Hard-core/soft shell (HCSS) particles have been shown to self-assemble into a remarkably rich variety of structures under compression due to the simple interplay between the hard-core and soft-shoulder length scales in their interactions. Most studies in this area model the soft shell interaction as a square shoulder potential. Although appealing from a theoretical point of view, the potential is physically unrealistic because there is no repulsive force in the soft shell regime, unlike in experimental HCSS systems. To make the model more realistic, here we consider HCSS particles with a range soft shell potential profiles beyond the standard square shoulder form and study the model using both minimum energy calculations and Monte Carlo simulations. We find that by tuning density and the soft shell profile, HCSS particles in the thin shell regime (i.e., shell to core ratio $r_1/r_0 \leq \sqrt{3}$) can form a large range of structures, including hexagons, chains, squares, rhomboids and two distinct zig-zag structures. Furthermore, by tuning the density and $r_1/r_0$, we find that HCSS particles with experimentally realistic linear ramp soft shoulder repulsions can form honeycombs and quasicrystals with 10-fold and 12-fold symmetry. Our study therefore suggests the exciting possibility of fabricating these exotic 2D structures experimentally through colloidal self-assembly.
A lattice model with soft repulsion followed by attraction is developed for a monolayer of hybrid core-shell particles self-assembling at an interface. The model is solved exactly in one dimension. One, two or three periodic structures and variety of shapes of the pressure-density isotherms may occur in different versions of the model. For strong interactions the isotherm consists of vertical segments separated by plateaus. The range of order depends strongly on the strength of attraction and on the density. Our results agree with experimental observations.
The influence of shape fluctuations on deformable thermosensitive microgels in aqueous solution is investigated by dynamic light scattering (DLS) and depolarized dynamic light scattering (DDLS). The systems under study consist of a solid core of polystyrene and a thermosensitive shell of cross-linked poly(N-isopropylacrylamide) (PNIPA) without and with embedded palladium nanoparticles. PNIPA is soluble in water, but has a lower critical solution temperature at 32 C (LCST). Below the LCST the PNIPA shell is swollen. Here we find that besides translational and rotational diffusion, the particles…
We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of hard-core--penetrable-shell particles. The shells are in general inhomogeneous and characterized by a radially-symmetrical, piecewise-continuous conductivity profile. The local value of the conductivity is determined by the shortest distance from the point of interest to the nearest particle. The effective conductivity is expressed in terms of the constituents'…
The optically induced oscillatory response of a spherical two-component, shell-core structured, nanoparticle by nodeless elastic vibrations of soft peripheral shell against hard and dynamically immobile inner core is considered. The eigenfrequencies of the even-parity, spheroidal and odd-parity torsional vibrational modes trapped in the finite-depth shell are obtained which are of practical interest for modal specification of individual resonances in spectra of resonant scattering of long wavelength electromagnetic waves by ultrafine particles.
We use numerical simulations to show how noninteracting hard particles binding to a deformable elastic shell may self-assemble into a variety of linear patterns. This is a result of the nontrivial elastic response to deformations of shells. The morphology of the patterns can be controlled by the mechanical properties of the surface, and can be fine-tuned by varying the binding energy of the particles. We also repeat our calculations for a fully flexible chain and find that the chain conformations follow patterns similar to those formed by the nanoparticles under analogous conditions. We propos…
Anisotropic, submicrometer sized particles are versatile systems providing interesting features in creating ordering in 2-dimensional systems. Combining hard ellipsoids with a soft shell further enhances the opportunities to trigger and control order and alignment. In this work, we report a rich 2D phase behavior and show how softness affects the ordering of anisotropic particles at fluid oil-water interfaces. Three different core-shell systems were synthesized such that they have the same elliptical hematite-silica core but differ with respect to thickness and stiffness of the soft microgel s…
Instability patterns of rolling up a sleeve appear more intricate than the ones of walking over a rug on floor, both characterized as uniaxially compressed soft-film/stiff-substrate systems. This can be explained by curvature effects. To investigate pattern transitions on a curved surface, we study a soft shell sliding on a rigid cylinder by experiments, computations and theoretical analyses. We reveal a novel post-buckling phenomenon involving multiple successive bifurcations: smooth-wrinkle-ridge-sagging transitions. The shell initially buckles into periodic axisymmetric wrinkles at the thre…
