Lifshitz Theory Research Articles

ℱ(P) quantum mechanics

We explore the possibility to extend the Heisenberg’s uncertainty principle to a nonlinear extension of the quantum algebra related to a functional operator of the momenta as [Formula: see text]. We show that such an extension of quantum mechanics is intimately connected to the non-commutative space-time algebra and the Lorentz symmetry deformations. We show that a large class of [Formula: see text] models can introduce superluminal modes in the quantized theories. We also show that the Hořava–Lifshitz theory is related to a large class of [Formula: see text] Quantum Mechanics.

Modulation of substrate van der Waals forces using varying thicknesses of polymer overlayers

Thin polymeric coatings are commonly used for altering surface properties and modulating the interfacial performance of materials. Possible contributions from the substrate to the interfacial forces and effects are, however, usually ignored and are not well understood, nor is it established how the coating thickness modulates and eventually eliminates contributions from substrates to the van der Waals (vdW) interfacial force. In this study we quantified, by colloid-probe atomic force microscope (AFM) and by theoretical calculations, the interfacial vdW contributions from substrates acting through ethanol plasma polymer (EtOHpp) coatings of a range of thicknesses on Au and Si bulk materials. In approach force curves against EtOHpp-coated Au substrates the magnitude of the vdW force decreased as the EtOHpp coating thickness increased to 18 nm and then plateaued with further increases in coating thickness, providing direct evidence for a contribution to the total interfacial vdW force from the Au substrate acting through thin coatings. The experimental observations accord with theoretical calculations of the thickness dependence of Hamaker coefficients derived from rigorous simulation using the Lifshitz theory. In addition, the measured forces agree well with theoretical predictions including correction for finite roughness. Thus, our experimental and theoretical results establish how the thickness of polymer thin film coatings modulates the total interfacial vdW force and how this can be used to tune the net vdW force so as to either contain a large substrate contribution or arise predominantly from the polymeric overlayer. Our findings enable rational design of coating thickness to tailor interfacial interactions and material performance.

Non-retarded room temperature Hamaker constants between elemental metals

The Lifshitz theory of van der Waals forces is utilized for the systematic calculation of the non-retarded room temperature Hamaker constants between 26 identical isotropic elemental metals that are embedded in vacuum or in pure water. The full spectral method, complemented with a Drude-like low frequency extrapolation, is employed for the elemental metals benefitting from the availability of extended-in-frequency reliable dielectric data. The simple spectral method is employed for pure water and three dielectric representations are explored. Numerical truncation and low frequency extrapolation effects are shown to be negligible. The accuracy of common Lifshitz approximations is quantified. The Hamaker constants for 100 metal combinations are reported; the geometric mixing rule is revealed to be highly accurate in vacuum & water.

Multi-Foulant-Resistant Material Design by Matching Coating-Fluid Optical Properties.

The buildup of corrosion deposits, known as fouling, seriously hinders large-scale energy production. From nuclear power plants to geothermal reservoirs, fouling increases system pressure drops, impedes heat transfer, and accelerates corrosion, leading to derating and early failure. Here, we investigate the collodial interactions between multiple foulants and coated surfaces, with the aim of discovering principles for minimizing the adhesion of foulants to them. We hypothesize that matching the full refractive index spectrum of a coating to its surrounding fluid minimizes the adhesion of all foulants entrained within and that the Lifshitz theory is sufficient to predict which materials will be multi-foulant-resistant. First-principle calculations of Hamaker constants and refractive indices of six foulants on six coatings in water correlate well to direct measurements of adhesion by atomic force microscopy (AFM)-based force spectroscopy. Amorphous 2% fluorine-doped tin oxide, crystalline SiO2, CaF2, and Na3AlF6, which all nearly match the refractive index spectrum of water, successfully resisted adhesion of six diverse foulant materials in aqueous AFM measurements. The validation of this design principle may be expanded to design multi-fouling-resistant coatings for any system in which van der Waals forces are the dominant adhesion mechanism.

Casimir effect in optoelectronic devices using ferrofluids

Some of the modern electronic and optoelectronic devices exploit ferrofluids contained in narrow gaps between two material plates. When the width of the gap becomes below a micrometer, the boundary plates are subjected to the Casimir force arising from the zero-point and thermal fluctuations of the electromagnetic field. These forces should be taken into account in microdevices with the dimensions decreased to below a micrometer. In this paper, we review recently performed calculations of the attractive Casimir pressure in three-layer systems containing a ferrofluid. We also find the ferrofluidic system where the Casimir pressure is repulsive. This result is obtained in the framework of the fundamental Lifshitz theory of van der Waals and Casimir forces. The conclusion is made that enhanced repulsion due to the presence of a ferrofluid may prevent from sticking of closely spaced elements of a microdevice.

