2D Phase Transition Research Articles

Long-wavelength fluctuations and the glass transition in two dimensions and three dimensions

Phase transitions significantly differ between 2D and 3D systems, but the influence of dimensionality on the glass transition is unresolved. We use microscopy to study colloidal systems as they approach their glass transitions at high concentrations and find differences between two dimensions and three dimensions. We find that, in two dimensions, particles can undergo large displacements without changing their position relative to their neighbors, in contrast with three dimensions. This is related to Mermin-Wagner long-wavelength fluctuations that influence phase transitions in two dimensions. However, when measuring particle motion only relative to their neighbors, two dimensions and three dimensions have similar behavior as the glass transition is approached, showing that the long-wavelength fluctuations do not cause a fundamental distinction between 2D and 3D glass transitions.

Design of Highly Stable Echogenic Microbubbles through Controlled Assembly of Their Hydrophobin Shell.

Dispersing hydrophobin HFBII under air saturated with perfluorohexane gas limits HFBII aggregation to nanometer-sizes. Critical basic findings include an unusual co-adsorption effect caused by the fluorocarbon gas, a strong acceleration of HFBII adsorption at the air/water interface, the incorporation of perfluorohexane into the interfacial film, the suppression of the fluid-to-solid 2D phase transition exhibited by HFBII monolayers under air, and a drastic change in film elasticity of both Gibbs and Langmuir films. As a result, perfluorohexane allows the formation of homogenous populations of spherical, narrowly dispersed, exceptionally stable, and echogenic microbubbles.

Design of Highly Stable Echogenic Microbubbles through Controlled Assembly of Their Hydrophobin Shell

AbstractDispersing hydrophobin HFBII under air saturated with perfluorohexane gas limits HFBII aggregation to nanometer‐sizes. Critical basic findings include an unusual co‐adsorption effect caused by the fluorocarbon gas, a strong acceleration of HFBII adsorption at the air/water interface, the incorporation of perfluorohexane into the interfacial film, the suppression of the fluid‐to‐solid 2D phase transition exhibited by HFBII monolayers under air, and a drastic change in film elasticity of both Gibbs and Langmuir films. As a result, perfluorohexane allows the formation of homogenous populations of spherical, narrowly dispersed, exceptionally stable, and echogenic microbubbles.

Adsorption of Formate on Au(111) in Acid Solution: Relevance for Electro-Oxidation of Formic Acid

The behavior of formic acid on Au(111) in perchloric acid solution at room temperature has been investigated by electrochemical methods and in situ scanning tunneling microscopy (STM) in the potential region negative to surface oxidation. Specific adsorption of formate lifts the reconstruction of the Au(111) surface. Currents for formate adsorption have been separated from those of formic acid oxidation by varying the sweep rate between 0.01 and 50 V s–1. A 2D phase transition within the formate layer adsorbed on long-range Au(111) terraces gives rise to a characteristic voltammetric needle-peak. Parallel chains of strongly bound formate have been imaged by in situ STM. Steady-state voltammetry at different formic acid concentrations shows a characteristic bell-shaped current maximum and a pronounced current jump related with the adlayer phase transition at more positive potentials. Oxidation kinetics of formic acid strongly depends on formate adsorption, which is determined by the electrode potential, th...

On the 2D-transition, hysteresis and thermodynamic equilibrium of Kr adsorption on a graphite surface

