1
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Sorichetti V, Ninarello A, Ruiz-Franco J, Hugouvieux V, Zaccarelli E, Micheletti C, Kob W, Rovigatti L. Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks. J Chem Phys 2023; 158:074905. [PMID: 36813705 DOI: 10.1063/5.0134271] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.
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Affiliation(s)
- Valerio Sorichetti
- Laboratoire Charles Coulomb (L2C), Univ. Montpellier, CNRS, F-34095 Montpellier, France
| | | | | | | | | | - Cristian Micheletti
- SISSA-Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy
| | - Walter Kob
- Laboratoire Charles Coulomb (L2C), Univ. Montpellier, CNRS, F-34095 Montpellier, France
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2
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Jonas H, Schall P, Bolhuis PG. Extended Wertheim theory predicts the anomalous chain length distributions of divalent patchy particles under extreme confinement. J Chem Phys 2022; 157:094903. [DOI: 10.1063/5.0098882] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Colloidal patchy particles with divalent attractive interaction can self-assemble into linear polymer chains. Their equilibrium properties in 2D and 3D are well described by Wertheim's thermodynamic perturbation theory which predicts a well-defined exponentially decaying equilibrium chain length distribution. In experi- mental realizations, due to gravity, particles sediment to the bottom of the suspension forming a monolayer of particles with a gravitational height smaller than the particle diameter. In accordance with experiments, an anomalously high monomer concentration is observed in simulations which is not well understood. To account for this observation, we interpret the polymerization as taking place in a highly confined quasi-2D plane and extend the Wertheim thermodynamic perturbation theory by defining addition reactions constants as functions of the chain length. We derive the theory, test it on simple square well potentials, and apply it to the experimental case of synthetic colloidal patchy particles immersed in a binary liquid mixture that are described by an accurate effective critical Casimir patchy particle potential. The important interaction parameters entering the theory are explicitly computed using the integral method in combination with Monte Carlo sampling. Without any adjustable parameter, the predictions of the chain length distribution are in excellent agreement with explicit simulations of self-assembling particles. We discuss generality of the approach, and its application range.
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Affiliation(s)
- Hannah Jonas
- University of Amsterdam Van 't Hoff Institute for Molecular Sciences, Netherlands
| | - Peter Schall
- Institute of Physics, Universiteit van Amsterdam Faculteit der Natuurwetenschappen Wiskunde en Informatica, Netherlands
| | - Peter G. Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam Van 't Hoff Institute for Molecular Sciences, Netherlands
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3
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Russo J, Leoni F, Martelli F, Sciortino F. The physics of empty liquids: from patchy particles to water. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:016601. [PMID: 34905739 DOI: 10.1088/1361-6633/ac42d9] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2021] [Accepted: 12/14/2021] [Indexed: 06/14/2023]
Abstract
Empty liquids represent a wide class of materials whose constituents arrange in a random network through reversible bonds. Many key insights on the physical properties of empty liquids have originated almost independently from the study of colloidal patchy particles on one side, and a large body of theoretical and experimental research on water on the other side. Patchy particles represent a family of coarse-grained potentials that allows for a precise control of both the geometric and the energetic aspects of bonding, while water has arguably the most complex phase diagram of any pure substance, and a puzzling amorphous phase behavior. It was only recently that the exchange of ideas from both fields has made it possible to solve long-standing problems and shed new light on the behavior of empty liquids. Here we highlight the connections between patchy particles and water, focusing on the modelling principles that make an empty liquid behave like water, including the factors that control the appearance of thermodynamic and dynamic anomalies, the possibility of liquid-liquid phase transitions, and the crystallization of open crystalline structures.
