Abstract
The solid-phase diagram of binary systems consisting of particles of diameter σA = σ and σB = γσ (γ ≤ 1) interacting with an inverse p = 12 power law is investigated as a paradigm of a soft potential. In addition to the diameter ratio γ that characterizes hard-sphere models, the phase diagram is a function of an additional parameter that controls the relative interaction strength between the different particle types. Phase diagrams are determined from extremes of thermodynamic functions by considering 15 candidate lattices. In general, it is shown that the phase diagram of a soft repulsive potential leads to the morphological diversity observed in experiments with binary nanoparticles, thus providing a general framework to understand their phase diagrams. Particular emphasis is given to the two most successful crystallization strategies so far: evaporation of solvent from nanoparticles with grafted hydrocarbon ligands and DNA programmable self-assembly.
Highlights
The solid-phase diagram of binary systems consisting of particles of diameter σA = σ and σB = γσ (γ ≤ 1) interacting with an inverse p = 12 power law is investigated as a paradigm of a soft potential
Over the recent years there has been a spectacular success in the assembly of nanoparticle superlattice (NPS), with the two most successful strategies consisting of evaporation of a solvent from NPs with grafted hydrocarbon chains [1,2,3,4] [solvent evaporation (SE) systems] or the programmable self-assembly of DNA grafted NPs [5,6,7] in water (DNA systems)
It has been observed that different binary systems with the same NP hydrodynamic radius do not exhibit the same equilibrium phase [19], clearly pointing to a phase diagram that depends on other parameters besides the ratio of the two NPs diameters, which completely determines the phase diagram of the HS system [15]
Summary
The solid-phase diagram of binary systems consisting of particles of diameter σA = σ and σB = γσ (γ ≤ 1) interacting with an inverse p = 12 power law is investigated as a paradigm of a soft potential. In addition to the diameter ratio γ that characterizes hard-sphere models, the phase diagram is a function of an additional parameter that controls the relative interaction strength between the different particle types. It has been observed that different binary systems with the same NP hydrodynamic radius (with different hydrocarbon chain length, for example) do not exhibit the same equilibrium phase [19], clearly pointing to a phase diagram that depends on other parameters besides the ratio of the two NPs diameters, which completely determines the phase diagram of the HS system [15]. Motivated by the partial success of HS models, namely the imperfect but clear correlation between experimental equilibrium structures and those with high packing fraction (PF) and the need, for the reasons exposed (see ref. 19), to consider a soft potential, we examine particles of different diameters interacting with an inverse power law (IPL): Vj,h ðrÞ
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