A fractal model for determining oxygen effective diffusivity of gas diffusion
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一、文学常识1. 《红楼梦》的作者是谁?2. 《三国演义》中谁被称为“卧龙”?3. 《西游记》中唐僧师徒四人分别是谁?4. 《水浒传》中梁山好汉共有多少人?5. 《骆驼祥子》的作者是谁?二、文言文阅读1. 下列句子中,哪一句是出自《论语》?a. 己所不欲,勿施于人。
b. 学而时习之,不亦说乎?c. 三人行,必有我师焉。
d. 人无远虑,必有近忧。
2. 下列词语中,哪一个是出自《庄子》?a. 鹏程万里b. 神龙见首不见尾c. 朝三暮四d. 破釜沉舟3. 下列句子中,哪一句是出自《孟子》?a. 得道多助,失道寡助。
b. 非礼勿视,非礼勿听,非礼勿言,非礼勿动。
c. 人之初,性本善。
d. 己所不欲,勿施于人。
4. 下列词语中,哪一个是出自《诗经》?a. 桃之夭夭,灼灼其华。
b. 春风得意马蹄疾,一日看尽长安花。
c. 人生得意须尽欢,莫使金樽空对月。
d. 床前明月光,疑是地上霜。
三、现代文阅读1. 下列文章中,哪一篇文章是鲁迅的作品?a. 《背影》b. 《荷塘月色》c. 《故乡》d. 《背影》2. 下列词语中,哪一个是出自朱自清的作品?a. 美不胜收b. 烟花三月下扬州c. 水天一色d. 风花雪月3. 下列句子中,哪一句是出自茅盾的作品?a. 世间万物皆有毒,唯有爱不可挡。
b. 人生如梦,岁月如歌。
c. 人生自古谁无死,留取丹心照汗青。
d. 人生得意须尽欢,莫使金樽空对月。
4. 下列词语中,哪一个是出自巴金的作品?a. 美不胜收b. 烟花三月下扬州c. 水天一色d. 风花雪月四、诗词鉴赏1. 下列诗句中,哪一句是出自唐代诗人杜甫的作品?a. 春风得意马蹄疾,一日看尽长安花。
b. 人生得意须尽欢,莫使金樽空对月。
c. 会当凌绝顶,一览众山小。
d. 床前明月光,疑是地上霜。
2. 下列诗句中,哪一句是出自宋代诗人苏轼的作品?a. 春风得意马蹄疾,一日看尽长安花。
b. 人生得意须尽欢,莫使金樽空对月。
c. 会当凌绝顶,一览众山小。
fractal and fractional 水平-回复Fractals and Fractionals in Mathematics: A Comprehensive ExplorationFractals and fractionals are fascinating concepts within the realm of mathematics. Both terms describe mathematical objects that exhibit intricate patterns and structures. In this article, we will delve into the world of fractals and fractionals, exploring their definitions, properties, and applications.To begin, let us first understand what a fractal is. A fractal is a complex geometric shape that can be split into parts, each of which is a reduced-scale replica of the whole. This self-similarity is a fundamental characteristic of fractals. The term "fractal" was coined by mathematician Benoit Mandelbrot in 1975, although the concept itself has been around for centuries.Fractals can be generated through simple mathematical equations or algorithms. One of the most well-known fractals is the Mandelbrot set, named after its creator. It consists of a collection of points in the complex plane that do not escape to infinity after iteratively applying a specific equation. The resulting shape of theMandelbrot set is incredibly intricate, revealing intricate patterns and details when zoomed in.Fractals have numerous properties that make them intriguing to mathematicians and scientists alike. One of these properties is called infinite complexity. Fractals possess structures that are infinitely detailed, regardless of the level of magnification. This attribute is seen in the self-similarity of fractals, where each part resembles the whole. The complexity of fractals often leads to a phenomenon known as "aesthetic appeal," where the observer finds beauty and harmony in the intricate patterns.Another property of fractals is their fractional dimension. Unlike traditional geometric shapes like squares or triangles, which have integer dimensions, fractals have fractional dimensions. This means that fractal objects occupy a fraction of a dimension between whole numbers. For example, the Cantor set, a simple fractal constructed by removing a middle third of a line segment and repeating the process infinitely, has a dimension of approximately 0.631.Fractionals, on the other hand, refer to mathematical objects thatinvolve fractional numbers. In mathematics, fractions represent parts of a whole. They consist of a numerator (which signifies the number of parts) and a denominator (which signifies the total number of parts required to make a whole). Fractions are essential in everyday life and are commonly used in various fields, such as physics, finance, and engineering.The relationship between fractals and fractionals lies in their shared utilization of fractions. Fractals often exhibit fractional dimensions, as discussed earlier. This fractional dimension is calculated using methods similar to those used in determining the value of a fraction. In essence, the fractional dimension of a fractal represents the part of a whole that it occupies within a given space or set.Fractals and fractionals have a wide range of applications in various scientific and technological fields. In physics, fractal theories have been used to model complex systems, such as weather patterns or the behavior of fluids. In computer graphics, fractals are employed to generate realistic and complex natural landscapes or textures. They are also used in data compression methods, allowing for efficient storage and transmission of information.In conclusion, fractals and fractionals are fascinating mathematical concepts with far-reaching applications. Fractals exhibit infinite complexity and possess fractional dimensions, while fractionals represent parts of a whole using fractions. The interplay between these two concepts allows for the exploration and understanding of complex systems and patterns in nature and science. From the mesmerizing patterns of the Mandelbrot set to the practical applications in various fields, fractals and fractionals continue to captivate our imagination and expand our understanding of the mathematical world.。
化学化工英语试题及答案一、选择题(每题2分,共20分)1. Which of the following is a chemical element?A. WaterB. OxygenC. HydrogenD. Carbon答案:B, C, D2. The chemical formula for table salt is:A. NaOHB. NaClC. HClD. NaHCO3答案:B3. What is the process called when a substance changes from a solid to a liquid?A. SublimationB. VaporizationC. MeltingD. Condensation答案:C4. In the periodic table, which group contains alkali metals?A. Group 1B. Group 2C. Group 17D. Group 18答案:A5. What is the name of the process where a substance decomposes into two or more substances due to heat?A. CombustionB. OxidationC. ReductionD. Decomposition答案:D6. Which of the following is a physical property of a substance?A. ColorB. TasteC. SolubilityD. Reactivity答案:A7. What is the term for a compound that releases hydrogen ions (H+) when dissolved in water?A. BaseB. AcidC. SaltD. Neutral答案:B8. The law of conservation of mass states that in a chemical reaction:A. Mass is lostB. Mass is gainedC. Mass remains constantD. Mass can be converted into energy答案:C9. Which of the following is a type of chemical bond?A. Ionic bondB. Covalent bondC. Hydrogen bondD. All of the above答案:D10. What is the name of the process where a substance absorbs energy and changes from a liquid to a gas?A. MeltingB. VaporizationC. SublimationD. Condensation答案:B二、填空题(每题2分,共20分)1. The symbol for the element iron is ________.答案:Fe2. The pH scale ranges from ________ to ________.答案:0 to 143. A compound that produces a basic solution when dissolvedin water is called a ________.答案:base4. The smallest particle of an element that retains its chemical properties is called a ________.答案:atom5. The process of separating a mixture into its individual components is known as ________.答案:separation6. The study of the composition, structure, and properties of matter is called ________.答案:chemistry7. The process of a substance changing from a gas to a liquid is called ________.答案:condensation8. A(n) ________ reaction is a type of chemical reactionwhere two or more substances combine to form a single product. 答案:synthesis9. The volume of a gas at constant temperature and pressureis directly proportional to the number of ________.答案:moles10. The process of converting a solid directly into a gas without passing through the liquid phase is known as ________. 答案:sublimation三、简答题(每题10分,共30分)1. Explain what is meant by the term "stoichiometry" in chemistry.答案:Stoichiometry is the calculation of the relative quantities of reactants and products in a chemical reaction.It is based on the law of conservation of mass and involvesthe use of balanced chemical equations and the molar massesof substances to determine the amounts of reactants needed to produce a certain amount of product or the amounts ofproducts formed from a given amount of reactant.2. Describe the difference between a physical change and a chemical change.答案:A physical change is a change in the state or form of a substance without altering its chemical composition. Examples include melting, freezing, and boiling. A chemical change, on the other hand, involves a change in the chemical composition of a substance, resulting in the formation of new substances. Examples include combustion and rusting.3. What are the three main types of chemical bonds, and givean example of each.答案:The three main types of chemical bonds are ionic bonds, covalent bonds, and metallic bonds. An ionic bond is formed when electrons are transferred from one atom to another, resulting in the formation of oppositely charged ions. An example is the bond between sodium (Na) and chloride (Cl) in table salt (NaCl). A covalent bond is formed when two atoms share electrons, as seen in water (H2O) where hydrogen atoms share electrons with oxygen. Metallic bonds occur in metals, where a "sea" of delocalized electrons is shared among positively charged metal ions, as in sodium metal。
高三英语化学元素与化学反应单选题60题1. Which element has the symbol "O" and is essential for respiration?A. OxygenB. OsmiumC. GoldD. Silver答案:A。
解析:题干问的是符号为“O”且对呼吸至关重要的元素。
A选项Oxygen(氧),符号为“O”,是呼吸作用必需的元素;B选项Osmium((锇),符号为“Os”;C选项Gold((金),符号为“Au”;D选项Silver(银),符号为“Ag”,所以正确答案是A。
2. The element with the symbol "Na" is named _.A. NeonB. NickelC. SodiumD. Nitrogen答案:C。
解析:符号为“Na”的元素是Sodium((钠)。
A选项Neon (氖),符号为“Ne”;B选项Nickel((镍),符号为“Ni”;D选项Nitrogen (氮),符号为“N”,所以答案为C。
3. Which element is in Group 17 and has 7 valence electrons?A. FluorineB. ChlorineC. BromineD. All of the above答案:D。
解析:氟(Fluorine)、氯(Chlorine)、溴(Bromine)都属于第17族((卤族元素),它们的最外层都有7个电子,所以这三个选项都正确,答案为D。
4. The element whose atomic number is 6 is _.A. CarbonB. CalciumC. CobaltD. Copper答案:A。
解析:原子序数为6的元素是Carbon(碳)。
B选项Calcium(钙)原子序数为20;C选项Cobalt(钴)原子序数为27;D选项Copper(铜)原子序数为29,所以答案为A。
High pressure adsorption of hydrogen,nitrogen,carbon dioxide and methane on the metal–organic framework HKUST-1J.Moellmer a ,A.Moeller a ,F.Dreisbach b ,R.Glaeser a ,c ,R.Staudt d ,⇑aInstitut für Nichtklassische Chemie e.V.,Permoserstr.15,D-04318Leipzig,Germany bRubotherm GmbH,Universitätsstr.142,D-44799Bochum,Germany cInstitute of Chemical Technology,University of Leipzig,Linnéstr.3,D-04103Leipzig,Germany dUniversity of Applied Sciences Offenburg,Badstraße 24,D-77652Offenburg,Germanya r t i c l e i n f o Article history:Received 20April 2010Received in revised form 30August 2010Accepted 19September 2010Available online 25September 2010Keywords:Surface excessAbsolute amount adsorbed High pressure MOFIsosteric heata b s t r a c tHigh pressure adsorption phenomena are discussed for different gases on HKUST-1(Cu 3(BTC)2,commer-cially available product Basolite TM C300).Sorption isotherms for hydrogen,nitrogen,methane and carbon dioxide on HKUST-1were measured in the temperature range of 273–343K and at pressures up to 50MPa.The calculated surface excess adsorption capacities for all four adsorptive are one of the highest reported in the literature for HKUST-1samples.All surface excess data were further calculated from the experimental data by using the helium buoyancy correction.A detailed description was given.Also a procedure to calculate the absolute amount adsorbed from the surface excess amount by using two different models is ing one model,the density and the volume of the adsorbed phase can be calculated.The density of the adsorbed phase q ads corresponds to the liquid density of the adsorptive at its boiling point q liq,BP .In case of hydrogen no excess maximum was found up to 50MPa,so that one model could not be applied.Finally,the isosteric heat of adsorption for each gas was calculated by using the Clausius–Clapeyron equation.