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Search results for: COULOMB GREEN FUNCTION
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Dynamic polarizability of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the Dirac-Coulomb Green function
PublicationWe utilize the Sturmian expansion of the Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B 30, 825 (1997)] to obtain components of the dynamic dipole polarizability tensor of the relativistic hydrogenlike atom in the ground state. It is found that the tensor may be expressed in terms of two independent quantities: a scalar polarizability and a vector polarizability, the latter being of the relativistic origin. In the static...
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Magnetizability of the relativistic hydrogen-like atom: applicayion of the Sturmian expansion of the first-order Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla magnetyzowalności relatywistycznego atomu wodoro-podobnego w stanie podstawowym.
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Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B 30 (1997) 825; erratum 30 (1997) 2747] is exploited to derive a closed-form expression for the magnetizability of an arbitrary discrete state of the relativistic one-electron atom with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric...
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Magnetic-field-induced electric quadrupole moments for relativistic hydrogenlike atoms: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe consider a Dirac one-electron atom placed in a weak, static, uniform magnetic field. We show that, to the first order in the strength of the external field, the only electric multipole moments, which are induced by the perturbation in the atom, are those of an even order. Using the Sturmian expansion of the generalized Dirac-Coulomb Green function we derive a closed-form expression for the electric quadrupole moment induced...
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Static magnetic multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationWe study far- and near-field magnetic and electric multipole moments induced in the ground state of the Dirac one-electron atom placed in a weak 2L-pole magnetostatic field. The analysis is carried out within the framework of the first-order Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian expansion of the generalized Dirac-Coulomb Green function [Szmytkowski, J. Phys. B 30, 825 (1997);J. Phys. B 30, 2747(E)...
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Static electric multipole susceptibilities of the relativistic hydrogenlike atom in the ground state: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationThe ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite $2^{L}$ polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997); erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997)] is used to derive closed-form analytical...
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Stark-induced magnetic anapole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationZnaleziono magnetyczny moment anapolowy indukowany w stanie podstawowym relatywistycznego atomu jednoelektronowego przez zewnętrzne stałe, słabe, jednorodne pole elektryczne. Podano wyrażenie analityczne dla polaryzowalności anapolowej takiego atomu. Obliczenia wykonano, stosując rozwinięcie sturmowskie uogólnionej funkcji Greena-Diraca-Coulomba.
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Gordon decomposition of the static dipole polarizability of the relativistic hydrogen-like atom: application of the Sturmian expansion of the first-order Dirac-Coulomb Green function.
PublicationWyprowadzono analityczne wyrażenie dla statycznej polaryzowalności dipolowej relatywistycznego atomu jednoelektronowego w stanie podstawowym. Dokonano rozkładu Gordona polaryzowalności. Pokazano, że polaryzowalność ma charakter czysto konwekcyjny.
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Electric-field-induced magnetic quadrupole moment in the ground state of the relativistic hydrogenlike atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie uogólnionej funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla magnetycznego momentu kwadrupolowego, indukowanego przez zewnętrzne słabe, stałe, jednorodne pole elektryczne w stanie podstawowym relatywistycznego atomujednoelektronowego.
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Electric and magnetic dipole shielding constans for the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla stałych ekranowania elektrycznego i magnetycznego relatywistycznego atomu wodoropodobnego w stanie podstawowym.
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Magnetic field-induced electric quadrupole moment in the ground state of the relativistic hydrogen-like atom: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function
PublicationStosując rozwinięcie sturmowskie funkcji Greena-Diraca-Coulomba, znaleziono wyrażenie analityczne dla elektrycznego momentu kwadrupolowego, indukowanego przez zewnętrzne pole magnetyczne w relatywistycznym atomie wodoropodobnym w stanie podstawowym. Wykazano, że jest to efekt czysto relatywistyczny.
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Closed-form expression for the magnetic shielding constant of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac–Coulomb Green function
PublicationWe present analytical derivation of the closed-form expression for the dipole magnetic shielding constant of a Dirac one-electron atom being in an arbitrary discrete energy eigenstate. The external magnetic field, by which the atomic state is perturbed, is assumed to be weak, uniform, and time independent. With respect to the atomic nucleus we assume that it is pointlike, spinless, motionless, and of charge Ze. Calculations are...
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Green function diagonal for a class of heat equations
PublicationA construction of the heat kernel diagonal is considered as element of generalized zeta function theory, which gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expressions of the Green function in the case of finite-gap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...
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Green`s function methods for Mathematical modeling of unidirectional diffusion process in isothermal metals bonding process
PublicationPodano wykorzystanie funkcji Greena w rozwiązaniu matematycznego modelu dyfuzji jednowymiarowej podczas izotermicznego łączenia metali.
