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Percolation and high density percolation in binary mixtures of patchy particles

By: José Maria Tavares
From: Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa; e Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa, Portugal
At: Building C3, room 3.2.16
[2023-10-31] 11:00

Mean field percolation theory can be extended to the case of binary
mixtures where bonds are formed between particles of two species. This
extension will be illustrated using a particular model of patchy
particles: one of the species (the particles) has fC patches of type C
and the other species (the linkers) has two patches of type A and fB
patches of type B. The case in which linkers can self-assemble into
linear chains (forming AA bonds) while still promoting the aggregation
of particles is considered. Percolation thermodynamic diagrams (i.e. the
conditions under which equilibrium gelation takes place) are obtained by
combining the generalized mean field percolation theory with Wertheim’s
theory for thermodynamics. Percolation theory predicts a rich and
unexpected behaviour: the self-assembly of linkers into chains reduces
the fraction of particles needed for percolation to occur and may induce
percolation when the fraction of particles is high; percolation by
heating and percolation loops in temperature–composition diagrams are
obtained when the formation of chains is energetically favourable, by
increasing the entropic gain of branching.

High density percolation (or m- percolation) is a generalization of
usual percolation. It occurs when a non-zero fraction of particles with
valence f (or f patches) forms an infinite cluster that only contains
particles bonded to m or more particles. This concept is extended to the
case of binary mixtures. The derivation of the mean field expressions
for the m-percolation probability threshold and for the fraction of
particles in an infinite m-cluster is presented.