Mathematical modeling of controlled-release systems of herbicides using lignins as matrices

The herbicides applied in soils can be easily lost, owing to leaching, volatilization, and bio-and photodegradation. Controlled-release systemsusing polymeric matrices claim to solve these problems. The movement of the herbicides in the soilisalso an important phenomenon to be studied in order to evaluate the loss processes. The development of mathematical models is a relevantrequirement for simulation and optimization of such systems. This study reviews mathematical models as an initial step for modeling data obtained for controlled-release systems of herbicides (diuron, 2,4-dichlorophenoxyacetic acid, and ametryn) using sugarcane bagasse lignin as a polymeric matrix. The release kinetic studies were carried out using several acceptorsystems includinga water bath, soil, and soil-packed columns. Generally, these models take into account phenomena such as unsteady-state mass transfer by diffusion (Fick'slaw) and convection, consumption by several processes, and partitioning processes, resulting in partial differential equations with respect to time and space variables.     

Discrete-time stochastic modeling and simulation of biochemical networks

Since inherent randomness in chemically reacting systems is evident, stochastic modeling and simulation are exceedingly important for investigating complex biological networks. Within the most common stochastic approach a network is modeled by a continuous-time Markov chain governed by the chemical master equation. We show how the continuous-time Markov chain can be converted to a stochastically identical discrete-time Markov chain and obtain a discrete-time version of the chemical master equation. Simulating the discrete-time Markov chain is equivalent to the Gillespie algorithm but requires less effort in that it eliminates the generation of exponential random variables. Thus, exactness as possessed by the Gillespie algorithm is preserved while the simulation can be performed more efficiently.     

Redox flow batteries for energy storage: their promise,achievements and challenges

Redox flow batteries continue to be developed for utility-scale energy storage applications. Progress on standardisation, safety and recycling regulations as well as financing has helped to improve their commercialisation. The technical progress of redox flow batteries has not considered adequately the significance of electrolyte flow velocity, mass transfer and plug flow reactor modelling, despite steps in the right direction. 3D simulations of fluid flow, pressure drop, current distribution and mechanical resistance using commercial software are becoming more common, but satisfactory validation by experiments is still unusual. The majority of research tends to report short-term studies on small electrodes, often in poorly defined flow channels; long-term evaluation of electrode and membrane durability on a pilot scale is needed. Digital imaging of electrode structure using X-ray computed tomography is increasingly being used. Much activity is directed to organic and non-aqueous systems. However, scale-up and high, sustained charge capacity using electrolytes of moderate cost, which are environmentally acceptable to source, store, transport and handle, require considerable attention. Recommendations for future work are discussed.     

Diafiltration of Eucalyptus wood autohydrolysis liquors: Mathematical modeling

Liquors from the aqueous processing of Eucalyptus wood were diafiltered through a nanofiltration ceramic membrane, and experimental data concerning the time-course of flux and concentrations of the different compounds present in the medium (monosaccharides, oligosaccharides, oligosaccharide substituents and other non-volatile compounds) were determined. A mathematical model based on a combination of osmotic pressure and an additional in-series resistance provided a quantitative interpretation of experimental data.     

Mathematical modeling of the graft reaction between polystyrene and polyethylene

Polystyrene (PS) and polyethylene (PE) are two major components of household plastic waste whose blends are immiscible. Recycling them together is an attractive option that requires a compatibilization process to improve the blend mechanical properties. If a PE/PS copolymer is added or formed in situ, it may act as compatibilizer. The structure and molecular properties of this copolymer are key factors to assure its effectivity as a compatibilizer. In this work, we study the graft copolymerization reaction between polystyrene and polyethylene using the catalytic system composed of AlCl₃ and styrene. We develop a model of this process which considers that PE/PS grafting and PS degradation occur simultaneously. We propose a kinetic mechanism for the whole process and apply the method of moments to solve the mass balance equations. The model is able to calculate average molecular weights as well as the amount of grafted PS. It accurately describes the available experimental data, constituting a valuable tool for simulation and optimization purposes.     

