How close to two dimensions does a Lennard-Jones system need to be to produce a hexatic phase?

We report on a computer simulation study of a Lennard-Jones liquid confined in a narrow slit pore with tunable attractive walls. In order to investigate how freezing in this system occurs, we perform an analysis using different order parameters. Although some of the parameters indicate that the system goes through a hexatic phase, other parameters do not. This shows that to be certain whether a system of a finite particle number has a hexatic phase, one needs to study not only a large system, but also several order parameters to check all necessary properties. We find that the Binder cumulant is the most reliable one to prove the existence of a hexatic phase. We observe an intermediate hexatic phase only in a monolayer of particles confined such that the fluctuations in the positions perpendicular to the walls are less than 0.15 particle diameters, i.e., if the system is practically perfectly 2D.     

Melting in two-dimensional Yukawa systems: a Brownian dynamics simulation

We studied the melting behavior of two-dimensional colloidal crystals with a Yukawa pair potential by Brownian dynamics simulations. The melting follows the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario with two continuous phase transitions and a middle hexatic phase. The two phase-transition points were accurately identified from the divergence of the translational and orientational susceptibilities. Configurational temperatures were employed to monitor the equilibrium of the overdamped system and the strongest temperature fluctuation was observed in the hexatic phase. The inherent structure obtained by rapid quenching exhibits three different behaviors in the solid, hexatic, and liquid phases. The measured core energy of the free dislocations, E(c) = 7.81 ± 0.91 k(B)T, is larger than the critical value of 2.84 k(B)T, which consistently supports the KTHNY melting scenario.     

Experimental characterization of hexatic smectic phases through electro-optic studies and dielectric relaxation spectroscopy

The electro-optic and complex dielectric behaviour of an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4'-(n-butanoyloxyprop-1-oxy)biphenyl-4-carboxylate, having chiral SmC_A* and hexatic smectic phases, have been investigated. Complex dielectric permittivities were measured as a function of frequency, d.c. bias field and temperature. Spontaneous polarization was measured by the current reversal technique; tilt angle was measured under a polarizing microscope using a low frequency electric field. The electro-optic properties and dielectric behaviour of the material are compared with results obtained by DSC and polarizing optical microscopy. Dielectric relaxation processes in SmC_A* and hexatic smectic phases were determined. The dielectric strength at the SmC_A* to hexatic smectic phase transition is discussed in terms of coupling between the long range bond orientational order and smectic C director. It seems from the results of spontaneous polarization and dielectric relaxation spectroscopy that the material might possess an additional phase between the SmC_A* and hexatic smectic I* phases.     

Observation of a liquid-gas phase transition in monolayers of alkyltrimethylammonium alkyl sulfates adsorbed at the air/water interface

The equilibrium adsorption layers of symmetric chain alkyltrimethylammonium alkyl sulfates (Cn+.Cn- for n = 8, 12) were investigated at the air/water interface by sum-frequency vibrational spectroscopy in the function of the bulk surfactant concentration. To ensure the surface purity of the solutions investigated, an improved version of the foam fractionation method was used for the purification of the constituent ionic surfactants and the surface purity of the solutions was also checked. In the monolayer of the C12+.C12- surfactant, a two-dimensional first-order gas/liquid phase transition was observed. At surfactant bulk concentrations just exceeding the concentration corresponding to the phase transition, the monolayer is conformationally disordered, liquidlike, but with increasing bulk surfactant concentration the conformational order of the monolayer increases. The SFG spectra of the C8+.C8- monolayer did not indicate the occurrence of phase transition at room temperature.     

