Viscoelastic properties, linear

Linear viscoelasticity is the simplest type of viscoelastic behavior, in which viscoelastic properties are independent of the magnitude of applied stress or strain (Barnes et al., 1989 Gunasekaran and Ak, 2002). Linear viscoelasticity is usually exhibited by food materials at very small strains (Rao, 1992) that cause negligible damage to the food s structure the phenomenon must therefore be investigated experimentally using small deformation test methods. 

Linear viscoelastic properties can be measured in two ways by static methods or by dynamic methods (Barnes et al., 1989). 

The most common dynamic method is oscillatory testing, in which the sample is subjected to a sinusoidal oscillatory strain, and the resulting oscillatory stress measured. The more sophisticated rotational viscometers have the additional capability of dynamically testing liquid-like materials using small angle oscillatory shear. A parallel disc viscometer can be set up for testing solid-like materials (e.g., butter), in oscillatory shear. Some UTM-type solids rheometers, in which the moving crosshead can be made to reciprocate sinusoidally, can be used to test solid-like materials in oscillatory deformation in compression, tension or shear. 

A number of highly sophisticated commercial rheometers, rather different in design from the traditional UTM, are now available in which dynamic and static tests on solids in compression, tension, shear and bending can all be carried out using the same instrument. 

The four variables in dynamic oscillatory tests are strain amplitude (or stress amplitude in the case of controlled stress dynamic rheometers), frequency, temperature and time (Gunasekaran and Ak, 2002). Dynamic oscillatory tests can thus take the form of a strain (or stress) amplitude sweep (frequency and temperature held constant), a frequency sweep (strain or stress amplitude and temperature held constant), a temperature sweep (strain or stress amplitude and frequency held constant), or a time sweep (strain or stress amplitude, temperature and frequency held constant). A strain or stress amplitude sweep is normally carried out first to determine the limit of linear viscoelastic behavior. In processing data from both static and dynamic tests it is always necessary to check that measurements were made in the linear region. This is done by calculating viscoelastic properties from the experimental data and determining whether or not they are independent of the magnitude of applied stresses and strains. 

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Investigation of the linear viscoelastic properties of SDIBS with branch MWs exceeding the critical entanglement MW of PIB (about -7000 g/mol ) revealed that both the viscosity and the length of the entanglement plateau scaled with B rather than with the length of the branches, a distinctively different behavior than that of star-branched PIBs. However, the magnitude of the plateau modulus and the temperature dependence of the terminal zone shift factors were found to... 

C. Friedrich, K. Mattes, and D. Schulze, Non-linear Viscoelastic Properties of Polymer Melts as Analyzed by LAOS-FT Experiments, lUPAC Macro 2004, Paris, France, July 4—9, 2004, Paper 6.1.3. 

The surface characteristics of these species are determined by the particulates and stress transfer across the membrane will tend to be low, reducing internal circulation within the drop. The structure of the interface surrounding the drop plays a significant role in determining the characteristics of the droplet behaviour. We can begin our consideration of emulsion systems by looking at the role of this layer in determining linear viscoelastic properties. This was undertaken by... 

Contents Chain Configuration in Amorphous Polymer Systems. Material Properties of Viscoelastic Liquids. Molecular Models in Polymer Rheology. Experimental Results on Linear Viscoelastic Behavior. Molecular Entan-lement Theories of Linear iscoelastic Behavior. Entanglement in Cross-linked Systems. Non-linear Viscoelastic-Properties. 

To compile the definitions, a number of sources have been used. A number of the definitions were adapted from an International Organization for Standardization (ISO) manuscript on Plastics Vocabulary [1]. Where possible, the names for properties, their definitions and the symbols for linear viscoelastic properties were checked against past compilations of terminology [2-6]. Other documents consulted include ASTM publications [7-13]. 

Analyses of the results obtained depend on the shape of the specimen, whether or not the distribution of mass in the specimen is accounted for and the assumed model used to represent the linear viscoelastic properties of the material. The following terms relate to analyses which generally assume small deformations, specimens of uniform cross-section, non-distributed mass and a Voigt-Kelvin solid. These are the conventional assumptions. 

