Processing math: 100%

基于Co/β-Mo2C修饰碳纸阳极的高性能微生物燃料电池

陈妹琼, 郭文显, 肖红飞, 蔡志泉, 张敏, 程发良

陈妹琼, 郭文显, 肖红飞, 蔡志泉, 张敏, 程发良. 基于Co/β-Mo2C修饰碳纸阳极的高性能微生物燃料电池[J]. 华南师范大学学报(自然科学版), 2021, 53(3): 15-21. DOI: 10.6054/j.jscnun.2021038
引用本文: 陈妹琼, 郭文显, 肖红飞, 蔡志泉, 张敏, 程发良. 基于Co/β-Mo2C修饰碳纸阳极的高性能微生物燃料电池[J]. 华南师范大学学报(自然科学版), 2021, 53(3): 15-21. DOI: 10.6054/j.jscnun.2021038
CHEN Meiqiong, GUO Wenxian, XIAO Hongfei, CAI Zhiquan, ZHANG Min, CHENG Faliang. Co/β-Mo2C-decorated Carbon Paper Anode for High-performance Microbial Fuel Cells[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(3): 15-21. DOI: 10.6054/j.jscnun.2021038
Citation: CHEN Meiqiong, GUO Wenxian, XIAO Hongfei, CAI Zhiquan, ZHANG Min, CHENG Faliang. Co/β-Mo2C-decorated Carbon Paper Anode for High-performance Microbial Fuel Cells[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(3): 15-21. DOI: 10.6054/j.jscnun.2021038

基于Co/β-Mo2C修饰碳纸阳极的高性能微生物燃料电池

基金项目: 

国家自然科学基金项目 21775022

国家自然科学基金项目 52002068

广东省基础与应用基础研究基金联合基金项目 2019A1515110314

广东省自然科学基金项目 2017A030310603

东莞理工学院城市学院重大科研培育项目 2017YZD003Z

2019年广东省本科高校教学质量与教学改革工程建设项目 实验教学示范中心No.30

详细信息
    通讯作者:

    肖红飞,Email:xiaohf@ccdgut.edu.cn

    程发良,Email:chengfl@dgut.edu.cn

  • 中图分类号: TM911.45; O646

Co/β-Mo2C-decorated Carbon Paper Anode for High-performance Microbial Fuel Cells

  • 摘要: 采用热处理辅助的化学法制备了Co/β-Mo2C双金属碳化物,将其作为微生物燃料电池(MFCs)阳极催化剂. 采用扫描电子显微镜(SEM),X-射线衍射(XRD)和X射线光电子能谱(XPS)等手段研究了形貌和组成,采用电化学交流阻抗(EIS)法、循环伏安(CV)法和单室空气阴极微生物燃料电池(MFC)研究了其电化学性能. 结果表明:Co/β-Mo2C具有良好的电催化性能以及出色的微生物相容性. 含有3 mg/cm2 Co/β-Mo2C的阳极MFC最大输出功率密度和库伦效率分别为483.3 mW/cm2和3.7%,分别是未修饰的碳纸阳极MFC的1.30倍和1.68倍. 该研究可为开发高性能的微生物燃料电池阳极催化材料提供新思路.
    Abstract: Bimetallic carbide Co/β-Mo2C was prepared with the thermal treatment-assisted chemical method and used as an anode catalyst for Microbial Fuel Cells (MFCs). The morphology and content of Co/β-Mo2C was studied with the scanning electron microscope (SEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS). Furthermore, the cyclic voltammetry (CV), the electrochemical impedance spectroscopy (EIS) and a single-chamber air-cathode Microbial Fuel Cell(MFC) were used to study the electrochemical performance of Co/β-Mo2C. The results showed that due to the prominent electrochemical activity and excellent biocompatibility, the MFC device equipped with 3 mg/cm2 Co/β-Mo2C-decorated carbon paper anode delivered a power density of 483.3 mW/cm2, and a coulomb efficiency of 3.7%, which are 1.30 and 1.68 times those of the pristine carbon paper anode MFCs respectively. This work provides a new path for the explorer of high-performance anodic catalysts for MFCs application.
  • 链回归点、非游荡点集、极限点集和回归点集是动力系统中重要的定义,在动力系统的发展中有着重要的作用,与系统的混沌、链传递密不可分。