The Casimir-Polder interaction of an atom and real graphene sheet: Verification of the Nernst heat theorem

We find the low-temperature behavior of the Casimir-Polder free energy and entropy for an atom interacting with real graphene sheet possessing nonzero energy gap and chemical potential. Employing the formalism of the polarization tensor, it is shown that the Casimir-Polder entropy goes to zero by the power law with vanishing temperature, i.e., the Nernst heat theorem is satisfied. This result is discussed in connection with the problems connected with account of free charge carriers in the Lifshitz theory.

Large excitonic effect on van der Waals interaction between two-dimensional semiconductors.

An exceptionally large excitonic effect on the van der Waals (vdW) interaction between two-dimensional semiconductors is unraveled using the Lifshitz theory in conjunction with the ab initio GW plus Bethe-Salpeter equation formalism. Upon consideration of the electron-hole interaction, the vdW energy between two atomistic layers separated by 10 000 angstroms can be larger by a ratio of ∼30%, which is an order of magnitude greater than that seen for semi-infinite silicon surfaces. The large influence of the short-range electron-hole interaction on the long-range effect of quantum fluctuations is rooted in the ultra-thin nature of two-dimensional semiconductors which results in not only large exciton binding energy but also amplified roles of low-frequency dielectric responses.

Comparison of Casimir forces and electrostatics from conductive SiC-Si/C and Ru surfaces

Comprehensive knowledge of Casimir forces and associated electrostatics from conductive SiC and Ru surfaces can be essential in diverse areas ranging from micro/nanodevice operation in harsh environments to multilayer coatings in advanced lithography technologies. Hence, the Casimir force was measured between an Au-coated microsphere and N-doped SiC samples with Si- and C-terminated faces, and the results were compared with the measurements using the same microsphere and a metallic Ruthenium surface. Electrostatic calibration showed that the Si- and C-faces behave differently with a nearly ~0.6-0.7 V difference in the contact potentials V0Si/C. We attribute this to a higher incorporation of N on the C-terminated face in the near surface region resulting in the formation of NOx and an increased work function compared to the Si-terminated surface which is in agreement with x-ray photoelectron spectroscopy data. Notably, the contact potential of the SiC-C face was closer to the metallic Ru-Au system. However, the measured optical properties of the SiC-Si/C terminated surfaces with ellipsometry did not show any substantial differences indicating that the effective depth of the Si/C terminating surface layers are significantly smaller than the photon penetration depth not leading to any differences in the calculated forces via Lifshitz theory. Nonetheless, the measured Casimir forces, after compensation of the electrostatics contributions, showed differences between the Si/C faces, whereas the comparison with the Lifshitz theory prediction shows better agreement for the SiC-Si face. Finally, comparison of the Casimir forces below 40 nm separations between the SiC-Si/C and Ru surfaces indicated that the short-range roughness effects on the Casimir force increase in magnitude with increasing metallic behavior of the plate surface.

Relating bulk to boundary entanglement

Quantum many-body systems have a rich structure in the presence of boundaries. We study the groundstates of conformal field theories (CFTs) and Lifshitz field theories in the presence of a boundary through the lens of the entanglement entropy. For a family of theories in general dimensions, we relate the universal terms in the entanglement entropy of the bulk theory with the corresponding terms for the theory with a boundary. This relation imposes a condition on certain boundary central charges. For example, in $2+1$ dimensions, we show that the corner-induced logarithmic terms of free CFTs and certain Lifshitz theories are simply related to those that arise when the corner touches the boundary. We test our findings on the lattice, including a numerical implementation of Neumann boundary conditions. We also propose an ansatz, the boundary Extensive Mutual Information model, for a CFT with a boundary whose entanglement entropy is purely geometrical. This model shows the same bulk-boundary connection as Dirac fermions and certain supersymmetric CFTs that have a holographic dual. Finally, we discuss how our results can be generalized to all dimensions as well as to massive quantum field theories.

Precision measurements of the gradient of the Casimir force between ultraclean metallic surfaces at larger separations

We report precision measurements of the Casimir interaction at larger separation distances between the Au-coated surfaces of a sphere and a plate in ultrahigh vacuum using a much softer cantilever of the dynamic atomic-force-microscope-based setup and two-step cleaning procedure of the vacuum chamber and test body surfaces by means of UV light and Ar-ion bombardment. Compared to the previously performed experiment, two more measurement sets for the gradient of the Casimir force are provided, which confirmed and slightly improved the results. Next, additional measurements have been performed with a factor-of-two larger oscillation amplitude of the cantilever. This allowed the obtainment of meaningful results at much larger separation distances. The comparison of the measurement data with theoretical predictions of the Lifshitz theory using the dissipative Drude model to describe the response of Au to the low-frequency electromagnetic field fluctuations shows that this theoretical approach is experimentally excluded over the distances from 250 to 1100 nm (i.e., a major step forward compared to the previous work where it was excluded up to only 820 nm). The theoretical approach using the dissipationless plasma model at low frequencies is shown to be consistent with the data over the entire measurement range from 250 to 1300 nm. The possibilities to explain these puzzling results are discussed.

