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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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2
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Stuij SG, Jonas HJ, Gong Z, Sacanna S, Kodger TE, Bolhuis PG, Schall P. Revealing viscoelastic bending relaxation dynamics of isolated semiflexible colloidal polymers. SOFT MATTER 2021; 17:8291-8299. [PMID: 34550152 DOI: 10.1039/d1sm00556a] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
The viscoelastic properties of filaments and biopolymers play a crucial role in soft and biological materials from biopolymer networks to novel synthetic metamaterials. Colloidal particles with specific valency allow mimicking polymers and more complex molecular structures at the colloidal scale, offering direct observation of their internal degrees of freedom. Here, we elucidate the time-dependent viscoelastic response in the bending of isolated semi-flexible colloidal polymers, assembled from dipatch colloidal particles by reversible critical Casimir forces. By tuning the patch-patch interaction strength, we adjust the polymers' viscoelastic properties, and follow spontaneous bending modes and their relaxation directly on the particle level. We find that the elastic response is well described by that of a semiflexible rod with persistence length of order 1000 μm, tunable by the critical Casimir interaction strength. We identify the viscous relaxation on longer timescales to be due to internal friction, leading to a wavelength-independent relaxation time similar to single biopolymers, but in the colloidal case arising from the contact mechanics of the bonded patches. These tunable mechanical properties of assembled colloidal filaments open the door to "colloidal architectures", rationally designed (network) structures with desired topology and mechanical properties.
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Affiliation(s)
- Simon G Stuij
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
| | - Hannah J Jonas
- van't Hoff Institute for Molecular Sciences, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
| | - Zhe Gong
- Molecular Design Institute, Department of Chemistry, New York University, 29 Washington Place, New York 10003, USA
| | - Stefano Sacanna
- Molecular Design Institute, Department of Chemistry, New York University, 29 Washington Place, New York 10003, USA
| | - Thomas E Kodger
- Physical Chemistry and Soft Matter, Wageningen University, Stippeneng 4, 6708 WE Wageningen, The Netherlands
| | - Peter G Bolhuis
- van't Hoff Institute for Molecular Sciences, University of Amsterdam, 1098 XH Amsterdam, The Netherlands
| | - Peter Schall
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
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3
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Marino E, Vasilyev OA, Kluft BB, Stroink MJB, Kondrat S, Schall P. Controlled deposition of nanoparticles with critical Casimir forces. NANOSCALE HORIZONS 2021; 6:751-758. [PMID: 34268545 PMCID: PMC8381518 DOI: 10.1039/d0nh00670j] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 05/20/2021] [Indexed: 05/28/2023]
Abstract
Nanocrystal assembly represents the key fabrication step to develop next-generation optoelectronic devices with properties defined from the bottom-up. Despite numerous efforts, our limited understanding of nanoscale interactions has so far delayed the establishment of assembly conditions leading to reproducible superstructure morphologies, therefore hampering integration with large-scale, industrial processes. In this work, we demonstrate the deposition of a layer of semiconductor nanocrystals on a flat and unpatterned silicon substrate as mediated by the interplay of critical Casimir attraction and electrostatic repulsion. We show experimentally and rationalize with Monte Carlo and molecular dynamics simulations how this assembly process can be biased towards the formation of 2D layers or 3D islands and how the morphology of the deposited superstructure can be tuned from crystalline to amorphous. Our findings demonstrate the potential of the critical Casimir interaction to direct the growth of future artificial solids based on nanocrystals as the ultimate building blocks.
