1
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Xu S, Zhang H, Qiao B, Wang Y. Insights into solvent-dependent nucleation behavior of benzoic acid from metastable zone widths. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.117634] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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2
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Mura E, Ding Y. Nucleation of melt: From fundamentals to dispersed systems. Adv Colloid Interface Sci 2021; 289:102361. [PMID: 33561567 DOI: 10.1016/j.cis.2021.102361] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2020] [Revised: 01/12/2021] [Accepted: 01/13/2021] [Indexed: 11/28/2022]
Abstract
The most evident aspects of a first order transition of a system from an old to a new phase, are the presence of a discontinuity at the interface between both phases and the thermal effects related to the latent heat exchanged with the surrounding environment. These effects are the result of a sequence of events promoted by thermodynamic conditions persisting over the equilibrium in a metastable state. The breakdown of metastability is promoted by infinitesimal energy fluctuations resulting in the germination of clusters of the new phase that can grow to a critical size (nucleus) and then develop or vanish. Examples of these sequences are common in various technological fields such as combustion, food processing, pharmaceutical manufacturing, condensation, and phase change heat transfer, etc. This work aims to highlight a logical path that leads the readers from the fundamental phenomenology to the most intricated aspects of the nucleation within dispersed systems such as oil-in-water emulsions. Differences between the homogeneous and heterogeneous mechanisms are, under the light of the Classical Nucleation Theory (CNT), presented in bulk and confined systems until defining a minimum confinement size. By collecting insights coming from a rich scientific literature mostly focused on the stability of emulsified systems, the discussion is then on the aspects related to the surface related mechanisms. Two main aspects are then considered: a) the wettability of the nucleating cluster by the surrounding melt; b) the affinity between the adsorbed layer, where a surfactant is located, and the oil melt phase (mainly n-alkanes and triacylglycerols with different moieties). In cases where nucleation is dominating over the dewetting of the nucleus, the contact angle can be considered as a constant value. The affinity in terms of molecular features between the surfactant and the oil phase can promote the template effect. Several factors seem to play a role in this interaction such as the thermal characteristics of the surfactant and comparable dimensions between the molecule (or fractions) of the dispersed compound and the tail of the surfactant.
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Affiliation(s)
- Ernesto Mura
- Global Energy Interconnection Research Institute Europe GmbH, Kantstr. 162, 10623 Berlin, Germany.
| | - Yulong Ding
- Birmingham Centre for Energy Storage & School of Chemical Engineering, Univ. of Birmingham, B15 2TT, UK
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3
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Xu S, Hou Z, Chuai X, Wang Y. Overview of Secondary Nucleation: From Fundamentals to Application. Ind Eng Chem Res 2020. [DOI: 10.1021/acs.iecr.0c03304] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Shijie Xu
- Tianjin Key Laboratory of Brine Chemical Engineering and Ecological Utilization of Resources, Tianjin Engineering Center of Marine Chemical Engineering & Technology, College of Chemical Engineering and Materials Science, Tianjin University of Science and Technology, Tianjin 300457, China
| | - Zhongbi Hou
- Tianjin Key Laboratory of Brine Chemical Engineering and Ecological Utilization of Resources, Tianjin Engineering Center of Marine Chemical Engineering & Technology, College of Chemical Engineering and Materials Science, Tianjin University of Science and Technology, Tianjin 300457, China
| | - Xiaoyu Chuai
- Tianjin Key Laboratory of Brine Chemical Engineering and Ecological Utilization of Resources, Tianjin Engineering Center of Marine Chemical Engineering & Technology, College of Chemical Engineering and Materials Science, Tianjin University of Science and Technology, Tianjin 300457, China
| | - Yanfei Wang
- Tianjin Key Laboratory of Brine Chemical Engineering and Ecological Utilization of Resources, Tianjin Engineering Center of Marine Chemical Engineering & Technology, College of Chemical Engineering and Materials Science, Tianjin University of Science and Technology, Tianjin 300457, China
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4
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Affiliation(s)
- Peter G. Vekilov
- Department of Chemical and Biomolecular Engineering and Department of Chemistry, University of Houston, Houston, Texas 77204, United States
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5
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Hopkins SS, Chakrabarti A, Schmit JD. Effects of non-pairwise repulsion on nanoparticle assembly. J Chem Phys 2019; 151:034901. [PMID: 31325921 DOI: 10.1063/1.5092130] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Electrostatic interactions provide a convenient way to modulate interactions between nanoparticles, colloids, and biomolecules because they can be adjusted by the solution pH or salt concentration. While the presence of salt provides an easy method to control the net interparticle interaction, the nonlinearities arising from electrostatic screening make it difficult to quantify the strength of the interaction. In particular, when charged particles assemble into clusters or aggregates, nonlinear effects render the interactions strongly non-pairwise. Here, we report Brownian dynamics simulations to investigate the effect that the non-pairwise nature of electrostatic interactions has on nanoparticle assembly. We compare these simulations to a system in which the electrostatics are modeled by a strictly pairwise Yukawa potential. We find that both systems show a narrow range in parameter space where the particles form well-ordered crystals. Bordering this range are regions where the net interactions are too weak to stabilize aggregated structures or strong enough that the system becomes kinetically trapped in a gel. The non-pairwise potential differs from the pairwise system in the appearance of an amorphous state for strongly charged particles. This state appears because the many-body electrostatic interactions limit the maximum density achievable in an assembly.
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Affiliation(s)
- Sawyer S Hopkins
- Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA
| | | | - Jeremy D Schmit
- Department of Physics, Kansas State University, Manhattan, Kansas 66506, USA
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6
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Royall CP, Williams SR, Tanaka H. Vitrification and gelation in sticky spheres. J Chem Phys 2018; 148:044501. [PMID: 29390812 DOI: 10.1063/1.5000263] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Glasses and gels are the two dynamically arrested, disordered states of matter. Despite their importance, their similarities and differences remain elusive, especially at high density, where until now it has been impossible to distinguish them. We identify dynamical and structural signatures which distinguish the gel and glass transitions in a colloidal model system of hard and "sticky" spheres. It has been suggested that "spinodal" gelation is initiated by gas-liquid viscoelastic phase separation to a bicontinuous network and the resulting densification leads to vitrification of the colloid-rich phase, but whether this phase has sufficient density for arrest is unclear [M. A. Miller and D. Frenkel, Phys. Rev. Lett. 90, 135702 (2003) and P. J. Lu et al., Nature 435, 499-504 (2008)]. Moreover alternative mechanisms for arrest involving percolation have been proposed [A. P. R. Eberle et al., Phys. Rev. Lett. 106, 105704 (2011)]. Here we resolve these outstanding questions, beginning by determining the phase diagram. This, along with demonstrating that percolation plays no role in controlling the dynamics of our system, enables us to confirm spinodal decomposition as the mechanism for gelation. We are then able to show that gels can be formed even at much higher densities than previously supposed, at least to a volume fraction of ϕ = 0.59. Far from being networks, these gels apparently resemble glasses but are still clearly distinguished by the "discontinuous" nature of the transition and the resulting rapid solidification, which leads to the formation of inhomogeneous (with small voids) and far-from-equilibrium local structures. This is markedly different from the glass transition, whose continuous nature leads to the formation of homogeneous and locally equilibrated structures. We further reveal that the onset of the attractive glass transition in the form of a supercooled liquid is in fact interrupted by gelation. Our findings provide a general thermodynamic, dynamic, and structural basis upon which we can distinguish gelation from vitrification.
