Nano- and microparticles at fluid and biological interfaces

Soft and Deformable Thermoresponsive Hollow Rod-Shaped Microgels

Depending on their aspect ratio, rod-shaped particles exhibit a much richer 2D and 3D phase behavior than their spherical counterparts, with additional nematic and smectic phases accompanied by defined orientational ordering. While the phase diagram of colloidal hard rods is extensively explored, little is known about the influence of softness in such systems, partly due to the absence of appropriate model systems. Additionally, investigating higher volume fractions for long rods is usually complicated because non-equilibrium dynamical arrest is likely to precede the formation of more defined states. This has motivated us to develop micrometric rod-like microgels with limited sedimentation that can respond to temperature and reversibly reorganize into defined phases via annealing and seeding procedures. A detailed procedure is presented for synthesizing rod-shaped hollow poly(N-isopropylacrylamide) microgels using micrometric silica rods as sacrificial templates. Their morphological characterization is conducted through a combination of microscopy and light scattering techniques, evidencing the unconstrained swelling of rod-shaped hollow microgels compared to core-shell microgel rods. Different aspects of their assembly in dispersion and at interfaces are further tested to illustrate the opportunities and challenges offered by such systems that combine softness, anisotropy, and thermoresponsivity.

The wetting of H2O by CO2

Biphasic interfaces are complex but fascinating regimes that display a number of properties distinct from those of the bulk. The CO2-H2O interface, in particular, has been the subject of a number of studies on account of its importance for the carbon life cycle as well as carbon capture and sequestration schemes. Despite this attention, there remain a number of open questions on the nature of the CO2-H2O interface, particularly concerning the interfacial tension and phase behavior of CO2 at the interface. In this paper, we seek to address these ambiguities using ab initio-quality simulations. Harnessing the benefits of machine-learned potentials and enhanced statistical sampling methods, we present an ab initio-level description of the CO2-H2O interface. Interfacial tensions are predicted from 1 to 500 bars and found to be in close agreement with experiment at pressures for which experimental data are available. Structural analyses indicate the buildup of an adsorbed, saturated CO2 film forming at a low pressure (20 bars) with properties similar to those of the bulk liquid, but preferential perpendicular alignment with respect to the interface. The CO2 monolayer buildup coincides with a reduced structuring of water molecules close to the interface. This study highlights the predictive nature of machine-learned potentials for complex macroscopic properties of biphasic interfaces, and the mechanistic insight obtained into carbon dioxide aggregation at the water interface is of high relevance for geoscience, climate research, and materials science.

Elastocapillary interaction for particles trapped at the isotropic-nematic liquid crystal interface

We present numerical simulations on pairwise interactions between particles trapped at an isotropic-nematic liquid crystal (Iso-N) interface. The particles are subject to elastocapillary interactions arising from interfacial deformations and elastic distortions of the nematic phase. We use a recent model based on a phase-field approach [see Qiu et al., Phys. Rev. E 103, 022706 (2021)2470-004510.1103/PhysRevE.103.022706] to take into account the coupling between elastic and capillary phenomena. The pair potential is computed in a two-dimensional geometry for a range of particle separations and two anchoring configurations. The first configuration leads to the presence of an anchoring conflict at the three-phase contact line, whereas such a conflict does not exist for the second one. In the first case, the results show that significant interfacial deformations and downward particle displacements occur, resulting in sizable attractive capillary interactions able to overcome repulsive elastic forces at intermediate separations. The pair potential exhibits an equilibrium distance since elastic repulsions prevail at short range and prevent the clustering of particles. However, in the absence of any anchoring conflict, the interfacial deformations are very small and the capillary forces have a negligible contribution to the pair potential, which is fully repulsive and overwhelmed by elastic forces. These results suggest that the self-assembly properties of particles floating at Iso-N interfaces might be controlled by tuning anchoring conflicts.

Structure of liquid-vapor interfaces: Perspectives from liquid state theory, large-scale simulations, and potential grazing-incidence x-ray diffraction

Grazing-incidence x-ray diffraction (GIXRD) is a scattering technique that allows one to characterize the structure of fluid interfaces down to the molecular scale, including the measurement of surface tension and interface roughness. However, the corresponding standard data analysis at nonzero wave numbers has been criticized as to be inconclusive because the scattering intensity is polluted by the unavoidable scattering from the bulk. Here, we overcome this ambiguity by proposing a physically consistent model of the bulk contribution based on a minimal set of assumptions of experimental relevance. To this end, we derive an explicit integral expression for the background scattering, which can be determined numerically from the static structure factors of the coexisting bulk phases as independent input. Concerning the interpretation of GIXRD data inferred from computer simulations, we extend the model to account also for the finite sizes of the bulk phases, which are unavoidable in simulations. The corresponding leading-order correction beyond the dominant contribution to the scattered intensity is revealed by asymptotic analysis, which is characterized by the competition between the linear system size and the x-ray penetration depth in the case of simulations. Specifically, we have calculated the expected GIXRD intensity for scattering at the planar liquid-vapor interface of Lennard-Jones fluids with truncated pair interactions via extensive, high-precision computer simulations. The reported data cover interfacial and bulk properties of fluid states along the whole liquid-vapor coexistence line. A sensitivity analysis shows that our findings are robust with respect to the detailed definition of the mean interface position. We conclude that previous claims of an enhanced surface tension at mesoscopic scales are amenable to unambiguous tests via scattering experiments.