Ó2010Elsevier Inc.All rights reserved.1.IntroductionA new group of porous materials was developed in the mid 90ties by Yaghi and co-workers [1–3],the so called metal–organic frameworks or coordination polymers.Such materials consist of metal atoms or metal/oxygen-cluster,which are connected by or-ganic linkers.Several linkers and also motifs have been described to form hundreds of different porous materials [4–9].One of the most important specimens of this class of materials is HKUST-1(also named Cu 3(BTC)2or,as a commercially available product,Basolite TM C300)[10–12].As already mentioned in the Refs.[10,11],HKUST-1consists of Cu–Cu-dimers which are connected by 1,3,5-tricarboxylate linkers to form a 3-dimensional network with micropores in a range of 0.7–0.9nm.Spectroscopic analysis of the commercially available HKUST-1prepared by electrochemical synthesis is given in Ref.[11].During the last decade,the well known material HKUST-1has been widely studied in adsorption processes and adsorptive sepa-rations by several groups.Among those,adsorption applications like purification and separation processes [11,13–17],gas storage,especially hydrogen storage under ambient or cryogenic tempera-tures [18–22]or gas capture in the presence of environmental applications or for vehicle industry [23,24]are of the main interest.To the best of our knowledge,only one recent publication by Senkovska and Kaskel [25]has dealt with high pressure adsorption data of gases (>15MPa at T =298K for methane)on HKUST-1at room temperature up to 20MPa.These authors have reported stor-age capacities for methane in synthetic HKUST-1-samples of about 15.7wt.%at 303K.Thus,we report for the first time high pressure (>20MPa)adsorption data for the MOF-type material HKUST-1.In this study,we measured the sorption capacities of HKUST-1(Basolite TM C300)for the supercritical gases hydrogen,nitrogen,methane and carbon dioxide in a temperature range of 303–343K and pressures up to 50MPa.However,the adsorption of a supercritical gas on a microporous solid up to high pressures has been widely studied [26–41].It is therefore known,that the adsorption isotherm of a supercritical fluid on a microporous material consists of a maximum in the sur-face excess amount at a certain pressure.The experimental surface excess amount should be the starting point for the calculation of the absolute amount adsorbed for an experimentally working sci-entist,because it is not possible to determine the absolute ad-sorbed quantities by experimental techniques.This is of interests,when experimental data have to be compared with results from simulation experiments,where the absolute amount adsorbed1387-1811/$-see front matter Ó2010Elsevier Inc.All rights reserved.doi:10.1016/j.micromeso.2010.09.013⇑Corresponding author.E-mail addresses:moeller@inc.uni-leipzig.de (A.Moeller),dreisbach@rubotherm.de (F.Dreisbach),staudt@inc.uni-leipzig.de ,Reiner.Staudt@fh-offenburg.de (R.Staudt).can be obtained.Therefore,modelsabsolute amount adsorbed from the face excess.The major aim of this work two different models for the calculation sorbed from the surface excess amount. models.On the one hand,we use the adsorbent to calculate the absolutethe other hand,a second model gives us sity of adsorbed phase[38,46–49].The were further compared to each other. can be used to characterize specific phase.Furthermore,the isosteric heat of (hydrogen,nitrogen,methane andusing the Clausius–Clapeyron equation of the isotherms.2.Materials and experimental2.1.MaterialsThe adsorbent HKUST-1was used in cially available material,Basolite TM Aldrich(US).For a more detailedalso Ref.[11].All used gases were obtained from Air Products(US)with variable purity(CO299.995%,N299.995%,CH499.5%,H299.995%and He 99.9992%).Finally,methanol was purchased from Fluka(Germany) with a purity of99.9%.2.2.Low pressure adsorption isotherms2.2.1.Nitrogen physisorption at77KNitrogen adsorption isotherms at77K on HKUST-1were ob-tained by using the commercially available volumetric sorption analyzer BELSORP-miniII from Bel Japan Inc.equipped with a high resolution pressure sensor.2.2.2.Methanol adsorption at298KMethanol adsorption measurements at298K were performed on a magnetic suspension balance(Rubotherm,Germany) equipped with a dosage system for methanol from the vapor phase. Details are shown in Fig.1.Highly accurate pressure transducers (MKS Baratron,US and Newport Omega,US)were used in a range from vacuum up to10kPa and from10kPa up to0.1MPa.Prior to the analysis,all samples were outgassed at423K for 12h under turbomolecular pump vacuum(<1Pa).2.3.High pressure gravimetric adsorption measurementsHigh pressure sorption isotherms of carbon dioxide,nitrogen, methane,hydrogen and helium were recorded in a magnetic sus-pension balance(Rubotherm,Germany[50])that can be operated up to50MPa.In Fig.1,a scheme of the balance including temper-ature and pressure sensors and various gas supplies(additionally, the dosage system for methanol)is shown.Various pressure trans-ducers(Newport Omega,US)were used in a range from vacuum up to50MPa with an accuracy of0.05%.In a typical experiment,a stainless steel sample holder was filled with about1g of HKUST-1and the balance was evacuated for12h at423K and0.3Pa until constant mass was achieved. For measuring the sorption capacity,the gas was dosed into the balance chamber to elevated pressures.Equilibrium was achieved within30min for each gas,which is characterized by constant weight and pressure.The temperature was kept constant with an accuracy of±0.5K for each measurement.Additionally,for each isotherm,a minimum of two measure-ments were carried out with a fresh sample.The high pressure adsorption isotherms presented in the following consist of the en-tirety of all measured values at elevated temperatures.For the determination of the density for all gases,the program FLUIDCAL was used[51–54].3.Results and discussion3.1.Determination of the specific pore volumeGenerally,the textural properties of nanoporous solids such as MOFs,can be investigated by physisorption experiments,e.g.,by nitrogen(77K)or argon(87K)sorption isotherms[42–45].Not only the specific surface area and the pore size distribution are of interest,but also the specific pore volume is an important param-eter,especially for the determination of the absolute amount ad-sorbed from the surface excess amount[45].A detailed analysis of such procedures can be found in Ref.[42]for an In-based MOF with soc topology(soc=square octahedral).In this study,the pore volume was calculated using the adsorp-tion isotherms of three different adsorptive in the temperature range of77–298K up to the saturation pressure P S of each gas.In Fig.2,the isotherms of nitrogen(77K,P S=0.097,152MPa),carbon dioxide(273K,P S=3.4851MPa)and methanol(298K, P S=0.016,981MPa)are shown.All isotherms are type-I isotherms according to the IUPAC classification[55].In the case of the carbon dioxide adsorption isotherm,the surface excess mass at higher pressures(P>0.1MPa)was converted into the absolute amount adsorbed using the procedure described in Ref.[42]and also in Section3.3.The Gurvitch rule(P/P0=0.95)was used to determine the spe-cific pore volume from the isotherms shown in Fig.2[43–45].In the case of nitrogen,the slope of the isotherm can be seen at lower relative pressures as in the case of carbon dioxide and methanol, respectively.Evidently,the interaction for carbon dioxide and methanol with the surface of the porous material is equal.This is Fig. 1.Scheme of a gravimetric magnetic suspension balance(Rubotherm, Germany)equipped with a dosage system of vapor(here for methanol)as an option.J.obvious from the identical slope of the isotherm for both gases in the same relative pressure region(0.001<P/P0<0.1).This is remarkable because carbon dioxide is nonpolar but has a quadru-pol moment and a high polarizability,while methanol is polar with a similar polarizability[56].However,the effective adsorption po-tential of the inner surface of HKUST-1to methanol and carbon dioxide is equal.The calculated specific pore volumes for nitrogen(V Pore= 0.71cm3gÀ1calculated with q N2=0.80,770cm3gÀ1)and methanol (V Pore=0.69cm3gÀ1calculated with q methanol=0.78,624cm3 gÀ1)are in good agreement with each other.However,the pore volume determined from the carbon dioxide high pressure adsorp-3À1sample volume by using the helium buoyancy correction is esti-mated in a wrong way.To avoid this effect,several measurements have to be carried out and compared to each other.Alternatively,a helium buoyancy correction at high temperature can be used,if the adsorbent(surface)at the higher temperature can be assumed to remain unchanged.Secondly,the density of helium is usually lower than the den-sity of the gas to be measured[58].The buoyancy effect is propor-tional to the density of the bulk phase of the adsorptive.The density of helium during buoyancy measurements is in most cases (not for hydrogen)several times lower than the density of other adsorptives,e.g.,Ar,Kr,Xe,N2,O2,CO2or CH4,at the same pres-sure.This behavior can be seen in Fig.3a,where the adsorption iso-therms for hydrogen,methane and nitrogen at303K and also the helium buoyancy measurement up to50MPa are plotted over their corresponding densities.For a buoyancy correction,the surface ex-cess of helium should have to be known over the whole density re-gime of the adsorptive,i.e.,up to q bulk,methane=0.3g cmÀ3for methane(corresponding pressure P0.3,helium=560MPa)and q bulk,nitrogen=0.4g cmÀ3for nitrogen(corresponding pressure P0.4,helium=1075MPa).Since the helium surface excess is known for lower densities only,a direct buoyancy correction is possible only for hydrogen(see Fig.3a).Herein,we used the so called reduced mass X,which wasfirstly described by Staudt et al.[59]in1993,for a better understanding of the buoyancy correction.The reduced mass can be considered as a direct experimental value and is a function of the sample mass, temperature,pressure/density and,of course,of the adsorption capacity[57].Here,the surface excess was obtained by using the reduced mass X corrected by the product of bulk density of thefluid q bulk and the specific adsorbent volume V HeAs(according to Eq.(1)),calcu-lated from helium measurements.m r¼Xþq bulk V He As;ð1ÞFig.2.Nitrogen(77K),carbon dioxide(273K)and methanol(298K)adsorptionisotherms on HKUST-1up to their corresponding saturation pressure.Fig.3a.Surface excess amount of nitrogen,methane,hydrogen and heliumadsorption at303K on HKUST-1as a function of density.Materials138(2011)140–148the surface excess amount for each gas in the above mentioned procedure.3.3.Density of the adsorbed phase and calculation of the absolute amount adsorbedAs already mentioned before,the surface excess mass is the quantity,which can be calculated in a simple way from the re-duced mass(Eq.(1)).However,also the absolute amount adsorbed is of interest.Here,we use two different ways to determine the absolute amount adsorbed from the surface excess data.First,the absolute amount adsorbed m ads can be described as:m ads¼m rþq bulk V ads;ð2Þwhere m r is the surface excess mass,q bulk is the density of the gas phase and V ads is the volume of the adsorbed phase[37,57].The volume of the adsorbed phase is unknown,but can easily be obtained as V ads=m ads/q ads,where q ads is the density of the ad-sorbed phase.Then,Eq.(2)becomes m r¼m adsð1Àq bulk=q adsÞ:ð3ÞWith the assumption,that the adsorbed phase is in a liquid-like state(q ads=q liq)[57],this expression can now be used to determine the absolute amount adsorbed at high pressures(P>0.1MPa),but only forfluids below their critical point.This was already used for the carbon dioxide adsorption isotherm at273K(shown before, see section3.1).Generally,Eq.