    学者们对链回归点、非游荡点集、极限点集和回归点集的拓扑结构和动力学性质进行了研究[1-11]。如:证明了在群作用下的逆极限空间中移位映射的G-回归点集等于自映射在其G-回归点集形成的逆极限空间[1];在正上密度回归点集稠密的条件下,证明了可迁系统等价于E系统[2];证明了在群作用下的逆极限空间中移位映射的G-链回归点集等于自映射在其G-链回归点集形成的逆极限空间[3];证明了转移映射的强非游荡点集等于自映射f在其强非游荡点集形成的逆极限空间[4];研究了右高类帐篷映射链回归点集和强链回归点集的关系[5];指出映射f的每个负轨道的a-极限集是G上某个点的w-极限集[6];讨论了强一致收敛下序列映射非游荡点的保持性[7];在广义树上研究了连续自映射f回归点集的拓扑结构[8];证明了回归点集对映射f强不变[9];证明了x是一致回复点当且仅当x是Birkhoff回复点[10];在具备一定条件下的可交换的C-系统中,证明了任意传递点是等度连续点[11]

    链回归点一定是G-链回归点,非游荡点一定是G-非游荡点,极限点一定是G-极限点,回归点一定是G-回归点集,但反之不成立。本文尝试将链回归点、非游荡点集、极限点集和回归点集的动力学性质进行推广,在映射fG-等度连续的条件下,在度量G-空间中研究了G-链回归点、G-非游荡点、G-极限点和G-回归点之间的动力学关系,拟充实度量G-空间中G-链回归点、G-非游荡点、G-极限点和G-回归点的理论。

    定义1[1]  设X是度量空间,G是拓扑群。若映射φ: G×XX满足

    (1) ∀xX,有φ(e, x)=x,其中eG的单位元;

    (2) ∀xXg1, g2G, 有

    φ(g1,φ(g2,x))=φ(g1g2,x),

    则称(X, G, φ)是度量G-空间,简称X是度量G-空间。为了书写方便,通常将φ(g, x)简写为gx

    X是紧致度量空间,则称X是紧致度量G-空间。

    定义2[1]  设(X, d)是度量空间,如果f: XX是一一映射且ff-1都是连续的,则称f是同胚映射。

    定义3[1]  设(X, d)是度量G-空间,f: XX连续。如果∀x, yX,∃{ni}⊂N+,∃{gi}⊂G,使得limigifni(x)=y,则称yxG-极限点,用wG(x, f)表示。记WG(f)xXwG(x,f),称WG(f)为fG-极限点集。

    定义4[1]  设(X, d)是度量G-空间,f: XX连续,xX。如果对任意包含x的开集U,∃nN+,∃gG,使得gfn(x)∈U,则称xfG-回归点。fG-回归点集用RG(f)表示。

    定义5[3]  设(X, d)是度量G-空间,f: XX连续,xX。如果对任意包含x的开集U,∃nN+,∃gG,使得gfn(U)∩U≠Ø,则称xfG-非游荡点。fG-非游荡点集用ΩG(f)表示。

    定义6[12]  设(X, d)是度量G-空间,f: XX连续。如果∀gG,∀xX,有f(gx)=gf(x),则称f是等价映射。

    定义7[12]  设(X, d)是度量G-空间,f: XX连续。如果∀gG,∀xX,∃hG,有f(gx)=hf(x),则称f是伪等价映射。

    定义8[13]  设(X, d)是度量G-空间,f: XX连续。如果∀ε>0,∃δ>0,当d(x, y) < δ时,∀nN+,∃gn, pnG,有d(fn(gnx), fn(pny)) < ε,则称fG-等度连续。

