Ebook: Soft Matter Self-Assembly

Self-assembly is one of the key concepts in contemporary soft condensed matter. An umbrella term encompassing the various modes of spontaneous organization of micrometer- and submicrometer-size particles into ordered structures of various degrees of complexity, it often relies on remarkably simple interactions and mechanisms. During the past decade we have witnessed a fascinating progress in the field, probably best epitomized by the advent of Janus and DNA-coated colloids. In turn, self-assembly is one of the key principles used by nature to construct living matter, where it frequently takes place in a hierarchical fashion —viruses, for example, consist of genetic material packed into strikingly regular capsids made from proteins. Many of the self-assembly experiments and techniques developed within the soft-matter domain rely on physics and physical chemistry to mimic natural processes, and in these cases the close connection between physics, chemistry, and molecular biology is rather evident.

This School was conceived so as to review the different aspects of self-assembly as comprehensively as possible at an advanced level, complementing the more standard MSc and PhD courses in soft condensed matter physics given at many Universities. As such, the School aimed to bring forward the ways in which the textbook-level behavior of polymers, liquid crystals, and colloids can be used to steer the formation of complex structures by relying, e.g., on forces mediated by an anisotropic, partly ordered solvent or produced by various external fields and on molecular or particle recognition. Also addressed were selected topics in colloid hydrodynamics, wetting and behavior at interfaces in general, given that many experiments and applications involve an ambient fluid, either as the continuum phase in a colloidal dispersion or in the form of a thin film. The School combined lectures describing experimental and practical achievements with the more theoretical and computational views of the field, helping participants to appreciate how closely intertwined they really are.

The School was organized and supported by the Marie-Sklodowska-Curie European Training Network COLLDENSE. The program included nine minicourses consisting of four lectures each, five seminars discussing special topics, and a lively poster session where the students presented their own work. We were happy to see that many of the posters resonated very well with the topics discussed at lectures, which convinced us that the School was indeed timely. We were also very happy to see that the participants included students from Europe as well as from India, Japan, Mexico, USA, and elsewhere, and quite a few observers.

We are certain that the participants' memories of the splendid Villa Monastero in Varenna, which provided an excellent environment for discussions and work, are as pleasant as ours — not only because of science, natural beauty, and rich cultural heritage but also because of the outstanding local organization. Barbara Alzani, Ramona Brigatti, and Marta Pigazzini made sure that everything was very smooth and that we all felt welcome. With their experience and dedication, they really made the School a memorable event. A part of the organizational duties was taken care of by Roberta Comastri and the production of this Volume of the Proceedings was in the hands of Monica Bonetti and Marcella Missiroli. We are sincerely grateful to all of them for their help, and we thank the Italian Physical Society (SIF) for including our School in their Varenna program.

We trust that the material collected in these Proceedings will be appreciated both by students and by experts. The proceedings also include two reprints from Reviews of Modern Physics, and we encourage the readers to consult the original works cited in the Chapters as well as the different textbooks written by the lecturers including the superb Polymer Physics by Michael Rubinstein and Ralph Colby.

C. N. Likos, F. Sciortino, E. Zaccarelli and P. Ziherl

In this brief contribution we review the basic elements of self-assembly, calling attention on the competition between the energetic gain of forming a bond and the loss of translational entropy. We show how to calculate theoretically the distribution of cluster sizes, in the hypothesis of an ideal gas of cluster, and discuss how the cluster partition functions can be calculated numerically. Building on the thermodynamic formalism, we discuss some analytically soluble simple models of self-assembly: equilibrium and cooperative polymerization and micelle formation. Finally, we discuss the importance of directional interactions for self-assembly, its role in the bonding entropy reduction, in the suppression of the driving force for phase-separation and in the possibility of forming aggregates that do not expose attractive surfaces, thus minimizing inter-cluster attractive interactions.