Experimental characterization of hexatic smectic phases through electro-optic studies and dielectric relaxation spectroscopy

The electro-optic and complex dielectric behaviour of an antiferroelectric liquid crystal 4-(1-methylheptyloxycarbonyl)phenyl 4′-(n-butanoyloxyprop-1-oxy)biphenyl-4-carboxylate, having chiral SmC_A* and hexatic smectic phases, have been investigated. Complex dielectric permittivities were measured as a function of frequency, d.c. bias field and temperature. Spontaneous polarization was measured by the current reversal technique; tilt angle was measured under a polarizing microscope using a low frequency electric field. The electro-optic properties and dielectric behaviour of the material are compared with results obtained by DSC and polarizing optical microscopy. Dielectric relaxation processes in SmC_A* and hexatic smectic phases were determined. The dielectric strength at the SmC_A* to hexatic smectic phase transition is discussed in terms of coupling between the long range bond orientational order and smectic C director. It seems from the results of spontaneous polarization and dielectric relaxation spectroscopy that the material might possess an additional phase between the SmC_A* and hexatic smectic I* phases.     

Phase transitions in the liquid-vapor interface of dilute alloys of Bi in Ga: new experimental studies

We report the results of measurements of x-ray reflectivity and grazing incidence x-ray diffraction from the liquid-vapor interfaces of four dilute alloys of Bi in Ga with mole fractions x(Bi)=0.0032, 0.0023, 0.00037, and 0.000037. The monolayer coverage of the alloys with x(Bi)=0.0023, and x(Bi)=0.00037 is about 0.85 and only very slightly temperature dependent. The monolayer coverage in the lowest-concentration alloy, with x(Bi)=0.000037, ranged from 0.82 at 29 degrees C to 0.58 at 110 degrees C. In none of these alloys, down to the lowest temperature used, 29 degrees C, can we find any evidence for crystallization of the Bi monolayer that segregates as the outermost stratum of the liquid-vapor interface. Drawing on theoretical arguments we propose that the transitions inferred from the second-harmonic generation and plasma generation studies of dilute Bi in Ga alloys are from the liquid state to the hexatic state of the Bi monolayer. The data for the alloy with x(Bi)=0.000037 suggest that near 80 degrees C there is a disordered phase-to-disordered phase transition.     

Fatty-acid monolayers at the nematic/water interface: phases and liquid-crystal alignment

The two-dimensional (2D) phases of fatty-acid monolayers (hexadecanoic, octadecanoic, eicosanoic, and docosanoic acids) have been studied at the interface of a nematic liquid crystal (LC) and water. When observed between crossed polarizers, the LC responds to monolayer structure owing to mesoscopic alignment of the LC by the adsorbed molecules. Similar to Langmuir monolayers at the air/water interface, the adsorbed monolayer at the nematic/water interface displays distinct thermodynamic phases. Observed are a 2D gas, isotropic liquid, and two condensed mesophases, each with a characteristic anchoring of the LC zenithal tilt and azimuth. By varying the monolayer temperature and surface concentration we observe reversible first-order phase transitions from vapor to liquid and from liquid to condensed. A temperature-dependent transition between two condensed phases appears to be a reversible swiveling transition in the tilt azimuth of the monolayer. Similar to monolayers at the air/water interface, the temperature of the gas/liquid/condensed triple-point temperature increased by about 10 degrees C for a two methylene group increase in chain length. However, the absolute value of the triple-point temperatures are depressed by about 40 degrees C compared to those of analogous monolayers at the air/water interface. We also observe a direct influence by the LC layer on the mesoscopic and macroscopic structure of the monolayer by analyzing the shapes and internal textures of gas domains in coexistence with a 2D liquid. An effective anisotropic line tension arises from elastic forces owing to deformation of the nematic director across phase boundaries. This results in the deformation of the domain from circular to elongated, with a distinct singularity. The LC elastic energy also gives rise to transition zones displaying mesoscopic realignment of the director tilt or azimuth between adjacent regions with a sudden change in anchoring.     