    备注1  G-等度连续点的概念见文献[13], 交换群的概念见文献[14]。

    定义9[15]  设(X, d)是度量G-空间,f: XX连续,ε>0。如果∀i(0≤i < n),∃giG,使得d(gif(xi), xi+1) < ε,则称{xi}i=0nf作用下的(G, ε)链。

    定义10[3]  设(X, d)是度量G-空间,f: XX连续。如果∀ε>0,存在f作用下的(G, ε)链{xi}i=0n,其中x0=xn=x,则称xfG-链回归点。fG-链回归点集用CRG(f)表示。

    引理1[1]  设(X, d)是紧致度量G-空间,G是紧致,则∀ε>0,∃0 < δ < ε,当d(u, v) < δ时,∀gG,有d(gu, gv) < ε

    引理2[3]  设(X, d)是度量G-空间,G是紧致的,f: XX同胚等价,则f(WG(f))=WG(f)。

    引理3[3]  设(X, d)是紧致度量G-空间,G是紧致的,f: XX同胚等价,则f(CRG(f))=CRG(f)。

    定理1  设(X, d)是紧致度量G-空间,G是可交换的紧致群,f: XX伪等价。若fG-等度连续的,则RG(f)=WG(f)=ΩG(f)。

    证明  由G-回归点、G-极限点和G-非游荡点的定义易知,RG(f)⊂WG(f)⊂ΩG(f)。下证:ΩG(f)⊂RG(f)。由引理1知,∀ε>0,∃0 < ε0 < ε,当d(z1, z2) < ε0时,∀sG,有

    d(sz1,sz2)<ε (1)

    ∃0 < ε1 < ε0,当d(z1, z2) < ε1时,∀sG,有

    d(sz1,sz2)<ε02 (2)

    fG-等度连续的,则对ε1>0,∃0 < ε2 < ε1,当d(z1, z2) < ε2时,∀n≥0,∃gn, knG,使得

    d(fn(gnz1),fn(knz2))<ε12 (3)

    xΩG(f), 则∃m>1,∃gG,∃yX,使得

    d(x,y)<ε2, (4)
    d(gfm(y),x)<ε2 (5)

    由式(3)和式(4)知

    d(fm(gmx),fm(kmy))<ε12

    由于f是伪等价映射,故∃pm, tmG,使得

    d(pmfm(x),tmfm(y))<ε12 (6)

    由式(2)和式(5)知

    d(tmgfm(y),tmx)<ε02 (7)

    由式(2)和式(6)知

    d(gpmfm(x),gtmfm(y))<ε02

    由于G是可交换的,故

    d(gpmfm(x),tmgfm(y))<ε02 (8)

    由式(7)和式(8)知

    d(gpmfm(x),tmx)<d(gpmfm(x),tmgfm(y))+d(tmgfm(y),tmx)<ε0

    由式(1)知

    d((tm)1gpmfm(x),x)<ε,

    xRG(f),从而有ΩG(f)⊂RG(f),故RG(f)=WG(f)=ΩG(f)。证毕。

    定理2  设(X, d)是紧致度量G-空间,G是紧致的,f: XX同胚等价。若fG-等度连续的,则WG(f)=CRG(f)=n=1fn(X)。

    证明  由引理2知,∀n≥1,有

    fn(WG(f))=WG(f)

    fn(WG(f))⊂fn(X),则∀n≥1,有WG(f)⊂fn(X)。因此

    WG(f)n=1fn(X)

    由引理1知,∀ε>0,∃0 < ε0 < ε,当d(z1, z2) < ε0时,∀sG,有

    d(sz1,sz2)<ε (9)

    fG-等度连续的,则对上述ε0>0,∃0 < δ < ε0,当d(z1, z2) < δ时,∀n≥0,∃gn, knG,使得

    d(fn(gnz1),fn(knz2))<ε0 (10)

    yn=1fn(X),则∀n≥1,∃xnX,使得

    y=fn(xn) (11)

