Complex viscosity defined

For sodium/hexamethylene-l,6-bis-carbamidocaprolactam system, Sibal et al. [64] found the value of the constant k in Equation 1.4 to be 17.5. Note that the values of the constant k in Equation 1.4 that defines the relative complex viscosity rise during anionic ring opening polymerization of caprolactam are comparable for both caprolactam-magnesium-bromide/isophthaloyl-bis-caprolactam and sodium/hexamethylene-l,6-bis-carbamidocapro-lactam as the catalyst/initiator systems even though the kinetic constants for anionic polymerization for these systems are extremely different (see Table 1.2). 

From Equation 1.4, the complex viscosity at 57 percent conversion of the caprolactam monomer, which may be defined as solidification or gel point, is 100Pas (1000 Poise). Combining the information on conversion at the gel point with the data presented in Figures 1.20 and 1.21, the time to gel formation during pultrusion can be estimated. 

The rheokinetics of polycaprolactam polymerizing in the monomer shows that below 50 percent conversion, the relative complex viscosity versus conversion of the nylon 6 homopolymerization is defined by the phenomenological equation ri / t]Q = exp(19.6 X), where // is the complex viscosity of nylon 6 anionically polymerizing in its monomer, 0 is the viscosity of caprolactam monomer, and X is fractional conversion. 

Viscosity is the ratio of a stress to a strain rate [Eq. (I l-9)j. Since the complex modulus G has the units of stress, it is possible to define a complex viscosity t] as the ratio of G to a complex rate of strain ... 

Since the complex Auscosity is concentration-dependent just in the same manner as the steady-state viscosity, one can define a complex viscosity increment, v, and a complex intrinsic viscosity, [ ], similar to that for steady-state viscosity... 

Dynamic-shear measurements are of the complex viscosity rj ) as a function of the dynamic oscillation rate (o), at constant temperature. These tests are defined as isothermal dynamic frequency sweeps. Since the dynamic frequency sweeps are conducted at a given amplitude of motion, or strain, it is necessary to ensure that the sweeps are conducted in the region where the response is strain-independent, which is defined as the linear viscoelastic region. This region of strain independence is determined by an isothermal strain sweep, which measures the complex viscosity as a function of applied strain at a given frequency. This ensures that a strain at which the dynamic frequency sweep may be conducted in the linear viscoelastic region is selected. 

The complex viscosity as a function of frequency, maximum strain and temperature is generally determined with one rheometer. Standard ASTM 4440-84/90 defines the measurement of rheological parameters of polymer samples using dynamic oscillation. This standard reiterates the importance of determining the linear viscoelastic region prior to performing dynamic frequency sweeps. 

The nse of carboxymethylcelluloses has also been suggested. These are a group of complex, poorly-defined products with various properties. Their effectiveness seems to vary according to the type of wine, bnt especially in relation to the presence of protective colloids. Carboxymethylcelluloses modify a wine s viscosity. They have not as yet been developed on an industrial scale. 

In marked contrast to measurements of shear rheological properties, such as apparent viscosity in steady shear, or of complex viscosity in small amplitude oscillatory shear, extensional viscosity measurements are far from straightforward. This is particularly so in the case of mobile elastic liquids whose rheology can mitigate against the generation of well-defined extensional flow fields. 

From the expressions corresponding to the shear rate and shear stress, a complex viscosity can also be defined as ... 

Rheology is not just about viscosity, but also about another important property, namely the elasticity. Complex fluids also exhibit elastic behaviour. Similar to the viscosity defined above being similar to the definition of a Newtonian viscosity, the elasticity of a complex material can be defined similar to its idealised counterpart, the Hookean solid. The modulus of elasticity is defined as... 

Periodic or oscillatory viscosity experiments provide a powerful rheological analogue to dynamic mechanical experiments. The theoretical relations are, in fact, closely interlocked. The complex viscosity, rj, is defined as (10)... 

The system can be further characterised by measurement of the mechanical spectrum at a strain within the linear viscoelastic region defined by the strain sweep. Here the storage (G ) and loss (G") modulus, and complex viscosity (r) ) are measured as a function of frequency (u)) and plotted on double logarithmic plots. Typical mechanical spectrum of entanglement solutions are shown in Figure 2.9. 

Since viscosity is the quantity of interest in rheology, it is a simple matter to define a complex viscosity (q ) in a dynamic rheological test based on a complex form of Newton s law of viscosity... 

It is also possible to define a dynamic complex viscosity in terms of G and G" as follows ... 

The amplitude ratio is equal to co r], where the magnitude of the complex viscosity is defined... 

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