Rafael S Zola

Rafael S Zola
Federal University of Technology of Paraná | UTFPR · Departamento Acadêmico de Física (DAFIS)

PhD

About

112
Publications
14,521
Reads
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2,243
Citations
Additional affiliations
August 2012 - January 2013
State University of Maringá
Position
  • Professor (Assistant)
August 2007 - March 2012
Kent State University
Position
  • PhD Student

Publications

Publications (112)
Article
Full-text available
We investigate the diffusion phenomenon of particles in the vicinity of a spherical colloidal particle where particles may be adsorbed/desorbed and react on the surface of the colloidal particle. The mathematical model comprises a generalized diffusion equation to govern bulk dynamics and kinetic equations which can describe non-Debye relaxations a...
Article
Helical twists exist in liquid crystals as a result of the addition of chiral dopants or boundary conditions and play a role in several liquid-crystal phenomena and devices. To date, various methodologies have been explored, albeit with varying degrees of precision and complexity, often resulting in the measurement of just one parameter, such as he...
Article
Full-text available
We investigate the H-theorem for a class of generalized kinetic equations with fractional time-derivative, hyperbolic term, and nonlinear diffusion. When the H-theorem is satisfied, we demonstrate that different entropic forms may emerge due to the equation’s nonlinearity. We obtain the entropy production related to these entropies and show that it...
Article
We consider a nematic liquid crystal film confined to a flat cell with homeotropic and planar patterned hybrid anchoring and show, using Monte Carlo simulations, the possibility of the system to stabilize line and point defects. The planar anchoring surface is patterned with a chessboardlike grid of squares with alternating random or parallel homog...
Article
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Many fundamental physical problems are modeled using differential equations, describing time- and space-dependent variables from conservation laws. Practical problems, such as surface morphology, particle interactions, and memory effects, reveal the limitations of traditional tools. Fractional calculus is a valuable tool for these issues, with appl...
Article
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Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-near...
Article
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The interplay of diffusion with phenomena like stochastic adsorption–desorption, absorption, and reaction–diffusion is essential for life and manifests in diverse natural contexts. Many factors must be considered, including geometry, dimensionality, and the interplay of diffusion across bulk and surfaces. To address this complexity, we investigate...
Preprint
Full-text available
Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k-near...
Article
Full-text available
In this study, we investigate a nonlinear diffusion process in which particles stochastically reset to their initial positions at a constant rate. The nonlinear diffusion process is modeled using the porous media equation and its extensions, which are nonlinear diffusion equations. We use analytical and numerical calculations to obtain and interpre...
Article
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We study the entropy production in a fractal system composed of two subsystems, each of which is subjected to an external force. This is achieved by using the H-theorem on the nonlinear Fokker–Planck equations (NFEs) characterizing the diffusing dynamics of each subsystem. In particular, we write a general NFE in terms of Hausdorff derivatives to t...
Article
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We analyze the electrical impedance response established in terms of the time-fractional approach formulation of the Poisson-Nernst-Planck model by considering a general boundary condition. The total current across the sample is solenoidal, as the Maxwell equations require, and the boundary conditions can be related to different scenarios. We also...
Article
We used Monte Carlo simulations with an elastically anisotropic pairwise potential to simulate the equilibrium structure of chiral and achiral nematic liquid crystals in spherical confinement under perpendicular and tangential strong anchoring. The stable structures are obtained by a quenching process, where the temperature is a parameter of the sy...
Article
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We investigate the solutions of a generalized diffusion-like equation by considering a spatial and time fractional derivative and the presence of non-local terms, which can be related to reaction or adsorption–desorption processes. We use the Green function approach to obtain solutions and evaluate the spreading of the system to show a rich class o...
Article
Twist-coupled elastic deformations are ubiquitous and in the limelight of interest for next-generation self-shaping materials. Here, we describe how twist dynamics under fixed anchoring lead to bend deformation and defect dynamics in a field-unwound chiral liquid crystal material. We use the Q-tensor dynamics under the Landau–de Gennes formalism in...
