Loss modulus behavior

The loss moduli (E") of the latex IPN s shown in Figures 4, 7 and 10 are lower than that of PEMA with its broad secondary loss maximum. A summary of the loss modulus behavior of all the materials is given in Table IV in the form of the temperature bandwidths and the temperature bandwidth constants, as determined by equation 1. The value of E was assumed to be the same for all the materials because of the unavailability of accurate E data and because the calculation of the temperature bandwidth constant is very sensitive to the selection of E . 

Relaxations of a-PVDF have been investigated by various methods including dielectric, dynamic mechanical, nmr, dilatometric, and piezoelectric and reviewed (3). Significant relaxation ranges are seen in the loss-modulus curve of the dynamic mechanical spectmm for a-PVDF at about 100°C (a ), 50°C (a ), —38° C (P), and —70° C (y). PVDF relaxation temperatures are rather complex because the behavior of PVDF varies with thermal or mechanical history and with the testing methodology (131). 

There are also some far-fetched proposals for the LST a maximum in tan S [151] or a maximum in G" [152] at LST. However, these expectations are not consistent with the observed behavior. The G" maximum seems to occur much beyond the gel point. It also has been proposed that the gel point may be reached when the storage modulus equals the loss modulus, G = G" [153,154], but this is contradicted by the observation that the G — G" crossover depends on the specific choice of frequency [154], Obviously, the gel point cannot depend on the probing frequency. Chambon and Winter [5, 6], however, showed that there is one exception for the special group of materials with a relaxation exponent value n = 0.5, the loss tangent becomes unity, tan Sc = 1, and the G — G" crossover coincides with the gel point. This shows that the crossover G = G" does not in general coincide with the LST. 

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. 

The effect of the side chain bulkiness has been further studied on a series of chloro derivatives of poly(ethyl methacrylate)(PEMA). Though poly(2-chloroethyl methacrylate) exhibits69 a pronounced peak at Ty = 117 K, poly(2,2,2-trichloroethyl methacrylate), poly(2,2,2-trichloro-l-methoxyethyl methacrylate), and poly(2,2,2-trichloro-l-ethoxyethyl methacrylate) do not show (Fig. 6) any low-temperature loss maximum above the liquid nitrogen temperature157. However, these three polymers probably display a relaxation process below 77 K as indicated by the decrease in the loss modulus with rising temperature up to 100 K. Their relaxation behavior seems to be similar to that of PEMA rather than of poly(2-chloroethyl methacrylate) which is difficult to explain. 

Experiments with the /3-lg/Tween 20 system were performed at a macroscopic a/w interface at a /3-lg concentration of 0.2 mg/ml [40]. The data obtained relate to the properties of the interface 20 minutes after formation. Up to R = 1, the storage modulus (dilational elasticity) was large and relatively constant, whereas the loss modulus (dilational viscosity) increased with increasing R. As R was increased to higher values there was a marked decrease in the storage modulus (dilational elasticity) and a gradual increase in the loss modulus (dilational viscosity). In summary, the data show the presence of a transition in surface dilational behavior in this system at a solution composition of approximately R = 1. At this point, there is a transformation in the adsorbed layer properties from elastic to viscous. 

Thus, mechanical measurements such as DMA or TBA are more common with the latter being used on reactive systems to gather reaction kinetics data [120]. These methods relate changes in the responsive modulus of the material to an impressed sinusoidal vibration. From this Tg, the physical thermomechanical behavior of the system can be related by a quantity termed tan 8 (storage modulus/loss modulus) which passes through a maximum at the Tg. These relaxations occur at certain frequencies at characteristic temperatures. 

It is necessary to state more precisely and to clarify the use of the term nonlinear dynamical behavior of filled rubbers. This property should not be confused with the fact that rubbers are highly non-linear elastic materials under static conditions as seen in the typical stress-strain curves. The use of linear viscoelastic parameters, G and G", to describe the behavior of dynamic amplitude dependent rubbers maybe considered paradoxical in itself, because storage and loss modulus are defined only in terms of linear behavior. 

The (L-N-B)-model represents a highly sophisticated approach to the nonlinear behavior of dynamically excited, filled rubbers. However, it must be criticized that fittings of the storage - and loss - modulus could not be obtained with a single distribution function/la (y). The physical meaning of the density distribution function gla (y) remains unclear, indicating that the consideration of energy dissipation in the (L-N-B)-model is uncompleted. 

This section examines the dynamic behavior and the electrical response of a TSM resonator coated with a viscoelastic film. The elastic properties of viscoelastic materials must be described by a complex modulus. For example, the shear modulus is represented by G = G + yG", where G is the storage modulus and G" the loss modulus. Polymers are viscoelastic materials that are important for sensor applications. As described in Chapter S, polymer films are commmily aj lied as sorbent layers in gas- and liquid-sensing applications. Thus, it is important to understand how polymer-coated TSM resonators respond. 

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