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Affiliation(s)
- Emanuele Marino
- Department of Chemistry, University of PennsylvaniaPhiladelphiaPennsylvania 19104USA
- van der Waals-Zeeman Institute, University of AmsterdamAmsterdamThe Netherlands
| | - Oleg A. Vasilyev
- Max-Planck-Institut für Intelligente SystemeHeisenbergstraße 3D-70569 StuttgartGermany
- IV. Institut für Theoretische Physik, Universität StuttgartPfaffenwaldring 57D-70569 StuttgartGermany
| | - Bas B. Kluft
- van der Waals-Zeeman Institute, University of AmsterdamAmsterdamThe Netherlands
| | - Milo J. B. Stroink
- van der Waals-Zeeman Institute, University of AmsterdamAmsterdamThe Netherlands
| | - Svyatoslav Kondrat
- Max-Planck-Institut für Intelligente SystemeHeisenbergstraße 3D-70569 StuttgartGermany
- IV. Institut für Theoretische Physik, Universität StuttgartPfaffenwaldring 57D-70569 StuttgartGermany
- Institute of Physical Chemistry, Polish Academy of SciencesKasprzaka 44/5201-224 WarsawPoland
| | - Peter Schall
- van der Waals-Zeeman Institute, University of AmsterdamAmsterdamThe Netherlands
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Mahdisoltani S, Golestanian R. Long-Range Fluctuation-Induced Forces in Driven Electrolytes. PHYSICAL REVIEW LETTERS 2021; 126:158002. [PMID: 33929248 DOI: 10.1103/physrevlett.126.158002] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2020] [Revised: 01/20/2021] [Accepted: 03/02/2021] [Indexed: 06/12/2023]
Abstract
We study the stochastic dynamics of an electrolyte driven by a uniform external electric field and show that it exhibits generic scale invariance despite the presence of Debye screening. The resulting long-range correlations give rise to a Casimir-like fluctuation-induced force between neutral boundaries that confine the ions; this force is controlled by the external electric field, and it can be both attractive and repulsive with similar boundary conditions, unlike other long-range fluctuation-induced forces. This work highlights the importance of nonequilibrium correlations in electrolytes and shows how they can be used to tune interactions between uncharged biological or synthetic structures at large separations.
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Affiliation(s)
- Saeed Mahdisoltani
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
- Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
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5
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Vasilyev OA, Marino E, Kluft BB, Schall P, Kondrat S. Debye vs. Casimir: controlling the structure of charged nanoparticles deposited on a substrate. NANOSCALE 2021; 13:6475-6488. [PMID: 33885527 DOI: 10.1039/d0nr09076j] [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
Fine-tuning the interactions between particles can allow one to steer their collective behaviour and structure. A convenient way to achieve this is to use solvent criticality to control attraction, via critical Casimir forces, and to control repulsion via the Debye screening of electrostatic interactions. Herein, we develop a multiscale simulation framework and a method for controlled deposition of quantum dots to investigate how these interactions affect the structure of charged nanoparticles deposited on a substrate, altogether immersed in a binary liquid mixture intermixed with salt. We consider nanoparticles and substrates favouring the same component of the mixture and find that the critical Casimir interactions between the nanoparticles become drastically reduced at the substrate. In particular, the interactions can become a few kBT weaker and their decay length a few orders of magnitude smaller than in the bulk. At off-critical compositions, the decay length increases upon approaching criticality, as expected, but the interaction strength decreases. With molecular dynamics simulations and experiments, we reveal that the nanoparticles can self-assemble into crystalline clusters which form superstructures resembling cluster fluids and spinodal morphology. The simulations additionally predict the formation of fractal-like nanoparticle gels and bicontinuous phases. Our results demonstrate that charged nanoparticles in a salty binary liquid mixture provide exciting opportunities to study the formation of complex structures experimentally and theoretically, which may lead to applications in optoelectronics and photonics.
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Affiliation(s)
- Oleg A Vasilyev
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany.
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Vasilyev OA, Labbé-Laurent M, Dietrich S, Kondrat S. Bridging transitions and capillary forces for colloids in a slit. J Chem Phys 2020; 153:014901. [PMID: 32640823 DOI: 10.1063/5.0005419] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Capillary bridges can form between colloids immersed in a two-phase fluid, e.g., in a binary liquid mixture, if the surface of the colloids prefers the species other than the one favored in the bulk liquid. Here, we study the formation of liquid bridges induced by confining colloids to a slit, with the slit walls having a preference opposite to the one of the colloid surface. Using mean field theory, we show that there is a line of first-order phase transitions between the bridge and the no-bridge states, which ends at a critical point. By decreasing the slit width, this critical point is shifted toward smaller separations between the colloids. However, at very small separations and far from criticality, we observe only a minor influence of the slit width on the location of the transition. Monte Carlo simulations of the Ising model, which mimics incompressible binary liquid mixtures, confirm the occurrence of the bridging transitions, as manifested by the appearance of "spinodal" regions where both bridge and no-bridge configurations are stable or metastable. Interestingly, we find that there is no such spinodal region in the case of small colloids, but we observe a sharpening of the transition when the colloid size increases. In addition, we demonstrate that the capillary force acting between the colloids can depend sensitively on the slit width and varies drastically with temperature, thus achieving strengths orders of magnitude higher than at criticality of the fluid.
