1
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Vogel P, Palberg T. Electrokinetic effects of ambient and excess carbonization of dielectric surfaces in aqueous environments. J Colloid Interface Sci 2023; 656:280-288. [PMID: 37995398 DOI: 10.1016/j.jcis.2023.10.056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2023] [Revised: 10/09/2023] [Accepted: 10/12/2023] [Indexed: 11/25/2023]
Abstract
The charge state of surfaces in contact with aqueous electrolytes is crucial for the performance and stability of dielectric surfaces in general and lyophobic colloids in particular. Thus far the role of adsorbed molecular CO2 remained largely unexplored. The aim of the present investigation is to study the de-charging and re-charging for two model surfaces upon addition of CO2 and/or 1:1 electrolytes (NaCl, HCl) under precisely controlled boundary conditions up to millimolar concentrations of additives. Starting from the salt- and CO2-free state, the ζ-potential magnitudes drop linearly with the logarithm of the CO2-concentrations over several orders of magnitude in CO2-concentrations. Hydrophobic Polystyrene nearly fully discharges, hydrophilic SiO2 reveals a 60% charge reduction. From the surface specific effects of instead adding NaCl or HCl, we discriminate and parameterize empirically the relative contribution of three individual mechanisms for decreasing the ζ-potential magnitudes (screening, pH-driven charge regulation, dielectric charge regulation) combining during CO2-addition. Moreover, depending on the achieved CO2-induced de-charging, the behavior upon subsequent addition of NaCl and HCl switches between two limiting cases. Screening dominates for surfaces in the native state without CO2, but a significant re-charging is observed for surfaces conditioned under excess CO2-concentrations.
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Affiliation(s)
- Peter Vogel
- Institute of Physics, Johannes Gutenberg University, 55128 Mainz, Germany.
| | - Thomas Palberg
- Institute of Physics, Johannes Gutenberg University, 55128 Mainz, Germany
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2
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Bakhshandeh A, Levin Y. Charge fluctuations in charge-regulated systems: dependence on statistical ensemble. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:65. [PMID: 37522995 DOI: 10.1140/epje/s10189-023-00325-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Accepted: 07/18/2023] [Indexed: 08/01/2023]
Abstract
We investigate charge regulation of nanoparticles in concentrated suspensions, focusing on the effect of different statistical ensembles. We find that the choice of ensemble does not affect the mean charge of nanoparticles, but significantly alters the magnitude of its fluctuation. Specifically, we compared the behaviors of colloidal charge fluctuations in the semi-grand canonical and canonical ensembles and identified significant differences between the two. The choice of ensemble-whether the system is isolated or is in contact with a reservoir of acid and salt-will, therefore, affect the Kirkwood-Shumaker fluctuation-induced force inside concentrated suspensions. Our results emphasize the importance of selecting an appropriate ensemble that accurately reflects the experimental conditions when studying fluctuation-induced forces between polyelectrolytes, proteins, and colloidal particles in concentrated suspensions.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, 91501-970, Brazil
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, 91501-970, Brazil.
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3
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Vernin NS, Gillespie D. Surface charge regulation using classical density functional theory: the effect of divalent potential determining ions. Phys Chem Chem Phys 2023; 25:1023-1031. [PMID: 36533726 DOI: 10.1039/d2cp03644d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The charge regulation approach has been used to describe the charge of surfaces susceptible to the presence of protons and other ions. Conventionally, this model is used with the Poisson-Boltzmann equation, which generally neglects the finite size of the ions and the electrostatic correlations. Recently, progress has been made by coupling charge regulation with classical density functional theory (DFT), which explicitly includes these correlations. However, little is known about charge regulation at surfaces with both acid-base equilibria and complexation with multivalent ions. The main purpose of this work is to investigate the role divalent ions play in charge regulation. Using DFT, we show that the size of the divalent ion has significant consequences on the surface charge density and it should not be neglected. For the surface reactions investigated, the larger the size of the divalent cation, the greater the charge on the surface due to higher divalent concentration there. At low divalent concentration, the ion correlations play a second-order but non-negligible role; using Poisson-Boltzmann theory with point ions cannot recover the DFT surface charge. At high concentrations, ion correlations play a dominant role by creating charge inversion.
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Affiliation(s)
- Nathalia Salles Vernin
- Department of Sanitary and Environmental Engineering, Rio de Janeiro State University, Rio de Janeiro, RJ 20550-900, Brazil.
| | - Dirk Gillespie
- Department of Physiology and Biophysics, Rush University Medical Center, Chicago, IL 60612, USA.
