1
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Shen X, Bourg IC. Interaction between Hydrated Smectite Clay Particles as a Function of Salinity (0-1 M) and Counterion Type (Na, K, Ca). THE JOURNAL OF PHYSICAL CHEMISTRY. C, NANOMATERIALS AND INTERFACES 2022; 126:20990-20997. [PMID: 37881773 PMCID: PMC10595998 DOI: 10.1021/acs.jpcc.2c04636] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Revised: 11/11/2022] [Indexed: 10/27/2023]
Abstract
Swelling clay minerals control the hydrologic and mechanical properties of many soils, sediments, and sedimentary rocks. This important and well-known phenomenon remains challenging to predict because it emerges from complex multiscale couplings between aqueous chemistry and colloidal interaction mechanics in nanoporous clay assemblages, for which predictive models remain elusive. In particular, the predominant theory of colloidal interactions across fluid films, the widely used Derjaguin-Landau-Verwey-Overbeek model, fails to predict the ubiquitous existence of stable swelling states at interparticle distances below 3 nm that are stabilized by specific inter-atomic interactions in overlapping electrical double layers between the charged clay surfaces. Atomistic simulations have the potential to generate detailed insights into the mechanisms of these interactions. Recently, we developed a metadynamics-based molecular dynamics simulation methodology that can predict the free energy of interaction between parallel smectite clay particles in a wide range of interparticle distances (from 0.3 to 3 nm) and salinities (from 0.0 to 1.0 M NaCl). Here, we extend this work by characterizing the sensitivity of interparticle interactions to counterion type (Na, K, Ca). We establish a detailed picture of the free energy of interaction of parallel clay particles across water films as the sum of five interaction mechanisms with different sensitivities to salinity, counterion type, and interparticle distance.
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Affiliation(s)
- Xinyi Shen
- Department of Civil and Environmental
Engineering and High Meadows Environmental Institute, Princeton University, Princeton, New Jersey08544, United States
| | - Ian C. Bourg
- Department of Civil and Environmental
Engineering and High Meadows Environmental Institute, Princeton University, Princeton, New Jersey08544, United States
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2
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Prudente FV, Marques JMC. Thermodynamic Signatures of Structural Transitions and Dissociation of Charged Colloidal Clusters: A Parallel Tempering Monte Carlo Study. MOLECULES (BASEL, SWITZERLAND) 2022; 27:molecules27082581. [PMID: 35458778 PMCID: PMC9032479 DOI: 10.3390/molecules27082581] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Revised: 03/30/2022] [Accepted: 04/14/2022] [Indexed: 01/05/2023]
Abstract
Computational simulation of colloidal systems make use of empirical interaction potentials that are founded in well-established theory. In this work, we have performed parallel tempering Monte Carlo (PTMC) simulations to calculate heat capacity and to assess structural transitions, which may occur in charged colloidal clusters whose effective interactions are described by a sum of pair potentials with attractive short-range and repulsive long-range components. Previous studies on these systems have shown that the global minimum structure varies from spherical-type shapes for small-size clusters to Bernal spiral and “beaded-necklace” shapes at intermediate and larger sizes, respectively. In order to study both structural transitions and dissociation, we have organized the structures appearing in the PTMC calculations by three sets according to their energy: (i) low-energy structures, including the global minimum; (ii) intermediate-energy “beaded-necklace” motifs; (iii) high-energy linear and branched structures that characterize the dissociative clusters. We observe that, depending on the cluster, either peaks or shoulders on the heat–capacity curve constitute thermodynamics signatures of dissociation and structural transitions. The dissociation occurs at T=0.20 for all studied clusters and it is characterized by the appearance of a significant number of linear structures, while the structural transitions corresponding to unrolling the Bernal spiral are quite dependent on the size of the colloidal system.
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Affiliation(s)
- Frederico V. Prudente
- Instituto de Física, Universidade Federal da Bahia, Salvador 40170-115, BA, Brazil
- Correspondence: (F.V.P.); (J.M.C.M.)
| | - Jorge M. C. Marques
- CQC–IMS, Department of Chemistry, University of Coimbra, 3004-535 Coimbra, Portugal
- Correspondence: (F.V.P.); (J.M.C.M.)