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Affiliation(s)
- Oleg A Vasilyev
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany
| | - Marcel Labbé-Laurent
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany
| | - Svyatoslav Kondrat
- Department of Complex Systems, Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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Farahmand Bafi N, Nowakowski P, Dietrich S. Effective pair interaction of patchy particles in critical fluids. J Chem Phys 2020; 152:114902. [PMID: 32199445 DOI: 10.1063/5.0001293] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
We study the critical Casimir interaction between two spherical colloids immersed in a binary liquid mixture close to its critical demixing point. The surface of each colloid prefers one species of the mixture with the exception of a circular patch of arbitrary size, where the other species is preferred. For such objects, we calculate, within the Derjaguin approximation, the scaling function describing the critical Casimir potential, and we use it to derive the scaling functions for all components of the forces and torques acting on both colloids. The results are compared with available experimental data. Moreover, the general relation between the scaling function for the potential and the scaling functions for the force and the torque is derived.
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Affiliation(s)
- N Farahmand Bafi
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - P Nowakowski
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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Rohwer CM, Squarcini A, Vasilyev O, Dietrich S, Gross M. Ensemble dependence of critical Casimir forces in films with Dirichlet boundary conditions. Phys Rev E 2019; 99:062103. [PMID: 31330655 DOI: 10.1103/physreve.99.062103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2018] [Indexed: 06/10/2023]
Abstract
In a recent study [Phys. Rev. E 94, 022103 (2016)2470-004510.1103/PhysRevE.94.022103] it has been shown that, for a fluid film subject to critical adsorption, the resulting critical Casimir force (CCF) may significantly depend on the thermodynamic ensemble. Here we extend that study by considering fluid films within the so-called ordinary surface universality class. We focus on mean-field theory, within which the order parameter (OP) profile satisfies Dirichlet boundary conditions and produces a nontrivial CCF in the presence of external bulk fields or, respectively, a nonzero total order parameter within the film. Additionally, we study the influence of fluctuations by means of Monte Carlo simulations of the three-dimensional Ising model. We show that, in the canonical ensemble, i.e., when fixing the so-called total mass within the film, the CCF is repulsive for large absolute values of the total OP, instead of attractive as in the grand canonical ensemble. Based on the Landau-Ginzburg free energy, we furthermore obtain analytic expressions for the order parameter profiles and analyze the relation between the total mass in the film and the external bulk field.
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Affiliation(s)
- Christian M Rohwer
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany and 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Alessio Squarcini
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany and 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Oleg Vasilyev
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany and 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - S Dietrich
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany and 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Markus Gross
- Max Planck Institute for Intelligent Systems, Heisenbergstr. 3, 70569 Stuttgart, Germany and 4th Institute for Theoretical Physics, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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9
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Kondrat S, Vasilyev OA, Dietrich S. Probing interface localization-delocalization transitions by colloids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:414002. [PMID: 30178756 DOI: 10.1088/1361-648x/aadead] [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
Interface localization-delocalization transitions (ILDT) occur in two-phase fluids confined in a slit with competing preferences of the walls for the two fluid phases. At low temperatures the interface between the two phases is localized at one of the walls. Upon increasing temperature it unbinds. Although intensively studied theoretically and computationally, such transitions have not yet been observed experimentally due to severe challenges in resolving fine details of the fluid structure. Here, using mean field theory and Monte Carlo simulations of the Ising model, we propose to detect these ILDT by using colloids. We show that the finite-size and fluctuation induced force acting on a colloid confined in such a system experiences a vivid change if, upon lowering the temperature, the interface localizes at one of the walls. This change can serve as a more easily accessible experimental indicator of the transition.
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Affiliation(s)
- Svyatoslav Kondrat
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
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10
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Vasilyev OA, Dietrich S, Kondrat S. Nonadditive interactions and phase transitions in strongly confined colloidal systems. SOFT MATTER 2018; 14:586-596. [PMID: 29264614 DOI: 10.1039/c7sm01363a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The behaviour of colloids can be controlled effectively by tuning the solvent-mediated interactions among them. An extensively studied example is the temperature-induced aggregation of suspended colloids close to the consolute point of their binary solvent. Here, using mean field theory and Monte Carlo simulations, we study the behaviour of colloids confined to a narrow slit containing a nearly-critical binary liquid mixture. We found that the effective interactions in this system are highly non-additive. In particular, the effective interactions among the colloids can be a few times stronger than the corresponding sum of the effective pair potentials. Inter alia, this non-additivity manifests itself in the phase behaviour of confined colloids, which depends sensitively on the slit width and temperature. In addition, we demonstrate the possibility of a first-order bridging transition between colloids confined to a slit and suspended in a phase-separated fluid well below the critical point of the solvent and at its critical composition in the bulk. This transition is accompanied by a remarkably large hysteresis loop, in which the force between the colloids varies by two orders of magnitude.
