Effective structure of a system with continuous polydispersity

In a system of N particles, with continuous size polydispersity there exists N(N-1) number of partial structure factors making it analytically less tractable. A common practice is to treat the system as an effective one component system which is known to exhibit an artificial softening of the structure. The aim of this study is to describe the system in terms of M pseudo species such that we can avoid this artificial softening but at the same time have a value of M << N. We use potential energy and pair excess entropy to estimate an optimum number of species, M_{0}. We find that systems with polydispersity width, {\Delta}{\sigma}_{0} can be treated as a monodisperse system. We show that M_{0} depends on the degree and type of polydispersity and also on the nature of the interaction potential, whereas, {\Delta}{\sigma}_{0} weakly depends on the type of the polydispersity, but shows a stronger dependence on the type of interaction potential. Systems with softer interaction potential have a higher tolerance with respect to polydispersity. Interestingly, M_{0} is independent of system size, making this study more relevant for bigger systems. Our study reveals that even 1% polydispersity cannot be treated as an effective monodisperse system. Thus while studying the role of polydispersity by using the structure of an effective one component system care must be taken in decoupling the role of polydispersity from that of the artificial softening of the structure.