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3
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Cheng R, Li J, Ríos de Anda I, Taylor TWC, Faers MA, Anderson JLR, Seddon AM, Royall CP. Protein-polymer mixtures in the colloid limit: Aggregation, sedimentation, and crystallization. J Chem Phys 2021; 155:114901. [PMID: 34551522 DOI: 10.1063/5.0052122] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
While proteins have been treated as particles with a spherically symmetric interaction, of course in reality, the situation is rather more complex. A simple step toward higher complexity is to treat the proteins as non-spherical particles and that is the approach we pursue here. We investigate the phase behavior of the enhanced green fluorescent protein (eGFP) under the addition of a non-adsorbing polymer, polyethylene glycol. From small angle x-ray scattering, we infer that the eGFP undergoes dimerization and we treat the dimers as spherocylinders with aspect ratio L/D - 1 = 1.05. Despite the complex nature of the proteins, we find that the phase behavior is similar to that of hard spherocylinders with an ideal polymer depletant, exhibiting aggregation and, in a small region of the phase diagram, crystallization. By comparing our measurements of the onset of aggregation with predictions for hard colloids and ideal polymers [S. V. Savenko and M. Dijkstra, J. Chem. Phys. 124, 234902 (2006) and Lo Verso et al., Phys. Rev. E 73, 061407 (2006)], we find good agreement, which suggests that the behavior of the eGFP is consistent with that of hard spherocylinders and ideal polymers.
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Affiliation(s)
- Rui Cheng
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Jingwen Li
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | | | - Thomas W C Taylor
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | | | - J L Ross Anderson
- School of Biochemistry, University of Bristol, Bristol BS8 1TD, United Kingdom
| | - Annela M Seddon
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - C Patrick Royall
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
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4
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Royall CP, Faers MA, Fussell SL, Hallett JE. Real space analysis of colloidal gels: triumphs, challenges and future directions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:453002. [PMID: 34034239 DOI: 10.1088/1361-648x/ac04cb] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 05/25/2021] [Indexed: 06/12/2023]
Abstract
Colloidal gels constitute an important class of materials found in many contexts and with a wide range of applications. Yet as matter far from equilibrium, gels exhibit a variety of time-dependent behaviours, which can be perplexing, such as an increase in strength prior to catastrophic failure. Remarkably, such complex phenomena are faithfully captured by an extremely simple model-'sticky spheres'. Here we review progress in our understanding of colloidal gels made through the use of real space analysis and particle resolved studies. We consider the challenges of obtaining a suitable experimental system where the refractive index and density of the colloidal particles is matched to that of the solvent. We review work to obtain a particle-level mechanism for rigidity in gels and the evolution of our understanding of time-dependent behaviour, from early-time aggregation to ageing, before considering the response of colloidal gels to deformation and then move on to more complex systems of anisotropic particles and mixtures. Finally we note some more exotic materials with similar properties.
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Affiliation(s)
- C Patrick Royall
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
- School of Chemistry, University of Bristol, Cantock Close, Bristol, BS8 1TS, United Kingdom
- Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, United Kingdom
| | - Malcolm A Faers
- Bayer AG, Crop Science Division, Formulation Technology, Alfred Nobel Str. 50, 40789 Monheim, Germany
| | - Sian L Fussell
- School of Chemistry, University of Bristol, Cantock Close, Bristol, BS8 1TS, United Kingdom
- Bristol Centre for Functional Nanomaterials, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, United Kingdom
| | - James E Hallett
- Physical and Theoretical Chemistry Laboratory, South Parks Road, University of Oxford, OX1 3QZ, United Kingdom
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5
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Lindquist BA. Inverse design of equilibrium cluster fluids applied to a physically informed model. J Chem Phys 2021; 154:174907. [PMID: 34241069 DOI: 10.1063/5.0048812] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inverse design strategies have proven highly useful for the discovery of interaction potentials that prompt self-assembly of a variety of interesting structures. However, often the optimized particle interactions do not have a direct relationship to experimental systems. In this work, we show that Relative Entropy minimization is able to discover physically meaningful parameter sets for a model interaction built from depletion attraction and electrostatic repulsion that yield self-assembly of size-specific clusters. We then explore the sensitivity of the optimized interaction potentials with respect to deviations in the underlying physical quantities, showing that clustering behavior is largely preserved even as the optimized parameters are perturbed.