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Affiliation(s)
- Oleg A Vasilyev
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany.
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Valchev G, Dantchev D. Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces. Phys Rev E 2017; 96:022107. [PMID: 28950495 DOI: 10.1103/physreve.96.022107] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2017] [Indexed: 11/07/2022]
Abstract
We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. The latter arise as an effective force between bodies when immersed in a near-critical medium, say a nonpolar one-component fluid or a binary liquid mixture. They are due to the fact that the presence of the bodies modifies the order parameter profile of the medium between them as well as the spectrum of its allowed fluctuations. We study the interplay between these forces, as well as the total force (TF) between a spherical colloid particle and a thick planar slab and between two spherical colloid particles. We do that using general scaling arguments and mean-field-type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance L from each other, confining the fluctuating fluid medium characterized by its temperature T and chemical potential μ. The surfaces of the colloid particles and the slab are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called (+,+) boundary conditions. On the other hand, the core region of the slab and the particles influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloids-fluid, slab-fluid, and fluid-fluid coupling parameters, the competition between the effects due to the coatings and the core regions of the objects involved result, when one changes T, μ, or L, in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab, as well as between the colloids. This can be used for governing the behavior of objects, say colloidal particles, at small distances, say in colloid suspensions for preventing flocculation. It can also provide a strategy for solving problems with handling, feeding, trapping, and fixing of microparts in nanotechnology. Data for specific substances in support of the experimental feasibility of the theoretically predicted behavior of the CF and TF have been also presented.
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Affiliation(s)
- Galin Valchev
- Institute of Mechanics-Bulgarian Academy of Sciences, Academic Georgy Bonchev Strasse, building 4, 1113 Sofia, Bulgaria
| | - Daniel Dantchev
- Institute of Mechanics-Bulgarian Academy of Sciences, Academic Georgy Bonchev Strasse, building 4, 1113 Sofia, Bulgaria.,Max-Planck-Institut für Intelligente Systeme, Heisenbergstrasse 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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12
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Labbé-Laurent M, Law AD, Dietrich S. Liquid bridging of cylindrical colloids in near-critical solvents. J Chem Phys 2017; 147:104701. [DOI: 10.1063/1.4986149] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
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13
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Stuij SG, Labbé-Laurent M, Kodger TE, Maciołek A, Schall P. Critical Casimir interactions between colloids around the critical point of binary solvents. SOFT MATTER 2017; 13:5233-5249. [PMID: 28574564 DOI: 10.1039/c7sm00599g] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Critical Casimir interactions between colloidal particles arise from the confinement of fluctuations of a near-critical solvent in the liquid gap between closely-spaced particles. So far, the comparison of theoretical predictions and experimental measurements of critical Casimir forces (CCFs) has focused on the critical solvent composition, while it has been lacking for off-critical compositions. We address this issue by investigating CCFs between spherical colloidal particles around the critical point of a binary solvent through a combination of experiments, previous Ising Monte Carlo simulation results and field-theoretical methods. By measuring the correlation length of the near-critical solvent and the pair potentials of the particles in terms of radial distribution functions and by determining the second virial coefficient, we test in detail theoretical predictions. Our results indicate that the critical Casimir theory gives quantitative correct predictions for the interaction potential between particles in a near critical binary mixture if weak preferential adsorption of the particle surface is taken into account.
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Affiliation(s)
- S G Stuij
- Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands.
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14
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Flachi A, Nitta M, Takada S, Yoshii R. Sign Flip in the Casimir Force for Interacting Fermion Systems. PHYSICAL REVIEW LETTERS 2017; 119:031601. [PMID: 28777594 DOI: 10.1103/physrevlett.119.031601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2017] [Indexed: 06/07/2023]
Abstract
In this work we consider a fermionic chain of finite length ℓ. Fermions are allowed to interact and are forced to obey boundary conditions, thus altering the process of condensation. Our goal is to explore how this affects the quantum vacuum energy for this system. We approach this problem by using a self-consistent method and observe a nontrivial behavior in the Casimir force, displaying a switch from an attractive to a repulsive regime. This flip stems from the competition between the attractive contribution from the usual fermionic Casimir effect and a repulsive one coming from the condensate.
