DNA electrophoresis in confined, periodic geometries: a new lakes-straits model

We present a method to study the dynamics of long DNA molecules inside a cubic array of confining spheres, connected through narrow openings. Our method is based on the coarse-grained, lakes-straits model of Zimm and is therefore much faster than Brownian dynamics simulations. In contrast to Zimm's approach, our method uses a standard stochastic kinetic simulation to account for the mass transfer through the narrow straits and the formation of new lakes. The different rates, or propensities, of the reactions are obtained using first-passage time statistics and a Monte Carlo sampling to compute the total free energy of the chain. The total free energy takes into account the self-avoiding nature of the chain as well as confinement effects from the impenetrable spheres. The mobilities of various chains agree with biased reptation theory at low and high fields. At moderate fields, confinement effects lead to a new regime of reptation where the mobility is a linear function of molecular weight and the dispersion is minimal.     

Molecular dynamics of confined glucose solutions

Silica gels containing solutions of glucose in heavy water at different concentrations have been prepared by a sol-gel method. Dynamical studies with quasielastic neutron scattering, compared with previous results on bulk solutions, show that the dynamics of the glucose molecules are not appreciably affected by the confinement, even though the gels behave macroscopically as solid materials. Small-angle neutron-scattering spectra on the same systems, fitted with a fractal model, yield a correlation length that decreases from 20 to 2.5 nm with increasing glucose concentration, suggesting a clustering of glucose molecules in concentrated solutions that is consistent with the dynamical measurements. These two sets of results imply that 20 nm is an upper limit for the scale at which the dynamics of glucose molecules in solution are affected by confinement.     

Ionic liquids in confined geometries

Over recent years the Surface Force Apparatus (SFA) has been used to carry out model experiments revealing structural and dynamic properties of ionic liquids confined to thin films. Understanding characteristics such as confinement induced ion layering and lubrication is of primary importance to many applications of ionic liquids, from energy devices to nanoparticle dispersion. This Perspective surveys and compares SFA results from several laboratories as well as simulations and other model experiments. A coherent picture is beginning to emerge of ionic liquids as nano-structured in pores and thin films, and possessing complex dynamic properties. The article covers structure, dynamics, and colloidal forces in confined ionic liquids; ionic liquids are revealed as a class of liquids with unique and useful confinement properties and pertinent future directions of research are highlighted.     

Carbohydrate clustering in aqueous solutions and the dynamics of confined water

We use molecular dynamics simulations to investigate structure and dynamics of fructose aqueous solutions in the 1-5 M concentration range at ambient conditions. We analyze hydration structures, H-bond statistics, and size distribution of H-bonded carbohydrate clusters as functions of concentration. We find that the local tetrahedral order of water is reasonably well-preserved and that the solute tends to appear as scattered "isolated" molecules at low concentrations and as H-bonded clusters for less diluted solutions. The sugar cluster size distribution exhibits a sharp transition to a percolated cluster between 3.5 and 3.8 M. The percolated cluster forms an intertwined network of H-bonded saccharides that imprisons water. For the dynamics, we find good agreement between simulation and available experimental results for the self-diffusion coefficients. Water librational dynamics is little affected by sugar concentration, whereas reorientational relaxation is described by a concentration-independent bulk-like component attributed to noninterfacial water molecules and a slower component (strongly concentration dependent) that arises from interfacial solvent molecules and, hence, depends on the dynamics of the cluster structure itself. Analysis of H-bonding survival probability functions indicates that the formation of carbohydrate clusters upon increasing concentration enhances the H-bond relaxation time and slows down the entire system dynamics. We find that multiexponential or stretched-exponential fits alone cannot describe the H-bond survival probabilities for the entire postlibrational time span of our data (0.1-100 ps), as opposed to a combined stretched-plus-biexponential function, which provides excellent fits. Our results suggest that water dynamics in concentrated fructose solutions resembles in many ways that of protein hydration water.     

Columnar discotics in confined geometries

The influence of geometric confinement on the state of order and on the glass relaxation process was investigated for a triphenylene derivative able to display a highly ordered plastic columnar phase in the bulk. The compound was incorporated into porous glasses - characterized by a narrow size distribution - with average pore diameters of 20, 7.5, 5 and 2.5 nm. The X-ray diagrams revealed the presence of a hexagonal order, yet the lattice spacing is significantly reduced with decreasing pore size and the reflections become broad. The X-ray doublet reflection, superimposed on the halo which is characteristic for the bulk plastic columnar phase, is absent in all cases. It is replaced by a single broad intracolumnar reflection which indicates that the confinement destabilizes the plastic phase in favour of the hexagonal ordered phase. A further observation is that the intracolumnar correlation length is reduced with decreasing pore size. The confinement was furthermore found to cause a transition from a strong glass (bulk material) to a fragile glass former, obviously induced by the structural modification.     