Line tension of alkane lenses on aqueous surfactant solutions at phase transitions of coexisting interfaces

Alkane droplets on aqueous solutions of surfactants exhibit a first-order wetting transition as the concentration of surfactant is increased. The low-concentration or “partial wetting” state corresponds to an oil lens in equilibrium with a two-dimensional dilute gas of oil and surfactant molecules. The high-concentration or “pseudo-partial wetting” state consists of an oil lens in equilibrium with a mixed monolayer of surfactant and oil. Depending on the combination of surfactant and oil, these mixed monolayers undergo a thermal phase transition upon cooling, either to a frozen mixed monolayer or to an unusual bilayer structure in which the upper leaflet is a solid layer of pure alkane with hexagonal packing and upright chains while the lower leaflet remains a disordered liquid-like mixed monolayer. Additionally, certain long-chain alkanes exhibit a surface freezing transition at the air–oil interface where the top monolayer of oil freezes above its melting point. In this review, we summarize our previous studies and discuss how these wetting and surface freezing transitions influence the line tension of oil lenses from both an experimental and theoretical perspective.     

Phase transition of lipid-like monolayer characterized by second harmonic generation

Phase transition of a lipid-like hemicyanine compound characterized by second harmonic generation is studied carefully. The phase transition is assigned as the first order transition between solid state and liquid state. The transition temperature increases with an increase in the surface molecular concentration. A monolayer structure parameter a which is very sensitive to the phase transition is introduced.     

Predicting the phase diagram of two-dimensional colloidal systems with long-range interactions

The phase diagram of a two-dimensional model system for colloidal particles at the air-water interface was determined using Monte Carlo computer simulations in the isothermic-isobaric ensemble. The micrometer-range binary colloidal interaction has been modeled by hard disklike particles interacting via a secondary minimum followed by a weaker longer-range repulsive maximum, both of the order of kBT. The repulsive part of the potential drives the clustering of particles at low densities and low temperatures. Pinned voids are formed at higher densities and intermediate values of the surface pressure. The analysis of isotherms, translational and orientational correlation functions as well as structure factor gives clear evidence of the presence of a melting first-order transition. However, the melting process can be also followed by a metastable route through a hexatic phase at low surface pressures and low temperatures, before crystalization occurs at higher surface pressure.     

Progress in characterization of Langmuir monolayers by consideration of compressibility

Over decades, information about the rheological properties of the condensed monolayer phases has been obtained by introduction of a two-dimensional compressibility which is defined on the basis of the surface pressure-molecular area (Pi-A) features of the monolayer. Since the last decade, fundamental progress was attained in the experimental determination of the main characteristics of Langmuir monolayers in microscopic and molecular scale. Already smallest changes in the molecular structure of the amphiphile can result in changes in the molecular arrangement in the monolayer and thus, in changes of the main characteristics of the monolayer such as, the surface pressure-area per molecule (Pi-A) isotherms, the shape and texture of the condensed phase domains and the two-dimensional lattice structure. As the classical equations of state allowed only characterisation of the fluid (gaseous, liquid-expanded) state, thermodynamically based equations of state, which consider also the aggregation of the monolayer material to the condensed phase, have been developed. The present review focuses particularly to amphiphilic monolayers, the Pi-A isotherms of which indicate the existence of two condensed phases. For this case, the experimental results of the differences in the structure features and phase properties are discussed. The generalisation of the equation of state for Langmuir monolayers developed for the case that one, two or more phase transitions in the monolayer take place, is in agreement with the experimental results that the two-dimensional compressibility of the condensed phases undergoes a jump at the phase transition, whereas the compressibility is proportional to the surface pressure within one of the condensed phases. An example is presented which explains the procedure of the theoretical analysis of Pi-A isotherms indicating the existence of two condensed phases. An element of the procedure is the application of the general principle that the behaviour of any thermodynamic system is determined by the stability condition. An interesting anisotropy of the compressibility is revealed by GIXD studies of the S-phase of octadecanol monolayers. However, similar studies performed close to the LS-S-phase transition would result in a thermodynamically impossible negative compressibility. Close to this phase transition, the compressibility cannot be determined from the positions of the maxima because the monolayer is in a disordered state attributed to elastic distortions by fluctuations with the structure of the new phase in the surrounding matrix without destroying the quasi-long-range positional order.     