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Affiliation(s)
- Antonino Flachi
- Department of Physics, Keio University, 4-1-1 Hiyoshi, Kanagawa 223-8521, Japan
- Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Kanagawa 223-8521, Japan
| | - Muneto Nitta
- Department of Physics, Keio University, 4-1-1 Hiyoshi, Kanagawa 223-8521, Japan
- Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Kanagawa 223-8521, Japan
| | - Satoshi Takada
- Earthquake Research Institute, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan and Department of Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
| | - Ryosuke Yoshii
- Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Kanagawa 223-8521, Japan
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15
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Eisenriegler E, Burkhardt TW. Casimir interaction of rodlike particles in a two-dimensional critical system. Phys Rev E 2016; 94:032130. [PMID: 27739769 DOI: 10.1103/physreve.94.032130] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2016] [Indexed: 11/07/2022]
Abstract
We consider the fluctuation-induced interaction of two thin, rodlike particles, or "needles," immersed in a two-dimensional critical fluid of Ising symmetry right at the critical point. Conformally mapping the plane containing the needles onto a simpler geometry in which the stress tensor is known, we analyze the force and torque between needles of arbitrary length, separation, and orientation. For infinite and semi-infinite needles we utilize the mapping of the plane bounded by the needles onto the half plane, and for two needles of finite length we use the mapping onto an annulus. For semi-infinite and infinite needles the force is expressed in terms of elementary functions, and we also obtain analytical results for the force and torque between needles of finite length with separation much greater than their length. Evaluating formulas in our approach numerically for several needle geometries and surface universality classes, we study the full crossover from small to large values of the separation to length ratio. In these two limits the numerical results agree with results for infinitely long needles and with predictions of the small-particle operator expansion, respectively.
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Affiliation(s)
- E Eisenriegler
- Theoretical Soft Matter and Biophysics, Institute of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - T W Burkhardt
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
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16
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Labbé-Laurent M, Dietrich S. Critical Casimir interactions between Janus particles. SOFT MATTER 2016; 12:6621-6648. [PMID: 27444691 DOI: 10.1039/c6sm00990e] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Recently there has been strong experimental and theoretical interest in studying the self-assembly and the phase behavior of patchy and Janus particles, which form colloidal suspensions. Although in this quest a variety of effective interactions have been proposed and used in order to achieve a directed assembly, the critical Casimir effect stands out as being particularly suitable in this respect because it provides both attractive and repulsive interactions as well as the potential of a sensitive temperature control of their strength. Specifically, we have calculated the critical Casimir force between a single Janus particle and a laterally homogeneous substrate as well as a substrate with a chemical step. We have used the Derjaguin approximation and compared it with results from full mean field theory. A modification of the Derjaguin approximation turns out to be generally reliable. Based on this approach we have derived the effective force and the effective potential between two Janus cylinders as well as between two Janus spheres.
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Affiliation(s)
- M Labbé-Laurent
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany.
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17
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Nowakowski P, Napiórkowski M. Lateral critical Casimir force in two–dimensional inhomogeneous Ising strip. Exact results. J Chem Phys 2016; 144:214703. [DOI: 10.1063/1.4952977] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Piotr Nowakowski
- Max–Planck–Institut für Intelligente Systeme, Heisenbergstr. 3, 70569 Stuttgart, Germany and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - Marek Napiórkowski
- Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02–093 Warszawa, Poland
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18
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Abstract
In soft condensed matter physics, effective interactions often emerge due to the spatial confinement of fluctuating fields. For instance, microscopic particles dissolved in a binary liquid mixture are subject to critical Casimir forces whenever their surfaces confine the thermal fluctuations of the order parameter of the solvent close to its critical demixing point. These forces are theoretically predicted to be nonadditive on the scale set by the bulk correlation length of the fluctuations. Here we provide direct experimental evidence of this fact by reporting the measurement of the associated many-body forces. We consider three colloidal particles in optical traps and observe that the critical Casimir force exerted on one of them by the other two differs from the sum of the forces they exert separately. This three-body effect depends sensitively on the distance from the critical point and on the chemical functionalisation of the colloid surfaces. The critical Casimir force, rising from fluctuating field confined between surfaces, is predicted to be nonadditive, but there is no experimental verification to date. Here the authors provide data support by quantifying the forces between three interacting colloidal particles using holographic traps.