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4
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Vogel P, Möller N, Qaisrani MN, Bista P, Weber SAL, Butt HJ, Liebchen B, Sulpizi M, Palberg T. Charging of Dielectric Surfaces in Contact with Aqueous Electrolytes─the Influence of CO 2. J Am Chem Soc 2022; 144:21080-21087. [DOI: 10.1021/jacs.2c06793] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Affiliation(s)
- Peter Vogel
- Institute of Physics, Johannes Gutenberg University, 55128Mainz, Germany
| | - Nadir Möller
- Institute of Physics, Johannes Gutenberg University, 55128Mainz, Germany
| | | | - Pravash Bista
- Max Planck Institute for Polymer Research, 55128Mainz, Germany
| | | | | | - Benno Liebchen
- Institute for Condensed Matter Physics, Technische Universität Darmstadt, 64289Darmstadt, Germany
| | - Marialore Sulpizi
- Department of Physics, Ruhr Universität Bochum, 44780Bochum, Germany
| | - Thomas Palberg
- Institute of Physics, Johannes Gutenberg University, 55128Mainz, Germany
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5
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Allahyarov E, Löwen H, Denton AR. Structural correlations in highly asymmetric binary charged colloidal mixtures. Phys Chem Chem Phys 2022; 24:15439-15451. [PMID: 35708479 DOI: 10.1039/d2cp01343f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We explore structural correlations of strongly asymmetric mixtures of binary charged colloids within the primitive model of electrolytes considering large charge and size ratios of 10 and higher. Using computer simulations with explicit microions, we obtain the partial pair correlation functions between the like-charged colloidal macroions. Interestingly the big-small correlation peak amplitude is smaller than that of the big-big and small-small macroion correlation peaks, which is unfamiliar for additive repulsive interactions. Extracting optimal effective microion-averaged pair interactions between the macroions, we find that on top of non-additive Yukawa-like repulsions an additional shifted Gaussian attractive potential between the small macroions is needed to accurately reproduce their correct pair correlations. For small Coulomb couplings, the behavior is reproduced in a coarse-grained theory with microion-averaged effective interactions between the macroions. However, the accuracy of the theory deteriorates with increasing Coulomb coupling. We emphasize the relevance of entropic interactions exerted by the microions on the macroions. Our results are experimentally verifiable in binary mixtures of micron-sized colloids and like-charge nanoparticles.
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Affiliation(s)
- Elshad Allahyarov
- Theoretical Department, Joint Institute for High Temperatures, Russian Academy of Sciences (IVTAN), 13/19 Izhorskaya Street, Moscow 125412, Russia. .,Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine Universität Düsseldorf, Universitätstrasse 1, 40225 Düsseldorf, Germany.,Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7202, USA
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine Universität Düsseldorf, Universitätstrasse 1, 40225 Düsseldorf, Germany
| | - Alan R Denton
- Department of Physics, North Dakota State University, Fargo, ND 58108-6050, USA
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6
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Bakhshandeh A, Frydel D, Levin Y. Charge regulation of colloidal particles in aqueous solutions. Phys Chem Chem Phys 2020; 22:24712-24728. [PMID: 33104140 DOI: 10.1039/d0cp03633a] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
We study the charge regulation of colloidal particles inside aqueous electrolyte solutions. To stabilize a colloidal suspension against precipitation, colloidal particles are synthesized with either acidic or basic groups on their surface. On contact with water, these surface groups undergo proton transfer reactions, resulting in colloidal surface charge. The charge is determined by the condition of local chemical equilibrium between hydronium ions inside the solution and at the colloidal surface. We use a model of Baxter sticky spheres to explicitly calculate the equilibrium dissociation constants and to construct a theory which is able to quantitatively predict the effective charge of colloidal particles with either acidic or basic surface groups. The predictions of the theory for the model are found to be in excellent agreement with the results of Monte Carlo simulations. This theory is further extended to treat colloidal particles with a mixture of both acidic and basic surface groups.
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Affiliation(s)
- Amin Bakhshandeh
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970, Porto Alegre, RS, Brazil.
