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Polyamide membranes, such as nanofiltration (NF) and reverse osmosis (RO) membranes, are widely used for water desalination and purification. However, the mechanisms of solute transport and solute rejection due to charge interactions remain unclear at the molecular level. Here we use molecular dynamics (MD) simulations to examine the transport of single-solute feeds through charged nanofiltration membranes with different membrane charge concentrations of COO$^{\text{-}}$ and NH$_2\!^+$ corresponding to different pH levels. Results show that Na$^+$ and Cl$^{\text{-}}$ solute ions are better rejected when the membrane has a higher concentration of negatively charged groups, corresponding to a higher pH, whereas CaCl$_2$ is well-rejected at all pH levels studied. These results are consistent with experimental findings which are performed at the same pH conditions as simulation setup. Moreover, solute transport behavior depends on the membrane functional group distribution. When COO$^{\text{-}}$ functional groups are concentrated at membrane feed surface, ion permeation into the membrane is reduced. Counter-ions tend to associate with charged functional groups while co-ions seem to pas

Polymeric membranes, including Polysulfone (PSf) membranes, are routinely used for water treatment. To enhance water permeation of above membranes, it is common to synthesize polymeric membranes with carbon nanotubes (CNTs) embedded in them. It is seen that water permeability of membranes having vertically aligned CNTs is higher, as compared to those where CNTs are not aligned. It is of interest to examine if the dielectric constant of a CNT based nanocomposite membrane is sensitive to alignment of CNTs or not. This paper reports dielectric properties of PSf-MWCNT membranes, both, for aligned and unaligned MWCNTs. Multi Walled Carbon Nanotubes (MWCNTs) based polysulfone membranes were synthesized using standard methods. MWCNTs in above membranes were aligned by casting the membrane in presence of magnetic field. The present paper, for the first time, shows that the above result is valid for membranes also.

The multiferroic properties of TbMnO3 demonstrate high versatility under applied pressure, making the material potentially suitable for use in flexible electronics. Here, we report on the preparation of elastic freestanding TbMnO3 membranes with dominant (001) or (010) crystallographic out-of-plane orientation. Membranes with thickness of 20 nm display orthorhombic bulk-like relaxed lattice parameters with strong suppression of twinning for the (010) oriented membranes. Strain in flexible membranes was tuned by using a commercial strain cell device and characterized by Raman spectroscopy. The B1g out-of-phase oxygen-stretching mode, representative for the Mn-O bond distance, systematically shifts to lower energy with increasing strain (epsilon{max} ~ 0.5 %). The flexibility and elastic properties of the membranes allow for specific manipulation of the multiferroic state by strain, whereas the choice of the crystallographic orientation gives possibility for an in- or out-of-plane electric polarization.

The signature of a membrane is a sequence of tensors whose entries are iterated integrals. We study algebraic properties of membrane signatures, with a focus on signature matrices of polynomial and piecewise bilinear membranes. Generalizing known results for path signatures, we show that the two families of membranes admit the same set of signature matrices and we examine the corresponding affine varieties. In particular, we prove that there are no algebraic relations on signature matrices of membranes, in contrast to the path case. We complement our results by a linear time algorithm for the computation of signature tensors for piecewise bilinear membranes.

How internal forces are transduced into motion through soft, fluid membranes remains a fundamental question in the study of active systems. To investigate this coupling, we develop a minimal system consisting of a single ferromagnetic particle encapsulated within a lipid vesicle with controlled membrane composition and phase behavior. An external rotating magnetic field actuates the particle, which rotates and translates along the inner membrane leaflet. This motion generates local slip in the membrane; near a substrate, the slip creates a shear gradient across the lubrication gap that propels the vesicle forward. Propulsion is intermittent and strongest when the particle moves near the vesicle bottom, where stress transmission is most effective. We find that the coupling between internal flows and vesicle motion is highly sensitive to membrane elasticity, excess area, and phase coexistence. Local membrane deformation and flow dissipate part of the stress, limiting the efficiency of force transduction. Additionally, membrane fluctuations and external boundaries reduce particle mobility, and in phase-separated membranes, line tension at domain boundaries deflects the particle and gr

We perform numerical simulations of active ideal and self-avoiding tethered membranes. Passive ideal membranes with bending interactions are known to exhibit a continuous crumpling transition between a low temperature flat phase and a high temperature crumpled phase. Conversely, self-avoiding membranes remain in an extended (flat) phase for all temperatures even in the absence of a bending energy. We find that the introduction of active fluctuations into the system produces a phase behavior that is overall consistent with that observed for passive membranes. The phases and the nature of the transition for ideal membranes is unchanged and active fluctuations can be remarkably accounted for by a simple rescaling of the temperature. For the self-avoiding membrane, we find that the extended phase is preserved even in the presence of very large active fluctuations.

