softmatter:Yukawa Potential

The hard=core formulation of the Yukawa Potential for several combinations of ε and κ.

The Yukawa pair potential is used to model the interaction between charge stabilized colloids. It is a purely repulsive potential when considered two particles with like charge; oppositely charged particles will exhibit an attraction.

The typical formulation of the Yukawa potential is as follows [1]:

$U_{Yukawa} (r; \kappa)=\epsilon\frac{exp[-\kappa(r/\sigma)]}{r/\sigma}$

Often in Monte Carlo Simulation (MC) studies, the hard-core formulation of the Yukawa potential is used [1]:

$U_{Yukawa}(r; \kappa)= \begin{cases} \infty &r<\sigma\\ \epsilon\frac{exp[-\kappa \sigma (r/\sigma-1)]}{r/\sigma} & r \geq \sigma \end{cases}$

Where in both cases σ, κ, and ε are the particle diameter, inverse screening length (inverse Debye length), and surface potential respectively[1].

This potential is shown to the right for various combinations of κ and ε. It is important to note that ε adjusts the height at the surface. A large value for κ results to a short-range potential, where as a small value results in a long-range potential.

The phase behavior has been investigated in two [2] and three dimensions [1,3,4] using Monte Carlo Simulation (MC).

References

• [1] El Azhar F, Baus M, Ryckaert JP, et al. Line of triple points for the hard-core Yukawa model: A computer simulation study, JOURNAL OF CHEMICAL PHYSICS 112 (11): 5121-5126 MAR 15 (2000)
• [2] LOWEN H. STRUCTURE AND BROWNIAN DYNAMICS OF THE 2-DIMENSIONAL YUKAWA FLUID, JOURNAL OF PHYSICS-CONDENSED MATTER 4 (50): 10105-10116 DEC 14 1992
• [3] Auer S, Frenkel D. Crystallization of weakly charged colloidal spheres: a numerical study, JOURNAL OF PHYSICS-CONDENSED MATTER 14 (33): 7667-7680 AUG 26 2002
• [4] HAGEN MHJ, FRENKEL D. DETERMINATION OF PHASE-DIAGRAMS FOR THE HARD-CORE ATTRACTIVE YUKAWA SYSTEM , JOURNAL OF CHEMICAL PHYSICS 101 (5): 4093-4097 SEP 1 1994