Thermodynamics of phase transitions in langmuir monolayers observed by vibrational sum frequency spectroscopy

Vibrational sum-frequency spectroscopy (VSFS) was used to study gauche defects in octadecylamine (ODA) monolayers at the air/water interface. The VSFS spectra provide unique insights into phase transitions that occur as a result of changes in the structure of the monolayer's hydrophobic region. These changes can be attributed to the increased presence of gauche conformers in the ODA alkyl chains during the monolayer's transition from the solid to liquid phase. Temperature-dependent spectra from monolayers at several different pressures were used to assign the phase transition temperature based on the observed changes in microscopic structure. Through application of a two-dimensional form of the Clapeyron equation, the first in situ measurements of the entropy and enthalpy changes associated with gauche conformers in a monolayer were made.     

Monolayers of mono- and bipolar palmitic acid derivatives

Monopolar and bipolar derivatives of hexadecanoic acid (HA), 16-hydroxyhexadecanoic acid (HHA), methyl hexadecanoate (MH) and methyl 16-hydroxyhexadecanoate (MHH) have been investigated on pure water and NaCl solutions with different ion concentrations (1, 2 and 3 mol l⁻¹). Surface pressure area isotherms show that HA forms a fully condensed monolayer on pure water at 20 °C [E. Teer, C.M. Knobler, S. Siegel, D. Vollhardt, G. Brezesinski, J. Phys. Chem., B104, 43, 2000, pp. 10053–10058] whereas in the case of the corresponding bipolar HHA the hydroxy group as a second polar moiety leads to a destabilization of the monolayer. The presence of two relatively strong hydrophilic polar groups at opposite ends of the chain prevents the formation of condensed films. The esterification of the carboxyl group (MH) changes the phase sequence from L₂–Ov–LS for HA to L₂–LS. Inserting a hydroxy group at the end of the chain (MHH) shifts the liquid expanded/liquid condensed (LE/LC) phase transition to higher surface pressures but does not change the phase sequence, however it increases the chain tilt. The pressure of the first-order phase transition LE/LC is strongly temperature dependent for MH, while the transition pressure of MHH is almost temperature independent. The phase behavior of MHH and MH on pure water was further studied by surface potential, Brewster angle microscopy (BAM), fluorescence microscopy and grazing incidence X-ray diffraction (GIXD) measurements. The LC domains of MHH on pure water are so small that no inner texture can be observed by BAM in contrast to the LC domains of MH. 3M NaCl in the subphase does not change the MH textures, while it increases the size of the LC domains of MHH. The influence of the hydroxy group on the monolayer behavior is discussed in terms of the formation of hydrogen bonds. The presence of NaCl in the subphase expands the monolayers. The results obtained are explained by changes in monolayer–monolayer and monolayer–subphase interactions.     

Freedericksz transition in polymeric hexatic liquid crystals

The threshold voltage for the Freedericksz transition of a polymer hexatic liquid crystal depends on the film thickness. This behaviour is attributed to the coupling of the director and the bonds defined by the hexatic order. We fit the results of a simple elastic continuum model to threshold data. The fit is suitable for the estimation of several material constants.     

Wetting and freezing of hexadecane on an aqueous surfactant solution: triple point in a 2-D film

Wetting of water by hexadecane has been investigated by ellipsometry as a function of the concentration of the cationic surfactant dodecyltrimethylammonium bromide (DTAB) in the aqueous phase and temperature. Three phases are identified: a 2-D gas of hexadecane molecules and DTAB molecules, a 2-D liquid comprising a mixed monolayer of hexadecane and DTAB, and a 2-D 'solid' phase. Evidence is presented to support the hypothesis that the liquid-solid phase transition is actually a wetting transition in which a surface-frozen layer of pure hexadecane wets the liquid-like mixed monolayer of hexadecane and DTAB. The triple point, at which the three phases coexist, is located at a temperature of 17.3 degrees C and DTAB concentration of 0.75 mmol kg (-1). The slopes of the three phase boundaries are analyzed thermodynamically.     