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Mechanical Properties, Microstructure and Surface Quality of Polypropylene Green Composites as a Function of Sunflower Husk Waste Filler Particle Size and Content
PublicationAgricultural waste is a still untapped source of materials that can, in case of proper utilization, significantly improve the sustainability of polymers and their composites. In this work, polymer composites based on isotactic polypropylene were produced incorporating ground sunflower husk in the amount of 10 wt% and 20 wt%. The work’s main objective is to evaluate how preliminary fractioning of this agricultural waste filler affects...
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Relativistic two-dimensional hydrogen-like atom in a weak magnetic field
PublicationA two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh–Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are...
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Two-dimensional hydrogen-like atom in a weak magnetic field
PublicationWe consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr¨odinger perturbation theory, using the Sturmian expansion of the generalized radial Coulomb Green function, we derive explicit analytical expressions for corrections to an arbitrary planar hydrogenic bound-state energy level, up to the fourth...
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Jednoelektronowy atom Diraca w słabym polu magnetycznym
PublicationW rozprawie przedstawiono opis wpływu zewnętrznego stałego, słabego, jednorodnego pola magnetycznego na jednoelektronowy atom Diraca. Wykorzystując funkcje gęstości ładunku elektrycznego oraz gęstości prądu elektrycznego, rozważono procesy indukowania się w atomie dodatkowych elektromagnetycznych momentów multipolowych. Dokonano analizy indukowanego momentu dipolowego, w wyniku której uzyskano wyrażenie dla magnetyzowalności atomu....
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Properties and Formation of Mineralized Veins in an Organic-Rich Shale Formation
PublicationAn earlier paper defined mineral and organic matter constituents in weak interfaces in shale formations (Ptaszynska, et. al., 2016). The formation studied in the earlier work and here is the Jurassic, early-Cretaceous Vaca Muerta formation in the Neuquen basin in Argentina. In this earlier work, mineralized "veins" were noted to be prevalent and complicated, sometimes being shear weak interfaces while in other cases they were not....
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Green and equitable analytical chemistry
PublicationGreen analytical chemistry introduces the ideas of reduction ofanalytical activities impact on the environment. However, to bemore sustainable, analytical chemistry should include socialaspects in greater manner. In this light‘equitable’analyticalprocedures, which are easily available in terms of price andapplicability by everyday user, are developed. These positivetrends are observed as many procedures, based on commonlyused for...
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Complementary green analytical procedure index (ComplexGAPI) and software
PublicationIt is not easy to find appropriate tools for the evaluation of the “green”nature of analytical methodologies which involve the use of compounds, materials, or chemicals manufactured prior to the analytical step. Here, we propose a new metric for the evaluation of analytical procedures based on the GAC attributes. The proposed solution expands on the well-known green analytical procedure index by adding additional fields pertaining...
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Evaluation of Green Sample Preparation Techniques for Organic Compounds
PublicationNowadays, Green Analytical Chemistry (GAC) idea is of high importance, with impact on the rapid growth in the sample preparation area with special emphasis on sample preparation simplification, miniaturization and automation. Due to the fact that GAC is of high importance today, this study is focused on the evaluation of green sample preparation techniques for organic compounds. It is well known that sample preparation is considered...
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THE FUNCTION OF GREENERY IN A SKYSCRAPER: THE PLACEMENT AND ITS INFLUENCE
PublicationThe contrast between the high rise buildings; with their mostly geometric shapes, and the organic form of the greenery was visible even in the idea of a skyscraper. Yet the realizations and recent projects show emerging interest and the link between them. To better understand the developing function of the greenery in the context of a skyscraper, both literature and case studies are conducted. The aim is to relate the location...
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Green Chemistry Metrics with Special Reference to Green Analytical Chemistry
PublicationThe concept of green chemistry is widely recognized in chemical laboratories. To properly measure an environmental impact of chemical processes, dedicated assessment tools are required. This paper summarizes the current state of knowledge in the field of development of green chemistry and green analytical chemistry metrics. The diverse methods used for evaluation of the greenness of organic synthesis, such as eco-footprint, E-Factor,...
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Trends in the new generation of green solvents in extraction processes
PublicationAnalytical chemistry, like other scientific fields, has undergone a number of changes to make it more consistent with the concept of sustainable development. Among the various steps of chemical analysis, without a doubt, sample preparation is the bottleneck in regard to following a green protocol, especially in terms of solvent consumption. Therefore, many attempts have been made to improve the environmental friendliness of this...
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Superconductivity at 2.2 K in the layered oxypnictide La3Ni4P4O2
PublicationW pracy przedstawiamy odkrycie nowego, warstwowego, związku nadprzewodzącego La3Ni4P4O2.
