The inherent structure landscape for a system of hard spheres confined to a hard cylindrical channel, such that spheres can only contact their first and second neighbours, is studied using an analytical model that extends previous results [Phys. Rev. Lett. 115, 025702 (2015)] to provide a comprehensive picture of jammed packings over a range of packing densities. In the model, a packing is described as an arrangement of $k$ helical sections, separated by defects, that have alternating helical twist directions and where all spheres satisfy local jamming constraints. The structure of each helical section is determined by a single helical twist angle, and a jammed packing is obtained by minimizing the length of the channel per particle with respect to the $k$ helical section angles. An analysis of a small system of $N=20$ spheres shows that the basins on the inherent structure landscape associated with these helical arrangements split into a number of distinct jammed states separated by low barriers giving rise to a degree of hierarchical organization. The model accurately predicts the geometric properties of packings generated using the Lubachevsky and Stillinger compression scheme ($N=10^4$) and provides insight into the nature of the probability distribution of helical section lengths.
An exact description of the complete jamming landscape is developed for a system of hard discs of diameter $σ$, confined between two lines separated by a distance $1+\sqrt{3/4} < H/σ< 2$. By considering all possible local packing arrangements, the generalized ensemble partition function of jammed states is obtained using the transfer matrix method, which allows us to calculate the configurational entropy and the equation of state for the packings. Exploring the relationship between structural order and packing density, we find that the geometric frustration between local packing environments p…
We use numerical modelling to study the flow patterns of an active nematic confined in a cylindrical capillary, considering both planar and homeotropic boundary conditions. We find that active flow emerges not only along the capillary axis but also within the plane of the capillary, where radial vortices are formed. If topological defects are imposed by the boundary conditions, they act as local pumps driving the flow. At higher activity we demonstrate escape of the active defects and flow into the third dimension, indicating the importance of dimensionality in active materials. We argue that …
We derive, from the dimensional cross-over criterion, a fundamental-measure density functional for parallel hard curved rectangles moving on a cylindrical surface. We derive it from the density functional of circular arcs of length $σ$ with centers of mass located on an external circumference of radius $R_0$. The latter functional in turns is obtained from the corresponding 2D functional for a fluid of hard discs of radius $R$ on a flat surface with centers of mass confined onto a circumference of radius $R_0$. Thus the curved length of closest approach between two centers of mass of hard disc…
By evaporating a drop of lipid dispersion we generate the myelin morphology often seen in dissolving surfactant powders. We explain these puzzling nonequilibrium structures using a geometric argument: The bilayer repeat spacing increases and thus the repulsion between bilayers decreases when a multilamellar disk is converted into a myelin without gain or loss of material and with number of bilayers unchanged. Sufficient reduction in bilayer repulsion can compensate for the cost in curvature energy, leading to a net stability of the myelin structure. A numerical estimate predicts the degree of …
We present a neutron scattering analysis of the density and the static structure factor of confined methanol at various temperatures. Confinement is performed in the cylindrical pores of MCM-41 silicates with pore diameters D=24 angstrom and D=35 angstrom. A change of the thermal expansivity of confined methanol at low temperature is the signature of a glass transition, which occurs at higher temperature for the smallest pore. This is an evidence of a surface induced slowing down of the dynamics of the fluid. The structure factor presents a systematic evolution with the pore diameter, which ha…
Manipulating the self-assembly nanostructures with combined different control measures is emerging as a promising route for numerous applications to generate templates and scaffolds for nanostructured materials. Here, the two different control measures are a cylindrical confinement and an oscillatory shear flow. We study the phase behavior of diblock copolymer confined in nanopore under oscillatory shear by considering different $D/L_0$ ($D$ is the diameter of the cylindrical nanopore, $L_0$ is the domain spacing) and different shears via Cell Dynamics Simulation. Under different $D/L_0$, in t…
