Diffusive Regime Research Articles

Friction, mobility, and thermophoresis of carbon nanoparticles on a graphene sheet

It is shown using the method of molecular dynamics that the motion of carbon nanoparticles (rectangular graphene flakes, spherical fullerenes of size $L<10$ nm) on the surface of a thermalized graphene sheet lying on a flat substrate can be described as the motion of particles in a viscous medium with a constant coefficient of friction, the value of which depends on the temperature and particle size. It has been shown that there are two types of effective friction: diffusion and ballistic. In ballistic regime of motion (at velocities $v>100$ m/s), deceleration occurs due to the interaction of moving nanoparticles with thermal out-of-plane bending vibrations of a graphene sheet. Because of this, with the increasing temperature, the coefficient of friction monotonically increases. In the diffusion regime of motion (at $v<10$ m/s), friction arises due to the need for the particle to overcome local energy barriers, therefore it decreases with increasing emperature. The difference between ballistic and diffusion friction is most pronounced at low temperatures, since the mobility of nanoparticles in the ballistic regime of motion decreases with increasing temperature, while in the diffusion regime it monotonously increases. It is shown that the presence of a normal force pressing the nanoparticle to the substrate leads to an increases in its friction with the substrate.

Stochastic dynamics with multiplicative dichotomic noise: Heterogeneous telegrapher’s equation, anomalous crossovers and resetting

We analyze diffusion processes with finite propagation speed in a non-homogeneous medium in terms of the heterogeneous telegrapher’s equation. In the diffusion limit of infinite-velocity propagation we recover the results for the heterogeneous diffusion process. The heterogeneous telegrapher’s process exhibits a rich variety of diffusion regimes including hyperdiffusion, ballistic motion, superdiffusion, normal diffusion and subdiffusion, and different crossover dynamics characteristic for complex systems in which anomalous diffusion is observed. The anomalous diffusion exponent in the short time limit is twice the exponent in the long time limit, in accordance to the crossover dynamics from ballistic diffusion to normal diffusion in the standard telegrapher’s process. We also analyze the finite-velocity heterogeneous diffusion process in presence of stochastic Poissonian resetting. We show that the system reaches a non-equilibrium stationary state. The transition to this non-equilibrium steady state is analyzed in terms of the large deviation function.

Apparent permeability of organic matter in shale considering pore size distribution

The gas flow in shale nanopores is a crucial factor for shale gas exploitation. Organic matter in shale is an important constituent of gas shale reservoirs because of its gas storage ability. Current apparent permeability (Kapp) models focus on permeability calculations derived from pores with a given diameter or given mathematical distribution instead of pore size distribution. We confirmed the gas mass flux in organic matter by modifying the molecular diffusion coefficient and adsorption amount related to surface diffusion and flow regime transformation critical conditions such as pore size and pressure. Then, Kapp was calculated by coupling the mass flux with the pore size distribution. Our research shows that steps occur in the Kapp curves of organic matter owing to the flow regime transformation from transition flow to slip flow. Additionally, porosity, dominant pore diameter and frequency were the main factors affecting the Kapp of organic matter.

Legitimacy Without Democracy? Sources of Diffuse Regime Support in Post-Colonial Hong Kong

The resilience of non-democratic regimes in the past decades demonstrates that some authoritarian regimes have figured out ways to consolidate regime support without democratic elections. Hong Kong is a remarkable case of “legitimacy without democracy” as the system of government enjoyed a certain level of legitimacy since colonial days without being democratically elected. Using Hong Kong as a case and based on data from several waves of Asian Barometer Survey (ABS), this study analyzes the impact of citizens’ evaluation of the economic conditions, perception of freedoms, perceived procedural justice and institutional trust, and stability concerns on diffuse regime support in Hong Kong. There are three key findings of this study. First, economic performance is not a significant predictor of diffuse regime support in the case of Hong Kong, whereas, second, institutional trust and perceived civil liberties are. Finally, we found indirect evidence for the role of stability in shaping regime support, although its importance seems far less important than institutional trust and civil liberties.

