear... 

In an earlier procedure applying universal calibration, viscosities of the four most concentrated fractions eluting about the peak were measured, and the intrinsic viscosities were plotted against count. The intrinsic viscosities of all the fractions were obtained by extrapolation of the plot for use in the calculations to obtain degree of polymerization (DP). In the present method the DP of each fraction is obtained from the relationship MW = (cod size/K)1/1+ derived from Benoit s concept and the Mark-Houwink equation. Results from the new procedure are in excellent agreement with those obtained independently on cotton by others. Anomalies in results obtained previously on some samples disappear while marked improvement is noted for others. The determination is speeded up greatly by computer processing of data, and experimental error is reduced. 

Ohm26,78-79), among others, called attention to the anomalous viscosity behavior of polymer solutions at very low concentration. Plots of j sp/C against C were found to curve either down or up at such concentrations, and the anomaly was attributed to the adsorption of polymer molecules onto the capillary wall. In order to calculate the thickness of the adsorbed polymer layer, Ohrn used the equation... 

The viscosities of many binary liquid systems display minima as functions of composition at constant temperature, so that negative values of D are also possible. Yajnik and his coworkers (265 ) long ago observed that very frequently an extremum in the isothermal vapor pressure-composition curve is accompanied by an extremum of the opposite sense in the viscosity-concentration curve. Data are apparently not available for solutions of very low-molecular-weight paraffins in carbon tetrachloride, but minima are found for the viscosities of solutions of CC14 with ethyl iodide, ethyl acetate and acetone, so that a minimum appears quite probable for mixtures of small aliphatic hydrocarbons with carbon tetrachloride. If this were true, the downward trend of the Meyer-Van der Wyk data on C17—C31 paraffins, earlier discussed in connection with the polyethylene plots of Fig. 14, would be understood. It will be recognized that such a trend is also precisely what is to be expected from the draining effect of the hydrodynamic theories of Debye and Bueche (79), Brinkman (45 ) and Kirkwood and Riseman (139). However, the absence of such a trend in the case of polyethylene... 

Solutions of these substances at first show the normal increase of viscosity with concentration. Above a certain critical concentration, however, the viscosity decreases rapidly. This phenomenon is explained by orientation of the rod-like macromolecules in the flow direction. An analogous behaviour is observed, if the viscosity is plotted as a function of molecular weight at constant concentration. 

A peculiar four-stage scheme of a structure formation course of different protein-based systems, high in protein concentration was assessed by Rbck and Kulozik (2006) by an inline viscosity assessment in a small scale reaction chamber with the stirrer as a probe directly linked to the rheometer. A typical new structure formation course, not been reported until now, was obtained. The apparent viscosity is plotted as a function of the processing time. This typical progression is explained in Figure... 

Figure 12-26). At low concentrations, plots of relative viscosity versus concentration are indeed usually linear, but, as might be expected, show deviations from linearity at higher concentrations. 

The solution viscosity y5 concentration plots do not exhiUt a maximum in contrast to ical polymer liquid ciystal solutions. As noted in the introduction, this same behavior is exhibited by other cellulose-solvent systems (.9,14) and, as discussed in the introduction, suggests the mesophase is metastable. 

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. 

Ounkovsky and Volovai found that the viscosity-compositioii plots of binary mixtures of liquids having equal viscosities are not usually linear. Lautie found for dilute solutions of non-electrolytes that the relative viscosity 97/770 naay be represented as a linear or quadratic function of concentration. 

These conclusions are supported by the viscosity data plotted in Figure 1. The reduced viscosity of the hexyl copolymer is presented as a function of a in 0.2M solutions of TMACl, NaCl, and LiCl. The polymer concentration of 3.2 X 10"3 monomole/l was low enough to allow interpretation of the results in terms of the molecular dimensions of the polymer molecules. The findings demonstrate strikingly the differences in the effects of the TMA+ ion and the alkali metal ions. Whereas the polyacid showed an enormous expansion with increasing a in the presence of TMA+ ion, this expansion was suppressed almost completely by the alkali metal ions. The difference between the effects of... 

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