3.2.2. Payne Effect

Payne [108] reported that the effects of changes due to deformation of the microstructure of the material were due to breakage and reform of weak physical bonds connecting neighboring filler clusters. This analysis has been applied for the elastomeric composites where the filler particles are connected to the elastomer in the microstructural viewpoint. As the strain amplitude increases, the distance between the CI particles increases and the bond between the elastomer and the particle breaks. For this reason, G' decreases as the structure breaks. In other words, if the bond strength of particles and matrix is strong, the change of G' will be small due to the change of strain amplitude. If the bond strength of particles and elastomer is weak, the change of G' will be large due to strain amplitude. In other words, the Payne effect represents the bond strength between the elastomeric medium and the filler particles. Many researchers have evaluated the properties of MREs through the Payne effect of anisotropic and isotropic MREs [109–112]. The Payne effect is measured by the change of G' according to the change of strain amplitude under cyclic loading conditions and calculated using Equation (1),

$$\text{Payne Effect} = \frac{\text{G}\_0'-\text{G}\_\text{\textphi}'}{\text{G}\_0'} \times 100\tag{1}$$

where *G*0 is the G' at an initial strain and *G*∞ is the G' at the infinite strain. Figure 4 is a graph showing the G' of both pure CI based MRE and PGMA coated CI-based MRE as a function of strain [60]. The Payne effect of the CI-based MRE was calculated to be 84%, while that of PGMA coated CI-based MRE was 78%. MRE with PGMA coated CI had a lower Payne effect. This confirms that CI coated with PGMA has a stronger bond strength with the rubber matrix than the CI-based MRE.

**Figure 4.** The storage moduli CI/PGMA and pure CI based magnetorheological (MR) elastomers [60].
