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Madhavan N, Deshpande AP, Mani E, Basavaraj MG. Electrostatic Heteroaggregation: Fundamentals and Applications in Interfacial Engineering. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:2112-2134. [PMID: 36727572 DOI: 10.1021/acs.langmuir.2c02681] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
The aggregation of oppositely charged soft materials (particles, surfactants, polyelectrolytes, etc.) that differ in one or more physical or chemical attributes, broadly referred to as electrostatic heteroaggregation, has been an active area of research for several decades now. While electrostatic heteroaggregation (EHA) is relevant to diverse fields such as environmental engineering, food technology, and pharmaceutical formulations, more recently there has been a resurgence to explore various aspects of this phenomenon in the context of interface stabilization and the development of functional materials. In this Feature Article, we provide an overview of the recent contributions of our group to this exciting field with particular emphasis on fundamental studies of electrostatic heteroaggregation between oppositely charged systems in the bulk, at interfaces, and across the bulk/interface. The influence of the size and shape of particles and the surface charge of heteroaggregates on the formation of Pickering emulsions and their utilization in the development of porous ceramics is discussed.
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Affiliation(s)
- Nithin Madhavan
- Polymer Engineering and Colloid Sciences Laboratory, Department of Chemical Engineering, Indian Institute of Technology Madras, Sardar Patel Road, Adyar, IIT P.O., Chennai600036, India
| | - Abhijit P Deshpande
- Polymer Engineering and Colloid Sciences Laboratory, Department of Chemical Engineering, Indian Institute of Technology Madras, Sardar Patel Road, Adyar, IIT P.O., Chennai600036, India
| | - Ethayaraja Mani
- Polymer Engineering and Colloid Sciences Laboratory, Department of Chemical Engineering, Indian Institute of Technology Madras, Sardar Patel Road, Adyar, IIT P.O., Chennai600036, India
| | - Madivala G Basavaraj
- Polymer Engineering and Colloid Sciences Laboratory, Department of Chemical Engineering, Indian Institute of Technology Madras, Sardar Patel Road, Adyar, IIT P.O., Chennai600036, India
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2
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Yuan J, Takae K, Tanaka H. Impact of Charge Regulation on Self-Assembly of Zwitterionic Nanoparticles. PHYSICAL REVIEW LETTERS 2022; 128:158001. [PMID: 35499868 DOI: 10.1103/physrevlett.128.158001] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
Zwitterionic modification of colloids with weak acids and bases represents a promising strategy in creating functional materials with tunable properties and modeling the self-organization of charged proteins. However, accurate incorporation of the dynamic dissociation or association of ionization groups known as charge regulation (CR) is often intractable in theoretical and computational investigations since charge redistribution and configuration need to be evolved self-consistently. Using hybrid Monte Carlo and molecular dynamics simulations, we demonstrate that a dilute suspension of overall charge-neutral zwitterionic Janus nanoparticles shows a conformational transition from an open assembly of string or bundle to compact cluster along with the variation in pH. The behavior under CR is qualitatively different from the commonly employed constant charge condition where the transition is absent. The CR-induced clustering is due to the inhomogeneous and fluctuating charges localized near the equatorial boundary of the Janus particle. These features are enhanced particularly at low salt concentration and high electrostatic coupling strength. Our results indicate the critical role of charge regulation in the spatial self-organization of zwitterionic nanoparticles.
