Polymer chains in a soft nanotube: a Monte Carlo study

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D相似文献   

Polymer brushes in cylindrical pores: simulation versus scaling theory

The structure of flexible polymers endgrafted in cylindrical pores of diameter D is studied as a function of chain length N and grafting density sigma, assuming good solvent conditions. A phenomenological scaling theory, describing the variation of the linear dimensions of the chains with sigma, is developed and tested by molecular dynamics simulations of a bead-spring model. Different regimes are identified, depending on the ratio of D to the size of a free polymer N(3/5). For D>N(3/5) a crossover occurs for sigma=sigma*=N(-6/5) from the "mushroom" behavior (R(gx)=R(gy)=R(gz)=N(35)) to the behavior of a flat brush (R(gz)=sigma(1/3)N,R(gx)=R(gy)=sigma(-1/12)N(1/2)), until at sigma**=(D/N)3 a crossover to a compressed state of the brush, [R(gz)=D,R(gx)=R(gy)=(N(3)D/4sigma)(1/8)相似文献   

How Does a Polymer Brush Repel Proteins？

The captioned question has been addressed by the steric effect; namely, the adsorption of proteins on a surface grafted with linear polymer chains decreases monotonically as the grafting density increases. However, there is no quantitative and satisfactory explanation why the adsorption starts to increase when the grafting density is sufficiently high and why polyethylene glycol（PEG） still remains as one of the best polymers to repel proteins. After considering each grafted chain as a molecular spring confined inside a ＂tube＂ made of its surrounding grafted chains, we estimated how its free energy depends on the grafting density and chain length, and calculated its thermal energy-agitated chain conformation fluctuation, enabling us to predict an adsorption minimum at a proper grafting density, which agrees well with previous experimental results. We propose that it is such a chain fluctuation that slows down the adsorption kinetically.     

Transient Surface Tension of an Expanding Liquid Sheet

We address the problem of dynamic surface tension using measurements of sheet diameters that results from the impact of a liquid jet of diameter d(0) on a small disk of diameter d(i) (d(i)/d(0) approximately 4). At low velocities, the sheet diameter D is related to d(0) by the Weber number We, constructed with the liquid density rho, the jet velocity u(0), and the surface tension sigma at the rim: D/d(0)=18 We=18 [rho u(0)(2)/(sigma/d(0))]. This relation expresses the equilibrium between inertial forces and surface tension forces at the sheet rim. When a surfactant has been dissolved in the bulk of the liquid prior to the formation of the initial jet, the rim surface tension, and therefore the sheet diameter, depends on the amount of surfactant adsorbed at the rim. This amount is fixed by a competition between surface formation induced by radial extension and repopulation of the liquid interface in surfactant. The experimental setup proposed here provides a method to measure dynamic surface tension from sheet diameter measurements and symmetrically to monitor the adsorption of a surfactant on a liquid surface. The available adsorption time ranges from 10 to 100 ms. Experimental data obtained with two surfactants are in agreement with a model of a diffusion-controlled adsorption at the interface. Copyright 2000 Academic Press.     

Draining Collars and Lenses in Liquid-Lined Vertical Tubes

The speed at which an annular liquid collar drains under gravity g in a vertical tube of radius a, when the tube has an otherwise thin viscous liquid lining on its interior, is determined by a balance between the collar's weight and viscous shear stresses confined to narrow regions in the neighborhood of the collar's effective contact lines. Whether a collar grows or shrinks in volume as it drains depends on the modified Bond number B=rho g a(2)/(sigmaepsilon), where rho is the fluid density, sigma is its surface tension, and epsilona is the thickness of the thin film immediately ahead of the collar. Asymptotic methods are used here to determine the following nonlinear stability criteria for an individual collar, valid in the limit of small epsilon. For 0相似文献   

Thin-thick surface phase coexistence and boundary tension of the square-well fluid on a weak attractive surface

Prewetting transition is studied for the square-well fluid of attractive-well diameter lambda(ff)sigma(ff)=1.5 in the presence of a homogeneous surface modeled by the square-well potential of attractive well from 0.8sigma(ff) to 1.8sigma(ff). We investigate surface phase coexistence of thin-thick film transition using grand-canonical transition matrix Monte Carlo (GC-TMMC) and histogram reweighting techniques. Molecular dynamics (MD) and GC-TMMC are utilized to predict the properties of the fluid for various surface fluid affinities. Occurrences of prewetting transition with the variation of surface affinity are observed for a domain of reduced temperature from T(*)=0.62 to 0.75. We have used MD and GC-TMMC+finite size scaling (FSS) simulations to calculate the boundary tension as a function of temperature as well as surface affinity. Boundary tensions via MD and GC-TMMC+FSS methods are in good agreement. The boundary tension increases with the decrease of wall-fluid affinity. Prewetting critical properties are calculated using rectilinear diameter approach and scaling analysis. We found that critical temperature and density increase with the decrease of wall-fluid affinity.     