Impact of Biogenic and Chemogenic Selenium Nanoparticles on Model Eukaryotic Lipid Membranes

Microbial nanotechnology is an expanding research area devoted to producing biogenic metal and metalloid nanomaterials (NMs) using microorganisms. Often, biogenic NMs are explored as antimicrobial, anticancer, or antioxidant agents. Yet, most studies focus on their applications rather than the underlying mechanism of action or toxicity. Here, we evaluate the toxicity of our well-characterized biogenic selenium nanoparticles (bSeNPs) produced by the Stenotrophomonas maltophilia strain SeITE02 against the model yeast Saccharomyces cerevisiae comparing it with chemogenic SeNPs (cSeNPs). Knowing from previous studies that the biogenic extract contained bSeNPs in an organic material (OM) and supported here by Fourier transform infrared spectroscopy, we removed and incubated it with cSeNPs (cSeNPs_OM) to assess its influence on the toxicity of these formulations. Specifically, we focused on the first stages of the eukaryotic cell exposure to these samples─i.e., their interaction with the cell lipid membrane, which was mimicked by preparing vesicles from yeast polar lipid extract or phosphatidylcholine lipids. Fluidity changes derived from biogenic and chemogenic samples revealed that the bSeNP extract mediated the overall rigidification of lipid vesicles, while cSeNPs showed negligible effects. The OM and cSeNPs_OM induced similar modifications to the bSeNP extract, reiterating the need to consider the OM influence on the physical-chemical and biological properties of bSeNP extracts.

Nanoscale Porosity in Microellipsoids Cloaks Interparticle Capillary Attraction at Fluid Interfaces

Anisotropic particles pinned at fluid interfaces tend toward disordered multiparticle configurations due to large, orientationally dependent, capillary forces, which is a significant barrier to exploiting these particles to create functional self-assembled materials. Therefore, current interfacial assembly methods typically focus on isotropic spheres, which have minimal capillary attraction and no dependence on orientation in the plane of the interface. In order to create long-range ordered structures with complex configurations via interfacially trapped anisotropic particles, control over the interparticle interaction energy via external fields and/or particle engineering is necessary. Here, we synthesize colloidal ellipsoids with nanoscale porosity and show that their interparticle capillary attraction at a water-air interface is reduced by an order of magnitude compared to their smooth counterparts. This is accomplished by comparing the behavior of smooth, rough, and porous ellipsoids at a water-air interface. By monitoring the dynamics of two particles approaching one another, we show that the porous particles exhibit a much shorter-range capillary interaction potential, with scaling intriguingly different than theory describing the behavior of smooth ellipsoids. Further, interferometry measurements of the fluid deformation surrounding a single particle shows that the interface around porous ellipsoids does not possess the characteristic quadrupolar symmetry of smooth ellipsoids, and quantitatively confirms the decrease in capillary interaction energy. By engineering nanostructured surface features in this fashion, the interfacial capillary interactions between particles may be controlled, informing an approach for the self-assembly of complex two-dimensional microstructures composed of anisotropic particles.

Effect of Particle Size on the Orientation and Order of Assemblies of Functionalized Microscale Cubes Formed at the Water/Air Interface

The impact of the particle size and wettability on the orientation and order of assemblies obtained by self-organization of functionalized microscale polystyrene cubes at the water/air interface is reported. An increase in the hydrophobicity of 10- and 5-μm-sized self-assembled monolayer-functionalized polystyrene cubes, as assessed by independent water contact angle measurements, led to a change of the preferred orientation of the assembled cubes at the water/air interface from face-up to edge-up and further to vertex-up, irrespective of microcube size. This tendency is consistent with our previous studies with 30-μm-sized cubes. However, the transitions among these orientations and the capillary force-induced structures, which change from flat plate to tilted linear and further to close-packed hexagonal arrangements, were observed to shift to larger contact angles for smaller cube size. Likewise, the order of the formed aggregates decreased significantly with decreasing cube size, which is tentatively attributed to the small ratio of inertial force to capillary force for smaller cubes in disordered aggregates, which results in more difficulties to reorient in the stirring process. Experiments with small fractions of larger cubes added to the water/air interface increased the order of smaller homo-aggregates to values similar to neat 30 μm cube assemblies. Hence, collisions of larger cubes or aggregates are shown to play a decisive role in breaking metastable structures to approach a global energy minimum assembly.

