Viscosities, calculating concentrated polymer solution

Calculation of Concentrated Polymer Solution Viscosities A New Approach... 

The heat of dissociation in hexane solution of lithium polyisoprene, erroneously assumed to be dimeric, was reported in a 1984 review 71) to be 154.7 KJ/mole. This value, taken from the paperl05> published in 1964 by one of its authors, was based on a viscometric study. The reported viscometric data were shown i06) to yield greatly divergent AH values, depending on what value of a, the exponent relating the viscosity p of a concentrated polymer solution to DPW of the polymer (q DP ), is used in calculation. As shown by a recent compilation 1071 the experimental a values vary from 3.3 to 3.5, and another recent paper 108) reports its variation from 3.14 to 4. Even a minute variation of oe results in an enormous change of the computed AH, namely from 104.5 KJ/mole for oe = 3.38 to 209 KJ/mole for oe = 3.42. Hence, the AH = 154.7 KJ/mole, computed for a = 3.40, is meaningless. For the same reasons the value of 99.5 KJ/mole for the dissociation of the dimeric lithium polystyrene reported in the same review and obtained by the viscometric procedure is without foundation. 

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

The zero-shear viscosity of a concentrated polymer solution can be treated by a modified version of the method used to calculate the zero-shear viscosity of a polymer melt. The modifications take the two effects of the solvent (plasticization and true dilution of the polymer) into account. Approximations are involved, however, in determining the appropriate mixing rules for the plasticization effect and the magnitude of the true dilution effect. The zero-shear viscosity of concentrated polymer solutions will be discussed briefly in Section 13.G. 

Step 22. Calculate the viscosity of a polymer melt and/or the zero-shear viscosity of a concentrated polymer solution. The molecular weight dependence of the zero-shear viscosity is given by equations 13.2 and 13.3, where the critical molecular weight Mcr (Equation 13.6) is... 

A model for calculating viscosities of concentrated polymer solutions has been formulated and used successfully to predict viscosities of alkyd resin solutions in both pure aromatic solvents and in mixtures of hydrocarbons and oxygenated materials. It was also found to describe viscosity trends in polystyrene-diethylbenzene solutions accurately. The formulation explicitly accounts for the observation that concentrated solution viscosities increase markedly with decreasing compatibility between resin and diluent. The proposal of an empirical relationship which interprets the viscosity enhancement in poorer solvents in terms of increased chain-chain interactions is of interest. The model contains three constants which are fixed for a particular resin and are independent of diluent type. These are the Mark-HouuAnk constant, the parameter in the Martin viscosity equation, and the constant relating the postulated clustering to the solution thermodynamics of a particular solution. 

A new approach to calculating viscosities of concentrated polymer solutions has been presented. It consists of the derivation of a semi-empirical computational model containing three parameters characteristic of a particular polymer. Once these parameters have been established, the viscosity of any solution of the polymeric material in a solvent or solvent blend may be calculated. The method should be of particular interest to the coatings industry, where they often require a screening estimate of the potential viscosity-reducing power of a new solvent blend. 

Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

The following is a brief review of the viscosity pareimeters that are commonly used in polymer analyses. The relative viscosity (ripgi) of a polymer saitple solution as defined in Equation 1 can be determined experimentally from the measured viscosity value for the polymer saitple solution (h) and that of the solvent (h )- From the h -1 value and the polymer sanple concentration (c), tne calculations for the other viscosity parameters are possible in accordance to Equations 2 through 5 ... 

Gamma radiation can be used with macroscopic amounts of polymer. This is particularly welcome when polymers are not compatible with the GPC technique. Larger samples can be characterized by viscosity changes, usually measured in dilute solutions. All that is needed is a suitable solvent. If the Mark-Houwink parameters are known, it is possible to calculate viscosity-average molecular weight, Mv, from dilute solution viscosities. However, even the raw viscosity-concentration data in terms of the reduced viscosity may be enough to indicate the sensitivity of a given polymer in qualitative terms. The reduced viscosity at concentrations c is isp/c where t]sp — (solution viscosity — solvent viscosity)/solvent viscosity. 

Figure 8 illustrates the relationship between inherent viscosity (IV) and concentration for PBI/PAr/NMP solutions. It is interesting to note that the IV of all solution blends exhibited normal polymer solution characteristics. At a fixed concentration (0.5%), it was noted that the IV of the solution blends exceeded the rule of mixtures (see Fig. 9) suggesting that PBI and PAr exhibit specific interactions in a dilute solution, such that the resulting hydrodynamic sizes of the blends were greater than that of the calculated averages based on each component. 

An alternative method has been used by Morton (73, 74) which involves an independent measurement of the degree of association of polyisoprenyllithium. Measurements were made of the concentrated solution viscosity of active and terminated polymer solutions. An approximately ten-fold decrease in viscosity was observed on discharging the ion-pair. This corresponds to two-fold association for polyisoprenyllithium in hexane, since in concentrated solutions v) = KMffl. A careful study established that the association numbers were slightly less than two and decreased with temperature. From the data, K2 can be calculated and hence k . In this way it was found that in hexane kp — 3.4 X 103 exp. (— 4100/RT) at 30°, kp = 4.7 litre/mole sec. For practical reasons,... 

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 concentrated solution viscosity measurement yields the weight-average degree of association of active chain ends rather than the more conventional number-average (mole fraction) value. However, the calculation of the equilibrium constant for association, K, can be accomplished if Mw and the heterogeneity index of the polymer sample are known. The latter parameter can be determined via postpolymerization characterization. 

The viscosity of dilute polymer solutions is considerably higher than that of the pure solvent. The viscosity increase depends on the temperature, the nature of the solvent and polymer, the polymer concentration, and the sizes of the polymer molecules. This last dependence permits estimation of an average molecular weight from solution viscosity. The average molecular weight which is measured is the viscosity average A/v, which differs from those described so far in this text. Before viscosity increase data are used to calculate Afv of the solute it is necessary, however, to eliminate the effects of solvent viscosity and polymer concentration. The methods whereby this is achieved are described in this section. 

The increase in viscosity with the addition of a polymer into a solvent is an important property. By measuring the solution viscosity as a function of polymer concentration, useful information about the polymer s molecular properties can be determined. From the solution data, the intrinsic viscosity (also known as the limiting viscosity number or Staudinger index) can be calculated ... 

The dilute solution viscosity measurements were conducted using Ubbelohde viscometers generally conducted at 25 + 0.05°C in a thermo-stated bath. The reduced viscosity or viscosity number [defined as (t -ri0)/ri0c, where 0 is the viscosity of the polymer solution, 0o is the viscosity of the solvent (or mixed solvent), and c is the concentration of polymer in g/100 mL] was calculated for each solution measured. 

The model has been tested for its ability to predict Newtonian solution viscosities at polymer concentrations in the range of 30-60 wt % in a number of pure solvents and solvent blends. The calculated results generally agree with the experimental data. 

As it is known, the plots of Fig. 39 allow one to determine the values of intrinsic viscosity [rj] by the extrapolation to the polymer zero concentration c. Another method of [r ] evaluation is Shultz-Blashke Eq. (48). In Table 12, the comparison of [q] values, evaluated by two indicated methods, is adduced for polyarylate F-1 at three testing temperatures and polyamidobenzymidazole [94] at two concentrations of solution in sulfuric acid. As it follows from the data of Table 12, the values [q], calculated according to the Eqs. (47) and (48) showed a good correspondence, that allows one to use Shultz-Blashke equation for [q] values of semirigid- and rigid-chain polymers estimation. 

---