Dilute solution method viscosity

We report here the results of our recent studies of poly(alkyl/arylphosphazenes) with particular emphasis on the following areas (1) the overall scope of, and recent improvements in, the condensation polymerization method (2) the characterization of a representative series of these polymers by dilute solution techniques (viscosity, membrane osmometry, light scattering, and size exclusion chromatography), thermal analysis (TGA and DSC), NMR spectroscopy, and X-ray diffraction (3) the preparation and preliminary thermolysis reactions of new, functionalized phosphoranimine monomers and (4) the mechanism of the polymerization reaction. 

The dilute solution methods have been used for characterising polymers since day one of polymer science. Measurements of dilute solution viscosity, osmotic pressure and light scattering have been well-established in theory as well as in practice. They are described practically in every textbook and in many review articles. More than 30 years have passed since the introduction of size exclusion chromatography (or gel permeation chromatography CPC), which provides fractionation data very conveniently. This chapter is not intended to be a review of these methods. It is directed to examining how useful these methods are with respect to sensitivity, reproducibility, and reliability. Stated differently, the question is whether or not differences in processability can be explained on the basis of information available from the dilute solution methods. 

The Mooney index is often called Mooney viscosity hut there is no rationale that the index represents viscosity. It is an expression of some aspect of viscoelasticity in that there may be some relationship to the processability. The method uses an instrument with a particular design, which provides a simple operation and a quick result. Compared to the dilute solution method, the sample size required is much larger so that it is more representative of the commercial lot. The Mooney index has been used worldwide as a specification for gum rubbers. 

Analytical and test methods for the characterization of polyethylene and PP are also used for PB, PMP, and polymers of other higher a-olefins. The C-nmr method as well as k and Raman spectroscopic methods are all used to study the chemical stmcture and stereoregularity of polyolefin resins. In industry, polyolefin stereoregularity is usually estimated by the solvent—extraction method similar to that used for isotactic PP. Intrinsic viscosity measurements of dilute solutions in decahn and tetraHn at elevated temperatures can provide the basis for the molecular weight estimation of PB and PMP with the Mark-Houwiok equation, [rj] = KM. The constants K and d for several polyolefins are given in Table 8. 

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. 

The extremely low rates of solution of polymers and the high viscosities of their solutions present serious problems in the application of the delicate calorimetric methods required to measure the small heats of mixing or dilution. This method has been applied successfully only to polymers of lower molecular weight where the rate of solution is rapid and the viscosity of the concentrated solution not intolerably great.22 The second method requires very high precision in the measurement of the activity in order that the usually small temperature coefficient can be determined with sufficient accuracy. 

The terms in Eq. (6) include the gravitational constant, g, the tube radius, R, the fluid viscosity, p, the solute concentration in the donor phase, C0, and the penetration depth, The density difference between the solution and solvent (ps - p0) is critical to the calculation of a. Thus, this method is dependent upon accurate measurement of density values and close temperature control, particularly when C0 represents a dilute solution. This method has been shown to be sensitive to different diffusion coefficients for various ionic species of citrate and phosphate [5], The variability of this method in terms of the coefficient of variation ranged from 19% for glycine to 2.9% for ortho-aminobenzoic acid. 

The viscosity of a dilute solution of polymer depends on the molecular weight of the polymer. This gives us a simple method for measuring molecular weight based on viscosity, which is readily measured. 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

The dominating working mode of polymer HPLC is the straight elution of small volume of sample solution along the column. There were attempts to introduce the differential and vacancy procedures in SEC. In both cases, the eluent was a diluted solution of the polymer while either a proper sample or a reference polymer [314] or even pure eluent [315] was injected. A broader application of these proposals was hindered by both the high eluent viscosity and the large sample consumption. Moreover, the dependences of log M vs. Vr (Equation 16.12) obtained by the conventional and the differential/vacancy methods are mutually shifted. The deviation between both dependences was attributed to the nonequilibrium situation in the vacancy polymer HPLC [316],... 

The model parameters q and ML can be estimated from experimental data for radius of gyration, intrinsic viscosity, sedimentation coefficient, diffusion coefficient and so on in dilute solutions. The typical methods are expounded in several recent articles and books [20-22], Here we refer only to the results of the application to representative liquid-crystalline polymers (See Table 1). 