Capillary Assembly of Anisotropic Particles at Cylindrical Fluid-Fluid Interfaces

The unique behavior of colloids at liquid interfaces provides exciting opportunities for engineering the assembly of colloidal particles into functional materials. The deformable nature of fluid-fluid interfaces means that we can use the interfacial curvature, in addition to particle properties, to direct self-assembly. To this end, we use a finite element method (Surface Evolver) to study the self-assembly of rod-shaped particles adsorbed at a simple curved fluid-fluid interface formed by a sessile liquid drop with cylindrical geometry. Specifically, we study the self-assembly of single and multiple rods as a function of drop curvature and particle properties such as shape (ellipsoid, cylinder, and spherocylinder), contact angle, aspect ratio, and chemical heterogeneity (homogeneous and triblock patchy). We find that the curved interface allows us to effectively control the orientation of the rods, allowing us to achieve parallel, perpendicular, or novel obliquely orientations with respect to the cylindrical drop. In addition, by tuning particle properties to achieve parallel alignment of the rods, we show that the cylindrical drop geometry favors tip-to-tip assembly of the rods, not just for cylinders, but also for ellipsoids and triblock patchy rods. Finally, for triblock patchy rods with larger contact line undulations, we can achieve strong spatial confinement of the rods transverse to the cylindrical drop due to the capillary repulsion between the contact line undulations of the particle and the pinned contact lines of the sessile drop. Our capillary assembly method allows us to manipulate the configuration of single and multiple rod-like particles and therefore offers a facile strategy for organizing such particles into useful functional materials.

Membrane-Mediated Interactions Between Nonspherical Elastic Particles

The transport of particles across lipid-bilayer membranes is important for biological cells to exchange information and material with their environment. Large particles often get wrapped by membranes, a process which has been intensively investigated in the case of hard particles. However, many particles in vivo and in vitro are deformable, e.g., vesicles, filamentous viruses, macromolecular condensates, polymer-grafted nanoparticles, and microgels. Vesicles may serve as a generic model system for deformable particles. Here, we study nonspherical vesicles with various sizes, shapes, and elastic properties at initially planar lipid-bilayer membranes. Using the Helfrich Hamiltonian, triangulated membranes, and energy minimization, we predict the interplay of vesicle shapes and wrapping states. Increasing particle softness enhances the stability of shallow-wrapped and deep-wrapped states over nonwrapped and complete-wrapped states. The free membrane mediates an interaction between partial-wrapped vesicles. For the pair interaction between deep-wrapped vesicles, we predict repulsion. For shallow-wrapped vesicles, we predict attraction for tip-to-tip orientation and repulsion for side-by-side orientation. Our predictions may guide the design and fabrication of deformable particles for efficient use in medical applications, such as targeted drug delivery.

Forces Controlling the Assembly of Particles at Fluid Interfaces

The interaction of particles with fluid interfaces is ubiquitous in synthetic and natural work, involving two types of interactions: particle-interface interactions (trapping energy) and interparticle interactions. Therefore, it is urgent to gain a deep understanding of the main forces controlling the trapping of particles at fluid interfaces, and their assembly to generate a broad range of structures characterized by different degrees of order. This Perspective tries to provide an overview of the main contributions to the energetic landscape controlling the assembly of particles at fluid interfaces, which is essential for exploiting this type of interfacial systems as platforms for the fabrication of interface-based soft materials with technological interest.

Understanding Interfacial Nanoparticle Organization through Simulation and Theory: A Review

Understanding the behaviors of nanoparticles at interfaces is crucial not only for the design of novel nanostructured materials with superior properties but also for a better understanding of many biological systems where nanoscale objects such as drug molecules, viruses, and proteins can interact with various interfaces. Theoretical studies and tailored computer simulations offer unique approaches to investigating the evolution and formation of structures as well as to determining structure-property relationships regarding the interfacial nanostructures. In this feature article, we summarize our efforts to exploit computational approaches as well as theoretical modeling in understanding the organization of nanoscale objects at the interfaces of various systems. First, we present the latest research advances and state-of-the-art computational techniques for the simulation of nanoparticles at interfaces. Then we introduce the applications of multiscale modeling and simulation methods as well as theoretical analysis to explore the basic science and the fundamental principles in the interfacial nanoparticle organization, covering the interfaces of polymer, nanoscience, biomacromolecules, and biomembranes. Finally, we discuss future directions to signify the framework in tailoring the interfacial organization of nanoparticles based on the computational design. This feature article could promote further efforts toward fundamental research and the wide applications of theoretical approaches in designing interfacial assemblies for new types of functional nanomaterials and beyond.

Ion-bridges and lipids drive aggregation of same-charge nanoparticles on lipid membranes

The control of the aggregation of biomedical nanoparticles (NP) in physiological conditions is crucial as clustering may change completely the way they interact with the biological environment. Here we show that Au nanoparticles, functionalized by an anionic, amphiphilic shell, spontaneously aggregate in fluid zwitterionic lipid bilayers. We use molecular dynamics and enhanced sampling techniques to disentangle the short-range and long-range driving forces of aggregation. At short inter-particle distances, ion-mediated, charge-charge interactions (ion bridging) stabilize the formation of large NP aggregates, as confirmed by cryo-electron microscopy. Lipid depletion and membrane curvature are the main membrane deformations driving long-range NP-NP attraction. Ion bridging, lipid depletion, and membrane curvature stem from the configurational flexibility of the nanoparticle shell. Our simulations show, more in general, that the aggregation of same-charge membrane inclusions can be expected as a result of intrinsically nanoscale effects taking place at the NP-NP and NP-bilayer soft interfaces.

