Lifshitz Theory Research Articles

Surface Forces between Titanium Dioxide Surfaces in the Presence of Cationic Surfactant as a Function of Surfactant Concentration, Electrolyte Concentration, and pH

Titanium dioxide (titania) surfaces produced by atomic layer deposition (ALD) are suitable for surfactant adsorption and surface force measurements. Adsorption isotherms for cetyltrimethylammonium bromide (CTAB) on ALD titanium dioxide surfaces were measured using optical reflectometry (OR), and surface force measurements between ALD titanium dioxide surfaces in aqueous CTAB solutions were measured using the colloid probe technique at different pH and electrolyte concentrations. Measurements were performed at a range of concentrations below and above the common intersection point (CIP) where adsorption is dominated by electrostatic and hydrophobic interactions, respectively. An examination of surfactant adsorption above and below the isoelectric point (IEP) was performed. Interestingly, significant levels of adsorption were observed below the IEP where the electrostatic interactions are unfavorable. The adsorption results are used to interpret the force data, which is dependent upon the amount of surfactant adsorbed and the electrolyte concentration and pH. The surface force data is compared to DLVO theory. Poor fits are obtained when Lifshitz theory is used to describe the dispersion forces. However, all of the data are fit well with a dispersion force of reduced magnitude. The kinetics of adsorption was measured and reveals very slow adsorption kinetics below the critical micelle concentration as a result of the monomer-by-monomer formation of aggregates on the surface.

Probing Atom-Surface Interactions by Diffraction of Bose-Einstein Condensates

In this article we analyze the Casimir-Polder interaction of atoms with a solid grating and an additional repulsive interaction between the atoms and the grating in the presence of an external laser source. The combined potential landscape above the solid body is probed locally by diffraction of Bose-Einstein condensates. Measured diffraction efficiencies reveal information about the shape of the Casimir-Polder interaction and allow us to discern between models based on a pairwise-summation (Hamaker) approach and Lifshitz theory.

BLACK HOLE THERMODYNAMIC FLUCTUATIONS AND PHASE TRANSITION OF IR MODIFIED HOŘAVA–LIFSHITZ GRAVITY

Hořava–Lifshitz theory as a renormalizable model of gravity might be an ultraviolet (UV) completion of general relativity (GR) and it reduces to Einstein gravity with a nonvanishing cosmological constant in infrared (IR) approximation. Kehagias and Sfetsos have added a relevant operator proportional to the three-dimensional (3D) geometry Ricci scalar to the original Hořava–Lifshitz theory action and obtained a spherically symmetric asymptotically flat black hole solution called Kehagias–Sfetsos (KS) black hole. Nonequilibrium thermodynamic fluctuations based on the metric of a KS black hole in IR modified Hořava–Lifshitz gravity have been calculated. It is concluded that the second-order momentum of mass flux is nondivergent and phase transition does not occur at the extremal case, while phase transition occurs at some other case, which is also different from the common case when the heat capacity is divergent.

On the effect of van der Waals attractions on the critical salt concentration for inhibiting bubble coalescence

The coalescence of gas bubbles in many salt solutions such as NaCl is significantly inhibited if the salt concentration exceeds a critical concentration which is unique for each salt. It has been predicted as a function of the Hamaker constants of van der Waals attractions between two bubbles. In this paper, the Lifshitz theory on the van der Waals interaction energy and the available spectrum for water dielectric permittivity are applied to determine the Hamaker constants for liquid films between bubbles in pure water and salt solutions. Using the new values for Hamaker constants for thin films of saline solutions, we show that the effect of van der Waals attractions on the critical salt concentration is significantly weaker than previously hypothesized. The predictions based on van der Waals attractions significantly under-estimate the experimental critical concentrations. The failure of the van der Waals attraction in predicting the critical salt concentration highlights the urgent need of revising the available theories on bubble coalescence in salt solutions and saline water.

New constraints on Yukawa-type corrections to Newtonian gravity at short separations

We discuss the strongest constraints on Yukawa-type corrections to Newton’s gravitational law within a submicrometer interaction range, following from measurements of the Casimir force. In this connection, the complicated problems arising when comparing the measurement data with the Lifshitz theory are analyzed. Special attention is paid to the results of two recent experiments on measuring the Casimir interaction between ferromagnetic surfaces and sinusoidally corrugated surfaces at various angles between corrugations.

