Parallel Repulsive Walls Research Articles

Cholesteric and screw-like nematic phases in systems of helical particles.

Recent numerical simulations of hard helical particle systems unveiled the existence of a novel chiral nematic phase, termed screw-like, characterised by the helical organization of the particle C2 symmetry axes round the nematic director with periodicity equal to the particle pitch. This phase forms at high density and can follow a less dense uniform nematic phase, with relative occurrence of the two phases depending on the helix morphology. Since these numerical simulations were conducted under three-dimensional periodic boundary conditions, two questions could remain open. First, the real nature of the lower density nematic phase, expected to be cholesteric. Second, the influence that the latter, once allowed to form, may have on the existence and stability of the screw-like nematic phase. To address these questions, we have performed Monte Carlo and molecular dynamics numerical simulations of helical particle systems confined between two parallel repulsive walls. We have found that the removal of the periodicity constraint along one direction allows a relatively-long-pitch cholesteric phase to form, in lieu of the uniform nematic phase, with helical axis perpendicular to the walls while the existence and stability of the screw-like nematic phase are not appreciably affected by this change of boundary conditions.

Ring polymer chains confined in a slit geometry of two parallel walls: the massive field theory approach

The investigation of a dilute solution of phantom ideal ring polymer chains confined in a slit geometry of two parallel repulsive walls, two inert walls, and for the mixed case of one inert and the other one repulsive wall, was performed. Taking into account the well known correspondence between the field theoretical O(n)-vector model in the limit and the behaviour of long-flexible polymer chains in a good solvent, the investigation of a dilute solution of long-flexible ring polymer chains with the excluded volume interaction (EVI) confined in a slit geometry of two parallel repulsive walls was performed in the framework of the massive field theory approach at fixed space dimensions d = 3 up to one-loop order. For all the above mentioned cases, the correspondent depletion interaction potentials, the depletion forces and the forces which exert the phantom ideal ring polymers and the ring polymers with the EVI on the walls were calculated, respectively. The obtained results indicate that the phantom ideal ring polymer chains and the ring polymer chains with the EVI due to the complexity of chain topology and because of the entropical reason demonstrate completely different behaviour in confined geometries than linear polymer chains. For example, the phantom ideal ring polymers prefer to escape from the space not only between two repulsive walls but also in the case of two inert walls, which leads to the attractive depletion forces. The ring polymer chains with less complex knot types (with the bigger radius of gyration) in a ring topology in the wide slit region exert higher forces on the confining repulsive walls. The depletion force in the case of mixed boundary conditions becomes repulsive in contrast to the case of linear polymer chains.

Investigation of ring polymers in confined geometries

The investigation of a dilute solution of phantom ideal ring polymers and ring polymers with excluded volume interaction (EVI) in a good solvent confined in a slit geometry of two parallel repulsive walls and in a solution of colloidal particles of big size were performed. Taking into account the correspondence between the field theoretical ϕ4 O(n)-vector model in the limit n → 0 and the behavior of long-flexible polymers, the depletion forces and the forces which exert phantom ideal ring and ring polymer with EVI on the walls were obtained in the framework of the massive field theory approach at fixed space dimensions d=3 up to one-loop order. Additionally, the investigation of a dilute solution of phantom ideal ring polymers in the slit geometry of two inert walls and mixed walls with one repulsive and one inert wall were performed. Taking into account the Derjaguin approximation the depletion forces between big colloidal particle and a wall as well as between two big colloidal particles were calculated. The obtained results give possibility to understand the complexity of physical effects arising from confinement and chain topology and can find practical application in new types of micro- and nano-electromechanical devices.

Capillary Nematization of Semiflexible Polymers

Semiflexible polymers under good solvent conditions confined by two planar parallel repulsive walls are investigated for a wide range of monomer concentrations and distances between the walls, for a case where persistence length and contour length of the macromolecules are almost equal. Chain conformations and local nematic ordering near the walls are studied by both molecular dynamics methods and density functional theory, putting it in perspective with the recent work where the isotropic phase of semiflexible polymer solutions in the vicinity of a single repulsive wall in semi‐infinite geometry is considered. Profiles of the total density of monomers as well as densities of end‐ and middle‐monomers and also the local orientational order parameter across the slit are computed. For small distances between the walls, the increase of monomer density causes a gradual onset of nematic order without a sharp transition while for large distances between the walls a first‐order “capillary nematization” transition is found at a monomer concentration somewhat smaller than needed for the onset of nematic order in the bulk. A brief comparison with related treatments for other models is made.image