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Green Lean in Services
PublicationThe study presents the basic aspects of the improvement of the company useing Green Lean concept. The authors refer to the basics of the concept, present its theoretical aspects together with a revew of possible actions to eliminate the green waste. All these considerations refer to the service activities of any kind in order to maintain holistic approach of the research.
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Simplified Dirac--Coulomb Equations
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The 12 principles of green analytical chemistry and the SIGNIFICANCE mnemonic of green analytical practices
PublicationThe current rapid development of green analytical chemistry (GAC) requires clear, concise guidelines in the form of GAC principles that will be helpful in greening laboratory practices. The existing principles of green chemistry and green engineering need revision for their use in GAC because they do not fully meet the needs of analytical chemistry. In this article we propose a set of 12 principles consisting of known concepts...
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Green analytical chemistry as an integral part of sustainable education development
PublicationGreen chemistry is an important way of thinking in the field of chemistry and aims to conduct processes in accordance with the principles of sustainable development. It is the application of a wide range of principles that minimize the impact of both chemical processes and products on the environment. And what about analytical chemistry? Without a doubt, analytical chemistry plays an important role in the sustainable development...
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Application of multivariate statistics in assessment of green analytical chemistry parameters of analytical methodologies
PublicationThe study offers a multivariate statistical analysis of a dataset, including the major metrological, “greenness” and methodological parameters of 43 analytical methodologies applied for aldrin determination (a frequently analyzed organic compound) in water samples. The variables (parameters) chosen were as follows: metrological (LOD, recovery, RSD), describing the “greenness” (amount of the solvent used, amount of waste generated)...
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Green and Sustainable Membranes: A review
PublicationMembranes are ubiquitous tools for modern water treatment technology that critically eliminate hazardous materials such as organic, inorganic, heavy metals, and biomedical pollutants. Nowadays, nano-membranes are of particular interest for myriad applications such as water treatment, desalination, ion exchange, ion concentration control, and several kinds of biomedical applications. However, this state-of-the-art technology suffers...
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Green, blue and energy in cities
PublicationThe article refers to the implementation of blue-green infrastructure in cities, with particular emphasis on the aspect of rainwater and energy management. The article presents the advantages of water and greenery in the city and gives examples of engineering solutions used, both the more popular (including green and biosolar roofs), as well as experimental solutions, which are an interesting and necessary alternative in the era...
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History and Milestones of Green Analytical Chemistry
PublicationDue to the increased environmental consciousness, Green Analytical Chemistry (GAC) is an important concept steadily gaining popularity, as its implementation facilitates the decrease the detrimental effect analytical chemistry methodologies may have on the environment. In this chapter, a brief overview of the history of Green Analytical Chemistry (GAC) and its milestones was given. Emphasis has been put on the beginnings of green...
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The implementation of green transformation through clusters
PublicationThe paper addresses a poorly documented issue in the literature, namely the role of clusters in green transformation, including processes related to green, low-carbon, and circular economies. The purpose was to identify and understand the practices of clusters in this area. The adopted mixed research strategy consisted of both qualitative and quantitative research. Both research phases were conducted in a group of Polish Key National...
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Green Sample Collection
PublicationThe term of “green sample collection” is directly associated with both passive and dynamic analytical tools which allow for simultaneous management of the stage of collection and isolation and/or enrichment of a broad spectrum of chemical compounds from environmental samples. The use of passive sampling techniques at the stage of sample collection makes it possible to obtain in a simple yet inexpensive manner an analytical information...
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Green analytical chemistry : theory and practice
PublicationThis tutorial review summarises the current state of green analytical chemistry with special emphasis on environmentally friendly sample preparation techniques. Green analytical chemistry is a part of the sustainable development concept; its history and origins are described. Miniaturisation of analytical devices and shortening the time elapsing between performing analysis and obtaining reliable analytical results are important...
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Green chromatography
PublicationAnalysis of organic compounds in samples characterized by different composition of the matrix is very important in many areas. A vast majority of organic compound determinations are performed using gas or liquid chromatographic methods. It is thus very important that these methods have negligible environmental impact. Chromatographic techniques have the potential to be greener at all steps of the analysis, from sample collection...
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Metrics for green analytical chemistry
PublicationGreen analytical chemistry, although not being a new concept, does not have a greenness metrics system. Green chemistry metrics are not suitable for analytical procedure assessment because they often refer to the mass of the product. Some efforts have been made to develop suitable metrics for analytical chemistry. Some are simple to use but do not cover all aspects of analytical methods’ environmental impact. Others are more comprehensive...
