Isolated anisotropic particle

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

Most commercially available anisotropically conductive adhesives are formulated on the bridging concept, as illustrated in Fig. 1. A concentration of conductive particles far below the percolation threshold is dispersed in an adhesive. The composite is applied to the surface either by screen printing a paste or laminating a film. When a device is attached to a PWB, the placement force displaces the adhesive composite such that a layer the thickness of a single particle remains. Individual particles span the gap between device and PWB and form an electrical interconnection. For successful implementation of anisotropically conductive adhesives, the concentration of metal particles must be carefully controlled such that a sufficient number of particles is present to assure reliable electrical conductivity between the PWB and the device (Z direction) while electrical isolation is maintained between adjacent pads (X,Y directions). 

The goal in formulating anisotropically conductive adhesives is to maximize particle concentration without compromising electrical isolation in the X Y plane. Higher particle loadings increase the probability that an electrical interconnection will be made (especially for relatively small contact areas) and decrease contact resistance. Typical concentrations range from 5 to 15 vol % (30 to 60 wt % based on pure silver particles). The size of the particles usually ranges from 10 to 20 pm in diameter. Smaller particles offer the best results for very fine pitch applications. 

In the present paper, we first review briefly the rigid rod models for liquid crystalline phase transitions. In these models, emphasis is placed on the anisotropic form and on the orientation dependent intermolecular interactions between rigid particles. Conformational studies on isolated chains have shown that liquid crystalline polymers are rather semi-rigid in character although only a narrow range of deformations is possible due to intrachain interactions. The effect of chain flexibility on the formation of liquid crystalline phases has been pointed out both experimentally and the-oretically J. 

With the high resolution of the TIRM technique, one should be aware of several physical phenomena that are active on length scales comparable to the penetration depth. When an isolated particle is in the vicinity of a solid boundary, its Brownian motion is hindered due to an increase in hydrodynamic drag. The presence of the solid wall decreases the diffusion coefficient, resulting in hindered, anisotropic Brownian motion [7]. 

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