Casimir Attraction Research Articles

Statistical Thermodynamic Description of Self-Assembly of Large Inclusions in Biological Membranes.

Recent studies revealed anomalous underscreening in concentrated electrolytes, and we suggest that the underscreened electrostatic forces between membrane proteins play a significant role in the process of self-assembly. In this work, we assumed that the underscreened electrostatic forces compete with the thermodynamic Casimir forces induced by concentration fluctuations in the lipid bilayer, and developed a simplified model for a binary mixture of oppositely charged membrane proteins with different preference to liquid-ordered and liquid-disordered domains in the membrane. In the model, like macromolecules interact with short-range Casimir attraction and long-range electrostatic repulsion, and the cross-interaction is of the opposite sign. We determine energetically favored patterns in a system in equilibrium with a bulk reservoir of the macromolecules. Different patterns consisting of clusters and stripes of the two components and of vacancies are energetically favorable for different values of the chemical potentials. Effects of thermal flutuations at low temperature are studied using Monte Carlo simulations in grand canonical and canonical ensembles. For fixed numbers of the macromolecules, a single two-component cluster with a regular pattern coexists with dispersed small one-component clusters, and the number of small clusters depends on the ratio of the numbers of the molecules of the two components. Our results show that the pattern formation is controlled by the shape of the interactions, the density of the proteins, and the proportion of the components.

Universal Casimir attraction between filaments at the cell scale

The electromagnetic Casimir interaction between dielectric objects immersed in salted water includes a universal contribution that is not screened by the solvent and therefore long-ranged. Here, we study the geometry of two parallel dielectric cylinders. We derive the Casimir free energy by using the scattering method. We show that its magnitude largely exceeds the thermal energy scale for a large parameter range. This includes length scales relevant for actin filaments and microtubules in cells. We show that the Casimir free energy is a universal function of the geometry, independent of the dielectric response functions of the cylinders, at all distances of biological interest. While multiple interactions exist between filaments in cells, this universal attractive interaction should have an important role in the cohesion of bundles of parallel filaments.

Nonlocal Timoshenko shear beam model for multilayer curved graphene nano-switches

Graphene sheets are the basis of nano-electromechanical switches, which offer a unique insight into the world of quantum mechanics. In this paper, we proposed a new size-dependent multi-beam shear model for investigating the pull-in instability of multilayer graphene/substrate nano-switches within the context of the Timoshenko beam theory. As the graphene/substrate bemas bent toward the graphene layer due to the thermomechanical mismatch, the impact of curvature is considered in the proposed model. Also, the impact of the Casimir attraction is incorporated in the developed model by taking into account the limited conductivity of interacting surfaces. The scale dependency of the materials is considered in the framework of the nonlocal elasticity. To simulate the nano-switch and explore the pull-in instability, a finite element procedure is developed. The proposed approach is verified by comparing the pull-in voltage to published data. Finally, the role of influential parameters, including size dependency, length, initial gap, curvature, and the number of graphene layers on instability voltage of nano-switch, are investigated.

An improved fuzzy controller on electromechanical nano-tweezers

This paper aims to develop an improved fuzzy controller for position controlling of nano-wire-based electromechanical nano-tweezers. The nonlinear governing equation is developed by incorporating the Euler–Bernoulli beam model and Hamilton’s principle. Also, the quantum vacuum fluctuations are assimilated in the developed model in terms of Casimir attraction. The nonlinear constitutive equation is transformed into a nonlinear state-space form by employing the Galerkin method. Based on the linguistic explanation of the system, an improved fuzzy controller is designed to control the nano-tweezers for manipulating desired objects. The Taguchi technique has been used to decrease the number of independent experiments and improve the structure of membership functions, consequently. The designed controller is employed for both controlling and path tracking of nano-tweezers. The outcomes indicate that the proposed improved fuzzy controller has excellent performance for stabilizing the nano-tweezers at any desired gap.

