Nanopores in solid-state membranes have been used to detect, identify, filter, and characterize nanoparticles and biological molecules. In this work, we simulate an ionic flow through a nanopore while an ellipsoidal nanoparticle translocates through a pore. We numerically solve the Poisson-Nernst-Planck equations to obtain the ionic current values for different aspect ratios, sizes, and orientations of a translocating particle. By extending the existing theoretical model for the ionic current in the nanopore to the particles of ellipsoidal shape, we propose semiempirical fitting formulas which describe our computed data within 5% accuracy. We also demonstrate how the derived formulas can be used to identify the dimensions of nanoparticles from the available experimental data which may have useful applications in bionanotechnology.

When a nanoparticle (or a biomolecule) translocates through a nanopore in a solid-state membrane submereged in an electrolyte solution, the ionic current changes and the ionic current blockadeIonic current blockade appears. In this work we elucidate how the concentration polarizationConcentration polarization, the surface charge on the nanopore and nanoparticle as well as the applied voltage affect the ionic current blockadeIonic current blockade. We use Brownian dynamics approach in conjunction with a full three-dimensional self-consistent solution of the Poisson-Nernst-Planck and Navier-Stockes system of equations to describe realistic ionic current response arising due to the random motion of a nanoparticle through a nanopore. We then derive a closed form expression for the ionic current blockadeIonic current blockade ratio and apply it to analyze the computed and experimentally measured ionic current blockadesIonic current blockade.

Nanoporous membranes may provide an approach for rapidly filtering proteins at high throughput volume, a goal that many fields of study would find useful. Creating a system to separate proteins quickly would require an extensive knowledge of protein-nanopore and protein-protein dynamics. To further this knowledge, we use Brownian dynamics simulations to model the motion of two similarly sized proteins (insulin and ubiquitin) coarse-grained and interacting with each other in a system with a cylindrical nanopore (of radius ranging from 30 to 60 Å), an electrically biased membrane (−1 and 1 V), and a zero electrolyte bias. The time each protein takes to move from one side of the membrane to the other (cis chamber to the trans chamber) is compared in order to find the system that best encourages the separation of the two proteins. Additionally, we studied the interaction of two spherical beads of various sizes and charges in order to determine the favorable/viable circumstances of separating proteins. We use the results of these simple cases to gain insight on the more complex dynamics present in modeling specific proteins.

We present a novel computational approach to self-consistently describe a nanoparticle moving through a nanopore embedded in a solid-state membrane. We calculate the electrostatic and hydrodynamic forces a particle experiences at various locations within a nanopore and incorporate these forces into a Brownian dynamics model at each time step. The value of the ionic current through the pore is determined based on the particle's location, and in conjunction with our Brownian dynamics model, a realistic ionic current trace is obtained due to the motion of a nanoparticle through a nanopore. We find that in addition to the usual geometric blockade, the variations of the current along the axis of the pore are largely caused by a concentration polarization induced by the presence of the translocating nanoparticle in the nanopore while the current changes in the radial (perpendicular to the axis) direction occur because of the local buildup of the ionic charge between the particle and the nanopore surface.

The ability to separate proteins is desirable for many fields of study, and nanoporous membranes may offer a method for rapid protein filtration at high throughput volume, provided there is an understanding of the protein dynamics involved. In this work, we use Brownian dynamics simulations to study the motion of coarse-grained proteins insulin and ubiquitin in an electrically biased membrane. In our model, the protein is subjected to various biases applied to the silicon membrane equipped with a nanopore of different radii. The time each protein takes to find a cylindrical nanopore embedded in a thin silicon membrane, attempt to translocate it (waiting time), and successfully translocate it in a single attempt (translocation time) is calculated. We observe insulin finding the nanopore and translocating it faster than the electrically neutral ubiquitin due to insulin's slightly smaller size and net negative charge. While ubiquitin's dynamics is also affected by the size of the pore, surprisingly, its translocation process is also noticeably changed by the membrane bias. By investigating the protein's multipole moments, we demonstrate that this behavior is largely due to the protein's dipole and quadrupole interactions with the membrane potential.

The ability to separate proteins is desirable for many fields of study and nanoporous membranes may offer a method for rapid protein filtration at high throughput volume provided there is an understanding of the protein dynamics involved. We use Brownian dynamics simulations to model the motion of coarse-grained proteins insulin and ubiquitin in an electrically biased membrane under zero electrolyte bias. The time each protein takes to find a cylindrical nanopore embedded in a thin silicon dioxide membrane (waiting time) and successfully translocate it in a single attempt (translocation time) are calculated. In our model, each protein is subjected to various biases applied to the silicon membrane equipped with a nanopore of different radii. We observe insulin finding the nanopore and translocating it faster than the electrically neutral ubiquitin due insulin's slightly smaller size and net negative charge. While ubiquitin's dynamics is also affected by the size of the pore, surprisingly, its translocation process is noticably changed by the membrane bias. By investigating the protein's dipole and quadrupole moments, we demonstrate that its waiting and translocation time dependency on the membrane bias is due to the protein's charge distribution.

