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1.
Chemphyschem ; 25(14): e202300730, 2024 Jul 15.
Artículo en Inglés | MEDLINE | ID: mdl-38411619

RESUMEN

Prolonged exposure to alcohol vapors can have detrimental effects on human health, potentially leading to eye irritation, dizziness, and in some cases, damage to the nervous system. The present article aims to provide a comprehensive understanding on the synthesis and characterization of zinc ferrite (ZnFe2O4) nanoparticles, as well as their interactions with a range of alcohol vapors, including methanol, ethanol, n-propanol, and isopropanol. These alcohols differ in their molecular weight, boiling points, diffusivity, and other properties. The study reveals the semiconducting ZnFe2O4 nanoparticulate sensor's capability for reversible, repeatable, and sensitive detection of alcohol vapors. The sensor exhibits the highest response to ethanol within operating temperature range (225-300 °C). An attempt is made to establish a correlation between the properties of the target analytes and the observed sensing signals. Additionally, the response conductance transients of ZnFe2O4 under the exposure to the studied alcohol vapors are modeled based on the Langmuir-Hinshelwood adsorption mechanism. The characteristic time constants obtained from this modeling are justified with respect to the properties of the analytes.

2.
Nanotechnology ; 35(40)2024 Jul 17.
Artículo en Inglés | MEDLINE | ID: mdl-38959867

RESUMEN

The number of layers present in a two-dimensional (2D) nanomaterial plays a critical role in applications that involve surface interaction, for example, gas sensing. This paper reports the synthesis of 2D WS2nanoflakes using the facile liquid exfoliation technique. The nanoflakes were exfoliated using bath sonication (BS-WS2) and probe sonication (PS-WS2). The thickness of the BS-WS2was found to range between 70 and 200 nm, and that of PS-WS2varied from 0.6 to 80 nm, indicating the presence of single to few layers of WS2when characterized using atomic force microscope. All the WS2samples were thoroughly characterized using electron microscopes, x-ray diffractometer, Raman spectroscopy, UV-Visible spectroscopy, Fourier transform infrared spectroscope, and thermogravimetric analyser. Both the nanostructured samples were exposed to 2 ppm of NO2at room temperature. Interestingly, BS-WS2which comprises of a greater number of WS2layers exhibited -14.2% response as against -3.4% response of PS-WS2, the atomically thin sample. The BS-WS2sample was found to be highly selective towards NO2but was slower (with incomplete recovery) as compared to PS-WS2. The PS-WS2sample was observed to exhibit -11.9% to -27.4% response to 2-10 ppm of CO and -3.4%-35.2% response to 2-10 ppm of NO2at room temperature, thereby exhibiting the potential to detect two gases simultaneously. These gases could be accurately predicted and quantified if the response times of the PS-WS2sample were considered. The atomically thin WS2-based sensor exhibited a limit of detection of 131 and 81 ppb for CO and NO2, respectively.

3.
Int J Mol Sci ; 24(12)2023 Jun 17.
Artículo en Inglés | MEDLINE | ID: mdl-37373431

RESUMEN

Defective molybdenum disulfide (MoS2) monolayers (MLs) modified with coinage metal atoms (Cu, Ag and Au) embedded in sulfur vacancies are studied at a dispersion-corrected density functional level. Atmospheric constituents (H2, O2 and N2) and air pollutants (CO and NO), known as secondary greenhouse gases, are adsorbed on up to two atoms embedded into sulfur vacancies in MoS2 MLs. The adsorption energies suggest that the NO (1.44 eV) and CO (1.24 eV) are chemisorbed more strongly than O2 (1.07 eV) and N2 (0.66 eV) on the ML with a cooper atom substituting for a sulfur atom. Therefore, the adsorption of N2 and O2 does not compete with NO or CO adsorption. Besides, NO adsorbed on embedded Cu creates a new level in the band gap. In addition, it was found that the CO molecule could directly react with the pre-adsorbed O2 molecule on a Cu atom, forming the complex OOCO, via the Eley-Rideal reaction mechanism. The adsorption energies of CO, NO and O2 on Au2S2, Cu2S2 and Ag2S2 embedded into two sulfur vacancies were competitive. Charge transference occurs from the defective MoS2 ML to the adsorbed molecules, oxidizing the later ones (NO, CO and O2) since they act as acceptors. The total and projected density of states reveal that a MoS2 ML modified with copper, gold and silver dimers could be used to design electronic or magnetic devices for sensing applications in the adsorption of NO, CO and O2 molecules. Moreover, NO and O2 molecules adsorbed on MoS2-Au2s2 and MoS2-Cu2s2 introduce a transition from metallic to half-metallic behavior for applications in spintronics. These modified monolayers are expected to exhibit chemiresistive behavior, meaning their electrical resistance changes in response to the presence of NO molecules. This property makes them suitable for detecting and measuring NO concentrations. Also, modified materials with half-metal behavior could be beneficial for spintronic devices, particularly those that require spin-polarized currents.