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Affiliation(s)
- Beth A Lindquist
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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6
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Kurka DW, Niehues M, Ravoo BJ. Self-Assembly of Colloidal Molecules Based on Host-Guest Chemistry and Geometric Constraints. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:3924-3931. [PMID: 32182073 DOI: 10.1021/acs.langmuir.9b03891] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The preparation of colloidal molecules (CMs), that is, clusters of colloids with a defined aggregation number and configuration, is of continued and significant interest in colloid chemistry and materials science and numerous interactions have been utilized to drive their (self-)assembly. However, only very few reports are available on the assembly of CMs based on host-guest chemistry. In this paper, we investigate the assembly of like-charged silica particles into well-defined, core-satellite ABn-type CMs in water, mediated by host-guest interactions and geometric constraints. Exploiting the inherent dynamics of noncovalent attraction and making use of a soft polymer shell to enhance multivalent host-guest interactions, we successfully synthesized AB3, AB4, and AB6 CMs by selecting the appropriate size ratio of satellite to core particles.
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Affiliation(s)
- Dustin W Kurka
- Organic Chemistry Institute and Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
| | - Maximilian Niehues
- Organic Chemistry Institute and Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
| | - Bart Jan Ravoo
- Organic Chemistry Institute and Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany
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7
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Dong J, Meissner M, Faers MA, Eggers J, Seddon AM, Royall CP. Opposed flow focusing: evidence of a second order jetting transition. SOFT MATTER 2018; 14:8344-8351. [PMID: 30298898 DOI: 10.1039/c8sm00700d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We propose a novel microfluidic "opposed-flow" geometry in which the continuous fluid phase is fed into a junction in a direction opposite to the dispersed phase. This pulls out the dispersed phase into a micron-sized jet, which decays into micron-sized droplets. As the driving pressure is tuned to a critical value, the jet radius vanishes as a power law down to sizes below 1 μm. By contrast, the conventional "coflowing" junction leads to a first order jetting transition, in which the jet disappears at a finite radius of several μm, to give way to a "dripping" state, resulting in much larger droplets. We demonstrate the effectiveness of our method by producing the first microfluidic silicone oil emulsions with a sub micron particle radius, and utilize these droplets to produce colloidal clusters.
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Affiliation(s)
- Jun Dong
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, UK. and Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, UK
| | - Max Meissner
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, UK. and Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, UK
| | | | - Jens Eggers
- Mathematics Department, University of Bristol, BS8 1TW, Bristol, UK
| | - Annela M Seddon
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, UK. and Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, UK and Bristol Centre for Functional Nanomaterials, University of Bristol, Bristol, BS8 1TL, UK
| | - C Patrick Royall
- H. H. Wills Physics Laboratory, University of Bristol, Bristol, BS8 1TL, UK. and Centre for Nanoscience and Quantum Information, Tyndall Avenue, Bristol, BS8 1FD, UK and Chemistry Department, University of Bristol, Bristol, BS8 1TS, UK
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8
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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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9
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Royall CP. Hunting mermaids in real space: known knowns, known unknowns and unknown unknowns. SOFT MATTER 2018; 14:4020-4028. [PMID: 29767188 DOI: 10.1039/c8sm00400e] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We review efforts to realise so-called mermaid (or short-ranged attraction/long ranged repulsion) interactions in 3d real space. The repulsive and attractive contributions to these interactions in charged colloids and colloid-polymer mixtures, may be accurately realised, by comparing particle-resolved studies with colloids to computer simulation. However, when we review work where these interactions have been combined, despite early indications of behaviour consistent with predictions, closer analysis reveals that in the non-aqueous systems used for particle-resolved studies, the idea of summing the attractive and repulsive components leads to wild deviations with experiment. We suggest that the origin lies in the weak ion dissociation in these systems with low dielectric constant solvents. Ultimately this leads even to non-centro-symmetric interactions and a new level of complexity in these systems.