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7
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Ong GMC, Gallegos A, Wu J. Modeling Surface Charge Regulation of Colloidal Particles in Aqueous Solutions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:11918-11928. [PMID: 32921060 DOI: 10.1021/acs.langmuir.0c02000] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Colloidal particles are mostly charged in an aqueous solution because of the protonation or deprotonation of ionizable groups on the surface. The surface charge density reflects a complex interplay of ion distributions within the electric double layer and the surface reaction equilibrium. In this work, we present a coarse-grained model to describe the charge regulation of various colloidal systems by an explicit consideration of the inhomogeneous ion distributions and surface reactions. With the primitive model for aqueous solutions and equilibrium constants for surface reactions as the inputs, the theoretical model is able to make quantitative predictions of the surface-charge densities and zeta potentials for diverse colloidal particles over a wide range of pH and ionic conditions. By accounting for the ionic size effects and electrostatic correlations, our model is applicable to systems with multivalent ions that exhibit charge inversion and provides a faithful description of the interfacial properties without evoking the empirical Stern capacitance or specific ion adsorptions.
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Affiliation(s)
- Gary M C Ong
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
| | - Alejandro Gallegos
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
| | - Jianzhong Wu
- Department of Chemical and Environmental Engineering, University of California, Riverside, California 92521, United States
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8
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Botin D, Carrique F, Ruiz-Reina E, Palberg T. Non-monotonic concentration dependence of the electro-phoretic mobility of charged spheres in realistic salt free suspensions. J Chem Phys 2020; 152:244902. [PMID: 32610949 DOI: 10.1063/5.0010692] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Using super-heterodyne Doppler velocimetry with multiple scattering correction, we extend the optically accessible range of concentrations in experiments on colloidal electro-kinetics. Here, we measured the electro-phoretic mobility and the DC conductivity of aqueous charged sphere suspensions covering about three orders of magnitude in particle concentrations and transmissions as low as 40%. The extended concentration range for the first time allows the demonstration of a non-monotonic concentration dependence of the mobility for a single particle species. Our observations reconcile previous experimental observations made on other species over restricted concentration ranges. We compare our results to the state-of-the-art theoretical calculations using a constant particle charge and the carefully determined experimental boundary conditions as input. In particular, we consider the so-called realistic salt free conditions, i.e., we respect the release of counterions by the particles, the solvent hydrolysis, and the formation of carbonic acid from dissolved neutral CO2. We also compare our results to previous results obtained under similarly well-defined conditions. This allows identification of three distinct regions of differing density dependence. There is an ascent during the build-up of double layer overlap, which is not expected by theory, an extended plateau region in quantitative agreement with theoretical expectation based on a constant effective charge and a sudden decrease, which occurs way before the expected gradual decrease. Our observations suggest a relation of the non-monotonic behavior to a decrease in particle charge, and we tentatively discuss possibly underlying mechanisms.
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Affiliation(s)
- Denis Botin
- Institute of Physics, Johannes Gutenberg University, 55128 Mainz, Germany
| | - Felix Carrique
- Institute Carlos I for Theoretical and Computational Physics (iC1), Departamento de Física Aplicada I, Facultad de Ciencias, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain
| | - Emilio Ruiz-Reina
- Institute Carlos I for Theoretical and Computational Physics (iC1), Departamento de Física Aplicada II, Escuela de Ingenierías Industriales, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain
| | - Thomas Palberg
- Institute of Physics, Johannes Gutenberg University, 55128 Mainz, Germany
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9
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Bakhshandeh A, Frydel D, Diehl A, Levin Y. Charge Regulation of Colloidal Particles: Theory and Simulations. PHYSICAL REVIEW LETTERS 2019; 123:208004. [PMID: 31809122 DOI: 10.1103/physrevlett.123.208004] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2019] [Indexed: 06/10/2023]
Abstract
To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem with the NP approach is traced back to the use of a bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is nontrivially related to the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of pH and salt concentration.
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Affiliation(s)
- Amin Bakhshandeh
- Programa de Pós-Graduação em Física, Instituto de Física e Matemática, Universidade Federal de Pelotas, Caixa Postal 354, CEP 96010-900 Pelotas, Rio Grande do Sul, Brazil
| | - Derek Frydel
- Department of Chemistry, Federico Santa Maria Technical University, Campus San Joaquin, 7820275 Santiago, Chile
| | - Alexandre Diehl
- Departamento de Física, Instituto de Física e Matemática, Universidade Federal de Pelotas, Caixa Postal 354, CEP 96010-900 Pelotas, Rio Grande do Sul, Brazil
| | - Yan Levin
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, CEP 91501-970 Porto Alegre, Rio Grande do Sul, Brazil
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10
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Bareigts G, Labbez C. Jellium and cell model for titratable colloids with continuous size distribution. J Chem Phys 2019; 149:244903. [PMID: 30599741 DOI: 10.1063/1.5066074] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A good understanding and determination of colloidal interactions is paramount to comprehend and model the thermodynamic and structural properties of colloidal suspensions. In concentrated aqueous suspensions of colloids with a titratable surface charge, this determination is, however, complicated by the density dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addition, colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper, we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided. The methods, inspired by the seminal work of Torres et al., [J. Chem. Phys. 128, 154906 (2008)] are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various commercially available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calculated. The importance of size and charge polydispersity as well as the validity of these two models is discussed in light of the results.
