Self-Consistent Screening Approximation for Flexible Membranes: Application to Graphene

Crystalline membranes at finite temperatures have an anomalous behavior of the bending rigidity that makes them more rigid in the long wavelength limit. This issue is particularly relevant for applications of graphene in nano- and micro-electromechanical systems. We calculate numerically the height-height correlation function $G(q)$ of crystalline two-dimensional membranes, determining the renormalized bending rigidity, in the range of wavevectors $q$ from $10^{-7}$ \AA$^{-1}$ till 10 \AA$^{-1}$ in the self-consistent screening approximation (SCSA). For parameters appropriate to graphene, the calculated correlation function agrees reasonably with the results of atomistic Monte Carlo simulations for this material within the range of $q$ from $10^{-2}$ \AA$^{-1}$ till 1 \AA$^{-1}$. In the limit $q\rightarrow 0$ our data for the exponent $\eta$ of the renormalized bending rigidity $\kappa_R(q)\propto q^{-\eta}$ is compatible with the previously known analytical results for the SCSA $\eta\simeq 0.82$. However, this limit appears to be reached only for $q<10^{-5}$ \AA$^{-1}$ whereas at intermediate $q$ the behavior of $G(q)$ cannot be described by a single exponent.Comment: 5 pages, 4 figure

Atomistic simulations of structural and thermodynamic properties of bilayer graphene

We study the structural and thermodynamic properties of bilayer graphene, a prototype two-layer membrane, by means of Monte Carlo simulations based on the empirical bond order potential LCBOPII. We present the temperature dependence of lattice parameter, bending rigidity and high temperature heat capacity as well as the correlation function of out-of-plane atomic displacements. The thermal expansion coefficient changes sign from negative to positive above $\approx 400$ K, which is lower than previously found for single layer graphene and close to the experimental value of bulk graphite. The bending rigidity is twice as large than for single layer graphene, making the out-of-plane fluctuations smaller. The crossover from correlated to uncorrelated out-of-plane fluctuations of the two carbon planes occurs for wavevectors shorter than $\approx 3$ nm$^{-1}$Comment: 6 pages, 7 figures

Thermomechanical properties of graphene: valence force field model approach

Using the valence force field model of Perebeinos and Tersoff [Phys. Rev. B {\bf79}, 241409(R) (2009)], different energy modes of suspended graphene subjected to tensile or compressive strain are studied. By carrying out Monte Carlo simulations it is found that: i) only for small strains ($|\varepsilon| \lessapprox 0.02$) the total energy is symmetrical in the strain, while it behaves completely different beyond this threshold; ii) the important energy contributions in stretching experiments are stretching, angle bending, out-of-plane term and a term that provides repulsion against $\pi-\pi$ misalignment; iii) in compressing experiments the two latter terms increase rapidly and beyond the buckling transition stretching and bending energies are found to be constant; iv) from stretching-compressing simulations we calculated the Young modulus at room temperature 350$\pm3.15$\,N/m, which is in good agreement with experimental results (340$\pm50$\,N/m) and with ab-initio results [322-353]\,N/m; v) molar heat capacity is estimated to be 24.64\,J/mol$^{-1}$K$^{-1}$ which is comparable with the Dulong-Petit value, i.e. 24.94\,J/mol$^{-1}$K$^{-1}$ and is almost independent of the strain; vi) non-linear scaling properties are obtained from height-height correlations at finite temperature; vii) the used valence force field model results in a temperature independent bending modulus for graphene, and viii) the Gruneisen parameter is estimated to be 0.64.Comment: 8 pages, 5 figures. To appear in J. Phys.: Condens. Matte

Scaling Properties of Flexible Membranes from Atomistic Simulations: Application to Graphene

Structure and thermodynamics of crystalline membranes are characterized by the long wavelength behavior of the normal-normal correlation function G(q). We calculate G(q) by Monte Carlo and Molecular Dynamics simulations for a quasi-harmonic model potential and for a realistic potential for graphene. To access the long wavelength limit for finite-size systems (up to 40000 atoms) we introduce a Monte Carlo sampling based on collective atomic moves (wave moves). We find a power-law behaviour $G(q)\propto q^{-2+\eta}$ with the same exponent $\eta \approx 0.85$ for both potentials. This finding supports, from the microscopic side, the adequacy of the scaling theory of membranes in the continuum medium approach, even for an extremely rigid material like graphene

Finite temperature lattice properties of graphene beyond the quasiharmonic approximation

The thermal and mechanical stability of graphene is important for many potential applications in nanotechnology. We calculate the temperature dependence of lattice parameter, elastic properties and heat capacity by means of atomistic Monte Carlo simulations that allow to go beyond the quasiharmonic approximation. We predict an unusual, non-monotonic, behavior of the lattice parameter with minimum at temperature about 900 K and of the shear modulus with maximum at the same temperature. The Poisson ratio in graphene is found to be small ~0.1 in a broad temperature interval.Comment: 4 pages, 5 figure

Effect of Laser Optoperforation of the Zona Pellucida on Mouse Embryo Development in vitro

