Dynamic mechanical modulus

Figure 1. Typical Dynamic Mechanical Modulus and Loss Tangent a Function of Temperature.

Figure 1. Typical dynamic mechanical modulus and loss tangent data as a junction of temperature. Key a, glassy region b, transition region and c, rubbery...

In order to investigate the viscoelastic behavior of crosslinked EVA, rheological measurements were made to determine at what temperatures the phase transitions occur and their effect on the dynamic mechanical modulus. The complex dynamic modulus E expression is given by Eq. (6). 

Here ait) is the stress at time t and s is the strain E is the complex dynamic mechanical modulus, E is the ratio of in-phase stress to the applied strain, and E" is the ratio of out-of-phase stress to strain. The out-of-phase stress leads the strain by 90°. Further, it can be shown thatE is related to the mechanical energy stored per cycle and E" is related to the energy converted to heat throngh viscous dissipation. As a result, E is referred to as the storage modulus and E" is called the loss modulus. The material loss factor or loss tangent is... 

On the basis of the complex representation for the dynamic mechanical modulus, the relationships between stress and strain can be considered on a complex plane in terms of vectors (74), as shown in Figure 32c. The applied strain of magnitude o is out of phase with the resulting stress of magnitude ctq by an amoimt represented by angle 5. The stress components of a are resolved as a, in-phase, and a", 90° out-of-phase with e = o-... 

Dynamic mechanical measurements were made on PTEE samples saturated with various halocarbons (88). The peaks in loss modulus associated with the amorphous relaxation near —90°C and the crystalline relaxation near room temperature were not affected by these additives. An additional loss peak appeared near —30° C, and the modulus was reduced at all higher temperatures. The amorphous relaxation that appears as a peak in the loss compliance at 134°C is shifted to 45—70°C in the swollen samples. 

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). 

Transparent, homogeneous hybrids using a 50 50 PVAc-to-TEOS mixture and an acid-catalyzed reaction have been produced and characterized by dsc and dms (46). Dsc indicated only a slight increase in the T of the hybrid with incorporation of sihca. Dynamic mechanical tan 8 responses indicate a strong interaction between the organic and inorganic phases and, hence, weU-dispersed phases that lead to high modulus mbbery plateaus. 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

The dynamic mechanical properties of VDC—VC copolymers have been studied in detail. The incorporation of VC units in the polymer results in a drop in dynamic modulus because of the reduction in crystallinity. However, the glass-transition temperature is raised therefore, the softening effect observed at room temperature is accompanied by increased brittleness at lower temperatures. These copolymers are normally plasticized in order to avoid this. Small amounts of plasticizer (2—10 wt %) depress T significantly without loss of strength at room temperature. At higher levels of VC, the T of the copolymer is above room temperature and the modulus rises again. A minimum in modulus or maximum in softness is usually observed in copolymers in which T is above room temperature. A thermomechanical analysis of VDC—AN (acrylonitrile) and VDC—MMA (methyl methacrylate) copolymer systems shows a minimum in softening point at 79.4 and 68.1 mol % VDC, respectively (86). 

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). 

The excellent low temperature properties of FZ have been iadicated ia Table 1. Modulus curves were obtained usiag dynamic mechanical spectroscopy to compare several elastomer types at a constant 75 durometer hardness. These curves iadicate the low temperature flexibiUty of FZ is similar to fluorosihcone and ia great contrast to that of a fluorocarbon elastomer (vinyUdene fluoride copolymer) (Fig. 3) (15). 

Tackifying resins enhance the adhesion of non-polar elastomers by improving wettability, increasing polarity and altering the viscoelastic properties. Dahlquist [31 ] established the first evidence of the modification of the viscoelastic properties of an elastomer by adding resins, and demonstrated that the performance of pressure-sensitive adhesives was related to the creep compliance. Later, Aubrey and Sherriff [32] demonstrated that a relationship between peel strength and viscoelasticity in natural rubber-low molecular resins blends existed. Class and Chu [33] used the dynamic mechanical measurements to demonstrate that compatible resins with an elastomer produced a decrease in the elastic modulus at room temperature and an increase in the tan <5 peak (which indicated the glass transition temperature of the resin-elastomer blend). Resins which are incompatible with an elastomer caused an increase in the elastic modulus at room temperature and showed two distinct maxima in the tan <5 curve. 

In conclusion, the different thermal histories imposed to PTEB have a minor effect on the /3 and y relaxations, while the a. transition is greatly dependent on the annealing of the samples, being considerably more intense and narrower for the specimen freshly quenched from the melt, which exhibits only a liquid crystalline order. The increase of the storage modulus produced by the aging process confirms the dynamic mechanical results obtained for PDEB [24], a polyester of the same series, as well as the micro-hardness increase [22] (a direct consequence of the modulus rise) with the aging time. 

Figure 6 Typical plots from dynamic mechanical thermal analysis showing storage modulus and tan6 variation with temperature [27]. SO (---), S2 (--).

Dynamic mechanical tests measure the response or deformation of a material to periodic or varying forces. Generally an applied force and its resulting deformation both vary sinusoidally with time. From such tests it is possible to obtain simultaneously an elastic modulus and mechanical damping, the latter of which gives the amount of energy dissipated as heat during the deformation of the material. 

Torsion property As noted, the shear modulus is usually obtained by using pendulum and oscillatory rheometer techniques. The torsional pendulum (ASTM D 2236 Dynamic Mechanical Properties of Plastics by Means of a Torsional Pendulum Test Procedure) is a popular test, since it is applicable to virtually all plastics and uses a simple specimen readily fabricated by all commercial processes or easily cut from fabricated products. 

A technique for performing dynamic mechanical measurements in which the sample is oscillated mechanically at a fixed frequency. Storage modulus and damping are calculated from the applied strain and the resultant stress and shift in phase angle. 

Adsorption of rubber over the nanosilica particles alters the viscoelastic responses. Analysis of dynamic mechanical properties therefore provides a direct clue of the mbber-silica interaction. Figure 3.22 shows the variation in storage modulus (log scale) and tan 8 against temperature for ACM-silica, ENR-silica, and in situ acrylic copolymer and terpolymer-silica hybrid nanocomposites. 

Dynamic mechanical properties of the nanocomposites are shown in Figure 4.6. There is 10% improvement of the storage modulus at 20°C by incorporating only 4 wt% of the nanombe. 

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