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Affiliation(s)
- Jiaxing Yuan
- Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan
| | - Kyohei Takae
- Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
| | - Hajime Tanaka
- Research Center for Advanced Science and Technology, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan
- 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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Study of the aggregation behavior of Janus particles by coupling experiments and Brownian dynamics simulations. J Colloid Interface Sci 2021; 583:222-233. [PMID: 33002694 DOI: 10.1016/j.jcis.2020.09.031] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Revised: 09/09/2020] [Accepted: 09/10/2020] [Indexed: 11/23/2022]
Abstract
HYPOTHESIS New colloids such as inverse patchy particles or Janus particles are considered as smart building blocks in the development of innovative and performant materials. For example, the control of the self-assembly of oxide-based charged Janus particles is interesting for ceramic shaping. Thus, the synthesis of silica based Janus particles as well as a detailed study of their behavior in suspension are presented in this paper. EXPERIMENTS Fluorescent silica particles are partially modified in surface by grafting amine groups using a Pickering emulsion route. Zeta potential measurements, sedimentation tests and confocal microscopy observations are carried out to analyze the aggregation of the obtained particles in aqueous suspension as a function of the patch size and of the pH. Brownian dynamics simulations are also performed to better understand the aggregate structures. FINDINGS The aggregation of the synthesized silica-based Janus particles can be tuned by modifying the experimental parameters, and elongated or on the contrary more compact structures could be observed. This control of aggregation makes such particles promising to build new ceramic materials.
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Frungieri G, Babler MU, Vanni M. Shear-Induced Heteroaggregation of Oppositely Charged Colloidal Particles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:10739-10749. [PMID: 32814425 PMCID: PMC8011919 DOI: 10.1021/acs.langmuir.0c01536] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
This paper investigates numerically the shear-induced aggregation of mixed populations of colloidal particles leading to the formation of clusters. Suspensions with different amounts of positively and negatively charged colloidal particles are simulated. To resolve the aggregation kinetics and structural properties of the formed clusters, we resort to a mixed deterministic-stochastic simulation method. The method is built on a combination of a Monte Carlo algorithm to sample a statistically expected sequence of encounter events between the suspended particles and a discrete element method built in the framework of Stokesian dynamics to simulate the encounters in a fully predictive manner. Results reveal a strong influence of the composition of the population on both the aggregation kinetics and the aggregate structure. In particular, we observe a size-stabilization phenomenon taking place in the suspension when the relative concentration of the majority particles lies in the range 80-85%; i.e., starting from primary particles, after a short growth period, we observed a cessation of aggregation. Inspection of the aggregate morphology shows that the formed clusters are composed of few minority particles placed in the inner region, while the aggregate surface is covered by majority particles, acting to provide a shielding effect against further growth.
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Affiliation(s)
- Graziano Frungieri
- Department of Applied
Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
| | - Matthaus U. Babler
- Department of Chemical Engineering, KTH
Royal Institute of Technology, Teknikringen 42, SE-10044 Stockholm, Sweden
| | - Marco Vanni
- Department of Applied
Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Turin, Italy
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Laganapan A, Cerbelaud M, Ferrando R, Tran CT, Crespin B, Videcoq A. Computer simulations of heteroaggregation with large size asymmetric colloids. J Colloid Interface Sci 2018; 514:694-703. [PMID: 29310099 DOI: 10.1016/j.jcis.2017.12.071] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2017] [Revised: 12/22/2017] [Accepted: 12/26/2017] [Indexed: 11/24/2022]
Abstract
HYPOTHESIS Hetero-aggregation of inorganic colloids is influenced by numerous parameters, which dictate the suspension properties. When particles are different in size, the suspension can be either stable or unstable according to concentration of components, ionic strength, and pH. Experimentally, understanding the role of each parameter is sometimes difficult because parameters cannot easily be modified independently. Numerical simulations are thus very useful to discriminate between different effects. SIMULATIONS Brownian dynamics simulations are used here to study the heteroaggregation of dilute suspensions composed of two populations of colloids with large size asymmetry. Special attention is paid to the effect of small-particle concentration, surface potentials, and ionic strength. FINDINGS The simulation results show that hetero-aggregation can be tuned by modifying these different parameters, and that the resulting aggregate structures depend more on the surface properties of small particles than on those of large particles. The simulations shed light on a further parameter crucially influencing hetero-aggregation, i.e. the mobility of small particles when adsorbed on large ones. The present results rationalize numerous experimental observations reported in the literature and can be used as reference to explain future experimental observations.