Article
Full-text available
In this work, we investigate the effect of the number of available adsorption sites for diffusing particles in a liquid confined between walls where the adsorption (desorption) phenomena occur. We formulate and numerically solve a model for particles governed by Fickian’s law of diffusion, where the dynamics at the surfaces obey the Langmuir kineti...
Article
We investigate an extension of the Schrödinger equation by considering a fractional differential operator for the spatial variable, which simultaneously takes the heterogeneity of the media and Lévy like distributions into account. By using the Green’s function method, we obtain solutions to the equation in the case of the free particle and when it...
Article
The approaches developed for studying the polarization of molecules and the dynamics of ions in dielectric materials are usually considered separately. The two effects are often believed to take place in different frequency ranges. The low frequency response is usually dominated by ionic migration, whereas the high frequency response is played by m...
Article
In this paper we present Marlics (Maringá Liquid Crystal Simulator), a software written in C++ to obtain either the system dynamics, by using the Runge-Kutta method, or the minimum energy states with the Fast Inertial Relaxation Engine (FIRE) for both achiral and chiral nematic liquid crystals. The system solved by Marlics consists in the dynamical...
Preprint
Machine learning methods are becoming increasingly important for the development of materials science. In spite of this, the use of image analysis in the development of these systems is still recent and underexplored, especially in materials often studied via optical imaging techniques such as liquid crystals. Here we apply the recently proposed me...
Article
Machine learning methods are becoming increasingly important for the development of materials science. In spite of this, the use of image analysis in the development of these systems is still recent and underexplored, especially in materials often studied via optical imaging techniques such as liquid crystals. Here we apply the recently proposed me...
Article
Full-text available
We investigate particle diffusion in a heterogeneous medium limited by a surface where sorption–desorption processes are governed by a kinetic equation. We consider that the dynamics of the particles present in the medium are governed by a diffusion equation with a spatial dependence on the diffusion coefficient, i.e., K(x) = D|x|−η, with −1 < η an...
Article
We simulated nematic liquid crystal confined under patterned substrates. In one of the simulated surfaces, the easy axis is planar and uniform, while the other one offers a periodic alignment, with well-defined modulation. We use Monte Carlo simulations within a lattice model to determine the molecular organization of the confined sample built to p...
Article
We revisit the electrochemical impedance spectroscopy problem in the framework of the Poisson-Nernst-Planck model for a semi-infinite electrolytic cell, using the Gouy-Chapman interface approximation. The drift-diffusion problem is formulated in terms of fractional differential operators having singular and non-singular kernels. These operators are...
Article
We review and extend some results for the fractional Schrödinger equation by considering nonlocal terms or potential given in terms of delta functions. For each case, we have obtained the solution in terms of the Green function approach.
Article
The complex arrangement of layered structures in curved geometries is a ubiquitous problem in soft condensed matter systems. In general, cholesteric liquid crystals (CLCs) in spherical droplets have been studied...
Article
We study diffusing particles in a confined liquid whose diffusion coefficient periodically varies across the sample. The limiting substrates may adsorb-desorb particles when memory effects are also considered. We show how the bulk modulation (amplitude and number of turns) affects bulk and surface distributions. The diffusing regimes are also studi...
Article
General diffusion processes involve one or more diffusing species and are usually modelled by Fick’s law, which assumes infinite propagation velocity. In this article, searching for the effect of finite propagation speeds in a system with two reacting species, we investigate diffusing and reacting particles governed by a hyperbolic diffusion equati...
Article
Diffusion processes occurring in a myriad of systems sparkle great interest in understanding their general properties and applications. In this work, we investigate a broad set of diffusive systems that can be governed by a generalized diffusion equation and subjected to a surface that can promote sorption and, consequently, desorption, thus releas...
Article
Full-text available
Machine learning algorithms have been available since the 1990s, but it is much more recently that they have come into use also in the physical sciences. While these algorithms have already proven to be useful in uncovering new properties of materials and in simplifying experimental protocols, their usage in liquid crystals research is still limite...
