The effect of boundary adaptivity on hexagonal ordering and bistability in circularly confined quasi hard discs

Williams, Ian H.; Oğuz, Erdal C.; Jack, Robert L.; Bartlett, Paul; Löwen, Hartmut; Royall, C. Patrick

doi:10.1063/1.4867785

Cited by 16 publications

(22 citation statements)

References 67 publications

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“…[5][6][7][8][9][10]). On the other hand, in many circumstances the experimental setup is naturally realizing the canonical ensemble [11][12][13], which easily justifies corresponding theoretical studies. For instance, important consequences of the conservation of the particle number arise concerning the structure and the phase transitions of (offcritical) fluids confined in nanoscopic pores or capillaries [14][15][16][17][18][19][20][21][22][23], which motivated the development of canonical density functional methods [24,25].…”

Section: Introductionmentioning

confidence: 65%

Critical adsorption and critical Casimir forces in the canonical ensemble

et al. 2016

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Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean field theory (MFT) based on a Ginzburg-Landau free energy functional as well as via Monte Carlo simulations of the threedimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a non-integrable divergence of the mean field order parameter (OP) profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.

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Section: Introductionmentioning

confidence: 65%

Critical adsorption and critical Casimir forces in the canonical ensemble

et al. 2016

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“…Time is scaled by the rotation period, t rot . In all but the central region, ψ 6 explores a large range, indicating that the local structure is alternately driven between highly hexagonal and disordered arrangements -rotating the boundary drives the internal structure between the two bistable configurations observed in the quiescent system [28,29]. Furthermore, in all but the central region, this occurs with some characteristic frequencyfastest in the wall-adjacent layer, and more slowly in the third and second layers.…”

Section: Mechanism Of Transmission Controlmentioning

confidence: 90%

Transmission of torque at the nanoscale

et al. 2015

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In macroscopic mechanical devices, torque is transmitted through gearwheels and clutches. In the construction of devices at the nanoscale, torque and its transmission through soft materials will be a key component. However, this regime is dominated by thermal fluctuations leading to dissipation. Here we demonstrate the principle of torque transmission for a disc-like colloidal assembly exhibiting clutch-like behaviour, driven by 27 particles in optical traps. These are translated on a circular path to form a rotating boundary that transmits torque to additional particles confined to the interior. We investigate this transmission and find that it is determined by solid-like or fluid-like behaviour of the device and a stick-slip mechanism reminiscent of macroscopic gearwheels slipping. The transmission behaviour is predominantly governed by the rotation rate of the boundary and the density of the confined system. We determine the e ciency of our device and thus optimize conditions to maximize power output.C lassical thermodynamics evolved in response to the need to understand, predict and optimize the steam engines responsible for driving the industrial revolution 1 . In contrast to these macroscopic devices, 'soft' engines at the nanoscale operate in the presence of thermal fluctuations. When the thermal energy is of the same order as the work done, these fluctuations pose a fundamental challenge and call for new design principles. Nanomachines have been studied theoretically 2 , particularly in the case of molecular motors 3,4 . Experimentally, colloidal and nanoparticle systems provide insight into fundamental thermodynamic processes in the presence of stochastic Brownian noise 5,6 . Single colloidal particles manipulated by optical forces have been used to, for example, realize the analogue of a Stirling engine 7 , to explore the nanoscopic manifestation of the second law of thermodynamics 8,9 and to emulate memory devices testing Landauer's principle for the work dissipated when erasing information 10 . The next stage is to exploit these insights from model systems to engineer devices that perform predictably in the presence of thermal fluctuations.An important step in this direction would be a microscopic gearbox or transmission system. Although rotational devices have been fabricated 11-13 , and nanoscopic gearwheels realized 14,15 , such devices are typically single rigid objects driven to rotate by, for example, optical forces 12-14 , magnetic forces 16 , rectified bacterial motion 15 or asymmetric catalytic activity 17,18 . However, nanoscale devices are frequently engineered using soft components, and the self-or directed assembly of nanometric building blocks into soft mesostructures represents an exciting opportunity for the realization of microscopic machines [19][20][21][22][23][24][25] . The response of a soft material to an external force is fundamentally different from that of a rigid body and the transmission of torque through soft materials remains little explored despite its clear importance if...

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“…However, due to its discrete nature, the tissue is susceptible to having shear deformations in addition. This is because, the circular confinement does not permit all the cells to have a preferred co-ordination number z = 6 [88], thus leading to distortion of the tissue, since the triangles formed by cell-cell connections (springs) cannot be all equilateral. The presence of motility forces further distorts the tissue by contributing additional shear strains.…”

Section: Confinement Contributes To the Distortion Of The Tissuementioning

confidence: 99%

Coherent Motion of Monolayer Sheets under Confinement and Its Pathological Implications

Gupta

Cugno

et al. 2015

PLoS Comput Biol

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Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed, remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements.

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The effect of boundary adaptivity on hexagonal ordering and bistability in circularly confined quasi hard discs

Cited by 16 publications

References 67 publications

Critical adsorption and critical Casimir forces in the canonical ensemble

Critical adsorption and critical Casimir forces in the canonical ensemble

Transmission of torque at the nanoscale

Coherent Motion of Monolayer Sheets under Confinement and Its Pathological Implications

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