Laser operations on cells and embryos are an important field of current photobiology and biophotonics. The high power density of tightly focused laser irradiation provides an efficient impact on matter of cells or embryos. Precise focusing of the laser spot allows strictly controlled perforation of the membrane. The present work was devoted to studying the influence of optoperforation of mammalian embryonic zona pellucida with a tightly focused laser beam with 1.48-µm wavelength on further development of the embryo. Such a laser operation was proposed for application in in vitro fertilization (IVF) practice and intracytoplasmic sperm injection into the oocyte (ICSI). For cultured in vitro oocytes and embryos, the process of natural exiting from the zona pellucida (&quot;hatching&quot;) is often impaired, which decreases probability of implantation and pregnancy The goals of the present work were to determine the influence of different manipulations on development of embryos in vitro until blastocyst formation and on the ISSN 0006-2979, Biochemistry (Moscow), 2015, Vol. 80, No. 6, pp. 769-775. © Pleiades Publishing, Ltd., 2015. Original Russian Text © E. O. Zakharchenko, A. D. Zalessky, A. A. Osychenko, A. S. Krivokharchenko, A. K. Shakhbazyan, A. V. Ryabova, V. A. Nadtochenko, 2015, published in Biokhimiya, 2015 769 * To whom correspondence should be addressed. Abstract-The effect of laser optical perforation of the zona pellucida on the viability and development of mouse embryos has been studied. Operations of zona pellucida thinning and single or double perforation were carried out on 2-cell embryo, morula, and blastocyst stages with a laser pulse (wavelength 1.48 µm, pulse duration 2 ms). Embryo development up to the blastocyst stage and hatching efficiency were statistically analyzed. It was found that 2-cell or morula stage embryo zona pellucida thinning or single perforation did not affect development to the blastocyst stage and number of hatched embryos, but it accelerated embryo hatching compared to control groups one day earlier in vitro. Double optoperforation on 2-cell embryo or morula stage did not significantly affect development to the blastocyst stage, but it strongly decreased the number of hatched embryos. Also, zona pellucida perforation at the blastocyst stage had a negative effect: hatching did not occur after this manipulation. Blastocyst cell number calculation after single zona pellucida perforation at 2-cell and morula stages showed that cell number of hatching or hatched blastocysts did not differ from the same control groups. This fact points out that the laser single optoperforation method is a useful and safe experimental tool that allows further manipulations within the zona pellucida. Effect of Laser Optoperforation of the Zon

Determination of the Bending Rigidity of Graphene via Electrostatic Actuation of Buckled Membranes

The small mass and atomic-scale thickness of graphene membranes make them highly suitable for nanoelectromechanical devices such as e.g. mass sensors, high frequency resonators or memory elements. Although only atomically thick, many of the mechanical properties of graphene membranes can be described by classical continuum mechanics. An important parameter for predicting the performance and linearity of graphene nanoelectromechanical devices as well as for describing ripple formation and other properties such as electron scattering mechanisms, is the bending rigidity, {\kappa}. In spite of the importance of this parameter it has so far only been estimated indirectly for monolayer graphene from the phonon spectrum of graphite, estimated from AFM measurements or predicted from ab initio calculations or bond-order potential models. Here, we employ a new approach to the experimental determination of {\kappa} by exploiting the snap-through instability in pre-buckled graphene membranes. We demonstrate the reproducible fabrication of convex buckled graphene membranes by controlling the thermal stress during the fabrication procedure and show the abrupt switching from convex to concave geometry that occurs when electrostatic pressure is applied via an underlying gate electrode. The bending rigidity of bilayer graphene membranes under ambient conditions was determined to be $35.5^{+20}_{-15}$ eV. Monolayers have significantly lower {\kappa} than bilayers

Анализ неоднородности химического состава снежного покрова с использованием методов кластеризации (k-means) и ГИС-технологии

The purpose of the work is a comparative analysis of the geochemical spectra of melt water and dust in the snow cover of the city of Tyumen and its surroundings. Sampling was carried out in 2020 using standard methods. Content of macro-elements (Na, Mg, Al, P, S, K, Ca, Fe, Mn) was determined by the ICP-AES atomic emission method (iCAP-6500, Thermo Scientific, USA), microelements – by mass spectrometry with inductively coupled plasma ICP- MS (X-7 Thermo Elemental, USA). The main method of analyzing the inhomogeneity of the territory was multidimensional cluster analysis (k-means). If sampling points have a high (or low) content of individual chemical elements, but are located among the points with lower (or higher) content, then the problem of formation of them arises. The problem points of water-soluble macro-elements have a high content of Na, Ca and Mg that results from the use of different anti-icing reagents. Macro-elements of the solid phase of snow are mostly similar in composition to background soils; the problem points are more often found in the northern part of the city, however some of them may be observed in other sites. According to the geochemical spectrum, microelements of the liquid phase of the snow cover are divided into four clusters. Background cluster С1 is located at the maximum distance (20–35 km) from the city center. It is distinguished by higher contents of Ni, Cu, Pb, Li, Sn, W relative to the background cluster С2. The cluster С2 has the lowest content of microelements and combines some points of the background also in the central part of the city. Cluster С3 (2 points) is located in the industrial area. By the composition of microelements, the cluster С4 has a geochemical spectrum similar to the С2 cluster, but with a higher content of them. According to the content of microelements in the solid phase, the C1 cluster combines the background and partly urban areas. Clusters С2 and С3 are similar in geochemical spectrum, but differ in the content of heavy metals. Geographically, they tend to the northern part of the city. Problem points are notable in cluster C4. They are located far from the industrial zone and main roads. Their localization may be caused by the precipitation of snow dust from the atmosphere during its regional transport.Исследован химический состав снежного покрова в г. Тюмень и его окрестностях. Для изучения неоднородности территории использовался кластерный анализ (k-means). Его результаты отражают концентрирование на местности точек, схожих по геохимическому спектру, вокруг некоторых сравнительно однородных ядер. Обнаружены точки с высоким содержанием тяжёлых металлов, удалённые от источников загрязнения. Предполагается, что вымывание аэрозолей жидкими осадками из атмосферы может создавать повышенную концентрацию некоторых элементов в снежном покрове в виде мозаичных пятен. Кластеризация позволяет выявлять неоднородность химического состава снега, а использование ГИС-технологий – визуализировать расположение выделенных кластеров