In this work, the ionic current blockades due to the translocation of a neutral spherical nanoparticle through a nanopore in a solid state membrane are computed. We use a Brownian dynamics approach, in conjunction with a full three-dimensional self-consistent solution of the Poisson-Nernst-Planck and Navier-Stockes system of equations to describe realistic ionic current response arising due to the random motion of a nanoparticle through a nanopore. We find that in addition to the usual geometric blockade, the variations of the current along the axis of the pore are largely caused by a concentration polarization induced by the presence of the translocating nanoparticle in the nanopore while the current changes in the radial (perpendicular to the axis) direction occur because of the local build up of the ionic charge between the particle and the nanopore surface. By performing statistical analysis of the current traces, we also observe that, in general, smaller current blockade values correspond to faster translocation times, while increased dwell times result in a larger current decrease.

We study the movement of a polymer attached to a large protein inside a nanopore in a thin silicon dioxide membrane submerged in an electrolyte solution. We use Brownian dynamics to describe the motion of a negatively charged polymer chain of varying lengths attached to a neutral protein modeled as a spherical bead with a radius larger than that of the nanopore, allowing the chain to thread the nanopore but preventing it from translocating. The motion of the protein-polymer complex within the pore is also compared to that of a freely translocating polymer. Our results show that the free polymer's standard deviations in the direction normal to the pore axis is greater than that of the protein-polymer complex. We find that restrictions imposed by the protein, bias, and neighboring chain segments aid in controlling the position of the chain in the pore. Understanding the behavior of the protein-polymer chain complex may lead to methods that improve molecule identification by increasing the resolution of ionic current measurements.

We theoretically study how the electro-osmotic fluid velocity in a charged cylindrical nanopore in a thin solid state membrane depends on the pore's geometry, membrane charge, and electrolyte concentration. We find that when the pore's length is comparable to its diameter, the velocity profile develops a concave shape with a minimum along the pore axis unlike the situation in very long nanopores with a maximum velocity along the central pore axis. This effect is attributed to the induced pressure along the nanopore axis due to the fluid flow expansion and contraction near the exit or entrance to the pore and to the reduction of electric field inside the nanopore. The induced pressure is maximal when the pore's length is about equal to its diameter while decreasing for both longer and shorter nanopores. A model for the fluid velocity incorporating these effects is developed and shown to be in a good agreement with numerically computed results.

In this work, we theoretically study the interaction between a solid-state membrane equipped with a nanopore and a tethered, negatively charged polymer chain subjected to a time-dependent applied electrolyte bias. In order to describe the movement of the chain in the biomolecule-membrane system immersed in an electrolyte solution, Brownian dynamics is used. We show that we can control the polymer’s equilibrium position with various applied electrolyte biases: for a sufficiently positive bias, the chain extends inside the pore, and the removal of the bias causes the polymer to leave the pore. Corresponding to a driven process, we find that the time it takes for a biomolecular chain to enter and extend into a nanopore in a positive bias almost increases linearly with chain length while the time it takes for a polymer chain to escape the nanopore is mainly governed by diffusion. In addition to attaching the polymer chain to the mouth of the nanopore, the chain is attached to a molecule with a radius larger than that of the nanopore’s, acting as a molecular stop. This allows the polymer to thread the nanopore but not translocate it. In this new system, the chain’s variation of movement was compared to that of the freely translocating polymer chain. The results show the free polymer having greater variation in the radial direction, indicating the restrictions imposed by the molecular stop and bias aid in controlling the position and movement of the polymer chain in the nanopore.

This article examines the spin and charge properties of double and triple quantum dots (QDs) populated containing just a few electrons, with particular emphasis on laterally coupled QDs. It first describes the theoretical approach, known as exact diagonalization method, utilized on the example of the two-electron system in coupled QDs that are modelled as two parabolas. The many-body problem is solved via the exact diagonalization method as well as variational Heitler–London and Monte Carlo methods. The article proceeds by considering the general characteristics of the two-electron double-QD structure and limitations of the approximate methods commonly used for its theoretical description. It also discusses the stability diagram for two circular dots and investigates how its features are affected by the QD elliptical deformations. Finally, it assesses the behavior of the two-electron system in the realistic double-dot confinement potentials.

