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Kroll R, Gottlieb M, Tsori Y. Surface tension between liquids containing antagonistic and regular salts. Eur Phys J E Soft Matter 2023; 46:116. [PMID: 38019306 DOI: 10.1140/epje/s10189-023-00378-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 11/13/2023] [Indexed: 11/30/2023]
Abstract
We investigate theoretically the surface tension between two immiscible liquids containing antagonistic and regular salts. The mean-field model includes the electrostatic energy and the Gibbs transfer energy of the ions. We find the Donnan potential difference between the liquids and solve the Poisson-Boltzmann equation to calculate the potential and ion density profiles. When the liquids contain only a regular salt, the surface tension increases when compared to the no-salt case; in contrast, the surface tension is reduced when they contain only an antagonistic salt. When both salts are present, the surface tension can either further decrease or increase depending on the preferential solvation of the ions, in agreement with published experimental observations.
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Affiliation(s)
- Roni Kroll
- Chemical Engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel.
| | - Moshe Gottlieb
- Chemical Engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel
| | - Yoav Tsori
- Chemical Engineering, Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel
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Seal A, Tiwari U, Gupta A, Govind Rajan A. Incorporating ion-specific van der Waals and soft repulsive interactions in the Poisson-Boltzmann theory of electrical double layers. Phys Chem Chem Phys 2023; 25:21708-21722. [PMID: 37551893 DOI: 10.1039/d3cp00745f] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/09/2023]
Abstract
Electrical double layers (EDLs) arise when an electrolyte is in contact with a charged surface, and are encountered in several application areas including batteries, supercapacitors, electrocatalytic reactors, and colloids. Over the last century, the development of Poisson-Boltzmann (PB) models and their modified versions have provided significant physical insight into the structure and dynamics of the EDL. Incorporation of physics such as finite-ion-size effects, dielectric decrement, and ion-ion correlations has made such models increasingly accurate when compared to more computationally expensive approaches such as molecular simulations and classical density functional theory. However, a prominent knowledge gap has been the exclusion of van der Waals (vdW) and soft repulsive interactions in modified PB models. Although short-ranged as compared to electrostatic interactions, we show here that vdW and soft repulsive interactions can play an important role in determining the structure of the EDL via the formation of a Stern layer and in modulating the differential capacitance of an electrode in an electrolyte. To this end, we incorporate ion-ion and wall-ion vdW attraction and soft repulsion via a 12-6 Lennard-Jones (LJ) potential, resulting in a modified PB-LJ approach. The wall-ion LJ interactions were found to have a significant effect on the electrical potential and concentration profiles, especially close to the wall. However, ion-ion LJ interactions do not affect the EDL structure at low bulk ion concentrations (<1 M). We also derive dimensionless numbers to quantify the impact of ion-ion and wall-ion LJ interactions on the EDL. Furthermore, in the pursuit of capturing ion-specific effects, we apply our model by considering various ions such as Na, K+, Mg2+, Cl-, and SO42-. We observe how varying parameters such as the electrolyte concentration and electrode potential affect the structure of the EDL due to the competition between ion-specific LJ and electrostatic interactions. Lastly, we show that the inclusion of vdW and soft repulsion interactions, as well as hydration effects, leads to a better qualitative agreement of the PB models with experimental double-layer differential capacitance data. Overall, the modified PB-LJ approach presented herein will lead to more accurate theoretical descriptions of EDLs in various application areas.
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Affiliation(s)
- Aniruddha Seal
- School of Chemical Sciences, National Institute of Science Education and Research Bhubaneswar, Homi Bhabha National Institute, Khurda, Odisha 752050, India
- Department of Chemical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012, India.
| | - Utkarsh Tiwari
- Department of Chemical Engineering, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Zuarinagar, Goa 403726, India
- Department of Chemical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012, India.
| | - Ankur Gupta
- Department of Chemical and Biological Engineering, University of Colorado Boulder, Boulder, Colorado 80309, USA
| | - Ananth Govind Rajan
- Department of Chemical Engineering, Indian Institute of Science, Bengaluru, Karnataka 560012, India.