General Relativity without paradigm of space-time covariance, and resolution of the problem of time

The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full space-time covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical structure, yield transparent physical dynamics and a resolution of the problem of time. The deep divide between quantum mechanics and conventional canonical formulations of quantum gravity is overcome with a Schrodinger equation for quantum geometrodynamics that describes evolution in intrinsic time. Unitary time development with gauge-invariant temporal ordering is also viable. All Kuchar observables become physical; and classical space-time, with direct correlation between its proper times and intrinsic time intervals, emerges from constructive interference. The framework not only yields a physical Hamiltonian for Einstein’s theory, but also prompts natural extensions and improvements towards a well behaved quantum theory of gravity. It is a consistent canonical scheme to discuss Horava–Lifshitz theories with intrinsic time evolution, and of the many possible alternatives that respect 3-covariance (rather thanthemorerestrictive4-covariance ofEinstein’stheory), Horava’s “detailed balance” form of the Hamiltonian constraint is essentially pinned down by this framework. Issues in quantum gravity that depend on radiative corrections and the rigorous definition and regularization of the Hamiltonian operator are not addressed in this work.

Repulsive interactions of a lipid membrane with graphene in composite materials

The van der Waals interaction between a lipid membrane and a substrate covered by a graphene sheet is investigated using the Lifshitz theory. The reflection coefficients are obtained for a layered planar system submerged in water. The dielectric response properties of the involved materials are also specified and discussed. Our calculations show that a graphene covered substrate can repel the biological membrane in water. This is attributed to the significant changes in the response properties of the system due to the monolayer graphene. It is also found that the van der Waals interaction is mostly dominated by the presence of graphene, while the role of the particular substrate is secondary.

Casimir interaction between two magnetic metals in comparison with nonmagnetic test bodies

We present the complete results for the dynamic experiment on measuring the gradient of the Casimir force between magnetic (Ni-coated) surfaces of a plate and a sphere. Special attention is paid to the description of some details of the setup, its calibration, error analysis, and background effects. Computations are performed in the framework of the Lifshitz theory at nonzero temperature with an account of analytic corrections to the proximity force approximation and of surface roughness using both the Drude and the plasma model approaches. The theory of magnetic interaction between a sphere and a plate due to domain structure of their surfaces is developed for both out-of-plane and in-plane magnetizations in the absence and in the presence of spontaneous magnetization. It is shown that in all cases the magnetic contribution to the measured force gradients is much smaller than the total experimental error. The comparison between experiment and theory is done using the rigorous statistical method. It is shown that the theoretical approach taking into account dissipation of free electrons is excluded by the data at a 95% confidence level. The approach neglecting dissipation is confirmed by the data at more than 90% confidence level. We prove that the results of experiments with Ni-Ni, Ni-Au, and Au-Au surfaces taken together cannot be reconciled with the approach including free electrons dissipation by the introduction of any unaccounted background force, either attractive or repulsive.

Computations of Lifshitz–van der Waals interaction energies between irregular particles and surfaces at all separations for resuspension modelling

The phenomenon of particle resuspension plays a vital role in numerous fields. Among many aspects of particle resuspension dynamics, a dominant concern is the accurate description and formulation of the van der Waals (vdW) interactions between the particle and substrate. Current models treat adhesion by incorporating a material-dependent Hamaker's constant which relies on the heuristic Hamaker's two-body interactions. However, this assumption of pairwise summation of interaction energies can lead to significant errors in condensed matter as it does not take into account the many-body interaction and retardation effects. To address these issues, an approach based on Lifshitz continuum theory of vdW interactions has been developed to calculate the principal many-body interactions between arbitrary geometries at all separation distances to a high degree of accuracy through Lifshitz's theory. We have applied this numerical implementation to calculate the many-body vdW interactions between spherical particles and surfaces with sinusoidally varying roughness profile and also to non-spherical particles (cubes, cylinders, tetrahedron etc) orientated differently with respect to the surface. Our calculations revealed that increasing the surface roughness amplitude decreases the adhesion force and non-spherical particles adhere to the surfaces more strongly when their flatter sides are oriented towards the surface. Such practical shapes and structures of particle–surface systems have not been previously considered in resuspension models and this rigorous treatment of vdW interactions provides more realistic adhesion forces between the particle and the surface which can then be coupled with computational fluid dynamics models to improve the predictive capabilities of particle resuspension dynamics.

On the computation of Casimir stresses in open media and Lifshitz theory

A classification of the electromagnetic modes on open and closed spatial domains containing media with piecewise homogeneous permittivities is used to facilitate the derivation of quantum induced Casimir stresses in dielectrics. By directly exploiting the complex analytic properties of solutions of the macroscopic Maxwell equations for open systems it is shown how regular expressions for such stresses can be expressed in terms of double integrals involving either real or pure imaginary frequencies associated with harmonic modes in conformity with the Lifshitz theory for separated planar dielectric half-spaces. The derivation is self-contained without recourse to the Krein formula for a density of states or mode regularization and offers a more direct approach to other open systems.