Perspective on antiferroelectrics for energy storage and conversion applications

As a close relative of ferroelectricity,antiferroelectricity has received a recent resurgence of interest driven by technological aspirations in energy-efficient applications,such as energy storage capacitors,solid-state cooling devices,explosive energy conversion,and displacement transducers.Though prolonged efforts in this area have led to certain progress and the discovery of more than 100 antiferroelectric materials over the last 70 years,some scientific and technological issues remain unresolved.Herein,we provide perspectives on the development of antiferroelectrics for energy storage and conversion applications,as well as a comprehensive understanding of the structural origin of antiferroelectricity and field-induced phase transitions,followed by design strategies for new lead-free antiferroelectrics.We also envision unprecedented challenges in the development of promising antiferroelectric materials that bridge materials design and real applications.Future research in these directions will open up new possibilities in resolving the mystery of antiferroelectricity,provide opportunities for comprehending structure-property correlation and developing antiferroelectric/ferroelectric theories,and suggest an approach to the manipulation of phase transitions for real-world applications.     

Mathematical modeling and sustained release property of a 5-fluorouracil imprinted vehicle

In the present research, a type of imprinted hydrogels, in which 5-fluorouracil is complexed non-covalently to the monomers and cross-linked into the hydrogel matrix, is synthesized in order to evaluate the possibility of their applications in sustaining the release of 5-fluorouracil due to the drug’s heightened interactions with the imprinted binding sites. Because of the hydrophility, hydrogels can absorb large amounts of water. As a result, drug release mechanisms are different from hydrophobic polymers. Mathematical model has been established to predict the drug release from the hydrogel matrix as a function of time. The drug release mechanism when immersed in release medium is discussed based on mathematical analysis. Swelling studies are performed and the capability of the hydrogels to reload 5-fluorouracil in aqueous solutions is evaluated. In vitro release studies after reloading are conducted. Mathematical analysis suggest that drug release kinetics from the hydrogels fit Fickian mechanism, further evaluation of the fitness for different hydrogel types reveal that the conformation of binding sites can play a very important role in deciding the kind of drug release mechanism. Experiments reveal that all hydrogels show swelling property. The imprinted hydrogels bind much more 5-fluorouracil than non-imprinted ones, and they sustain 5-fluorouracil release better than non-imprinted hydrogels. This research indicates that the imprinted hydrogels would be a potential promising device for drug delivery.     

Mathematical modeling and simulation of inulinase adsorption in expanded bed column

A mathematical model for an expanded bed column was developed to predict breakthrough curves for inulinase adsorption on Streamline SP ion-exchange adsorbent, using a crude fermentative broth with cells as the feedstock. The kinetics and mass transfer parameters were estimated using the PSO (particle swarm optimization) heuristic algorithm. The parameters were estimated for each expansion degree (ED) using three breakthrough curves at initial inulinase concentrations of 65.6 U mL⁻¹. In sequence, the model parameters for an ED of 2.5 were validated using the breakthrough curve at an initial concentration of 114.4 U mL⁻¹. The applicability of the validated model in process optimization was investigated, using the model as a process simulator and experimental design methodology to optimize the column and process efficiencies. The results demonstrated the usefulness of this methodology for expanded bed adsorption processes.     

Direct chlorine determination in crude oils by energy dispersive X-ray fluorescence spectrometry: An improved method based on a proper strategy for sample homogenization and calibration with inorganic standards

Official guidelines to perform chlorine determination in crude oil are (i) American Society for Testing and Materials (ASTM) D6470, which is based on the extraction of water from the oil and subsequent determination of the chloride by potentiometry, (ii) ASTM D3230, that measures the conductivity of a solution of crude oil in a mixture of organic solvents and (iii) US Environmental Protection Agency (EPA) 9075 that uses energy dispersive X-ray fluorescence spectrometry to quantify chlorine and it is applicable for the range from 200 μg g^− 1 to percent levels of the analyte. The goal of this work is to propose method to quantify lower amounts of chlorine in crude oil using energy dispersive X-ray fluorescence spectrometry using a simple calibration strategy. Sample homogenization procedure was carefully studied in order to enable accurate results. The calibration curve was made with standards prepared by diluting aqueous NaCl standard in glycerin. The method presented a linear response that covers the range from 8 to at least 100 μg g^− 1 of chlorine. Chlorine in crude oil samples from Campos Basin - Brazil were quantified by the proposed method and by potentiometry after extraction of chlorine from the oil. Results achieved using both methods were statistically the same at 95% confidence level.     

Mathematical modeling of controlled-relase kinetics of herbicides in a dynamic-water-bath system

Applied Biochemistry and Biotechnology - Release of herbicides from lignin-based formulations follows a diffusion-controlled mechanism. For mathematical modeling of diffusive transport, the...     