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Nakayama Y. Nonlinear dielectric decrement of electrolyte solutions: An effective medium approach. J Colloid Interface Sci 2023; 646:354-360. [PMID: 37201463 DOI: 10.1016/j.jcis.2023.05.046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2023] [Revised: 04/28/2023] [Accepted: 05/07/2023] [Indexed: 05/20/2023]
Abstract
HYPOTHESIS The dielectric constant of an electrolyte solution, which determines electrostatic interactions between colloids and interfaces, depends nonlinearly on the salinity and also on the type of salt. The linear decrement at dilute solutions is due to the reduced polarizability in the hydration shell around an ion. However, the full hydration volume cannot explain the experimental solubility, which indicates the hydration volume should decrease at high salinity. Volume reduction of the hydration shell is supposed to weaken dielectric decrement and thus should be relevant to the nonlinear decrement. SIMULATIONS According to the effective medium theory for the permittivity of heterogeneous media, we derive an equation which relates the dielectric constant with the dielectric cavities created by the hydrated cations and anions, and the effect of partial dehydration at high salinity is taken into account. FINDINGS Analysis of experiments on monovalent electrolytes suggests that weakened dielectric decrement at high salinity originates primarily from the partial dehydration. Furthermore, the onset volume fraction of the partial dehydration is found to be salt-specific, and is correlated with the solvation free energy. Our results suggest that while the reduced polarizability of the hydration shell determines the linear dielectric decrement at low salinity, ion-specific tendency of dehydration is responsible for nonlinear dielectric decrement at high salinity.
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Affiliation(s)
- Yasuya Nakayama
- Department of Chemical Engineering, Kyushu University, Nishi-ku, Fukuoka, 819-0395, Japan.
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Park YS, Kang IS. Multi-ionic effects on the equilibrium and dynamic properties of electric double layers based on the Bikerman correction. J Electroanal Chem (Lausanne) 2021; 880:114923. [DOI: 10.1016/j.jelechem.2020.114923] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Gupta A, Stone HA. Electrical Double Layers: Effects of Asymmetry in Electrolyte Valence on Steric Effects, Dielectric Decrement, and Ion-Ion Correlations. Langmuir 2018; 34:11971-11985. [PMID: 30153029 DOI: 10.1021/acs.langmuir.8b02064] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the effects of asymmetry in electrolyte valence (i.e., non z: z electrolytes) on mean field theory of the electrical double layer. Specifically, we study the effect of valence asymmetry on finite ion-size effects, the dielectric decrement, and ion-ion correlations. For a model configuration of an electrolyte near a charged surface in equilibrium, we present comprehensive analytical and numerical results for the potential distribution, electrode charge density, capacitance, and dimensionless salt uptake. We emphasize that the asymmetry in electrolyte valence significantly influences the diffuse-charge relations, and prior results reported in the literature are readily extended to non z: z electrolytes. We develop scaling relations and invoke physical arguments to examine the importance of asymmetry in electrolyte valence on the aforementioned effects. We conclude by providing implications of our findings on diffuse-charge dynamics and other electrokinetic phenomena.
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Affiliation(s)
- Ankur Gupta
- Department of Mechanical and Aerospace Engineering , Princeton University , Princeton , New Jersey 08544 , United States
| | - Howard A Stone
- Department of Mechanical and Aerospace Engineering , Princeton University , Princeton , New Jersey 08544 , United States
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6
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López-García J, Horno J, Grosse C. Ion size effects on the dielectric and electrokinetic properties in aqueous colloidal suspensions. Curr Opin Colloid Interface Sci 2016. [DOI: 10.1016/j.cocis.2016.05.006] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Abstract
The nonlinear phenomena that occur in the electric double layer (EDL) that forms at charged surfaces strongly influence electrokinetic effects, including electro-osmosis and electrophoresis. In particular, saturation effects due to either dielectric decrement or ion crowding effects are of paramount importance. Dielectric decrement significantly influences the ionic concentration in the EDL at high ζ potential, leading to the formation of a condensed layer near the particle's surface. In this article, we present a model incorporating both steric effects due to the finite size of ions and dielectric decrement to describe the physics in the electric double layer. The model remains valid in both weakly and strongly nonlinear regimes, as long as the electric double layer remains in quasiequilibrium. We apply this model to the study of two archetypal problems in electrokinetics, namely the electrophoresis of particles with fixed surface charges and the electrophoresis of ideally polarizable particles.
