The relevance of curvature-induced quadrupolar interactions in dipolar chain aggregation.

The aggregation of dipolar chains driven by thermal fluctuations in an external strong (electric or magnetic) field is investigated theoretically. We discover a new simple electrostatic mechanism that rationalizes the counter-intuitive lateral coalescence of dipolar chains. There, we first demonstrate that two bent dipolar chains can either attract or repel each other depending if they possess similar or opposite curvatures, respectively. Upon bending, dipolar chains become the siege of polarization-induced local charges that in turn lead to quadrupolar couplings. This striking feature is then exploited to understand our conducted Monte Carlo simulations at finite temperature where thermal fluctuations cause local curvatures in the formed dipolar chains. The related quadrupolar attractive mode with correlated chain-curvatures is clearly identified in the simulation snapshots. Our findings shed new light on a longstanding problem in soft matter and related areas.

Columnar dipolar clusters defying gravity.

A striking and highly versatile feature of magnetic (nano)particles is their ability to be manipulated at will at a distance by external fields. In this paper, the influence of gravity on the self-assembly of dipolar particles near a surface in the presence of a strong vertical magnetic field is investigated theoretically. A rich ground-state phase diagram stems from the effects of the number of particles N and gravity. Two distinct regimes are discovered for the gravity-mediated breakup of a standing chain. When N is small, there is a chain fragmentation (with two widely separated repulsive chain fragments) above a critical value for the gravity, whereas for higher chains, ribbonization (with two cohesive chain fragments) sets in. In both scenarios, simple algebraic decays for the transition gravity as a function of N are analytically predicted and accurately corroborate the exact numerical results. Further intricate chain fragmentations and internal ribbon transformations operate upon further increasing the gravity until all N constitutive particles lie on the surface. Our findings shed additional light on various recent experiments and computer simulations on magnetic colloids and granular media.

Magnetic dimer at a surface: Influence of gravity and external magnetic fields.

The interaction of two dipolar hard spheres near a surface and under the influence of gravity and external perpendicular magnetic fields is investigated theoretically. The full ground-state phase diagram as a function of gravity and magnetic field strengths is established. A dimer (i.e., two touching beads) can only exist when the gravity and magnetic field strengths are simultaneously not too large. Thereby, upon increasing the magnetic field strength, three dimeric states emerge: a lying state (dimer axis parallel to the substrate), an inclined state (intermediate state between the lying and standing ones) and a standing state (dimer axis normal to the substrate). It is found that the orientation angles of the dimer axis and the dipole moment in the newly discovered inclined phase are related by a strikingly simple Snell-Descartes-like law. We argue that our findings can be experimentally verified in colloidal and granular systems.

Helical Superstructure of Intermediate Filaments.

Intermediate filaments are the least explored among the large cytoskeletal elements. We show here that they display conformational anomalies in narrow microfluidic channels. Their unusual behavior can be understood as the consequence of a previously undetected, large-scale helically curved superstructure. Confinement in a channel orders the otherwise soft, strongly fluctuating helical filaments and enhances their structural correlations, giving rise to experimentally detectable, strongly oscillating tangent correlation functions. We propose an explanation for the detected intrinsic curving phenomenon-an elastic shape instability that we call autocoiling. The mechanism involves self-induced filament buckling via a surface stress located at the outside of the cross section. The results agree with ultrastructural findings and rationalize for the commonly observed looped intermediate filament shapes. Beyond curvature, explaining the molecular origin of the detected helical torsion remains an interesting challenge.

Ordering of sedimenting paramagnetic colloids in a monolayer.