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Affiliation(s)
- Guillaume Bareigts
- ICB UMR 6303 CNRS, University of Bourgogne Franche-Comté, FR-21000 Dijon, France
| | - Christophe Labbez
- ICB UMR 6303 CNRS, University of Bourgogne Franche-Comté, FR-21000 Dijon, France
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11
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Takae K, Tanaka H. Hydrodynamic simulations of charge-regulation effects in colloidal suspensions. SOFT MATTER 2018; 14:4711-4720. [PMID: 29850748 DOI: 10.1039/c8sm00579f] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Self-organization of charged soft matter is of crucial importance in biology. However, it is an extremely complex phenomenon due to dynamical couplings between the hydrodynamic flow, ions, and charges of soft matter. For colloidal suspensions, the coupling between the former two has already been studied by numerical simulations, with the colloid surface charge being fixed. However, the self-organization of colloids and/or the application of an external electric field make the electrostatic environment of each colloid inhomogeneous in both space and time. Thus, this leads to inhomogenisation of the surface charge of each colloid under ionisation equilibrium conditions. This effect is known as "charge regulation" and is of great importance in various electrostatic and electrokinetic phenomena not only in colloid suspensions but also in solutions of biomolecules. However, there has so far been no success in taking the charge regulation effect into account in numerical simulations of colloidal electrokinetics. Here, we extend the fluid particle dynamics (FPD) method to incorporate the charge regulation effect. We present a theoretical formulation of the method and its application to two types of problems, where charge regulation plays an important role: (i) cluster formation of colloid particles and (ii) a single colloid particle under an external field. By these examples, we show not only the importance of considering charge-regulation effects in the self-organization of charged systems but also the applicability of our simulation method to more complex problems of charged soft matter systems.
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Affiliation(s)
- Kyohei Takae
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.
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12
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Heinen M. Calculating particle pair potentials from fluid-state pair correlations: Iterative ornstein-zernike inversion. J Comput Chem 2018; 39:1531-1543. [DOI: 10.1002/jcc.25225] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2017] [Revised: 03/22/2018] [Accepted: 03/24/2018] [Indexed: 11/08/2022]
Affiliation(s)
- Marco Heinen
- División de Ciencias e Ingenierías, Departamento de Ingeniería Física; University of Guanajuato, Loma del Bosque 103; León 37150 Mexico
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13
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Banchio AJ, Heinen M, Holmqvist P, Nägele G. Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles. J Chem Phys 2018; 148:134902. [PMID: 29626910 DOI: 10.1063/1.5017969] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, fc(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of fc(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with fc(q, t), there is indication of long-time exponential decay of fc(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of fc(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for fc(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, fs(q, t), and its non-Gaussian parameter α2(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from fc(q, t) is theoretically validated.
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Affiliation(s)
- Adolfo J Banchio
- Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, Córdoba, Argentina
| | - Marco Heinen
- División de Ciencias e Ingenierías, Universidad de Guanajuato, 37150 León, Guanajuato, Mexico
| | - Peter Holmqvist
- Division of Physical Chemistry, Lund University, Lund SE-221 00, Sweden
| | - Gerhard Nägele
- Institut für Theoretische Physik II, Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany
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14
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Denton AR. Effective electrostatic interactions in colloid-nanoparticle mixtures. Phys Rev E 2017; 96:062610. [PMID: 29347449 DOI: 10.1103/physreve.96.062610] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Indexed: 06/07/2023]
Abstract
Interparticle interactions and bulk properties of colloidal suspensions can be substantially modified by the addition of nanoparticles. Extreme asymmetries in size and charge between colloidal particles and nanoparticles present severe computational challenges to molecular-scale modeling of such complex systems. We present a statistical mechanical theory of effective electrostatic interactions that can greatly ease large-scale modeling of charged colloid-nanoparticle mixtures. By applying a sequential coarse-graining procedure, we show that a multicomponent mixture of charged colloids, nanoparticles, counterions, and coions can be mapped first onto a binary mixture of colloids and nanoparticles and then onto a one-component model of colloids alone. In a linear-response approximation, the one-component model is governed by a single effective pair potential and a one-body volume energy, whose parameters depend nontrivially on nanoparticle size, charge, and concentration. To test the theory, we perform molecular dynamics simulations of the two-component and one-component models and compute structural properties. For moderate electrostatic couplings, colloid-colloid radial distribution functions and static structure factors agree closely between the two models, validating the sequential coarse-graining approach. Nanoparticles of sufficient charge and concentration enhance screening of electrostatic interactions, weakening correlations between charged colloids and destabilizing suspensions, consistent with experiments.