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Affiliation(s)
- B Figliuzzi
- Mines ParisTech, PSL Research University, Center for Mathematical Morphology, 35 rue Saint-Honoré 77305 Fontainebleau Cedex, France
| | - W H R Chan
- Mechanical Engineering Department, Stanford University, 450 Serra Mall CA94305 Stanford, USA
| | - C R Buie
- Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue MA02139 Cambridge, USA
| | - J L Moran
- Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue MA02139 Cambridge, USA
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López-garcía JJ, Horno J, Grosse C. Influence of steric interactions on the dielectric and electrokinetic properties in colloidal suspensions. J Colloid Interface Sci 2015; 458:273-83. [DOI: 10.1016/j.jcis.2015.07.060] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2015] [Revised: 07/24/2015] [Accepted: 07/25/2015] [Indexed: 11/18/2022]
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Maroni P, Montes Ruiz-Cabello FJ, Cardoso C, Tiraferri A. Adsorbed Mass of Polymers on Self-Assembled Monolayers: Effect of Surface Chemistry and Polymer Charge. Langmuir 2015; 31:6045-6054. [PMID: 25993382 DOI: 10.1021/acs.langmuir.5b01103] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The adsorbed mass of polymers on surfaces with different chemistry is presented, and the related adsorption mechanism is discussed. Strong and weak polyelectrolytes of negative and positive charge are studied, as well as an uncharged polymer. Self-assembled monolayers of alkanethiols on gold are used in reflectometry and quartz crystal microbalance (QCM-D) experiments as adsorbing substrates bearing different terminal moieties, namely, methyl, hydroxyl, carboxyl, and amine groups. The various polymer-surface combinations allow the systematic investigation of the role of surface chemistry and polymer charge on adsorbed amount. Interactions of different nature and range drive polymer adsorption: the measured adsorbed amounts reveal information about their relative contribution. When electrostatic chain-surface attraction is present, the largest adsorbed masses are observed. However, significant mass is measured even when an electrostatic barrier to adsorption is present, suggesting the importance of forces of nonelectrostatic origin, which include both hydrophobic interactions and specific forces acting at short distances. This mechanism results in large adsorbed amounts for the adsorption of weak polyelectrolytes, and it is apparent especially in the adsorption behavior of a neutral polymer.
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Affiliation(s)
- Plinio Maroni
- †Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, Quai Ernest-Ansermet 30, 1205 Geneva, Switzerland
| | - Francisco Javier Montes Ruiz-Cabello
- †Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, Quai Ernest-Ansermet 30, 1205 Geneva, Switzerland
- ‡Biocolloid and Fluid Physics Group, Applied Physics Department, Faculty of Sciences, University of Granada, Fuente Nueva s/n, 18071 Granada, Spain
| | - Catia Cardoso
- †Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, Quai Ernest-Ansermet 30, 1205 Geneva, Switzerland
| | - Alberto Tiraferri
- †Department of Inorganic and Analytical Chemistry, University of Geneva, Sciences II, Quai Ernest-Ansermet 30, 1205 Geneva, Switzerland
- §Department of Land, Environment and Infrastructure Engineering (DIATI), Polytechnic University of Turin, C.so Duca degli Abruzzi 24, 10129 Torino, Italy
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Nakayama Y, Andelman D. Differential capacitance of the electric double layer: The interplay between ion finite size and dielectric decrement. J Chem Phys 2015; 142:044706. [DOI: 10.1063/1.4906319] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Affiliation(s)
- Yasuya Nakayama
- Department of Chemical Engineering, Kyushu University, Nishi-ku, Fukuoka 819-0395, Japan
| | - David Andelman
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel
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11
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Spruijt E, Biesheuvel PM, de Vos WM. Adsorption of charged and neutral polymer chains on silica surfaces: the role of electrostatics, volume exclusion, and hydrogen bonding. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:012601. [PMID: 25679636 DOI: 10.1103/physreve.91.012601] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2014] [Indexed: 06/04/2023]
Abstract
We develop an off-lattice (continuum) model to describe the adsorption of neutral polymer chains and polyelectrolytes to surfaces. Our continuum description allows taking excluded volume interactions between polymer chains and ions directly into account. To implement those interactions, we use a modified hard-sphere equation of state, adapted for mixtures of connected beads. Our model is applicable to neutral, charged, and ionizable surfaces and polymer chains alike and accounts for polarizability effects of the adsorbed layer and chemical interactions between polymer chains and the surface. We compare our model predictions to data of a classical system for polymer adsorption: neutral poly(N-vinylpyrrolidone) (PVP) on silica surfaces. The model shows that PVP adsorption on silica is driven by surface hydrogen bonding with an effective maximum binding energy of about 1.3k(B)T per PVP segment at low pH. As the pH increases, the Si-OH groups become increasingly dissociated, leading to a lower capacity for H bonding and simultaneous counterion accumulation and volume exclusion close to the surface. Together these effects result in a characteristic adsorption isotherm, with the adsorbed amount dropping sharply at a critical pH. Using this model for adsorption data on silica surfaces cleaned by either a piranha solution or an O(2) plasma, we find that the former have a significantly higher density of silanol groups.
