Self-propelled particles with fluctuating speed and direction of motion

Controlled molecular assembly of self-propelled colloid motors and their biomedical applications 林显坤, 吴志光, 司铁岩 and 贺强Citation: 中国科学 : 化学 4747, 3 (2017); doi: 10.1360/N032016-00156View online: /doi/10.1360/N032016-00156View Table of Contents: /publisher/scp/journal/SSC/47/1Published by the 《中国科学》杂志社Articles you may be interested inRecent advances in self-propelled particlesSCIENCE CHINA Chemistry 6060, 1293 (2017);An energetics analysis of fish self-propelled swimmingSCIENCE CHINA Physics, Mechanics & Astronomy 6161, 074721 (2018);Numerical simulations of self-propelled swimming of 3D bionic fish schoolScience in China Series E-Technological Sciences 5252, 658 (2009);A study of a three-dimensional self-propelled flying bird with flapping wingsSCIENCE CHINA Physics, Mechanics & Astronomy 5858, 594701 (2015);Numerical simulations and vorticity dynamics of self-propelled swimming of 3D bionic fishSCIENCE CHINA Physics, Mechanics & Astronomy 5555, 272 (2012);引用格式： 林显坤,吴志光,司铁岩,贺强.可控分子组装的自驱动胶体马达及其生物医学应用.中国科学:化学,2017,47:3–13Lin X,Wu Z,Si T,He Q.Controlled molecular assembly of self-propelled colloid motors and their biomedical applications.Sci Sin Chim ,2017,47:3–13,doi:10.1360/N032016-00156© 2016 《中国科学》杂志社可控分子组装的自驱动胶体马达及其生物医学应用林显坤,吴志光,司铁岩,贺强*哈尔滨工业大学微系统与微结构制造教育部重点实验室,微纳米技术研究中心,哈尔滨150080*通讯作者,E-mail:qianghe@收稿日期:2016-07-29;接受日期:2016-09-23;网络版发表日期:2016-12-20国家自然科学基金(编号:21573053,21674029,21603047)资助项目摘要 人造胶体马达是能够将不同形式的能量转化为流体中机械运动的微纳米机器.自2012年以来,将自下而上的可控分子组装与自上而下的方法有效结合已成为可控构筑胶体马达的重要策略之一.基于可控分子组装(如层层组装)的胶体马达具有易于实现规模化制备、能够对外界刺激作出响应、便于实现多功能化等优点.本文综述了通过将各种功能性构筑基元集成到组装结构中进而实现胶体马达的可控构筑、运动控制以及生物医学应用等方面的研究进展.主要介绍了基于不同层层组装结构的气泡驱动马达的可控构筑,基于聚电解质多层膜微胶囊及纳米管的近红外光驱动马达的构筑,生物界面化马达的制备,实现对胶体马达运动速度、方向及状态有效控制的主要方法,以及马达在药物靶向递送、光热治疗和生物毒素清除等生物医学领域中的应用.关键词 胶体马达,可控分子组装,层层组装,自驱动,生物医学1 引言胶体马达是指能够将化学能、光能、声能或其他形式的能量转化为机械运动并完成复杂任务的微纳米系统[1~8],通常也被称为微纳米机器人.近年来,胶体马达(即人造微纳米马达)已逐渐成为微纳米技术等相关领域中的研究热点和难点之一.这是由于递送、分离以及传感等多种应用领域迫切需要微纳米粒子具有在微纳米乃至宏观尺寸进行高速运动的能力.胶体马达的研究将有望给药物靶向递送[9~12]、细胞的捕获与分离[13]、分析检测[14]、环境净化[15]以及纳米印刷术[16]等领域带来具有革命性的解决方案.胶体马达的常见形态包括阴阳型(Janus)球形粒子、纳米管、纳米线以及纳米棒等结构(图1)[7].通常,可将胶体马达按驱动能量的来源分为化学驱动和非化学驱动两类.化学驱动主要依赖于原位的化学反应,并且往往需要催化剂和化学燃料(如H 2O 2)的参与,而非化学驱动主要借助外界的电场、超声场以及光照等来提供能量,需要外界设备的参与.针对不同的情况,研究者已经提出了气泡驱动、界面张力梯度驱动、自电泳、自扩散泳、渗透压驱动、超声驱动、自热泳以及聚合反应驱动等多种驱动机理[17].中国科学:化学2017 年 第 47卷 第 1 期: 3 ~ 13SCIENTIA SINICA Chimica评述自驱动微马达专题林显坤等: 可控分子组装的自驱动胶体马达及其生物医学应用4图1 几类典型的胶体马达及其主要的运动机理示意图[7](网络版彩图)美国哈佛大学Whitesides 等[18]于2002年制备了厘米尺度的化学催化马达.该马达是由半圆柱形的聚二甲基硅氧烷(polydimethylsiloxane,PDMS)薄片构成,在薄片上固定着Pt 覆盖的多孔玻璃.金属Pt 可以催化H 2O 2的分解,从而释放出氧气泡并推动马达在溶液中进行运动.尽管该马达具有厘米级的尺寸,但在胶体马达发展历史上仍具有里程碑意义.随后,Sen 等[19]和Ozin 等[20]成功地将自驱动马达的尺寸降到了微纳米量级,从而证明了利用化学反应驱动微纳米尺寸粒子在流体中运动的可行性[7].近年来,运用自上而下与自下而上方法有效结合来构筑基于可控组装结构的胶体马达已成为一种重要的马达构筑策略.2012年,本课题组[21]和Wilson 等[22]分别率先运用可控组装方法制备了自驱动胶体马达.本课题组[21]利用层层组装(layer-by-layer assembly,LbL)结合微接触印刷技术制备了气泡驱动的阴阳型聚电解质多层微胶囊马达,实现了集自驱动运动能力和装载能力于一身.Wilson 等[22]构筑了基于嵌段共聚物自组装体的纳米马达.通过控制实验条件,他们使两亲嵌段共聚物自组装所形成的囊泡转变为类裂口红细胞结构,并进一步实现了Pt 纳米粒子的包裹,从而制备了化学催化的自组装纳米马达.自此,自下而上方法(如层层组装、大分子自组装等)与自上而下方法(如微接触印刷、金属真空溅射等)相结合的构筑策略在胶体马达的可控制备、运动控制以及应用等方面已取得了长足的进步[23,24].可控组装[25]在胶体马达构筑方面具有诸多优势.首先,可控组装为未来实现具有精确结构的胶体马达的宏量制备提供了可能.其次,基于组装结构的马达可以对外界刺激具有良好的响应性.最后,可控组装结构提供了一个易于集成多种功能性组分从而实现多功能化的平台.胶体马达自驱动运动往往要求其结构具有不对称性等特征,因而目前仍需通过结合自上而下的方法来集成纳米构筑基元,从而实现智能胶体马达的可控制备.在各种组装方法中,LbL [26~28]是一种可控制备不同结构胶体马达的重要方法.通过分别带正、负电荷的聚电解质在不同模板上的交替沉积可以很容易地制备聚电解质多层膜(polyelectrolyte multilayers,PEM).所采用的模板将决定所制备PEM 的结构,以分散的胶体颗粒为模板可制得空心胶囊[29],在多孔模板的通道内进行交替沉积可获得PEM 纳米管[30],在固体基底表面沉积可获得多层薄膜.LbL 技术可以赋予所制备组装体以良好的结构和组成可控性,并且通过非共价相互作用可以将不同种类的功能性基元[31]集成到组装结构的内部或表面,从而使基于LbL 组装结构的胶体马达具有良好的多功能性和刺激响应性.本文主要介绍本课题组通过可控组装(尤其是LbL)方法以及多功能性纳米构筑基元可控集成,进而实现智能胶体马达可控构筑的研究进展.涉及气泡驱动、光驱动以及超声驱动胶体马达的可控制备,马达运动速度、方向以及状态控制,马达在生物医学等领域中的应用等内容.2 胶体马达的可控制备2.1 气泡驱动胶体马达框架结构的制备以及实现催化剂在组装结构中的不对称分布是构筑基于可控组装结构的气泡驱动胶体马达的重要步骤.框架结构决定了马达的形状和尺寸,并提供了集成纳米尺度构筑基元的平台.对于以H 2O 2为燃料通过气泡驱动的马达,Pt 纳米粒子或过氧化氢酶(catalase,CAT)是常用的催化剂.Pt 纳米粒子或CAT 能够催化H 2O 2分解为O 2和H 2O,而释放的氧气中国科学: 化学 2017 年 第 47 卷 第 1 期5泡能够推动胶体马达进行高速运动.本课题组[21]率先报道了基于LbL 技术的阴阳型微胶囊马达.该胶囊是由5个聚苯乙烯磺酸盐(poly(styrene sulfonate),PSS)/聚烯丙胺盐酸盐(poly(allylamine hy-drochloride),PAH)双层膜构成的,其直径约为8μm (图2).该研究中采用了树枝状Pt 纳米粒子,因其具有更大的比表面积以及催化活性,有利于实现马达的高速运动.可通过微接触印刷技术将树枝状Pt 纳米颗粒覆盖在已制备的胶囊表面,制备出了具有不对称结构的阴阳型微胶囊.简要地,将一个蘸有Pt 纳米粒子“墨水”的PDMS 图章放置于覆盖有PEM 的模板微球所形成的自组装单层表面,而后将修饰后的微球分散于水中,并用HF 移除二氧化硅粒子模版,即可获得Pt 纳米粒子不对称修饰的空心微胶囊.所得微胶囊马达可在15%的H 2O 2溶液中高速运动,并主要呈现出两种典型的运动轨迹,即圆形运动和螺旋形运动,其运动速度可分别达140和110μm s −1.此外,该马达在30%的H 2O 2溶液中可达到1mm s −1(相当于每秒125倍身长)的超快运动速度.除了微接触印刷技术,也可以利用真空溅射技术将Pt 覆盖在微胶囊的上半部分来制备具有阴阳型结构的微胶囊马达(图2)[32].在这种方法中,为使催化剂金属层与PEM 牢固地结合在一起,通常需要在两者之间填充Ti 或Cr 金属层做黏合剂层.与微接触印刷技术相比,真空溅射方法的优点在于可以通过控制金属溅射时间等参数构建厚度可调的多层结构,而且直接使用金属原子,不需要催化剂Pt 纳米粒子的合成.Bonchio 等[33]进一步将Pt 纳米粒子替换为可催化降解H 2O 2燃料的多金属氧簇,并将其组装于PEM 微胶囊中,从而获得了微胶囊马达,其运动速度可达25μm s −1.由于在该马达中,催化剂多金属氧簇是被夹在聚电解质多层内部的,即形成了三明治结构,因而易发生由氧气泡快速释放造成的微胶囊不可逆性破坏.同时可以用生物酶来代替作为催化剂的Pt 制备基于PEM 微胶囊的生物催化胶体马达[34].首先,在二氧化硅微球模板表面构筑(PSS/PAH)5多层膜,而后将所得粒子滴加到硅基底表面形成自组装单层,通过真空溅射依次在粒子的上半部覆盖Ni 和Au,最后将粒子从硅基底表面释放下来并用HF 刻蚀溶解二氧化硅模板,即可获得Au 金属层不对称修饰的空心微胶囊.进一步,在Au 层表面修饰3-巯基丙酸,利用化学反应便可实现CAT 的固定化.该生物催化胶体马达可在生理温度下在1%H 2O 2溶液中进行自驱动运动.如此低浓度的H 2O 2溶液对细胞具有较小的毒性.因此,CAT 可以作为Pt 纳米粒子催化剂的替代物,从而提高微胶囊马达的生物相容性.类似地,我们还制备了气泡驱动的PEM 壳状马达[35].该马达具有与微胶囊马达类似的结构,不同之处在于其催化剂层位于囊壁内侧且胶囊不是全封闭的(图3).首先,使直径约为20μm 的二氧化硅粒子在玻璃基底上形成自组装单层,而后将该自组装单层转移到Parafilm 薄膜上.通过轻微的按压以及在80℃下加热20min,使得冷却至室温后二氧化硅粒子部分嵌入到Parafilm 薄膜中.接下来,通过真空溅射技术在粒子表面覆盖一层金属Pt,并通过LbL 进一步覆盖(PSS/PAH)10多层膜.最后利用四氢呋喃溶解Parafilm 薄膜,并利用HF 溶解二氧化硅粒子模板,即可获得PEM 壳状马达.该马达的运动速度可达260μm s −1,在水中带电有机物的快速分离与检测方面具有潜在的应用.由多孔模板辅助LbL 技术制备的PEM 纳米管也可以转变为管状胶体马达.这种气泡驱动的管状胶体马达可被形象地称为“纳米火箭”[36].本课题组[37]率先报道了自驱动的PEM 纳米火箭(图4).在该研究中,选取图2 LbL 结合微接触印刷[21]或金属真空溅射[32]构筑阴阳型PEM 微胶囊马达的制备过程示意图(网络版彩图)图3 PEM 壳状马达[35]合成过程示意图(网络版彩图)林显坤等: 可控分子组装的自驱动胶体马达及其生物医学应用6图4 通过多孔模板辅助LbL 技术可控构筑纳米火箭[37]的制备过程示意图(网络版彩图)了两种可生物降解的天然高分子作为马达框架结构材料,即带正电荷的壳聚糖(chitosan,CHI)和带负电荷的海藻酸钠(sodium alginate,ALG),并选取了多孔的聚碳酸酯薄膜(polycarbonate,PC)为模板,以Pt 纳米粒子为分解H 2O 2燃料的催化剂.首先,将CHI 和ALG 交替地沉积在PC 模板孔道内,进一步将Pt 纳米粒子沉积在多层膜的内表面,最后经过打磨处理并用有机溶剂去除模板,即可获得分散的纳米火箭.所采用的PC 模板孔道具有不对称性,并使得所得纳米管具有锥形结构,即纳米管具有直径不同的两个开口端.这将促使氧气泡倾向于从较大的开口端被释放,进而推动纳米火箭的高速运动.该纳米火箭的运动速度可达74μm s −1(相当于每秒运动10倍体长).以具有良好生物相容性的牛血清白蛋白(bovine serum albumin,BSA)和聚赖氨酸(poly(L-lysine),PLL)为壁材可构筑生物可降解的纳米火箭[38].该研究还利用生物相容的明胶(gelatin)所具有的溶胶-凝胶相转变能力实现了对CAT 、Au 纳米粒子以及模型药物阿霉素(doxorubicin,DOX)的装载.在40℃将上述材料的混合水溶液填充进入已组装了PEM 的多孔模板孔道内,待温度降低至4℃时明胶将发生从溶液到凝胶的转变,从而实现各种功能基元的装载.该纳米火箭在生理温度下在0.5%H 2O 2溶液中可达4μm s −1的运动速度.利用与α胰凝乳蛋白酶(α-chymotrypsin)共培养可测试纳米火箭的生物可降解性.研究发现,共培养24h 后,该纳米火箭可降解为薄片状结构.通过LbL 方法与微接触印刷技术的有效结合还可以制备二维盘状的PEM 胶体马达(图5)[39~42].首先,直接在PDMS 印章上组装PEM,而后利用微接触印刷技术将PEM 转移到聚乙烯醇(polyvinylalcohol,PV A)薄膜上并形成PEM 二维盘状结构阵列.进一步,利用真空溅射技术在盘状结构表面覆盖Pt 金属层,并利用热水溶解PV A 薄膜,即可获得二维盘状的PEM 胶体马达.该图5 二维盘状的PEM 胶体马达[39]的制备过程示意图(网络版彩图)胶体马达可因氧气气泡成核位置的区别而呈现出不同的运动行为.2.2 光驱动胶体马达因为近红外光(near-infrared light,NIR)在人体组织中具有良好的透过性,由NIR 来驱动胶体马达的运动对于其在生物医学等领域中的应用具有重要的意义.以光能作为马达运动的能量源可以有效避免有毒化学燃料(如H 2O 2)的使用,并可实现马达运动的远程供能与控制.将Au 纳米棒或Au 纳米壳层不对称地修饰在微胶囊或PEM 纳米管上,并利用其在NIR 照射下光热效应所产生的温度梯度已成为一种实现NIR 驱动马达运动的重要途径.本课题组[43]制备了由CHI 和ALG 多层膜构成的NIR 驱动的阴阳型微胶囊马达.CHI/ALG 微胶囊马达是通过常规的模板辅助LbL 技术结合微接触印刷技术制备的(图6).