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Affiliation(s)
- C Patrick Royall
- HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
| | - Stephen R Williams
- Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia
| | - Hajime Tanaka
- 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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7
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Tsurusawa H, Russo J, Leocmach M, Tanaka H. Formation of porous crystals via viscoelastic phase separation. NATURE MATERIALS 2017; 16:1022-1028. [PMID: 28759032 DOI: 10.1038/nmat4945] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Accepted: 06/26/2017] [Indexed: 06/07/2023]
Abstract
Viscoelastic phase separation of colloidal suspensions can be interrupted to form gels either by glass transition or by crystallization. With a new confocal microscopy protocol, we follow the entire kinetics of phase separation, from homogeneous phase to different arrested states. For the first time in experiments, our results unveil a novel crystallization pathway to sponge-like porous crystal structures. In the early stages, we show that nucleation requires a structural reorganization of the liquid phase, called stress-driven ageing. Once nucleation starts, we observe that crystallization follows three different routes: direct crystallization of the liquid phase, the Bergeron process, and Ostwald ripening. Nucleation starts inside the reorganized network, but crystals grow past it by direct condensation of the gas phase on their surface, driving liquid evaporation, and producing a network structure different from the original phase separation pattern. We argue that similar crystal-gel states can be formed in monatomic and molecular systems if the liquid phase is slow enough to induce viscoelastic phase separation, but fast enough to prevent immediate vitrification. This provides a novel pathway to form nanoporous crystals of metals and semiconductors without dealloying, which may be important for catalytic, optical, sensing, and filtration applications.
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Affiliation(s)
- Hideyo Tsurusawa
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
| | - John Russo
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
- School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
| | - Mathieu Leocmach
- Univ Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France
| | - Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
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8
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Zhou RB, Cao HL, Zhang CY, Yin DC. A review on recent advances for nucleants and nucleation in protein crystallization. CrystEngComm 2017. [DOI: 10.1039/c6ce02562e] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
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9
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Russo J, Tanaka H. Crystal nucleation as the ordering of multiple order parameters. J Chem Phys 2016; 145:211801. [DOI: 10.1063/1.4962166] [Citation(s) in RCA: 79] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Affiliation(s)
- John Russo
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
- School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
| | - Hajime Tanaka
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
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10
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Bera MK, Antonio MR. Crystallization of Keggin Heteropolyanions via a Two-Step Process in Aqueous Solutions. J Am Chem Soc 2016; 138:7282-8. [DOI: 10.1021/jacs.5b13375] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Affiliation(s)
- Mrinal K. Bera
- Chemical
Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
| | - Mark R. Antonio
- Chemical
Sciences and Engineering
Division, Argonne National Laboratory, Argonne, Illinois 60439, United States
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11
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Li YW, Sun ZY. The relationship between local density and bond-orientational order during crystallization of the Gaussian core model. SOFT MATTER 2016; 12:2009-2016. [PMID: 26777751 DOI: 10.1039/c5sm02712h] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Whether nucleation is triggered by density or by bond-orientational order is one of the most hotly debated issues in recent investigations of the crystallization process. Here, we present a numerical study of the relationship between them for soft particles within the isothermal-isobaric ensemble. We compress the system and thus obtain the fluid-solid transition. By investigating locally dense-packed particles and particles with a relatively high bond-orientational order in the compressing process, we find a sharp increase of the spatial correlations for both densely packed particles and highly bond-orientational ordered particles at the phase transition point, which provide new characterization methods for the liquid-crystal transition. We also find that it is the bond-orientational order rather than density that triggers the nucleation process. The relationship between the local density and the bond-orientational order parameter is strongly affected by the characterization methods used. The local bond order parameter (q6) shows clear correlation with the local density (ρ) in the fluid stage, while the coarse-grained form (q[combining macron]6) does not correlate with ρ at all, owing to the comparable spatial scales of q6 and ρ. Nevertheless, q[combining macron]6 shows an obvious advantage in distinguishing between solid and liquid particles in our work. These results may elevate our understanding of the mechanism of the crystallization process.
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Affiliation(s)
- Yan-Wei Li
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China.
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12
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Haxton TK, Hedges LO, Whitelam S. Crystallization and arrest mechanisms of model colloids. SOFT MATTER 2015; 11:9307-9320. [PMID: 26428696 DOI: 10.1039/c5sm01833a] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We performed dynamic simulations of spheres with short-range attractive interactions for many values of interaction strength and range. Fast crystallization occurs in a localized region of this parameter space, but the character of crystallization pathways is not uniform within this region. Pathways range from one-step, in which a crystal nucleates directly from a gas, to two-step, in which substantial liquid-like clusters form and only subsequently become crystalline. Crystallization can fail because of slow nucleation from either gas or liquid, or because of dynamic arrest caused by strong interactions. Arrested states are characterized by the formation of networks of face-sharing tetrahedra that can be detected by a local common neighbor analysis.