The adsorption and desorption of Kr on graphite at temperatures in the range 60–88K, was systematically investigated using a combination of several simulation techniques including: Grand Canonical Monte Carlo (GCMC), Canonical kinetic-Monte Carlo (C-kMC) and the Mid-Density Scheme (MDS). Particular emphasis was placed on the gas–solid, gas–liquid and liquid–solid 2D phase transitions. For temperatures below the bulk triple point, the transition from a 2D-liquid-like monolayer to a 2D-solid-like state is manifested as a sub-step in the isotherm. A further increase in the chemical potential leads to another rearrangement of the 2D-solid-like state from a disordered structure to an ordered structure that is signalled by (1) another sub-step in the monolayer region and (2) a spike in the plot of the isosteric heat versus density at loadings close to the dense monolayer coverage concentration. Whenever a 2D transition occurs in a grand canonical isotherm it is always associated with a hysteresis, a feature that is not widely recognised in the literature. We studied in details this hysteresis with the analysis of the canonical isotherm, obtained with C-kMC, which exhibits a van der Waals (vdW) type loop with a vertical segment in the middle. We complemented the hysteresis loop and the vdW curve with the analysis of the equilibrium transition obtained with the MDS, and found that the equilibrium transition coincides exactly with the vertical segment of the C-kMC isotherm, indicating the co-existence of two phases at equilibrium. We also analysed adsorption at higher layers and found that the 2D-coexistence is also observed, provided that the temperature is well below the triple point. Finally the 2D-critical temperatures were obtained for the first three layers and they are in good agreement with the experimental data in the literature.

Two-dimensional phase transition in a strongly nonideal dusty plasma

We consider the results of experimental observation of melting of a plasma-dust monolayer (2D phase transition) in a low-pressure gas discharge. Pair and bond-angular correlation functions as well as the number of topological defects in the monolayer are measured and analyzed. The change of profile of the bond-angular correlation functions confirms the existence of the solid-hexatic phase-liquid phase transition, which completely correlates with the Berezinskii-Kosterlitz-Thouless theory.

Evidence for magnetic (AF SDW) 2D-phase transition in doped ferropnictides and ferroselenides

The evidence for magnetic (AF SDW) 2D phase transition preceding a superconducting one (Tc < Tm) is presented for the plane of the FeAs(Se) layers of doped ferropnictides (-selenides). In contrast to the parent undoped compounds, the incommensurability of SDW and the lattice period leads to the formation of CDW with one-half wavelength. The magnetic phase (H-T) diagram of doped ferropnictides (-selenides) is characteristic of systems in which dielectric (e-h) and superconducting (e-e) pairings coexist.

Effective and accurate approach for modeling of commensurate-incommensurate transition in krypton monolayer on graphite.

Commensurate-incommensurate (C-IC) transition of krypton molecular layer on graphite received much attention in recent decades in theoretical and experimental researches. However, there still exists a possibility of generalization of the phenomenon from thermodynamic viewpoint on the basis of accurate molecular simulation. Recently, a new technique was developed for analysis of two-dimensional (2D) phase transitions in systems involving a crystalline phase, which is based on accounting for the effect of temperature and the chemical potential on the lattice constant of the 2D layer using the Gibbs-Duhem equation [E. A. Ustinov, J. Chem. Phys. 140, 074706 (2014)]. The technique has allowed for determination of phase diagrams of 2D argon layers on the uniform surface and in slit pores. This paper extends the developed methodology on systems accounting for the periodic modulation of the substrate potential. The main advantage of the developed approach is that it provides highly accurate evaluation of the chemical potential of crystalline layers, which allows reliable determination of temperature and other parameters of various 2D phase transitions. Applicability of the methodology is demonstrated on the krypton-graphite system. Analysis of phase diagram of the krypton molecular layer, thermodynamic functions of coexisting phases, and a method of prediction of adsorption isotherms is considered accounting for a compression of the graphite due to the krypton-carbon interaction. The temperature and heat of C-IC transition has been reliably determined for the gas-solid and solid-solid system.