Effects of viscous and capillary forces on the growth rates of gas bubbles in supersaturated liquid–gas​ solutions

An analytical and numerical study of diffusion growth of overcritical gas bubbles at degassing of the supersaturated-by-gas solution with the explicit full-scale influence of viscous and capillary forces on internal pressure in the bubbles has been presented. This study is based on our recent semi-analytical approach to the same problem (Kuchma and Shchekin, 2021). Generally, this approach allows one to find how the growth rate of overcritical bubbles depends on gas supersaturation, its diffusivity and solubility in solution, solution viscosity, surface tension at bubble surface and how it changes from zero for critical bubbles at unstable equilibrium with solution to sufficiently large values for large overcritical bubbles. A special question concerns approaching the widely used in kinetics of bubble nucleation stationary diffusion regime of growth and not so widely used self-similar non-stationary diffusion regime. As a first step, we have found analytical formulas for the bubble growth rate and the correction function (which takes into account the balance in the number of gas molecules that have left the liquid solution and came into the growing bubble) of small overcritical gas bubbles at strong viscosity of the solution and full account of capillary pressure in the bubbles as a function of the bubble radius. As a second step, we derived asymptotic formulas for the case of low viscosity and small radii of bubbles. As a third step, we obtained the formulas for the bubble growth rate and the correction function at large overcritical radii. Finally, we numerically evaluated the joint effects of viscous and capillary forces on the rate of gas bubble growth at any radius of the overcritical bubble within the wide range of viscosities of the supersaturated-by-gas solution and confirmed all the asymptotic analytical results.

Dynamics of plosive consonants via imaging, computations, and soft electronics

A quantitative understanding of the coupled dynamics of flow and particles in aerosol and droplet transmission associated with speech remains elusive. Here, we summarize an effort that integrates insights into flow-particle dynamics induced by the production plosive sounds during speech with skin-integrated electronic systems for monitoring the production of these sounds. In particular, we uncover diffusive and ballistic regimes separated by a threshold particle size and characterize the Lagrangian acceleration and pair dispersion. Lagrangian dynamics of the particles in the diffusive regime exhibit features of isotropic turbulence. These fundamental findings highlight the value in skin-interfaced wireless sensors for continuously measuring critical speech patterns in clinical settings, work environments, and the home, based on unique neck biomechanics associated with the generation of plosive sounds. We introduce a wireless, soft device that captures these motions to enable detection of plosive sounds in multiple languages through a convolutional neural network approach. This work spans fundamental flow-particle physics to soft electronic technology, with implications in monitoring and studying critical speech patterns associated with aerosol and droplet transmissions relevant to the spread of infectious diseases.

Time delay in 1D disordered media with high transmission

We study the time delay of reflected and transmitted waves in 1D disordered media with high transmission. Highly transparent and translucent random media are found in nature or can be synthetically produced. We perform numerical simulations of microwaves propagating in disordered waveguides to show that reflection amplitudes are described by complex Gaussian random variables with the remarkable consequence that the time-delay statistics in reflection of 1D disordered media are described as in random media in the diffusive regime. For transmitted waves, we show numerically that the time delay is an additive quantity and its fluctuations thus follow a Gaussian distribution. Ultimately, the distributions of the time delay in reflection and transmission are physical illustrations of the central limit theorem at work.

Transport properties of diffusive particles conditioned to survive in trapping environments

We consider a one-dimensional Brownian motion with diffusion coefficient D in the presence of n partially absorbing traps with intensity β, separated by a distance L and evenly spaced around the initial position of the particle. We study the transport properties of the process conditioned to survive up to time t. We find that the surviving particle first diffuses normally, before it encounters the traps, then undergoes a period of transient anomalous diffusion, after which it reaches a final diffusive regime. The asymptotic regime is governed by an effective diffusion coefficient D eff, which is induced by the trapping environment and is typically different from the original one. We show that when the number of traps is finite, the environment enhances diffusion and induces an effective diffusion coefficient that is systematically equal to D eff = 2D, independently of the number of the traps, the trapping intensity β and the distance L. On the contrary, when the number of traps is infinite, we find that the environment inhibits diffusion with an effective diffusion coefficient that depends on the traps intensity β and the distance L through a non-trivial scaling function , for which we obtain a closed-form. Moreover, we provide a rejection-free algorithm to generate surviving trajectories by deriving an effective Langevin equation with an effective repulsive potential induced by the traps. Finally, we extend our results to other trapping environments.