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Affiliation(s)
| | | | - Riccardo Ferrando
- Dipartimento di Chimica e Chimica Industriale and CNR-IMEM, I-16146 Genova, Italy
| | - Công Tâm Tran
- Univ. Limoges, CNRS, SPCTS, UMR 7315, F-87000 Limoges, France; Univ. Limoges, CNRS, XLIM, UMR 7252, F-87000 Limoges, France
| | - Benoît Crespin
- Univ. Limoges, CNRS, XLIM, UMR 7252, F-87000 Limoges, France
| | - Arnaud Videcoq
- Univ. Limoges, CNRS, SPCTS, UMR 7315, F-87000 Limoges, France.
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6
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Jeżewski W. Aggregation and fragmentation in liquids with dispersed nanoparticles. Phys Chem Chem Phys 2018; 20:18879-18888. [DOI: 10.1039/c8cp01594e] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
Nanoparticle-induced aggregation and fragmentation phenomena in liquid media are investigated by applying a model of preferential attachment of dispersing molecules to randomly chosen nanoparticles and larger particles, each containing a single nanoparticle.
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Affiliation(s)
- Wojciech Jeżewski
- Institute of Molecular Physics
- Polish Academy of Sciences
- 60-179 Poznań
- Poland
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7
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Bansal P, Deshpande AP, Basavaraj MG. Hetero-aggregation of oppositely charged nanoparticles. J Colloid Interface Sci 2017; 492:92-100. [DOI: 10.1016/j.jcis.2016.12.059] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2016] [Revised: 12/22/2016] [Accepted: 12/25/2016] [Indexed: 10/20/2022]
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8
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Park JD, Myung JS, Ahn KH. A review on particle dynamics simulation techniques for colloidal dispersions: Methods and applications. KOREAN J CHEM ENG 2016. [DOI: 10.1007/s11814-016-0229-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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9
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Zong Y, Yuan G, Han CC. Asymmetrical phase separation and gelation in binary mixtures of oppositely charged colloids. J Chem Phys 2016; 145:014904. [DOI: 10.1063/1.4954993] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yiwu Zong
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Guangcui Yuan
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Department of Polymer Engineering, The University of Akron, Akron, Ohio 44325, USA
| | - Charles C. Han
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
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10
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Lee J, Lee SJ, Ahn KH, Lee SJ. Nanoparticle-Induced Gelation of Bimodal Slurries with Highly Size-Asymmetric Particles: Effect of Surface Chemistry and Concentration. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:13639-13646. [PMID: 26634946 DOI: 10.1021/acs.langmuir.5b03752] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
A systematic study has been performed to investigate the effect of surface potential of nanoparticles on the rheological behavior of bimodal suspensions, using a model system consisting of polystyrene latex (primary size ∼530 nm) and alumina-coated silica (primary size ∼12 nm) particles. The surface potential of small particles was tuned by varying the solution pH, causing them to be repulsive to each other, attractive to each other, and oppositely charged to the large particles, while the large particles remained electrostatically stabilized. We found that the rheological properties could be dramatically changed from viscous to gel-like depending on the surface potential and concentration of small particles. A colloidal gel was induced by small particles when the small particles had the opposite charge to the large particles and a volume fraction of 10(-4) < ϕsmall < 10(-3), and when the small particles were attractive to each other above a critical threshold, ϕsmall > 10(-4). Cryo-SEM distinguished the gel structures to be either short bridging gels produced by oppositely charged small particles or long bridging gels or dense gels produced by attractive small particles. On the basis of this rheological behavior and microstructure, we prepared a phase diagram of highly size-asymmetric bimodal colloids with respect to the surface chemistry and concentration of small particles.
