### Abstract

No exact solution for the free energy of electrostatic interaction for a charged sphere and rod geometry in an electrolyte solution has yet been proposed. This geometry is interesting because it can be applied to describe macromolecules interacting with a random fiber-matrix for modeling of hindered transport in diffusional systems. Here we present an analytical approach that yields an exact solution to the problem for ion-penetrable - also called 'soft' - sphere and infinitely long rod. This solution is compared to a published finite-element analysis of the same system with nonpenetrable - also called 'hard' - sphere and infinitely long rod maintaining a constant surface charge density restriction. For any ionic strength or ratio of rod radius to sphere radius the ion-penetrable method yields an electrostatic free energy of interaction which is lower than that given by the analysis for hard bodies. This free energy is significantly lower for most parameter value combinations and therefore suggests that one should carefully examine the system being modeled to determine if it is approximated better by a hard body or ion-penetrable body approach. (C) 2000 Academic Press.

Original language | English |
---|---|

Pages (from-to) | 102-106 |

Number of pages | 5 |

Journal | Journal of Colloid and Interface Science |

Volume | 229 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 2000 |

### Fingerprint

### Keywords

- Double-layer interaction
- Electrostatic interaction
- Fiber-matrix
- Ion-penetrable bodies
- Poisson-Boltzmann equation

### ASJC Scopus subject areas

- Colloid and Surface Chemistry
- Physical and Theoretical Chemistry
- Surfaces and Interfaces

### Cite this

**An exact solution to the electrostatic interaction between an ion-penetrable sphere and an ion-penetrable rod.** / Mark, Lawrence; Kaplan, Jerome L.; Williams, James.

Research output: Contribution to journal › Article

*Journal of Colloid and Interface Science*, vol. 229, no. 1, pp. 102-106. https://doi.org/10.1006/jcis.2000.6975

}

TY - JOUR

T1 - An exact solution to the electrostatic interaction between an ion-penetrable sphere and an ion-penetrable rod

AU - Mark, Lawrence

AU - Kaplan, Jerome L.

AU - Williams, James

PY - 2000/9/1

Y1 - 2000/9/1

N2 - No exact solution for the free energy of electrostatic interaction for a charged sphere and rod geometry in an electrolyte solution has yet been proposed. This geometry is interesting because it can be applied to describe macromolecules interacting with a random fiber-matrix for modeling of hindered transport in diffusional systems. Here we present an analytical approach that yields an exact solution to the problem for ion-penetrable - also called 'soft' - sphere and infinitely long rod. This solution is compared to a published finite-element analysis of the same system with nonpenetrable - also called 'hard' - sphere and infinitely long rod maintaining a constant surface charge density restriction. For any ionic strength or ratio of rod radius to sphere radius the ion-penetrable method yields an electrostatic free energy of interaction which is lower than that given by the analysis for hard bodies. This free energy is significantly lower for most parameter value combinations and therefore suggests that one should carefully examine the system being modeled to determine if it is approximated better by a hard body or ion-penetrable body approach. (C) 2000 Academic Press.

AB - No exact solution for the free energy of electrostatic interaction for a charged sphere and rod geometry in an electrolyte solution has yet been proposed. This geometry is interesting because it can be applied to describe macromolecules interacting with a random fiber-matrix for modeling of hindered transport in diffusional systems. Here we present an analytical approach that yields an exact solution to the problem for ion-penetrable - also called 'soft' - sphere and infinitely long rod. This solution is compared to a published finite-element analysis of the same system with nonpenetrable - also called 'hard' - sphere and infinitely long rod maintaining a constant surface charge density restriction. For any ionic strength or ratio of rod radius to sphere radius the ion-penetrable method yields an electrostatic free energy of interaction which is lower than that given by the analysis for hard bodies. This free energy is significantly lower for most parameter value combinations and therefore suggests that one should carefully examine the system being modeled to determine if it is approximated better by a hard body or ion-penetrable body approach. (C) 2000 Academic Press.

KW - Double-layer interaction

KW - Electrostatic interaction

KW - Fiber-matrix

KW - Ion-penetrable bodies

KW - Poisson-Boltzmann equation

UR - http://www.scopus.com/inward/record.url?scp=0034283817&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034283817&partnerID=8YFLogxK

U2 - 10.1006/jcis.2000.6975

DO - 10.1006/jcis.2000.6975

M3 - Article

VL - 229

SP - 102

EP - 106

JO - Journal of Colloid and Interface Science

JF - Journal of Colloid and Interface Science

SN - 0021-9797

IS - 1

ER -