在这里,采用含有Au 纳米棒的CHI/ALG 多层膜作为微接触印刷的“墨水”,从而使得Au 纳米棒仅富集于微胶囊马达的一侧.所使用的Au 纳米棒在近红外区(850nm)具有等离子共振吸收.在NIR 激光照射下所产生的热梯度推动了马达的运动,从而避免了有毒化学燃料的使用.该马达在9.6J cm −2激光照射下的运动速率可达23.27μm s −1.本课题组[44]进一步报道了超快的NIR 驱动的PEM 纳米火箭.该纳米火箭的框架结构是通过PSS 和PAH 在PC 模板的孔道内进行LbL 沉积而获得的.随后,利用静电相互作用将直径约为20nm 的Au 纳米粒子组装在所制备的(PSS/PAH)20纳米管内部.进一步, 通过种中国科学: 化学 2017 年 第 47 卷 第 1 期7图6 光驱动的阴阳型微胶囊马达[43]的制备过程示意图(网络版彩图)子生长过程可将Au 纳米粒子转变为Au 纳米壳层,最后使用二氯甲烷溶解PC 模板后,即可获得NIR 驱动的PEM 纳米火箭.这种NIR 驱动的火箭可以在水中进行沿火箭轴向的前进运动,其速度可高达160μm s −1(相当于每秒13倍体长).理论模拟研究表明,这种具有不对称结构的纳米火箭在NIR 照射下,内部的Au 纳米壳将光能转化为热能从而在火箭的附近区域产生了不对称的热梯度.这种热梯度所带来的热泳作用是该纳米火箭运动的主要驱动力.此外,这种NIR 驱动的PEM 纳米火箭可以在细胞培养基中进行有效运动并且NIR 在驱动马达运动过程中不会对细胞造成影响.2.3 生物界面化胶体马达细胞膜可以被看作是自然界创造的一类特殊组装结构.通过将细胞膜或仿生膜与胶体马达进行有机结合可以获得生物界面化的胶体马达.各种细胞膜已被融合到介孔硅纳米胶囊、Au 纳米壳层结构、阴阳型微胶囊等结构表面用以改善这些微纳米结构在药物递送、光热治疗等应用中的生物相容性等[45~53].同样,通过生物界面化可以有效地提高胶体马达的生物相容性,使其在生物介质中仍然可以进行高速的运动,并避免生物体组织的排异与吞噬,进而可以实现马达在生物体内的长时间循环.此外,通过生物界面化还可以提高马达的靶向识别能力.这些改进都有利于促进胶体马达在生物医学等领域中的应用.本课题组[54]率先实现了直径仅75nm 的自驱动阴阳型纳米马达的制备,并利用自行研制的高分辨光学显微镜对纳米马达的运动行为进行了系统研究.这是国际上较早开展100nm 尺寸以下的胶体马达研究的代表性工作之一.尽管这种纳米尺寸的胶体马达给其运动的观察带来了困难,但其在生物医学应用中,尤其是药物递送等领域,却具有重要的意义,因为理想的药物载体应能够穿过人体内的屏障.该纳米马达由直径约为65nm 的介孔二氧化硅纳米粒子制备而成.利用真空溅射在这种纳米粒子的部分表面覆盖了Pt 金属帽,使得马达可在过氧化氢降解所释放的氧气泡推动下进行自驱动运动,并达到20.2μm s −1(相当于每秒267倍身长)的运动速度.因其所具有的孔道结构,这种纳米马达还可用于药物的装载及在细胞内的释放.为此,需在该纳米马达表面组装混有叶酸的卵磷脂双层.这种仿生膜有利于促进马达与癌细胞的识别,并保持模型药物在该马达孔道内的装载.最近的研究表明,如果将Pt 金属层替换为Au 金属层,还可以构筑NIR 驱动的介孔硅纳米马达.该马达可以实现每秒950倍身长的超高速运动[55].本课题组还与张良方课题组[56]合作,通过利用一种低渗溶血的方法将Fe 3O 4纳米粒子组装到红细胞内构筑了以天然红细胞(red blood cells,RBC)为基础的微马达.这种微马达可在外源超声场下实现自驱动运动,并且可通过外源磁场控制其运动方向.在超声场下,红细胞马达的不对称结构以及磁性纳米粒子在红细胞马达内部的不均匀分布造成了压力梯度差,这种压力差是红细胞马达运动的主要驱动力.这种红细胞马达保留了天然红细胞的结构和生物特征,具有良好的生物相容性,可以免于巨噬细胞的吞噬.进一步,还可以在红细胞内同时引入量子点、DOX 和磁性纳米粒子等多种组分,从而在良好的生物相容性基础上实现多通道荧光成像、外加磁场导航的超声驱动以及药物递送等多种功能(图7)[57].除了将纳米粒子装入细胞内而将细胞转变为胶体马达,将由细胞膜制备得到的囊泡融合到纳米结构的表面也是一种构筑生物界面化胶体马达的有效方法.通过将由新鲜红细胞制备得到的囊泡融合到Au 纳米线的表面可以构筑具有良好生物相容性的超声驱动马达[58].这种Au 纳米线是通过模板辅助的电化学沉积技术制备的,具有独特的内凹形末端,可在超声场存在下进行自驱动运动.以超声场作为自驱动运动的能量来源,可有效避免有毒燃料的使用,是一种生物友好的驱动方式.此外, 采用与制备PEM 壳状马达类林显坤等: 可控分子组装的自驱动胶体马达及其生物医学应用8图7 通过同时引入量子点、DOX 和磁性纳米粒子等多种功能基元将红细胞转变为仿生的胶体马达[57](网络版彩图)似的方法,将Mg 微粒部分嵌入Parafilm 薄膜,并在裸露的表面依次沉积Au 纳米粒子、ALG 以及红细胞膜,而后溶解除去Parafilm 薄膜,可以制备以水为燃料气泡驱动的生物界面化阴阳型胶体马达[59].该马达可在生物介质中运动,而不会被污损,可用于细胞毒素的清除.3 胶体马达的运动控制3.1 运动速度控制对于气泡驱动的胶体马达,在一定燃料浓度范围内,通常随着燃料浓度的增加,马达的速度也将增加.我们发现当H 2O 2浓度从1%增加至15%时,纳米火箭的运动速度可增加14倍[37].这种运动速度的增加是与氧气泡释放频率的增加紧密相关的.研究发现,在同样的H 2O 2浓度范围内,氧气泡的释放频率由2Hz 增加到了30Hz.该研究同时也发现增加溶液温度可以急剧加速马达的运动.这是由于温度的增加加速了催化反应速率,并提高了传质速率.对于光驱动的胶体马达,调控NIR 激光的辐照强度是控制其运动速度的有效途径.NIR 驱动微胶囊马达的平均运动速度可随着辐照激光强度的增加而从1.3μm s −1增加至23.27μm s −1(图8(a))[43].而对于超声驱动的胶体马达,可以通过调控超声换能器的电压来方便地控制超声场的强度,进而控制胶体马达的运动速度.红细胞膜修饰的Au 纳米线马达的平均运动速度可随超声换能器电压从1V 增至6V 而从5μm s −1增加至43μm s −1(图8(b))[58].该研究也表明红细胞膜修饰对超声驱动纳米线马达的运动速度影响很小.3.2 运动方向控制胶体马达运动轨迹与方向的控制对于其在靶向运图8 (a)NIR 驱动微胶囊马达的运动速度与激光辐照能量之间的依赖关系[43];(b)红细胞膜修饰的(虚线)及未修饰(实线)的超声驱动Au 纳米线马达的运动速度与超声换能器电压之间的依赖关系[58]输或分离等方面的应用是至关重要的.引入磁性组分(如磁性纳米粒子)是一条实现对胶体马达运动方向控制的简便途径.本课题组[37]通过LbL 技术将Fe 3O 4纳米粒子集成到了聚合物纳米火箭中,并实现了在外加磁场远程控制下纳米火箭向HeLa 癌细胞的靶向运动.扫描电子显微镜结果表明,该纳米火箭可进一步贴附在细胞表面,甚至刺入细胞内部.在利用微接触印刷制备微胶囊胶体马达的过程中可以将柠檬酸稳定的Fe 3O 4纳米粒子组装进入PEM 中,从而实现了在外加磁场下对微胶囊马达运动方向的控制[21].需要指出的是,对磁场强度可以进行一定的控制,使其仅可以改变马达的运动方向,而基本不会对马达自身的运动速度产生影响.除了引入磁性纳米粒子外,也可以利用真空溅射的方法在微胶囊马达表面部分覆盖具有磁性的Ni 金属层来实现对胶体马达运动方向的控制[34].研究还发现,当外加磁场强度处于一定范围内时可以导致微胶囊马达阴阳型结构取向的变化,而不会改变其位置,也即可实现马达可控的旋转.由于引入了不对称分布的磁性Fe 3O 4纳米粒子,基于红细胞的超声驱动胶体马达在外加磁场条件下可产生净磁场,进而通过外加磁场的开关可以实现对马达运动方向的周期性控制(图9)[56].而在外加磁场开关的条件下,天然红细胞的运动方向几乎不受影响(图9(c)).3.3 运动状态控制对胶体马达运动的启停状态进行有效的远程控制对于马达在药物递送与释放等生物医学领域中的应用具有重要意义.应用NIR 可对气泡驱动PEM 纳米火箭的运动状态进行远程控制[60].首先,将Pt 纳米粒子组。

钙钛矿催化剂英语Perovskite Catalysts: A Promising Pathway to a Sustainable FuturePerovskite materials have emerged as a remarkable class of catalysts, offering a versatile and efficient solution to a wide range of environmental and energy-related challenges. These materials, with their unique crystal structure and tunable properties, have captured the attention of researchers worldwide, paving the way for innovative applications in various fields including renewable energy, pollution control, and chemical synthesis.At the heart of perovskite catalysts lies their exceptional ability to facilitate critical chemical reactions. The perovskite structure, consisting of a central metal cation surrounded by an octahedron of anions, provides a highly customizable platform for tailoring catalytic performance. By substituting different elements into the perovskite lattice, researchers can fine-tune the material's electronic structure, surface properties, and catalytic activity, enabling targeted optimization for specific applications.One of the most promising applications of perovskite catalysts is in the realm of renewable energy. Perovskite materials havedemonstrated exceptional efficiency in the water-splitting reaction, a crucial process for the generation of clean hydrogen fuel. By leveraging the unique redox properties of perovskites, researchers have developed highly active and stable catalysts for both the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER), the two half-reactions that comprise water splitting. These perovskite-based catalysts have shown superior performance compared to traditional precious metal-based catalysts, making them a cost-effective and sustainable alternative for large-scale hydrogen production.Moreover, perovskite catalysts have also found applications in the field of carbon dioxide (CO2) reduction, a vital process for mitigating greenhouse gas emissions and achieving a circular carbon economy. Perovskite-based electrocatalysts have demonstrated the ability to selectively convert CO2 into valuable chemicals and fuels, such as carbon monoxide, formic acid, and methanol, with high efficiency and selectivity. This capability holds immense promise for the development of integrated CO2 capture and utilization systems, contributing to a more sustainable and environmentally-friendly future.Beyond renewable energy applications, perovskite catalysts have also made significant strides in the field of pollution control. These materials have shown remarkable catalytic activity in the removal ofvarious air and water pollutants, including nitrogen oxides (NOx), sulfur oxides (SOx), volatile organic compounds (VOCs), and heavy metals. Perovskite-based catalysts can effectively oxidize or reduce these harmful substances, transforming them into less toxic or even benign compounds. This versatility makes perovskite catalysts a promising solution for addressing pressing environmental challenges, such as urban air pollution and water contamination.In the realm of chemical synthesis, perovskite catalysts have also showcased their potential. These materials have been employed in a wide range of organic transformations, including hydrogenation, oxidation, and coupling reactions. Perovskite catalysts have demonstrated superior activity, selectivity, and stability compared to traditional metal-based catalysts, opening up new avenues for the development of more efficient and sustainable chemical processes.The remarkable performance of perovskite catalysts can be attributed to their unique structural and electronic