Magneto-Hemodynamic of Blood Flow Having Impact of Radiative Flux Due to Infrared Magnetic Hyperthermia: Spectral Relaxation Approach

Hyperthermia therapy is an adjuvant procedure during which perfused body tissues is subjected to elevated range of temperature in bid to achieve improved drug potency and efficacy of cancer treatment. While a selected class of hyperthermia techniques is shouldered on the thermal radiations derived from single-sourced electro-radiation measures, there are deliberations on conjugating dual radiation field sources in an attempt to improve the delivery of therapy procedure. This paper numerically explores the thermal effectiveness of combined infrared hyperemia having nanoparticle recirculation in the vicinity of imposed magnetic field on subcutaneous strata of a model lesion as ablation scheme. An elaborate Spectral relaxation method (SRM) was formulated to handle equation of coupled momentum and thermal equilibrium in the blood-perfused tissue domain of a spongy fibrous tissue. Thermal diffusion regimes in the presence of external magnetic field imposition were described leveraging on the renowned Roseland diffusion approximation to delineate the impact of radiative flux within the computational domain. The contribution of tissue sponginess was examined using mechanics of pore-scale porosity over a selected of clinical informed scenarios. Our observations showed for a substantial depth of spongy lesion, magnetic field architecture constitute the control regimes of hemodynamics in the blood-tissue interface while facilitating thermal transport across the depth of the model lesion. This parameter-indicator could be utilized to control the dispensing of hyperthermia treatment in intravenous perfused tissue.

Quantitative analysis of diffusion regimes in iron ore with low field NMR

SUMMARY The use of nuclear magnetic resonance (NMR) techniques allows in situ characterization of geophysical properties such as moisture content, permeability and wettability. However, the accuracy and applicability of such measurements is limited by internal magnetic field gradients which are a consequence of magnetic susceptibility differences at solid–fluid interfaces. Such effects are particularly prominent in iron ore rock samples which contain ferrimagnetic and ferromagnetic mineralogy leading to high magnetic susceptibility. Multiple echo time Carr–Purcell–Meiboom–Gill (CPMG) NMR pulse sequences are commonly used to capture the influence of internal gradients, with the intention of deconvoluting diffusion in effective internal gradients (geff) from true transver relaxation (T2). The interpretation of such measurements is complicated by the presence of multiple diffusive regimes: the short-time (ST), motionally averaged and localization regimes respectively. We introduce a new model for diffusive NMR signal attenuation, called the multiregime model which is intended to better capture diffusive behaviour across the three regimes. The multiregime model is compared against previous methods for quantifying diffusive decay (the ST only and generalized inversion models). Multi-echo measurements of iron ore samples are fit with each model in order to quantify 2-D T2–geff distributions. The resulting distributions demonstrate how the multiregime model can provide insight into the relative influence of the different diffusive regimes in a given sample. This assists in understanding the influence of diffusive decay on measurement accuracy, for example the increased measurement error with increasing prevalence of the localization regime. The multiregime model provides a key step in accurately segregating surface relaxation and diffusive relaxation, which is crucial for accurately estimating pore size distributions, permeability and wettability in high magnetic susceptibility samples using NMR.

How to estimate the memory of the elephant random walk

We introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entire history. Our estimator is nothing more than a quasi-maximum likelihood estimator, based on a second order Taylor approximation of the log-likelihood function. We show the almost sure convergence of our estimate in the diffusive, critical and superdiffusive regimes. The local asymptotic normality of our statistical procedure is established in the diffusive regime, while the local asymptotic mixed normality is proven in the superdiffusive regime. Asymptotic and exact confidence intervals as well as statistical tests are also provided. All our analysis relies on asymptotic results for martingales and the quadratic variations associated.

Diffusive regimes in a two-dimensional chiral fluid

Diffusion is a fundamental aspect of transport processes in biological systems, and thus, in the development of life itself. And yet, the diffusive dynamics of active fluids with directed rotation, known as chiral fluids, has not been analyzed in detail so far. Here, we describe the diffusive regimes of a two-dimensional chiral fluid, composed in this case of a set of identical disk-shaped rotors. We found strong experimental evidence of odd diffusion. This odd diffusion emerges in the form of a two-dimensional tensor with an antisymmetric part. In particular, we show that chiral diffusion is complex, featuring transitions between super, quasi-normal, and sub diffusion, and very slowly aging. Moreover, we show that the diffusion tensor elements, including off-diagonal elements; i.e., odd diffusion coefficient, change sign according to flow vorticity. Therefore, the chiral fluid has a self regulated diffusion, controlled by its vorticity.