The term “self-assembly” refers to the situation where many building blocks spontaneously form well-defined aggregates. Building blocks can be molecules, macromolecules (such as proteins, DNA), or colloids. In these notes I make use of statistical thermodynamics to address self-assembly in relatively complex situations. These situations are allostery, transcription regulation, virus capsid assembly, and the formation of charged, finite-size colloidal clusters. The first two situations can be reduced to a problem of adsorption onto substrates or templates. In the case of allostery, the state of the substrate couples to the binding affinity, leading to potentially strong “collective” effects. In transcription regulation, the adsorption of transcription factors (proteins) onto the promoter regions on DNA is proportional to the level of transcription of a gene. There, the main complication is that there are other substrates on which transcription factors may adsorb, a competition effect that may dramatically influence the level of transcription. The last two paragraphs are about virus capsid stability and finite-size, charged colloidal aggregates, respectively. In theses situations, finite-size aggregates occur without the presence of templates. In the case of virus capsids, finite size is presumed, and the question is addressed under what conditions (temperature, ionic strength) capsids are stable relative to the non-assembled state. For colloidal cluster, on the other hand, the building blocks are assumed to interact by short-range attraction and long-range repulsion, the magnitude of the latter being determined self-consistently from properties of the colloids and the solvent.

In this Chapter, we discuss novel aspects of the depletion interaction, which arise in situations in which the large colloidal particles in the mixture are not hard but rather soft, penetrable spherical aggregates. Given the fact that true hard-sphere interactions are extremely challenging to realize experimentally, soft colloids are indeed the rule in complex, soft matter fluids, and not the exception. We adopt star polymers as prototypes of soft colloids and we consider depleting agents at the two extremes of the colloid-polymer spectrum: linear homopolymer chains, on the one hand, and small, hard spherical colloids, on the other. We analyze in detail the quantitative characteristics of the ensuing depletion interactions and we demonstrate that they have novel and unexpected features, stemming from the softness of the depleted particles and their penetrability to the additives. The implications of these characteristics on the thermodynamics and rheology of the mixtures are also critically discussed.

During the past few years we have seen an impressive number of studies using directed self-assembly in soft matter research with a surprisingly wide range of underlying aims and goals. Here we will focus on field-driven colloidal self-assembly, and demonstrate how we can apply external electromagnetic fields in order to modulate the intrinsic interparticle interactions and induce additional directional ones in order to tune the subtle balance between thermal motion and the action of interparticle forces and thus generate new self-assembled structures. We describe two interesting classes of responsive particles, ionic microgels and hematite core-shell colloids, and use various real and reciprocal space techniques to monitor the particles in situ and time resolved while they assemble into the targeted structures. We show in particular how we can use field-driven self-assembly to induce phase transitions, cycle through various equilibrium and non-equilibrium phases, and study the underlying mechanisms of these phase transitions. Moreover, we demonstrate the effect of particle anisotropy in field-driven assembly.

In this Chapter we describe the self-assembly and interparticle correlations in dipolar soft matter. Following the historical development of the ideas, we start with an ideal dipolar gas, describe mean-field approaches, and several hierarchical steps in self-assembly. We study all of these phenomena in order to understand how to tune the response of dipolar soft matter to an external magnetic field. Apart from “traditional spherical magnetic colloids” we also briefly address the possibilities to alter the magnetic response by changing the shape or the structure of magnetic colloids.

A particle placed in soft matter distorts its host and creates an energy landscape. This can occur, for example, for particles in liquid crystals, for particles on lipid bilayers or for particles trapped at fluid interfaces. Such energies can be used to direct particles to assemble with remarkable degrees of control over orientation and structure. These notes explore that concept for capillary interactions, beginning with particle trapping at fluid interfaces, addressing pair interactions on planar interfaces and culminating with curvature capillary migration. Particular care is given to the solution of the associated boundary-value problems to determine the energies of interaction. Experimental exploration of these interactions on planar and curved interfaces is described. Theory and experiment are compared. These interactions provide a rich toolkit for directed assembly of materials, and, owing to their close analogy to related systems, pave the way to new explorations in materials science.

