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 repulsive and one inert wall are obtained. Besides, taking into account the Derjaguin approximation the layer monomer density profiles for dilute polymer solution confined in semi-infinite space containing mesoscopic spherical particle of big radius are calculated. 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. The obtained results are in good agreement with previous theoretical results and with the results of Monte Carlo simulations.
We present results from molecular dynamics simulations of a spherically confined neutral polymer in the presence of crowding agents, studying polymer shapes and conformations as a function of the confining potential, solvent quality and the density of crowders. The conformations of the polymer under good solvent conditions are largely independent of crowder density, even when the polymer is strongly confined. However, for poor solvents and attractive walls, the polymer shows a transition between an adsorbed extended state to a globular conformation on the surface as a function of crowder parti…
Nano-scale confinement of polymer in cone-shaped geometries occurs in many experimental situations. A flexible polymer confined in a cone-shaped nano-channel is studied theoretically and using molecular dynamics simulations. Distribution of the monomers inside the channel, configuration of the confined polymer, entropic force acting on the polymer, and their dependence on the channel and the polymer parameters are investigated. The theory and the simulation results are in very good agreement. The entropic force on the polymer that results from the asymmetric shape of the channel is measured in…
Equilibration of polymer melts containing highly entangled long polymer chains in confinement or with free surfaces is a challenge for computer simulations. We approach this problem by first studying polymer melts based on the soft-sphere coarse-grained model confined between two walls with periodic boundary conditions in two directions parallel to the walls. Then we apply backmapping to reinsert the microscopic details of the underlying bead-spring model. Tuning the strength of the wall potential, the monomer density of confined polymer melts in equilibrium is kept at the bulk density even ne…
We revisit the classical problem of the behavior of an isolated linear polymer chain in confined spaces, introducing the distinction between two different confinement regimes (the {\it weak} and the {\it strong} confinement regimes, respectively). We then discuss some recent experimental findings concerning the partitioning of individual polymers into protein pores. We also generalize our study to the case of branched polymers, and study the flow-injection properties of such objects into nanoscopic pores, for which the strong confinement regime plays an important role.
We investigate condensation of a long confined chiral nematic polymer inside a spherical enclosure, mimicking condensation of DNA inside a viral capsid. The Landau-de Gennes nematic free energy {\sl Ansatz} appropriate for nematic polymers allows us to study the condensation process in detail with different boundary conditions at the enclosing wall that simulate repulsive and attractive polymer-surface interactions. Increasing the chirality, we observe a transformation of the toroidal condensate into a closed surface with an increasing genus, akin to the ordered domain formation observed in cr…
We consider an inextensible, semiflexible polymer or worm-like chain which is confined in the transverse direction by a parabolic potential and subject to a longitudinal force at the ends, so that the polymer is stretched out and backfolding is negligible. Simple analytic expressions for the partition function, valid in this regime, are obtained for chains of arbitrary length with a variety of boundary conditions at the ends. The spatial distribution of the end points or radial distribution function is also analyzed.
We consider a fully directed self-avoiding walk model on a cubic lattice to mimic the conformations of an infinitely long confined flexible polymer chain; and the confinement condition is achieved by two parallel athermal plates. The confined polymer system is under good solvent condition and we revisit this problem to solve the real polymer's model for any length of chain and also for any separation in between the plates. The equilibrium statistics of the confined polymer chain is derived using an analytical calculations based on the generating function technique. The force of the confinement…
Using Langevin dynamics simulations in three dimensions (3D), we investigate the dynamics of polymer translocation into the regions between two parallel plane walls with separation $R$ under a driving force $F$, respectively. Compared with an unconfined environment, the translocation dynamics is greatly changed due to the crowding effect of the partially translocated monomers. Translocation time $τ$ initially decreases rapidly with increasing $R$ and then saturates for larger $R$, and the confined environment leads to a nonuniversal dependence of $τ$ on $F$.