Detection of 2D phase transitions at the electrode/electrolyte interface using electrochemical impedance spectroscopy

The capacitance of the electric double layer, CDL, formed at the electrode/electrolyte interface is generally determined by electrochemical impedance spectroscopy (EIS). However, CDL values obtained using EIS data often depend on the ac frequency of the potential perturbation used in EIS. The reasons for the observed frequency dispersions can be various, and hence extracting valuable information about the status of the electrified interface is not possible with the required certainty. In this work, using well-understood electrochemical systems, namely Pt(111) electrodes in contact with a series of acidic sulfate ions containing electrolytes, we provide strong evidence that 2D phase transitions in the adsorbate layers and, in general, structural effects at the electrode/electrolyte interface are in many cases responsible for the frequency dispersion of the double layer capacitance. These empirical findings open new opportunities for the detection and evaluation of 2D phase transition processes and other structural effects using EIS, even in presence of simultaneously occurring electrochemical processes. However, further theoretical elaboration of this effect is necessary.

Luminescence modulation in liquid crystalline phases containing a dispiro[fluorene-9,11′-indeno[1,2-b]fluorene-12′,9′′-fluorene] core

Luminescence modulations of a bulky dispiro[fluorene-9,11′-indeno[1,2-b]fluorene-12′,9′′-fluorene] (DSF-IF) core embedded in thermotropic liquid crystal phases.

Semimetal–superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having π-flux per plaquette. The reason for such a choice is that the π-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, tz), these Dirac points are unaltered: it is then possible to study the 3D–2D interpolation towards the π-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2D π-flux square lattice and the honeycomb geometry. We investigate by a mean-field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and half-filling, there is a quantum phase transition occurring at a critical (negative) interaction Uc presenting a linear critical exponent for the gap as a function of |U − Uc|. We show that in three dimensions, this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of tz.

The constant phase element reveals 2D phase transitions in adsorbate layers at the electrode/electrolyte interfaces

Using one of the most understood and well-characterized electrochemical systems, Pt(111) surface in contact with H2SO4, we provide evidences that specific adsorption, 2D phase transitions in the adsorbate layers and, in general, structural effects in the double layer are largely responsible for the so-called frequency dispersion of the double layer. The results also show promise that parameters of the constant phase element (which is used in impedance spectroscopy to account for the frequency dispersion) obtained as a function of the electrode potential can be reasonably used to detect 2D phase transitions at the electrode/electrolyte interfaces. This would provide a better insight into the interface, increasing the impact of measurements made by electrochemical impedance spectroscopy.

Pressure-Induced Order Transition in Nanodot-Forming Diblock Copolymers at the Air/Water Interface

Understanding and controlling the processes in block copolymer (BC) monolayers at the air/water interface during surface area compression is a key issue for producing ultrathin films of predetermined morphology with well-defined order and known dimensions. Langmuir isotherms of nanodot-forming BC monolayers generally display a plateau indicative of a 2D phase transition, which has been the subject of various interpretations in the literature. Here, based on investigations of Langmuir-Blodgett and Langmuir-Schaefer nanodot films of PS-P4VP mixed with 3-n-pentadecylphenol (PDP), we show by atomic force microscopy (AFM) that it involves a change in nanodot packing order (from quasi-hexagonal to quasi-square), argued to be a general phenomenon for nanodot BC monolayers. It is accompanied by system-specific conformational changes (as discussed in previous literature), which, in the present case, implicate PDP alkyl chain ordering, as deduced previously from in situ infrared data and indirectly supported here by AFM imaging.

On the Heat of Adsorption at Layering Transitions in Adsorption of Noble Gases and Nitrogen on Graphite