Design and parameterization of a stochastic cellular automaton describing a chemical reaction

Although most of the work concerned with reaction kinetics concentrates on empirical findings, stochastic models, and differential equations, a growing number of researchers is exploring other methods to elucidate reaction kinetics. In this work, the parameterization of an utter discrete spatio-temporal model, more specifically, a cellular automaton (CA), describing the reaction of HCl with CaCO(3) , is suggested. Furthermore, a system of partial differential equations (PDE), deduced from a set of CA rules, is implemented to compare both modeling paradigms. In this article, the experimental setup to acquire time series of data is explained, a stochastic CA-based model and a continuous PDE-based model capable of describing the reaction are proposed, the models are parameterized using the experimental data and, finally, the relationship between a discrete time step of the CA-based model and the physical time is studied. Essentially, the parameterization of both models can be traced back to the quest for a solution of the inverse problem in which a (set of) rule(s), respectively a system of PDE, is deduced starting from the observed data. It is demonstrated that the proposed CA- and PDE-based models are capable of describing the considered chemical reaction with a high accuracy, which is confirmed by a root mean squared error between the simulated and observed data of 0.388 and 0.869 g CO(2) , respectively. Further, it is shown that an exponential or linear relationship can be used to link the physical time to a discrete time step of the CA-based model.     

Mathematical modeling of the catalytic degradation of polystyrene in the presence of aluminum chloride

We model the effect of the catalyst AlCl₃ on polystyrene (PS). Detailed experimental studies were previously carried out on the effect of AlCl₃ on PS, as part of an effort to understand how to minimize the degradation of PS during the Friedel-Crafts alkylation performed to obtain a graft copolymer from immiscible blends of PS and a polyolefin (PO). In the present work three mathematical models for the catalytic degradation of PS are proposed, all of which consider that reaction starts with the elimination of a phenyl group from the PS chain, followed by either chain scission or a change in the chain structure. The models vary in the way they consider the strength of the main chain bonds, or the reactivity of modified PS chains. Kinetic parameters for each model are estimated. Although the three proposed models could be used to represent our own experimental data, one is more accurate. Experimental data from other authors are used to evaluate its capabilities. Based on the predictions of the better model, we discuss conditions to minimize PS scission, such as operating at low temperatures and AlCl₃ concentrations, and using short processing times.     

Two-dimensional hybrid nanomaterials derived from MXenes(Ti_3C_2T_x)as advanced energy storage and conversion applications

The development of two-dimensional hybrid nanomaterial derived from MXenes as high performance electrode material is the key component for the advanced ene rgy storage and conversion systems.In the past decades,MXene derived nanomaterials have attracted greatly interest in scientific activity and potential applications because of their unique synergistic properties such as high thermal stability,excellent electrical conductivity,large surface area,easy to handle and outstanding electro and photo chemical properties.This review is focused on the synthesis of hybrid nanomaterials from MXene(Ti_3C_2T_x) for renewable energy conversion and storage application including hydrogen evolution reaction,supercapacitor,lithium-ion batteries and photocatalysis.Finally,we also summarized the prospect and opportunities of novel two-dimensional hybrid nanomaterials derived MXene(Ti_3C_2T_x) fo r futuristic sustainable energy technology.     

Mathematical modeling of the role of bone turnover in pH regulation in bone interstitial fluid

Background and aimsBone turnover is strongly affected by pH of surrounding fluid, and in turn plays a role in maintaining systemic pH, however the quantitative contribution of bone processes to pH regulation is not known. Our goal was to develop a mathematical model describing pH regulation in the interstitial fluid and to examine the contribution of hydroxyapatite dissolution and precipitation to pH regulation.Materials and methodsWe modeled twelve reversible equilibrium reactions of sixteen calcium, phosphate, hydrogen and carbonate species in the interstitial fluid and examined the buffering capacity and range. The effect of hydroxyapatite dissolution and precipitation was modeled by assuming that the calcium, phosphate and hydroxide contained in the bone volume adjacent to the interstitial fluid is instantaneously added to or removed from the interstitial fluid.ResultsThe carbonate buffer was found to dominate electrochemical buffering system of the bone interstitial fluid. Nevertheless, the phosphate added during dissolution of bone hydroxyapatite significantly improved the interstitial fluid buffering capacity. In contrast, hydroxyapatite precipitation had limited effect on the interstitial fluid pH regulation.ConclusionThis study provides mechanistic insights into the physicochemical processes underlying the known role of bone turnover processes in regulation of body pH homeostasis.     

