# Soft Matter Roadmap

Jean-Louis Barrat, Emanuela del Gado, Stefan Egelhaaf, Xiaoming Mao, Marjolein Dijkstra, David Pine, Sanat Kumar, Kyle Bishop, Oleg Gang, Allie Obermeyer, et al.

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Jean-Louis Barrat, Emanuela del Gado, Stefan Egelhaaf, Xiaoming Mao, Marjolein Dijkstra, et al. Soft Matter Roadmap. Journal of Physics: Materials, 2023, 10.1088/2515-7639/ad06cc. hal-04260533

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Soft Matter Roadmap

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# Soft Matter Roadmap

Jean-Louis Barrat¹,⁴,⁹,⁵⁰, Emanuela Del Gado²,⁴,⁹,⁵⁰, Stefan U. Egelhaaf³,⁴,⁹,⁵⁰, Xiaomiing Mao⁴,⁴,⁹,⁵⁰, Marjolein Dijkstra⁵, David J. Pine⁶,⁷, Sanat K Kumar⁸, Kyle Bishop⁸, Oleg Gang⁸, Allie Obermeyer⁸, Christine M. Papadakis⁹, Constantinos Tsitsilianis¹⁰, Ivan I. Smalyukh¹¹,¹², Aurelie Hourlier-

Fargette¹³, Sebastien Andrieux¹³, Wiebke Drenckhan¹³, Norman Wagner¹⁴, Ryan P. Murphy¹⁵, Eric R. Weeks¹⁶, Roberto Cerbino¹⁷, Yilong Han¹⁸, Luca Cipelletti¹⁹,²⁰, Laurence Ramos¹⁹, Wilson C.K.

Poon²¹, James A. Richards²¹, Itai Cohen²², Eric M. Furst²³, Alshakim Nelson²⁴, Stephen L. Craig²⁵, Rajesh Ganapathy²⁶, Ajay Kumar Sood²⁷, Francesco Sciortino²⁸, Muhittin Mungan²⁹,³⁰, Srikanth Sastry³¹, Colin Scheibner³²,³³, Michel Fruchart³²,³³, Vincenzo Vitelli³²,³³,³⁴, S. A. Ridout³⁵,³⁸, M.

Stern³⁵, I. Tah³⁵,³⁷, G. Zhang³⁵,³⁶, Andrea J. Liu³⁵,³⁹, Chinedum O. Osuji⁴⁰, Yuan Xu⁴¹, Heather M.

Shewan⁴¹, Jason R. Stokes⁴¹, Matthias Merkel⁴², Pierre Ronceray⁴³, Jean-François Rupprecht⁴², Olga Matsarskaia⁴⁴, Frank Schreiber⁴⁵, Felix Roosen-Runge⁴⁶, Marie-Eve Aubin-Tam⁴⁷, Gijsje H.

Koenderink⁴⁷, Rosa M. Espinosa-Marzal⁴⁸, Joaquin Yus⁴⁸ and Jiheon Kwon⁴⁸

## Author affiliations

¹ Université Grenoble Alpes, CNRS, LIphy, 38000 Grenoble, France

² Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, 20057 Washington DC, USA

³ Condensed Matter Physics Laboratory, Heinrich Heine University, 40225 Düsseldorf, Germany

⁴ Department of Physics, University of Michigan, MI, USA

⁵ Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, the Netherlands

⁶ Department of Physics, University of New York, New York, USA

⁷ Department of Chemical and Biological Engineering, University of New York, New York, USA

⁸ Soft Matter Group, Department of Chemical Engineering, Columbia University, New York, NY, USA

⁹ Technical University of Munich, Physics Department, Soft Matter Physics Group, James-Franck-Str. 1, 85748 Garching, Germany

¹⁰ Department of Chemical Engineering, University of Patras, 26500 Patras, Greece

¹¹ Department of Physics and Materials Science Engineering Program, University of Colorado, Boulder, CO 80309, USA

¹² Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, CO 80309, USA

¹³ Institut Charles Sadron, Université de Strasbourg – CNRS UPR22, France

¹⁴ Center for Neutron Science, Dept. of Chemical and Biomolecular Engineering, University of Delaware, Newark, DE, USA

¹⁵ NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA

¹⁶ Emory University, Atlanta GA 30322, USA

¹⁷ University of Vienna, 1090 Vienna, Austria
¹⁸ Department of Physics, The Hong Kong University of Science and Technology, Hong Kong

¹⁹ Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France

²⁰ Institut Universitaire de France (IUF), France

²¹ Edinburgh Complex Fluids Partnership, School of Physics and Astronomy, The University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Edinburgh EH9 3FD, UK

²² Department of Physics, Cornell University, Ithaca, NY, USA

²³ Department of Chemical and Biomolecular Engineering, University of Delaware, Newark, DE, USA

²⁴ Department of Chemistry, University of Washington, Seattle, WA

²⁵ Department of Chemistry, Duke University, Durham, North Carolina, USA

²⁶ Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India

²⁷ Indian Institute of Science, Bangalore 560012, India

²⁸ Department of Physics, Sapienza Universita' di Roma, Piazzale Aldo Moro, 5, 00185 Rome, Italy

²⁹ Institute for Biological Physics, University of Cologne, Zülpicher Straße 77, 50937 Köln, Germany

³⁰ Institute for Applied Mathematics, University of Bonn, Endenicher Allee 60, 53115 Bonn, Germany

³¹ Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkar Campus, 560064 Bengaluru, India

³² James Franck Institute, The University of Chicago, Chicago, IL 60637, USA

³³ Department of Physics, The University of Chicago, Chicago, IL 60637, USA

³⁴ Kadanoff Center for Theoretical Physics, The University of Chicago, Chicago, IL 60637, USA

³⁵ Department of Physics, University of Pennsylvania, Philadelphia PA 19104 USA

³⁶ Department of Physics, City University of Hong Kong, 83 Tat Chee Ave., Kowloon Tong, Hong Kong

³⁷ Speciality Glass Division, CSIR-Central Glass and Ceramic Research Institute, Kolkata 700032, India

³⁸ Department of Physics, Emory University, Atlanta GA 30322 USA

³⁹ Flatiron Institute, Simons Foundation, New York NY 10010 USA

⁴⁰ Department of Chemical and Biomolecular Engineering, University of Pennsylvania, USA

⁴¹ School of Chemical Engineering, The University of Queensland, Australia

⁴² Aix Marseille Univ, Université de Toulon, CNRS, CPT (UMR 7332), Turing Centre for Living Systems (CENTURI), Marseille, France

⁴³ Aix Marseille Univ, CNRS, CINaM (UMR 7325), Turing Centre for Living Systems (CENTURI), Marseille, France

⁴⁴ Institut Laue-Langevin, Grenoble, France

⁴⁵ Institute of Applied Physics, University of Tübingen, Germany

⁴⁶ Department of Biomedical Science and Biofilms-Research Center for Biointerfaces, University of Malmö, Sweden

⁴⁷ Department of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, 2629 HZ Delft, The Netherlands

⁴⁸ University of Illinois at Urbana-Champaign, Illinois, USA

⁴⁹ Guest editors of the Roadmap.

⁵⁰ Author to whom any correspondence should be addressed.
## Author emails

Jean-Louis.Barrat@univ-grenoble-alpes.fr, ed610@georgetown.edu, stefan.egelhaaf@hhu.de,maox@umich.edu.

## Contents

Introduction

### Section 1 – New building blocks, synthesis and functionalities

1.1 Complex colloidal materials – Marjolein Dijkstra

1.2 Engineered colloidal carticles – David Pine

1.3 Soft polymer materials – Sanat K Kumar, Kyle Bishop, Oleg Gang and Allie Obermeyer

1.4 Complex polymer hydrogels – Christine M.Papadakis and Constantinos Tsitsilianis

1.5 Liquid crystalline materials – Ivan I. Smalyukh

1.6 Solid foams, interface-based materials – Aurelie Hourlier-Fargette, Sebastien Andrieux and Wiebke Drenckhan

### Section 2 – New experimental tools to characterize soft materials

2.1 Rheo-SANS: Small Angle Neutron Scattering (SANS) with in situ rheometry– Norman Wagner and Ryan P. Murphy

2.2 Imaging microscopic processes – Eric R. Weeks

2.3 New microscopy techniques – Roberto Cerbino

### Section 3 – New experimental tools to manipulate soft materials

3.1 Phase transition studies in colloids – Yilong Han

3.2 Large mechanical deformation – Luca Cipelletti and Laurence Ramos

3.3 Suspension rheology: A smooth past, rough present and sticky future? – Wilson C.K. Poon and James A. Richards

3.4 Driven liquid to solid transitions – Itai Cohen

3.5 Electric and magnetic field control – Eric M. Furst

3.6 Stimuli-responsive materials – Alshakim Nelson and Stephen L. Craig

### Section 4 – New theoretical concepts and modelling tools

4.1 Linking Hard and Soft Matter Physics – Rajesh Ganapathy and Ajay Kumar Sood

4.2 Glasses and gels – Francesco Sciortino

4.3 Memory in soft matter – Muhittin Mungan and Srikanth Sastry

4.4 Soft metamaterials: Adaptation and intelligence – Colin Scheibner, Michel Fruchart and Vincenzo Vitelli

4.5 Machine learning for soft matter learning– S. A. Ridout, M. Stern, I. Tah, G. Zhang and Andrea J. Liu
## Section 5 – New problems and emerging challenges

5.1 Soft materials for energy – Chinedum O. Osuji

5.2 Soft materials and food structure – Yuan Xu, Heather M. Shewan and Jason R. Stokes

## Section 6 – From soft to bio and vice versa

6.1 Active biological materials – Matthias Merkel, Pierre Ronceray and Jean-François Rupprecht

6.2 Protein self-assembly – Olga Matsarskaia, Frank Schreiber and Felix Roosen-Runge

6.3 Biosourced soft materials – Marie-Eve Aubin-Tam and Gijsje H. Koenderink

6.4 Reinforced hydrogels via mineralization: Next generation bioscaffolds – Rosa M. Espinosa-Marzal, Joaquin Yus and Jiheon Kwon

## Abstract

Soft materials are usually defined as materials made of mesoscopic entities, often self-organized, sensitive to thermal fluctuations and to weak perturbations. Archetypal examples are colloids, polymers, amphiphiles, liquid crystals, foams. The importance of soft materials in everyday commodity products, as well as in technological applications, is enormous, and controlling or improving their properties is the focus of many efforts. From a fundamental perspective, the possibility of manipulating soft material properties, by tuning interactions between constituents and by applying external perturbations, gives rise to an almost unlimited variety in physical properties. Together with the relative ease to observe and characterize them, this renders soft matter systems powerful model systems to investigate statistical physics phenomena, many of them relevant as well to hard condensed matter systems.

Understanding the emerging properties from mesoscale constituents still poses enormous challenges, which have stimulated a wealth of new experimental approaches, including the synthesis of new systems with, e.g., tailored self-assembling properties, or novel experimental techniques in imaging, scattering or rheology. Theoretical and numerical methods, and coarse-grained models, have become central to predict physical properties of soft materials, while computational approaches that also use machine learning tools are playing a progressively major role in many investigations.

This roadmap paper intends to give a broad overview of recent and possible future activities in the field of soft materials, with experts covering various developments and challenges in material synthesis and characterization, instrumental, simulation and theoretical methods as well as general concepts.
Introduction

Jean Louis Barret¹, Emanuela Del Gado², Stefan U. Egelhaaf³ and Xiaoming Mao⁴

¹ Université Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France

² Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, 20057 Washington DC, USA.

³ Condensed Matter Physics Laboratory, Heinrich Heine University, 40225 Düsseldorf, Germany

⁴ Department of Physics, University of Michigan, MI, USA

**Status** Thirty years ago, in his 1992 Nobel Laureate lecture¹, PG de Gennes talked about a “sentimental journey in the wonderland of soft matter”, characterized by complexity and flexibility. Indeed, the complex world of soft matter is probably better suited for such an impressionist journey than for a rigid roadmap. Nevertheless, in this roadmap, we have tried to find a compromise by gathering 26 contributions from leading groups worldwide, illustrating the many directions in which the field is presently developing. These contributions cover a very broad range, from fundamental aspects of statistical physics to engineering applications in fields as diverse as energy, biomaterials, or food science. In this field, and this is also a legacy of the “founding fathers” PG de Gennes and S Edwards, theory and experiment, fundamental and applicative research, are intimately linked, and the new experimental techniques and theoretical tools very rapidly find their ways to new applications. de Gennes and Edwards have often taken forward ideas and concepts developed in other areas such as quantum field theory and hard condensed matter, to build a more rigorous and insightful understanding of the properties of soft materials. Edwards’ clear vision of how theoretical science can help resolve practical engineering and industrial problems has had a permanent imprint in soft matter science, bringing on many occasions theorists and industrialists to work together, a legacy still carried over through initiatives such as the Edwards Symposia in Cambridge among others². How many of the topics highlighted in this roadmap could have been anticipated 30 years ago? Probably very few. Even if the basic ingredients of soft matter have not changed, surprising behaviours are still being discovered in fields that were considered as mostly understood, such as polymer networks³. The soft matter field once considered synonymous with “complex fluids” has evolved to encompass a growing number of “soft materials” such as dispersions, plastics, membranes, foams, active materials, metamaterials, biomaterials, as illustrated in various contributions of this roadmap. On a fundamental side, the study of soft matter systems has been essential in improving our understanding of major open issues in statistical physics with relevance for applications, such as the mechanism underlying the glass transition⁴.

**New building blocks, synthesis, and functionalities** With the advent of well-defined model systems, systematic and quantitative experiments became possible⁵,⁶ They were dedicated to, e.g., the equilibrium and non-equilibrium behaviour of colloidal, polymeric and surfactant systems and represented benchmarks for theoretical models. Over the years, systems were developed which
possess a more complex architecture, show tunable properties, respond to external stimuli as well as their local environment, show a specific, e.g., chemical functionality, or use energy from their environment to sustain a directed motion. For example, introducing mechanophores or stress sensitive molecules⁷ allows one to follow complex processes such as crystallization, deformation, and rupture of soft materials. Self-healing materials⁸ with polymer or gel like properties can be achieved through supramolecular chemistry. Although many phenomena have already been observed to emerge from these properties, it is expected that additional, so far unexplored behaviour will be discovered and that the potential for modifications and extensions to the existing building blocks will be explored further. Recent developments and possible future directions in this area are illustrated with a few examples in this roadmap (Sections 1.1 to 1.6; Figure 1).

<figure><img src="image_3.png" /><figcaption>**Figure 1** A graphic to demonstrate the areas covered within the Roadmap article</figcaption></figure>

**New experimental tools to characterize and manipulate soft materials** To fully characterize soft materials, a broad range of length and time scales needs to be covered. During the last decades a range of experimental techniques have been developed, and are still being developed, specifically devoted to and motivated from the investigation of soft materials. The utilization of techniques has changed over the years: for example, to investigate the microscopic structure and dynamics of soft materials, scattering is more and more complemented and sometimes replaced by microscopy (in this case rather due to increasing computational power than developments of the measurement techniques). In addition, especially in non-equilibrium situations, a simultaneous determination of
several parameters is advantageous to, e.g., link the microscopic structure and dynamics to macroscopic properties. This is reflected in the development of equipment and measurement procedures which combine different (existing or new) measurement techniques, a trend which is expected to continue in future. Moreover, combinations of distinct measurement techniques as such have been explored, a prominent and powerful example being Digital Fourier Microscopy, which benefits from advantages of microscopy and scattering experiments⁹ (Sections 2.1 to 2.3; Figure 1). In addition, due to the susceptibility of soft matter to external fields, it is desirable to, on one hand, perform measurements while the samples are manipulated by, e.g., mechanical, electrical, magnetic, or optical fields, and, on the other hand, precisely set the sample conditions, ranging from temperature and other parameters to sample loading (Sections 3.1 to 3.6; Figure 1).

**New theoretical concepts and modeling tools.** Fundamental advances in theory and modeling as well as establishing new concepts have been an important component in the development of soft matter science. Indeed, soft matter is an exciting playground for new fundamental theories owing to the rich interplay between disorder, strong fluctuations, the hierarchy of length scales, as well as the excellent controllability of the building blocks of soft matter, e.g., nano, colloidal, and granular particles, where interactions can be fine-tuned to explore a plethora of new phases of matter. In the early days of theoretical studies of soft matter, concepts from statistical mechanics and hard condensed matter have been borrowed, ranging from renormalization, criticality, to frustrated interactions, which led to great successes in explaining basic phenomena of unique phases in soft matter. As our understandings of soft matter deepened, and more experimental probes became available in the past few decades, completely new fundamental notions are emerging from soft matter, from mesophases with partially broken symmetry, unique kinetics on rugged free-energy landscapes, nonlocality in rigidity transitions, to more recent advances in using artificial intelligence to understand and manipulate complex materials¹⁰. These new concepts are being shared with other branches of physics¹¹, leading to a much richer knowledge base of physics, mathematics, materials science and engineering, and biology (Sections 4.1 to 4.5; Figure 1).

