Zinc doped g C3N4/BiVO4 as a Z scheme photocatalyst system for water splitting under visible light

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Chinese Journal of Catalysis 39 (218) 472 478 催化学报 218 年第 39 卷第 3 期 www.cjcatal.org available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/chnjc Article (Special Issue of Photocatalysis for Solar Fuels) Zinc doped g C3N4/BiVO4 as a Z scheme photocatalyst system for water splitting under visible light Zhen Qin, Wenjian Fang, Junying Liu, Zhidong Wei, Zhi Jiang, Wenfeng Shangguan * Research Center for Combustion and Environmental Technology, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 24, China A R T I C L E I N F O A B S T R A C T Article history: Received 28 September 217 Accepted 29 October 217 Published 5 March 218 Keywords: g C3N4 BiVO4 Z scheme Shuttle redox mediator Water splitting A two step photocatalytic water splitting system, termed a Z scheme system, was achieved using Zn doped g C3N4 for H2 evolution and BiVO4 for O2 evolution with Fe 2+ /Fe 3+ as a shuttle redox mediator. H2 and O2 were evaluated simultaneously when the doping amount of zinc was 1%. Moreover, Zn doped (1%) g C3N4 synthesized by an impregnation method showed superior active ability to form the Z scheme with BiVO4 than by in situ synthesis. X ray diffraction, UV Vis spectroscopy, scanning electron microscopy, and X ray photoelectron spectroscopy were used to characterize the samples. It was determined that more Zn N bonds could be formed on the surface of g C3N4 by impregnation, which could facilitate charge transfer. 218, Dalian Institute of Chemical Physics, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved. 1. Introduction As the dramatic increase in the development of industry proceeds with overuse of fossil fuels, environmental problems and energy crises may become ever more serious. To help alleviate this situation, water splitting using semiconducting photocatalysts has been shown, since the discovery of the Honda Fujishima effect, to be a promising method to generate H2, as an environmentally friendly energy source, directly from the sun [1]. A new type of metal free semiconductor material, g C3N4, has received attention because of its non toxicity, visible light response, and thermal chemical stability [2 5]. Its low cost and simple synthesis make g C3N4 easily obtainable from calcining melamine, dicyandiamide, urea, or other raw materials [6 8]. However, because of the high binding energy of g C3N4 and its low crystallinity, it is difficult to separate the photogenerated electron hole pair and it suffers from fast recombination of photoexcited charge carriers [9,1]. Researchers have been working on modifications to g C3N4, and several metal containing carbon nitride compounds have been reported to greatly improve the performance of g C3N4 under visible light [2,4,5,11]. However, such doping modification cannot solve the problem of recombination. To solve that, coupling g C3N4 with other materials to form a composite structure shows some promise [12]. Examples include CdS/g C3N4 [13], TiO2/g C3N4 [14], WO3/g C3N4 [15], g C3N4/Ag3PO4 [16], Cd.5Zn.5S/g C3N4 [17], and CoTiO3/g C3N4 [18], but all of these works focused only on enhancing H2 evolution and no O2 was observed. So called Z scheme principled photocatalyst has stirred the interest of scientists because of its charge transport mechanism, similar to the natural green plant photosynthesis, and its Z scheme charge transfer path. In this system, two different photocatalysts are combined using an appropriate shuttle re * Corresponding author. Tel: +86 21 34262; E mail:shangguan@sjtu.edu.cn This work was supported by the National Natural Science Foundation of China (21773153). DOI: 1.116/S1872 267(17)62961 9 http://www.sciencedirect.com/science/journal/1872267 Chin. J. Catal., Vol. 39, No. 3, March 218

