Domain-array melting in the dipolar lattice gas

Core-softened colloid under extreme geometrical confinement

Geometrical constraints offer a promising strategy for assembling colloidal crystal structures that are not typically observed in bulk or under 2D conditions. Core-softened colloids, in particular, have emerged as versatile chemical building blocks with applications across various scientific and technological areas. In this study, we investigate the behavior of a core-softened model confined between two parallel walls. Employing molecular dynamics simulations, we analyze the system's response under extreme confinement, where only one or two layers of colloids are permitted. The system comprises particles modeled by a ramp-like potential confined within slit nanoslits created by two flat, purely repulsive walls with a lateral side L separated by a distance Lz. Through a systematic analysis of the phase behavior as Lz increases, or as the system undergoes decompression, for different values of L, we identified a mono-to-bilayer transition associated with changes in the colloidal structure. In the monolayer regime, we observed solid phases at lower densities than those observed in the 2D case. Importantly, we demonstrated that confinement at specific Lz values, allowing particle arrangement into two layers, can lead to the emergence of the square phase, which was not observed under monolayer or 2D conditions. By correlating thermodynamic, translational, and orientational ordering, as well as the dynamics of this confined colloidal system, our findings offer valuable insights into the utilization of geometrical constraints to induce and manipulate structural changes.

Lattice-gas model of a charge regulated planar surface

In this work, we consider a lattice-gas model of charge regulation with electrostatic interactions within the Debye-Hückel level of approximation. In addition to long-range electrostatic interactions, the model incorporates the nearest-neighbor interactions for representing non-electrostatic forces between adsorbed ions. The Frumkin-Fowler-Guggenheim isotherm obtained from the mean-field analysis accurately reproduces the simulation data points.

Time-structuring in the evolution of 2D nanopatterns through interactions with substrate

Hydrophobic dodecanethiol capped gold nanoparticles (AuNPs) are found to self-assemble into two-dimensional patterns in monolayers of amphiphiles spread at the air-water interface of a Langmuir trough. In this communication we investigate the role of the nanoparticle-monolayer (FNMA) and monolayer-monolayer (FMMA) lipophilic attraction in influencing morphology and dynamics of AuNP cluster patterns in fatty acid monolayers. FNMA and FMMA are progressively varied by changing n, where n is the number of -CH2 groups in the alkyl tails of the amphiphilic fatty acid (CH3(CH2)nCOOH) molecules forming the monolayer. Compressibility measurements on the pristine and nanoparticle-laden monolayers show that, while the compressibility of the pristine monolayer decreases with increasing n, pointing to a progressive increase in FMMA, the effect of nanoparticles (increase in compressibility or lowering of FMMA) is discernible only for 14 < n < 22. The corresponding pattern morphology, observed with a Brewster Angle Microscope (BAM) at an in-plane resolution of 450 nm for 6 hours, reveals that there are essentially three stages in pattern evolution, lamellae of Au nanoclusters spread over the fatty-acid monolayer background (the λ state) followed by a network of nanoclusters with high node density (the ν state) and finally rings (circular/elongated) of random sizes with very low node density (the ρ state), evolving from an initial unsegregated state, without appreciable change in the average nanoparticle number density over the field of view. Increasing FNMA alongwith FMMA is found to shift a certain state to later times, thus playing the role of a viscous drag and introducing a delay in the timeline. The mean square fluctuation of BAM intensity remains flat and then decays as f(ξ) = ξ(2H) over smaller length scales, where ξ is the spatial separation and H the Hurst exponent. The study of f(ξ) over time reveals the growth of a sub-diffusive regime (H < 0.5) at the intermediate length scale, in almost all the films coinciding with the emergence of the ρ state. The growth of this sub-diffusive regime is slower for stronger FNMA and FMMA, the interactions thus acting as control parameters in dictating the time structure of the spatio-temporal patterns.

