Search

Transfer entropy in information theory was recently demonstrated [Basak et al., Phys. Rev. E 102, 012404 (2020)] to enable us to elucidate the interaction domain among interacting elements solely from an ensemble of trajectories. Therefore, only pairs of elements whose distances are shorter than some distance variable, termed cutoff distance, are taken into account in the computation of transfer entropies. The prediction performance in capturing the underlying interaction domain is subject to the noise level exerted on the elements and the sufficiency of statistics of the interaction events. In this paper, the dependence of the prediction performance is scrutinized systematically on noise level and the length of trajectories by using a modified Vicsek model. The larger the noise level and the shorter the time length of trajectories, the more the derivative of average transfer entropy fluctuates, which makes the identification of the interaction domain in terms of the position of global minimum of the derivative of average transfer entropy difficult. A measure to quantify the degree of strong convexity at the coarse-grained level is proposed. It is shown that the convexity score scheme can identify the interaction distance fairly well even while the position of the global minimum of the derivative of average transfer entropy does not. We also derive an analytical model to explain the relationship between the interaction domain and the change in transfer entropy that supports our cutoff distance technique to elucidate the underlying interaction domain from trajectories. [ABSTRACT FROM AUTHOR]

As expected, the asymptotic persistence lengths are the same in these two cases, as both converge toward the same HT ht for large m. However, the I B i SB I i sb are determined by the boundary contributions of short segments (small m). This relation holds approximately for the values reported by Wu I et al. i :[1] HT ht nm, I A i = 450 nm, and I B i = 10. Note that expression (2) contains one parameter less than (1), implying that HT ht . [Extracted from the article]

We present a computer simulation study of polymer translocation in a situation where the chain is initially confined to a closed cylindrical cavity in order to reduce the impact of conformational diversity on the translocation times. In particular, we investigate how the coefficient of variation of the distribution of translocation times can be minimized by optimizing both the volume and the aspect ratio of the cavity. Interestingly, this type of confinement sometimes increases the number and impact of hairpin conformations such that the fluctuations in the translocation process do not follow a power law in time (for instance, these fluctuations can even vary non-monotonically with time).We develop a tension-propagation model for a polymer compressed into such a confining volume and find that its predictions are in good agreement with our simulation results in the experimentally relevant strongly driven limit. Both the theoretical calculations and the simulation data yield a minimum in the coefficient of variation of the distribution of translocation times for a cylindrical cavity with an aspect ratio that makes it similar to a hemisphere. This provides guidance for the design of new devices based on the preconfinement of the target polymer into cavities. [ABSTRACT FROM AUTHOR]

Flexibility of short DNA helices is important for the biological functions such as nucleosome formation and DNA-protein recognition. Recent experiments suggest that short DNAs of tens of base pairs (bps) may have apparently higher flexibility than those of kilo bps, while there is still the debate on such high flexibility. In the present work, we have studied the flexibility of short DNAs with finite-length of 5-50 bps by the all-atomistic molecular dynamics simulations and Monte Carlo simulations with the worm-like chain model. Our microscopic analyses reveal that short DNAs have apparently high flexibility which is attributed to the significantly strong bending and stretching flexibilities of ~6 bps at each helix end. Correspondingly, the apparent persistence length lp of short DNAs increases gradually from ~29 nm to ~45 nm as DNA length increases from 10 to 50 bps, in accordance with the available experimental data. Our further analyses show that the short DNAs with excluding ~6 bps at each helix end have the similar flexibility with those of kilo bps and can be described by the worm-like chain model with lp ~ 50 nm. [ABSTRACT FROM AUTHOR]

Studies on confined water are important not only from the viewpoint of scientific interest but also for the development of new nanoscale devices. In this work, we aimed to clarify the properties of confined water in the cylindrical pores of single-walled carbon nanotubes (SWCNTs) that had diameters in the range of 1.46 to 2.40 nm. A combination of x-ray diffraction (XRD), nuclear magnetic resonance, and electrical resistance measurements revealed that water inside SWCNTs with diameters between 1.68 and 2.40 nm undergoes a wet-dry type transition with the lowering of temperature; below the transition temperature Twd, water was ejected from the SWCNTs. Twd increased with increasing SWCNT diameter D. For the SWCNTs with D = 1.68, 2.00, 2.18, and 2.40 nm, Twd obtained by the XRD measurements were 218, 225, 236, and 237 K, respectively. We performed a systematic study on finite length SWCNT systems using classical molecular dynamics calculations to clarify the effect of open ends of the SWCNTs and water content on the water structure. It was found that ice structures that were formed at low temperatures were strongly affected by the bore diameter, a = D - σOC, where σOC is gap distance between the SWCNT and oxygen atom in water, and the number of water molecules in the system. In small pores (a < 1.02 nm), tubule ices or the so-called ice nanotubes (ice NTs) were formed irrespective of the water content. On the other hand, in larger pores (a > 1.10 nm) with small water content, filled water clusters were formed leaving some empty space in the SWCNT pore, which grew to fill the pore with increasing water content. For pores with sizes in between these two regimes (1.02 < a < 1.10 nm), tubule ice also appeared with small water content and grew with increasing water content. However, once the tubule ice filled the entire SWCNT pore, further increase in the water content resulted in encapsulation of the additional water molecules inside the tubule ice. Corresponding XRD measurements on SWCNTs with a mean diameter of 1.46 nm strongly suggested the presence of such a filled structure. [ABSTRACT FROM AUTHOR]