Asunto(s)
Cobre , Gases , Adsorción , Molibdeno , Oro , Azufre
4.
Small ; 18(11): e2104984, 2022 03.
Artículo en Inglés | MEDLINE | ID: mdl-34894075

RESUMEN

With the demanding detection of unique toxic gas, semiconductor gas sensors have attracted tremendous attention due to their intriguing features, such as, high sensitivity, online detection, portability, ease of use, and low cost. Triethylamine, a typical gas of volatile organic compounds, is an important raw material for industrial development, but it is also a hazard to human health. This review presents a concise compilation of the advances in triethylamine detection based on chemiresistive sensors. Specifically, the testing system and sensing parameters are described in detail. Besides, the sensing mechanism with characterizing tactics is analyzed. The research status based on various chemiresistive sensors is also surveyed. Finally, the conclusion and challenges, as well as some perspectives toward this area, are presented.


Asunto(s)
Etilaminas , Compuestos Orgánicos Volátiles , Humanos , Semiconductores
5.
Sensors (Basel) ; 22(3)2022 Jan 24.
Artículo en Inglés | MEDLINE | ID: mdl-35161641

RESUMEN

Nitric oxide (NO) is a highly reactive toxic gas that forms as an intermediate compound during the oxidation of ammonia and is used for the manufacture of hydroxylamine in the chemical industry. Moreover, NO is a signaling molecule in many physiological and pathological processes in mammals, as well as a biomarker indicating the course of inflammatory processes in the respiratory tract. For this reason, the detection of NO both in the gas phase and in the aqueous media is an important task. This review analyzes the state of research over the past ten years in the field of applications of phthalocyanines, porphyrins and their hybrid materials as active layers of chemical sensors for the detection of NO, with a primary focus on chemiresistive and electrochemical ones. The first part of the review is devoted to the study of phthalocyanines and porphyrins, as well as their hybrids for the NO detection in aqueous solutions and biological media. The second part presents an analysis of works describing the latest achievements in the field of studied materials as active layers of sensors for the determination of gaseous NO. It is expected that this review will further increase the interest of researchers who are engaged in the current level of evaluation and selection of modern materials for use in the chemical sensing of nitric oxide.


Asunto(s)
Porfirinas , Indoles , Isoindoles , Óxido Nítrico
6.
Angew Chem Int Ed Engl ; 60(34): 18666-18672, 2021 Aug 16.
Artículo en Inglés | MEDLINE | ID: mdl-34032341

RESUMEN

2D conjugated metal-organic frameworks (2D c-MOFs) are emerging as electroactive materials for chemiresistive sensors, but selective sensing with fast response/recovery is a challenge. Phthalocyanine-based Ni2 [MPc(NH)8 ] 2D c-MOF films are presented as active layers for polarity-selective chemiresisitors toward water and volatile organic compounds (VOCs). Surface-hydrophobic modification by grafting aliphatic alkyl chains on 2D c-MOF films decreases diffused analytes into the MOF backbone, resulting in a considerably accelerated recovery progress (from ca. 50 to ca. 10 s) during humidity sensing. Toward VOCs, the sensors deliver a polarity-selective response among alcohols but no signal for low-polarity aprotic hydrocarbons. The octadecyltrimethoxysilane-modified Ni2 [MPc(NH)8 ] based sensor displays high-performance methanol sensing with fast response (36 s)/recovery (13 s) and a detection limit as low as 10 ppm, surpassing reported room-temperature chemiresistors.