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Affiliation(s)
- Evan Spruijt
- ESPCI ParisTech, Physique et Mécanique des Milieux Hétérogènes, UMR 7636 du CNRS, 10 rue Vauquelin, 75005 Paris, France and Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
| | - P M Biesheuvel
- Wetsus, European Centre of Excellence for Sustainable Water Technology, Oostergoweg 9, 8911 MA Leeuwarden, The Netherlands and Wageningen University, Laboratory of Physical Chemistry and Colloid Science, Dreijenplein 6, 6703 HB The Netherlands
| | - Wiebe M de Vos
- University of Twente, Membrane Science and Technology, MESA+ Institute of Nanotechnology, P.O. Box 217, 7500 AE Enschede, The Netherlands
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12
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López-García JJ, Horno J, Grosse C. Influence of the finite size and effective permittivity of ions on the equilibrium double layer around colloidal particles in aqueous electrolyte solution. J Colloid Interface Sci 2014; 428:308-15. [DOI: 10.1016/j.jcis.2014.04.065] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2014] [Revised: 04/29/2014] [Accepted: 04/30/2014] [Indexed: 10/25/2022]
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13
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López-García JJ, Horno J, Grosse C. Equilibrium properties of charged spherical colloidal particles suspended in aqueous electrolytes: Finite ion size and effective ion permittivity effects. J Colloid Interface Sci 2012; 380:213-21. [DOI: 10.1016/j.jcis.2012.05.012] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2012] [Revised: 05/07/2012] [Accepted: 05/08/2012] [Indexed: 11/26/2022]
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Xu GK, Feng XQ, Li B, Gao H. Controlled Release and Assembly of Drug Nanoparticles via pH-Responsive Polymeric Micelles: A Theoretical Study. J Phys Chem B 2012; 116:6003-9. [DOI: 10.1021/jp3007816] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Guang-Kui Xu
- Institute of Biomechanics and
Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Xi-Qiao Feng
- Institute of Biomechanics and
Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Bo Li
- College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, China
| | - Huajian Gao
- School of Engineering, Brown University, Providence, Rhode Island 02912, United
States
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15
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López-García JJ, Horno J, Grosse C. Poisson-Boltzmann description of the electrical double layer including ion size effects. Langmuir 2011; 27:13970-13974. [PMID: 22035520 DOI: 10.1021/la2025445] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The electrical double layer is examined using a generalized Poisson-Boltzmann equation that takes into account the finite ion size by modeling the aqueous electrolyte solution as a suspension of polarizable insulating spheres in water. We find that this model greatly amplifies the steric effects predicted by the usual modified Poisson-Boltzmann equation, which imposes only a restriction on the ability of ions to approach one another. This amplification should allow for an interpretation of the experimental results using reasonable effective ionic radii (close to their well-known hydrated values).
