Relaxation filled rubbers

An important feature of filled elastomers is the stress softening whereby an elastomer exhibits lower tensile properties at extensions less than those previously applied. As a result of this effect, a hysteresis loop on the stress-strain curve is observed. This effect is irreversible it is not connected with relaxation processes but the internal structure changes during stress softening. The reinforcement results from the polymer-filler interaction which include both physical and chemical bonds. Thus, deforma-tional properties and strength of filled rubbers are closely connected with the polymer-particle interactions and the ability of these bonds to become reformed under stress. 

Below a characteristic temperature, T0, of about 15° to 16°C, the shift factors appear to follow the WLF equation, Equation 2, with C = 7.1, C2 = 135.9°C, and Tr — 0°C. The coefficients were determined in the usual way (6). The temperature dependence of both the relaxation moduli and the creep compliances could be described with the same WLF equation within the experimental scatter. It appears that below T0 the triblock copolymer behaves essentially as a filled rubber, the polystyrene domains acting only as inert filler. However, the WLF equation which describes the temperature dependence of the mechanical properties in this region is not identical with that of pure 1,4-polybutadiene, for which Maekawa, Mancke, and Ferry (20) find cx — 4.20, c = 161.5°C,... 

Experimental studies of filled rubbers are complicated by several things, such as the effect of the magnetic susceptibility of the filler, the effect of free radicals present at the surface of carbon black, the complex shape of the decay of the transverse magnetisation relaxation of elastomeric materials due to the complex origin of the relaxation function itself [20, 36, 63-66], and the structural heterogeneity of rubbery materials. 

The amount of radicals in carbon black filled rubbers decreases significantly upon extraction of free rubber with the aid of a solvent containing a free radical scavenger. The extraction nevertheless causes a substantial increase in the fraction of the T2 relaxation component with the decay time of about 0.02-0.03 ms [62], This increase is apparently caused by an increase in the total rubber-carbon black interfacial area per volume unit of the rubber due to the removal of free rubber. The T2 relaxation component with a short decay time is also observed in poly(dimethyl siloxane) (PDMS) filled with fumed silicas [88], whose particles contain a minor amount of paramagnetic impurities. Apparently, free radicals hardly influence the interpretation of NMR data obtained for carbon-black rubbers in any drastic way [62, 79]. 

Solid state NMR offers several advantages for the investigation of filled rubbers since molecular properties of elastomer chains can be measured selectively by NMR e>q)eriments. The method is very sensitive to the molecular scale heterogeneity in a sample. The network structure which is composed of chemical, physical and topological junctions can also be andyzed by NMR relaxation experiments [11,12,14,15],... 

Proton spin resonance measurements on carbon black filled rubbers confirm the relatively small effect of the black on local segmental mobility. Waldrop and Kraus (107) were unable to find evidence for two spin-lattice relaxation times (one for surface rubber and one for bulk rubber) and found very little effect of carbon blacks on the position of the minimum in the spin-lattice relaxation time (7j) vs. temperature curve. The shape of the curve was also substantially unaffected (107). Extraction of free rubber from an uncross-linked SBR-HAF black mix did not accentuate the effect of the carbon black. More recently Kaufmann, Slichter and Davis (108) reported the observation of two spin-spin relaxation times (T2) in the bound rubber phases of polybutadiene and ethylene-propylene rubber, each reinforced with 50 phr of an SAF black (155 m2/g surface area). The amount of fully immobilized polymer was only 4% of the total, but the remainder of the bound rubber displayed... 

The effects of HAF black on the stress relaxation of natural rubber vulcanizates was studied by Gent (178). In unfilled networks the relaxation rate was independent of strain up to 200% extension and then increased with the development of strain induced crystallinity. In the filled rubber the relaxation rate was greatly increased, corresponding to rates attained in the gum at much higher extensions. The results can be explained qualitatively in terms of the strain amplification effect In SBR, which does not crystallize under strain and in cis-polybutadiene, vulcanizates of which crystallize only at very high strains, the large increase in relaxation rate due to carbon black is not found (150). 

For small strains the stress-relaxation rate of vulcanized rubbers at long times is proportional to tan 8 (178). This will also be true at large strains if strain-time factorization applies. The implication of this for the results of Cotten and Boonstra (150) is that tan 8 in unswollen vulcanizates is only little affected by carbon black-polymer interactions at strain levels between 75 and 250% elongation (and at very low frequencies) and suggests that the substantial increases in tan 8 observed in filled rubbers at small strains are due primarily to the effects of secondary filler aggregation. 

It is certain that the relaxation behavior of filled rubbers at large strains involves numerous complications beyond the phenomena of linear viscoelasticity in unfilled amorphous polymers. Breakdown of filler structure, strain amplification, failure of the polymer-filler bond, scission of highly extended network chains and changes in network chain configuration probably all play important roles in certain ranges of time, strain rate, and temperature. A clear understanding of the interplay of these effects is not yet at hand. 

Payne [55] investigated the dynamic relaxation of the filled rubber by changing the amplitude and found a peak of the loss occurring at the very small amplitude of about 1 mm. This is called the Payne effect. It is regarded as the energy loss due to the destruction of the chain structure of carbon black by extension. The magnitude of the loss is often used as a measure of the structure, because it is found to run parallel to the reinforcement of rubber. 

The non linear viscoelasticity of various particles filled rubber is addressed in range of studies. It is found that the carbon black filled-elastomer exhibit quasi-static and dynamic response of nonlinearity. Hartmann reported a state of stress which is the superposition of a time independent, long-term, response (hyperelastic) and a time dependent, short-term, response in carbon black filled-rubber when loaded with time-dependent external forces. The short term stresses were larger than the long term hyperelastic ones. The authors had done a comparative study for the non linear viscoelastic models undergoing relaxation, creep and hysteresis tests [20-22]. For reproducible and accurate viscoelastic parameters an experimental procedure is developed using an ad hoc nonlinear optimization algorithm. 

Indeed, carbon black-filled rubber, when loaded with time-dependent external forces, suffers a state of stress which is the superposition of two different aspects a time independent, long-term, behavior (sometimes improperly called hyperelastic ) opposed to a time dependent, short-term, response. Step-strain relaxation tests suggest that short term stresses are larger than the long term or quasi-static ones [117]. Moreover, oscillatoiy (sinusoidal) tests indicate that dissipative anelastic effects are significant, which leads to the consideration of a constitutive relation which depends not only on the current value of the strain but on the entire strain history. This assumption must be in accordance with some principles which restrict the class of rehable constitutive equations. These restrictions can be classified as physical and constitutive . The former are restrictirMis to which every rational physical theory must be subjected to, e.g., frame indifference. The latter, on the other hand, depends upon the material under consideration, e.g., internal symmetries. 

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