Molecular dynamics simulations and a stochastic Fokker-Planck equation based approach are used to illuminate how position-dependent solvent mobility near one or more tracer particle(s) is affected when tracer-solvent interactions are rationally modified to affect corresponding solvation structure. For tracers in a dense hard-sphere fluid, we compare two types of tracer-solvent interactions: (1) a hard-sphere-like interaction; and (2) a soft repulsion extending beyond the hard core designed via statistical mechanical theory to enhance tracer mobility at infinite dilution by suppressing coordina…
This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches do not need any numerical integration and so they are computationally more efficient. The formulation is designed for large deformations and allows for geometrical and material nonlinearities, which makes it very suitable for the modeling of soft tissues. Furthermore, six different isotropic and anisotropic material models, which are commonly used to model …
Micron-sized hard core-soft shell hybrid microgels are promising model systems for studies of soft matter as they enable in-situ optical investigations and their structures/morphologies can be engineered with a great variety. Yet, protocols that yield micron-sized core-shell microgels with a tailorable shell-to-core size ratio are rarely available. In this work, we report on the one-pot synthesis protocol for micron-sized silica-poly(N-isopropylacrylamide) core-shell microgels that has excellent control over the shell-to-core ratio. Small-angle light scattering and microscopy of 2- and 3-dimen…
Manipulating the shape of nanoscale objects in a controllable fashion is at the heart of designing materials that act as building blocks for self-assembly or serve as targeted drug delivery carriers. Inducing shape deformations by controlling external parameters is also an important way of designing biomimetic membranes. In this paper, we demonstrate that electrostatics can be used as a tool to manipulate the shape of soft, closed membranes by tuning environmental conditions such as the electrolyte concentration in the medium. Using a molecular dynamics-based simulated annealing procedure, we …
To explore dense packings of soft colloids, scattering experiments are ideal to access the structure factor. However, for soft microgels determination of the structure factor is difficult because of the low contrast of the polymer network and potential microgel interpenetration and deformation that change the form factor contribution. Here, we employ small-angle X-ray scattering (SAXS) to study soft, thermoresponsive microgels with poly-N-isopropylacrylamide (PNIPAM) shells and gold nanoparticle cores. The scattering of the gold cores dominates the scattering patterns and allows precise determ…
The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study th…
We study an elasticity model for compressed protein monolayers or particle rafts at a liquid interface. Based on the microscopic view of hard-core particles with soft shells, a bead-spring model is formulated and analyzed in terms of continuum elasticity theory. The theory can be applied, for example, to hydrophobin-coated air-water interfaces or, more generally, to liquid interfaces coated with an adsorbed monolayer of interacting hard-core particles. We derive constitutive relations for such particle rafts and describe the buckling of compressed planar liquid interfaces as well as their appa…
We study the (near or close to) ground state distribution of N softly repelling particles trapped in the interior of a spherical box. The charges mutually interact via an inverse power law potential of the form $1/r^γ$. We study three regimes in which the charges form an single spherical shell at the edge of the box ($γ=1$), a series of concentric shells of increasing density ($γ=2$) and $γ=12$ for which the charges form shells with a more uniform charge distribution. We conduct numerical simulations for clusters containing up to 5000 charges and compare charge density across the system with c…
The behavior of colloidal particles with a hard core and a soft shell has attracted the attention for researchers in the physical-chemistry interface not only due the large number of applications, but due the unique properties of these systems in bulk and at interfaces. The adsorption at the boundary of two phases can provide information about the molecular arrangement. In this way, we perform Langevin Dynamics simulations of polymer-grafted nanoparticles. We employed a recently obtained core-softened potential to analyze the relation between adsorption, structure and dynamic properties of the…
Triangular lattice models for pattern formation by hard-core soft-shell particles at interfaces are introduced and studied in order to determine the effect of the shell thickness and structure. In model I, we consider particles with hard-cores covered by shells of cross-linked polymeric chains. In model II, such inner shell is covered by a much softer outer shell. In both models, the hard cores can occupy sites of the triangular lattice, and nearest-neighbor repulsion following from overlapping shells is assumed. The capillary force is represented by the second- or the fifth neighbor attractio…
Unraveling the Mechanisms of Ultrasound-Induced Mechanical Degradation of Microgels: Effects of Mechanoresponsive Crosslinks, Softness, and Core-Shell Architecture