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Affiliation(s)
- Thomas K Haxton
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
| | - Lester O Hedges
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. and Department of Physics, University of Bath, Bath, BA2 7AY, UK
| | - Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
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13
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Wedekind J, Xu L, Buldyrev SV, Stanley HE, Reguera D, Franzese G. Optimization of crystal nucleation close to a metastable fluid-fluid phase transition. Sci Rep 2015; 5:11260. [PMID: 26095898 PMCID: PMC4476038 DOI: 10.1038/srep11260] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2015] [Accepted: 04/09/2015] [Indexed: 11/15/2022] Open
Abstract
The presence of a metastable fluid-fluid critical point is thought to dramatically influence the crystallization pathway, increasing the nucleation rate by many orders of magnitude over the predictions of classical nucleation theory. We use molecular dynamics simulations to study the kinetics of crystallization in the vicinity of this metastable critical point and throughout the metastable fluid-fluid phase diagram. To quantitatively understand how the fluid-fluid phase separation affects the crystal nucleation, we evaluate accurately the kinetics and reconstruct the thermodynamic free-energy landscape of crystal formation. Contrary to expectations, we find no special advantage of the proximity of the metastable critical point on the crystallization rates. However, we find that the ultrafast formation of a dense liquid phase causes the crystallization to accelerate both near the metastable critical point and almost everywhere below the fluid-fluid spinodal line. These results unveil three different scenarios for crystallization that could guide the optimization of the process in experiments
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Affiliation(s)
- Jan Wedekind
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Limei Xu
- International Center for Quantum Materials and School of Physics, Peking University, Beijing 100871, China
| | - Sergey V Buldyrev
- Department of Physics, Yeshiva University, 500 West 185th Street, New York, NY 10033 USA
| | - H Eugene Stanley
- Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215 USA
| | - David Reguera
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
| | - Giancarlo Franzese
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
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14
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Habasaki J, Ishikawa M. Molecular dynamics study of coagulation in silica-nanocolloid-water-NaCl systems based on the atomistic model. Phys Chem Chem Phys 2014; 16:24000-17. [PMID: 25285911 DOI: 10.1039/c4cp02984d] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In the present work, large scale molecular dynamics (MD) simulations of nanocolloidal silica in aqueous NaCl solutions were performed using a fully atomistic model to study the microscopic structures and dynamics of the systems that lead to aggregation or gelation. Our attention is focused on the self-organizations that occur in the structures of the colloidal silica and water for various concentrations of NaCl. As the salt concentration increased, coagulation developed through the direct bonding of SiO4 units. The trend was explained by the systematic changes in the pair correlation functions related to the barrier height in the potential of mean force [J. G. Kirkwood, J. Chem. Phys., 1935, 3, 300]. Network structures of silica were visualised, and their fractal dimensions were examined by computing the running coordination numbers of Si-Si pairs and also by the analysis of two dimensional images. The calculated dimension by the former method was comparable to the experimental observations for the aggregation of silica colloids, and at longer length scales, super-aggregation was evident in the gelation process. The result from the 2D images is found to be insensitive to the differences in the structure. Clear changes in both the structure and mobility of the water were observed as the NaCl concentration increased, suggesting the importance of the solvent structures to these processes, although such a feature is lacking in the conventional models and most simulations of colloids.
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Affiliation(s)
- Junko Habasaki
- Department of Innovative and Engineered Materials, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Nagatsuta 4259, Yokohama 226-8502, Japan.
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15
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Vekilov PG. Phase diagrams and kinetics of phase transitions in protein solutions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:193101. [PMID: 22495288 DOI: 10.1088/0953-8984/24/19/193101] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The phase behavior of proteins is of interest for fundamental and practical reasons. The nucleation of new phases is one of the last major unresolved problems of nature. The formation of protein condensed phases (crystals, polymers, and other solid aggregates, as well as dense liquids and gels) underlies pathological conditions, plays a crucial role in the biological function of the respective protein, or is an essential part of laboratory and industrial processes. In this review, we focus on phase transitions of proteins in their properly folded state. We first summarize the recently acquired understanding of physical processes underlying the phase diagrams of the protein solutions and the thermodynamics of protein phase transitions. Then we review recent findings on the kinetics of nucleation of dense liquid droplets and crystals. We explore the transition from nucleation to spinodal decomposition for liquid-liquid separation and introduce the new concept of solution-to-crystal spinodal. We review the two-step mechanism of protein crystal nucleation, in which mesoscopic metastable protein clusters serve as precursors to the ordered crystal nuclei. The concepts and mechanisms reviewed here provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.
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Affiliation(s)
- Peter G Vekilov
- Department of Chemical and Biomolecular Engineering and Department of Chemistry, University of Houston, Houston, TX 77204-4004, USA.
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16
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The Two-Step Mechanism and The Solution-Crystal Spinodal for Nucleation of Crystals in Solution. ADVANCES IN CHEMICAL PHYSICS 2012. [DOI: 10.1002/9781118309513.ch4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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17
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Li W, Liu Y, Perez T, Gunton JD, Sorensen CM, Chakrabarti A. Kinetics of nanochain formation in a simplified model of amelogenin biomacromolecules. Biophys J 2011; 101:2502-6. [PMID: 22098749 PMCID: PMC3218329 DOI: 10.1016/j.bpj.2011.09.056] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2011] [Revised: 07/25/2011] [Accepted: 09/02/2011] [Indexed: 10/15/2022] Open
Abstract
We show that the kinetics of nanochain formation of amelogenin molecules is well described by a combination of translational and rotational diffusion of a simplified anisotropic bipolar model consisting of hydrophobic spherical colloid particles and a point charge located on each particle surface. The colloid particles interact via a standard depletion attraction whereas the point charges interact through a screened Coulomb repulsion. We study the kinetics via a Brownian dynamics simulation of both translational and rotational motions and show that the anisotropy brought in by the charge dramatically affects the kinetic pathway of cluster formation and our simple model captures the main features of the experimental observations.
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Affiliation(s)
- Wei Li
- Department of Physics, Lehigh University, Bethlehem, Pennsylvania, USA.
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18
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Knott BC, Doherty MF, Peters B. A simulation test of the optical Kerr mechanism for laser-induced nucleation. J Chem Phys 2011; 134:154501. [DOI: 10.1063/1.3574010] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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19
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Li W, Gunton JD, Khan SJ, Schoelz JK, Chakrabarti A. Brownian dynamics simulation of insulin microsphere formation from break-up of a fractal network. J Chem Phys 2011; 134:024902. [DOI: 10.1063/1.3517865] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Abstract
Crystallization starts with nucleation and control of nucleation is crucial for the control of the number, size, perfection, polymorphism and other characteristics of crystalline materials. This is particularly true for crystallization in solution, which is an essential part of processes in the chemical and pharmaceutical industries and a major step in physiological and pathological phenomena. There have been significant recent advances in the understanding of the mechanism of nucleation of crystals in solution. The foremost of these are the two-step mechanism of nucleation and the notion of the solution-crystal spinodal. According to the two-step mechanism, the crystalline nucleus appears inside pre-existing metastable clusters of size several hundred nanometers, which consist of dense liquid and are suspended in the solution. While initially proposed for protein crystals, the applicability of this mechanism has been demonstrated for small molecule organic materials, colloids, polymers, and biominerals. This mechanism helps to explain several long-standing puzzles of crystal nucleation in solution: nucleation rates which are many orders of magnitude lower than theoretical predictions, the significance of the dense protein liquid, and others. At high supersaturations typical of most crystallizing systems, the generation of crystal embryos occurs in the spinodal regime, where the nucleation barrier is negligible. The solution-crystal spinodal helps to understand the role of heterogeneous substrates in nucleation and the selection of crystalline polymorphs. Importantly, these ideas provide powerful tools for control of the nucleation process by varying the solution thermodynamic parameters.
