Patchy Colloidal Particles Research Articles

Re-entrant phase behavior in confined two-patch colloidal particles.

We present a version of density functional approach for the system of patchy colloidal particles confined in slitlike pores with hard walls. Each particle possesses two off-center sites of the types A and B, and in addition to single A-A and B-B bonds, formation of the double A-B-A and B-A-B bonds is allowed. The proposed approach is based on the fundamental measure theory and the second order perturbation theory of Wertheim. For the model in question, a re-entrant phase behavior in a bulk system has been found [Kalyuzhnyi Y. V.; Cummings, P. T., J. Chem. Phys. 2013, 139, 104905] . Our calculations revealed that the re-entrant phase diagrams are also observed in confined systems. The upper critical temperature decreases with the pore width, while the lower critical temperature increases very slightly.

Self-assembly of three-dimensional open structures using patchy colloidal particles.

Open structures can display a number of unusual properties, including a negative Poisson's ratio, negative thermal expansion, and holographic elasticity, and have many interesting applications in engineering. However, it is a grand challenge to self-assemble open structures at the colloidal scale, where short-range interactions and low coordination number can leave them mechanically unstable. In this paper we discuss the self-assembly of three-dimensional open structures using triblock Janus particles, which have two large attractive patches that can form multiple bonds, separated by a band with purely hard-sphere repulsion. Such surface patterning leads to open structures that are stabilized by orientational entropy (in an order-by-disorder effect) and selected over close-packed structures by vibrational entropy. For different patch sizes the particles can form into either tetrahedral or octahedral structural motifs which then compose open lattices, including the pyrochlore, the hexagonal tetrastack and the perovskite lattices. Using an analytic theory, we examine the phase diagrams of these possible open and close-packed structures for triblock Janus particles and characterize the mechanical properties of these structures. Our theory leads to rational designs of particles for the self-assembly of three-dimensional colloidal structures that are possible using current experimental techniques.

Properties of patchy colloidal particles close to a surface: A Monte Carlo and density functional study

We investigate the behavior of a patchy particle model close to a hard-wall via Monte Carlo simulation and density functional theory (DFT). Two DFT approaches, based on the homogeneous and inhomogeneous versions of Wertheim's first order perturbation theory for the association free energy are used. We evaluate, by simulation and theory, the equilibrium bulk phase diagram of the fluid and analyze the surface properties for two isochores, one of which is close to the liquid side of the gas-liquid coexistence curve. We find that the density profile near the wall crosses over from a typical high-temperature adsorption profile to a low-temperature desorption one, for the isochore close to coexistence. We relate this behavior to the properties of the bulk network liquid and find that the theoretical descriptions are reasonably accurate in this regime. At very low temperatures, however, an almost fully bonded network is formed, and the simulations reveal a second adsorption regime which is not captured by DFT. We trace this failure to the neglect of orientational correlations of the particles, which are found to exhibit surface induced orientational order in this regime.

Surface roughness directed self-assembly of patchy particles into colloidal micelles

Colloidal particles with site-specific directional interactions, so called "patchy particles", are promising candidates for bottom-up assembly routes towards complex structures with rationally designed properties. Here we present an experimental realization of patchy colloidal particles based on material independent depletion interaction and surface roughness. Curved, smooth patches on rough colloids are shown to be exclusively attractive due to their different overlap volumes. We discuss in detail the case of colloids with one patch that serves as a model for molecular surfactants both with respect to their geometry and their interactions. These one-patch particles assemble into clusters that resemble surfactant micelles with the smooth and attractive sides of the colloids located at the interior. We term these clusters "colloidal micelles". Direct Monte Carlo simulations starting from a homogeneous state give rise to cluster size distributions that are in good agreement with those found in experiments. Important differences with surfactant micelles originate from the colloidal character of our model system and are investigated by simulations and addressed theoretically. Our new "patchy" model system opens up the possibility for self-assembly studies into finite-sized superstructures as well as crystals with as of yet inaccessible structures.

Self-assembly scenarios of patchy colloidal particles

The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is extremely difficult to predict the large variety of ordered equilibrium structures that these particles are able to undergo, under the variation of external parameters such as temperature or pressure. Here we show that, by a novel combination of two theoretical tools, it is indeed possible to predict the self-assembly scenario of patchy colloidal particles: on one hand, a reliable and efficient optimization tool based on the ideas of evolutionary algorithms helps to identify the ordered equilibrium structures to be expected at T = 0; on the other hand, suitable simulation techniques allow us to estimate via free energy calculations the phase diagram at finite temperature. With these powerful approaches we are able to identify the broad variety of emerging self-assembly scenarios for spherical colloids decorated with four patches and we investigate and discuss the stability of the crystal structures on modifying in a controlled way the tetrahedral arrangement of the patches.