**New problems and emerging challenges** Because of soft matter versatility, soft matter processes and concepts enter also non-soft materials, famous examples being water purification¹², batteries production¹³ or self-assembly of photonic materials as well as building materials¹⁴. Beyond this, new questions related to the sustainability of material resources and of material processing, and to their environmental impact are emerging. Understanding how to recycle, repurpose and sustainably use plastics as well as biopolymer fibers present in, e.g., agricultural waste, how to reduce the use of toxic and polluting solvents, or, in general, to design more sustainable, stronger or more adaptable materials are all, in the end, soft matter problems and point to the key role that soft materials can play in reducing the human environmental footprint on our planet¹⁵,¹⁶ as well as safeguarding a sufficient but also sustainable food production (Sections 5.1 and 5.2; Figure 1).
**Analyzing and sharing (huge amounts of) data** Among the new challenges that the science of soft materials is facing, one of the most important and urgent is the sheer volume of data being produced, or to be produced, by advanced techniques, especially those combining different types of measurements. This renders it interesting to exploit the potential of AI based approaches (Section 4.5; Figure 1). In addition, how to share data properly and efficiently, how to develop shared benchmark soft materials, whose softness and frequently intrinsically non equilibrium nature make sample preparation and control particularly delicate, have become among the most pressing questions the soft materials community is working to address¹⁷.

**Conclusion** In the beginning, soft matter systems were mainly studied in chemistry and chemical engineering. With the advent of well-defined, reproducible, and 'simple' model systems, physicists became interested in soft matter. Meanwhile, the range of systems has been extended to quite complex particles and samples as well as experimental conditions. Approaching the complexity of real-world systems, the developed concepts and models can hence be applied in chemistry, biology, and medicine as well as in material, food, and environmental science and in technological and industrial applications. Therefore, ideas developed in the context of soft matter systems can now be found in many other areas of science where they show a significant impact and relevance (Sections 6.1 to 6.4; Figure 1).

The 26 contributions to this roadmap are intended to illustrate the central position of soft matter science at the crossroad of disciplines, and to highlight recent developments and perspectives in the field, ranging from novel conceptual insights to modern applications. To help the reader navigate the breadth of materials, themes and disciplines covered, we have organized the content into 6 sections that highlight novelty in classical soft materials (1), connections with biomaterials and biological systems (2), applications and technology based on soft materials (3), new exploration tools (4), soft materials manipulation (5), and new concepts that have emerged in fundamental studies of soft materials (6).
References

1. P.G. de Gennes, Nobel lecture (1992) https://doi.org/10.1002/anie.199208421

2. Stealing the Gold A celebration of the pioneering physics of Sam Edwards"
Paul Goldbart, Nigel Goldenfeld, and David Sherrington, Clarendon Press, Oxford 2004. The Sam Edwards
symposiums are organized at the Cambridge centre for mathematical science, see
https://gateway.newton.ac.uk/event/tgm129 for the 2023 edition.

3. Creton, C., 50th Anniversary Perspective: Networks and Gels: Soft but Dynamic and Tough.
Macromolecules, 2017. 50(21): p. 8297-8316.

4. L. Berthier and G. Biroli, "Theoretical perspective on the glass transition and amorphous materials" Rev. Mod. Phys. 83, 587.

5. P. N. Pusey and W. van Megen, Phase behaviour of concentrated suspensions of nearly hard colloidal spheres, Nature 320, 340 (1986).

6. D. J. Mitchell, G. J. T. Tiddy, L. Waring, T. Bostock, M. P. McDonald, Phase behaviour of polyoxyethylene surfactants with water, J. Chem. Soc. Faraday Trans., 79, 975 (1983).

7. D.A. Davis et al, Force-induced activation of covalent bonds in mechanoresponsive polymeric materials, Nature, 459, 68 (2009)

8. T. Aida, T, EW Meijer, SI Stupp, Functional Supramolecular Polymers Science, 335, 813 (2012)

9. Digital Fourier microscopy for soft matter dynamics
Fabio Giavazzi and Roberto Cerbino, Journal of Optics, 083001 (2014).

10. Gabriele M Coli, Emanuele Boattini, Laura Filion, Marjolein Dijkstra, Inverse design of soft materials via a deep learning-based evolutionary strategy, Science Advances 8, eabj6731 (2022).

11. Jishnu N Nampoothiri, Yinqiao Wang, Kabir Ramola, Jie Zhang, Subhro Bhattacharjee, Bulbul Chakraborty, Emergent elasticity in amorphous solids, Physical review letters 125, 118002 (2020).

12. S. Bolisetty, M. Peydayesh, R Mezzenga Sustainable technologies for water purification from heavy metals: review and analysis Chem. Soc. Rev., 48, 463 (2019)

13. Ying Wang, Curt J Zanelotti, Xiaoen Wang, Robert Kerr, Liyu Jin, Wang Hay Kan, Theo J Dingemans, Maria Forsyth, Louis A Madsen, Solid-state rigid-rod polymer composite electrolytes with nanocrystalline lithium-ion pathways, Nature Materials 20, 1255 (2021).

14. A. Goyal et al, The physics of cement cohesion, Science advances 7, eabg5882 (2021)

15. Jan-George Rosenboom, Robert Langer and Giovanni Traverso, Bioplastics for a circular economy, Nature Reviews Materials 7, 117 (2022).

16. The National Academies of Sciences, Engineering and Medicine, "Frontiers of Materials Research: A Decadal Survey", 2019. The National Academies Press, Washington, DC. https://doi.org/10.17226/25244. https://doi.org/10.17226/25244.

17. National Institute of Standards and Technologies, Materials Data Repository, https://materialsdata.nist.gov; Material Genome Initiative, https://www.mgi.gov/; Community Resource for Innovation in Polymer Technology, https://cript.mit.edu/.
# Section 1.1 – Complex colloidal materials

Marjolein Dijkstra

Soft Condensed Matter, Debye Institute for Nanomaterials Science, Utrecht University, the Netherlands

**Status** The field of colloid science has undergone a revolutionary transformation in the 20th century. Advancements in the chemical synthesis and fabrication techniques have resulted in the creation of a dazzling variety of novel colloidal building blocks, while novel imaging, tracking, and manipulation techniques of colloidal particles have provided us with a wealth of fundamental insights into physical phenomena, such as melting, freezing, (de)mixing, glass transitions, nucleation, jamming, random packings, two-dimensional melting, and structure formation. These phenomena can be spontaneous or externally driven by gravity, templates, electric or magnetic fields, or other external forces.

From a theoretical point of view, not only the advent of computer simulations in the 1960s as a new scientific tool for studying highly correlated many-body systems, but also the exploitation of thermodynamics and statistical physics for predicting equilibrium properties of colloidal suspensions, have contributed significantly to our increased understanding and exploitation of colloids. Computer simulations enabled us to study with unprecedented microscopic detail the structure and phase behaviour of colloidal systems, whereas the high level of control in colloid synthesis resulted in well-defined experimental model systems, allowing for direct comparisons between experiments, simulations, and theory.

To illustrate the power of synergy between experiments, simulations, and theory, we refer to the freezing transition of hard-sphere fluids into face-centered cubic(fcc) solid phases, predicted theoretically in 1951 [1], and observed in early Molecular Dynamics and Monte Carlo simulations in 1957 [2, 3], but which was received with quite some scepticism at that time. The existence of such a phase transition was eventually proven once and forever by experiments on micron-sized sterically stabilized polymethyl methacrylate hard spheres in 1986 [4]. More interestingly, in contrast to atomic and molecular systems, the effective interactions between colloidal particles can be tuned by the addition of salt to a suspension of charged-stabilized colloids, giving rise to not only fcc but also body-centered cubic (bcc) phases for sufficiently long-range repulsive interactions [5]. Alternatively, an effective depletion attraction can be induced between the colloids by the addition of depletants or non-adsorbing polymer [6]. As the range and strength of the depletion interaction can be tuned by the size and concentration of the polymer, such mixtures serve as excellent model systems to test [7] the theoretical predictions on condensation of gases into liquids as laid down in the dissertation of Van der Waals in 1873 [8].

In addition, the field has shifted its attention from micron-sized colloids to nanometre-sized particles since the seminal work of Bentzon et al. who reported in 1989 the self-assembly of metaloxide nanoparticles into superlattice structures [9]. This study instigated a very active
research field, driven by the potential of creating new nanostructured materials with unprecedented functionalities using colloidal self-assembly of for instance semiconductor, metal, perovskite, and metal organic framework particles [10].

<figure><img src="image_4.png" /><figcaption>**Figure 1** The dazzling variety of novel colloidal building blocks can be divided into A) anisotropic particles such as 1) colloidal molecules: colloidal silica dumbbells, scale bar 180 nm [11], colloidal clusters of polystyrene microspheres, scale bar 1 µm [12], colloidal (semi)flexible polystyrene bead chains, scale bar 4 µm [13], 2) rods and plates: Au nanorods, scale bar 100 nm [14], colloidal polymethylmethacrylate ellipsoids, scale bar 5 µm [15], colloidal polystyrene discs, scale bar 2 µm [16], 3) branched particles: colloidal CdS/CdSe octapod-shaped nanocrystals [17], colloidal CdTe tetrapod-shaped nanocrystals, scale bar 100 nm [18], branched cubic silica particle, scale bar 1 µm [19], 4) polyhedral-shaped particles: slightly truncated silver nanocubes [20], octahedral metal organic framework particles, scale bar 0.5 µm [21], hollow silica cubes, scale bar 1 µm [22], B) programmed functionalized particles: 2 µm silica triblock Janus spheres [23], polystyrene patchy dumbbells with different surface roughness, scale bar 10 µm [24], lock and key colloids, scale bar 2 µm [25], DNA functionalized tetrahedral polystyrene clusters, scale bar 5 µm [26], di-patch DNA functionalized colloids, scale bar 5 µm [27], DNA functionalized nanocubes and spheres, scale bar 100 nm [28],</figcaption></figure>
bar 100 nm [28] and C) active self-propelled particles: 3-methacryloxypropyl trimethoxysilane (TPM) polymer colloidal sphere with a protruding hematite cube, scale bar 1 µm [29], colloidal Quincke rollers, scale bar 50 µm [30], Pt-coated active polystyrene bead chains, scale bar 2 µm [31]

However, the self-assembly of colloidal spheres with isotropic interactions is limited to lattice structures with simple symmetries such as fcc and bcc. To increase the structural diversity, one may resort to binary mixtures that form surprisingly exotic crystal structures analogous to their atomic counterparts like NaCl, AlB2, NaZn13, MgZn2, MgCu2, MgNi2 phase [32, 33] or to mixtures of oppositely charged colloids forming colloidal analogues of ionic crystals like NaCl, CsCl, CuAu, but also novel structures that do not have an atomic or molecular analogue [34, 35].

Another way to increase the diversity of self-assembled structures is to develop novel classes of colloidal particles with anisotropic shapes and varying interaction potentials, see Figure 1. Over the past decades a spectacular variety of novel colloidal building blocks have been fabricated [10, 36, 37] from different materials like dielectric, metal, semiconductor, and combinations thereof, with sizes ranging from the nanometer to the micrometer scale, and with a plethora of shapes such as clusters of spheres, so-called "colloidal molecules", rod-like, platelike, branched particles, polyhedral-shaped particles, hollow objects, microcapsules, nanostars, etc. Theoretically, the effect of shape on the interaction of colloidal particles already started in the 1950s with the seminal work by Lars Onsager [38].

More recently, these particles can also be functionalized so that instructions for self-assembly are programmed in the shape, e.g., lock and key colloids [25] or shape-shifting particles [39], in the surface pattern, e.g., Janus colloids, triblock Janus colloids, and patchy particles using e.g., regioselective depletion [40] or surface functionalization by DNA or proteins. Especially, the hybridization of complementary DNA strands grafted on the surface of colloidal building blocks, pioneered by the works of [41, 42], has proven to be a successful and versatile route for programming the self-assembly of structures as complex as diamond and clathrates [26, 43]. In addition, the self-assembly can be aided or altered by the application of external fields such as electric fields, gravity, templates, and by the structure of the solvent. For instance, self-assembly of colloidal particles can be tuned in situ by solvent-mediated interactions upon approaching the critical point of a solvent mixture [44], bicontinuous gel networks are formed in the case of an arrested phase separation of the solvent mixture due to jamming of the adsorbed colloids at the liquid-liquid interface [45], and topological structures like strings, knots, and links are formed due to the anchoring of a (chiral) nematic solvent at the colloidal surfaces [46, 47]. This vast array of colloidal building blocks and self-assembly protocols can be exploited for the fabrication of nanostructured materials with interesting optical, mechanical, and catalytic properties. To accelerate the design of self-assembled nanomaterials, the experimental efforts can be guided by theory and simulations. Over the past decades, huge progress has been made in the development of algorithms to predict the candidate structures of these novel colloidal building blocks, determining the thermodynamically stable phases by calculating free energies, to the point where
thermodynamic phase diagrams can be calculated in theory and simulations for any particle shape and interaction using the tools of thermodynamics and statistical mechanics.

## Current and future challenges

### (a) Designer soft matter

**High throughput screening** We have arrived at the brink of exciting times, where we can synthesize or fabricate colloidal building blocks with (nearly) any shape and interaction potential, from any material on demand. From a theoretical side, tremendous efforts have been devoted over the past decades to the “forward design” problem: Which structures with what properties are formed for a given colloidal building block under what circumstances? A major drawback of this approach is that the number of possible building blocks and thermodynamic conditions is vast, calling for the development of efficient high-throughput protocols to quickly conduct many experiments or simulations simultaneously and to test systematically many combinations of parameters. For instance, automated microfluidic and robotic synthesis platforms can be used to conduct many experiments in a high-dimensional parameter space in a very efficient way. On the other hand, surrogate models based on e.g., machine-learned many-body interactions can significantly accelerate the exploration of large search spaces in computer simulations [48]. Using these data-driven approaches, machine learning can be used to find a mapping between the input parameters, e.g., different thermodynamic conditions, on the one hand and the outcomes of the experiments on the other hand. Such machine-learned models can be used to make predictions for unexplored parameter combinations, thereby enabling rapid identification of promising building blocks, interaction potentials, and thermodynamic conditions for targeted self-assembly of colloidal structures with specific properties and functionalities. Additionally, the analysis of large amounts of data produced by high-throughput screening with novel machine-learning algorithms may result in the development of reliable and generic design rules that can be used to create soft advanced materials by design with certain electronic, optical or catalytic properties, or mechanical or rheological responses. A combined high-throughput screening and machine learning protocol can be used to provide suggestions for the next experiments/simulations to improve the machine-learned models or to optimize the conditions for a certain outcome. Very recently, a mobile robotic chemist was developed that could autonomously execute multiple experiments in a chemical lab and that uses machine learning to optimize a certain property based on the experiments done so far [49].

**Inverse design** The holy grail of designer soft matter is the development of a protocol for solving the so-called inverse design problem: What kind of colloidal building

blocks should we make and under what thermodynamic conditions should they self-assemble to realize a desired structure with a specific property? While state-of-the-art computational and theoretical statistical mechanics methods have been very successful in solving the so-called “forward” design problem, a robust, versatile algorithm for solving the inverse problem remains a
significant challenge. The lack of a reliable and efficient inverse design method remains a significant obstacle for the full exploitation of colloidal self-assembly in the development of next-gen materials. A variety of inverse-design approaches has been developed recently based on machine learning approaches or optimization techniques such as evolutionary strategies to optimize interaction potentials for targeted self-assembly, albeit often resulting into colloid interactions that are not always experimentally realisable [50]. This can be solved by restricting the search space to experimentally realistic potentials.

**Kinetics** Despite the availability of a wide variety of colloidal building blocks, the number of successfully self-assembled structures is still limited. To better understand and control the self-assembly, it is essential to also investigate the kinetic pathways for the formation of the thermodynamically stable phases, proceeding either via nucleation and growth or through spinodal decomposition.

**Nucleation** Homogeneous nucleation of colloidal particles has been the subject of many studies in the past decades. Several scenarios have been proposed in the literature such as one-step or two-step crystallization mechanisms, devitrification, spinodal-like processes, etc., but consensus has not been reached. Nucleation of the stable phase may also be hampered by the formation of competing polymorphs. To gain control over the formation of certain polymorphs requires a better understanding of the nucleation pathways and of the selection mechanisms that determines the pathway towards a certain self-assembled structure.