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Affiliation(s)
- Alan R Denton
- Department of Physics, North Dakota State University, Fargo, North Dakota 58108-6050, USA
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15
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Vangara R, Brown D, van Swol F, Petsev D. Electrolyte solution structure and its effect on the properties of electric double layers with surface charge regulation. J Colloid Interface Sci 2017; 488:180-189. [DOI: 10.1016/j.jcis.2016.10.084] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2016] [Revised: 10/26/2016] [Accepted: 10/27/2016] [Indexed: 10/20/2022]
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16
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García de Soria MI, Álvarez CE, Trizac E. Renormalized jellium model for colloidal mixtures. Phys Rev E 2016; 94:042609. [PMID: 27841649 DOI: 10.1103/physreve.94.042609] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2016] [Indexed: 11/07/2022]
Abstract
In an attempt to quantify the role of polydispersity in colloidal suspensions, we present an efficient implementation of the renormalized jellium model for a mixture of spherical charged colloids. The different species may have different size, charge, and density. Advantage is taken from the fact that the electric potential pertaining to a given species obeys a Poisson's equation that is species independent; only boundary conditions do change from one species to the next. All species are coupled through the renormalized background (jellium) density, that is determined self-consistently. The corresponding predictions are compared to the results of Monte Carlo simulations of binary mixtures, where Coulombic interactions are accounted for exactly, at the primitive model level (structureless solvent with fixed dielectric permittivity). An excellent agreement is found.
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Affiliation(s)
| | - Carlos E Álvarez
- Facultad de Ciencias Naturales y Matemáticas, Universidad del Rosario, Calle 12C No. 6-25, Bogotá, Colombia
| | - Emmanuel Trizac
- LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
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17
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Okamoto R, Onuki A. Ionization at a solid-water interface in an applied electric field: Charge regulation. J Chem Phys 2016; 145:124706. [PMID: 27782653 DOI: 10.1063/1.4963100] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate ionization at a solid-water interface in an applied electric field. We attach an electrode to a dielectric film bearing silanol or carboxyl groups with an areal density Γ0, where the degree of dissociation α is determined by the proton density in water close to the film. We show how α depends on the density n0 of NaOH in water and the surface charge density σm on the electrode. For σm > 0, the protons are expelled away from the film, leading to an increase in α. In particular, in the range 0 < σm < eΓ0, self-regulation occurs to realize α ≅ σm/eΓ0 for n0 ≪ nc, where nc is 0.01 mol/L for silica surfaces and is 2 × 10-5 mol/L for carboxyl-bearing surfaces. We also examine the charge regulation with decreasing the cell thickness H below the Debye length κ-1, where a crossover occurs at the Gouy-Chapman length. In particular, when σm ∼ eΓ0 and H ≪ κ-1, the surface charges remain only partially screened by ions, leading to a nonvanishing electric field in the interior.
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Affiliation(s)
- Ryuichi Okamoto
- Department of Chemistry, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
| | - Akira Onuki
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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18
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Fleharty ME, van Swol F, Petsev DN. Solvent Role in the Formation of Electric Double Layers with Surface Charge Regulation: A Bystander or a Key Participant? PHYSICAL REVIEW LETTERS 2016; 116:048301. [PMID: 26871358 DOI: 10.1103/physrevlett.116.048301] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2015] [Indexed: 06/05/2023]
Abstract
The charge formation at interfaces involving electrolyte solutions is due to the chemical equilibrium between the surface reactive groups and the potential determining ions in the solution (i.e., charge regulation). In this Letter we report our findings that this equilibrium is strongly coupled to the precise molecular structure of the solution near the charged interface. The neutral solvent molecules dominate this structure due to their overwhelmingly large number. Treating the solvent as a structureless continuum leads to a fundamentally inadequate physical picture of charged interfaces. We show that a proper account of the solvent effect leads to an unexpected and complex system behavior that is affected by the molecular and ionic excluded volumes and van der Waals interactions.
