Equilibrium Process Research Articles

Influence of Ammonia Concentration on Solvay Soda Process Parameters and Associated Environmental and Energetic Effects

Modifying the absorption process in soda production by the Solvay method requires performing many calculations and determining a new equilibrium process. An increase in ammonia concentration in the reaction solution causes kinetic changes in equilibrium. Changes to the Solvay soda production technology were determined using chemical and instrumental analysis methods. A modification of the process in the form of SAB was introduced. Information allowing the design of an additional absorber and its location in the network of technological devices was presented in the form of parameters using typical chemical engineering assumptions. Spectroscopic and electrochemical techniques were used for this purpose. The increase in total alkalinity due to the addition of ammonia to 135 mmol·20 cm−3 resulted in cooling savings of about 152.4 MJ·Mg−1 of soda. The ammonia desorption rate and process energy parameters were determined for the new system. The temperature requirements for the carbonation column were defined, and in particular, a technique was developed to minimize the cooling of the lower part of the reactor, which reduces the consumption of process energy. Emissions of CO2 were reduced from 11.70 to 7.85% and NH3 from 5.52 to 4.89% in exhaust gases from the carbonation column.

Soya bean derived activated carbon as an efficient adsorbent for capture of valuable heavy metals from waste aqueous solution

Abstract The removal of hazardous metal ions from liquid waste effluents is very important for water as well as environmental safety. In this regard, this article discusses in detail the U(VI) uptake from aquatic environment using biomass-based Soya Bean activated carbon (labeled as AC-SB). XRD, SEM, FTIR, Raman, and BET analysis were used to characterize the synthesized AC-SB sorbent. Batch-type experiments were used to investigate the effect of various parameters on adsorption efficiency, including pH, metal-ion concentration, temperature, and contact time. The sorption experimental data have been described well with pseudo-second-order kinetic mathematical equations. The equilibrium state of the uptake reaction was 120 min. The Langmuir isotherm model accurately described the equilibrium process which declares that the uranium sorption is a monolayer and homogeneous process. The sorption capacity of the prepared AC was 32.7 mg g−1. Thermodynamic analysis explore that the U(VI) uptake process is endothermic, feasible and spontenous process. The displayed results demonstrate that the prepared AC-SB sorbent could be used as the proper material for uranium sorption from real matrix samples.

Out of Equilibrium Chemical Systems Fueled by Trichloroacetic Acid

Dissipative systems are based on the supply of energy to a system by fuel pulses and dissipation of this energy through the fuel decomposition, resulting in repetition of a given physical or biological function. Such out of equilibrium processes are at the heart of all living organisms, and in the past decade, researchers have attempted to transpose these principles to purely synthetic systems. However, upon fuel decomposition, the resulting waste generated tends to accumulate in the system, rapidly inhibiting the machinery after a few cycles of fuel pulses. In order to solve this issue, trichloroacetic acid has appeared as a fuel of choice to reversibly change the acidity of a system, liberating volatile chloroform and CO2 upon fuel decomposition. In this Perspective, we present the advantages of this fuel and successful applications ranging from conformational switches to rotary motors to temporal control over crystallization or smart materials.

Time to reach the maximum for a stationary stochastic process.

We consider a one-dimensional stationary time series of fixed duration T. We investigate the time t_{m} at which the process reaches the global maximum within the time interval [0,T]. By using a path-decomposition technique, we compute the probability density function P(t_{m}|T) of t_{m} for several processes, that are either at equilibrium (such as the Ornstein-Uhlenbeck process) or out of equilibrium (such as Brownian motion with stochastic resetting). We show that for equilibrium processes the distribution of P(t_{m}|T) is always symmetric around the midpoint t_{m}=T/2, as a consequence of the time-reversal symmetry. This property can be used to detect nonequilibrium fluctuations in stationary time series. Moreover, for a diffusive particle in a confining potential, we show that the scaled distribution P(t_{m}|T) becomes universal, i.e., independent of the details of the potential, at late times. This distribution P(t_{m}|T) becomes uniform in the "bulk" 1≪t_{m}≪T and has a nontrivial universal shape in the "edge regimes" t_{m}→0 and t_{m}→T. Some of these results have been announced in a recent letter [Europhys. Lett. 135, 30003 (2021)0295-507510.1209/0295-5075/ac19ee].

