Direct observation of domain structure in condensed monolayer phases

Hierarchical structure growth across different length scales in the two-phase coexistence region of myristic acid Langmuir monolayers: correlation of static and dynamic heterogeneities

We investigated the hierarchical structure growth of myristic acid monolayers at the air-water interface across different length scales in the two-phase coexistence region of the first order liquid expanded (LE)-liquid condensed (LC) phase transition. A combined study of surface pressure-area (π-A) isotherm measurements with Brewster angle microscopy (BAM) observations was done at different temperatures. At the nanometer scale, the analysis of the π-A isotherm by application of a thermodynamic cluster equation allowed us to obtain the π dependence of cluster size (cluster distribution) in the LE-LC coexistence region. The cluster distributions showed a peak at the midpoint pressure of the transition. At higher temperature the larger nanocluster size was obtained at the transition midpoint. At the micrometer scale, BAM showed that LC domains have characteristic textures depending on the temperature. At low temperature domain density was lower and the average size of circular domains was larger. A large number of circular domains revealed a virtual boojum texture from the initial to the late stage of the transition. At the final stage some circular domains coalesced to form larger circular stripe domains and others coalesced to each other without the formation of stripe domains, finally resulting in a uniform texture over the entire water surface. At high temperature the domain texture was predominantly uniform, and a small number of domains only included straight line defects from the intermediate to the late stage of the transition. All domains coalesced to each other without the development of any texture including the stripe, different from the case at low temperature. The phase boundary line tension is highly likely to play a key role for understanding the hierarchical growth and coarsening (coalescence) process in the LE-LC transition between the different length scales from the nanometer to the micrometer scale consistently together.

Molecular Explanation for the Abnormal Flux of Material into a Hot Spot in Ester Monolayers

Langmuir monolayers of certain surfactants show a negative derivative of the surface pressure with respect to temperature. In these monolayers, a local temperature gradient leads to local yielding of the solid phase to a kinetically flowing liquid, so that the material flows toward the hotter regions that act as sinks. The accumulation of material leads to the formation of nonequilibrium multilamellar bubbles of different sizes. Here we investigate the molecular factors leading to such a peculiar behavior. First, we identify the required structural molecular moieties, and second we vary the composition of the subphase in order to analyze its influence. We conclude that esters appear to be unique in two key aspects: they form monolayers whose compression isotherms shift to lower areas as the temperature increases, and thus collapse into a hot spot; and they bind weakly to the aqueous subphase, i.e., water does not attach to the monolayer at the molecular level, but only supports it. Molecular simulations for a selected system confirm and help explain the observed behavior: surfactant molecules form a weak hydrogen bonding network, which is disrupted upon heating, and also the molecular tilting changes with temperature, leading to changes in the film density.

Dislocation-Mediated Deformation in Solid Langmuir Monolayers: Plastic Bending and Tilt Boundary

The shear response of three types of textures (mosaic, striation, and stripe) in 10,12-pentacosadiynoic acid solid Langmuir monolayers has been investigated with Brewster angle microscopy. Low temperature mosaic textures respond to an applied stress elastically. Upon the application of shear the change of contrast appears in the form of propagation of fronts roughly perpendicularly to the shear direction within a single domain reversibly, while the domain shape keeps constant since it is presumably frozen kinetically. The striation and stripe textures at high temperatures show a viscoplastic behavior (plastic bending) in its rheological response, being consistent with the formation of a dislocation wall (tilt boundary) through dislocation dynamics (dislocation glide and climb). The stress-induced formation of a tilt boundary provides a manifestation of the collective motion of a number of dislocations.