Self-assembly of colloidal cube superstructures with critical Casimir attractions

The structure of self-assembled materials is determined by the shape and interactions of the building blocks. Here, we investigate the self-assembly of colloidal ‘superballs’, i.e. cubes with rounded corners, by temperature-tunable critical Casimir forces to obtain insight into the coupling of a cubic shape and short range attractions. The critical Casimir force is a completely reversible and controllable attraction that arises in a near-critical solvent mixture. Using confocal microscopy and particle tracking, we follow the self-assembly dynamics and structural transition in a quasi-2D system. At low attraction, we observe the formation of small clusters with square symmetry. When the attraction is increased, a transition to a rhombic Λ1-lattice is observed. We explain our findings by the change in contact area at faces and corners of the building blocks combined with the increase in attraction strength and range of the critical Casimir force. Our results show that the coupling between the rounded cubic shape and short-range attraction plays a crucial role for the superstructures that form and provide new insights for the active assembly control of micro and nanocubes.

Chiral Anomaly-Enhanced Casimir Interaction between Weyl SemimetalsSupported by the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000), the National Natural Science Foundation of China (Grant Nos. 61674145, 11974340, and 11504106), the National Key R&D Program of China (Grant Nos. 2017YFA0303400 and 2018YFA0306101), the Chinese Academy of Sciences (Grant No. QYZDJ-SSW-SYS001 and XDPB22).

We theoretically study the Casimir interaction between Weyl semimetals. When the distance a between semi-infinite Weyl semimetals is in the micrometer regime, the Casimir attraction can be enhanced by the chiral anomaly. The Casimir attraction depends sensitively on the relative orientations between the separations ( b 1, b 2) of Weyl nodes in the Brillouin zone and show anisotropic behavior for the relative orientation of these separations ( b 1, b 2) when they orient parallel to the interface. This anisotropy is quite larger than that in conventional birefringent materials. The Casimir force can be repulsive in the micrometer regime if the Weyl semimetal slabs are sufficiently thin and the direction of Weyl nodes separations ( b 1, b 2) is perpendicular to the interface. The Casimir attraction between Weyl semimetal slabs decays slower than 1/a 4 when the Weyl nodes separations b 1 and b 2 are both parallel to the interface.

Probing the screening of the Casimir interaction with optical tweezers

We measure the colloidal interaction between two silica microspheres in aqueous solution in the distance range from $0.2\,\mu$m to $0.5\,\mu$m with the help of optical tweezers. When employing a sample with a low salt concentration, the resulting interaction is dominated by the repulsive double-layer interaction which is fully characterized. The double-layer interaction is suppressed when adding $0.22\,$M of salt to our sample, thus leading to a purely attractive Casimir signal. When analyzing the experimental data for the potential energy and force, we find good agreement with theoretical results based on the scattering approach. At the distance range probed experimentally, the interaction arises mainly from the unscreened transverse magnetic contribution in the zero-frequency limit, with nonzero Matsubara frequencies providing a negligible contribution. In contrast, such unscreened contribution is not included by the standard theoretical model of the Casimir interaction in electrolyte solutions, in which the zero-frequency term is treated separately as an electrostatic fluctuational effect. As a consequence, the resulting attraction is too weak in this standard model, by approximately one order of magnitude, to explain the experimental data. Overall, our experimental results shed light on the nature of the thermal zero-frequency contribution and indicate that the Casimir attraction across polar liquids has a longer range than previously predicted.

Debye vs. Casimir: controlling the structure of charged nanoparticles deposited on a substrate.