Equilibrium model for the ablation response of silicone-coated PICA

A novel equilibrium ablation and thermal response model for NASA’s Phenolic Impregnated Carbon Ablator (PICA) is presented. For the first time, the model accounts for the effect of NuSil, a silicone overcoat applied as contamination control during assembly, test, and launch operations for both the Mars Science Laboratory and the Mars 2020 heatshields. The protective effect of NuSil against atomic oxygen is discussed based on experimental results collected under arc jet environment. A detailed mass and heat transfer analysis for PICA-NuSil was implemented in the Porous material Analysis Toolbox based on OpenFOAM, PATO. The model includes specific boundary conditions for the coating removal and surface equilibrium processes using representative elements of the NuSil-environment system. The charred NuSil surface was modeled as SiO2 based on the observation that a silicon oxycarbide layer, formed during the decomposition of NuSil, transforms into domains of pure silica and charred PICA. Two-dimensional material response simulations were performed to compare PICA and PICA-NuSil using boundary conditions calibrated with arc jet data. The present work constitutes the first demonstration of a multi-dimensional ablation response of a silicone-coated carbon-phenolic ablator. It is shown that simulations agree with experiments, and the model reproduces measured temperature and recession. Differences between the PICA-NuSil response under Earth and Mars atmospheres are discussed.

State estimation for aoristic models

AbstractAoristic data can be described by a marked point process in time in which the points cannot be observed directly but are known to lie in observable intervals, the marks. We consider Bayesian state estimation for the latent points when the marks are modeled in terms of an alternating renewal process in equilibrium and the prior is a Markov point process. We derive the posterior distribution, estimate its parameters and present some examples that illustrate the influence of the prior distribution. The model is then used to estimate times of occurrence of interval censored crimes.

Friction induced mechanochemistry: self-adaptive lubrication through in-situ tribo-click system

The friction, which commonly exist on moving mechanical interfaces, accounts for structure damage and energy consumption. Traditional lubricating protection strategy mainly focus on the active additives and functional surface with high entropy as well as low friction. Here, an ingenious and groundbreaking mechanochemistry method of friction induced in-situ synthesis of lubricating and anti-wear materials is proposed in this paper. This interfacial friction modulation revolves around the configuration of a mechanical tribo-chemical reaction in combination with the classical ‘click reaction’, occurring locally on the copper sliding asperity present in the base oil. In particular, the process of friction functions as the fundamental stimulator of this tribochemical reaction, where the in-situ tribo-click product compensates for the frictional loss and instantly safeguards the tribo-interface. As an unforeseen outcome, the said resultant is found to exhibit premium friction-reducing effect under shear stress, along with a refined adaptability. It is evident that this tribo-click reaction demonstrates a distinctively efficient dynamic equilibrium process for the formation, consumption, and supply of tribo-film, which is attributable to the predominance shown by the in-situ tribo-click reaction and the self-adaptive tribological performance of the interfacial friction modulation system.

Low-Cost Adsorbents for the Removal of Phenol/Phenolics, Pesticides, and Dyes from Wastewater Systems: A Review