properties. The flexibility of the perovskite structure allows for the incorporation of a diverse range of elements, enabling the fine-tuning of catalytic activity and selectivity. Additionally, the strong metal-oxygen bonds in perovskites confer excellent thermal and chemical stability, crucial for maintaining catalytic performance under harsh reaction conditions.Furthermore, the scalable and cost-effective synthesis methods for perovskite materials have made them increasingly attractive for industrial applications. Compared to traditional precious metal-based catalysts, perovskite catalysts can be produced using more abundant and less expensive raw materials, making them a more economically viable option for large-scale deployment.As the field of perovskite catalysts continues to evolve, researchers are exploring innovative strategies to further enhance their performance and broaden their applications. This includes the development of nanostructured perovskite catalysts with increased surface area and active site density, the integration of perovskites with other functional materials to create hybrid catalytic systems, and the exploration of novel perovskite compositions for targeted catalytic reactions.In conclusion, perovskite catalysts have emerged as a transformative technology, offering a promising pathway towards a more sustainable future. Their versatility, efficiency, and cost-effectiveness have positioned them as a game-changing solution in renewable energy, pollution control, and chemical synthesis. As research and development in this field continue to advance, the impact of perovskite catalysts is poised to extend far beyond their current applications, contributing to a cleaner, more environmentally-friendly, and resource-efficient world.。

以英文命名的物理学现象
以下是一些以英文命名的物理学现象：
1. Doppler Effect（多普勒效应）：描述当波源相对于观察者运动时，观察到的波的频率和波长发生变化的现象。

2. Photoelectric Effect（光电效应）：指的是当光照射到金属表面时，光子的能量足够大时，可以将金属中的电子从原子中解离出来形成电流的现象。

3. Quantum Tunneling（量子隧道效应）：是指在经典物理学下不可能发生的情况下，由于量子力学的特性，粒子可以穿越能量势垒的现象。

4. Superconductivity（超导现象）：指的是在极低温度下，某些特定材料的电阻消失，可以使电流在其中无阻碍地流动的现象。

5. Bose-Einstein Condensation（玻色-爱因斯坦凝聚）：是指在极低温下，玻色子（一种基本粒子）的量子态出现互不冲突的大量粒子处于相同量子态的集体行为。

请注意，以上内容仅为物理学现象的一部分，如您对其他领域的命名有需要，请提供更具体的问题。

CHAPTER 2BASIC PLASMA EQUATIONS AND EQUILIBRIUM2.1INTRODUCTIONThe plasma medium is complicated in that the charged particles are both affected by external electric and magnetic fields and contribute to them.The resulting self-consistent system is nonlinear and very difficult to analyze.Furthermore,the inter-particle collisions,although also electromagnetic in character,occur on space and time scales that are usually much shorter than those of the applied fields or the fields due to the average motion of the particles.To make progress with such a complicated system,various simplifying approxi-mations are needed.The interparticle collisions are considered independently of the larger scale fields to determine an equilibrium distribution of the charged-particle velocities.The velocity distribution is averaged over velocities to obtain the macro-scopic motion.The macroscopic motion takes place in external applied fields and in the macroscopic fields generated by the average particle motion.These self-consistent fields are nonlinear,but may be linearized in some situations,particularly when dealing with waves in plasmas.The effect of spatial variation of the distri-bution function leads to pressure forces in the macroscopic equations.The collisions manifest themselves in particle generation and loss processes,as an average friction force between different particle species,and in energy exchanges among species.In this chapter,we consider the basic equations that govern the plasma medium,con-centrating attention on the macroscopic system.The complete derivation of these 23Principles of Plasma Discharges and Materials Processing ,by M.A.Lieberman and A.J.Lichtenberg.ISBN 0-471-72001-1Copyright #2005John Wiley &Sons,Inc.equations,from fundamental principles,is beyond the scope of the text.We shall make the equations plausible and,in the easier instances,supply some derivations in appendices.For the reader interested in more rigorous treatment,references to the literature will be given.In Section2.2,we introduce the macroscopicfield equations and the current and voltage.In Section2.3,we introduce the fundamental equation of plasma physics, for the evolution of the particle distribution function,in a form most applicable for weakly ionized plasmas.We then define the macroscopic quantities and indicate how the macroscopic equations are obtained by taking moments of the fundamental equation.References given in the text can be consulted for more details of the aver-aging procedure.Although the macroscopic equations depend on the equilibrium distribution,their form is independent of the equilibrium.To solve the equations for particular problems the equilibrium must be known.In Section2.4,we introduce the equilibrium distribution and obtain some consequences arising from it and from thefield equations.The form of the equilibrium distribution will be shown to be a consequence of the interparticle collisions,in Appendix B.2.2FIELD EQUATIONS,CURRENT,AND VOLTAGEMaxwell’s EquationsThe usual macroscopic form of Maxwell’s equations arerÂE¼Àm0@H@t(2:2:1)rÂH¼e0@E@tþJ(2:2:2)e0rÁE¼r(2:2:3) andmrÁH¼0(2:2:4) where E(r,t)and H(r,t)are the electric and magneticfield vectors and wherem 0¼4pÂ10À7H/m and e0%8:854Â10À12F/m are the permeability and per-mittivity of free space.The sources of thefields,the charge density r(r,t)and the current density J(r,t),are related by the charge continuity equation(Problem2.1):@rþrÁJ¼0(2:2:5) In general,J¼J condþJ polþJ mag24BASIC PLASMA EQUATIONS AND EQUILIBRIUMwhere the conduction current density J cond is due to the motion of the free charges, the polarization current density J pol is due to the motion of bound charges in a dielectric material,and the magnetization current density J mag is due to the magnetic moments in a magnetic material.In a plasma in vacuum,J pol and J mag are zero and J¼J cond.If(2.2.3)is integrated over a volume V,enclosed by a surface S,then we obtain its integral form,Gauss’law:e0þSEÁd A¼q(2:2:6)where q is the total charge inside the volume.Similarly,integrating(2.2.5),we obtaind q d t þþSJÁd A¼0which states that the rate of increase of charge inside V is supplied by the total currentflowing across S into V,that is,that charge is conserved.In(2.2.2),thefirst term on the RHS is the displacement current densityflowing in the vacuum,and the second term is the conduction current density due to the free charges.We can introduce the total current densityJ T¼e0@E@tþJ(2:2:7)and taking the divergence of(2.2.2),we see thatrÁJ T¼0(2:2:8)In one dimension,this reduces to d J T x=d x¼0,such that J T x¼J T x(t),independent of x.Hence,for example,the total currentflowing across a spatially nonuniform one-dimensional discharge is independent of x,as illustrated in Figure2.1.A generalization of this result is Kirchhoff’s