Particle trapped at the isotropic-nematic liquid crystal interface: Elastocapillary phenomena and drag forces

We present numerical simulations of a particle trapped at the isotropic-nematic liquid crystal (Iso-N) interface. We use our recent model, based on a phase-field approach [see Qiu et al., Phys. Rev. E 103, 022706 (2021)10.1103/PhysRevE.103.022706], to couple the capillary forces acting on the interface with the elastic stresses in the nematic phase along with topological defects. A range of floating configurations are first investigated as a function of the contact angle and various anchoring conditions at the fluid interface. The results show that the response of the system is driven by the existence of an anchoring conflict at the contact line. Substantial particle displacements and/or interfacial deformations may occur in this case even for moderate anchoring strengths. These findings highlight the coupling between elastic and capillary forces. In a second part, we compute drag forces exerted on a particle that moves along the Iso-N interface for several contact angles and a moderate Ericksen number. Because of the coupling between the velocity and order parameter fields, topological defects are swept downstream of the particle by the flow and sometimes escape from the particle or merge with the interface. We also find linear force-velocity laws, with drag forces at the Iso-N interface being slightly greater than their isotropic counterparts due to director distortions. We discuss these results in light of past studies on the behavior of particles being dragged in the bulk of a liquid crystal matrix.

A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve.

Biomimetic Curvature and Tension-Driven Membrane Fusion Induced by Silica Nanoparticles

Fusion events in living cells are intricate phenomena that require the coordinate action of multicomponent protein complexes. However, simpler synthetic tools to control membrane fusion in artificial cells are highly desirable. Native membrane fusion machinery mediates fusion, driving a delicate balance of membrane curvature and tension between two closely apposed membranes. Here, we show that silica nanoparticles (SiO₂ NPs) at a size close to the cross-over between tension-driven and curvature-driven interaction regimes initiate efficient fusion of biomimetic model membranes. Fusion efficiency and mechanisms are studied by Förster resonance energy transfer and confocal fluorescence microscopy. SiO₂ NPs induce a slight increase in lipid packing likely to increase the lateral tension of the membrane. We observe a connection between membrane tension and fusion efficiency. Finally, real-time confocal fluorescence microscopy reveals three distinct mechanistic pathways for membrane fusion. SiO₂ NPs show significant potential for inclusion in the synthetic biology toolkit for membrane remodeling and fusion in artificial cells.

Amphiphilic nanoparticles generate curvature in lipid membranes and shape liposome-liposome interfaces

We show by molecular dynamics that amphiphilic Au nanoparticles (NP) with a diameter of 4 nm generate curvature in phosphatidylcholine lipid membranes. NPs generate negative curvature when they adsorb on the membrane surface but, as they get spontaneously and progressively embedded into the membrane core, the curvature turns positive. As membrane embedding is kinetically slow, both configurations can be observed by Cryo-EM. NP-induced curvature explains the peculiar structure of liposome-liposome interfaces in presence of NPs.

Effect of malaria parasite shape on its alignment at erythrocyte membrane

During the blood stage of malaria pathogenesis, parasites invade healthy red blood cells (RBC) to multiply inside the host and evade the immune response. When attached to RBC, the parasite first has to align its apex with the membrane for a successful invasion. Since the parasite’s apex sits at the pointed end of an oval (egg-like) shape with a large local curvature, apical alignment is in general an energetically unfavorable process. Previously, using coarse-grained mesoscopic simulations, we have shown that optimal alignment time is achieved due to RBC membrane deformation and the stochastic nature of bond-based interactions between the parasite and RBC membrane (Hillringhaus et al., 2020). Here, we demonstrate that the parasite’s shape has a prominent effect on the alignment process. The alignment times of spherical parasites for intermediate and large bond off-rates (or weak membrane-parasite interactions) are found to be close to those of an egg-like shape. However, for small bond off-rates (or strong adhesion and large membrane deformations), the alignment time for a spherical shape increases drastically. Parasite shapes with large aspect ratios such as oblate and long prolate ellipsoids are found to exhibit very long alignment times in comparison to the egg-like shape. At a stiffened RBC, a spherical parasite aligns faster than any other investigated shape. This study shows that the original egg-like shape performs not worse for parasite alignment than other considered shapes but is more robust with respect to different adhesion interactions and RBC membrane rigidities.

Particle rotation speeds up capillary interactions

We use dynamic numerical simulations to investigate the role of particle rotation in pairwise capillary interactions of particles trapped at a fluid interface. The fluid interface is modeled with a phase-field method which is coupled to the Navier-Stokes equations to solve for the flow dynamics. Numerical solutions are found using a finite element scheme in a bounded two-dimensional geometry. The interfacial deformations are caused by the buoyant weight of the particles, which are allowed to both translate and rotate due to the capillary and viscous forces and torques at play. The results show that the capillary attraction is faster between freely rotating particles than if particle rotation is inhibited, and the higher the viscosity mismatch, the greater the effect. To explain this result, we analyze the drag force exerted on the particles and find that the translational drag force on a rotating particle is always less than its non-rotating counterpart due to attenuated velocity gradients in the vicinity of the particle. We also find that the influence of interfacial deformations on particle rotation is minute.

