[Zurück]

S. Wagner, E. G. Noya, Y. Kalyuzhnyi, G. Kahl:
"Crystallization and melting of two-dimensional patchy particles - theory vs simulation";
Poster: 11th Liquid Matter Conference 2021, Prague; 19.07.2021.

In the following work we consider a system of patchy particles on a two dimensional plane. The
particles are impenetrable disks and have a single patch with a patch-patch interaction of a Kern-
Frenkel type potential [1]. The opening angle θ and the interaction range δ enter the model as
parameters. In the solid phase particles arrange on a hexagonal lattice and can form bonding pat-
terns throughout the lattice. Within the model dimer- and trimer-structures, straight and zig-zag
lines may be formed. The type of bonding pattern depends on the number of possible bonds per
particle. As an example of possible bonding patterns and snapshots of the system see Fig. 1a and
Fig. 1b.
The phase transitions and phase diagrams of these patchy particles in two dimensions were
studied by Shin and Schweizer within a theoretical framework [2]. Their methods comprise a
self-consistent phonon theory (SCP) from which conclusions for the phase behaviour of patchy
particles with variable patch size in the solid regime were drawn. Solid phases include all before-
mentioned orientational structures as well as a plastic crystal phase.
In an attempt to verify the conclusions from this work, an extensive Monte-Carlo simula-
tion study was carried out as well as a different theoretical approach by using multidensity re-
summed thermodynamic perturbation theory for fluids with central-force type of associative po-
tential (RTPT-CF) [3,4]. Predictions made by Shin and Schweizer include solid phases only;
using simulations includes also the lower denisity regime; the theoretical approach (RTPT-CF)
used here aims at solid and fluid phases as well. In Fig. 2 a comparison of the RTPT-CF and
Monte-Carlo simulation method can be seen. Simulation methods used to predict the phase tran-
sitions between liquid and solid structures are the Replica Exchange method and for the gas-liquid
phase coexistence the Gibbs-Ensemble method. Free energies are calculated using the Einstein-
Molecule method [5].
The free accessible volume will greatly be affected by the type of bonds the particles form
and also their lattice arrangements. In contrast to the preceding theoretical study of this system
[2] results of the simulation study also allow a prediction of the spatial distribution of phases in
coexistence.
References
[1] N. Kern and D. Frenkel, J. Chem. Phys., 118, 9882 (2003)
[2] H. Shin and K.S. Schweizer, Soft Matter, 10, 262 (2014)
[3] Y. V. Kalyuzhnyi, G. Stell, Mol. Phys. 78, 1247 (1993)
[4] Y. V. Kalyuzhnyi, H. Docherty, P. T. Cummings, J. Chem. Phys. 135, 014501 (2011)
[5] C. Vega, E.G. Noya, J. Chem. Phys. 127, 154113 (2007)
[6] S. Whitelam and P.L. Geissler, J. Chem. Phys., 127, 154101 (2007)
[7] K.W. Wojciechiowski, A.C. Branka and D. Frenkel, Physica A, 196, 519-545 (1993)

patchy particles, dimers, trimers

https://publik.tuwien.ac.at/files/publik_302038.pdf