Sedimentation enables self-assembly of colloidal particles into crystalline structures, as needed for catalysis or photonics applications. Here we combine experiments, theory, and simulations to investigate the equilibrium structure of a colloidal monolayer with tunable interparticle repulsion via an applied external magnetic field. Experimental observations of the equilibrium structure are in excellent agreement with density functional theory. Within a (zero-temperature) local density approximation, we derive a simple analytical expression that quantitatively captures the inhomogeneous ordering ranging from solid to liquidlike states. Monte Carlo simulations corroborate these findings and explore an even wider range of sedimentation conditions, thus providing a global view of the sedimentation-mediated ordering in colloidal monolayers with tunable long-ranged interparticle repulsions. Our findings shed further light on the classical sedimentation problem in colloidal science and related areas.

Dipolar Crystals: The Crucial Role of the Clinohexagonal Prism Phase.

We report a new phase called clinohexagonal prism (CHP) that accounts for all the ground states of dipolar hard spheres prepared at any density. This phase merely consists of an oblique prismatic lattice with a hexagonal base. Our calculations show that at intermediate densities, a special close packed body-centered orthorhombic phase coincides with the CHP phase in the ground state for a wide density window. In the high packing regime, i.e., in the vicinity of the density of the hexagonal close packed phase, it is a limiting case of the CHP phase with vanishing obliquity that emerges. These findings provide a unified and clarified view of the solid-solid transitions occurring at zero temperature in dipolar systems and should be relevant in other related molecular or soft matter systems governed by anisotropic (and possibly isotropic) soft potentials.

On the interaction of dipolar filaments.

The interactions of dipolar filaments such as magnetic needles and chains in strong homogeneous magnetic/electric field are investigated theoretically. Revisiting the case of uniformly magnetized/polarized parallel needles of finite size L and separated by a distance R , all the relevant regimes of attraction and/or repulsion are properly addressed and discussed. At short inter-needle separation ( R/L ≲ 0.2, the repuive pair potential of two facing needles is governed by R(-1) in strong contrast with R(-3) at long separations (R/L ≳ 2.5). This softening is attributed to an efficient long-range screening owing to the relatively long needle extension in this regime. This whole understanding of dipolar needles effective interaction is then used to grasp that of dipolar chains made up of spherical dipolar beads. When excluded-volume correlations are weak (i.e., the chains are a few beads apart), chains and needles possess virtually the same effective interaction. However, at short separation there is a remarkable hardening upon approaching two chains in registry in qualitative contrast to the needles case.

Structure and cohesive energy of dipolar helices.

This paper deals with the investigation of cohesive energy in dipolar helices made up of hard spheres. Such tubular helical structures are ubiquitous objects in biological systems. We observe a complex dependence of cohesive energy on surface packing fraction and dipole moment distribution. As far as single helices are concerned, the lowest cohesive energy is achieved at the highest surface packing fraction. Besides, a striking non-monotonic behavior is reported for the cohesive energy as a function of the surface packing fraction. For multiple helices, we discover a new phase, exhibiting markedly higher cohesive energy. This phase is referred to as ZZ tube consisting of stacked crown rings (reminiscent of a pile of zig-zag rings), resulting in a local triangular arrangement with densely packed filaments parallel to the tube axis.

Quantitatively mimicking wet colloidal suspensions with dry granular media.

Athermal two-dimensional granular systems are exposed to external mechanical noise leading to Brownian-like motion. Using tunable repulsive interparticle interaction, it is shown that the same microstructure as that observed in colloidal suspensions can be quantitatively recovered at a macroscopic scale. To that end, experiments on granular and colloidal systems made up of magnetized particles as well as computer simulations are performed and compared. Excellent agreement throughout the range of the magnetic coupling parameter is found for the pair distribution as well as the bond-orientational correlation functions. This finding opens new ways to efficiently and very conveniently explore phase transitions, crystallization, nucleation, etc in confined geometries.

Reply to "Comment on 'Self-assembly of magnetic balls: From chains to tubes' ".

