A density-functional theory investigation of cluster formation in an effective-potential model of dendrimers

TL;DR

This study uses density-functional theory to explore how particles with soft-core repulsive interactions form various crystal structures, revealing phase transitions and cluster behaviors without assuming specific density profiles.

Contribution

It provides a comprehensive DFT analysis of cluster formation in dendrimer models without predefined density functional forms, capturing multiple phase transitions.

Findings

Identified fluid to bcc, hcp, and fcc phase transitions with increasing density.

Particles form localized clusters with nearly density-independent lattice constants.

Approximate density profiles yield results close to unconstrained DFT minimization.

Abstract

We consider a system of particles interacting via a purely repulsive, soft-core potential recently introduced to model effective pair interactions between dendrimers, which is expected to lead to the formation of crystals with multiple occupancy of the lattice sites. The phase diagram is investigated by density-functional theory (DFT) without making any a priori assumption on the functional form of the density profile or on the type of crystal lattice. As the average density $\rho$ is increased, the system displays first a transition from a fluid to a bcc phase, and subsequently to hcp and fcc phases. In the inhomogeneous region, the behavior is that found in previous investigations of this class of cluster-forming potentials. Specifically, the particles arrange into clusters strongly localized at the lattice sites, and the lattice constant depends very weakly on $\rho$, leading to an occupancy number of the sites which is a nearly linear function of $\rho$. These results are compared to those predicted by the more widespread approach, in which the DFT minimization is carried out by representing the density profile by a given functional form depending on few variational parameters. We find that for the model potential studied here, the latter approach recovers most of the predictions of the unconstrained minimization.