Persistence lengths and structure factors of wormlike polymers under confinement

The behavior of semiflexible chains modeling wormlike polymers such as DNA and actin in confined spaces was explored by coarse-grained Monte Carlo simulations. The persistence length P, mean end-to-end distance R2, mean radius of gyration Rg2, and the size ratio R2/Rg2 were computed for chains in slits, cylinders, and spheres. It was found that the intrinsic persistence length of a free chain undergoes on confinement substantial alteration into the apparent persistence length. The qualitative differences were found in trends of the apparent persistence lengths between slits and cylinders on one side and spheres on the other side. The quantities P, R2, Rg2, and R2/Rg2 display similar dependences upon squeezing the chains in nanopores. The above quantities change nonmonotonically with confinement in slits and cylinders, whereas they drop smoothly with decreasing radius of a sphere. For elongation of a chain in a cylinder, two regimes corresponding to strong and moderate confinements were found and compared to experiments and predictions of the blob and Odijk theories. In a spherical cavity, the toroidal chain structure with a hole in the center was detected under strong confinements. The scattering form factor S(q) computed for semiflexible confined chains revealed three regimes of behavior in a slit and a cylinder that matched up well with the scaling theory. The complex form of the function S(q) computed for a sphere was interpreted as a sign of the toroidal structure. A reasonable agreement was found between the simulations and measurements of DNA and actin filaments, confined in nano- and microfluidic channels and spherical droplets, pertaining to the changes of the persistence lengths, chain elongation, and toroidal structure formation.     

分散体系中任意形状的胶粒模型与相互作用能——Ⅲ. 园柱体型颗粒

在分散体系的研究中,也经常遇到园柱体型胶粒,例如蛋白质分子,海泡石和凸凹棒石粘土颗粒,它们都能用带电的园柱体型采近似处理。这种类型的颗粒以往研究不多,其原因大约有二,一是处理这类颗粒时,数学上的困难很大;二是这类颗粒之间的相互作用,和它们之间的取向有关。Sparnaay首先用Derjaguin法得出园柱体型颗粒处于平行和垂直位置时,相互排斥能的近似表达式。Brenner和McQuarrie(BM)对颗粒外的电位分布采     

Monte Carlo Simulations of Polymers in Nanoslits

Summary: Monte Carlo computer simulations have been performed for model polymers confined in slits of thickness comparable to the transverse diameter of the chains. The density of polymer within the slits is allowed to vary with the slit thickness in such a way that the content of the slits is always in equilibrium with a large reservoir of bulk polymer. The calculations reveal the presence of polymer‐mediated attractive or repulsive interactions between the slit plates, oscillating with the slit thickness in good agreement with experimental results.

The base cell used in the simulations.     

Tangential and nondiagonal components of pressure in a circular slit

Two local tangential and one nondiagonal components of the pressure tensor have been calculated inside circular plane-parallel empty slits with dispersion forces. Symmetric and asymmetric slits have been considered. The spatial dependences have the same character for both tangential components, although their absolute values are somewhat different. It has been shown that, in the symmetric slit, the corrections for its finite size to the tangential pressure appear to be larger than those to the normal pressure. The nondiagonal pressure component becomes noticeable only near the edges of narrow slits.     

Diffusion in the presence of cylindrical obstacles arranged in a square lattice analyzed with generalized Fick-Jacobs equation

The generalized Fick-Jacobs equation is widely used to study diffusion of Brownian particles in three-dimensional tubes and quasi-two-dimensional channels of varying constraint geometry. We show how this equation can be applied to study the slowdown of unconstrained diffusion in the presence of obstacles. Specifically, we study diffusion of a point Brownian particle in the presence of identical cylindrical obstacles arranged in a square lattice. The focus is on the effective diffusion coefficient of the particle in the plane perpendicular to the cylinder axes, as a function of the cylinder radii. As radii vary from zero to one half of the lattice period, the effective diffusion coefficient decreases from its value in the obstacle free space to zero. Using different versions of the generalized Fick-Jacobs equation, we derive simple approximate formulas, which give the effective diffusion coefficient as a function of the cylinder radii, and compare their predictions with the values of the effective diffusion coefficient obtained from Brownian dynamics simulations. We find that both Reguera-Rubi and Kalinay-Percus versions of the generalized Fick-Jacobs equation lead to quite accurate predictions of the effective diffusion coefficient (with maximum relative errors below 4% and 7%, respectively) over the entire range of the cylinder radii from zero to one half of the lattice period.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

Molecular arrangements and conformations of liquid unbranched alkanes in narrow slits

Realistic, atomistic models of liquid tridecane in broad slits (>3 nm) and in narrow slits of thickness 1,2 nm and 1,0 nm have been obtained using the Monte Carlo technique. The setup of the models is such that the molecules in the slits are in equilibrium with the bulk liquid. The surfaces of the plates are modelled as two-dimensional arrays of hexagonally packed units having the same size and interaction parameters of a methylene group. The regions adjacent to the plates in slits with thickness > 3 nm are characterized by a well defined tendency to form partially ordered layer structures, while molecules at a distance from the plates larger than 1,5 nm are unperturbed. The simultaneous presence of two plates increases the tendency to form layer structures when their distance is 1,2 nm, while this tendency is almost totally destroyed when the slit is squeezed down to a thickness of 1,0 nm. This is also associated with a 10% decrease of the density in the latter slit.     