**Vitrification** Additionally, the self-assembly may be suppressed by kinetic effects such as vitrification, gelation, defects, stacking faults, and grain boundaries. Upon increasing the volume fraction, colloidal suspensions may undergo a glass transition where the viscosity increases by orders of magnitude and the system macroscopically behaves as a solid, yet its structure is still disordered. Despite the amount of research devoted to understanding glasses, the microscopic origin of the glass transition remains controversial and heavily debated. The main problem is that the structural relaxation time increases rapidly upon approaching the glass transition, making it difficult to unravel the physical phenomena underlying the glass transition. Recently, significant progress has been made in understanding the glass transition using machine-learning protocols to relate local structures hidden in the glass to the dynamics of the particles [51] as well as by employing algorithms that considerably speed up the equilibration deep in the glass [52]. It is clear that the kinetics and competition with other polymorphs, glass transitions, and gelation should be taken into account in the design and inverse design of self-assembly routes for specific target structures, e.g., by exploring the free-energy landscapes using data-driven methods and sculpting it towards the formation of the desired polymorph [53, 54].

**(b) Soft materials and machines with lifelike properties** The self-assembled materials mentioned so far are, however, passive. The next step would be to develop hierarchically structured soft materials and machines that can autonomously assemble, sense, respond, and reconfigure on demand. Nature displays a plethora of self-assembled dynamic materials that respond to external
stimuli, e.g., Chameleons change colour for camouflage, plants have the ability to bend towards sunlight, pinecones can change shape for a sudden seed release, and geckos stick to surfaces and change adhesion due to a self-regulated cooperative motion of tiny hairs (setae) on their feet. In all these cases, the ability to respond and adapt is encoded in a hierarchically structured material, where active and passive components are coupled in a non-trivial way. The design of soft materials and machines that function far from equilibrium requires insight in the dynamical behaviour of self-organizing active elements.

**Active matter** In the last decade, a diversity of active or self-propelled particles [55] have been produced ranging from chemically fuelled phoretic swimmers, light activated self-propelled colloids, magnetic swimmers, Marangoni-driven active droplets, Quincke rollers, etc. The exact mechanism responsible for the self-propulsion of these particles varies with the details of the colloidal system, and may be driven by transport phenomena like electrophoresis, diffusiophoresis, or thermophoresis when the activity is generated by gradients in the electric field, concentrations of solutes, or temperature, respectively. A precise control of out-of-equilibrium active matter systems requires a thorough understanding of the self-propulsion mechanism. The collective behaviour of many interacting and self-propelling particles can give rise to fascinating phenomena and a plethora of self-organized structures, which are not observed in passive systems. Examples of such structures include clustering, motility induced phase separation, living crystals, dynamical superstructures of synchronized microgears, and chiral fluids, among others [55]. Since these particles incessantly convert energy into active motion, these systems are intrinsically out of equilibrium. In contrast to the collective behaviour of passive systems, which is well-described by the laws of equilibrium thermodynamics and statistical physics, there is no such framework yet for active matter. New theoretical approaches are required to describe the collective dynamic behaviour of active systems [56].

**Hierarchical self-assembly** Nature is rife of beautiful examples of hierarchically organized structures, where active and passive elements function in a cooperative way. For instance, macromolecules like lipids, DNA, and proteins self-assemble into cells, individual cells into tissues, tissues into organs, and organs into organisms such as birds and fish that can in turn dynamically organize into flocks and schools. These hierarchical, dynamical structures aspire researchers to also self-assemble colloidal matter hierarchically. A better insight in the laws and possibilities of hierarchical self-assembly will enable us to structure matter over multiple length scales and to add new (dynamic) properties and functionalities at each self-assembly step. Examples of hierarchically self-assembly include the fabrication of colloidal molecules [12], supraparticles [57], patchy particles [58], or the co-assembly of different colloidal particles in hierarchical multicomponent materials [59]. The ultimate aim is to create self-assembling micromachines [60, 61] that are motile, self-healing, responsive, and shapeshifting, which can autonomously assemble into complex and interesting dynamical structures.
**Concluding remarks** The theoretical tools to understand the equilibrium behaviour of colloids were developed in the 19th and 20th century, before the advent of computer simulations in the 1960s and our ability to conduct controlled experiments since colloidal particles with accurately defined shapes, interactions, and surface functionalizations were only synthesized from the 1990s. However, applying the methods from statistical physics, thermodynamics, and liquid-state theory frequently led to equations that are too hard to solve analytically or numerically, and computer simulations gained ground over the past decades. While the equilibrium behaviour of colloidal matter is well described by equilibrium statistical physics, there is no such framework yet to describe out-of-equilibrium systems. The focus of the 21st century will be on the development of a theoretical framework that encompasses non-equilibrium statistical mechanics and non-linear dynamics. Recently, machine learning has become the fourth pillar of science, next to theory, experiments, and simulations. The use of machine learning as a scientific tool is picking up with an incredible speed. In the next years, we will see that large data sets from simulations and experiments will be combined to find mappings between input parameters, such as thermodynamic conditions, particle interactions, etc. on the one hand, and the macroscopic equilibrium or out-of-equilibrium behaviour on the other hand by training machine-learning algorithms with the available data. These machine-learned models can be used to make predictions for unseen input parameters and to optimize materials designs. An important question that arises is whether or not these machine-learning algorithms can deliver any scientific understanding, or should they solely be considered as black box models, and more provocatively, do we still need theory to obtain a physical understanding of the phenomena at hand. Time will provide us with an answer. What we do know is that the study of colloids has already provided us with a wealth of insights into physical phenomena such as freezing, nucleation, and glass transitions. In the coming years, this rapidly evolving field will turn its attention to the bottom-up self-assembly of bio-inspired complex materials and machines, where passive and active components function far from equilibrium together in an intricately cooperative and hierarchical way. Studying these new materials with life-like properties will lead to exciting new physics and will give us insights in the dynamic and collective behaviour of out-of-equilibrium systems, requiring the development of new theoretical frameworks to describe these fascinating systems with self-healing, responsive, and adaptive properties.

**Acknowledgements** Financial support from ERC Advanced Grant No. 884902 'SoftML' is acknowledged.
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# Section 1.2 – Engineering colloidal particles

David Pine<fnref n="1" />, <fnref n="2" />

**Status** Until recently, most synthetic colloidal particles were spheres that were suspended in a liquid and stabilized against aggregation by surface charges or by a polymer brush adsorbed or grafted to the particle surface. Such particles found widespread use in cosmetics, paints, medicine, and in fundamental studies of phase transitions and self-assembly. Interest in engineered colloidal particles was sparked in the mid-nineties by the realization that colloidal crystals might be useful for new optical applications including materials with photonic band gaps. Early work focused on close-packed FCC photonic crystals of spheres, but attention shifted to cubic diamond crystals, or structures with similar symmetry, which are needed to realize the large band gaps and the insensitivity to disorder required to achieve robust optical properties. This led to the development of particle clusters preassembled into dimers, tetrahedra, or other aggregates [1] that could serve as building blocks for assembling colloidal crystals more complex than the familiar FCC, BCC, and related structures. It also led to the development of patchy particles [2,3], especially 4-patch colloids that mimic the valence and tetrahedral bonding symmetry of diamond-forming atoms like carbon. However, patches alone proved inadequate to form cubic diamond crystals as they do not constrain the bond conformations of neighbouring particles. The requisite “staggered” bond conformations were achieved very recently by synthesizing patchy particles with tetrahedral lobes, which led to the first self-assembled cubic diamond colloidal crystals suitable for templating 3D photonic crystals [3].

Interest in colloidal self-assembly spurred several other innovations, including the development of Janus particles (particles with two dissimilar faces) that self-assemble into structures resembling those formed by molecular amphiphiles [1] and also into fascinating new structures like a 2D honeycomb lattice [4]. The development of oppositely charged ionic colloids stabilized by a thin polymer brush has produced colloidal crystals of unprecedented size and stability, with millimetre-size crystals in a variety of structures that can be permanently fixed, removed from aqueous suspension, and dried while maintaining their crystallinity [1].

The periodic spatial variation of the refractive index in colloidal crystals gives rise to structural colour that depends strongly on viewing angle due to Bragg scattering from different crystalline planes. The desire for colour independent of viewing angle thus led to intense activity on developing disordered arrangements of colloidal spheres with structural colour [5]. Hyperuniform arrangements of colloidal particles, which can be achieved through periodic shearing [6], also emerged as another significant idea for producing not only structural colour but also photonic band gaps from isotropic structures.

<footnote n="1">¹Department of Physics, University of New York, New York, USA</footnote>

<footnote n="2">²Department of Chemical and Biological Engineering, University of New York, New York, USA</footnote>
Research on colloidal self-assembly focused on developing new attractive orthogonal programmable interactions between colloids, the most versatile being those derived from DNA-coated colloids, whose hybridizing sticky ends can be manipulated to control phase behaviour as well as to dynamically reconfigure colloidal structures using toehold displacement strands [7]. The development of roughness-controlled depletion attraction [8] as well as critical Casimir forces [9] also added to the expanding toolset for controlling self-assembly.

Another important direction was the development of lithographic methods for making structured particles, particularly hydrogel particles, which has led to a vast library of particle shapes and applications in photonics and medicine [10].

**Current and Future Challenges** Although a vast new toolset of colloidal interactions and particle shapes has been introduced recently, few new crystal structures have been realised. Ideally, one would like to be able to program virtually any multiparticle structure, crystalline or otherwise. The programmability and orthogonality of DNA-mediated colloidal interactions would seem to make this possible, but their potential has yet to be tapped. One problem is simultaneously controlling the relative melting (i.e., collective dehybridization) temperatures of many different complementary DNA sticky ends on differently functionalized particles [7]. This involves not only programming the DNA base-pair sequences of the sticky ends, but also controlling and understanding the role of areal grafting density, flexibility, and length of the polymers that tether the sticky ends. Some progress on this front has been made using DNA toehold displacement strands [1,7].

Making colloidal structures that dynamically reconfigure based on external cues like temperature or chemical environment is highly desirable. Here again, DNA toehold displacement strands [1,7] have been a powerful tool, with demonstrations of reentrant colloidal phase transitions and sequential self-assembly, but their potential for making colloidal micromachines remains largely unexplored.

While new particles with different shapes have been realized [1,3,10], many more will be required to realize complex non-crystalline structures such as fully three-dimensional quasicrystals. Moreover, of the particle shapes that can be realised, producing many of them in bulk quantities remains a challenge [1,10]. While there have been some notable advances in synthesizing patchy particles in bulk quantities [1,10], most remain difficult to produce in quantities needed for manufacturing [2,4,9].

A key challenge is fabricating patches, lobes, cavities, or other features with different functionalities so that different parts of a particle can interact with other particles, both through shape-specific lock-and-key interactions and chemically derived interactions. The challenge is to make arbitrary structures similar to those routinely realized with proteins in biological systems [1,7,10].
Many applications in photonics, require control over structure—crystallinity, hyperuniformity—at long length scales; doing so remains a challenge. Current methods for annealing grain boundaries are crude and very slow. Creating hyperuniform colloidal structures over much more than a decade in length scale remains challenging [6].

**Advances in Science and Technology to Meet Challenges** Future progress requires advances on several fronts. Developing new approaches for the fabrication of multifunctional colloidal particles with control over patchiness and interactions is vitally important. Taking a cue from proteins, one promising approach is to develop the ability to make linear chains of different colloids in any desired sequence such that they subsequently fold in to a desired “globular” aggregate with preprogrammed patchy interactions. Such a project need not be overly ambitious: sequences from four to about a dozen particles would suffice to create multifunctional patchy particles significantly more complex and versatile than currently available. Using DNA origami to this end provides one approach [7], although the differences in length scales—micrometre vs. tens of nanometres—poses a challenge. Other developing approaches include using liquid colloidal particles (emulsions) or colloids with mobile DNA bound by a liquid bilayer to make flexible colloidal chains that can fold [11].

Developing quantitative models for the binding between DNA-coated colloids as well as a more quantitative understanding of their crystallization kinetics is needed, as crystallization is notoriously slow in these systems. Similarly, understanding the phase behaviour and kinetics of multifunctional patchy colloids could provide invaluable guidance for colloidal design.

A great deal of progress has been achieved in producing structural colour using colloidal glasses. Recent work suggests that modifying the packing protocol to control structural correlations and using core-shell particles to independently tune Mie scattering and structural correlations are important, but so are many other factors so that attaining maximal colour saturation while maintaining angle independence remains a challenge [5].

**Concluding Remarks** The field of engineered colloidal particles has exploded over the past decade with many new particles and fabrication techniques having been proposed and demonstrated. Lithographically manufactured hydrogel particles are finding ever-expanding medical applications. New colloidal crystals such as diamond have been fabricated for the first time, which could lead to the realization of materials with robust photonic band gaps. Understanding of structural colour and the means to produce it have moved forward significantly. New reconfigurable colloidal materials have been made. All of this opens up new opportunities for colloidal self-assembly. Many of these advances have been motivated by scientific curiosity. Going forward, the field will need to focus more of its efforts towards applications and do so more aggressively in order to realize them.

**Acknowledgements** DJP acknowledges support from the US Army Research Office (Award No. W911NF-17-1-0328) and the US Department of Energy (Award No. DE-SC0007991).
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## Section 1.3 – Soft polymer materials

Sanat K Kumar, Kyle Bishop, Oleg Gang and Allie Obermeyer

Soft Matter Group, Department of Chemical Engineering, Columbia University, New York, NY, USA

**Status** Polymeric materials have been the focus of research for well over 100 years, and as in the case of many topics at the intersection of science and engineering advances are driven by and motivated by applications. Particularly germane examples today are the use of polymers in emerging energy technologies (carbon sequestration, battery applications, water purification membranes), in creating a circular economy (polymer upcycling), in understanding the context of biological relevant polymers (particularly the topic of coacervation relevant to membrane-less organelles; out of equilibrium – or active -materials) and in the bottom up creation of materials with desired properties (using for example DNA guided assembly of nanostructures). We elaborate on each of these aspects below but an important point we stress is that the future of polymer science and engineering are intimately related to the sustainability of life on this planet.

**Emerging Energy Technologies** Polymer membranes are critical to the efficient separation of gas mixtures, carbon capture, the separation of ions and in water purification. Despite their widespread use, important challenges remain in the use of membranes in this context - primarily the need to selectively improve the transport of different mixture components while enhancing strength and aging behaviour. The important figures of merit here are the flux of the desired component, which is proportional to the permeability, $P_i = D_i \times S_i$ ($D_i$ is the gas diffusivity and $S_i$ its solubility coefficient) and selectivity (i.e., gas purity) which is defined as $\alpha_{ij} = P_i/P_j$. The goal is to maximize both $P_i$ and $\alpha_{ij}$. Most of the research in this area has empirically targeted the development of new polymers with improved separation performance.¹⁻³ Additionally mechanical robustness is critical, e.g., having mechanically strong materials to stand the pressure driven flows typically encountered, the ability to resist lithium dendrite formation in batteries, and the ability to minimize aging effects which typically unfavourably affect performance. The ability to *a priori* design polymers with enhanced separation and mechanical properties remains open. In this context we point to the new direction of creating mixed matrix membranes (mixed of MOF particles with polymers⁴; using polymer grafted nanoparticles⁵, ⁶) as superior constructs for such separations. Other cutting-edge technologies, and their underpinning science, need to be developed in this rapidly evolving field.
**Circular Economy** While plastics use grows, US recycling rates have stagnated at 10%. There is thus a need to develop the science that will facilitate the difficult deconstruction of polymers into value-added small molecules.⁷,⁸ These small molecules can be independently useful, or, alternately, they could be repolymerized into value added polymers (“circularity”). Depolymerizing plastics requires sizable energy inputs because this process has to overcome the very favourable free energy of the forward process of polymerization. The polymer ceiling temperature, Tceiling, is a

convenient proxy for this important metric. For T<Tceiling, the free energy of polymerization ΔG = ΔH(1 − T/Tceiling), is negative, with typical enthalpies of polymerization being ΔH~50-100 kJ/mol of monomer depending on the particular chemistry in question. For polymers with low Tceiling (e.g., PET, PS, PMMA, Table 1), ΔG is moderately favorable and hence breaking them down into monomers is relatively inexpensive – this is why a large body of research has focused on those particular materials.⁹ In contrast, a large fraction of ubiquitous, engineering polymers have

high Tceiling, e.g., polyolefins, polyisoprene (rubber tires), polyurethanes, polyimides, polyamides and most thermosets, the breakdown pathway is inherently energetically expensive. The free energy to depolymerize polyethylene (≈ 60 kJ/mol ~ 25RT) is high. Since this free energy is large, concurrently the activation barrier, Eα, to go from polymer to monomer is even larger. Thus, reaction rates to go from polymer to monomers are very small, even with the use of catalysts. To alleviate this major bottleneck, we hypothesize that external field(s) need to be judiciously used to flatten the free energy surface so that the polymer and monomer's free

energy become closer; further, the activation energy between the two states can also be reduced by this external field. When combined with suitably chosen catalysts, such external drivers can be used to dramatically increase depolymerization rates and thus make recycling pathways viable. Of course, one cannot overcome basic thermodynamic constraints, and hence the external field, which flattens the free energy surface provides the energy that is required to raise the free energy of the polymer and makes it easier to depolymerize.

