The Complete Phase Diagram of Monolayers of Enantiomeric N-Stearoyl-threonine Mixtures with Preferred Heterochiral Interactions.

Langmuir monolayers of chiral amphiphiles are well-controlled model systems for the investigation of phenomena related to stereochemistry. Here, we have investigated mixed monolayers of one pair of enantiomers (l and d) of the amino-acid-based amphiphile N-stearoyl-threonine. The monolayer characteristics were studied by pressure-area isotherm measurements and grazing incidence X-ray diffraction (GIXD) over a wide range of mixing ratios defined by the d-enantiomer mole fraction xD. While the isotherms provide insights into thermodynamical aspects, such as transition pressure, compression/decompression hysteresis, and preferential homo- and heterochiral interactions, GIXD reveals the molecular structural arrangements on the Ångström scale. Dominant heterochiral interactions in the racemic mixture lead to compound formation and the appearance of a nonchiral rectangular lattice, although the pure enantiomers form a chiral oblique lattice. Miscibility was found to be limited to mixtures with 0.27 ≲ xD ≲ 0.73, as well as to both outer edges (xD ≲ 0.08 and xD ≳ 0.92). Beyond this range, coexistence of oblique and rectangular lattices occurs, as is clearly seen in the GIXD patterns. Based on the results, a complete phase diagram with two eutectic points at xD ≈ 0.25 and xD ≈ 0.75 is proposed. Moreover, N-stearoyl-threonine was found to have a strong tendency to form a hydrogen-bonding network between the headgroups, which promotes superlattice formation.

Quantum chemical assessment of the molecular area corresponding to the onset of the LE-LC phase transition for amphiphilic 2D monolayers at the air/water interface.

An approach for the assessment of the area per surfactant molecule in a monolayer at the onset of the LE-LC phase transition (Ac) is proposed based on the quantum chemical approach and a thermodynamic model for amphiphilic monolayers, which takes into account the nonideality of the mixing entropy. The values of the Gibbs' clusterization energy for small surfactant associates, as well as the geometric parameters of the monolayer unit cells, were used, previously calculated using the semiempirical PM3 method for eight classes of amphiphilic compounds: saturated and ethoxylated alcohols, saturated and unsaturated cis-carboxylic acids, α-hydroxylic and α-aminoacids, N-acyl-substituted alanine and dialkyl-substituted melamine. The obtained Ac values are in satisfactory agreement with the available experimental data. This allows using the proposed approach for prognostic purposes in the cases where there are no corresponding π-A isotherms for necessary surfactants, but there are calculated thermodynamic and structural parameters of its clusterization.

Quantum-chemical analysis of hexagonal crystalline monolayers of ethoxylated nonionic surfactants at the air/water interface.

In the framework of the quantum chemical semiempirical PM3 method the monolayers of the monoethoxylated normal alcohols CnH2n+1OCH2CH2OH with n = 6-16 (CnE1) at the air/water interface are described. The optimized structures of small clusters (dimers, trimers, tetramers, pentamers, hexamers and heptamers) comprising the hexagonal monolayer are obtained. For these aggregates thermodynamic parameters of formation and clusterization are calculated. The correlation dependencies of the clusterization enthalpy, entropy and Gibbs energy on the number of CHHC interactions and interactions between the functional groups realized in the cluster are obtained on the basis of calculated data. The calculated parameters of the hexagonal monolayer unit cell are: a = 4.02 Å; b = 7.94 Å, t = 4°, close to those for an aliphatic alcohol monolayer according to GIXD experiments: a = 5.0 Å; b = 7.5 Å, t = 0-9°. Spontaneous clusterization of monoethoxylated alcohols at the air/water interface under standard conditions is shown to be possible for molecules possessing more than 14 carbon atoms in the alkyl chain, in good agreement with the characteristics of the surface pressure-molecular area (π-A) isotherms. It is found that addition of the -O-CH2-CH2- unit to the hydrophilic part of aliphatic alcohols results in a shift of their spontaneous clusterization threshold to that of the compounds with hydrocarbon chains 3 methylene units longer. The temperature effect of CnE1 is assessed. It corresponds to the spontaneous clusterization temperature decrease of 10-20 K per two methylene units taken from the alkyl chain in agreement with experimental data. The comparison of clusterization Gibbs energy dependencies for small aggregates of CnE1 confirms the experimental fact that the crystalline monolayers are formed by preferential aggregation of trimers.