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Affiliation(s)
- Peter G Vekilov
- Department of Chemical and Biomolecular Engineering and Department of Chemistry, University of Houston, Houston Texas, 77204-4004, USA
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22
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Campi G, Mari A, Amenitsch H, Pifferi A, Cannas C, Suber L. Monitoring early stages of silver particle formation in a polymer solution by in situ and time resolved small angle X-ray scattering. NANOSCALE 2010; 2:2447-2455. [PMID: 20938556 DOI: 10.1039/c0nr00390e] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Silver particles have been prepared by reduction of silver nitrate with ascorbic acid in acidic aqueous solution containing a low concentration of a commercial polynaphthalene sulfonate polymer (Daxad 19) as dispersant agent. The reduction has been induced and controlled by the slow addition of ascorbic acid at a fixed rate; in this way, we were able to monitor the formation of a silver crystalline colloidal dispersion by in situ and time resolved Small Angle X-ray Scattering measurements. Modeling the scattering intensity with interacting spherical particles in a polymer-Ag like-fractal template allowed us to distinguish different stages involving liquid-like ordered cluster nucleation, cluster growth up to primary particle formation and particle coalescence. Between primary particle formation and particle coalescence, we observed the occurrence of a transient phase of core-shell type structures having primary particles as stable cores in expanding shells built by the organic polymer. We discuss these results in a twofold perspective pertaining both to technology, relative to controlled fabrication of metal nanoparticles and to basic chemical physics, dealing with non standard stepwise crystallization from solutions.
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Affiliation(s)
- Gaetano Campi
- CNR-Istituto di Cristallografia, Via Salaria, Km 29.300, Monterotondo Stazione, RM I-00015, Italy.
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23
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Abstract
The formation of crystalline nanoparticles starts with nucleation and control of nucleation is crucial for the control of the number, size, perfection, polymorph modification and other characteristics of particles. Recently, there have been significant advances in the understanding of the mechanism of nucleation of crystals in solution. The most significant of these is the two-step mechanism of nucleation, according to which the crystalline nucleus appears inside pre-existing metastable clusters of size several hundred nanometers, which consist of dense liquid and are suspended in the solution. While initially proposed for protein crystals, the applicability of this mechanism has been demonstrated for small-molecule organic and inorganic materials, colloids, and biominerals. This mechanism helps to explain several long-standing puzzles of crystal nucleation in solution: nucleation rates which are many orders of magnitude lower than theoretical predictions, nucleation kinetic dependencies with steady or receding parts at increasing supersaturation, the role of heterogeneous substrates for polymorph selection, the significance of the dense protein liquid, and others. More importantly, this mechanism provides powerful tools for control of the nucleation process by varying the solution thermodynamic parameters so that the volume occupied by the dense liquid shrinks or expands.
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Affiliation(s)
- Peter G Vekilov
- Department of Chemical and Biomolecular Engineering and Department of Chemistry, University of Houston, Houston, Texas 77204-4004, USA
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24
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Furukawa A, Tanaka H. Key role of hydrodynamic interactions in colloidal gelation. PHYSICAL REVIEW LETTERS 2010; 104:245702. [PMID: 20867312 DOI: 10.1103/physrevlett.104.245702] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2009] [Revised: 05/07/2010] [Indexed: 05/16/2023]
Abstract
Colloidal gelation is caused by the formation of a percolated network of colloidal particles suspended in a liquid. Thus far the major transport process leading to gelation has been believed to be the brownian diffusion of particles. Contrary to this common belief, we reveal by numerical simulations that many-body hydrodynamic interactions between colloidal particles also play an essential role in gelation: They significantly promote gelation, or lower the colloid volume fraction threshold for percolation, as compared to their absence. We find that the incompressible nature of a liquid component and the resulting self-organization of hydrodynamic flow with a transverse (rotational) character are responsible for this enhancement of network-forming ability.
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Affiliation(s)
- Akira Furukawa
- Institute of Industrial Science, University of Tokyo, Meguro-ku, Tokyo 153-8505, Japan
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Duff N, Peters B. Nucleation in a Potts lattice gas model of crystallization from solution. J Chem Phys 2009; 131:184101. [DOI: 10.1063/1.3250934] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Erdemir D, Lee AY, Myerson AS. Nucleation of crystals from solution: classical and two-step models. Acc Chem Res 2009; 42:621-9. [PMID: 19402623 DOI: 10.1021/ar800217x] [Citation(s) in RCA: 546] [Impact Index Per Article: 36.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Crystallization is vital to many processes occurring in nature and in the chemical, pharmaceutical, and food industries. Notably, crystallization is an attractive isolation step for manufacturing because this single process combines both particle formation and purification. Almost all of the products based on fine chemicals, such as dyes, explosives, and photographic materials, require crystallization in their manufacture, and more than 90% of all pharmaceutical products contain bioactive drug substances and excipients in the crystalline solid state. Hence control over the crystallization process allows manufacturers to obtain products with desired and reproducible properties. We judge the quality of a crystalline product based on four main properties: size, purity, morphology, and crystal structure. The pharmaceutical industry in particular requires production of the desired crystal form (polymorph) to assure the bioavailability and stability of the drug substance. In solution crystallization, nucleation plays a decisive role in determining the crystal structure and size distribution. Therefore, understanding the fundamentals of nucleation is crucial to achieve control over these properties. Because of its analytical simplicity, researchers have widely applied classical nucleation theory to solution crystallization. However, a number of differences between theoretical predictions and experimental results suggest that nucleation of solids from solution does not proceed via the classical pathway but follows more complex routes. In this Account, we discuss the shortcomings of classical nucleation theory and review studies contributing to the development of the modern two-step model. In the two-step model that was initially proposed for protein crystallization, a sufficient-sized cluster of solute molecules forms first, followed by reorganization of that cluster into an ordered structure. In recent experimental and theoretical studies, we and other researchers have demonstrated the applicability of the two-step mechanism to both macromolecules and small organic molecules, suggesting that this mechanism may underlie most crystallization processes from solutions. Because we have observed an increase in the organization time of appropriate lattice structures with greater molecular complexity, we propose that organization is the rate-determining step. Further development of a clearer picture of nucleation may help determine the optimum conditions necessary for the effective organization within the clusters. In addition, greater understanding of these processes may lead to the design of auxiliaries that can increase the rate of nucleation and avoid the formation of undesired solid forms, allowing researchers to obtain the final product in a timely and reproducible manner.