Cell membranes separate the cell interior from the external environment. They are constituted by a variety of lipids; their composition determines the dynamics of membrane proteins and affects the ability of the cells to adapt. Even though the study of model membranes allows to understand the interactions among lipids and the overall mechanics, little is known about these properties in native membranes. To combine topology and nanomechanics analysis of native membranes, I designed a method to investigate the plasma membranes isolated from a variety of single cells. Five cell types were chosen and tested, revealing 20\% variation in membrane thickness. I probed the resistance of the isolated membranes to indent, finding their line tension and spreading pressure. These results show that membranes isolated from neurons are stiffer and less diffusive than brain cancer cell membranes. This method gives direct quantitative insights on the mechanics of native cell membranes.

We present Monte Carlo simulations of an ultra coarse-grained lipid bilayer with different number of lipids on both leaflets. In the simulations, we employ a new method for measuring the elastic parameters of the membrane, including the area per lipid, area elasticity modulus, and bending rigidity. The method also allows to measure the spontaneous curvature and non-local bending modulus, which are not accessible by standard computer simulations with periodic boundary conditions. For membranes with lipid densities much smaller than the liquid to gel transition density, $ρ_g$, we find a very good agreement between the simulation results and the theory expressing the bilayer elastic free energy as the sum of quadratic free energies in the strains associated with the area density and the local curvature of the monolayers. The theory fails when the lipid area density (in the symmetric reference case) is only slightly smaller than $ρ_g$. Increasing the degree of asymmetry and changing the density of the condensed leaflet to a value larger than $ρ_g$, causes the layer to phase separate between regions with distinct densities which, in turn, may also induce density variations in the dilate

An introduction to the defects which dominate the physics of superfluid He$^4$ films, of superconducting slabs and of crystalline and hexatic membranes is given. We first review point vortices in two-dimensional neutral superfluids and discuss the unusual screening which arises when the bosons are charged, as in superconducting films. Dislocation and disclination defects in crystalline membranes are discussed from a similar point of view. There is little or no screening in ``monolayer'' crystals, which are strongly constrained to lie in a flat two-dimensional plane. A strong nonlinear screening effect arises, however, in 2d membranes allowed to buckle into the third dimension. This screening drastically lowers dislocation and disclination energies, and forces crystalline membranes to melt at any finite temperature. We point out that buckled 5- and 7-fold disclinations in hexatic membranes have in general different logarithmically divergent energies. A similar asymmetry exists in the energies of 5- and 7-fold defects in {\it liquid} membranes. This difference determines the sign of the Gaussian bending rigidity, and has important consequences in membranes which can change their topo

Membranes are of great technological and biological as well as theoretical interest. Two main classes of membranes can be distinguished: Fluid membranes and polymerized, tethered membranes. Here, we review progress in the theoretical understanding of polymerized membranes, i.e. membranes with a fixed internal connectivity. We start by collecting basic physical properties, clarifying the role of bending rigidity and disorder, theoretically and experimentally as well as numerically. We then give a thorough introduction into the theory of self-avoiding membranes, or more generally non-local field theories with delta-like interactions. Based on a proof of perturbative renormalizability for non-local field-theories, renormalization group calculations can be performed up to 2-loop order, which in 3 dimensions predict a crumpled phase with fractal dimension of about 2.4. The tricritical behavior of membranes is discussed and shown to be quite different from that of polymers. Dynamical properties are studied in the same frame-work. Along the same lines, disorder can be included leading to interesting applications. We also construct a generalization of the O(N)-model, which in the limit N-&

We demonstrate, on the basis of molecular dynamics simulations, the possibility of an efficient water-ethanol separation using nanoporous carbon membranes, namely carbon nanotube membranes, nanoporous graphene sheets, and multilayer graphene membranes. While these carbon membranes are in general permeable to both pure liquids, they exhibit a counter-intuitive "self-semi-permeability" to water in the presence of water-ethanol mixtures. This originates in a preferred ethanol adsorption in nanoconfinement that prevents water molecules from entering the carbon nanopores. An osmotic pressure is accordingly expressed across the carbon membranes for the water-ethanol mixture, which agrees with the classic van't Hoff type expression. This suggests a robust and versatile membrane-based separation, built on a pressure-driven reverse-osmosis process across these carbon-based membranes. In particular, the recent development of large-scale 'graphene-oxide' like membranes then opens an avenue for a versatile and efficient ethanol dehydration using this separation process, with possible application for bio-ethanol fabrication.