Numerical solution of the t-J model with random exchange couplings in d=∞ dimensions.

To explore the nature of the metallic state near the transition to a Mott insulator, we investigate the t-J model with random exchange interaction in d=∞ dimensions. A numerically exact solution is obtained by an extension of the continuous-time quantum Monte Carlo method to the case of a vector bosonic field coupled to a local spin. We show that the paramagnetic solution near the Mott insulator describes an incoherent metal with a residual moment, and that single-particle excitations produce an additional band, which is separated from the Mott-Hubbard band.

Emergence of a common energy scale close to the orbital-selective Mott transition.

We calculate the spectra and spin susceptibilities of a Hubbard model with two bands having different bandwidths but the same on-site interaction, with parameters close to the orbital-selective Mott transition, using dynamical mean-field theory. If the Hund's rule coupling is sufficiently strong, one common energy scale emerges which characterizes both the location of kinks in the self-energy and extrema of the diagonal spin susceptibilities. A physical explanation of this energy scale is derived from a Kondo-type model. We infer that for multiband systems local spin dynamics rather than spectral functions determine the location of kinks in the effective band structure.

On the inclusion of alkanes into the monolayer of aliphatic alcohols at the water/alkane vapor interface: a quantum chemical approach.

In the framework of the quantum chemical semiempirical PM3 method thermodynamic and structural parameters of the formation and clusterization of aliphatic alcohols C(n)H(2n+1)OH (n(OH) = 8-16) at 298 K at the water/alkane vapor C(n)H(2n+2), (n(CH(3)) = 6-16) interface were calculated. The dependencies of enthalpy, entropy and Gibbs' energy of clusterization per one monomer molecule of 2D films on the alkyl chain length of corresponding alcohols and alkanes, the molar fraction of alkanes in the monolayers and the immersion degree of alcohol molecules into the water phase were shown to be linear or stepwise. The threshold of spontaneous clusterization of aliphatic alcohols at the water/alkane vapor interface was 10-11 carbon atoms at 298 K which is in line with experimental data at the air/water interface. It is shown that the presence of alkane vapor does not influence the process of alcohol monolayer formation. The structure of these monolayers is analogous to those obtained at the air/water interface in agreement with experimental data. The inclusion of alkane molecules into the amphiphilic monolayer at the water/alkane vapor interface is possible for amphiphiles with the spontaneous clusterization threshold at the air/water interface (n(s)(0)) of at least 16 methylene units in the alkyl chain, and it does not depend on the molar fraction of alkanes in the corresponding monolayer. The inclusion of alkanes from the vapor phase into the amphiphilic monolayer also requires that the difference between the alkyl chain lengths of alcohols and alkanes is not larger than n(s)(0) - 15 and n(s)(0) - 14 for the 2D film 1 and 2D film 2, respectively.

Quantification of correlations in quantum many-particle systems.

We introduce a well-defined and unbiased measure of the strength of correlations in quantum many-particle systems which is based on the relative von Neumann entropy computed from the density operator of correlated and uncorrelated states. The usefulness of this general concept is demonstrated by quantifying correlations of interacting electrons in the Hubbard model and in a series of transition-metal oxides using dynamical mean-field theory.

Route to ferromagnetism in organic polymers.

Employing a rigorous theoretical method for the construction of exact many-electron ground states we prove that interactions can be employed to tune a bare dispersive band structure such that it develops a flat band. Thereby, we show that pentagon-chain polymers with electron densities above half filling may be designed to become ferromagnetic or half metallic.

Relationship between the Bulk and Surface Basicity of Aliphatic Amines: A Quantum Chemical Approach.