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Affiliation(s)
- John Russo
- Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Fabio Leoni
- Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
| | - Fausto Martelli
- IBM Research Europe, Hartree Centre, Daresbury WA4 4AD, United Kingdom
| | - Francesco Sciortino
- Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
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4
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Sorichetti V, Hugouvieux V, Kob W. Dynamics of Nanoparticles in Polydisperse Polymer Networks: from Free Diffusion to Hopping. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c01394] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Valerio Sorichetti
- Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), CNRS, Université Paris-Saclay, F-91405 Orsay, France
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, F-34095 Montpellier, France
- IATE, Université Montpellier, INRAE, Institut Agro, F-34060 Montpellier, France
| | - Virginie Hugouvieux
- IATE, Université Montpellier, INRAE, Institut Agro, F-34060 Montpellier, France
| | - Walter Kob
- Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, F-34095 Montpellier, France
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5
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Jonas HJ, Stuij SG, Schall P, Bolhuis PG. A temperature-dependent critical Casimir patchy particle model benchmarked onto experiment. J Chem Phys 2021; 155:034902. [PMID: 34293902 DOI: 10.1063/5.0055012] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Synthetic colloidal patchy particles immersed in a binary liquid mixture can self-assemble via critical Casimir interactions into various superstructures, such as chains and networks. Up to now, there are no quantitatively accurate potential models that can simulate and predict this experimentally observed behavior precisely. Here, we develop a protocol to establish such a model based on a combination of theoretical Casimir potentials and angular switching functions. Using Monte Carlo simulations, we optimize several material-specific parameters in the model to match the experimental chain length distribution and persistence length. Our approach gives a systematic way to obtain accurate potentials for critical Casimir induced patchy particle interactions and can be used in large-scale simulations.
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Affiliation(s)
- H J Jonas
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
| | - S G Stuij
- Institute of Physics, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
| | - P Schall
- Institute of Physics, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
| | - P G Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, P.O. Box 94157, 1090 GD Amsterdam, The Netherlands
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6
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Cai Z, Li Z, Ravaine S, He M, Song Y, Yin Y, Zheng H, Teng J, Zhang A. From colloidal particles to photonic crystals: advances in self-assembly and their emerging applications. Chem Soc Rev 2021; 50:5898-5951. [PMID: 34027954 DOI: 10.1039/d0cs00706d] [Citation(s) in RCA: 117] [Impact Index Per Article: 39.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Over the last three decades, photonic crystals (PhCs) have attracted intense interests thanks to their broad potential applications in optics and photonics. Generally, these structures can be fabricated via either "top-down" lithographic or "bottom-up" self-assembly approaches. The self-assembly approaches have attracted particular attention due to their low cost, simple fabrication processes, relative convenience of scaling up, and the ease of creating complex structures with nanometer precision. The self-assembled colloidal crystals (CCs), which are good candidates for PhCs, have offered unprecedented opportunities for photonics, optics, optoelectronics, sensing, energy harvesting, environmental remediation, pigments, and many other applications. The creation of high-quality CCs and their mass fabrication over large areas are the critical limiting factors for real-world applications. This paper reviews the state-of-the-art techniques in the self-assembly of colloidal particles for the fabrication of large-area high-quality CCs and CCs with unique symmetries. The first part of this review summarizes the types of defects commonly encountered in the fabrication process and their effects on the optical properties of the resultant CCs. Next, the mechanisms of the formation of cracks/defects are discussed, and a range of versatile fabrication methods to create large-area crack/defect-free two-dimensional and three-dimensional CCs are described. Meanwhile, we also shed light on both the advantages and limitations of these advanced approaches developed to fabricate high-quality CCs. The self-assembly routes and achievements in the fabrication of CCs with the ability to open a complete photonic bandgap, such as cubic diamond and pyrochlore structure CCs, are discussed as well. Then emerging applications of large-area high-quality CCs and unique photonic structures enabled by the advanced self-assembly methods are illustrated. At the end of this review, we outlook the future approaches in the fabrication of perfect CCs and highlight their novel real-world applications.
