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Gambassi A, Dietrich S. Critical Casimir forces in soft matter. SOFT MATTER 2024; 20:3212-3242. [PMID: 38573318 DOI: 10.1039/d3sm01408h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/05/2024]
Abstract
We review recent advances in the theoretical, numerical, and experimental studies of critical Casimir forces in soft matter, with particular emphasis on their relevance for the structures of colloidal suspensions and on their dynamics. Distinct from other interactions which act in soft matter, such as electrostatic and van der Waals forces, critical Casimir forces are effective interactions characterised by the possibility to control reversibly their strength via minute temperature changes, while their attractive or repulsive character is conveniently determined via surface treatments or by structuring the involved surfaces. These features make critical Casimir forces excellent candidates for controlling the equilibrium and dynamical properties of individual colloids or colloidal dispersions as well as for possible applications in micro-mechanical systems. In the past 25 years a number of theoretical and experimental studies have been devoted to investigating these forces primarily under thermal equilibrium conditions, while their dynamical and non-equilibrium behaviour is a largely unexplored subject open for future investigations.
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Affiliation(s)
- A Gambassi
- SISSA-International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy.
| | - S Dietrich
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany
- IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany.
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Jonas HJ, Schall P, Bolhuis PG. Activity affects the stability, deformation and breakage dynamics of colloidal architectures. SOFT MATTER 2024; 20:2162-2177. [PMID: 38351836 DOI: 10.1039/d3sm01255g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/29/2024]
Abstract
Living network architectures, such as the cytoskeleton, are characterized by continuous energy injection, leading to rich but poorly understood non-equilibrium physics. There is a need for a well-controlled (experimental) model system that allows basic insight into such non-equilibrium processes. Activated self-assembled colloidal architectures can fulfill this role, as colloidal patchy particles can self-assemble into colloidal architectures such as chains, rings and networks, while self-propelled colloidal particles can simultaneously inject energy into the architecture, alter the dynamical behavior of the system, and cause the self-assembled structures to deform and break. To gain insight, we conduct a numerical investigation into the effect of introducing self-propelled colloids modeled as active Brownian particles, into self-assembling colloidal dispersions of dipatch and tripatch particles. For the interaction potential, we use a previously designed model that accurately can reproduce experimental colloidal self-assembly via the critical Casimir force [Jonas et al., J. Chem. Phys., 2021, 135, 034902]. Here, we focus primarily on the breakage dynamics of three archetypal substructures, namely, dimers, chains, and rings. We find a rich response behavior to the introduction of self-propelled particles, in which the activity can enhance as well as reduce the stability of the architecture, deform the intact structures and alter the mechanisms of fragmentation. We rationalize these findings in terms of the rate and mechanisms of breakage as a function of the direction and magnitude of the active force by separating the bond breakage process into two stages: escaping the potential well and separation of the particles. The results set the stage for investigating more complex architectures.
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Affiliation(s)
- H J Jonas
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, PO Box 94157, 1090 GD Amsterdam, The Netherlands.
| | - P Schall
- van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, PO Box 94485, 1090 GL Amsterdam, The Netherlands
| | - P G Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, PO Box 94157, 1090 GD Amsterdam, The Netherlands.
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Swinkels PJM, Sinaasappel R, Gong Z, Sacanna S, Meyer WV, Sciortino F, Schall P. Networks of Limited-Valency Patchy Particles. PHYSICAL REVIEW LETTERS 2024; 132:078203. [PMID: 38427857 DOI: 10.1103/physrevlett.132.078203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Revised: 11/27/2023] [Accepted: 01/17/2024] [Indexed: 03/03/2024]
Abstract
Equilibrium gels provide physically attractive counterparts of nonequilibrium gels, allowing statistical understanding and design of the equilibrium gel structure. Here, we assemble two-dimensional equilibrium gels from limited-valency "patchy" colloidal particles and follow their evolution at the particle scale to elucidate cluster-size distributions and free energies. By finely adjusting the patch attraction with critical Casimir forces, we let a mixture of two-valent and pseudo-three-valent patchy particles approach the percolated network state through a set of equilibrium states. Comparing this equilibrium route with a deep quench, we find that both routes approach the percolated state via the same equilibrium states, revealing that the network topology is uniquely set by the particle bond angles, independent of the formation history. The limited-valency system follows percolation theory remarkably well, approaching the percolation point with the expected universal exponents.
