Crystalline Membranes Research Articles

Dislocations and crowdions in two-dimensional crystals. Part III: Plastic deformation of the crystal as a result of defect movement and defect interaction with the field of elastic stresses

A continuation of the theoretical study of the intrinsic properties of dislocation and crowdion structural defects in 2D crystals [V. D. Natsik and S. N. Smirnov, Fiz. Nizk. Temp. 40, 1366 (2014) and V. D. Natsik and S. N. Smirnov, Fiz. Nizk. Temp. 41, 271 (2015)]. The atomic lattice model of conservative (glide) and non-conservative (climb) defect movement is discussed in detail. It is shown that given a continuum description of the 2D crystal, an individual defect can be examined as a point carrier of plastic deformation, its value being determined by the topological charge, which is compliant with the crystal geometry defect parameters. It is found that the strain rate depends on the rate at which the defect center moves, as well as its topological charge. The elastic forces acting on the dislocation and crowdion centers in the field of applied mechanical stresses, and the forces of elastic interaction between defects, are calculated in terms of the linear theory of elasticity of a 2D crystal. The non-linear effect pertaining to the interaction between defects and bending deformation of the crystalline membrane, which is specific to 2D crystals, is also discussed.

Phenomenology of ripples in graphene

A recent experimental study has shown that the flat geometry of graphene is unstable, leading to the formation of a corrugated structure: topological defects and ripples [1]. Graphene can be viewed as a crystalline membrane. An ideal flat 2D-crystal could not exist at a finite temperature [1], and the long range order in graphene’s structure occurs because of ripples and topological defects. Both of these factors facilitate the achievement of thermodynamic stability in grapheme [2] and they could be induced to relieve the membrane’s strain. As far as we know, no widely accepted model for ripples in monolayer graphene exists. The crumpled membrane theory does not work for graphene at relevant temperatures. Some authors try to obtain a ripplelike solution from the renormalization group approach, but the only result is the appearance of some characteristic length of a correct magnitude. The phenomenon under consideration looks too simple to be described with a use of the sophisticated fluctuation theory: we assume that the ripple theory has to be the mean field one. The somewhat similar problem of undulations in biological membranes was solved by taking into account the internal degrees of freedom [3]. One such fluctuating degree of freedom was the membrane thickness. In the case of graphene, a natural candidate on this position is the in-plane transverse optical phonon. The spatial period of the ripple is determined by the ratio of the coefficients in the thermodynamic potential derivative expansion. The out-of-plane subsystem acquires periodicity due to the interaction between the subsystems. Two interaction mechanisms: bilinear and biquadratic were considered. Only solutions with vanishing Gaussian curvature are admissible. The suggested phenomenological description needs to be justified by future microscopic theory.

Free-standing gallium nitride membrane-based sensor for the impedimetric detection of alcohols

We report on the fabrication and characterization of single-crystal Gallium Nitride (GaN) membrane organic gas sensor. The sensing device is based on the highly stable free-standing III-nitride membrane, and it is probed using non-destructive impedance spectroscopy. Monitoring the effect of a series of polar organic molecules on the electrochemical impedance spectrum of the sensing membrane in the frequency range of 1 mHz to 0.1 MHz at room temperature, we concluded that the sensor is highly sensitive to alcohols, in the gas phase, with selectivity that depends on the molecular weight and vapor pressure of the molecules. The highly robust and stable GaN crystalline membrane and the ability to test these sensors using impedance spectroscopy and electrochemical probing techniques suggest that single crystal GaN-based sensors can find a wide range of applications in harsh and extreme environments.

Universal behavior of crystalline membranes: Crumpling transition and Poisson ratio of the flat phase.

We revisit the universal behavior of crystalline membranes at and below the crumpling transition, which pertains to the mechanical properties of important soft and hard matter materials, such as the cytoskeleton of red blood cells or graphene. Specifically, we perform large-scale Monte Carlo simulations of a triangulated two-dimensional phantom network which is freely fluctuating in three-dimensional space. We obtain a continuous crumpling transition characterized by critical exponents which we estimate accurately through the use of finite-size techniques. By controlling the scaling corrections, we additionally compute with high accuracy the asymptotic value of the Poisson ratio in the flat phase, thus characterizing the auxetic properties of this class of systems. We obtain agreement with the value which is universally expected for polymerized membranes with a fixed connectivity.

