Halloysite is an alumosilicate tubular clay with a diameter of 50 nm, an inner lumen of 15 nm and a length of 600–900 nm. It is a natural biocompatible nanomaterial available in thousands of tons at ...low price, which makes it a good candidate for nanoarchitectural composites. The inner lumen of halloysite may be adjusted by etching to 20–30% of the tube volume and loading with functional agents (antioxidants, anticorrosion agents, flame‐retardant agents, drugs, or proteins) allowing for formulations with sustained release tuned by the tube end‐stoppers for hours and days. Clogging the tube ends in polymeric composites allows further extension of the release time. Thus, antioxidant‐loaded halloysite doped into rubber enhances anti‐aging properties for at least 12 months. The addition of 3–5 wt% of halloysite increases the strength of polymeric materials, and the possibility of the tube's orientation promises a gradient of properties. Halloysite nanotubes are a promising mesoporous media for catalytic nanoparticles that may be seeded on the tube surface or synthesized exclusively in the lumens, providing enhanced catalytic properties, especially at high temperatures. In vitro and in vivo studies on biological cells and worms indicate the safety of halloysite, and tests for efficient adsorption of mycotoxins in animals' stomachs are also carried out.
Halloysite, 50 nm diameter tubular clay, is a natural biocompatible material available in thousands of tons. Its inner lumen may be etched, doubling the lumen's volume, and loaded with functional agents, such as antioxidants, anticorrosion materials, flame‐retardants, catalysts, drugs, or proteins, enabling sustained controlled release tuned for hours, days, or months.
We consider the original β-Fermi-Pasta-Ulam-Tsingou system; numerical simulations and theoretical arguments suggest that, for a finite number of masses, a statistical equilibrium state is reached ...independently of the initial energy of the system. Using ensemble averages over initial conditions characterized by different Fourier random phases, we numerically estimate the time scale of equipartition and we find that for very small nonlinearity it matches the prediction based on exact wave-wave resonant interaction theory. We derive a simple formula for the nonlinear frequency broadening and show that when the phenomenon of overlap of frequencies takes place, a different scaling for the thermalization time scale is observed. Our result supports the idea that the Chirikov overlap criterion identifies a transition region between two different relaxation time scalings.
We analyse analytically and numerically the scale-invariant stationary solution to the internal-wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading-order ...contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-collinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale-invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wavenumbers in both the vertical and the horizontal directions. Our results compare favourably with the finescale parametrization of ocean mixing that was proposed in Polzin et al. (J. Phys. Oceanogr., vol. 25, issue 3, 1995, pp. 306–328).
Significance Despite the fact that more than 60 years have passed, the α -Fermi–Pasta–Ulam (FPU) system has not yet been fully understood. Their seminal work stimulated many interdisciplinary ...research topics in mathematics and physics like integrable systems, soliton theory, ergodic theory, and chaos. In this article, we theoretically investigate the original problem by applying the wave–wave interaction theory. By using this mathematical approach, we are able to explain why the emergence of equipartition requires very long times (inaccessible when the original numerical experiments were performed but nowadays recently observed using computer power). Our approach is general and can be used to attack other problems of weakly nonlinear dispersive waves.
We study the original α -Fermi–Pasta–Ulam (FPU) system with N = 16, 32, and 64 masses connected by a nonlinear quadratic spring. Our approach is based on resonant wave–wave interaction theory; i.e., we assume that, in the weakly nonlinear regime (the one in which Fermi was originally interested), the large time dynamics is ruled by exact resonances. After a detailed analysis of the α -FPU equation of motion, we find that the first nontrivial resonances correspond to six-wave interactions. Those are precisely the interactions responsible for the thermalization of the energy in the spectrum. We predict that, for small-amplitude random waves, the timescale of such interactions is extremely large and it is of the order of 1/ ϵ ⁸, where ϵ is the small parameter in the system. The wave–wave interaction theory is not based on any threshold: Equipartition is predicted for arbitrary small nonlinearity. Our results are supported by extensive numerical simulations. A key role in our finding is played by the Umklapp (flip-over) resonant interactions, typical of discrete systems. The thermodynamic limit is also briefly discussed.
Halloysite is natural tubular clay suitable as a component of biocompatible nanosystems with specific functionalities. The selective modification of halloysite inner/outer surfaces can be achieved by ...exploiting supramolecular and covalent interactions resulting in controlled colloidal stability adjusted to the solvent polarity. The functionalized halloysite nanotubes can be employed as reinforcing filler for polymers as well as carriers for the sustained release of active molecules, such as antioxidants, flame-retardants, corrosion inhibitors, biocides and drugs. The tubular morphology makes halloysite a perspective template for core-shell metal supports for mesoporous catalysts. The catalysts can be incorporated with selective and unselective metal binding on the nanotubes' outer surface or in the inner lumens. Micropatterns of self-assembled nanotubes have been realized by the droplet casting method. The selective modification of halloysite has been exploited to increase the nanotubes' ordering in the produced patterns. Pickering emulsions, induced by the self-assembly of halloysite nanotubes on oil-water interface, can be used for petroleum spill bioremediation and catalysis.