The authors of the Comment [Phys. Rev. E 91, 057201 (2015)] propose compact round clusters as, energetically, better candidates than stacked rings found in Messina et al. [Phys. Rev. E 89, 011202 (2014)] (forming open tubes) at a pretty large number of constitutive magnets, typically for N≳1300. Our new findings show that elongated rodlike structures can even outmatch the reported structures in Friedrich et al. [Phys. Rev. E 91, 057201 (2015)] and in Messina et al. [Phys. Rev. E 89, 011202 (2014)] from typically N≳460.

Self-assembly of magnetic balls: from chains to tubes.

The self-assembly of spherical magnets (magnetic balls) is addressed theoretically. Minimal energy structures are obtained by optimization procedures as well as Monte Carlo computer simulations. Three typical shapes are obtained depending on the number of constitutive magnets N. In the regime of small N, chains are stable as dimers or trimers (i.e., N≤3), then rings become stable for (4≤N≤13) where dipole vectors adopt a vortexlike arrangement. A major finding concerns the stacking of rings as soon as N is large enough (N≥14). The number of stacked rings is found to increase as N^{2/3}, leading to a tubular structure at large N. All the relevant predicted shapes are experimentally reproduced by manipulating millimetric magnets.

Packing confined hard spheres denser with adaptive prism phases.

We show that hard spheres confined between two parallel hard plates pack denser with periodic adaptive prismatic structures which are composed of alternating prisms of spheres. The internal structure of the prisms adapts to the slit height which results in close packings for a range of plate separations, just above the distance where three intersecting square layers fit exactly between the plates. The adaptive prism phases are also observed in real-space experiments on confined sterically stabilized colloids and in Monte Carlo simulations at finite pressure.

Soft repulsive mixtures under gravity: brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking.

A binary mixture of particles interacting via long-ranged repulsive forces is studied in gravity by computer simulation and theory. The more repulsive A-particles create a depletion zone of less repulsive B-particles around them reminiscent to a bubble. Applying Archimedes' principle effectively to this bubble, an A-particle can be lifted in a fluid background of B-particles. This "depletion bubble" mechanism explains and predicts a brazil-nut effect where the heavier A-particles float on top of the lighter B-particles. It also implies an effective attraction of an A-particle towards a hard container bottom wall which leads to boundary layering of A-particles. Additionally, we have studied a periodic inversion of gravity causing perpetuous mutual penetration of the mixture in a slit geometry. In this nonequilibrium case of time-dependent gravity, the boundary layering persists. Our results are based on computer simulations and density functional theory of a two-dimensional binary mixture of colloidal repulsive dipoles. The predicted effects also occur for other long-ranged repulsive interactions and in three spatial dimensions. They are therefore verifiable in settling experiments on dipolar or charged colloidal mixtures as well as in charged granulates and dusty plasmas.

Statistics of polymer adsorption under shear flow.

Using nonequilibrium Brownian dynamics computer simulations, we have investigated the steady state statistics of a polymer chain under three different shear environments: (i) linear shear flow in the bulk (no interfaces), (ii) shear vorticity normal to the adsorbing interface, and (iii) shear gradient normal to the adsorbing interface. The statistical distribution of the chain end-to-end distance and its orientational angles are calculated within our computer simulations. Over a wide range of shear rates, this distribution can be mapped onto a simple theoretical finite-extensible-nonlinear-elastic dumbbell model with fitted anisotropic effective spring constants. The tails of the angular distribution functions are consistent with scaling predictions borrowed from the bulk dumbbell model. Finally, the frequency of the characteristic periodic tumbling motion has been investigated by simulation as well and was found to be sublinear with the shear rate for the three setups, which extends earlier results done in experiments and simulations for free and tethered polymer molecules without adsorption.

Ultrafast quenching of binary colloidal suspensions in an external magnetic field.

An ultrafast quench is applied to binary mixtures of superparamagnetic colloidal particles confined at a two-dimensional water-air interface by a sudden increase of an external magnetic field. This quench realizes a virtually instantaneous cooling which is impossible in molecular systems. Using real-space experiments, the relaxation behavior after the quench is explored. Local crystallites with triangular and square symmetry are formed on different time scales, and the correlation peak amplitude of the small particles evolves nonmonotonically in time in agreement with Brownian dynamics computer simulations.

