Stress-strain isotherm

Direct measurements of equilibrium stress-strain isotherms of SAH are complicated by the gel softness. Nevertheless, a number of experiments on compression and tension of the gels has been reported (see, for example, Refs. [18, 21, 42]). The method of dynamic light scattering is free from such inconveniences... 

These Monte Carlo distributions can be used in the standard three-chain model for rubber-like elasticity to generate, for example, stress-strain isotherms [5]. Non-Gaussian effects can cause large increases in modulus at high... 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

Figure 9 Illustrative stress-strain isotherms for poly(diethylsiloxane), as a function of the amount of mesophase present. 

The equilibrium stress-strain isotherms in elongation, and the swelling ratios in benzene, were measured at 25°C for these networks. Network chain densities calculated from these measurements exceeded the values predicted from stoichiometry. 

The two network precursors and solvent (if present) were combined with 20 ppm catalyst and reacted under argon at 75°C to produce the desired networks. The sol fractions, ws, and equilibrium swelling ratio In benzene, V2m, of these networks were determined according to established procedures ( 1, 4. Equilibrium tensile stress-strain Isotherms were obtained at 25 C on dumbbell shaped specimens according to procedures described elsewhere (1, 4). The data were well correlated by linear regression to the empirical Mooney-Rivlin (6 ) relationship. The tensile behavior of the networks formed In solution was measured both on networks with the solvent present and on networks from which the oligomeric PEMS had been extracted. 

Temperature. The effect of temperature on the stress-strain isotherms is of particular importance with regard to the... 

Figure 2. Typical stress-strain isotherms for PDMS networks prepared by tetra-functionally end-linking very short and relatively long chains.

Figure 5. Stress-strain isotherms obtained for bimodal (600-11,300), PDMS networks containing 75.2 mol % short chains (20).

Also relevant here are some force-temperature ("thermoelastic") results obtained at elongations sufficiently large to give large increases in [f ] in the stress-strain isotherm (16). 

Hydroxyl-terminated POET chains are end-linked into noncrystallizable trifunctional networks using an aromatic triisocyanate. The networks thus obtained are studied with regard to their stress-strain isotherms. The analysis of the temperature coefficient of PDET in terms of the RIS model confirms the results obtained from NMR studies, according to which the gauche states... 

Mark,J.E., Flory.P.J. Stress-strain isotherms for poly-(dimethylsiloxane) networks. J. Appl. Phys. 37,4635-4639 (1966). 

For this reason, stress-strain isotherms are frequently represented by the semi-empirical Mooney-Rivlin relationship81,85... 

Figure 8.3 Stress-strain isotherms for PDMS-silica in situ reinforced elastomers in elongation (region to the left of the vertical dashed line, with or1 < 1), and in biaxial extension (compression) (to the right, with or1 > l).38 The filled symbols represent the data obtained out of sequence to test for reversibility. 

Figure 8.4 Stress-strain isotherms for PDMS networks reinforced with in situ generated titania particles.39 Each curve is labeled with the wt % of filler introduced, and filled circles locate results used to test for reversibility.

Figure 8.8 Stress-strain isotherms for PDMS-polystyrene (PS) composites.50 Each curve is labeled with the wt % PS present in the composite, and the dashed fines locate the relatively linear portions of the curves useful for quantitative interpretations.129...

Figure 8.9 Stress-strain isotherms of the PDMS-PS composites described in the preceding figure.59 Values of the draw ratio and testing directions are indicated on each curve. The symbols with small tabs attached represent data used to test for reversibility.

Figure 8.10 Stress-strain isotherms for PDMS composites containing magnetically responsive particles.73 Each curve is identified by the wt % filler present, the strength of the magnetic field (in Gauss) applied during cross-linking, and the orientation (parallel or perpendicular) of the sample strip relative to the lines of force of the magnetic field.

Figyre 3.16 Mooney-Rivlin plots [Eq. (3.38)] showing the effect of the temperature on stress-strain isotherms for model PDMS networks (15,16). The filled circles represent the reversibility of the elastic measurements, and the vertical lines locate the fracture points. (From Ref. 15.)... 

Figure 3. Some typical stress-strain isotherms...

Uniaxial stress-strain measurements are often used to characterize polymer networks both in the dry state and in equilibrium with a diluent. The analysis of the stress-strain isotherms is usually performed in terms of the reduced force... 

In general, experimental stress-strain isotherms differ from the predictions of the simple statistical theories. 

---