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Affiliation(s)
- Deniz Erdemir
- Department of Chemical & Biological Engineering, Illinois Institute of Technology, Chicago, Illinois 60616
- Process Research and Development, Bristol-Myers Squibb Company, One Squibb Drive, New Brunswick, New Jersey 08903, and
| | - Alfred Y. Lee
- Chemical and Physical Sciences, Schering-Plough Research Institute, 556 Morris Avenue, Summit, New Jersey 07901
| | - Allan S. Myerson
- Department of Chemical & Biological Engineering, Illinois Institute of Technology, Chicago, Illinois 60616
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Savage JR, Dinsmore AD. Experimental evidence for two-step nucleation in colloidal crystallization. PHYSICAL REVIEW LETTERS 2009; 102:198302. [PMID: 19519003 DOI: 10.1103/physrevlett.102.198302] [Citation(s) in RCA: 102] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2008] [Indexed: 05/27/2023]
Abstract
We investigated the freezing of colloidal spheres in two dimensions with single-particle resolution. Using micron-size, charge-stabilized polystyrene spheres with a temperature-dependent depletion attraction induced by surfactant micelles, we supercooled an initially amorphous (gaslike) system. Particle motions were monitored as crystallization proceeded. At low concentrations, freezing occurred in a single step in a manner consistent with classical nucleation theory. In other samples two-step nucleation was found, in which amorphous clusters grew to approximately 30 particles, then rapidly crystallized. Measured free energies show the role of metastable gas-liquid coexistence, which also enhanced the rate of nucleation following deeper quenches.
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Affiliation(s)
- J R Savage
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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28
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Babu S, Gimel JC, Nicolai T. Crystallization and dynamical arrest of attractive hard spheres. J Chem Phys 2009; 130:064504. [DOI: 10.1063/1.3074310] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Khan SJ, Sorensen CM, Chakrabarti A. Kinetics and morphology of cluster growth in a model of short-range attractive colloids. J Chem Phys 2009; 131:194908. [DOI: 10.1063/1.3262311] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Lovette MA, Browning AR, Griffin DW, Sizemore JP, Snyder RC, Doherty MF. Crystal Shape Engineering. Ind Eng Chem Res 2008. [DOI: 10.1021/ie800900f] [Citation(s) in RCA: 261] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michael A. Lovette
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080
| | - Andrea Robben Browning
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080
| | - Derek W. Griffin
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080
| | - Jacob P. Sizemore
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080
| | - Ryan C. Snyder
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080
| | - Michael F. Doherty
- Department of Chemical Engineering, University of California, Santa Barbara, California 93106-5080
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31
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Cerdà JJ, Sintes T, Holm C, Sorensen CM, Chakrabarti A. Shear effects on crystal nucleation in colloidal suspensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:031403. [PMID: 18851034 DOI: 10.1103/physreve.78.031403] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2008] [Indexed: 05/26/2023]
Abstract
Extensive two-dimensional Langevin dynamics simulations are used to determine the effect of steady shear flows on the crystal nucleation kinetics of charge stabilized colloids and colloids whose pair potential possess an attractive shallow well of a few k_{B}T 's (attractive colloids). Results show that in both types of systems small amounts of shear speeds up the crystallization process and enhances the quality of the growing crystal significantly. Moderate shear rates, on the other hand, destroy the ordering in the system. The very high shear rate regime where a reentering transition to the ordered state could exist is not considered in this work. In addition to the crystal nucleation phenomena, the analysis of the transport properties and the characterization of the steady state regime under shear are performed.
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Affiliation(s)
- Juan J Cerdà
- Frankfurt Institute for Advanced Studies, J. W. Goethe-Universität, Ruth-Moufang-Strasse 1, D-60438, Frankfurt am Main, Germany
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32
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Chen B, Nellas RB, Keasler SJ. Fractal aggregates in protein crystal nucleation. J Phys Chem B 2008; 112:4725-30. [PMID: 18358033 DOI: 10.1021/jp8002728] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Monte Carlo simulations of homogeneous nucleation for a protein model with an exceedingly short-ranged attractive potential yielded a nonconventional crystal nucleation mechanism, which proceeds by the formation of fractal, low-dimensional aggregates followed by a concurrent collapse and increase of the crystallinity of these aggregates to become compact ordered nuclei. This result corroborates a recently proposed two-step mechanism for protein crystal nucleation from solution.
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Affiliation(s)
- Bin Chen
- Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803-1804, USA.
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33
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Zhang TH, Liu XY. How Does a Transient Amorphous Precursor Template Crystallization. J Am Chem Soc 2007; 129:13520-6. [DOI: 10.1021/ja073598k] [Citation(s) in RCA: 125] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Tian Hui Zhang
- Contribution from the Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542
| | - Xiang Yang Liu
- Contribution from the Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542
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34
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Tóth GI, Gránásy L. Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: II. Nucleation in the metastable liquid immiscibility region. J Chem Phys 2007; 127:074710. [PMID: 17718630 DOI: 10.1063/1.2752506] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In the second part of our paper, we address crystal nucleation in the metastable liquid miscibility region of eutectic systems that is always present, though experimentally often inaccessible. While this situation resembles the one seen in single component crystal nucleation in the presence of a metastable vapor-liquid critical point addressed in previous works, it is more complex because of the fact that here two crystal phases of significantly different compositions may nucleate. Accordingly, at a fixed temperature below the critical point, six different types of nuclei may form: two liquid-liquid nuclei: two solid-liquid nuclei; and two types of composite nuclei, in which the crystalline core has a liquid "skirt," whose composition falls in between the compositions of the solid and the initial liquid phases, in addition to nuclei with concentric alternating composition shells of prohibitively high free energy. We discuss crystalline phase selection via exploring/identifying the possible pathways for crystal nucleation.
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Affiliation(s)
- Gyula I Tóth
- Research Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary
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35
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Hecht M, Harting J, Herrmann HJ. Stability diagram for dense suspensions of model colloidal Al2O3 particles in shear flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:051404. [PMID: 17677062 DOI: 10.1103/physreve.75.051404] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2006] [Indexed: 05/16/2023]
Abstract
In Al2O3 suspensions, depending on the experimental conditions, very different microstructures can be found, comprising fluidlike suspensions, a repulsive structure, and a clustered microstructure. For technical processing in ceramics, the knowledge of the microstructure is of importance, since it essentially determines the stability of a workpiece to be produced. To enlighten this topic, we investigate these suspensions under shear by means of simulations. We observe cluster formation on two different length scales: the distance of nearest neighbors and on the length scale of the system size. We find that the clustering behavior does not depend on the length scale of observation. If interparticle interactions are not attractive the particles form layers in the shear flow. The results are summarized in a stability diagram.