Critical behavior of a two-dimensional complex fluid: Macroscopic and mesoscopic views

Liquid disordered (L_{d}) to liquid ordered (L_{o}) phase transition in myristic acid [MyA, CH_{3}(CH_{2})_{12}COOH] Langmuir monolayers was studied macroscopically as well as mesoscopically to locate the critical point. Macroscopically, isotherms of the monolayer were obtained across the 20^{∘}C-38^{∘}C temperature (T) range and the critical point was estimated, primarily from the vanishing of the order parameter, at ≈38^{∘}C. Mesoscopically, domain morphology in the L_{d}-L_{o} coexistence regime was imaged using the technique of Brewster angle microscopy (BAM) as a function of T and the corresponding power spectral density function (PSDF) obtained. Monolayer morphology passed from stable circular domains and a sharp peak in PSDF to stable dendritic domains and a divergence of the correlation length as the critical point was approached from below. The critical point was found to be consistent at ≈38^{∘}C from both isotherm and BAM results. In the critical regime the scaling behavior of the transition followed the two-dimensional Ising model. Additionally, we obtained a precritical regime, over a temperature range of ≈8^{∘}C below T_{c}, characterized by fluctuations in the order parameter at the macroscopic scale and at the mesoscopic scale characterized by unstable domains of fingering or dendritic morphology as well as proliferation of a large number of small sized domains, multiple peaks in the power spectra, and a corresponding fluctuation in the peak q values with T. Further, while comparing temperature studies on an ensemble of MyA monolayers with those on a single monolayer, the system was found to be not strictly ergodic in that the ensemble development did not strictly match with the time development in the system. In particular, the critical temperature was found to be lowered in the latter. These results clearly show that the critical behavior in fatty acid monolayer phase transitions have features of both complex and nonequilibrium systems.

Labyrinthine instability in freely suspended films of a polarization-modulated smectic phase

We report on fingering and labyrinthine instabilities of the layer dislocation lines in freely suspended polar liquid-crystalline films. These polar fingerlike and labyrinth structures reversibly form upon a transition into a modulated phase. External electric fields of several kV/m applied in the film plane can reversibly influence the formation of the finger textures. We show that the labyrinthine pattern is intrinsically related to regular splay deformations of the polarization.

Reversible shape transition of pb islands on Cu(111)

Using low-energy electron microscopy, we have observed a reversible transition in the shape of Pb adatom and vacancy islands on Cu(111). With increasing temperature, circular islands become elongated in one direction. In previous work we have shown that surface stress domain patterns are observed in this system with a characteristic feature size which decreases with increasing temperature. We show that the island shape transition occurs when the ratio of the island size to this characteristic feature size reaches a particular value. The observed critical ratio matches the value expected from stress domains.

Patterns in melting snow and vapor deposited layers

We have observed a natural periodic pattern occurring in partially melted snow lying on the ground under certain atmospheric conditions. We explain this phenomenon quantitatively by considering heat flow through this layer coexisting in two phases (snow and water). Our model equations exhibit a range of patterns depending on the average density of snow. Strikingly similar patterns have been observed by Plass and co-workers in monolayer depositions of Pb on heated PbCu substrates. We argue that the physics of the two phenomena, differing in length scales by 7 orders of magnitude, is similar.

Thermal motion and energetics of self-assembled domain structures: Pb on Cu(111)

Low energy electron microscope measurements of the thermal motion of 50-200 nm diameter Pb islands on Cu(111) are used to establish the nature and determine the strength of interactions that give rise to self-assembly in this two-dimensional, two-phase system. The results show that self-assembled patterns arise from a temperature-independent surface stress difference of approximately 1.2 N/m between the two phases. With increasing Pb coverage, the domain patterns evolve in a manner consistent with models based on dipolar repulsions caused by elastic interactions due to a surface stress difference.