Fine-tuning the interactions between particles can allow one to steer their collective behaviour and structure. A convenient way to achieve this is to use solvent criticality to control attraction, via critical Casimir forces, and to control repulsion via the Debye screening of electrostatic interactions. Herein, we develop a multiscale simulation framework and a method for controlled deposition of quantum dots to investigate how these interactions affect the structure of charged nanoparticles deposited on a substrate, altogether immersed in a binary liquid mixture intermixed with salt. We consider nanoparticles and substrates favouring the same component of the mixture and find that the critical Casimir interactions between the nanoparticles become drastically reduced at the substrate. In particular, the interactions can become a few kBT weaker and their decay length a few orders of magnitude smaller than in the bulk. At off-critical compositions, the decay length increases upon approaching criticality, as expected, but the interaction strength decreases. With molecular dynamics simulations and experiments, we reveal that the nanoparticles can self-assemble into crystalline clusters which form superstructures resembling cluster fluids and spinodal morphology. The simulations additionally predict the formation of fractal-like nanoparticle gels and bicontinuous phases. Our results demonstrate that charged nanoparticles in a salty binary liquid mixture provide exciting opportunities to study the formation of complex structures experimentally and theoretically, which may lead to applications in optoelectronics and photonics.

Effect of increased stability of peptide-based coatings in the Casimir regime via nanoparticle doping

We find that thin peptide films and coatings doped with metallic nanoparticles are more stable due to the role of electromagnetic fluctuations. It is shown that for the doped freestanding in vacuum peptide film the Casimir attraction becomes larger in magnitude. For dielectric substrates coated with peptide films, the nanoparticle doping leads to a wider range of film thicknesses where the Casimir pressure is attractive and to larger pressure magnitudes at the points of extremum. The doping of peptide coatings with magnetic nanoparticles preserves all the advantages of nonmagnetic ones and simultaneously imparts superparamagnetic properties to the coating which could extend significantly the application areas of bioelectronics.

Nonlinear dynamic stability of piezoelectric thermoelastic electromechanical resonators

This research work deals with analyzing instability and nonlinear behaviors of piezoelectric thermal nano-bridges. An adjustable thermo-elastic model with the ability to control stability conditions is developed to examine the system behavior at different temperatures. To increase the performance range and improve system characteristics, a piezovoltage is applied and a spring is connected to the sliding end of the deformable beam as design parameters. The partial differential equations (PDEs) are derived using the extended Hamilton’s principle and Galerkin decomposition is implemented to discretize the nonlinear equations, which are solved via a computational method called the step-by-step linearization method (SSLM). To improve the accuracy of the solution, the number of mode shapes and the size of voltage increments are analyzed and sufficient values are employed in the solution. The validity of the formulation and solution method is verified with experimental, analytical, and numerical data for several cases. Finally, the vibration and eigenvalue problem of the actuated nano-manipulator subjected to electrostatic and Casimir attractions are investigated. It is concluded that the fringing-fields correction changes the system frequency, static equilibrium, and pull-in characteristics significantly. The results are expected to be instrumental in the analysis, design, and operation of numerous adjustable advanced nano-systems.

Scale-dependent dynamic stability analysis of nanowire-fabricated nanotweezers

Dynamic stability analysis of nanowire-fabricated nanotweezers is examined in this paper using a new nonlinear model. A novel size dependent model based on the strain gradient theory (SGT) and the Gurtin–Murdoch elasticity (GME) is presented for simulating the simultaneous effects of scale-dependent phenomena (i.e. microstructure dependency and surface energies). Moreover, the impacts of rare field gas damping, structural damping, intermolecular force and Casimir attraction are included in the proposed model. An analytical solution is developed for investigating the dynamic instability. It is established that the proposed model exhibit significant scale-dependence effect on the stability characteristics of nanotweezers.

Graphene cantilever under Casimir force

The stability of graphene cantilever under Casimir attraction to an underlying conductor is investigated. The dependence of the instability threshold on temperature and flexural rigidity is obtained. Analytical work is supplemented by numerical computation of the critical temperature above which the graphene cantilever irreversibly bends down and attaches to the conductor. The geometry of the attachment and exfoliation of the graphene sheet is discussed. It is argued that graphene cantilever can be an excellent tool for precision measurements of the Casimir force.

A corrected model for static and dynamic electromechanical instability of narrow nanotweezers: Incorporation of size effect, surface layer and finite dimensions

Herein, a corrected theoretical model is proposed for modeling the static and dynamic behavior of electrostatically actuated narrow-width nanotweezers considering the correction due to finite dimensions, size dependency and surface energy. The Gurtin–Murdoch surface elasticity in conjunction with the modified couple stress theory is employed to consider the coupling effect of surface stresses and size phenomenon. In addition, the model accounts for the external force corrections by incorporating the impact of narrow width on the distribution of Casimir attraction, van der Waals (vdW) force and the fringing field effect. The proposed model is beneficial for the precise modeling of the narrow nanotweezers in nano-scale.