current law,which states that the sum of the currents entering a node,where many current-carrying conductors meet,is zero.This is also shown in Figure2.1,where I rf¼I TþI1.If the time variation of the magneticfield is negligible,as is often the case in plasmas,then from Maxwell’s equations rÂE%0.Since the curl of a gradient is zero,this implies that the electricfield can be derived from the gradient of a scalar potential,E¼Àr F(2:2:9)2.2FIELD EQUATIONS,CURRENT,AND VOLTAGE25Integrating (2.2.9)around any closed loop C givesþC E Ád ‘¼ÀþC r F Ád ‘¼ÀþC d F ¼0(2:2:10)Hence,we obtain Kirchhoff’s voltage law ,which states that the sum of the voltages around any loop is zero.This is illustrated in Figure 2.1,for which we obtainV rf ¼V 1þV 2þV 3that is,the source voltage V rf is equal to the sum of the voltages V 1and V 3across the two sheaths and the voltage V 2across the bulk plasma.Note that currents and vol-tages can have positive or negative values;the directions for which their values are designated as positive must be specified,as shown in the figure.If (2.2.9)is substituted in (2.2.3),we obtainr 2F ¼Àre 0(2:2:11)Equation (2.2.11),Poisson’s equation ,is one of the fundamental equations that we shall use.As an example of its application,consider the potential in the center (x ¼0)of two grounded (F ¼0)plates separated by a distance l ¼10cm and con-taining a uniform ion density n i ¼1010cm 23,without the presence of neutralizing electrons.Integrating Poisson’s equationd 2F d x 2¼Àen i eFIGURE 2.1.Kirchhoff’s circuit laws:The total current J T flowing across a nonuniform one-dimensional discharge is independent of x ;the sum of the currents entering a node is zero (I rf ¼I T þI 1);the sum of voltages around a loop is zero (V rf ¼V 1þV 2þV 3).26BASIC PLASMA EQUATIONS AND EQUILIBRIUMusing the boundary conditions that F ¼0at x ¼+l =2and that d F =d x ¼0at x ¼0(by symmetry),we obtainF ¼12en i e 0l 22Àx 2"#The maximum potential in the center is 2.3Â105V,which is impossibly large for a real discharge.Hence,the ions must be mostly neutralized by electrons,leading to a quasi-neutral plasma.Figure 2.2shows a PIC simulation time history over 10210s of (a )the v x –x phase space,(b )the number N of sheets versus time,and (c )the potential F versus x for 100unneutralized ion sheets (with e /M for argon ions).We see the ion acceleration in (a ),the loss of ions in (b ),and the parabolic potential profile in (c );the maximum potential decreases as ions are lost from the system.We consider quasi-neutrality further in Section 2.4.Electric and magnetic fields exert forces on charged particles given by the Lorentz force law :F ¼q (E þv ÂB )(2:2:12)FIGURE 2.2.PIC simulation of ion loss in a plasma containing ions only:(a )v x –x ion phase space,showing the ion acceleration trajectories;(b )number N of ion sheets versus t ,with the steps indicating the loss of a single sheet;(c )the potential F versus x during the first 10210s of ion loss.2.2FIELD EQUATIONS,CURRENT,AND VOLTAGE 2728BASIC PLASMA EQUATIONS AND EQUILIBRIUMwhere v is the particle velocity and B¼m0H is the magnetic induction vector.The charged particles move under the action of the Lorentz force.The moving charges in turn contribute to both r and J in the plasma.If r and J are linearly related to E and B,then thefield equations are linear.As we shall see,this is not generally the case for a plasma.Nevertheless,linearization may be possible in some cases for which the plasma may be considered to have an effective dielectric constant;that is,the “free charges”play the same role as“bound charges”in a dielectric.We consider this further in Chapter4.2.3THE CONSERVATION EQUATIONSBoltzmann’s EquationFor a given species,we introduce a distribution function f(r,v,t)in the six-dimensional phase space(r,v)of particle positions and velocities,with the interpret-ation thatf(r,v,t)d3r d3v¼number of particles inside a six-dimensional phasespace volume d3r d3v at(r,v)at time tThe six coordinates(r,v)are considered to be independent variables.We illus-trate the definition of f and its phase space in one dimension in Figure2.3.As particles drift in phase space or move under the action of macroscopic forces, theyflow into or out of thefixed volume d x d v x.Hence the distribution functionaf should obey a continuity equation which can be derived as follows.InFIGURE2.3.One-dimensional v x–x phase space,illustrating the derivation of the Boltzmann equation and the change in f due to collisions.time d t,f(x,v x,t)d x a x(x,v x,t)d t particlesflow into d x d v x across face1f(x,v xþd v x,t)d x a x(x,v xþd v x,t)d t particlesflow out of d x d v x across face2 f(x,v x,t)d v x v x d t particlesflow into d x d v x across face3f(xþd x,v x,t)d v x v x d t particlesflow out of d x d v x across face4where a x v d v x=d t and v x;d x=d t are theflow velocities in the v x and x directions, respectively.Hencef(x,v x,tþd t)d x d v xÀf(x,v x,t)d x d v x¼½f(x,v x,t)a x(x,v x,t)Àf(x,v xþd v x,t)a x(x,v xþd v x,t) d x d tþ½f(x,v x,t)v xÀf(xþd x,v x,t)v x d v x d tDividing by d x d v x d t,we obtain@f @t ¼À@@x(f v x)À@@v x(fa x)(2:3:1)Noting that v x is independent of x and assuming that the acceleration a x¼F x=m of the particles does not depend on v x,then(2.3.1)can be rewritten as@f @t þv x@f@xþa x@f@v x¼0The three-dimensional generalization,@f@tþvÁr r fþaÁr v f¼0(2:3:2)with r r¼(^x@=@xþ^y@=@yþ^z@=@z)and r v¼(^x@=@v xþ^y@=@v yþ^z@=@v z)is called the collisionless Boltzmann equation or Vlasov equation.In addition toflows into or out of the volume across the faces,particles can “suddenly”appear in or disappear from the volume due to very short time scale interparticle collisions,which are assumed to occur on a timescale shorter than the evolution time of f in(2.3.2).Such collisions can practically instantaneously change the velocity(but not the position)of a particle.Examples of particles sud-denly appearing or disappearing are shown in Figure2.3.We account for this effect,which changes f,by adding a“collision term”to the right-hand side of (2.3.2),thus obtaining the Boltzmann equation:@f @t þvÁr r fþFmÁr v f¼@f@tc(2:3:3)2.3THE CONSERVATION EQUATIONS29The collision term in integral form will be derived in Appendix B.The preceding heuristic derivation of the Boltzmann equation can be made rigorous from various points of view,and the interested reader is referred to texts on plasma theory, such as Holt and Haskel(1965).A kinetic theory of discharges,accounting for non-Maxwellian particle distributions,must be based on solutions of the Boltzmann equation.We give an introduction to this analysis in Chapter18. Macroscopic QuantitiesThe complexity of the dynamical equations is greatly reduced by averaging over the velocity coordinates of the distribution function to obtain equations depending on the spatial coordinates and the time only.The averaged quantities,such as species density,mean velocity,and energy density are called macroscopic quantities,and the equations describing them are the macroscopic conservation equations.To obtain these