2D Phase Transition Research Articles

Isotope effects and the manifestation of 2D phase transitions in the kinetics of low-temperature (down to 5 K) hydrogen adsorption

The adsorption–desorption characteristics of hydrogen isotopes on the (110) surfaces of W and Mo are investigated at a temperature Ts∼5 K. It is found that the characteristics for hydrogen and deuterium are very different. Isothermal desorption from W(110) at Ts∼5 K is observed in the case of H2, while that of D2 is practically absent. The desorption of H2 is suppressed as the flux of molecules to the surface increases; this, in the opinion of the authors, is a consequence of phase transition from a 2D gas to a 2D condensate. The initial sticking probability of H2 on W(110) depends strongly on the flux, while that of D2 is nearly independent of flux; in the H2 case this is explained by the formation of nuclei of the 2D condensed phase during the lifetime of the molecule in the precursor state. In the case of H2 adsorption on Mo(110) a sharp and deep minimum is observed in the dependence of the sticking probability on the coverage, which is absent in the case of D2. These isotope effects are explained by the deeper position of the levels of the zero-point vibrations of the heavier molecule D2.

Electrochemistry of Langmuir–Blodgett and self-organized monolayers of an azocrown ether, both pure and mixed with a phospholipid

The electrochemical behavior of monolayers of an azocrown ether (L16), both pure and mixed with dioleoylphosphatidylcholine (DOPC) was investigated using a mercury electrode. The monolayers formed at the air ∣ water interface were transferred onto the electrode using the Langmuir–Blodgett approach. The reversibility of the electrode processes depends on the surface pressure during the transfer of the monolayer. The reduction mechanism of the azo to the hydrazo group was studied in acidic medium by cyclic voltammetry and potential-step chronocoulometry. The dependence of the faradaic charge due to azo group reduction at constant pH upon scan rate (for voltammetry) or upon electrolysis time (for chronocoulometry) was examined on the basis of a general kinetic approach. The same approach was used to interpret the dependence of the faradaic charge upon pH at constant scan rate or electrolysis time. The reduction of the azo to the hydrazo group takes place via the reversible uptake of one electron, followed by the rate determining protonation of the resulting radical anion. When L16 is in the form of a pure monolayer its electroreduction is accompanied by a 2D phase transition involving the passage from a liquid-like to a solid-like structure. No such phase transition is observed in mixed L16–DOPC monolayers. At intermediate compositions of this mixture, strong attractive interactions between L16 and DOPC molecules decrease the mean area per molecule with respect to the ideal behavior at the air ∣ water interface, and prevent complete electroreduction of the L16 molecules in the monolayer.

Structural and thermodynamic characteristics of natural marine films derived from force–area studies

Natural marine film experiments in shallow offshore waters of the Baltic and Mediterranean Seas were carried out over the period 1990–1996 under calm sea conditions using a novel device for sampling and force–area studies. The sampler-Langmuir trough-Wilhelmy filter paper plate system ‘cuts out’ an undisturbed film-covered sea area (8 cm thick) to perform π– A studies without any initial physico-chemical sample processing. The limiting specific area A lim (268–3157 Å 2 per molecule) and mean molecular weight (0.65–9.7 kDa) of microlayer surfactants were determined from the 2D virial equation of state applied to the isotherms. The π – A isotherms recorded in the temperature range 5–35°C exhibited several plateaus and ‘kinks’ corresponding to 2D phase transitions that allowed for the first time completing the phase diagram ( π– T) of natural films. Enthalpy Δ H and entropy Δ S t of the first-order phase transitions (G → LE → LC) were evaluated using the Clausius–Clapeyron equation applied to the isotherms. Additional information on the film structure were derived from the entropy change Δ S c attributed to the π – A hysteresis, and the polymer film scaling theory adopted to marine films. The results obtained suggest that natural films are a complex mixture of biomolecules covering a wide range of solubilities, surface activity and molecular weight with an apparent structural organisation.

New vortex-matter size effect observed in Bi(2)Sr(2)CaCu(2)O(8 + delta).