Steady state pressure driven flow of liquid argon through a finite length cylindrical nanopore was investigated numerically by classical Navier-Stokes (NS) hydrodynamic models and nonequilibrium molecular dynamics (MD) simulations. In both approaches, the nanopore was nominally 2.2 nm in diameter and 6 nm long. For the MD simulations, the intermolecular properties of the walls were specified independently from the liquid. Comparisons between the approaches were made in terms of the gross feature of total flow rate through the nanopore, as well as the more refined considerations of the spatial distributions of pressure, density, and velocity. The results showed that for the NS equations to predict the same trends in total flow rate with increasing pressure difference as the MD simulation, submodels for variations in density and viscosity with pressure are needed to be included. The classical NS boundary conditions quantitatively agreed with the flow rate predictions from MD simulations only under the condition of having a neutral-like solid-liquid interaction. Under these conditions, the NS and MD models also agreed well in streamwise distributions of pressure, density, and velocity, but not in the radial direction. [ABSTRACT FROM AUTHOR]

A statistical mechanical model is presented which explicitly accounts for the fluctuations, the electrostatic, and the excluded volume correlations for ions bound to a polyelectrolyte such as DNA. The method can be employed to treat a wide range of ionic conditions including multivalent ions. The microscopic framework of the theory permits the use of realistic finite length and grooved structural model for the polyelectrolyte and modeling of the finite size of the bound ions. Test against Monte Carlo simulations suggests that the theory can give accurate predictions for the ion distribution and the thermodynamic properties. For multivalent ions, the theory makes improved predictions as compared with the mean-field approach. Moreover, for long polyelectrolyte and dilute salt concentration, the theory predicts ion binding properties that agree with the counterion condensation theory.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The orientation-dependent electrical double-layer interaction between two thin rodlike macroions of finite length is considered. Starting from an expression for the interaction free energy as a double integral of the Green’s function for the linearized Poisson–Boltzmann equation, we obtain several useful analytical approximations. For certain rod configurations, we obtain simple analytical approximations to the double-layer interaction that are quantitatively accurate at physically relevant rod separations and electrolyte concentrations. For a general rod configuration, specified by the separation and three angles, we develop a generalized multipole expansion of the double-layer interaction energy, which converges rapidly if the rod length is not much larger than the center-of-mass rod separation or the Debye length. The orientation dependence of the double-layer repulsion can then be quantitatively accounted for in terms of the screened charge–quadrupole and quadrupole–quadrupole interactions. Furthermore, we show that the double-layer repulsion between finite rods depends on the rod orientations even at arbitrarily large separation. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The statistical properties of the autocorrelation function from a time series composed of independently and identically distributed stochastic variables has been studied. Analytical expressions for the autocorrelation function’s variance have been derived. It has been found that two common ways of calculating the autocorrelation, moving-average and Fourier transform, exhibit different uncertainty characteristics. For periodic time series, the Fourier transform method is preferred because it gives smaller uncertainties that are uniform through all time lags. Based on these analytical results, a statistically robust method has been proposed to test the existence of correlations in a time series. The statistical test is verified by computer simulations and an application to single-molecule fluorescence spectroscopy is discussed. [ABSTRACT FROM AUTHOR]

By means of the Rutherford method it is found that in zigzag carbon nanotubes with an even number n=2j of hexagons in a tube ring the gap between occupied and empty single-electron levels disappears. The frontier level is shown to be at least doubly degenerate. The reason for the loss of the zero level (for n=2j) upon reaching the infinite length limit is discussed. The existence of a lot of states, specific for finite nanotubes, with the energy very close to the Fermi level is shown, and the number of these states is estimated. The existence of a narrow (of order 10-4 eV) conduction band, formed by edge states, is demonstrated in tight binding approximation. If the Coulomb interaction is taken into account, the half-filled degenerate π-electronic level continues to exist. The open shell Hartree–Fock theory demonstrates the degenerate configuration splitting onto three equidistant terms: two singlets with the seniority numbers 0 and 1, and the lowest triplet in accordance with the Hund rule. The behavior of the single-electron gap is alike for all three terms: the gap is of the order 0.2–0.01 eV. The Rutherford method gives analytical results for armchair nanotubes as well, which explains the gap oscillations as a function of the tube length with a period of three rings. Application of the degenerate open shell Hartree–Fock theory supports this explanation. [ABSTRACT FROM AUTHOR]