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Affiliation(s)
- Zhongyu Cai
- Research Institute for Frontier Science, Beijing Advanced Innovation Center for Biomedical Engineering, School of Space and Environment, Beihang University, Beijing 100191, China. and Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, 117576, Singapore and Department of Chemistry, University of Pittsburgh, Pittsburgh, PA 15260, USA
| | - Zhiwei Li
- Department of Chemistry, University of California, Riverside, CA 92521, USA
| | - Serge Ravaine
- CNRS, Univ. Bordeaux, CRPP, UMR 5031, F-33600 Pessac, France
| | - Mingxin He
- Department of Physics, Center for Soft Matter Research, New York University, New York, NY 10003, USA
| | - Yanlin Song
- Beijing National Laboratory for Molecular Sciences (BNLMS), Key Laboratory of Green Printing, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Yadong Yin
- Department of Chemistry, University of California, Riverside, CA 92521, USA
| | - Hanbin Zheng
- CNRS, Univ. Bordeaux, CRPP, UMR 5031, F-33600 Pessac, France
| | - Jinghua Teng
- Institute of Materials Research and Engineering, Agency for Science, Technology, and Research (A*STAR), 2 Fusionopolis Way, Innovis, #08-03, Singapore 138634, Singapore.
| | - Ao Zhang
- Research Institute for Frontier Science, Beijing Advanced Innovation Center for Biomedical Engineering, School of Space and Environment, Beihang University, Beijing 100191, China.
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7
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Tagliabue A, Landsgesell J, Mella M, Holm C. Can oppositely charged polyelectrolyte stars form a gel? A simulational study. SOFT MATTER 2021; 17:1574-1588. [PMID: 33351002 DOI: 10.1039/d0sm01617a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We present a Langevin molecular dynamics study of an equimolar mixture of monodispersed oppositely charged di-block four-armed polyelectrolyte stars. We used an implicit solvent coarse-grained representation of the polyelectrolyte stars, and varied the length of the terminal charged blocks that reside on each arm. By varying the polymer concentration, we computed PV diagrams and determined the free-swelling equilibrium concentration with respect to a pure water reservoir as a function of the charged block length. We investigated various structural properties of the resulting equilibrium structures, like the number of ionic bonds, dangling arms, isolated stars, and cluster sizes. The ionic bonds featured a broad distribution of the number of arms involved and also displayed a distribution of net charges peaked around the neutral ionic bond. Our main result is that for charged block length equal to 4 and 5 ionized beads the resulting macro-aggregate spans the box and forms a network phase. Furthermore, we investigated the restructuring dynamics of ionic bonds; the results suggested both short bond lifetimes and a high frequency of ballistic association/dissociation events. Bonds result strong enough to yield a stable gel phase, but they are still weak enough to allow network restructuring under thermal fluctuations.
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Affiliation(s)
- Andrea Tagliabue
- Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 9, 22100, Como, Italy
| | - Jonas Landsgesell
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, Stuttgart, 70569, Germany.
| | - Massimo Mella
- Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell'Insubria, via Valleggio 9, 22100, Como, Italy
| | - Christian Holm
- Institute for Computational Physics, University of Stuttgart, Allmandring 3, Stuttgart, 70569, Germany.
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8
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Singh RK, Mahato J, Chowdhury A, Sain A, Nandi A. Non-Gaussian subdiffusion of single-molecule tracers in a hydrated polymer network. J Chem Phys 2020; 152:024903. [PMID: 31941310 DOI: 10.1063/1.5128743] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Single molecule tracking experiments inside a hydrated polymer network have shown that the tracer motion is subdiffusive due to the viscoelastic environment inside the gel-like network. This property can be related to the negative autocorrelation of the instantaneous displacements at short times. Although the displacements of the individual tracers exhibit Gaussian statistics, the displacement distribution of all the trajectories combined from different spatial locations of the polymer network exhibits a non-Gaussian distribution. Here, we analyze many individual tracer trajectories to show that the central portion of the non-Gaussian distribution can be well approximated by an exponential distribution that spreads sublinearly with time. We explain all these features seen in the experiment by a generalized Langevin model for an overdamped particle with algebraically decaying correlations. We show that the degree of non-Gaussianity can change with the extent of heterogeneity, which is controlled in our model by the experimentally observed distributions of the motion parameters.