The huge development of industrial production and human activities throughout the world has resulted in serious water pollution. Pesticides, dyes, phenol, and phenolic compounds may be life-threatening to humans and marine aquatic animals, even at low concentrations. These pollutants must be removed by using different techniques to provide high-quality water. So far, the adsorption process has been considered an effective method to remove pollutants from an aqueous solution. The adsorption method has several advantages, such as low cost, easy operation, and high performance. This article reviewed the removal of dye, pesticides, phenol, and phenolic compounds through zeolite, activated carbon, clay, ash fly, and carbon nanotubes by reviewing the existing literature from 2000 to 2022. The properties of the adsorbent, adsorption studies, the method of design, and optimization conditions were reported. The thermodynamic studies were conducted to determine Gibbs free energy change, standard entropy change, and standard enthalpy change. Adsorption isotherms (Langmuir, Freundlich, and Temkim models) revealed the relationship between the amount of adsorbates per unit adsorbent in the equilibrium process. The adsorption kinetic investigations (pseudo-first-order and pseudo-second-order kinetic model) were carried out to determine the rate of adsorption and correlate the experimental data. Experimental results indicated that a higher adsorption capacity can be observed when the adsorbents have a high surface area and high-porosity structure. The removal percentage of pollutants increased when the adsorbent dosage was increased due to the availability of a larger number of adsorption sites. In conclusion, cheaper adsorbents can be used in wastewater treatment to improve water quality and protect the environment.

Quantum mechanics of open systems: Dissipaton theories.

This Perspective presents a comprehensive account of the dissipaton theories developed in our group since 2014, including the physical picture of dissipatons and the phase-space dissipaton algebra. The dissipaton-equation-of-motion-space (DEOM-space) formulations cover the Schrödinger picture, the Heisenberg picture, and further the imaginary-time DEOM. Recently developed are the dissipaton theories for studying equilibrium and nonequilibrium thermodynamic mixing processes. The Jarzynski equality and Crooks relation are accurately reproduced numerically. It is anticipated that dissipaton theories would remain essential toward a maturation of quantum mechanics of open systems.

(Invited) Accelerating Electrochemistry: The Development of Rapid Impedance Methods and High-Throughput Screening of Novel Oxide Electrodes for Fuel Cells and Electrolyzers

As electrochemical technologies rise to ever greater prominence in the global energy landscape, new techniques to accelerate the discovery, design, and characterization of novel electrochemical materials and devices are needed. Motivated by this opportunity, here we present our recent work in the development of novel rapid multi-dimensional impedance characterization using the Distribution of Relaxation Times (DRT) combined with high-throughput impedance-based screening of electrocatalysts for ceramic fuel cells and electrolyzers, both of which offer opportunities to accelerate electrochemical materials research and development.The DRT has been established as a versatile tool for analysis of electrochemical impedance spectroscopy (EIS) data, providing insight into the relevant electrochemical processes of fuel cells, batteries, and other devices without the constraints of an a priori model. Here, we present a method for obtaining the DRT directly from rapid time-domain measurements. This technique provides the DRT on a time-scale that is 1-2 orders of magnitude faster than conventional EIS measurements, and opens new avenues for characterization and analysis that are inaccessible and/or impractical with conventional EIS. We demonstrate how this technique can be used to construct multidimensional DRT maps as a function of variables such as applied bias, temperature, changing gas conditions, or state-of-charge (Figure 1). In addition, the model can be adapted to account for time-varying sample states, enabling meaningful analysis of unstable samples and transient phenomena such as equilibration or degradation processes. Finally, we demonstrate how hardware sampling-rate limitations can be overcome via hybrid frequency- and time-domain measurements to scan a broad range of timescales without sacrificing measurement speed. The capability of this method to resolve the DRT along additional dimensions promises to enhance the interpretability of the DRT and provide new insight to guide materials and device optimization.We then discuss how rapid impedance characterization and analysis methods can be coupled to combinatorial thin-film synthesis and high-throughput automated characterization to investigate a large family of catalytically-active triple-ionic-electronic conducting oxide perovskite materials based on the Ba(Co,Fe,Zr,Y)O3-δ (BCFZY) compositional system, which show great promise for catalyzing the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) for ceramic fuel cells and electrolyzers (Figure 2). In total, we collected and analyzed more than 2,500 impedance spectra from three combinatorial thin-film electrode libraries, comprising 432 distinct compositions. These libraries were synthesized by pulsed laser deposition and measured at three temperatures under two different gas atmospheres, enabling a new scientific insight into the trends governing electrochemical performance. Our combinatorial experiments demonstrate that Co-rich compositions achieve the lowest overall polarization resistance under both dry air and humid N2, while high Fe content may impede the performance at low-to-intermediate temperatures. Reuslts from the combinatorial experiments are supported by isotope-labled SIMS trace diffusion studies as well as by protonic-ceramic fuel cell and electrolysis cell testing of both symmetric cells and full cells that incorporated select compositions of interest. Hierarchical Bayesian analysis indicates that the performance-limiting process depends on the chemical composition, measurement temperature, and atmospheric humidity. Thus, by combining rapid analysis methods with combinatorial experimentation, we achieve a composition map of the condition-dependent electronic properties of materials in the BCFZY perovskite family for application as air electrodes in protonic ceramic fuel cell and electrolyzers. Figure 1

