Spherical Substrate Research Articles

Crystallization of self-propelled particles on a spherical substrate

In this paper, we investigate the self-propelled particles confined on a spherical substrate and explore the structural and dynamic properties of self-propelled particles by controlling the packing fraction and activity. We find that these self-propelled particles freeze into the crystal with the increase in the packing fraction. We observe the pattern evolution of inevitable topological defects due to the geometric constraints of the spherical substrate. During the process of freezing, there is a transition from twelve isolated grain boundaries to the uniform distribution of defects with the increase in the self-propelled velocity. Finally, we establish a phase diagram of the freezing process. These results may deepen our understanding of active particles in complex and crowded environments.

Adhesion of tungsten particles on rough tungsten surfaces using Atomic Force Microscopy

Adhesion forces between tungsten spherical microparticles and tungsten substrates with different roughnesses have been measured using the Atomic Force Microscopy (AFM) colloidal probe technique. Mean roughnesses of the tungsten substrates were measured by AFM and were ranked in three categories i.e. nanoscale, sub-microscale and microscale roughnesses. Experimental Hamaker constant of 37±3.5×10−20 J has been obtained using a spherical tungsten particle of 10.5 μm in radius and a tungsten substrate with nanoscale root-mean-square roughness of rms=11.5 nm. It was shown that larger roughness of the order rms=712 nm induces a two order of magnitude decrease on the adhesion of tungsten microparticles compared to a smooth tungsten surface with nanoscale roughness. Comparison with the van der Waals-based adhesion force model of Rabinovich which integrates the roughness of surfaces showed good agreement with experimental pull-off forces even when roughness of the substrate is close to the micrometer range. In such case, measurements have shown that dependency of adhesion force with particle size (in the micrometer range) has a secondary influence compared to the roughness of surfaces.

Chitosan based self-assembled nanocapsules as antibacterial agent

Creating an appropriate antibacterial disinfection system without forming any harmful compounds is still a major challenge and calls for new technologies for efficient disinfection and microbial control. Towards this aim, we report on the elaboration of biodegradable and biocompatible polymeric nanocapsules, also called hollow nanoparticles, for potential applications in antibiotic therapy. These nanomaterials are based on the self-assembly of charged polysaccharides, namely chitosan and alginate, onto gold nanoparticles as a sacrificial matrix (60 nm). Electrostatic interactions between the protonated amine groups of chitosan (+35 mV) and the carboxylate groups of alginate (- 20 mV) are the driving attraction force enabling the elaboration of well-ordered multilayer films onto the spherical substrate. The removal of the colloidal gold, via cyanide-assisted hydrolysis, is evidenced by time-dependent variation of the gold spectroscopic signature (30 min is required). TEM shows the obtention of nanocapsules. An inhibitory effect of these particles has been demonstrated during the growth of two representative bacteria in a liquid medium: Staphylococcus aureus (Gram-positive) (from 4.6% to 16.3% for gold nanomaterials + and from 18.6% to 34.9% for (chi+/alg−)n-chi+ nanocapsules) and Escherichia coli (Gram-negative) (from 5.4% to 20% for gold nanomaterials and from 23.7% to 40% for (chi+/alg−)n-chi+ nanocapsules). Acridine orange staining demonstrated the bactericidal effect of chitosan-based capsules. These findings demonstrate that (chitosan/alginate)n capsules can be exploited as new antibacterial material. Thus, we present a complementary approach to classical nanoparticles prepared by complexation between alginate and chitosan or other materials.

Patchy particles by self-assembly of star copolymers on a spherical substrate: Thomson solutions in a geometric problem with a color constraint.