(2)can also be used to describe the surface excess mass of a supercriticalfluid[26,57,60–62]by substitution of the adsorbed mass with m ads=V ads q ads.Then,Eq.(2)can be written in the following way:m r¼ðq adsÀq bulk V adsÞ:ð4ÞA similar approach was used by Poirier et al.[46].These authors used the Dubinin-Astakhov equation for the calculation of the ad-sorbed mass m ads.Nevertheless,the surface excess isotherm of a microporous material shows a maximum at the point,where the difference be-tween the density of the adsorbed phase q ads and the bulk phase q bulk is maximal[61,62].For higher pressures,the bulk phase ismore compressible than the adsorbed phase and the surface excess decreases.In the same way,the surface excess isotherm decreases as well.The surface excess isotherm at high pressures is mainly influenced by the equation of state of the adsorptive and after the maximum an inflection point of such isotherms(surface excess plotted against pressure and density)is evident[26,27,35].The location of this inflection point depends on the adsorbate/adsor-bent interaction and also on the thermodynamic state of the adsorptive.This can be nicely seen in the high pressure adsorption isotherms reported in Refs.[26,32,35].In this study,the surface excess isotherms of carbon dioxide(T/ T C=1.01(308K),T/T C=1.03(313K),T/T C=1.08(328K),T/T C=1.13 (343K)),methane(T/T C=1.59(303K),T/T C=1.67(318K),T/T C= 1.754(333K))and nitrogen(T/T C=2.40(303K),T/T C=2.52 (318K),T/T C=2.64(333K))show a maximum below50MPa.Here, wefit the experimental surface excess masses against the density of carbon dioxide,methane and nitrogen in the linear range after the maximum of the surface excess by using Eq.(4).In an optimal procedure,thefirst derivative at the inflection point of the surface excess(surface excess plotted against the density)has to befitted. From thisfit,the adsorbed volume V ads and the density of the ad-sorbed phase q ads can be easily obtained.In Table2,all data from thefitting procedure are summarized.Additionally,thefit param-eters of Eq(40,for carbon dioxide,methane and nitrogen data,can also be taken from Figs.4a,4b and4c,respectively.The estimated values of the density of the adsorbed phase,i.e., the intersection of thefit curve with the x-axis,for methane (q ads=0.44–0.45g cmÀ3)are in the range of its liquid density at its boiling point q liq,BP(q liq,BP=0.4226g cmÀ3).According to its phase diagram[51]it is not possible to specify the liquid density at its boiling point for carbon dioxide.Here,the liquid density be-tween its triple point(T p=216.6K)and its critical point (T C=304.1K)was calculated to q liq,Tp=1.18g cmÀ3and q liq,T c=0.54g cmÀ3[51].Nevertheless,an adsorbed density of q ads=1.07–1.08g cmÀ3was calculated by using Eq.(4)for carbon dioxide,which is within its liquid density regime and insignificant lower than the liquid density at its triple point.This indicates strongly the consistency of the model for methane and carbon dioxide and makes also clear that at50MPa(methane)and 30MPa(carbon dioxide)the inflection point of the surface excess isotherm(plotted against the density)is already achieved.However,for nitrogen(q ads=1.16–1.17g cmÀ3)the calculated density of the adsorbed phase is somewhat higher than the liquid density at its boiling point(q liq,BP=0.8085g cmÀ3for nitrogen). The higher values of the density of the adsorbed phase for nitrogenMaterials138(2011)140–148143(estimated byfitting the linear part of the isotherm above the max-imum)indicate,that up to50MPa the inflection point for the sur-face excess isotherm of nitrogen is not achieved(see Fig.4c Consequently,the calculated densities of the adsorbed phase for nitrogen are30%higher than the liquid density at its boiling.Be-cause of that,measurements of nitrogen above50MPa are highly desired.In case of adsorbed carbon dioxide and methane,the calculated adsorbed volume(V ads=0.60–0.75cm3gÀ1for carbon dioxide andads =0.38–0.44cm3gÀ1for methane,respectively)are much high-Table2Carbon dioxide,methane and nitrogen data obtained from surface excess using the Fit with equation4(Details can be also found in Fig.5a and5b).Specific Volume of the adsorbed phase bV ads/(cm3gÀ1)Porefilling factor bV ads/V PoreDensity of the adsorbedphase q ads/(g cmÀ3)Reduced density of theadsorbed phase q ads/q critReducedtemperature T/T critCO2(308K)0.750.95 1.07 2.29 1.01 CO2(313K)0.720.91 1.08 2.31 1.03 CO2(328K)0.670.85 1.07 2.29 1.08 CO2(343K)0.600.76 1.07 2.29 1.13CH4(303K)0.440.630.44 2.71 1.59 CH4(318K)0.410.590.44 2.71 1.67 CH4(333K)0.380.540.45 2.77 1.75Fig.4b.Methane adsorption isotherms in temperature range303–333K on HKUST-Each isotherm wasfitted in the linear range above the maximum of the surface excess with Eq.(4).Fig.4c.Nitrogen adsorption isotherms in temperature range303–333K on HKUST-Each isotherm wasfitted in the linear range above the maximum of the surface excess with Eq.(4).144J.Moellmer et al./Microporous and Mesoporous Materials138(2011)140–148V Pore=0.79cm3gÀ1from carbon dioxide adsorption isotherm at 273K)for carbon dioxide,0.54–0.63for methane and0.26–0.31 for nitrogen were observed.The porefilling factor for carbon diox-ide at308K is near1,because carbon dioxide is only slightly above its critical temperature.The pore volume V P for HKUST-1was cal-culated using the Gurvitch rule(see Section3.1)by using the car-bon dioxide adsorption isotherm at273K.This value of the pore volume V P=0.79cmÀ3gÀ1is the starting value of the adsorbed vol-ume of a supercriticalfluid.With increasing temperature,the cal-culated adsorbed volume decreases,because of the increasing adsorbate–adsorbate interactions.This means also,that in the sat-uration regime of an isotherm,a supercriticalfluidfills the whole micropore volume of the adsorbent,but the estimated values of the pore volume and therefore the porefilling factor seem to be a function of temperature,according to the higher adsorbate–adsorbate interactions.Furthermore,the higher porefilling factors for methane are also due to the fact that methane is near its bulk critical temperature as it is for nitrogen.In case of hydrogen no maximum can be observed up to an adsorptive density of0.03g cmÀ3(and pressures up to50MPa). This can be seen in Fig.4d,while carbon dioxide,methane and nitrogen exhibit a maximum,which are shown in Figs.4a,4b and4c,respectively.This is also due to the fact,that at tempera-tures of303K to333K,hydrogen is far above its critical tempera-ture(T/T C=9.13(303K);T/T C=9.58(318K);T/T C=10.03(333K)). Thus,at these temperatures,a maximum could not be observed until50MPa and it is not possible to calculate the absolute amount adsorbed using Eq.(4).Poirier et al.[47–49]discussed high pres-sure hydrogen adsorption isotherms at lower reduced tempera-tures(between35K(T/T C=1.05)and100K(T/T C=3.01))in the context of adsorbed phase densities of hydrogen on different MOF materials.For all materials,no maximum was found at tem-peratures higher than100K and pressures up to8MPa.By using a modified Dubinin-Astakhov approach,they showed for different in its saturation regime of the isotherm can be assumed to be that of a liquid-like state.With the approach given by Eq.(4),the absolute amount ad-sorbed for hydrogen was calculated by using the liquid density at its boiling point to specify the density of the adsorbed phase.Thus, the adsorbed volume for hydrogen at each temperature was calcu-lated by using the liquid density and by extrapolating the methane data.These data can also be found in supplementary Table2.By adopting the volume of the adsorbed phase,the absolute amount adsorbed was then ing Eq.(4)(model1),the linear range after the maximum of the surface excess mass against the density was shifted into the saturation regime.It is thus clear,that with this approach the lowest value of the absolute amount ad-sorbed can be calculated.Further,a second model was used to calculate the absolute amount adsorbed.By using Eq.(2)and by adopting the specific pore volume(which was obtained from the N2/77K and metha-nol/298K adsorption isotherm to give V Pore=0.7cm3gÀ1),as the volume of the adsorbate(Section3.1).Here,we assume that the to-tal pore volume isfilled with adsorbate.By applying this approach, the resulting absolute amount adsorbed can be understood as the maximum adsorption capacity(total adsorbed amount)or as an overall limiting value.All results,for both models are shown in Figs.5a,5b,5c and5d,respectively,where the absolute amount ad-sorbed are plotted against the pressure.Allfits were done by using the Padèequation.A detailed description of the model can be found in the supplementary datafile.3.4.Determination of the isosteric heat of adsorptionFor all industrial adsorption processes,information about the temperature dependency of adsorption isotherms is necessary. From this dependency,the isosteric heat of adsorption can be cal-Fig.4d.Hydrogen adsorption isotherms in temperature range303–333K onHKUST-1.No surface excess maximum could be obtained until50MPa.J.Moellmer et al./Microporous and Mesoporous Materials138(2011)140–148145range between303and333K using Eq.(4)and V ads)for calculation of the isosteric heat of adsorption.In Fig.6,all estimated values forthe isosteric heat of adsorption are shown as a function of loading. Additionally,the calculated values for all gases are constant over a wide range of loadings(up to10mmol gÀ1),but decrease slightly in case of carbon dioxide and methane.At higher loading the adsorbate–adsorbate interactions become more important and thus,the isosteric heat of adsorption has to increase rapidly.How-ever,up to10mmol gÀ1the maximum adsorption capacities for carbon dioxide,methane and nitrogen are not observed,and no in-crease is found up to10mmol gÀ1.Nevertheless,all calculated isosteric heats of adsorption at zero coverage are higher than the corresponding values of the heat of vaporization of each adsorptive.For carbon dioxide a value of ca.29.2kJ molÀ1at zero loading was determined.This is lower than the value given by Wang et al.[16](ca.35kJ molÀ1)calculated from experimental sorption isosteres for carbon dioxide on HKUST-1samples.Also,a high affinity for methane on HKUST-1was observed.A value of ca.20.7kJ molÀ1at zero loading indicates strong binding between thefluid molecules and the surface area of HKUST-1.Both values, for carbon dioxide and methane,are higher than for several com-mercially activated carbons(16–25kJ molÀ1for carbon dioxide at zero loading and16–20kJ molÀ1for methane at zero loading, respectively)[65].However,not only adsorption measurements can be used to determine the isosteric heats,but indeed also grand canonical Monte Carlo simulations(GCMC)methods are useful for estimation of the heat of adsorption.Walton et al.