A reactive force field simulation of liquid–liquid phase transitions in phosphorus

Abstract

A force field model of phosphorus has been developed based on density functional ͑DF͒ computations and experimental results, covering low energy forms of local tetrahedral symmetry and more compact ͑simple cubic͒ structures that arise with increasing pressure. Rules tailored to DF data for the addition, deletion, and exchange of covalent bonds allow the system to adapt the bonding configuration to the thermodynamic state. Monte Carlo simulations in the N-P-T ensemble show that the molecular (P 4 ) liquid phase, stable at low pressure P and relatively low temperature T, transforms to a polymeric ͑gel͒ state on increasing either P or T. These phase changes are observed in recent experiments at similar thermodynamic conditions, as shown by the close agreement of computed and measured structure factors in the molecular and polymer phases. The polymeric phase obtained by increasing pressure has a dominant simple cubic character, while the polymer obtained by raising T at moderate pressure is tetrahedral. Comparison with DF results suggests that the latter is a semiconductor, while the cubic form is metallic. The simulations show that the T-induced polymerization is due to the entropy of the configuration of covalent bonds, as in the polymerization transition in sulfur. The transition observed with increasing P is the continuation at high T of the black P to arsenic ͑A17͒ structure observed in the solid state, and also corresponds to a semiconductor to metal transition.

Quantitative analysis of bonding in P4 clusters

“…In this case, the formation of the red phosphorus polymers of both linear and three-dimensional structure is possible. Experimental data [9] and Monte Carlo simulations [10] have shown that the P 4 liquid phase, while being stable at low pressure, P, and relatively low temperature, T, transforms to a polymeric state by increasing either P or T. These phase changes were observed in recent experiments with similar thermodynamic conditions, as shown by a close agreement of computed and measured structure factors in the molecular and polymer phases [10].…”

Revealing the importance of surface morphology of nanomaterials to biological responses: Adsorption of the villin headpiece onto graphene and phosphorene

“…The phosphorus and carbon atoms were modeled as uncharged Lennard-Jones particles. The cross sections r for phosphorus and carbon atoms are r pp = 3.33 Å [7] and r cc = 3.4 Å [8], respectively. The depth of potential well for phosphorus and carbon atoms are e pp = 0.400 kcal/mol [7] and e cc = 0.086 kcal/mol [8], respectively.…”

“…The cross sections r for phosphorus and carbon atoms are r pp = 3.33 Å [7] and r cc = 3.4 Å [8], respectively. The depth of potential well for phosphorus and carbon atoms are e pp = 0.400 kcal/mol [7] and e cc = 0.086 kcal/mol [8], respectively. The bond strength constants for phosphorus and carbon atoms are 297 kcal mol À1 Å 2 [7] and 938 kcal mol À1 Å 2 [8], respectively.…”

“…This is different from graphene where the chemical bond results from the sp 2 hybridization of carbon atoms [5,6]. (3) Lennard-Jones (LJ) potential: the LJ potential well depth of phosphorene [7] is about four times larger than that of graphene [8] and hence could influence the hydrophobicity directly. (4) Band gap: phosphorene possesses a direct band gap (a range of energy states in which electrons cannot exist freely) which makes it a natural semiconducting nanomaterial [9], whereas graphene is a semimetal.…”

Structure and dynamics in liquid bismuth and Bin clusters: A density functional study

“…They showed that the open structures could be interpreted as a modulation of random packing by oscillations in the effective potentials. Ballone and Jones 26 studied the liquid-liquid phase transition in a 4000 atom sample of P using a classical force field fit to an extensive set of density functional (DF) calculations on phosphorus clusters. The first molecular dynamics (MD)/DF simulation of liquid Bi was performed by de Wijs et al 27 on a 60-atom sample over 4.15 ps at 1000 K. Souto et al 28 carried out simulations at 600 K (124 atoms, 600 K, 40 ps, local density approximation for exchange and correlation) and discussed the static and dynamical structure factors, the pair distribution function, and the nature of the collective modes.…”