Zhen Qin et al. / Chinese Journal of Catalysis 39 (218) 472 478 473 dox mediator [19]. Its unique energy gap, structure, and charge transfer mode make the electrons and holes separately spaced [2]. The Z scheme method also makes it possible to combine photocatalysts for either water reduction or oxidation potential to the system [19]. For example, BiVO4, whose conduction band is.3 V versus NHE, and which has no ability to produce H2, is capable of oxidizing from a solution containing appropriate electron acceptors, as will be discussed vide infra. Some work to date has focused on using BiVO4 to reinforce the oxidation capacity of g C3N4 [21 25], whose conduction band (CB) is 1.42 V and valence band (VB) is 1.25 V versus NHE. However, most of these studies only formed a heterojunction that results in a more negative VB and more positive CB, which is undesirable for water splitting. Herein, we report on the overall water splitting using Zn doped g C3N4 for H2 evolution and BiVO4 photocatalyst for O2, with Fe 3+ /Fe 2+ redox couple as an electron mediator. Our photocatalytic experiments indicate that g C3N4 can be used in a typical Z scheme water splitting system with both H2 and O2 gases evolved in a stoichiometric ratio (H2/O2 2). 2. Experimental Urea (>99.%), Ethanol (99.7%), NH4VO3 (>99%), ZnCl2 (>98.%), HCl (>36.% to aqueous solution), dicyandiamide (>99%), Bi(NO3)3 5H2O (>98%), HNO3 (65% 68%), NH3 H2O (28% to aqueous solution), and H2PtCl6 6H2O were purchased from Sinopharm Chemical Reagent Co., Ltd. (China). FeCl2 (>98%) was purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. (China). All reagents were used without further purification. 2.1. Photocatalyst preparation The photocatalyst of g C3N4 was synthesized according to the procedure presented in Ref. [26]. Typically, 16 g urea was heated to 873 K at a heating rate of 2.5 K/min in an alumina crucible with aluminum foil as a cover. After naturally cooling to room temperature, the light yellow colored g C3N4 was obtained without further treatment. The as prepared g C3N4 (1 g) was then mixed with 1 ml of ethanol and different proportions of ZnCl2 (e.g..1 g ZnCl2 for CN 1 U, where U represents use of urea as the precursor) were added to the mixed solution. A few drops of HCl (36%) were added to avoid hydrolysis of ZnCl2. This solution was heated and stirred at 353 K to remove ethanol. It was then heated to 673 K at a rate of 5 K/min under nitrogen flow and kept at this temperature for 4 h. Zinc containing g C3N4 was then produced after naturally cooling in a nitrogen atmosphere. Different methods have been used to realize Zn doping. Wang s group [4] used dicyandiamide and ZnCl2 as precursors, combined with a polycondensation process at elevated temperatures. Meanwhile, Ye s group [22] mixed as prepared g C3N4 with ZnCl2 and then dried this under nitrogen flow. In the Wang and Ye work, the materials used are the same and the only difference is the synthetic method employed. Our research uses the same synthetic method as Ye s work except that we use urea instead of dicyandiamide. Three different types of g C3N4 doped with zinc (1%) were synthesized and denoted as CN 1 D2, CN 1 D1, and CN 1 U. BiVO4 catalyst was synthesized using a hydrothermal method [27] as follows. First, 3 mmol Bi(NO3)3 5H2O and 3 mmol NH4VO3 were dissolved in 4 ml HNO3 (2 mol/l) with vigorous stirring. The ph was then adjusted to 2. using ammonia and dilute nitric acid to form a yellowish suspension that was kept under stirring for 1 h. Then, the resulting suspension was transferred into a Teflon recipient, which was performed at 473 K for 24 h. 2.2. Characterization X ray diffraction (XRD) patterns of the as prepared samples were measured on a D8 DA VINCE (Bruker) X ray diffractometer using Cu Kα radiation under 4 kv and 4 ma. The scanning speed was 6 /min and 2θ = 1 8. The morphologies of the samples were revealed by scanning electron microscopy (SEM, JEOL JSM 638LV). The XPS patterns were measured on an AXIS UltraDLD electronic energy spectrometer (Kratos group) at 3 W using Mg Kα X rays as the excitation source. 