Spontaneous assembly of a hybrid crystal-liquid phase in inverse patchy colloid systems

Simulating inverse patchy colloid models

Nano- to micro-sized particles with differently charged surface areas exhibit complex interaction patterns, characterized by both opposite-charge attraction and like-charge repulsion. While several successful models have been proposed in the literature to describe directional attraction, models accounting for both directional attraction and directional repulsion are much less numerous and often tailored to specific microscopic systems. Here, we present a simple and versatile patchy model, where the interaction energy of a pair of particles is a sum of interactions between sites of different types located within the particle volume. We implement different formulations of this model in both a self-developed Monte Carlo code and the widely used LAMMPS molecular dynamics simulation software, providing basic toolkits for both simulation methods and, in the latter case, for different algorithms. By comparing physical observables and code performances, we discuss the different models, methods, and algorithms, offering insights into optimization strategies and tricks of trade.

Patchy Charge Distribution Affects the pH in Protein Solutions during Dialysis

When using dialysis ultra- or diafiltration to purify protein solutions, a dialysis buffer in the permeate is employed to set the pH in the protein solution. Failure to achieve the target pH may cause undesired precipitation of the valuable product. However, the pH in the permeate differs from that in the retentate, which contains the proteins. Experimental optimization of the process conditions is time-consuming and expensive, while accurate theoretical predictions still pose a major challenge. Current models of dialysis account for the Donnan equilibrium, acid-base properties, and ion-protein interactions, but they neglect the patchy distribution of ionizable groups on the proteins and its impact on the solution properties. Here, we present a simple computational model of a colloidal particle with weakly acidic sites on the surface, organized in patches. This minimalistic model allows systematic variation of the relevant parameters, while simultaneously demonstrating the essential physics governing the acid-base equilibria in protein solutions. Using molecular simulations in the Grand-Reaction ensemble, we demonstrate that interactions between ionizable sites significantly affect the nanoparticle charge and thereby contribute to pH difference between the permeate and retentate. We show that the significance of this contribution increases if the ionizable sites are located on a smaller patch. Protein solutions are governed by the same physics as our simple model. In this context, our results show that models which aim to quantitatively predict the pH in protein solutions during dialysis need to account for the patchy distribution of ionizable sites on the protein surface.

Liquid-liquid phase separation driven by charge heterogeneity

Despite the intrinsic charge heterogeneity of proteins plays a crucial role in the liquid-liquid phase separation (LLPS) of a broad variety of protein systems, our understanding of the effects of their electrostatic anisotropy is still in its early stages. We approach this issue by means of a coarse-grained model based on a robust mean-field description that extends the DLVO theory to non-uniformly charged particles. We numerically investigate the effect of surface charge patchiness and net particle charge on varying these features independently and with the use of a few parameters only. The effect of charge anisotropy on the LLPS critical point is rationalized via a thermodynamic-independent parameter based on orientationally averaged pair properties, that estimates the particle connectivity and controls the propensity of the liquid phase to condensate. We show that, even though directional attraction alone is able to lower the particle bonding valence-thus shifting the critical point towards lower temperatures and densities-directional repulsion significantly and systematically diminishes the particle functionality, thus further reducing the critical parameters. This electrostatically-driven shift can be understood in terms of the additional morphological constraints introduced by the directional repulsion, that hinder the condensation of dense aggregates.

Features of heterogeneously charged systems at their liquid-liquid critical point

Recently synthesized colloids and biological systems such as proteins, viruses and monoclonal antibodies are heterogeneously charged, i.e., different regions of their surfaces carry different amounts of positive or negative charge. Because of charge inhomogeneity, electrostatic interactions between these units through the surrounding medium are intrinsically anisotropic, meaning that they are characterized not only by the attraction between oppositely charged regions but also by the repulsion between like-charged areas. Recent experiments have shown that the liquid-liquid phase separation of these systems can be driven by anisotropic electrostatic interactions, but it is not clear how the emerging aggregates are affected by charge imbalance and charge patchiness. The ability to experimentally control these two quantities calls for a theoretical understanding of their interplay, which we address here at the critical point. We consider a coarse-grained model of anisotropically charged hard spheres whose interaction potential is grounded in a robust mean field theory and perform extensive numerical Monte Carlo simulations to understand the aggregation behavior of these units at the critical point. Stemming from the simplicity of the model, we address the interplay between charge imbalance and charge patchiness with the use of three parameters only and fully rationalize how these features impact the critical point of the model by means of thermodynamic-independent pair properties.

Synthesis of patchy particles using gaseous ligands

The collective self-assembly of colloidal particles can be influenced by the composition of the suspending medium, the bulk material of the particles themselves and, importantly, by their surface chemistry. This can be inhomogeneous or patchy to give an orientational dependence to the interaction potential between the particles. These additional constraints to the energy landscape then steer the self-assembly towards configurations of fundamental or applicational interest. We present a novel approach to modify the surface chemistry of colloidal particles to give them two polar patches, using gaseous ligands. In particular, we synthesize polar inverse patchy colloids, i.e., charged particles with two (fluorescent) patches of the opposite charge on their poles. We characterize the dependence of these charges on the pH of the suspending solution.