<table><caption>**Table 1:** Ceiling Temperature for Select Polymers</caption><thead><tr><td>Monomer</td><td>Tceiling</td></tr></thead><tbody><tr><td>α-Methylstyrene (PαMS)</td><td>66° C</td></tr><tr><td>Isobutylene (PIB)</td><td>175° C</td></tr><tr><td>Methylmethacrylate (PMMA)</td><td>198° C</td></tr><tr><td>Ethyleneterephthalate (PET)</td><td>300° C</td></tr><tr><td>Styrene (PS)</td><td>395° C</td></tr><tr><td>Isoprene (PI)</td><td>466° C</td></tr><tr><td>Ethylene (PE)</td><td>610° C</td></tr><tr><td>Tetrafluoroethylene (PTFE)</td><td>1100° C</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>**Figure 1** Schematic illustration of external forces that can aid in polymer upcycling.</figcaption></figure>
**Coacervation** The ability to understand how living organisms emerged provides fundamental insight into life on earth and paves the way for polymer scientists and engineers to mimic the emergent properties of cells and organisms to create more sustainable materials. For example, understanding how cells originally delineated self and other and gained the ability to grow, divide, and self-replicate could guide the design of autonomous polymeric materials capable of both healing and self-destruction as needed. Recent evidence has shown that short oligomers and polyions can form a condensed phase with a distinct chemical environment than the surroundings – providing a potential mimic of original protocells.¹⁰ These condensed droplets can be imbued with catalytic activity, which makes their formation and dissolution sensitive to the presence of chemical fuel.¹¹ Theoretical efforts have also demonstrated the potential of droplets of condensed phases, fuelled by chemical reactions, to grow and divide¹² or control their size.¹³ In addition to the potential role of oligomer and biopolymer phase separation in the origins of life, the condensation of biomacromolecules plays a key role in both bacterial and eukaryotic cell biology. The formation of these intracellular biomolecular condensates has received extensive attention over the past decade with numerous condensed compartments identified¹⁴, ¹⁵ and more recently their functional implications on biomolecular and cellular activity revealed.¹⁶ As understanding of the design rules for the formation of cellular condensates has improved, condensates have been engineered with specificity and metabolic activity.¹⁷, ¹⁸

**Active Soft Matter** Living matter performs complex functions such as force generation, energy conversion, and information processing that rely on complex biopolymer materials animated by chemical reactions.¹⁹ These dynamic functions are characterized by flows of energy and matter, which are notably absent from passive equilibrium materials. Inspired by biological systems, the pursuit of synthetic soft matter operating outside the constraints of thermodynamic equilibrium aims to advance our fundamental understanding and deliver new material capabilities (e.g., artificial muscles,²⁰ colloidal robots.²¹, ²² There are several strategies for driving materials out of equilibrium. Arguably the simplest relies on initializing the system in an otherwise improbable configuration—for example, glass formation by melt. Alternatively, control variables such as external fields can be modulated in time on scales commensurate with that of material relaxation as to stabilize (or destabilize) new structures.²³, ²⁴ The use of time-dependent drivers that break time reversal symmetry enables steady currents underlying ratcheted transport and force generation. Another route to nonequilibrium uses multiple reservoirs to drive currents of mass, energy, and momentum that couple to and direct material organization. Common examples include polymer systems subject to mechanical shear, ionic currents, or gas fluxes. In addition to external currents and fields imposed at material boundaries, distributed energy input to the individual components of a material system (e.g., via chemical reactions) provides a basis for new phenomena known as active matter.²⁵ Experimental realizations include nematic liquid crystals with internal stresses powered by molecular motors²⁶, ²⁷ as well as self-propelled colloids driven by phoretic flows.²⁸, ²⁹ The latter highlight yet another route to nonequilibrium whereby non-conservative forces that do not derive from a global potential give rise to non-reciprocal interactions that violate Newton's third
law of action-reaction symmetry.<sup>30, 31</sup> In the context of self-assembly, the use of chemically fuelled reactions to activate components for assembly enables active polymers<sup>32, 33</sup> and droplets<sup>34, 35</sup> inspired by the cytoskeleton and condensates of living cells.

**Bottoms Up Assembly of Functional Materials** Various nanomaterial classes can spontaneously self-assemble into ordered nanostructures, including nanoparticles (NP), polymers, and biomolecules. The ability to guide self-assembly processes through DNA-based methods stand out due their ability to encode information for specificity and directionality of interactions, which is critical for enabling *designability* of self-assembled nanomaterials. Starting from the early ideas of DNA organization of nanoscale matter<sup>36</sup> and DNA motifs for linking inorganic particles<sup>37, 38</sup>, DNA-based assembly methods<sup>39-41</sup> have provided an ability to assemble nanoscale structures, including planar<sup>42, 43</sup> and isolated DNA architectures<sup>41, 44 45, 46</sup>, and NP clusters<sup>47, 48</sup>. However, establishing methods for forming the *desired complex 3D organization* of inorganic NPs (*functional payloads*), has met a fundamental challenge: an inevitable coupling between the nature of NP (size, shape, interactions, grafted ligands) and the self-assembly process. Although a rich diversity of 3D inorganic NP lattices<sup>49-51</sup> have been demonstrated, the organizations are typically limited to: (i) mimicking atomic systems, (ii) mono and binary compositions, (iii) single-scale periodicity, and a simple architecture. Thus, a new fabrication platform that incorporates wet-chemistry derived payloads, offers means for creating designed nano-organizations with control on multiple scales and provides integration of different nanomaterial types is needed.

Recent demonstrated integration of polyhedral DNA frames with encoded NP into “material voxel”<sup>52</sup> open possibilities for rational assembly of though directional and encoded interaction of voxels. This assembly strategy permits us to assemble different types of lattice organization in a completely rational way<sup>52</sup>. Moreover, it allows us to decouple a nano-object nature from assembly process that is fully governed by directional bonds of voxel, thus, we built lattices form inorganic NP, proteins and enzymes using practically the same voxel assembly process<sup>52</sup>. Importantly, this realization promises a practically realizable assembly platform that will use inverse design strategy for creating targeted 3D nanoscale organization through the coordination of between voxels based on the encoding of their bonds.

<figure><img src="image_6.png" /><figcaption>**Figure 2** Programming material formation from DNA folding to nanoparticles and protein integration and to large-scale architectures.</figcaption></figure>
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## Section 1.4 - Complex Polymer Hydrogels

Christine M. Papadakis<fnref n="1" /> and Constantinos Tsitsilianis<fnref n="2" />

**Status** Complex polymer hydrogels are ubiquitous, the most prominent example being the oxygen-permeable soft contact lenses invented in 1960, that consist of hydrophilic and hydrophobic block copolymers. They are significantly more versatile than the classical simple hydrogels, which consist of one type of water-soluble polymers that are cross-linked chemically and/or physically, typically retain a large amount of water and are mechanically soft [1]. The term 'complex hydrogel' does not only refer to a combination of building blocks having different properties, but also to their diverse functionalities, including the constituents they carry, e.g., payloads such as magnetic nanoparticles, quantum dots or stem cells. Network architectures that feature superior properties compared to classical polymer hydrogels, e.g., enhanced toughness, are based on, e.g., slidable, or high-functionality cross-links or on double interpenetrating networks (Figure 1a-c), and on cross-links having tunable strength (Figure 1d-f, [2,3]). Complex polymer hydrogels featuring multiple physical interactions may have extraordinary mechanical properties, such as high toughness (Figure 1g).

<figure><img src="image_7.png" /></figure>

<footnote n="1">¹Technical University of Munich, Physics Department, Soft Matter Physics Group, James-Franck-Str. 1, 85748 Garching, Germany</footnote>

<footnote n="2">²Department of Chemical Engineering, University of Patras, 26500 Patras, Greece</footnote>
**Figure 1** Crosslinks in complex polymer hydrogels: Types of crosslinks: (a) slidable crosslinks, (b) high-functionality crosslinks and (c) interpenetrating polymer networks. Examples for strong physical crosslinks: helical association (d), weak physical crosslinks: coordination complexes (e), and dynamic covalent crosslinks: hydrazine bonds (f) Reprinted with permission from [2]. Copyright 2021 American Chemical Society. (g) Double network featuring multiple physical interactions. Upper left: Design principle. The first network is a physically cross-linked hydrogel from agar, while the second network is formed by a water-soluble polyanion with Fe³⁺ counterions. Green lines: Agar, forming double helix structures; blue lines: water-soluble polymer; magenta stars: Fe³⁺. Upper right: Physical interactions at play in the second network. Bottom left: Mechanical behaviour under stress. Bottom right: Stress-strain curves proving the high toughness of the double network with ionic interactions (black curve). Reprinted with permission from [6]. Copyright 2020 American Chemical Society.

Motivated by healthcare needs and other modern technologies, such as robotics, immense progress on network design has been made in recent years through various disciplines, namely advanced chemistry including computational methods, macromolecular engineering, and recombinant DNA technologies. Synthetic model macromolecule precursors prepared by advanced polymerization techniques, such as “living”, controlled polymerization, comprising various repeating units and functionalities, introduced via post-polymerization reactions, and featuring various architectures, such as linear, star or graft polymers, have been designed to satisfy combined requirements, namely dynamic association self-assembly, dynamic covalent bonding and multi-responsiveness to various environmental stimuli. The specific design of these polymeric species (e.g., amphiphilic 4-armed star block copolymers, [4]) can lead to well-defined “ideal” networks with tunable structures, mechanical response, and stimuli responsiveness [5]. A multitude of recent developments results in novel multifunctional hydrogels, that combine several properties and are perfectly tailored to the specific application, such as specific mechanical properties with sensing capability (Figure 1g, [7-9]).

**Current and Future Challenges** For several applications, hydrogels are needed, that not only feature appropriate mechanical properties, such as extremely high fracture toughness and tensile strength, but also particular physical properties, such as high electrical conductivity [2]. In addition, the interfacial properties, like adhesion, are of importance, especially when complex hydrogels are used together with other materials [6]. Hydrogels having multiple combined mechanical, physical, chemical and biological properties can only be achieved by designing complex networks. For instance, portable and wearable electronics require materials for energy storage that are highly stretchable [7-9]. Sensors in soft robotics require gels with high stretchability and sensing capability [10]. For long-term applications in rough environments, these gels need to be highly durable, i.e., self-healing. For applications as components of, e.g., drug delivery systems, microfluidic devices, tissue implants, contact lenses, chemo-mechanical sensors and actuators, materials are needed that mimic artificial muscles, i.e., they are supposed to swell, shrink, or bend in response to environmental stimuli [11]. Tunable hydrogels were proposed for the use in clean water production by solar desalination and in solar desalination and atmospheric water harvesting [9].
Network design principles targeting modern biomedical applications require additional combined
properties like biocompatibility, biodegradability, and bioactivity. Natural polymers, namely
polysaccharides, polypeptides, hydrophobically modified peptides (self-assembled to nanofibers)
and protein-like motifs, combined with biocompatible synthetic polymers are well-suited as
network precursor biomaterials for the rational design of advanced, tailor-made complex networks,
devoted to specific healthcare applications, such as drug/gene delivery, wound healing, and
regenerative medicine.

For tissue engineering, adaptable hydrogels [12] formed by reversible crosslinks of more than one
crosslinking mechanism, e.g., dual crosslinking [13], have been accomplished. This kind of networks,
that have mechanical properties adapted to the specific tissue and create a suitable dynamic
microenvironment (4D biology) approaching the natural extracellular matrices, allow cellular
functions to take place, such as adhesion, migration, and proliferation [14]. For non-invasive or
minimally invasive methods into the body, injectable and self-healable hydrogels have been
proposed [15], that have specific mechanical properties during injection (protecting cells) and at
rest in the host tissue along with suitable stress relaxation and controlled erosion rates. To provide
these properties, responsive dynamic linkages based on a combination of triggers like shear or
change of temperature or pH have been integrated to the network structure [16].

Hydrogels have been also designed as high-loading, multi-drug carriers for therapeutic purposes [17]. Particularly for cancer therapies, they can cause less severe side effects than systemic chemotherapy and can achieve sustained controlled delivery of drugs at tumour sites. However, these systems are faced with additional challenges related to clinical applications namely long-term biocompatibility, release rates and metabolism in vivo, specificity to patients and tissues [18].

**Advances in Science and Technology to Meet Challenges** A multitude of recent developments result in novel multifunctional hydrogels, that combine several properties and are perfectly tailored to the specific application. For instance, complex polymer gels have been proposed to be part of electroluminescent devices [7], supercapacitors [8] or in sensors in soft robotics [10]. The use of (interpenetrated) double networks, for instance, ensures the durability of the gels, which is of importance in long-term applications in rough environments. Design principles to achieve high electrical conductivity comprise hydrogels with percolated electrically conductive fillers, e.g., carbon nanotubes, hydrogels with ionically conductive salt solvents serving as electrodes, and hydrogels based on conducting polymers, that may be used as stretchable sensors in prosthetics [2]. Combination of properties is possible in an orthogonal way, e.g., by using a stretchy polymer network and percolating electrically conductive phases [2]. A synergistic way of combining properties could be to use stiffening elements, such as micro- or nanofibers that feature high electrical conductivity themselves [2].

Hydrogels have attracted particular attention as materials, that can change shape following an
external stimulus, since they can exhibit complex swelling behaviours triggered by variations of
external parameters, such as pH, temperature, light, electric fields, ionic strength, antigens, and glucose [19]. Due to such unique responsiveness, good biocompatibility and degradability, hydrogels have gained substantial interest and attention for a variety of potential applications, such as components of drug delivery systems, microfluidic devices, tissue implants, contact lenses, chemo-mechanical sensors and actuators.

The further development of dynamic hydrogel multifunctional platforms for basic and translational biomedical applications is faced with new challenges. The complexity of the emerging novel network platforms increases as to fulfil all the required structural, biocompatible, and final functional properties. This might generate some contradictions. For instance, microscopic structural dynamics and macroscopic long-term stability need to be balanced. Other important issues are the real-time characterization under microscopic resolution and the monitoring of the structural and physical properties along with the cell behaviour during long periods of time, requiring the development of advanced methodologies and novel techniques. In some applications, the hydrogel erosion rates must be rationally designed. The programmable orthogonal hydrogel erosion through distinct triggers, e.g., by sonication or light, targeting dissociation of specific crosslinks might be a solution. Although a plethora of promising network systems devoted to specific applications have been developed and studied in vivo with model animals, not many of them have reached clinical trials [20], which constitutes the final criterion for real biomedical applications and emerges as a new challenge.
<figure><img src="image_8.png" /><figcaption>**Figure 2** Complex hydrogels for (a) energy applications and (b) biomedical applications. (a) A flexible supercapacitor incorporated with solid-state double network hydrogel electrolytes. Loading-unloading testing cycles show that, while the first network breaks during the first cycle, the second network is rapidly recovered. After 7000 charge/discharge cycles, 80% of the initial capacitance is retained. A light-emitting diode can be lightened up. Reprinted with permission from [8]. Copyright 2021 American Chemical Society. (b) Schematic representation of the design strategy of the physicochemical double cross-linked multifunctional hydrogel prepared by Schiff base and catechol-Fe³⁺ chelation bonds, capable of healing deep second-degree burn wounds. The hydrogel shortened the healing time of burn wounds to 13 days and accelerated the reconstruction of skin structure and function. Reprinted with permission from [21]. Copyright 2021 Elsevier.</figcaption></figure>

**Concluding Remarks** Complex networks in the form of hydrogels have been systematically developed the recent years due to the vast variety of promising applications in various fields of technology. Unambiguously there are still several challenges that must be addressed to achieve real and safe applications. The increasing complexity of hydrogels needed to meet the different requirements in daily life applications, raises both fundamental and technological questions, which motivate further interdisciplinary developments of these soft materials. Systematic advancement and optimization of design principles combined with specialized implementation bottom-up strategies are expected to emerge in the years to come.
**Acknowledgements** C. M. P. gratefully acknowledges Deutsche Forschungsgemeinschaft for funding (PA 771/19-1). C. M. P. and C. T. thank DAAD and IKY for funding within the IKYDA program.