2.3. Photocatalytic experiment for water splitting The photocatalytic activities were evaluated in a Pyrex reaction cell connected to a closed gas circulation and evacuation system. Particulate Pt was photodeposited onto the photocatalyst samples as a water reduction cocatalyst as the reaction progressed. Specifically, 1.8 g FeCl2 was dissolved in 8 ml deionized water and 1 wt% Pt (1 mg Pt for.1g CN x U, for example) was added into this solution..1 g of CN x U (x =, 5, 1, or 2) and.5 g of BiVO4 was then suspended in the solution. The suspension was thoroughly degassed and irradiated by a 3 W Xe arc lamp. The amount of H2 and O2 was analyzed every hour using online gas chromatography. The photodeposition method was also used to load Pt co catalyst onto g C3N4 doped with Zinc. An aqueous solution of H2PtCl6 (containing 1 wt% Pt) was added to 8 ml aqueous solution suspended in the CN 1 U powder, and then the solution was irradiated using a Xe lamp (3 W). The Pt cocatalyst was deposited in metallic form according to previous descriptions [28]. 3. Results and discussion 3.1. Characterization of as prepared samples The diffraction patterns for the Zn doped g C3N4 with different amounts of zinc, as can be seen in Fig. 1(a), shows two peaks at 13.4 and 27.4, corresponding to the () and diffraction planes, respectively [3,21,29]. The main peak at 27.4 can be indexed as the distance of.681 nm between nitride pores in C3N4, which indicates a two dimensional carbon nitride structure both in the modified and unmodified samples [2,4,22]. Its intensity gradually decreases as the Zn content increases, and the same trend can be observed in the peak at

474 Zhen Qin et al. / Chinese Journal of Catalysis 39 (218) 472 478 (a) (b) Intensity (a.u.) CN-2-U CN-15-U CN-1-U CN-5-U Intensity (a.u.) g-c 3 N 4 1 2 3 4 6 2 /( o ) 1 2 3 4 6 2 /( o ) Fig. 1. XRD patterns of (a) the CN x U catalyst samples with different x values and pristine g C3N4 and (b) BiVO4 JCPDS 14 688. 13.4. This peak can be ascribed to the interplanar distance of.326 nm, and this may indicate that there is a deterioration of crystallinity upon Zn doping and it may strongly impact the distance between g C3N4 hosts [2,23]. No heterogeneous phase, such as zinc, its oxide or chloride, was observed from the XRD data [5]. The phase and purity of the synthesized BiVO4 can be observed from Fig. 1(b), which were consistent with JCPDS card No. 14 688 (pure phase monoclinic point group). For the purpose of studying the optical absorption of the as prepared g C3N4 based samples, the UV Vis absorption spectra are provided in Fig. 2. The light absorption edges of the CN x U with different Zn contents gave a small change to the short wavelength range compared to the pristine g C3N4 (the maximum light absorption edge was obtained with the CN 1 U samples). 3.2. Overall water splitting by Z scheme photocatalysis system Fig. 3 shows the changes in photocatalytic activity as various amounts of Zn was doped into g C3N4. It has been revealed previously that the hydrogen yield is a non monotonic function of the Zn content [11]; therefore, the overall water splitting was only obtained when 1% of Zn was loaded. This can be explained from when there is too much doped Zn, they may unite as reaction sites for the recombination of photoelectric electron hole pairs, resulting in a decrease in the redox ability of g C3N4 [2]. To make sure that the CN 1 U was combined with BiVO4 through a shuttle redox mediator, Fig. 4 shows the photocatalytic activity of the different components in aqueous FeCl2 solution. Overall water splitting (H2 and O2 gases generated in a stoichiometric ratio) was only observed when both CN 1 U and BiVO4 was added to the aqueous FeCl2 solution with a certain amount of H2PtCl4. However, there is another theory which purports that Pt nanoparticles would be formed and play a key role in overall water splitting when H2PtCl6 is added to the original solution and deposited as the reaction progresses [3]. To ascertain whether the overall water splitting actually contributed to g C3N4 doped with zinc and BiVO4, pre photodeposed g C3N4 was tested and the results can be seen in Fig. 5. As the picture shows, stoichiometric H2 and O2 gases can be observed in the Z scheme system built by both pre photodeposed (CN 1(Pt)/BiVO4) and when it is photodeposed during the 3 Absorbance (a.u.) g-c 3 N 4 CN-1-U CN-5-U CN-15-U CN-2-U 3 4 6 7 Wavelength (nm) Fig. 2. UV Vis diffuse reflectance spectra (DRS) of CN x U (x = 5, 1, 15, or 2) and g C3N4 samples. CN--U/Pt/BiVO4 CN-5-U/Pt/BiVO4 CN-1-U/Pt/BiVO4 CN-2-U/Pt/BiVO4 Fig. 3. Photocatalytic activity of CN x U/Pt/BiVO4 Z scheme systems (x =, 5, 1 or 2).