Crystallization, a prototypical self-organization process during which a disordered state spontaneously transforms into a crystal characterized by a regular arrangement of its building blocks, usually proceeds by nucleation and growth. In the initial stages of the transformation, a localized nucleus of the new phase forms in the old one due to a random fluctuation. Most of these nuclei disappear after a short time, but rarely a crystalline embryo may reach a critical size after which further growth becomes thermodynamically favorable and the entire system is converted into the new phase. In these lecture notes, we will discuss several theoretical concepts and computational methods to study crystallization. More specifically, we will address the rare event problem arising in the simulation of nucleation processes and explain how to calculate nucleation rates accurately. Particular attention is directed towards discussing statistical tools to analyze crystallization trajectories and identify the transition mechanism.

The ability to form orientationally highly selective bonds makes the so-called inverse patchy colloids (IPCs) — i.e., spherical colloids with heterogeneously charged surfaces — excellent building entities in targeted self-assembly processes into highly complex, ordered structures. IPCs turn out to be ideal candidates to form highly stable layered phases, i.e., structures that are difficult to self-assemble with conventional patchy particles. In this chapter we trace this particular ability of IPCs starting out from two-dimensional setups and arriving eventually at the phase diagram of three dimensional systems. Static and dynamic properties of the ensuing phases are discussed.

The ordered phases formed by polymeric nanocolloidal particles with a core-shell architecture are typically very different from those seen in classical hard colloids. The differences must invariably be related to softness of particles. Here we discuss the T=0 phase diagram of a 2D model of core-softened particles represented by the hard-core/square-shoulder pair potential. The aim of the analysis is to show that a simple generalization of the hard-core potential is sufficient to induce several rather complex crystalline and quasicrystalline phases, and to illustrate how these structures can be systematically constructed and compared using a geometric scheme based on canonical local packings of the particles.

One of the crucial challenges in nanoscience is gaining control over the formation of the desired nanoscale structures. Such structural control provides access to the novel material functions. While many functional nanoscale blocks are inorganic, soft matter components, i.e. surfactants, macromolecules, polymers, and biopolymers, can play an important role in defining structures formed from those blocks via self-assembly. In recent years DNA-based self-assembly approaches emerged as powerful means for nanoscale fabrications: DNA can direct inter-particle binding, can be used as a scaffold for particle positioning and can regulate a structural self-assembly. We review here the major areas of DNA-based nanoscale self-assembly, including systems formed purely from the DNA strands and structures formed by particles with the help of DNA. The methods for particles functionalized with DNA are elaborated. The assembly approaches that exploit DNA programmability for the creation of desired clusters, lattices and dynamically tunable systems are discussed.

This is a series of four lectures presented at the 2015 Enrico Fermi Summer School in Varenna. The aim of the lectures is to give an introduction to the hydrodynamics of active matter concentrating on low-Reynolds-number examples such as cells and molecular motors. Lecture 1 introduces the hydrodynamics of single active particles, covering the Stokes equation and the Scallop Theorem, and stressing the link between autonomous activity and the dipolar symmetry of the far flow field. In lecture 2 I discuss applications of this mathematics to the behaviour of microswimmers at surfaces and in external flows, and describe our current understanding of how swimmers stir the surrounding fluid. Lecture 3 concentrates on the collective behaviour of active particles, modelled as an active nematic. I write down the equations of motion and motivate the form of the active stress. The resulting hydrodynamic instability leads to a state termed “active turbulence” characterised by strong jets and vortices in the flow field and the continual creation and annihilation of pairs of topological defects. Lecture 4 compares simulations of active turbulence to experiments on suspensions of microtubules and molecular motors. I introduce lyotropic active nematics and discuss active anchoring at interfaces.

We outline the necessary background to understand the interaction of colloids in liquid crystals through boundary conditions and topology. Colloids create new boundaries in the sample and, in turn, generate boundary conditions that can be frustrated by the existing boundary conditions on the sample wall. Irrespective of energy, the topology often requires additional defects and textures. We give some fundamental examples of this in the situation of nematic liquid crystals.