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Affiliation(s)
- José Juan López-García
- Departamento de Física, Universidad de Jaén, Campus Las Lagunillas, Ed. A-3, 23071 Jaén, Spain
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Saito T, Koopal LK, Nagasaki S, Tanaka S. Adsorption of Heterogeneously Charged Nanoparticles on a Variably Charged Surface by the Extended Surface Complexation Approach: Charge Regulation, Chemical Heterogeneity, and Surface Complexation. J Phys Chem B 2008; 112:1339-49. [DOI: 10.1021/jp076621x] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Takumi Saito
- Department of Quantum Engineering and Systems Science, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan, Nuclear Professional School, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, and Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703HB Wageningen, The Netherlands
| | - Luuk K. Koopal
- Department of Quantum Engineering and Systems Science, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan, Nuclear Professional School, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, and Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703HB Wageningen, The Netherlands
| | - Shinya Nagasaki
- Department of Quantum Engineering and Systems Science, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan, Nuclear Professional School, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, and Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703HB Wageningen, The Netherlands
| | - Satoru Tanaka
- Department of Quantum Engineering and Systems Science, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan, Nuclear Professional School, School of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, and Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703HB Wageningen, The Netherlands
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Biesheuvel PM, Lindhoud S, Cohen Stuart MA, de Vries R. Phase behavior of mixtures of oppositely charged protein nanoparticles at asymmetric charge ratios. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 73:041408. [PMID: 16711801 DOI: 10.1103/physreve.73.041408] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2006] [Indexed: 05/09/2023]
Abstract
We present experimental and theoretical results for the phase behavior of mixtures of oppositely charged globular protein molecules in aqueous solutions containing monovalent salt. These colloidal mixtures are interesting model systems, on the one hand for electrolyte solutions ("colloidal ionic liquids"), and on the other for mixtures of oppositely charged (bio)macromolecules, colloids, micelles, etc., with the range of the electrostatic interactions (Debye length) easily tunable from much smaller to much larger than the particle size, simply by adding different amounts of monovalent salt. In this paper we investigate the phase behavior of such mixtures in the case that equally sized colloids have a large difference in charge magnitude. This is possible at any mixing ratio because small ions compensate any colloidal charge asymmetry. Our experimental system is based on lysozyme, a positively charged "hard" globular protein molecule, and succinylated lysozyme, a chemical modification of lysozyme which is negatively charged. By changing the solution pH we can adjust the ratio of charge between the two molecules. To describe phase separation into a dilute phase and a dense "complex" phase, a thermodynamic model is set up in which we combine the Carnahan-Starling-van der Waals equation of state with a heterogeneous Poisson-Boltzmann cell model and include the possibility that protein molecules adjust their charge when they move from one phase to the other (charge regulation). The theory uses the nonelectrostatic attraction strength as the only adjustable parameter and reasonably well reproduces the data in that complexation is only possible at intermediate , not too asymmetric mixing ratios, and low enough ionic strength and temperature.
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Affiliation(s)
- P Maarten Biesheuvel
- Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, The Netherlands
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Abstract
The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction dominates, the boundary condition is the same as that of the neutral polymer adsorption. For highly charged polymer (compressed state) in which the electrostatic interaction dominates, the linear relationship (electrostatic boundary condition) between the surface monomer density and the surface charge density needs to be modified.
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Affiliation(s)
- Chi-Ho Cheng
- Institute of Physics, Academia Sinica, Taipei, Taiwan.
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Biesheuvel PM, Leermakers FAM, Stuart MAC. Self-consistent field theory of protein adsorption in a non-Gaussian polyelectrolyte brush. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 73:011802. [PMID: 16486177 DOI: 10.1103/physreve.73.011802] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2005] [Indexed: 05/06/2023]
Abstract
To describe adsorption of globular protein molecules in a polyelectrolyte brush we use the strong-stretching approximation of the Edwards self-consistent field equation, combined with corrections for a non-Gaussian brush. To describe chemical potentials in this mixture of (globular) species of widely varying sizes (ions, brush polyelectrolyte segments, globular protein molecules), we use the Boublik-Mansoori-Carnahan-Starling-Leland equation of state derived for polydisperse mixtures of spherical particles. The polyelectrolyte chain is described in this approach as a string of beads with the beads of a size related to the chain diameter. We use the one-dimensional Poisson equation to describe the electrostatic field and include the ionizable character of both the brush polyions and the protein molecules. This model explains the experimental observation of high amounts of protein adsorption in a polyacid brush for values above the isoelectric point of the protein as being due to charge reversal of the protein molecules upon entry in the brush. We find a distinct minimum in protein concentration near the edge of the brush. With increasing this barrier to protein transfer becomes larger, but much less so when we increase the ionic strength, a difference that might relate to an experimentally observed difference in the protein release rate in these two cases. A free energy analysis shows that the release of small ions from the brush and the increase of brush ionization are the two driving forces for protein adsorption in a like-charged brush.
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Affiliation(s)
- P Maarten Biesheuvel
- Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, The Netherlands.
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