(Invited) A Formalism Relating the Relative Humidity to the Proton Conductivity Mechanism of Membranes

The relationship between relative humidity of gas phase and proton conductivity in proton exchange membranes has been subject of extensive investigations [1],[2]. Herein, a theoretical framework is presented which describes proton transport in relation to stepwise equilibria that reflect the water uptake. In the proposed model, at first, the hydration process is treated as a stepwise equilibrium process, in agreement with experimental observations. Several hierarchical levels of structure evolve with increasing hydration. These levels are easily confirmed by the analysis of the electric response of perfluorinated based membranes by complex dielectric and conductivity spectra. Thus, a wide range of literature data on hydration of Nafion as a function of activity and temperature has been analyzed by means of the proposed model to extract chemical parameters diagnostic of the type of interactions characterizing the hydrophilic domains of membranes.These parameters, which are crucial in order to modulate the ion transport phenomena in ionomers, are then introduced into the model to describe the functional dependence of conductivity on water activity in gas phase. The treatment of proton conductivity is built on the approaches commonly adopted to describe transport in solids [3]. Key proton migration phenomena appropriate to the levels of the structural hierarchy are considered. The conductivity model is used to describe a set of conductivity vs. water uptake data as a function of temperature, with data taken to exceptionally low water contents. The formalism is then used to analyze a set of data for a perfluorosulfonic acid (PFSA) membrane as a function of hydration, temperature and polymer equivalent weight. The main advantage of the proposed framework is the possibility of a straightforward application to multiple membrane types based on the energetics of water uptake. Actually, the focus on chemical interactions allows to better correlate the effects of the morphology and relaxation events of the matrix to the proton migration phenomena of the membrane. Acknowledgements This work has received funding from: (a) the European Union’s Horizon 2020 research and innovation program under grant agreement 881603; (b) the project ‘Advanced Low-Platinum hierarchical Electrocatalysts for low-T fuel cells’ funded by EIT Raw Materials.

Statistical complexity and the road to equilibrium in many-body chaotic quantum systems.

In this work we revisit the problem of equilibration in isolated many-body interacting quantum systems. We pay particular attention to quantum chaotic Hamiltonians, and rather than focusing on the properties of the asymptotic states and how they adhere to the predictions of the Eigenstate Thermalization Hypothesis, we focus on the equilibration process itself, i.e., the road to equilibrium. Along the road to equilibrium the diagonal ensembles obey an emergent form of the second law of thermodynamics and we provide an information theoretic proof of this fact. With this proof at hand we show that the road to equilibrium is nothing but a hierarchy in time of diagonal ensembles. Furthermore, introducing the notions of statistical complexity and the entropy-complexity plane, we investigate the uniqueness of the road to equilibrium in a generic many-body system by comparing its trajectories in the entropy-complexity plane to those generated by a random Hamiltonian. Finally, by treating the random Hamiltonian as a perturbation we analyzed the stability of entropy-complexity trajectories associated with the road to equilibrium for a chaotic Hamiltonian and different types of initial states.