Synthesis of TiO2 nanostructure membrane and influence of ZrO2 addition on microstructure, thermal stability and membrane properties

A technique for the synthesis of crystalline TiO2 nano-structured membranes by the sol–gel method is determined. Macroporous α-alumina support was used as substrate and intermediate layer was gained by coating and calcination of the colloidal titania sol on the mechanical support. The effect of several processing variables on particle size and sol stability of titania was studied. The influence of 20 mol% zirconia doping on microstructure, liquid permeability, thermal and mechanical stability of composite titania/zirconia membranes was investigated. The thermal and mechanical stability, phase transformation, surface morphology, pore size distribution and permeation of the defect-free titania–zirconia membrane were investigated using X-ray diffraction, atomic force microscopy, gas adsorption analyzer, TG–DTA analysis, scanning electron microscope, FTIR analysis and water permeation apparatus, respectively. It was shown that zirconia retards the phase transformation of anatase to rutile until at least 700 °C. The pore size decreases to 1.2 nm by addition of up to 20 mol% zirconia, while nitrogen sorption experiments shows that the porosity, BET surface area and pore connectivity increases.

Marked inducing effects of metal oxide supports on the hydrothermal stability of zeolitic imidazolate framework (ZIF) membranes

The hydrothermal stability of crystalline ZIF membranes markedly depend on the surface chemistry of the metal oxide supports.

イオンや分子を輸送する液晶性自己組織化膜の構築

イオンや分子を輸送する液晶性自己組織化膜の構築

MD simulation and cluster analyses of the gas permeability of parylene AF4 membranes

In poly-p-xylylene (parylene) AF4 membranes, amorphous and crystalline areas were constructed by a novel computational technique: a combination of NVT + NPT-molecular dynamics (MD) and “gradually reduce the size” (GRS) methods. The corresponding free volume was determined via the homology cluster method. Crystalline parylene AF4 membranes were found to provide less free volume for the adsorption and transfer of gases than amorphous parylene AF4. The permeability results showed that amorphous and crystalline parylene AF4 membranes have different permeation properties, and the corresponding permeability coefficients approach those observed experimentally. This work determined the behaviours and directions of diffusing gases via a cluster analysis technique. Gas diffusion occurs only along the y-axis in the crystalline area and randomly in the amorphous area. The relative permeability was close to the experimental value.

Electrochemical Reduction of Carbon Dioxide on Single-Crystal Copper Membrane

The selective electrochemical reduction of carbon dioxide (CO2) was demonstrated over single-crystal copper membranes. The crystalline copper membranes were deposited on specific support substrates that were c-plane sapphire for Cu(111), MgO(100) for Cu(100), and MgO(110) for Cu(110). Methane (CH4) and ethylene (C2H4) formation in CO2 electrochemical reduction was more favorable on Cu(111) membranes than that on polycrystalline copper plates. The electrolyte type that CO2 gas was effectively dissolved in, was important to significantly maintain electrochemical activity. The product selectivity for CO2 conversion was strongly dependent on the crystal structure of the copper surface.

Theory of thermal expansion in 2D crystals

The thermal expansion in layered crystals is of fundamental and technological interest. As suggested by I. M. Lifshitz in 1952, in thin solid films (crystalline membranes) a negative contribution to is due to anharmonic couplings between in-plane stretching modes and out-of-plane bending (flexural modes). Genuine in-plane anharmonicities give a positive contribution to . The competition between these two effects can lead to a change of sign (crossover) from a negative value of in a temperature (T) range to a positive value of for in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a two-dimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The in-plane and out-of-plane contributions to the thermal expansion are studied as functions of T for crystals of different sizes. Besides, renormalization of the flexural mode frequencies plays a crucial role in determining the crossover temperature . Numerical examples are given for graphene where the anharmonic couplings are determined from experiments. The theory is applicable to other layer crystals wherever the anharmonic couplings are known.

Glass is a Viable Substrate for Precision Force Microscopy of Membrane Proteins.

Though ubiquitous in optical microscopy, glass has long been overlooked as a specimen supporting surface for high resolution atomic force microscopy (AFM) investigations due to its roughness. Using bacteriorhodopsin from Halobacterium salinarum and the translocon SecYEG from Escherichia coli, we demonstrate that faithful images of 2D crystalline and non-crystalline membrane proteins in lipid bilayers can be obtained on microscope cover glass following a straight-forward cleaning procedure. Direct comparison between AFM data obtained on glass and on mica substrates show no major differences in image fidelity. Repeated association of the ATPase SecA with the cytoplasmic protrusion of SecYEG demonstrates that the translocon remains competent for binding after tens of minutes of continuous AFM imaging. This opens the door for precision long-timescale investigations of the active translocase in near-native conditions and, more generally, for integration of high resolution biological AFM with many powerful optical techniques that require non-birefringent substrates.