Role of MXene surface terminations in electrochemical energy storage: A review

MXenes are a group of recently discovered 2D materials and have attracted extensive attention since their first report in 2011; they have shown excellent prospects for energy storage applications owing to their unique layered microstructure and tunable electrical properties. One major feature of MXenes is their tailorable surface terminations (e.g., −F, −O, −OH). Numerous studies have indicated that the composition of the surface terminations can significantly impact the electrochemical properties of MXenes. Nonetheless, the underlying mechanisms are still poorly understood, mainly because of the difficulties in quantitative analysis and characterization. This review summarizes the latest research progress on MXene terminations. First, a systematic introduction to the approaches for preparing MXenes is presented, which generally dominates the surface terminations. Then, theoretical and experimental efforts regarding the surface terminations are discussed, and the influence of surface terminations on the electronic and electrochemical properties of MXenes are generalized. Finally, we present the significance and research prospects of MXene terminations. We expect this review to encourage research on MXenes and provide guidance for usingthese materials for batteries and supercapacitors.     

Improving breakdown strength and energy storage efficiency of poly(vinylidene fluoride-co-chlorotrifluoroethylene) and polyurea blend films by double layer structure design

All-organic composites are widely used in energy storage application due to the high breakdown strength performance, but the improvement of energy storage was limited by the relatively low dielectric constant. Therefore, to satisfy the high demands of dielectric materials, energy storage properties of polymer composites should be further enhanced. In this article, poly(vinylidene fluoride-co-chlorotrifluoroethylene) (P(VDF-CTFE)) and polyurea (PUA), which are known as high dielectric ferroelectric material and linearly high energy storage efficiency material respectively, are composited through double layer (DL) casting method for the first time. The properties of DL structured composite film is contrasted with solution blending structure especially in energy storage efficiency, and the results demonstrate that DL structure design can make great use of advantages of two materials and also can avoid the influence of phase separation between P(VDF-CTFE) and PUA efficiently. Moreover, high breakdown strength (6180 kV/cm) and high energy storage efficiency (77%) of DL composites can be realized simultaneously by incorporating PUA as an insulating layer, and the mechanism is discussed in detail. This work provides an effective route to improve the energy storage properties of polymer dielectric materials and shows great application potential.     

Formation of lithium fluoride/metal nanocomposites for energy storage through solid state reduction of metal fluorides

In order to utilize high energy metal fluoride electrode materials as direct replacement electrode materials for lithium ion batteries in the future, a methodology to prelithiate the cathode or anode must be developed. Herein, we introduce the use of a solid state Li₃N route to achieve the lithiation and mechanoreduction of metal fluoride based nanocomposites. The resulting prelithiation was found to be effective with the formation of xLiF:Me structures of very fine nanodimensions analogous to what is found by electrochemical lithiation. Physical and electrochemical properties of these nanocomposites for the bismuth and iron lithium fluoride systems are reported.     

Membraneless energy conversion and storage using immiscible electrolyte solutions

Breakthrough alternative technologies are urgently required to alleviate the critical need to decarbonise our energy supply. We showcase non-conventional approaches to battery and solar energy conversion and storage (ECS) system designs that harness key attributes of immiscible electrolyte solutions, especially the membraneless separation of redox active species and ability to electrify certain liquid–liquid interfaces. We critically evaluate the recent development of membraneless redox flow batteries based on biphasic systems, where one redox couple is confined to an immiscible ionic liquid or organic solvent phase, and the other couple to an aqueous phase. Common to all solar ECS devices are the abilities to harvest light, leading to photo-induced charge carrier separation, and separate the products of the photo-reaction, minimising recombination. We summarise recent progress towards achieving this accepted solar ECS design using immiscible electrolyte solutions in photo-ionic cells, to generate redox fuels, and biphasic “batch” water splitting, to generate solar fuels.     

Mathematical Modeling of Chemical Reactors—Development and Implementation of Novel Technologies

Mathematical modeling is an important tool for rapid and reliable reactor development and design. The models are built up from basic studies of the reaction mechanism and kinetics, the transfer processes, and the interactions within the system. A detailed understanding of the elementary processes enables the construction of powerful and complex models for dynamic and steady-state simulation. With the aid of experimentally determined parameter values one can develop new processes or improve existing ones. Excellent results obtained in experimental work under idealized laboratory conditions can seldom be fully realized in practice. This is due to factors such as transfer resistances, local gradients, fluctuating conditions, and constructional and other limitations which lead to unsatisfactory parameter values and higher costs to compensate for these shortcomings. Some recommendations are made for circumventing these deficiencies.