Zhen Qin et al. / Chinese Journal of Catalysis 39 (218) 472 478 475 3 Fig. 6. (a) SEM and (b) TEM images of the mixture obtained after the reaction on CN 1 U and BiVO4 (2:1, 12 h). CN-1-U/Pt BiVO4/Pt CN-1-U/Pt/BiVO4 Fig. 4. Photocatalytic activity of catalyst CN 1 U/Pt, BiVO4/Pt, and Z scheme CN 1 U/Pt/BiVO4. Thus, we obtained a stable Z scheme system for overall water splitting by combining Zn doped (1%) g C3N4 and BiVO4 though a Fe 3+ /Fe 2+ redox couple. Pt was used as a cocatalyst for H2 revolution. CN-1-U(Pt)/BiVO4 CN-1-U/Pt/BiVO4 Fig. 5. Photocatalytic activity of Z scheme system with CN 1 U (Pt)/BiVO4 for pre photodeposed Pt and CN 1 U/Pt/BiVO4 for Pt photodeposed as the reaction proceeds. reaction (CN 1/Pt/BiVO4). The formation of a complex is supported by TEM images (Fig. 6(b)) of the CN 1/Pt example. These results indicate that CN 1 U can be applied to a typical Z scheme water splitting system as H2 evolving photocatalysts via a shuttle redox mediator. A typical SEM image of the suspension of CN 1 U and BiVO4 (2:1; 12 h), as illustrated in Fig. 6(a), also supports this. CN 1 U and BiVO4 are separated in this mixture without any obvious form of heterojunction. The stability of the as prepared Z scheme system can be observed in Fig. 7. We can see that the system retains a stable stoichiometric H2 and O2 production over a long time period. Under visible light the H2 production was very low, and this may be due to the poor activity of g C3N4 decomposed by urea, which was also shown by the UV DRS data (Fig. 2). There is no obvious difference in O2 production over the initial two hours, which can be attributed to the high capability of BiVO4 under visible light. However, after six hours of radiation, the production of O2 using aqueous NaNO2 as a light filter slowly decreased. This can be explained by the low production of H2, which influences the interchange of the Fe 3+ /Fe 2+ redox couple. The low production of H2 might also lead to an accumulation of ferrous ion, a potential competitor to the oxidation reaction. 3.3. Possible function of zinc doped in g C3N4 According to previous research [4,11], there are two different ways to realize doping with Zn. Specifically, Zn doped g C3N4 can be synthesized by an impregnation method (CN 1 U and CN 1 D1) or by in situ synthesis (CN 1 D2). These three types of Z scheme were constructed and tested, with the results shown in Fig. 8. Overall water splitting can be observed in the Z scheme using both CN 1 U and CN 1 D1. The difference in the production between CN 1 U and CN 1 D1 may contribute to the introduction of pores in g C3N4 by using urea as the precursor. The high surface area and continuous porosity, which can be active centers, are important requirements for catalysis [12]. The chemical state and surface chemical composition were characterized by XPS (Fig. 9). There are significant differences in the C 1s and N 1s peaks for Zn doped g C3N4 synthesized by the impregnation method (CN 1 D1) relative to the in situ synthesized CN 1 D2, as discussed vide infra. A Zn 2p3/2 binding energy (BE) peak at 12.3 ev in both Zn doped samples is revealed in Fig. 9(d). This is lower than the 121.9 ev value measured for Zn(II) in ZnCl2, and there are no Cl peaks detected Amount of evolved gases ( mol) Full Band, Full Band, Visible, Visible, 1 2 3 4 5 6 7 8 9 1 11 12 13 Time (h) Fig. 7. Photocatalytic activity of the CN 1 U/Pt/BiVO4 Z scheme system for 12 h. Visible light was used with aqueous NaNO2 as a light filter.