Chains of cubic colloids at fluid-fluid interfaces

Inspired by recent experimental observations of spontaneous chain formation of cubic particles adsorbed at a fluid-fluid interface, we theoretically investigate whether capillary interactions can be responsible for this self-assembly process. We calculate adsorption energies, equilibrium particle orientations, and interfacial deformations, not only for a variety of contact angles but also for single cubes as well as an infinite 2D lattice of cubes at the interface. This allows us to construct a ground-state phase diagram as a function of areal density for several contact angles, and upon combining the capillary energy of a 2D lattice with a simple expression for the entropy of a 2D fluid we also construct temperature-density or size-density phase diagrams that exhibit large two-phase regions and triple points. We identify several regimes with stable chainlike structures, in line with the experimental observations.

Tunable Collective Dynamics of Active Inclusions in Viscous Membranes

We study hydrodynamic interactions and clustering mechanisms of active membrane inclusions within lipid bilayers. Pairs of inclusions display unique oscillatory dynamics that disappear when the 3D fluid adjacent to the membrane is confined. We reduce the governing equations to a coupled dynamical system whose phase behavior reveals the striking role of bulk confinement in enhancing cluster formation within the membrane. Using numerical simulations, we then extend this finding to demonstrate the role of confinement in controlling large-scale aggregation of membrane inclusions.

Interfacial viscoelasticity and jamming of colloidal particles at fluid-fluid interfaces: a review

Colloidal particles can be adsorbed at fluid-fluid interfaces, a phenomenon frequently observed in particle-stabilized foams, Pickering emulsions, and bijels. Particles adsorbed at interfaces exhibit unique physical and chemical behaviors, which affect the mechanical properties of the interface. Therefore, interfacial colloidal particles are of interest in terms of both fundamental and applied research. In this paper, we review studies on the adsorption of colloidal particles at fluid-fluid interfaces, from both thermodynamic and mechanical points of view, and discuss the differences as compared with surfactants and polymers. The unique particle interactions induced by the interfaces as well as the particle dynamics including lateral diffusion and contact line relaxation will be presented. We focus on the rearrangement of the particles and the resultant interfacial viscoelasticity. Particular emphasis will be given to the effects of particle shape, size, and surface hydrophobicity on the interfacial particle assembly and the mechanical properties of the obtained particle layer. We will also summarize recent advances in interfacial jamming behavior caused by adsorption of particles at interfaces. The buckling and cracking behavior of particle layers will be discussed from a mechanical perspective. Finally, we suggest several potential directions for future research in this area.

Wrapping of Microparticles by Floppy Lipid Vesicles

Lipid membranes, the barrier defining living cells and many of their subcompartments, bind to a wide variety of nano- and micrometer sized objects. In the presence of strong adhesive forces, membranes can strongly deform and wrap the particles, an essential step in crossing the membrane for a variety of healthy and disease-related processes. A large body of theoretical and numerical work has focused on identifying the physical properties that underly wrapping. Using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure a wrapping phase diagram and make quantitative comparisons to theoretical models. Our data are consistent with a model of membrane-particle interactions accounting for the adhesive energy per unit area, membrane bending rigidity, particle size, and vesicle radius.

Static and dynamic behavior of magnetic particles at fluid interfaces

This perspective work reviews the current status of research on magnetic particles at fluid interfaces. The article gives both a unified overview of recent experimental advances and theoretical studies centered on very different phenomena that share a common characteristic: they involve adsorbed magnetic particles that range in size from a few nanometers to several millimeters. Because of their capability of being remotely piloted through controllable external fields, magnetic particles have proven essential as building blocks in the design of new techniques, smart materials and micromachines, with new tunable properties and prospective applications in engineering and biotechnology. Once adsorbed at a fluid-fluid interfase, in a process that can be facilitated via the application of magnetic field gradients, these particles often result sorely confined to two dimensions (2D). In this configuration, inter-particle forces directed along the perpendicular to the interface are typically very small compared to the surface forces. Hence, the confinement and symmetry breaking introduced by the presence of the surface play an important role on the response of the system to the application of an external field. In monolayers of particles where the magnetic is predominant interaction, the states reached are strongly determined by the mode and orientation of the applied field, which promote different patterns and processes. Furthermore, they can reproduce some of the dynamic assemblies displayed in bulk or form new ones, that take advantage of the interfacial phenomena or of the symmetry breaking introduce by the confining boundary. Magnetic colloids are also widely used for unraveling the guiding principles of 2D dynamic self-assembly, in designs devised for producing interface transport, as tiny probes for assessing interfacial rheological properties, neglecting the bulk and inertia contributions, as well as actuated stabilizing agents in foams and emulsions.

Interaction of Particles with Langmuir Monolayers of 1,2-Dipalmitoyl-Sn-Glycero-3-Phosphocholine: A Matter of Chemistry?

