{"title":"Dynamic Process Flexibility Analysis Using Neural Networks and a Volumetric Flexibility Index","authors":"Zhongyu Zhang, Biao Huang, Zukui Li","doi":"10.1021/acs.iecr.4c04545","DOIUrl":"https://doi.org/10.1021/acs.iecr.4c04545","url":null,"abstract":"Uncertain parameters are common in real-world chemical processes due to inherent variations, underscoring the essential need for operational flexibility. In dynamic process systems, the feasible operation region evolves over time, complicating the assessment of flexibility. Current approaches for evaluating dynamic process flexibility are largely adaptations of techniques used for steady-state flexibility analysis, including the extended active set method and the extended vertex method. These strategies aim to identify the maximum allowable deviations of uncertain parameters from their nominal values. However, such conventional indices may lack reliability when the selected nominal point significantly deviates from the central position and/or when the feasible region exhibits nonconvex characteristics. In this paper, we propose a volumetric flexibility index to the dynamic systems and combine Physics-Informed Neural Network for Control (PINNC) and Convolutional Neural Network (CNN) to determine the flexibility index value. The PINNC model acts as a surrogate for the system’s dynamic model, while the CNN classification network model identifies the feasible region for uncertain parameters. The proposed framework effectively handles nonconvex feasible regions. Its effectiveness and advantages are highlighted through comparisons with existing methods.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"58 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143736914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bin Lan, Yuzhi Liu, Shuang Wu, Junlong Yang, Qi Yang
{"title":"Adhesive Mechanism of Polymer Patches with Densely Populated Convex and Concave Micropatterns in Dry and Wet Environments","authors":"Bin Lan, Yuzhi Liu, Shuang Wu, Junlong Yang, Qi Yang","doi":"10.1021/acs.iecr.5c00135","DOIUrl":"https://doi.org/10.1021/acs.iecr.5c00135","url":null,"abstract":"Fabricating polymer patches with highly adhesive properties through physical bonding methods offers the advantage of facile mass production, while avoiding the complexities and potential toxicity associated with chemical reactions and reagents. The adhesive performance of physically bonded polymer patches is intricately linked to their microstructural features. However, a significant knowledge gap persists regarding the influence of microstructures on the adhesive strength. Designing and controlling microstructures to achieve highly adhesive strength, particularly in wet environments, remains a critical challenge. In this study, we designed two simple yet representative micropattern patches utilizing van der Waals force and suction effect. The adhesion behavior was systematically analyzed in dry and wet environments by considering key structural dimensions and external stress. We explored the underlying adhesion mechanisms, developed a theoretical model to calculate the interfacial adhesion strength, and compared the performance of different microstructures in wet environments. These findings provided insights into optimizing interfacial adhesion, offering theoretical and empirical guidance for developing advanced adhesive patches with potential clinical applications.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"32 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143745620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hailin Huang, Zhiyi Huang, Xingshan Yin, Xiaofeng Lin, Lei Ji, Yingjuan Sun, Wenjing Lin, Jianxiong He, Jiahui He, Guobin Yi
{"title":"Construction of Polyurethane with Excellent Water-Tolerant and Self-Healing Properties by the Efficient Synergy of Imine Bonds and Aliphatic Long Chains","authors":"Hailin Huang, Zhiyi Huang, Xingshan Yin, Xiaofeng Lin, Lei Ji, Yingjuan Sun, Wenjing Lin, Jianxiong He, Jiahui He, Guobin Yi","doi":"10.1021/acs.iecr.5c00332","DOIUrl":"https://doi.org/10.1021/acs.iecr.5c00332","url":null,"abstract":"Thermoplastic polyurethane (TPU) elastomers are widely used as substrates for flexible sensing due to their excellent toughness and self-healing properties. However, water interference seriously impacts the mechanical and self-healing performance of TPU. Herein, a novel hydroxy-terminated polybutadiene-based polyurethane (HPU) with water tolerance and self-healing properties was constructed by the synergy of water-sensitive dynamic imine bond and aliphatic long side chains (glycidyl methacrylate (GM)). The introduction of GM enhances the water tolerance of HPU and reduces the polymer segment symmetry. This enables segment mobility to activate the dynamic imine bond metathesis, crucial for the self-healing of HPU. With this unique structure, HPU exhibits outstanding water tolerance, remaining stable underwater for 3 days without significant mechanical property decay. It also has a high self-healing efficiency, over 95% at 35 °C in 24 h and 79% underwater. In addition, HPU shows excellent mechanical properties (tensile strain: 1171%, tensile strength: 4.2 MPa, toughness: 34.9 MJ/m<sup>3</sup>). These excellent properties endow HPU with great potential in practical applications, especially in humidity-sensing. The humidity-sensing application based on HPU has a broad detection range (11–95% relative humidity (RH)) and stable signals in water. This elastomer, with excellent water tolerance and high self-healing, is expected to expand the practical applications of flexible sensing materials in harsh humidity or underwater environments.