Viscometry

The methodology of capillary viscometry of liquids rests on the laws of flow through a fine-bore tube. The viscosity is determined from the measured flow rate under a known applied pressure through a tube of known dimensions. 

Fora pure solvent, the flow time to can be related to the viscosity rj in a similar manner. Of particular interest is the relative viscosity 

The relative viscosity is a function of the solvent viscosity and the concentration of the polymer solution. It is possible to use the measured flow-time data for the solvent and polymer solutions to arrive at a quantity known as the intrinsic viscosity (IV) which is characteristic of the polymer molecular 

In these equations f/,p is defined as the specific viscosity, is the relative viscosity, is the reduced viscosity and [ ] is the intrinsic viscosity. The relative and specific viscosities are dimensionless and the intrinsic viscosity is either expressed in decilitres per gram or millilitres per gram, i.e. the inverse of concentration. 

It is good practice to extrapolate both rj /c and ( / i/c— 1) to infinite dilution (c- 0) in order to obtain a better estimate of the magnitude of [ /]. 

The viscosity-average molecular weight of a polymer sample may be computed from the chromatogram hi of the polymer by the formula  

Mao and co-workers [189] have developed a new method for the determination of polymer viscosity-average molecular weights using flow piezoelectric quartz crystal (PQC) viscosity sensing. Experimental apparatus with a 9 MHz AT-cut quartz crystal and a flow detection cell was constructed and shown to give highly reproducible data at a temperature of 25 0.1 °C and fluid flow rate of 1.3-1.6 ml/min. A response model for the PQC in contact with the dilute polymer solutions (concentration less than 0.01 g/ml) was proposed in which the frequency change from the pure solvents, Af, follows Af = + kj, where 

Til is absolute viscosity of dilute polymer solution and and kj are the proportionality constants. This model was investigated with PEG samples (PEG-20000 and PEG-10000) under the aforementioned experimental conditions using water as solvent. Based on this model, the method was developed and tested with an unknown polyvinyl alcohol sample against the conventional capillary viscosity method. There was good agreement between this method and the conventional method. The method proposed by Mao and co-workers [189] has a number of advantages over the conventional viscosity method it 

Lukhovitskii and Karpo [191] established that, in the concentration range accessible for viscometry, the efflux time of a polymer solution is a linear function of the polymer concentration. This is consistent with the Einstein-Simha equation. In the general case, the efflux time of a solution with a polymer concentration tending to zero, T, does not coincide with the efflux time of the pure solvent, T, When the efflux time of a polymer solution is reduced by rather than by (as is done in the standard method), the reduced viscosity becomes independent of the polymer concentration and equal to the intrinsic viscosity. The advantages of the proposed method are especially important for the determination of the intrinsic viscosity (M ) of ultra-high molecular weight polymers. 

Intrinsic viscosity measurements have been used to determine the molecular weight of PP [192-195], PET [196, 197], PE [198-204], PVC [203], polyacrylamide [205, 206], polyvinyl pyrrolidone [207], and styrene-methyl methacrylate copolymers [208]. 

The most common instrument used for viscosity measurements in low-viscosity liquids is the capillary viscometer. In this instrument, a liquid is made to flow under its own potential head through a narrow capillary with a weU-defined length and cross section. The volumetric flow rate Qota simple Newtonian liquid undergoing laminar flow in a capillary of diameter d and length / is given by Poiseuille s equation  

Ap is the pressure difference between the fluid at the inlet and the outlet 

FIGURE 7.7 Ostwald viscometer. Viscosity is determined by measuring the time rrequired for fluid level to fall from the upper to the lower mark. 

A = nd gh/128Vl is a constant that depends on the geometry of the instrument and can be determined from calibration experiments using liquids with known q and p 

by simply measuring t, the kinematic viscosity v = q/p of any low-viscosity Newtonian liquid can be determined. It is important to note that because the lower bulb contains liquid during the measnrement, h depends on the liquid level in both arms of the viscometer. Calibration experiments must therefore be performed with the same initial head of liquid as the actual measuranents to yield accurate results. In practice, Equation 7.17 leads to small but systanatic errors in viscosity data, particularly for low viscosity liquids. The source of errors can be traced to omission of the energy required to accelerate the liquid as it enters and leaves the capillary. When this effect is taken into account, Equation 7.17 reads [30] 

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In addition to the apparent viscosity two other material parameters can be obtained using simple shear flow viscometry. These are primary and secondary nomial stress coefficients expressed, respectively, as... 

Figure 5,16. It is assumed that by using an exactly symmetric cone a shear rate distribution, which is very nearly uniform, within the equilibrium (i.e. steady state) flow held can be generated (Tanner, 1985). Therefore in this type of viscometry the applied torque required for the steady rotation of the cone is related to the uniform shearing stress on its surface by a simplihed theoretical equation given as...

Petera, J. and Nassehi, V., 1995. Use of the finite element modelling technique for the improvement of viscometry results obtained by cone-and-plate rheometers. J. Non-Newtonian Fluid Mech. 58, 1-24. 

At 25°C, the Mark-Houwink exponent for poly(methyl methacrylate) has the value 0.69 in acetone and 0.83 in chloroform. Calculate (retaining more significant figures than strictly warranted) the value of that would be obtained for a sample with the following molecular weight distribution if the sample were studied by viscometry in each of these solvents ... 