Lipid layers are considered among the first protective barriers of the human body against pollutants, e.g., skin, lung surfactant, or tear film. This makes it necessary to explore the physico-chemical bases underlying the interaction of pollutants and lipid layers. This work evaluates using a pool of surface-sensitive techniques, the impact of carbon black and fumed silica particles on the behavior of Langmuir monolayers of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). The results show that the incorporation of particles into the lipid monolayers affects the surface pressure–area isotherm of the DPPC, modifying both the phase behavior and the collapse conditions. This is explained considering that particles occupy a part of the area available for lipid organization, which affects the lateral organization of the lipid molecules, and consequently the cohesion interactions within the monolayer. Furthermore, particles incorporation worsens the mechanical performance of lipid layers, which may impact negatively in different processes presenting biological relevance. The modification induced by the particles has been found to be dependent on their specific chemical nature. This work tries to shed light on some of the most fundamental physico-chemical bases governing the interaction of pollutants with lipid layers, which plays an essential role on the design of strategies for preventing the potential health hazards associated with pollution.

Osmotic Concentration-Controlled Particle Uptake and Wrapping-Induced Lysis of Cells and Vesicles

In vivo, high protein and ion concentrations determine the preferred volumes of cells, organelles, and vesicles. Deformations of their lipid-bilayer membranes by nanoparticle wrapping reduce the interior volumes available to solutes and thus induce large osmotic pressure differences. Osmotic concentration can therefore be an important control parameter for wrapping of nanoparticles. We employ a curvature-elasticity model of the membrane and contact interaction with spherical particles to study their wrapping at initially spherical vesicles. Although the continuous particle-binding transition is independent of the presence of solutes, the discontinuous envelopment transition shifts to higher adhesion strengths and the corresponding energy barrier increases with increasing osmotic concentration. High osmotic concentrations stabilize partial-wrapped, membrane-bound states for both, particle attachment to the inside and the outside. In this regime, wrapping of particles controls membrane tension, with power-law dependencies on osmotic concentration and adhesion strength. For high adhesion strengths, particle wrapping can lead to the opening of mechanosensitive channels in cell membranes and to lysis. Membrane tension-induced stabilization of partial-wrapped states as well as wrapping-induced lysis play important roles not only for desired mechano-bacteriocidal effects of engineered nanomaterials but may also determine viral burst sizes of bacteria and control endocytosis for mammalian cells.

Drag force on a particle straddling a fluid interface: Influence of interfacial deformations

We numerically investigate the influence of interfacial deformations on the drag force exerted on a particle straddling a fluid interface. We perform finite element simulations of the two-phase flow system in a bounded two-dimensional geometry. The fluid interface is modeled with a phase-field method which is coupled to the Navier-Stokes equations to solve for the flow dynamics. The interfacial deformations are caused by the buoyant weight of the particle, which results in curved menisci. We compute drag coefficients as a function of the three-phase contact angle, the viscosity ratio of the two fluids, and the particle density. Our results show that, for some parameter values, large drag forces are not necessarily correlated with large interfacial distortions and that a lower drag may actually be achieved with non-flat interfaces rather than with unperturbed ones.

Colloids at Fluid Interfaces

Over the last two decades, understanding of the attachment of colloids to fluid interfaces has attracted the interest of researchers from different fields. This is explained by considering the ubiquity of colloidal and interfacial systems in nature and technology. However, to date, the control and tuning of the assembly of colloids at fluid interfaces remain a challenge. This review discusses some of the most fundamental aspects governing the organization of colloidal objects at fluid interfaces, paying special attention to spherical particles. This requires a description of different physicochemical aspects, from the driving force involved in the assembly to its thermodynamic description, and from the interactions involved in the assembly to the dynamics and rheological behavior of particle-laden interfaces.

Impact of Surface Amphiphilicity on the Interfacial Behavior of Janus Particle Layers under Compression

Langmuir monolayers of silica/gold Janus particles with two different degrees of amphiphilicity have been examined to study the significance of particle surface amphiphilicity on the structure and mechanical properties of the interfacial layers. The response of the layers to the applied compression provides insight into the nature and strength of the interparticle interactions. Different collapse modes observed for the interfacial layers are linked to the amphiphilicity of Janus particles and their configuration at the interface. Molecular dynamics simulations on nanoparticles with similar contact angles provide insight on the arrangement of particles at the interface and support our conclusion that the interfacial configuration and collapse of anisotropic particles at the air/water interface are controlled by particle amphiphilicity.

Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces

At the heart of the structured architecture and complex dynamics of biological systems are specific and timely interactions operated by biomolecules. In many instances, biomolecular agents are spatially confined to flexible lipid membranes where, among other functions, they control cell adhesion, motility and tissue formation. Besides being central to several biological processes, multivalent interactions mediated by reactive linkers confined to deformable substrates underpin the design of synthetic-biological platforms and advanced biomimetic materials. Here we review recent advances on the experimental study and theoretical modelling of a heterogeneous class of biomimetic systems in which synthetic linkers mediate multivalent interactions between fluid and deformable colloidal units, including lipid vesicles and emulsion droplets. Linkers are often prepared from synthetic DNA nanostructures, enabling full programmability of the thermodynamic and kinetic properties of their mutual interactions. The coupling of the statistical effects of multivalent interactions with substrate fluidity and deformability gives rise to a rich emerging phenomenology that, in the context of self-assembled soft materials, has been shown to produce exotic phase behaviour, stimuli-responsiveness, and kinetic programmability of the self-assembly process. Applications to (synthetic) biology will also be reviewed.