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19
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Toldin FP, Tröndle M, Dietrich S. Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:214010. [PMID: 25966039 DOI: 10.1088/0953-8984/27/21/214010] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Recent experimental realizations of the critical Casimir effect have been implemented by monitoring colloidal particles immersed in a binary liquid mixture near demixing and exposed to a chemically structured substrate. In particular, critical Casimir forces have been measured for surfaces consisting of stripes with periodically alternating adsorption preferences, forming chemical steps between them. Motivated by these experiments, we analyze the contribution of such chemical steps to the critical Casimir force for the film geometry and within the Ising universality class. By means of Monte Carlo simulations, mean-field theory and finite-size scaling analysis we determine the universal scaling function associated with the contribution to the critical Casimir force due to individual, isolated chemical steps facing a surface with homogeneous adsorption preference or with Dirichlet boundary condition. In line with previous findings, these results allow one to compute the critical Casimir force for the film geometry and in the presence of arbitrarily shaped, but wide stripes. In this latter limit the force decomposes into a sum of the contributions due to the two homogeneous parts of the surface and due to the chemical steps between the stripes. We assess this decomposition by comparing the resulting sum with actual simulation data for the critical Casimir force in the presence of a chemically striped substrate.
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Affiliation(s)
- Francesco Parisen Toldin
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
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20
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Tröndle M, Harnau L, Dietrich S. Critical Casimir forces between planar and crenellated surfaces. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:214006. [PMID: 25965585 DOI: 10.1088/0953-8984/27/21/214006] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We study critical Casimir forces between planar walls and geometrically structured substrates within mean-field theory. As substrate structures, crenellated surfaces consisting of periodic arrays of rectangular crenels and merlons are considered. Within the widely used proximity force approximation, both the top surfaces of the merlons and the bottom surfaces of the crenels contribute to the critical Casimir force. However, for such systems the full, numerically determined critical Casimir forces deviate significantly from the pairwise addition formalism underlying the proximity force approximation. A first-order correction to the proximity force approximation is presented in terms of a step contribution arising from the critical Casimir interaction between a planar substrate and the right-angled steps of the merlons consisting of their upper and lower edges as well as their sidewalls.
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Affiliation(s)
- M Tröndle
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstrasse 3, D-70569 Stuttgart, Germany. Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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21
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Mattos TG, Harnau L, Dietrich S. Three-body critical Casimir forces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:042304. [PMID: 25974488 DOI: 10.1103/physreve.91.042304] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2015] [Indexed: 06/04/2023]
Abstract
Within mean-field theory we calculate universal scaling functions associated with critical Casimir forces for a system consisting of three parallel cylindrical colloids immersed in a near-critical binary liquid mixture. For several geometrical arrangements and boundary conditions at the surfaces of the colloids we study the force between two colloidal particles in the direction normal to their axes, analyzing the influence of the presence of a third particle on that force. Upon changing temperature or the relative positions of the particles we observe interesting features such as a change of sign of this force caused by the presence of the third particle. We determine the three-body component of the forces acting on one of the colloids by subtracting the pairwise forces from the total force. The three-body contribution to the total critical Casimir force turns out to be more pronounced for small surface-to-surface distances between the colloids as well as for temperatures close to criticality. Moreover, we compare our results with similar ones for other physical systems such as three atoms interacting via van der Waals forces.
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Affiliation(s)
- T G Mattos
- Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, Av. Amazonas 7675, 30510-000 Belo Horizonte, Brazil; Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany; and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - L Harnau
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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22
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Parisen Toldin F. Critical Casimir force in the presence of random local adsorption preference. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:032105. [PMID: 25871052 DOI: 10.1103/physreve.91.032105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Indexed: 06/04/2023]
Abstract
We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter p, which measures, on average, the portion of the surface that prefers one component, so that p=0,1 correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimir force. We show that by tuning the disorder parameter p, the system exhibits a crossover between an attractive and a repulsive force. At p=1/2, disorder allows to effectively realize Dirichlet boundary conditions, which are generically not accessible in classical fluids. Our results are relevant for the experimental realizations of the critical Casimir force in binary liquid mixtures.