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Affiliation(s)
- Martin Hecht
- Institute for Computational Physics, Pfaffenwaldring 27, Stuttgart, Germany
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36
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Tanaka H, Araki T. Viscoelastic phase separation in soft matter: Numerical-simulation study on its physical mechanism. Chem Eng Sci 2006. [DOI: 10.1016/j.ces.2004.02.025] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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37
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Zaccarelli E, Saika-Voivod I, Buldyrev SV, Moreno AJ, Tartaglia P, Sciortino F. Gel to glass transition in simulation of a valence-limited colloidal system. J Chem Phys 2006; 124:124908. [PMID: 16599726 DOI: 10.1063/1.2177241] [Citation(s) in RCA: 80] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We numerically study a simple model for thermoreversible colloidal gelation in which particles can form reversible bonds with a predefined maximum number of neighbors. We focus on three and four maximally coordinated particles, since in these two cases the low valency makes it possible to probe, in equilibrium, slow dynamics down to very low temperatures T. By studying a large region of T and packing fraction phi we are able to estimate both the location of the liquid-gas phase separation spinodal and the locus of dynamic arrest, where the system is trapped in a disordered nonergodic state. We find that there are two distinct arrest lines for the system: a glass line at high packing fraction, and a gel line at low phi and T. The former is rather vertical (phi controlled), while the latter is rather horizontal (T controlled) in the phi-T plane. Dynamics on approaching the glass line along isotherms exhibit a power-law dependence on phi, while dynamics along isochores follow an activated (Arrhenius) dependence. The gel has clearly distinct properties from those of both a repulsive and an attractive glass. A gel to glass crossover occurs in a fairly narrow range in phi along low-T isotherms, seen most strikingly in the behavior of the nonergodicity factor. Interestingly, we detect the presence of anomalous dynamics, such as subdiffusive behavior for the mean squared displacement and logarithmic decay for the density correlation functions in the region where the gel dynamics interferes with the glass dynamics.
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Affiliation(s)
- E Zaccarelli
- Dipartimento di Fisica and CNR-INFM-SOFT, Universitá di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185, Roma, Italy.
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38
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Babu S, Rottereau M, Nicolai T, Gimel JC, Durand D. Flocculation and percolation in reversible cluster-cluster aggregation. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2006; 19:203-11. [PMID: 16505949 DOI: 10.1140/epje/e2006-00022-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2005] [Indexed: 05/06/2023]
Abstract
Off-lattice dynamic Monte-Carlo simulations were done of reversible cluster-cluster aggregation for spheres that form rigid bonds at contact. The equilibrium properties were found to be determined by the life time of encounters between two particles (te). te is a function not only of the probability to form or break a bond, but also of the elementary step size of the Brownian motion of the particles. In the flocculation regime the fractal dimension of the clusters is df=2.0 and the size distribution has a power law decay with exponent tau=1.5. At larger values of te transient gels are formed. Close to the percolation threshold the clusters have a fractal dimension df=2.7 and the power law exponent of the size distribution is tau=2.1. The transition between flocculation and percolation occurs at a characteristic weight average aggregation number that decreases with increasing volume fraction.
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Affiliation(s)
- S Babu
- Polymères Colloïdes Interfaces, UMR 6120 CNRS - Université du Maine, 72085, Le Mans Cedex 9, France
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39
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Huang H, Ruckenstein E. Thermodynamically stable dispersions induced by depletion interactions. J Colloid Interface Sci 2005; 290:336-42. [PMID: 15987641 DOI: 10.1016/j.jcis.2005.04.059] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2004] [Revised: 04/20/2005] [Accepted: 04/20/2005] [Indexed: 11/30/2022]
Abstract
When small particles are added to a colloidal dispersion of large particles, a depletion interaction between large particles occurs because the small ones are depleted from the gaps between the former particles. In the present paper, a cell model is employed to examine the behavior of a dispersion of large particles immersed in an electrolyte solution containing small particles. In this model, each cell consists of one large particle in its center and an associated atmosphere. Double-layer, van der Waals, and depletion interactions, as well as entropic effects, have been taken into account. When the change of the free energy with respect to that of the electrolyte solution is negative (and this happens in most cases), the dispersions of large particles are stable from a thermodynamic point of view. With increasing volume fraction of the small particles, the free energy change becomes more negative. The formation of gels observed experimentally in concentrated emulsions is explained through the formation of a thermodynamically stable dispersion.
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Affiliation(s)
- Haohao Huang
- Department of Chemical and Biological Engineering, State University of New York at Buffalo, Buffalo, NY 14260, USA
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40
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Zaccarelli E, Buldyrev SV, La Nave E, Moreno AJ, Saika-Voivod I, Sciortino F, Tartaglia P. Model for reversible colloidal gelation. PHYSICAL REVIEW LETTERS 2005; 94:218301. [PMID: 16090355 DOI: 10.1103/physrevlett.94.218301] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2004] [Indexed: 05/03/2023]
Abstract
We report a numerical study, covering a wide range of packing fraction Phi and temperature T, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number n(max) of bonded interactions. We show that, when n(max)<6, the liquid-gas coexistence region shrinks, giving access to regions of low Phi where dynamics can be followed down to low T without an intervening phase separation. We characterize these arrested states at low densities (gel states) in terms of structure and dynamical slowing down, pointing out features which are very different from the standard glassy states observed at high Phi values.
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Affiliation(s)
- E Zaccarelli
- Dipartimento di Fisica and INFM-CRS SOFT, Università di Roma "La Sapienza", Piazzale Aldo Moro 2, I-00185 Roma, Italy
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41
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Cerdà JJ, Sintes T, Sorensen CM, Chakrabarti A. Structure factor scaling in colloidal phase separation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:051405. [PMID: 15600616 DOI: 10.1103/physreve.70.051405] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2004] [Indexed: 05/24/2023]
Abstract
The dynamical scaling hypothesis for the structure factor, S (q) , in depletion-driven colloidal phase separation is studied by carrying out Brownian dynamics simulations. A true dynamical scaling is observed for shallow quenches into the two-phase coexistence region. In such a quench, compact clusters nucleate and grow with time and there is only one characteristic length scale in the system after an initial transient period. Scaling is satisfied beyond this initial period. In contrast, deep quenches lead to fractal cluster growth, and the system is controlled by two characteristic lengths that evolve differently in time [Huang, Oh, and Sorensen (HOS), Phys. Rev. E 57, 875 (1998)]. True dynamical scaling thus cannot be expected to hold. However, an apparent scaling for the structure factor is observed over some period of time when these two characteristic length scales become comparable to each other. We compare our simulation results for the total structure factor to theoretical predictions by HOS by writing it as a product of cluster-cluster and the averaged single-cluster structure factors, each with its own characteristic length.