Scattering and absorption of ultracold atoms by nanotubes

We investigate theoretically how cold atoms, including Bose–Einstein condensates, are scattered from, or absorbed by, nanotubes with a view to analysing recent experiments. In particular, we consider the role of potential strength, quantum reflection, atomic interactions and tube vibrations on atom loss rates. Lifshitz theory calculations deliver a significantly stronger scattering potential than that found in experiment and we discuss possible reasons for this. We found that the scattering potential for dielectric tubes can be calculated to a good approximation using a modified pairwise summation approach, which is efficient and easily extendable to arbitrary geometries. Quantum reflection of atoms from a nanotube may become a significant factor at low temperatures, especially for non-metallic tubes. Interatomic interactions are shown to increase the rate at which atoms are lost to the nanotube and lead to non-trivial dynamics. Thermal nanotube vibrations do not significantly increase loss rates or reduce condensate fractions, but lower frequency oscillations can dramatically heat the cloud.

Measuring the Casimir force gradient from graphene on a SiO2substrate

The gradient of the Casimir force between a Si-SiO${}_{2}$-graphene substrate and an Au-coated sphere is measured by means of a dynamic atomic force microscope operated in the frequency shift technique. It is shown that the presence of graphene leads to up to a $9%$ increase in the force gradient at the shortest separation considered. This is in qualitative agreement with the predictions of Lifshitz theory using the dielectric permittivities of Si and SiO${}_{2}$ and the Dirac model of graphene.

THERMODYNAMIC STABILITY OF WATER-IN-OIL EMULSIONS

It is well known that colloids can show phase transitions similar to the ones observed in molecular systems. Colloid-diluted and colloid-concentrated phases can coexist in thermodynamic equilibrium at certain conditions. In a previous work, the authors of this research have used this concept to study petroleum emulsions stability, applying thermodynamic perturbation theories to calculate a phase diagram of water-in-oil emulsions under the influence of an electric field. In this work, it was used a similar thermodynamic formalism coupled with the Lifshitz theory to perform a qualitative analysis of the influence of some variables on emulsion stability. Among the variables studied were temperature, applied electric field, and salt concentration. This research found that droplet diameter is a key parameter in studying thermodynamic stability. Variables like temperature and oil composition can have an opposite effect on thermodynamic and kinetic stability. The application of an electric field can destabilize thermodynamically the emulsion. It can also induce meta-stable transitions, which are important for the calculation of droplet coagulation rate. The results presented in this work are in accordance with trends of experimental and industrial observations, and seek to promote a better understanding of water-in-oil emulsion stability.

Measurements of screening length in salt solutions by total internal reflection microscopy: Influence of van der Waals forces and instrumental noise

Total internal reflection microscopy (TIRM) measurements of colloidal spheres in aqueous electrolyte solutions have been carried out with focus on screening properties of various electrolytes and methods and analyses for reliably extracting them from TIRM measurements. Approximations based on Lifshitz theory of flat plates are found to yield van der Waals interactions that are too strong compared to measured interaction potentials. Allowing for some attenuation of these interactions due to surface roughness, a consistent set of screening lengths can be extracted by fitting a model of the interaction, comprising screened Coulomb, van der Waals, and gravitational interactions, to the TIRM data. With the exception of the 2:2 electrolytes, the screening lengths extracted from the TIRM measurements are well described by Debye–Hückel theory, including some surfactants below their critical micelle concentration and electrolytes with large size asymmetries between anion and cation. In 2:2 electrolytes the screening lengths are found to be larger than the corresponding Debye length by as much as 50% at the highest salt concentrations studied. While this deviation is significantly larger than predictions of theory based on the primitive model of electrolytes, similar magnitudes are found from analysis of BD simulations with added noise at realistic levels in the incident intensity. The work shows that care has to be taken when extracting parameters governing potentials in the presence of noise, particularly at high ionic strengths when potentials become steep at short separations.

Demonstration of the Casimir Force between Ferromagnetic Surfaces of a Ni-Coated Sphere and a Ni-Coated Plate

We demonstrate the Casimir interaction between two ferromagnetic boundary surfaces using the dynamic atomic force microscope. The experimental data are found to be in excellent agreement with the predictions of the Lifshitz theory for magnetic boundary surfaces combined with the plasma model approach. It is shown that for magnetic materials the role of hypothetical patch potentials is opposite to that required for reconciliation of the data with the Drude model.

Lifshitz field theories with SDiff symmetries

Abstract We consider Lifshitz field theories with a dynamical critical exponent z equal to the dimension of space d and with a large group of base space symmetries, concretely space coordinate transformations with unit determinant (“Special Diffeomorphisms”). The field configurations of the theories considered may have the topology of skyrmions, vortices or monopoles, although we focus our detailed investigations on skyrmions. The resulting Lifshitz field theories have a BPS bound and exact soliton solutions saturating the bound, as well as time-dependent topological Q-ball solutions. Finally, we investigate the U(1) gauged versions of the Lifshitz field theories coupled to a Chern-Simons gauge field, where the BPS bound and soliton solutions saturating the bound continue to exist.