The vortex-matter 3D to 2D phase transition is studied in micron-sized Bi(2)Sr(2)CaCu(2)O(8 + delta) single crystals using local Hall magnetization measurements. At a given temperature, the second magnetization peak, the signature of a possible 3D--2D vortex phase transition, disappears for samples smaller than a critical length. We suggest that this critical length should be equated with the 2D vortex lattice ab-plane correlation length R(2D)(c). The magnitude and temperature dependence of R(2D)(c) agree well with Larkin-Ovchinnikov collective pinning theory.

Viscoelastic Behavior of 1-Dodecanol Monolayers Undergoing a Liquid−Solid Phase Transition. A Surface Quasielastic Light Scattering Study

A surface quasielastic light scattering (SQELS) and electrocapillary wave (ECW) study of a monolayer of 1-dodecanol, obtained by placing a reservoir drop of the alcohol on top of a water surface, has been carried out as a function of temperature at different wavevectors. This monolayer goes through a liquid−solid phase transition at 312.1 K, more than 14 K above the freezing of bulk 1-dodecanol. The fit of the SQELS spectra gives the frequency, ωc, and the temporal damping, Δωc, of thermally induced capillary waves. In all the temperature range ωc follows Kelvin-like behavior (i.e., ωc ∼ q3/2) leading to values of the apparent dynamic surface tension lower than the static ones. In addition the damping follows, Δωc ∼ q1.2-1.4 very far from the expected ∼q2 dispersion behavior. Both wave parameters show temperature trends compatible with the expected liquid−solid 2D phase transition at around 312 K. The expansion of the frequency range by using the ECW technique, shows that our experimental results cover the regions q ≤ qR ≤ q, where qR is the wavevector at which capillary-dilational resonance takes place. Within the classical elasto-hydrodynamic theory, our results can be accounted for if the dilational viscosity, κ, takes a negative sign. In these conditions mode mixing takes place for q ≥ qR. Alternatively the experimental results can be quantitatively explained with κ = 0 if an extra hydrodynamic coupling is included in the dispersion equation. From a physicochemical point of view this coupling may arise from the vicinity of the phase transition and/or molecular orientational effects promoted by the dilational wave. The small values of the dynamic elasticity, ε(ω), found in this work can be rationalized in terms of a monolayer−subsurface material transport, within the Lucassen−Van de Tempel model.

2D Phase Transitions in Langmuir Monolayers of the Aromatic 4‘,5‘-Diphenyl-1,1‘:3‘,1‘ ‘-terphenyl-4-carboxylic Acid

Langmuir monolayers of 4‘,5‘-diphenyl-1,1‘:3‘,1‘ ‘-terphenyl-4-carboxylic acid (in short DTCA) were studied under different experimental conditions. The π−A isotherms displayed a broad plateau on a pure water subphase and two plateaus on a neutral aqueous subphase containing Cd2+ ions. DTCA monolayers were transferred as LB multilayer films and characterized by FTIR, X-ray diffraction, and electric surface potential measurements. From the analysis of surface potentials for LB films transferred at surface pressures corresponding to different parts of the π−A isotherm it was possible to infer that molecular orientational changes are the probable cause for the plateau in the isotherm.

Modeling analysis of molecular chiral effect detected by Maxwell-displacement-current measurements

Based on Maxwell displacement current (MDC) and surface pressure measurements by monolayer compression, the physicochemical properties of chiral and racemic phospholipid [α-phosphatidylcholine dipalmitoyl (DPPC)] monolayers at the air–water interface were investigated. It was found that at a temperature of 20 °C, the chiral and racemic phospholipid monolayers exhibited similar pressure-area isotherms with a pressure plateau between 65 and 85 Å2, usually attributed to the two-dimensional (2D) phase transition from expanded monolayer to condensed one. Nevertheless, with MDC measurement some critical peaks in the 2D pressure plateau region with different amplitude and sign were detected related to the chirality of the phospholipid samples. This result clearly demonstrates that microscopic chirality affects the electrical properties of monolayers. To investigate the chiral effect theoretically, a twist-conformation molecular model was raised by a modification of the simple rodlike model and biaxial rodlike model, which were developed in our previous work. The analysis based on this modified model reveals that the monolayer properties, especially the MDC behavior by compression, are profoundly influenced by the chirality of molecules.