Determination of McGowan volumes for ions and correlation with van der Waals volumes

The McGowan volume has been widely used for the analysis of physicochemical and biochemical properties in chemistry and drug industry. Because McGowan volumes are not available for ions, its application is limited to only neutral compounds. Pauling radii of metallic ions have been collected and studied to obtain McGowan volumes for ions. Regression analysis was carried out between Pauling radii (R(p)) and McGowan radii (R(x)) for a wide range of compounds. It was found that Pauling radii and McGowan radii derived from McGowan volumes by using a volume-radius formula are linearly related (R(x) = 1.115R(p) + 0.0623, r(2) = 0.995). This equation is then used to calculate McGowan volumes for various ions and charged groups. McGowan volumes have been calculated for inorganic, organic, and organometallic compounds and correlated with van der Waals volumes. Results show that McGowan volumes (V(x)) are entirely equivalent to computer-calculated van der Waals volumes.     

On gauging and control of grainy materials by gamma-ray absorptiometry in hydraulic transport of solids in pipes

Grain-size effects on γ-ray absorptiometry in non-destructive assay of rainy solid materials with uniform grain radii are widely investigated. In many applications the grain radii are not uniform, but follow more or less a distribution function. The present work offers a Monte Carlo model for γ-ray attenuation in materials with grain-size distributions. Suitable correction functions for grain-size effects have been derived. A comparison between the Monte Carlo results and those from analytical calculations shows a good agreement when the grain sizes are uniform, but a disagreement appears when grain sizes are statistically distributed. This disagreement between the two results may be due to the several approximations introduced in the analytical calculations.     

Comparison of transition probabilities calculated using different parameters on WBEPM theory for some p‐d and d‐p transitions in excited atomic nitrogen

The transition probabilities between individual and multiplet lines for some quartet terms of excited p‐d and d‐p transition arrays of nitrogen atom have been calculated using the weakest bound electron potential model (WBEPM) theory. For determination relevant parameters, we employed both numerical Coulomb approximation (NCA) method and numerical nonrelativistic Hartree–Fock (NRHF) wave functions for expectation values of radii. The necessary energy values have been taken from experimental energy data in the literature. The expectation values of radii obtained using the two different methods have been employed in the calculation of transition probabilities of all transition arrays. The results obtained have been compared with either each other or NIST data. Good agreement with accepted values taken from NIST has been observed for related excited transitions. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Entropic selectivity of binary mixtures in cylindrical pores

We show that a simple model consisting of a binary hard-sphere mixture in a narrow cylindrical pore can lead to strong size selectivity by considering a situation where each species of the mixture sees a different radius of the cylinder. Two mechanisms are proposed to explain the observed results depending on the radius of the cylinder: for large radii the selectivity is driven by an enhancement of the depletion forces at the cylinder walls whereas for the narrowest cylinders excluded-volume effects lead to a shift of the effective chemical potential of the particles in the pore.     

Mathematical modelling for equilibrium configurations of concentric gold nanoparticles

Nanotechnology is a promising research area, and it is believed that the unique properties of molecules at the nano-scale will benefit mankind especially in the medical exploration. Here we utilize an applied mathematical modelling to investigate spherical and cylindrical concentric structures of gold nanoparticles, with the aim of maximising the free space for which to improve amount of drug or gene to bind on the nanoparticle surfaces and deliver to the target cells. The energy between two gold molecules is modelled by the 6–12 Lennard-Jones potential function, and the total potential between two layers for such particles is calculated using the continuous approximation. On minimising the energy function, the radii for five layers for the concentric sphere and likewise for the cylinder are presented. Further, the equilibrium spacing between any two layers is predicted to lie in the range 2.94–2.96 Å, for both concentric structures. There are at present no experimental or simulation results for comparison with the theoretical equilibrium configurations for concentric gold nanoparticles predicted by this study.     

The Electrochemical Oxidation of N,N‐Diethyl‐p‐Phenylenediamine in DMF and Analytical Applications. Part I: Mechanistic Study

The electrochemical oxidation of N,N‐diethyl‐p‐phenylenediamine in dimethylformamide has been studied at platinum and gold microdisk electrodes of various radii between 6.7 and 66 μm. The voltammetric responses revealed two electrochemically reversible waves the second of which becomes larger at higher concentrations and bigger electrode radii. The voltammetric signals have been modelled and the electrochemical oxidation reaction is not inconsistent with an EC_revECE reaction. Kinetic parameters are reported.     

