Deformation, loss modulus

Similar information can be obtained from analysis by dynamic mechanical thermal analysis (dmta). Dmta measures the deformation of a material in response to vibrational forces. The dynamic modulus, the loss modulus, and a mechanical damping are deterrnined from such measurements. Detailed information on the theory of dmta is given (128). 

Gels are viscoelastic bodies, the rheological properties of which can be described by two parameters, the storage modulus (G, which is a measure of its elasticity) and the loss modulus (G", which is a measure of its viscous nature). The combined viscoelastic modulus (G ) is a measure of the overall resistance of a gel to deformation. These moduli are often highly dependent on the time-scale of deformation. Another important parameter of a food gel is its yield stress. 

It turns out that stress relaxation following a simple shear deformation is seldom employed experimentally. A more common technique is to measure the steady state response to small sinusoidal deformations as a function of angular frequency to. The dynamic storage modulus G (to) and loss modulus G"(to) in small sinusoidal deformations are related to G(t) ... 

The imaginary part of the modulus, also called the loss modulus, is a damping term which determines the dissipation of energy as heat upon deformation. G"/G is called the dissipation factor and is proportional to the ratio of energy dissipated per cycle to the maximum potential energy stored during a cycle. 

Eqs. (1.16) are, of course, very well-known. G is known as the storage modulus in shear. It describes that part of the shear stress, which is in phase with the deformation. G" is the loss modulus in shear. It describes that part of shear stress which is 90 degrees out of phase. 6 is the loss angle. These definitions will be used occasionally in this review. 

Dynamic mechanical experiments, where the material is periodically strained, are common methods to characterize the visco-elastic behavior of elastomers by measuring the storage modulus G and loss modulus G". G is a measure for the maximal, reversibly stored energy for a periodical deformation and G" is proportional to the dissipated energy for the oscillation cycle. It is obvious to investigate, whether the l.c. state of the l.c. elastomers influences the dynamic mechanical properties and whether different modes of linking the mesogenic moieties to the backbone can be detected. 

Fibrin is a viscoelastic polymer, which means that it has both elastic and viscous properties (Ferry, 1988). Thus, the properties of fibrin may be characterized by stiffness or storage modulus (representing its elastic properties) and creep compliance or loss modulus/loss tangent (representing its inelastic properties). These parameters will determine how the clot responds to the forces applied to it in flowing blood. For example, a stiff clot will not deform as much as a less stiff one with applied stress. 

The physical properties of barrier dressings were evaluated using the Seiko Model DMS 210 Dynamic Mechanical Analyzer Instrument (see Fig. 2.45). Referring to Fig. 2.46, dynamic mechanical analysis consists of oscillating (1 Hz) tensile force of a material in an environmentally (37°C) controlled chamber (see Fig. 2.47) to measure loss modulus (E") and stored modulus (E ). Many materials including polymers and tissue are viscoelastic, meaning that they deform (stretch or pull) with applied force and return to their original shape with time. The effect is a function of the viscous property (E") within the material that resists deformation and the elastic property (E )... 

Dynamic mechanical load on elastomer products is often exerted at small deformations and low deformation rates but over extended time periods. Then part of the mechanical energy is dissipated into heat depending on the value of the loss modulus. As a consequence, a temperature profile is established within the sample. Then the modulus... 

It demonstrates the highly elastic behaviour. At small deformation amplitudes the storage modulus G is one order of magnitude larger than the loss modulus G" and independent of the frequency. This is the behaviour of a solid body. 

The term s0E sin (cot) in Eq. (13.54) is the part of the stress that is in phase with the deformation and thus represents the elastic part of the stress, i.e. the part of the stress where energy is stored. For that reason E is called the (tensile) storage modulus. The term e0E"cos(cot) in Eq. (13.54) is the part of the stress that is re/2 rad out of phase with the deformation and thus represents the viscous part of the stress, i.e. the part of the stress where energy is dissipated. For that reason E" is called the (tensile) loss modulus. 

Models of viscoelastic behaviours, 412 Modes of deformation, 526 Modulus, 396 bulk, 395,405, 447,514 complex, 410, 418 dynamic, 451 loss, 408... 

Fig. 1 a,b. Strain amplitude dependence of the complex dynamic modulus E E l i E" in the uniaxial compression mode for natural rubber samples filled with 50 phr carbon black of different grades a storage modulus E b loss modulus E". The N numbers denote various commercial blacks, EB denotes non-commercial experimental blacks. The different blacks vary in specific surface and structure. The strain sweeps were performed with a dynamical testing device EPLEXOR at temperature T = 25 °C, frequency f = 1 Hz, and static pre-deformation of -10 %. The x-axis is the double strain amplitude 2eo... 

A very convincing piece of evidence for agglomeration-deagglomeration as an important loss mechanism is the close empirical relationship between the maximum value of the loss modulus, G"m, and the height of the step in the storage modulus G (y0) as a function of deformation amplitude ... 

When using small deformation rheology there are several useful parameters that may be obtained to describe a material the complex modulus (G ), storage modulus (G ), loss modulus (G") and the tangent of the phase shift or phase angle (tan 5). These values must be taken from within the LVR, and are obtained using a dynamic oscillatory rheometer (Rao 1999). Outside the LVR, important information may be obtained such as the yield stress and yield strain. 

When the stress is decomposed into two components the ratio of the in-phase stress to the strain amplitude (j/a, maximum strain) is called the storage modulus. This quantity is labeled G (co) in a shear deformation experiment. The ratio of the out-of-phase stress to the strain amplitude is the loss modulus G"(co). Alternatively, if the strain vector is resolved into its components, the ratio of the in-phase strain to the stress amplitude t is the storage compliance J (m), and the ratio of ihe out-of-phase strain to the stress amplitude is the loss compliance J"(wi). G (co) and J ((x>) are associated with the periodic storage and complete release of energy in the sinusoidal deformation process. Tlie loss parameters G" w) and y"(to) on the other hand reflect the nonrecoverable use of applied mechanical energy to cause flow in the specimen. At a specified frequency and temperature, the dynamic response of a polymer can be summarized by any one of the following pairs of parameters G (x>) and G" (x>), J (vd) and or Ta/yb (the absolute modulus G ) and... 

The development of a maximum in tan 5 or ihe loss modulus at the glass-to-rubber transition is explained as follows. At temperatures below Tg the polymer behaves elastically, and there is little or no flow to convert the applied energy into internal work in the material. Now It, the energy dissipated as heat per unit volume of material per unit time because of flow in shear deformation, is... 

---