Heinrich-Heine University（海因里希·海涅大学）；DWI – Leibniz Institute for Interactive Materials（DWI–莱布尼茨交互材料研究所）；RWTH Aachen University（亚琛工业大学）；Lund University（隆德大学）
In this work, a two dimensional system of polymer grafted nanoparticles is analyzed using large-scale Langevin Dymanics simulations. Effective core-softened potentials were obtained for two cases: one where the polymers are free to rotate around the nanoparticle core and a second where the polymers are fixed, with a $45^\circ$ angle between them. The use of effective core-softened potentials allow us to explore the complete system phase space. In this way, the $PT$, $Tρ$ and $Pρ$ phase diagrams for each potential were obtained, with all fluid and solid phases. The phase boundaries were defined…
We investigate the conformation, position, and dynamics of core-shell nanoparticles (CSNPs) composed of a silica core encapsulated in a cross-linked poly-N-isopropylacrylamide shell at a water-oil interface for a systematic range of core sizes and shell thicknesses. We first present a free-energy model that we use to predict the CSNP wetting behavior at the interface as a function of its geometrical and compositional properties in the bulk phases, which gives good agreement with our experimental data. Remarkably, upon knowledge of the polymer shell deformability, the equilibrium particle posit…
Within an Onsager-like density functional theory we explore the thermodynamic and structural properties of an isotropic and nematic fluid of hard needle-like colloids in contact with a hard substrate coated with a soft short-ranged attractive or repulsive layer. As a function of the range and the strength of the soft interactions we find wetting and drying transitions, a pre-drying line, and a symmetry-breaking transition from uniaxial to biaxial in the wetting and drying film.
This study uses a combination of stochastic optimization, statistical mechanical theory, and molecular simulation to test the extent to which the long-time dynamics of a single tracer particle can be enhanced by rationally modifying its interactions--and hence static correlations--with the other particles of a dense fluid. Specifically, a simulated annealing strategy is introduced that, when coupled with test-particle calculations from an accurate density functional theory, finds interactions that maximize either the tracer's partial molar excess entropy or a related pair-correlation measure (…
The packing of hard spheres (HS) of diameter $σ$ in a cylinder has been used to model experimental systems, such as fullerenes in nanotubes and colloidal wire assembly. Finding the densest packings of HS under this type of confinement, however, grows increasingly complex with the cylinder diameter, $D$. Little is thus known about the densest achievable packings for $D>2.873σ$. In this work, we extend the identification of the packings up to $D=4.00σ$ by adapting Torquato-Jiao's adaptive-shrinking-cell formulation and sequential-linear-programming (SLP) technique. We identify 17 new structures,…
Microgels, cross-linked polymers with submicrometer size, are ideal soft model systems. While spherical microgels have been studied extensively, anisotropic microgels have been hardly investigated. In this study, we compare the interfacial deformation and assembly of anisotropic core-shell and hollow microgels. The core-shell microgel consists of an elliptical core of hematite covered with a thin silica layer and a thin shell made of PNiPAM. The hollow microgels were obtained after a two step etching procedure of the inorganic core. The behavior of these microgels at the oil-water interface wa…
We study the dynamical decay of the van Hove function of Brownian hard spheres using event-driven Brownian dynamics simulations and dynamic test particle theory. Relevant decays mechanisms include deconfinement of the self particle, decay of correlation shells, and shell drift. Comparison to results for the Lennard-Jones system indicates the generality of these mechanisms for dense overdamped liquids. We use dynamical density functional theory on the basis of the Rosenfeld functional with self interaction correction. Superadiabatic forces are analysed using a recent power functional approximat…
Short-time dynamics and high-frequency rheology for suspensions of non-overlapping core-shell particles with thin shells were analyzed. In the thin-shell limit, the single-particle scattering coefficients were derived and shown to define a unique effective radius. This result was used to justify theoretically (in the thin-shell limit) the accuracy of the annulus approximation with the inner radius equal to the effective hydrodynamic radius of the core-shell particle. The two-particle virial expansion of the translational & rotational self-diffusion, sedimentation and viscosity was performed. T…
We show how to incorporate the possibility of kinetic control in the conceptual Density Functional Theory formalism. This allow us to prove that the hard/soft acid/base principle will likely fail when the reactions are not thermodynamically-driven.
In this paper we consider different models for soft modes in jammed hard spheres. We show how one can construct mean field models that can be solved analytically. The analytic solution of these models displays an excess of low energy soft modes that become more and more localized by decreasing the energy. A simple solution of these models is found in the infinite dimensional limit.