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Affiliation(s)
- Mark E Fleharty
- Department of Chemical and Biological Engineering, and Center for Micro-Engineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Frank van Swol
- Department of Chemical and Biological Engineering, and Center for Micro-Engineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Dimiter N Petsev
- Department of Chemical and Biological Engineering, and Center for Micro-Engineered Materials, University of New Mexico, Albuquerque, New Mexico 87131, USA
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Trefalt G, Behrens SH, Borkovec M. Charge Regulation in the Electrical Double Layer: Ion Adsorption and Surface Interactions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2016; 32:380-400. [PMID: 26599980 DOI: 10.1021/acs.langmuir.5b03611] [Citation(s) in RCA: 168] [Impact Index Per Article: 21.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Charge regulation in the electrical double layer has important implications for ion adsorption, interparticle forces, colloidal stability, and deposition phenomena. Although charge regulation generally receives little attention, its consequences can be major, especially when considering interactions between unequally charged surfaces. The present article discusses common approaches to quantify such phenomena, especially within classical Poisson-Boltzmann theory, and pinpoints numerous situations where a consideration of charge regulation is essential. For the interpretation of interaction energy profiles, we advocate the use of the constant regulation approximation, which summarizes the surface properties in terms of two quantities, namely, the diffuse layer potential and the regulation parameter. This description also captures some pronounced regulation effects observed in the presence of multivalent ions.
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Affiliation(s)
- Gregor Trefalt
- Department of Inorganic and Analytical Chemistry, University of Geneva , Sciences II, 30 Quai Ernest-Ansermet, 1205 Geneva, Switzerland
| | - Sven Holger Behrens
- School of Chemical and Biomolecular Engineering, Georgia Institute of Technology , Atlanta, Georgia 30332-0100, United States
| | - Michal Borkovec
- Department of Inorganic and Analytical Chemistry, University of Geneva , Sciences II, 30 Quai Ernest-Ansermet, 1205 Geneva, Switzerland
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Makuch K, Heinen M, Abade GC, Nägele G. Rotational self-diffusion in suspensions of charged particles: simulations and revised Beenakker-Mazur and pairwise additivity methods. SOFT MATTER 2015; 11:5313-5326. [PMID: 26054032 DOI: 10.1039/c5sm00056d] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a comprehensive joint theory-simulation study of rotational self-diffusion in suspensions of charged particles whose interactions are modeled by the generic hard-sphere plus repulsive Yukawa (HSY) pair potential. Elaborate, high-precision simulation results for the short-time rotational self-diffusion coefficient, D(r), are discussed covering a broad range of fluid-phase state points in the HSY model phase diagram. The salient trends in the behavior of D(r) as a function of reduced potential strength and range, and particle concentration, are systematically explored and physically explained. The simulation results are further used to assess the performance of two semi-analytic theoretical methods for calculating D(r). The first theoretical method is a revised version of the classical Beenakker-Mazur method (BM) adapted to rotational diffusion which includes a highly improved treatment of the salient many-particle hydrodynamic interactions. The second method is an easy-to-implement pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a full two-body level with lubrication corrections included. The static pair correlation functions required as the only input to both theoretical methods are calculated using the accurate Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it significantly underestimates D(r). In contrast, the PA method agrees well with the simulation results for D(r) even for intermediately concentrated systems. A simple improvement of the PA method is presented which is applicable for large concentrations.
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Affiliation(s)
- Karol Makuch
- Faculty of Physics, Institute of Theoretical Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland.
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Gapinski J, Nägele G, Patkowski A. Freezing lines of colloidal Yukawa spheres. II. Local structure and characteristic lengths. J Chem Phys 2014; 141:124505. [DOI: 10.1063/1.4895965] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jacek Gapinski
- Molecular Biophysics Division, Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
- NanoBioMedical Center, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
| | - Gerhard Nägele
- Institute of Complex Systems (ICS-3), Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Adam Patkowski
- Molecular Biophysics Division, Faculty of Physics, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
- NanoBioMedical Center, A. Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland
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Palberg T. Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2014; 26:333101. [PMID: 25035303 DOI: 10.1088/0953-8984/26/33/333101] [Citation(s) in RCA: 51] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.
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Affiliation(s)
- Thomas Palberg
- Institut für Physik, Johannes Gutenberg Universität Mainz, 55099 Mainz, Germany
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