### Abstract

In simulating charged systems, it is often useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of solving the PB equation at each step of the simulation can be bypassed using variational methods that treat the electrostatic potential as a dynamic variable. But such approaches require the access to a true free-energy functional: a functional that not only provides the correct solution of the PB equation upon extremization, but also evaluates to the true free energy of the system at its minimum. Moreover, the numerical efficiency of such procedures is further enhanced if the free-energy functional is local and is expressed in terms of the electrostatic potential. Existing PB functionals of the electrostatic potential, while possessing the local structure, are not free-energy functionals. We present a variational formulation with a local free-energy functional of the potential. In addition, we also construct a nonlocal free-energy functional of the electrostatic potential. These functionals are suited for employment in simulation schemes based on the ideas of dynamical optimization.

Original language | English (US) |
---|---|

Article number | 022305 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 88 |

Issue number | 2 |

DOIs | |

State | Published - Aug 12 2013 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability
- Medicine(all)

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*88*(2), [022305]. https://doi.org/10.1103/PhysRevE.88.022305

**Free-energy functionals of the electrostatic potential for Poisson-Boltzmann theory.** / Jadhao, Vikram; Solis, Francisco; De La Cruz, Monica Olvera.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 88, no. 2, 022305. https://doi.org/10.1103/PhysRevE.88.022305

}

TY - JOUR

T1 - Free-energy functionals of the electrostatic potential for Poisson-Boltzmann theory

AU - Jadhao, Vikram

AU - Solis, Francisco

AU - De La Cruz, Monica Olvera

PY - 2013/8/12

Y1 - 2013/8/12

N2 - In simulating charged systems, it is often useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of solving the PB equation at each step of the simulation can be bypassed using variational methods that treat the electrostatic potential as a dynamic variable. But such approaches require the access to a true free-energy functional: a functional that not only provides the correct solution of the PB equation upon extremization, but also evaluates to the true free energy of the system at its minimum. Moreover, the numerical efficiency of such procedures is further enhanced if the free-energy functional is local and is expressed in terms of the electrostatic potential. Existing PB functionals of the electrostatic potential, while possessing the local structure, are not free-energy functionals. We present a variational formulation with a local free-energy functional of the potential. In addition, we also construct a nonlocal free-energy functional of the electrostatic potential. These functionals are suited for employment in simulation schemes based on the ideas of dynamical optimization.

AB - In simulating charged systems, it is often useful to treat some ionic components of the system at the mean-field level and solve the Poisson-Boltzmann (PB) equation to get their respective density profiles. The numerically intensive task of solving the PB equation at each step of the simulation can be bypassed using variational methods that treat the electrostatic potential as a dynamic variable. But such approaches require the access to a true free-energy functional: a functional that not only provides the correct solution of the PB equation upon extremization, but also evaluates to the true free energy of the system at its minimum. Moreover, the numerical efficiency of such procedures is further enhanced if the free-energy functional is local and is expressed in terms of the electrostatic potential. Existing PB functionals of the electrostatic potential, while possessing the local structure, are not free-energy functionals. We present a variational formulation with a local free-energy functional of the potential. In addition, we also construct a nonlocal free-energy functional of the electrostatic potential. These functionals are suited for employment in simulation schemes based on the ideas of dynamical optimization.

UR - http://www.scopus.com/inward/record.url?scp=84883865866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883865866&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.88.022305

DO - 10.1103/PhysRevE.88.022305

M3 - Article

C2 - 24032831

AN - SCOPUS:84883865866

VL - 88

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 2

M1 - 022305

ER -