1. Introduction Despite the technological significance of the Payne effect in rubber applications [1], this strain-induced softening phenomenon is often regarded as a spe- cial area of physics specific to filled elastomers [2]. Practically, the effect is measured as decreasing storage modulus with increasing strain amplitude at fixed temperature and fixed frequency during dynamic-mechanical testing of filled rubbers. Par- allel, the corresponding loss modulus runs through a maximum value with increasing strain amplitude. Basic characteristics of the relationships between dynamic modulus and strain amplitude are similar for all kinds of investigated rubbers filled with con- ventional fillers like carbon black and silica (see, for example, reference [2]), or even for non-conven- tional rubber nanocomposites which were prepared, for example, via clay–NR latex dispersion and sub- sequent vulcanization [3, 4]. It is essential to note that dynamic strain-induced decrease of the stiffness of filled rubbers shows a striking similarity to what is known phenomenolog- ically about the glass transition of solid materials and the jamming transition of granular materials [5, 6]. This analogy stems from the reality that shear strain in dynamic mechanical measurements intro- duces fluctuations in a filler network by forcing the system to explore different configurations. Such fluctuations can be described by an ‘effective tem- perature’ that has many attributes of a true tempera- ture, and particularly is proportional to the strain amplitude [7, 8]. Thus, filled rubbers with respect to strain will display many unusual phenomena that are usually observed in glass-forming materials, but now demonstrated in filled rubbers, including asym- metric kinetics, crossover effects, and glasslike kinetic transitions [2, 5–7]. Indeed, the increase of the particle concentration may lead to jamming and 291 A statistical mechanical approach to the Payne effect in filled rubbers G. Heinrich 1* , T. A. Vilgis 2 1 Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Str. 6, 01069 Dresden, Germany 2 Max-Planck-Institut für Polymerforschung Mainz, Postfach 3148, 55021 Mainz, Germany Received 1 October 2014; accepted in revised form 30 November 2014 Abstract. In this paper we apply and discuss some new aspects to the steric interaction of filler particles in reinforced elas- tomers under dynamic mechanical loading conditions. At certain concentration the filler particles (for example, carbon black, or silica) form loose clusters which themselves interact with each other and form a filler network with a significant contri- bution to the dynamic modulus of the rubber material. The filler concentration is relatively high, so that it is likely that the clusters undergo a ‘jamming transition’. With increasing strain amplitude under periodic mechanical deformation the disrup- tion of the filler network resp. of finite filler cluster configurations leads to dejamming observed as softening of the rubber. As a theoretical approach we map the problem on a simple one dimensional Ising model. We present here a static model of this jamming (dejamming) and discuss the consequences on the mechanical and deformation properties of the filled rubber. Keywords: rubber, mechanical properties, Payne effect, statistical mechanics eXPRESS Polymer Letters Vol.9, No.3 (2015) 291–299 Available online at www.expresspolymlett.com DOI: 10.3144/expresspolymlett.2015.26 * Corresponding author, e-mail: gheinrich@ipfdd.de © BME-PT