In order to examine the validity of the reptation model of motion in a dense collection of polymers, dynamic Monte Carlo (MC) simulations of polymer chains composed of n beads confined to a diamond lattice were undertaken as a function of polymer concentration [lowercase_phi_synonym] and degree of polymerization n. We demonstrate that over a wide density range these systems exhibit the experimentally required molecular weight dependence of the center-of-mass self-diffusion coefficient D∼n-2.1 and the terminal relaxation time of the end-to-end vector τR∼n3.4. Thus, these systems should represent a highly entangled collection of polymers appropriate to look for the existence of reptation. The time dependence of the average single bead mean-square displacement, as well as the dependence of the single bead displacement on position in the chain were examined, along with the time dependence of the center-of-mass displacement. Furthermore, to determine where in fact a well-defined tube exists, the mean-square displacements of a polymer chain down and perpendicular to its primitive path defined at zero time were calculated, and snapshots of the primitive path as a function of time are presented. For an environment where all the chains move, no evidence of a tube, whose existence is central to the validity of the reptation model, was found. However, if a single chain is allowed to move in a partially frozen matrix of chains (where all chains but one are pinned every ne beads, and where between pin points the other chains are free to move), reptation with tube leakage is recovered for the single mobile chain. The dynamics of these chains possesses aspects of Rouse-like motion; however, unlike a Rouse chain, these chains undergo highly cooperative motion that appears to involve a backflow between chains to conserve constant average density. While these simulations cannot preclude the onset of reptation at higher molecular weight, they strongly... [ABSTRACT FROM AUTHOR]

Reports on molecular dynamics simulation results for single-file self-diffusion in pores of infinite and finite length. Moderately dense, non-overtaking, hard-sphere fluids in cylindrical pores; Investigation of particle mobility as a function of time and pore length; Stationary Fickian diffusion in infinitely long pores with diffusely reflecting pore walls; Definition of a diffusivity.

Flexibility of short DNA helices is important for the biological functions such as nucleosome formation and DNA-protein recognition. Recent experiments suggest that short DNAs of tens of base pairs (bps) may have apparently higher flexibility than those of kilo bps, while there is still the debate on such high flexibility. In the present work, we have studied the flexibility of short DNAs with finite-length of 5-50 bps by the all-atomistic molecular dynamics simulations and Monte Carlo simulations with the worm-like chain model. Our microscopic analyses reveal that short DNAs have apparently high flexibility which is attributed to the significantly strong bending and stretching flexibilities of ∼6 bps at each helix end. Correspondingly, the apparent persistence length lp of short DNAs increases gradually from ∼29 nm to ∼45 nm as DNA length increases from 10 to 50 bps, in accordance with the available experimental data. Our further analyses show that the short DNAs with excluding ∼6 bps at each helix end have the similar flexibility with those of kilo bps and can be described by the worm-like chain model with lp ∼ 50 nm.

Steady state pressure driven flow of liquid argon through a finite length cylindrical nanopore was investigated numerically by classical Navier-Stokes (NS) hydrodynamic models and nonequilibrium molecular dynamics (MD) simulations. In both approaches, the nanopore was nominally 2.2 nm in diameter and 6 nm long. For the MD simulations, the intermolecular properties of the walls were specified independently from the liquid. Comparisons between the approaches were made in terms of the gross feature of total flow rate through the nanopore, as well as the more refined considerations of the spatial distributions of pressure, density, and velocity. The results showed that for the NS equations to predict the same trends in total flow rate with increasing pressure difference as the MD simulation, submodels for variations in density and viscosity with pressure are needed to be included. The classical NS boundary conditions quantitatively agreed with the flow rate predictions from MD simulations only under the condition of having a neutral-like solid-liquid interaction. Under these conditions, the NS and MD models also agreed well in streamwise distributions of pressure, density, and velocity, but not in the radial direction.

The Onsager-type theory for nematic ordering described in an earlier paper [J. Chem. Phys. 87, 4932 (1987)] is applied to a liquid-density fluid of hard ellipsoids of revolution, and an accurate calculation that agrees very well with the main features of computer simulations of this system is presented. For larger geometrical anisotropies, the isotropic-nematic transition properties are in better agreement with simulation results. [ABSTRACT FROM AUTHOR]

Diffusion in complex heterogeneous media, such as biological tissues or porous materials, typically involves constrained displacements in tortuous structures and sticky environments. Therefore, diffusing particles experience both entropic (excluded-volume) forces and the presence of complex energy landscapes. In this situation, one may describe transport through an effective diffusion coefficient. In this paper, we examine comb structures with finite-length 1D and finite-area 2D fingers, which act as purely diffusive traps. We find that there exists a critical width of 2D fingers, above which the effective diffusion along the backbone is faster than for an equivalent arrangement of 1D fingers. Moreover, we show that the effective diffusion coefficient is described by a general analytical form for both 1D and 2D fingers, provided the correct scaling variable is identified as a function of the structural parameters. Interestingly, this formula corresponds to the well-known general situation of diffusion in a medium with fast reversible adsorption. Finally, we show that the same formula describes diffusion in the presence of dilute potential energy traps, e.g., through a landscape of square wells. While diffusion is ultimately always the result of microscopic interactions (with particles in the fluid, other solutes, and the environment), effective representations are often of great practical use. The results reported in this paper help clarify the microscopic origins and the applicability of global, integrated descriptions of diffusion in complex media. [ABSTRACT FROM AUTHOR]