476 Zhen Qin et al. / Chinese Journal of Catalysis 39 (218) 472 478 3 CN-1-U/Pt/BiVO4 CN-1-D1/Pt/BiVO4 CN-1-D2/Pt/BiVO4 Fig. 8. Photocatalytic activity of Z scheme system using g C3N4 with various methods to dope Zn and BiVO4. in either sample. Hence, it can be speculated that Zn(II) was successfully linked to the g C3N4 framework in both samples through a Zn N bond without Cl ions [11]. The reason for the different catalytic ability between the two types of Zn doped g C3N4 may be ascertained from the C 1s (Fig. 9(a)) and N 1s (Fig. 9(b)) peaks. The C 1s and N 1s peaks of the two samples in Fig. 1 are both clear, but the ways in which they were modified by zinc differ. In Fig. 1(a) and (b), the C 1s peaks can be convoluted as several binding energies. The main peak at 287.7 ev (C1) corresponds to the triazine ring of the N=C N group [4,3,31]. The peak at 285.4 ev (C3) can be assigned to the sp 3 C N bond, and the peak at 284.2 ev (C2) corresponds to the sp 2 C=C bond. The weak peak at 289. ev (C4) can be attributed to C O groups caused by inevitable oxidation [11]. Zn doped g C3N4 obtained by in situ synthesis shows a significantly weaker C2 peak than that obtained via impregnation. For the N 1s signal, a similar trend is observed, as shown in Fig. 8(c) and (d). The N 1s XPS peak can also be deconvoluted into three typical peaks. The dominant peak at 398.2 ev (N1) can be attributed to the C N=C group, which is a manifestation of the triazine ring. The peak at 399.3 (N2) and 4.5 ev (N3) can be assigned, respectively, to the N and N bonds [32]. Compared to CN 1 D1, the integral strength of the N 1s signal of the CN 1 D2 sample is reduced. From these observations, we conclude that Zn might be doped by forming Zn N bonds, which promote carrier transport from Zn to the g C3N4 bodies [4,31,33]. Also, by using the impregnation method, Zn can be combined more homogeneously without distorting the triazine ring. This method could be a way to better improve the redox ability of g C3N4 to dope zinc and make it suitable for forming a Z scheme water splitting system with bismuth vanadate. 4. Conclusions A typical Z scheme system composed of a Fe 3+ /Fe 2+ redox mediator that splits water into H2 and O2 by using zinc doped (1%) g C3N4 for H2 production and BiVO4 as O2 photocatalyst was reported. The Z scheme system showed a stoichiometric (a) C 1s (b) N 1s 295 29 285 28 275 41 45 4 395 (c) O 1s (d) Zn 2p 54 535 53 525 16 1 14 13 12 Fig. 9. XPS analysis of (a) C 1s, (b) N 1s, (c) O 1s, and (d) Zn 2p peaks. CN 1 D1; CN 1 D2. 11