Connecting the Phase State and Volatility of Dicarboxylic Acids at Elevated Temperatures

The partitioning of semivolatile organic molecules between condensed phases and the vapor phase has broad application across a range of scientific disciplines, with significant impacts in atmospheric chemistry for regulating the evolving composition of aerosol particles. Vapor partitioning depends on the molecular interactions and phase state of the condensed material and shows a well-established dependence on temperature. The phase state of solid organic material is not always well-defined, and many examples can be found for the formation of amorphous subcooled liquid states rather than crystalline solids. This can lead to significant changes to vapor equilibrium processes by modifying the thermodynamics and kinetics of evaporation. Here, we explore the influence of phase state on the evaporation dynamics of a series of straight-chain dicarboxylic acids across a range of above-ambient temperatures. These molecules show an odd/even alteration in some of their properties based on the number of carbon atoms that may be connected to their phase state under dry conditions. Using a newly developed linear-quadrupole electrodynamic balance, we levitate single particles containing the sample and expose them to dry conditions across a range of temperatures (ambient to ∼350 K). Using the rate of evaporation measured from the change in the size or relative mass, we derive the vapor pressure and enthalpy of vaporization. Light scattering data allows for unambiguous identification of the phase of the particles (crystal vs amorphous) allowing the vapor equilibrium properties to be attributed to a particular state. This work highlights a new experimental method for characterizing vapor pressures of low volatility substances and extends the temperature range of available data for the vapor pressure of terminal dicarboxylic acids. These measurements show that crystalline and subcooled liquid states persist at elevated temperatures and provide a direct comparison between subcooled and crystal phases under the same experimental conditions.

Triazolyl- vs Pyridyl-Functionalized N-Heterocyclic Carbene Complexes: Impact of the Pendant N-Donor Ligand on Intramolecular C-C Bond Formation.

Organometallic Rh(Cp*) (Cp* = η5-pentamethylcyclopentadienyl) complexes with monodentate N-heterocyclic carbene (NHC) ligands bearing a pendant anthracenyl substituent have been shown to undergo intramolecular C-C coupling reactions. Herein, two bidentate NHC ligands substituted with pyridyl or triazolyl donor groups were prepared along with the corresponding MII/III (M = RuII, OsII, RhIII, IrIII) complexes. While the Rh(Cp*) complex featuring an NHC-triazole bidentate ligand underwent the equivalent reaction as the monodentate Rh(NHC) complex, i.e., it formed a polydentate ligand, the pyridyl-pendant derivative was unequivocally shown to be unreactive. This contrasting behavior was further investigated by density functional theory (DFT) calculations that highlighted significant differences between the two types of Rh(III) complexes with pendant pyridyl or triazolyl N-coordinating groups. Modeling of the reaction pathways suggests that the initial formation of a dicationic Rh(III) species is unfavorable and that the internal ligand transformation proceeds first by dissociation of the coordinated N atom of the pendant group from the Rh center. After the formation of a neutral η4-fulvene ligand via combined proton/single electron transfer, a cycloaddition occurs between the exo-ene bond of fulvene and the 9' and 10' positions on the pendant anthracenyl group. The resulting experimental UV-visible spectrum recorded in methanol of the polydentate triazolyl-based Rh species revealed the loss of the vibronic coupling typically associated with an anthracenyl functional group. Moreover, TD-DFT modeling indicates the presence of an equilibrium process whereby the N-coordination of the pendant triazolyl group to the RhIII center appears to be highly labile. Charge decomposition analysis (CDA) of the DFT-modeled species with the dissociated triazolyl group revealed a pseudo-η3-allylic interaction between the π-type MOs of the transformed anthracenyl group and the RhIII center; thus, the singly attached chelating ligand is classified as having rare nonadenticity.

