Cluster Simulation Algorithm for Complex Fluids
A very high efficiency Monte Carlo method known as the geometric cluster algorithm has been developed to simulate the behavior of colloids. Typically, suspensions of colloids contain particles of widely different sizes, which move at vastly different time scales. Geometric cluster simulation is the first to account accurately for structures with a range of particle sizes, allowing large particles to move appropriately without having to simulate all of the particle-by-particle random attempts that fail to move the large object.
The primary difficulty in previous methods arises from the fact that displacement of a large particle forces displacement of nearby small particles. Thus, large particles become effectively immobile, as their movement is a collective process involving both their movement and that of many surrounding particles. Conventional approaches can not deal effectively with collective motions on a rational computational time scale. In the new method, collective movements are realized via reflection of particles or clusters of particles around a randomly-chosen point in the liquid. (In other words, the particles are moved a fixed distance and direction toward the random point and then the same distance and direction beyond it.) When the shift of more than one particle lowers the energy of the system while the shift of a single particle does not, multiple particles move by the reflection motion.
It has been demonstrated mathematically that thermodynamic and structural properties computed by means of the geometric cluster algorithm are identical to results obtained from conventional, more computationally-intensive approaches. Because the details of how large clusters of particles move is ignored, the calculation is accelerated enormously. The result is an efficient algorithm that has been shown to properly simulate colloidal behavior for the first time.
Material suspensions known as colloids are ubiquitous in the world around us — drilling muds, abrasives used in microfabrication, heat management fluids, and cells in suspension with serum proteins provide interesting examples that illustrate their diverse nature. Such liquids have numerous applications, optimization of which depends on a fundamental understanding of the physics of the processes. Bridging the entangled time scales needed to simulate their dynamical behavior has been a daunting challenge that has made predictive simulations impossible. The current work provides a completely general tool for simulations of complex materials. Applications are as broad as the range of colloids in our environment. Thus, this model will, for the first time, allow true design of new colloidal materials rather than a hit-or-miss approach to their creation. A concrete application of the geometric cluster algorithm is the simulation of the nanoparticle haloing technique for the stabilization of colloidal suspensions, discovered by J. Lewis and co-workers at the FSMRL. It is anticipated that the simulations will clarify the underlying physical mechanism of this phenomenon.
Senior FSMRL PI: E. Luijten
This work was featured on the cover of the March 2004 issue of Physics Today.