    根据X的紧致性,存在子列{xni}i=0满足xnix(i→∞)。因此,对上述δ>0,∃m>0,当i>m时,有

    d(xni,x)<δ

    由式(10)知,当i>m时,有

    d(fni(gnix),fni(knixni))<ε0

    由式(11)和f是等价映射知

    d(fni(gnix),kniy)<ε0

    由式(9)和f是等价映射知,当i>m时,有

    d((kni)1gnifni(x),y)<ε

    从而有yWG(f),则n=1fn(X)WG(f),故

    WG(f)=n=1fn(X)

    下证CRG(f)=WG(f)。由G-极限点和G-链回归点的定义知,WG(f)⊂CRG(f)。由引理3知,∀n≥1,有

    fn(CRG(f))=CRG(f)

    fn(CRG(f))⊂fn(X),则∀n≥1,有

    CRG(f)fn(X)

    从而有

    CRG(f)n=1fn(X),

    则CRG(f)⊂WG(f),故CRG(f)=WG(f)。因此WG(f)=CRG(f)=n=1fn(X)。证毕。

    定理3  设(X, d)是紧致度量G-空间,G是可交换的紧致群,f: XX伪等价,则WG(f)中的所有点都是G-等度连续点当且仅当fG-等度连续的。

    证明  (⇒)假设WG(f)中的所有点都是G-等度连续点。∀xX, 则wG(x, f)≠Ø。取ywG(x, f),则yG-等度连续点。由引理1知,∀ε>0,∃0 < ε0 < ε,当d(z1, z2) < ε0时,∀sG,有

    d(sz1,sz2)<ε (12)

    yG-等度连续点知,对ε0>0,∃0 < δ0 < ε0,当d(z, y) < δ0时,∀n≥0,∃gn, knG,使得

    d(fn(gnz),fn(knz))<ε02 (13)

    由引理1和yG-等度连续点知,对上述δ0>0,∃0 < δ1 < δ0,当d(z, y) < δ1时,∀n≥0,∃tn, hnG,使得

    d(fn(tnz),fn(hny))<δ02 (14)

    d(z1, z2) < δ1时,∀sG,有

    d(sz1,sz2)<δ02 (15)

    ywG(x, f)知,∃g′G,∃m>0,使得

    d(gfm(x),y)<δ12 (16)

    由式(14)和式(16)知,∀n≥0,有

    d(fn(tngfm(x)),fn(hny))<δ02

    由于f是伪等价映射,故∃t′n, h′mG,使得

    d(tnfn+m(x),hnfn(y))<δ02 (17)

    f是一致连续的,故∀0≤im,∃0 < δ2 < δ1,当d(z1, z2) < δ2时,有

    d(fm(z1),fm(z2))<δ12 (18)

    d(z, x) < δ2,由式(18)知,∀0≤im,有

    d(fi(z),fi(x))<δ12 (19)

    再结合式(15)知

    d(gfm(z),gfm(x))<δ02 (20)

    结合式(16)和式(20)知

    d(gfm(z),y)<d(gfm(z),gfm(x))+d(gfm(x),y)<δ0

    由式(13)知

    d(fn(gngfm(z)),fn(kny))<ε02

    由于f是伪等价映射,故∃g′n, k′nG,使得

    d(gnfn+m(z),knfn(y))<ε02

    由式(12)知

    d(hngnfn+m(z),hnknfn(y))<ε2 (21)

    由式(12)和式(17)知

    d(kntnfn+m(x),knhnfn(y))<ε2

    由于G是可交换的,故

    d(kntnfn+m(x),hnknfn(y))<ε2 (22)