Computer simulations of a two-dimensional system with competing interactions

The results and methodology of large scale computer simulations of the two-dimensional dipolar Ising model with long-range interactions are reported. Systems as large as 117,649 particles were studied to elucidate the elementary excitations and phase diagram of two-dimensional systems, such as Langmuir monolayers, thin garnet films, and adsorbed films on solid surfaces, which spontaneously form patterns of stripes, bubbles, and intermediately shaped domains. The challenging numerical investigations of large scale systems with long-range interactions at low temperatures were made possible by combining the fast multipole method and a non-Metropolis Monte Carlo sampling technique. Our simulations provide evidence that, at sufficiently high ratios of the repulsive to the attractive coupling constant for the model, twofold stripe order in the systems of interest is lost through a defect-mediated mechanism. Heat capacity data and the excitations observed in our simulations as the system disorders indicate that it is most likely an instance of a Kosterlitz-Thouless phase transition. The results from simulations with and without external field are in excellent agreement with the predictions of an analytic scaling theory [A. D. Stoycheva and S. J. Singer, Phys. Rev. E 64, 016118 (2001)], confirming the phase diagram furnished by the analytic model. The scaling theory suggests that, under certain conditions, defect-mediated stripe melting may be supplanted by Ising like disordering within stripes for small repulsion strength. A qualitative discussion of a model that supports both disordering mechanisms is presented.

Nanostructures. Self-assembled domain patterns

The ordered domain patterns that form spontaneously in a wide variety of chemical and physical systems as a result of competing interatomic interactions can be used as templates for fabricating nanostructures. Here we describe a new self-assembling domain pattern on a solid surface that involves two surface structures of lead on copper. The evolution of the system agrees with theoretical predictions, enabling us to probe the interatomic force parameters that are crucial to the process.

Scaling theory for two-dimensional systems with competing interactions

We derive an analytic scaling theory for a two-dimensional system in which spontaneous patterns of stripes, bubbles, and intermediately shaped domains arise due to the competition of short-range attractions and long-range dipolar repulsions. The theory predicts temperature and domain-size scaling as a function of the relative repulsion strength eta, the ratio of the repulsive to the attractive coupling constant in the system's Hamiltonian. As eta decreases, the domain size explodes exponentially and the melting temperature for a system of ordered stripes increases. Our findings shed new light on the phase diagram and critical excitations for the dipolar Ising ferromagnet or lattice gas and their continuum analogs. We show that the features described by the scaling theory are insensitive to details like cutoffs for the dipolar interactions and, therefore, should be widely applicable. Our corresponding states analysis explains the experimentally observed stripe melting upon compression in a Langmuir monolayer. A phenomenological extension of the analytic scaling theory describes how the system's behavior is modified in the presence of magnetization or density fluctuations. Fluctuations are found to suppress domain size and the stripe melting temperature. In regimes where fluctuations are important, we predict that domain size will decrease with increasing temperature.

Stripe melting in a two-dimensional system with competing interactions

A model with competing short-ranged attractions and long-ranged repulsions that describes self-organized patterns in systems like Langmuir monolayers, magnetic films, and adsorbed monolayers is studied using numerical simulations and analytic theory. Simulations provide strong evidence confirming that the stripe phase order is destroyed in a defect unbinding transition. Large scale computer simulations are in agreement with an analytic scaling theory, which also predicts an eventual crossover from defect-mediated stripe melting to a spin-disordering (or particle-mixing) mechanism with decreasing repulsion strength.

Spontaneous patterning of quantum dots at the air-water interface

Nanoparticles deposited at the air-water interface are observed to form circular domains at low density and stripes at higher density. We interpret these patterns as equilibrium phenomena produced by a competition between an attraction and a longer-ranged repulsion. Computer simulations of a generic pair potential with attractive and repulsive parts of this kind, reproduce both the circular and stripe patterns. Such patterns have a potential use in nanoelectronic applications.

Domain Shapes and Patterns: The Phenomenology of Modulated Phases

A wide variety of two- and three-dimensional physical-chemical systems display domain patterns in equilibrium. The phenomenology of these patterns, and of the shapes of their constituent domains, is reviewed here from a point of view that interprets these patterns as a manifestation of modulated phases. These phases are stabilized by competing interactions and are characterized by periodic spatial variations of the pertinent order parameter, the corresponding modulation period generally displaying a dependence on temperature and other external fields. This simple picture provides a unifying framework to account for striking and substantial similarities revealed in the prevalent "stripe" and "bubble" morphologies as well as in commonly observed, characteristic domain-shape instabilities. Several areas of particular current interest are discussed.