Viscoelasticity Method

The U-shaped tube method is used for thermoreversible gels with relatively low modulus ( 100dyne/cm ). As shown in Fig. 4, by preparing a gel in such a way that there are differences in meniscus height, the melting point is determined fix)m the change in height. In the experiment reported by Harrison et al. [16], the amount of the sample used was as little as 0.3 ml when a capillary 0.25-1 mm in diameter is used at the bottom of the tube and the distance between the two vertical tubes is 20 mm. 

They measured the difference in the meniscus Ah by increasing the temperature of the gels, such as methyl acrylate-vinylidene chloride copolymer and determined the melting point from the breakpoint of the log A/j-temperature plot. It was reported that the melting point was not affected by the inner diameter of the capillary or the Ah prior to melting. 

The three methods described thus far are simple methods for measming the loss of the fluidity of sol and the appearance of elasticity [21]. However, they merely observe apparent phenomena. In other words, as viscosity and elasticity of polymeric materials depend on measurement time, it is necessary to observe the loss of fluidity and appearance of elasticity of materials with long relaxation time, such as gels, over a long period of time. In this sense, dynamic mechanical spectroscopy is useful. Readers are referred to monographs on dynamic mechanical spectroscopy [22-24]. In this section, a few examples of viscoelastic behaviors observed at the gel point will be discussed. 

What kind of viscoelastic behavior can be observed in samples that are intermittently removed during tiie gel formation process  

This kind of G and G behavior is regarded as the reflection of the structural variation due to the crosslink network formation via the cross- 

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In a parallel with the theoretical advancement of gel research, a notable, new discovery was recently made in experimental polymer science. Tung and Dynes [62] could show that the viscoelastic method is a useful tool to determine the gel point. What is mentioned below is the essence of the Tung and Dynes work. 

Modulus MPa Modulus at glassy state viscoelastic method 2200 (31)... 

Viscoelastic methods for the characterisation of gum rubbers are extended to rubber compounds, and the ways in which the viscoelastic properties of gum rubbers are manifested in the properties of the corresponding compounds are examined. The development of a method for evaluating strain amplification and strain rate amplification is described. Examples are presented of the characterisation of compounds with respect to variations in gum rubbers and carbon black grades, and consideration is given to the unique characteristics of compounds which are not observed in gum rubbers. Quality control tests for gum rubbers and compounds based on viscoelasticity are reviewed. 32 refs. 

Battiato, G., Varga, G. (1982) The AGIP Viscoelastic Method for Asphalt Pavement Design , in Proceedings of the Fifth International Conference on the Structural Design of Asphalt Pavements (The Study Centre for Road Construction, The Netherlands) pp. 59-66... 

Characterisation of a gum rubber requires determination of the amount of gel fraction, unless it is known to be gel-free. The most direct means of determining gel content is the filtration of the solution. However, the absolute value of gel content is difficult to assess, because the value depends upon the pore size of the filter. Also, the gel is not necessarily distributed uniformly throughout a given lot so that the data are only approximate measures. The viscoelastic method is relative but more reproducible than filtration because the sample size is larger. For a critical examination of the presence of gel, the viscoelastic method provides a better comparison among samples the filtration results may be used as supplementary information. 

The Computation of Polymeric Material s Viscoelastic Properties by Dynamic Indentation Method. 

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

Depending on the method of analysis, constitutive models of viscoelastic fluids can be formulated as differential or integral equations. 

Application of the weighted residual method to the solution of incompressible non-Newtonian equations of continuity and motion can be based on a variety of different schemes. Tn what follows general outlines and the formulation of the working equations of these schemes are explained. In these formulations Cauchy s equation of motion, which includes the extra stress derivatives (Equation (1.4)), is used to preseiwe the generality of the derivations. However, velocity and pressure are the only field unknowns which are obtainable from the solution of the equations of continuity and motion. The extra stress in Cauchy s equation of motion is either substituted in terms of velocity gradients or calculated via a viscoelastic constitutive equation in a separate step. 

In viscoelastic models in addition to the described conditions, stresses at the inlet should be given. As already mentioned there is no universal method to define such conditions, however, the following options may be considered (Tanner, 2000) ... 

Crochet, M. J., 1982, Numerical simulation of die-entry and die-exit flow of a viscoelastic fluid. In Numerical Methods in Forming Processes, Pineridge Press, Swansea. 

Petera, J. and Nassehi, V., 1996. Finite element modelling of free surface viscoelastic flows with particular application to rubber mixing. Int. J. Numer. Methods Fluids 23, 1117-1132. 

In principle, the relaxation spectrum H(r) describes the distribution of relaxation times which characterizes a sample. If such a distribution function can be determined from one type of deformation experiment, it can be used to evaluate the modulus or compliance in experiments involving other modes of deformation. In this sense it embodies the key features of the viscoelastic response of a spectrum. Methods for finding a function H(r) which is compatible with experimental results are discussed in Ferry s Viscoelastic Properties of Polymers. In Sec. 3.12 we shall see how a molecular model for viscoelasticity can be used as a source of information concerning the relaxation spectrum. 

Much more information can be obtained by examining the mechanical properties of a viscoelastic material over an extensive temperature range. A convenient nondestmctive method is the measurement of torsional modulus. A number of instmments are available (13—18). More details on use and interpretation of these measurements may be found in references 8 and 19—25. An increase in modulus value means an increase in polymer hardness or stiffness. The various regions of elastic behavior are shown in Figure 1. Curve A of Figure 1 is that of a soft polymer, curve B of a hard polymer. To a close approximation both are transpositions of each other on the temperature scale. A copolymer curve would fall between those of the homopolymers, with the displacement depending on the amount of hard monomer in the copolymer (26—28). 

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