Confinement or geometric frustration is known to alter the structure of soft matter, including copolymeric melts, and can consequently be used to tune structure and properties. Here we investigate the self-assembly of ABC and ABB 3-miktoarm star copolymers confined to a spherical shell using coarse-grained dissipative particle dynamics simulations. In bulk and flat geometries the ABC stars form hexagonal tilings, but this is topologically prohibited in a spherical geometry which normally is alleviated by forming pentagonal tiles. However, the molecular architecture of the ABC stars implies an additional 'color constraint' which only allows even tilings (where all polygons have an even number of edges) and we study the effect of these simultaneous constraints. We find that both ABC and ABB systems form spherical tiling patterns, the type of which depends on the radius of the spherical substrate. For small spherical substrates, all solutions correspond to patterns solving the Thomson problem of placing mobile repulsive electric charges on a sphere. In ABC systems we find three coexisting, possibly different tilings, one in each color, each of them solving the Thomson problem simultaneously. For all except the smallest substrates, we find competing solutions with seemingly degenerate free energies that occur with different probabilities. Statistically, an observer who is blind to the differences between B and C can tell from the structure of the A domains if the system is an ABC or an ABB star copolymer system.

Geometrically incompatible confinement of solids

The complex morphologies exhibited by spatially confined thin objects have long challenged human efforts to understand and manipulate them, from the representation of patterns in draped fabric in Renaissance art to current-day efforts to engineer flexible sensors that conform to the human body. We introduce a theoretical principle, broadly generalizing Euler's elastica-a core concept of continuum mechanics that invokes the energetic preference of bending over straining a thin solid object and that has been widely applied to classical and modern studies of beams and rods. We define a class of geometrically incompatible confinement problems, whereby the topography imposed on a thin solid body is incompatible with its intrinsic ("target") metric and, as a consequence of Gauss' Theorema Egregium, induces strain. By focusing on a prototypical example of a sheet attached to a spherical substrate, numerical simulations and analytical study demonstrate that the mechanics is governed by a principle, which we call the "Gauss-Euler elastica" This emergent rule states that-despite the unavoidable strain in such an incompatible confinement-the ratio between the energies stored in straining and bending the solid may be arbitrarily small. The Gauss-Euler elastica underlies a theoretical framework that greatly simplifies the daunting task of solving the highly nonlinear equations that describe thin solids at mechanical equilibrium. This development thus opens possibilities for attacking a broad class of phenomena governed by the coupling of geometry and mechanics.

Four stages of droplet spreading on a spherical substrate and in a spherical cavity: Surface tension versus line tension and viscous dissipation versus frictional dissipation

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a completely wettable spherical substrate is theoretically studied. Both convex spherical substrates and concave spherical cavities with smooth or rough surfaces are considered. The droplet on a rough substrate is modeled by either the Wenzel or the Cassie-Baxter model. The two sources of driving force of spreading by the surface-tension and the line tension are considered. Also, the two channels of energy dissipation by the viscous dissipation within the bulk and the frictional dissipation at the contact line are considered. A combined theory of spreading on a spherical substrate is constructed by including those four factors. The spreading process is divided into four stages, each of which is governed by one of two driving forces and one of two dissipations. It is found that the dynamic contact angle $\theta$ has a characteristic time ($t$) dependence at each stage. It does not necessarily follow the standard power law $\theta \sim t^{-\alpha}$. Instead, the relaxation can be a power-law with the exponent $\alpha$ different from that on a flat substrate, or it can be exponential or it can finish within a finite time. Therefore, various spreading scenarios on a spherical substrate and in a spherical cavity are predicted.

Hierarchical Reduced Graphene Oxide Ridges for Stretchable, Wearable, and Washable Strain Sensors.

Recently, flexible and wearable devices are increasingly in demand and graphene has been widely used due to its exceptional chemical, mechanical and electrical properties. Building complex buckling patterns of graphene is an essential strategy to increase its flexible and stretchable properties. Herein, a facile dimensionally controlled four-dimensional (4D) shrinking method was proposed to generate hierarchical reduced graphene oxide (rGO) buckling patterns on curved substrates mimicking different parts of the uniforms. The reduced graphene oxide ridges (rGORs) generated on the spherical substrate seem isotropic, while those generated on the cylindrical substrate are obviously more hierarchical or oriented, especially when the cylindrical substrate are shrinking via two steps. The oriented rGORs are superhydrophobic and strain sensitive but obviously anisotropic along the axial and circumferential directions. The sensitivity of rGORs along the axial direction is much higher than those along the circumferential direction. In addition, the intrinsic solvent barrier property of graphene enables the crack-free rGORs an excellent chemical protective performance, withstanding DCM immersion for more than 2.5 h. The flexible rGORs-based strain sensors can be used to detect both large and subtle human motions and activities by achieving high sensitivity (maximum gauge factor up to 48), high unidirectional stretchability (300-530%), and ultrahigh areal stretchability (up to 2690%). Excellent durability was also demonstrated for human motion monitoring with resistance to hand rubbing, ultrasonic cleaning, machine washing, and chemical immersion.