Colloidal phase transition driven by alternating electric field

The transverse two-dimensional assembly of colloidal particles near an electrode surface subjected to ac polarization is studied by varying the frequency and field strength in the absence and presence of an added electrolyte. The variation of the translational and bond-orientational correlation functions with frequency suggests the existence of a hexatic phase in which the particles retain the remnants of the crystalline long-range orientational order, but has a liquidlike translational order. The electrohydrodynamic (EHD) flow is analyzed in the light of the existing theoretical models. The equilibrium distribution of particles is considered to be the resultant of the two opposing forces--Stoke's force due to EHD flow and the screened Coulomb interaction between the colloidal particles. Several features of the experimental results are discussed, such as the role played by the EHD flow in the particle aggregation, the dependence of the equilibrium interparticle separation on ionic strength, zeta potential, and particle size.     

Fluorescence microscopy observation of self-organized microstructure formed by a rare earth compound

The morphologies of monolayers containing Eu(TTA)3Phen (TTA=thenoyltrifluoroace-tone, Phen = 1, 10-phenanthroline) were studied at the air/liquid interface on different subphases by fluorescence microscopy (FM). The composite subphase was the basic premise for the stable existence of the rare earth compound at air/liquid interface. The process that rare earth compound phase changes from liquid expanded state to liquid condensed state corresponded to a plateau in the π-A isotherm. In the pure Eu(TTA)3Phen monolayer, rod domains of Eu(TTA)3Phen formed and packed with no order. In the mixed monolayers with stearic acid (SA), phase transition of SA occurred first and formed domains with an electric gradient field, which induced the rare earth compound to form luminescent ring domains. Influence of intermolecular interaction on the self-organized microstructure was revealed.     

Adsorption and micellar properties of a mixed system of nonionic-nonionic surfactants

We study the surface adsorption and bulk micellization of a mixed system of two nonionic surfactants, namely, ethylene glycol mono-n-dodecyl ether (C12E1) and tetraethylene glycol mono-n-tetradecyl ether (C14E4), at different mixing ratios at 15 degrees C. The pure C14E4 monolayer cannot show any indicative features of phase transition because of both hydration-induced and dipolar repulsive interactions between the bulky head groups. On the other hand, the monolayers of pure C12E1 and its mixture with C14E4 undergo a first-order phase transition, showing a variety of surface patterns in the coexistence region between the liquid expanded (LE) and liquid condensed (LC) phases under the same experimental conditions. For pure C12E1, the domains are of a fingering pattern while those for the C12E1/C14E4 mixed system are found to be compact circular and small irregular structures at 2:1 and 1:1 molar ratios, respectively. The critical micelle concentration (cmc) values of both the pure and the mixed systems were measured to understand the micellar behavior of the surfactants in the mixture. The cmc values of the mixed system were also calculated assuming ideal behavior of the surfactants in the mixture. The experimental and calculated values are found to be very close to each other, suggesting an almost ideal nature of mixing. The interaction parameters for mixed monolayer and micelle formation were calculated to understand the mutual behavior of the surfactants in the mixture. It is observed that the interaction parameters for mixed monolayer formation are more negative than those of micelle formation, indicating a stronger interaction between the surfactants during monolayer formation. It is concluded that since both the surfactants bear EO units in their head groups, structural parity and hydrogen bonding between the surfactants allow them to be closely packed during monolayer and micelle formation.     

The influence of structural changes of the N‐substituent on liquid crystalline behaviour of ester imides

Several new ester imide derivatives with different N‐substituents in the imide ring were synthesized and their mesogenic properties investigated by thermal analysis, optical microscopy and X‐ray diffraction. All the esters of N‐4‐[(4′‐decyloxybiphenyl‐4‐yl)oxycarbonyl]phthalimideacetic acid and aliphatic alcohols exhibited monolayer SmA and SmC phases. In addition, for the ethyl and propyl esters a monotropic hexatic (F or I) phase was observed. The introduction of additional substituents at the carbon atom in the methylenemethoxycarbonyl group (in the vicinity of the nitrogen atom) substantially influenced liquid crystalline properties: the compounds with a flexible chain exhibited monotropic SmA–SmB dimorphism, but liquid crystalline properties vanished for the substituent containing the more rigid phenyl ring.