Chiroptical vesicles and disks that originated from achiral molecules

We report a chiral gel of vesicles and disklike micelles that originated from achiral molecules. The supramolecular chirality was obtained via regulating pH, in which a sol-gel-sol transition in a colloidal system consisting of a gelator, 4,4-di(2,3-dicarboxylphenoxyl)azobenzene (AzoNa4), and a zwitterionic surfactant, tetradecyldimethylamine oxide (C14DMAO), happened. The supramolecular chirality was related to the state of aggregation, i.e., only the condensed gels show chiral sense and sols are chiral-silent. The coexistence of vesicles and disklike micelles was captured for the first time in supramolecular chiral hydrogels by cryo- and freeze-fracture transmission electron microscopy (cryo- and FF-TEM) observations. Ascribed to the photoisomerization of the azobenzene units, upon alternative UV/visible light irradiation, the gel chirality can be switched reversibly with the macroscopic changes between vesicles/disks and wormlike micelles. A pH- and light-dual-responsive chiroptical switch can be constructed, which may require understanding the regulating membrane permeability and reagent release of structural transformation through photoisomerization and also require understanding the origin of gelation-induced supramolecular chirality completely based on achiral molecules.

Chiral structures from achiral liquid crystals in cylindrical capillaries

We study chiral symmetry-broken configurations of nematic liquid crystals (LCs) confined to cylindrical capillaries with homeotropic anchoring on the cylinder walls (i.e., perpendicular surface alignment). Interestingly, achiral nematic LCs with comparatively small twist elastic moduli relieve bend and splay deformations by introducing twist deformations. In the resulting twisted and escaped radial (TER) configuration, LC directors are parallel to the cylindrical axis near the center, but to attain radial orientation near the capillary wall, they escape along the radius through bend and twist distortions. Chiral symmetry-breaking experiments in polymer-coated capillaries are carried out using Sunset Yellow FCF, a lyotropic chromonic LC with a small twist elastic constant. Its director configurations are investigated by polarized optical microscopy and explained theoretically with numerical calculations. A rich phenomenology of defects also arises from the degenerate bend/twist deformations of the TER configuration, including a nonsingular domain wall separating domains of opposite twist handedness but the same escape direction and singular point defects (hedgehogs) separating domains of opposite escape direction. We show the energetic preference for singular defects separating domains of opposite twist handedness compared with those of the same handedness, and we report remarkable chiral configurations with a double helix of disclination lines along the cylindrical axis. These findings show archetypally how simple boundary conditions and elastic anisotropy of confined materials lead to multiple symmetry breaking and how these broken symmetries combine to create a variety of defects.

Theory of Defects in Condensed Phases of Langmuir Monolayers

Recent fluorescence-microscopy experiments have observed two types of defects—star defects and striped textures-in the liquid—condensed phases of Langmuir monolayers. These defects can be understood through a continuum elastic theory. This theory predicts both splay stripes, which are driven by the asymmetry between molecular heads and tails, and bend stripes, which are driven by a spontaneous breaking of chiral symmetry in the monolayer. These predictions are compared with experimental observations.

Domain Structures and Phase Transitions in Langmuir Monolayers

A variety of recent measurements has shown that the phase diagrams of Langmuir monolayers of relatively simple amphiphiles such as fatty acids and their methyl and ethyl esters are remarkably complex. Nine condensed phases have been identified; their structures can be related to those of known smectic phases. A key distinction between phases is the orientation of the molecular tilt azimuth with respect to the local hexagonal order of the head groups. When monolayers are examined by fluorescence microscopy, regions of uniform tilt can be observed if the exciting radiation is polarized with respect to the surface normal. The tilt regions form patterns similar to those observed in freely suspended films of smectic liquid crystals. The patterns can be changed by compressing the film and by changing the temperature. Transitions between different phases can be observed.

Chiral Symmetry Breaking and Pattern Formation in Two-Dimensional Films

Thin films of organic molecules, such as Langmuir monolayers and freely suspended smectic films, can exhibit a spontaneous breaking of chiral symmetry. This chiral symmetry breaking can occur through at least three possible mechanisms: (1) the relation between tilt order and bond-orientational order in a tilted hexatic phase, (2) a special packing of non-chiral molecules on a two-dimensional surface, and (3) phase separation of a racemic mixture. Because the chiral order parameter is coupled to variations in the direction of molecular tilt, chiral symmetry breaking leads to the formation of patterns in the tilt direction with one-dimensional or two-dimensional order. Using a Landau theory, we investigate these patterns and predict the critical behavior near the chiral symmetry breaking transition.