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Affiliation(s)
- Juan J Cerdà
- Departament de Física and IMEDEA (CSIC-UIB), Universitat de les Illes Balears and Consejo Superior de Investigaciones Científicas, 07071 Palma de Mallorca, Spain
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42
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Saika-Voivod I, Zaccarelli E, Sciortino F, Buldyrev SV, Tartaglia P. Effect of bond lifetime on the dynamics of a short-range attractive colloidal system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:041401. [PMID: 15600402 DOI: 10.1103/physreve.70.041401] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2004] [Revised: 06/10/2004] [Indexed: 05/24/2023]
Abstract
We perform molecular dynamics simulations of short-range attractive colloid particles modeled by a narrow (3% of the hard sphere diameter) square well potential of unit depth. We compare the dynamics of systems with the same thermodynamics but different bond lifetimes, by adding to the square well potential a thin barrier at the edge of the attractive well. For permanent bonds, the relaxation time tau diverges as the packing fraction phi approaches a threshold related to percolation, while for short-lived bonds, the phi dependence of tau is more typical of a glassy system. At intermediate bond lifetimes, the phi dependence of tau is driven by percolation at low phi , but then crosses over to glassy behavior at higher phi . We also study the wave vector dependence of the percolation dynamics.
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Affiliation(s)
- I Saika-Voivod
- Dipartimento di Fisica and Istituto Nazionale per la Fisica della Materia, Università di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185, Roma, Italy
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43
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Cerdà JJ, Sintes T, Sorensen CM, Chakrabarti A. Kinetics of phase transformations in depletion-driven colloids. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:011405. [PMID: 15324049 DOI: 10.1103/physreve.70.011405] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2004] [Indexed: 05/24/2023]
Abstract
We present results from a detailed numerical study of the kinetics of phase transformations in a model two-dimensional depletion-driven colloidal system. Transition from a single, dispersed phase to a two-phase coexistence of monomers and clusters is obtained as the depth of the interaction potential among the colloidal particles is changed. Increasing the well depth further, fractal clusters are observed in the simulation. These fractal clusters have a hybrid structure in the sense that they show hexagonal closed-packed crystalline ordering at short length scales and a ramified fractal nature at larger length scales. For sufficiently deep potential wells, the diffusion-limited cluster-cluster aggregation model is recovered in terms of the large-scale fractal dimension Df of the clusters, the kinetic exponent z, and the scaling form of the cluster size distribution. For shallower well depths inside the two-phase coexistence region, simulation results for the kinetics of cluster growth are compared with intermediate-stage phase separation in binary mixtures. In the single-phase region, growth kinetics agree well with a mean-field aggregation-fragmentation model of Sorensen, Zhang, and Taylor.
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Affiliation(s)
- Juan J Cerdà
- Departament de Física and IMEDEA (CSIC-UIB), Universitat de les Illes Balears and Consejo Superior de Investigaciones Científicas, 07122 Palma de Mallorca, Spain
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44
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Bonanomi E, Sandkühler P, Sefcik J, Morari M, Morbidelli M. Precursor Aggregate Distributions for Particulate Gels. Ind Eng Chem Res 2004. [DOI: 10.1021/ie0342006] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eleonora Bonanomi
- Institut für Automatik, ETH, Swiss Federal Institute of Technology, ETHZ - ETL, CH 8092 Zurich, Switzerland, and Institut für Chemie- und Bioingenieurswissenschaften, Swiss Federal Institute of Technology Zurich, ETH Hönggerberg/HCI, CH 8093 Zurich, Switzerland
| | - Peter Sandkühler
- Institut für Automatik, ETH, Swiss Federal Institute of Technology, ETHZ - ETL, CH 8092 Zurich, Switzerland, and Institut für Chemie- und Bioingenieurswissenschaften, Swiss Federal Institute of Technology Zurich, ETH Hönggerberg/HCI, CH 8093 Zurich, Switzerland
| | - Jan Sefcik
- Institut für Automatik, ETH, Swiss Federal Institute of Technology, ETHZ - ETL, CH 8092 Zurich, Switzerland, and Institut für Chemie- und Bioingenieurswissenschaften, Swiss Federal Institute of Technology Zurich, ETH Hönggerberg/HCI, CH 8093 Zurich, Switzerland
| | - Manfred Morari
- Institut für Automatik, ETH, Swiss Federal Institute of Technology, ETHZ - ETL, CH 8092 Zurich, Switzerland, and Institut für Chemie- und Bioingenieurswissenschaften, Swiss Federal Institute of Technology Zurich, ETH Hönggerberg/HCI, CH 8093 Zurich, Switzerland
| | - Massimo Morbidelli
- Institut für Automatik, ETH, Swiss Federal Institute of Technology, ETHZ - ETL, CH 8092 Zurich, Switzerland, and Institut für Chemie- und Bioingenieurswissenschaften, Swiss Federal Institute of Technology Zurich, ETH Hönggerberg/HCI, CH 8093 Zurich, Switzerland
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45
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Borodich A, Rojdestvenski I, Cottam M. Lateral heterogeneity of photosystems in thylakoid membranes studied by Brownian dynamics simulations. Biophys J 2003; 85:774-89. [PMID: 12885627 PMCID: PMC1303201 DOI: 10.1016/s0006-3495(03)74519-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/05/2002] [Accepted: 04/01/2003] [Indexed: 10/21/2022] Open
Abstract
The aggregation and segregation of photosystems in higher plant thylakoid membranes as stromal cation-induced phenomena are studied by the Brownian dynamics method. A theoretical model of photosystems lateral movement within the membrane plane is developed, assuming their pairwise effective potential interaction in aqueous and lipid media and their diffusion. Along with the screened electrostatic repulsive interaction the model accounts for the van der Waals-type, elastic, and lipid-induced attractive forces between photosystems of different sizes and charges. Simulations with a priori estimated parameters demonstrate that all three studied repulsion-attraction alternatives might favor the local segregation of photosystems under physiologically reasonable conditions. However, only the lipid-induced potential combined with the size-corrected screened Coulomb interaction provides the segregated configurations with photosystems II localized in the central part of the grana-size simulation cell and photosystems I occupying its margins, as observed experimentally. Mapping of thermodynamic states reveals that the coexistence curves between isotropic and aggregated phases are the sigmoidlike functions regardless of the effective potential type. It correlates with measurements of the chlorophyll content of thylakoid fragments. Also the universality of the phase curves characterizes the aggregation and segregation of photosystems as order-disorder phase transitions with the Debye radius as a governing parameter.
