De Gennes Research Articles

Annihilation of Highly-Charged Topological Defects

We studied numerically external stimuli enforced annihilation of a pair of daughter nematic topological defect (TD) assemblies bearing a relatively strong topological charge |m|=3/2. A Landau- de Gennes phenomenological approach in terms of tensor nematic order parameter was used in an effectively two-dimensional Cartesian coordinate system, where spatial variations along the z-axis were neglected. A pair of {m=3/2,m=−3/2} was enforced by an appropriate surface anchoring field, mimicking an experimental sample realization using the atomic force microscope (AFM) scribing method. Furthermore, defects were confined within a rectangular boundary that imposes strong tangential anchoring. This setup enabled complex and counter-intuitive annihilation processes on varying relevant parameters. We present two qualitatively different annihilation paths, where we either gradually reduced the relative surface anchoring field importance or increased an external in-plane spatially homogeneous electric field E. The creation and depinning of additional defect pairs {12,−12} mediated the annihilation in such a geometry. Furthermore, we illustrate the absorption of TDs by sharp edges of the confining boundary, accompanied by m=±1/4↔∓1/4 winding reversal of edge singularities, and also E-driven zero-dimensional to one-dimensional defect core transformation.

Perfectly matched layers for Schrödinger-type equations with nontrivial energy–momentum dispersion

The construction of perfectly-matched-layer (PML) boundary conditions is extended to wave equations with non-trivial energy–momentum dispersion relation. Complex coordinate extension is based upon the relative sign between the surface-normal component of group velocity and the k-vector. This ensures selective damping of propagating and counter-propagating modes at the simulation boundaries. Moreover, the technical complexity of the PML method can be inferred from the energy–momentum dispersion relation of the underlying wave equation, respectively, the finite-difference scheme employed. The PML transform is derived for selected Schrödinger-type (i.e. first-order-in-time) kinetic transport equations. Spectral analysis demonstrates proper damping behaviour of out-propagating modes. Results are presented for the Schrödinger equation for particles and holes, the s- and p-wave Bogoliubov–de Gennes equation, the Dirac equation, and the Dohnal k⋅p model. Where available, a comparison to previous PML formulations is made.

Breathing modes of repulsive polarons in Bose–Bose mixtures

We consider impurity atoms embedded in a two-component Bose–Einstein condensate in a quasi-one dimensional regime. We study the effects of repulsive coupling between the impurities and Bose species on the equilibrium of the system for both miscible and immiscible mixtures by numerically solving the underlying coupled Gross–Pitaevskii equations. Our results reveal that the presence of impurities may lead to a miscible–immiscible phase transition due to the interaction of the impurities and the two condensates. Within the realm of the Bogoliubov–de Gennes equations we calculate the quantum fluctuations due to the different types of interactions. The breathing modes and the time evolution of harmonically trapped impurities in both homogeneous and inhomogeneous binary condensates are deeply discussed in the miscible case using variational and numerical means. We show in particular that the self-trapping, the miscibility and the inhomogeneity of the trapped Bose mixture may strongly modify the low-lying excitations and the dynamical properties of impurities. The presence of phonons in the homogeneous Bose mixture gives rise to the damping of breathing oscillations of impurities width.

Discontinuous Galerkin finite element methods for the Landau–de Gennes minimization problem of liquid crystals

Abstract We consider a system of second-order nonlinear elliptic partial differential equations that models the equilibrium configurations of a two-dimensional planar bistable nematic liquid crystal device. Discontinuous Galerkin (dG) finite element methods are used to approximate the solutions of this nonlinear problem with nonhomogeneous Dirichlet boundary conditions. A discrete inf–sup condition demonstrates the stability of the dG discretization of a well-posed linear problem. We then establish the existence and local uniqueness of the discrete solution of the nonlinear problem. A priori error estimates in the energy and $\mathbf{L}^2$ norms are derived and a best approximation property is demonstrated. Further, we prove the quadratic convergence of the Newton iterates along with complementary numerical experiments.

Investigation of eigenvalues and scattering problem for the Bogoliubov – de Gennes Hamiltonian near the superconducting gap edge

Investigation of eigenvalues and scattering problem for the Bogoliubov – de Gennes Hamiltonian near the superconducting gap edge

Crystal structure and complex magnetic properties of R11Pd4In9 compounds (R = Y, Gd–Er)