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Affiliation(s)
- C Patrick Royall
- School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK.
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10
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Hernández-Rojas J, Calvo F. Temperature- and field-induced structural transitions in magnetic colloidal clusters. Phys Rev E 2018; 97:022601. [PMID: 29548195 DOI: 10.1103/physreve.97.022601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2017] [Indexed: 06/08/2023]
Abstract
Magnetic colloidal clusters can form chain, ring, and more compact structures depending on their size. In the present investigation we examine the combined effects of temperature and external magnetic field on these configurations by means of extensive Monte Carlo simulations and a dedicated analysis based on inherent structures. Various thermodynamical, geometric, and magnetic properties are calculated and altogether provide evidence for possibly multiple structural transitions at low external magnetic field. Temperature effects are found to overcome the ordering effect of the external field, the melted stated being associated with low magnetization and a greater compactness. Tentative phase diagrams are proposed for selected sizes.
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Affiliation(s)
- J Hernández-Rojas
- Departamento de Física and IUdEA, Universidad de La Laguna, 38205, La Laguna, Tenerife, Spain
| | - F Calvo
- Laboratoire Interdisciplinaire de Physique, Université Grenoble Alpes and CNRS, 140 Av. de la physique, 38402 St Martin d'Hères, France
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11
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Santos AP, Pȩkalski J, Panagiotopoulos AZ. Thermodynamic signatures and cluster properties of self-assembly in systems with competing interactions. SOFT MATTER 2017; 13:8055-8063. [PMID: 29052681 DOI: 10.1039/c7sm01721a] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Colloidal particles, amphiphiles and functionalized nanoparticles are examples of systems that frequently exhibit short-range attraction coupled with long-range repulsion. We vary the ratio of attraction and repulsion in a simple isotropic model with competing interactions, using molecular simulations, and observe significant differences in the properties of the self-assembled clusters that form. We report conditions that lead to the self-assembly of clusters of a preferred size, accompanied by a change in the slope of the pressure with respect to density, similar to micelles formed by amphiphilic molecules. We also report conditions where repulsion dominates, clusters of a preferred size form and the pressure vs. density slope is unaffected by self-assembly. We investigate cluster structure by calculating the size distributions, free colloid density, cluster shape and density profiles. The system dynamics are characterized by cluster life-times. We do not find qualitative differences in structure or dynamics of the clusters, regardless the pressure behavior. Therefore, thermodynamic and structural quantities are required to classify the different clustering characteristics that are observable in systems with competing interactions. Our results have implications in terms of development of design principles for stable cluster self-assembly.
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Affiliation(s)
- Andrew P Santos
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA.
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12
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Liu J, Shen T, Yang ZH, Zhang S, Sun GY. Multistep Heterogeneous Nucleation in Binary Mixtures of Charged Colloidal Spheres. J Phys Chem Lett 2017; 8:4652-4658. [PMID: 28893063 DOI: 10.1021/acs.jpclett.7b02096] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Nucleation plays a decisive role in determining the crystal structure and size distribution; however, understanding of the fundamentals of nucleation is quite limited. In particular, it is unclear whether a nucleus forms spontaneously from solution via a single- or multiple-step process. Here we show how a binary mixture of charged colloidal spheres nucleates heterogeneously on a flat substrate by means of Bragg microscopy, laser diffraction, and laser microscopy. In contrast with the conventional one-step and two-step nucleation mechanisms, a novel pathway of multistep heterogeneous nucleation under certain experimental conditions is highlighted by four steps: initial homogeneous fluid → prenucleation clusters → preordered prenucleation clusters → intermediate ordered phase → final crystal. It is expected that the obtained results would be helpful in rationalizing the rich phase behavior exhibited by the binary mixture systems and in developing better and broadly applicable nucleation models as well as in designing defect-free single-crystal alloys.