References

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# Section 1.5 - Liquid crystalline materials

Ivan I. Smalyukh<fnref n="1" />,<fnref n="2" />

**Status** Early documented observations of liquid crystals (LCs) go back some 160 years [1], when they provided evidence of LC phase behaviour in cholesterol derivatives extracted from animals. Nowadays, LCs form a basis of many advanced technologies, ranging from displays to electro-optic, photonic and biomedical devices. These states of soft condensed matter combine various degrees of orientational and partial positional order with fluidity and exhibit structural diversity exceeding that of solid crystals. They can have uninhibited fluidity combined with orientational order alone, like in the so-called nematic LC phases, or exhibit one- or two-dimensional partial positional order or quasi-crystalline organization co-existing with fluidity, like in smectic and columnar phases, respectively. Being highly experimentally accessible, LCs often serve as model systems to understand behaviour of less accessible physical systems, ranging from elementary particles to the Early Universe cosmology [2].

With nearly two centuries of research history and LC-enabled technologies all around us, the LC research field recently exhibits a renaissance of its development [2-12]. For example, more nematic LC phases have been discovered over the recent period of about 10 years than during the rest of LC history. New application opportunities promise a means of addressing the global energy demand and climate-related challenges [3]. Old-textbook classifications need re-writing as entire new classes of LCs continue emerging, including the ones previously thought to be impossible. Recent breakthroughs in nanoscience enable molecular-colloidal LCs that combine thermotropic and lyotropic sub-classes [4,5], where rich phase behaviour stems from stimuli-tuneable molecular and colloidal interactions at the hierarchy of length scales ranging from angstroms to micrometres [4-9]. These LCs reveal unexpected combinations of order and fluidity, like the monoclinic and orthorhombic symmetries [4,5], uniaxial and monoclinic ferromagnetic and other polar LCs [8,9], twist-bend and splay-bend nematic phases [10], etc. Materials with ferroelectric LC fluid phases have been synthesized [11,12] and are actively studied [13-15]. A series of recent breakthroughs in LC elastomers, polymers and gels promise revolutionizing soft robotics, biomimetic smart window films [3], as well as various sensors and actuators. LC sub-classes of active and driven matter exhibit particularly intriguing behaviour of topological defects [16]. On the other hand, LCs are found hosting zoos of topological solitons with particle-like behaviour manifesting in the formation of solitonic crystals and unusual forms of active and driven matter [2,17]. From yet another perspective, manifestations of LC behaviour continue being observed in various biological and active matter systems, as well as new biomedical applications such as biodetection, drug delivery and cancer treatment [18-22].

**Current and Future Challenges** While structure of crystalline solids is fully classified in textbooks, the diversity of structures of LC fluids is still being explored. Much like in the Planer's experiment [1], LCs were often discovered accidentally. To increase the odds of discovery, a common recipe

<footnote n="1">¹Department of Physics and Materials Science Engineering Program, University of Colorado, Boulder, CO 80309, USA.</footnote>

<footnote n="2">²Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, CO 80309, USA.</footnote>
was to design building blocks with symmetries of anticipated LC phases and hope that interactions between them will lead to such phase behaviours. Yet, recent findings reveal more complex relations between symmetries of building blocks and those of LC phases. For example, organic molecular dimers of building blocks of conventional uniaxial nematic phases organize into very different mesophases, the so-called twist-bend and splay-bend nematic states [10]. While brick-like molecules commonly exhibited high-symmetry uniaxial rather than highly thought after orthorhombic nematic LCs, an emergent behaviour of high-symmetry disc- and rod-like colloidal and molecular building blocks led to not only orthorhombic but also monoclinic nematic phases (Figure 1a) [4], where the molecular and colloidal subsystems order along obliquely oriented directions in the latter case. Could there be ways of discovering LCs by design? Hypothetically, fluid-like orientational order of colloidal nanoparticles within a molecular nematic host could lead to a series of symmetry-breaking transformations (Figure 1b), but one needs to discover the physical design rules to make these molecular-colloidal assemblies the energetic ground states.

<figure><img src="image_9.png" /><figcaption>**Figure 1** Demonstrated and anticipated diversity of molecular-colloidal LC fluids. (a) Monoclinic nematic formed by thin colloidal discs dispersed in a common molecular nematic host with molecular ordering direction depicted by magenta lines. The symmetry plane and axis are marked; green regions next to particle edges show the localized regions where nematic order of the molecular host medium is perturbed by the colloidal disc surfaces with conically degenerate surface anchoring. (b) Point group symmetries and transformations of orientational order that can emerge in mesostructured nematic LCs formed by a uniaxial $D_{hh}$ molecular nematic host doped with colloidal particles with various geometric shapes. Chiral and nonchiral phases are depicted with magenta and yellow colours, respectively.</figcaption></figure>

While topology recently plays important roles in phase discovery in hard condensed matter, blue phases of chiral LCs show how topologically nontrivial field configurations can arise in soft matter, enriching behaviour beyond that of a chiral nematic (cholesteric) LC phase (Fig. ure2a). Cubic blue phases comprise periodic arrays of fractional skyrmions (double twist tubes) and disclinations [2]. 3D particle-like topological solitons can be building blocks of exotic phases too [2]. Figure 2 shows examples of crystalline arrays and phases of the so-called “heliknotons” [12], a type of 3D topological solitons with a dual nature of being a non-singular Hopf soliton in the material director field $n(r)$ and a vortex (disclination) knot in the immaterial fields of helical axis $\chi(r)$ and $\tau(r) \perp n(r) \perp \chi(r)$. Such heliknotons form various crystalline lattices, open and closed, including triclinic crystals [12]. Curiously, like blue phases, under appropriate conditions, these heliknoton states can emerge in LC materials with “old” chemical composition, including the ones extracted from animals
[1], showing how exotic LC states with nontrivial topology could have been overlooked. In a similar way, for many years, polar LC phases with uninhibited 3D fluidity were assumed to be impossible, but several different embodiments of such phases in purely molecular [11-15] and molecular-colloidal [8,9] systems were recently discovered. Technological needs and fundamental curiosity call for research to reveal LC materials with different symmetries, topological diversity and varying combinations of order and fluidity.

<figure><img src="image_10.png" /></figure>

Figure 2 Topology and self-assembled crystals of heliknotons. (a) Helical field comprising a triad of orthonormal **n**(r), **χ**(r) and **τ**(r). (b) Preimages in the smoothly vectorized **n**(r) of a heliknoton coloured according to their orientations on S² (inset). (c) Knotted skyrmionics structure in the director field **n**(r) is co-located with knots of vortex lines in **χ**(r) and **τ**(r). Gray isosurfaces in (b,c) show regions of distorted helical background. (d) Primitive cell of a triclinic

**Advances in Science and Technology to Meet Challenges** The design rules for obtaining molecular-colloidal hybrid LCs with various unusual symmetries of orientational order and fluidity, like triclinic nematics (with uninhibited fluidity and low-symmetry order that has no symmetry operations apart from trivial ones), remain to be revealed. For example, the emergent order with various symmetries can arise from a thermal self-reconfiguration of relative orientations of the molecular and colloidal subsystems, supplemented with competing anisotropic elastic, steric and electrostatic colloidal interactions [4]. Unlike in solids, where symmetries of the crystal basis are required to be compatible with crystallographic lattices, no such constraints apply to nematic fluids that can adopt even a larger variety of symmetries yet to be discovered [4]. The diagram in Fig. 1b shows different symmetries, and transitions between them, which all potentially are realizable in the molecular-colloidal hybrid LCs.

Approaches of recent LC discovery can be combined to open even more opportunities. For example, one can imagine dispersing anisotropic colloidal nanoparticles in twist-bend and splay-bend LCs and stabilizing various topological soliton and defect arrays within them. For example, particularly interesting high-dimensional order parameter spaces are SO(3)=S³/Z₂ of the monoclinic biaxial colloidal ferromagnets [4,9] and SO(3)/D₂=S³/Q₈ of orthorhombic biaxial nematics [4,5]. The allowed topological solitons in these systems are understood based on homotopy theory, but little is known about their stability and interactions. What types of solitonic knotted field configurations can exist in these soft matter systems? For example, π₃(S³/Q₈)=Z and π₃(S³/Z₂)=Z topological solitons in biaxial nematic and ferromagnetic LCs would be rather interesting analogues of the π₃(S³)=Z Skyrme solitons in high energy physics, but can they emerge as global or local free energy
minima in these soft matter systems and can they form space-filling crystalline or other arrays, like in the LC blue phases?

New symmetries could impart designable ferroelectric, ferromagnetic, piezoelectric, and other properties on the ensuing LC materials, expanding the scope of technological and fundamental science utility even further. Promising significant new discovery, these emergent LC materials require dealing with a hierarchy of length and time scales as well as with creation of entirely new concepts, laws, and generalizations. LC discovery requires an interdisciplinary research effort that is not purely physics, chemistry, biology, or material science, nor that is a subfield of engineering, but rather is an intrinsically interdisciplinary mixture of these, a pursuit in which substantial progress is made simultaneously in the context of all these fields.

**Concluding Remarks** LCs with novel structure and physical properties are essential for reducing energy demand, slowing down climate change and improving quality of life. The future LC research will need to focus on understanding and control of molecular and nanoparticle self-assembly, as well as on material behaviour arising from their ordered mesoscale co-organization and self-alignment. The LC research transcends the traditional disciplinary boundaries of physics, topology, chemistry, engineering, and materials science, advancing the knowledge of self-organization of importance to advancing the emergent new technologies. While the examples above touched only the state of art and prospects for new discoveries in LCs of the nematic type, with uninhibited 3D fluidity and orientational order only, similarly exciting opportunities exist for other sub-classes of LCs, like smectics and columnar phases with partial one- and two-dimensional positional order co-existing with fluidity. The road of LC discovery ahead of us is promising entirely new worlds of these beautiful and technologically useful states of condensed matter.

**Acknowledgements** I.I.S. is grateful to students and postdocs in his research group who worked on liquid crystals and colloids. I.I.S. acknowledges the support by the U.S. Department of Energy, Office of Basic Energy Sciences, under contract DE-SC0019293, and the National Science Foundation grant DMR-1810513.
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## Section 1.6 - Solid foams, interface-based materials

Aurelie Hourlier-Fargette, Sebastien Andrieux and Wiebke Drenckhan
Institut Charles Sadron, Université de Strasbourg – CNRS UPR22, France

**Status** Characterised by their remarkably rich properties, solid foams are exploited in a vast range of applications, ranging from food foams, mechanical protection, thermal and acoustic insulation, filtering and lightweight applications to electromagnetic shielding or tissue engineering (Figure 1). Despite their longstanding use, these aerated materials continue to raise many challenging scientific questions and offer great potential for innovation. Solid foams are a specific sub-class of cellular- and macro-porous materials. They consist of a close-packed assembly of gas pores in a solidified matrix whose morphology is determined during an initially fluid-like state where interfacial energies play a decisive role in fixing the pore shapes [1]. This is particularly evident when foams are obtained through "liquid foam templating", whereby a liquid foam in mechanical equilibrium is solidified [2]. Other pore-shaping energies enter into the foaming process when an initially viscoelastic matrix is foamed. The resulting gas fractions of solid foams are commonly above 0.64, with closely packed spherical pores at the lower limit and polyhedral pores for gas fractions close to one (Figure 1). Typical pore sizes range from micrometers to millimeters (Figure 2), with pores being closed (Figures 2a,b) or connected (Figures 2c,d). Pores can be polydisperse and disordered (Figures 2a-d) or monodisperse and ordered (Figures 2e-j).

The astounding properties of solid foams are governed by a complex interplay between the foam morphology, the gas fraction, and the properties of the solid matrix (Figure 1 & Figure 2). Amongst the wide range of modern materials, foams stand out due to their unique multi-scale nature, ranging from the molecular scale of the interfaces (potentially containing stabilising agents) and thin films, to the macro-scale of the full hierarchical material. A vast variety of materials is already routinely foamed, including bio- and synthetic polymers, metals, ceramics, concrete, or glass. Many different techniques have been developed for foam generation, relying on physical or (electro)chemical mechanisms for pore formation [3]. Increasingly, bi-liquid foams (emulsions) are used as templates, resulting in solid foams after removal of the dispersed phase.

<figure><img src="image_11.png" /><figcaption>**Figure 1** Foams are multi-scale materials, whose rich properties are governed by a complex interplay between the matrix material and the morphology.</figcaption></figure>
**Current and Future Challenges** One of the key challenges in foam research remains to establish a predictive understanding of their complex, multi-scale structure-property relations (Figure 1) with emphasis on their largely non-linear response. This requires the development of efficient and reliable structural analysis tools and reverse engineering approaches to predict and design optimal foam morphologies. While foam morphologies in the limit of high and low gas fractions are now routinely treated, important challenges subsist in the description of intermediate gas fractions.

The dominant role of interfacial effects in the initially fluid-like matrix puts important constraints on the foam morphology which limits the accessible range of material properties. Recent advances in 3D printing (Figure 2q) have shown the value of a more flexible control of cellular architectures - yet with limitations for producing large volumes of multi-scale materials at low cost. Solid foams will therefore remain the material of choice for many applications, although they need to be pushed beyond their current limits, for example, to turn them into acoustic/electromagnetic (Figures 2g,q) or mechanical (Figure 2k) metamaterials. Researchers are therefore actively working on developing new strategies to enlarge the range of accessible foam morphologies, either by explicitly controlling the interactions between bubbles in the assembly process (adhesion, friction, interfacial viscoelasticity) (Figures 2g-j), or by exploring the use of hybrid foams of initially liquid-solid composites, involving elastocapillary interactions (Figures 2m,n). Foams with intriguing properties are also obtained using controlled property gradients (Figure 2o), by combining different characteristic length scales (Figure 2n), or by shaping them into simple (Figure 2p) or into complex forms through 3D printing (Figure 2r). Last but not least, better morphology control also involves the need to reach nanoscale pore sizes (Figure 2l) for extraordinary thermal insulation and ultra-large surface to volume ratios.

One of the major challenges in the effort to foam new materials arises from the fact that the mechanisms which control foam stability in the initially fluid-like template remain far from understood [4]. Moreover, each new material requires the development of an appropriate foaming process. Other open questions concern the mechanisms arising at the different material scales during the fluid-solid transition. For example, to control the pore opening process, a better understanding of the thinning and stability of the solidifying thin films is required (10-1000 nm), evoking timely questions related to fluid dynamics and solidification in the presence of complex interfaces and under (soft) confinement. In the race towards high-performance and smart materials, future progress on foams must be intimately linked with the rapidly growing fields of stimuli-responsive materials, soft robotics, and life-like materials, of particular relevance for biomedical applications.
<figure><img src="image_12.png" /><figcaption>**Figure 2** Modern foams come in a wide range of morphologies: Isotropic (a) and non-isotropic (b), closed-cell polymer foams. Low- (c) and high density (d) open-cell polyurethane foams. Periodic open- (e) and closed-cell (f) polystyrene foams obtained by emulsion-templating [5]. Unbuckled (g,h) and buckled (i,j) periodic hydrogel foams of interest for acoustic/electromagnetic metamaterials. (k) Re-entrant foam for mechanical metamaterials [6]. (l) Nano-foam/sponge[7]. Hybrid polyurethane foams containing fibres (m) or a second foam (n). (o) Graded foam [8] and (p) foamed fibres. (q) 3D-printed foam structure as optical metamaterial [9]. (r) 3D-printing with foamed resin [10]. [Credits: a,b,c,d,g,h,i,j,m,n,p – courtesy of ICS MIM team (C. Gauthier, D. Favier, A. Egele, T. Roland, H. Pelletier, A. Hourlier-Fargette, S. Andrieux, W. Drenckhan)]</figcaption></figure>

**Advances in Science and Technology to Meet Challenges** The evolution of the strongly market-driven research on foam materials is an excellent example that a close link between applied and fundamental research encourages rapid progress. The inherently interdisciplinary nature of this research area requires convergence of diverse communities from academia and industry (mechanics, physics, physical-chemistry, chemistry, biomedical/chemical engineering, etc.) and between different emerging fields (metamaterials, extreme mechanics, soft robotics, ...). Improving the interactions between these communities and providing high-quality training of scientists at their interfaces is thus essential to ensure efficient progress. To accompany this progress, advances in experimental, computational, and theoretical tools are crucial to understand and optimise structure-properties relations of multi-scale materials – and to push them beyond current limits with a reverse engineering approach. Computational tools need to cover the multiple length, time and energy scales naturally present in foams, often with strong out-of-equilibrium elements. An example is the efficient coupling of molecular-dynamics-type simulations with finite elements, which remains a challenging issue. Computational and experimental foam research will greatly profit from the rapidly growing progress in Artificial Intelligence tools. For example, they will provide important input in the optimisation of complex formulations and structure/property relations. The development of sufficiently complete mean field theories remains a particularly difficult exercise and its usefulness is sometimes questioned in the light of rapidly evolving computational tools. Experimentally, advances in chemistry and physical chemistry need to provide new stabilising agents and responsive materials suitable for foaming, while advances in the development of new foaming processes need to allow the production of large foam volumes with fine control over the foam morphology. Simpler tools to characterize reliably static and dynamic properties of complex thin films and interfaces need to be developed and their use needs to be
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harmonised across the different research laboratories. Efficient 3D-characterisation of the foam
morphology needs to be ensured through technological innovations including lab-based, multi-
scale X-ray tomography and associated software for image analysis. The exploitation of large-
instrument facilities (X-ray/Neutron scattering and tomography) remains a heavy exercise and
hence restricted to a small group of experts despite its unequalled analytic power. Dedicated
structures may be put in place to accompany researchers with more ready-to-use solutions.