Electrostatics in soft matter.

Recent progress in understanding the effect of electrostatics in soft matter is presented. A vast number of materials contain ions, ranging from the molecular scale (e.g. electrolyte) to the meso/macroscopic one (e.g. charged colloidal particles or polyelectrolytes). Their (micro)structure and physico-chemical properties are especially dictated by the famous and redoubtable long-ranged Coulomb interaction. In particular, theoretical and simulational aspects, including the experimental motivations, will be discussed.

Binary crystals in two-dimensional two-component Yukawa mixtures.

The zero-temperature phase diagram of binary mixtures of like-charge particles interacting via a screened Coulomb pair potential is calculated as a function of composition and charge ratio. The potential energy obtained by a Lekner summation is minimized among a variety of candidate two-dimensional crystals. A wealth of different stable crystal structures is identified including A, B, AB(2), A(2)B, and AB(4) structures [A (B) particles correspond to large (small) charge.] Their elementary cells consist of triangular, square, or rhombic lattices of the A particles with a basis comprising various structures of A and B particles. For small charge asymmetry there are no intermediate crystals besides the pure A and B triangular crystals. The predicted structures are detectable in experiments on confined mixtures of like-charge colloids or dusty plasma sheets.

Macroion adsorption: the crucial role of excluded volume and co-ions.

The adsorption of charged colloids (macroions) onto an oppositely charged planar substrate is investigated theoretically. Taking properly into account the finite size of the macroions, unusual behaviors are reported. It is found that the role of the co-ions (the little salt-ions carrying the same sign of charge as that of the substrate) is crucial in understanding the mechanisms involved in the process of macroion adsorption. In particular, the co-ions can accumulate near the substrate's surface and lead to a counterintuitive surface charge amplification.

Confined colloidal bilayers under shear: steady state and relaxation back to equilibrium.

Crystalline bilayers of charged colloidal suspensions which are confined between two parallel plates and sheared via a relative motion of the two plates are studied by extensive Brownian dynamics computer simulations. The charge-stabilized suspension is modeled by a Yukawa pair potential. The unsheared equilibrium configuration is two crystalline layers with a nested quadratic in-plane structure. For increasing shear rates (.)gamma, we find the following steady states: First, up to a threshold of the shear rate, there is a static solid which is elastically sheared. Above the threshold, there are two crystalline layers sliding on top of each other with a registration procedure. Higher shear rates melt the crystalline bilayers and even higher shear rates lead to a reentrant solid stratified in the shear direction. This qualitative scenario is similar to that found in previous bulk simulations. We have then studied the relaxation of the sheared steady state back to equilibrium after an instantaneous cessation of shear and found a nonmonotonic behavior of the typical relaxation time as a function of the shear rate (.)gamma. In particular, application of high shear rates accelerates the relaxation back to equilibrium since shear-ordering facilitates the growth of the equilibrium crystal. This mechanism can be used to grow defect-free colloidal crystals from strongly sheared suspensions. Our theoretical predictions can be verified in real-space experiments of strongly confined charged suspensions.

Behavior of rodlike polyelectrolytes near an oppositely charged surface.

The behavior of highly charged short rodlike polyelectrolytes near oppositely charged planar surfaces is investigated by means of Monte Carlo simulations. A detailed microstructural study, including monomer and fluid charge distributions and chain orientation, is provided. The influence of chain length, substrate's surface-charge density, and image forces is considered. Due to the lower chain entropy (compared to flexible chains), our simulation data show that rodlike polyelectrolytes can, in general, better adsorb than flexible ones do. Nonetheless, at low substrate-dielectric constant, it is found that repulsive image forces tend to significantly reduce this discrepancy.