The molecular kink paradigm for rubber elasticity: numerical simulations of explicit polyisoprene networks at low to moderate tensile strains

Based on recent molecular dynamics and ab initio simulations of small isoprene molecules, we propose a new ansatz for rubber elasticity. We envision a network chain as a series of independent molecular kinks, each comprised of a small number of backbone units, and the strain as being imposed along the contour of the chain. We treat chain extension in three distinct force regimes: (Ia) near zero strain, where we assume that the chain is extended within a well defined tube, with all of the kinks participating simultaneously as entropic elastic springs, (II) when the chain becomes sensibly straight, giving rise to a purely enthalpic stretching force (until bond rupture occurs) and, (Ib) a linear entropic regime, between regimes Ia and II, in which a force limit is imposed by tube deformation. In this intermediate regime, the molecular kinks are assumed to be gradually straightened until the chain becomes a series of straight segments between entanglements. We assume that there exists a tube deformation tension limit that is inversely proportional to the chain path tortuosity. Here we report the results of numerical simulations of explicit three-dimensional, periodic, polyisoprene networks, using these extension-only force models. At low strain, crosslink nodes are moved affinely, up to an arbitrary node force limit. Above this limit, non-affine motion of the nodes is allowed to relax unbalanced chain forces. Our simulation results are in good agreement with tensile stress vs. strain experiments.     

Solvation force, structure and thermodynamics of fluids confined in geometrically rough pores

The effect of periodic surface roughness on the behavior of confined soft sphere fluids is investigated using grand canonical Monte Carlo simulations. Rough pores are constructed by taking the prototypical slit-shaped pore and introducing unidirectional sinusoidal undulations on one wall. For the above geometry our study reveals that the solvation force response can be phase shifted in a controlled manner by varying the amplitude of roughness. At a fixed amplitude of roughness, a, the solvation force for pores with structured walls was relatively insensitive to the wavelength of the undulation, lambda for 2.3/=0.5. The predictions of the superposition approximation, where the solvation force response for the rough pores is deduced from the solvation force response of the slit-shaped pores, was in excellent agreement with simulation results for the structured pores and for lambda/sigma(ff)>/=7 in the case of smooth walled pores. Grand potential computations illustrate that interactions between the walls of the pore can alter the pore width corresponding to the thermodynamically stable state, with wall-wall interactions playing an important role at smaller pore widths and higher amplitudes of roughness.     

Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: evaluation of the surface tension of critical nucleus

The homogeneous nucleation of bismuth supersaturated vapor is studied in a laminar flow quartz tube nucleation chamber. The concentration, size, and morphology of outcoming aerosol particles are analyzed by a transmission electron microscope (TEM) and an automatic diffusion battery (ADB). The wall deposit morphology is studied by scanning electron microscopy. The rate of wall deposition is measured by the light absorption technique and direct weighting of the wall deposits. The confines of the nucleation region are determined in the "supersaturation cut-off" measurements inserting a metal grid into the nucleation zone and monitoring the outlet aerosol concentration response. Using the above experimental techniques, the nucleation rate, supersaturation, and nucleation temperature are measured. The surface tension of the critical nucleus and the radius of the surface of tension are determined from the measured nucleation parameters. To this aim an analytical formula for the nucleation rate is used, derived from author's previous papers based on the Gibbs formula for the work of formation of critical nucleus and the translation-rotation correction. A more accurate approach is also applied to determine the surface tension of critical drop from the experimentally measured bismuth mass flow, temperature profiles, ADB, and TEM data solving an inverse problem by numerical simulation. The simulation of the vapor to particles conversion is carried out in the framework of the explicit finite difference scheme accounting the nucleation, vapor to particles and vapor to wall deposition, and particle to wall deposition, coagulation. The nucleation rate is determined from simulations to be in the range of 10(9)-10(11) cm(-3) s(-1) for the supersaturation of Bi(2) dimers being 10(17)-10(7) and the nucleation temperature 330-570 K, respectively. The surface tension σ(S) of the bismuth critical nucleus is found to be in the range of 455-487 mN/m for the radius of the surface of tension from 0.36 to 0.48 nm. The function σ(S) changes weakly with the radius of critical nucleus. The value of σ(S) is from 14% to 24% higher than the surface tension of a flat surface.     