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"58 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143745442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kazuki Arima, Yuta Aoki, Mito Hotta, Nobuyoshi Koga
{"title":"Multistep Reaction Pathway and Kinetics of the Thermal Decomposition of Catalyst Precursors: Copper(II)–Zinc Hydroxycarbonates","authors":"Kazuki Arima, Yuta Aoki, Mito Hotta, Nobuyoshi Koga","doi":"10.1021/acs.iecr.5c00217","DOIUrl":"https://doi.org/10.1021/acs.iecr.5c00217","url":null,"abstract":"The Cu–Zn hydroxycarbonates serve as precursors for the preparation of CuO–ZnO and Cu–ZnO catalysts for methanol synthesis. In this study, the multistep thermal decomposition of Cu–Zn hydroxycarbonates with varying Cu:Zn ratios was investigated using a methodologically sound kinetic analysis procedure. The objective was to provide fundamental data regarding the heterogeneous reaction scheme and kinetics of multistep thermal decomposition. It is expected that the fundamental kinetic data will subsequently be optimized for the specific Cu–Zn hydroxycarbonate under specific reaction conditions and utilized for refining the processing conditions to prepare CuO–ZnO and Cu–ZnO. The Cu–Zn hydroxycarbonates with different Cu:Zn ratios were characterized as malachite, zincian malachite, aurichalcite, and hydrozincite, as well as these mixtures depending on the Cu:Zn ratio. For all Cu–Zn hydroxycarbonate samples, the multistep thermal decomposition was individually modeled as a partially overlapping five-step process to produce CuO–ZnO via poorly crystalline intermediate oxycarbonates or carbonates. The contribution and kinetic parameters of each reaction step in individual samples with specific Cu:Zn ratios were tabulated, which were correlated to the stoichiometry of the multistep reaction and compared between different samples.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"183 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143745443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pedro Velho, Eduardo Sousa, José T. Coelho, Diogo Moreira, Eugénia A. Macedo
{"title":"New ATPSs Containing Choline Salts and Propan-1-ol: Phase Equilibria, eNRTL Modeling, and Partitioning Studies","authors":"Pedro Velho, Eduardo Sousa, José T. Coelho, Diogo Moreira, Eugénia A. Macedo","doi":"10.1021/acs.iecr.5c00145","DOIUrl":"https://doi.org/10.1021/acs.iecr.5c00145","url":null,"abstract":"In this work, the liquid–liquid equilibria (LLE) of the Aqueous Two-Phase Systems (ATPSs) {propan-1-ol (1) + choline bicarbonate ([Ch][Bic]) or choline dihydrogen citrate ([Ch][H<sub>2</sub>Cit]) (2) + water (3)} were assessed at 298.15 K and 0.1 MPa. Solubility curves were estimated by the “cloud-point” method, while tie-line composition data were determined using third-degree polynomials of liquid density (ρ) and electrical conductivity (κ). The obtained LLE data were correlated with low standard deviations (σ<sub>SD</sub>) using various empirical models, such as the ones of Han et al. for solubility data (3.8 < σ<sub>SD</sub> × 10<sup>3</sup> < 11) and Bancroft-Hubard for tie-line composition data (3.4 < σ<sub>SD</sub> × 10<sup>2</sup> < 4.6). Tie-line composition data were also described with the electrolyte-Non-Random Two-Liquid (eNRTL) model, considering the ATPSs as mixed solvent media with strong salts and obtaining low standard deviations (7.3 < σ<sub>SD</sub> × 10<sup>7</sup> < 7.7). Although very successful, this modeling approach required a significant number of adjustable parameters to describe all the interacting species, which may be intensive from a computational point of view. Moreover, during thermodynamic modeling, nonrandomness factors based on calculations at the Density Functional Theory (DFT) level were applied for propan-1-ol (α = 0.1970) and water (α = 0.3333), while a fixed value was used for the choline salts (α = 0.2). Finally, to demonstrate the practical potential of these ATPSs for removing pharmaceutical pollutants from water, partition studies of salicylic acid (Sa) were conducted in these systems, attaining promising partition coefficients (2.1 ± 0.3 < <i>K</i> < 5.6 ± 0.9) and extraction efficiencies (53 ± 2 < <i>E</i>/% < 87 ± 3), specially for the system containing [Ch][H<sub>2</sub>Cit] (4.4 ± 0.5 < <i>K</i> < 5.6 ± 0.9) and (77 ± 2 < <i>E</i>/% < 87 ± 3). Moreover, a positive effect on these performance indicators was observed with growing lengths of tie-line (TLLs), for which a significant affinity exists between the target solute and propan-1-ol.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"70 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143736414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chinmay Patil, Sumit Hazare, Vivek Vitankar, Aniruddha J. Joshi, Ashwin Wasudeo Patwardhan, Jyeshtharaj B. Joshi