Casimir forces for inhomogeneous planar media

Casimir forces arise from vacuum fluctuations. They are fully understood only for simple models, and are important in nano- and microtechnologies. We report our experience of computer algebra calculations towards the Casimir force for models involving inhomogeneous dielectrics. We describe a methodology that greatly increases confidence in any results obtained, and use this methodology to demonstrate that the analytic derivation of scalar Green's functions is at the boundary of current computer algebra technology. We further demonstrate that Lifshitz theory of electromagnetic vacuum energy can not be directly applied to calculate the Casimir stress for models of this type, and produce results that have led to alternative regularisations. Using a combination of our new computational framework and the new theory based on our results, we provide specific calculations of Casimir forces for planar dielectrics having permittivity that declines exponentially. We discuss the relative strengths and weaknesses of computer algebra systems when applied to this type of problem, and describe a combined numerical and symbolic computational framework for calculating Casimir forces for arbitrary planar models.

Dynamical stability of the quantum Lifshitz theory in 2+1 dimensions

The roles of magnetic and electric perturbations in the quantum Lifshitz model in $2+1$ dimensions are examined in this paper. The quantum Lifshitz model is an effective field theory for quantum multicritical systems, which include generalized two-dimensional (2D) quantum dimer models in bipartite lattices and their generalizations. It describes a class of quantum phase transitions between ordered and topological phases in $2+1$ dimensions. Magnetic perturbations break the dimer conservation law. Electric excitations, the condensation of which leads to ordered phases, have been studied extensively both in the classical three-dimensional model and in the quantum 2D model. The role of magnetic vortex excitations, the condensation of which drives these systems into a ${\mathbb{Z}}_{2}$ topological phase, has been largely ignored. Recent numerical studies claim that the quantum theory has a peculiar feature: the dynamical exponent $z$ flows continuously and the quantum theory is hence unstable to magnetic vortices. To study the interplay of both excitations, we perform a perturbative renormalization group study to one-loop order and study the stability of the theory away from quantum multicriticality. This is done by generalizing the operator-product expansion to anisotropic models. It is found that the dynamical exponent does not appear to flow, in contrast to the classical Monte Carlo study. Possible reasons for this difference are discussed at length.

The Relationship Between Contact Mechanics and Adhesion in Nanoscale Contacts Between Non-Polar Molecular Monolayers

Atomic and friction force microscopy were employed to examine adhesion and friction between dodecanethiol self-assembled monolayers in pure media as well as in two-component heptane/acetone mixtures. In media that did not contain hydrogen bond donors, the pull-off forces were found to be in very good agreement with theoretic predictions based on the Lifshitz theory. As the hydrogen bond donor ability of the medium increased, the adhesion energy was found to be increasingly underestimated by the model, illustrating the importance of the medium–medium interactions outside the contact area in determining the adhesive properties of the contact at the nanoscale. Exceptionally, in n-octanol, the pull-off forces were considerably lower than predicted and a dual slope linear friction–load relation was observed. These observations were rationalized by the formation of physisorbed layers of octanol on the surfaces. The friction–load relationship in the other media was found to be dependent on the magnitude of adhesion. For weakly adhering systems, the friction–load relationship was linear, but as adhesion increased, a sublinear relationship was observed. The data were rationalized by treating the friction as the sum of an adhesion-dependent shear term characterized by a surface shear strength τ and a molecular plowing term characterized by a coefficient of friction μ. Thus, Amontons’ law appears to describe the limiting case of very weak adhesion where viscoelastic plowing is primarily responsible for energy dissipation, while a sublinear friction–load relationship emerges in other situations due to the dissipation of energy in shearing adhesive contacts.

Holographic fermions in charged Lifshitz theory

We investigate the properties of holographic fermions in charged Lifshitz black holes at finite temperature through the AdS/CFT correspondence. In the charged Lifshitz background with the dynamical exponent $z=2$, we find that the dispersion relation is linear. The scaling behavior of the imaginal part of the Green function relative to ${k}_{\ensuremath{\perp}}=k\ensuremath{-}{k}_{F}$ is also discussed. We find, although the system has a linear dispersion relation and quadratic quasiparticle width, it does not satisfy Luttinger's theorem. We also find that the variation of the scaling parameters $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ is small as the charge $q$ varies. Furthermore, we also discuss the effect of the dynamical exponent $z$ by considering the cases $z=4$ and $z=6$ and show that $\mathrm{Im}{G}_{ii}$ become smooth when the dynamical exponent $z$ increases.