The isosteric heat versus loading of simple fluids (noble gases and nitrogen) adsorbed on a graphitic surface at a range of temperatures is investigated with GCMC simulations. At low temperatures (usually below the bulk triple point) the adsorption isotherms show a distinct 2D-phase transition in the first layer and possibly in higher layers and then has a more complex pattern. For densities less than the gaseous 2D-density, the heat increases linearly with loading. For loadings across the 2D-transition, the isosteric heat is constant, and when loadings are greater than the liquid-like density of the 2D-transition the isosteric heat again increases linearly with loading up to monolayer concentration, beyond which the isosteric heat decreases sharply, indicating the onset of adsorption into the second layer. Grand canonical Monte Carlo simulation shows that the constant heat observed in the 2D-transition is because of the increase in the number of clusters of similar size, rather than the increase in the cluster size. At very low temperature, a dense layer forms before the onset of the next layer and there is no heat spike in the plot of the isosteric heat versus loading because there are no gaps large enough in the dense layer for further addition of a particle. Moreover, there is no heat spike in these plots at high temperatures because of the increase in thermal motion of the molecules. Therefore, there is a narrow range of temperature from which we can see an isosteric heat spike, resulting from the squeezing of molecules into the lower layers, which increases both the solid-fluid interaction and the fluid-fluid interaction. We have found that the 2D-critical temperatures of the first three layers correlate well with the well depth of the fluid-fluid interaction, and interestingly the 2D-critical temperature of the third layer is between those of the first and second layers. © 2010 American Chemical Society.

Histogram of number of particles as an indicator for 2D phase transition in adsorption of gases on graphite

Grand canonical Monte Carlo simulation is used to study the adsorption of gases with strong and weak molecular interaction on graphite. We choose nitrogen adsorption at 77 K, ethylene at 104 K, methanol at 240 K and ammonia at 300 K as model examples. The adsorption mechanism of these species can be studied by analysing the radial distribution and the ‘number of particles histogram’ as a function of loading. At low pressures, at which the surface is barely covered with molecules, nitrogen and ethylene adsorb in a similar manner, while ammonia and methanol show a distinct difference because of the formation of clusters, resulted from the hydrogen bonding. Small clusters are observed for methanol and larger ones for ammonia, which is in agreement with the fact that hydrogen bonding is more significant in ammonia than in methanol. Analysis of the number of particles distribution can identify 2D phase transition as a sudden shift of the peak in the number histogram as exemplified with the adsorption of ethylene at 104 K and ammonia at 300 K.

Entropy Variation in the Two-dimensional Phase Transition of Anthracene Adsorbed at the Hg Electrode/Ethylene Glycol Solution Interface

The adsorption of anthracene (C14H10), at the mercury electrode/ethylene glycol (EG) solution interface, is characterized by a low and almost constant capacity (about 8 μF cm−2) region (capacitive “pit” or “plateau”) in capacity vs. potential curves, upon selection of suitable values of temperature, bulk concentration and applied potential values. This result is rationalized assuming the occurrence of a 2D phase transition between two distinct adsorbed phases: (i) a “disordered” phase, characterized by a flat “parallel” disposition of the aromatic moiety on the electrode surface (ii) an “ordered” phase, characterized by a “perpendicular” disposition of the aromatic moiety on the electrode surface. The experimental evidence is rationalized by considering the chemical potential as an explicit function of the “electric field/adsorbed molecule” interaction. Such a modelistic approach enables the determination of the relevant standard entropy variation.

The experimental realization of a two-dimensional colloidal model system

We present the technical details of an experimental method to realize a model system for two-dimensional (2D) phase transitions and the glass transition. The system consists of several hundred thousand colloidal superparamagnetic particles confined by gravity at a flat water-air interface of a pending water droplet where they are subjected to Brownian motion. The dipolar pair potential and, therefore, the system temperature are not only known precisely but also directly and instantaneously controllable via an external magnetic field H. In the case of a one-component system of monodisperse particles the system can crystallize upon application of H whereas in a two component system it undergoes a glass transition. Up to 10,000 particles are observed by video microscopy and image processing provides their trajectories on all relative length and time scales. The position of the interface is actively regulated thereby reducing surface fluctuations to less than 1 microm and the setup inclination is controlled to an accuracy of +/-1 murad. The sample quality being necessary to enable the experimental investigation of the 2D melting scenario, 2D crystallization, and the 2D glass transition, is discussed.