The methods of measuring the liquid phase properties were described previously [1], It was observed that heat was evolved during the preparation of all these mixtures. It should be mentioned that the electrical conductivities of the sulphuric acid-nitromethane mixtures were not constant, but were found to increase with time. Reliable data could therefore not be obtained. This is due to the fact that nitromethane reacts with sulphuric acid in dilute solutions, as has been recently discussed by Gillespie and Solomons [6]. All other properties of these mixtures were constant at 25° and measurements were restricted to this temperature. For the other four systems the viscosity, electrical conductivity and density were investigated at two temperatures 25° and 40°), because of the importance of the temperature coefficients of viscosity and electrical conductivity. The refractive indexes were measured only at 25°. The investigation of the liquid phase properties of the system with p-nitro toluene at these temperatures was possible only up to 50 mole % of p-nitrotoluene, i.e. until the solutions became saturated with respect to p-nitrotoluene. The refractive indexes of these solutions were not measured. 

Viscosity determinations at the highest convenient concentration are of practical value, because in most of the applications of nitrocellulose, solutions of these concentrations are used, and there is usually little difference between the concentration in use and that used for the determination. All nitrocellulose solutions that are not very dilute show more or less abnormal viscosity, i.e. the rate of flow is not proportional to the applied stress or pressure. The ease of flow of a solution at one degree of stress cannot then be inferred from a viscosity determined at another. Nevertheless the measured viscosity of a comparatively concentrated solution is in general useful information. This advantage is sacrificed in what is the most rational of all viscosity systems, the German I.G. Method. Measurements are made in dilute solutions and the results are expressed in terms of the Eigenviscositat (k) of Fikentscher and Mark [99] a function which to a large extent is independent of concentration ... 

This unit describes a method for measuring the viscosity (r ) of Newtonian fluids. For a Newtonian fluid, viscosity is a constant at a given temperature and pressure, as defined in unit hi. i common liquids under ordinary circumstances behave in this way. Examples include pure fluids and solutions. Liquids which have suspended matter of sufficient size and concentration may deviate from Newtonian behavior. Examples of liquids exhibiting non-Newtonian behavior (unit hi. i) include polymer suspensions, emulsions, and fruit juices. Glass capillary viscometers are useful for the measurement of fluids, with the appropriate choice of capillary dimensions, for Newtonian fluids of viscosity up to 10 Pascals (Newtons m/sec 2) or 100 Poise (dynes cm/sec 2). Traditionally, these viscometers have been used in the oil industry. However, they have been adapted for use in the food industry and are commonly used for molecular weight prediction of food polymers in very dilute solutions (Daubert and Foegeding, 1998). There are three common types of capillary viscometers including Ubelohde, Ostwald, and Cannon-Fenske. These viscometers are often referred to as U-tube viscometers because they resemble the letter U (see Fig. HI.3.1). 

The characterization of surface activity of fillers is obtained by use of several analytical techniques [1]. Examples of them are inverse gas chromatography [1, 2], the adsorption of a low molecular weight analog of elastomers [3], the adsorption of elastomer chains fi om dilute solutions [4], the wettability, viscosity of PDMS fluids in the boundary layer at the surface of solids [5], the determination of the specific surface area, and the analysis of surface groups [1]. It should, however, be mentioned that the results obtained by these methods do not provide direct information on the elastomer behavior at the interface, due to the use of small probe molecules or the presence of a solvent in the systems studied. 

Rheology is a powerful method for the characterization of HA properties. In particular, rotational rheometers are particularly suitable in studying the rheological properties of HA. In such rheometers, different geometries (cone/plate, plate/plate, and concentric cylinders) are applied to concentrated, semi-diluted, and diluted solutions. A typical rheometric test performed on a HA solution is the so-called "flow curve". In such a test, the dynamic viscosity (q) is measured as a function of the shear rate (7) at constant strain (shear rate or stress sweep). From the flow curve, the Newtonian dynamic viscosity (qo), first plateau, and the critical shear rate ( 7 c), onset of non-Newtonian flow, could be determined. 

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