averaged quantities we take velocity moments of the distribution func-tion,and the equations are obtained from the moments of the Boltzmann equation.The average quantities that we are concerned with are the particle density,n(r,t)¼ðf d3v(2:3:4)the particlefluxG(r,t)¼n u¼ðv f d3v(2:3:5)where u(r,t)is the mean velocity,and the particle kinetic energy per unit volumew¼32pþ12mu2n¼12mðv2f d3v(2:3:6)where p(r,t)is the isotropic pressure,which we define below.In this form,w is sumof the internal energy density32p and theflow energy density12mu2n.Particle ConservationThe lowest moment of the Boltzmann equation is obtained by integrating all terms of(2.3.3)over velocity space.The integration yields the macroscopic continuity equation:@n@tþrÁ(n u)¼GÀL(2:3:7)The collision term in(2.3.3),which yields the right-hand side of(2.3.7),is equal to zero when integrated over velocities,except for collisions that create or destroy 30BASIC PLASMA EQUATIONS AND EQUILIBRIUMparticles,designated as G and L ,respectively (e.g.,ionization,recombination).In fact,(2.3.7)is transparent since it physically describes the conservation of particles.If (2.3.7)is integrated over a volume V bounded by a closed surface S ,then (2.3.7)states that the net number of particles generated per second within V ,either flows across the surface S or increases the number of particles within V .For common low-pressure discharges in the steady state,G is usually due to ioniz-ation by electron–neutral collisions:G ¼n iz n ewhere n iz is the ionization frequency.The volume loss rate L ,usually due to recom-bination,is often negligible.Hencer Á(n u )¼n iz n e (2:3:8)in a typical discharge.However,note that the continuity equation is clearly not sufficient to give the evolution of the density n ,since it involves another quantity,the mean particle velocity u .Momentum ConservationTo obtain an equation for u ,a first moment is formed by multiplying the Boltzmann equation by v and integrating over velocity.The details are complicated and involve evaluation of tensor elements.The calculation can be found in most plasma theory texts,for example,Krall and Trivelpiece (1973).The result is mn @u @t þu Ár ðÞu !¼qn E þu ÂB ðÞÀr ÁP þf c (2:3:9)The left-hand side is the species mass density times the convective derivative of the mean velocity,representing the mass density times the acceleration.The convective derivative has two terms:the first term @u =@t represents an acceleration due to an explicitly time-varying u ;the second “inertial”term (u Ár )u represents an acceleration even for a steady fluid flow (@=@t ;0)having a spatially varying u .For example,if u ¼^xu x (x )increases along x ,then the fluid is accelerating along x (Problem 2.4).This second term is nonlinear in u and can often be neglected in discharge analysis.The mass times acceleration is acted upon,on the right-hand side,by the body forces,with the first term being the electric and magnetic force densities.The second term is the force density due to the divergence of the pressure tensor,which arises due to the integration over velocitiesP ij ¼mn k v i Àu ðÞv j Àu ÀÁl v (2:3:10)2.3THE CONSERVATION EQUATIONS 31where the subscripts i,j give the component directions and kÁl v denotes the velocity average of the bracketed quantity over f.ÃFor weakly ionized plasmas it is almost never used in this form,but rather an isotropic version is employed:P¼p000p000p@1A(2:3:11)such thatrÁP¼r p(2:3:12) a pressure gradient,withp¼13mn k(vÀu)2l v(2:3:13)being the scalar pressure.Physically,the pressure gradient force density arises as illustrated in Figure2.4,which shows a small volume acted upon by a pressure that is an increasing function of x.The net force on this volume is p(x)d AÀp(xþd x)d A and the volume is d A d x.Hence the force per unit volume isÀ@p=@x.The third term on the right in(2.3.9)represents the time rate of momentum trans-fer per unit volume due to collisions with other species.For electrons or positive ions the most important transfer is often due to collisions with neutrals.The transfer is usually approximated by a Krook collision operatorf j c¼ÀXbmn n m b(uÀu b):Àm(uÀu G)Gþm(uÀu L)L(2:3:14)where the summation is over all other species,u b is the mean velocity of species b, n m b is the momentum transfer frequency for collisions with species b,and u G and u L are the mean velocities of newly created and lost particles.Generally j u G j(j u j for pair creation by ionization,and u L%u for recombination or charge transfer lossprocesses.We discuss the Krook form of the collision operator further in Chapter 18.The last two terms in(2.3.14)are generally small and give the momentum trans-fer due to the creation or destruction of particles.For example,if ions are created at rest,then they exert a drag force on the moving ionfluid because they act to lower the averagefluid velocity.A common form of the average force(momentum conservation)equation is obtained from(2.3.9)neglecting the magnetic forces and taking u b¼0in theÃWe assume f is normalized so that k f lv ¼1.32BASIC PLASMA EQUATIONS AND EQUILIBRIUMKrook collision term for collisions with one neutral species.The result is mn @u @t þu Ár u !¼qn E Àr p Àmn n m u (2:3:15)where only the acceleration (@u =@t ),inertial (u Ár u ),electric field,pressure gradi-ent,and collision terms appear.For slow time variation,the acceleration term can be neglected.For high pressures,the inertial term is small compared to the collision term and can also be dropped.Equations (2.3.7)and (2.3.9)together still do not form a closed set,since the pressure tensor P (or scalar pressure p )is not determined.The usual procedure to close the equations is to use a thermodynamic equation of state to relate p to n .The isothermal relation for an equilibrium Maxwellian distribution isp ¼nkT(2:3:16)so thatr p ¼kT r n (2:3:17)where T is the temperature in kelvin and k is Boltzmann’s constant (k ¼1.381Â10223J /K).This holds for slow time variations,where temperatures are allowed to equilibrate.In this case,the fluid can exchange energy with its sur-roundings,and we also require an energy conservation equation (see below)to deter-mine p and T .For a room temperature (297K)neutral gas having density n g and pressure p ,(2.3.16)yieldsn g (cm À3)%3:250Â1016p (Torr)(2:3:18)p FIGURE 2.4.The force density due to the pressure gradient.2.3THE CONSERVATION EQUATIONS 33Alternatively,the adiabatic equation of state isp¼Cn g(2:3:19) such thatr p p ¼gr nn(2:3:20)where g is the ratio of specific heat at constant pressure to that at constant volume.The specific heats are defined in Section7.2;g¼5/3for a perfect gas; for one-dimensional adiabatic motion,g¼3.The adiabatic relation holds for fast time variations,such as in waves,when thefluid does not exchange energy with its surroundings;hence an energy conservation equation is not required. For almost all applications to discharge analysis,we use the isothermal equation of state.Energy ConservationThe energy conservation equation is obtained by multiplying the Boltzmannequation