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Bedolla-Montiel EA, Lange JT, Pérez de Alba Ortíz A, Dijkstra M. Inverse design of crystals and quasicrystals in a non-additive binary mixture of hard disks. J Chem Phys 2024; 160:244902. [PMID: 38916271 DOI: 10.1063/5.0210034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2024] [Accepted: 06/07/2024] [Indexed: 06/26/2024] Open
Abstract
The development of new materials typically involves a process of trial and error, guided by insights from past experimental and theoretical findings. The inverse design approach for soft-matter systems has the potential to optimize specific physical parameters, such as particle interactions, particle shape, or composition and packing fraction. This optimization aims to facilitate the spontaneous formation of specific target structures through self-assembly. In this study, we expand upon a recently introduced inverse design protocol for monodisperse systems to identify the required conditions and interactions for assembling crystal and quasicrystal phases within a binary mixture of two distinct species. This method utilizes an evolution algorithm to identify the optimal state point and interaction parameters, enabling the self-assembly of the desired structure. In addition, we employ a convolutional neural network (CNN) that classifies different phases based on their diffraction patterns, serving as a fitness function for the desired structure. Using our protocol, we successfully inverse design two-dimensional crystalline structures, including a hexagonal lattice and a dodecagonal quasicrystal, within a non-additive binary mixture of hard disks. Finally, we introduce a symmetry-based order parameter that leverages the encoded symmetry within the diffraction pattern. This order parameter circumvents the need for training a CNN and is used as a fitness function to inverse design an octagonal quasicrystal.
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Affiliation(s)
- Edwin A Bedolla-Montiel
- Soft Condensed Matter and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
| | - Jochem T Lange
- Soft Condensed Matter and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
| | - Alberto Pérez de Alba Ortíz
- Soft Condensed Matter and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
- Computational Soft Matter Lab, Computational Chemistry Group and Computational Science Lab, van 't Hoff Institute for Molecular Science and Informatics Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands
| | - Marjolein Dijkstra
- Soft Condensed Matter and Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, Netherlands
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2
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Schmidt MM, Ruiz-Franco J, Bochenek S, Camerin F, Zaccarelli E, Scotti A. Interfacial Fluid Rheology of Soft Particles. PHYSICAL REVIEW LETTERS 2023; 131:258202. [PMID: 38181345 DOI: 10.1103/physrevlett.131.258202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Revised: 08/18/2023] [Accepted: 11/20/2023] [Indexed: 01/07/2024]
Abstract
In situ interfacial rheology and numerical simulations are used to investigate microgel monolayers in a wide range of packing fractions, ζ_{2D}. The heterogeneous particle compressibility determines two flow regimes characterized by distinct master curves. To mimic the microgel architecture and reproduce experiments, an interaction potential combining a soft shoulder with the Hertzian model is introduced. In contrast to bulk conditions, the elastic moduli vary nonmonotonically with ζ_{2D} at the interface, confirming long-sought predictions of reentrant behavior for Hertzian-like systems.
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Affiliation(s)
- Maximilian M Schmidt
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52074 Aachen, Germany
| | - José Ruiz-Franco
- Laboratory of Physical Chemistry and Soft Matter, Wageningen University & Research, Stippeneng 4, 6708 WE Wageningen, The Netherlands
| | - Steffen Bochenek
- Institute of Physical Chemistry, RWTH Aachen University, Landoltweg 2, 52074 Aachen, Germany
| | - Fabrizio Camerin
- Soft Condensed Matter & Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, Princetonplein 1, 3584 CC Utrecht, The Netherlands
| | - Emanuela Zaccarelli
- Italian National Research Council-Institute for Complex Systems (CNR-ISC), Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Rome, Italy
- Department of Physics, Sapienza University of Rome, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Andrea Scotti
- Department of Biomedical Science, Faculty of Health and Society, Malmö University, SE-205 06 Malmö, Sweden
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3
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Kuk K, Abgarjan V, Gregel L, Zhou Y, Carrasco Fadanelli V, Buttinoni I, Karg M. Compression of colloidal monolayers at liquid interfaces: in situ vs. ex situ investigation. SOFT MATTER 2023; 19:175-188. [PMID: 36426847 DOI: 10.1039/d2sm01125e] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
The assembly of colloidal particles at liquid/liquid or air/liquid interfaces is a versatile procedure to create microstructured monolayers and study their behavior under compression. When combined with soft and deformable particles such as microgels, compression is used to tune not only the interparticle distance but also the underlying microstructure of the monolayer. So far, the great majority of studies on microgel-laden interfaces are conducted ex situ after transfer to solid substrates, for example, via Langmuir-Blodgett deposition. This type of analysis relies on the stringent assumption that the microstructure is conserved during transfer and subsequent drying. In this work, we couple a Langmuir trough to a custom-built small-angle light scattering setup to monitor colloidal monolayers in situ during compression. By comparing the results with ex situ and in situ microscopy measurements, we conclude that Langmuir-Blodgett deposition can alter the structural properties of the colloidal monolayers significantly.