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Affiliation(s)
- Francesco Parisen Toldin
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
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23
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Law AD, Harnau L, Tröndle M, Dietrich S. Effective interaction between a colloid and a soft interface near criticality. J Chem Phys 2014; 141:134704. [DOI: 10.1063/1.4896383] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
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24
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Nowakowski P, Napiórkowski M. Lateral critical Casimir force in 2D Ising strip with inhomogeneous walls. J Chem Phys 2014; 141:064704. [DOI: 10.1063/1.4892343] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Mohry TF, Kondrat S, Maciołek A, Dietrich S. Critical Casimir interactions around the consolute point of a binary solvent. SOFT MATTER 2014; 10:5510-5522. [PMID: 24954395 DOI: 10.1039/c4sm00622d] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Spatial confinement of a near-critical medium changes its fluctuation spectrum and modifies the corresponding order parameter distribution, resulting in effective, so-called critical Casimir forces (CCFs) acting on the confining surfaces. These forces are attractive for like boundary conditions of the order parameter at the opposing surfaces of the confinement. For colloidal particles dissolved in a binary liquid mixture acting as a solvent close to its critical point of demixing, one thus expects the emergence of phase segregation into equilibrium colloidal liquid and gas phases. We analyze how such phenomena occur asymmetrically in the whole thermodynamic neighborhood of the consolute point of the binary solvent. By applying field-theoretical methods within mean-field approximation and the semi-empirical de Gennes-Fisher functional, we study the CCFs acting between planar parallel walls as well as between two spherical colloids and their dependence on temperature and on the composition of the near-critical binary mixture. We find that for compositions slightly poor in the molecules preferentially adsorbed at the surfaces, the CCFs are significantly stronger than at the critical composition, thus leading to pronounced colloidal segregation. The segregation phase diagram of the colloid solution following from the calculated effective pair potential between the colloids agrees surprisingly well with experiments and simulations.
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Affiliation(s)
- T F Mohry
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany.
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26
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Labbé-Laurent M, Tröndle M, Harnau L, Dietrich S. Alignment of cylindrical colloids near chemically patterned substrates induced by critical Casimir torques. SOFT MATTER 2014; 10:2270-2291. [PMID: 24652197 DOI: 10.1039/c3sm52858h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Recent experiments have demonstrated a fluctuation-induced lateral trapping of spherical colloidal particles immersed in a binary liquid mixture near its critical demixing point and exposed to chemically patterned substrates. Inspired by these experiments, we study this kind of effective interaction, known as the critical Casimir effect, for elongated colloids of cylindrical shape. This adds orientational degrees of freedom. When the colloidal particles are close to a chemically structured substrate, a critical Casimir torque acting on the colloids emerges. We calculate this torque on the basis of the Derjaguin approximation. The range of validity of the latter is assessed via mean-field theory. This assessment shows that the Derjaguin approximation is reliable in experimentally relevant regimes, so that we extend it to Janus particles endowed with opposing adsorption preferences. Our analysis indicates that critical Casimir interactions are capable of achieving well-defined, reversible alignments both of chemically homogeneous and of Janus cylinders.
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Affiliation(s)
- M Labbé-Laurent
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany.
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27
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Zubaszewska M, Maciołek A, Drzewiński A. Critical Casimir forces along the isofields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052129. [PMID: 24329236 DOI: 10.1103/physreve.88.052129] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/23/2013] [Indexed: 06/03/2023]
Abstract
Using quasiexact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field h≠0. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two disks. We find that varying the temperature along the isofields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a qualitatively different functional dependence on the temperature than along h=0. These findings might be of relevance for biomembranes, whose heterogeneity is recently interpreted as being connected with a critical behavior belonging to the 2D Ising universality class.
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Affiliation(s)
- M Zubaszewska
- Institute of Physics, University of Zielona Góra, ul. Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
| | - A Maciołek
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, D-70569 Stuttgart, Germany and IV Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany and Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, PL-01-224 Warsaw, Poland
| | - A Drzewiński
- Institute of Physics, University of Zielona Góra, ul. Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
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28
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Parisen Toldin F, Tröndle M, Dietrich S. Critical Casimir forces between homogeneous and chemically striped surfaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052110. [PMID: 24329217 DOI: 10.1103/physreve.88.052110] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2013] [Revised: 08/08/2013] [Indexed: 06/03/2023]
Abstract
Recent experiments have measured the critical Casimir force acting on a colloid immersed in a binary liquid mixture near its continuous demixing phase transition and exposed to a chemically structured substrate. Motivated by these experiments, we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically striped, such that there is a laterally alternating adsorption preference for the two species of the binary liquid mixture, which is implemented by surface fields. For the opposite wall we employ alternatively a homogeneous adsorption preference or homogeneous Dirichlet boundary conditions, which within a lattice model are realized by open boundary conditions. By means of mean-field theory, Monte Carlo simulations, and finite-size scaling analysis we determine the critical Casimir force acting on the two parallel walls and its corresponding universal scaling function. We show that in the limit of stripe widths small compared with the film thickness, on the striped surface the system effectively realizes Dirichlet boundary conditions, which generically do not hold for actual fluids. Moreover, the critical Casimir force is found to be attractive or repulsive, depending on the width of the stripes of the chemically patterned surface and on the boundary condition applied to the opposing surface.