by12m v2and integrating over velocity.The integration and some othermanipulation yield@ @t32pþrÁ32p uðÞþp rÁuþrÁq¼@@t32pc(2:3:21)Here32p is the thermal energy density(J/m3),32p u is the macroscopic thermal energyflux(W/m2),representing theflow of the thermal energy density at thefluid velocityu,p rÁu(W/m3)gives the heating or cooling of thefluid due to compression orexpansion of its volume(Problem2.5),q is the heatflow vector(W/m2),whichgives the microscopic thermal energyflux,and the collisional term includes all col-lisional processes that change the thermal energy density.These include ionization,excitation,elastic scattering,and frictional(ohmic)heating.The equation is usuallyclosed by setting q¼0or by letting q¼Àk T r T,where k T is the thermal conduc-tivity.For most steady-state discharges the macroscopic thermal energyflux isbalanced against the collisional processes,giving the simpler equationrÁ32p u¼@32pc(2:3:22)Equation(2.3.22),together with the continuity equation(2.3.8),will often prove suf-ficient for our analysis.34BASIC PLASMA EQUATIONS AND EQUILIBRIUMSummarySummarizing our results for the macroscopic equations describing the electron and ionfluids,we have in their most usually used forms the continuity equationrÁ(n u)¼n iz n e(2:3:8) the force equation,mn @u@tþuÁr u!¼qn EÀr pÀmn n m u(2:3:15)the isothermal equation of statep¼nkT(2:3:16) and the energy-conservation equationrÁ32p u¼@@t32pc(2:3:22)These equations hold for each charged species,with the total charges and currents summed in Maxwell’s equations.For example,with electrons and one positive ion species with charge Ze,we haver¼e Zn iÀn eðÞ(2:3:23)J¼e Zn i u iÀn e u eðÞ(2:3:24)These equations are still very difficult to solve without simplifications.They consist of18unknown quantities n i,n e,p i,p e,T i,T e,u i,u e,E,and B,with the vectors each counting for three.Various simplifications used to make the solutions to the equations tractable will be employed as the individual problems allow.2.4EQUILIBRIUM PROPERTIESElectrons are generally in near-thermal equilibrium at temperature T e in discharges, whereas positive ions are almost never in thermal equilibrium.Neutral gas mol-ecules may or may not be in thermal equilibrium,depending on the generation and loss processes.For a single species in thermal equilibrium with itself(e.g.,elec-trons),in the absence of time variation,spatial gradients,and accelerations,the2.4EQUILIBRIUM PROPERTIES35Boltzmann equation(2.3.3)reduces to@f @tc¼0(2:4:1)where the subscript c here represents the collisions of a particle species with itself. We show in Appendix B that the solution of(2.4.1)has a Gaussian speed distribution of the formf(v)¼C eÀj2m v2(2:4:2) The two constants C and j can be obtained by using the thermodynamic relationw¼12mn k v2l v¼32nkT(2:4:3)that is,that the average energy of a particle is12kT per translational degree offreedom,and by using a suitable normalization of the distribution.Normalizing f(v)to n,we obtainCð2p0d fðpsin u d uð1expÀj2m v2ÀÁv2d v¼n(2:4:4)and using(2.4.3),we obtain1 2mCð2pd fðpsin u d uð1expÀj2m v2ÀÁv4d v¼32nkT(2:4:5)where we have written the integrals over velocity space in spherical coordinates.The angle integrals yield the factor4p.The v integrals are evaluated using the relationÃð10eÀu2u2i d u¼(2iÀ1)!!2ffiffiffiffipp,where i is an integer!1:(2:4:6)Solving for C and j we havef(v)¼nm2p kT3=2expÀm v22kT(2:4:7)which is the Maxwellian distribution.Ã!!denotes the double factorial function;for example,7!!¼7Â5Â3Â1. 36BASIC PLASMA EQUATIONS AND EQUILIBRIUMSimilarly,other averages can be performed.The average speed vis given by v ¼m =2p kT ðÞ3=2ð10v exp Àv 22v 2th !4p v 2d v (2:4:8)where v th ¼(kT =m )1=2is the thermal velocity.We obtainv ¼8kT p m 1=2(2:4:9)The directed flux G z in (say)the þz direction is given by n k v z l v ,where the average is taken over v z .0only.Writing v z ¼v cos u we have in spherical coordinatesG z ¼n m 2p kT 3=2ð2p 0d f ðp =20sin u d u ð10v cos u exp Àv 22v 2th v 2d v Evaluating the integrals,we findG z ¼14n v (2:4:10)G z is the number of particles per square meter per second crossing the z ¼0surfacein the positive direction.Similarly,the average energy flux S z ¼n k 1m v 2v z l v in theþz direction can be found:S z ¼2kT G z .We see that the average kinetic energy W per particle crossing z ¼0in the positive direction isW ¼2kT (2:4:11)It is sometimes convenient to define the distribution in terms of other variables.For example,we can define a distribution of energies W ¼12m v 2by4p g W ðÞd W ¼4p f v ðÞv 2d vEvaluating d v =d W ,we see that g and f are related byg W ðÞ¼v (W )f ½v (W ) m (2:4:12)where v (W )¼(2W =m )1=2.Boltzmann’s RelationA very important relation can be obtained for the density of electrons in thermal equilibrium at varying positions in a plasma under the action of a spatially varying 2.4EQUILIBRIUM PROPERTIES 3738BASIC PLASMA EQUATIONS AND EQUILIBRIUMpotential.In the absence of electron drifts(u e;0),the inertial,magnetic,and fric-tional forces are zero,and the electron force balance is,from(2.3.15)with@=@t;0,en e Eþr p e¼0(2:4:13) Setting E¼Àr F and assuming p e¼n e kT e,(2.4.13)becomesÀen e r FþkT e r n e¼0or,rearranging,r(e FÀkT e ln n e)¼0(2:4:14) Integrating,we havee FÀkT e ln n e¼constorn e(r)¼n0e e F(r)=kT e(2:4:15)which is Boltzmann’s relation for electrons.We see that electrons are“attracted”to regions of positive potential.We shall generally write Boltzmann’s relation in more convenient unitsn e¼n0e F=T e(2:4:16)where T e is now expressed in volts,as is F.For positive ions in thermal equilibrium at temperature T i,a similar analysis shows thatn i¼n0eÀF=T i(2:4:17) Hence positive ions in thermal equilibrium are“repelled”from regions of positive potential.However,positive ions are almost never in thermal equilibrium in low-pressure discharges because the ion drift velocity u i is large,leading to inertial or frictional forces in(2.3.15)that are comparable to the electricfield or pressure gra-dient forces.Debye LengthThe characteristic length scale in a plasma is the electron Debye length l De.As we will show,the Debye length is the distance scale over which significant charge densities can spontaneously exist.For example,low-voltage(undriven)sheaths are typically a few Debye lengths wide.To determine the Debye length,let us intro-duce a sheet of negative charge having surface charge density r S,0C/m2into an。