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Affiliation(s)
- Jianing Liu
- School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology , Nanjing 210044, China
- Jiangsu Key Laboratory for Optoelectronic Detection of Atmosphere and Ocean, Nanjing University of Information Science & Technology , Nanjing 210044, China
| | - Tong Shen
- School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology , Nanjing 210044, China
- Jiangsu Key Laboratory for Optoelectronic Detection of Atmosphere and Ocean, Nanjing University of Information Science & Technology , Nanjing 210044, China
| | - Zhao Hua Yang
- School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology , Nanjing 210044, China
| | - Shu Zhang
- School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology , Nanjing 210044, China
| | - Guang Yu Sun
- School of Physics and Optoelectronic Engineering, Nanjing University of Information Science & Technology , Nanjing 210044, China
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13
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Morphew D, Chakrabarti D. Clusters of anisotropic colloidal particles: From colloidal molecules to supracolloidal structures. Curr Opin Colloid Interface Sci 2017. [DOI: 10.1016/j.cocis.2017.05.006] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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14
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Capellmann RF, Valadez-Pérez NE, Simon B, Egelhaaf SU, Laurati M, Castañeda-Priego R. Structure of colloidal gels at intermediate concentrations: the role of competing interactions. SOFT MATTER 2016; 12:9303-9313. [PMID: 27801925 DOI: 10.1039/c6sm01822j] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Colloidal gels formed by colloid-polymer mixtures with an intermediate volume fraction (ϕc ≈ 0.4) are investigated by confocal microscopy. In addition, we have performed Monte Carlo simulations based on a simple effective pair potential that includes a short-range attractive contribution representing depletion interactions, and a longer-range repulsive contribution describing the electrostatic interactions due to the presence of residual charges. Despite neglecting non-equilibrium effects, experiments and simulations yield similar gel structures, characterised by, e.g., the pair, angular and bond distribution functions. We find that the structure hardly depends on the strength of the attraction if the electrostatic contribution is fixed, but changes significantly if the electrostatic screening is changed. This delicate balance between attractions and repulsions, which we quantify by the second virial coefficient, also determines the location of the gelation boundary.
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Affiliation(s)
- Ronja F Capellmann
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Néstor E Valadez-Pérez
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Guanajuato, Mexico.
| | - Benedikt Simon
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Stefan U Egelhaaf
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstr. 1, 40225 Düsseldorf, Germany
| | - Marco Laurati
- Condensed Matter Physics Laboratory, Heinrich Heine University, Universitätsstr. 1, 40225 Düsseldorf, Germany and División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Guanajuato, Mexico.
| | - Ramón Castañeda-Priego
- División de Ciencias e Ingenierías, Campus León, Universidad de Guanajuato, Loma del Bosque 103, Lomas del Campestre, 37150 León, Guanajuato, Mexico.
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15
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Zhuang Y, Charbonneau P. Recent Advances in the Theory and Simulation of Model Colloidal Microphase Formers. J Phys Chem B 2016; 120:7775-82. [DOI: 10.1021/acs.jpcb.6b05471] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yuan Zhuang
- Department
of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Patrick Charbonneau
- Department
of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department
of Physics, Duke University, Durham, North Carolina 27708, United States
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16
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Okuzono T, Odai K, Masuda T, Toyotama A, Yamanaka J. Numerical study of cluster formation in binary charged colloids. Phys Rev E 2016; 94:012609. [PMID: 27575181 DOI: 10.1103/physreve.94.012609] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2016] [Indexed: 05/25/2023]
Abstract
Cluster formation of oppositely charged colloidal particles is studied numerically. A simple Brownian dynamics method with a screened-Coulomb (Yukawa) potential is employed for numerical simulations. An equilibrium phase which consists of clusters and unassociated particles is obtained. It is shown that the equilibrium association number of clusters and their shapes are determined by charge numbers and charge ratio of the binary particles. The phase diagram of cluster formation for various charge numbers and their ratios is obtained. A simple relation between the association number and the charge ratio is found. It is demonstrated that in the case of high charge ratio the cluster takes a multilayer structure which is highly symmetric. It is also pointed out that the cluster-particle interaction changes dynamically in the cluster formation process, which is involved in the selection of final cluster structure.