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Affiliation(s)
- R K Singh
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Jaladhar Mahato
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Arindam Chowdhury
- Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Anirban Sain
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
| | - Amitabha Nandi
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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9
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Ciarella S, Biezemans RA, Janssen LMC. Understanding, predicting, and tuning the fragility of vitrimeric polymers. Proc Natl Acad Sci U S A 2019; 116:25013-25022. [PMID: 31767770 PMCID: PMC6911242 DOI: 10.1073/pnas.1912571116] [Citation(s) in RCA: 28] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Fragility is an empirical property that describes how abruptly a glass-forming material solidifies upon supercooling. The degree of fragility carries important implications for the functionality and processability of a material, as well as for our fundamental understanding of the glass transition. However, the microstructural properties underlying fragility still remain poorly understood. Here, we explain the microstructure-fragility link in vitrimeric networks, a novel type of high-performance polymers with unique bond-swapping functionality and unusual glass-forming behavior. Our results are gained from coarse-grained computer simulations and first-principles mode-coupling theory (MCT) of star-polymer vitrimers. We first demonstrate that the vitrimer fragility can be tuned over an unprecedentedly broad range, from fragile to strong and even superstrong behavior, by decreasing the bulk density. Remarkably, this entire phenomenology can be reproduced by microscopic MCT, thus challenging the conventional belief that existing first-principles theories cannot account for nonfragile behaviors. Our MCT analysis allows us to rationally identify the microstructural origin of the fragile-to-superstrong crossover, which is rooted in the sensitivity of the static structure factor to temperature variations. On the molecular scale, this behavior stems from a change in dominant length scales, switching from repulsive excluded-volume interactions to intrachain attractions as the vitrimer density decreases. Finally, we develop a simplified schematic MCT model which corroborates our microscopically founded conclusions and which unites our findings with earlier MCT studies. Our work sheds additional light on the elusive structure-fragility link in glass-forming matter and provides a first-principles-based platform for designing amorphous materials with an on-demand dynamic response.
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Affiliation(s)
- Simone Ciarella
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Rutger A Biezemans
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Liesbeth M C Janssen
- Theory of Polymers and Soft Matter, Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
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10
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Liu SJ, Li JT, Gu F, Wang HJ. Crystallization, vitrification, and gelation of patchy colloidal particles. CHINESE J CHEM PHYS 2019. [DOI: 10.1063/1674-0068/cjcp1810231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Shu-jing Liu
- College of Chemistry and Environmental Science, Hebei University, Baoding 071002, China
- College of Science, Agricultural University of Hebei, Baoding 071001, China
| | - Jiang-tao Li
- College of Chemistry and Environmental Science, Hebei University, Baoding 071002, China
| | - Fang Gu
- College of Chemistry and Environmental Science, Hebei University, Baoding 071002, China
| | - Hai-jun Wang
- College of Chemistry and Environmental Science, Hebei University, Baoding 071002, China
- Chemical Biology Key Laboratory of Hebei Province, Hebei University, Baoding 071002, China
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11
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Handle PH, Rovigatti L, Sciortino F. q-Independent Slow Dynamics in Atomic and Molecular Systems. PHYSICAL REVIEW LETTERS 2019; 122:175501. [PMID: 31107067 DOI: 10.1103/physrevlett.122.175501] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2018] [Indexed: 06/09/2023]
Abstract
Investigating million-atom systems for very long simulation times, we demonstrate that the collective density-density correlation time (τ_{α}) in simulated supercooled water and silica becomes wave-vector independent (q^{0}) when the probing wavelength is several times larger than the interparticle distance. The q independence of the collective density-density correlation functions, a feature clearly observed in light-scattering studies of some soft-matter systems, is thus a genuine feature of many (but not all) slow-dynamics systems, either atomic, molecular, or colloidal. Indeed, we show that when the dynamics of the density fluctuations includes particle-type diffusion, as in the case of the Lennard-Jones binary-mixture model, the q^{0} regime does not set in and the relaxation time continues to scale as τ_{α}∼q^{-2} even at small q.