Entropic interaction between fluctuating twin boundaries

Nanotwinned metals have opened up exciting avenues for the design of high-strength, high-ductility materials owing to the extraordinary properties of twin boundaries. The recent advances in the fabrication of nanostructured materials with twin lamella on the order of a mere few atomic layers call for a closer examination of the stability of these structural motifs, especially at high temperatures. This paper presents a study of the entropic interaction between fluctuating twin boundaries by way of atomistic simulations and statistical mechanics based analysis. The simulations reveal that fluctuations of twin boundaries are considerably enhanced in the presence of adjoining twin boundaries as their spacing, d, decreases. In addition, the theoretical analysis shows that fluctuating twin boundaries indeed exhibit an attractive entropic interaction which enhances their thermal fluctuations and that the entropic force decreases as 1/d2. This finite temperature interaction between twin boundaries is fundamentally distinct from the well-known repulsive entropic interaction followed by fluctuating lipid membranes as well as many crystalline membranes and interfaces. This rather surprising attraction between fluctuating twin boundaries is attributed to their shear coupled normal motion.

Effect of the Cu-substrate thickness on the hardness variation of flame-heated Cr–C deposits

Cr–C deposits were electroplated on a pure Cu substrate in a Cr+3-based plating bath. After electroplating, the Cr–C deposits with and without a Cu substrate were flame-heated for 2 s to increase their hardness. Experimental results show that the hardness and crack density of a flame-heated Cr–C deposit were strongly affected by the Cu-substrate thickness. The hardness of as-plated Cr–C deposit with a Cu substrate increased from 750 to 1600 Hv after flame heating, while a low hardness value of 970 Hv was detected from the flame-heated Cr–C deposit without a Cu substrate. Increase in hardness values of flame-heated Cr–C deposits is attributed to precipitation of crystalline diamond membranes. Fully crystalline diamond-like membranes were found in the flame-heated Cr–C deposit with a Cu substrate; while semi-crystalline diamond-like membranes were detected in the flame-heated deposit without a Cu substrate. The constraint effect of the Cu substrate induced a high internal tension stress in the Cr–C deposit during and after flame heating, leading to widening through-deposit cracks and increasing the deposit hardness.

Theory of anharmonic phonons in two-dimensional crystals

Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semi-empirical model for anharmonic couplings of third and fourth order, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Gr\"uneisen parameters, the thermal tension and the thermal expansion coefficients as function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions we obtain the renormalization and decay rate of in-plane and flexural phonons as function of temperature, wave vector and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There we find that the transition temperature from negative to positive thermal expansion is lowered with smaller system size and by renormalization of the flexural mode frequency. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of Normal and Umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals.

Fourier Monte Carlo renormalization-group approach to crystalline membranes

The computation of the critical exponent η characterizing the universal elastic behavior of crystalline membranes in the flat phase continues to represent challenges to theorists as well as computer simulators that manifest themselves in a considerable spread of numerical results for η published in the literature. We present additional insight into this problem that results from combining Wilson's momentum shell renormalization-group method with the power of modern computer simulations based on the Fourier Monte Carlo algorithm. After discussing the ideas and difficulties underlying this combined scheme, we present a calculation of the renormalization-group flow of the effective two-dimensional Young modulus for momentum shells of different thickness. Extrapolation to infinite shell thickness allows us to produce results in reasonable agreement with those obtained by functional renormalization group or by Fourier Monte Carlo simulations in combination with finite-size scaling. Moreover, our method allows us to obtain a decent estimate for the value of the Wegner exponent ω that determines the leading correction to scaling, which in turn allows us to refine our numerical estimate for η previously obtained from precise finite-size scaling data.

Electrical properties and strain distribution of Ge suspended structures

Germanium membranes and microstructures of 50–1000nm thickness have been fabricated by a combination of epitaxial growth on a Si substrate and simple etching processes. The strain in these structures has been measured by high-resolution micro-X-ray diffraction and micro-Raman spectroscopy. The strain in these membranes is extremely isotropic and the surface is observed to be very smooth, with an RMS roughness below 2nm. The process of membrane fabrication also serves to remove the misfit dislocation network that originally forms at the Si/Ge interface, with benefits for the mechanical, optical and electrical properties of the crystalline membranes.