Boojum and stripe textures in long-range orientationally ordered monolayers on solid substrates

Long-range organization of molecular tilt azimuth is a striking feature in monolayers at the air-water interface. We show that the boojum and stripe textures of pentadecanoic acid (PDA) with the continuous variations of molecular tilt azimuth formed at the air-water interface at temperatures lower than room temperature can be preserved after being transferred to glass substrates at low dipping speeds. The long-range tilt order in the transferred boojums and stripes is resolved by frictional force microscopy at room temperature, suggesting that the tilt order is "frozen" through the interaction of PDA molecules with the glass surface. The transferred stripe structure can be used as a unique alignment layer to induce a continuously azimuthal orientation of nematic liquid crystals.

Spatiotemporal patterns in a Langmuir monolayer due to driven molecular precession

Langmuir monolayers of chiral liquid crystals on the surface of water exhibit orientational waves with complex spatiotemporal patterns. These patterns arise from a collective precession of the mesogenic molecules, driven by the evaporation of water through the monolayer. We investigate the behavior of these orientational waves around topological defects in the molecular orientation. Through Brewster angle microscopy, we find that the waves form a reversing spiral pattern, which rotates about the central vortex. With increasing relative humidity, the rotation slows and then stops. We model the system theoretically, and show that predicted patterns are in good agreement with the experiments.

Swelling of a cluster phase in Langmuir monolayers containing semi-fluorinated phosphonic acids

Langmuir monolayers of semi-fluorinated nonadecylphosphonic acid (F8H11PO), hexadecylphosphonic acid (H16PO), and their mixtures were investigated by Brewster angle microscopy (BAM), atomic force microscopy (AFM) and surface-pressure measurements. Nanometre-scale two-dimensional clusters were observed by AFM in a spread monolayer of pure F8H11PO transferred to mica. Two different organized arrangements of clusters were observed. AFM and BAM observations showed that the mixture exhibits a solid phase over a large range of mole fraction and surface pressure, sometimes in coexistence with clusters. With increasing mole fraction of H16PO, the lateral shape of these clusters remains the same while their organization and their height change.

Two-dimensional facets in Langmuir monolayers of 1-O-hexadecyl-rac-glycerol at the air–water interface

We study the surface phase behavior in Langmuir monolayers of 1-O-hexadecyl-rac-glycerol (C16G) by film balance and Brewster angle microscopy over a wide range of temperatures. A cusp point followed by a pronounced plateau region in the pressure-area (pi-A) isotherm indicates a first-order phase transition between a lower density liquid expanded (LE) phase and a higher density liquid condensed (LC) phase at the air-water interface. A wide variety of condensed domains are found to form just after the appearance of the cusp point. The observed surface morphology was compared with that of ethylene glycol mono-n-hexadecyl ether (C16E1) that bears an ethylene oxide (EO) unit in the head-group. As usually observed, the domains of C16E1 are found to be circular at lower temperatures and fractal at higher temperatures. Contrary to this usual behavior, the domains of C16G are found to be strip-like structures at lower temperatures, which attain increasingly compact shape as the temperature increases and finally attain faceted structures at > or = 25 degrees C. It is concluded that a higher degree of dehydration around the head-group region of C16G appreciably reduces the hydration-induced repulsive interactions between the head-groups and imparts to the molecules an increase in hydrophobicity, thereby a closer molecular packing. As a result, the molecules form increasingly compact domains as the temperature increases. Since the head-group of C16E1 is much smaller than that of C16G, dehydration effect cannot appreciably increase its hydrophobic character. Rather, increases in subphase temperature result in a decrease in the line tension of the interface giving fractal structures at higher temperatures. In addition, the changes in enthalpy (deltaH) and entropy (deltaS) values were also calculated to understand the thermodynamic nature of condensation of the molecules in the LE-LC transition region.