Using self-consistent field and density-functional theories, we first investigate colloidal self-assembling of colloid/polymer films confined between two soft surfaces grafted by polymers. With the increase of colloidal concentrations, the film undergoes a series of transitions from disordered liquid $\to$ sparse square $\to$ hexagonal (or mixed square-hexagonal) $\to$ dense square $\to$ cylindric structures in plane, which results from the competition between the entropic elasticity of polymer brushes and the steric packing effect of colloidal particles. A phase diagram displays the stable re…
Experiments using nanofluidic devices have proven effective in characterizing the physical properties of polymers confined to small cavities. Two recent studies using such methods examined the organization and dynamics of two DNA molecules in box-like cavities with strong confinement in one direction and with square and elliptical cross sections in the lateral plane. Motivated by these experiments, we employ Monte Carlo and Brownian dynamics simulations to study the physical behaviour of two polymers confined to small cavities with shapes comparable to those used in the experiments. We quantif…
We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer {\sl via} the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy {\sl ansatz} is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and …
A number of recent experiments have provided detailed observations of the configurations of long DNA strands under nano-to-micrometer sized confinement. We therefore revisit the problem of an excluded volume polymer chain confined between two parallel plates with varying plate separation. We show that the non-monotonic behavior of the overall size of the chain as a function of plate-separation, seen in computer simulations and reproduced by earlier theories, can already be predicted on the basis of scaling arguments. However, the behavior of the size in a plane parallel to the plates, a quanti…
Monte Carlo simulations are used to study the conformational properties of a folded semiflexible polymer confined to a long channel. We measure the variation in the conformational free energy with respect to the end-to-end distance of the polymer, and from these functions we extract the free energy of the hairpin fold, as well as the entropic force arising from interactions between the portions of the polymer that overlap along the channel. We consider the scaling of the free energies with respect to varying the persistence length of the polymer, as well as the channel dimensions for confineme…
Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance 1 << D << N^ν(ν= 3/4 is the Flory exponent). For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. We measure the densities of monomers and of end points as functions of the distance from the walls, the longitudinal extent of the chain, and the forces exerted on the walls. Their scaling with D and the universal ratio between force and…
From studies via Molecular Dynamics simulations, we report results on structure and dynamics in mixtures of active colloids and passive polymers that are confined inside a spherical container with a repulsive boundary. Such systems mimic the presence of bacteria in the background of bio-polymers. All interactions in the fully passive case are chosen in such a way that in equilibrium coexistence between colloid-rich and polymer-rich phases occurs. For most part of the studies the chosen compositions give rise to Janus structure; one side of the sphere is occupied by the colloids and the rest by…
Employing Molecular Dynamics simulations of a chemically realistic model of 1,4-polybutadiene between graphite walls we show that the mass exchange between layers close to the walls is a slow process already in the melt state. For the glass transition of confined polymers this process competes with the slowing down due to packing effects and intramolecular rotation barriers.
The paper presents a short overview of the theoretical, numerical and experimental works on the critical behavior of a dilute polymer solution of long-flexible polymer chains confined in semi-infinite space restricted by a surface or in a slit geometry of two parallel walls with different adsorbing or repelling properties in respect for polymers as well as in a solution of mesoscopic spherical colloidal particles of one sort or two different sorts. We discuss the application of the massive field theory approach in a fixed space dimensions d=3 up to one loop order for such topics as:(a) the inv…
We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical str…
We study the conformations of a self-avoiding polymer confined to a channel by computing the cross-sectional distributions of the positions of its monomers. By means of Monte-Carlo simulations for a self-avoiding, freely-jointed chain we determine how the cross-sectional distribution for a given monomer depends on its location in the polymer, and how strongly this distribution is affected by self avoidance. To this end we analyze how the frequency of intra-chain collisions between monomers depends on their spatial position in the channel and on their location within the polymer. We show that m…
A theoretical study on the phase behaviors of a polymer solution confined between two coaxial cylindrical walls is presented. For the case of a neutral inner cylinder, the spinodal point derived through the Gaussian fluctuation theory is confinement-independent because of the existence of a free dimension in the system. The kinetic analysis indicates that the fluctuation modes always have a component of a plane wave along the axial direction, which can lead to the formation of a periodic-like concentration pattern. On the other hand, the equilibrium structure of the system is obtained by using…
This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the interaction of defects with the underlying curvature. This chapter concludes with two cases of three-dimensional nematic phases confined to spaces with curved boundaries, namely a torus and a spherical shell.
We study the dynamics of a knot in a semiflexible polymer confined to a narrow channel of width comparable to the polymers' persistence length. Using a combination of Brownian dynamics simulations and a coarse-grained stochastic model, we characterize the coupled dynamics of knot size variation and knot diffusion along the polymer, which ultimately leads to spontaneous unknotting. We find that the knot grows to macroscopic size before disappearing. Interestingly, an external force applied to the ends of the confined polymer speeds up spontaneous unknotting.