The complexity and unpredictability of postbuckling responses in even simple thin shells have raised great challenges to emerging technologies exploiting buckling transitions. Here we comprehensively survey the buckling landscapes to show the full complexity of the stable buckling states and the transition mechanisms between each of them. This is achieved by combining a simple and versatile triangulated lattice model for modelling the shell morphologies with efficient high-dimensional free-energy minimisation and transition path finding algorithms. We show how the simple free energy landscapes…
We derive an unbiased information theoretic energy landscape for chromosomes at metaphase using a maximum entropy approach that accurately reproduces the details of the experimentally measured pair-wise contact probabilities between genomic loci. Dynamical simulations using this landscape lead to cylindrical, helically twisted structures reflecting liquid crystalline order. These structures are similar to those arising from a generic ideal homogenized chromosome energy landscape. The helical twist can be either right or left handed so chiral symmetry is broken spontaneously. The ideal chromoso…
Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology $3_1$, $4_1$, or $5_1$, as well as unknotted polymers that are capable of forming S-loops. We measure the variation of the free energy $F$ with the end-to-end polymer extension length $X$ and examine the effect of varying the polymer topology, persistence length $P$ and cyl…
Phyllotactic states are regular lattice-like structures on cylinders and are a botanical classification scheme. In this communication, we report a sequence of transitions between phyllotactic states for particles with a repulsive particle-particle interaction on a cylindrical geometry at zero temperature. We can infer the transition points as a function of density via Monte Carlo simulations, as well as the mathematical descriptions of the ground states. The lattices we generate are described as phyllotactic states that fit onto the cylindrical surface as a set of helical chains. Our analysis …
Using novel micro-printing techniques, we develop a versatile experimental setup that allows us to study how lateral confinement tames the active flows and defect properties of the microtubule/kinesin active nematic system. We demonstrate that the active length scale that determines the self-organization of this system in unconstrained geometries loses its relevance under strong lateral confinement. Dramatic transitions are observed from chaotic to vortex lattices and defect-free unidirectional flows. Defects, which determine the active flow behavior, are created and annihilated on the channel…
The behavior of confined cylindrical micelle-forming surfactants under the influence of shear has been investigated using Monte Carlo simulations. The surfactants are modeled as coarse-grained lattice polymers, while the Monte Carlo shear flow is implemented with an externally imposed potential energy field which induces a linear drag velocity on the surfactants. It is shown that in the absence of shear, cylindrical micelles confined within a monolayer coarsen gradually with Monte Carlo "time" t, the persistence length of the micelles scaling as t^{0.24}, in agreement with the scaling obtained…
The orientational and translational order of a thermotropic ferroelectric liquid crystal (2MBOCBC) imbibed in self-organized, parallel, cylindrical pores with radii of 10, 15, or 20 nm in anodic aluminium oxide monoliths (AAO) are explored by high-resolution linear and circular optical birefringence as well as neutron diffraction texture analysis. The results are compared to experiments on the bulk system. The native oxidic pore walls do not provide a stable smectogen wall anchoring. By contrast, a polymeric wall grafting enforcing planar molecular anchoring results in a thermal-history indepe…
We investigate a longitudinally loaded elastic nanorod inside a cylindrical channel and show within the context of classical elasticity theory that the Euler buckling instability leads to a helical postbuckling form of the rod within the channel. The local pitch of the confined helix changes along the channel and so does the longitudinal force transmitted along the rod, diminishing away from the loaded end. This creates a possibility of jamming of the nanorod within the channel.