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Deep eutectic solvents – based green absorbents for effective volatile organochlorine compounds removal from biogas
PublicationVolatile organochlorine compounds (VOXs) presented in biogas can cause many technological and environmental problems. During the combustion of biogas containing VOXs, the corrosion of installation, as well as the formation of toxic by-products (polyhalogenated dioxins and furans) and further emission to the atmosphere, may occur. Therefore, in this study, a new procedure based on physical absorption was developed. In order to meet...
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Green Therapy w projektowaniu ośrodków medycznych Green Therapy in complex design of health centres
PublicationKoncepcja przestrzenna ogrodu terapeutycznego podporządkowana jest generalnej idei otwierania się projektantów na poszukiwanie nowych możliwości poprawy samopoczucia odbiorcy - poprzez zapewnienie użytkownikom poczucia bezpieczeństwa, komfortu i odprężenia, harmonii. Dotyczy to nie tylko grupy osób chorych, które dręczone są przez niepokoje i napięcia wywołane przez niepełnosprawność czy chorobę, ale także pacjentów w różnym wieku...
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Developments in Green Chromatography
PublicationGreen analytical chemistry is a widely recognized concept that has led to the development of new analytical methods with reduced environmental impact and minimized analyst occupational exposure. Achievements include the development of microextraction, ultrasound-assisted extraction (UAE), and microwave-assisted extraction (MAE) techniques. Research towards greener separation processes focuses on the elimination of toxic solvents...
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CONDITIONS OF THE GREEN TRANSFORMATION. THE CASE OF THE EUROPEAN UNION
PublicationThe main purpose of the paper is to identify the factors that determine the course of green transformation and to assess the current stage and possible directions of change in subsequent years in EU countries. The literature lacks comprehensive studies that show the impact of diverse types of factors on the course of green transformation. For this purpose, two perspectives of the research – economic and environmental – are usually...
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Green analytical chemistry metrics: A review
PublicationGreen analytical chemistry encourages reducing the use of toxic chemicals/reagents, using energy-efficient equipment, and generating minimal waste. The recent trends in analytical method development focus on the miniaturization of the sample preparation devices, the development of solventless or solvent-minimized extraction techniques, and the utilization of less toxic solvents. The twelve principles of GAC serve as a basic guideline...
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The smoothness test for a density function
PublicationThe problem of testing hypothesis that a density function has no more than μ derivatives versus it has more than μ derivatives is considered. For a solution, the L2 norms of wavelet orthogonal projections on some orthogonal ‘‘differences’’ of spaces from a multiresolution analysis is used. For the construction of the smoothness test an asymptotic distribution of a smoothness estimator is used. To analyze that asymptotic distribution,...
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A procedure for elastoplastic hardening function identification.
PublicationThe inverse analysis method for identifying a nonlinear hardening function,which governs a plastic yielding of soil and rock materials in the framework of elastoplastic theory is presented. A concept of two stage finite element based on spatial discretization of computational space and hardening function space is introduced. The proposed inverse analysis can be classified as the output least squares method. The Levenberg Marquard...
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Green Polymer Nanocomposites for Skin Tissue Engineering
PublicationFabrication of an appropriate skin scaffold needs to meet several standards related to the mechanical and biological properties. Fully natural/green scaffolds with acceptable biodegradability, biocompatibility, and physiological properties quite often suffer from poor mechanical properties. Therefore, for appropriate skin tissue engineering and to mimic the real functions, we need to use synthetic polymers and/or additives as complements...
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Don't forget the dark side of green transformation
PublicationDesign/methodology/approach – The study is a continuation of the research by Durst and Zieba (2019) related to knowledge risks and their potential outcomes. This present study makes an update on the literature on knowledge risks and green transformation and describes knowledge risks that can be faced in this process. Originality/value – The paper offers new insights for researchers dealing with the topic of knowledge risks in...
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Diethyl carbonate as a green extraction solvent for chlorophenol determination with dispersive liquid–liquid microextraction
PublicationThe principles of green analytical chemistry indicate that the search for greener organic solvents for extraction applications is crucial. In this study diethyl carbonate (DEC) is proved to be a green solvent, as it is relatively nontoxic, obtainable from renewable resources and biodegradable. Here it is applied as an extraction solvent for chlorophenol determination in water samples with dispersive liquid–liquid microextraction....
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Green Analytical Chemistry: Summary of Existing Knowledge and Future Trends
PublicationAnalysis of recent publications in green analytical chemistry shows the current trends and future needs in this area. The main issues are related with search for cheaper, more efficient, more accurate, greener and miniaturized alternatives. Miniaturization is perhaps, the most notable current trend in analytical chemistry. Rapid developments and improvements in instrumentation have led to impressive range of benchtop technology...