Bicontinuous and mixed gels in binary mixtures of patchy colloidal particles

We investigate the thermodynamics and percolation regimes of model binary mixtures of patchy colloidal particles. The particles of each species have three sites of two types, one of which promotes bonding of particles of the same species while the other promotes bonding of different species. We find up to four percolated structures at low temperatures and densities: two gels where only one species percolates, a mixed gel where particles of both species percolate but neither species percolates separately, and a bicontinuous gel where particles of both species percolate separately forming two interconnected networks. The competition between the entropy and the energy of bonding drives the stability of the different percolating structures. Appropriate mixtures exhibit one or more connectivity transitions between the mixed and bicontinuous gels, as the temperature and/or the composition changes.

The vibrational density of states of a disordered gel model

We investigate the vibrational density of states (vDOS) in harmonic approximation of a binary mixture of colloidal patchy particles with two and three patches for different relative compositions x(2). At low temperature, this system forms a thermo-reversible gel, i.e., a fully bonded network of chains of two-patches particles, in which the branching points are provided by three-patches particles. For all the compositions, we find in the vDOS a pronounced peak at low frequency whose height grows on increasing the fraction of two-functional particles or equivalently with the average length of the chains. To identify the various spectral features, we compare the vDOS of the whole system with the one of small representative structures of the network and with the vDOS of a long linear chain of two-patches particles and we find that these structures are indeed able to rationalize the various peaks in the vDOS of the full system. At large x(2) the vDOSs of the gel and of the long chain show remarkable similarities. Analyzing the dispersion relations and the spectrum of the linear chain we show that the excess of low frequency modes, the analog of the boson peak in glassy disordered systems, arises from the strong coupling between rotations and translations.

Patchy colloids: state of the art and perspectives

Recently, an increasing experimental effort has been devoted to the synthesis of complex colloidal particles with chemically or physically patterned surfaces and possible specific shapes that are far from spherical. These new colloidal particles with anisotropic interactions are commonly named patchy particles. In this Perspective article, we focus on patchy systems characterized by spherical neutral particles with patchy surfaces. We summarize most of the patchy particle models that have been developed so far and describe how their basic features are connected to the physical systems they are meant to investigate. Patchy models consider particles as hard or soft spheres carrying a finite and small number of attractive sites arranged in precise geometries on the particle's surface. The anisotropy of the interaction and the limited valence in bonding are the salient features determining the collective behavior of such systems. By tuning the number, the interaction parameters and the local arrangements of the patches, it is possible to investigate a wide range of physical phenomena, from different self-assembly processes of proteins, polymers and patchy colloids to the dynamical arrest of gel-like structures. We also draw attention to charged patchy systems: colloidal patchy particles as well as proteins are likely charged, hence the description of the presence of heterogeneously distributed charges on the particle surface is a promising perspective for future investigations.

Self-assembly scenarios of patchy colloidal particles in two dimensions

We have investigated the self-assembly scenario of patchy colloidal particles in atwo-dimensional system. The energetically most favourable ordered particle arrangementshave been identified via an optimization tool that is based on genetic algorithms. Assumingdifferent simple models for patchy colloidal particles, which include binary mixtures aswell as attraction and repulsion between the patches, we could identify a broadvariety of highly non-trivial ordered structures. The strategies of the systems toself-assemble become evident from a systematic variation of the pressure: (i) saturationof patch bonds at low pressure and close packing at high pressure and (ii) forintermediate pressure values, the strategy is governed by a trade-off between thesetwo energetic aspects. The present study is yet another demonstration of theefficiency and the high reliability of genetic algorithms as versatile optimization tools.

Primitive models of patchy colloidal particles. A review

In this article I will review some recent studies of the phase behavior and of the self-assembly of patchy colloidal particles. These studies have been based on simple primitive models for colloid–colloid interactions, effectively extending to soft matter the seminal work of I. Nezbeda on associated fluids. I will discuss the possibilities offered by the study of the self-assembly of particles with limited valence in deepening our understanding of the onset of the liquid state, of the differences between gels and glasses and of the possible connection between physical and chemical gels. A review with 55 references.

A Simple Method to Produce Trivalent Colloidal Particles

Trivalent patchy colloidal particles are synthesized using a two-step mu-contact printing method. First, one pole of a particle is modified, then the other. With the center portion of the particle left intact, the final chemical makeup consists of three distinct patches of different chemical composition whose relative areas can be controlled. This method depends on preparing stamps with sufficient adhesion to lift off particles yet mild enough adhesion for their subsequent detachment. Furthermore, this method adjusts stamp stiffness, allowing the respective areas of the two printed poles to be controlled separately. To check the efficacy of the method, the shapes of the chemically modified poles were examined using scanning electron microscopy (SEM) after Au nanoparticle adsorption. Fluorescence imaging further confirmed the trivalent patchy particle geometry.

Reversible gels of patchy particles: Role of the valence

We simulate a binary mixture of colloidal patchy particles with two and three patches, respectively, for several relative concentrations and hence relative average valences. For these limited-valence systems, it is possible to reach low temperatures, where the lifetime of the patch-patch interactions becomes longer than the observation time without encountering phase separation in a colloid-poor (gas) and a colloid rich (liquid) phase. The resulting arrested state is a fully connected long-lived network where particles with three patches provide the branching points connecting chains of two-patch particles. We investigate the effect of the valence on the structural and dynamic properties of the resulting gel and attempt to provide a theoretical description of the formation and of the resulting gel structure based on a combination of the Wertheim theory for associated liquids and the Flory-Stockmayer approach for modeling chemical gelation.

