Anisotropic magnetoresistivity in structured elastomer composites: modelling and experiments

Abstract

A constitutive model for the anisotropic magnetoresistivity in structured elastomer composites (SECs) is proposed. The SECs considered here are oriented pseudo-chains of conductive-magnetic inorganic materials inside an elastomer organic matrix. The pseudo-chains are formed by fillers which are simultaneously conductive and magnetic dispersed in the polymer before curing or solvent evaporation. The SEC is then prepared in the presence of a uniform magnetic field, referred to as <strong>H</strong><small>_curing</small>. This procedure generates the pseudo-chains, which are preferentially aligned in the direction of <strong>H</strong><small>_curing</small>. Electrical conduction is present in that direction only. The constitutive model for the magnetoresistance considers the magnetic pressure, <em>P</em><small>_mag</small>, induced on the pseudo-chains by an external magnetic field, <em>H</em>, applied in the direction of the pseudo-chains. The relative changes in conductivity as a function of <em>H</em> are calculated by evaluating the relative increase of the electron tunnelling probability with <em>P</em><small>_mag</small>, a magneto-elastic coupling which produces an increase of conductivity with magnetization. The model is used to adjust experimental results of magnetoresistance in a specific SEC where the polymer is polydimethylsiloxane, PDMS, and fillers are microparticles of magnetite?silver (referred to as Fe<small>₃</small>O<small>₄</small>[Ag]). Simulations of the expected response for other materials in both superparamagnetic and blocked magnetic states are presented, showing the influence of the Young´s modulus of the matrix and filler´s saturation magnetization.