A Multi-Scale Approach to Membrane Remodeling Processes

We present a multi-scale simulation procedure to describe membrane-related biological processes that span over a wide range of length scales. At macroscopic length-scale, a membrane is described as a flexible thin film modeled by a dynamic triangulated surface with its spatial conformations governed by an elastic energy containing only a few model parameters. An implicit protein model allows us to include complex effects of membrane-protein interactions in the macroscopic description. The gist of this multi-scale approach is a scheme to calibrate the implicit protein model using finer scale simulation techniques e.g., all atom and coarse grain molecular dynamics. We previously used this approach and properly described the formation of membrane tubular invaginations upon binding of B-subunit of Shiga toxin. Here, we provide a perspective of our multi-scale approach, summarizing its main features and sketching possible routes for future development.

Entry modes of ellipsoidal nanoparticles on a membrane during clathrin-mediated endocytosis

The membrane wrapping and internalization of nanoparticles, such as viruses and drug nanocarriers, through clathrin-mediated endocytosis (CME) are vitally important for intracellular transport. During CME, the shape of the particle plays crucial roles in the determination of particle-membrane interactions, but much of the previous work has been focused on spherical particles. In this work, we develop a stochastic model to study the CME of ellipsoidal particles. In our model, the deformation of the membrane and wrapping of the nanoparticles are driven by the accumulation of clathrin lattices, which is stimulated by the ligand-receptor interactions. Using our model, we systematically investigate the effect of particle shape (ellipsoids with different aspect ratios) on the CME. Our results show three entry modes: tip-first, tilted, and laying-down modes, used by ellipsoidal nanoparticles for internalization depending on the aspect ratio. Certain ellipsoids are able to take multiple entry modes for internalization. Interestingly, the prolate ellipsoid with an aspect ratio of 0.42 can be internalized with a significantly reduced number of ligand-receptor bonds. Particles which can be internalized with fewer bonds are excellent candidates for transcellular drug delivery. Moreover, our results demonstrate that internalization of ellipsoids with intermediate aspect ratios is easier than that of particles with low and high aspect ratios. Our model and simulations provide critical mechanistic insights into CME of ellipsoidal particles, and represent a viable platform for optimal design of nanoparticles for targeted drug delivery applications.

Assembling responsive microgels at responsive lipid membranes

Directed colloidal self-assembly at fluid interfaces can have a large impact in the fields of nanotechnology, materials, and biomedical sciences. The ability to control interfacial self-assembly relies on the fine interplay between bulk and surface interactions. Here, we investigate the interfacial assembly of thermoresponsive microgels and lipogels at the surface of giant unilamellar vesicles (GUVs) consisting of phospholipids bilayers with different compositions. By altering the properties of the lipid membrane and the microgel particles, it is possible to control the adsorption/desorption processes as well as the organization and dynamics of the colloids at the vesicle surface. No translocation of the microgels and lipogels through the membrane was observed for any of the membrane compositions and temperatures investigated. The lipid membranes with fluid chains provide highly dynamic interfaces that can host and mediate long-range ordering into 2D hexagonal crystals. This is in clear contrast to the conditions when the membranes are composed of lipids with solid chains, where there is no crystalline arrangement, and most of the particles desorb from the membrane. Likewise, we show that in segregated membranes, the soft microgel colloids form closely packed 2D crystals on the fluid bilayer domains, while hardly any particles adhere to the more solid bilayer domains. These findings thus present an approach for selective and controlled colloidal assembly at lipid membranes, opening routes toward the development of tunable soft materials.

Density functional theory for the microscopic structure of nanoparticles at the liquid-liquid interface

We propose an extension of the density functional approach to study the structure and thermodynamic properties of a system comprising a certain amount of nanoparticles at the interface between two partially miscible liquids. Model calculations have been carried out for a binary symmetric mixture of Yukawa fluids and hard-sphere nanoparticles. Despite its simplicity, the model captures the principal features of this type of system. The results indicate that nanoparticles form layers and the number of layers depends on the amount of nanoparticles and on their diameters. For the systems studied the formation of the layers evidences strong localization of the nanoparticles at the interface.

Density functional approach to the description of the structure of dimer nanoparticles at liquid–liquid interfaces

A density functional approach to the description of the structure of dimer nanoparticles at liquid–liquid interfaces.

