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Yang X, Scacchi A, Vahid H, Sammalkorpi M, Ala-Nissila T. Interaction between two polyelectrolytes in monovalent aqueous salt solutions. Phys Chem Chem Phys 2022; 24:21112-21121. [PMID: 36018307 DOI: 10.1039/d2cp02066a] [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 use the recently developed soft-potential-enhanced Poisson-Boltzmann (SPB) theory to study the interaction between two parallel polyelectrolytes (PEs) in monovalent ionic solutions in the weak-coupling regime. The SPB theory is fitted to ion distributions from coarse-grained molecular dynamics (MD) simulations and benchmarked against all-atom MD modelling for poly(diallyldimethylammonium) (PDADMA). We show that the SPB theory is able to accurately capture the interactions between two PEs at distances beyond the PE radius. For PDADMA positional correlations between the charged groups lead to locally asymmetric PE charge and ion distributions. This gives rise to small deviations from the SPB prediction that appear as short-range oscillations in the potential of mean force. Our results suggest that the SPB theory can be an efficient way to model interactions in chemically specific complex PE systems.
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Affiliation(s)
- Xiang Yang
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland.
| | - Alberto Scacchi
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland. .,Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.,Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
| | - Hossein Vahid
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland. .,Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.,Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
| | - Maria Sammalkorpi
- Department of Chemistry and Materials Science, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.,Academy of Finland Center of Excellence in Life-Inspired Hybrid Materials (LIBER), Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland.,Department of Bioproducts and Biosystems, Aalto University, P.O. Box 16100, FI-00076 Aalto, Finland
| | - Tapio Ala-Nissila
- Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland. .,QTF Center of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11000, FI-00076 Aalto, Finland.,Interdisciplinary Center for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, UK
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Investigation about validity of the Derjaguin approximation for electrostatic interactions for a sphere-sphere system. Colloid Polym Sci 2019. [DOI: 10.1007/s00396-019-04469-7] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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3
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Relaxation Effect on Intrapore Diffusivities of Highly Charged Colloidal Particles Confined in Porous Membranes. Transp Porous Media 2018. [DOI: 10.1007/s11242-018-1046-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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An innovative approach to preparation of particles with optimal size distribution: an example of SiO2. J Taiwan Inst Chem Eng 2011. [DOI: 10.1016/j.jtice.2010.08.004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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A novel method to control inner and outer haze of an anti-glare film by surface modification of light-scattering particles. J Colloid Interface Sci 2010; 350:421-6. [DOI: 10.1016/j.jcis.2010.07.014] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2010] [Revised: 07/08/2010] [Accepted: 07/09/2010] [Indexed: 11/20/2022]
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7
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Liu BT, Hsu JP. Analytic expressions for electrical energy and electrical force of two spheres. J Chem Phys 2009; 130:044106. [DOI: 10.1063/1.3067877] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Tseng S, Wong NB, Liu PC, Hsu JP. Approximate analytical expressions for the electrical potential in a cavity containing salt-free medium. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2007; 23:10448-54. [PMID: 17854213 DOI: 10.1021/la7017456] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
The electrical potential in a closed surface such as a cavity containing counterions only is derived for the cases of constant surface potential and constant surface charge density. The results obtained have applications in, for example, microemulsion-related systems in which ionic surfactants are introduced to maintain the stability of a dispersion and electroosmotic flow-related analysis. An analytical expression for the electrical potential is derived for a planar slit, and the methodology used is modified to derive approximate analytical expressions for spherical and cylindrical cavities. The higher the surface potential, the better the performance of these expressions. For the case where the surface potential is above ca. 50 mV, the performance of the approximate analytical expressions can further be improved by multiplying a correction function.
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Affiliation(s)
- Shiojenn Tseng
- Department of Mathematics, Tamkang University, Tamsui, Taipei, Taiwan 25137
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Hsu JP, Yu HY, Tseng S. Approximate Analytical Expressions for the Electrical Potential between Two Planar, Cylindrical, and Spherical Surfaces. J Phys Chem B 2006; 110:25007-12. [PMID: 17149923 DOI: 10.1021/jp062704m] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Approximate analytical expressions for the electrical potential of planar, cylindrical, and spherical surfaces are derived for the case in which the dispersion medium contains counterions only. On the basis of the results for single surfaces, those for two identical surfaces can be derived. The curvature effect of a surface on the electrical potential distribution can be neglected when the order of its radius exceeds approximately 100 times the thickness of the corresponding double layer. If this effect needs to be considered, it can be taken into account by multiplying a correction function by the electrical potential of a planar surface. The electrical potential at the center between two derived surfaces is readily applicable to the evaluation of the electrostatic force per unit area between two surfaces, or the osmotic pressure. For the same set of parameters, the magnitudes of the osmotic pressure for various types of surfaces rank as follows: planar surface > cylindrical surfaces > spherical surfaces.
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Affiliation(s)
- Jyh-Ping Hsu
- Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617
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10
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Thermodynamics of the solid/liquid interface - its application to adsorption and colloid stability. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/s1573-4285(06)80050-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
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11
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Chun MS, Bowen WR. Rigorous calculations of linearized Poisson–Boltzmann interaction between dissimilar spherical colloids and osmotic pressure in concentrated dispersions. J Colloid Interface Sci 2004; 272:330-9. [PMID: 15028495 DOI: 10.1016/j.jcis.2003.12.005] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2003] [Accepted: 12/02/2003] [Indexed: 11/22/2022]
Abstract
We present computational results on the static properties of concentrated dispersions of bidisperse colloids. The long-range electrostatic interactions between dissimilar spherical colloids are determined using the singularity method, which provides rigorous solutions to the linearized electrostatic field. The NVT Monte Carlo simulation is applied to the bulk suspension to obtain the radial distribution function for the concentrated system. The increasing trend of osmotic pressure with increasing total particle concentration is reduced as the concentration ratio between large and small particles is increased. The increase of electrostatic interaction between similarly charged particles caused by the Debye screening effect provides an increase in the osmotic pressure. From the estimation of total structure factor, we observe the strong correlations developed between dissimilar spheres, and the small spheres are expected to tend to fit into the spaces between the larger ones. As the particle concentration increases at a given ionic strength, the magnitude of the first peak in structure factors increases and also moves to higher wavenumber values.