Influence of temperature and alkyl chain length on phase behavior in Langmuir monolayers of some oxyethylenated nonionic surfactants

We study the surface phase behavior in Langmuir monolayers of a series of nonionic surfactants of the general formula CnE1 with n=14, 16, and 18 by film balance and Brewster angle microscopy (BAM) over a wide range of temperatures. A cusp point followed by a pronounced plateau region in the pressure-area (pi-A) isotherms indicates a first-order phase transition in the coexisting state between a lower density liquid expanded (LE) phase and a higher density liquid condensed (LC) phase at the air-water interface. The formation of bright two-dimensional (2D) LC domains in a dark background visualized by BAM further confirms this observation. In addition to the cusp point at the onset of the LE-LC coexistence state, another cusp point followed by a small plateau is observed for the C14E1 and C18E1 monolayers, indicating a second phase transition between two condensed phases of different compressibility and tilt orientation of the molecules. This unusual two-step phase transition is explained by the Ostwald step rule. The C16E1 and C18E1 monolayers show a kink in their respective isotherms, after which the surface pressure increases steeply with only a little decrease in the molecular area, suggesting that the molecules undergo a transition from a tilted to an almost vertical orientation with respect to the water surface. The thermodynamic parameters for the condensation of the molecules in the LE-LC coexistence state were calculated by employing the 2D Clapeyron equation. The temperature coefficient of the critical surface pressure dpi(c)/dT values shows a decreasing trend from C14E1 to C18E1, suggesting that the condensation process becomes less and less prone to thermal perturbation as the chain length increases. For all the amphiphiles, the DeltaH values are found to be negative, suggesting an exothermic nature of condensation. The negative DeltaS values obtained from the relation DeltaH/T probably come from the restriction on the rotational and translational motion of the molecules constrained in a confined area in the LE-LC transition region.

Influence of temperature and headgroup size on condensed-phase patterns in langmuir monolayers of some oxyethylenated nonionic surfactants

The surface phase behavior in Langmuir monolayers of some oxyethylenated nonionic surfactants of the general formula C16En, with n = 1, 2, 3, and 4, at the air-water interface has been studied by film balance and Brewster angle microscopy (BAM) over a wide range of temperatures. The C16E4 monolayers cannot show any indicative features of phase transition because of strong dipolar as well as hydration-induced repulsive interactions between the bulky headgroups. On the other hand, the monolayers of C16E1, C16E2, and C16E3 show a sharp cusp point followed by a pronounced plateau region in their respective isotherms with subsequent formation of a variety of structures in the two-phase coexistence region between the liquid expanded (LE) and liquid condensed (LC) phases at different temperatures. As usually observed, the domains of C16E1, which bears only one ethylene oxide (EO) unit in the headgroup, are circular at lower temperatures while fractal at higher temperatures. On the other hand, those for C16E2 and C16E3 are initially found to be irregular structures, which attain increasingly compact shape with increasing temperature, and finally become circular when the subphase temperature is 26 and 15 degrees C for C16E2 and C16E3, respectively. It is concluded that a higher degree of dehydration around the headgroup region appreciably reduces the headgroup size, which imparts to the molecules an increase in hydrophobicity, thereby a closer molecular packing. Consequently, the line tension of the interface increases, showing compact structures at higher temperatures. Since C16E1 bears only one EO unit in its headgroup, the dehydration effect cannot appreciably raise its hydrophobicity to overcome the increases in thermal motion and chain flexibility of the molecules. Rather, increases in subphase temperature result in a decrease in the line tension of the interface, giving fractal structures at higher temperatures.

String Defects Connecting Pairs of Half-Integer Disclinations and Tilting Transition of a Langmuir Monolayer

The static and dynamic string defect textures connecting pairs of half-integer disclinations have been observed by Brewster angle microscopy in the solid phase of pentacosadiynoic acid Langmuir monolayers. The static string defect structures have appeared coexisting with two kinds of point disclinations that have four and two black brushes. The use of local laser heating has allowed one to observe kinetics of creation and annihilation of string defects connecting the two-half-integer disclinations in the splitting process of an s = 1 point disclination into fractional disclinations. These kinetics have been analyzed by studying the competition between the orientational elasticity of the molecules and the line tension of the string and the drag force of the disclinations.