A Non-Equilibrium multiphysics model for coal seam gas extraction

Current permeability models are normally derived on the assumption of local equilibrium between coal matrixes and fracture within the representative elementary volume (REV) during gas extraction/injection. Under this assumption, the gas pressure and its associated swelling strain will distribute uniformly throughout the entire REV irrespective of the equilibration process between coal matrixes and fracture. This uniform distribution has long been considered as the reason why current permeability models cannot explain permeability data as widely reported. Significant efforts have been made to resolve this issue for the last decade but all these efforts ignore the transient nature of local equilibration evolution from initial to ultimate equilibrium states. In this study, we developed a concept of local non-equilibrium index (LNEI) to define a complete permeability model under the influence of gas extraction/injection. The application of this concept transforms equilibrium permeability models to non-equilibrium ones. Equilibrium models represent only two end points (before gas extraction/injection and after the completion of gas extraction/injection) while our non-equilibrium one represents the complete evolution of coal permeability between two end points. Our non-equilibrium model is degenerated to replicate all equilibrium models as reported in the literature and used as a key cross-coupling relation to formulate the non-equilibrium multiphysics model. Our non-equilibrium multiphysics model is verified against two rare experimental data sets and applied to predict the effects of the local equilibration process on both the evolution of coal permeability and the gas production under field conditions.

Dynamic compressive response of porcine muscle measured using a split Hopkinson bar system with a pair of PVDF force transducers

The classic metallic Split Hopkinson Pressure Bar (SHPB) cannot capture the transmitted signal accurately when measuring soft biological tissue, because of the very low wave impedance and strength of this material. So the dynamic compressive response of porcine muscle has been investigated by using a modified SHPB. The forces on both ends of the sample measured using Polyvinylidene fluor (PVDF) transducers were applied to calculate the stress in the specimen instead of the strain gauge signal on the transmitted bar. Moreover, a circular cardboard disk pulse shaper was applied for generating a suitable incident pulse to achieve stress equilibrium and constant strain rates in the specimens. Then, the dynamic mechanical properties of porcine muscle parallel and perpendicular to the fiber directions were measured, and the stress equilibrium process during loading was analyzed, as well as the inertia-induced extra stress being corrected. Furthermore, quasi-static tests were conducted at two different strain rates to investigate the strain rate dependence using a universal material testing machine. The results show that the stress-strain curves are sensitive to strain rate in the two different loading directions. The compressive stress perpendicular to the fiber direction is stiffer than that parallel to the fiber direction. In addition, a strain rate-dependent constitutive model was developed based on the mechanical response of the muscle at different strain rates and fitted to the experimental data. The results show that the overall fit is good, and the constitutive model could describe the muscle's dynamic mechanical properties.

Real-time computer assisted measurement of oocyte and embryo volume for assessment of transport parameters

Cryopreservation of gametes has revolutionized both animal agriculture and human reproductive medicine. Although many new technologies have tremendously improved the cryopreservation of oocytes and embryos, osmotic stress encountered during the equilibration process can cause their loss of function. Rational cryoprotective agent (CPA) equilibration strategies can be used to minimize this stress but require trained personnel to monitor the process in individual oocytes or embryos or require the use of suboptimal average transport parameter values in mathematically guided protocols. To enable individually optimized equilibration of CPAs in individual cells, here we establish experimental and computational techniques to track the osmotic behavior of individual bovine oocytes and embryos during CPA equilibration in real time. We designed a microfluidic device to provide a controlled flow of CPA and modified standard image analysis techniques to estimate real-time cell volume changes. In particular, we used a level-set method to define a boundary within a contour plot which could automate the image analysis process. A colour based level set algorithm coupled with contour smoothing not only provided the best fit but also reduced the segmentation time to well under a second per image. The accuracy of the automated method was comparable to human segmented images for both oocytes and embryos. This technology should enable both rapid evaluation of key biophysical parameters in oocytes and embryos undergoing CPA equilibration and the development of real-time feedback-control of CPA equilibration, enabling individual oocyte- and embryo-specific optimal protocols.