Preprint
Full-text available
Machine learning algorithms have been available since the 1990s, but it is much more recently that they have come into use also in the physical sciences. While these algorithms have already proven to be useful in uncovering new properties of materials and in simplifying experimental protocols, their usage in liquid crystals research is still limite...
Article
The adsorption-desorption phenomena play a pivotal role in several industrial and scientific processes, deserving attention from research groups across several fields of knowledge. In this article, we study adsorption-desorption of neutral particles scattered in a confined liquid when memory effects are present in both processes, the adsorption and...
Article
The twist-bend nematic (NTB) phase is a doubly degenerated heliconical structure with nanometric pitch and spontaneous bend and twist deformations. It is favored by symmetry-breaking molecular structures, such as bent dimers and bent-core molecules, and it is currently one of the burgeoning fields of liquid-crystal research. Although tremendous adv...
Article
We investigate the diffusion phenomenon in a heterogeneous system composed by two different media in contact. We consider the dynamics of the particles for each medium governed by generalized diffusion equations, which can be related to fractional diffusion equations. The interface separating the different media defines the boundary conditions to b...
Article
Here, we have demonstrated the production and characterization of hydrogel scaffolds based on chitosan/gellan gum (CS/GG) assemblies, without any covalent and metallic crosslinking agents, conventionally used to yield non-soluble polysaccharide-based materials. The polyelectrolyte complexes (physical hydrogels called as PECs) are characterized by F...
Article
This study reports the synthesis, characterization and biological properties of films based on poly(vinyl alcohol) (PVA) and a cationic tannin polymer derivative (TN). Films are obtained from polymeric blends by tuning the PVA/TN weight ratios. The materials are characterized through infrared spectroscopy, X-ray photoelectron spectroscopy, contact...
Article
We investigate possible connections between two different implementations of the Poisson-Nernst-Planck (PNP) anomalous models used to analyze the electrical response of electrolytic cells. One of them is built in the framework of the fractional calculus, and considers integro-differential boundary conditions also formulated by using fractional deri...
Article
We investigate diffusive phenomena governed by fractional diffusion equations in the presence of a spatial dependent diffusion coefficient and external forces. We consider a fractional operator which enables us to analyze, in a unified way, different types of fractional time derivatives. This approach opens the possibility of considering new situat...
Article
Full-text available
Imaging techniques are essential tools for inquiring a number of properties from different materials. Liquid crystals are often investigated via optical and image processing methods. In spite of that, considerably less attention has been paid to the problem of extracting physical properties of liquid crystals directly from textures images of these...
Preprint
Full-text available
Imaging techniques are essential tools for inquiring a number of properties from different materials. Liquid crystals are often investigated via optical and image processing methods. In spite of that, considerably less attention has been paid to the problem of extracting physical properties of liquid crystals directly from textures images of these...
Article
Full-text available
The ability to control light direction with tailored precision via facile means is long‐desired in science and industry. With the advances in optics, a periodic structure called diffraction grating gains prominence and renders a more flexible control over light propagation when compared to prisms. Today, diffraction gratings are common components i...
Article
We investigate alignment and electro-optical properties of a room temperature dye-doped antiferroelec-tric liquid-crystal mixture. We achieve uniform alignment on a macroscopic scale of thin cells with the combination of proper surface alignment and electric field treatment. We also successfully demonstrate that two films of dye-doped antiferroelec...
Article
Full-text available
Recent discoveries of advanced photocontrolled materials have kindled a great deal of interest on their use as command surfaces that switch easy axis under light radiation. One noticeable point when using switchable surfaces on any application is how the dynamical process propagates to the bulk directors. In this paper, we theoretically study the e...
Article
The recent experimental observation of twist-bend nematic phases has kindled interest on this new class of materials. The natural twist-bend deformations of the director results in a nanoscale pitch (pseudo-layers) probed by freeze-fracture transmission electron microscopy (FFTEM) and very recently it was verified by resonant soft x-ray scattering...