Faceted structures in Langmuir monolayers of diethylene glycol mono-n-octadecyl ether at the air--water interface

We have concurrently studied the surface pressure (pi) versus area (A) isotherms and microscopic surface morphological features of Langmuir monolayers of diethylene glycol mono-n-octadecyl ether (C18E2) by film balance and Brewster angle microscopy (BAM) over a wide range of temperature. At temperatures < or =10 degrees C, the monolayers exist in the form of condensed phase even just after the evaporation of the spreading solvent, suggesting that the melting point of the condensed phase is above this temperature. At > or =15 degrees C, the monolayers can exist as gas (G), liquid expanded (LE), and liquid condensed (LC) phases and undergo a pressure-induced first-order phase transition between LE and LC phases showing a sharp cusp point followed by a plateau region in the pi-A isotherms. A variety of 2-D structures, depending on the subphase temperature, are observed by BAM just after the appearance of the cusp point. It is interesting to note here that the domains attain increasingly large and compact shape as the subphase temperature increases and finally give faceted structures with sharp edges and corners at > or =30 degrees C. The BAM observations were coupled with polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS) to gain better understanding regarding the conformational order and subcell packing of the molecules. The constancy of the methylene stretching modes over the studied temperature range suggests that the hydrocarbon chains do not undergo any conformational changes upon compression of the monolayer. However, the full width at half-maximum (fwhm) values of the asymmetric methylene stretching mode (nu(as)(CH(2))) are found to respond differently with changes in temperature. It is concluded that even though the trans/gauche ratio of the hydrocarbon chains remains virtually constant, the LE-LC phase transition upon compression of the monolayer is accompanied by a loss of the rotational freedom of the molecules.

Reflection of light at structured chiral interfaces

Modified boundary conditions and general surface constitutive equations are derived for a very thin interface with some internal structure that separates two different media. The modified boundary conditions are reduced to the standard ones for an idealized steplike sharp interface without additional structure. These modified boundary conditions together with surface constitutive equations and Maxwell equations in the bulk form a complete set of macroscopic equations to describe optical properties of planar interfaces with thicknesses much less then the wavelength of light. In particular, two-dimensional chiral surfaces are considered that are characterized by surface gyrotropic coefficients even if the two different bulk media and the interface are made of nonchiral materials. It is shown that the rotation of the polarization state should occur for the light reflected from such a surface. This result is supported by recent experimental data.

Surface phase behavior in Langmuir monolayers of diethylene glycol mono-n-hexadecyl ether at the air-water interface

The surface phase behavior of condensed-phase domains formed during a first-order phase transition in Langmuir monolayers of diethylene glycol mono-n-hexadecyl ether at the air-water interface has been investigated by Brewster angle microscopy and polarization modulation infrared reflection absorption spectroscopy (PM-IRRAS). A variety of two-dimensional (2D) structures are observed just after the appearance of the phase transition at different temperatures. At 10 and 15 degrees C, the domains are found to be small nuclei of irregular structures. Spiral structures are observed at 20 and 22 degrees C, while striplike structures at 24 degrees C. The spiral domains attain increasingly compact shape with increasing temperature, and finally become circular at >or=26 degrees C. Increases in temperature result in dehydration in the ethylene oxide chain, which increases the hydrophobicity, and impart to the molecules a longer-chain-like character. As a result line tension increases with increasing temperature, which probably outweighs the dipole-dipole repulsions showing circular domains at higher temperatures. The PM-IRRAS measurement reveals that the nu(as)(CH(2)) mode moves to lower wave numbers indicating that the LE-LC (liquid expanded-liquid condensed) phase transition during the compression of the monolayer involves changes in the conformational order of the molecules with a preferential increase in the planner trans zigzag conformation of the hydrocarbon chains. The nu(as)(CH(2)) mode in the LC region of the isotherm shows a constant value around 2917.8 cm(-1) indicating a stable state of the monolayer with an almost all-trans conformation of the hydrocarbon chains. The downward band at 1124 cm(-1) assigned to the nu(as)(C-O-C) mode indicates that the corresponding transition dipole moment is oriented perpendicular to the water surface.

Orientational structures in confined smectic-C domains in Langmuir monolayers

Droplet smectic-C domains in films of surfactant molecules exhibit different orientational textures. For these systems we formulate a kinetic model based on a free energy functional containing bulk (elastic) and surface interactions. Numerical simulations for the corresponding relaxational equation show the existence of two different equilibrium configurations with a centered defect. In particular, when the elastic terms dominate, bend-shaped textures appear, whereas for strong boundary effects mixed bend/splay conformations are displayed. A variational analysis for the free energy functional confirms the validity of the above numerical results. The stability of textures with centered defects with respect to the formation of periferic defects (boojums) is also discussed qualitatively. The above theoretical predictions are compared with experimental results from Brewster angle microscopy imaging of azobenzene Langmuir monolayers.

