skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Effective charges and virial pressure of concentrated macroion solutions

Abstract

The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin-Landau-Verwey-Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. In this paper, we show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations ofmore » macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion-macroion spatial correlation and the virial pressure obtained with the EPC model. Finally, our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.« less

Authors:
 [1];  [2];  [3];  [1]
  1. Northwestern Univ., Evanston, IL (United States)
  2. Northwestern Univ., Evanston, IL (United States); Univ. Autonoma de San Luis Potosi (Mexico)
  3. Univ. of Utrecht (Netherlands)
Publication Date:
Research Org.:
Northwestern Univ., Evanston, IL (United States); Energy Frontier Research Centers (EFRC) (United States). Center for Bio-Inspired Energy Science (CBES)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1349033
Grant/Contract Number:  
SC0000989
Resource Type:
Accepted Manuscript
Journal Name:
Proceedings of the National Academy of Sciences of the United States of America
Additional Journal Information:
Journal Volume: 112; Journal Issue: 30; Journal ID: ISSN 0027-8424
Publisher:
National Academy of Sciences
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; colloids; DLVO; macroions; electrolytes; cell model

Citation Formats

Boon, Niels, Guerrero-García, Guillermo Ivan, van Roij, René, and Olvera de la Cruz, Monica. Effective charges and virial pressure of concentrated macroion solutions. United States: N. p., 2015. Web. doi:10.1073/pnas.1511798112.
Boon, Niels, Guerrero-García, Guillermo Ivan, van Roij, René, & Olvera de la Cruz, Monica. Effective charges and virial pressure of concentrated macroion solutions. United States. doi:10.1073/pnas.1511798112.
Boon, Niels, Guerrero-García, Guillermo Ivan, van Roij, René, and Olvera de la Cruz, Monica. Mon . "Effective charges and virial pressure of concentrated macroion solutions". United States. doi:10.1073/pnas.1511798112. https://www.osti.gov/servlets/purl/1349033.
@article{osti_1349033,
title = {Effective charges and virial pressure of concentrated macroion solutions},
author = {Boon, Niels and Guerrero-García, Guillermo Ivan and van Roij, René and Olvera de la Cruz, Monica},
abstractNote = {The stability of colloidal suspensions is crucial in a wide variety of processes, including the fabrication of photonic materials and scaffolds for biological assemblies. The ionic strength of the electrolyte that suspends charged colloids is widely used to control the physical properties of colloidal suspensions. The extensively used two-body Derjaguin-Landau-Verwey-Overbeek (DLVO) approach allows for a quantitative analysis of the effective electrostatic forces between colloidal particles. DLVO relates the ionic double layers, which enclose the particles, to their effective electrostatic repulsion. Nevertheless, the double layer is distorted at high macroion volume fractions. Therefore, DLVO cannot describe the many-body effects that arise in concentrated suspensions. In this paper, we show that this problem can be largely resolved by identifying effective point charges for the macroions using cell theory. This extrapolated point charge (EPC) method assigns effective point charges in a consistent way, taking into account the excluded volume of highly charged macroions at any concentration, and thereby naturally accounting for high volume fractions in both salt-free and added-salt conditions. We provide an analytical expression for the effective pair potential and validate the EPC method by comparing molecular dynamics simulations of macroions and monovalent microions that interact via Coulombic potentials to simulations of macroions interacting via the derived EPC effective potential. The simulations reproduce the macroion-macroion spatial correlation and the virial pressure obtained with the EPC model. Finally, our findings provide a route to relate the physical properties such as pressure in systems of screened Coulomb particles to experimental measurements.},
doi = {10.1073/pnas.1511798112},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = 30,
volume = 112,
place = {United States},
year = {2015},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

The Role of Attractive and Repulsive Forces in the Formation of Tactoids, Thixotropic Gels, Protein Crystals and Coacervates
journal, December 1938

  • Langmuir, Irving
  • The Journal of Chemical Physics, Vol. 6, Issue 12
  • DOI: 10.1063/1.1750183

The discrete-ion effect in ionic double-layer theory
journal, February 1967

  • Levine, S.; Mingins, J.; Bell, G. M.
  • Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, Vol. 13, Issue 3
  • DOI: 10.1016/0022-0728(67)80125-6

Theory of the Diffuse Double Layer
journal, November 1960

  • Stillinger, Frank H.; Kirkwood, John G.
  • The Journal of Chemical Physics, Vol. 33, Issue 5
  • DOI: 10.1063/1.1731401

Statistical mechanical theories of the electric double layer
journal, June 1981

  • Levine, Samuel; Outhwaite, Christopher W.; Bhuiyan, Lutful B.
  • Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, Vol. 123, Issue 1
  • DOI: 10.1016/S0022-0728(81)80046-0