Rayleigh-Taylor instability under a spherical substrate

The Rayleigh-Taylor instability of a thin viscous film coating the inside of a spherical substrate is studied. The instability properties are investigated by performing a linear optimal transient growth analysis. The pattern formation is further analyzed using nonlinear numerical simulations.

Performance optimization of 193 nm antireflective coatings with wide incident angle ranges on strongly curved spherical substrates.

A method to optimize the spectral performance of 193 nm antireflective (AR) coating with a broad range of angle of incidence (AOI) on strongly curved spherical substrates is described. In this method, the actual film thickness on test plates for single-layer LaF3 and MgF2 films are corrected by measuring the relationship between the film thickness on test plates and that on quartz crystal microbalance. Interface roughness in multi-layer AR coating is obtained from atomic force microscopy measurements and its effect on the spectrum of the multi-layer is taken into account in this method by being simulated as a homogeneous sublayer. Porosities of the sublayers in AR coatings are obtained by reversely engineering the residual reflectance of the coatings/substrate/coating stacks. The obtained refractive indices and thicknesses in the multilayer are then used for analysis and optimization of the spectrum of 193 nm AR coatings. For strongly curved spherical surfaces, spectrum uniformity of the AR coating is optimized by taking into consideration simultaneously the merit functions at different positions of spherical substrates. This work provides a general solution to the performance optimization of 193 nm AR coatings with broad AOI range and on strongly curved spherical substrates.

Superconducting Niobium Coatings Deposited on Spherical Substrates in Molten Salts

The interaction of substrates from ceramics, beryllium, and carbopyroceram with the electrolyte for the electrodeposition of niobium coatings was investigated. The corrosion resistance of spherical ceramic and beryllium samples with the protective molybdenum films obtained by magnetron sputtering was studied. The exfoliation of molybdenum film from ceramics and beryllium samples was observed after the experiments due to the interaction of substrates with the melt. It was found that the carbopyroceram did not corrode in the niobium containing melt and this material was chosen as the substrate for the electrodeposition of superconducting niobium coatings. The influence of the oxide ions on the electrochemical behavior of niobium complexes in the NaCl–KCl–NaF–K2NbF7 melt was studied. A special form of the cathode was constructed for the electrodeposition of niobium coatings on spherically shaped substrates. Electrodeposition of the niobium coatings on spheres 10 mm in diameter manufactured from carbopyroceram was carried out at 750 °C with the cathodic current density of 5 × 10−3–2 × 10−2 A·cm−2 and the electrolysis time of 8–12 h. Influence of the cathodic current density on the microstructure of niobium coatings was studied. The roughness, nonsphericity, and superconductive properties of niobium coatings were determined.

Glassy dynamics of dense particle assemblies on a spherical substrate.

We study by molecular dynamics simulation a dense one-component system of particles confined on a spherical substrate. We more specifically investigate the evolution of the structural and dynamical properties of the system when changing the control parameters, the temperature and the curvature of the substrate. We find that the dynamics become glassy at low temperature, with a strong slowdown of the relaxation and the emergence of dynamical heterogeneity. The prevalent local 6-fold order is frustrated by curvature and we analyze in detail the role of the topological defects in the statics and the dynamics of the particle assembly.

Pseudo-magnetic fields of strongly-curved graphene nanobubbles

We use the [Formula: see text]-orbital axis vector (POAV) analysis to deal with large curvature effect of graphene in the tight-binding model. To test the validities of pseudo-magnetic fields (PMFs) derived from the tight-binding model and the model with Dirac equation coupled to a curved surface, we propose two types of spatially constant-field topographies for strongly-curved graphene nanobubbles, which correspond to these two models, respectively. It is shown from the latter model that the PMF induced by any spherical graphene nanobubble is always equivalent to the magnetic field caused by one magnetic monopole charge distributed on a complete spherical surface with the same radius. Such a PMF might be attributed to the isometry breaking of a graphene layer attached conformably to a spherical substrate with adhesion.