7.
Sensors (Basel) ; 20(7)2020 Mar 29.
Artículo en Inglés | MEDLINE | ID: mdl-32235349

RESUMEN

In this work, thin films of vanadyl phthalocyanines (VOPc and VOPcF4) are studied as active layers for the detection of gaseous ammonia and hydrogen. The effect of F-substituents on the structural features of vanadyl phthalocyanine films and their sensor response toward ammonia (10-50 ppm) and hydrogen (100-500 ppm) is investigated by X-ray diffraction (XRD) and chemiresistive methods, respectively. It is shown that the sensor response of VOPcF4 films to ammonia is 2-3 times higher than that of VOPc films. By contrast, the sensor response to hydrogen is higher in the case of VOPc films. Apart from this, the hybrid structures of vanadyl phthalocyanine films with Pd nanoparticles deposited on their surface by a chemical vapor deposition method are also tested to reveal the effect of Pd nanoparticles on the sensitivity of VOPc films to hydrogen. Deposition of Pd nanoparticles on the surface of VOPc films leads to the noticeable increase of their sensitivity to hydrogen.

8.
Sensors (Basel) ; 19(3)2019 Jan 23.
Artículo en Inglés | MEDLINE | ID: mdl-30678070

RESUMEN

Treating diseases at their earliest stages significantly increases the chance of survival while decreasing the cost of treatment. Therefore, compared to traditional blood testing methods it is the goal of medical diagnostics to deliver a technique that can rapidly predict and if required non-invasively monitor illnesses such as lung cancer, diabetes, melanoma and breast cancer at their very earliest stages, when the chance of recovery is significantly higher. To date human breath nalysis is a promising candidate for fulfilling this need. Here, we highlight the latest key achievements on nanostructured chemiresistive sensors for disease diagnosis by human breath with focus on the multi-scale engineering of both composition and nano-micro scale morphology. We critically assess and compare state-of-the-art devices with the intention to provide direction for the next generation of chemiresistive nanostructured sensors.


Asunto(s)
Técnicas Biosensibles/métodos , Nanoestructuras/química , Semiconductores , Pruebas Respiratorias , Humanos
9.
Sensors (Basel) ; 18(7)2018 Jul 03.
Artículo en Inglés | MEDLINE | ID: mdl-29970853

RESUMEN

In this work, the sensor response of MPcFx (M = Cu, Co, Zn; x = 0, 4, 16) films toward gaseous NH3 (10⁻50 ppm) was studied by a chemiresistive method and compared to that of unsubstituted MPc films to reveal the effects of central metals and F-substituents on the sensing properties. A combination of atomic force microscopy and X-ray diffraction techniques have been used to elucidate the structural features of thin MPcFx films deposited by organic molecular beam deposition. It has been shown that the sensor response of MPcF4 films to ammonia is noticeably higher than that of MPc films, which is in good correlation with the values of binding energy between the metal phthalocyanine and NH3 molecules, as calculated by the density functional theory (DFT) method. At the same time, in contrast to the DFT calculations, MPcF16 demonstrated the lesser sensor response compared with MPcF4, which appeared to be connected with the different structure and morphology of their films. The ZnPcF4 films were shown to exhibit a sensitivity to ammonia up to concentrations as low as 0.1 ppm, and can be used for the selective detection of ammonia in the presence of some reducing gases and volatile organic compounds. Moreover, the ZnPcF4 films can be used for the detection of NH3 in the gas mixture simulating exhaled air (N2 76%, O2 16%, H2O 5%, and CO2 3%).

10.
Small ; 12(7): 911-20, 2016 Feb 17.
Artículo en Inglés | MEDLINE | ID: mdl-26728087

RESUMEN

A novel catalyst functionalization method, based on protein-encapsulated metallic nanoparticles (NPs) and their self-assembly on polystyrene (PS) colloid templates, is used to form catalyst-loaded porous WO3 nanofibers (NFs). The metallic NPs, composed of Au, Pd, or Pt, are encapsulated within a protein cage, i.e., apoferritin, to form unagglomerated monodispersed particles with diameters of less than 5 nm. The catalytic NPs maintain their nanoscale size, even following high-temperature heat-treatment during synthesis, which is attributed to the discrete self-assembly of NPs on PS colloid templates. In addition, the PS templates generate open pores on the electrospun WO3 NFs, facilitating gas molecule transport into the sensing layers and promoting active surface reactions. As a result, the Au and Pd NP-loaded porous WO3 NFs show superior sensitivity toward hydrogen sulfide, as evidenced by responses (R(air)/R(gas)) of 11.1 and 43.5 at 350 °C, respectively. These responses represent 1.8- and 7.1-fold improvements compared to that of dense WO3 NFs (R(air)/R(gas) = 6.1). Moreover, Pt NP-loaded porous WO3 NFs exhibit high acetone sensitivity with response of 28.9. These results demonstrate a novel catalyst loading method, in which small NPs are well-dispersed within the pores of WO3 NFs, that is applicable to high sensitivity breath sensors.


