Multiple fine particle model

Kinetics models of gas-solid non-catalytic reaction include uniform conversion model (UCN), multiple fine particle model (GPM), crack core model (CCM), phase-change model (PCM), change void model (CVM), thermal decomposition model (TDM), shrinking core model with multi-step reactions, and multi-step reaction model of formation porous structure in reaction etc. Among these models, the shrinking core model (SCM) is the most important and most widely used. For conversion of solid it is also the most simple and practical model. Commonly it is suitable for experimental data. However, it can only be used in some reactions of many solid reactions. A more complex model must be used in other cases. 

Higher-order multipole moments enhance the forces between particles at short distances and their neglect is extremely questionable, especially if fine effects are looked at, as for instance the ground-state properties of close-packed lattice structures [244,246-251] or the viscosity To go beyond the point dipole approximation Klingenberg and co-workers [ 173,252] developed an empirical force expression for the interaction between two dielectric spheres in a uniform external field from the munerical solution of Laplace s equation [253]. Recently, Yu and co-workers [254,255] proposed a computationally efficient (approximate) dipole-induced-dipole model based on a multiple image method which accounts partially for multipolar interactions. 

---