Preparation of High-Density Polymer Brushes with a Multihelical Structure.

It is well-known that a mixture of isotactic and syndiotactic polymethyl methacrylate (PMMA) forms a stereocomplex consisting of a multihelical structure in which an isotactic chain is surrounded by a syndiotactic chain. Here, we report the basic structure of the stereocomplex formed when the syndiotactic PMMA chains are tethered to a silicon substrate and form a high-density polymer brush. The influence of geometric confinement was investigated by preparing the high-density polymer brushes on a flat and spherical substrate. In both cases, mixing the untethered isotactic PMMA with the grafted syndiotactic PMMA led to the formation of a stereocomplex with a multihelical structure. Static contact angle measurements showed a hindered surface mobility at the outermost surface of the polymer brush, indicating that the stereocomplex forms a crystalline structure. A syndiotactic polymer brush with substituted fluoroalkyl groups was prepared to increase the contrast for grazing incidence wide-angle X-ray diffraction (GIWAXD) measurements. The GIWAXD results verified that the stereocomplex forms a crystalline structure oriented perpendicular to the substrate with a relatively low degree of orientation.

Adsorption and fusion of hybrid lipid/polymer vesicles onto 2D and 3D surfaces.

We investigated the formation of hybrid lipid/polymer (1,2-dioleoyl-sn-glycero-3-phosphocholine and poly(ethylene oxide-b-butadiene); DOPC/EO22Bd37) films onto planar silica surfaces. Using laser scanning confocal microscopy, atomic force microscopy, and quartz crystal microbalance analysis, we monitored the adsorption and fusion of hybrid lipid/polymer vesicles onto planar borosilicate glass cleaned via chemical etching or RF/air plasma treatment. In addition we used cryo-electron microscopy to characterize film formation on mesoporous silica nanoparticles. As the polymer content in the vesicles increased, the resulting hybrid lipid/polymer films on borosilicate glass - cleaned by chemical etching or plasma treatment - were more heterogeneous, indicating a large number of adsorbed vesicles rather than continuous bilayer films at higher polymer loadings. The observed lateral fluidity of both DOPC and hybrid lipid/polymer films also decreased substantially with increasing polymer fraction and was found to be relatively insensitive to changes in pH. Films prepared from vesicles with higher polymer loadings were completely immobile. We also found that polymer vesicles did not interact with clean plasma-treated glass surfaces, which may be due to elevated OH and Si-OH on plasma-treated surfaces. Conformal hybrid lipid/polymer coatings consistent with bilayers could be formed on mesoporous silica nanoparticles and imaged via cryo-electron microscopy. These results expand the library of biocompatible materials that can be used for coating silica-based materials and nanoparticles.

Topography- and topology-driven spreading of non-Newtonian power-law liquids on a flat and a spherical substrate.

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids on a flat and a spherical rough and textured substrate is theoretically studied in the capillary-controlled spreading regime. A droplet whose scale is much larger than that of the roughness of substrate is considered. The equilibrium contact angle on a rough substrate is modeled by the Wenzel and the Cassie-Baxter model. Only the viscous energy dissipation within the droplet volume is considered, and that within the texture of substrate by imbibition is neglected. Then, the energy balance approach is adopted to derive the evolution equation of the contact angle. When the equilibrium contact angle vanishes, the relaxation of dynamic contact angle θ of a droplet obeys a power-law decay θ∼t^{-α} except for the Newtonian and the non-Newtonian shear-thinning liquid of the Wenzel model on a spherical substrate. The spreading exponent α of the non-Newtonian shear-thickening liquid of the Wenzel model on a spherical substrate is larger than others. The relaxation of the Newtonian liquid of the Wenzel model on a spherical substrate is even faster showing the exponential relaxation. The relaxation of the non-Newtonian shear-thinning liquid of Wenzel model on a spherical substrate is fastest and finishes within a finite time. Thus, the topography (roughness) and the topology (flat to spherical) of substrate accelerate the spreading of droplet.