To assess the surface basicity constant (pK b) of aliphatic amine films, the use of a theoretical approach recently developed to evaluate the pK a of carboxylic acid monolayers on the water surface is tested. The present paper gives a new full picture of the change of acid-base properties of surfactants during their aggregation at the air/water interface. The exploited approach is simple because it does not involve the construction of thermodynamic cycles but uses the Gibbs energies of the formation and dimerization of surfactant monomers in neutral and ionized forms in the aqueous and gaseous phases. The quantum chemical semiempirical PM3 method is applied to perform calculations using a conductor-like screening model, which takes into account the aqueous phase. The calculation shows that aliphatic amines, as well as carboxylic acids, are characterized by a change of the value of the basicity/acidity constant during the film formation. The film formation of surfactants leads to a decrease in their acid-base properties, i.e., the surface pK a values of carboxylic acids and pK b values of amines increase. However, unlike carboxylic acids, there is practically no dependence of the surface pK b value on the alkyl chain length of the aliphatic amine, which is caused by almost identical contributions of one CH2 fragment to the solvation Gibbs energy of neutral and ionized monomers within the calculation error. The obtained results agree with existing experimental data.

Theoretical Description of Mixed Film Formation at the Air/Water Interface: Carboxylic Acids-Alcohols.

The thermodynamic parameters of formation and clusterization of aliphatic alcohols C n H2n+1OH and carboxylic acids C n H2n+1COOH (n = 6-16) are calculated using the quantum-chemical semiempirical PM3 method. Four types of dimers are constructed in two directions of the spread monolayer comprising the most energetically advantageous monomer structures. The hydrophobic chains of alcohol and carboxylic acid molecules in the regarded dimers are found to be tilted within 12° to the normal of the spread monolayer. The structures of the mixed and pure surfactant dimers are the basis for the mixed alcohol-carboxylic acid monolayers of the following types: two dimensional (2D) film 1 with single distribution of the individual component in the other one, when the molecules of the first component do not interact with each other but are completely surrounded by the molecules of the second component; 2D film 2 with domain structure, when the film consists of "islands" of the individual components. The dependences of the clusterization Gibbs' energy per one monolayer molecule on the molar fraction of the components for the mixed 2D films 1 formed by surfactants with equal alkyl chain length are found to be limited from top to bottom by the corresponding dependences for pure components. This indicates the absence of synergetic interaction between the hydrophilic head groups of carboxylic acids and alcohols and conforms to the available experimental data. The formation of the described types of mixed films is competitive. The preferential formation of 2D films 1 with single distribution of the first component among the molecules of the second one is possible when the length of the carboxylic acid hydrocarbon chain is longer by Δn = 1-2 methylene units than that of the corresponding alcohol alkyl chain. According to the fractionally linear law, the highest possible content of the carboxylic acids in such 2D films 1 depends on the Δn value and does not exceed 33.3%.

Local electron-electron interaction strength in ferromagnetic nickel determined by spin-polarized positron annihilation.

We employ a positron annihilation technique, the spin-polarized two-dimensional angular correlation of annihilation radiation (2D-ACAR), to measure the spin-difference spectra of ferromagnetic nickel. The experimental data are compared with the theoretical results obtained within a combination of the local spin density approximation (LSDA) and the many-body dynamical mean-field theory (DMFT). We find that the self-energy defining the electronic correlations in Ni leads to anisotropic contributions to the momentum distribution. By direct comparison of the theoretical and experimental results we determine the strength of the local electronic interaction U in ferromagnetic Ni as 2.0 ± 0.1 eV.

Helfrich's concept of intrinsic force and its molecular origin in bilayers and monolayers.