Asunto(s)
Apoferritinas/química , Biomarcadores/análisis , Coloides/química , Nanofibras/química , Óxidos/química , Poliestirenos/química , Tungsteno/química , Animales , Catálisis , Caballos , Sulfuro de Hidrógeno/análisis , Nanofibras/ultraestructura
11.
Adv Sci (Weinh) ; : e2405694, 2024 Aug 13.
Artículo en Inglés | MEDLINE | ID: mdl-39135514

RESUMEN

Sensors that can accurately assess oxygen (O2) concentrations in real time are crucial for a wide range of applications spanning personal health monitoring, environmental protection, and industrial process development. Here a high-performance chemiresistive sensor that allows for the rapid detection of O2 at room temperature under visible light illumination is described. Inspired by the operating principles of dye-sensitized solar cells, the chemiresistor is based on a single-walled carbon nanotube-titania hybrid (SWCNT-TiO2) bearing a molecular Re-based photosensitizer [(Pbpy)(CO)3ReBr] (Pbpy = 4,4'-[P(O)(OH)2]2-2,2'-bipyridine). The resulting SWCNT-TiO2-Re composite undergoes photoinduced charge transfer that is sensitive to ppb levels of O2, thereby yielding a rapid and reversible chemiresistive response. Owing to its unique mode of operation and robust components, the sensor shows a high degree of selectivity for O2 over a range of interferants, humidity tolerance, and multimonth benchtop stability. The approach presented herein demonstrates the translatability of concepts in light harvesting to the development of robust, rapid, and low-power sensing technologies.

12.
Micromachines (Basel) ; 14(9)2023 Sep 15.
Artículo en Inglés | MEDLINE | ID: mdl-37763935

RESUMEN

Halogenated metal phthalocyanines are promising materials for the manufacture of active layers of chemiresistive sensors for the detection of various gases. Despite the high interest in such sensors, there are few systematic studies of the position of halogen substituents in phthalocyanine macroring on the chemiresistive response of their films to gases. In this work, we prepared and studied films of novel tetrachlorosubstituted vanadyl phthalocyanine derivatives with Cl substituents in the peripheral (VOPcCl4-p) and nonperipheral (VOPcCl4-np) positions of the phthalocyanine ring as active layers of chemiresistive sensors to reveal the effect of the position of substituents on their structure and sensor response to low concentrations of NH3. It was shown that the films of VOPcCl4-p exhibited a noticeably higher sensor response to NH3 than the VOPcCl4-np ones. The limit of detection of NH3 was 0.7 ppm. The sensing layers demonstrated a reversible sensor response at room temperature with fairly low response/recovery times. It was also demonstrated that NH3 can be detected in the presence of various interfering gases (CO2 and H2) and some volatile organic vapors, as well as in a mixture of gases with a composition close to exhaled air.