Diffuse photon remission associated with thecenter-illuminated-area-detection geometry: PartI, an approach to the steady-state model.

Diffuse photon remission associated with the center-illuminated-area-detection (CIAD) geometry has been useful for non-contact sensing and may inform single-fiber reflectance (SfR). This series of work advances model approaches that help enrich the understanding and applicability of the photon remission by CIAD. The general approach is to derive the diffuse photon remission by the area integration of the radially resolved diffuse reflectance while limiting the analysis to a medium exhibiting only the Heyney-Greenstein (HG) scattering phase function. Part I assesses the steady-state photon remission in CIAD over a reduced scattering scaled diameter of μ s ' d a r e a ∈[0.5×10-3,103] that covers the range extensively modeled for SfR. The corresponding radially resolved diffuse reflectance is obtained by concatenating an empirical expression for the semi-ballistic region near the point-of-illumination and a formula utilizing a master-slave dual-source scheme over the semi-diffusive to a diffusive regime while being constrained by an extrapolated zero-boundary condition. The terminal algebraic photon remission is examined against Monte Carlo simulations for an absorption coefficient over [0.001,1]m m -1, a reduced scattering coefficient over [0.01,1000]m m -1, a HG scattering anisotropy factor within [0.5,0.95], and a diameter of the area of collection ranging [50,1000]µm. The algebraic model is also applied to phantom data acquired over a ∼2c m non-contact CIAD configuration and with a 200µm SfR probe. The model approach will be extended in a subsequent work towards the time-of-flight characteristics of CIAD.

Impact of the Non-Uniform Catalyst Particle Size on Product Selectivities in Consecutive Reactions

The analysis of consecutive reactions A→B→C in porous catalyst particles, where the simultaneous processes of diffusion and chemical reactions take place and both reactant and products are subjected to diffusion limitations, was performed for catalyst particles with non-uniform sizes, a fact that has not been considered so far. The system comprises first-order consecutive irreversible reactions that proceed on spherical catalyst particles with a log-normal volume particle size distribution (PSD), which is typical in many catalytic applications. Regardless of the prevailing diffusion regime (chemical control, transition situation or intraparticle diffusion control), the yield of the intermediate product (B) reaches a maximum value as a function of the conversion of reactant (A), then decreases as a consequence of the prevalence of the secondary reaction that converts it into the secondary product (C). If intraparticle diffusion resistances affect the reactant species, given the relationship between the kinetic constants and the mean particle size, the selectivity to the intermediate product is negatively affected by the dispersion in PSD. The larger the dispersion in PSD, the stronger the negative impact.