Linear splay elasticity in surface-induced films of tilted smectic liquid crystals

The prefrozen films that may be observed at the surface of isotropic liquid crystal droplets, close to the isotropic-smectic phase transition, or surface-induced films, are essentially asymmetric. If moreover, the molecules are tilted inside the smectic layers, as in the smectic-C (SmC) or smectic-C(A) (SmC(A)) phases, the c director that we may define as the order parameter of the film, is a real vector. Thus, the surface-induced films of MHTAC exhibit vectorial or polar properties, though the molecules are not chiral. The film free energy therefore contains a surface-elasticity term, K(1)c(2) c, that is a linear function of the splay distortion, and that may be negative enough to promote a mechanical instability. A spontaneous c distortion, or c modulation, then invades the whole film and produces an array of parallel stripes, with a typical four-fringe periodicity when observed between crossed polarisers. Here, we present optical measurements of the distortion for different film thicknesses, and we propose a linear analysis of the data to test our model. Due to the limitations inherent to the Fourier expansion that we use, the calculations are valid only between two limits: a large q limit where splay domains collapse into disclination lines, and a small q borderline below which the distortion evolves towards a system of independent solitons. We find that the sign of the spontaneous splay elastic constant K1 alternates as a function of the number of layers, N, a property that is reminiscent of the alternate structure of the SmC(A) phase. We argue that the two-dimension elastic constant, K1, originates from the interactions between the molecules in contact to the isotropic phase, and we deduce K1 approximately -(-1)(N)x10(-11) N and the elastic anisotropy, with a ratio of the splay over bend elastic constants K(s)/K(b) approximately 4.5. Similar properties could be observed also in other types of ultrathin films, e.g., in free-standing, ferroelectric (SmC*) or antiferroelectric (SmC(*)(A)), films, in Langmuir films, and even in particular biological films. In some cases, a second, electric instability may occur and superimpose onto the elastic one.

Orientational ordering and chiral symmetry breaking in organic monolayers composed of disklike mesogenic molecules: molecular theory and computer simulations

Orientational ordering of disklike molecules on a flat surface is investigated using a molecular-statistical theory and Monte-Carlo simulations. The theory is based on the two-dimensional orientational order parameter for molecules with a threefold symmetry axis, and on a simple model interaction potential which has been derived taking into consideration only the symmetry of basic molecular structure. The theory reveals three different anisotropic phases. One of them exactly corresponds to the structure which has recently been observed experimentally in self-assembling monolayers of discotic mesogenic molecules on a pyrolitic graphite surface. This is a two-dimensional (2D) chiral anisotropic phase composed of nonchiral molecules. The phase consists of three sublattices with different orientational order. One sublattice is orientationally disordered, while the other two sublattices are ordered with the same scalar order parameter and different orientations of the ordering tensor. Both order parameters of the directions of ordering are determined self-consistently by minimizing the total free energy of the system. The detailed structure of this unusual phase is also confirmed by the results of Monte Carlo simulations based on the same model interaction potential. The results of the theory qualitatively explain existing experimental data and also shed some light on the origin of supramolecular structures observed in 3D columnar phases composed of similar molecules.

Chiral sign induction by vortices during the formation of mesophases in stirred solutions

Achiral diprotonated porphyrins, forming homoassociates in aqueous solution, lead to spontaneous chiral symmetry breaking. The unexpected result is that the chirality sign of these homoassociates can be selected by vortex motion during the aggregation process. This result is confirmed by means of circular dichroism spectra. These experimental findings are rationalized in terms of the asymmetric influence of macroscopic forces on bifurcation scenarios and by considering the specific binding characteristics of the porphyrin units to form the homoassociates.