{"title":"Leveraging Machine Learning for Heat Transfer Coefficient Estimation in Gas–Liquid and Gas–Liquid–Solid Bubble Columns","authors":"Chinmay Patil, Sumit Hazare, Vivek Vitankar, Aniruddha J. Joshi, Ashwin Wasudeo Patwardhan, Jyeshtharaj B. Joshi","doi":"10.1021/acs.iecr.4c04741","DOIUrl":"https://doi.org/10.1021/acs.iecr.4c04741","url":null,"abstract":"For a precise design of the bubble column, it is crucial to accurately estimate design parameters, such as heat and mass transfer coefficient. The heat transfer coefficient in the bubble column or slurry bubble column can be calculated by empirical or semiempirical correlations. These correlations fail to correlate the multidimensional nature of the data and lack generalization, whereas machine learning (ML) models have the advantage of doing the same. Most of the correlations in the existing literature are for gas–liquid bubble columns. In the present study, a regressive ML model for the estimation of the heat transfer coefficient for gas–liquid as well as gas–liquid–solid bubble columns was developed on published experimental data. Three different ML methods, artificial neural networks (ANN), random forest (RF), and support vector regression (SVR), were used to train the data set. Models were trained on the data set with individual parameters and dimensionless numbers. The data set consists of 962 data points with individual features such as column diameter, height of clear liquid, sparger type, sparger hole diameter, % free area, pressure, temperature, superficial gas and liquid velocity, gas density, mixture density, viscosity, specific heat capacity and thermal conductivity, surface tension, particle diameter, and heat transfer measurement location. The present study shows that SVR trained on dimensionless numbers performed better than SVR, RF, and ANN trained on individual parameters and RF and ANN trained on dimensionless numbers. The overall mean absolute percentage error (MAPE), <i>R</i><sup>2</sup>, and number of outliers for the SVR model were 8.42%, 0.983, and 85 outliers out of 962 data points, respectively. The SVR model trained with dimensionless numbers could predict the effects of pressure and particle concentration.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"36 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143736481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimizing Polyacrylonitrile Membranes with Polyethylene Glycol-1000 for Efficient Municipal Wastewater Treatment","authors":"Mahesh Manikantan Sandhya, Animesh Jana, Akshay Modi","doi":"10.1021/acs.iecr.5c00095","DOIUrl":"https://doi.org/10.1021/acs.iecr.5c00095","url":null,"abstract":"This study investigates the effect of polyethylene glycol (<i>M</i><sub>w</sub>: 1000 Da, PEG-1000) incorporation on polyacrylonitrile (PAN) membranes for enhanced municipal wastewater treatment. Surface functionality analysis confirmed successful integration, while morphological studies revealed a transformation from finger-like cavities (pristine PAN membrane) to a spongy structure with PEG-1000. Increased PEG-1000 concentration enhanced hydrophilicity and maintained thermal stability while increasing surface roughness. However, pure water flux decreased marginally. Remarkably, PAN membranes blended with ≥2 wt % PEG-1000 exhibited significant improvements in antifouling performance when tested with simulated and real municipal wastewater, achieving flux recovery values of >80% compared to 73.8% for pristine membranes. Bovine serum albumin (BSA) rejection values exceeded 99% across all membranes. Long-term evaluations (up to 10 cycles) demonstrated excellent antifouling stability for membranes containing 2 wt % PEG-1000. These findings suggest that incorporating 2 wt % PEG-1000 is optimal for enhancing PAN membrane performance in municipal wastewater treatment.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"36 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Experimental and Numerical Analysis of an Interactive Motion Drum for Enhanced Mixing and Segregation of Mixtures","authors":"Leqi Lin, Kaiyuan Yang, Xin Zhang, Chengbo Liu, Kun Hong, Xizhong Chen","doi":"10.1021/acs.iecr.5c00591","DOIUrl":"https://doi.org/10.1021/acs.iecr.5c00591","url":null,"abstract":"Rotating drums are widely used in particle processing, where internal obstacles play a crucial role in controlling particle mixing and segregation dynamics. Traditional designs often struggle with stagnant zones and inconsistent mixing dynamics, particularly under varying rotational conditions. This study addresses this gap by proposing an innovative interactive motion design between the drum and obstacles, creating reverse rolling waves that disrupt stagnant zones and enhance mixing efficiency. By employing counter-rotation (where the drum and obstacles rotate in opposite directions), the design effectively disrupts