Relaxation carbon-black-filled rubbers

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]. 

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 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. 

Several NMR relaxation studies using carbon-black-filled natural rubber (NR), EPDM and butadiene (BR) rubbers have shown that a layer of immobilised, tightly bound rubber is formed on the carbon black surface [20, 62, 79, 87, 89] (Figure 10.9). 

H NMR transverse magnetisation relaxation experiments have been used to characterise the interactions between NR, isoprene rubber, BR, EPDM and polyethylacrylate rubbers with hydrophilic silica and silicas modified with coupling agents [124-129]. These studies showed that the physical interactions and the structures of the physical networks in rubbers filled with carbon black and rubbers filled with silicas are very similar. In both cases the principal mechanism behind the formation of the bound rubber is physical adsorption of rubber molecules onto the filler surface. 

Elastomer-filler interactions were the subject of many intensive investigations. Kaufmann and co-workers [17] investigated carbon-black-filled EPDM by nuclear spin relaxation time measurements and found three distinct regions in the material. These regions are characterised by different mobility of the elastomer chains a mobile region in which the polymer chains have no interaction with the filler particles, loosely bound rubber in an outer shell around the carbon black particles and an inner shell of tightly bound elastomer chain with limited mobility. 

The characterization of the elastomer-filler interactions at a molecular level may be cairied out by spectroscopic techniques such as IR and NMR spectroscopy. X-ray and neutron scattering, dynamic mechanical and dielectric spectroscopy, and molecular dynamics simulations [6]. Up to now, the most comprehensive studies of silica filled PDMS [4, 7-22] and carbon black filled conventional rubbers [23] have been carried out by H [4, 7—20, 23], [21], and C NMR relaxation experiments [22],... 

Of particular importance for detection of chemical or physical change in polymer materials are mobility filters, which are sensitive to differences in the numbers of molecules within a given window of correlation times. Within reasonable approximation such filters are relaxation filters. Here, Tj filters are sensitive to differences in the fast motion regime while T2 and Tip filters are sensitive to the slow motion regime. Which time window is of importance can be seen from Fig. 5.7 [101]. It shows a double-logarithmic plot of the mechanical relaxation strengths Hi(t) for two carbon-black filled styrene-butadiene rubber (SBR) samples as a function of the mechanical relaxation time T. They have been measured by dynamic mechanical relaxation spectroscopy. In terms of NMR, the curves correspond to spectral densities of motion. But the spectral densities relevant to NMR are mainly those referring... 

Fig. 18. Anomalous stress relaxation of carbon black-filled SBR following rapid extension. By comparison note the normal relaxation behavior of the unfilled rubber. After Kraus, Childers and Rollmann (16)...

The identification of material heterogeneities based on differences in molecular motion is an important feature of NMR imaging. The importance of slow molecular motion for image contrast is demonstrated in Figure 31 with relaxation time parameter images through a partially aged sheet of carbon-black-filled styrene-co-butadiene rubber (SBR) (147). 

In the original paper [47], the authors reported work on the uniaxial tension of plasticised poly(vinyl chloride), sulfur vulcanisates of butyl rubber, and polyisobutylene. Very successful predictions were made at extension ratios up to approximately five. Zapas and Craft [48] applied their formulation to multi-step stress relaxation and creep and recovery of both plasticised poly(vinyl chloride) and polyisobutylene. McKenna and Zapas applied a modified form of the model to the torsional deformation of PMMA [49]. McKenna and Zapas [50] have used the model in the analysis of the tensile behaviour of carbon-black-filled butyl rubbers. 

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 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 has now been shown that recent studies of relaxation, sorptive, and diffusive behavior in many filled polymer systems amply confirm earlier observations of deviations from values predicted by simple additivity (Kumins, 1965). Such effects are not confined to high-surface-area fillers such as certain carbon blacks and fillers (typical reinforcing fillers for rubber) they are also observed frequently with low-surface-area fillers, such as pigments and even glass beads with average diameters in the range of tens of micrometers. 

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