The production of sequence-specific copolymers using copolymer templates is fundamental to the synthesis of complex biological molecules and is a promising framework for the synthesis of synthetic chemical complexes. Unlike the superficially similar process of self-assembly, however, the development of synthetic systems that implement templated copying of copolymers under constant environmental conditions has been challenging. The main difficulty has been overcoming product inhibition or the tendency of products to adhere strongly to their templates—an effect that gets exponentially stronger with the template length. We develop coarse-grained models of copolymerization on a finite-length template and analyze them through stochastic simulation. We use these models first to demonstrate that product inhibition prevents reliable template copying and then ask how this problem can be overcome to achieve cyclic production of polymer copies of the right length and sequence in an autonomous and chemically driven context. We find that a simple addition to the model is sufficient to generate far longer polymer products that initially form on, and then separate from, the template. In this approach, some of the free energy of polymerization is diverted into disrupting copy–template bonds behind the leading edge of the growing copy copolymer. By additionally weakening the final copy–template bond at the end of the template, the model predicts that reliable copying with a high yield of full-length, sequence-matched products is possible over large ranges of parameter space, opening the way to the engineering of synthetic copying systems that operate autonomously. [ABSTRACT FROM AUTHOR]

The modular path integral methodology is used to extend the well-known spin-boson dynamics to finite-length quantum Ising chains, where each spin is coupled to a dissipative harmonic bath. The chain is initially prepared in the ferromagnetic phase where all spins are aligned, and the magnetization is calculated with spin–spin coupling parameters corresponding to the paramagnetic phase, mimicking a quantum quench experiment. The observed dynamics is found to depend significantly on the location of the tagged spin. In the absence of a dissipative bath, the time evolution displays irregular patterns that arise from multiple frequencies associated with the eigenvalues of the chain Hamiltonian. Coupling of each spin to a harmonic bath leads to smoother dynamics, with damping effects that are stronger compared to those observed in the spin-boson model and more prominent in interior spins, a consequence of additional damping from the spin environment. Interior spins exhibit a transition from underdamped oscillatory to overdamped monotonic dynamics as the temperature, spin–bath, or spin–spin coupling is increased. In addition to these behaviors, a new dynamical pattern emerges in the evolution of edge spins with strong spin–spin coupling at low and intermediate temperatures, where the magnetization oscillates either above or below the equilibrium value. [ABSTRACT FROM AUTHOR]

Dissipative systems often exhibit novel and unexpected properties. This is, for instance, the case of simple liquids, which, when subjected to shear and after reaching a steady state, can exhibit a negative entropy production over finite length scales and timescales. This result, among others, is captured by nonequilibrium relations known as fluctuation theorems. Using nonequilibrium molecular dynamics simulations, we examine how, by fine-tuning the properties of the components of a complex fluid, we can steer the nonequilibrium response of the fluid. More specifically, we show how we control the nonequilibrium probability distribution for the shear stress and, in turn, how often states with a negative entropy production can occur. To achieve this, we start by characterizing how the size for the liquid matrix impacts the probability of observing negative entropy states, as well as the timescale over which these can be observed. We then measure how the addition of larger particles to this liquid matrix, i.e., simulating a model colloidal suspension, results in an increase in the occurrence of such states. This suggests how modifications in the composition of the mixture and in the properties of its components lead to an increase in the probability of observing states of negative entropy production and, thus, for the system to run in reverse. [ABSTRACT FROM AUTHOR]