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Affiliation(s)
- P J M Swinkels
- Institute of Physics, University of Amsterdam, 1098XH Amsterdam, The Netherlands
| | - R Sinaasappel
- Institute of Physics, University of Amsterdam, 1098XH Amsterdam, The Netherlands
| | - Z Gong
- Molecular Design Institute, Department of Chemistry, New York University, New York, NY 10003-6688, USA
| | - S Sacanna
- Molecular Design Institute, Department of Chemistry, New York University, New York, NY 10003-6688, USA
| | - W V Meyer
- Universities Space Research Association, with GEARS, NASA Glenn Research Center, 2001 Aerospace Parkway, Brook Park, Ohio 44152, USA
| | | | - P Schall
- Institute of Physics, University of Amsterdam, 1098XH Amsterdam, The Netherlands
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Swinkels PJM, Gong Z, Sacanna S, Noya EG, Schall P. Visualizing defect dynamics by assembling the colloidal graphene lattice. Nat Commun 2023; 14:1524. [PMID: 36934102 PMCID: PMC10024684 DOI: 10.1038/s41467-023-37222-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 03/07/2023] [Indexed: 03/20/2023] Open
Abstract
Graphene has been under intense scientific interest because of its remarkable optical, mechanical and electronic properties. Its honeycomb structure makes it an archetypical two-dimensional material exhibiting a photonic and phononic band gap with topologically protected states. Here, we assemble colloidal graphene, the analogue of atomic graphene using pseudo-trivalent patchy particles, allowing particle-scale insight into crystal growth and defect dynamics. We directly observe the formation and healing of common defects, like grain boundaries and vacancies using confocal microscopy. We identify a pentagonal defect motif that is kinetically favoured in the early stages of growth, and acts as seed for more extended defects in the later stages. We determine the conformational energy of the crystal from the bond saturation and bond angle distortions, and follow its evolution through the energy landscape upon defect rearrangement and healing. These direct observations reveal that the origins of the most common defects lie in the early stages of graphene assembly, where pentagons are kinetically favoured over the equilibrium hexagons of the honeycomb lattice, subsequently stabilized during further growth. Our results open the door to the assembly of complex 2D colloidal materials and investigation of their dynamical, mechanical and optical properties.
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Affiliation(s)
- Piet J M Swinkels
- Institute of Physics, University of Amsterdam, Amsterdam, the Netherlands
| | - Zhe Gong
- Molecular Design Institute, Department of Chemistry, New York University, New York, NY, USA
| | - Stefano Sacanna
- Molecular Design Institute, Department of Chemistry, New York University, New York, NY, USA
| | - Eva G Noya
- Instituto de Química Física Rocasolano, CSIC, Madrid, Spain
| | - Peter Schall
- Institute of Physics, University of Amsterdam, Amsterdam, the Netherlands.
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Popov A, Hernandez R. Bottom-Up Construction of the Interaction between Janus Particles. J Phys Chem B 2023; 127:1664-1673. [PMID: 36780204 PMCID: PMC9969965 DOI: 10.1021/acs.jpcb.2c07858] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Revised: 12/29/2022] [Indexed: 02/14/2023]
Abstract
While the interaction between two uniformly charged spheres─viz colloids─is well-known, the interaction between nonuniformly charged spheres such as Janus particles is not. Specifically, the Derjaguin approximation relates the potential energy between two spherical particles with the interaction energy Vpl per unit area between two planar surfaces. The formalism has been extended to obtain a quadrature expression for the screened electrostatic interaction between Janus colloids with variable relative orientations. The interaction is decomposed into three zones in the parametric space, distinguished by their azimuthal symmetry. Different specific situations are examined to estimate the contributions of these zones to the total energy. The effective potential Vpl is renormalized such that the resulting potential energy is identical with the actual one for the most preferable relative orientations between the Janus particles. The potential energy as a function of the separation distance and the mutual orientation of a pair of particles compares favorably between the analytical (but approximate) form and the rigorous point-wise computational model used earlier. Coarse-grained models of Janus particles can thus implement this potential model efficiently without loss of generality.