Adsorption of heavy metal ions from aqueous solution by polyrhodanine-encapsulated magnetic nanoparticles

The influence of salt concentration on the terminal velocities of gravity-driven single bubbles sliding along an inclined glass wall has been investigated, in an effort to establish whether surface forces acting between the wall and the bubble influence the latter's mobility. A simple sliding bubble apparatus was employed to measure the terminal velocities of air bubbles with radii ranging from 0.3 to 1.5 mm sliding along the interior wall of an inclined Pyrex glass cylinder with inclination angles between 0.6 and 40.1°. Experiments were performed in pure water, 10 mM and 100 mM KCl solutions. We compared our experimental results with a theory by Hodges et al. which considers hydrodynamic forces only, and with a theory developed by two of us which considers surface forces to play a significant role. Our experimental results demonstrate that the terminal velocity of the bubble not only varies with the angle of inclination and the bubble size but also with the salt concentration, particularly at low inclination angles of ～1-5°, indicating that double-layer forces between the bubble and the wall influence the sliding behavior. This is the first demonstration that terminal velocities of sliding bubbles are affected by disjoining pressure.     

Self-avoiding walks in slits and slabs with interactive walls

Self-avoiding walk models of a polymer confined between two parallel attractive walls in two and three dimensions (slits and slabs, respectively) have recently had a revival of interest. They were first studied as simple models of steric stabilisation and sensitised flocculation in colloids. The revival has been catalysed by new exact solution techniques, that have allowed the solution of directed walk models in two dimensions in full generality, and by new Monte Carlo techniques that have allowed the simulation of the full parameter space in the three-dimensional slab model. Additionally, rigorous techniques applied to the slab problem have also yielded new results. The contributions to the study of this problem that have been recently added include a novel phase diagram for the “infinite-slab” (when the walls are a macroscopic distance apart but both walls may still “see” the polymer) the delineation of the repulsive and attractive regimes of the parameter space, and a conjectured scaling theory for the problem in general dimensions.     

Radii of Redox Components from Absolute Redox Potentials Compared with Covalent and Aqueous Ionic Radii

Aqueous standard potentials, referred to that of the SHE as zero, were recently shown to vary linearly with gaseous ionization potentials, with the absolute potential of SHE as the intercept. This enabled arriving at the absolute redox potentials of elements. Here, the distances between the oxidized and reduced forms in aqueous solutions have been evaluated. From the linear dependence of these distances on the covalent radii of atoms, the radii of the redox components have been obtained. The latter also vary linearly with the aqueous ionic radii estimated earlier from ion‐water distances, and indicate the presence of aqueous molecular anions.     

Covalent radii revisited

A new set of covalent atomic radii has been deduced from crystallographic data for most of the elements with atomic numbers up to 96. The proposed radii show a well behaved periodic dependence that allows us to interpolate a few radii for elements for which structural data is lacking, notably the noble gases. The proposed set of radii therefore fills most of the gaps and solves some inconsistencies in currently used covalent radii. The transition metal and lanthanide contractions as well as the differences in covalent atomic radii between low spin and high spin configurations in transition metals are illustrated by the proposed radii set.     

Charge induced pattern formation on surfaces: segregation in cylindrical micelles of cationic-anionic peptide-amphiphiles

Micelles, vesicles, and films composed of two species of incompatible heterogeneous molecules exhibit full internal segregation of the component species. This macroscopic segregation can be inhibited by oppositely charging the two different molecular species. The degree of compatibility achieved by the charges leads to either fully homogenous mixtures or to local segregation and the possible formation of regular patterns. We investigate the induction of periodic surface patterns by the presence of opposite charges in flat films and cylindrical micelles. In the strong segregation limit the incompatibility between species can be described by a line tension parameter gamma. The size of the patterns formed is of the order of a characteristic size L approximately (gamma/sigma(2))(1/2), where sigma is the surface charge density. The pattern symmetry on flat surfaces is function only of the fraction of area covered by the components, f: lamellar for 0.34相似文献   

On the size dependence of the surface energy of metal nanoclusters

The many-particle tight-binding potential has been employed to calculate the specific surface energy of icosahedral nanoclusters of transition metals. The equimolecular surface has been considered as the dividing surface. The surface energy has been shown to linearly increase with particle size at nanocluster radii smaller than five radii of the first coordination sphere. As the nanocluster radius is further enlarged, the surface energy passes through a maximum and approaches an asymptotic macroscopic value. The coefficients of proportionality between the specific surface energy and nanocluster radius have been found and compared with the data available from the literature.     

Correction of random surface roughness on colloidal probes in measuring adhesion

Atomic force microscopes (AFM) are commonly used to measure adhesion at nanoscale between two surfaces. To avoid uncertainties in the contact areas between the tip and the surface, colloidal probes have been used for adhesion measurements. We measured adhesion between glass spheres and silicon (100) surface using colloidal probes of different radii under controlled conditions (relative humidity of < 3%, temperature of 25 +/- 1 degrees C). Results showed that the adhesion forces did not correlate with the radii of the spheres as suggested by elastic contact mechanics theories. Surface roughness and random surface features were found on the surfaces of the colloidal probes. We evaluated various roughness parameters, Rumpf and Rabinovich models, and a load-bearing area correction model in an attempt to correct for the roughness effects on adhesion, but the results were unsatisfactory. We developed a new multiscale contact model taking into account elastic as well as plastic deformation in a successive contacting mode. The new model was able to correct for most of the surface roughness features except for surface ridges with sharp angular features, limited by the spherical asperity assumption made in the model.