Instability Characteristics of Free-Standing Nanowires Based on the Strain Gradient Theory with the Consideration of Casimir Attraction and Surface Effects

AbstractSize-dependent dynamic instability of cylindrical nanowires incorporating the effects of Casimir attraction and surface energy is presented in this research work. To develop the attractive intermolecular force between the nanowire and its substrate, theproximity force approximation(PFA) for small separations, and the Dirichlet asymptotic approximation for large separations with a cylinder-plate geometry are employed. A nonlinear governing equation of motion for free-standing nanowires – based on the Gurtin-Murdoch model – and a strain gradient elasticity theory are derived. To overcome the complexity of the nonlinear problem in hand, a Garlerkin-based projection procedure for construction of a reduced-order model is implemented as a way of discretization of the governing differential equation. The effects of length-scale parameter, surface energy and vacuum fluctuations on the dynamic instability threshold and adhesion of nanowires are examined. It is demonstrated that in the absence of any actuation, a nanowire might behave unstably, due to the Casimir induction force.

Electromechanical Performance of NEMS Actuator Fabricated from Nanowire under quantum vacuum fluctuations using GDQ and MVIM

The Casimir attraction can significantly interfere the physical response of nanoactuators. The intensity of the Casimir force depends on the geometries of interacting bodies. The present paper is dedicated to model the influence of the Casimir attraction on the electrostatic stability of nanoactuators made of cylindrical conductive nanowire/nanotube. An asymptotic solution, based on path-integral approach, is employed to consider the Casimir force. The continuum theory is employed to derive the constitutive equation of the actuator. The governing nonlinear equations are solved by three different approaches. Various perspectives of the issue including comparison with the van der Waals (vdW) force regime, the variation of instability parameters and effect of geometry are addressed.

Influence of electrical double-layer dispersion forces and size dependency on pull-in instability of clamped microplate immersed in ionic liquid electrolytes

Plate-type clamped microplate is of the most common constructive elements for developing in-liquid-operating devices. While the electromechanical behavior of clamped microplate in non-liquid environments has exclusively been addressed in the literature, no theoretical studies have yet been conducted on precise modeling of the clamped microplate in electrolyte liquid. Herein, the electromechanical response and instability of the clamped microplate immersed in ionic electrolyte media are investigated. The electrochemical force field is determined using double layer theory and linearized Poisson–Boltzmann equation. The presence of dispersion forces, i.e., Casimir and van der Waals attractions, are included in the theoretical model considering the correction due to the presence of liquid media between the interacting surfaces (three-layer model). To this end, a kind of microplate has been designed, i.e., a square microplate with all edges clamped supported. The strain gradient elasticity is employed to model the size-dependent structural behavior of the clamped microplate. To solve the nonlinear constitutive equation of the system, Extended Kantorovich Method, is employed and the pull-in parameter of the microplate are extracted. Impacts of the dispersion forces and size effect on the instability characteristics are discussed as well as the effect of ion concentration and potential ratio. It is found that the significant difference between the pull-in instability parameters in the modified strain gradient theory and the classical theory for thin microplates is merely due to the consideration of size effect parameter in the modified strain gradient theory. To confirm the validity of formulations, the numerical values of the results are compared. The results predicted via the aforementioned approach are in excellent agreement with those in the literature. Some new examples are solved to demonstrate the applicability of the procedure.