Before we are in a position to discuss the viscosity of polymer melts, we must first give a quantitative definition of what is meant by viscosity and then say something about how this property is measured. This will not be our only exposure to experimental viscosity in this volume—other methods for determining bulk viscosity will be taken up in the next chapter and the viscosity of solutions will be discussed in Chap. 9—so the discussion of viscometry will only be introductory. Throughout we shall be concerned with constant temperature experiments conducted under nonturbulent flow conditions. 

Slurry Viscosity. Viscosities of magnesium hydroxide slurries are determined by the Brookfield Viscometer in which viscosity is measured using various combinations of spindles and spindle speeds, or other common methods of viscometry. Viscosity decreases with increasing rate of shear. Fluids, such as magnesium hydroxide slurry, that exhibit this type of rheological behavior are termed pseudoplastic. The viscosities obtained can be correlated with product or process parameters. Details of viscosity deterrnination for slurries are well covered in the Hterature (85,86). 

Analysis for Poly(Ethylene Oxide). Another special analytical method takes advantage of the fact that poly(ethylene oxide) forms a water-insoluble association compound with poly(acryhc acid). This reaction can be used in the analysis of the concentration of poly(ethylene oxide) in a dilute aqueous solution. Ereshly prepared poly(acryhc acid) is added to a solution of unknown poly(ethylene oxide) concentration. A precipitate forms, and its concentration can be measured turbidimetricaHy. Using appropriate caUbration standards, the precipitate concentration can then be converted to concentration of poly(ethylene oxide). The optimum resin concentration in the unknown sample is 0.2—0.4 ppm. Therefore, it is necessary to dilute more concentrated solutions to this range before analysis (97). Low concentrations of poly(ethylene oxide) in water may also be determined by viscometry (98) or by complexation with KI and then titration with Na2S202 (99). 

FIGURE 10.14 Analysis of polyvinylpyridines on SynChropak CATSEC 100,300, and 1000 columns in series (250 X 4.6 mm i.d.). Flow rate 0.37 ml/min. Mobile phase 0.1 % trifluoroacetic acid in 0.2 N sodium nitrate. Detection by differential viscometry. (Reprinted from Ref. 9 with permission.)... 

Many proteins and polymers have been analyzed on SynChropak GPC and CATSEC columns. Table 10.6 lists some of the published applications. The use of a surfactant to analyze the caseins in milk is illustrated in Eig. 10.12. Viruses have also been analyzed on SynChropak GPC columns, as seen in the chromatogram from Dr. Jerson Silva of the University of Illinois (Pig. 10.13). Dr. Nagy and Mr. Terwilliger analyzed cationic polymers on a series of CATSEC columns using differential viscometry as detection (Pig. 10.14) (9). 

Synthetic, nonionic polymers generally elute with little or no adsorption on TSK-PW columns. Characterization of these polymers has been demonstrated successfully using four types of on-line detectors. These include differential refractive index (DRI), differential viscometry (DV), FALLS, and MALLS detection (4-8). Absolute molecular weight, root mean square (RMS) radius of gyration, conformational coefficients, and intrinsic viscosity distributions have... 

TABLE 20.4 Mark-Houwink Constants for PEG, PEO, and PSC from SEC/Viscometry Using TSK-PW Columns... 

FIGURE 20.4 Differential viscometry chromatogram of fully hydrolyzed PVA using TSK-PW columns. 

Synchropak columns are very useful for characterizing hydrophilic, anionic, and nonionic, water-soluble polymers, CATSEC columns work best for characterizing cationic polymers utilizing both light scattering and/or differential viscometry detection over a wide range of molecular weights. 

Nagy, D. J. (1994). First International GPC-Viscometry Symposium, Houston, TX. 

The presence of a critical St content in ASt-x can also be seen in fluorescence spectra [29], This copolymer in aqueous solution shows an excimer emission peaking at 325 nra. As shown in Fig. 8, the intensity of the excimer emission increases, while the monomer emission decreases, with increasing St content. Eventually the excimer dominates the monomer emission at an St content of 72 mol%. The excimer emission becomes apparent at an St content of about 50 mol%, which agrees with the critical St content estimated by viscometry and NMR spectroscopy. The existence of the critical St content suggests the hydro-phobic self-aggregation to be a cooperative process. 

Using IR spectroscopy and NMR, one can analyze the chemical structure of PA. The molecular weight and molecular weight distribution can be analyzed by endgroup analysis, viscometry, and high-pressure liquid chromatography (HPLC). The crystalline order can be analyzed by WAXS, small-angle X-ray spectroscopy... 

Hie hydrolytic depolymerization of nylon-6 was followed by gel permeation chromatography (GPC), viscometry, and gravimetry. GPC determinations were performed on a Waters 150C chromatography system using benzyl alcohol as die eluant, two Plgel 10-p.m crosslinked polystyrene columns, and a differential refractometer detector. The flow rate was 1 mL/min. The concentration of the polymer solutions was 0.5 wt% and dissolution was accomplished at 130°C. 

Virtually crosslinked (VC) products, 201 Viscometry, of polyamides, 161-162 Viscosity, molecular weight and, 3 VK column reactor, 175 Volatile organic compounds (VOCs), 206, 207... 

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