**Concluding Remarks** Even though mankind started producing solid foams more than a thousand years ago, progress in the optimisation and exploitation of these "interface-driven", aerated materials will continue to require high-quality, innovative research. Solid foams provide an excellent scientific playground to advance our fundamental tools and our understanding of systems with complex, multi-hierarchical structure-property relations, while providing a natural access to industrial applications in the search for solutions to societal problems.

**Acknowledgements** We acknowledge discussions with numerous researchers from academia and industry. We acknowledge funding from an ERC Consolidator Grant (agreement 819511 – METAFOAM), from the region Grand Est (Young Investigator Grant), and from the Interdisciplinary Institute "Hierarchical Functional Materials" supported by IdEx Unistra (ANR-10-IDEX-0002) and SFRI (STRAT'US project, ANR-20-SFRI-0012) under the framework of the French Investments for the Future Program.

**References**

[1] W. Drenckhan and S. Hutzler, "Structure and energy of liquid foams," *Adv. Colloid Interface Sci.*, vol. 224, pp. 1-16, 2015, doi: http://dx.doi.org/10.1016/j.cis.2015.05.004.

[2] S. Andrieux, A. Quell, C. Stubenrauch, and W. Drenckhan, "Liquid foam templating – A route to tailor-made polymer foams," *Adv. Colloid Interface Sci.*, vol. 256, pp. 276-290, Jun. 2018, doi: 10.1016/j.cis.2018.03.010.

[3] W. Drenckhan and A. Saint-Jalmes, "The science of foaming," *Adv. Colloid Interface Sci.*, vol. 222, pp. 228-259, 2015, doi: http://dx.doi.org/10.1016/j.cis.2015.04.001.

[4] D. Langevin, "Coalescence in foams and emulsions: Similarities and differences," *Curr. Opin. Colloid Interface Sci.*, vol. 44, pp. 23-31, 2019, doi: https://doi.org/10.1016/j.cocis.2019.09.001.

[5] A. Quell, S. Heitkam, W. Drenckhan, and C. Stubenrauch, "Creating Honeycomb Structures in Porous Polymers by Osmotic Transport," *Chemphyschem*, vol. 18, no. 5, pp. 451-454, 2017, doi: 10.1002/cphc.201600834.

[6] R. Lakes, "Foam Structures with a Negative Poisson's Ratio," *Science (80-).*, vol. 235, pp. 1038-1040, 1987.

[7] Q. Weinbach et al., "Efficient Control of a Mesoporous Fibrillar PEDOT:PSS Aerogel Structure for Promising Thermoelectric Applications," *Frontiers in Electronic Materials*, vol. 2. 2022, [Online]. Available: https://www.frontiersin.org/articles/10.3389/femat.2022.875856.

[8] M. Costantini et al., "3D-Printing of Functionally Graded Porous Materials Using On-Demand Reconfigurable Microfluidics," *Angew. Chemie - Int. Ed.*, vol. 58, no. 23, pp. 7620-7625, Jun. 2019, doi: 10.1002/anie.201900530.

[9] J. Haberko and F. Scheffold, "Fabrication of mesoscale polymeric templates for three-dimensional disordered photonic materials," *Opt. Express*, vol. 21, no. 1, pp. 1057-1065, 2013, doi: 10.1364/OE.21.001057.

[10] C. W. Visser, D. Amato, J. Mueller, and J. Lewis, "Architected Polymer Foams via Direct Bubble Writing," *Adv. Mater.*, Sep. 2019, doi: 10.1002/adma.201904668.
# Section 2.1 – Rheo-SANS: Small Angle Neutron Scattering (SANS) with in situ rheometry

Norman Wagner<fnref n="1" /> and Ryan P. Murphy<fnref n="2" />

**Status** Development of “structure-property” relationships in colloid, polymer, and surfactant science is a central concept for understanding both equilibrium and non-equilibrium complex fluids and soft materials. The need to understand these structure-property relationships drove the development of neutron scattering sample environments capable of measuring the flow of complex fluids and viscoelastic polymers at the nanoscale<fnref n="1" />. In comparison to X-rays or polarized light, the unique ability of neutrons to penetrate many materials and to provide contrast (isotope substitution) opened fundamentally new avenues of research. The first flow-SANS instrumentation was developed in the 1980’s at neutron scattering facilities in France (ILL)<fnref n="2" /> and the US (NIST).³ Investigators quickly recognized the need for simultaneous measurements of rheological properties and *in situ* structural changes to address ever more complex systems showing memory, thixotropy and hysteresis. As shown in Figure 1, the application of a shear field breaks structural symmetry. Consequently, measurements in all three scattering planes defined by the shear flow are needed to reconstruct the flowing microstructure.⁴ A commercial Rheo-SANS instrument from Anton Paar is now widely available as a neutron scattering sample environment for the radial and tangential experiments.⁵ However, the velocity-velocity gradient plane (1-2 plane, Fig. 1) is the most informative, yet challenging, configuration to measure, and current access to the 1-2 plane is restricted to flow-SANS without simultaneous rheometry.⁶, ⁷

Significant advances in neutron scattering instruments, increases in neutron flux, broader q-range, and time-resolved data acquisition now enable Rheo-SANS methods to probe materials across a wide range of shear flow conditions, over length scales spanning nanometres to micrometres, and under time scales down to 10 ms.⁸ New scientific opportunities in soft matter, biology, and materials development are driving the improvement of scattering environments that can cover greater ranges of shear rate (Fig. 2), broader temperature ranges, complementary *in situ* methods such as dielectric spectroscopy,⁹ and more complex flows with extensional components.¹⁰, ¹¹

<footnote n="1">¹Center for Neutron Science, Dept. of Chemical and Biomolecular Engineering, University of Delaware, Newark, DE, USA</footnote>

<footnote n="2">²NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA</footnote>
<figure><img src="image_13.png" /><figcaption>**Figure 1** Rheo-SANS schematic (courtesy of Dr. Keyi Xu) showing the planes of flow accessed by neutrons (red arrows). The SANS patterns shown reflect the highly non-equilibrium, highly anisotropic microstructure of a shear thickening colloidal suspension. These spectra are combined with Stress-SANS theory to elucidate the underlying mechanism of the continuous shear thickening phenomenon. SANS data from Ref. 4, used with permission of Cambridge University Press.</figcaption></figure>

**Current and Future Challenges** One current challenge being addressed is to develop a single Rheo-SANS device capable of measuring the structure and rheology in all three orthogonal flow planes as a function of time. A "4D Rheo-SANS" instrument must be able to easily change orientation with respect to the stationary neutron beam path, as well as provide accurate stress measurements and thermal control to fully characterize the behaviour of sheared materials. Improvements must also be addressed to quantify the time-dependent behaviour of various materials, including their memory effects, relaxations, and hysteresis. Increasing rheometer complexity and higher neutron fluxes requires the ability to synchronize rheological and neutron scattering data across long sequences of repeated experiments for higher time resolution. For instances where the sample microstructure becomes inhomogenous under flow,¹² it is still challenging to measure and verify the structure of highly nonlinear, shear-banding materials where the local concentration,
microstructure, rheology and flow-field are coupled. Also, it is of significant interest to understand mechanisms by which yield stress fluids transition from elastic gels to flowing liquids.¹³

Another challenge is to measure complex fluids at extreme shear rates and under industrially relevant pressure driven flows. Generating shear rates up to 10⁶ s⁻¹ and beyond necessitates high flow velocities, high pressures, and precision geometries on micrometre scales. Pressure-driven flows also produce additional complexity in data analysis, as the projected scattering pattern is inherently convoluted by multiple scattering planes.

Additional advances in Rheo-SANS environments are required for limited biological sample volumes, as well as for samples that require specialized environmental conditions, such as humidity or evaporation control, extreme temperatures and pressure, electric fields, or magnetic fields. Integrating additional metrology with Rheo-SANS, such as dielectric and light scattering methods, can widen the length scale of structures probed, measure dynamic processes on the micro to millisecond scale, and detect flow instabilities.

As instrumentation upgrades continue to generate larger datasets more rapidly, new, and faster data analysis methods will be critical. The growing data size requires integration of new simulation tools for designing experiments, on-the-fly analysis of 2D scattering data sets, and tomographic reconstruction of the full 3D microstructure obtained from multiple 2D scattering projections. Standard procedures and calibrations for Rheo-SANS sample environments would also promote consistency across different beamlines, providing a more user-friendly and accessible experiment for the Rheo-SANS user community.

**Advances in Science and Technology to Meet Challenges** Development is underway to build a true 4D Rheo-SANS sample environment capable of measuring stress and microstructure in all three plans of flow (Fig.1) with the same instrument and with time resolution down to 10ms. A key goal is to provide the Rheo-SANS user community with a commercial 4D Rheo-SANS instrument that is integrated with beamline data acquisition software (SBIR Phase II DE-SC0019595).

Recently, various other Rheo-SANS environments have been developed with different advantages. Capillary Rheo-SANS (CRSANS) measures complex fluids at high shear rates up to 10⁶ s⁻¹.¹⁴ The high-shear capillary geometry, together with traditional concentric cylinder Rheo-SANS geometries, can now provide structural and rheological signatures across eight orders of magnitude in shear rate. Dielectric spectroscopy methods have already been integrated *in situ* with Rheo-SANS,⁹ and more complex flows with extensional components have also been recently developed.¹⁰, ¹¹ Orthoganol integration of optical microrheology methods, such as diffusing wave spectroscopy, together with SANS can provide linear rheological characterization under extreme temperatures and pressures or under applied electric or magnetic fields.

The recently developed Very Small-Angle Neutron Scattering (VSANS) instrument at NIST provides unique neutron collimation and detector options that will help address challenges in measuring
hierarchical materials from the nanometre to micrometre scales.¹⁵ Multiple detectors are positioned at different distances to capture a broader q-range within a single measurement. In addition to accessing a lower q-range with a 2D detector, VSANS will be particularly advantageous for time-resolved rheological measurements, low volume geometries, reacting systems, and stopped-flow mixing experiments.

Ongoing developments in community-driven software tools such as SasView (www.sasview.org), computational power, and recent statistical methods to determine orientation distribution functions from anisotropic scattering data¹⁶ will help the broader scattering community extract more structural information from two-dimensional scattering projections and with different applied flow fields. Advances in computing, machine learning algorithms, AI pattern recognition, and 3D data visualization will help meet challenges in extracting, analyzing, and presenting data-rich Rheo-SANS measurements.

Finally, advances in complementary methods, such as rheo-NMR, ¹⁷ rheo-light scattering, ¹⁸ rheo-X-ray scattering¹⁹, ²⁰, ²¹, and rheo-confocal microscopy,²² provide additional information for some systems that can be combined with Rheo-SANS to extend the range of length scales covered or to examine different species within the structure due to differences in scattering contrast. A more extensive review of measurements of microstructure under flow can be found in a recent monograph. ²³

<figure><img src="image_14.png" /><figcaption>**Figure 2** Capillary Rheo-SANS instrument for measuring the rheology and nanostructure of complex fluids at high shear rates. (a) Capillary rheometer setup on a SANS beamline at NIST, (b) capillary coil scattering cell composed of (c) fused silica capillary. (d) Shear-dependent viscosity of worm-like micelles (sodium lauryl ether</figcaption></figure>
sulfate in brine) as measured with traditional Rheo-SANS (open symbols) and Capillary Rheo-SANS (closed symbols). (e-i) Inset 2D SANS patterns correspond to different shear rates designated by arrows. Reproduced and adapted from Ref. 14 with permission from the Royal Society of Chemistry.

**Concluding Remarks** The user community and beamline facilities are advancing neutron scattering sample environments for Rheo-SANS. Instrument commercialization promises wider availability and standardization of metrology. Advances in simulation and theory enable mechanistic interpretation of structure-property relationships for flowing systems. Extensions of the Rheo-SANS method to a broader range of shear rates, extreme pressures and temperatures, broader time and length scales, more complex flows, and confined flows are ongoing developments desired by the user community. Opportunities for full 3D structure-under-flow reconstruction with time resolution (4D Rheo-SANS), paradigm changes in data analysis afforded by advances in machine learning, and the coupling with complementary *in situ* metrologies, will improve structure-property relationships and help verify theory and simulation. Increased neutron flux and SANS instrumentation such as VSANS, coupled with advanced data acquisition and analysis methods, will increase user accessibility to address broader scientific challenges in soft matter and biology.

**Acknowledgements** This manuscript was prepared under cooperative agreements 70NANB20H133 & 370NANB17H302 from NIST, U.S. Department of Commerce, as well as DOE SBIR/STTR RPM acknowledges support from the Center for High Resolution Neutron Scattering (CHRNS) which is jointly funded by the NCNR and NSF under Agreement No. DMR-2010792. Identification of commercial equipment or materials in this work does not imply recommendation or endorsement by the National Institute of Standards and Technology.

**References**

[1] A. P. R. Eberle and L. Porcar, Curr Opin Colloid In 17 (1), 33-43 (2012).

[2] P. Lindner and R. C. Oberthur, Revue De Physique Appliquee 19 (9), 759-763 (1984).

[3] G. C. Straty, Journal of Research of the National Institute of Standards and Technology 94 (4), 259-261 (1989).

[4] A. K. Gurnon, P. D. Godfrin, N. J. Wagner, A. P. R. Eberle, P. Butler and L. Porcar, JoVE (84), e51068 (2014).

[5] L. Porcar, D. Pozzo, G. Langenbucher, J. Moyer and P. D. Butler, Review of Scientific Instruments 82 (8), 083902 (2011).

[6] J. C. Vanderwerff, B. J. Ackerson, R. P. May and C. G. Dekruif, Physica A 165 (3), 375-398 (1990).

[7] M. W. Liberatore, F. Nettesheim, N. J. Wagner and L. Porcar, Physical Review E 73 (2), 020504 (2006).

[8] M. A. Calabrese, N. J. Wagner and S. A. Rogers, Soft Matter 12 (8), 2301-2308 (2016).

[9] J. J. Richards, C. V. L. Gagnon, J. R. Krzywon, N. J. Wagner and P. D. Butler, Jove-Journal of Visualized Experiments (122), 55318 (2017).

[10] A. Bharati, S. D. Hudson and K. M. Weigandt, Current Opinion in Colloid & Interface Science 42, 137-146 (2019).
[11] P. T. Corona, N. Ruocco, K. M. Weigandt, L. G. Leal and M. E. Helgeson, Scientific Reports 8 (1), 15559 (2018).

[12] M. E. Helgeson, L. Porcar, C. Lopez-Barron and N. J. Wagner, Physical Review Letters 105 (8) (2010).

[13] J. M. Kim, A. P. R. Eberle, A. K. Gurnon, L. Porcar and N. J. Wagner, Journal of Rheology 58 (5), 1301-1328 (2014).

[14] R. P. Murphy, Z. W. Riedel, M. A. Nakatani, P. F. Salipante, J. S. Weston, S. D. Hudson and K. M. Weigandt, Soft Matter 16 (27), 6285-6293 (2020).

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[16] P. T. Corona, K. S. Silmore, R. Adkins, C. Lang, M. P. Lettinga, J. W. Swan, L. G. Leal and M. E. Helgeson, Physical Review Materials 5 (6), 065601 (2021).

[17] P. T. Callaghan, Emagres 1 (1), 155-168 (2012).

[18] S. Kuczera, L. Gentile, T. I. Brox, U. Olsson, C. Schmid and P. Galvosas, Langmuir 34 (28), 8314-8325 (2018).

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[23] N. J. Wagner, "Microstructure Under Flow" in *Theory and Applications of Colloidal Suspension Rheology*, edited by N. J. Wagner and J. Mewis (Cambridge University Press, Cambridge UK, 2021), pp. 155-172.
## Section 2.2 – Imaging Microscopic Processes

Eric R. Weeks

Emory University, Atlanta GA 30322, USA

**Status** In March 2022, for the first time the American Physical Society March Meeting featured a "Gallery of Soft Matter" to showcase the visual beauty of soft matter systems. While some fraction of the submitted images were from simulations, many came from experimental images. And while soft matter science is known for beautiful static images such as fractal gels and dry foams, there are equally pleasing images and movies of dynamical processes such as colloidal suspensions undergoing phase transitions (Fig. 1A,B) and flowing soft materials (Fig. 1C).