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Affiliation(s)
- Philip H Handle
- Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Lorenzo Rovigatti
- Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, I-00185 Roma, Italy
- CNR-ISC, UoS Sapienza, Piazzale Aldo Moro 5, I-00185 Roma, Italy
| | - Francesco Sciortino
- Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 5, I-00185 Roma, Italy
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12
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Stopper D, Hirschmann F, Oettel M, Roth R. Bulk structural information from density functionals for patchy particles. J Chem Phys 2018; 149:224503. [DOI: 10.1063/1.5064780] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Daniel Stopper
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Frank Hirschmann
- Institute for Applied Physics, University of Tübingen, Auf der Morgenstelle 16, 72076 Tübingen, Germany
| | - Martin Oettel
- Institute for Applied Physics, University of Tübingen, Auf der Morgenstelle 16, 72076 Tübingen, Germany
| | - Roland Roth
- Institute for Theoretical Physics, University of Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
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13
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Bleibel J, Habiger M, Lütje M, Hirschmann F, Roosen-Runge F, Seydel T, Zhang F, Schreiber F, Oettel M. Two time scales for self and collective diffusion near the critical point in a simple patchy model for proteins with floating bonds. SOFT MATTER 2018; 14:8006-8016. [PMID: 30187060 DOI: 10.1039/c8sm00599k] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Using dynamic Monte Carlo and Brownian dynamics, we investigate a floating bond model in which particles can bind through mobile bonds. The maximum number of bonds (here fixed to 4) can be tuned by appropriately choosing the repulsive, nonadditive interactions among bonds and particles. We compute the static and dynamic structure factor (intermediate scattering function) in the vicinity of the gas-liquid critical point. The static structure exhibits a weak tetrahedral network character. The intermediate scattering function shows a temporal decay deviating from a single exponential, which can be described by a double exponential decay where the two time scales differ approximately by one order of magnitude. This time scale separation is robust over a range of wave numbers. The analysis of clusters in real space indicates the formation of noncompact clusters and shows a considerable stretch in the instantaneous size distribution when approaching the critical point. The average time evolution of the largest subcluster of given initial clusters with 10 or more particles also shows a double exponential decay. The observation of two time scales in the intermediate scattering function at low packing fractions is consistent with similar findings in globular protein solutions with trivalent metal ions that act as bonds between proteins.
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Affiliation(s)
- J Bleibel
- Institut für Angewandte Physik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany.
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14
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Rovigatti L, Russo J, Romano F. How to simulate patchy particles ⋆. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:59. [PMID: 29748868 DOI: 10.1140/epje/i2018-11667-x] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Accepted: 04/16/2018] [Indexed: 06/08/2023]
Abstract
Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed significantly to our understanding of the behaviour of patchy particles, but, although simple in principle, advanced simulation techniques are often required to sample the low temperatures and long time-scales associated with their self-assembly behaviour. In this work we review the most popular simulation techniques that have been used to study patchy particles, with a special focus on Monte Carlo methods. We cover many of the tools required to simulate patchy systems, from interaction potentials to biased moves, cluster moves, and free-energy methods. The review is complemented by an educationally oriented Monte Carlo computer code that implements all the techniques described in the text to simulate a well-known tetrahedral patchy particle model.
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Affiliation(s)
- Lorenzo Rovigatti
- CNR-ISC, Uos Sapienza, Piazzale A. Moro 2, 00185, Roma, Italy.
- Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, 00185, Roma, Italy.
| | - John Russo
- School of Mathematics, University of Bristol, BS8 1TW, Bristol, UK
| | - Flavio Romano
- Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca' Foscari di Venezia, Via Torino 155, 30172, Venezia Mestre, Italy
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15
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Rovigatti L, Nava G, Bellini T, Sciortino F. Self-Dynamics and Collective Swap-Driven Dynamics in a Particle Model for Vitrimers. Macromolecules 2018. [DOI: 10.1021/acs.macromol.7b02186] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Lorenzo Rovigatti
- CNR-ISC,
Uos Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy
- Department
of Physics, Sapienza, Universitá di Roma, Piazzale Aldo
Moro 2, I-00185, Roma, Italy
| | - Giovanni Nava
- Department
of Medical Biotechnology and Translational Medicine, Universita degli Studi di Milano, via Fratelli Cervi 93, I-20090 Segrate, MI, Italy
| | - Tommaso Bellini
- Department
of Medical Biotechnology and Translational Medicine, Universita degli Studi di Milano, via Fratelli Cervi 93, I-20090 Segrate, MI, Italy
| | - Francesco Sciortino
- Department
of Physics, Sapienza, Universitá di Roma, Piazzale Aldo
Moro 2, I-00185, Roma, Italy
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16
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Dias CS, Araújo NAM, Telo da Gama MM. Dynamics of network fluids. Adv Colloid Interface Sci 2017; 247:258-263. [PMID: 28802478 DOI: 10.1016/j.cis.2017.07.001] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/08/2017] [Revised: 05/16/2017] [Accepted: 07/02/2017] [Indexed: 11/20/2022]
Abstract
Network fluids are structured fluids consisting of chains and branches. They are characterized by unusual physical properties, such as, exotic bulk phase diagrams, interfacial roughening and wetting transitions, and equilibrium and nonequilibrium gels. Here, we provide an overview of a selection of their equilibrium and dynamical properties. Recent research efforts towards bridging equilibrium and non-equilibrium studies are discussed, as well as several open questions.
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Affiliation(s)
- C S Dias
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal; Centro de Física Teórica e Computacional, Universidade de Lisboa, Lisboa 1749-016, Portugal.
| | - N A M Araújo
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal; Centro de Física Teórica e Computacional, Universidade de Lisboa, Lisboa 1749-016, Portugal
| | - M M Telo da Gama
- Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, 1749-016 Lisboa, Portugal; Centro de Física Teórica e Computacional, Universidade de Lisboa, Lisboa 1749-016, Portugal
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Roldán É, Gupta S. Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement. Phys Rev E 2017; 96:022130. [PMID: 28950574 DOI: 10.1103/physreve.96.022130] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2017] [Indexed: 06/07/2023]
Abstract
We study the dynamics of overdamped Brownian particles diffusing in conservative force fields and undergoing stochastic resetting to a given location at a generic space-dependent rate of resetting. We present a systematic approach involving path integrals and elements of renewal theory that allows us to derive analytical expressions for a variety of statistics of the dynamics such as (i) the propagator prior to first reset, (ii) the distribution of the first-reset time, and (iii) the spatial distribution of the particle at long times. We apply our approach to several representative and hitherto unexplored examples of resetting dynamics. A particularly interesting example for which we find analytical expressions for the statistics of resetting is that of a Brownian particle trapped in a harmonic potential with a rate of resetting that depends on the instantaneous energy of the particle. We find that using energy-dependent resetting processes is more effective in achieving spatial confinement of Brownian particles on a faster time scale than performing quenches of parameters of the harmonic potential.
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Affiliation(s)
- Édgar Roldán
- Max-Planck Institute for the Physics of Complex Systems, cfAED and GISC, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Shamik Gupta
- Department of Physics, Ramakrishna Mission Vivekananda University, Belur Math, Howrah 711 202, West Bengal, India
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