Molecular Dynamics simulations of water molecules in nanometre sized cylindrical channels connecting two reservoirs show that the permeation of water is very sensitive to the channel radius and to electric polarization of the embedding material. At threshold, the permeation is {\emph{intermittent}} on a nanosecond timescale, and strongly enhanced by the presence of an ion inside the channel, providing a possible mechanism for gating. Confined water remains surprisingly fluid and bulk-like. Its behaviour differs strikingly from that of a reference Lennard-Jones fluid, which tends to contract in…
We extensively study the phase diagram of a diblock copolymer melt confined in a cylindrical nanopore using real-space self-consistent mean-field theory. We discover a rich variety of new two-dimensional equilibrium structures that have no analog in the unconfined system. These include non-hexagonally coordinated cylinder phases and structures intermediate between lamellae and cylinders. We map the stability regions and phase boundaries for all the structures we find. As the pore radius is decreased, the pore accommodates fewer cylindrical domains and structural transitions occur as cylinders …
The effect of cylindrical confinement on the phase behaviour of a system of parallel hard rods is studied using Onsager's second virial theory. The hard rods are represented as hard cylinders of diameter $D$ and length $L$, while the cylindrical pore is infinite with diameter $W$. The interaction between the wall and the rods is hard repulsive, and it is assumed that molecules are parallel to the surface of the pore (planar anchoring). In very narrow pores ($D<W<2 D$), the structure is homogeneous and the system behaves as a one-dimensional Tonks gas. For wider pores, inhomogeneous fluid struc…
We explore the optical birefringence of the nematic binary mixtures 6CB$_{1-x}$7CB$_x$ ($0~\le~x~\le~1$) imbibed into parallel-aligned nanochannels of mesoporous alumina and silica membranes for channel radii of $3.4~\le~R~\le 21.0$ nm. The results are compared with the bulk behavior and analyzed with a Landau-de-Gennes model. Depending on the channel radius the nematic ordering in the cylindrical nanochannels evolves either discontinuously (subcritical regime, nematic ordering field $σ<1/2$) or continuously (overcritical regime, $σ>1/2$), but in both cases with a characteristic paranematic pr…
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…
We use a series of molecular dynamics simulations, and analytical theory, to demonstrate that a system of hard spheres confined to a narrow cylindrical channel exhibits a continuous phase transition from an isotropic fluid at low densities, to an orientationally ordered, but translationally disordered, helical fluid at high densities. The ordered fluid phase contains small sections of helix separated by topological defects that change the direction of the twist, altering the local chirailty. The defects break up the translational order, but the fluid develops long range orientational order. An…
We show that a system of hard discs confined to a narrow channel exhibits a fragile-strong fluid crossover located at the maximum of the isobaric heat capacity and that the relaxation times for different channel widths fall onto a single master curve when rescaled by the relaxation times and temperatures of the crossover. Calculations of the configurational entropy and the inherent structure equation of state find that the crossover is related to properties of the jamming landscape for the model but that the Adams-Gibbs relation does not predict the relaxation behavior. We also show that a fac…
We use virial series to study the equilibrium properties of confined soft-spheres fluids interacting through the inverse-power potentials. The confinement is induced by hard walls with planar, spherical and cylindrical shapes. We evaluate analytically the coefficients of order two in density of the wall-fluid surface tension $γ$ and analyze the curvature contributions to the free energy. Emphasis is in bending and Gaussian rigidities, which are found analytically at order two in density. Their contribution to $γ(R)$ and the accuracy of different truncation procedures to the low curvature expan…
To enlighten the nature of the order-disorder and order-order transitions in block copolymer melts confined in narrow capillaries we analyze peculiarities of the conventional Landau weak crystallization theory of systems confined to cylindrical geometry. This phenomenological approach provides a quantitative classification of the cylindrical ordered morphologies by expansion of the order parameter spatial distribution into the eigenfunctions of the Laplace operator. The symmetry of the resulting ordered morphologies is shown to strongly depend both on the boundary conditions (wall preference) …