Macroscopic chirality of a liquid crystal from nonchiral molecules

The transfer of chirality from nonchiral polymer networks to the racemic B2 phase of nonchiral banana-shaped molecules is demonstrated. This corresponds to the transfer of chirality from an achiral material to another achiral material. There are two levels of chirality transfers. (a) On a microscopic level the presence of a polymer network (chiral or nonchiral) favors a chiral state over a thermodynamically stable racemic state due to the inversion symmetry breaking at the polymer-liquid crystal interfaces. (b) A macroscopically chiral (enantimerically enriched) sample can be produced if the polymer network has a helical structure, and/or contains chemically chiral groups. The chirality transfer can be locally suppressed by exposing the liquid crystal to a strong electric field treatment.

Chiral hedgehog textures in two-dimensional XY-like ordered domains

The textures associated with a point defect centered in a circular domain of a thin film with XY-like ordering have been analyzed. The family of equilibrium textures, both stable and metastable, can be classified by a new radial topological number in addition to the winding number of the defect. Chiral textures are supported in an achiral system as a result of spontaneously broken chiral symmetry. Among these chiral textures, our theoretical analysis accurately describes two categories of recently discovered "reversing spiral" textures, ones that are energetically stable and metastable.

Numerical studies of domains and bubbles of langmuir monolayers

A numerical algorithm based on the finite element method has been developed to accurately determine the shape of the boundary of a domain containing "boojum" textures, which are order-parameter distributions that resemble the structure of the orbital angular momentum in a superfluid 3He droplet [N.D. Mermin, in Quantum Fluids and Solids, edited by S.B. Trickey, E. Adams, and J.Duffy (Plenum, New York, 1997)]. Within the context of the simple model we adopt, the effects of both bulk elastic anisotropy and line-tension anisotropy on the domain boundary can be examined. It is found that line-tension anisotropy must be present in order to account for domains with protruding features. Both elastic anisotropy and anisotropic line tension can result in domains with indentations. The numerical algorithm has been extended to investigate the problem of a bubble in an extended region ordered phase.

Analysis of compression-induced chiral phase separation in Langmuir monolayers

We analyze the compression-induced chiral phase separation (CPS) in Langmuir films, taking into account the elastic theory of liquid crystals and the mixing energy of the two constituent enantiomers. The difference between the Selinger-Wang-Bruinsma-Knobler theory [J. V. Selinger et al., Phys. Rev. Lett. 70, 1139 (1993)] and our treatment is that we do not introduce the concentration-square-gradient term in the free energy, but alternatively take into account a line tension at CPS boundaries. Our model predicts that a two-domain pattern with opposite chiralities is energy minimized, but a multistripe pattern with two alternate constant chiralities is also possible, though metastable. This offers a tentative explanation for the CPS pattern consisting of homogeneously oriented stripes with diverse widths observed by Eckhardt et al. [Nature (London) 362, 614 (1993)].

Long-range tilt orientational order in phospholipid monolayers: a comparative study

Monolayers of dipalmitoyl-phosphatidyl-N-monomethylethanolamine (DPP(Me)E) and dipalmitoyl-phosphatidyl-N,N-dimethylethanolamine (DPP(Me2)E) are studied and compared with dipalmitoyl-phosphatidylethanolamine (DPPE), dimyristoyl-phosphatidylethanolamine (DMPE), and dipalmitoyl-phosphatidylcholine (DPPC) to characterize the influence of the headgroup size. The properties of the condensed phases of DPP(Me2)E and DPP(Me)E are between those of DPPC and DMPE or DPPE. DPPC domains are elongated and the orientation changes continuously, whereas DMPE domains are compact and the orientation jumps at curved lines. The domains of DPP(Me2)E and DPP(Me)E are compact, and not elongated. The orientation changes continuously by 360 degrees around a point in the centered domains, and jumps of the orientation occur only in the case of twinning. Furthermore, the size of the headgroup influences the erection of the aliphatic chains. For DPPC and (DPP(Me2)E), no complete erection of chains occurs, whereas for DPP(Me)E the surface pressure required for the complete erection of chains is much higher than for DPPE. The same tendency is found for the collapse. DPPC monolayers do not collapse. DPP(Me2)E monolayers collapse at a much higher surface pressure than those of DPP(Me)E and DPPE.