Article
Periodic modulations in chiral nematic liquid crystals (CLCs) are used in several optical and photonic devices. A remarkable way of fabricating and controlling such patterns is in a thin wetting layer that grows as temperature is decreased. Here, we study this stripe formation process experimentally and by means of Monte Carlo simulations. We repor...
Article
Surface driven pattern formation is an intriguing phenomenon in the liquid crystals field. Owing to its ability to transmit torque, one can generate different patterns by propagating distortions on the optical wavelength scale in the sample from the surface. Here, we theoretically investigate (from the elasticity point of view) twist deformations i...
Chapter
This chapter covers the unique chiral nematic liquid crystal (LC) phase. It discusses how stimuli-directing changes to the helical axis's orientation of a chiral nematic phase can be used for smart, functional materials that respond in accordance to device's need, including one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) cont...
Article
Modulated phases as variational solutions in liquid-crystalline systems All authors J. A. Reyes, M. P. Rosseto, L. R. Evangelista, R. R. Ribeiro de Almeida & R. S. Zola https://doi.org/10.1080/15421406.2017.1403231 Published online 18 January 2018 Representation of the oblique helicoidal structure with a nanometric pitch of typical of the twist-...
Article
Role of the surface anchoring energy on the spontaneous modulated pattern formation of hybrid aligned cholesteric liquid crystals All authors R. L. Biagio, R. Teixeira de Souza, L. R. Evangelista & R. S. Zola https://doi.org/10.1080/15421406.2017.1403791 Published online 18 January 2018
Article
Optically reconfigurable monodisperse chiral microspheres of self-organized helical superstructures with dynamic chirality were fabricated via a capillary-based microfluidic technique. Light-driven handedness-invertible transformations between different configurations of microspheres were vividly observed...
Article
Zigzag pattern formation is a common and important phenomenon in nature serving a multitude of purposes. For example, the zigzag-shaped edge of green leaves boosts the transportation and absorption of nutrients. However, the elucidation of this complicated shape formation is challenging in fluid mechanics and soft condensed matter systems. Herein,...
Article
Full-text available
The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulate structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase $N_{TB}$ is characterized by a heliconical structure with a pitch in the nano-metr...
Preprint
Full-text available
The extended Frank elastic energy density is used to investigate the existence of a stable periodically modulate structure that appears as a ground state exhibiting a twist-bend molecular arrangement. For an unbounded sample, we show that the twist-bend nematic phase $N_{TB}$ is characterized by a heliconical structure with a pitch in the nano-metr...
Article
Full-text available
From the elastic point of view, the twist-bend nematic phase, (NTB), has a ground state characterised by a spontaneous bend with a precession of the director n along the direction of an axis t. The tilt angle θ formed between the director n and the axis t gives rise to a heliconical structure with a nanometric helical pitch p. Using an elastic cont...
Article
We argue that ion motion in electrolytic cells containing Milli--Q water, weak electrolytes, or liquid crystals may exhibit unusual diffusive regimes that deviate from the expected behavior, leading the system to present anomalous diffusion. Our arguments lie on the investigation of the electrical conductivity and its relation with the mean square...
Article
Broken symmetry of any kind in natural or synthetic systems is a burgeoning area of science. In this article, the temporal behavior of the bulk density, electric potential inside the sample, and the adsorbed ionic particles density in an electrolytic cell are shown to be non-symmetric and strongly affected by the surfaces dynamics. These parameters...
Article
Full-text available
Diffusion of particles in a heterogeneous system separated by a semipermeable membrane is investigated. The particle dynamics is governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. The kinetic equations are solved by incorporating memory effec...
Article
Full-text available
The recently discovered twist-bend nematic phase, Ntb, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, n, on a conical helix with a tilt angle θ and helical pitch P. The stability of the Ntb phase has been recently demonstrated from the elastic point of view by extending the Fra...
Article
A self-organized helical superstructure was found to exhibit thermally tunable, reversible selective reflection of light across the whole visible region upon doping with an achiral bent-core hybrid trimer having a twist-bend nematic phase.