[66]calculated the isosteric heat for several gases such as carbon monoxide,hydrogen(ca.6.3kJ molÀ1),methane(ca.18.7kJ molÀ1)and nitrogen(ca.13.0kJ molÀ1)on HKUST-1at zero loading at298K.These data are consistent with the calculated values in this study.Further-more,the values of the isosteric heat of adsorption for HKUST-1 are higher than for zeolite–imidazolate frameworks, e.g.ZIF-8, ZIF-69or ZIF-76,and also for MOF-5[70,71]and an In-based Fig.5d.Hydrogen adsorption isotherms in temperature range303–333K HKUST-1(Surface excess vs.absolute amount adsorbed using two different models, plotted lines arefits with Padèequation).soc-MOF[42].The values of the isosteric heat of adsorption ob-tained in this study are shown in Fig.6.Additionally,a detailed comparison with values from other materials could be found in Table3.4.ConclusionPure gas adsorption data of nitrogen,hydrogen,carbon dioxide and methane on the commercially available metal–organic frame-work HKUST-1(Basolite TM C300)were measured at temperatures between303and343K and pressures up to50MPa by using the gravimetric method.Textural informations were obtained from adsorption isotherms of several adsorptives at different tempera-tures and pressures,e.g.,nitrogen adsorption at77K and carbon dioxide adsorption at273K.A detailed description of the effect of buoyancy for high pres-sure data correction was given.The approach was then used to cal-culate the surface excess mass from the experimental data,the reduced mass.The absolute amount adsorbed,given by extrapola-tion of the surface excess isotherm in the linear range after the maximum,can be seen as the lowest limit for the absolute amount adsorbed.From this model,information about the adsorbed vol-ume was received,which was then also used to determine the absolute amount adsorbed.The calculated adsorbed volumes of carbon dioxide,methane and nitrogen decrease with increasing temperature.This is due to the fact,that at higher temperature an increase of adsorbate–adsorbate interactions can be assumed. Another important aspect is the calculation of the density of the adsorbed phase using this model.For carbon dioxide and methane, densities of 1.07–1.08g cmÀ3and0.44g cmÀ3were calculated, which corresponds to the assumption that the adsorbedfluid is in a liquid-like state.In a second model the specific pore volume from nitrogen mea-surement at77K and methanol adsorption at298K (V Pore=0.7cm3gÀ1)was used for calculation of the absolute ad-sorbed amount.The obtained values can be understood as the overall or total adsorption capacities.In summary,both concepts show the lowest and the highest value of the absolute amount adsorbed.Additionally,the isosteric heat of adsorption for hydrogen (6.9kJ molÀ1),nitrogen(12.8kJ molÀ1),methane(20.5kJ molÀ1) and carbon dioxide(33.9kJ molÀ1)was calculated using the Padèequation and applying the Clausius–Clapeyron equation up to its saturation regime of the isotherms.The obtained values are in good agreement with data from the literature calculated by using experimental data and as well for simulation data. AcknowledgementThe authors thank the‘‘Deutsche Forschungsgemeinschaft”DFG-project SPP1362MOF(STA428/17-1)forfinancial support. Appendix A.Supplementary dataSupplementary data associated with this article can be found,in the online version,at doi:10.1016/j.micromeso.2010.09.013. 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2024年07版小学三年级下册英语第3单元测验试卷考试时间:80分钟(总分:140)A卷考试人:_________题号一二三四五总分得分一、综合题(共计100题共100分)1. 听力题:The ______ teaches us about music.2. 听力题:The chemical formula for potassium iodide is ______.3. 填空题:The first female pharaoh of Egypt was __________ (哈特谢普苏特).4. 选择题:What is the name of the famous sculpture by Michelangelo?A. The ThinkerB. DavidC. Venus de MiloD. The Kiss答案: B5. 听力题:A _______ is a chemical substance that can donate protons.6. 听力题:The chemical symbol for titanium is _______.7. 选择题:What do you call the process of water falling from the sky?A. EvaporationB. PrecipitationC. CondensationD. Collection答案: BWhich fruit is yellow and curved?A. AppleB. OrangeC. BananaD. Grape答案:C9. 听力题:The ______ has a long tongue.10. 填空题:The kitten loves to chase its _______ (尾巴).11. 听力填空题:During summer vacation, I plan to __________. I’m excited about exploring new places and having adventures with my family!12. 听力题:She is _____ (learning) to cook.13. 填空题:The capybara is known as the world's largest ______ (啮齿动物).14. 填空题:My favorite subject is __________. (数学)15. 听力题:A chemical change produces substances with different ______.16. 听力题:Chemical reactions can occur at different ______.17. 填空题:I call my pet fish “.”18. 填空题:The _____ (植物主题) can inspire creative projects.19. 选择题:What is the opposite of 'hard'?A. ToughB. SoftC. FirmD. Solid答案:BWhat is the sum of 1 + 2 + 3?A. 5B. 6C. 7D. 8答案:B21. 填空题:The __________ (历史的回声) resonates deeply.22. 填空题:I saw a ________ walking along the path.23. 听力题:Chemical processes can be influenced by ______ and temperature.24. 选择题:What is the primary color of the sun?A. BlueB. YellowC. RedD. Green答案:B25. 填空题:________ (植物观察) is a fun hobby.26. 选择题:What is the capital of Austria?A. ViennaB. SalzburgC. InnsbruckD. Linz答案:A27. 选择题:Which instrument has keys and is played by pressing them?A. GuitarB. DrumsC. PianoD. Violin答案:C28. 听力题:His favorite food is ________.The chemical symbol for chlorine is ______.30. 选择题:How do you say "good morning" in Italian?A. BuongiornoB. BuonaseraC. BuonanotteD. Ciao31. 听力题:The main gas emitted by decaying organic matter is __________.32. 填空题:The ________ (环境保护政策) can influence growth.33. 听力题:I see a _____ (出租车) on the street.34. 选择题:What is the color of a typical kiwi fruit?A. BrownB. GreenC. YellowD. Red35. 填空题:The _______ (羊) produces wool.36. 听力题:The Age of Exploration began in the ________ century.37. 填空题:I want to learn about ________ in science class.38. 选择题:Which bird is known for its colorful tail?a. Crowb. Sparrowc. Peacockd. Pigeon答案:c39. 听力题:She is ___ a song. (singing)Recognizing plant ______ can help you manage your garden effectively. (识别植物的需求可以帮助你有效管理花园。
第42卷 第23期 包 装 工 程2021年12月PACKAGING ENGINEERING ·92·收稿日期:2021-07-07作者简介:浦广益(1972—),男,硕士,江南大学讲师,主要研究方向为材料成型技术与机械。
通信作者:潘嘹(1986—),男,博士,江南大学副教授,主要研究方向为食品药品包装。
预测相融共混膜氧气透过率的分形渝渗模型浦广益1, 2,潘嘹1, 2,GE Chang-feng 3,卢立新1, 2,王军1, 2,丘晓琳1, 2(1.江南大学,无锡 214122;2.江苏省食品先进制造装备技术重点实验室,无锡 214122;3.罗切斯特理工大学,罗切斯特 14623)摘要:目的 预测相融体系共混膜氧气透过率,为高阻氧共混膜的生产和设计提供理论依据。
方法 应用分形与渝渗理论提出一种氧气透过率预测模型,该模型能够在高阻氧材料体积分数条件下更准确地估算相融体系共混膜的氧气透过率。
以聚酯/聚萘二甲酸乙二醇酯(PET/PEN )共混膜为例,通过扫描电镜分析共混膜微观形貌,确定PET/PEN 共混膜中氧气渗透维数,并根据渗透维数结合文中提出的预测模型计算PET/PEN 共混膜氧气透过率,最后通过实验数据验证该模型的有效性。
结果 氧气在PET/PEN 混合膜中的渗透可以简化为二维渗透。
在低PEN 体积分数条件下,现有模型和文中提出的预测模型均与实验结果高度吻合。
该模型在高PEN 体积分数条件下展现出了现有其他模型所没有的曲线趋势,能够更准确地描述高阻氧材料在共混膜体系中对氧气的阻隔作用。
结论 文中提出的预测模型能够用于预测相融体系共混膜的氧气透过率。
关键词:氧气透过率;预测模型;分形理论;渝渗理论;相融体系共混膜中图分类号:TS206.4;TB332 文献标识码:A 文章编号:1001-3563(2021)23-0092-08DOI :10.19554/ki.1001-3563.2021.23.013 Fractal and Percolation Model for Predicting the Oxygen Permeability ofMiscibility Blended FilmPU Guang-yi 1, 2, PAN Liao 1, 2, GE Chang-feng 3, LU Li-xin 1,2, WANG Jun 1,2, QIU Xiao-lin 1, 2(1.Jiangnan University, Wuxi 214122, China; 2.Jiangsu Key Laboratory of Advanced Food Manufacturing Equipmentand Technology, Wuxi 214122, China; 3.Rochester Institute of Technology, Rochester 14623, USA) ABSTRACT: The work aims to predict the oxygen permeability of miscibility blended film, and provide a theoretical support for the manufacture and design of high oxygen barrier blended film. In this research, a prediction model of oxygen permeability was proposed according to the application of fractal theory and percolation theory. This model can predict oxygen permeability of miscibility blended films more accurately at a high content (mass fraction) of oxygen barrier po-lymer. A scanning electron microscopy (SEM) was used to analyze the micro-structure of PET/PEN blended films, deter-mine the dimension of oxygen permeability in PET/PEN blended films. Then the oxygen permeability of PET/PEN blended film was calculated according to the permeability dimension combined with the prediction model pro-posed in this work. Finally, the validity of the model was verified by experimental data. The results indicated that the oxygen permeation in PET/PEN blended films can be simplified into a 2-D percolation. Both the existing model and the proposed model had a good agreement with the experimental data at low PEN content (volume fraction). However, the proposed model showed a unique curve trend which had a more accurate prediction to experimental data at the high PEN. All Rights Reserved.第42卷第23期浦广益等:预测相融共混膜氧气透过率的分形渝渗模型·93·content (volume fraction) in blended films and can describe the barrier effect of high oxygen barrier polymer on oxygen in the blended film system more accurately. The proposed model can be used to predict the oxygen permeability of miscibil-ity blended film.KEY WORDS: oxygen permeability; prediction model; fractal theory; percolation theory; miscibility blended films阻氧性能是产品包装薄膜的重要性能之一,高阻氧薄膜能够有效延缓包装内食品的氧化过程,延长易氧化食品货架期。
化学专业外语练习题1、c Which of the following belongs to phosphate?( sodium phosphite)(a) PH3 (b) Na3PO3(c) Na3PO4 (d) P2、b 1H and 2H are ____ and occupy the same position in periodic Table.(a) isomers (b) isotopes (c) redox bodies (d) amphoteric compounds3、d The ____ of a carbon is 12(a) the weight of molecule (b) molecular number(c) the weight of atom (d) atomic weight4、Which of the following belong to nitrate? C(a) NH3 (b) KNO3 (c) KNO2 (d) NO5、Which of the following belongs to secondary amine? B4、The number of outmost electron in carbon atom is _C_.(a) 1 (b) 2 (c) 4 (d) 65、In reaction H2 + CuO — H2O + Cu, __B__ is reduced.(a) H2 (b) CuO (c) Cu (d) H2O6、Which of the following is charged? _C_(a) atom (b) molecule (c) proton (d) neutron7、Who first presented Periodic Table of elements? C(a) Democritus (b) Boyle (c) Mendeleev (d) Dalton8、Which of the following is classified into amine? B(a) NH3 (b) CH3NH2 (c) NaNH2 (d) N29、The substances on the left side of the chemical equation are known as __d_ .(a) reactant (b) reactor (c) reductant (d) reaction10、Who first present the model of an atom in 1900s? b(a) Plato (b) Dalton (c) Mendeleev (d) Boyle11、Which of the following belongs to nitrite? b(a) HNO2 (b) KNO2 (c) Mg3N2 (d) NH312、Which of the following belongs to metal? b(a) selenium (b) sodium (c) Tellurium (d) Helium13、d The elementary particle of ____ is uncharged. d(a) proton (b) electron (c) ion (d) neutron14、d Bromine has ____ electrons in its outermost energy level. d(a) 2 (b) 3 (c) 8 (d) 715、a Which of the following is non-metal?(a) chlorine (b) lead (c) copper (d) mercury16、a The atomic number of helium is ____.(a) 2 (b) 4 (c) 3 (d) 017、d The horizontal rows of the periodic table are called ____.(a) energy level (b) groups (c) electron configuration (d) periods18、a The symbol for element silver is ____.(a) Ag (b) Sn (c) Hg (d) Au19、c The atomic number of carbon is ____.(a) 13 (b) 6 (c) 12 (d) 120、b Which of the following is inert element?(a) hydrogen (b) helium (c) tellurium (d) potassium21、c Which of the following belongs to halogen?(a) carbon (b) lithium (c) fluorine (d) neon22、a Which of the following belongs to noble gas?(a) neon (b) potassium (c) iodine (d) lead23、a Which of the following belongs to alkali metal?(a) silver (b) sodium (c) tellurium (d) bromine24、b Which of the following belongs to metal halide?(a) KClO3 (b) KCl (c) HCl (d) Cl225、a The ____ of carbon is is 1s22s22p2(a) electron configuration (b) periodicity (c) general property (d) inertness26、b The general property of metal is ____.(a) soft (b) lustrous (c) flammable (d) toxic27、c Fluorine, chlorine, bromine and iodine belong to ____ group.(a) alkaline metal (b) transition metal (c) halogen (d) alkaline earth metal28、b Few reactions occur on helium and argon, so the two elements are chemically ____.(a) reactive (b) inert (c) mild (d) strong29、a The standard enthalpy for normal oxygen is ____.(a) 0 (b) >0 (c) <0 (d) ≠030、c The maximum electronegative element in Periodic Table is ____.(a) H (b) Na (c) F (d) He31、b Which of the following belongs to the complex?(a) FeF3 (b) Na3[FeF6] (c) Fe3O4 (d) Fe32、d When solid NaCl is put into water, the solid ―disappears‖. The whole system is called ____.