<figure><img src="image_15.png" /></figure>

**Figure 1** (A,B) Video microscopy image from dense colloidal sample of ellipsoids with aspect ratio = 6 at area fraction $\phi = 0.70$. The most mobile 8% of the particles are highlighted in color for translational (A) and rotational (B) motion. (A) and (B) reprinted with permission from Zheng, Wang, and Han, *Phys. Rev. Lett.* **107**, 065702 (2011) [1]. Copyright 2011 by the American Physical Society. (C) Velocity profile of a flowing colloidal gel, exhibiting plug-like flow. The gel is at volume fraction $\phi = 0.27$. Data are taken with confocal microscopy. L = 25 µm is the half-width of the capillary tube, which has a square cross-section. Reprinted with permission from Conrad and Lewis 2008, *Langmuir* **24** 7628-7634 [2]. Copyright 2008 American Chemical Society.

A starting point for visualizing soft materials is video microscopy, which became useful once inexpensive CCD cameras became available in the 1990's. Video microscopy uses a conventional optical microscope to view samples. From this starting point, important developments for soft matter included the use of fast confocal microscopes to take three-dimensional images (reviewed in [3]) and holographic microscopy as an alternative method of fast 3D imaging [4]. Some soft matter scientists now use super-resolution microscopy to directly image nm-sized objects [5]. The main advantage of microscopy is that it allows localized study of spatially heterogeneous samples, and in many cases also temporally heterogeneous processes.

A now-classic method for turning microscope movies into quantitative measurements is multiple particle tracking, launched in the soft matter community by the 1996 work of Crocker and Grier [6]. Their open-source particle tracking code has since been translated into several different programming languages. The original algorithm is optimized for particles that move via Brownian motion. Several groups have modified the algorithm for flowing situations [7] or active particles which have a directional bias to their motion. Other codes have arisen for specific purposes such as tracking live cells [8] or tracking polydisperse objects (reviewed in [9]). Nowadays the main challenge an experimentalist faces is identifying the particle tracking method that is easiest to use,
is written in a desired programming language, and/or is optimized for the particular experimental needs [9-12].

**Current and Future Challenges** Recent developments in imaging microscopic processes in soft materials can be roughly divided into two buckets: software and hardware.

The software side consists of clever ways to squeeze more information out of images. Particle tracking specifically requires particles that can be easily seen and distinguished against the background. This visibility constraint is circumvented by Differential Dynamic Microscopy (DDM). This method uses any microscopy technique one likes to take a movie, and then Fourier analysis of the sequence of images allows one to obtain dynamical data like that measured by dynamic light scattering [13]. This method works on quite challenging samples; for example, the original article demonstrates a measurement of the diffusivity of particles that are much smaller than the optical resolution limit of the microscope. The method also works for highly scattering samples where there is an index of refraction mismatch between the particles and the solvent. A fascinating variety of other analysis techniques for microscopic movies are reviewed in [9], which also makes the point that analysis techniques are cheaper than investing in new microscopy hardware.

The hardware side starts with new and/or more widely available microscopy techniques, such as the above-mentioned confocal microscopy and holographic microscopy methods. The next step is combining instruments and techniques. An excellent illustration is boundary stress microscopy [14]. The method starts by combining a rheometer and a confocal microscope, as shown in Fig. 2; this combination has been used by several groups [7]. The rheometer uses a transparent bottom plate atop an inverted microscope, so that the microscope looks upward into the rheometer. The sample thus can be sheared by the rheometer, allowing for precise control over strains and simultaneous measurements of stresses, while the sample is imaged by the confocal microscope (potentially even in 3D for slow strain rates). To visualize boundary stresses, an additional idea from traction force microscopy is added. Directly on the transparent bottom plate, a thin gel substrate is added with embedded tracer particles. The sample then contacts this gel substrate, rather than directly the bottom plate. When the sample is sheared, stresses are transmitted to the gel substrate which responds elastically (see Fig. 1B). The elastic displacements of the tracer particles reveal the stresses exerted on the substrate.

**Advances in Science and Technology to Meet Challenges** Challenges for the future, then, are to devise clever new analysis techniques, and to find new ways to merge experimental hardware techniques. Progress is most likely to come from collaborations that bring together ideas and complementary expertise.

For example, one could imagine a colloidal chemist designing novel tracer particles that allow one to measure new properties inside a sample. DNA-based mechanosensors can be sensitive to pN-scale tension forces, for example [15], and other mechanosensitive molecules are even more sensitive [16]. Might colloids coated with such sensors be useful to soft matter scientists? Colloids
of a wide variety of shapes are possible (as reviewed in [17]) and have led to observations of rotational diffusion (for example [18]); what might one do with more exotic shapes?

<figure><img src="image_16.png" /><figcaption>**Figure 2** (A) Illustration of the boundary stress microscopy method, using a "rheoscope" that combines a rheometer and a confocal microscope. In this sketch the red tendrils represent a collagen network. (B) A confocal image of sheared collagen fibers along with yellow vectors representing boundary displacements which indicate boundary stresses. Scale bar = 25 µm. Image from [14], copyright 2015, open access under the Creative Commons Attribution License.</figcaption></figure>

The above example of boundary stress microscopy challenges us to consider new mergers of experimental techniques. One needs to find appropriate techniques to match to interesting scientific questions in soft matter science. Indeed, one way to state the challenge is the need to stay aware of the increasing variety of clever experimental techniques.

An additional challenge is to implement real-time analysis of microscopy images with real-time feedback. This has been done in many cases, but the speed is limited based on computer speed and the complexity of the analysis required. One can speculate that as computer speeds continue to improve, and as faster algorithms are developed, that there is room for new science to be done where the computer is an important component to the experimental instrument beyond just storing data for later analysis.

**Concluding Remarks** Imaging dynamical processes in soft matter systems often starts with your eye and brain. You see something interesting, and then you try to quantify it; to show that what you see is not just an accidental event. Other times one starts with imagination: if we could design the
proper instrument or engineer the right sample, what might we be able to image and measure?
Ambitious experimentalists should read broadly, look for techniques that one can bring to soft
matter (whether hardware or analysis ideas), and be open to collaborations especially outside one's
own field.

**Acknowledgements** This work was supported by the National Science Foundation under Grant No. CBET-1804186. The author thanks Y. Han, J. C. Conrad, and D. L. Blair for providing copies of their figures and for helpful discussions, and J. C. Crocker for introducing him to the joys of microscopy a while ago.

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## Section 2.3 – New microscopy techniques

Roberto Cerbino

University of Vienna, 1090 Vienna, Austria

**Status** Optical microscopy is a prominent technique to study soft matter structure and dynamics: it is easily implemented, and it matches the relevant spatiotemporal scales. Despite early applications, such as the study of Brownian motion by Jean Perrin, the urge of increasing the spatiotemporal resolution toward the molecular scales have relegated optical microscopy in the underwood of qualitative methods for quite some time, with light, x-ray, and neutron scattering techniques dominating the scene of quantitative tools for soft matter characterization.

Starting from the 1970s, the invention and development of CCD cameras, in combination with the introduction of a plethora of novel microscopy techniques (e.g., confocal, light-sheet, super-resolution...) brought optical microscopy back to the stage as a major player for the quantitative characterization of soft matter. Nowadays, soft matter experimentalists can use light to observe samples in direct space with various techniques and contrast mechanisms (e.g. absorption, scattering, fluorescence...) to perform accurate quantitative experiments [1]–[3]. Alternatively, static and dynamic light scattering (SLS and DLS) remain unbeatable tools to capture fast dynamics or to obtain robust ensemble information, at the expense of losing access to a space-resolved characterization of the sample.

An intermediate approach, known as Digital Fourier Microscopy (DFM) [4], obtains scattering information from Fourier analysis of images acquired in direct space, transforming a microscope into a light scattering instrument, while at the same time retaining the original movies for alternative analyses. DFM techniques - and in particular Differential Dynamic Microscopy (DDM) that is based on Fourier transforming differences between images acquired at different times [5], [6] - are increasingly gaining popularity, with applications covering classical soft matter systems such as polymers, colloids and liquid crystals, as well as biological ones, including proteins, bacteria and eukaryotic cells [7].

Besides representing a convenient and accessible alternative to light scattering, DDM has several key qualities, among which special mention goes to its capability to probe dynamic entities that are abundantly smaller than the wavelength of light. Compared to DLS, DDM is more robust against optical imperfections and multiple scattering. One main drawback is the heavy post-processing of large stacks of images.
<figure><img src="image_17.png" /><figcaption>Figure 1 **Differential dynamic microscopy is relatively insensitive to multiple scattering:** Hydrodynamic diameter (closed symbols) measured by DDM and optical transmission (open symbols) of a sample of PMMA particles dispersed in water as a function of particle concentration. The red line is a fit to the data using a model that accounts for particle interactions. Reprinted with permission from Kathrin Eitel, Gary Bryant, and Hans Joachim Schöpe Langmuir 2020 36 (35), 10307-10320 DOI: 10.1021/acs.langmuir.0c00709. Copyright 2020 American Chemical Society.</figcaption></figure>

**Current and Future Challenges** Robustness of DDM against multiple scattering makes it the tool of choice to study optically dense samples, such as the interior of living cells or non-dilute colloids [7]. A case in point is shown in Figure 1, where Eitel et al. [8] prove that for optical transmission conditions under which DLS would fail, DDM can correctly size colloidal particles suspended in a liquid. However, beyond a generic consensus that the relative insensitivity of DDM to multiple scattering is due to the partial limited spatial and temporal coherence of the typical light source used (e.g halogen lamps or LEDs), a systematic study of the optimal working conditions is still lacking.

Other challenges that researchers will need to face are related to the wide spatiotemporal range that needs to be accessed when studying soft matter. Theoretically, the smallest accessible timescale in DFM experiments is the inverse of the acquisition frame rate, whereas the largest one is typically the duration of the experiment. Similarly, the pixel and the image size (including optical magnification) set the lower and upper spatial scales, respectively, with the additional degree of freedom that the magnification can be changed in a wide range (typically from 1x to 100x).

Once a camera is chosen, the brute force approach to cover a wide range of space and time scales implies performing very long, fast image acquisitions of megapixel images obtained with different magnifications. Clearly, this approach becomes very rapidly unfeasible: for instance, modern
sCMOS cameras acquiring 3200x3200 8-bits images at 500 fps produce about 5 GB/s (~17 TB/h) of data to be saved on disk and later analysed, where the images are post-processed to compute suitable correlation functions at different Fourier wave vectors $q$.

Extracting maximum information would thus benefit from: 1) accessing fast dynamics with slow cameras; 2) accessing slow dynamics and large spatial scales with minimal disk occupancy; 3) shortening the computational time needed to analyse large amounts of data, possibly in real-time; 4) automating image analysis to reach the level typical of commercial DLS instruments. Progress in all these areas would tremendously favour the massification of DFM techniques.

**Advances in Science and Technology to Meet Challenges** As far as multiple scattering is concerned, some progress has been made by using DDM in combination with spatially-selective fluorescence microscopy techniques, such as light sheet [9] and confocal [10], [11]. It would be crucial to understand whether multiple scattering suppression schemes typical of DLS and based on cross-correlation, can also be extended to DDM, which would further push the range of applicability to strongly scattering systems normally studied only with Diffusing Wave Spectroscopy or x-ray scattering.

The development of novel image acquisition protocols is a very promising area. For example, access to dynamics faster than the inverse acquisition rate has been obtained by Philippe et al. with a variable-delay temporal scheme [12], by Arko and Petelin with two randomly triggered cameras acquiring two sequences of images of the same region in the sample [13], and by You and McGorty, who used a color camera to acquire images obtained by sequentially pulsing blue and then red light separated by a variable lag time much smaller than the camera's exposure time [14] (see Figure 2). Some of these protocols also lead to a reduction of the disk occupancy [12].

To hopefully bring DDM closer to real-time analysis as in DLS, optimization of the image processing algorithms is also desirable. Using GPUs instead of CPUs can lower the time to complete image analysis by two orders of magnitude [10], [15]. Without resorting to GPUs, one can employ a Fourier transform in time instead of performing differences of images (as in the original DDM algorithm) to reach speed-up factors up to 300 [16]. Adopting a probabilistic approach to downsample the imaging data before processing can lead to a dramatic reduction (up to a factor of ~100) of the computational load, with virtually no loss of information on the estimated, physically relevant, quantities [17]. Further progress is likely and will allow us to run DDM in real time minimizing or cancelling the need to store the images, paving the way to its massive use as standard technique in every soft matter laboratory.
<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

Figure 2 **Two-colour DDM for capturing fast dynamics**: (a) Schematic of an optical microscope showing two LED light sources (one with a peak wavelength of 625 nm, the other 455 nm) used to illuminate an aqueous suspension of 180 nm diameter polystyrene particles prepared at 0.02% mass fraction. A 40× objective and tube lens image the sample onto a colour CMOS camera. (b) Images are acquired at 10 Hz and, within a single exposure time of the camera, each LED is pulsed for about 1 ms. The time interval between pulses is varied and, for the data shown in (c), ranges from 3 to 91 ms. (c) The relaxation rate, τ⁻¹, characterizing the particle dynamics is determined with standard DDM plotted versus the squared wave vector q². The solid line shows a diffusive dynamics τ⁻¹ = Dq², with D = 2.48 µm²/s. Data from the standard DDM method (violet diamonds) starts deviating from this straight line just after the expected decay rate exceeds 10 s⁻¹, as anticipated given the images were acquired at 10 Hz. Data from the two-color DDM method follows the expected linear relationship up to around 70 s⁻¹. In the low-q region, the two-color method does not accurately detect data fluctuations slower than about 10 s⁻¹. (Figure panels are reproduced and adapted under CC BY 4.0 license from arXiv:2101.12147)

**Concluding Remarks** The incessant advances in microscopy, combined with the development of novel experimental schemes, and with the constant technological progress leading to faster, less noisy, and more sensitive image detectors, will ensure further development of DFM methods in the next years. It is not difficult to imagine a near future in which users without a strong background in optics and image processing will be able to run real-time, high-throughput, automated DFM experiments on a variety of samples that would be hardly accessible with other techniques. At the
same time, new possibilities will arise from combining DFM with other experimental tools, such as rheology, electrophoresis, chromatography, microfluidics, to perform a characterization of the microscopic dynamics of externally manipulated soft matter. Finally, applications to biology have been many, and initial successes point to a possible wider use for the characterization of crowded biological systems ranging from the cell interior to cellular tissues.

## Acknowledgements

I acknowledge useful and inspiring discussions with Fabio Giavazzi.

## References

[1] R. Cerbino, "Quantitative optical microscopy of colloids: The legacy of Jean Perrin," *Curr. Opin. Colloid Interface Sci.*, vol. 34, 2018, doi: 10.1016/j.cocis.2018.03.003.

[2] B. D. Leahy, N. Y. C. Lin, and I. Cohen, "Quantitative light microscopy of dense suspensions: Colloid science at the next decimal place," *Curr. Opin. Colloid Interface Sci.*, vol. 34, pp. 32–46, Mar. 2018, doi: 10.1016/J.COCIS.2018.03.002.

[3] A. Aloi and I. K. Voets, "Soft matter nanoscopy," *Curr. Opin. Colloid Interface Sci.*, vol. 34, pp. 59–73, Mar. 2018, doi: 10.1016/J.COCIS.2018.03.001.

[4] F. Giavazzi and R. Cerbino, "Digital Fourier microscopy for soft matter dynamics," *J. Opt.*, vol. 16, no. 8, p. 083001, 2014, doi: 10.1088/2040-8978/16/8/083001.

[5] R. Cerbino and V. Trappe, "Differential dynamic microscopy: Probing wave vector dependent dynamics with a microscope," *Phys. Rev. Lett.*, vol. 100, no. 18, 2008, doi: 10.1103/PhysRevLett.100.188102.

[6] F. Giavazzi, D. Brogioli, V. Trappe, T. Bellini, and R. Cerbino, "Scattering information obtained by optical microscopy: Differential dynamic microscopy and beyond," *Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys.*, vol. 80, no. 3, 2009, doi: 10.1103/PhysRevE.80.031403.

[7] R. Cerbino and P. Cicuta, "Perspective: Differential dynamic microscopy extracts multi-scale activity in complex fluids and biological systems," *J. Chem. Phys.*, vol. 147, no. 11, 2017, doi: 10.1063/1.5001027.

[8] K. Eitel, G. Bryant, and H. J. Schöpe, "A Hitchhiker's Guide to Particle Sizing Techniques," *Langmuir*, vol. 36, no. 35, pp. 10307–10320, Sep. 2020, doi: 10.1021/ACS.LANGMUIR.0C00709.

[9] D. M. Wulstein, K. E. Regan, R. M. Robertson-Anderson, and R. Mcgorty, "Light-sheet microscopy with digital Fourier analysis measures transport properties over large field-of-view," *Opt. Express*, vol. 24, no. 18, p. 20881, 2016, doi: 10.1364/OE.24.020881.