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Affiliation(s)
- Keumkyung Kuk
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany.
| | - Vahan Abgarjan
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany.
| | - Lukas Gregel
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany.
| | - Yichu Zhou
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany.
| | - Virginia Carrasco Fadanelli
- Institut für Experimentelle Physik der kondensierten Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany
| | - Ivo Buttinoni
- Institut für Experimentelle Physik der kondensierten Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany
| | - Matthias Karg
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany.
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4
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Menath J, Mohammadi R, Grauer JC, Deters C, Böhm M, Liebchen B, Janssen LMC, Löwen H, Vogel N. Acoustic Crystallization of 2D Colloidal Crystals. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2023; 35:e2206593. [PMID: 36281801 DOI: 10.1002/adma.202206593] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2022] [Revised: 10/13/2022] [Indexed: 06/16/2023]
Abstract
2D colloidal crystallization provides a simple strategy to produce defined nanostructure arrays over macroscopic areas. Regularity and long-range order of such crystals is essential to ensure functionality, but difficult to achieve in self-assembling systems. Here, a simple loudspeaker setup for the acoustic crystallization of 2D colloidal crystals (ACDC) of polystyrene, microgels, and core-shell particles at liquid interfaces is introduced. This setup anneals an interfacial colloidal monolayer and affords an increase in average grain size by almost two orders of magnitude. The order is characterized via the structural color of the colloidal crystal, the acoustic annealing process is optimized via the frequency and the amplitude of the applied sound wave, and its efficiency is rationalized via the surface coverage-dependent interactions within the interfacial colloidal monolayer. Computer simulations show that multiple rearrangement mechanisms at different length scales, from the local motion around voids to grain boundary movements via consecutive particle rotations around common centers, collude to remove defects. The experimentally simple ACDC process, paired with the demonstrated applicability toward complex particle systems, provides access to highly defined nanostructure arrays for a wide range of research communities.
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Affiliation(s)
- Johannes Menath
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058, Erlangen, Germany
| | - Reza Mohammadi
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058, Erlangen, Germany
| | - Jens Christian Grauer
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, D-40225, Düsseldorf, Germany
| | - Claudius Deters
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, D-40225, Düsseldorf, Germany
| | - Maike Böhm
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058, Erlangen, Germany
| | - Benno Liebchen
- Institute of Physics: Theory of Soft Matter, Technical University of Darmstadt, Hochschulstraße 12, 64289, Darmstadt, Germany
| | - Liesbeth M C Janssen
- Soft Matter and Biological Physics, Department of Applied Physics, Eindhoven University of Technology, Eindhoven, 5600 MB, The Netherlands
| | - Hartmut Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, D-40225, Düsseldorf, Germany
| | - Nicolas Vogel
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058, Erlangen, Germany
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Feller D, Karg M. Fluid interface-assisted assembly of soft microgels: recent developments for structures beyond hexagonal packing. SOFT MATTER 2022; 18:6301-6312. [PMID: 35993260 DOI: 10.1039/d2sm00872f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Microgels adsorb to air/water and oil/water interfaces - a process driven by a significant reduction in interfacial tension. Depending on the available interface area per microgel, strong lateral deformation can be observed. Typically, hexagonally ordered structures appear spontaneously upon contact of the microgel shells. Transfer from the interface to solid substrates gives access to macroscopically sized microgel monolayers that are interesting for photonic and plasmonic studies as well as colloid-based lithography, for example. Significant efforts have been made to understand the phase behavior of microgels at different interfaces and to explore the available parameter space for achieving complex tessellations. In this review, we will discuss the most recent developments in the realization of microgel monolayers with structures beyond hexagonal packing.
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Affiliation(s)
- Déborah Feller
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany.
| | - Matthias Karg
- Institut für Physikalische Chemie I: Kolloide und Nanooptik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, 40225 Düsseldorf, Germany.