Hydrodynamic mechanisms of spinodal decomposition in confined colloid-polymer mixtures: A multiparticle collision dynamics study

A multiscale model for a colloid-polymer mixture is developed. The colloids are described as point particles interacting with each other and with the polymers with strongly repulsive potentials, while polymers interact with each other with a softer potential. The fluid in the suspension is taken into account by the multiparticle collision dynamics method (MPC). Considering a slit geometry where the suspension is confined between parallel repulsive walls, different possibilities for the hydrodynamic boundary conditions (b.c.) at the walls (slip versus stick) are treated. Quenching experiments are considered, where the system volume is suddenly reduced (keeping the density of the solvent fluid constant, while the colloid and polymer particle numbers are kept constant) and thus an initially homogeneous system is quenched deeply into the miscibility gap, where it is unstable. For various relative concentrations of colloids and polymers, the time evolution of the growing colloid-rich and polymer-rich domains are studied by molecular dynamics simulation, taking hydrodynamic effects mediated by the solvent into account via MPC. It is found that the domain size [script-l](d)(t) grows with time t as [script-l](d)(t) [proportionality] t(1/3) for stick and (at late stages) as [script-l](d)(t) [proportionality] t(2/3) for slip b.c., while break-up of percolating structures can cause a transient "arrest" of growth. While these findings apply for films that are 5-10 colloid diameters wide, for ultrathin films (1.5 colloid diameters wide) a regime with [script-l](d)(t) [proportionality] t(1/2) is also identified for rather shallow quenches.

Star polymers confined in a nanoslit: a simulation test of scaling and self-consistent field theories

The free energy cost of confining a star polymer where f flexible polymer chains containing N monomeric units are tethered to a central unit in a slit with two parallel repulsive walls a distance D apart is considered, for good solvent conditions. Also the parallel and perpendicular components of the gyration radius of the star polymer, and the monomer density profile across the slit are obtained. Theoretical descriptions via Flory theory and scaling treatments are outlined, and compared to numerical self-consistent field calculations (applying the Scheutjens–Fleer lattice theory) and to Molecular Dynamics results for a bead-spring model. It is shown that Flory theory and self-consistent field (SCF) theory yield the correct scaling of the parallel linear dimension of the star with N, f and D, but cannot be used for estimating the free energy cost reliably. We demonstrate that the same problem occurs already for the confinement of chains in cylindrical tubes. We also briefly discuss the problem of a free or grafted star polymer interacting with a single wall, and show that the dependence of confining force on the functionality of the star is different for a star confined in a nanoslit and a star interacting with a single wall, which is due to the absence of a symmetry plane in the latter case.

Monomer density profiles of real polymer chains in confined geometries

The universal density–force relation is analyzed and the correspondent universal amplitude ratio B real is obtained using the massive field theory approach in fixed space dimensions d = 3 up to one-loop order. The layer monomer density profiles of ideal chains and real polymer chains with excluded volume interaction in a good solvent between two parallel repulsive walls, one inert and one repulsive wall and for the case of wall and a mesoscopic spherical particle of a big radius are obtained using the massive field theory approach up to one-loop order. The last mentioned situation is analyzed for both cases when wall and particle are repulsive and for the mixed case of repulsive wall and inert particle. Besides, the layer monomer density profiles of polymer chains with one end fixed at the surface and other free are analyzed near the repulsive and inert wall up to two-loop order. The obtained results are in qualitative agreement with previous theoretical investigations and with the results of Monte Carlo simulations.

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

Taking into account the well known correspondence between the field theoretical ϕ(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.

Polymer chains in confined geometries: Massive field theory approach

The massive field theory approach in fixed space dimensions d<4 is applied to investigate a dilute solution of long-flexible polymer chains in a good solvent between two parallel repulsive walls, two inert walls, and for the mixed case of one inert and one repulsive wall. The well-known correspondence between the field theoretical phi4 O(n) -vector model in the limit n-->0 and the behavior of long-flexible polymer chains in a good solvent is used to calculate the depletion interaction potential and the depletion force up to one-loop order. In order to make the theory UV finite in renormalization-group sense in 3<or=d<4 dimensions we performed the standard mass renormalization and additional surface-enhancement constants renormalization. Besides, our investigations include modification of renormalization scheme for the case of two inert walls. The obtained results confirm that the depletion interaction potential and the resulting depletion force between two repulsive walls are weaker for chains with excluded volume interaction (EVI) than for ideal chains because the EVI effectively reduces the depletion effect near the walls. Our results are in qualitative agreement with previous theoretical investigations, experimental results, and with the results of Monte Carlo simulations.