An analytic expression is derived for the distribution $G(\vec{R})$ of the end-to-end distance $\vec{R}$ of semiflexible polymers in external potentials to elucidate the effect of confinement on the mechanical and statistical properties of biomolecules. For parabolic confinement the result is exact whereas for realistic potentials a self-consistent ansatz is developed, so that $G(\vec{R})$ is given explicitly even for hard wall confinement. The theoretical result is in excellent quantitative agreement with fluorescence microscopy data for actin filaments confined in rectangularly shaped microc…
We consider a long, semiflexible polymer, with persistence length $P$ and contour length $L$, fluctuating in a narrow cylindrical channel of diameter $D$. In the regime $D\ll P\ll L$ the free energy of confinement $ΔF$ and the length of the channel $R_\parallel$ occupied by the polymer are given by Odijk's relations $ΔF/R_\parallel=A_\circ k_BTP^{-1/3}D^{-2/3}$ and $R_\parallel=L[1-α_\circ(D/P)^{2/3}]$, where $A_\circ$ and $α_\circ$ are dimensionless amplitudes. Using a simulation algorithm inspired by PERM (Pruned Enriched Rosenbluth Method), which yields results for very long polymers, we de…
We have examined the behaviors of a knotted linear polymer in narrow tubes using Langevin dynamics simulation to investigate the knot localization property in one-dimensional (1D) geometry. We have found that the knot is strongly localized in such a geometry. By observing the distribution function of the size of localized knot, we found the scaling behavior of the fluctuation around the most probable size with radius of confinement. Based on the analysis of the probability distribution of the knot size, we show that the strong localization behavior and the fluctuation around the most probable …
Diffusion properties of a self-avoiding polymer embedded in regularly distributed obstacles with spacing a=20 and confined in two dimensions is studied numerically using the extended bond fluctuation method which we have developed recently. We have observed for the first time to our knowledge, that the mean square displacement of a center monomer $ϕ_{M/2}(t)$ exhibits four dynamical regimes, i.e., $ϕ_{M/2}(t) \sim t^{ν_m}$ with $ν_m\sim 0.6$, 3/8, 3/4, and 1 from the shortest to longest time regimes. The exponents in the second and third regimes are well described by segmental diffusion in the…
We show that the problem of describing the conformations of a semiflexible polymer confined to a channel can be mapped onto an exactly solvable model in the so-called extended de Gennes regime. This regime (where the polymer is neither weakly nor strongly confined) has recently been studied intensively experimentally and by means of computer simulations. The exact solution predicts precisely how the conformational fluctuations depend upon the channel width and upon the microscopic parameters characterising the physical properties of the polymer.
We investigate the influence of confinement on phase separation in colloid-polymer mixtures. To describe the particle interactions, the colloid-polymer model of Asakura and Oosawa [J. Chem. Phys. 22, 1255 (1954)] is used. Grand canonical Monte Carlo simulations are then applied to this model confined between two parallel hard walls, separated by a distance D=5 colloid diameters. We focus on the critical regime of the phase separation and look for signs of crossover from three-dimensional (3D) Ising to two-dimensional (2D) Ising universality. To extract the critical behavior, finite size scalin…
We present molecular dynamics friction calculations for confined hydrocarbon solids with molecular lengths from 20 to 1400 carbon atoms. Two cases are considered: (a) polymer sliding against a hard substrate, and (b) polymer sliding on polymer. We discuss the velocity dependence of the frictional shear stress for both cases. In our simulations, the polymer films are very thin (approx. 3 nm), and the solid walls are connected to a thermostat at a short distance from the polymer slab. Under these circumstances we find that frictional heating effects are not important, and the effective temperatu…
Polymer systems in slab geometries are studied on the basis of the recently presented Gaussian Ellipsoid Model [J. Chem. Phys. 114, 7655 (2001)].The potential of the confining walls has an exponential shape. For homogeneous systems in thermodynamic equilibrium we discuss density, orientation and deformation profiles of the polymers close to the walls. For strongly segregated mixtures of polymer components A and B equilibrium profiles are studied near a planar interface separating A and B rich regions. Spinodal decomposition processes of the mixtures in the presence of neutral walls show upon s…
We report on the linear viscoelastic properties of mixtures comprising multiarm star (as model soft colloids) and long linear chain homopolymers in a good solvent. In contrast to earlier works, we investigated symmetric mixtures (with a size ratio of 1) and showed that the polymeric and colloidal responses can be decoupled. The adopted experimental protocol involved probing the linear chain dynamics in different star environments. To this end, we studied mixtures with different star mass fraction, which was kept constant while linear chains were added and their entanglement plateau modulus ($G…
Polymers confined to a narrow channel are subject to strong entropic forces that tend to drive the molecules apart. In this study, we use Monte Carlo computer simulations to study the segregation behavior of two flexible hard-sphere polymers under confinement in a cylindrical channel. We focus on the effects of using polymers of different lengths. We measure the variation of the conformational free energy, $F$, with the center-of-mass separation distance, $λ$. The simulations reveal four different separation regimes, characterized by different scaling properties of the free energy with respect…
We identify problems with the standard complex order parameter formalism for smectic-A (SmA) liquid crystals, and discuss possible alternative descriptions of smectic order. In particular, we suggest an approach based on the real smectic density variation rather than a complex order parameter. This approach gives reasonable numerical results for the smectic layer configuration and director field in sample geometries, and can be used to model smectic liquid crystals under nanoscale confinement for technological applications.