XIX meeting of the Italian Society of Pure and Applied Biophysics

This special issue of the European Biophysics Journal contains papers presented as invited lectures or oral contributions at the XIX meeting of the Italian Society of Pure and Applied Biophysics, also known as SIBPA. The conference was held in Rome, 17–20 September 2008 at the “Sacro Cuore” Catholic University. For the second time, the Wrst was in 2006, the articles presented at the conference appear in this journal that is the major point of reference for the European Biophysical Societies’ Association (EBSA) and once again witness of the interesting development of the Italian Biophysics. The main topics of the meeting were organized in seven sessions, with two invited lectures per session, and a special lecture concerning the renewable energies obtained from biological sources performed by J. Barber of the Wolfson Labs (Imperial College, London). During the Biomolecular aggregate session M. Di Carlo (CNR-Palermo) and M. Digman (CA Univ. at Irvine) have interested the participants in the eVect on live cells of aggregation of beta-amyloid peptide and huntingtin, respectively. The session of Processes and mechanisms of the biological membranes has had its main points in the lectures concerning the studies of membrane permeability of ion channels (A. Moroni, Milano Univ.) or to antimicrobial peptides (G. Rispoli, Ferrara Univ.). For the session of Biomaterials and nano-biophysics O. Cavalleri (Genoa Univ.) and L. Cordone (Palermo Univ.) have discussed the possibility of a Wne control of protein folding/unfolding to build molecular nanostructures or the preservation properties of trehalose–water matrixes, respectively. The development of a framework for the registration of 3D imaging data for clinical heart investigations (R. Antolini, Trento Univ.) and the attempt to extend the results obtained on a charged, functionalized and patchy colloidal particles to globular protein solutions (F. Sciortino, Roma La Sapienza Univ.) have been discussed during the Theoretical and computational biophysics topic. In the session Photobiophysics and photoprocesses, T. Kottke (Bielefeld Univ.) has discussed the mechanism of blue light reception in plant and animal cryptochromes and D. Dell’Orco (Modena and Reggio Emilia Univ.) the molecular systems biology approaches to phototransduction in vertebrate rods. The investigation of a new biological scenario in which gene expression and regulation largely depend on a complex posttranscriptional network signals acting on mRNAs (A. Quattrone, Trento Univ.) and the relationship between structure and function in the P450 cytochrome involved in the erythromycin biosynthesis (B. Vallone, Roma La Sapienza Univ.) have been debated during the session regarding the Structure and function of proteins and nucleic acids. The biophysical mechanisms of regulation of CLC chloride channels and transporters (M. Pusch, Genoa CNR) and the application of optical and Xuorescence microscopies for dynamical tracking from cellular to molecular resolution (M. Faretta, Milan Eur. Inst. Oncol.) have been discussed during the Molecular and cellular biophysics session. The last day of the meeting, four young scientists have received the prize for their research: D. Giacomazza (&) Institute of Biophysics, National Research Council, Via U. La Malfa 153, Palermo, Italy e-mail: daniela.giacomazza@pa.ibf.cnr.it

A spherical model with directional interactions. I. Static properties

We introduce a simple spherical model whose structural properties are similar to the ones generated by models with directional interactions, by employing a binary mixture of large and small hard spheres, with a square-well attraction acting only between particles of different sizes. The small particles provide the bonds between the large ones. With a proper choice of the interaction parameters, as well as of the relative concentration of the two species, it is possible to control the effective valence. Here we focus on a specific choice of the parameters which favors tetrahedral ordering and study the equilibrium static properties of the system in a large window of densities and temperatures. Upon lowering the temperature we observe a progressive increase in local order, accompanied by the formation of a four-coordinated network of bonds. Three different density regions are observed: At low density the system phase separates into a gas and a liquid phase; at intermediate densities a network of fully bonded particles develops; at high densities--due to the competition between excluded volume and attractive interactions--the system forms a defective network. The very same behavior has been previously observed in numerical studies of nonspherical models for molecular liquids, such as water, and in models of patchy colloidal particles. Different from these models, theoretical treatments devised for spherical potentials, e.g., integral equations and ideal mode coupling theory for the glass transition, can be applied in the present case, opening the way for a deeper understanding of the thermodynamic and dynamic behavior of low valence molecules and particles.

Phase Diagram of Patchy Colloids: Towards Empty Liquids

We report theoretical and numerical evaluations of the phase diagram for patchy colloidal particles of new generation. We show that the reduction of the number of bonded nearest neighbors offers the possibility of generating liquid states (i.e., states with temperature T lower than the liquid-gas critical temperature) with a vanishing occupied packing fraction (phi), a case which can not be realized with spherically interacting particles. Theoretical results suggest that such reduction is accompanied by an increase of the region of stability of the liquid phase in the (T-phi) plane, possibly favoring the establishment of homogeneous disordered materials at small phi, i.e., stable equilibrium gels.