Article
Full-text available
Civil construction has grown inadvertently in Brazil, and, consequently, its demands for raw material. The production of such materials, as to any industrial process, yields wastewater effluents and has as destination, in general, water resources such as rivers and lakes. Nonetheless, government inspection cannot keep up with the number of starting...
Article
Civil construction has grown inadvertently in Brazil, and, consequently, its demands for raw material. The production of such materials, as to any industrial process, yields wastewater effluents and has, in general, as destination water resources such as rivers and lakes. Nonetheless, government inspection can not keep up with the number of startin...
Article
Full-text available
The recently discovered twist-bend nematic phase, $\rm N_{tb}$, is a non-uniform equilibrium nematic phase that presents a spontaneous bend with a precession of the nematic director, $\textbf{n}$, on a conical helix with a tilt angle $\theta$ and helical pitch $P$. The stability of the $\rm N_{tb}$ phase has been recently demonstrated from the elas...
Chapter
Full-text available
An extension of the anomalous Poisson - Nernst - Planck (PNP) diffusional model for an electrolytic cell containing two groups of ions by considering fractional time derivatives of distributed order and nonusual boundary conditions is discussed. The equations are solved exactly in the small AC signal approximation and exhibit a rich variety of beha...
Article
Full-text available
The twist-bend nematic phase, NTB, may be viewed as a heliconical molecular arrangement in which the director n precesses uniformly about an extra director field, t. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a natural extension of the...
Article
We investigate a sorption process where one substance spreads out through another having possibility of chemical reaction between them. So as to describe this process, we have considered the bulk dynamics governed by a fractional diffusion equation, where the reaction term may describe an irreversible or a reversible process. This reaction term rep...
Article
Self-organized 3D photonic superstructures loaded with plasmonic hybrid nanorods were found to undergo structural transformations from body-centered cubic to simple cubic upon NIR-light irradiation resulting from the “photothermal effect” of nanorods. Furthermore, dynamic NIR light-directed red, green and blue reflections of the 3D photonic nanocom...
Article
Full-text available
The twist-bend nematic phase, $N_{\rm TB}$, may be viewed as a heliconical molecular arrangement in which the director $\bf n$ precesses uniformly about an extra director field, $\bf t$. It corresponds to a nematic ground state exhibiting nanoscale periodic modulation. To demonstrate the stability of this phase from the elastic point of view, a nat...
Article
A confined liquid with dissolved neutral particles is theoretically studied when the limiting surfaces present different dynamics for the adsorption--desorption phenomena. The investigation considers different non-singular kernels in the kinetic equations at the walls, where the suitable choice of the kernel can account for the relative importance...
Article
We experimentally observed that the photonic band gap (reflection band) of polymer stabilized cholesteric liquid crystals with negative dielectric anisotropies can be greatly broadened under DC electric fields. We explored the underlying mechanism. We found that the dispersed polymer network moved when DC voltages were applied across the liquid cry...
Article
Constructing and tuning self-organized three-dimensional (3D) superstructures with tailored functionality is crucial in the nanofabrication of smart molecular devices. Herein we fabricate a self-organized, phototunable 3D photonic superstructure from monodisperse droplets of one-dimensional cholesteric liquid crystal (CLC) containing a photosensiti...
Article
Constructing and tuning self-organized three-dimensional (3D) superstructures with tailored functionality is crucial in the nanofabrication of smart molecular devices. Herein we fabricate a self-organized, phototunable 3D photonic superstructure from monodisperse droplets of one-dimensional cholesteric liquid crystal (CLC) containing a photosensiti...
Article
The reaction process occurring on a solid surface where active sites are present is investigated. The phenomenon is described by a linear kinetic equation capable of accounting for memory effects in the adsorption–desorption and a first order reaction process. In order to broaden the formulation of the problem, the surface is in contact with a syst...
Article
Full-text available
The comb model is a simplified description for anomalous diffusion under geometric constraints. It represents particles spreading out in a two-dimensional space where the motions in the x-direction are allowed only when the y coordinate of the particle is zero. Here, we propose an extension for the comb model via Langevin-like equations driven by f...