stagnant zones, enhances convection and diffusion, and significantly improves mixing efficiency across different speeds. At higher rotational speeds, cascading effects intensify, reducing particle clusters while maintaining high mixing efficiency. Conversely, synchronous rotation (drum and obstacles rotating in the same direction) favors segregation, with obstacles disrupting particle flow, leading to localized velocity reductions and eventual separation. To quantitatively assess these effects, machine learning algorithms, including Segment Anything, were employed to analyze experimental and simulation results, providing robust validation of particle dynamics. Additionally, a 3D-printed, self-designed rotating drum was utilized to experimentally validate the optimized flow patterns predicted through simulations. This study offers new insights into designing advanced rotating drum systems with enhanced control over mixing and segregation dynamics, bridging the gap between computational modeling and experimental validation for improved particle processing performance.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"30 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Emmanuel N. Skountzos, Ashwin Ravichandran, Maricela Lizcano, John W. Lawson
{"title":"Molecular Dynamics Simulations for the Prediction of the Conformational, Dynamic, and Thermal Properties of Poly(phenylsulfone) (PPSU) and Their Dependence on Molecular Weight","authors":"Emmanuel N. Skountzos, Ashwin Ravichandran, Maricela Lizcano, John W. Lawson","doi":"10.1021/acs.iecr.4c04601","DOIUrl":"https://doi.org/10.1021/acs.iecr.4c04601","url":null,"abstract":"Atomistic configurations of model poly(phenylsulfone) (PPSU) systems, with molecular lengths ranging from <i>N</i> = 5 to <i>N</i> = 50 monomers, were thoroughly relaxed by subjecting them to detailed molecular dynamics (MD) simulations. We present results for their thermal properties, including the thermal expansion coefficient (<i>a</i><sub>P</sub>) and the thermal conductivity (λ). Our simulation predictions for both properties align relatively closely with experimental values, and no significant correlation with the PPSU chain length was recorded. Prior to examining the thermal properties at <i>T</i> = 300 K, we conducted an extensive analysis of the thermodynamic, structural, conformational, and dynamic properties of these models in the molten state at <i>T</i> = 700 K. This provided valuable microscopic insights, such as the dependence of the mean-squared radius of gyration, mean-squared end-to-end distance, self-diffusion coefficient, and total relaxation time on molecular weight, which were subsequently correlated with the zero-rate shear viscosity. During the quenching process from high temperatures to ambient conditions, we estimated the glass transition temperature (<i>T</i><sub>g</sub>) of all model systems, and the predicted values relatively matched the experimental data within the expected range, considering the high cooling rates in the MD simulations. Our simulations effectively captured the important dependence of <i>T</i><sub>g</sub> on molecular weight.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"15 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143734096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamic Control to Maximize the Performance of Protein A Resin in Antibody Extraction","authors":"Fred Ghanem, Kirti M. Yenkie","doi":"10.1021/acs.iecr.4c03098","DOIUrl":"https://doi.org/10.1021/acs.iecr.4c03098","url":null,"abstract":"Antibody therapies are critical in treating various diseases such as cancer and autoimmune diseases. Affinity chromatography is the most expensive and necessary step in the purification of antibodies. Therefore, optimizing this step is critical to maintaining downstream operations and minimizing costs. This work uses an accurate sigmoidal model to represent the resin process condition. Unfortunately, variations in antibody concentrations and the inherent process uncertainties in biological systems make the process optimization task challenging. Therefore, we capture the uncertainties of the process via utilization of the Ito processes. After several candidate Ito processes were tested, the Brownian motion with drift was found to be most suitable for capturing the uncertainties. Thus, the deterministic ordinary differential equation model based on the method of moments is then modified into a stochastic model, which can be optimized via the stochastic optimal control strategy. Pontryagin’s maximum principle is implemented and solved for the objective function of maximizing the theoretical plate number. Successful control via flow rate adjustments led to higher antibody extraction compared to fixed flow rates, which was also confirmed experimentally. Improvements in the affinity chromatography capacity for antibodies allow for less resin use and therefore smaller systems.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":"30 1","pages":""},"PeriodicalIF":4.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143723827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}