Magnetic properties of the R11Pd4In9 compounds (R = Y, Gd–Er) were investigated by means of X-ray diffraction and magnetic measurements. Three of these compounds, namely those with R = Y, Ho and Er, are newly synthesized. The compounds crystallize in the orthorhombic Nd11Pd4In9-type crystal structure (oC48, Cmmm) in which the rare earth atoms occupy five nonequivalent sublattices. Magnetic properties of the investigated compounds are related mainly to the R3+ ions, except the case of Y11Pd4In9 which is a Pauli paramagnet. For R = Gd-Er, the values of effective magnetic moments in the paramagnetic state are close to the free R3+ ion values while the moments in the ordered state at T = 2 K and H = 90 kOe are lower than the respective R3+ moments. The compounds have complex magnetic properties. All paramagnetic Curie temperatures are positive suggesting that the ferromagnetic interactions are predominant. However, the low temperature data indicate an antiferromagnetic order. With increase of temperature the magnetic properties change from antiferro-to ferrimagnetic and finally to paramagnetic ones. The critical temperatures of magnetic ordering do not fulfill the de Gennes scaling, indicating a crystalline electric field contribution to stabilization of the magnetic order at low temperatures. The neutron diffraction measurements, performed for Ho11Pd4In9, reveal a coexistence of two magnetic phases at low temperatures: the antiferromagnetic with propagation vector k = [0,0,½] and the ferrimagnetic one with k = [0,0,0]. The antiferromagnetic order is predominant at low temperatures while the ferrimagnetic one dominates at intermediate temperatures.

Long Tails with Flower-like Conformations Undergo an Escape Transition in Homopolymer Adsorption Layers.

De Gennes predicted that homopolymer adsorption on a solid–liquid interface results in an adsorption profile with a proximal, a central, and a distal region, wherein, for a good solvent, the central region has a self-similar structure with a density profile that decays as a power law with a coefficient of −4/3. Recent numerical self-consistent field (SCF) predictions for the long-chain length (N) limit revealed a more complex central region with an inner part, where the loops dominate the layer, with a (mean-field) power-law coefficient of −2 and an outer part, where tails dominate, with a “de Gennes” scaling of −4/3. The tails with length t < t* contribute to the inner part of the central region, and these have similar conformations as the loops. The outer part is populated by tails with a length t > t*, and these behave differently. With the increasing length of the tails, there exists a weak escape transition at t = tescape ≈ N/10. Long tails in the adsorption profile (t ≳ t* ∝ N0.733) show enhanced fluctuations due to this nearby escape transition, and this explains the excluded volume scaling for the outer part of the central region in SCF. With this interpretation, the −2 scaling found by SCF for the inner part should be classified as a mean-field result.

Simulating the Effects of Excluded-Volume Interactions in Polymer Solutions

Excluded-volume interactions are ubiquitous to modeling the average size of polymers in solution. This paper shows how simulations can be used by students to explore the emergence of mathematical scaling relations from excluded-volume interactions. Simulations provide robust visual representations of the system, and can be used to investigate a wide scope of problems and scenarios. The simulations were built with the free VPython coding environment and relatively basic algorithms. The results align with the mathematical theories of Flory and De Gennes and provide access to additional insights that are less obvious in the mathematical treatments. Students with relatively basic programming knowledge were able to extend and modify these models and to examine their alignment with mathematical theories. These examples extend the growing literature on simulation-based approaches for teaching and learning chemistry.

Superconducting proximity effect in flat band systems

We study theoretically proximity-induced superconductivity and its inverse effect in dice lattice flat band model by considering Josephson junction with an s-wave pairing in the superconducting leads. Using self-consistent tight-binding Bogoliubov–de Gennes method, we show that there is a critical value for chemical potential of the superconductors depending on paring interaction strength over which for undoped normal region the proximity effect is enhanced. Whereas if the supserconductor chemical potential is less than the critical one the proximity effect decreases regardless of normal region doping and in the meanwhile, the pairing amplitude of superconducting region increases significantly. Furthermore, we unveil that the supercurrent passing through the junction is large (vanishingly small) when the superconductor chemical potential is smaller (larger) than the critical value which increases as a function of normal region chemical potential.

Nonlocality of Majorana zero modes and teleportation: Self-consistent treatment based on the Bogoliubov–de Gennes equation

The nonlocal nature of the Majorana zero modes implies an inherent teleportation channel and unique transport signatures for Majorana identification. In this work we make an effort to eliminate some inconsistencies between the Bogoliubov-de Gennes equation based treatment and the method using the associated regular fermion number states of vacancy and occupation within the `second quantization' framework. We first consider a rather simple `quantum dot--Majorana wire--quantum dot' system, then a more experimentally relevant setup by replacing the quantum dots with transport leads. For the latter setup, based on the dynamical evolution of electron-hole excitations, we develop a single-particle-wavefunction approach to quantum transport, which renders both the conventional quantum scattering theory and the steady-state nonequilibrium Green's function formalism as its stationary limit. Further, we revisit the issue of Majorana tunneling spectroscopy and consider in particular the two-lead coupling setup. We present comprehensive discussions with detailed comparisons, and predict a zero-bias-limit conductance of $e^2/h$ (for symmetric coupling to the leads),which is a half of the popular result of the zero-bias-peak, or, the so-called Majorana quantized conductance ($2e^2/h$). The present work may arouse a need to reexamine some existing studies and the proposed treatment is expected to be involved in analyzing future experiments in this fast developing field.