Capillary Interaction and Self-Assembly of Tilted Magnetic Ellipsoidal Particles at Liquid Interfaces

Magnetic ellipsoidal particles adsorbed at a liquid interface provide exciting opportunities for creating switchable functional materials, where self-assembly can be switched on and off using an external field [Davies et al., Adv. Mater., 2014, 26, 6715]. In order to gain a deeper understanding of this novel system in the presence of an external field, we study the capillary interaction and self-assembly of tilted ellipsoids using analytical theory and finite element simulations. We derive an analytical expression for the dipolar capillary interaction between tilted ellipsoids in elliptical polar coordinates, which exhibits a 1/r ² power law dependence in the far field (i.e., large particle separations r) and correctly captures the orientational dependence of the capillary interactions in the near field. Using this dipole potential and finite element simulations, we further analyze the energy landscape of particle clusters consisting of up to eight tilted ellipsoids in contact. For clusters of two particles, we find that the side-to-side configuration is stable, whereas the tip-to-tip configuration is unstable. However, for clusters of more than three particles, we find that circular loops of side-to-side particles become globally stable, whereas linear chains of side-to-side particles become metastable. Furthermore, the energy barrier for the linear-to-loop transition decreases with increasing particle number. Our results explain both thermodynamically and kinetically why tilted ellipsoids assemble side-to-side locally but have a strong tendency to form loops on larger length scales.

Simulating the interaction between a descending super-quadric solid object and a soap film

We investigate the interaction that occurs between a light solid object and a horizontal soap film of a ‘bamboo’ foam contained in a cylindrical tube. We vary the shape of the descending object from a sphere to a cube by changing a single shape parameter. We investigate in detail how the soap film deforms and determine the forces that the film exerts on the object, depending on the radius of the cylindrical tube, and the shape, orientation and position of the object. We show that a cubic particle in a particular orientation experiences the largest drag force, and that this orientation is also the most likely outcome of dropping a cube from an arbitrary orientation through a bamboo foam.

Aggregation of nanoparticles regulated by mechanical properties of nanoparticle-membrane system

The aggregation of nanoparticles (NPs) on the cell membrane is crucial for the cellular uptake process and has important biological implications in protein-membrane interactions. In this paper, we systematically investigate how the aggregation is regulated by the mechanical properties of the NP-membrane system, including the membrane tension, and the size and shape of the NPs. Results show that when NPs aggregate parallel to the cell membrane, increasing the membrane tension will modulate the membrane-mediated interaction between the NPs from attractive to attractive-repulsive and finally to purely repulsive. In contrast, the membrane-mediated interaction is attractive and independent of the membrane tension when the NPs aggregate to a tubular configuration. For the aggregation of NPs of different sizes, the large-size NP is wrapped to a greater extent than the small-size NP. For the aggregation of nonspherical NPs, low aspect ratio and weak NP-membrane adhesion strength lead to the side-to-side configuration, whereas a system with a high aspect ratio and strong NP-membrane adhesion strength prefers the tip-to-tip configuration. Importantly, NPs of different sizes and anisotropic shapes are found to facilitate the aggregation process by reducing the energy barrier that should be overcome during the aggregation. The results reveal the mechanism of the aggregation of NPs on the cell membrane and provide guidelines to the design of NP-based drug delivery systems.

Controlling Cargo Trafficking in Multicomponent Membranes

Biological membranes typically contain a large number of different components dispersed in small concentrations in the main membrane phase, including proteins, sugars, and lipids of varying geometrical properties. Most of these components do not bind the cargo. Here, we show that such "inert" components can be crucial for the precise control of cross-membrane trafficking. Using a statistical mechanics model and molecular dynamics simulations, we demonstrate that the presence of inert membrane components of small isotropic curvatures dramatically influences cargo endocytosis, even if the total spontaneous curvature of such a membrane remains unchanged. Curved lipids, such as cholesterol, as well as asymmetrically included proteins and tethered sugars can, therefore, actively participate in the control of the membrane trafficking of nanoscopic cargo. We find that even a low-level expression of curved inert membrane components can determine the membrane selectivity toward the cargo size and can be used to selectively target membranes of certain compositions. Our results suggest a robust and general method of controlling cargo trafficking by adjusting the membrane composition without needing to alter the concentration of receptors or the average membrane curvature. This study indicates that cells can prepare for any trafficking event by incorporating curved inert components in either of the membrane leaflets.

Detaching Microparticles from a Liquid Surface

The work required to detach microparticles from fluid interfaces depends on the shape of the liquid meniscus. However, measuring the capillary force on a single microparticle and simultaneously imaging the shape of the liquid meniscus has not yet been accomplished. To correlate force and shape, we combined a laser scanning confocal microscope with a colloidal probe setup. While moving a hydrophobic microsphere (radius 5-10  μm) in and out of a 2-5  μm thick glycerol film, we simultaneously measured the force and imaged the shape of the liquid meniscus. In this way we verified the fundamental equations [D. F. James, J. Fluid Mech. 63, 657 (1974)JFLSA70022-112010.1017/S0022112074002126; A. D. Scheludko, A. D. Nikolov, Colloid Polymer Sci. 253, 396 (1975)] that describe the adhesion of particles in flotation, deinking of paper, the stability of Pickering emulsions and particle-stabilized foams. Comparing experimental results with theory showed, however, that the receding contact angle has to be applied, which can be much lower than the static contact angle obtained right after jump in of the particle.