Payne effect amplitudes

Filler-filler interaction (Payne effect) - The introduction of reinforcing fillers into rubbery matrices strongly modifies the viscoelastic behavior of the materials. In dynamic mechanical measurements, with increasing strain amplitude, reinforced samples display a decrease of the storage shear modulus G. This phenomenon is commonly known as the Payne effect and is due to progressive destruction of the filler-filler interaction [46, 47]. The AG values calculated from the difference in the G values measured at 0.56% strain and at 100% strain in the unvulcanized state are used to quantify the Payne effect. 

The temperature dependence of the Payne effect has been studied by Payne and other authors [28, 32, 47]. With increasing temperature an Arrhe-nius-like drop of the moduli is found if the deformation amplitude is kept constant. Beside this effect, the impact of filler surface characteristics in the non-linear dynamic properties of filler reinforced rubbers has been discussed in a review of Wang [47], where basic theoretical interpretations and modeling is presented. The Payne effect has also been investigated in composites containing polymeric model fillers, like microgels of different particle size and surface chemistry, which could provide some more insight into the fundamental mechanisms of rubber reinforcement by colloidal fillers [48, 49]. 

The pronounced amplitude dependence of the complex modulus, referred to as the Payne effect, has also been observed in low viscosity media, e.g., composites of carbon black with decane and liquid paraffin [50], carbon black suspensions in ethylene vinylacetate copolymers [51], and clay/water suspensions [52, 53]. It was found that the storage modulus decreases with... 

The effect of amplitude-dependence of the dynamic viscoelastic properties of carbon black filled rubbers has been known for some 50 years, but was brought into clear focus by the work of Payne in the 1960s [1-7]. Therefore, this effect is often referred as the Payne-effect. It has been also investigated intensively by... 

Even dynamic measurements have been made on mixtures of carbon black with decane and liquid paraffin [22], carbon black suspensions in ethylene vinylacetate copolymers [23], or on clay/water systems [24,25]. The corresponding results show that the storage modulus decreases with dynamic amplitude in a manner similar to that of conventional rubber (e.g., NR/carbon blacks). This demonstrates the existence and properties of physical carbon black structures in the absence of rubber. Further, these results indicate that structure effects of the filler determine the Payne-effect primarily. The elastomer seems to act merely as a dispersing medium that influences the magnitude of agglomeration and distribution of filler, but does not have visible influence on the overall characteristics of three-dimensional filler networks or filler clusters, respectively. The elastomer matrix allows the filler structure to reform after breakdown with increasing strain amplitude. 

The discussion in the Introduction led to the convincing assumption that the strain-dependent behavior of filled rubbers is due to the break-down of filler networks within the rubber matrix. This conviction will be enhanced in the following sections. However, in contrast to this mechanism, sometimes alternative models have been proposed. Gui et al. theorized that the strain amplitude effect was due to deformation, flow and alignment of the rubber molecules attached to the filler particle [41 ]. Another concept has been developed by Smith [42]. He has indicated that a shell of hard rubber (bound rubber) of definite thickness surrounds the filler and the non-linearity in dynamic mechanical behavior is related to the desorption and reabsorption of the hard absorbed shell around the carbon black. In a similar way, recently Maier and Goritz suggested a Langmuir-type polymer chain adsorption on the filler surface to explain the Payne-effect [43]. 

The modulus at minimum and low strain amplitudes is due to the so-called filler network and it is accepted that the filler surface area, as well as the surface activity, play a major role in establishing a filler network, determining the effective contact area between filler particles and between filler particles and the elastomer matrix. The stress assisted disruption of the filler network causes the reduction of the modulus as the strain amplitude increases, giving rise to the non-linearity of the dynamic-mechanical behaviour of the rubber composite. This phenomenon is known as the Payne effect and it is (to a certain extent) reversible. The disruption and re-formation of the filler network is... 

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. 

However, according to the pseudo-cross-link model, the Payne effect can be ascribed to the interaction between the surface of carbon black and the chemical group at the polymer terminal, which is also adsorbed on the black surface but more strongly than the pseudolink in a chain. This causes a larger loss when the terminal begins to slip. The relaxation time or relaxation distance are almost the same as that of the B-chain. This assumption is compatible with the constant critical amplitude, the parallels between the dynamic loss, the reinforcing ability of carbon black, and the independence of the amplitude on the molecular weight of matrix rubbers. The relaxation time T and the distance d are to be expressed respectively as... 

The dynamic properties of filled rubbers are widely studied by many researchers in this field of which the contribution made by Payne is the most significant. The dependence of strain amplitude on the storage modulus in filled mbbers is known as the Payne effect [27]. At a strain more than 0.1 %, the storage modulus of filled rubber collapses from a plateau value of G O to a minimum value Goo and this decrease is accompanied by a maximum of the loss modulus, G". The variation in this storage modulus value with respect to the minimum value is called amplitude of the Payne effect, and this increases with the filler content, specific surface and properties of the filler and its dispersion within the matrix. The amplitude inversely changes with temperature. A lot of investigations were performed in order to explain the Payne effect and reasons behind it. Payne neglected the contribution... 

The authors also describe the effect of temperature on the Payne effect. With increasing temperature the amplitude of the Payne effect decreases significantly (Fig. 12). Very surprisingly, enhanced Payne-like behavior was observed for rubber vulcanizates at room temperature where filler-filler and filler-polymer interaction are not observed in comparison to the typically filled vulcanizates. The authors concluded that in addition to the contribution from the filler-filler network, there are many other factors that affect the nonlinear viscoelastic behavior. Nevertheless, the Payne effect is assumed to arise from the elementary mechanism consisting of adsorption-desorption of polymer chains from the surface of the particles [50]. Besides the experimental investigation, the authors have applied the Maier... 

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