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478 Zhen Qin et al. / Chinese Journal of Catalysis 39 (218) 472 478 Graphical Abstract Chin. J. Catal., 218, 39: 472 478 doi: 1.116/S1872 267(17)62961 9 Zinc doped g C3N4/BiVO4 as a Z scheme photocatalyst system for water splitting under visible light Zhen Qin, Wenjian Fang, Junying Liu, Zhidong Wei, Zhi Jiang, Wenfeng Shangguan * Shanghai Jiao Tong University A two step photocatalytic water splitting system, so called Z scheme system, was achieved using Zn doped g C3N4 for H2 evolution and BiVO4 for O2 evolution with Fe 2+ /Fe 3+ as a shuttle redox mediator. Potential (V vs. NHE) -1.42 H + /.3 Fe 3+ /Fe 2+.77 /O 1.23 1.25 2.76 Light O, H + CB e - h + VB BiVO 4 Light Fe 2+ Fe 3+ CB e - h + VB g-c 3 N 4 :Zn Pt H + [3] N. Zhang, C. Han, Y. J. Xu, J. J. Foley, D. T. Zhang, J. Codrington, S. K. Gray, Y. G. Sun, Nat. Photonics, 216, 1, 473 482. [31] A. Thomas, A. Fischer, F. Goettmann, M. Antonietti, J. O. Müller, R. Schlögl, J. M. Carlsson, J. Mater. Chem., 8, 18, 4893 498. [32] E. Raymundo Pinero, D. Cazorla Amorós, A. Linares Solano, J. Find, U. Wild, R. Schlögl, Carbon, 2, 4, 597 68. [33] M. Futsuhara, K. Yoshioka, O. Takai, Thin Solid Films, 1998, 322, 274 281. 基于掺 Zn 氮化碳和 BiVO 4 构建 Z 型光催化系统实现完全分解水 * 秦臻, 房文健, 刘军营, 韦之栋, 江治, 上官文峰上海交通大学燃烧与环境技术研究中心, 上海 24 摘要 : 随着现代工业的迅猛发展和化石燃料的过量使用, 全球范围内能源和环境问题日益严峻, 因此利用丰富的太阳光能 分解水来直接制取清洁的氢气具有诱人的应用前景. 目前, 聚合物半导体石墨相氮化碳 (g-c 3 N 4 ) 因其廉价 稳定 不含金 属组分和独特的电子能带结构已被广泛应用于光解水产氢研究. 然而, 氮化碳具有结晶度差 光生载流子易复合的缺点. 众所周知, Z 型体系可以很好地减少电子和空穴的复合问题. 同时, 催化剂只需分别满足光解水过程的一端, 这使得半导体 光催化剂的选择非常丰富, 可以大大拓宽材料体系. 因此, 将 g-c 3 N 4 运用到 Z 型体系中的研究得到了广泛关注. 然而, 这些 研究多集中在如何增强 g-c 3 N 4 的产氢能力方面, 对实现水的完全分解的研究鲜见报道. 本实验设计了这样一种 Z 型体系 : 使用掺 Zn 的 g-c 3 N 4 作为产氢端, BiVO 4 作为产氧端, Fe 3+ /Fe 2+ 作为氧化还原对. 实验 结果表明, 该体系可以在全波段下实现水的完全分解 ( 氢氧比为 2:1), 并且保持相当高的稳定性. 实验所使用的氮化碳为固相法烧结尿素制得, Zn 的掺杂采用浸渍法, 同时通过水热法合成 BiVO 4, 使用 Pt 作为助催化 剂. 通过搭建含有不同组成成分的 Z 型体系, 将它们的性能和表征结果进行比较分析. 通过 XRD, UV-Vis, SEM 和 XPS 等测试手段对催化剂进行表征. XRD 分析结果表明成功合成了掺杂 Zn 的石墨相氮化 碳. UV-Vis 则显示随着 Zn 浓度的提高, 吸收边发生变化. 通过改变掺杂 Zn 的浓度, 得到了能够实现完全分解水的 Z 型体系, 其最佳掺杂比例为 : ZnCl 2 和氮化碳的质量比为 1:1. 为了排除单催化剂和 Pt 颗粒对完全分解水性能的影响, 分别作了单独 产氢端 单独产氧端 预负载 Pt 和光沉积 Pt 的性能测试. 从 SEM 中没有发现 g-c 3 N 4 和 BiVO 4 的异质结结构. 这些结果表明 所搭建的是典型的利用氧化还原离子对为中间电子传输载体的 Z 型体系, 经长达 12 h 的持续测试证明其具有较高的稳定性. 为了研究 Zn 在构建 Z 型中所起的作用, 分别采用文献中报道的原位和浸渍法实现 Zn 的掺杂. 对这两种掺杂方式的性能 测试表明, 只有采用浸渍法时, 所构建的 Z 型体系具有完全分解水的能力. 对这两种方法得到的掺 Zn 氮化碳进行表面化学 组成和价态 (XPS) 的分析. 结果显示, 两种掺杂方法都可以通过形成 Zn=N 键的形式实现 Zn 的掺杂, 但浸渍法使 Zn 在 g-c 3 N 4 表面分布更均匀, 同时对氮化碳原本三嗪环的破坏较小, 因此具有更好的还原能力, 可以与 BiVO 4 匹配以构成 Z 型体系. 实验通过采用掺杂 Zn 的氮化碳作为产氢催化剂, BiVO 4 作为产氧催化剂, Fe 3+ /Fe 2+ 作为氧化还原中间体, 构建了典型的 Z 型体系. 该体系在 Zn 的掺杂浓度为 1% 时能够实现长时间稳定的完全分解水. 关键词 : 氮化碳 ; 钒酸铋 ; Z 型 ; 氧化还原介质 ; 分解水 收稿日期 : 217-9-28. 接受日期 : 217-1-29. 出版日期 : 218-3-5. * 通讯联系人. 电话 : (21)34262; 电子信箱 : shangguan@sjtu.edu.cn 基金来源 : 国家自然科学基金 (21773153). 本文的全文电子版由 Elsevier 出版社在 ScienceDirect 上出版 (http://www.sciencedirect.com/science/journal/1872267).