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Affiliation(s)
- Jooyoung Lee
- School of Chemical and Biological Engineering, Institute of Chemical Process, Seoul National University , Seoul 151-744, Korea
| | - Seong Jae Lee
- Department of Polymer Engineering, The University of Suwon , Gyeonggi 445-743, Korea
| | - Kyung Hyun Ahn
- School of Chemical and Biological Engineering, Institute of Chemical Process, Seoul National University , Seoul 151-744, Korea
| | - Seung Jong Lee
- School of Chemical and Biological Engineering, Institute of Chemical Process, Seoul National University , Seoul 151-744, Korea
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11
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How colloid–colloid interactions and hydrodynamic effects influence the percolation threshold: A simulation study in alumina suspensions. J Colloid Interface Sci 2015; 458:241-6. [DOI: 10.1016/j.jcis.2015.07.058] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2015] [Revised: 07/24/2015] [Accepted: 07/24/2015] [Indexed: 11/23/2022]
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12
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Koroleva M, Tokarev A, Yurtov E. Simulation of flocculation in W/O emulsions and experimental study. Colloids Surf A Physicochem Eng Asp 2015. [DOI: 10.1016/j.colsurfa.2015.05.005] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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13
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Cerbelaud M, Lestriez B, Ferrando R, Videcoq A, Richard-Plouet M, Caldes MT, Guyomard D. Numerical and experimental study of suspensions containing carbon blacks used as conductive additives in composite electrodes for lithium batteries. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:2660-2669. [PMID: 24564804 DOI: 10.1021/la404693s] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Suspensions of carbon blacks and spherical carbon particles are studied experimentally and numerically to understand the role of the particle shape on the tendency to percolation. Two commercial carbon blacks and one lab-synthesized spherical carbon are used. The percolation thresholds in suspensions are experimentally determined by two complementary methods: impedance spectroscopy and rheology. Brownian dynamics simulations are performed to explain the experimental results taking into account the fractal shape of the aggregates in the carbon blacks. The results of Brownian dynamics simulations are in good agreement with the experimental results and allow one to explain the experimental behavior of suspensions.
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Affiliation(s)
- Manuella Cerbelaud
- Institut des Matériaux Jean Rouxel (IMN), Université de Nantes, CNRS , 2 rue de la Houssinière, BP32229, 44322 Nantes cedex 3, France
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14
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Tomilov A, Videcoq A, Cerbelaud M, Piechowiak MA, Chartier T, Ala-Nissila T, Bochicchio D, Ferrando R. Aggregation in Colloidal Suspensions: Evaluation of the Role of Hydrodynamic Interactions by Means of Numerical Simulations. J Phys Chem B 2013; 117:14509-17. [DOI: 10.1021/jp407247y] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. Tomilov
- SPCTS, UMR 7315,
ENSCI, CNRS; Centre Européen de la Céramique, 12 rue Atlantis, 87068 Limoges cedex, France
| | - A. Videcoq
- SPCTS, UMR 7315,
ENSCI, CNRS; Centre Européen de la Céramique, 12 rue Atlantis, 87068 Limoges cedex, France
| | - M. Cerbelaud
- Institut
des Matériaux Jean Rouxel (IMN), Université de Nantes, CNRS, 2 rue de la Houssinière, BP32229, 44322 Nantes cedex 3, France
| | - M. A. Piechowiak
- SPCTS, UMR 7315,
ENSCI, CNRS; Centre Européen de la Céramique, 12 rue Atlantis, 87068 Limoges cedex, France
| | - T. Chartier
- SPCTS, UMR 7315,
ENSCI, CNRS; Centre Européen de la Céramique, 12 rue Atlantis, 87068 Limoges cedex, France
| | - T. Ala-Nissila
- Department
of Applied Physics and COMP CoE, Aalto University School of Science, P.O. Box 11000, FI-00076 Aalto, Espoo, Finland
- Department
of Physics, Brown University, Providence, Rhode Island 02912-8143, United States
| | - D. Bochicchio
- Dipartimento
di
Fisica and CNR-IMEM, Via Dodecaneso
33, Genova I-16146, Italy
| | - R. Ferrando
- Dipartimento
di
Fisica and CNR-IMEM, Via Dodecaneso
33, Genova I-16146, Italy
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15
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Dickinson E. Structure and rheology of colloidal particle gels: insight from computer simulation. Adv Colloid Interface Sci 2013; 199-200:114-27. [PMID: 23916723 DOI: 10.1016/j.cis.2013.07.002] [Citation(s) in RCA: 41] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2013] [Revised: 07/08/2013] [Accepted: 07/09/2013] [Indexed: 10/26/2022]
Abstract
