Ising Model for Conductive Percolation in Electrically Conductive Adhesives by Considering Random Arrangement of Conducting Particles

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doi:10.3844/ajassp.2012.1113.1123

Abstract

Problem statement: Thermodynamically, particles in composites will arrange in a way such that the Helmholtz free energy is minimized. However, even a single structure has the lowest free energy, it should not ignore the probability of other structures having larger energies to occur, although at small chances. Approach: All possible arrangements of particles in the composites, therefore, must be taken into account in the theory or simulation development. Results: The composite energy depends on the interaction between components in the composites. To consider the effect of interactions on energy, in this study we used a simple Ising model incorporated with the Bragg-Williams approximation. We used the model to predict the average packing fraction and the percolation threshold in composites as well as other quantities related to percolation phenomenon. Conclusion/Recommendations: We found several predictions that have not been reported by previous authors. This model can be important in the understanding conductivity development in electrically conductive adhesive composites.

Highlights

One interesting phenomenon exhibited by these composites is the occurrence of percolation threshold, a quantity which divides two strongly different states, such as conductive and insulating states (Mikrajuddin et al, 2000; 1999), magnetic and nonmagnetic states (Thorpe, 1978), crystal and amorphous states, Surprisingly, in recent progress, the percolation phenomena are applied to other fields, in the past of which likely did not show any relation with material composites such as communication systems such as the internet and other Peer-To-Peer networks (PastorSatorras and Vespignani, 2007), dynamics of epidemic spreading (Anderson and May, 1992; Meyers, 2007), HIV infection to AIDS (Kamp and Bornholdt, 2002), social networks (Chen et al, 2007a; 2007b)
Using the modified effective medium approximation, we previously reported that the percolation threshold occurs at vc = f / 2 / γ, with f is the packing fraction (Mikrajuddin et al, 1999) and by adopting a theory for sol-gel development in polymerization for describing
The binding energy between particle and matrix is more positive than the binding energy between particles, so that in order to minimize the composite free energy, the arrangement of particles in the composite must be in such a way that the contact area between particles and matrix is as small as possible and this is found when the arrangement is in small coordination number

Summary

INTRODUCTION

The properties of composites of particles dispersed in continuum media have been reported by many authors several decades, covering numerous composites, such as conductive particles dispersed in insulating adhesives (electrically conductive adhesives) for microelectronic applications (Mikrajuddin et al, 2000; Yim et al, 2008; Lin and Chen, 2008; Li et al, 2008; Lin and Chiu, 2008; Morris and Lee, 2008; Zenner et al, 2008; Novak et al, 2004; Inoue et al, 2008; 2009; Inoue and Suganuma, 2007; 2009; Kim and Paik, 2008; Mundlein et al, 2002; Li et al, 1993; Tongxiang et al, 2008; Lee et al, 2005; Sander et al, 2002; 2003), insulating particles dispersed in Ionic adhesive for use in solid batteries or fuel cells (Mikrajuddin et al, 2000; 1999), colloidal systems (Lu et al, 2006; 2008), pharmaceutical tablets (Stromme et al, 2003) and other composites such as fibers in concrete (Newman, 2002) and fly ash-concrete (Mohan et al, 2012). Some authors treated the particles have been average coordination number is logically accepted arranged in a simple cubic structure and other authors when we consider some previous reports related to assumed the particles have been arranged in a body average bond connection between particles per nodes centered cubic structure, prior to theory or simulation (Dhydkov, 2009; Blumenfeld et al, 2005) and the development. This assumption may raise some concept of non permanent bonds

MATERIALS AND METHODS

RESULTS

CONCLUSION