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Affiliation(s)
- Andrei Borodich
- Umeå Plant Science Center, Department of Plant Physiology, Umeå University, Umeå, Sweden
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46
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d'Arjuzon RJM, Frith W, Melrose JR. Brownian dynamics simulations of aging colloidal gels. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:061404. [PMID: 16241223 DOI: 10.1103/physreve.67.061404] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/14/2002] [Indexed: 05/04/2023]
Abstract
The aging of colloidal gels is investigated using very long duration Brownian dynamics simulations. The Asakura-Oosawa description of the depletion interaction is used to model a simple colloid polymer mixture. Several regimes are identified during gel formation. The intermediate scattering function displays a double decay characteristic of systems where some kinetic processes are frozen. The beta relaxation at short times is explained in terms of the Krall-Weitz model for the decorrelation due to the elastic modes present. The alpha relaxation at long times is well described by a stretched exponential, showing a wide spectrum of relaxation times for which the q dependence is tau(alpha)=q(-2.2), lower than for diffusion. For the shortest waiting times, a combination of two stretched exponentials is used, suggesting a bimodal distribution. The extracted relaxation times vary with waiting time as tau(alpha)=tau(0.66)(w), more slowly than in the simple aging case. The real space displacements are found to be strongly non-Gaussian, correlated in space and time. We were unable to find clear evidence that the gel aging was driven by internal stresses. Rather, we hypothesize that in this case of weakly interacting gels, the aging behavior arises due to the thermal diffusion of strands, constrained by the percolating network, which ruptures discontinuously. Although the mechanisms differ, the similarity of some of the results to aging of glasses is striking.
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Gimel JC, Nicolai T, Durand D. Relation between aggregation and phase separation: three-dimensional Monte Carlo simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:061405. [PMID: 12513283 DOI: 10.1103/physreve.66.061405] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2002] [Revised: 08/26/2002] [Indexed: 05/24/2023]
Abstract
We study phase separation of particles in solution using Monte Carlo simulations of reversible aggregation on a cubic lattice. Two stages of the phase separation can be clearly distinguished: initial random aggregation and subsequent densification. Step one leads to a distribution of fractal aggregates close to the binodal and to a temporary gel for large attractive interaction. Step two leads to isolated spherical dense domains close to the binodal and branched wormlike strands for large attractive interactions. The transition between the two types of structure is gradual and there is no clear feature that shows the existence of a spinodal. The first stage of the phase separation is metastable very close to the binodal or at very large interaction energy. In the latter case, the second step can be viewed as an aging process of the gel formed in the first step.
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Affiliation(s)
- Jean Christophe Gimel
- Polymères Colloïdes Interfaces, CNRS UMR6120, Université du Maine, F-72085 Le Mans cedex 9, France.
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Galkin O, Chen K, Nagel RL, Hirsch RE, Vekilov PG. Liquid-liquid separation in solutions of normal and sickle cell hemoglobin. Proc Natl Acad Sci U S A 2002; 99:8479-83. [PMID: 12070342 PMCID: PMC124280 DOI: 10.1073/pnas.122055299] [Citation(s) in RCA: 140] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
We show that in solutions of human hemoglobin (Hb)--oxy- and deoxy-Hb A or S--of near-physiological pH, ionic strength, and Hb concentration, liquid-liquid phase separation occurs reversibly and reproducibly at temperatures between 35 and 40 degrees C. In solutions of deoxy-HbS, we demonstrate that the dense liquid droplets facilitate the nucleation of HbS polymers, whose formation is the primary pathogenic event for sickle cell anemia. In view of recent results that shifts of the liquid-liquid separation phase boundary can be achieved by nontoxic additives at molar concentrations up to 30 times lower than the protein concentrations, these findings open new avenues for the inhibition of the HbS polymerization.
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Affiliation(s)
- Oleg Galkin
- Department of Chemical Engineering, University of Houston, Houston, TX 77204, USA
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Anderson VJ, Lekkerkerker HNW. Insights into phase transition kinetics from colloid science. Nature 2002; 416:811-5. [PMID: 11976674 DOI: 10.1038/416811a] [Citation(s) in RCA: 589] [Impact Index Per Article: 26.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Colloids display intriguing transitions between gas, liquid, solid and liquid crystalline phases. Such phase transitions are ubiquitous in nature and have been studied for decades. However, the predictions of phase diagrams are not always realized; systems often become undercooled, supersaturated, or trapped in gel-like states. In many cases the end products strongly depend on the starting position in the phase diagram and discrepancies between predictions and actual observations are due to the intricacies of the dynamics of phase transitions. Colloid science aims to understand the underlying mechanisms of these transitions. Important advances have been made, for example, with new imaging techniques that allow direct observation of individual colloidal particles undergoing phase transitions, revealing some of the secrets of the complex pathways involved.
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Affiliation(s)
- V J Anderson
- Van't Hoff Laboratory for Physical and Colloid Chemistry, Debye Institute, Utrecht University, Padualaan 8, 3584 CH Utrecht, The Netherlands
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Evans RM, Poon WC, Renth F. Classification of ordering kinetics in three-phase systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:031403. [PMID: 11580335 DOI: 10.1103/physreve.64.031403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2001] [Indexed: 05/23/2023]
Abstract
Though equations of motion containing transport coefficients are required to quantitatively predict the phase-ordering dynamics of any given system, a great deal can be gleaned just from the shape of the free-energy landscape. We demonstrate how to extract the most information concerning phase-ordering phenomenology from a knowledge of a system's free-energy function, or phase diagram. Many putative pathways to equilibrium can be ruled out on the grounds of the second law of thermodynamics. In some parts of the phase diagram, these considerations are sufficient to completely determine the phase-ordering process without ever having to calculate a transport coefficient, even when three phases are present. The results include a large number of regions of the phase diagram with distinct phase-ordering kinetics, and some surprisingly elaborate routes to the equilibrium state. A process is found whereby a crystalline condensation nucleus becomes coated with a shell of gas, buffering it from a majority metastable liquid phase. Our results, based on thermodynamic arguments, are supported by numerical solution of model B, which describes diffusive phase-ordering kinetics. Some of our predictions are tested against experimental observations of colloid-polymer mixtures, described in more detail in the preceding paper [F. Renth, W. C. K. Poon, and R. M. L. Evans, Phys. Rev. E 64, 031402 (2001)]. A compact notation is developed to represent intricate phase-ordering pathways.
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Affiliation(s)
- R M Evans
- Department of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland, United Kingdom
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