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Affiliation(s)
- Tohru Okuzono
- Graduate School of Pharmaceutical Sciences, Nagoya City University, Nagoya 467-8603, Japan
| | - Kana Odai
- Graduate School of Pharmaceutical Sciences, Nagoya City University, Nagoya 467-8603, Japan
| | - Tatsuhiro Masuda
- Graduate School of Pharmaceutical Sciences, Nagoya City University, Nagoya 467-8603, Japan
| | - Akiko Toyotama
- Graduate School of Pharmaceutical Sciences, Nagoya City University, Nagoya 467-8603, Japan
| | - Junpei Yamanaka
- Graduate School of Pharmaceutical Sciences, Nagoya City University, Nagoya 467-8603, Japan
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17
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Zhuang Y, Charbonneau P. Equilibrium Phase Behavior of the Square-Well Linear Microphase-Forming Model. J Phys Chem B 2016; 120:6178-88. [DOI: 10.1021/acs.jpcb.6b02167] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Yuan Zhuang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department
of Physics, Duke University, Durham, North Carolina 27708, United States
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18
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Cruz SMA, Marques JMC. A Detailed Study on the Low-Energy Structures of Charged Colloidal Clusters. J Phys Chem B 2016; 120:3455-66. [PMID: 26986933 DOI: 10.1021/acs.jpcb.6b01233] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The target of this investigation is the systematic characterization of the low-energy structures of charged colloidal clusters that may be important to understand the self-assembling process of biomolecules. The aggregation of charged colloidal particles is governed by the attractive short-ranged Morse potential and the Yukawa repulsive tail to describe the long-range charge effect. A global optimization strategy, based on our own evolutionary algorithm, was adopted to discover the low-energy structures of colloidal clusters composed of up to 20 particles. A detailed analysis of the low-energy structures involving charged particles shows that the appearance of the Bernal spiral as the most stable motif occurs, first, at N = 6, but it is favored for larger clusters (N ≥ 13); for 6 ≤ N ≤ 12, there is a competition between the spiral (which is favored for higher charges) and more spherical-like structures. Finally, we study binary clusters composed by two sets of differently charged colloidal particles. Although a great diversity of low-energy structures is observed (especially for aggregates with one of the components in excess), the global minimum is disputed by three structural motifs depending on the composition of the cluster and, in some cases, on the range of the Morse potential.
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Affiliation(s)
- S M A Cruz
- Departamento de Química, Universidade de Coimbra , 3004-535 Coimbra, Portugal
| | - J M C Marques
- Departamento de Química, Universidade de Coimbra , 3004-535 Coimbra, Portugal
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Spontaneous Formation of Eutectic Crystal Structures in Binary and Ternary Charged Colloids due to Depletion Attraction. Sci Rep 2016; 6:23292. [PMID: 26984298 PMCID: PMC4794737 DOI: 10.1038/srep23292] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2015] [Accepted: 03/01/2016] [Indexed: 11/18/2022] Open
Abstract
Crystallization of colloids has extensively been studied for past few decades as models to study phase transition in general. Recently, complex crystal structures in multi-component colloids, including alloy and eutectic structures, have attracted considerable attention. However, the fabrication of 2D area-filling colloidal eutectics has not been reported till date. Here, we report formation of eutectic structures in binary and ternary aqueous colloids due to depletion attraction. We used charged particles + linear polyelectrolyte systems, in which the interparticle interaction could be represented as a sum of the electrostatic, depletion, and van der Waals forces. The interaction was tunable at a lengthscale accessible to direct observation by optical microscopy. The eutectic structures were formed because of interplay of crystallization of constituent components and accompanying fractionation. An observed binary phase diagram, defined by a mixing ratio and inverse area fraction of the particles, was analogous to that for atomic and molecular eutectic systems. This new method also allows the adjustment of both the number and wavelengths of Bragg diffraction peaks. Furthermore, these eutectic structures could be immobilized in polymer gel to produce self-standing materials. The present findings will be useful in the design of the optical properties of colloidal crystals.