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Affiliation(s)
- Myung-Suk Chun
- Complex Fluids and Membrane Team, Korea Institute of Science and Technology, P.O. Box 131, Cheongryang, Seoul 130-650, South Korea.
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Kallay N, Zalac S. Stability of Nanodispersions: A Model for Kinetics of Aggregation of Nanoparticles. J Colloid Interface Sci 2002; 253:70-6. [PMID: 16290832 DOI: 10.1006/jcis.2002.8476] [Citation(s) in RCA: 108] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2001] [Accepted: 05/09/2002] [Indexed: 11/22/2022]
Abstract
In the course of aggregation of very small colloid particles (nanoparticles) the overlap of the diffuse layers is practically complete, so that one cannot apply the common DLVO theory. Since nanopoarticles are small compared to the extent of the diffuse layer, the process is considered in the same way as for two interacting ions. Therefore, the Brønsted concept based on the Transition State Theory was applied. The charge of interacting nanoparticles was calculated by means of the Surface Complexation Model and decrease of effective charge of particles was also taken into account. Numerical simulations were performed using the parameters for hematite and rutile colloid systems. The effect of pH and electrolyte concentration on the stability coefficient of nanosystems was found to be more pronounced but similar to that for regular colloidal systems. The effect markedly depends on the nature of the solid which is characterized by equilibrium constants of surface reactions responsible for surface charge, i.e., by the point of zero charge, while the specificity of counterions is described by their association affinity, i.e., by surface association equilibrium constants. The most pronounced is the particle size effect. It was shown that extremely small particles cannot be stabilized by an electrostatic repulsion barrier. Additionally, at the same mass concentration, nanoparticles aggregate more rapidly than ordinary colloidal particles due to thier higher number concentration.
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Affiliation(s)
- Nikola Kallay
- Department of Chemistry, Faculty of Science, University of Zagreb, Marulićev trg 19, P.O. Box 163, Zagreb, HR 10000, Croatia.
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Interparticle force between like-charged colloidal systems: a numerical study. Colloids Surf A Physicochem Eng Asp 2001. [DOI: 10.1016/s0927-7757(00)00819-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Sun N, Walz JY. A Model for Calculating Electrostatic Interactions between Colloidal Particles of Arbitrary Surface Topology. J Colloid Interface Sci 2001; 234:90-105. [PMID: 11161495 DOI: 10.1006/jcis.2000.7248] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
A numerical model for calculating the electrostatic interaction between two particles of arbitrary shape and topology is described. A key feature of the model is a generalized discretization program, capable of simulating any desired analytical shape as a set of flat, triangular elements. The relative sizes of the elements are adjusted using a density function to better match the desired shape and the spatial variation of the electrical surface properties on each particle. The distribution of either surface potential or surface charge density is then calculated using a boundary element approach to solve the linearized Poisson-Boltzmann equation. Example interaction energy profiles are calculated for three different types of roughness-bumps, pits, and surface waves. It is found that the interaction energy between rough particles remains different from that between two equivalent smooth spheres at all separations, even for gap widths much larger than either the solution Debye length or the characteristic roughness size. This behavior at large gap widths arises from the nature of the decay of the electric potential away from each particle. In addition, the magnitude of the roughness effect is found to depend greatly on the size and shape of the nonuniformity as well as the electrostatic boundary conditions. For example, for a sphere containing asperities of height equal to 0.2 times the particle radius, the interaction energy can be as much as 50% greater than that between two equivalent spheres under the condition of constant surface potential. At constant surface charge density, the ratio of the interaction energies between rough and smooth spheres was found to either diverge or become zero as contact between the two particles is approached, depending on the nature of the roughness. Changes of this magnitude could clearly have a substantial impact on the stability behavior of a dispersion of such particles. Copyright 2001 Academic Press.
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Affiliation(s)
- Ning Sun
- Department of Chemical Engineering, Yale University, New Haven, Connecticut, 06520
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Gu Y. The Electrical Double-Layer Interaction between a Spherical Particle and a Cylinder. J Colloid Interface Sci 2000; 231:199-203. [PMID: 11082267 DOI: 10.1006/jcis.2000.7110] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Based on the well-known Debye-Hückel approximation and the Derjaguin's integration method, this paper presents an integral solution for the electrical double-layer (EDL) interaction between a spherical particle and a cylinder. The effects of the relative dimensions of the cylinder to the sphere on the EDL interaction are studied using this numerical solution. The detailed numerical results indicate that, in general, the curvature effect on the EDL interaction cannot be neglected at small separation distances. The widely used sphere-flat plate approximation will considerably overestimate the actual EDL interaction between a spherical particle and a cylinder. The ratio of the radius of the particle to the EDL thickness, tau=kappaa(p), also plays an important role in determining the EDL interaction at small dimensionless separation distances (</=3tau(-1)). In addition, it is found that at small separation distances, the EDL interaction can become attractive between two asymmetric EDLs, even though their zeta potentials have the same polarity. Copyright 2000 Academic Press.
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Affiliation(s)
- Y Gu
- Faculty of Engineering, University of Regina, Regina, Saskatchewan, S4S 0A2, Canada
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