Instability threshold of rippled carbon nanotube nanotweezers in the low vacuum gas flow incorporating Dirichlet and Neumann modes of Casimir energy

The aim of this research work is to address the influences of dispersion forces and rippled configuration on the instability threshold of carbon nanotube (CNT) based nanotweezers. To this end, the Dirichlet and Neumann modes of Casimir force arisen from the electric and magnetic energies is developed for cylinder–cylinder geometry. Moreover, the CNTs rippling deformation which experimentally revealed is included in the Euler-Bernoulli beam model to modify the governing equations. The differential quadrature method (DQM) in conjunction with the 4th-order Runge-Kutta algorithm is employed to numerically simulate the non-linear partial differential equations. It is interestingly demonstrated that these phenomena remarkably affect the electromechanical behavior of nanotweezers fabricated from CNTs. By taking the rippling configuration and Casimir attraction between tubes into account, the pull-in voltage decreases. On the other hand, when the gas damping effect due to low vacuum environment is taken into consideration, the pull-in value increases. The accuracy of the present modeling is compared with those experimentally published in the literature, giving excellent results.

Modeling the nonlinear pull-in behavior of tunable nano-switches

Double-sided nano-devices can potentially be used as tuning switches and variable capacitors. In this paper, the pull-in behavior of double-sided cantilever nano-wires, including the Casimir and partial electrostatic attractions are developed. To increase the tunability, only a piece of substrate plates is electrostatically actuated and conductors’ voltage can be different. Herein, the governing nonlinear equation is derived via extended Hamilton's principle. The Galerkin method is used to discretize the differential EOM and the step-by-step linearization method is employed to solve them numerically. The validity of the presented model is confirmed by comparing the theoretical results with the experimental reported ones. The influence of geometrical parameters, i.e. stationary electrodes distance (initial gaps), non-actuated piece length/location as well as wire diameter and length on the instability is investigated. Furthermore, the effect of surface elasticity, residual surface tension and length-scale on the free vibration is examined. It is concluded that the geometric configuration characteristics play significant roles in the pull-in deflection and voltage of nano-structures, which should be considered in applying design and tuning applications.

Enhancing Casimir repulsion via topological insulator multilayers

We propose to observe the enhanced Casimir repulsion between two parallel multilayer walls made of alternating layers of a topological insulator (TI) and a normal insulator. Based on the transfer matrix method, the Fresnel coefficients matrix is generalized to apply to the TI multilayer structure. The Casimir repulsion under the influence of the magnetization orientation in the magnetic coatings on TI layer surfaces, the layer thicknesses, and the topological magnetoelectric polarizability, is investigated. We show that, for the multilayer structures with parallel magnetization on the TI layer surfaces, it is possible to enhance the repulsion by increasing the TI layer number, which is due to the accumulation of the contribution to the repulsion from the polarization rotation effect occurring on each TI layer surface. Generally, in the distance region where there is Casimir attraction between semi-infinite TIs, the force may turn into repulsion in TI multilayer structure, and in the region of repulsion for semi-infinite TI, the repulsive force can be enhanced in magnitude, the enhancement tends to a maximum while the structure contains sufficiently many layers.

A modified model for dynamic instability of CNT based actuators by considering rippling deformation, tip-charge concentration and Casimir attraction

The tip charge concentration and rippling phenomenon can substantially affect the electromechanical performance of actuators fabricated from cantilever carbon nanotube (CNT). However, these important phenomena are often ignored in the theoretical beam models. In this article, the influence of rippling deformation, Casimir attraction and tip concentration charge on the dynamic pull-in characteristics of nanotube actuators is investigated using a modified Euler–Bernoulli beam theory. To express the Casimir attraction of cylinder-plate geometry, two approaches e.g. proximity force approximation (PFA) for small separations and Drichlet asymptotic approximation for large separations are considered. The charge concentration at the CNT tip is included in the governing equation using Dirac delta function. It is demonstrated that the rippling deformation and tip charge concentration can substantially decrease the dynamic pull-in voltage of the nano-actuator. The rippling deformation of CNT increases the pull-in time while the concentrated charge at the CNT end reduces the pull-in time of the nano-system. Results of the present study are beneficial to precise design and fabrication of electromechanical CNT actuators. Comparison between the obtained results and those reported in the literature by experiments and molecular dynamics, verifies the integrity of the present analysis.