Study of Fractal Characteristics of Individual Macromolecular Tangles

The fractal characteristics of individual macromolecular tangles of block and random copolymers are investigated. It was found that the dependence of the mass of macromolecules on the radius of inertia of a statistically significant sample is well described by the de Gennes equation with a fractal dimension of 5/3. It was established that the fine structure of the polymer coil also has a fractal nature. The fractal dimension inside the macromolecular coil changes significantly with distance from the center of mass.

Superfluidity of fermionic pairs in a harmonic trap. Comparative studies: Local Density Approximation and Bogoliubov-de Gennes solutions

Experiments with ultracold gases on the lattice give the opportunity to realize superfluid fermionic mixtures in a trapping potential. The external trap modifies the chemical potential locally. Moreover, this trap also introduces non-homogeneity in the superconducting order parameter. There are, among other approaches, two methods which can be used to describe the system of two-component mixtures loaded into an optical lattice: the Local Density Approximation (LDA) and the self-consistent Bogoliubov–de Gennes equations. Here, we compare results obtained within these two methods. We conclude that the results can be distinguishable only in the case of a small value of the pairing interaction.

Influence of hydrophobic and electrostatic interactions on counterion-dissociation in sodium carboxymethylcellulose - polyethylene glycol (PEG) solutions

Counterion dissociation/condensation and related phenomena of sodium carboxymethylcellulose have been investigated in water with varying hydrophobicity by conductance measurements. Alteration of the hydrophobicity of the media was accomplished by adding varying amounts of polyethylene glycol with different molar masses to the solutions. Analyses of the specific conductances measured as a function of sodium carboxymethylcellulose concentration were performed taking into account the de Gennes scaling model which describes the configuration of polyion chains in semidilute solutions. Results indicate that polyions are the chief transporter of the electricity in the investigated solutions and that a major fraction of the counterions is accompanied by the polyion chains and performs concerted movement towards the positive electrode. Increasing molar mass of the polyethylene glycol samples added to aqueous sodium carboxymethylcellulose solutions containing a given amount of the additive promotes counterion-dissociation, whereas increasing amount of the additive with a given molar mass promotes counterion-condensation. Relative influences of electrostatic and hydrophobic forces have been taken into consideration in order to elucidate the observed dissociation/condensation behavior of counterions of aqueous sodium carboxymethylcellulose solutions. Analyses of the results provided important insight regarding the possible alterations of the conformation of the polyions originating from the subtle balance of hydrophobic and electrostatic interactions in these solutions.

Equilibrium Solvation, Electron-Transfer Reactions, and Stokes-Shift Dynamics in Ionic Liquids.

A microscopic theory of solvent response by room-temperature ionic liquids is formulated based on the dynamic longitudinal susceptibility of liquid's charge density. The susceptibility function combines the structural information in terms of reciprocal-space structure factors with the memory function responsible for solvation dynamics. The charge-density structure factors and corresponding intermediate scattering functions are analyzed here by molecular dynamics simulations. They show the existence of two drastically different time scales of charge-density fluctuations. Faster, stretched-exponential dynamics are consistent with dielectric measurements. It contributes to the Stokes-shift dynamics of coumarin-153 optical dye calculated with the new theory and compared to experimental reports. The second, much slower and exponential, relaxation shows the phenomenology of de Gennes narrowing: the relaxation time passes through a strong maximum at the wave vector representing the first peak of the structure factor. This peak, which is particularly sharp for the charge density, contributes significantly to the equilibrium free energy of solvation, thus invalidating dielectric theories of solvation for ionic liquids. Dynamics of charge density fluctuations at the length scale consistent with the sharp peak require long observation times. Electron-transfer reactions occurring on faster time-scales are not affected by these slow dynamics. Nonergodic reorganization energy of electron transfer, accounting for the observation window established by the reaction time, drops sharply when the reaction rate crosses the main peak in the Stokes-shift loss spectrum. The dependence of the reorganization energy on the reaction rate strongly affects the energy-gap law of electron transfer, with a tendency for a shallow or entirely disappearing inverted region.

Theoretical study on the effect of electric field for carbon nanotubes dispersed in nematic liquid crystal

Nematic liquid crystal (NLC) plays an important role in the controlled alignment of carbon nanotubes (CNTs). When nematogens are strongly anchored over the surfaces of CNTs, the Liquid Crystal (LC) order parameter is greatly influenced. Moreover, the electro-optic properties of the medium are significantly improved. Application of electric field further modifies these novel properties. The effect of electric field not only changes the phase behavior but also influences the ordering of both LC molecules and CNTs. Utilizing Doi and Landau–de Gennes type free energy mechanism, we have investigated in detail the changes incurred by the electric field. Order parameters of both LC and CNTs are calculated and modified phase diagrams are drawn. Finally, we have employed Landau–Khalatnikov equation to calculate rotational viscosity of the medium. It is found that rotational viscosity decreases with increasing volume fraction of CNTs in accordance with experimental results.