The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: The force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational chan…
The deformation and break-up of Newtonian/viscoelastic droplets are studied in confined shear flow. Our numerical approach is based on a combination of Lattice-Boltzmann models (LBM) and finite difference schemes, the former used to model two immiscible fluids with variable viscous ratio, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). We quantify the droplet response by changing the polymer relaxation time $τ…
We study structural properties of a ring polymeric melt confined in a film in comparison to a linear counterpart using molecular dynamics simulations. Local structure orderings of ring and linear polymers in the vicinity of the surface are similar to each other because the length scale of surface-monomer excluded volume interaction is smaller than the size of an ideal blob of the ring. In a long length scale, while the Silberberg hypothesis can be used to provide a physical origin of confined linear polymer results, it no longer holds for a ring polymer case. We also present different structur…
Shape transformations of hairy nanoparticles under confinement are studied using molecular dynamic simulations. We discuss the behavior of these particles in slits with inert or attractive walls. We assume that only chain-wall interactions are attractive. The impact of the strength of interactions with the walls and the width of the slits on the particle configuration is shown. In the case of attractive surfaces, we found new structures in which the chains are connected with both walls and form bridges between them: pillars, symmetrical and asymmetrical spools, and hourglasses. In wide pores w…
The longitudinal response of single semiflexible polymers to sudden changes in externally applied forces is known to be controlled by the propagation and relaxation of backbone tension. Under many experimental circumstances, realized, e.g., in nano-fluidic devices or in polymeric networks or solutions, these polymers are effectively confined in a channel- or tube-like geometry. By means of heuristic scaling laws and rigorous analytical theory, we analyze the tension dynamics of confined semiflexible polymers for various generic experimental setups. It turns out that in contrast to the well-kno…
We analyze static properties of a strongly confined semiflexible polymer, i.e. either trapped in a closed space or compressed by external forces, in an athermal solvent. Like a flexible polymer case, we can resort to an analogy with the semidilute solution, but a complication due to the additional length scale arising from the chain rigidity results in more diverse behaviours depending on system parameters. For each regime, scaling forms of the excess free energy of the confinement are derived. Effects of the confinement geometry and the solvent quality are briefly discussed.
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…
The spreading of one- and two-component polymer nanodroplets is studied using molecular dynamics simulation in a cylindrical geometry. The droplets consist of polymer chains of length 10, 40, and 100 monomers per chain described by the bead-spring model spreading on a flat surface with a surface-coupled Langevin thermostat. Each droplet contains ~350,000 monomers. The dynamics of the individual components of each droplet are analyzed and compared to the dynamics of single component droplets for the spreading rates of the precursor foot and bulk croplet, the time evolution of the contact angle,…
Single three dimensional polymers confined to a slab, i.e. to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by $N$-step walks on a simple cubic lattice confined to the region $1 \le z \le D$. The simulations cover both regions $D << R_F$ and $D >> R_F$ (where $R_F \sim N^ν$ is the Flory radius, with $ν\approx 0.587$), as well as the cross-over region in between. Chain lengths are up to $N=80,000$, slab widths up to D=120. In order to test the analysis program and to check for finite size corrections, we actually studied three different …
Using Gibbs ensemble Monte Carlo simulations and density functional theory we investigate the fluid-fluid demixing transition in inhomogeneous colloid-polymer mixtures confined between two parallel plates with separation distances between one and ten colloid diameters covering the complete range from quasi two-dimensional to bulk-like behavior. We use the Asakura-Oosawa-Vrij model in which colloid-colloid and colloid-polymer interactions are hard-sphere like, whilst the pair potential between polymers vanishes. Two different types of confinement induced by a pair of parallel walls are consider…
We investigate the motion of two overlapping polymers with self-avoidance confined in a narrow 2d box. A statistical model is constructed using blob free-energy arguments. We find spontaneous segregation under the condition: $L > R_{//}$, and mixing under $L < R_{//}$, where L is the length of the box, and $R_{//}$ the polymer extension in an infinite slit. Segregation time scales are determined by solving a mean first-passage time problem, and by performing Monte Carlo simulations. Predictions of the two methods show good agreement. Our results may elucidate a driving force for chromosomes se…
We employ computer simulations and thermodynamic integration to analyse the effects of bending rigidity and slit confinement on the free energy cost of tying knots, $ΔF_{\rm knotting}$, on polymer chains under tension. A tension-dependent, non-zero optimal stiffness $κ_{\rm min}$ exists, for which $ΔF_{\rm knotting}$ is minimal. For a polymer chain with several stiffness domains, each containing a large amount of monomers, the domain with stiffness $κ_{\rm min}$ will be preferred by the knot. A {\it local} analysis of the bending in the interior of the knot reveals that local stretching of cha…
Two-dimensional nematics possess peculiar properties that have been studied recently using computer simulation and various theoretical models. Here we review our own contribution to the field using density-functional theory, and present some preliminary simulation results on confined two-dimensional nematics. First we discuss the possible stable bulk phases and phase diagrams and the relation between phases and particle geometry. We then explore the adsorption properties on a single substrate and the confinement effects that arise when the fluid is confined between parallel walls. Next, confin…
We investigate the conformations of a semiflexible polymer confined to a square box. Results of Monte Carlo simulations show the existence of a shape transition when the persistence length of the polymer becomes comparable to the dimensions of box. An order parameter is introduced to quantify this behavior. A simple mean-field model is constructed to study the effect of the shape transition on the effective persistence length of the polymer.