[10] P. J. Lu et al., "Characterizing concentrated, multiply scattering, and actively driven fluorescent systems with confocal differential dynamic microscopy," *Phys. Rev. Lett.*, vol. 108, no. 21, 2012, doi: 10.1103/PhysRevLett.108.218103.

[11] M. Drechsler, F. Giavazzi, R. Cerbino, and I. M. Palacios, "Active diffusion and advection in Drosophila oocytes result from the interplay of actin and microtubules," *Nat. Commun.*, vol. 8, no. 1, 2017, doi: 10.1038/s41467-017-01414-6.
[12] A. Philippe et al., "An efficient scheme for sampling fast dynamics at a low average data acquisition rate," *J. Phys. Condens. Matter*, vol. 28, no. 7, pp. 1-17, 2015, doi: 10.1088/0953-8984/28/7/075201.

[13] M. Arko and A. Petelin, "Cross-differential dynamic microscopy," *Soft Matter*, vol. 15, no. 13, pp. 2791-2797, Mar. 2019, doi: 10.1039/C9SM00121B.

[14] R. You and R. McGorty, "Two-color differential dynamic microscopy for capturing fast dynamics," *Rev. Sci. Instrum.*, vol. 92, no. 2, p. 023702, Feb. 2021, doi: 10.1063/5.0039177.

[15] G. Cerchiari, F. Croccolo, F. Cardinaux, and F. Scheffold, "Note: Quasi-real-time analysis of dynamic near field scattering data using a graphics processing unit," *Rev. Sci. Instrum.*, vol. 83, no. 10, 2012, doi: 10.1063/1.4755747.

[16] M. Norouzisadeh, M. Chraga, G. Cerchiari, and F. Croccolo, "The modern structurator: increased performance for calculating the structure function," *Eur. Phys. J. E*, vol. 44, no. 12, pp. 146, 2021, doi: 10.1140/epje/s10189-021-00146-2

[17] M. Gu, Y. Luo, Y. He, M. E. Helgeson, and M. T. Valentine, "Uncertainty quantification and estimation in differential dynamic microscopy," *Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys.*, vol. 104, no. 3, 2021, doi: 10.1103/PhysRevE.104.034610
# Section 3.1 - Phase transition studies in colloids

Yilong Han

Department of Physics, The Hong Kong University of Science and Technology

**Status** Soft materials serve as powerful platforms for studies of phase transition because they exhibit rich phase behaviours. For example, liquid crystals exhibit various phases absent in atomic systems. Instead of focusing on discovering new phase transitions in soft materials, in this work, we focus on phase transition studies by using colloidal systems. Colloidal micro-particles move much slower than atoms and can be directly visualised by optical microscopy, even inside dense three-dimensional crystals or liquids (Figure 1a [1]). Single-particle kinetics can hardly be observed in atomic systems, making colloids important model systems of large atoms for the study of phase transitions [2]. The use of imaging analysis to track colloidal particles, which began in the 1990s, has afforded researchers important insights into microscopic structures and kinetics during phase transitions.

Most colloid phase-transition studies have focused on crystallisation [1,3] and glass transitions [4], and less studies have explored other transitions such as crystal melting, solid-solid transitions, and transitions of liquid crystal phases. The kinetic transition pathway depends on various factors and exhibits rich behaviours on complicated free-energy landscapes. Moreover, classical nucleation theory, which is based on certain oversimplified assumptions, can often be problematic in real systems. These make room for publications about kinetics of first-order transitions such as crystallization. Besides the initial nucleation stage, nuclei growth and coalesce, defects and stress effects, and transition of interfaces such as roughening have been explored. Some results obtained in colloids can guide studies of atomic systems; for example, the two-step nucleation in solid-solid transition from a parent crystal to a liquid to a product crystal was first observed in colloids and subsequently confirmed in metals.

New colloids, phases, and assembly and observation techniques (Figures 1b-d) have afforded additional opportunities for phase-transition studies. In particular, transitions between non-equilibrium steady states, which occur widely in nature, are much less understood than transitions between equilibrium phases. Specifically, the general theoretical framework and the categorisation of these transitions are unclear. Colloids can be controlled and observed at the single-particle level, rendering them an important research avenue.
<figure><img src="image_21.png" /><figcaption>**Figure 1** Examples of phase studies on colloids.</figcaption></figure>

(a) Nucleation in crystallisation [1].

(b) Nano-triangles forming a crystal, as observed by liquid electron microscopy [5].

(c) Colloidal quasicrystal by lithography [6].

(d) Crystal formed by active colloidal particles [7].

(e) Transitions between non-equilibrium states.

**Current and Future Challenges** Phase transitions occur under various conditions and have many aspects worth to study. For example, transitions in curved or confined spaces; in translational, rotational or other degrees of freedom; induced quasistatically or abruptly by changing effective temperature, pressure, shear or particle properties; and phase transition precursors (such as premelting and prefreezing). Finding poorly explored topics can be just a matter of combination of these aspects. For example, the structure of a phase can be ordered or disordered; while particles' motions can be liquid-like or solid-like. These produce 2x2=4 states: fluid, crystal, glass, and structural fluid with active particle swapping on a lattice. The last state has not been found in passive atomic systems but can nevertheless be formed by active particles.

Perhaps the most important topic is the non-equilibrium transitions such as the following:

(1) Transitions between metastable states such as conventional supercooled-liquid-to-glass transition. 'What is the nature of the glassy state? -- Where and why does liquid end and glass begin?' is ranked as the 125 most important scientific questions by *Science*. This question can be generalised to other non-equilibrium phases which similarly have blurry boundaries, e.g., between fine-grained polycrystals and glass [9] and between dense gels and glasses (Figure 1e).

(2) Transitions induced by athermal macro-parameters (e.g., shear-induce yielding transition).

(3) Transitions in systems with non-reciprocal interactions (i.e., breakdown of Newton's 3rd law), for example, in some active matters [10]. Active particles form rich states such as active nematic, crystal (Fig. 1d), and hyperuniform states. Their transitions have not been explored in conventional atomic or molecular systems.

Combinations of (1-3) can yield topics such as shear-induced polycrystal-glass transition in active systems. Combination of (1-3) with other aspects of transitions can produce even more topics; for example, glass melting in orientational degrees of freedom. Challenges are often in the fabrication
of high-quality samples with a large uniform phase and the tunability to quasi-statically drive the phase transition.

**Advances in Science and Technology to Meet Challenges** Many topics are yet to be explored using conventional repulsive colloidal spheres, which have been used in most previous phase-transition studies. New techniques of colloid fabrication, assembly, control, and imaging certainly provide additional opportunities. Recently synthesised novel colloids include particles of various shapes, soft deformable spheres, Janus, or patchy spheres with anisotropic interactions, oppositely charged particles without agglomeration, particles with anisotropic long-range interactions in liquid crystals, and active particles with ballistic translational or circular motions. In particular, arrays of arbitrarily shaped 2D colloidal platelets can be printed by photolithography and their designed structure can be maintained after dissolved into a solution (Figure 1c [6]). The study of phase behaviours on the free surfaces of solids or liquids requires attractive particles. Tunable attractions have been achieved by coating DNA molecules, adding thermal-sensitive depletants or dyes, using solvents near the phase separation point, and applying high-frequency magnetic fields. Electric, magnetic, optical, and ultrasonic fields can be used to manipulate individual particles or a group of particles and are helpful in testing related theories.

High-resolution optical microscopy and liquid-phase transmission electron microscopy (Figure 1b [5]) can resolve nm-sized particles. Smaller particles have relatively longer-range interactions and thus can form more types of crystalline phases. Particles of various shapes can be fabricated relatively more easily for nanoparticles. Their stronger Brownian motions are helpful for exploring slow dynamics in glasses and solid-solid transitions.

The recent non-reciprocal generalisations of synchronisation, flocking, and pattern formation provide a theoretical framework for transitions in active matters [10], which can guide further experimentation and simulation. Since the parameter space is too big to explore, we should focus on searching for the general features and providing a clear classification of non-equilibrium transitions.

**Concluding Remarks** Combination of various aspects of phase transitions can produce many topics that are yet to be well explored. Metallurgy is also a source of open questions. For example, the mechanisms of various mechanical transitions in crystalline and amorphous alloys are not clear. Transitions between non-equilibrium states are the least understood and most important. Colloids might provide valuable insights into the general features of non-equilibrium phase transitions in physical and biological systems.

Colloidal experiments have revealed important microscopic kinetic details of known phenomena (e.g., nucleation) and even discovered new phenomena (e.g., pre-solid-solid transition) which can guide the future studies in atomic systems. We should take advantage of the strengths of colloids, such as their tailorable size, shape, interaction, and self-propulsion. For example, colloidal solids are soft and thus can be used to explore transitions under ultrahigh pressure or shear levels inaccessible in atomic solids research.
## Acknowledgements

This work was supported by the Hong Kong RGC grant (CRF-C6016-20G). We thank Huijun Zhang for developing Figure 1e.

## References

[1] Gasser U, Weeks E R, Schofield A, Pusey P N and Weitz D A 2001 Real-space imaging of nucleation and growth in colloidal crystallization *Science* **292** 258

[2] Li B, Zhou D and Han Y 2016 Assembly and phase transitions within colloidal crystals *Nat. Rev. Mater.* **1** 15011

[3] Palberg T 2014 Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives *J. Phys. Condens. Matter* **26** 333101

[4] Hunter G L and Weeks E R 2012 The physics of the colloidal glass transition *Rep. Prog. Phys.* **75** 066501

[5] Ou Z, Wang Z, Luo B, Luijten E and Chen Q 2020 Kinetic pathways of crystallization at the nanoscale *Nat. Mater.* **19** 450

[6] Wang P Y and Mason T G 2018 A Brownian quasi-crystal of pre-assembled colloidal Penrose tiles *Nature* **561** 94

[7] Palacci J, Sacanna S, Steinberg A P, Pine D J and Chaikin P M 2013 *Living crystals of light-activated colloidal surfers Science* **339**, 936

[8] Zhang B and Snezhko A 2022 Hyperuniform active chiral fluids with tunable internal structure *Phys. Rev. Lett.* **128**, 218002

[9] Zhang H and Han Y 2018 Compression-induced polycrystal-glass transition in binary crystals *Phys. Rev. X* **8**, 041023

[10] Fruchart M, Hanai R, Littlewood P B and Vitelli V 2021 Non-reciprocal phase transitions *Nature* **592** 363
## Section 3.2 – Large mechanical deformation

Luca Cipelletti<fnref n="1" />,<fnref n="2" /> and Laurence Ramos<fnref n="1" />

**Status** The very term ‘Soft Matter’ indicates why we should care about large mechanical deformation (LMD): soft systems are easily deformed by even a modest stress. Thus, the LMD regime is of paramount importance in one or more steps of the life cycle of virtually all industrial and technological soft systems, in food production and sensory experience, as well as in active matter and biological systems (Fig. 1). Here, we use LMD as a proxy for the non-linear regime, where stress and strain, or strain rate, cease to be mutually proportional. Depending on the materials, the onset of non-linearity may occur for extremely large strain or strain rate. While LMD is relevant for both fluid- and solid-like systems (Fig. 1A), we shall focus mainly on soft solids, providing a (necessarily partial) glimpse of the research in the field.

Most early work addressed macroscopic quantities only (e.g. stress and strain). The pioneering investigation of bubble rafts by L. Bragg and J.F. Nye [1], by contrast, nicely exemplifies a research approach that is extremely up-to-date: the use of soft matter as a model system for hard condensed materials (in [1], the foam simulated the behaviour of a metal under strain), and the search of the microscopic origin of the macroscopic behaviour under LMD. The bubble rafts of Ref. [1] were crystalline, making it easy to identify structural changes, e.g. due to defect migration or annihilation. By contrast, most soft systems are amorphous, and detecting and quantifying structural changes is more arduous. Concepts such as the ‘shear transformation zones’ [2] have been introduced to address this challenge.

Other popular research lines include designing materials with outstanding properties under LMD (see the next section) and leveraging on transitions induced by a LMD to obtain new materials. Examples of the latter approach range from extrusion and spinning of polymers to manufacturing meat replacement by creating protein fibre, e.g. by electrospinning or mechanical elongation [3].

Theoretical work on LMD is very abundant and ranges from approaches drawing analogies with equilibrium statistical physics by introducing phase or state diagrams (jamming and shear banding transitions [4,5]), to models at the mean field level (soft glassy rheology [6], fluidity models [7]) or, on the contrary, emphasizing spatio-temporal fluctuations (rheo-chaos [8], viscoelastic instabilities [9]), to more microscopic approaches as in the Mode Coupling Theory [10]. As discussed below, such diversity reflects in part our lack of a general framework for the LMD regime.

<footnote n="1">¹Laboratoire Charles Coulomb (L2C), Université Montpellier, CNRS, Montpellier, France</footnote>

<footnote n="2">²Institut Universitaire de France (IUF), France</footnote>
<figure><img src="image_22.png" /><figcaption>**Figure 1** (A) Schematic behavior of a solid and a liquid under a mechanical load and definition of the large deformation regime. (B) X-ray images showing the large extension of the bolus (highlighted by the dashed red lines) during swallowing. Adapted from [11]. This is just one example of the large deformation of soft materials occurring in a variety of soft materials, from red blood cells in small blood capillaries, to wheat dough used in preparing pizza, to extrusion in the processing of polymers-based materials.</figcaption></figure>

## Current and Future Challenges

For small deformations, statistical physics tells us, even if it is generally not trivial and straightforward, how to relate the microscopic structure and dynamics to the macroscopic mechanical properties. Establishing an analogous link for systems under a LMD and, more generally, for systems driven out of equilibrium, is arguably one of the greatest challenges in modern material science and statistical physics. It also has implications for biology and medical science where the behaviour of the cell cortex, the extracellular matrix or of tissues under LMD is crucial. To reach this goal, several challenges must be addressed:

1) The most relevant quantities to be monitored experimentally or numerically and to be included in a theoretical approach need to be identified. In rheology, stress and strain often change smoothly across the linear/non-linear transition, while other quantities, e.g. extracted from Lissajous plots or inharmonicity analysis may carry more information. At the microscopic level, changes of the structure or the dynamics under LMD may be subtle, especially for amorphous, dense systems.
2) Several phenomena in LMD occur randomly in space and time (think e.g. of crack nucleation), or encompass a wide range of time- and length scales (e.g. in avalanche-like failure), or exhibit complex spatio-temporal patterns (e.g. due to flow and elastic instabilities). This complexity must be tracked.

3) Existing statistical mechanics tools and concepts developed for equilibrium systems need to be extended to the non-linear regime of LMD; new theoretical tools and paradigms will be likely required.

A thorough understanding of the relationship between the macroscopic mechanical behaviour and the microscopic structure and dynamics under LMD is a very ambitious and long-term goal. Closer on the horizon, challenges that are attracting an intense research effort include (but are not limited to):

1) Predicting failure: soft solids often exhibit sudden failure after a long induction time, e.g. under a constant load, as in creep, or as a result of cycling loading, as in fatigue. Identifying signals of failure as early as possible is of great practical importance. While rheological quantities exhibit little if any precursors of macroscopic failure, recent work has shown that changes at the microscopic level, e.g. in the dynamics, significantly anticipate material failure [12].

2) Designing new materials with outstanding mechanical properties under LMD, e.g. high extensibility coupled to a large stress at failure or self-healing capabilities. Ref. [13] discusses advances in various strategies deployed at this end, from interpenetrated networks to systems based on dynamic, reversible bonds.

3) Developing guidelines to design systems with a prescribed range of properties under LMD, which is of paramount importance, e.g., for mechanical metamaterials [14] or in the food industry [15,16].

**Advances in Science and Technology to Meet Challenges** To reach the goals outlined in the previous section, several technological and scientific advances are needed.

1) Most mechanical tests are performed under shear or traction. Other deformation geometries will be required to reach a general understanding of LMD and to test driving modes closer to those in technological applications. Examples include indentation, extensional flow or flow in constrictions, and drop impact (Fig. 2A). Geometries of this kind often allow for measuring the strain or strain rate, e.g. by imaging methods: a concomitant measurement of the stress will be a major advance. Advanced rheological methods will be needed to cope with the non-linear and time-varying response of soft matter under LMD. Recent improvements include fast mechanical spectroscopy via 'chirp rheometry' [17] and the popularization of orthogonal superposition rheometry, where a small-amplitude deformation is superimposed to a primary large deformation to probe non-linear moduli [18].

2) Experiments probing the microscopic structure and dynamics simultaneous to mechanical measurements are gaining momentum. Optical or confocal microscopes provide snapshots of the system with sub-micron resolution, but they are limited in terms of size of the field of view and viable samples (mostly particle-based and optically transparent). Advanced