Size Effect in Grand-canonical Monte-Carlo Simulation of Solutions of Electrolyte - Viet Duc, Nguyen (VNU Journal of Science: Mathematics - Physics; Vol 35 No 2DO - 10.25073/2588-1124/vnumap.4296, 2019)
Abstract: A Grand-canonical Monte-Carlo simulation method is investigated. Due to charge neutrality requirement of electrolyte solutions, ions must be added to or removed from the system in groups. It is then implemented to simulate solution of 1:1, 2:1 and 2:2 salts at different concentrations using the primitive ion model. We investigate how the finite size of the simulation box can influence statistical quantities of the salt system. Remarkably, the method works well down to a system as small as one salt molecule. Although the fluctuation in the statistical quantities increases as the system gets smaller, their average values remain equal to their bulk value within the uncertainty error. Based on this knowledge, the osmotic pressures of the electrolyte solutions are calculated and shown to depend linearly on the salt concentrations within the concentration range simulated. Chemical potential of ionic salt that can be used for simulation of these salts in more complex system are calculated. Keywords: GCMC, electrolyte solution simulation, primitive ion model, finite size effect. References [1] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Clarendon Press, Oxford, 1987. [2] P. Coveney, Computational biomedicine: modelling the human body, Oxford University Press, 2014. [3] M. Praprotnik, L.D. Site, Multiscale Molecular Modeling, in: L. Monticelli and E. Salonen, Biomolecular Simulations: Methods and Protocols, Humana Press, Hatfield, Hertfordshire, 2013, ch. III, pp. 567–583. [4] R. Potestio et al., Hamiltonian adaptive resolution simulation for molecular liquids, Phys. Rev. Lett. 110 (2013), 108301. https://doi.org/10.1103/PhysRevLett.110.108301. [5] M. Neri, C. Anselmi, M. Cascella, A. Maritan, A. Carloni, Coarse-Grained Model of Proteins Incorporating Atomistic Detail of the Active Site, Phys. Rev. Lett. 95 (2005), 218102. https://doi.org/10.1103/PhysRevLett.95.218102. [6] W.G. Noid, Perspective: Coarse-grained models for biomolecular systems, J. Chem. Phys. 139 (2013), 090901. https://doi.org/10.1063/1.4818908. [7] E. Brunk, U. Rothlisberger, Mixed Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations of Biological Systems in Ground and Electronically Excited States, Chemical reviews 115 (2015), 6217–6263. https://doi.org/10.1021/cr500628b. [8] Y. Ueda, H. Taketomi, N. Go, Studies on Protein Folding, Unfolding, and Fluctuations by Computer Simulation. II. A Three-Dimensional Lattice Model of Lysozyme, Biopolymers 17 (1978), 1531-1548. https://doi.org/10.1002/bip.1978.360170612. [9] T.X. Hoang, M. Cieplak, Molecular dynamics of folding of secondary structures in Go-type models of proteins, J. Chem. Phys. 112 (2000), 6851–6862. https://doi.org/10.1063/1.481261. [10] E. Villa, A. Balaeff, K. Schulten, Structural dynamics of the lac repressor–DNA complex revealed by a multiscale simulation, Proc. Nat. Acad. Science 102 (2005), 6783. https://doi.org/10.1073/pnas.0409387102. [11] J.P. Valleau, L.K. Cohen, Primitive model electrolytes. I. Grand canonical Monte Carlo computations, J. Chem. Phys. 72 (1980), 5935–5941. https://doi.org/10.1063/1.439092. [12] S. Lee, T.T. Le, T.T. Nguyen, Reentrant Behavior of Divalent-Counterion-Mediated DNA-DNA Electrostatic Interaction, Phys. Rev. Lett. 105 (2010), 248101. https://doi.org/10.1103/PhysRevLett.105.248101. [13] N.T. Toan, Strongly correlated electrostatics of viral genome packaging, J. Biol. Phys. 39 (2013), 247–265. https://doi.org/10.1007/s10867-013-9301-4. [14] T.T. Nguyen, Grand-canonical simulation of DNA condensation with two salts, effect of divalent counterion size, J. Chem. Phys. 144 (2016), 065102. https://doi.org/10.1063/1.4940312. [15] V. D. Nguyen, T. T. Nguyen, and P. Carloni, DNA like-charge attraction and overcharging by divalent counterions in the presence of divalent co-ions, J. Biol. Phys. 43 (2017), 185–195. https://doi.org/10.1007/s10867-017-9443-x. [16] P.P. Ewald, Evaluation of optical and electrostatic lattice potentials, Ann. Phys. 64 (1921), 253. [17] L. Nordenskiöld, A.P. Lyubartsev, Monte Carlo Simulation Study of Ion Distribution and Osmotic Pressure in Hexagonally Oriented DNA, J. Phys. Chem. 99 (1995), 10373–10382. https://doi.org/10.1021/j100025a046. [18] Lars Guldbrand, Lars G. Nilsson, and Lars Nordenskiöld, A Monte Carlo simulation study of electrostatic forces between hexagonally packed DNA double helices, J. Chem. Phys. 85 (1986), 6686 6698. https://doi.org/10.1063/1.451450. [19] L. Landau, E. Lifshitz, Statistical Physics, Elsevier Science, 2013.