Active transport of biomolecules assisted by motor proteins is imperative for the proper functioning of cellular activities. Inspired by the diffusion of active agents in crowded cellular channels, we computationally investigate the transport of an active tracer through a polymer grafted cylindrical channel by varying the activity of the tracer and stickiness of the tracer to the polymers. Our results reveal that the passive tracer exhibits profound subdiffusion with increasing stickiness by exploring deep into the grafted polymeric zone, while purely repulsive one prefers to diffuse through t…
A line of hard spheres confined by a transverse harmonic potential, with hard walls at its ends, exhibits a variety of buckled structures as it is compressed longitudinally. Here we show that these may be conveniently observed in a rotating liquid-filled tube (originally introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274 (2017)] to assemble ordered three dimensional structures at higher compressions). The corresponding theoretical model is transparent and easily investigated numerically, as well as by analytic approximations. Hence we explore a wide range…
We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau--de Gennes framework in terms of two geometry-dependent variables: half short edge length $λ$ and aspect ratio $b$. First, we analytically prove that, for any $b$ with a small enough $λ$ or for a large enough $b$ with a fixed domain size, there is a unique stable solution that has two line defects on the opposite short edges. Second, we numerically construct solution landscapes by varying $λ$ and $b$, and report a novel X state, which emerges from …
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 investigate cage breaking in dense hard disk systems using a model of three Brownian disks confined within a circular corral. This system has a six-dimensional configuration space, but can be equivalently thought to explore a symmetric one-dimensional free energy landscape containing two energy minima separated by an energy barrier. The exact free energy landscape can be calculated as a function of system size. Results of simulations show the average time between cage breaking events follows an Arrhenius scaling when the energy barrier is large. We also discuss some of the consequences of u…
Thin elastic solids are easily deformed into a myriad of three-dimensional shapes, which may contain sharp localized structures as in a crumpled candy wrapper, or have smooth and diffuse features like the undulating edge of a flower. Anticipating and controlling these morphologies is crucial to a variety of applications involving textiles, synthetic skins, and inflatable structures. Here we show that a "wrinkle-to-crumple" transition, previously observed in specific settings, is a ubiquitous response for confined sheets. This unified picture is borne out of a suite of model experiments on poly…
A recurring motif in the organization of biological tissues are networks of long, fibrillar protein strands effectively confined to cylindrical surfaces. Often, the fibers in such curved, quasi-2D geometries adopt a characteristic order: the fibers wrap around the central axis at an angle which varies with radius and, in several cases, is strongly bimodally distributed. In this Letter, we investigate the general problem of a 2D crosslinked network of semiflexible fibers confined to a cylindrical substrate, and demonstrate that in such systems the trade-off between bending and stretching energi…
We report the results of Monte Carlo simulations of the Lebwohl--Lasher model of nematic liquid crystals confined to cylindrical cavities with homeotropic anchoring. We show that the ratio of the bulk to surface couplings is not in general equal to the corresponding parameter K/W used in elastic theory (where K is the Frank elastic constant in the one constant approximation and W is the surface anchoring strength). By measuring the temperature dependence of K/W (which is equivalent to the surface extrapolation length) we are able to reconcile the results of our simulations as well as others wi…
We have investigated PLLA crystallization in lamellae-forming PS-b-PLLA confined to straight cylindrical nanopores under weak confinement (nanopore diameter D / equilibrium PS-b-PLLA period L0 larger than 4.8). Molten PS-b-PLLA predominantly forms concentric lamellae along the nanopores, but intertwined helices occur even for D/L0 = 7.3. Quenching PS-b-PLLA melts below TG(PS) results in PLLA cold crystallization strictly confined by the vitrified PS domains. Above TG(PS), PLLA crystallization is templated by the PS-b-PLLA melt domain structure in the nanopore centers, while adsorption on the n…
We present a coarse-grained model for ionic surfactants in explicit aqueous solutions, and study by computer simulation both the impact of water content on the morphology of the system, and the consequent effect of the formed interfaces on the structural features of the adsorbed fluid. On increasing the hydration level at ambient conditions, the model exhibits a series of three distinct phases: lamellar, cylindrical and micellar. We characterize the different structures in terms of diffraction patterns and neutron scattering static structure factors. We demonstrate that the rate of variation o…