Aggregates of cationic calix[4]arenes in aqueous solution as media for governing protolytic equilibrium, fluorescence, and kinetics

Many water-soluble ionic calixarenes readily form micelle-like aggregates in aqueous solution. Presently, it is firmly proved that such aggregates tend to shift the state of the acid-base equilibrium of indicator dyes just in the same manner as cationic surfactant micelles do. In this paper, we further the corresponding studies and report the peculiarities of several kinds of solvatochromic effects, fluorescence, acid-base equilibrium and kinetic processes in aqueous solutions of four cationic amphiphilic calix[4]arenes bearing hydrophilic choline groups at the upper rim: 5,11,17,23-tetra(N,N-dimethyl-N-hydroxyethylammonium)methylene-25,26,27,28-tetraalkyl-oxycalix[4]arene tetrachlorides. n-Propyl, n-hexyl, n-octyl, and n-dodecyl were used as alkyls, and the calixarenes were designated as of Cn-C4A-Ch, where n = 3, 6, 8, and 12, respectively. The principal colloidal properties, i.e., particle size and electrophoretic mobility of aggregates were characterized via dynamic light scattering. In parallel, the results were compared with those obtained in the presence of micelles of the common cationic surfactant cetyltrimethylammonium bromide and of large-sized aggregates of the calix[6]arene with six methoxy groups at the lower rim. As tools, molecular probes of triphenylmethine and fluorescein series, as well as the solvatochromic Reichardt’s dye were used. The obtained block of data sheds light upon the properties of calixarene aggregates as tools for governing chemical processes.

Discrete Sampling of Extreme Events Modifies Their Statistics.

Extreme value (EV) statistics of correlated systems are widely investigated in many fields, spanning the spectrum from weather forecasting to earthquake prediction. Does the unavoidable discrete sampling of a continuous correlated stochastic process change its EV distribution? We explore this question for correlated random variables modeled via Langevin dynamics for a particle in a potential field. For potentials growing at infinity faster than linearly and for long measurement times, we find that the EV distribution of the discretely sampled process diverges from that of the full continuous dataset and converges to that of independent and identically distributed random variables drawn from the process's equilibrium measure. However, for processes with sublinear potentials, the long-time limit is the EV statistics of the continuously sampled data. We treat processes whose equilibrium measures belong to the three EV attractors: Gumbel, Fréchet, and Weibull. Our Letter shows that the EV statistics can be extremely sensitive to the sampling rate of the data.

Crosslinked polyethylenimine/polyacrylonitrile blend membrane for multifunctional adsorption of heavy metals and endocrine disrupting chemicals in solution

A novel polyethylenimine/polyacrylonitrile blend membrane (PEI/PAN) was synthesized via crosslinking technology for removing multiple kinds of heavy metals and endocrine disrupting chemicals (EDCs) from aqueous solution including Cu(II), Cr(VI), bisphenol S (BPS), and 2,4-dichlorophenoxyacetic acid (2,4-D) in batch mode. Several characterization techniques were applied to identify the morphological and physicochemical characteristics of the synthesized PEI/PAN. The results show that the maximum adsorption capacities of Cu(II), Cr(VI), BPS, and 2,4-D reach up to 97.6, 136, 318, and 1303 mg/g at pH of 2.50, 4.89, 4.95 and 2.84, respectively, whereas the presence of salinity in the solution has affected the adsorption process. Moreover, the uptake of Cu(II) is more in line with Elovich kinetic model, and the kinetic processes for Cr(VI), BPS and 2,4-D can be described by the pseudo-first-order model. Freundlich model is more suitable for describing the adsorption isotherm behavior of PEI/PAN toward Cu(II) and Cr(VI), and Koble-Corrigan model can describe the adsorptive equilibrium processes for BPS and 2,4-D. Thermodynamic parameters are speculated that these adsorption processes are spontaneous and entropy-increasing, with endothermic processes for elimination of Cu(II), Cr(VI), and 2,4-D, while that of BPS is exothermic. PEI/PAN has possessed good reusability after five reuse cycles and has antibacterial property against gram-positive S. aureus. These adsorption processes may mainly occur due to the complexation for Cu(II), electrostatic force for Cr(VI), hydrogen bonding for BPS, as well as electrostatic attraction and hydrogen bonding for 2,4-D. Therefore, PEI/PAN membrane exhibits great potential to purify the wastewater polluted with heavy metals and EDCs.