Synthesis of spherical structured catalysts by dip‐coating: Application to n‐butane dehydrogenation

AbstractThis work analyzes the deposition conditions of thin layers of γ‐Al2O3 by dip‐coating on a spherical substrate of α‐Al2O3 spheres. Results showed that under controlled deposition conditions, a structured support of α‐Al2O3 spheres coated by a uniform γ‐Al2O3 layer (thickness ≈ 15 µm) of good adherence can be attained. Optimal preparation conditions for the coating, that involved pretreatment of the substrate, gel formation, deposition conditions, and thermal treatments, were obtained. Pt catalysts supported on this structured material can be used as promising dehydrogenation systems. In this sense, a monometallic structured catalyst showed both good metallic dispersion and catalytic performance in n‐butane dehydrogenation reaction compared to another conventional catalytic system.

Spreading law of non-Newtonian power-law liquids on a spherical substrate by an energy-balance approach.

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids, both shear-thickening and shear-thinning liquids, that completely wet a spherical substrate is theoretically investigated in the capillary-controlled spreading regime. The crater-shaped droplet model with the wedge-shaped meniscus near the three-phase contact line is used to calculate the viscous dissipation near the contact line. Then the energy balance approach is adopted to derive the equation that governs the evolution of the contact line. The time evolution of the dynamic contact angle θ of a droplet obeys a power law θ∼t^{-α} with the spreading exponent α, which is different from Tanner's law for Newtonian liquids and those for non-Newtonian liquids on a flat substrate. Furthermore, the line-tension dominated spreading, which could be realized on a spherical substrate for late-stage of spreading when the contact angle becomes low and the curvature of the contact line becomes large, is also investigated.

Gyrification-Inspired Highly Convoluted Graphene Oxide Patterns for Ultralarge Deforming Actuators

Gyrification in the human brain is driven by the compressive stress induced by the tangential expansion of the cortical layer, while similar topographies can also be induced by the tangential shrinkage of the spherical substrate. Herein we introduce a simple three-dimensional (3D) shrinking method to generate the cortex-like patterns using two-dimensional (2D) graphene oxide (GO) as the building blocks. By rotation-dip-coating a GO film on an air-charged latex balloon and then releasing the air slowly, a highly folded hydrophobic GO surface can be induced. Wrinkling-to-folding transition was observed and the folding state can be easily regulated by varying the prestrain of the substrate and the thickness of the GO film. Driven by the residue stresses stored in the system, sheet-to-tube actuating occurs rapidly once the bilayer system is cut into slices. In response to some organic solvents, however, the square bilayer actuator exhibits excellent reversible, bidirectional, large-deformational curling properties on wetting and drying. An ultralarge curvature of 2.75 mm-1 was observed within 18 s from the original negative bending to the final positive bending in response to tetrahydrofuran (THF). In addition to a mechanical hand, a swimming worm, a smart package, a bionic mimosa, and two bionic flowers, a crude oil collector has been designed and demonstrated, aided by the superhydrophobic and superoleophilic modified GO surface and the solvent-responsive bilayer system.

Spreading law on a completely wettable spherical substrate: The energy balance approach.

The spreading of a cap-shaped spherical droplet on a completely wettable spherical substrate is studied. The nonequilibrium thermodynamic formulation is used to derive the thermodynamic driving force of spreading including the line-tension effect. Then the energy balance approach is adopted to derive the evolution equation of the spreading droplet. The time evolution of the contact angle θ of a droplet obeys a power law θ∼t^{-α} with the exponent α, which is different from that derived from Tanner's law on a flat substrate. Furthermore, the line tension must be positive to promote complete wetting on a spherical substrate, while it must be negative on a flat substrate.

Development of an x-ray eight-image Kirkpatrick-Baez diagnostic system for China's laser fusion facility.

This article presents the development of an x-ray eight-image Kirkpatrick-Baez diagnostic system to be used at China's Shenguang-III (SG-III) laser facility in aspects of the optical design, multilayers, and online/offline tests. Six pieces of concave spherical substrates are used for constituting a special optical structure. Dual-periodic tungsten/carbon (W/C) multilayers are used for high reflectivity and large angular bandwidth of ∼0.1°. The global spatial resolution is ∼5 μm in the ±100 μm range. The schemes of system installation, transport, collimation, and image acquisition at China's SG-III facility are also discussed.