Formation of Ionic crystal

Coulomb and Modified Van der Waals interations

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Coulomb and Van der Waals interations (V_m=0):
U_ij(r)=4 f e²a_ij^-1 [(a_ij/r)¹² - (a_ij/r)⁶] + e²q_iq_j/r
a_ij=r_i+r_j, f=0.004

Modified Coulomb and Van der Waals interations (V_m=1):
U_ij(r)=4 f e²(2a_ij)^-1 {[2a_ij/(r+a_ij)]¹² - V_v[2a_ij/(r+a_ij)]⁶} + e²q_iq_j/(r+a_ij)
a_ij=r_i+r_j, f=0.004

In the simulation, the velocity of a particle is proportional to the force that act on the particle. The particles will settle into a configuration which locally minimize the total energy.

U_ij: The interaction potential between the i-th and j-th particles.
q_i, q_j: The charges of the i-th and j-th particles.
r_i, r_j: The radius of the i-th and j-th particles.
V_m: V_m=0 for standard Coulomb and Van der Waals interaction. V_m=1 for modified Coulomb and Van der Waals interaction.
V_v: V_v=1 for standard Van der Waals interaction. V_v=0 turns off the attractive part of Van der Waals interaction.

Usage

Restart: Restart simulation with a random particle configuration.
+/-N1,+/-N2: Increase/decrease N1 or N2, the number of the red or blue particles.*
+/-q1,+/-q2: Increase/decrease q1 or q2, the charges of the red or blue particles.*
+/-r1,+/-r2: Increase/decrease r1 or r2, the radii of the red or blue particles
+/-T: Increase/decrease temperature
Vv: toggles between Vv=1 and Vv=0
Vm: toggles between Vm=1 and Vm=0.*
In/Out: Zoom in/out
+/-Sp: Increase/decrease simulation speed. The simulation becomes unstable when Sp is too large. In this case, descrease Sp.

* The speed Sp is set to zero after clicking the button. Increase Sp to start the run.

Experiments

Click Restart many times (like ~ 20) to see if a nice crystal or other nice configurations can form.
Change Vm=0 to get the standard Van der Waals interaction. Now click Restart many times to see if a nice crystal or other nice configurations can form.
Change the charges to q1=5 and q2=-5. Now click Restart to see if a nice crystal or other nice configurations can form.
Increase temerature T to 1000, and then decrease T slowly back to 0.
Experiment with different q1/q2, N1/N2, r1/r2. Try to start with a few particles and then add particles one by one.