Protein filtration is important in many fields of science and technology such as medicine, biology, chemistry, and engineering. Recently, protein separation and filtering with nanoporous membranes has attracted interest due to the possibility of fast separation and high throughput volume. This, however, requires understanding of the protein's dynamics inside and in the vicinity of the nanopore. In this work, we utilize a Brownian dynamics approach to study the motion of the model protein insulin in the membrane-electrolyte electrostatic potential. We compare the results of the atomic model of the protein with the results of a coarse-grained and a single-bead model, and find that the coarse-grained representation of protein strikes the best balance between the accuracy of the results and the computational effort required. Contrary to common belief, we find that to adequately describe the protein, a single-bead model cannot be utilized without a significant effort to tabulate the simulation parameters. Similar to results for nanoparticle dynamics, our findings also indicate that the electric field and the electro-osmotic flow due to the applied membrane and electrolyte biases affect the capture and translocation of the biomolecule by either attracting or repelling it to or from the nanopore. Our computational model can also be applied to other types of proteins and separation conditions.

In this work, we theoretically study the interaction between a solid state membrane equipped with a nanopore and a tethered, negatively charged polymer chain subjected to a time-dependent applied electrolyte bias. In order to describe the movement of the chain in the biomolecule-membrane system immersed in an electrolyte solution, Brownian dynamics is used. We show that we can control the polymer's equilibrium position with various applied electrolyte biases: for a sufficiently positive bias, the chain extends inside the pore, and the removal of the bias causes the polymer to leave the pore. Corresponding to a driven process, we find that the time it takes for a biomolecular chain to enter and extend into a nanopore in a positive bias almost increases linearly with chain length while the amount of time it takes for a polymer chain to escape the nanopore is mainly governed by diffusion.

Nanochannels made in solid-state materials are used for various applications such as nanoparticle separation or DNA manipulation. In this work we examine the effects of the electric and dielectrophoretic forces on a charged nanoparticle confined in a nanochannel. To this end, we solve the Poisson equation for the nanochannel with a wedgelike geometry and consider how channel geometry and electrolyte concentration affect the electrostatic potential distribution and forces acting on nanoparticles of various sizes. On the basis of our calculations, we establish conditions necessary for the particle's attraction to the corners of a channel. We find that for large particles, the net force is attractive only for low concentrations of the electrolyte irrespective of the wedge angle, while small enough particles are attracted to the vertex for either larger electrolyte concentrations or small wedge angle.

We study the applicability of an electrically tunable nanoporous semiconductor membrane for the separation of nanoparticles by charge. We show that this type of membrane can overcome one of the major shortcomings of nanoporous membrane applications for particle separation: the compromise between membrane selectivity and permeability. The computational model that we have developed describes the electrostatic potential distribution within the system and tracks the movement of the filtered particle using Brownian dynamics while taking into consideration effects from dielectrophoresis, fluid flow, and electric potentials. We found that for our specific pore geometry, the dielectrophoresis plays a negligible role in the particle dynamics. By comparing the results for charged and uncharged particles, we show that for the optimal combination of applied electrolyte and membrane biases the same membrane can effectively separate same-sized particles based on charge with a difference of up to 3 times in membrane permeability.

We study the applicability of tunable nanoporous semiconductor membranes made of the heavily doped silicone for separation of nanoparticles and proteins by their size and charge. We demonstrate that this type of membrane can overcome one of the major shortcomings of membrane applications for particle separation: the compromise between membrane selectivity and permeability. The microscopic computational model that we have developed describes the translocation process of filtered objects with the translational-rotational Brownian Dynamics taking into consideration effects from the dielectrophoresis, the electrolyte solution flow, and the self-consistent electrostatic potential distribution within the continuum Poisson-Nernst-Planck approach. Our results indicate that the tunable local electric field arising inside the membrane can effectively control interaction of filtered objects with the nanopore to either block its passage or increase the translocation rate by modulating the electroosmotic flow direction and magnitude. By extracting the membrane permeability from our microscopic simulations, we compute the macroscopic sieving factors and show that the size and charge selectivity of the membrane can be tuned by the applied voltage in the broad range.

We have studied single-stranded DNA translocation through a semiconductor membrane consisting of doped p and n layers of Si forming a p–n-junction. Using Brownian dynamics simulations of the biomolecule in the self-consistent membrane–electrolyte potential obtained from the Poisson–Nernst–Planck model, we show that while polymer length is extended more than when its motion is constricted only by the physical confinement of the nanopore. The biomolecule elongation is particularly dramatic on the n-side of the membrane where the lateral membrane electric field restricts (focuses) the biomolecule motion more than on the p-side. The latter effect makes our membrane a solid-state analog of the α-hemolysin biochannel. The results indicate that the tunable local electric field inside the membrane can effectively control dynamics of a DNA in the channel to either momentarily trap, slow down or allow the biomolecule to translocate at will.