The discretized path integral expression for the reduced density matrix (RDM) of a system interacting with a dissipative harmonic bath is fully entangled because of influence functional terms that couple the variables at different time points. The iterative decomposition of the path integral, which exploits the finite length of influence functional memory, involves a tensor propagator whose size grows exponentially with the memory length. The present Communication disentangles the path integral by recursively spreading the temporal entanglement over longer path segments, while decreasing its contribution. Eventually, the entangled term becomes sufficiently small and may be neglected, leading to iterative propagation of the RDM through simple multiplication of matrices whose size is equal to that of the bare system. It is found that the temporal entanglement length is practically equal to the bath-induced memory length. The small matrix decomposition of the path integral (SMatPI) is stable and very efficient, extending the applicability of numerically exact real-time path integral methods to multi-state systems. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations are used to study the behavior of two polymers under confinement in a cylindrical tube. Each polymer is modeled as a chain of hard spheres. We measure the free energy of the system, F, as a function of the distance between the centers of mass of the polymers, λ, and examine the effects on the free energy functions of varying the channel diameter D and length L, as well as the polymer length N and bending rigidity κ. For infinitely long cylinders, F is a maximum at λ = 0, and decreases with λ until the polymers are no longer in contact. For flexible chains (κ = 0), the polymers overlap along the cylinder for low λ, while above some critical value of λ they are longitudinally compressed and non-overlapping while still in contact. We find that the free energy barrier height, ΔF = F(0) - F(∞), scales as ΔF/kBT ~ ND-1.93 ± 0.01, for N ≤ 200 and D ≤ 9σ, where σ is the monomer diameter. In addition, the overlap free energy appears to scale as F/kBT = Nf(λ/N; D) for sufficiently large N, where f is a function parameterized by the cylinder diameter D. For channels of finite length, the free energy barrier height increases with increasing confinement aspect ratio L/D at fixed volume fraction ɸ, and it decreases with increasing ɸ at fixed L/D. Increasing the polymer bending rigidity κ monotonically reduces the overlap free energy. For strongly confined systems, where the chain persistence length P satisfies D ≪ P, F varies linearly with λ with a slope that scales as F'(λ) ~ -kB TD-βP-α, where β ≈ 2 and a ≈ 0.37 for N = 200 chains. These exponent values deviate slightly from those predicted using a simple model, possibly due to insufficiently satisfying the conditions defining the Odijk regime. Finally, we use Monte Carlo dynamics simulations to examine polymer segregation dynamics for fully flexible chains and observe segregation rates that decrease with decreasing entropic force magnitude, f ≡ |dF/dλ|. For both infinite-length and finite-length channels, the polymers are not conformationally relaxed at later times during segregation. [ABSTRACT FROM AUTHOR]

Efforts to study the polymer physics of DNA confined in nanochannels have been stymied by a lack of consensus regarding its wall depletion length. We have measured this quantity in 38 nm wide, square silicon dioxide nanochannels for five different ionic strengths between 15 mM and 75 mM. Experiments used the Bionano Genomics Irys platform for massively parallel data acquisition, attenuating the effect of the sequence-dependent persistence length and finite-length effects by using nick-labeled E. coli genomicDNAwith contour length separations of at least 30 μm(88 325 base pairs) between nick pairs. Over 5 × 106 measurements of the fractional extension were obtained from 39 291 labeled DNA molecules. Analyzing the stretching via Odijk's theory for a strongly confined wormlike chain yielded a linear relationship between the depletion length and the Debye length. This simple linear fit to the experimental data exhibits the same qualitative trend as previously defined analytical models for the depletion length but now quantitatively captures the experimental data. [ABSTRACT FROM AUTHOR]

We study the exciton wave functions and the optical properties of cylindrical molecular aggregates. The cylindrical symmetry allows for a decomposition of the exciton Hamiltonian into a set of effective one-dimensional Hamiltonians, characterized by a transverse wave number k2. These effective Hamiltonians have interactions that are complex if the cylinder exhibits chirality. We propose analytical ansätze for the eigenfunctions of these one-dimensional problems that account for a finite cylinder length, and present a general study of their validity. A profound difference is found between the Hamiltonian for the transverse wave number k2=0 and those with k2≠0. The complex nature of the latter leads to chiral wave functions, which we characterize in detail. We apply our general formalism to the chlorosomes of green bacteria and compare the wave functions as well as linear optical spectra (absorption and dichroism) obtained through our ansätze with those obtained by numerical diagonalization as well as those obtained by imposing periodic boundary conditions in the cylinder’s axis direction. It is found that our ansätze, in particular, capture the finite-length effect in the circular dichroism spectrum much better than the solution with periodic boundary conditions. Our ansätze also show that in finite-length cylinders seven superradiant states dominate the linear optical response. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines effects of finite chain length on the collapse transition of stiff-chain macromolecules through a Monte Carlo simulation. Dependence of the coil-globule transition on chain stiffness for finite length chains; Existence of a region of parameters showing favorable toroidal structure.

We present a closed-form solution to the problem of elastic light scattering by a randomly oriented ensemble of cylinders of finite length. All the Mueller scattering matrix elements are calculated, so the solution is complete in the sense that all possible polarization effects are treated. The cylinders are assumed to be made of an isotropic material, which may be transparent or absorbing. Cylinder radius a and length L must obey a≤λmed/2π≤L, where λmed is the wavelength in the supporting fluid medium. Our solution includes all multipole effects due to the length of the cylinder, as well as all internal reflections at the boundary between the cylinder and the supporting medium. Nonzero values of the retardation elements M34 and M43 may be caused either by retardative internal reflections, or by absorption, or both. These elements are easily observable in experiments on scattering by rod-like viruses, but are completely missing in theories that ignore retardative contributions to the scattered amplitude. The curve M34(θ) is affected strongly in distinct ways by rod length, by index of refraction, and by absorptivity. [ABSTRACT FROM AUTHOR]

Anomalous diffusion is characterized by its asymptotic behavior for t → ∞. This makes it difficult to detect and describe in particle trajectories from experiments or computer simulations, which are necessarily of finite length. We propose a new approach using Bayesian inference applied directly to the observed trajectories sampled at different time scales. We illustrate the performance of this approach using random trajectories with known statistical properties and then use it for analyzing the motion of lipid molecules in the plane of a lipid bilayer. [ABSTRACT FROM AUTHOR]

