Phase field crystal model for patchy colloids
Final Report Abstract
We developed a two dimensional Phase Field Crystal (PFC) Theory for colloidal particles with a given rotational symmetry that is given by the directions along which the particles attract or repel each other. Our approach describes (ultra-)soft patchy particles. Free minimizations of the free energy functional reveal a rich phase behaviour where various complex phases occur as intermediate phases between nematic or cholesteric order and triangular or isotropic phases. For example, we observed different triangular, square, rhombic, and honeycomb phases. Furthermore, we even found a stable decagonal quasicrystal. Therefore, our PFC approach enables us to efficiently determine the possible orderings that occur for (ultra-)soft patchy particles. In addition, we performed simulations of patchy colloids and studied the stability and growth of twodimensional quasicrystalline structures that can be observed in such systems. We found that small patches with sharp binding angles are needed to observe octagonal or decagonal order while dodecagonal quasicrystals are also found for large patches. This might explain why in soft matter systems usually dodecagonal quasicrystals are observed in experiments and simulations while in metallic systems where binding angles are more important, decagonal order is reported more often. Concerning the growth of quasicrystals we found that the best structures are obtained for a growth at a high temperature just below the melting temperature. A comparison to the growth in systems with particles with isotropic interactions revealed that especially at intermediate temperatures there are less defects in case patchy colloids are considered. Interestingly, a comparison of the results of our PFC approach and our simulations shows that there are some major differences which are related to the fact that in our simulations we considered patchy colloids with a hard core while the PFC model describes (ultra-)soft particles that might overlap significantly. As a consequence, we have also developed a mean field model based on a Fundamental Measure approach for patchy particles with a hard core and want to study this new approach in the close future. We believe that the differences between (ultra-)soft particles and particles with a hard core will lead to a better insight to the different mechanisms for the stabilization and growth of quasicrystals that is based on the incommensurate length scales in case of the (ultra-)soft colloids while in case of a hard core local complex tilings might play an important role.
Publications
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Growth of two-dimensional dodecagonal colloidal quasicrystals: Particles with isotropic pair interactions with two length scales vs. patchy colloids with preferred binding angles. The European Physical Journal E, 41(10).
Gemeinhardt, Anja; Martinsons, Miriam & Schmiedeberg, Michael
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Stabilizing quasicrystals composed of patchy colloids by narrowing the patch width. EPL (Europhysics Letters), 126(3), 38001.
Gemeinhardt, A.; Martinsons, M. & Schmiedeberg, M.
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Active phase field crystal systems with inertial delay and underdamped dynamics. The European Physical Journal E, 43(7).
Arold, Dominic & Schmiedeberg, Michael
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Phasonic Diffusion and Self-confinement of Decagonal Quasicrystals in Hyperspace. Journal of Physics: Conference Series, 1458(1), 012018.
Hielscher, Johannes; Martinsons, Miriam; Schmiedeberg, Michael & Kapfer, Sebastian C.
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Stability of particles in two-dimensional quasicrystals against phasonic perturbations. Journal of Physics: Conference Series, 1458(1), 012019.
Martinsons, M. & Schmiedeberg, M.
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Phase field crystal model for particles with n-fold rotational symmetry in two dimensions. Modelling and Simulation in Materials Science and Engineering, 30(7), 074003.
Weigel, Robert F. B. & Schmiedeberg, Michael