(a) soluble (b) solvent (c) solubility (d) solution33、d Mn2+ can be ____ to MNO4- by (NH4)2S2O8 in acidic solution.(a) reduced (b) exchanged (c) substituted (d) oxidized34、a Charged atoms are called ____.(a) ions (b) protons (c) electrons (d) molecules35、b Which of the following is classified into oxo-anion ?(a) O2- (b) SO42- (c) S2- (d) S2-36、a Reaction CH4 +Cl2→ CH3Cl + HCl is called ____ reaction.(a) substitution (b) oxidation (c) reduction (d) exchange37、c Benzene is often used as ____ both in laboratory and in chemical industry.(a) solution (b) solvation (c) solvent (d) solute38、c Standard entropy of any species is ____.(a) 0 (b) ≤ 0 (c) > 0 (d) both (b) and (c)39、b If aqueous NaCl is wanted to separate, ____ is good choice.(a) substitution (b) distillation (c) coordination (d) bond40、b Alcohol is readily ____ and we smell it everywhere in air.(a) soluble (b) volatile (c) reactive (d) precipitated41、b As a general rule, the coordination compounds(the complex) with coordination number of six are observed _____ structure(a) tetrahedral (b) octahedral (c) octagonal (d) bipyridyl42、d The demanded energy that a gaseous neutral atom loses one electron at thermodynamic standard condition is called the first ____.(a) energy level (b) electron configuration (c) activation energy (d) ionization energy43、c NaCl is ____ in water.(a) solution (b) solvent (c) soluble (d) precipitated44、d When AgNO3 is mixed with NaCl, AgCl ____ is developed.(a) solution (b) solvent (c) soluble (d) precipitated45、b Which of the following belongs to hydrocarbon?(a) C11H22O11 (b) C8H18 (c) CH3COOH (d) H2SO446、a In K4[FeF6], the charge of the complex part is ____.(a) -4 (b) +2 (c) +1 (d) –147、b Which of the following belongs to substitution reaction?(a) H2 + Cl2— HCl (b) C6H6 + Cl2— C6H5Cl + HCl (c) H2O — H2 + O2 (d) S+ O2— SO248、a In K4[FeF6], the oxidation number(or state) of Fe is ____.(a) 2 (b) 0 (c) 6 (d) 449、__c__ is defined as required energy to break chemical bond into neutral species at thermodynamic standard condition. For example breaking H-H bond into two H· atom requires 104kJ/mol.(a) Lattice energy (b) Hydration energy (c) Bond energy (d) Activation energy50、a When gaseous HCl dissolves into water, ____ solution forms.(a) acidic (b) basic (c) salty (d) no51、b When ionic compounds dissolve in water, the ions interact with water molecules. Such process is called ____.(a) coprecipitation (b) ionization (c) hydration (d) coordination52、d When ions dissolve in water, they are surrounded by water molecules. Such process is called ____.(a) sublimation (b) substitution (c) ionization (d) solvation53、c When benzene is added in aqueous solution containing iodine, most of iodine then transfers into benzene because of the more solubility of iodine in benzene. Such process is called ___.(a) refinement (b) titration (c) extraction (d) diffraction54、d Which of the following is classified into transition element?(a) silicon (b) tin (c) helium (d) copper55、__b__ H2SO4 is often used in chemical experiment.(a) Volatile (b) Concentrated (c) Flammable (d) Inert56、a Electrolysis of aqueous solution will produce____.(a) H2 (b) H (c) water (d) OH-57、d Zinc reacts with ____ H2SO4 to generate hydrogen gas at room temperature.(a) concentrated (b) cold (c) hot (d) dilute58、a Which of the following belongs to oxoacid?(a) H2SO4 (b) H2S (c) H2O (d) HS-59、c Which of the following belongs to diatomic molecule?(a) HCN (b) KClO3 (c) HCl (d) C8H1060、c If solid NaCl is added into its saturation solution , ____ is developed.(a) transparent solution (b) colloidal (c) precipitate (d) dissolution61、c Which of the following belongs to alkali earth metal?(a) potassium (b) lead (c) calcium (d) boron62、b Which of the following belongs to hydride?(a) CuSO4·5H2O (b) H2S (c) C6H6 (d) H2SO463、a Which of the following belongs to carbohydrate?(a) C11H22O11 (b) C10H8 (c) HCHO (d) CO264、a Which of the following belongs to representative element?(a) carbon (b) iron (c) copper (d) zinc65、d Which of the following belongs to alkaline earth element?(a) potassium (b) mercury (c) boron (d) magnesium66、a Benzene usually carries out ____ reaction, as described belowC6H6 +Cl2---------C6H5Cl + HCl(a) substituent (b) substitution (c) displacement (d) alternative67、a The general formula of saturation alkane is ____(a) C n H2n+2 (b) C n H2n (c) C n H2n-2 (d) C n H2n-668、c There are ____ carbon atoms in parent chain of 2,3-dimethylbutane.(a) 2 (b) 5 (c) 4 (d) 669、c Which of the following is trans-2-butene?70、d The vinyl group has the structure of ____.(a) CH3CH2— (b) C6H5— (c) CH≡C— (d) CH2=CH—71、b Compounds that containing both hydroxyls and carbon-carbon double bonds are called ____(a) polyols (b) unsaturated alcohols (c) cyclols (d) thiol72、c Dienes contain ____ carbon-carbon double bonds.(a) di- (b) eth- (c) two (d) secondary73、a Which of the following is classified into alkenol?(a) CH2=CHCH2OH (b) CH3CH2CH2OH (c) CH≡CCH2OH (d) HOCH2CH2CH2OH74、b Vinylcyclopropane is classified into ____(a) alkane (b) alkene (c) alkyne (d) alkenyne75、c The functional group of alcohol is ____.(a) hydrate (b) hydroxide (c) hydroxyl (d) hydride76、a Alkynes contain carbon-carbon ____ bond(a) triple (b) three (c) tertiary (d) prop77、b Methylenecyclopentane is classified into ____(a) alkane (b) alkene (c) alkyne (d) alkenyne78、c Which of the following is the formula or general formula of ammonia?(a) C6H5OH (b) C6H5NH2 (c) NH3 (d) RNH279、a A primary amine contains ____ hydrogens attached to its nitrogen atom.(a) 2 (b) 3 (c) 4 (d) no80、d Reaction between methanamine and hydrochloric acid produces ___ salt.(a) imide (b) imine (c) amide (d) ammonium81、b The functional group of amine is ____.(a) ammonia (b) amino (c) ammonium (d) ammine82、a Alkanes contain carbon-carbon ____ bonds.(a) single (b) double (c) triple (d) both (b) and (c)83、d (+)-Glucose (C6H12O6) is ___ aldehyde, which contains hydroxyls and distinguishesfrom common aldehydes or alcohols in properties.(a) polyhydrate (b) many-hydrooxy (c) multihydroxyl (d) polyhydroxy84、b Compounds containing —OH and C=C groups are called ____ alcohols, because of the presence of carbon-carbon double bonds.(a) primary (b) unsaturated (c) monohydroxyl (d) polyolic85、b Oxacyclopropane contains ____ atom(a) nitrogen (b) oxygen (c) sulfur (d) phosphorus86、a azacyclopropane contains ____ atom(a) nitrogen (b) oxygen (c) sulfur (d) phosphorus87、 azacyclopropane is classified into ___?_(a) amine (b) ether (c) alkane (d) alkene88、a Oxacyclopropane contains ____ carbons(a) 2 (b) 3 (c) 4 (d) 589、d Which of the following belongs to tertiary amine?(a) CH3NH2 (b) (CH3)2NH (c) (NH3)3N (d) N(CH3)4+90、a Which of the following contains carbonyl group?(a) CH3COOH (b) CH3OCH3 (c) CH3CH2OH (d) CH3CH2Cl91/c Which of the following contains hydroxyl group?(a) CH3CHO (b) CH3OCH3 (c) CH3CH2OH (d) CH3CH2Cl92、c Which of the following belongs to saturated ketone?(a) CH3CHO (b) CH2=CHCOCH3 (c) CH3CH2COCH3 (d) CH3COOH93、c Carboxylic acids react with alcohols to form ____.(a) acid halides (b) acid anhydrides (c) esters (d) amides94、c The general formula of organic amides is ____.(a) RNH2 (b) RNH3+X- (c) RCONH2 (d) NaNH295、b Decarboxylation, elimination of the ___ as CO2is of importance for β-keto acid.(a) —OR (b) —COOH (c) —CHO (d) —CONH296、a Reaction of acid chloride with water forms ____.(a) carboxylic acid (b) chlorocarboxylic acid (c) ester (d) phenol97、b We can deduce that thiophene contains ___ element though its detailed structure is unknown.(a) O (b) S (c) N (d) C98、a Which of the following is neutralization reaction?(a) acid and base (b) salt and salt (c) salt and base (d) acid salt99、b Reaction of carboxylic acid with alcohol is defined as ____.(a) etherification (b) esterification (c) epoxide (d) elimination100、b Reaction of acid anhydrides with ammonia produce____(a) ammonium (b) amide (c) amine (d) amino101、d In K4[FeF6], the Fe is called ____.(a) dipole moment (b) coordination number (c) ligand (d) centre ion or atom102、a Concentration of concentrated sulfuric acid is ______(a) 18M (b) 12M (c) 6M (d) 2M103、a The detailed, step-by-step description of a chemical reaction is called ____, e.g., hydrogen reacts with oxygen to generate water. Such reaction involves the following step:H2→ H·H· +O2→ HO· + O·H· + HO·→ H2O(a) mechanism (b) dynamic equation (c) activation energy (d) process104、a Hydrolysis of FeCl3 shows ____(a) acidic (b) neutral (c) alkaline (d) amphoteric105、c Carbocation carries ____ charge.(a) no (b) neutral (c) positive (d) varying106、a A large excess of alcohol is added in the following reaction, CH3COOH +CH3CH2CH2OH------CH3COOC3H7 + H2O, the equilibrium shifts ____.(a) forwards (b) backwards (c) nothing (d) uncertainy107、c The reaction CH3COOH+ C2H5OH ----- CH3COOC2H5 is a ____ reaction because it proceeds in both direction.(a) forwards (b) backwards c) reversible d) reverse108、a If an entity combines with a proton, it is called ____.(a) protonation (b) protolysis (c) protophile (d) non-protic109、c The key raw material for chlor-alkali is ____.(a) lime (b) brine (c) soda ash (d) wood pulp110、a Soda ash is composed of ____.(a) sodium carbonate (b) sodium bicarbonate (c) ammonium bicarbonate (d) mixture between and sodium carbonate and sodium bicarbonate111、c According to the reaction 2NaCl +2 H2O ---------2NaOH + H2 +Cl2, the ration of caustic soda to chlorine is ____ (a) 1:2 (b )1:1 (c)2:1 (d)1:0112、c Sodium hydroxide, called ____ because of its corrosion, will burn or, even corrode our tissue and skin if it spots on them.(a) soda ash (b) caustic sodium (c) caustic soda (d) lime113、d Quicklime is manufactured by the thermal _______ (1200℃~1500℃) of limestone according to the equation: CaCO3 ------- CaO + CO2(a) combination (b) transfer (c) hydrolysis (d) decomposition114、b Which of the product derived from chlor-alkali industry?(a) electricity (b) chlorine (c) limestone (d) refractory115、c When an ammoniated solution of salt is bubbled by carbon dioxide, the process is called ____.(a) decomposition (b) calcine (c) carbonation (d) oxidation116、c In Solvay Process, separation between NaHCO3 precipitates and liquor should be carried out through ____. (a) drying (b) distillation (c) filtering (d) concentration117、c To remove some water from wet CaCO3, ____ is available.(a) electrolysis (b) metathesis (c) drying (d) solubility product118、c If you want to clear water from aqueous NaCl, the reasonable approach is ____.(a) cracking (b) humidification (c) distillation (d) agitation119、c If a solid NaCl is available from its aqueous solution, the reasonable method is ____ (a) lixiviation (b) sedimentation (c) crystallization (d)centrifugation120、d Which of the following is classified into metathesis?(a) H2 + O2— H2O (b) HCl + NaCl — NaCl + H2O(c) Zn + HCl — ZnCl2 + H2 (d) Na2SO4 + BaCl2— BaSO4 + NaCl121、d Silicate-gel is often used as ____ in chemical laboratory.(a) oxidant (b) packing material (c) initiator (d) drying agent122、b If we want to obtain solid NaCl from its aqueous solution, the reasonable operation is ____.(a) pyrolysis (b) crystallization (c) adsorption (d) adsorption123、d Which one of the following belongs to chloride?(a) Cl2 (b) NaClO3 (c) HClO3 (d) NaCl124、b All detergents, such as soap, contain ____.(a) chromatograph (b) surfactants (c) bleaching powder (d) catalysts125、Look at the following two electrode reaction(1) or (2):(1) Cl- -2e → Cl2(2) 2H2O +2 e → H2 +2OH-a Electrode (1) is ____(a) cathode (b) anode (c) negative electrode (d) electron127、c Bleaching powder is often used as ____ in public water supplies.