Theory of electrified interfaces
journal, January 1977


Colloid stability: The forces between charged surfaces in an electrolyte
journal, July 1991

  • Valleau, J. P.; Ivkov, R.; Torrie, G. M.
  • The Journal of Chemical Physics, Vol. 95, Issue 1
  • DOI: 10.1063/1.461452

The interaction between macrospheres in solution
journal, August 1992


Attractive Interaction between Similarly Charged Colloidal Particles
journal, December 1996

  • Chu, Xiaolin; Wasan, Darsh T.
  • Journal of Colloid and Interface Science, Vol. 184, Issue 1
  • DOI: 10.1006/jcis.1996.0620

Beyond Poisson-Boltzmann: Fluctuation effects and correlation functions
journal, January 2000


Phase Transitions in 2:1 and 3:1 Hard-Core Model Electrolytes
journal, January 2002


Ion-ion correlations and effective charges in electrolyte and macroion systems
journal, June 1996

  • Kjellander, Roland
  • Berichte der Bunsengesellschaft für physikalische Chemie, Vol. 100, Issue 6
  • DOI: 10.1002/bbpc.19961000635

Charge Inversion and Ion−Ion Correlation Effects at the Mercury/Aqueous MgSO 4 Interface: Toward the Solution of a Long-Standing Issue
journal, January 2010

  • Wernersson, Erik; Kjellander, Roland; Lyklema, Johannes
  • The Journal of Physical Chemistry C, Vol. 114, Issue 4
  • DOI: 10.1021/jp906759e

Tunable soft structure in charged fluids confined by dielectric interfaces
journal, March 2013

  • Zwanikken, J. W.; Olvera de la Cruz, M.
  • Proceedings of the National Academy of Sciences, Vol. 110, Issue 14
  • DOI: 10.1073/pnas.1302406110

On progress in forces since the DLVO theory
journal, December 1999


The electrostatic repulsion between charged spheres from exact solutions to the linearized poisson-boltzmann equation
journal, May 1983


Computation of Forces between Spherical Colloidal Particles: Nonlinear Poisson-Boltzmann Theory
journal, June 1994

  • Carnie, Steven L.; Chan, Derek Y. C.; Stankovich, Jim
  • Journal of Colloid and Interface Science, Vol. 165, Issue 1
  • DOI: 10.1006/jcis.1994.1212

Calculations of Double-Layer Electrostatic Interactions for the Sphere/Plane Geometry
journal, March 1997

  • Warszyński, P.; Adamczyk, Z.
  • Journal of Colloid and Interface Science, Vol. 187, Issue 2
  • DOI: 10.1006/jcis.1996.4671

Gas-liquid phase coexistence in colloidal suspensions?
journal, August 2001


Van der Waals–Like Instability in Suspensions of Mutually Repelling Charged Colloids
journal, October 1997


Ab initio description of counterion screening in colloidal suspensions
journal, February 1992


E FFECTIVE I NTERACTIONS B ETWEEN E LECTRIC D OUBLE L AYERS
journal, October 2000


Phase transitions in aqueous suspensions of spherical colloid particles
journal, October 1976


Crystallization and reentrant melting of charged colloids in nonpolar solvents
journal, March 2015


On the thermodynamics of micellar solutions
journal, January 1954


A hard sphere model for order-disorder transitions in colloidal dispersions
journal, September 1975


A semiempirical model for the phase transition in polystyrene latexes
journal, June 1976

  • Brenner, Stephen L.
  • The Journal of Physical Chemistry, Vol. 80, Issue 13
  • DOI: 10.1021/j100554a016

The order-disorder transition in latex dispersions
journal, December 1981


Renormalized jellium model for charge-stabilized colloidal suspensions
journal, March 2004


Charge renormalization, osmotic pressure, and bulk modulus of colloidal crystals: Theory
journal, June 1984

  • Alexander, S.; Chaikin, P. M.; Grant, P.
  • The Journal of Chemical Physics, Vol. 80, Issue 11
  • DOI: 10.1063/1.446600

Equation of State and Structure of Electrostatic Colloidal Crystals: Osmotic Pressure and Scattering Study
journal, April 1997

  • Reus, V.; Belloni, L.; Zemb, T.
  • Journal de Physique II, Vol. 7, Issue 4
  • DOI: 10.1051/jp2:1997142

Many-body interactions and the melting of colloidal crystals
journal, September 2003

  • Dobnikar, J.; Chen, Y.; Rzehak, R.
  • The Journal of Chemical Physics, Vol. 119, Issue 9
  • DOI: 10.1063/1.1595642

Testing the relevance of effective interaction potentials between highly-charged colloids in suspension
journal, November 2006

  • Dobnikar, J.; Castañeda-Priego, R.; Grünberg, H. H. von
  • New Journal of Physics, Vol. 8, Issue 11
  • DOI: 10.1088/1367-2630/8/11/277