A particle gel is a network of aggregated colloidal particles with soft solid-like mechanical properties. Its structural and rheological properties, and the kinetics of its formation, are dependent on the sizes and shapes of the constituent particles, the volume fraction of the particles, and the nature of the interactions between the particles before, during and after gelation. Particle gels may be permanent or transient depending on whether the colloidal forces between the aggregating particles lead to irreversible bonding or weak reversible interactions. With short-range reversible interactions, network formation is typically associated with phase separation or kinetic arrest due to particle crowding. Much existing knowledge has been derived from computer simulations of idealized model systems containing spherical particles interacting with well-defined pair potentials. The status of current progress is reviewed here by summarizing the underlying methodology and key findings from a range of simulation approaches: Monte Carlo, molecular dynamics, Brownian dynamics, Stokesian dynamics, dissipative particle dynamics, multiparticle collision dynamics, and fluid particle dynamics. Then it is described how the technique of Brownian dynamics simulation, in particular, has provided detailed insight into how different kinds of bonding and weak reversible interactions can affect the aggregate fractal structure, the percolation behaviour, and the small-deformation rheological properties of network-forming colloidal systems. A significant ongoing development has been the establishment and testing of efficient algorithms that are able to capture the subtle dynamic structuring effects that arise from effects of interparticle hydrodynamic interactions. This has led to an appreciation recently of the potentially important role of these particle-particle hydrodynamic effects in controlling the evolving morphology of simulated colloidal aggregates and in defining the location of the sol-gel phase boundary.
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16
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Bochicchio D, Videcoq A, Ferrando R. Kinetically driven ordered phase formation in binary colloidal crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022304. [PMID: 23496513 DOI: 10.1103/physreve.87.022304] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2012] [Revised: 01/17/2013] [Indexed: 06/01/2023]
Abstract
The aggregation of binary colloids of the same size and balanced charges is studied by Brownian dynamics simulations for dilute suspensions. It is shown that, under appropriate conditions, the formation of colloidal crystals is dominated by kinetic effects leading to the growth of well-ordered crystallites of the sodium-chloride (NaCl) bulk phase. These crystallites form with very high probability even when the cesium-chloride (CsCl) phase is more stable thermodynamically. Global optimization searches show that this result is not related to the most favorable structures of small clusters, which are either amorphous or of the CsCl structure. The formation of the NaCl phase is related to the specific kinetics of the crystallization process, which takes place by a two-step mechanism. In this mechanism, dense fluid aggregates form at first and then crystallization follows. It is shown that the type of short-range order in these dense fluid aggregates determines which phase is finally formed in the crystallites. The role of hydrodynamic effects in the aggregation process is analyzed by stochastic rotation dynamics - molecular dynamics simulations, and we find that these effects do not play a major role in the formation of the crystallites.
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Affiliation(s)
- D Bochicchio
- Dipartimento di Fisica and CNR-IMEM, Via Dodecaneso 33, Genova I-16146, Italy
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17
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Piechowiak MA, Videcoq A, Ferrando R, Bochicchio D, Pagnoux C, Rossignol F. Aggregation kinetics and gel formation in modestly concentrated suspensions of oppositely charged model ceramic colloids: a numerical study. Phys Chem Chem Phys 2012; 14:1431-9. [DOI: 10.1039/c1cp22980j] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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18
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Modulation of bulk physicochemical properties of emulsions by hetero-aggregation of oppositely charged protein-coated lipid droplets. Food Hydrocoll 2011. [DOI: 10.1016/j.foodhyd.2010.11.007] [Citation(s) in RCA: 59] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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19
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Dickinson E. Simple statistical thermodynamic model of the heteroaggregation and gelation of dispersions and emulsions. J Colloid Interface Sci 2011; 356:196-202. [DOI: 10.1016/j.jcis.2011.01.036] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2010] [Revised: 01/04/2011] [Accepted: 01/11/2011] [Indexed: 12/01/2022]
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