(a) infection (b) alkalisource (c) disinfectant (d) raw material128、a The raw material to produce sulfuric acid is____.(a) sulfide (b) sulfur (c) sulfate (d) sulfonate129、c Electrolysis of aqueous HCl will generate __?__.(a) hydride (b) hydrogen ion (c) hydrogen (d) hydrate130、b Which of the following shows alkaline?(a) chlorine (b) caustic soda (c) sulfuric acid (d) hydrogen131、a The method to produce industrially sulfuric acid is ____.(a) contact process (b) Solovy Process (c) electrolysis (d) lead chamber132、c Which of the following belongs to sulfide?(a) Na2S2O3 (b) Na2SO3 (c) Na2S (d) Na2SO4133、c If excess sulfur trioxide is dissolved into pure sulfuric acid, ____ forms.(a) concentrated sulfuric acid (b) dilute sulfuric acid(c) oleum (d) divanadium pentoxide134、b The method to synthesize ammonia is ____ .(a) Solvay Process (b) Habor Process(c) Catalytic Reforming (d) methanation135、d Prior to reforming reaction, the syngas requires _______ process, in which sulfur-containing compounds must be removed as they poison both the reforming catalysts and Harber catalysts.(a) sulfonation (b) sulfurization (c) sulfates (d) desulfurization136、d If a steam is required to be converted into liquid, _____ is available.(a) absorption tower (b) reformer (c) membrane cell (d) condenser137、c Benzene is ____ with concentrated nitric acid to form nitrobenzene, as described below: C6H6 + HNO3— C6H5NO2 + H2O(a) nitrogenated (b) nitrized (c) nitrated (d) nitricated138、b The following reaction is exothermic:4NH3 + 5O2— 4NO + 6H2O, therefore, low temperature favors the reaction ____.(a) backwards (b) forwards (c) no shift (d) uncertain139、a In the following reaction, Cu + 2H2SO4— CuSO4 + SO2 + 2H2O____ is oxidized.(a) Cu (b) H2SO4 (c) SO2 (d) H2O140、b The raw material to produce industrially nitric acid is ____.(a) nitrogen (b) ammonia (c) amine (d) ammine141、a Dehydration of pure nitric acid will give ____.(a) H2O (b) N2O5 (c) NO2 (d) NO142、c About 65% nitric acid reacts with ammonia to give ____.(a) nitrogen (b) ammonium nitrate (c) nitrogen dioxide (d) dinitrogen pentoxide.143、b Which of the following is an important precursor for petrochemicals?(a) ethane (b) ethylene (c) ethanol (d) ethanoic anhydride144、a Demethylation of methylcyclohexane gives ____.(a) cyclohexane (b) cyclohexyl (c) cyclohexene (d) benzene145、Dehydrogenation of cyclohexane gives __?__.(a) cyclohexene (b) cyclohexanone (c) cyclohexyl (d) cyclohexanecarboxylic acid146、a Precisely, the molecular weight of polymer, often greater than 107, equals to that of____ multiplied by degree of polymerization.(a) monomer (b) mole (c) covalent bond (d) radical147、b Vulcanization of rubber refers to addition of some ____ in the framework of rubber body.(a) vanadium (b) sulfur (c) chlorine (d) nitrogen148、c When the degree of polymerization reaches less than 20, we say the polymer is ____.(a) the intermediate (d) the distillate (c) oligomer (d) monomer149、c At the top of the distillation tower, there is a ____ to cool the vapor into reflux liquid and to recycle into the tower.(a) heat exchanger (b) furnace (c) working tank (c) condenser150、bIn sulfuric acid industry, elemental sulfur is combusted in ____ to general sulfur dioxide.(a) fractionating tower (b) furnace (c) steam stripper (d) working tank151、c At the bottom of the distillation tower, there is a(an) ____ to boil the liquid into vapor and to recycle into the tower.(a) still (b) auxiliary (c) tank (c) boiler152、d If a new bond between polymeric chains is developed, the process is called ____.(a) covalence (b) side-chain (c) fabrication (d) cross-linking153、a Which of following belongs to synthetic polymer?(a) plastic film (b) silk (c) cellulose (d) starch154、a Copolymers are derived from polymerization of ____ monomers, such as C6H5OH and HCHO.(a) different (b) usual (c) the same (d) conventional155、d Any commodity should have a technical ____ if they go into public commerce.(a) specific (b) specify (c) specialty (d) specification156、c The ____ of Zn-Cu alloy(solid solution) is as follow: 30%Zn and 70%Cu.(a) composite (b) component (c) composition (d) complex157、d As a convention, [Cu(NH3)4]SO4 is never considered a salt, but a ____.(a) composite (b) component (c) composition (d) complex158、b After synthesis of a product, the product must be ___ because the mixture contains the desirable products as well as the remaining reactants, catalysts, by-products.(a) pre-treated (b) post-treated (c) blended (d) eliminated159、a When ethanol is dissolved into water, a ____ solution is developed.(a) homogeneous (b) heterogeneous (c) viscose (d) latent160、a The reaction H2 + O2 -----H2O is ____.(a) exothermic (b) endothermic (c) isothermal (d) thermodynamic161、c Which of the follow is used as the semi-conductor material?(a) Fe (b) N2 (c) Si (d) He162、c Homopolymers are derived from polymerization of ____ monomers, such as polyethylene.(a) different (b) usual (c) the same (d) conventional163、a Activate carbon is often used as adsorbent in laboratory due to its large ____ surface.(a) specific (b) specify (c) specialty (d) specification164、b To obtain pure substance from the mixture, ____ is a good choice.(a) catalysis (b) purification (c) reactor design (d) solubility165、d If a reaction is carried out at a very high pressure, _____ is a good choice.(a) furnace (b) fractionating tower (c) heat exchanger (d) autoclave166、d Which of the following is classified into polymer?(a) formaldehyde (b) silica (c) sulfur trioxide (d) epoxy resin 167、a Which of the following is classified into synthetic polymer?(a) resin (b) vinyl chloride (c) epoxide (d) silica。
小学下册英语第六单元全练全测(含答案)英语试题一、综合题(本题有100小题,每小题1分,共100分.每小题不选、错误,均不给分)1.The __________ is a famous mountain in the Andes. (马丘比丘)2. A chemical reaction can produce _____ and heat.3.My aunt travels to ____ (different) countries each year.4.When i t’s foggy, I need to be extra __________ on the road. (小心的)5.What do you call a story that is told with pictures?A. ComicB. NovelC. BiographyD. Memoir6.I like to ride my _____ (自行车) around the neighborhood. 我喜欢在附近骑自行车。
7.What is the opposite of "hard"?A. SoftB. ToughC. StrongD. Heavy8.The chemical symbol for indium is __________.9.I love to make ________ (玩具类型) with clay.10.The __________ (历史的转折) signifies change.11.The ______ (狮子) is known for its courage.12.What is the opposite of 'happy'?A. ExcitedB. SadC. AngryD. Tired13.The ________ is a small but important insect.14.The __________ (地质) of the area is fascinating.15.I have a special box where I keep my favorite ________ (玩具名).16.The chemical symbol for neodymium is ______.17.The owl rests during the ______ (白天).18.The chemical symbol for aluminum is __________.19.What is the main source of energy for the Earth?A. MoonB. SunC. StarsD. Fire答案:B20.I can play make-believe with my ________ (玩具).21.The _______ has a unique texture.22.The ______ is a famous scientist.23.The main purpose of photosynthesis is to produce ______.24.The first successful kidney transplant was performed in ________.25. A light year measures ______ in space.26.Which animal has a pouch for carrying its young?A. DogB. KangarooC. CatD. Horse答案:B27.The fruit salad is ________ (新鲜).28._____ (农业) is important for food production.29.What do we call a scientist who studies human behavior?A. PsychologistB. SociologistC. AnthropologistD. Historian答案:A30.I enjoy ______ (写作) stories.31.The _____ (园艺师) designs beautiful landscapes.32.My ___ (小马) loves to run fast.33.What is the capital of Jamaica?A. KingstonB. Montego BayC. Ocho RiosD. Negril34.What do you call a large animal that has antlers?A. MooseB. DeerC. ElkD. All of the above答案:D35.What do we call a story that is made up?A. FactB. FictionC. HistoryD. Biography36.The Earth's surface is made up of various ______ ecosystems.37.The sun is ___ in the morning. (rising)38. A _____ is an area of land that rises sharply.39.Many different cultures can be found in _______.40.We will _______ (travel) to Italy next summer.41.What is the term for a group of galaxies held together by gravity?A. Galaxy ClusterB. SuperclusterC. Galaxy GroupD. Cosmic Cluster42.What do we call the process of using natural resources wisely?A. ConservationB. PollutionC. ExploitationD. Deforestation答案:A43.The chemical symbol for manganese is ________.44.What is the main ingredient in tofu?A. SoybeansB. PeasC. CornD. Wheat答案:A45.Astronomy is one of the oldest sciences in ______.46.What is the term for the remnants of a star that has exploded?A. Supernova RemnantB. Steller DustC. Cosmic AshD. Stellar Remains47. A chemical reaction can involve the transformation of _____.48.The __________ can affect the growth of plants.49. A ____(collaboration agreement) formalizes partnerships.50.The sun is shining ___ (brightly).51.Gases can fill any ______.52.Which continent is known for having kangaroos?A. AfricaB. AsiaC. AustraliaD. Europe答案:C53.I feel _______ when I play with my pets.54.Which animal is known for its stripes?A. LeopardB. ZebraC. LionD. Giraffe答案:B55.The crab scuttles across the _________. (沙滩)56.What do you call a young horse?A. CalfB. FoalC. KidD. Cub答案:B57.The _____ (乌鸦) is often seen perched on trees. 乌鸦常常栖息在树上。
A fractal model for determining oxygen effective diffusivity of gas diffusion layer under the dry and wet conditionsRui Wu,Qiang Liao,Xun Zhu ⇑,Hong WangInstitute of Engineering Thermophysics,Chongqing University,Chongqing 400044,ChinaKey Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University),Ministry of Education,Chongqing 400030,Chinaa r t i c l e i n f o Article history:Received 22February 2011Received in revised form 27April 2011Available online 15June 2011Keywords:Proton exchange membrane fuel cell Gas diffusion layerOxygen effective diffusivity Fractal theoryKnudsen diffusion Wettabilitya b s t r a c tIn this paper,we propose a new fractal model to determine the oxygen effective diffusivity of the porous gas diffusion layer (GDL)in proton exchange membrane fuel cell for both the dry and wet conditions.The model considers the GDL structure in terms of tortuosity and area fractal dimensions and also takes the Knudsen effect into account,which has no empirical constant but parameters with physical meanings.The fractal model is verified by the fair agreement with the experimental data and the results obtained from existing models.It is revealed that the Knudsen effect is essential for the understanding of the oxy-gen transport through the GDL.Under the dry condition,the oxygen effective diffusivity increases with higher area fractal dimension and lower tortuosity fractal dimension.For the wet condition,the water condensation in the GDL of mixed wettability is considered;and it is found that the behavior of oxygen effective diffusivity with liquid saturation depends on the GDL wettability.It is further revealed that for a given liquid saturation,the oxygen effective diffusivity increases with greater area fractal dimension;with the decrease of tortuosity fractal dimension,it also increases,except for the hydrophilic case at high liquid saturation.