Display omitted
•Stable colloids of functionalized halloysite can be doped into polymeric composites.•Tubes' lumen can encapsulate & sustainably release chemical inhibitors and drugs.•Halloysite makes excellent support for core-shell metal nanocatalysts.•Organized patterns on solid supports produced by clay nanotube self-assembly.•Pickering microemulsions for oil spill bioremediation also use similar self-assembly.
Selective fatty acid hydrophobization of the inner surface of tubule halloysite clay is demonstrated. Aqueous phosphonic acid was found to bind to alumina sites at the tube lumen and did not bind the ...tube's outer siloxane surface. The bonding was characterized with solid-state nuclear magnetic resonance (29Si, 13C, 31P NMR), Fourier transform infrared (FTIR), and X-ray photoelectron spectroscopy. NMR and FTIR spectroscopy of selectively modified tubes proved binding of octadecylphosphonic acid within the halloysite lumen through bidentate and tridentate P–O–Al linkage. Selective modification of the halloysite clay lumen creates an inorganic micelle-like architecture with a hydrophobic aliphatic chain core and a hydrophilic silicate shell. An enhanced capacity for adsorption of the modified halloysite toward hydrophobic derivatives of ferrocene was shown. This demonstrates that the different inner and outer surface chemistry of clay nanotubes can be used for selective modification, enabling different applications from water purification to drug immobilization and controlled release.
Abstract
We provide a first-principles analysis of the energy fluxes in the oceanic internal wave field. The resulting formula is remarkably similar to the renowned phenomenological formula for the ...turbulent dissipation rate in the ocean, which is known as the finescale parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber–frequency (
m
–
ω
) domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the finescale parameterization formula in functional form and in magnitude. These energy transfers are composed of a “local” and a “scale-separated” contributions; while the former is quantified numerically, the latter is dominated by the induced diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all nonzero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed “no-flux” solutions are reinstated to the status of “constant-downscale-flux” solutions. This is consequential for an understanding of energy fluxes, sources, and sinks that fits in the observational paradigm of the finescale parameterization, solving at once two long-standing paradoxes that had earned the name of “oceanic ultraviolet catastrophe.”
Significance Statement
The global circulation models cannot resolve the scales of the oceanic internal waves. The finescale parameterization of turbulent dissipation, a formula grounded in observations, is the standard tool by which the energy transfers due to internal waves are incorporated in the global models. Here, we provide an interpretation of this parameterization formula building on the first-principles statistical theory describing energy transfers between waves at different scales. Our result is in agreement with the finescale parameterization and points out a large contribution to the energy fluxes due to a type of wave interactions (local) usually disregarded. Moreover, the theory on which the traditional understanding of the parameterization is mainly built, a “diffusion approximation,” is known to be partly in contradiction with observations. We put forward a solution to this problem, visualized by means of “streamlines” that improve the intuition of the direction of the energy cascade.
We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed ...energy conservation of the triadic resonant interactions. In a first application to isotropic systems, we re-derive the previously used formula for the energy flux as a particular case for adjacent sets. We then exploit the new formalism to quantify the level of locality of the energy transfers in the example of surface capillary waves. A second application to anisotropic wave systems expands the currently available set of tools to investigate magnitude and direction of the energy fluxes in these systems. We illustrate the use of the formalism by characterizing the energy pathways in the oceanic internal wavefield. Our proposed approach, unlike traditional approaches, is not limited to stationarity, scale invariance and strict locality. In addition, we define a number $w$ that quantifies the scale separation necessary for two sets of modes to having negligible mutual energy exchange, with potential consequences in the interpretation of wave turbulence experiments. The methodology presented here provides a general, simple and systematic approach to energy fluxes in wave turbulence.
Layer-by-layer encapsulation of living biological cells and other microorganisms via sequential adsorption of oppositely charged functional nanoscale components is a promising instrument for ...engineering cells with enhanced properties and artificial microorganisms. Such nanoarchitectural shells assembled in mild aqueous conditions provide cells with additional abilities, widening their functionality and applications in artificial spore formation, whole-cell biosensors, and fabrication of three-dimensional multicellular clusters.
Halloysite is a naturally occurring clay mineral with submicron sized hollow cylindrical morphology. Halloysite morphology, structure and properties were characterized by using SEM, TEM, XRD, FT-IR ...spectroscopy, surface electrokinetic (zeta) potential and nitrogen adsorption isotherms. Comparison of the halloysite structure with imogolite was also provided. Halloysite toxicological studies revealed that it is environmentally friendly and biocompatible material. Due to its unique tubular shape and availability in thousands of tons halloysite has potential to be applied as nanocontainers for encapsulation of chemically and biologically active agents such as medicines, pharmaceuticals, antiseptics, corrosion inhibitors, antifouling agents, and doped with them plastics producing smart polymeric nanocomposites with improved mechanical strength. Finally possibility to synthesize metal nanorods within the halloysite lumen was demonstrated.
PDF
