TY - JOUR

T1 - Geometric frustration in small colloidal clusters

AU - Malins, Alex

AU - Williams, Stephen R.

AU - Eggers, Jens

AU - Tanaka, Hajime

AU - Royall, C. Patrick

PY - 2009

Y1 - 2009

N2 - We study the structure of clusters in a model colloidal system with competing interactions using Brownian dynamics simulations. A short-ranged attraction drives clustering, while a weak, long-ranged repulsion is used to model electrostatic charging in experimental systems. The former is treated with a short-ranged Morse attractive interaction, the latter with a repulsive Yukawa interaction. We consider the yield of clusters of specific structure as a function of the strength of the interactions, for clusters with m = 3,4,5,6,7,10 and 13 colloids. At sufficient strengths of the attractive interaction (around 10kBT), the average bond lifetime approaches the simulation timescale and the system becomes nonergodic. For small clusters, m≤5, where geometric frustration is not relevant, despite nonergodicity, for sufficient strengths of the attractive interaction the yield of clusters which maximize the number of bonds approaches 100%. However for m = 7 and higher, in the nonergodic regime we find a lower yield of these structures where we argue geometric frustration plays a significant role. m = 6 is a special case, where two structures, of octahedral and C2v symmetry, compete, with the latter being favoured by entropic contributions in the ergodic regime and by kinetic trapping in the nonergodic regime. We believe that our results should be valid as long as the one-component description of the interaction potential is valid. A system with competing electrostatic repulsions and van der Waals attractions may be such an example. However, in some cases, the one-component description of the interaction potential may not be appropriate.

AB - We study the structure of clusters in a model colloidal system with competing interactions using Brownian dynamics simulations. A short-ranged attraction drives clustering, while a weak, long-ranged repulsion is used to model electrostatic charging in experimental systems. The former is treated with a short-ranged Morse attractive interaction, the latter with a repulsive Yukawa interaction. We consider the yield of clusters of specific structure as a function of the strength of the interactions, for clusters with m = 3,4,5,6,7,10 and 13 colloids. At sufficient strengths of the attractive interaction (around 10kBT), the average bond lifetime approaches the simulation timescale and the system becomes nonergodic. For small clusters, m≤5, where geometric frustration is not relevant, despite nonergodicity, for sufficient strengths of the attractive interaction the yield of clusters which maximize the number of bonds approaches 100%. However for m = 7 and higher, in the nonergodic regime we find a lower yield of these structures where we argue geometric frustration plays a significant role. m = 6 is a special case, where two structures, of octahedral and C2v symmetry, compete, with the latter being favoured by entropic contributions in the ergodic regime and by kinetic trapping in the nonergodic regime. We believe that our results should be valid as long as the one-component description of the interaction potential is valid. A system with competing electrostatic repulsions and van der Waals attractions may be such an example. However, in some cases, the one-component description of the interaction potential may not be appropriate.

UR - http://www.scopus.com/inward/record.url?scp=70349320382&partnerID=8YFLogxK

U2 - 10.1088/0953-8984/21/42/425103

DO - 10.1088/0953-8984/21/42/425103

M3 - Article (Academic Journal)

C2 - 21715858

AN - SCOPUS:70349320382

SN - 0953-8984

VL - 21

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

IS - 42

M1 - 425103

ER -