Ó2011Elsevier Ltd.All rights reserved.1.IntroductionProton exchange membrane fuel cell is considered as one of the most promising candidates for the power sources of mobile,sta-tionary and portable devices,owing to its high efficiency,low emission,and rapid start capacity.At the cathode,oxygen is trans-ported through the gas diffusion layer (GDL)from the gas channel (GC)to the catalyst layer (CL),where it is combined with the pro-tons and electrons from the anode to produce water.The produced water could condense in the porous GDL,which blocks the oxygen transport and hence deteriorates the fuel cell performance.Numer-ical simulations based on the mass conservation equations have been widely employed to investigate the oxygen transport through the porous GDL that is partially filled with liquid water.Owing to the porous structure of GDL,it is needed to prescribe in these mod-els the oxygen effective diffusivity,the accurate determination of which is essential for the understating of oxygen transport through the GDL.Many experimental and numerical studies have been reported in literatures for determining the oxygen effective diffusivities of the porous GDL samples.Owing to the limitations of the present technology,most of the existing experimental measurements,e.g.[1–3],were performed under the dry condition with no regard for the impacts of liquid water in the GDL.These experimental studies,e.g.[1],have revealed that the oxygen effective diffusivity is determined not only by the GDL porosity but also by the GDL topology.Although these experimental studies are informative,they are phenomenal and cannot provide any insights into the impacts of GDL structure on oxygen transport.To gain a deep understanding of the oxygen effective diffusivity,pore scale direc-tion simulations of oxygen transport through the GDL have been conducted.In the simulations for the dry condition,e.g.[4,5],the detail structure of the GDL has been constructed.The dependency of oxygen effective diffusivity on liquid water in the GDL has also been numerically investigated by researchers using the pore net-work modeling approach in recent years [6–8].Notwithstanding the experimental and numerical studies men-tioned above,it is still scarce the definite relationship between the oxygen effective diffusivity and the structure of the porous GDL.The disorder nature of pore microstructure suggests that the inter-spaces in a real porous media have fractal character.Katz and Thompson [9]presented the experimental evidence that the pore spaces of a set of sandstones are fractal and self-similar.The fractal geometry theory has been proven to be a powerful means for the analysis of porous media with complex and random microstruc-tures [10].Interested readers can refer to reference [11]for a more0017-9310/$-see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.ijheatmasstransfer.2011.05.010⇑Corresponding author at:Institute of Engineering Thermophysics,ChongqingUniversity,Chongqing 400044,China.Tel./fax:+862365102474.E-mail address:zhuxun@ (X.Zhu).detailed review on this area.Recently,several researchers have implemented the fractal technology to compute the physical prop-erties of the porous GDL,e.g.,the gas permeability [12,13],the effective thermal conductivity [14],and the effective self diffusivity of hydrogen [15].Shi et al.[16]developed a fractal model for the oxygen transport through the dry GDL.Their model,however,sug-gested the ratio of oxygen effective diffusivity to oxygen diffusivity in air to be 0.701for the untreated TGP-H-060carbon paper,a va-lue that is much larger than the data 0.366obtained from the experimental measurement [1].Furthermore,in their model,the impacts of liquid in the GDL were not considered.In the present study,we develop a new fractal model,the pre-diction of which is in fair agreement with the experimental data and the results from the existing models,to elucidate how the oxy-gen effective diffusivity is affected by the GDL structure and wetta-bility under the dry and wet conditions.In Section 2,we introduce the oxygen effective diffusivity for the carbon paper GDLs.The de-duced fractal models are presented in Section 3,followed by the model validation and the parameter studies in Section 4.Finally,some interesting conclusions are drawn in Section 5.2.Oxygen effective diffusivity of carbon paper GDLTo take the GDL topology into account,the oxygen effective dif-fusivity D e is correlated with the GDL porosity e and the liquid sat-uration s as well as the GDL structure parameter U using the normalized function f (e ,U )and g (s ,U )as follows [8]:D e ¼D AB f ðe ;U Þg ðs ;U Þ;ð1Þwhere D AB is the bulk diffusivity of oxygen in the air.The normal-ized function f (e ,U )denotes the oxygen transport through the dry GDL samples and depends on only the intrinsic structure of theGDL.The normalized function g (s ,U )on the other hand character-izes the impacts of liquid water on oxygen transport through the wet GDL,which relies to not only the liquid saturation but also the distribution of liquid in the GDL (since the GDL topology con-trols the distribution of liquid therein,the normalized function g (s ,U )is also a function of GDL structure parameter).Up to now,many predictive models have been proposed for the normalized functions f (e ,U )and g (s ,U ),as listed in Tables 1and 2,respectively.Most of these models,however,are correlated with only e and s and do not indicate any physical meanings on how the GDL structure af-fects the oxygen transport.3.Fractal model for oxygen effective diffusivity of carbon paper GDL3.1.Theoretical baseBefore going to the detail of the deduction of fractal model for oxygen transport through the porous GDL,the basic concept of the fractal theory is introduced in this subsection.The carbon paper GDLs,e.g.,TGP-H-060carbon paper presented in Fig.1(a),are com-posed of randomly stacked carbon fibers and have numerous pores in the through-plane direction (i.e.,the transport direction).This type of GDL volume can be envisioned to be made up of a bundle of tortuous capillaries with various sizes,as shown in Fig.1(b).Here we set the diameter of a capillary as k and its tortuous length along the transport direction as L (k ).It has been shown that the relation-ship between them exhibits the similar fractal scaling law as fol-lows [17]:L ðk ÞL 0¼L 0kd t À1;ð2Þwhere L 0is the length of straight capillary,equal to the thickness ofthe GDL,and d t the tortuosity fractal dimension,characterizing the convolutedness of the capillaries,with 1<d t <2.The greater the va-lue of d t is,the higher the convolutedness of the capillary.The lim-iting case d t =1represents the straight capillary,i.e.,L (k )=L 0,while the other limiting case d t =2corresponds to a highly tortuous line that fills a plane.Besides the capillary convolutedness,the number of capillaries of diameter k is another important parameter for the fractal anal-ysis of porous media.It has been shown that the scaling relation-Table 1Existing models for the normalized function f (e ,U ).ModelTypeEffective medium theory [6]f (e ,U )=e 1.5Nam and Kaviany [6]f ðe ;U Þ¼e e À0:111À0:11ÀÁ0:785Das et al.[24]f ðe ;U Þ¼1À3ð1Àe Þe Wu et al.[8]f ðe ;U Þ¼e e À1=0:222À0:161C p ⁄⁄C p is the PTFE content by weight.4342R.Wu et al./International Journal of Heat and Mass Transfer 54(2011)4341–4348capillaries in the GDL;and the greater the value of d f is,the more the number of capillaries.Differentiating Eq.(3)with respect to k results in the number of capillaries that range from k to k +d k [17]:ÀdN ¼d f k dfmax k Àðd f þ1Þd kð4ÞandÀdN t¼d f k d fmin k Àðd f þ1Þd k ¼f ðk Þd k :ð5ÞThe minus in Eq.(4)indicates that the capillary population de-creases with increasing k .In Eq.(5),N t is the total number of capil-laries in the system,i.e.,N t =ðk max =k min Þd f ,and f (k )is the probability density function,which satisfies the following relationship [17]:f ðk Þ>0:ð6ÞBased on the probability theory,f (k )should also meet the following condition [17]:Z1À1f ðk Þd k ¼1:ð7ÞAccording to Eq.(5),we have [17]:Z1À1f ðk Þd k ¼Zk maxk min f ðk Þd k ¼Zk maxk mind f k dfmin k Àðd f þ1Þd k ¼1Àk mink maxd f:ð8ÞThis indicates that Eq.(7)holds if and only if following equation is satisfied [17]:k min k maxd f¼0:ð9ÞFor the carbon paper GDL samples,k min /k max is in general smaller than 10–2;therefore,Eq.(9)holds approximately,and the fractal technique can be used for the analysis of the oxygen transport through the carbon paper GDL samples.Eqs.(2)–(9)form the basis for the analysis of the porous media,which will be employed to de-rive the fractal oxygen effective model in the following subsections.3.2.Fractal model for the normalized function f (e ,U )in dry GDL Under the dry condition,the normalized function f (e ,U )=D e /D AB is calculated.For a given GDL porosity and structure,the oxygen effective diffusivity D e can be obtained based on Fick’s law:D e ¼QL 0D cA;ð10Þwhere D C is the oxygen concentration gradient across the GDL,A the cross sectional area of the GDL,and Q the total diffusion rate.Under the dry condition,the total diffusion rate through the GDL is the sum of the diffusion rate through each individual capillary in the system.The diffusion rate across a single capillary of diame-ter k can be determined using the following equation:q ðk Þ¼p4k 2D c ðk ÞD cL ðk Þ;ð11Þwhere D c (k )is the effective diffusivity of oxygen in the capillary,ex-pressed as [18]:D c ðk Þ¼1D AB þ1D k ðk ÞÀ1;ð12Þwhere D k (k )is the Knudsen diffusivity,which characterizes the col-lision between the oxygen molecular and the capillary wall and can be determined as:D k ðk Þ¼2k 2k B T p 12;ð13Þwhere k B is the Boltzmann constant,m the molecular mass,and Tthe temperature,assumed to be 353K in the present -bining Eqs.(2)and (11)–(13)leads to:q ðk Þ¼p4k1þd t1D AB þ1D k ðk ÞÀ1D c L d t 0:ð14ÞAfter q (k )is obtained,the total diffusion rate Q can be gained by integrating the individual diffusion rate over the entire range of capillary sizes from the minimum k min to the maximum k max :Q ¼ÀZk maxk minq ðk ÞdN :ð15ÞSubstituting Eq.(14)into Eq.(15)leads to:Q ¼Zk maxk minp4k 1þd t1D AB þ1D k ðk ÞÀ1D c L d t 0d f k d f max k Àðd f þ1Þd k ¼p d f k d fmax D c4L d t 0D AB 232k B T p m 1Z k max k min k 1þd t Àd f D AB þ2k 2k B T p 12d k ð16ÞandD e ¼QL 0D cA ¼p d f k d fmax 4AL d t À10D AB 232k B T p m 12Z k maxk mink 1þd t Àd fD AB þ2k 2k B T p 12d k :ð17ÞHere the cross sectional area A is determined based on the defini-tion of the GDL porosity e :e ¼A pA ;ð18Þwhere A p is the total area of pores in the cross section of the GDL:A p ¼ÀZk maxk minp4k 2dN ¼Zk maxk min p4d f k dfmaxk 1Àd f d k ¼p d f k d fmax k 2Àd f max Àk 2Àd f min 4ð2Àd f Þ:ð19ÞCombining Eqs.(18)and (19)results in:A ¼A p e ¼p d f k d f max k 2Àd f max Àk 2Àd fmin4e ð2Àd f Þ:ð20ÞSubstituting Eq.(20)into Eq.(17),we can arrive at the oxygen effec-tive diffusivity under the dry condition:D e ¼D ABe ð2Àdf ÞL d t À1k 2Àd f max Àk2Àd fmin232k B T p m 12Zk max k min k 1þd t Àd fD AB þ2k 2k B T p 1d k ð21Þand the normalized function f (e ,U ):f ðe ;U Þ¼D e D AB ¼e ð2Àd f ÞL d t À10k 2Àd f max Àk 2Àd f min 232k B T p m 12Zk max k min k 1þd t Àd f D AB þ23k 2k B T p m12d k :ð22ÞEq.