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Affiliation(s)
- Alexander Popov
- Department
of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Rigoberto Hernandez
- Department
of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
- Department
of Chemical & Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, United States
- Department
of Materials Science and Engineering, Johns
Hopkins University, Baltimore, Maryland 21218, United States
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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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Kennedy CL, Sayasilpi D, Schall P, Meijer JM. Self-assembly of colloidal cube superstructures with critical Casimir attractions. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022; 34:214005. [PMID: 35203069 DOI: 10.1088/1361-648x/ac5866] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 02/24/2022] [Indexed: 06/14/2023]
Abstract
The structure of self-assembled materials is determined by the shape and interactions of the building blocks. Here, we investigate the self-assembly of colloidal 'superballs', i.e. cubes with rounded corners, by temperature-tunable critical Casimir forces to obtain insight into the coupling of a cubic shape and short range attractions. The critical Casimir force is a completely reversible and controllable attraction that arises in a near-critical solvent mixture. Using confocal microscopy and particle tracking, we follow the self-assembly dynamics and structural transition in a quasi-2D system. At low attraction, we observe the formation of small clusters with square symmetry. When the attraction is increased, a transition to a rhombic Λ1-lattice is observed. We explain our findings by the change in contact area at faces and corners of the building blocks combined with the increase in attraction strength and range of the critical Casimir force. Our results show that the coupling between the rounded cubic shape and short-range attraction plays a crucial role for the superstructures that form and provide new insights for the active assembly control of micro and nanocubes.
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Affiliation(s)
- Chris L Kennedy
- Department of Applied Physics, Eindhoven University of Technology, Groene Loper 19, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Daphne Sayasilpi
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Peter Schall
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - Janne-Mieke Meijer
- Department of Applied Physics, Eindhoven University of Technology, Groene Loper 19, 5600 MB Eindhoven, The Netherlands
- Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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Stuij S, Rouwhorst J, Jonas HJ, Ruffino N, Gong Z, Sacanna S, Bolhuis PG, Schall P. Revealing Polymerization Kinetics with Colloidal Dipatch Particles. PHYSICAL REVIEW LETTERS 2021; 127:108001. [PMID: 34533362 DOI: 10.1103/physrevlett.127.108001] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Revised: 07/05/2021] [Accepted: 07/20/2021] [Indexed: 06/13/2023]
Abstract
Limited-valency colloidal particles can self-assemble into polymeric structures analogous to molecules. While their structural equilibrium properties have attracted wide attention, insight into their dynamics has proven challenging. Here, we investigate the polymerization dynamics of semiflexible polymers in 2D by direct observation of assembling divalent particles, bonded by critical Casimir forces. The reversible critical Casimir force creates living polymerization conditions with tunable chain dissociation, association, and bending rigidity. We find that unlike dilute polymers that show exponential size distributions in excellent agreement with Flory theory, concentrated samples exhibit arrest of rotational and translational diffusion due to a continuous isotropic-to-nematic transition in 2D, slowing down the growth kinetics. These effects are circumvented by the addition of higher-valency particles, cross linking the polymers into networks. Our results connecting polymer flexibility, polymer interactions, and the peculiar isotropic-nematic transition in 2D offer insight into the polymerization processes of synthetic two-dimensional polymers and biopolymers at membranes and interfaces.
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Affiliation(s)
- Simon Stuij
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Joep Rouwhorst
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Hannah J Jonas
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Nicola Ruffino
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Zhe Gong
- Molecular Design Institute, Department of Chemistry, New York University, New York, New York 10003-6688, USA
| | - Stefanno Sacanna
- Molecular Design Institute, Department of Chemistry, New York University, New York, New York 10003-6688, USA
| | - Peter G Bolhuis
- van 't Hoff Institute for Molecular Sciences, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Peter Schall
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
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