    由式(21)和式(22)知,当n>0时,有

    d(kntnfn+m(x),hngnfn+m(z))<d(kntnfn+m(x),hnknfn(y))+d(hnknfn(y),hngnfn+m(z))<ε (23)

    当0 < im时,取li=si=e。当im+1时,取li=k′imt′im, si=h′img′im。由式(19)和式(23)知,∀i≥0,有

    d(lifi(x),sifi(z))<ε,

    xG-等度连续点,因此X中的所有点都是G-等度连续点。

    假设映射f不是G-等度连续的,则∃δ3>0,∀nN+,∃kn≥0,∃x′n, y′nX且满足d(x′n, y′n) < 1/n,对∀s, tG,有

    d(fkn(sxn),fkn(tyn))δ3 (24)

    由于X是紧致的,因此,存在列{x′ni}和{y′ni},使得x′nix′, y′niy′。因为d(x′ni, y′ni) < 1/ni,所以x′=y′

    由于x′fG-等度连续点,则对δ3/2>0,∃0 < δ4 < δ3/2,∀nN+,∃gn, knG,当d(x′, z) < δ4时,有

    d(fn(gnz),fn(knx))<δ32 (25)

    m>0,满足d(x′m, x′) < δ4, d(y′m, x′) < δ4d(x′m, y′m) < 1/m。由式(25), 可得

    d(fn(gnxm),fn(knx))<δ32,
    d(fn(gnym),fn(knx))<δ32,

    则∀nN+, 有

    d(fn(gnxm),fn(gnym))<d(fn(gnxm),fn(knx))+d(fn(knx),fn(gnym))<δ3,

    与式(24)矛盾。因此fG-等度连续的。

    (⇐)由G-等度连续和G-等度连续点的定义立刻可以得到。证毕。

    本文首先引入G-链回归点、G-非游荡点集、G-极限点集和G-回归点集的定义,然后在G-等度连续的条件下研究了这些点集之间的关系。结论如下:(1)RG(f)=WG(f)=ΩG(f); (2)WG(f)=CRG(f)=n=1fn(X); (3)fG-等度连续的当且仅当WG(f)中的所有点都是G-等度连续点。这些结论推广了度量空间中链回归点、非游荡点集、极限点集和回归点集的结果,并为其在实际中的应用提供了理论支撑。

  • 图  1   Co/β-Mo2C的SEM和EDS谱

    Figure  1.   The SEM image and EDS spectrum of Co/β-Mo2C

    图  2   Co/β-Mo2C的XRD图谱

    Figure  2.   The XRD spectrum of Co/β-Mo2C

    图  3   Co/β-Mo2C的XPS谱

    Figure  3.   The XPS pattern of Co/β-Mo2C

    图  4   不同电极的CV曲线

    Figure  4.   The cyclic voltammogram curves of different electrodes

    图  5   不同电极的Nyquist图

    Figure  5.   The Nyquist plots of different electrodes

    图  6   不同阳极MFCs的极化曲线及功率密度曲线

    Figure  6.   The polarization curves and power output of MFCs with different anodes

    图  7   不同MFC在序批式运行中的电压输出

    Figure  7.   The voltage of MFC with different anodes operated in a batch-fed mode

    图  8   运行6周期后不同阳极的SEM图

    Figure  8.   The SEM images of different colonized anodes after six cycles

    表  1   Co/β-Mo2C的EDS结果

    Table  1   The EDS results of Co/β-Mo2C

    元素 质量分数/% 原子数百分比/%
    C 63.30 87.41
    O 6.51 6.75
    Co 5.73 1.61
    Mo 24.46 4.23
    下载: 导出CSV
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  • 期刊类型引用(1)

    1. 冀占江,刘海林. G-利普希茨跟踪性、G-等度连续和G-非游荡点集的研究. 华南师范大学学报(自然科学版). 2024(04): 111-115 . 百度学术

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  • 收稿日期:  2021-03-08
  • 网络出版日期:  2021-07-05
  • 刊出日期:  2021-06-24

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