(22)gives the fractal model of the normalized function f (e ,U ),which,as can be seen,has no empirical constants but parameters of physical meanings.Based on this equation,not only the oxygen effective diffusivity of the dry GDL is determined but also its depen-dency on GDL structure can be analyzed.3.3.Fractal model for the normalized function g(s,U )in wet GDL In fuel cell applications,the condensed liquid water in the GDL hinders the oxygen transport from the gas channel to the reactionR.Wu et al./International Journal of Heat and Mass Transfer 54(2011)4341–43484343sites.To facilitate the removal of liquid water,the cathode GDL is usually treated with PTFE to be hydrophobic.The anomaly of the PTFE treatment,however,generally renders the GDL mixed wetta-bility,i.e.,the hydrophilic and hydrophobic pores coexist.It has been shown that the hydrophilic and hydrophobic pores exhibit similar pore-size distributions [19].Sharing this scenario,we con-sider the porous carbon paper GDL as a system composed of hydro-philic and hydrophobic capillaries;and the number of hydrophilic capillaries with diameter greater than k is:N HI ðd P k Þ¼f HI k max kd f;ð23Þwhere f HI is the fraction of hydrophilic capillaries,characterizing thehydrophilicity of the GDL.Note that f HI =0denotes the hydrophobic GDL,and f HI =1characterizes the hydrophilic GDL.Under the wet condition,the saturated vapor pressure P r 0for the condensation in a capillary can be estimated using Kelvin equa-tion [20]:ln P r 00¼À4r M w cos hq w ;ð24Þwhere P 0is the saturated vapor pressure over a flat surface,r the surface tension,M w molecular weight of water,k the diameter of a single capillary,q w water density,R the gas constant,and h the contact angle which is P r 0=P 0>90 for the hydrophobic capillary and h <90°for the hydrophilic case.For the hydrophobic capillary,ln (P r 0/P 0)is positive and increases with smaller capillary,but it be-comes negative and decreases with smaller capillary when the GDL is hydrophilic.To this end,the capillaries in the system are occupied by liquid water according to the following order as the water vapor pressure increases:first the small hydrophilic capillaries,then the large hydrophilic capillaries followed by the large hydrophobic cap-illaries,and last the small hydrophobic capillaries.The filled capil-laries have no contribution to oxygen transport.Thus,when some capillaries are filled,i.e.,at a given liquid saturation,a new oxygen effective diffusivity D 0e can be obtained using the method mentioned in Section 3.2.The normalized function g (s ,U )then can be deter-mined as g ðs ;U Þ¼D 0e =D e ,for which D e is the oxygen effective diffu-sivity under the dry condition.As such,various values of g (s ,U )for different liquid saturation can be gained by increasing the water vapor pressure,with which the curve of g (s ,U )versus s is plotted.To determine the curve of g (s ,U )as a function of s using our fractal model,we first assume that water vapor condenses in the capillary of diameter k c .Based on this condition,a liquid saturation as well as an oxygen diffusivity D 0e can be calculated,with which a single point of g (s ,U )versus s is gained.By varying k c from k min to k max ,we can obtain a system data of g (s ,U )versus s ,from which the curve of g (s ,U )is achieved.Note that we consider the system of mixed wettability in the present study.When water condensation occurs in the hydrophilic capillaries of diameter k c ,all the hydro-philic tubes with diameter smaller than k c are occupied;and the li-quid water saturation s ,defined as the fraction of void space occupied by liquid phase,is:s ¼V o V t ¼ÀR k c k min p k 2L ðk ÞdN HIÀR k max k min p k 2L ðk ÞdN ¼f HI k 3Àd t Àd f c Àk 3Àd t Àd f min k 3Àd t Àd f max Àk 3Àd t Àd f min;ð25Þwhere V o is the volume of capillaries that are occupied by liquidwater,and V t the total volume of the capillaries.Owing to these occupied capillaries,the diffusion rate across the GDL unit cell becomes:Q ¼ÀZk maxk min q ðk ÞdN þZk ck minq ðk ÞdN HI :ð26ÞCombining Eqs.(14)and (26),we get the oxygen effective diffusiv-ity for this case:D 0e¼D ABe ð2Àdf ÞL d tÀ10k 2Àd fmax Àk 2Àd fmin ÀÁ232k B T p m12ÂR k maxk mink1þd t Àd f D AB þ23k 2k B T p mÀÁ12d k Àf HI R k ck mink1þd t Àd fD AB þ23k 2k B T p m ÀÁ12d k "#ð27Þand the normalized function g (s ,U ):g ðs ;U Þ¼D 0e D e¼R k maxk mink1þd t Àd fD AB þ23k 2k B T p mÀÁ12d k Àf HI R k ck mink1þd t Àd fD AB þ23k 2k B T p m ÀÁ12d kR k maxk mink1þd t Àd fD AB þ23k 2kB T p m ÀÁ12d k:ð28ÞHere D e is the oxygen effective diffusivity under the dry condition,Eq.(21).As for the condensation in the hydrophobic capillary of diameter k c ,not only all the hydrophilic capillaries but also all the hydrophobic capillaries with diameter greater than k c are filled with liquid water.Under this circumstance,the liquid saturation is:s ¼V o t¼ÀR k max k min p k 2L ðk ÞdN HI ÀR k max k c p k 2L ðk Þd ðN ÀN HI ÞÀR max k min p 4k 2L ðk ÞdN¼1Àð1Àf HI Þk 3Àd t Àd f cÀk 3Àd t Àd f min k 3Àd t Àd fmaxÀk 3Àd t Àd fminð29Þand the oxygen diffusion flux across the unit cell becomes:Q ¼ÀZk ck minq ðk Þd ðN ÀN HI Þ:ð30ÞCombining Eqs.(14)and (30)leads to the oxygen effective diffusiv-ity for this case:D 0e ¼D AB ð1Àf HI Þe ð2Àd f ÞL d t À1k 2Àd f max Àk 2Àd f min 232k B T p m 12Zk c k min k 1þd t Àd f D AB þ23k 2k B T p m12d k ð31Þand the normalized function g (s ,U ):g ðs ;U Þ¼D 0e D e¼ð1Àf HI ÞR k ck mink1þd t Àd fD AB þ2k 2k BT p mÀÁ12d k R k maxk mink1þd t Àd fD AB þ23k 2k B T p m ÀÁ12d k :ð32ÞEqs.(25)–(32)give the expressions of the normalized function g (s ,U )for studying the impacts of liquid water on oxygen transport through the GDL,with which we also can obtain the evolution of the oxygen effective diffusivity with liquid saturation for various GDL structures and wettabilities under the wet condition.4.Results and discussionFrom above fractal model,it can be seen that the oxygen diffusiv-ity is determined not only by GDL porosity /but also by the structure parameters (d t ,d f ,L 0,k min ,k max ).Actually,these parameters are not independent of each other.For example,Yu and Li [21]proposed that the area fractal dimension d f can be determined as:d f ¼d E Àln eln k min kmax;ð33Þwhere d E is the Euclidean dimension,which is d E =2in this study.Moreover,Yu [22]suggested that the value of tortuousity fractal dimension d t can be calculated using the following equation:d t ¼1þln s a v ln L 0a v;ð34Þ4344R.Wu et al./International Journal of Heat and Mass Transfer 54(2011)4341–4348where s a v and k a v are the average capillary tortuosity and the aver-aged capillary diameter,ing a simple geometry model,Yu and Li[23]derived that:s a v¼11þ1ffiffiffiffiffiffiffiffiffiffiffi1Àepþffiffiffiffiffiffiffiffiffiffiffi1Àepffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1ffiffiffiffiffiffi1ÀpÀ12þ1r1Àffiffiffiffiffiffiffiffiffiffiffi1Àp2 66 43775:ð35ÞAnd the average capillary diameter can be obtained according to its definition:k a v¼Z k maxk min kÁfðkÞd k¼d f k maxfk minmaxÀk minmaxd f"#:ð36ÞIn addition to this theoretical analysis,the fractal dimensions also can be experimentally measured using the box-counting method which is based on the image analysis of a unit cell of a porous sam-ple.Employing this method,Shi et al.[16]measured the fractal parameters of the untreated TGP-H-060carbon paper,as listed in Table3where the structure parameters of this GDL are also shown. In the present study,we consider these parameters as the baseline cases for the calculation of the normalized functions f(e,U)and g(s,U)based on the fractal analysis.4.1.The normalized function f(e,U)in dry carbon paperUnder the dry condition,the normalized function f(e,U)is determined.Before going to the detail of the parametric study,GDL.It also can be seen from thisfigure that most of the existing models over predict the normalized function f(e,U)significantly. Although the model of Wu et al.[8]agrees with our fractal model as well as the experimental data,it does not reveal any direct rela-tionship between f(e,U)and the GDL structure.From this point of view,we can conclude that the fractal theory points out a new way for the analysis of oxygen transport through the carbon paper GDL samples.The Knudsen effect,reflected by D k(k)in Eq.(12),is considered in our fractal model.To gain a better understand of the Knudsen ef-fect,we compare the values of f(e,U)obtained based on the models with and without Knudsen effect for the untreated TGP-H-060 carbon paper.Without the Knudsen diffusivity in Eq.(12),we can obtain the oxygen effective diffusivity:D e¼D ABeð2ÀdfÞk1þd tÀd fmaxÀk1þd tÀd fminL d tÀ1ð1þd tÀd fÞk2Àd fmaxÀk2Àd fminð37Þand the normalized function f(e,U):fðe;UÞ¼D eAB¼eð2ÀdfÞk1þd tÀd fmaxÀk1þd tÀd fminL d tÀ1ð1þd tÀd fÞk2Àd fmaxÀk2Àd fmin:ð38ÞAlthough Eq.(38)is simpler compared to Eq.(22),it gives the nor-malized function f(e,U)the value0.421,which is about15%higher than that obtained from Eq.(22)and the measured data.This result leads to the conclusion that the consideration of the Knudsen effect is essential for the understanding of oxygen transport through the GDL.Hence,in the rest calculations of this study,we always take the Knudsen effect into account.The impacts of GDL structure on oxygen transport under the dry condition can be obtained by investigating the dependency of the normalized function f(e,U)on fractal dimensions,as displayed in Fig.3wherein the variations of f(e,U)with d t for different d f are plotted.It can be seen from thisfigure that the normalized function f(e,U)increases as d f increases but decreases with the increase of d t.The decrease of f(e,U)with greater d t is attributed to the re-duced oxygen transport because of the increased capillary length. While with the increase of d f,the number of capillaries in the sys-Table3Geometric and fractal parameters of the untreated TGP-H-060carbon paper.Parameter Value[16]Descriptionk max8Â10À5m Maximum capillary diameterk min 3.079Â10À8m Minimum capillary diametere0.78PorosityL0 1.9Â10À4m GDL thicknessD AB 3.2Â10À5m2sÀ1Oxygen diffusivity in aird t 1.1447Tortuosity fractal dimensiond f 1.9669Area fractal dimensionThe normalized function f(e,U)obtained from the present fractal modelexisting models in Table1as well as the experimental measurements.R.Wu et al./International Journal of Heat and Mass Transfer54(2011)4341–43484345available for g(s,U);but several models with the form =(1Às)a have been proposed,Table2.For validation, present fractal model is compared with these existing models, displayed in Fig.4.Since all the current models are based on hydrophobic GDL hypothesis,only the fractal model for the hydro-phobic case is compared with them.As seen,the g(s,U) gained from the fractal model exhibits a similar trend as those models listed in Table2.For a given liquid saturation,bothg(s,U)at thefirst regime is attributed to the occupation of smallhydrophilic capillaries at the beginning of condensation.After this, the liquid willfill the large hydrophilic capillaries as well as the large hydrophobic capillaries,thereby leading to the fast drop of g(s,U)at the second regime.The slow reduction of g(s,U)at the last stage is contributed by the occupation of the rest small hydro-phobic capillaries in the system.Because of the continuous distri-bution of the capillary size in the fractal model,the transitions between each regime are smooth and cannot be characterized by some particular‘critical points’.The influences of liquid water on oxygen transport through the GDL of different structures can be gained by studying the variation of g(s,U)with s for different fractal dimensions.The impacts of tor-tuosity and area fractal dimensions on normalized function g(s,U) are displayed in Figs.6and7,respectively.It should be noticed here that the normalized function g(s,U)characterizes only the im-pacts of liquid water on oxygen transport,which is not affected by the oxygen transport under the dry condition(i.e.,the normalized function f(e,U)).As can be seen from thesefigures,the value of g(s,U)at a given liquid saturation is decreased with higher fractal dimensions for the hydrophobic GDL,while for the hydrophilic case,it is increased.The explanation for this result is as follows. With the increase of d t,the capillary length is increased,and theThe normalized function g(s,U)obtained from the present fractal modelexisting models in Table2.The impacts of the tortuosity fractal dimension on the normalized functionThe impacts of the area fractal dimension on the normalized function。