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Ickler M, Menath J, Holstein L, Rey M, Buzza DMA, Vogel N. Interfacial self-assembly of SiO 2-PNIPAM core-shell particles with varied crosslinking density. SOFT MATTER 2022; 18:5585-5597. [PMID: 35849635 DOI: 10.1039/d2sm00644h] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Spherical particles confined to liquid interfaces generally self-assemble into hexagonal patterns. It was theoretically predicted by Jagla two decades ago that such particles interacting via a soft repulsive potential are able to form complex, anisotropic assembly phases. Depending on the shape and range of the potential, the predicted minimum energy configurations include chains, rhomboid and square phases. We recently demonstrated that deformable core-shell particles consisting of a hard silica core and a soft poly(N-isopropylacrylamide) shell adsorbed at an air/water interface can form chain phases if the crosslinker is primarily incorporated around the silica core. Here, we systematically investigate the interfacial self-assembly behavior of such SiO2-PNIPAM core-shell particles as a function of crosslinker content and core size. We observe chain networks predominantly at low crosslinking densities and smaller core sizes, whereas higher crosslinking densities lead to the formation of rhomboid packing. We correlate these results with the interfacial morphologies of the different particle systems, where the ability to expand at the interface and form a thin corona at the periphery depends on the degree of crosslinking close to the core. We perform minimum energy calculations based on Jagla-type pair potentials with different shapes of the soft repulsive shoulder. We compare the theoretical phase diagram with experimental findings to infer to which extent the interfacial interactions of the experimental system may be captured by Jagla pair-wise interaction potentials.
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Affiliation(s)
- Maret Ickler
- Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstrasse 4, 91058 Erlangen, Germany.
- Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Haberstrasse 9a, 91058 Erlangen, Germany
| | - Johannes Menath
- Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstrasse 4, 91058 Erlangen, Germany.
- Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Haberstrasse 9a, 91058 Erlangen, Germany
| | - Laura Holstein
- Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstrasse 4, 91058 Erlangen, Germany.
- Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Haberstrasse 9a, 91058 Erlangen, Germany
| | - Marcel Rey
- Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstrasse 4, 91058 Erlangen, Germany.
- Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Haberstrasse 9a, 91058 Erlangen, Germany
- School of Physics & Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK
| | - D Martin A Buzza
- G W Gray Centre for Advanced Materials, Department of Physics & Mathematics, University of Hull, Hull HU6 7RX, UK
| | - Nicolas Vogel
- Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstrasse 4, 91058 Erlangen, Germany.
- Interdisciplinary Center for Functional Particle Systems (FPS), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Haberstrasse 9a, 91058 Erlangen, Germany
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7
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Nickel AC, Rudov AA, Potemkin II, Crassous JJ, Richtering W. Interfacial Assembly of Anisotropic Core-Shell and Hollow Microgels. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:4351-4363. [PMID: 35349289 DOI: 10.1021/acs.langmuir.2c00093] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Microgels, cross-linked polymers with submicrometer size, are ideal soft model systems. While spherical microgels have been studied extensively, anisotropic microgels have hardly been investigated. In this study, we compare the interfacial deformation and assembly of anisotropic core-shell and hollow microgels. The core-shell microgel consists of an elliptical core of hematite covered with a thin silica layer and a thin shell made of poly(N-isopropylacrylamide). The hollow microgels were obtained after a two-step etching procedure of the inorganic core. The behavior of these microgels at the oil-water interface was investigated in a Langmuir-Blodgett trough combined with ex situ atomic force microscopy. First, the influence of the architecture of anisotropic microgels on their spreading at the interface was investigated experimentally and by dissipative particle dynamic simulations. Hereby, the importance of the local shell thickness on the lateral and longitudinal interfacial deformation was highlighted as well as the differences between the core-shell and hollow architectures. The shape of the compression isotherms as well as the dimensions, ordering, and orientation of the microgels at the different compressions were analyzed. Due to their anisotropic shape and stiffness, both anisotropic microgels were found to exhibit significant capillary interactions with a preferential side-to-side assembly leading to stable microgel clusters at low interfacial coverage. Such capillary interactions were found to decrease in the case of the more deformable hollow anisotropic microgels. Consequently, anisotropic hollow microgels were found to distribute more evenly at high surface pressure compared to stiffer core-shell microgels. Our findings emphasize the complex interplay between the colloid design, anisotropy, and softness on the interfacial assembly and the opportunities it therefore offers to create more complex ordered interfaces.