Theoretical results for the extension of a polymer confined to a channel are usually derived in the limit of infinite contour length. But experimental studies and simulations of DNA molecules confined to nanochannels are not necessarily in this asymptotic limit. We calculate the statistics of the span and the end-to-end distance of a semiflexible polymer of finite length in the extended de Gennes regime, exploiting the fact that the problem can be mapped to a one-dimensional weakly self-avoiding random walk. The results thus obtained compare favourably with pruned-enriched Rosenbluth method (P…
If a semiflexible polymer confined to a narrow channel bends around by 180 degrees, the polymer is said to exhibit a hairpin. The equilibrium extension statistics of the confined polymer are well understood when hairpins are vanishingly rare or when they are plentiful. Here we analyze the extension statistics in the intermediate situation via experiments with DNA coated by the protein RecA, which enhances the stiffness of the DNA molecule by approximately one order of magnitude. We find that the extension distribution is highly non-Gaussian, in good agreement with Monte Carlo simulations of co…
Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. When these systems are confined their structural properties change. To understand these changes we study random close packing in finite-sized confined systems, in both two and three dimensions. Each packing consists of a 50-50 binary mixture with particle size ratio 1.4. The presence of confining walls significantly lowers the overall maximum area fraction (or volume fraction in three dimensions). A simple model is pres…
Phase separation of colloid-polymer mixtures, described by the Asakura-Oosawa (AO) model, confined in a thin slit pore is studied by grand-canonical Monte Carlo simulation. While one wall is a hard wall for both particles, at the other wall there acts an additional repulsive potential on the colloids only. Varying the strength of this potential, a crossover from capillary condensation to an interface localization transition is found. The latter occurs under conditions where in the bulk almost complete phase separation has occurred.
We investigate the pseudo-Casimir force in a slab of material composed of nematically ordered long polymers. We write the total mesoscopic energy together with the constraint connecting the local density and director fluctuations and evaluate the corresponding fluctuation free energy by standard methods. It leads to a pseudo-Casimir force of a different type than in the case of standard, short molecule nematic. We investigate its separation dependence and its magnitude and explicitly derive the relevant limiting cases.
In both nature and engineering, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We use the discrete element method to investigate the stress distribution developed within the granular packing as a result of compaction due to the displacement of a rigid piston. We observe that the stress within the packing increases exponentially with the length of accumulated grains, and show an extension to current analytic models which fits the measured st…
Motivated by recent experiments on the rod-like virus bacteriophage fd, confined to circular and annular domains, we present a theoretical study of structural transitions in these geometries. Using the continuum theory of nematic liquid crystals, we examine the competition between bulk elasticity and surface anchoring, mediated by the formation of topological defects. We show analytically that bulk defects are unstable with respect to defects sitting at the boundary. Moreover, in case of an annulus, whose topology does not require the presence of topological defects, under weak anchoring condi…
Hydrodynamic forces may significantly affect the motion of polymers. In sheet-like cavities, such as the cell's cytoplasm and microfluidic channels, the hydrodynamic forces are long-range. It is therefore expected that that hydrodynamic interactions will dominate the motion of polymers in sheets and will be manifested by Zimm-like scaling. Quite the opposite, we note here that although the hydrodynamic forces are long-range their overall effect on the motion of polymers vanishes due to the symmetry of the two-dimensional flow. As a result, the predicted scaling of experimental observables such…
