Concentrated polymer solutions viscosity measurements

PPS is well-recognized for its exceptional chemical resistance. There are no known solvents for PPS below 200°C. A comprehensive survey of solvents for PPS has been published (115). Extreme conditions are required to dissolve PPS in both common and exotic solvents. Solution viscosity measurements are made difficult by this high temperature requirement. Inherent viscosity measurements are performed in 1-chloronaphthalene at 206°C at a concentration of 0.4 g of polymer per deciliter of solution. The inherent viscosity of PPS solutions shows a usefiil response to increa sing molecular weight. Table 2 shows a correlation of inherent viscosity measurements with melt flow measurements. 

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. 

Depending on the concentration, the solvent, and the shear rate of measurement, concentrated polymer solutions may give wide ranges of viscosity and appear to be Newtonian or non-Newtonian. This is illustrated in Eigure 10, where solutions of a styrene—butadiene—styrene block copolymer are Newtonian and viscous at low shear rates, but become shear thinning at high shear rates, dropping to relatively low viscosities beyond 10 (42). The... 

Controlled stress viscometers are useful for determining the presence and the value of a yield stress. The stmcture can be estabUshed from creep measurements, and the elasticity from the amount of recovery after creep. The viscosity can be determined at very low shear rates, often ia a Newtonian region. This 2ero-shear viscosity, T q, is related directly to the molecular weight of polymer melts and concentrated polymer solutions. 

The experimental determination of polymer intrinsic viscosity is done through the measurement of polymer solution viscosity. The connotation of intrinsic viscosity [hi/ however, is very different from the usual sense of fluid viscosity. Intrinsic viscosity, or sometimes called the limiting viscosity number, carries a far more reaching significance of providing the size and MW information of the polymer molecule. Unlike the fluid viscosity, vdiich is commonly reported in the poise or centipoise units, the [h] value is reported in the dimension of inverse concentration xinits of dl/g, for exanple. The value of [hi for a linear polymer in a specific solvent is related to the polymer molecular weight (M) through the Mark-Houwink 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. 

Figure 2 shows the viscosities of the polymer solutions as measured at 25° 0.05 °C. in an Ubbelohde viscosimeter employing a concentration of 0.52 gram of polymer per 100 ml. of m-cresol. The viscosimeter had a flow time of more than 100 sec. for the pure solvent. 

Viscosity measurements alone cannot be directly used in the Mark-Houwink-Sakurada equation to relate absolute viscosity and polymer molecular weight, since additional unknowns, K and a must be determined. Therefore, viscometry does not yield absolute molecular weight values it rather gives only a relative measure of polymer s molecular weight. Viscosity measurements based on the principle of mechanical shearing are also employed, most commonly with concentrated polymer solutions or undiluted polymer these methods, however, are more applicable to flow properties of polymers, not molecular weight determinations. 

G. J. Coven, and B. J. Kinzig Entanglement effects in concentrated polymer solutions from viscosity measurements. J. Chem. Phys. 39, 128 (1963). 

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 relative viscosities of polymer solutions are measured at different concentrations and a plot of the reduced viscosity versus concentration is made, in order to extrapolate to zero concentration. The concentration dependence of the viscosity of polymer solutions, in the dilute regime, may be expressed by several linear equations. For practical extrapolation to zero concentration, the most commonly employed are the Huggins equation ... 

The zero-shear viscoelastic properties of concentrated polymer solutions or polymer melts are typically defined by two parameters the zero-shear viscosity (f]o) and the zero-shear recovery compliance (/ ). The former is a measure of the dissipation of energy, while the latter is a measure of energy storage. For model polymers, the infiuence of branching is best established for the zero-shear viscosity. When the branch length is short or the concentration of polymer is low (i.e., for solution rheology), it is found that the zero-shear viscosity of the branched polymer is lower than that of the linear. This has been attributed to the smaller mean-square radius of the branched chains and has led to the following relation... 

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. 

Polymer Solutions. All film-forming liquids are polymers or polymer solutions. The viscosity of these systems is constant only at extremely high dilution where the measurements leading to knowledge of molecular dimensions are made. At practical concentrations polymer solutions invariably become shear sensitive. 

Here t, 4, and 4 2 are three important material functions of a nonnewtonian fluid in steady shear flow. Experimentally, the apparent viscosity is the best known material function. There are numerous viscometers that can be used to measure the viscosity for almost all nonnewtonian fluids. Manipulating the measuring conditions allows the viscosity to be measured over the entire shear rate range. Instruments to measure the first normal stress coefficients are commercially available and provide accurate results for polymer melts and concentrated polymer solutions. The available experimental results on polymer melts show that , is positive and that it approaches zero as y approaches zero. Studies related to the second normal stress coefficient 4 reveal that it is much smaller than 4V and, furthermore, 4 2 is negative. For 2.5 percent polyacrylamide in a 50/50 mixture of water and glycerin, -4 2/4 i is reported to be in the range of 0.0001 to 0.1 [7]. 

G.S. Fulcher, Analysis of recent measurements of the viscosity data for concentrated polymer solutions, J. Am. Ceram. Soc. 1925, 8, 339-355, 789-794. 

Problems caused by the determination of the unoccupied vapor space were avoided by Haynes et al., since they measure the pressure difference as well as the absolute vapor pressure. Also, the concentration is determined independently by using a differential refractometer and a normalized relation between eoneentration and refractive index. Degassing of the liquids remains a necessity. Time for establishing thermodynamic equilibrium could be somewhat shortened by intensive stirring (slight problems with increasing polymer concentration and solution viscosity were reported). 

Low intrinsic viscosities and high ku values were determined by dilute solution viscosity measurements, indicative of large hydrodynamic interactions supporting the conclusions drawn from LS that intramolecular association does occur at low concentrations. Comparative examination of R and Rh values showed that Rvzwitterionic polymers, which was attributed to dissociation of the aggregates, to some extent, under the applied shear rate in the capillary. Because these forces are generally not very strong, it was concluded that the critical shear rate should be small. Compared to linear cB-fimctionalized polymers, the lower stability of the aggregates formed by the end-functionalized stars was attributed to the steric repulsion of the unfiinctionalized arms. 

The diffiisivities of low molecular weight solutes in polymer solutions do not appear to follow a predictable pattern as a function of polymer concentration. It is clear that the results cannot be predicted with the Wilke-Chang equation by merely using the increased viscosity of the solution. Diffiisivities have been reported to increase, decrease, or go through a maximum with increasing polymer concentration despite solution viscosity increases." Li and Gainer measured the diffiisivities of four solutes in seven... 

The intrinsic viscosity [n] of the polymer solution was measured with a capillary viscometer. A value of [n]=15dl/gr was obtained, i.e., the relative increase in viscosity, [n]c, was only 15% for the most concentrated solution of 100 ppm. The kinematic viscosity for calculation of Re was corrected according to the polymer concentration and changes in solution temperature. 

---