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Zhuang Y, Zhang K, Charbonneau P. Equilibrium Phase Behavior of a Continuous-Space Microphase Former. PHYSICAL REVIEW LETTERS 2016; 116:098301. [PMID: 26991204 DOI: 10.1103/physrevlett.116.098301] [Citation(s) in RCA: 61] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2015] [Indexed: 06/05/2023]
Abstract
Periodic microphases universally emerge in systems for which short-range interparticle attraction is frustrated by long-range repulsion. The morphological richness of these phases makes them desirable material targets, but our relatively coarse understanding of even simple models hinders controlling their assembly. We report here the solution of the equilibrium phase behavior of a microscopic microphase former through specialized Monte Carlo simulations. The results for cluster crystal, cylindrical, double gyroid, and lamellar ordering qualitatively agree with a Landau-type free energy description and reveal the nontrivial interplay between cluster, gel, and microphase formation.
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Affiliation(s)
- Yuan Zhuang
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
| | - Kai Zhang
- Department of Chemical Engineering, Columbia University, New York, New York 10027, USA
| | - Patrick Charbonneau
- Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
- Department of Physics, Duke University, Durham, North Carolina 27708, USA
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Hernández-Rojas J, Chakrabarti D, Wales DJ. Self-assembly of colloidal magnetic particles: energy landscapes and structural transitions. Phys Chem Chem Phys 2016; 18:26579-26585. [DOI: 10.1039/c6cp03085h] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The self-assembly of colloidal magnetic particles is of particular interest for the rich variety of structures it produces and the potential for these systems to be reconfigurable.
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Affiliation(s)
| | - D. Chakrabarti
- School of Chemistry
- University of Birmingham
- Birmingham B15 2TT
- UK
| | - D. J. Wales
- University Chemical Laboratories
- Cambridge CB2 1EW
- UK
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22
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Jadrich RB, Bollinger JA, Lindquist BA, Truskett TM. Equilibrium cluster fluids: pair interactions via inverse design. SOFT MATTER 2015; 11:9342-9354. [PMID: 26434352 DOI: 10.1039/c5sm01832c] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Inverse methods of statistical mechanics are becoming productive tools in the design of materials with specific microstructures or properties. While initial studies have focused on solid-state design targets (e.g., assembly of colloidal superlattices), one can alternatively design fluid states with desired morphologies. This work addresses the latter and demonstrates how a simple iterative Boltzmann inversion strategy can be used to determine the isotropic pair potential that reproduces the radial distribution function of a fluid of amorphous clusters with prescribed size. The inverse designed pair potential of this "ideal" cluster fluid, with its broad attractive well and narrow repulsive barrier at larger separations, is qualitatively different from the so-called SALR form most commonly associated with equilibrium cluster formation in colloids, which features short-range attractive (SA) and long-range repulsive (LR) contributions. These differences reflect alternative mechanisms for promoting cluster formation with an isotropic pair potential, and they in turn produce structured fluids with qualitatively different static and dynamic properties. Specifically, equilibrium simulations show that the amorphous clusters resulting from the inverse designed potentials display more uniformity in size and shape, and they also show greater spatial and temporal resolution than those resulting from SALR interactions.
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Affiliation(s)
- R B Jadrich
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
| | - J A Bollinger
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
| | - B A Lindquist
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
| | - T M Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA.