Quantitative evidence regarding chain entanglements comes from three principal sources, each solidly based in continuum mechanics linear viscoelastic properties, the non-linear properties associated with steady shearing flows, and the equilibrium moduli of crosslinked networks. Data on the effects of molecular structure are most extensive in the case of linear viscoelasticity. The phenomena attributed to chain entanglement are very prominent here, and the linear viscoelastic properties lend themselves most readily to molecular modeling since the configuration of the system is displaced for equilibrium only slightly by the measurement. 

The linear viscoelastic properties are often expressed in terms of an auxiliary function, the relaxation time distribution, H(x) H(x)dlnx is the portion of the initial modulus contributed by processes with relaxation times in the range lnt, InT + dlnt ... 

Only a few non-linear viscoelastic properties have been studied with polymers of well-characterized structure. The most prominent of these is the shear-rate dependence of viscosity. Considerable data have now been accumulated for several polymers, extending over a wide range of molecular weights and concen-... 

Rouse, P.E. A theory of the linear viscoelastic properties of dilute solutions of coiling polymers. J. Chem. Phys. 21,1272-1280 (1953). 

Theory for block copolymer rheology is still in its infancy. There are no models that can predict the rheological behaviour of a block copolymer from microscopic parameters. Fredrickson and Helfand (1988) considered fluctuation effects on the low frequency linear viscoelastic properties of block copolymers in the disordered melt near the ODT. They found that long-wavelength transverse momentum fluctuations couple only to compositional order parameter fluctua-... 

A. Guerrero, P. Partal, and C. Gallegos, Linear viscoelastic properties of sucrose ester-stabilized oil-in-water emulsions, J. Rheol., 42 (1998) 1375-1388. 

The derivation of fundamental linear viscoelastic properties from experimental data obtained in static and dynamic tests, and the relationships between these properties, are described by Barnes etal. (1989), Gunasekaran and Ak (2002) and Rao (1992). In the linear viscoelastic region, the moduli and viscosity coefficients from creep, stress relaxation and dynamic tests are interconvertible mathematically, and independent of the imposed stress or strain (Harnett, 1989). 

Different block length distributions in SBS and (SB)X block polymers and their mixtures can cause wide changes in domain morphology at constant overall monomer composition, which lead to characteristically different linear viscoelastic properties. 

The Fourier transform technique is perfectly general. It may be used also to study non-linear viscoelastic properties (29.30). ... 

The linear viscoelastic properties of all samples were characterized by dynamic shear measurements in the parallel-plate geometry. Experimental details have been previously published [9]. Using time-temperature equivalence, master curves for the storage and loss moduli were obtained. Fig. 1 shows the master curves at 140°C for the relaxation spectra and Table 3 gives the values of zero-shear viscosities, steady-state compliances and weight-average relaxation times at the same temperature. 

Measurement of the linear viscoelastic properties is the basic rheological characterization of polymer melts. These properties may he evaluated in the time domain (mainly creep and relaxation experiments) or in the frequency domain in this case we will talk about mechanical spectroscopy, where the sample experiences a harmonic stimulus (either stress or strain). 

Detailed derivation of linear viscoelastic properties of linear species [7]... 

Satisfactory agreement is achieved from these equations for depiction of the main features of linear viscoelastic properties that can be obtained with the experimental tools, either in transient or in oscillatory rheometry. 

The linear viscoelastic properties of hard-sphere suspensions have been measured by de Kruif, Mellema, and coworkers (van der Werff et al. 1989) and by Shikata and Pearson (1994). Figure 6-9 shows G and G" — r a>aT measured as a function of reduced frequency... 

It is remarkable that several predictions about linear viscoelastic properties in the terminal region can be obtained without special assumptions about the stress- orientation relationship. Thus, for a simple shear strain y which is small enough to evoke only a linear response, the shear stress after the rapid equilibratin process can be written... 

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