Spin-phonon interaction in thin magnetic films

The interaction between a ferromagnetic monolayer and nonmagnetic substrate is investigated. The characteristic dimension of superstructure arising in a film is estimated. New types of surface magnetoelastic waves are obtained near the 2D phase transition of a homogeneous magnetic state to the state with surface superstructure.

Pattern formation and chiral phase separation by compression: Racemic monolayer viewed as Bragg-Williams binary cholesterics

In nature, it is so abundant that the two molecular enantiomers of left- and right-handed chirality usually combine to form a racemic dimer. The means of separation of the dimers into distinct phases of optical activity, the chiral phase separation ~CPS!, are of critical importance in physics, chemistry, biology, and geology @1#, and have been realized through experiments going back to Pasteur in 1848 in isolation of enantiomers of sodium tartrate by crystallization @2#, and to Jungfleish in 1882 in the localization of crystallization of individual enantiomers on suitably disposed seeds @3#. However, the major challenge in the study is, on the theoretical side, to understand the mechanism of chiral symmetry breaking ~CSB! in CPS. The study of CPS in the threedimensional ~3D! state is especially difficult because both left- and right-handed chiral molecules have been classically regarded as exact mirror images and, therefore, are energetically equivalent in bulk due to the molecular rotation. It is natural to think that this difficulty may be reduced in a monolayer of racemic amphiphiles at the air/water interface, because the molecular rotation of the amphiphiles is limited due to the hydrophobic interaction between the amphiphiles and the water. In fact, a remarkable progress of the study in a 2D system was performed by Lundquist in the 1960s @4#. Recognizing the importance of steric factors in the living system, such as in the architecture of the lipoprotein membranes of cells, Lundquist found that at a temperature below 20 °C the racemic monolayer of the methyl ester of 2-methylhexacosanoic acid shows a pressure plateau in each pressure-area isotherm. This was interpreted as a 2D phase transition region, from the expanded phase to the condensed 2D crystalline phase. At that time, however, there were no methods available for the direct crystallographic study for the crystalline phase. In 1993, a significant advance was made by Eckhardt et al. @5#. By transferring such a monolayer of surface pressure from a water surface onto mica, and using atomic-force microscopy, they detected that the phase transition at the region of small molecular areas is a CPS transition, specifically a transition from rectangular lattices of a molecular packing structure ~racemic phase! into a chiral phase in which the enantiomers form two antipodal oblique lattices distinguished by some stripes ~see Figs. 1‐4 in @5#!. In physics, the CSB and stripe formation have been extensively studied in hexatic liquid-crystal ~LC! films @6#,

Replica Ornstein-Zernike equations and the structure of a simple fluid mixture in disordered porous media: application to a composite monomolecular adlayer

A two-dimensional (2D) model for a simple fluid mixture, consisting of spherical particles with different diameters that is adsorbed on a disordered porous medium, i.e., in a plane claiming hard discs in a frozen configuration, is studied by means of replica Ornstein–Zernike equations. The hypernetted chain and Percus–Yevick approximations are used. The structural and thermodynamic properties of the composite monomolecular adlayer are addressed, and the density and composition of the monolayer and their dependence on the presence of a disordered quenched 2D matrix in the plane of absorption at a fixed chemical potential is examined. It is shown that porous 2D media exhibit the effect of selectivity. The concentration of the smaller particles is larger on the porous media compared with the bulk phase. The model and methodology can be extended to study phase transitions in 2D partly quenched systems.

Replica Ornstein-Zernike equations and the structure of a simple fluid mixture in disordered porous media: application to a composite monomolecular adlayer

A two-dimensional (2D) model for a simple fluid mixture, consisting of spherical particles with different diameters that is adsorbed on a disordered porous medium, i.e., in a plane claiming hard discs in a frozen configuration, is studied by means of replica Ornstein–Zernike equations. The hypernetted chain and Percus–Yevick approximations are used. The structural and thermodynamic properties of the composite monomolecular adlayer are addressed, and the density and composition of the monolayer and their dependence on the presence of a disordered quenched 2D matrix in the plane of absorption at a fixed chemical potential is examined. It is shown that porous 2D media exhibit the effect of selectivity. The concentration of the smaller particles is larger on the porous media compared with the bulk phase. The model and methodology can be extended to study phase transitions in 2D partly quenched systems.