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Affiliation(s)
- Anne C Nickel
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany, European Union
| | - Andrey A Rudov
- DWI-Leibniz-Institute for Interactive Materials, 52056 Aachen, Germany, European Union
| | - Igor I Potemkin
- DWI-Leibniz-Institute for Interactive Materials, 52056 Aachen, Germany, European Union
| | - Jérôme J Crassous
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany, European Union
| | - Walter Richtering
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany, European Union
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8
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Guzmán E, Maestro A. Soft Colloidal Particles at Fluid Interfaces. Polymers (Basel) 2022; 14:polym14061133. [PMID: 35335463 PMCID: PMC8956102 DOI: 10.3390/polym14061133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Revised: 03/08/2022] [Accepted: 03/10/2022] [Indexed: 02/01/2023] Open
Abstract
The assembly of soft colloidal particles at fluid interfaces is reviewed in the present paper, with emphasis on the particular case of microgels formed by cross-linked polymer networks. The dual polymer/colloid character as well as the stimulus responsiveness of microgel particles pose a challenge in their experimental characterization and theoretical description when adsorbed to fluid interfaces. This has led to a controversial and, in some cases, contradictory picture that cannot be rationalized by considering microgels as simple colloids. Therefore, it is necessary to take into consideration the microgel polymer/colloid duality for a physically reliable description of the behavior of the microgel-laden interface. In fact, different aspects related to the above-mentioned duality control the organization of microgels at the fluid interface, and the properties and responsiveness of the obtained microgel-laden interfaces. This works present a critical revision of different physicochemical aspects involving the behavior of individual microgels confined at fluid interfaces, as well as the collective behaviors emerging in dense microgel assemblies.
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Affiliation(s)
- Eduardo Guzmán
- Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain
- Instituto Pluridisciplinar, Universidad Complutense de Madrid, Paseo de Juan XXIII, 28040 Madrid, Spain
- Correspondence: (E.G.); (A.M.)
| | - Armando Maestro
- Centro de Física de Materiales (CSIC, UPV/EHU), Paseo Manuel de Lardizabal 5, 20018 San Sebastian, Spain
- IKERBASQUE—Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
- Correspondence: (E.G.); (A.M.)
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9
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Ciarella S, Rey M, Harrer J, Holstein N, Ickler M, Löwen H, Vogel N, Janssen LMC. Soft Particles at Liquid Interfaces: From Molecular Particle Architecture to Collective Phase Behavior. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:5364-5375. [PMID: 33886318 DOI: 10.1021/acs.langmuir.1c00541] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Soft particles such as microgels can undergo significant and anisotropic deformations when adsorbed to a liquid interface. This, in turn, leads to a complex phase behavior upon compression. To date, experimental efforts have predominantly provided phenomenological links between microgel structure and resulting interfacial behavior, while simulations have not been entirely successful in reproducing experiments or predicting the minimal requirements for the desired phase behavior. Here, we develop a multiscale framework to link the molecular particle architecture to the resulting interfacial morphology and, ultimately, to the collective interfacial phase behavior. To this end, we investigate interfacial morphologies of different poly(N-isopropylacrylamide) particle systems using phase-contrast atomic force microscopy and correlate the distinct interfacial morphology with their bulk molecular architecture. We subsequently introduce a new coarse-grained simulation method that uses augmented potentials to translate this interfacial morphology into the resulting phase behavior upon compression. The main novelty of this method is the possibility to efficiently encode multibody interactions, the effects of which are key to distinguishing between heterostructural (anisotropic collapse) and isostructural (isotropic collapse) phase transitions. Our approach allows us to qualitatively resolve existing discrepancies between experiments and simulations. Notably, we demonstrate the first in silico account of the two-dimensional isostructural transition, which is frequently found in experiments but elusive in simulations. In addition, we provide the first experimental demonstration of a heterostructural transition to a chain phase in a single-component system, which has been theoretically predicted decades ago. Overall, our multiscale framework provides a phenomenological bridge between physicochemical soft-particle characteristics at the molecular scale and nanoscale and the collective self-assembly phenomenology at the macroscale, serving as a stepping stone toward an ultimately more quantitative and predictive design approach.
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Affiliation(s)
- Simone Ciarella
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
| | - Marcel Rey
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058 Erlangen, Germany
| | - Johannes Harrer
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058 Erlangen, Germany
| | - Nicolas Holstein
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058 Erlangen, Germany
| | - Maret Ickler
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058 Erlangen, Germany
| | - Hartmut Löwen
- Institute for Theoretical Physics II: Soft Matter, Heinrich-Heine University Düsseldorf, D-40225 Düsseldorf, Germany
| | - Nicolas Vogel
- Institute of Particle Technology, Friedrich-Alexander University Erlangen-Nürnberg, Cauerstrasse 4, 91058 Erlangen, Germany
| | - Liesbeth M C Janssen
- Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
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