13.
Nanomaterials (Basel) ; 13(18)2023 Sep 05.
Artículo en Inglés | MEDLINE | ID: mdl-37764530

RESUMEN

2D materials possess great potential to serve as gas-sensing materials due to their large, specific surface areas and strong surface activities. Among this family, transition metal chalcogenide materials exhibit different properties and are promising candidates for a wide range of applications, including sensors, photodetectors, energy conversion, and energy storage. Herein, a high-shear mixing method has been used to produce multilayered MoS2 nanosheet dispersions. MoS2 thin films were manufactured by vacuum-assisted filtration. The structural morphology of MoS2 was studied using ς-potential, UV-visible, scanning electron microscopy (SEM), atomic force microscopy (AFM), energy-dispersive X-ray spectroscopy (EDX), transmission electron microscopy (TEM), X-ray diffraction (XRD), and Raman spectroscopy (RS). The spectroscopic and microscopic analyses confirm the formation of a high-crystalline MoS2 thin film with good inter-sheet connectivity and relative thickness uniformity. The thickness of the MoS2 layer is measured to be approximately 250 nm, with a nanosheet size of 120 nm ± 40 nm and a number of layers between 6 and 9 layers. Moreover, the electrical characteristics clearly showed that the MoS2 thin film exhibits good conductivity and a linear I-V curve response, indicating good ohmic contact between the MoS2 film and the electrodes. As an example of applicability, we fabricated chemiresistive sensor devices with a MoS2 film as a sensing layer. The performance of the MoS2-chemiresistive sensor for NO2 was assessed by being exposed to different concentrations of NO2 (1 ppm to 10 ppm). This sensor shows a sensibility to low concentrations of 1 ppm, with a response time of 114 s and a recovery time of 420 s. The effect of thin-film thickness and operating temperatures on sensor response was studied. The results show that thinner film exhibits a higher response to NO2; the response decreases as the working temperature increases.

14.
ACS Sens ; 8(9): 3320-3337, 2023 09 22.
Artículo en Inglés | MEDLINE | ID: mdl-37602443

RESUMEN

Due to miscellaneous toxic gases in the vicinity, there is a burgeoning need for advancement in the existing gas sensing technology not only for the survival of mankind but also for the industries based in various fields such as beverage, forestry, health care, environmental monitoring, agriculture, and military security. A gas sensor must be highly selective toward a specific gas in order to avoid incorrect signals while responding to nontarget gases. This may lead to complex scenarios depicting sensor defects, such as low selectivity and cross-sensitivity. Therefore, a multiplex gas sensor is required to address the problems of cross selectivity by combining different gas sensors, signal processing, and pattern recognition techniques along with the currently employed gas sensing technologies. The different sensing materials used in these sensor arrays will produce a unique response signal for developing a set of identifiers as the input that can be used to recognize a specific gas by its "fingerprint". This review provides a comprehensive review of chemiresistive-based multiplex gas sensors, including various fabrication strategies from expensive to low-cost techniques, advances in sensing materials, and a gist of various pattern recognition techniques used for both rigid and flexible gas sensor applications. Finally, the review assesses the current state-of-the-art in multiplex gas sensor technology and discusses various challenges for future research in this direction.


Asunto(s)
Agricultura , Materiales Inteligentes , Bebidas , Monitoreo del Ambiente , Gases
15.
Biosensors (Basel) ; 12(7)2022 Jun 30.
Artículo en Inglés | MEDLINE | ID: mdl-35884279

RESUMEN

This work is aimed at the development of new heterostructures based on cobalt phthalocyanines (CoPc) and gold nanoparticles (AuNPs), and the evaluation of the prospects of their use to determine low concentrations of ammonia and nitric oxide. For this purpose, CoPc films were decorated with AuNPs by gas-phase methods (MOCVD and PVD) and drop-casting (DC), and their chemiresistive sensor response to low concentrations of NO (10-50 ppb) and NH3 (1-10 ppm) was investigated. A comparative analysis of the characteristics of heterostructures depending on the preparation methods was carried out. The composition, structure, and morphology of the resulting hybrid films were studied by X-ray photoelectron spectroscopy (XPS) and inductively coupled plasma atomic emission (ICP-AES) spectroscopy, as well as electron microscopy methods to discuss the effect of these parameters on the sensor response of hybrid films to ammonia and nitric oxide. It was shown that regardless of the fabrication method, the response of Au/CoPc heterostructures to NH3 and NO gases increased with an increase in the concentration of gold. The sensor response of Au/CoPc heterostructures to NH3 increased 2-3.3 times compared to CoPc film, whereas in the case of NO it increased up to 16 times. The detection limits of the Au/CoPc heterostructure with a gold content of ca. 2.1 µg/cm2 for NH3 and NO were 0.1 ppm and 4 ppb, respectively. It was shown that Au/CoPc heterostructures can be used for the detection of NH3 in a gas mixture simulating exhaled air (N2-74%, O2-16%, H2O-6%, CO2-4%).