We report the discovery of finite length scale effects on vibronic coupling in nanoscale α-Fe2O3 as measured by the behavior of vibronically activated d-d on-site excitations of Fe3+ as a function of size and shape. An oscillator strength analysis reveals that the frequency of the coupled symmetry-breaking phonon changes with size, a crossover that we analyze in terms of increasing three-dimensional character to the displacement pattern. These findings demonstrate the flexibility of mixing processes in confined systems and suggest a strategy for both enhancing and controlling charge-lattice interactions in other materials. [ABSTRACT FROM AUTHOR]

The conformational complexity of chain-like macromolecules such as proteins and other linear polymers is much larger than that of point-like atoms and molecules. Unlike particles, chains can bend, twist, and even become knotted. Thus chains might also display a much richer phase structure. Unfortunately, it is not very easy to characterize the phase of a long chain. Essentially, the only known attribute is the radius of gyration. The way how it changes when the degree of polymerization becomes different, and how it evolves when the ambient temperature and solvent properties change, is commonly used to disclose the phase. But in any finite length chain there are corrections to scaling that complicate the detailed analysis of the phase structure. Here we introduce a quantity that we call the folding angle to identify and scrutinize the phase structure, as a complement to the radius of gyration. We argue for a mean-field level relationship between the folding angle and the scaling exponent in the radius of gyration. We then estimate the value of the folding angle in the case of crystallographic α-helical protein structures in the Protein Data Bank. We also show how the experimental value of the folding angle can be obtained computationally, using a semiclassical Born-Oppenheimer description of α-helical chiral chains. [ABSTRACT FROM AUTHOR]

We employ the self-consistent field theory to study phase structures of brush-rod systems composed of two chemically distinct linear homopolymers. The polymer chains are uniformly grafted on the surface of a nanorod particle of finite length and comparable radius to the polymer radius of gyration. A 'masking' technique treating the cylindrical boundary is introduced to solve the modified diffusion equations with an efficient and high-order accurate pseudospectral method involving fast Fourier transform on an orthorhombic cell. A rich variety of structures for the phase separated brushes is predicted. Phase diagrams involving a series of system parameters, such as the aspect ratio of the nanorod, the grafting density, and the chain length are constructed. The results indicate that the phase structure of the mixed brush-rod system can be tailored by varying the grafted chain length and/or the aspect ratio of the rod to benefit the fabrication of polymeric nanocomposites. [ABSTRACT FROM AUTHOR]

We perform a numerical investigation of the transport of Brownian particles driven by a zero-mean periodic force across two-dimensional arrays of obstacles with finite length. By applying axial and transversal driving forces relative to the diffusion transport direction, the effective diffusivity is determined as function of the array geometry and the driving frequency, finding excess diffusion peaks at certain frequency ranges. The results indicate that a suitable selection of the axial and transversal frequencies yields enhanced diffusion transport along the axial direction. Symmetric and asymmetric arrays are considered, showing that the asymmetry has a detrimental effect in the magnitude of the excess diffusion peaks. This suggests that enhanced diffusion is obtained because the oscillatory driving force exploits preferential transport channels, whose effective obstacle spacing is maximized under symmetric configurations. [ABSTRACT FROM AUTHOR]

We derive an analytic description of the spin susceptibility in finite length zigzag carbon nanotubes (CNT) with chirality (n, 0). The spin susceptibility is proportional to the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions which describes indirect carrier mediated exchange coupling between localized magnetic moments. We show that the strongest RKKY interactions are along the edges of the nanotube and in the thermodynamic limit at half filling with spin symmetry the shape of the susceptibility curve about the edge of the CNT can be determined solely by the lattice geometry represented by the parameter n and a parameter L which describes the nanotube length. We also show that the introduction of Zeeman splitting or doping may have no effect on the spin susceptibility, provided n is small. A detailed knowledge of magnetic interactions, such as RKKY interactions, in CNT is of vital importance to the development of nanotechnology applications. [ABSTRACT FROM AUTHOR]

Elasticity of the polymer network, with nematic interactions between segments of all the system chains, is considered. The Maier and Saupe molecular mean-field is used for description of nematic interactions. Calculations are performed for non-Gaussian network containing chains of finite contour length. The network topological structure is taken into consideration via the system contraction coefficient. Values of thermodynamic parameters, necessary for the existence of the isotropic-nematic equilibrium, are calculated. The system free energy (Helmholtz function) is calculated for any direction of external elongation of the network. A relation between the deformation force and elongation ratio is obtained. The network can have isotropic as well as anisotropic elastic properties. It depends on the system internal orientations and chain lengths. For the network in isotropic phase, defined with respect to orientation of segments, elastic constants have the same values in any direction. It is independent of whether the chain length is finite or infinite. In the nematic phase, the network elastic constants have the same values for chains with infinite length, while they are many in various directions for finite length of chains. The problem of the nematic axis rotation under the system external deformation is considered. [ABSTRACT FROM AUTHOR]

Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities, and nanotubes. Here we introduce a novel finite length one dimensional Ising model to investigate the propagation and the annihilation of dynamical correlations in finite systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles. In our finite sized model, the two spins at the two end cells are oriented in the opposite directions to mimic the effects of surface that in real system fixes water orientation in the opposite directions. This produces opposite polarizations to propagate inside from the surface and to produce bulklike condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is nonexponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of relaxation of the spins undergoes a qualitative change with the emergence of a homogeneous dynamics where decay is predominantly exponential, again in agreement with experiments. [ABSTRACT FROM AUTHOR]

We employ all-electron ab initio time-dependent density functional theory based method to calculate the long-range dipole-dipole dispersion coefficient, namely, the van der Waals (vdW) coefficient (C6) between fullerenes and finite-length carbon nanotubes as well as between these structures and different small molecules. Our aim is to accurately estimate the strength of the long-range vdW interaction in terms of the C6 coefficients between these systems and also compare these values as a function of shape and size. The dispersion coefficients are obtained via Casimir–Polder relation. The calculations are carried out with the asymptotically correct exchange-correlation potential—the statistical average of orbital potential. It is observed from our calculations that the C6 coefficients of the carbon nanotubes increase nonlinearly with length, which implies a much stronger vdW interaction between the longer carbon nanostructures compared with the shorter ones. Additionally, it is found that the values of C6 and polarizability are about 40%–50% lower for the carbon cages when compared with the results corresponding to the quasi-one-dimensional nanotubes with equivalent number of atoms. From our calculations of the vdW coefficients between the small molecules and the carbon nanostructures, it is observed that for H2, the C6 value is much larger compared with that of He. It is found that the rare gas atoms have very low values of vdW coefficient with the carbon nanostructures. In contrast, it is found that other gas molecules, including the ones that are environmentally important, possess much higher C6 values. Carbon tetrachloride as well as chlorine molecule show very high C6 values with themselves as well as with the carbon nanostructures. This is due to the presence of the weakly bound seven electrons in the valence state for the halogen atoms, which makes these compounds much more polarizable compared with the others. [ABSTRACT FROM AUTHOR]

We calculate the linear and nonlinear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electronic polarization as a function of applied finite electric field—an approach we recently introduced and made possible by the use of a Berry-phase, many-body electric-enthalpy functional. Calculated susceptibilities and hypersusceptibilities are found to be in excellent agreement with the best estimates available from quantum chemistry—usually extrapolations to the infinite-chain limit of calculations for chains of finite length. It is found that while exchange effects dominate the proper description of the susceptibilities, second hypersusceptibilities are greatly affected by electronic correlations. We also assess how different approximations to the nodal surface of the many-body wave function affect the accuracy of the calculated susceptibilities. [ABSTRACT FROM AUTHOR]

We study the power spectrum of a random telegraphic noise with the distribution density of waiting times τ given by ψ(τ)∝1/τμ, with μ≈2. The condition μ<2 violates the ergodic hypothesis, and in this case the adoption of Wiener–Khintchine (WK) theorem for the spectrum evaluation requires some caution. We study this problem theoretically and numerically and we prove that the power spectrum obeys the prescription S(f)=K/fη, with η=3-μ, namely, the 1/f noise lives at border between the ergodic μ>2 and nonergodic μ<2 condition. We study sequences with the finite length L. In the case μ<2 the adoption of WK theorem is made legitimate by two different kinds of truncation effects: the physical and observation-induced effect. In the former case ψ(τ) is truncated at τ≈Tmax and L>Tmax ensures the condition of interrupted aging. In this case, we find that K is a number independent of L. The latter case, L≤Tmax, is more challenging. It was already solved by Margolin and Barkai, who used time asymptotic arguments based on the ergodicity breakdown and obtained K∝1/L2-μ, proving that the out-of-equilibrium nature of the condition μ<2 is signaled by the decrease of K with the increase of L. We use a generalized version of the Onsager principle that leads us to the same conclusion from a somewhat more extended view valid also for the transient out-of-equilibrium case of μ>2. We do not limit our treatment to the time asymptotic case, thereby producing a prediction that accounts for the transition from the 1/fη to the 1/f2 regime, recently observed in an experiment on blinking quantum dots. Our theoretical approach allows us to discuss some other recent experiments on molecular intermittent fluorescence and affords indications that should help to assess whether the spectrum is determined by the L≤Tmax or by the L≥Tmax condition. [ABSTRACT FROM AUTHOR]