ith the growing interest in sustainable energy sources siliconsolar cells offer opportunities to provide new capacitiesfor electricity generation with simultaneous reduction offorWgreenhouse gas emissions. Indeed, the photovoltaic industry undergoes a very dynamic development in the last few years, e.g. the volume of the solar cells produced worldwide is expected to increase by one and half order of magnitude in the next ten years (Varadi, 1998). This is expected to result in a signifi cant increase in the demand for pure silicon feedstock since polycrystalline silicon (poly-Si) based solar cells are the predominant solar cell technology. However, until now the photovoltaic industry has no independent feedstock source. It utilizes of-spec silicon from the semiconductor industry. Therefore a signifi cant shortage of solar grade silicon (s.g. Si) is expected in the next years. Assuming conservatively an annual growth rate for the photovoltaic industry of 15% and a share of thin fi lm technique on the photovoltaic market of 10% the defi ciency of s.g., Si will amount to more than 5000 t (metric ton) in 2010 (Block and Wagner, 2000). For the sustainable growth of the photovoltaic industry an independent feedstock supply of solar grade silicon is necessary.Against this background, several attempts have been made to establish new, independent processes for the low-cost production of solar grade silicon (Ikeda and Maeda, 1992; Block and Wagner, 2000). The main target is a signifi cant reduction of the production costs compared to the costs of electronic grade silicon. Different routes were proposed, among those consisting of consecutive hydrochlorination of metallurgical-grade silicon, purifi cation of chlorosilanes and fi nally their decomposition to pure silicon seems to be the most promising. In these routes that are also currently applied for production of the electronic grade silicon the reduction of the investment costs and energy consumption can be achieved mainly by the selection of the fi nal gaseous component, i.e. monosilane and dichlorosilane v.s trichlorosilane and the type of the decomposer. Along this, the Bayer route to low cost solar grade silicon was worked out (Block and Wagner, 2000). In the Bayer process, metallurgical silicon is converted by the reaction with silicon tetrachlorideand hydrogen to trichlorosilane. In the next reaction step, trichlorosilane is converted via dichlorosilane and monochlorosilane to monosilane. Resulting silicon tetrachloride is recycled to the hydrochlorination reaction. In the fi nal step, silane is decomposed to high purity granular silicon (according to Equation 1) and hydrogen that is recycled to the * Author to whom correspondence may be addressed. E-mail address: leslaw. mleczko.lm@bayer-ag.de hydrochlorination reactor. Production costs of < 10 €/ kg in a plant with capacity of 5000 t/y are targeted. SiH1H24kJ•molR,ST P4Si+i H→SH=−−∆23(1) In order to achieve this challenging goal the correct design of the fi nal reaction step is of primary importance. Although pyrolysis of silane is energetically proferable to the normally applied highly endothermic The fl uidized-bed chemical vapor deposition (CVD)process for polycrystalline silicon production is consid-ered to be the most attractive alternative to theconventional bell-jar process. In order to obtain stableoperation, high space-time-yields and high purity ofthe product several obstacles have to be eliminated.Reaction conditions must be optimized to avoid thehomogeneous decomposition of silane and minimizesilicon dust formation. The effect of temperature,silane partial pressure, gas velocity and the size ofbed particles has to be identifi ed. These dependen-cies and the interaction between hydrodynamics andkinetics of homogeneous and heterogeneous CVD-reactions were studied in a laboratory-scale fl uidized-bed reactor.Le procédé de production de silicone polycristallin pardéposition de vapeur chimique en lit fl uidisé (CVD) estconsidéré comme la méthode la plus intéressante parrapport au procédé à fi ole en cloche classique. Plusieursobstacles doivent être supprimés afi n d’obtenir unfonctionnement stable, des rendements en tempset en espace élevés et une pureté de produit élevée.Les conditions de réaction doivent être optimiséespour éviter la décomposition homogène du silaneet minimiser la formation de poussières de silicone.L’effet de la température, de la pression partielle dusilane, de la vitesse de gaz et de la taille des particulesde lit doit être déterminé. Ces dépendances etl’interaction entre l’hydrodynamique et la cinétiquedes réactions en CVD homogène et hétérogène ontété étudiées dans un réacteur à lit fl uidisé à l’échelledu laboratoire.keywords: silane, polycrystalline silicon, fl uidized bed.Optimization of Reaction Conditions in a Fluidized-Bed for Silane PyrolysisMaria P. Tejero-Ezpeleta1, Sigurd Buchholz2 and Leslaw Mleczko2*1 Chair of T echnical Chemistry, Ruhr-University Bochum, 44780, Germany2 Bayer AG, Corporate T echnology / Process T echnology, Leverkusen, 51368, Germanyreduction of trichlorosilane, a decrease in cost has to be achieved by replacing the traditional bell-jar reactor by another reactor type that will allow continuous operation at high space-time yields and lower energy consumption. As alternatives, an aerosol (free space) or a fl uidized-bed reactor were considered. An aerosol reactor is not suitable since extensive staging is necessary even for achieving particle size of the order of 20 µm (Dudukovich et al. 1986). A fl uidized bed with a large surface of solids that is available for chemical vapor deposition (CVD) was found to be the most attractive alternative to the conventional bell-jar process. This selection was supported by literature. Both means, i.e. the route and the reactor, allow to the reduction of the energy demand for production 1 kg Si from 300 kWh/kg for trichlorosilane reduction in a bell-jar (Siemens) reactor (Baysar, 1992) to 5 – 8 kWh/kg for pyrolysis of silane in a fl uidized bed (Ibrahim and Johnston, 1990).The main reaction pathways of silane decomposition in a fl uidized-bed reactor are presented schematically in Figure 1. Based on the current understanding, silane can be decomposed and silicon is formed via two major paths. One is the homogeneous decomposition into a gaseous precursor thatcan nucleate a new solid phase that is assumed to be silicon. The other is the heterogeneous decomposition of silane on the existing silicon seed particles or on the formed nuclei leading to a CVD of silicon. This reaction, i.e. deposition of silicon on the seed particles is responsible for the particle growth. Homogeneous reaction fi nes are formed as a product. Fluidized-bed reactors for pyrolysis of silane are usually operated in the bubbling or slugging regime. In the continuously operating reactor, seed particles with a diameter in the range of 100 µm are fed into a fl uidized bed. The bed is fl uidized by silane and an inert gas, usually hydrogen. Despite the light exothermicity of the pyrolysis reaction the reactor has to be heated. The granular product exhibits the same wide particle size distribution as in the bed, but the average particle diameter should be in the range of 900 µm.Several attempts were made to develop a fl uidized-bed silane/chlorosilane decomposer (Rohatgi, 1986 a, b; Kim et al., 1994; Ibrahim and Johnston, 1990; Block and Wagner, 2000). However, until now only MEMC Electronic Materials Inc. commercialized this technology (Ibrahim and Johnston, 1990). There are several reasons why CVD fl uidized-bed processes have not found wide spread application. One of the most important obstacles is