Methane adsorption on dichloromethane preplated graphite: 2D phase transitions on dual surfaces

Adsorbing increasing amounts of methane (CH 4) at 80 K on graphite preplated with one monolayer of dichloromethane (CH 2Cl 2) results in a succession of transitions: partial displacement of the preadsorbed film and replacement by a CH 4 monolayer; incorporation of CH 4 in the remaining CH 2Cl 2 patches so as to form a 2D solution; alternate layer-by-layer condensation on the resulting dual surface. When CH 2Cl 2 preplating is in the submonolayer range, CH 4 monolayer condensation occurs first on the bare part of the surface. When the graphite surface is saturated with CH 2Cl 2 the displacement is suppressed.

On the formation and dissolution kinetics of two-dimensional uracil ordered phases at the gold single crystal electrode-aqueous solution interface

The adsorption of uracil on Au(111) from a 0.5 M NaF electrolyte solution is characterized by the formation of various films delimited by 2D phase transitions. The kinetics of the interfacial rearrangements were investigated by means of current and charge transients using the potential step technique. The transients associated with the formation of the condensed physisorbed layer from an adsorbate free initial state can be well described by a model involving a three-stage process. The first part of the relaxation curves corresponds to the concomitant charging of the initial double layer capacitance and the fast adsorption of the surfactant. The remaining peaked current curves are analyzed in terms of the growth of pre-existing nuclei which at long times becomes diffusion limited. When the initial film is composed of chemisorbed molecules similar transients are obtained and attributed to the dissolution of the film which proceeds from holes growing with a rate becoming time dependent. The analysis of the kinetic results obtained at different temperatures confirms the distinct nature of the interfacial rearrangement leading to the same type of transients.

Effect of the crystallographic orientation of gold single-crystal electrodes on the occurrence of 2D phase transitions in adsorbed organic monolayers

The influence of the surface structure of a gold electrode on the occurrence of 2D phase transitions in adlayers of uracil and uridine has been studied by cyclic voltammetry. Au(111) surfaces with different step densities have been prepared by cutting the single crystals between 2 and 15.8° of their (111) axis. Results confirm that flat surfaces are a prerequisite for the formation of a 2D condensed physisorbed film.

Effect of Intermolecular and Interfacial Interactions on the Three- and Two-Dimensional Structure and Phase Behavior of Three-Block Liquid-Crystalline Siloxane Derivatives

Using several experimental techniques, we have investigated the thermodynamics and the structure of the bulk, monolayers, and multilayers of new three-block organosiloxanes based on the pentyloxy-4‘-cyanobiphenyl mesogenic unit. Compared to conventional amphiphiles or smectogens, these molecules contain an additional siloxane moiety whose bulkiness was gradually increased. This enables fine tuning of the steric effect imposed by the siloxane parts and allows determination of the balance between molecule−substrate and molecule−molecule interactions as well as of the effect of the siloxane end group on the microscopic structure, order, and film homogeneity. We show that the three- and two-dimensional behaviors are highly correlated and are determined by the subtle balance between these interactions. We particularly showed that surface effects induce a three-layer smectic film whatever the bulk state. Various 2D phenomena have been observed such as wetting, mono- and bilayer melting, liquid droplet freezing, several 2D phase transitions, and a tricritical point. These are reversible phenomena and easily controllable via lateral density change, making the present organosiloxane molecules a good model system to investigate in much more detail some challenging physical aspects in two dimensions.