The extension of Onsager’s second-virial theory [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for the orientational ordering of hard rods to mixtures of nonspherical hard bodies with finite length-to-breadth ratios is examined using the decoupling approximations of Parsons [Phys. Rev. A 19, 1225 (1979)] and Lee [J. Chem. Phys. 86, 6567 (1987); 89, 7036 (1988)]. Invariably the extension of the Parsons–Lee (PL) theory to mixtures has in the past involved a van der Waals one-fluid treatment in which the properties of the mixture are approximated by those of a reference one-component hard-sphere fluid with an effective diameter which depends on the composition of the mixture and the molecular parameters of the various components; commonly this is achieved by equating the molecular volumes of the effective hard sphere and of the components in the mixture and is referred to as the PL theory of mixtures. It is well known that a one-fluid treatment is not the most appropriate for the description of the thermodynamic properties of isotropic fluids, and inadequacies are often rectified with a many-fluid (MF) theory. Here, we examine MF theories which are developed from the virial theorem and the virial expansion of the Helmholtz free energy of anisotropic fluid mixtures. The use of the decoupling approximation of the pair distribution function at the level of a multicomponent hard-sphere reference system leads to our MF Parsons (MFP) theory of anisotropic mixtures. Alternatively the mapping of the virial coefficients of the hard-body mixtures onto those of equivalent hard-sphere systems leads to our MF Lee (MFL) theory. The description of the isotropic-nematic phase behavior of binary mixtures of hard Gaussian overlap particles is used to assess the adequacy of the four different theories, namely, the original second-virial theory of Onsager, the usual PL one-fluid theory, and the MF theories based on the Lee (MFL) and Parsons (MFP) approaches. A comparison with the simulation data for the mixtures studied by Zhou et al. [J. Chem. Phys. 120, 1832 (2004)] suggests that the Parsons MF description (MFP) provides the most accurate representation of the properties of the isotropic-nematic ordering transition and density (pressure) dependence of the order parameters. [ABSTRACT FROM AUTHOR]

We consider the mean field kinetic equations describing the relaxation dynamics of a lattice model of a fluid confined in a porous material. The dynamical theory embodied in these equations can be viewed as a mean field approximation to a Kawasaki dynamics Monte Carlo simulation of the system, as a theory of diffusion, or as a dynamical density functional theory. The solutions of the kinetic equations for long times coincide with the solutions of the static mean field equations for the inhomogeneous lattice gas. The approach is applied to a lattice gas model of a fluid confined in a finite length slit pore open at both ends and is in contact with the bulk fluid at a temperature where capillary condensation and hysteresis occur. The states emerging dynamically during irreversible changes in the chemical potential are compared with those obtained from the static mean field equations for states associated with a quasistatic progression up and down the adsorption/desorption isotherm. In the capillary transition region, the dynamics involves the appearance of undulates (adsorption) and liquid bridges (adsorption and desorption) which are unstable in the static mean field theory in the grand ensemble for the open pore but which are stable in the static mean field theory in the canonical ensemble for an infinite pore. [ABSTRACT FROM AUTHOR]

Stable and metastable fluid density distributions (FDDs) in a closed nanoslit between two identical parallel solid walls have been identified on the basis of a nonlocal canonical ensemble density functional theory. Similar to Monte Carlo simulations, periodicity of the FDD in one of the lateral (parallel to the walls surfaces) directions, denoted as the x direction, was assumed. In the other lateral direction, y direction, the FDD was considered uniform. It was found that depending on the average fluid density in the slit, both uniform as well as nonuniform FDDs in the x direction can occur. The uniform FDDs are either symmetric or asymmetric about the middle plane between walls; the latter FDD being the consequence of a symmetry breaking across the slit. The nonuniform FDDs in the x direction occur either in the form of a bump on a thin liquid film covering the walls or as a liquid bridge between those walls and provide symmetry breaking in the x direction. For small and large average densities, the stable state is uniform in the x direction and is symmetric about the middle plane between walls. In the intermediate range of the average density and depending on the length Lx of the FDD period, the stable state can be represented either by a FDD, which is uniform in the x direction and asymmetric about the middle of the slit (small values of Lx), or by a bump- and bridgelike FDD for intermediate and large values of Lx, respectively. These results are in agreement with the Monte Carlo simulations performed earlier by other authors. Because the free energy of the stable state decreases monotonically with increasing Lx, one can conclude that the real period is very large (infinite) and that for the values of the parameters employed, a single bridge of finite length over the entire slit is generated. [ABSTRACT FROM AUTHOR]

We develop a numerical scheme that calculates forces under given conformational states of a biomolecule by using a harmonic sampling potential. It can also be used for calculating the potential of mean force, as tested by random walks on Gaussian enthalpy barriers. Further, Brownian dynamics simulations of a finite-length freely jointed chain confirm the analytic expressions for its entropic elasticity that we derive. Our method, while generally applicable to many systems, will be particularly useful for studying the elasticity of biopolymers where various types of ensembles differ due to the finite size effect. [ABSTRACT FROM AUTHOR]

The depletion interactions of ellipsoidal colloidal particles in a solution of long polymer chains are analyzed. Of primary concern are the limiting cases in which the ellipsoid reduces to a cylinder of infinite length and finite radius and a “needle” of finite length and vanishing radius. Relations are obtained between the polymer effects induced by a needle that is much shorter than the polymer size and by a cylinder with radius much smaller than the polymer size. These imply exact quantitative results for the orientation-dependent depletion interaction between a short needle and a wall. Qualitative differences between the needle and thin disk are discussed. [ABSTRACT FROM AUTHOR]