Complex viscosity definition

In principle, any type of sample can be analysed by SEC provided that it can be solubilised and that there are no enthalpic interactions between sample and packing material. By definition then, this technique cannot be carried out on vulcanisates and even unvulcanised fully compounded rubber samples can present problems due to filler-rubber interactions. The primary use of SEC is to determine the whole MWD of polymers and the various averages (number, viscosity, weight, z-average) based on a calibration curve and to allow qualitative comparisons of different samples. Many commercial polymers have a broad MWD leading to strong peak overlap in the chromatography of complex multicomponent systems. 

This definition cannot be applied directly to mixtures, as phase equilibria of mixtures can be very complex. Nevertheless, the term supercritical is widely accepted because of its practicable use in certain applications [6]. Some properties of SCFs can be simply tuned by changing the pressure and temperature. In particular, density and viscosity change drastically under conditions close to the critical point. It is well known that the density-dependent properties of an SCF (e.g., solubihty, diffusivity, viscosity, and heat capacity) can be manipulated by relatively small changes in temperature and pressure (Sect. 2.1). 

Here t is the resulting shear stress, 6 is the phase shift often represented as tan(d), and (O is the frequency. The term 6 is often referred to as the loss angle. The in-phase elastic portion of the stress is To(cosd)sin(wt), and the out-of-phase viscous portion of the stress is To(sind)cos(complex modulus and viscosity, which can be used to extend the range of the data using the cone and plate rheometer [6] ... 

Skeggs innovative step, the introduction of air bubbles into the flowing stream, attempted to minimize the time taken for a steady-state condition to be reached in the detector. The definitive description of dispersion in segmented streams (Snyder [37]) showed a complex relationship between internal diameter, liquid flow rate, segmentation frequency, residence time in the flow system, viscosity of the hquid and surface tension. 

Phase diagrams from freezing point depressions show true compound formations for simpler amides—e.g., water-N-methylacetamide forms a compound at a mole ratio of 2 to 1, water-N,N-dimethylacetamide at 3 to 2 and 3 to 1, and water-N-methylpyrrolidone at 2 to 1. The heats of mixing and heat capacities at 25°C. of a number of water-amide systems were determined. All mixing curves were exothermic and possess maxima at definite mole ratios, while the heat capacities for the most part show distinct curvature changes at the characteristic mole ratios. Both experimental results point to the stability of the particular complexes even at room temperature. This is further supported by absolute viscosity studies over the whole concentration range where large maxima occur at these same mole ratios for disubsti-tuted amides and N-substituted pyrrolidones. 

Some papers60-61 have been devoted to phase separation of polyionic complexes from partially furated (PVA-S) and aminoacetylated (PVA-AAC)poly(vinyl alcohol) in aqueous salt solutions. The separation liquid-liquid or complex coacervation occurs at a definite value of the charge density on the macromolecule. From the concentration dependence of the reduced viscosity of the initial components PVA-S, PVA-AAc and their equivalent mixture in water it follows that the viscosity of the components noticeably increases with dilution, and the curve of the equivalent mixture is concentration independent. This fact confirms the formation of the neutral polymer salt, due to electrostatic interactions of PVA-S (strong polyadd) and PVA-AAc (weak polybase). 

The superscript indicates that the shear rate was increased from zero at time t = 0. This definition is only meaningful if the fluid at time r = 0 is in a well-defined state, usually a stress-free state, and if this starting state and the transient viscosity are reproducible from one run to the next. The superscript -p is sometimes omitted. Measurements of t) give information about rates of structural rearrangement within a deforming complex fluid. 

In analogy with the definition of viscosity given in transient experiments, the complex shear stress is related to the complex shear rate deformation by the expression... 

Information about physicochemical and complexation properties of polyvinylsulfonic acid (PVSH) or, more correctly, polyethylenesulfonic acid (PESH) [11] is much less available than that of the polyamines. PVSH (or PESH) is a simple, strong polyacid (see Fig. 6.6), so that partial ionization and possible hydrolysis effects, encountered with weak polyacids and their salts (e.g., polyacryfic acid and its salts), do not complicate the picture [76]. Commercially available sodium salt, PVSNa, is a brittle hygroscopic solid, soluble in water, but insoluble in organic solvents (methanol, dioxane, etc.) [77]. Viscosity behavior of the alkali metal salts was studied by several groups [28, 52, 75-77], but data are too scattered to be trustworthy. The PVS polyanion shows a definite selectivity in ion binding with alkali Li, Cs metals in the presence of Na, K hah des [78]. 

Additionally, Biot (1956a, b) introduced a complex correction function (F) which accounts for a frequency-dependent viscous flow resistance (r /K). In fact, while the assumption of an ideal Poiseuille flow is valid for lower frequencies, deviations of this law occnr at higher frequencies. For short wavelengths the inflnence of pore flnid viscosity confines to a thin skin depth close to the sediment frame, so that the pore fluid seems to be less viscous. To take these effects into account the complex fnnction (F) modifies the viscous flow resistance (p/K) as a fnnction of pore size, pore flnid density, viscosity and freqnency. A complete definition of (F) can be fonnd in Stoll (1989). 

---