Columnar discotics in confined geometries

The influence of geometric confinement on the state of order and on the glass relaxation process was investigated for a triphenylene derivative able to display a highly ordered plastic columnar phase in the bulk. The compound was incorporated into porous glasses - characterized by a narrow size distribution - with average pore diameters of 20, 7.5, 5 and 2.5 nm. The X-ray diagrams revealed the presence of a hexagonal order, yet the lattice spacing is significantly reduced with decreasing pore size and the reflections become broad. The X-ray doublet reflection, superimposed on the halo which is characteristic for the bulk plastic columnar phase, is absent in all cases. It is replaced by a single broad intracolumnar reflection which indicates that the confinement destabilizes the plastic phase in favour of the hexagonal ordered phase. A further observation is that the intracolumnar correlation length is reduced with decreasing pore size. The confinement was furthermore found to cause a transition from a strong glass (bulk material) to a fragile glass former, obviously induced by the structural modification.     

Molecular dynamics simulations of polymer transport in nanocomposites

Molecular dynamics simulations on the Kremer-Grest bead-spring model of polymer melts are used to study the effect of spherical nanoparticles on chain diffusion. We find that chain diffusivity is enhanced relative to its bulk value when polymer-particle interactions are repulsive and is reduced when polymer-particle interactions are strongly attractive. In both cases chain diffusivity assumes its bulk value when the chain center of mass is about one radius of gyration R(g) away from the particle surface. This behavior echoes the behavior of polymer melts confined between two flat surfaces, except in the limit of severe confinement where the surface influence on polymer mobility is more pronounced for flat surfaces. A particularly interesting fact is that, even though chain motion is strongly speeded up in the presence of repulsive boundaries, this effect can be reversed by pinning one isolated monomer onto the surface. This result strongly stresses the importance of properly specifying boundary conditions when the near surface dynamics of chains are studied.     

Molecular dynamics simulations of supramolecular polymer rheology

Using equilibrium and nonequilibrium molecular dynamics simulations, we studied the equilibrium and rheological properties of dilute and semidilute solutions of head-to-tail associating polymers. In our simulation model, a spontaneous complementary reversible association between the donor and the acceptor groups at the ends of oligomers was achieved by introducing a combination of truncated pseudo-Coulombic attractive potential and Lennard Jones repulsive potential between donor, acceptor, and neighboring groups. We have calculated the equilibrium properties of supramolecular polymers, such as the ring/chain equilibrium, average molecular weight, and molecular weight distribution of self-assembled chains and rings, which all agree well with previous analytical and computer modeling results. We have investigated shear thinning of solutions of 8- and 20-bead associating oligomers with different association energies at different temperatures and oligomer volume fractions. All reduced viscosity data for a given oligomer length can be collapsed into one master curve, exhibiting two power-law regions of shear-thinning behavior with an exponent of -0.55 at intermediate ranges of the reduced shear rate β and -0.8 (or -0.9) at larger shear rates. The equilibrium viscosity of supramolecular solutions with different oligomer lengths and associating energies is found to obey a power-law scaling dependence on oligomer volume fraction with an exponent of 1.5, in agreement with the experimental observations for several dilute or semidilute solutions of supramolecular polymers. This implies that dilute and semidilute supramolecular polymer solutions exhibit high polydispersity but may not be sufficiently entangled to follow the reptation mechanism of relaxation.     

Monomer density profiles for polymer chains in confined geometries: massive field theory approach

Taking into account the well known correspondence between the field theoretical ?(4) O(n)-vector model in the limit n → 0 and the behavior of long flexible polymer chains in a good solvent, the universal density-force relation is analyzed and the corresponding universal amplitude ratio B(real) is obtained using the massive field theory approach in fixed space dimensions d < 4. The monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one repulsive and one inert wall, are obtained in the framework of the massive field theory approach up to one-loop order. Besides, the monomer density profiles for the dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations.     

Molecular dynamics simulations of n-Alkane melts confined between solid surfaces

Molecular dynamics simulations of polyethylene chains (C_nH_2n+2 for n = 13, 16, 28, 60) have been carried out to investigate both equilibrium and dynamic properties of polymer melts confined between flat solid surfaces. We observe an oscillatory monomer density in the direction normal to the solid surfaces, which depends on the size of the monomers (i.e., on the volume density of the system). The packing manner of monomer segments, segment orientation, and local conformations of chains are found to be independent of chain length. In addition, preferential interfacial adsorption of chain ends is observed. The chains are flattened close to the surface and many molecules assume essentially two-dimensional train configurations even in the case of C₆₀H₁₂₂ melts. The apparent self-diffusivities of the centers of mass of the molecules depend on their distance from a surface. Molecules adjacent to a surface exhibit a reduced mobility perpendicular to the surface and an increased one parallel to it. The self-diffusion constant parallel to a surface depends strongly on the size of the monomers. An increase of the united atom diameter by 10% reduces the diffusion constant by a factor of three, in good agreement with the experimental value. © 1994 John Wiley & Sons, Inc.     

Liquid crystal phases in confined geometries

ABSTRACT

The orientation control of liquid crystal (LC) phases is essential for fundamental studies as well as practical applications. Surface treatment and topographic confinement have emerged as two of the most effective tools to control ordering and orientation of various types of LC phases. This review is intended to give an overview of the LC phases controlled in confined geometries at micro- and nanometre scales, in which the orientation control methods and the effective analytical techniques will be covered. Finally, the review closes with the applications using such confined LC phases.     