Asunto(s)
Oro , Nanopartículas del Metal , Amoníaco/análisis , Gases/análisis , Oro/química , Indoles , Nanopartículas del Metal/química , Óxido Nítrico , Compuestos Organometálicos
16.
ACS Sens ; 7(8): 2104-2131, 2022 08 26.
Artículo en Inglés | MEDLINE | ID: mdl-35914109

RESUMEN

The increasing demand for food production has necessitated the development of sensitive and reliable methods of analysis, which allow for the optimization of storage and distribution while ensuring food safety. Methods to quantify and monitor volatile and biogenic amines are key to minimizing the waste of high-protein foods and to enable the safe consumption of fresh products. Novel materials and device designs have allowed the development of portable and reliable sensors that make use of different transduction methods for amine detection and food quality monitoring. Herein, we review the past decade's advances in volatile amine sensors for food quality monitoring. First, the role of volatile and biogenic amines as a food-quality index is presented. Moreover, a comprehensive overview of the distinct amine gas sensors is provided according to the transduction method, operation strategies, and distinct materials (e.g., metal oxide semiconductors, conjugated polymers, carbon nanotubes, graphene and its derivatives, transition metal dichalcogenides, metal organic frameworks, MXenes, quantum dots, and dyes, among others) employed in each case. These include chemoresistive, fluorometric, colorimetric, and microgravimetric sensors. Emphasis is also given to sensor arrays that record the food quality fingerprints and wireless devices that operate as radiofrequency identification (RFID) tags. Finally, challenges and future opportunities on the development of new amine sensors are presented aiming to encourage further research and technological development of reliable, integrated, and remotely accessible devices for food-quality monitoring.


Asunto(s)
Nanotubos de Carbono , Materiales Inteligentes , Aminas Biogénicas , Calidad de los Alimentos , Inocuidad de los Alimentos
17.
ACS Appl Bio Mater ; 2(8): 3678-3685, 2019 Aug 19.
Artículo en Inglés | MEDLINE | ID: mdl-35030754

RESUMEN

Organic charge-transfer (CT) complexes with a unique electrical performance are attractive materials for organic electronics. However, achieving breakthroughs in the practical application of CT complexes through rational design have always been a challenge. For the first time, a chemiresistive sensor for nerve agent that mimics (diethyl chlorophosphate) vapor detection is rationally designed based on organic CT complexes. Such CT complex chemiresistive sensor realizes a subppb detection of diethyl chlorophosphate (DCP) within 5 s under atmospheric conditions at room temperature with a high selectivity. Meanwhile, based on the highly tunable characteristics of CT complexes, the influence of morphology and intermolecular interaction on the sensing response are investigated. It is worth noting that a stronger intermolecular interaction results in lower sensing responses for CT complexes with a different D/A combination but with the same ratio. The organic charge-transfer materials not only provide a highly tunable platform for the chemiresistive sensor but also have the special properties such as solution processability, flexibility, and molecular recognition, which provides more possibilities for the application of flexible and wearable biosensors.

18.
ACS Appl Mater Interfaces ; 10(18): 16169-16176, 2018 May 09.
Artículo en Inglés | MEDLINE | ID: mdl-29641171

RESUMEN

The primary objective of this work is to demonstrate a novel sensor system as a convenient vehicle for scaled-up repeatability and the kinetic analysis of a pixelated testbed. This work presents a sensor system capable of measuring hundreds of functionalized graphene sensors in a rapid and convenient fashion. The sensor system makes use of a novel array architecture requiring only one sensor per pixel and no selector transistor. The sensor system is employed specifically for the evaluation of Co(tpfpp)ClO4 functionalization of graphene sensors for the detection of ammonia as an extension of previous work. Co(tpfpp)ClO4 treated graphene sensors were found to provide 4-fold increased ammonia sensitivity over pristine graphene sensors. Sensors were also found to exhibit excellent selectivity over interfering compounds such as water and common organic solvents. The ability to monitor a large sensor array with 160 pixels provides insights into performance variations and reproducibility-critical factors in the development of practical sensor systems. All sensors exhibit the same linearly related responses with variations in response exhibiting Gaussian distributions, a key finding for variation modeling and quality engineering purposes. The mean correlation coefficient between sensor responses was found to be 0.999 indicating highly consistent sensor responses and excellent reproducibility of Co(tpfpp)ClO4 functionalization. A detailed kinetic model is developed to describe sensor response profiles. The model consists of two adsorption mechanisms-one reversible and one irreversible-and is shown capable of fitting experimental data with a mean percent error of 0.01%.

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