Physisorbed CO on ionic crystals: an extended BEG spin-lattice model of adsorbed dipolar molecules

The 2D dielectric phases and phase transitions of adsorbed dipolar molecules are studied using a dilute spin-one Ising model. The spin-one formulation assigns a spin S i =±1 to a (up/down) dipole occupying a lattice site I adsorbed perpendicular to the substrate surface and S i =0 to unoccupied sites. We relate the mean field expression for the spin-model interaction energy to a more detailed microscopic model involving dipolar, quadrupolar and repulsive interactions beyond nearest neighbor. Analytic solutions in the mean field approximation are discussed for dipole-orientation order–disorder transitions and ferroelectric-to-antiferroelectric transitions as a function of temperature and coverage. The model is applied to two prototypical dipolar physisorbed systems, CO on MgO(100) and CO on NaCl(100), using previous experimental and theoretical studies to determine the interaction energy parameters. We find for most of these model parameters that only temperature-dependent ferroelectric dipole order–disorder phase transitions can occur for these two systems. However, we find that phase transitions between the two ferroelectric states, driven by changes in coverage, should also be observed for some predicted values of the parameters. Phase diagrams are presented. Application of the model to other related adsorbed dipolar systems is also discussed.

2D Phase transition of organic molecules adsorbed at the Hg electrode/aqueous solution interface Part 2 Comparison of experimental data with model predictions

The 2D phase transition of thymine, uracil, guanine and coumarin, adsorbed at the Hg electrode/aqueous solution interface, is rationalised on the basis of the model proposed in Part 1, J. Chem. Soc., FaradayTrans., 1994, 90, 2925. The results together with that obtained for adenine, are compared with the relevant quantities calculated by using molecular descriptors (dipole moments and polarizabilities). Finally, a value of the standard enthalpy phase-transition variation, averaged over the results collected for the five compounds is estimated and discussed.

Comparison between charged, charged at the pzc and uncharged interfaces: a peculiar case related to the origin of the polarization catastrophe

Abstract The properties of charged, charged at the pzc and uncharged interfaces are studied by means of the semi-thermodynamic approach developed [Electrochim. Acta, 39 (1994) 865; Russ. J. Electrochem., 31 (1995) 747]. It is shown that an uncharged monolayer located between two conducting phases is mathematically equivalent to the corresponding charged one at the pzc. The free surface of solutions is equivalent to the previous ones, but only in the stable region. When a 2D phase transition occurs at an adsorbed layer, both the adsorption isotherms and the critical values of the interaction parameter are markedly different at the free surface from those at the uncharged metal|electrolyte solution interface. The origin of this difference is indicated and discussed. It is shown further that the conventional use of the canonical ensemble disregards the existence of two domains of different electrode charge density, both at the uncharged and the corresponding charged metal|electrolyte interface when the intermolecular interactions are treated approximately and the adsorbed layer undergoes a 2D phase transition. This is the real cause of the polarization catastrophe at charged interfaces and the reason why the canonical ensemble predicts totally artificial adsorption isotherms throughout the region of a 2D phase transition and higher and incorrect values for the critical interaction parameter at the uncharged metal|electrolyte interface. The existence of domains of different charge density is taken into account if we consider surface equilibria, and this eliminates these artifacts completely.

Phase transitions in 2D linearly stable coupled map lattices

Interface dynamics separating homogeneous phases is shown to be the main mechanism underlying irregular evolution in 2D linearly stable, coupled map lattices. In a fully deterministic model belonging to this class, we find evidence of at least two different regimes that we call weak and strong turbulence. The transition between the two regimes is carefully investigated revealing a direct connection with the destabilization of the interfaces separating homogeneous phases. The critical behaviour is analysed and compared with that of stochastic models like directed percolation.

Study of non-faradaic 2D phase transitions by use of cyclic voltammetry and capacitance-potential curves

Abstract Non-faradaic peaks produced by the two-dimensional (2D) condensation of organic molecules on an electrode were studied theoretically by using cyclic voltammetry. Under limiting conditions of low scan rate and overpotential, the classical and atomistic theories of nucleation were found to predict the same behaviour for this type of process. The model developed from the previous study was also used to predict hysteresis in capacitance-potential curves for this type of process. With slight nomenclature changes, the ensuing mathematical expressions are also applicable to 2D phase transitions involving the simultaneous exchange of electrons between deposited molecules and the electrode.