Cosmology from Newton–Chern–Simons gravity

We study a five-dimensional non-relativistic gravity theory whose action is composed of a gravitational sector and a sector of matter where the gravitational sector is given by the so called Newton–Chern–Simons gravity and where the matter sector is described by a perfect fluid. At time to do cosmology, the obtained field equations shows a close analogy with the projectable version of the Hořava–Lifshitz theory in (3+1)-dimensions. Solutions and their asymptotic limits are found. In particular a phantom solution with a future singularity reminiscent of a Litlle Big Rip future singularity is obtained.

Colloidal Gelation in Liquid Metals Enables Functional Nanocomposites of 2D Metal Carbides (MXenes) and Lightweight Metals.

Nanomaterials dispersed in different media, such as liquids or polymers, generate a variety of functional composites with synergistic properties. In this work, we discuss liquid metals as the nanomaterials' dispersion media. For example, 2D transition-metal carbides and nitrides (MXenes) can be efficiently dispersed in liquid Ga and lightweight alloys of Al, Mg, and Li. We show that the Lifshitz theory predicts strong van der Waals attraction between nanoscale objects interacting through liquid metals. However, a uniform distribution of MXenes in liquid metals can be achieved through colloidal gelation, where particles form self-supporting networks stable against macroscopic phase segregation. This network acts as a reinforcement boosting mechanical properties of the resulting metal-matrix composite. By choosing Mg-Li alloy as an example of ultralightweight metal matrix and Ti3C2Tx MXene as a nanoscale reinforcement, we apply a liquid metal gelation technique to fabricate functional nanocomposites with an up to 57% increase in the specific yield strength without compromising the matrix alloy's plasticity. MXenes largely retain their phase and 2D morphology after processing in liquid Mg-Li alloy at 700 °C. The 2D morphology enables formation of a strong semicoherent interface between MXene and metal matrix, manifested by biaxial strain of the MXene lattice inside the metal matrix. This work expands applications for MXenes and shows the potential for developing MXene-reinforced metal matrix composites for structural alloys and other emerging applications with metal-MXene interfaces, such as batteries and supercapacitors.

Lifshitz theory of the cosmological constant

Astrophysics has given empirical evidence for the cosmological constant that accelerates the expansion of the universe. Atomic, Molecular, and Optical Physics have proven experimentally that the quantum vacuum exerts forces – the van der Waals and Casimir forces – on neutral matter. It has long been conjectured (Zel’dovich, 1968) that the two empirical facts, the cosmological constant and the Casimir force, have a common theoretical explanation, but all attempts of deriving both from a unified theory in quantitative detail have not been successful so far. In AMO Physics, Lifshitz theory has been the standard theoretical tool for describing the measured forces of the quantum vacuum. This paper develops a version of Lifshitz theory that also accounts for the electromagnetic contribution to the cosmological constant. Assuming that the other fields of the Standard Model behave similarly, gives a possible quantum-optical explanation for what has been called dark energy.

Method for the Calculation of the Hamaker Constants of Organic Materials by the Lifshitz Macroscopic Approach with Density Functional Theory

The Hamaker constants, which are coefficients providing quantitative information on intermolecular forces, were calculated for a number of different materials according to the Lifshitz theory via simple DFT calculations without any experimental measurements being performed. The physical properties (polarizability, dipole moment, molecular volume, and vibrational frequency) of organic molecules were calculated using the B3LYP density functional and the aug-cc-pVDZ basis set. Values for the Hamaker constants were obtained using the approximation of the Lorentz-Lorenz equation and Onsager's equation with these properties. It was found that, in the case of "nonassociative" materials, such as hydrocarbons, ethers, ketones, aldehydes, carboxylic acids, esters, nitriles, and hydrosilanes, and halides, the calculated Hamaker constants were similar in value to their experimentally determined counterparts. Moreover, with this calculation method, it is easy to create the molecular model and the CPU time can be shortened.