Interatomic potential-based semiclassical theory for Lennard-Jones fluids

An interatomic potential based semiclassical theory is proposed to predict the concentration and potential profiles of a Lennard-Jones (LJ) fluid confined in a channel. The inputs to the semiclassical formulation are the LJ parameters of the fluid and the wall, the density of channel wall atoms, and the average concentration of the fluid inside the channel. Using the semiclassical formulation, fluid confinement in channel with widths ranging from 2sigma ff to 100sigma ff, where sigma ff is the fluid-fluid LJ distance parameter, is investigated. The concentration and potential predicted by the semiclassical formulation are found to be in good agreement with those from equilibrium molecular dynamics simulations. While atomistic simulations in large channels are computationally expensive, the proposed semiclassical formulation can rapidly and accurately predict the concentration and potential profiles. The proposed semiclassical theory is thus a robust and fast method to predict the interfacial and "bulk" fluid phenomena in channels with widths ranging from the macroscale down to the scale of a few atomic diameters.     

Density functional theory for semiflexible and cyclic polyatomic fluids

The effects of bond angle and chain stiffness on the structures of semiflexible polyatomic fluids are investigated by incorporating the bending potential into a density functional theory [Y. X. Yu and J. Z. Wu, J. Chem. Phys. 117, 2368 (2002)] that combines a modified fundamental measure theory for the excluded-volume effects and the first-order thermodynamics perturbation theory for the chain connectivity. The refined density functional theory faithfully reproduces the density profiles and conformational properties of a variety of triatomic fluids near a hard wall in which extensive Monte Carlo simulation data are available. In particular, the theory is able to capture the structures of rigid cyclic trimers where all segments are identical. The variation of local density profiles with respect to the chain length of confined polyatomic fluids is also explored. For quadratomic fluids confined in slit pores, the density profile of the middle segments exhibits novel double peaks that are absent in a fully flexible chain model. In addition, the density functional theory is applied to predicting the conformational properties and adsorption behavior of heterogeneous triatomic fluids of type "ABB" mimicking surfactant molecules. The competition between surface adsorption and self-association of trimers consisting of surface active and self-binding "A" segments and neutral "B" segment is explored.     

Tension and mobility of a DNA fragment in the lakes-straits model

We consider numerically, in the framework of the lakes-straits model, the mobility of a DNA chain under field-inversion gel-electrophoresis (FIGE). Here we investigate the role of the gel's structure on the mobility. We consider two situations: (i) a DNA chain fragment is bounded by two straits (narrow gateways) at a fixed distance, but is otherwise free, and (ii) the fragment is, in addition, confined with in a closed volume (pore). We calculate the tension on the DNA fragment in the two cases. For Gaussian chains we evaluate the corresponding statistical weights exactly, using a cellular automation algorithm. We find that the resulting tension differs drastically in the two models considered. Nonetheless this difference influences only weakly the overall FIGE mobility.     

Polymer conformation at the polymer melt surface

Due to the symmetry which characterizes the surroundings of each chain segment in the amorphous melt all (but end) segments are equivalent in their embedment in space. Energetic interactions between segments are confined to segments in contact. Hence, in the presence of a surface only the segments actually in the surface layer will be affected and will have a statistical weight and Boltzmann factor different from segments in the bulk. The number of segments so involved is fixed, since the extent of the surface is controlled. The partition function is comprised of factors which depend neither upon the order of the segments in the chain nor upon the conformation of any particular chain. Only segments finding themselves in the surface contribute to the surface tension, with the largest contribution deriving from the density transition in the interface. This, at most temperatures, is confined to a lamella one segment layer, or less, thick. For polymer of high enough molecular weight end-effects can be neglected and no allowance for the presence of ends is made here. It is then possible to reach a representation of surface tension in reduced coordinates, as shown already by Posner and Sanchez. Changes in chain conformation near the surface are calculated.     