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Nakamura Y, Okachi M, Toyotama A, Okuzono T, Yamanaka J. Controlled Clustering in Binary Charged Colloids by Adsorption of Ionic Surfactants. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:13303-11. [PMID: 26583431 DOI: 10.1021/acs.langmuir.5b02778] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We report on the controlled clustering of oppositely charged colloidal particles by the adsorption of ionic surfactants, which tunes charge numbers Z of particles. In particular, we studied the heteroclustering of submicron-sized polystyrene (PS) and silica particles, both of which are negatively charged, in the presence of cetylpyridinium chloride (CPC), a cationic surfactant. The surfactant concentration Csurf was selected below the critical micelle concentration. As CPC molecules were adsorbed, Z values of the PS and silica particles decreased, inverting to positive when Csurf exceeded the isoelectric point Ciep. Hydrophobic PS particles exhibited much lower Ciep than hydrophilic silica particles. At Csurf valuess between their Ciep values, the particles were oppositely charged, and clustering was enabled. To explain the clustering behavior, we investigated adsorption isotherms of the CPC and screened-Coulomb-type pair potential. Expected applications of the present findings are the control of colloidal associations and construction of various particle types into heterogeneous colloidal clusters.
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Affiliation(s)
- Yuki Nakamura
- Graduate School of Pharmaceutical Sciences, Nagoya City University , 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Japan
| | - Manami Okachi
- Graduate School of Pharmaceutical Sciences, Nagoya City University , 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Japan
| | - Akiko Toyotama
- Graduate School of Pharmaceutical Sciences, Nagoya City University , 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Japan
| | - Tohru Okuzono
- Graduate School of Pharmaceutical Sciences, Nagoya City University , 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Japan
| | - Junpei Yamanaka
- Graduate School of Pharmaceutical Sciences, Nagoya City University , 3-1 Tanabe, Mizuho, Nagoya, Aichi 467-8603, Japan
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Hoy RS. Structure and dynamics of model colloidal clusters with short-range attractions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012303. [PMID: 25679619 DOI: 10.1103/physreve.91.012303] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Indexed: 06/04/2023]
Abstract
We examine the structure and dynamics of small isolated N-particle clusters interacting via short-ranged Morse potentials. "Ideally prepared ensembles" obtained via exact enumeration studies of sticky hard-sphere packings serve as reference states allowing us to identify key statistical-geometrical properties and to quantitatively characterize how nonequilibrium ensembles prepared by thermal quenches at different rates T[over ̇] differ from their equilibrium counterparts. Studies of equilibrium dynamics show nontrivial temperature dependence: nonexponential relaxation indicates both glassy dynamics and differing stabilities of degenerate clusters with different structures. Our results should be useful for extending recent experimental studies of small colloidal clusters to examine both equilibrium relaxation dynamics at fixed T and a variety of nonequilibrium phenomena.
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Affiliation(s)
- Robert S Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
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González-Gutiérrez J, Carrillo-Estrada JL, Carvente O, Ruiz-Suárez JC. Free-energy landscapes of granular clusters grown by magnetic interaction. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:37. [PMID: 24839131 DOI: 10.1140/epje/i2014-14037-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2013] [Revised: 03/14/2014] [Accepted: 04/16/2014] [Indexed: 06/03/2023]
Abstract
We experimentally study the aggregation of small clusters made of non-Brownian dipolar beads in a vibro-fluidized system. The particles are paramagnetic spheres that add around a fixed magnetic seed inside a granular gas of glass beads. We observe that under appropriate physical conditions symmetric and asymmetric cluster configurations are created and, as the number of particles increases, the aggregation time obeys a power law. We use an ensemble statistics to evaluate the free-energies and entropies landscapes of the granular clusters. The correspondence between such landscapes shows that, even if the system is of macroscopic scale and not in strict equilibrium, our approach to understand the relationship between the cluster structures and the interactions that create them is reliable.
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26
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Malins A, Williams SR, Eggers J, Royall CP. Identification of structure in condensed matter with the topological cluster classification. J Chem Phys 2013; 139:234506. [DOI: 10.1063/1.4832897] [Citation(s) in RCA: 95] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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