Impact of casting conditions on PVDF/nanoclay nanocomposite membrane properties

In order to optimize the properties of PVDF/nanoclay nanocomposite membrane, the impact of casting conditions on membrane properties including PVDF crystalline phase, membrane morphology, mechanical strength and nanoclay retention were investigated. Nanoclays with hydrophilic modifiers tended to form membranes with larger macrovoids and higher beta-phase, and nanocomposite membranes with Nanomer® I.30E, which has a simple single alkyl group on the ammonium ion as organic modifier, had the highest nanoclay retention. Long air exposure time prior to immersion had a negative impact on nanoclay retention while adding sodium chloride to the quench bath helped retain nanoclay. Despite the slight changes, nanoparticle retentions varied from 32% to 48% for all membranes tested relative to the respective original concentration in the dope. Mechanical strength of the membranes was associated with membrane morphology, which was controlled by various casting conditions. Increases in air retention time, decreases in quench bath temperature and casting at high humidity increased the demixing rate which resulted in membranes with large macrovoids and poor mechanical properties including low tensile strength, ductility and stiffness. To form good membrane structure, polymer concentration and molecular weight of PVDF has to be high enough to provide the necessary viscosity in the dope. Casting conditions should be chosen carefully not only to retain more nanoclay for economic reasons but also for the morphology and mechanical strength needed for the required applications.

Thermodynamical Properties and Stability of Crystalline Membranes in the Quantum Regime

ABSTRACTWe study the thermodynamical properties and lattice dynamics of two-dimensional crystalline membranes, such as graphene and related compounds, in zero temperature limit, where quantum effects are dominant. We find out that, just as in the high temperature classical limit, a fundamental role is played by the anharmonic coupling between in-plane and out-of plane lattice modes, which leads to a strong reconstruction of the dispersion relation of the out-of-plane mode. We identify a crossover temperature, T*, bellow which quantum effects are dominant. We estimate that for graphene T* ∼ 70 - 90 K. Inclusion of anharmonic effects makes the thermal expansion finite in the thermodynamic limit, and below T* it tends to zero as a power law as T→0 as required by the third law of thermodynamics. The specific heat also goes to zero as a power law as T→0, but with a exponent that differs from the one predicted by the harmonic theory.

Glass: A Multi-Platform Specimen Supporting Substrate for Precision Single Molecule Studies of Membrane Proteins

High resolution (≈1 nm lateral resolution) biological AFM imaging has been carried out almost exclusively using freshly cleaved mica as a specimen supporting surface, but mica suffers from a fundamental limitation that has hindered AFM's broader integration with many modern optical methods. Mica exhibits biaxial birefringence; indeed, this naturally occurring material is used commercially for constructing optical wave plates. In general, propagation through birefringent material alters the polarization state and bifurcates the propagation direction of light in a manner which varies with thickness. This makes it challenging to incorporate freshly cleaved mica substrates with modern optical methods, many of which employ highly focused and polarized laser beams passing through then specimen plane. Using bacteriorhodopsin from Halobacterium salinarum and the translocon SecYEG from Escherichia coli, we demonstrate that faithful images of 2D crystalline and non-crystalline membrane proteins in lipid bilayers can be obtained on common microscope cover glass following a straight-forward cleaning procedure. Direct comparison between data obtained on glass and on mica show no significant differences in AFM image fidelity. This work opens the door for combining high resolution biological AFM with powerful optical methods that require optically isotropic substrates such as ultra-stable1 and direct 3D AFM2. In turn, this capability should enable long timescale conformational dynamics measurements of membrane proteins in near-native conditions. 1.King, G.M., Carter, A.R., Churnside, A.B., Eberle, L.S. & Perkins, T.T. Ultrastable atomic force microscopy: atomic-scale stability and registration in ambient conditions. Nano Letters 9, 1451 (2009). 2.Sigdel, K.P., Grayer, J.S. & King, G.M. Three-dimensional atomic force microscopy: interaction force vector by direct observation of tip trajectory. Nano Lett 13, 5106-5111 (2013).

Flexoelectricity in two-dimensional crystalline and biological membranes

The ability of a material to convert electrical stimuli into mechanical deformation, i.e. piezoelectricity, is a remarkable property of a rather small subset of insulating materials. The phenomenon of flexoelectricity, on the other hand, is universal. All dielectrics exhibit the flexoelectric effect whereby non-uniform strain (or strain gradients) can polarize the material and conversely non-uniform electric fields may cause mechanical deformation. The flexoelectric effect is strongly enhanced at the nanoscale and accordingly, all two-dimensional membranes of atomistic scale thickness exhibit a strong two-way coupling between the curvature and electric field. In this review, we highlight the recent advances made in our understanding of flexoelectricity in two-dimensional (2D) membranes-whether the crystalline ones such as dielectric graphene nanoribbons or the soft lipid bilayer membranes that are ubiquitous in biology. Aside from the fundamental mechanisms, phenomenology, and recent findings, we focus on rapidly emerging directions in this field and discuss applications such as energy harvesting, understanding of the mammalian hearing mechanism and ion transport among others.