Changes of Conformation in Albumin with Temperature by Molecular Dynamics Simulations.

This work presents the analysis of the conformation of albumin in the temperature range of –, i.e., in the physiological range. Using molecular dynamics simulations, we calculate values of the backbone and dihedral angles for this molecule. We analyze the global dynamic properties of albumin treated as a chain. In this range of temperature, we study parameters of the molecule and the conformational entropy derived from two angles that reflect global dynamics in the conformational space. A thorough rationalization, based on the scaling theory, for the subdiffusion Flory–De Gennes type exponent of unfolds in conjunction with picking up the most appreciable fluctuations of the corresponding statistical-test parameter. These fluctuations coincide adequately with entropy fluctuations, namely the oscillations out of thermodynamic equilibrium. Using Fisher’s test, we investigate the conformational entropy over time and suggest its oscillatory properties in the corresponding time domain. Using the Kruscal–Wallis test, we also analyze differences between the root mean square displacement of a molecule at various temperatures. Here we show that its values in the range of – are different than in another temperature. Using the Kullback–Leibler theory, we investigate differences between the distribution of the root mean square displacement for each temperature and time window.

Two-band superconducting square with a central defect: role of the deGennes extrapolation length

We present the influence of the deGennes extrapolation length on the vortex matter in a two band superconducting square with a central defect. This is determined by considering different values of the de Gennes extrapolation length b on the lateral surface of the sample. Our investigation was carried out by solving the two-dimensional time-dependent Ginzburg-Landau equations for a two-band system (2B-TDGL). We studied the density, magnetization, vorticity, and critical fields of the superconducting electrons as functions of the external applied magnetic field for different values of b on the surfaces of the sample and different sizes of the internal square defect. We show an unconventional vortex state due to the repulsive (attractive) short- (long-) range potential between the vortices. Finally, we show that at the limit of the thin film, a two-band system behaves like a three-band system.

Magnetic ordering at anomalously high temperatures in selected lanthanides: what about Pr?

Recent experiments have given evidence that for elemental Nd, Tb, and Dy the application of sufficient pressure pushes their magnetic ordering temperatures to anomalously high values. Pr metal has a dhcp structure and is trivalent with the 4f2 configuration. Its singlet ground state suppresses magnetic order from the 15 K anticipated from de Gennes scaling to 50 mK. Four-point electrical resistivity measurements were carried out on Pr for temperatures 1.5–295 K under pressures to 48 GPa. Although no clear evidence for magnetic order (or superconductivity) is observed above 1.5 K, the temperature dependence of the resistivity gives evidence that Pr may enter a dense Kondo state above 10 GPa.

What Is the Value of Water Contact Angle on Silicon?

Silicon is a widely applied material and the wetting of silicon surface is an important phenomenon. However, contradictions in the literature appear considering the value of the water contact angle (WCA). The purpose of this study is to present a holistic experimental and theoretical approach to the WCA determination. To do this, we checked the chemical composition of the silicon (1,0,0) surface by using the X-ray photoelectron spectroscopy (XPS) method, and next this surface was purified using different cleaning methods. As it was proved that airborne hydrocarbons change a solid wetting properties the WCA values were measured in hydrocarbons atmosphere. Next, molecular dynamics (MD) simulations were performed to determine the mechanism of wetting in this atmosphere and to propose the force field parameters for silica wetting simulation. It is concluded that the best method of surface cleaning is the solvent-reinforced de Gennes method, and the WCA value of silicon covered by SiO2 layer is equal to 20.7° (at room temperature). MD simulation results show that the mechanism of pure silicon wetting is similar to that reported for graphene, and the mechanism of silicon covered by SiO2 layer wetting is similar to this observed recently for a MOF.

Calculation of compositions of dispersed-filled polymer composites with different structures and properties

For the first time, calculations of compositions of dispersion-filled polymer composites with given structure parameters are presented, which take into account the construction of an infinite cluster, various types of lattices, the main parameters of lattices - coordination number (Z) and packing density (kуп) according to the De Gennes – Shklovsky model, as well as generalized parameters of structures (Θ), shape, size, maximum packaging (φm) and content of dispersed filler (φн).The dependencies and tabular data on the relationship of lattice parameters (Z, kуп) with the generalized parameter Θ (the proportion of the polymer matrix for the formation of a continuous interlayer between dispersed particles) of the composite structure are given, which determine the content of the filler to create a dispersed structure with specified parameters and properties.