A multiscale model of protein adsorption on a nanoparticle surface

We present a methodology to quantify the essential interactions at the interface between inorganic solid nanoparticles (NPs) and biological molecules. Our model is based on pre-calculation of the repetitive contributions to the interaction from molecular segments, which allows us to efficiently scan a multitude of molecules and rank them by their adsorption affinity. The interaction between the biomolecular fragments and the nanomaterial are evaluated using a systematic coarse-graining scheme starting from all-atom molecular dynamics simulations. The NPs are modelled using a two-layer representation, where the outer layer is parameterized at the atomistic level and the core is treated at the continuum level using Lifshitz theory of dispersion forces. We demonstrate that the scheme reproduces the experimentally observed features of the NP protein coronas. To illustrate the use of the methodology, we compute the adsorption energies for human blood plasma proteins on gold NPs of different sizes as well as the preferred orientation of the molecules upon adsorption. The computed energies can be used for predicting the composition of the NP-protein corona for the corresponding material.

Dispersion Forces between Metal and Dielectric Plates Separated by a Magnetic Fluid

The formalism of the Lifshitz theory has been used for determining the pressure exerted by dispersion forces between metal and dielectric plates separated by a thin layer of a magnetic fluid. Numerical calculations are performed for gold and quartz glass plates and the magnetic fluid consisting of kerosene and magnetite nanoparticles at room temperature. For this purpose, we have used familiar representations of dielectric properties of gold and quartz glass along the imaginary frequency axis; corresponding representations have also been obtained for magnetite and kerosene. The dispersion pressure has been analyzed as a function of the distance between the plates, the volume fraction of magnetite particles in the magnetic fluid, and their diameter. At large separations between the plates, simple analytic expressions for this pressure have been derived. Possible application of results has been considered.

Examining the Casimir puzzle with an upgraded AFM-based technique and advanced surface cleaning

We performed measurements of the gradient of the Casimir force between Au-coated surfaces of a sphere and a plate by means of significantly upgraded dynamic atomic force microscope (AFM) based technique. By introducing combined cleaning procedure of interior surfaces of the vacuum chamber and the test bodies by means of UV light and Ar ions, we reached higher vacuum and eliminated the role of electrostatic patches. Furthermore, the use of much softer cantilever allowed a sixfold decrease of the systematic error in measuring the force gradient. The experimental data are compared with theoretical predictions of the Lifshitz theory taking into account corrections due to the inaccuracy of the proximity force approximation and that due to surface roughness. It is shown that the theoretical approach accounting for the relaxation properties of free electrons is excluded by the data up to a larger than previous sphere-plate separation of 820~nm, whereas an alternative approach is found in a very good agreement with the data. Importance of these results in connection with the foundations of quantum statistical physics is discussed.

Fermionic Casimir effect in Horava–Lifshitz theories

In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava–Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.

Effect of agglomeration of magnetic nanoparticles on the Casimir pressure through a ferrofluid

The impact of agglomeration of magnetic nanoparticles on the Casimir pressure is investigated in the configuration of two material plates and a layer of ferrofluid confined between them. Both cases of similar and dissimilar plates are considered in the framework of the Lifshitz theory of dispersion forces. It is shown that for two dielectric (SiO_2) plates, as well as for one dielectric (SiO_2) and another one metallic (Au) plates, an agglomeration of magnetite nanoparticles results in only quantitative differences in the values of the Casimir pressure if the optical data for Au are extrapolated to low frequencies by means of the Drude model. If, however, an extrapolation by means of the plasma model is used in computations, which is confirmed in experiments on measuring the Casimir force, one finds that the pressure changes its sign when some share of magnetic nanoparticles of sufficiently large diameter is merged into clusters by two or three items. The revealed effect of sign change is investigated in detail at different separations between the plates, diameters of magnetic nanoparticles and shares of particles merged into clusters of different sizes. The obtained results may be useful when developing ferrofluid-based microdevices and for resolution of outstanding problems in the theory of Casimir forces.

Static coarsening behaviour of lamellar microstructure in selective laser melted Ti–6Al–4V

Static coarsening mechanism of selective laser melted (SLMed) Ti–6Al–4V with a lamellar microstructure was established at temperatures from 700 °C to 950 °C. Microstructure evolution revealed that high heat treatment temperature facilitated martensite decomposition and promoted lamellae growth. At each temperature, the growth rate decreased with increasing holding time. The static coarsening behaviour of SLMed Ti–6Al–4V can be interpreted by Lifshitz, Slyozov, and Wagner (LSW) theory. The coarsening coefficient were 0.33, 0.33–0.4, 0.4–0.5 for 700–800 °C, 900 °C and 950 °C, respectively. This indicated the coarsening mechanism was bulk diffusion at 700–800 °C, and a combination of bulk diffusion and interface reaction at 900 °C and 950 °C conditions.