Molecular-Scale Investigation of Structural Changes in Cyclohexanethiol Self-Assembled Monolayers on Au(111)

Two-dimensional ordered structures of cyclohexanethiol (CHT) self-assembled monolayers (SAMs) on Au(111) formed from different solution concentrations were investigated using scanning tunneling microscopy (STM). Molecular-scale STM imaging clearly revealed the 2D phase transitions of CHT SAMs from a (2 x 4 square root of 2)R20 degrees structure to a (5 x 2 square root of 3)R35 degrees structure via a intermediate phase of a (5 x square root of 15)R25 degrees structure depending on solution concentration used for SAM fabrication. The (5 x 2 square root of 3)R35 degrees phase was observed for high concentrations, after deposition at low temperature or after long-time immersion. Based on these results, we confirmed that the molecular packing arrangement can be regarded as a fully covered SAM structure. In addition, 2D SAM formation of CHT SAMs is markedly different from that of alkanethiol SAMs, which is a result of structural dynamics of the CHT ring in the process of molecular self-assembly. The molecular-scale STM results for CHT SAMs on Au(111) can provide very useful information on understanding structural behaviors of cyclic thiol SAMs.

Unconventional spin freezing and fluctuations in the frustrated antiferromagnetNiGa2S4

Muon spin rotation $(\ensuremath{\mu}\text{SR})$ experiments reveal unconventional spin freezing and dynamics in the two-dimensional (2D) triangular lattice antiferromagnet ${\text{NiGa}}_{2}{\text{S}}_{4}$. Long-lived disordered Ni-spin freezing (correlation time $\ensuremath{\gtrsim}{10}^{\ensuremath{-}6}\text{ }\text{s}$ at 2 K) sets in below ${T}_{f}=8.5\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{K}$ with a mean-field-like temperature dependence. The observed exponential temperature dependence of the muon spin relaxation above ${T}_{f}$ is strong evidence for 2D critical spin fluctuations. Slow Ni-spin fluctuations coexist with quasistatic magnetism at low temperatures but are rapidly suppressed for fields $\ensuremath{\gtrsim}10\text{ }\text{mT}$, in marked contrast with the field-independent specific heat. The $\ensuremath{\mu}\text{SR}$ and bulk susceptibility data indicate a well-defined 2D phase transition at ${T}_{f}$, below which ${\text{NiGa}}_{2}{\text{S}}_{4}$ is neither a conventional magnet nor a singlet spin liquid.

On the anatomy of the adsorption heat versus loading as a function of temperature and adsorbate for a graphitic surface

In this paper we review and classify the various patterns of isosteric heat versus loading for adsorption of gases on graphitised thermal carbon black at temperatures ranging from below the 3D triple point to temperatures above it, but less than the 3D critical point. We have identified the features of heat curve and highlighted the microscopic origin of these features. The patterns vary with temperature and with the relative strength of the fluid–fluid interaction and solid–fluid interaction. For simple adsorptives (by simple we meant there is no strong association between fluid particles), the heat curve is typified by fluid–fluid attraction and layering phenomena. For adsorptives showing strong association such as water, ammonia and methanol, the heat curve essentially begins below the condensation heat and then approaches it as loading is increased. This is mainly due to the strong hydrogen bonding in these fluids. A third group includes adsorptives such as benzene, where the heat curve is constant in the sub-monolayer coverage region (but is higher than the condensation heat) and then drops off to the condensation heat when higher layers are formed. The constant heat in the sub-monolayer region is due to the balance between the energy factor (from fluid–fluid interaction) and entropy factor (due to re-orientation of adsorbed molecules). Our proposed classification is supported by detailed GCMC simulations of various gases that have been reported in the literature, and we supplement these with new results for the adsorption of xenon on graphite to investigate in more detail the change in heat pattern with temperature. Xenon is chosen because of its high fluid–fluid interaction, allowing us to study the 2D-phase transition in the first as well as higher layers.