Bilayers and monolayers are excellent models of biological membranes. The constituents of the biological membranes such as lipids, cholesterols and proteins are chiral. Chiral molecules are abundant in nature (protein, nucleic acid and lipid). It is obvious that relationship between chirality and morphology (as well as function) of biological membrane is of interest for its fundamental importance and has technological implication regarding various membrane functions. The recent years have witnessed that a number of experimental studies in biomimetic systems have shown fascinating morphologies where chirality of the constituent molecule has decisive influence. Significant progress is made towards the understanding of these systems from the theoretical and computational studies. Helfrich's concept of intrinsic force arising from chirality is a milestone in understanding the biomimetic system such as bilayer and the related concepts, further progresses in molecular understanding made in recent years and experimental studies revealing the influence of chirality on morphology are the focus of the present review. Helfrich's concept of intrinsic force arising due to chirality is useful in understanding two-dimensional bilayers and one-dimensional monolayers and related mimetic systems. Various experimental techniques are used, which can probe the molecular architecture of these mimetic systems at different length scales and both macroscopic (thermodynamic) as well as microscopic (molecular) theories are developed. These studies are aimed to understand the role of chirality in the molecular interaction when the corresponding molecule is present in an aggregate. When one looks into the variety of morphologies exhibited by three-dimensional bilayer and two-dimensional monolayer, the later types of systems are more exotic in the sense that they show more diversity and interesting chiral discrimination. Helfrich's concept of intrinsic force may be considered useful in both cases. The intrinsic force due to chirality is the decisive factor in determining morphology which is explained by molecular approaches. Finally, biological and technological implications of such morphological variations are briefly mentioned.

Competition between Anderson localization and antiferromagnetism in correlated lattice fermion systems with disorder.

The magnetic ground state phase diagram of the disordered Hubbard model at half-filling is computed in dynamical mean-field theory supplemented with the spin resolved, typical local density of states. The competition between many-body correlations and disorder is found to stabilize paramagnetic and antiferromagnetic metallic phases at weak interactions. Strong disorder leads to Anderson localization of the electrons and suppresses the antiferromagnetic long-range order. Slater and Heisenberg antiferromagnets respond characteristically differently to disorder. The results can be tested with cold fermionic atoms loaded into optical lattices.

Ferromagnetism and Kondo insulator behavior in the disordered periodic Anderson model.

The effect of binary alloy disorder on the ferromagnetic phases of f-electron materials is studied within the periodic Anderson model. We find that disorder in the conduction band can drastically enhance the Curie temperature T{c} due to an increase of the local f moment. The effect may be explained qualitatively and even quantitatively by a simple theoretical ansatz. The emergence of an alloy Kondo insulator at noninteger filling is also pointed out.

Molecular interactions in amphiphilic assemblies: theoretical perspective.

In recent experimental studies, a number of morphological features have been revealed on amphiphilic assemblies that need consideration of the molecular chiral structure and the molecular polarity. Molecular chirality and polarity influence the intermolecular energy profile as a function of the distance and orientation between neighboring molecules in the condensed-phase aggregates of mono- and bilayers. After the experimental information is summarized, related microscopic theoretical works are presented. The molecular theory shows that the mesoscopic chiral shape of the condensed phase can be predicted from the molecular chiral structure studying the intermolecular energy profile. The theoretical insights have implications for related biological systems.

Exact many-electron ground states on the diamond Hubbard chain.

Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation-induced metallic, half-metallic, or insulating behavior. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density.

Mott-Hubbard transition versus Anderson localization in correlated electron systems with disorder.

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged ("typical") local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.

Phase behavior of 2,3-disubstituted methyl octadecanoate monolayers at the air-water interface.

The phase behavior of 2,3-disubstituted methyl octadecanoate monolayers at the air-water interface is studied by film balance and a Brewster angle microscope (BAM). The comparison of the surface pressure-molecular area (pi-A) isotherms with the corresponding BAM images provides information on the phase behavior of the monolayers. Variations in the phase behavior of different 2,3-disubstituted methyl octadecanoate monolayers can be correlated with the size of the headgroups, the interactions between the polar molecular moieties and the subphase, and the intermolecular interactions. The enlarging of the headgroups makes forming a condensed monolayer difficult for the molecules, even after introduction of substituents giving rise to the formation of hydrogen bonds between the molecules, which may balance the steric repulsion and stabilize the monolayers. Model calculations of the two-dimensional lattice structure of the 2,3-disubstituted methyl octadecanoates on basis of the pg and p1 space group are performed and correspond well with the experimental results.