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Affiliation(s)
- Francesco Parisen Toldin
- Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany
| | - Matthias Tröndle
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
| | - S Dietrich
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany and IV. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
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29
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Mattos TG, Harnau L, Dietrich S. Many-body effects for critical Casimir forces. J Chem Phys 2013; 138:074704. [PMID: 23445027 DOI: 10.1063/1.4791554] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within mean-field theory we calculate the scaling functions associated with critical Casimir forces for a system consisting of two spherical colloids immersed in a binary liquid mixture near its consolute point and facing a planar, homogeneous substrate. For several geometrical arrangements and boundary conditions we analyze the normal and the lateral critical Casimir forces acting on one of the two colloids. We find interesting features such as a change of sign of these forces upon varying either the position of one of the colloids or the temperature. By subtracting the pairwise forces from the total force we are able to determine the many-body forces acting on one of the colloids. We have found that the many-body contribution to the total critical Casimir force is more pronounced for small colloid-colloid and colloid-substrate distances, as well as for temperatures close to criticality, where the many-body contribution to the total force can reach up to 25%.
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Affiliation(s)
- T G Mattos
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstr. 3, D-70569 Stuttgart, Germany.
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30
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Hasenbusch M. Thermodynamic Casimir forces between a sphere and a plate: Monte Carlo simulation of a spin model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022130. [PMID: 23496482 DOI: 10.1103/physreve.87.022130] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2012] [Indexed: 06/01/2023]
Abstract
We study the thermodynamic Casimir force between a spherical object and a plate. We consider the bulk universality class of the three-dimensional Ising model, which is relevant for experiments on binary mixtures. To this end, we simulate the improved Blume-Capel model. Following Hucht, we compute the force by integrating energy differences over the inverse temperature. We demonstrate that these energy differences can be computed efficiently by using a particular cluster algorithm. Our numerical results for strongly symmetry breaking boundary conditions are compared with the Derjaguin approximation for small distances and the small sphere expansion for large distances between the sphere and the plate.
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Affiliation(s)
- Martin Hasenbusch
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.
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31
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Mohry TF, Maciołek A, Dietrich S. Phase behavior of colloidal suspensions with critical solvents in terms of effective interactions. J Chem Phys 2012; 136:224902. [PMID: 22713068 DOI: 10.1063/1.4722883] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We study the phase behavior of colloidal suspensions the solvents of which are considered to be binary liquid mixtures undergoing phase segregation. We focus on the thermodynamic region close to the critical point of the accompanying miscibility gap. There, due to the colloidal particles acting as cavities in the critical medium, the spatial confinements of the critical fluctuations of the corresponding order parameter result in the effective, so-called critical Casimir forces between the colloids. Employing an approach in terms of effective, one-component colloidal systems, we explore the possibility of phase coexistence between two phases of colloidal suspensions, one being rich and the other being poor in colloidal particles. The reliability of this effective approach is discussed.
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Affiliation(s)
- T F Mohry
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany.
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32
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Dantchev D, Valchev G. Surface integration approach: A new technique for evaluating geometry dependent forces between objects of various geometry and a plate. J Colloid Interface Sci 2012; 372:148-63. [DOI: 10.1016/j.jcis.2011.12.040] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/09/2011] [Revised: 11/14/2011] [Accepted: 12/12/2011] [Indexed: 10/14/2022]
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33
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Tröndle M, Zvyagolskaya O, Gambassi A, Vogt D, Harnau L, Bechinger C, Dietrich S. Trapping colloids near chemical stripes via critical Casimir forces. Mol Phys 2011. [DOI: 10.1080/00268976.2011.553639] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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