Electrochemical Detection of Cd(II) in Environmental Samples Using Nano-Ities

Heavy metals such as cadmium, lead, and arsenic have caused global health concerns that continue to rise yearly, which lead to several harmful diseases that primarily target organs such as kidneys and liver among other vital organs. Because of these well-known harmful effects, regulatory authorities have prescribed “permissible” levels of these metals in food, drinking water, and other possible sources to limit human exposure. However, increasing industrialization and inefficient recycling systems for industrially produced metal wastes have led to an increase in heavy metal exposure to humans. These toxins also bioaccumulate across the food chain, leaving us vulnerable to their harmful effects. Hence it is of great interest to develop systems that can detect metals efficiently to help set up effective metal mitigation protocols.Most conventional metal detecting tools, although highly accurate, require extensive sample pre-treatment steps which alter the speciation of the metal; a critical parameter for determining its toxicity. As(III) is known to be more toxic than As(V) and as such, they have separate medical remedies targeted toward the particular metal species. However, a conventional technique such as ICPMS is unable to differentiate between them. Furthermore, these conventional techniques require equipment that is bulky, expensive, and not user-friendly and limit real-time monitoring. Consequently, the development of a low-cost, portable, and robust sensor capable of providing accurate information on metal speciation will significantly aid in establishing metal mitigation systems efficiently. Low cost and user-friendliness will ensure that the sensor is within the economic and technological reach of most of the population and the portability of the sensor will enable testing in areas that are hard to access via a stationary lab. Such attributes coupled with accurate information on metal speciation will make an ideal metal sensor that will significantly aid the fight against heavy metal exposure.This study uses ion transfer between two immiscible electrolyte solutions (ITIES) to develop a Cd(II) sensor. Electrochemistry at ITIES is less complicated than other electrochemical techniques as it is based on the transfer of ions and does not include redox reactions; making it more attractive. Our electrode is a borosilicate glass electrode that is pulled using a carbon dioxide laser puller with an inner radius of ~300 nm. The nano-scale interface of our sensor follows a hemispherical diffusion regime which allows us to have a high mass transfer rate, which is essential for fast kinetic measurements. The nano-interface can also withstand various complex matrices consistently making it ideal for field applications. An ionophore- 1-10 phenanthroline was used to facilitate the Cd(II) transfer across the nano-interface. The sensor was calibrated n various matrices such as potassium chloride and artificial seawater to show its capability to withstand complex matrices without fouling. Stability and selectivity tests were done to showcase the sensor’s performance. It can also successfully detect Cd(II) when it is present in a complex form with strong ligands such as EDTA and NTA, etc. Our sensor’s analytical performance passed the ultimate test when we were able to accurately detect the dissolved Cd(II) ion concentrations in a water sample collected from the Indian River Lagoon in Melbourne, FL. The results from this test were in close agreement with the results reported by another research group that used ICPMS to quantify the amount of Cd(II) dissolved in the same environmental sample. However, ITIES does not require any sample pretreatment steps which is required for ICPMS.Thus, this study shows great promise for the development of an ideal electrochemical metal sensor for environmental samples. To the best of our knowledge, this is the first time a nanometer-scale glass electrode with ITIES to detect Cd(II) ions in complex matrices is being reported. Future studies will focus on the detection of metals in urine and blood samples and develop this into a portable point of care device.

Further results on the minimal random walk

The aim of this paper is to go further in the analysis of the asymptotic behavior of the so-called minimal random walk (MRW) using a new martingale approach. The MRW is a discrete-time random walk with infinite memory that has three regimes depending on the location of its two parameters. In the diffusive and critical regimes, we establish new results on the asymptotic behavior of the MRW such as quadratic strong laws and functional central limit theorems. In the superdiffusive regime, we prove the almost sure convergence of the MRW, properly normalized, to a nondegenerate random variable. Moreover, we show that the fluctuation of the MRW around its limiting random variable is still Gaussian. Finally, several results on the center of mass of the MRW are also provided.

Dispersion Processes in Weakly Dissipative Tidal Channels

AbstractWe report the results of an extensive experimental campaign dedicated to the analysis of turbulent dispersion owing to the circulations in tidal environments, characterized by a tidal inlet and a channel with lateral tidal flats. We focus on weakly‐convergent and weakly‐dissipative estuaries or tidal embankments, where the internal waters communicate with the open sea through an inlet mouth. Tides are reproduced as single or multiple harmonics waves. Particle Image Velocimetry is employed to measure two‐dimensional surface velocity fields. Large‐scale macro‐vortices, generated by vortex shedding during the flood phase from the inlet barrier, tend to occupy the entire tidal flats width and are completely flushed out during the ebb phase. In all experiments, an intense residual current, with shape influenced by the large‐scale flood vortices, is observed. The presence of large‐scale vortices and of a residual current strongly influences the Lagrangian auto‐correlation functions and the corresponding absolute dispersion time evolution. Looping auto‐correlations are the signature of both periodic forcing and vortices, ultimately, leading to super diffusive regimes. An asymptotic Brownian regime is always found for the investigated range of parameters allowing for an estimate of the horizontal dispersion coefficients which turn out to decrease with the friction parameter and tend to be enhanced when the semi‐diurnal constituents prevail. Finally, multiple particle statistics show multiple regimes depending on particle separations, compared to a typical injection length scale that seems to coincide with the inlet mouth dimension.