Ionic condensation and charge renormalization in colloidal suspensions
journal, September 1998


Simple Approach for Charge Renormalization in Highly Charged Macroions
journal, November 2002


Alexander's Prescription for Colloidal Charge Renormalization
journal, April 2003

  • Trizac, E.; Bocquet, L.; Aubouy, M.
  • Langmuir, Vol. 19, Issue 9
  • DOI: 10.1021/la027056m

Effective charge of colloidal particles
journal, December 2004

  • Diehl, Alexandre; Levin, Yan
  • The Journal of Chemical Physics, Vol. 121, Issue 23
  • DOI: 10.1063/1.1824013

Poisson–Boltzmann theory of charged colloids: limits of the cell model for salty suspensions
journal, August 2010


The viscoelastic properties of ordered latices: a self-consistent field theory
journal, September 1981


Pair structure of the hard-sphere Yukawa fluid: An improved analytic method versus simulations, Rogers-Young scheme, and experiment
journal, January 2011

  • Heinen, Marco; Holmqvist, Peter; Banchio, Adolfo J.
  • The Journal of Chemical Physics, Vol. 134, Issue 4
  • DOI: 10.1063/1.3524309

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995


Melting line of charged colloids from primitive model simulations
journal, December 2005

  • Hynninen, Antti-Pekka; Dijkstra, Marjolein
  • The Journal of Chemical Physics, Vol. 123, Issue 24
  • DOI: 10.1063/1.2138693

An exact method to obtain effective electrostatic interactions from computer simulations: The case of effective charge amplification
journal, August 2013

  • González-Mozuelos, P.; Guerrero-García, G. I.; Olvera de la Cruz, M.
  • The Journal of Chemical Physics, Vol. 139, Issue 6
  • DOI: 10.1063/1.4817776

Large Counterions Boost the Solubility and Renormalized Charge of Suspended Nanoparticles
journal, October 2013

  • Guerrero-García, Guillermo Iván; González-Mozuelos, Pedro; Olvera de la Cruz, Monica
  • ACS Nano, Vol. 7, Issue 11
  • DOI: 10.1021/nn404477b

Polarization Effects of Dielectric Nanoparticles in Aqueous Charge-Asymmetric Electrolytes
journal, July 2014

  • Guerrero García, Guillermo Iván; Olvera de la Cruz, Monica
  • The Journal of Physical Chemistry B, Vol. 118, Issue 29
  • DOI: 10.1021/jp5045173

Particle mesh Ewald: An N ⋅log( N ) method for Ewald sums in large systems
journal, June 1993

  • Darden, Tom; York, Darrin; Pedersen, Lee
  • The Journal of Chemical Physics, Vol. 98, Issue 12
  • DOI: 10.1063/1.464397

New, thermodynamically consistent, integral equation for simple fluids
journal, August 1984


Macroion correlation effects in electrostatic screening and thermodynamics of highly charged colloids
journal, November 2006


Freezing lines of colloidal Yukawa spheres. I. A Rogers-Young integral equation study
journal, January 2012

  • Gapinski, Jacek; Nägele, Gerhard; Patkowski, Adam
  • The Journal of Chemical Physics, Vol. 136, Issue 2
  • DOI: 10.1063/1.3675607

Freezing of Charge-Stabilized Colloidal Dispersions
journal, June 2003

  • Zhou, Shiqi; Zhang, Xiaoqi
  • The Journal of Physical Chemistry B, Vol. 107, Issue 22
  • DOI: 10.1021/jp027319l

Volume terms for charged colloids: A grand-canonical treatment
journal, February 2006


Nonlinear Screening and Gas-Liquid Separation in Suspensions of Charged Colloids
journal, December 2006


Electrostatic Interactions of Colloidal Particles at Vanishing Ionic Strength
journal, December 2008

  • Sainis, Sunil K.; Merrill, Jason W.; Dufresne, Eric R.
  • Langmuir, Vol. 24, Issue 23
  • DOI: 10.1021/la8024606

Surface Charge Density/Surface Potential Relationship for a Spherical Colloidal Particle in a Salt-Free Medium
journal, March 2002


Counterion-only electrical double layer: A constrained entropy approach
journal, September 2002

  • Briscoe, Wuge H.; Attard, Phil
  • The Journal of Chemical Physics, Vol. 117, Issue 11
  • DOI: 10.1063/1.1500359

Breakdown of the Yukawa model in de-ionized colloidal suspensions
journal, March 2008


Extended sedimentation profiles in charged colloids: the gravitational length, entropy, and electrostatics
journal, April 2005

  • Royall, C. P.; Roij, R. van; Blaaderen, A. van
  • Journal of Physics: Condensed Matter, Vol. 17, Issue 15
  • DOI: 10.1088/0953-8984/17/15/005