Spatial confinement effect on the atomic structure of solid argon

Molecules confined in nanopores show unusual behavior not seen in bulk systems. The present paper reports on molecular dynamics simulations of unusual freezing behavior in confined Ar. Similar to bulk Ar, liquid Ar confined in pores with a diameter D>15sigma (5.1 nm), where sigma is the diameter of the Ar atom, crystallizes when the cooling rate is lower than a critical value (Qc). We also find that the spatial confinement does not have significant influence on Qc when D>15sigma (5.1 nm). In the pore of 10sigma (3.4 nm) in diameter, on the other hand, the behavior is dramatically changed. Crystalline Ar does not appear inside the pore even when the system is cooled at a rate lower than the Qc in the bulk system by over two orders of magnitude. Instead, amorphous Ar characterized by local icosahedral configurations is formed in the pore. We further find that, even when crystalline Ar is formed outside the pore, it does not grow deeply into the pore. This supports that the amorphous Ar is actually the most stable phase in the pore. It is well known that Ar is a poor glass former. Our finding that even such an amorphous Ar is the most stable in the pore suggests that, in any system, it is possible to prepare amorphous structure selectively by using nano-molds.     

A small molecular size system giving unexpected surface effects: alpha-Cyclodextrin + sodium dodecyl sulfate in water

Maximum drop volumes (MDV) and the resultant surface tension values (sigma) of alpha-cyclodextrin (alpha-CD) + sodium dodecyl sulfate (SDS) aqueous mixtures have been determined over a broad concentration range of both solutes at 283.15, 293.15, 303.15, 313.15, and 323.15 K. Drops significantly larger than those of pure water (up to approximately 25% larger) were observed at low temperatures for solutions with [alpha-CD]/[SDS] concentration ratios, approximately > 2, producing unexpectedly high surface tension values. Our results indicate that at certain solute concentration ratios and temperatures, the drop volume method provides wrong values for equilibrium surface tensions. This is due to the high viscoelasticity of the surface film whose effect is important even though the injection rate of the drops was slow and the solutes molecular sizes are small.     

Streaming potential generated by a long viscous drop in a capillary

The streaming potential generated by motion of a long drop of viscosity mu(d) = lambdamu in a uniform circular capillary filled with fluid of viscosity mu is investigated by means of a model previously used to study electrophoresis of a charged mercury drop in water. The capillary wall is at potential zeta c relative to the bulk fluid within it, and the surface of the drop is at potential zeta(d). Potentials are assumed to be sufficiently small so that the charge cloud is described by the linearized Poisson-Boltzmann equation, and the Debye length characterizing the thickness of the charge cloud is assumed to be thin compared with the gap h(0) between the drop and the capillary wall. Ions in the external fluid are not allowed to discharge at the surface of the drop, and the wall of the capillary has a nonzero surface conductivity sigma c. The drop is assumed to be sufficiently long so that end effects can be neglected. Recirculation of fluid within the drop gives rise to an enhanced streaming current when zeta(d) is nonzero, leading to an anomalously high streaming potential. This vanishes as the drop viscosity becomes large. If V is the velocity of the drop and gamma is the coefficient of interfacial tension between the two fluids, then the capillary number is Ca = mu V/gamma, and the gap varies as h(0)planck'sCa(2/3). When Ca is small, the gap h(0) is small and electrical conduction along the narrow gap is dominated by the surface conductivity sigma(c) of the capillary wall, which is constant. The electrical current convected by flowing fluid is proportional to Ca, as is the change in streaming potential caused by the presence of the drop. If sigma(c) = 0, then the electrical conductance of the gap depends on its width h(0) and on the bulk fluid conductivity sigma and becomes small as h(0) approximately equal to Ca(2/3) --> 0. The streaming potential required to cancel the O(Ca) convection current therefore varies as Ca(1/3). If sigma(c) = 0 and the drop is rigid (lambda --> infinity), then the change in streaming potential over and above that expected due to the change in pressure gradient is proportional to the difference in potentials zeta(c)-zeta(d).     

Two interacting particles in a spherical pore

In this work we analytically evaluate, for the first time, the exact canonical partition function for two interacting spherical particles into a spherical pore. The interaction with the spherical substrate and between particles is described by an attractive square-well and a square-shoulder potential. In addition, we obtain exact expressions for both the one particle and an averaged two particle density distribution. We develop a thermodynamic approach to few-body systems by introducing a method based on thermodynamic measures [I. Urrutia, J. Chem. Phys. 134, 104503 (2010)] for nonhard interaction potentials. This analysis enables us to obtain expressions for the pressure, the surface tension, and the equivalent magnitudes for the total and Gaussian curvatures. As a by-product, we solve systems composed of two particles outside a fixed spherical obstacle. We study the low density limit for a many-body system confined to a spherical cavity and a many-body system surrounding a spherical obstacle. From this analysis we derive the exact first order dependence of the surface tension and Tolman length. Our findings show that the Tolman length goes to zero in the case of a purely hard wall spherical substrate, but contains a zero order term in density for square-well and square-shoulder wall-fluid potentials. This suggests that any nonhard wall-fluid potential should produce a non-null zero order term in the Tolman length.     