Directing Liquid Crystalline Self-Organization of Rodlike Particles through Tunable Attractive Single Tips

Dispersions of rodlike colloidal particles exhibit a plethora of liquid crystalline states, including nematic, smectic A, smectic B, and columnar phases. This phase behavior can be explained by presuming the predominance of hard-core volume exclusion between the particles. We show here how the self-organization of rodlike colloids can be controlled by introducing a weak and highly localized directional attractive interaction between one of the ends of the particles. This has been performed by functionalizing the tips of filamentous viruses by means of regioselectively grafting fluorescent dyes onto them, resulting in a hydrophobic patch whose attraction can be tuned by varying the number of bound dye molecules. We show, in agreement with our computer simulations, that increasing the single tip attraction stabilizes the smectic phase at the expense of the nematic phase, leaving all other liquid crystalline phases invariant. For a sufficiently strong tip attraction, the nematic state may be suppressed completely to get a direct isotropic liquid-to-smectic phase transition. Our findings provide insights into the rational design of building blocks for functional structures formed at low densities.

Mono-patchy zwitterionic microcolloids as building blocks for pH-controlled self-assembly

A directional molecular interaction between microcolloids can be achieved through pre-defined sites on their surface, "patches", which might make them follow each other in a controlled way and assemble into target structures of more complexity. In this article, we report the successful generation and characterization of mono-patchy melamine-formaldehyde microparticles with oppositely charged patches made of poly(methyl vinyl ether-alt-maleic acid) or polyethyleneimine via microcontact printing. The study of their self-aggregation behavior in solution shows that by change of pH, particle dimers are formed via attractive electrostatic force between the patchy and non-patchy surface of the particles, which reaches its optimum at a specific pH.

Tuning the order of colloidal monolayers: assembly of heterogeneously charged colloids close to a patterned substrate

We study the behavior of negatively charged colloids with two positively charged polar caps close to a planar patterned surface. The competition between the different anisotropic components of the particle-particle interaction is able by itself to give rise to a rich assembly scenario: colloids with charged surface patterns already form different crystalline domains when adsorbed to a homogeneously charged substrate. Here we consider substrates composed of alternating (negative/neutral, positive/neutral and positive/negative) parallel stripes and, by means of Monte Carlo simulations, we investigate the ordering of the colloids on changing the number of the stripes. We show that the additional competition between the two different lengths scales characterizing the system (i.e., the particle interaction range and the size of the stripes) gives rise to a plethora of distinct particle arrangements, where some well-defined trends can be observed. By accurately tuning the substrate charged motif it is possible to, e.g., promote specific particle arrangements, disfavor crystalline domains or induce the formation of extended, open clusters.

Molecular dynamics simulations of inverse patchy colloids

Inverse patchy colloids are patchy particles with differently charged surface regions. In this paper we focus on inverse patchy colloids with two different polar patches and an oppositely charged equatorial belt, and we describe a model and a reliable and efficient numerical algorithm that can be applied to investigate the properties of these particles in molecular dynamics simulations.

Aggregation kinetics of irreversible patches coupled with reversible isotropic interaction leading to chains, bundles and globules

In the present study we are performing simulation of simple model of two patch colloidal particles undergoing irreversible diffusion limited cluster aggregation using patchy Brownian cluster dynamics. In addition to the irreversible aggregation of patches, the spheres are coupled with isotropic reversible aggregation through the Kern–Frenkel potential. Due to the presence of anisotropic and isotropic potential we have also defined three different kinds of clusters formed due to anisotropic potential and isotropic potential only as well as both the potentials together. We have investigated the effect of patch size on self-assembly under different solvent qualities for various volume fractions. We will show that at low volume fractions during aggregation process, we end up in a chain conformation for smaller patch size while in a globular conformation for bigger patch size. We also observed a chain to bundle transformation depending on the attractive interaction strength between the chains or in other words depending on the quality of the solvent. We will also show that bundling process is very similar to nucleation and growth phenomena observed in colloidal system with short range attraction. We have also studied the bond angle distribution for this system, where for small patches only two angles are more probable indicating chain formation, while for bundling at very low volume fraction a tail is developed in the distribution. While for the case of higher patch angle this distribution is broad compared to the case of low patch angles showing we have a more globular conformation. We are also proposing a model for the formation of bundles which are similar to amyloid fibers using two patch colloidal particles.

Steering patchy particles using multivalent electrolytes

Proteins and many recently designed colloids can be regarded as patchy particles where directional interactions strongly influence and govern assembly behavior. Using explicit ion implicit solvent Metropolis Monte Carlo simulations, we investigate spherical model particles, carrying both charge and electric patches, in dilute aqueous 1 : 1, 1 : 3, and 3 : 1 electrolyte solutions. Striking differences in pair interaction free energies and orientational correlations are induced by three different salts which are discussed and rationalized in terms of ion-binding to surface groups, ion-ion correlations, and double layer forces. These findings suggest a general strategy where directional, intermolecular interactions can be invoked and tuned via small amounts of a carefully chosen electrolyte.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

Artistic representation of limited valance units consisting of a soft core (in blue) and a small number of flexible bonding patches (in orange).