Nonlinear dynamics of confined polymer melts with attractive walls

A scaling model is presented to analyze the reversible strain-hardening phenomenon in end-tethered polymer clay nanocomposites (Krishnamoorti, R.; Giannelis, E. P. Langmuir 2001, 17, 1448). It is assumed that for attractive clay-polymer interactions a fraction of the polymer chains that span the space between opposite clay plates get adsorbed on them, thereby bridging the plates. Under large amplitude oscillatory shear, such bridges are stretched, and this results in the strain-hardening behavior. The onset of strain hardening is predicted to be dependent only on the average distance separating the two plates and is independent of the frequency of the oscillations and the polymer molecular weight.     

Crystallization of tethered polyethylene in confined geometries

Ordered poly(ethylene)‐poly(vinylcyclohexane) (PE‐PVCH) block copolymers are employed to study the crystallization of tethered PE in confined geometries. The high T_g of the PVCH component of these materials forces PE chains to crystallize in well‐defined geometries dictated by the mesophase structure of the block copolymer. Effects of chain tethering on crystallization are examined through comparison of singly‐tethered PE chains in PE‐PVCH (EV) diblocks and doubly‐tethered PE in PVCH‐PE‐PVCH (VEV) triblocks. Crystallinity is independent of the block copolymer mesophase structure in both the EV and VEV systems, although crystallinity in VEV depends on the molecular weight of the PE block of the copolymer. Melting temperature data indicate that spatial confinement reduces crystallite size in EV and VEV, and that the double tethering of PE chains in VEV reduces crystallite size further through topological constraints. Crystal nucleation and growth depend strongly on the type of microstructure in both EV and VEV block copolymers. Differences in the overall rate of crystallization are correlated with the dimensional continuity of the PE microdomains. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37:2053–2068, 1999     

Molecular dynamics simulations of electroosmosis in perfluorosulfonic acid polymer

An atomistic MD simulation method has been developed to study the electroosmotic drag in the hydrated perfluorosulfonic acid polymer. The transport characteristics of the hydroniums and water molecules are evaluated from their velocity distribution functions with an electric field applied. It is shown that the microstructure of the hydrated perfluorosulfonic acid polymer is not perturbed significantly by the electric field up to 2 V/microm, and the velocity distribution functions obey the peak shifted Maxwell velocity distribution functions. The evaluated peak shifting velocities are only about 1% of the average thermal motion. The hydronium flow and water flow are evaluated from the average transport velocities or the peak shifting velocities. The electroosmotic drag coefficients from the MD simulations are in good correspondence with the experimental values. It is also shown that the electroosmotic drag coefficient has no or weak temperature dependence.     

Melting of Lennard-Jones clusters in confined geometries

The melting of Lennard-Jones (argon) clusters of various size (N = 500 to 10000 atoms), confined in a rigid matrix, is studied by molecular dynamics simulations. For spherical clusters we show the existence of a cluster size below which the dependence of the melting temperature cannot be described by the classical Gibbs-Thompson equation. We also provide evidence of the formation of a quasi-liquid layer at the surface of mesoscopic clusters. A good agreement is found between the theoretical model due to Celestini et al. and the simulation results obtained in this work. The melting of an ellipsoidal cluster is also investigated. We observe, in agreement with recent experimental and theoretical work, that the thickness of the molten layer is larger in the region of higher local curvature.     

Molecular dynamics simulations of osmosis and reverse osmosis in solutions

Computer simulation studies using the method of molecular dynamics have been carried out to investigate osmosis and reverse osmosis in solutions separated by semi-permeable membranes. The method has been used to study the dynamic approach to equilibrium in such systems from their initial nonequilibrium state. In addition density profiles of both the solute and solvent molecules have been investigated, especially near the walls for adsorption effects. Finally the diffusion coefficients and osmotic pressure have also been measured.Our results show both osmosis and reverse osmosis, as well as a smooth transition between the two when either the solution concentration is changed, or the density (pressure) difference between the solvent and solution compartments is varied. We believe this new method can be used to improve our understanding of these two important phenomena at the molecular level.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Molecular dynamics simulations of aqueous solutions of ethanolamines

We report on molecular dynamics simulations performed at constant temperature and pressure to study ethanolamines as pure components and in aqueous solutions. A new geometric integration algorithm that preserves the correct phase space volume is employed to study molecules having up to three ethanol chains. The most stable geometry, rotational barriers, and atomic charges were obtained by ab initio calculations in the gas phase. The calculated dipole moments agree well with available experimental data. The most stable conformation, due to intramolecular hydrogen bonding interactions, has a ringlike structure in one of the ethanol chains, leading to high molecular stability. All molecular dynamics simulations were performed in the liquid phase. The interaction parameters are the same for the atoms in the ethanol chains, reducing the number of variables in the potential model. Intermolecular hydrogen bonding is also analyzed, and it is shown that water associates at low water mole fractions. The force field reproduced (within 1%) the experimental liquid densities at different temperatures of pure components and aqueous solutions at 313 K. The excess and partial molar volumes are analyzed as a function of ethanolamine concentration.