Anisotropic ionic transport properties in solid PEO based electrolytes

Solid polymer electrolytes (SPE) based on dry poly(ethylene oxide) (PEO) are interesting candidates to develop solid-state lithium (Li) batteries thanks to their stability toward Li metal anode, mechanical properties and flexibility, as well as ionic conductivity high enough for a battery application at temperatures higher than the PEO melting temperatures. To optimize the ionic conductivity, one strategy is to favor in-plane conductivity thanks to its typical higher value in PEO homopolymer electrolyte compared to the through-plane one. Thus, there is the need to understand the in-plane ionic transport properties (ionic conductivity, transference number, and diffusion coefficient) of SPEs depending on their nature and architecture. Indeed, ionic transport in PEO based SPE is due to a complex interplay between different local mechanisms involving the interaction between the PEO chain segments and both cations and anions. The separation of the cationic and anionic mechanisms is thus necessary to distinguish their contributions on the ionic transport anisotropies. Here, we report on the determination by electrochemical methodologies of the cationic and anionic in-plane ionic conductivities, transference numbers and restricted diffusion coefficients for a series of SPEs made of PEO homopolymers (linear), composite (PEO with the addition of nanocellulose), binary (PS-PEO-PS) and single-ion (PSTFSI-PEO-PSTFSI) conducting triblock copolymer electrolytes. The methodology to get each parameter is presented and discussed while COMSOL simulations permit to take into account the geometries of the in-plane cell (positions of the electrodes and SPE dimension). In addition, an analytical model is presented to fit the experimental data of the in-plane cell relaxation (diffusion regime) with a simple equation to determine the in-plane ambipolar diffusion coefficient. We observed that the in-plane anionic transport in SPEs is strongly hindered by the presence of structural blocks leading to an overall in-plane conductivity lower than the through-plane one.

Opportunities and pitfalls in (sub)diffuse reflectance spectroscopy

For a long time, steady-state reflectance spectroscopy measurements have been performed so that diffusion theory could be used to extract tissue optical properties from the reflectance. The development of subdiffuse techniques, such as Single Fiber Reflectance Spectroscopy and subdiffuse SFDI, provides new opportunities for clinical applications since they have the key advantage that they are much more sensitive to the details of the tissue scattering phase function in comparison to diffuse techniques. Since the scattering phase function is related to the subcellular structure of tissue, subdiffuse measurements have the potential to provide a powerful contrast between healthy and diseased tissue. In the subdiffuse regime, the interrogated tissue volumes are much smaller than in the diffuse regime. Whether a measurement falls within the diffuse or subdiffuse regime depends on tissue optical properties and the distance between the source and detector fiber for fiber-optic techniques or the projected spatial frequency for hyperspectral imaging and SFDI. Thus, the distance between source and detector fibers or the projected spatial frequency has important implications for clinical applications of reflectance spectroscopy and should be carefully selected, since it influences which tissue optical properties the technique is sensitive to and the size of the tissue volume that is interrogated. In this paper, we will review the opportunities and pitfalls in steady-state reflectance spectroscopy in the subdiffuse and the diffuse regime. The discussed opportunities can guide the choice of either the diffuse or subdiffuse regime for a clinical application, and the discussed pitfalls can ensure these are avoided to enable the development of robust diagnostic algorithms. We will first discuss the relevant basics of light-tissue interaction. Next, we will review all the tissue scattering phase functions that have been measured and investigate which scattering phase function models are representative of tissue. Subsequently, we will discuss the sensitivity of diffuse and subdiffuse techniques to tissue optical properties and we will explore the difference in the interrogation depth probed by diffuse and subdiffuse techniques.

From gradient-index to step-index filters: A switch between the two types of photonic crystals induced by the amplitude and period of sinusoidal function applied during high-temperature anodisation of aluminium

Porous anodic alumina (PAA) holds promise for the realisation of high-quality optical filters with first-order photonic stop-bands (PSBλ1) located in the infrared spectral region, thereby expanding the possibility of its application in photonics and light-based industries. High-temperature (30 °C) sinusoidal pulse anodisation (SPA) of aluminium was applied to fabricate PAA with PSBλ1 in the range of 800–2500 nm. The systematic increase in the anodisation period (tp) and amplitude (A) caused a significant change in the optical properties of the PAAs, which were monitored by both transmittance and reflectance measurements. A switch from gradient-index to step-index optical filters was observed when A and tp were increased from the lowest (5 V and 100 s, respectively) to the highest (15 V and 300 s, respectively) values. The switch was ascribed to the transition between different self-ordering regimes. The finest filtering properties (PSBλ1 reflectance close to 100 %) were achieved when the SPA proceeded between diffusion and kinetic regimes, providing a better porosity/refractive index contrast within the periodic structure. The analysis under polarised light confirmed both the excellent filtering properties of the PAAs and the asymmetrical light reflectance produced through the robust and cost-effective SPA process.