Single crystal, nanoscale diamond membranes are highly sought after for a variety of applications including nanophotonics, nanoelectronics and quantum information science. However, so far, the availability of conductive diamond membranes remained an unreachable goal. In this work we present a complete nanofabrication methodology for engineering high aspect ratio, electrically active single crystal diamond membranes. The membranes have large lateral directions, exceeding 500x500 um2 and are only several hundreds of nanometers thick. We further realize vertical single crystal p-n junctions, made from the diamond membranes that exhibit onset voltages of ~ 10V and a current of several mA. Moreover, we deterministically introduce optically active color centers into the membranes, and demonstrate for the first time a single crystal nanoscale diamond LED. The robust and scalable approach to engineer the electrically active single crystal diamond membranes, offers new pathways for advanced nanophotonics, nanoelectronics and optomechanics devices employing diamond.

The dynamics of brane-like extended objects in spacetimes with torsion is derived from the conservation equations of stress-energy and spin tensors. Thus obtained world-sheet equations are applied to macroscopic test membranes made of spinning matter. Specifically, we consider membranes with maximally symmetric distribution of stress-energy and spin. These are characterized by two constants only: the tension and spin magnitude. By solving the world-sheet equations, we discover a similarity between such membranes in Riemann-Cartan backgrounds, and string theory membranes in low-energy string backgrounds. In the second part of the paper, we apply this result to cylindrical membranes wrapped around the extra compact dimension of a $(D+1)$-dimensional spacetime. In the narrow membrane limit, we discover how effective macroscopic strings couple to torsion. An observed similarity with the string sigma model is noted.

Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the development of molecular dynamics (MD), a variety of in silico methods have been proposed for the determination of elastic parameters of simulated lipid membranes. These MD methods allow for the consideration of details unattainable in experimental techniques and represent a distinct scientific field, which is rapidly developing. This work provides a review of these MD approaches with a focus on theoretical aspects. Two main challenges are identified: (i) the ambiguity in the transition from the continuum description of elastic theories to the discrete representation of MD simulations, and (ii) the d

We study the existence and stability of spherical membranes in curved spacetimes. For Dirac membranes in the Schwarzschild--de Sitter background we find that there exists an equilibrium solution. By fine--tuning the dimensionless parameter $ΛM^2,$ the static membrane can be at any position outside the black hole event horizon, even at the stretched horizon, but the solution is unstable. We show that modes having $l=0$ (and for $ΛM^2<16/243$ also $l=1$) are responsible for the instability. We also find that spherical higher order membranes (membranes with extrinsic curvature corrections), contrary to what happens in flat Minkowski space, {\it do} have equilibrium solutions in a general curved background and, in particular, also in the ``plain'' Schwarzschild geometry (while Dirac membranes do not have equilibrium solutions there). These solutions, however, are also unstable. We shall discuss a way of by--passing these instability problems, and we also relate our results to the recent ideas of representing the black hole event horizon as a relativistic bosonic membrane.

The statistical mechanics of flexible surfaces with internal elasticity and shape fluctuations is summarized. Phantom and self-avoiding isotropic and anisotropic membranes are discussed, with emphasis on the universal negative Poisson ratio common to the low-temperature phase of phantom membranes and all strictly self-avoiding membranes in the absence of attractive interactions. The study of crystalline order on the frozen surface of spherical membranes is also treated.

A feature of current membrane systems is the fact that objects and membranes are persistent. However, this is not true in the real world. In fact, cells and intracellular proteins have a well-defined lifetime. Inspired from these biological facts, we define a model of systems of mobile membranes in which each membrane and each object has a timer representing their lifetime. We show that systems of mutual mobile membranes with and without timers have the same computational power. An encoding of timed safe mobile ambients into systems of mutual mobile membranes with timers offers a relationship between two formalisms used in describing biological systems.

We investigate the recently developed theory of multiple membranes. In particular, we consider open membranes, i.e. the theory defined on a membrane world volume with a boundary. We first restrict our attention to the gauge sector of the theory. We obtain a boundary action from the Chern-Simons terms. Secondly, we consider the addition of certain boundary terms to various Chern-Simons theories coupled to matter. These terms ensure the full bulk plus boundary action has the correct amount of supersymmetry. For the ABJM model, this construction motivates the inclusion of a boundary quartic scalar potential. The boundary dynamics obtained from our modified theory produce Basu-Harvey type equations describing membranes ending on a fivebrane. The ultimate goal of this work is to throw light on the theory of fivebranes using the theory of open membranes.