Mesophase Separation of Diblock Copolymer Confined in a Cylindrical Tube Studied by Dissipative Particle Dynamics

Summary: The morphologies of diblock copolymers confined in a cylindrical tube have been investigated by the dissipative particle dynamics (DPD) method. Results indicate that the morphology depends on the volume ratio of the immiscible blocks, the diameter of the cylindrical tube and the interactions between the blocks and between the confinement wall and blocks. For symmetric diblock copolymers, when the tube wall is uniform toward the two blocks, perpendicular lamellae or a stacked disk morphology are generally formed except when the diameter of the cylindrical tube is very small; in that case, a special bi‐helix morphology forms because of the entropy effect. When the tube wall is non‐uniform, as the diameter of the tube increases, perpendicular lamellae are first formed, then changing to parallel lamellae and, finally, back to perpendicular lamellae again. An intermediate morphology characterizing the transition between perpendicular and parallel lamellae is observed. If the non‐uniformity of the wall is further enhanced, only parallel lamellae can be found. In the case of asymmetric diblock copolymers, more complex morphologies can be obtained. Multi‐cylindrical micro‐domains and a multilayer helical phase as well as other complex pictures are observed. Generally, the morphologies obtained could find their counterparts from experiments or Monte Carlo simulations; however, differences do exist, especially in some cases of asymmetric diblock copolymers.

Bi‐helix and stacked disks morphologies of A₅B₅ diblock copolymer confined in two different neutral nanocylinders.     

Nanoporous carbon nanotubes synthesized through confined hydrogen-bonding self-assembly

We report a simple and direct synthetic method for the preparation of nanoporous carbon nanotubes with larger pores (>10 nm) on the tube wall. The method combines the use of anodic aluminum oxide (AAO) as a template for the tube diameter and block copolymer/carbohydrates self-assembly within thin films confined inside AAO pore channels to form nanopores. It involves coating the AAO inner pore channel surface with block copolymer (polystyrene-co-poly(vinylpyridine)) and carbohydrates in dimethylformamide (DMF) solution. Drying of DMF induced microphase separation of PS-PVP and formation of ordered PS and PVP/carbohydrate domains. Within the coating, the carbohydrates stay specifically only in the pyridine domains surrounding PS domains due to the hydrogen bonding between carbohydrates and pyridine blocks. After carbonization at high temperature (>460 degrees C) in argon, PS was removed, forming the nanopores and carbohydrates, and PVP was carbonized, forming the framework of nanoporous carbon tubes within AAO channels. Removal of AAO led to the formation of individual monodisperse nanoporous carbon nanotubes with a tube wall of approximately 16 nm. The ease with which these nanoporous carbon nanotubes can be fabricated, and the ability to tune tube nanostructures and surface chemistry through the choice of block copolymers used and carbonization temperature, should facilitate investigations of their scope for practical applications.     

Diffusion on membrane tubes: a highly discriminatory test of the Saffman-Delbruck theory

The efficient transport of membrane proteins is vital in maintaining life. In this work, we investigate the transport of such membrane proteins along long thin membrane tubes or tethers. We calculate the diffusion constant to leading order in the low Reynolds number regime to be D = (4 pi eta)-1 log(r/a), with r and a being the tube and protein radii, respectively, and eta being the membrane viscosity. Thus we propose an exact limiting form for the controversial logarithmic correction, such as originally introduced by Saffman and Delbruck, that involves the tube radius rather than some "frame size". Our work suggests a test of this logarithmic correction could be achieved by measuring diffusion on membrane tubes, exploiting the fact that the equilibrium tube radius can be controlled by the membrane tension and varied over several orders of magnitude. We analyze the time taken for a protein to transit a membrane tube between cells and find that this can vary by an order of magnitude over physiological tensions. This is a strong effect in biological terms and suggests a possible regulatory coupling between membrane tension and signaling.