Soft colloids driven and sheared by traveling wave fields

We study the dynamics of soft colloids interacting via a Gaussian pair potential in an external moving potential which is periodic in the spatial coordinate of the direction of motion. Both dynamical density functional theory and Brownian dynamics computer simulations are used to predict the steady-state density profiles. Two different situations are investigated: the first corresponds to a light wave that travels with a constant velocity v through the quiescent solvent containing the colloidal suspension. The second setup consists of two parallel repulsive walls with a periodic topographical substructure. One of the walls is at rest relative to the solvent while the other is in motion, inducing a shearing of the suspension. In the first case, we find that the amplitude of the steady-state density behaves nonmonotonically with the traveling speed v of the wave if the shape of the wave contains an edge: for increasing v , it first grows and then decreases. In the second setup we show that a strongly confined suspension induces a shear resistance which is a nonmonotonic function of the wall velocity. These effects are verifiable in real-space experiments on colloidal suspensions exposed to external laser-optical fields. In both situations, the dynamical density functional theory is in good agreement with the Brownian dynamics simulation data.

Polymer depletion interaction between two parallel repulsive walls.

The depletion interaction between two parallel repulsive walls confining a dilute solution of long and flexible polymer chains is studied by field-theoretic methods. Special attention is paid to self-avoidance between chain monomers relevant for polymers in a good solvent. Our direct approach avoids the mapping of the actual polymer chains on effective hard or soft spheres. We compare our results with recent Monte Carlo simulations [A. Milchev and K. Binder, Eur. Phys. J. B 3, 477 (1998)] and with experimental results for the depletion interaction between a spherical colloidal particle and a planar wall in a dilute solution of nonionic polymers [D. Rudhardt, C. Bechinger, and P. Leiderer, Phys. Rev. Lett. 81, 1330 (1998)].

A polymer chain trapped between two parallel repulsive walls: A Monte-Carlo test of scaling behavior

An off-lattice bead-spring model of a polymer chain trapped between two parallel walls a distance D apart is studied by Monte-Carlo methods, using chain lengths N in the range $$32 \le N \le 512$$ and distances D from 4 to 32 (in units of the maximum spring extension). The scaling behavior of the coil linear dimensions parallel to the plates and of the force on the walls is studied and discussed with the help of current theoretical predictions. Also the density profiles of the monomers across the slit are obtained and it is shown that the predicted variation with the distance z from a wall, $$\rho (z) \propto {z^{1/\nu }}$$ , is obtained only when one introduces an extrapolation length λ in the description, $$\rho (z) \propto {[(z + \lambda )/D]^{1/\nu }}$$ , with $$\lambda \approx 0.35$$ . An analogous result is also obtained for Gaussian chains (where $$1/\nu = 2$$ ).

A polymer chain trapped between two parallel repulsive walls: A Monte-Carlo test of scaling behavior

A polymer chain trapped between two parallel repulsive walls: A Monte-Carlo test of scaling behavior

Scaling of confined membranes and interfaces

We have carried out Monte Carlo studies of the probability distribution functions (PDFS) for models of two- and three-dimensional membranes and interfaces confined between two parallel repulsive walls separated by a distance D. For two-dimensional interfaces it is known that the position PDF p(z), for conformally mapped binding potentials, scales and is characterized by a universal scaling function p(z) approximately sin pi z/Dtheta -1 (where theta is the short distance expansion critical exponent) for strong, weak and intermediate fluctuation regimes. Our simulation studies show that for a variety of membrane models the PDF has the expected scaling p(z)=U(z/D)/D, and we find that the same parametrization of the membrane PDFs gives an excellent fit to the numerical data.

Characterization of diffusive motion in anisotropic liquid systems

The translational motion of atoms in a liquid confined between two plane parallel repulsive walls is studied by computer simulation. It is shown that the motion perpendicular to the walls cannot be described in a strict sense by the conventional diffusion equation even if the diffusion constant is generalized to a space dependent diffusion tensor. Instead, for the anisotropic case, a system of linear coupled rate equations is proposed, whose time-independent rate transition matrix is shown to be necessarily spatially asymmetric, with the equilibrium mean static density as its zero eigenvalue eigenvector. This accurately describes the transverse atomic motion for times considerably larger than the velocity autocorrelation time without the need to empirically input the mean static density. This theory is tested by computer simulation and found within statistical error to be a valid quasi-microscopic description of the (slower) stochastic atomic motion. The evolution of the anisotropic self-diffusion propagators towards the quasi-periodic mean density profile is studied in detail as a function of the initial starting position.