a very expensive and time consuming scale-up of the pyrolysis reactor. Hereby a number of interconnected problems have to be solved, e.g. agglomeration of particles in the bed, contamination of the product with impurities during collision of particles with the reactor wall and the distributor, deposition of silicon on the reactor wall with the consequence of contamination of the product, damage of the reactor wall and limited times on stream, deposition of silicon in the gas distributor and plugging of the holes, formation of dust. Especially a low selectivity to dust is very important. In order to minimize homogeneous decomposition of monosilane reaction, conditions have be optimized—particularly the effect of the temperature, partial pressure of the silane, gas velocity and the size of bed particles has to be identifi ed. The problem of the selection of optimum reaction conditions was already addressed by academia (Rohatgi et al., 1982; Kojima et al., 1989; Kojima et al., 1991; Caussat, 1995). However conditions applied in those investigations differed signifi cantly from those expected in the industrial reactor.Against this background, an extended experimental research was started aiming at identifi cation, correlation and quantifi cation of the complex interrelations between reaction conditions, reactor design and performance. In the experiments reported in this paper, the identifi cation of the effect of reaction conditions, i.e. gas composition, particle diameter and gas velocity on the stability of the fl uidization, particle growth rate and on the reactor performance, i.e. yield to poly-Si will be described.ExperimentalLab-Scale Fluidized Bed ReactorA lab-scale fl uidized bed reactor (I.D. = 0.0524 m, h = 1.3 m) was designed for the investigation of silane pyrolysis in an operation range of = 773 – 1073 K and=T = 100 to 140 kPa.=pThe fl uidized bed stainless steel reactor is heated by electric heat on the outer reactor wall. The silane and further purge- or diluent gases are fed through separate, purge able gas lines and mass-fl ow controllers. The following gases were applied: SiH4 (Air-Products, ultrapure), He (Linde, 99.9990 %), N2(Linde, 99.9990%), Ar (Linde, 99.998%) and H2 (Linde, 99.9990%). Silane was taken out of a specially designed gas cabinet placed outside the laboratory with an integrated purge gas. The reactor consisted of three main parts connected via fl anges: a water-cooled bottom with a perforated-plate gas distributor, a heated reactor part (Sanicro 31HAT (1.4876), I.D. = 0.0524 m) and an expanded head (I.D = 0.1 m). The total height is approximately 1.5 m. At the bottom of the reactor, the gas is fed into the wind box and through the distributor (an exchangeable perforated plate of 0.003 m thickness). In order to prevent the distributor from plugging due to silane-decomposition, it is cooled by two water-cooled copper profi les inserted into the bottom part and a water-cooled steel shell positioned at the fl ange. The distributor temperature is recorded by a thermocouple located in the underside of the distributor plate. Several fi ttings are placed on the expanded head for thermocouples, pressure transmitters etc. as well as an outlet for the product gas. The thermocouples were fi xed to a thin rod and located at 0.005, 0.15, 0.30, 0.45 and 0.70 m above the gas distributor, on the central axis of the bed. The thermocouple located 0.15 m above Figure1.Scheme of Silane pyrolysis on seed particles in a fl uidized bed reactor.the gas distributor was used for controlling bed temperature. Elutriated particles are separated by a cyclone and a fi lter. The feed- and product-gas composition are analyzed online with respect to hydrogen, oxygen, nitrogen (He, Ar) and silane by GC-analysis (Siemens RGC 202). The analysis is carried out continuously and a magnetic three-way valve switches the streams online. In addition, a oxygen-analyzer (Systech, 0 ppm – 20 %) is employed to ensure a suffi cient purging prior to the experiments. The outlet gas is fed to a combustion system and residue silane and H 2 are burned. The effl uent of the combustion system is fed to a caustic scrubber in order to hold back solid SiO 2 formed during burning. The whole set-up is fully automated and a PC is employed for process control, measurements and data storage. A safety monitoring with a defi nite shut-down procedure is integrated into the process control unit. Several more hardware based safety monitoring devices (temperature sensors, gas sensors, pressure sensors) are installed to ensure process safety. A failure leads to an immediate shut down of the reactor unit. A schematic drawing of the lab scale equipment is given in Figure 2.Experimental ProcedureThe experimental procedure is described only in general. Details (molar fractions, temperatures, etc.) will be given in the results section and respective fi gure captions. At the beginning of each experiment, the fl uidized bed reactor was fi lled with 0.5 to 0.8 kg of metallurgical grade (m.g.) Si-seed particles (98 % Si) of a desired particle distribution (in-between 160 – 800 µm) while gas was fl owing through the distributor to prevent Si particles from falling through. The corresponding initial expanded bed heights varied from 0.3 to 0.8 m, as determined by cold-fl ow experiments. The inert gas stream was adjusted to a moderate fl uidization state (2-3 u /u ) and the bed was ) a mf heated to the desired reaction temperature (923 – 973 K) in a fl ow of nitrogen. Under these conditions the hydrodynamic residence times, calculated on the basis of the superfi cial gas velocity and expanded bed height, varied from 1.5 to 3 s. The fl uidization regimen under these conditions was identifi ed as slugging. The silane line was than purged with helium. In the case of hydrogen as fl uidizing gas, the nitrogen-stream was slowly replaced and a fl ow corresponding to the desired fl uidization state was adjusted. The silane molar fraction was than increased stepwise to the desired value. The pyrolysis ofsilane was carried out for 2 to 8 h depending on the conditions. In Figure 3, the time dependency of the temperature at different reactor heights in the bed and the molar-fraction profi les of silane and nitrogen during an experiment are shown. A lower but constant temperature (about 573 K) was measured at the gas-distributor level. This is due to the cooling effect of the silane-nitrogen-gas mixtures. Nevertheless, the temperature recorded 0.005 m over the gas distributor was only about 20 K lower than that in the bed at a height of about 0.15 m (heating controller) and 0.30 m over the gas distributor, i.e. the axial temperature profi le along the bed during the experiments was to be neglected. The pressure drop along the bed was monitored as well as the change in pressure fl uctuations in order to notice plugging and agglomeration of the bed during the experiments. The silane line was purged through the reactor (under reaction conditions) and the reactor was cooled down in a fl ow of nitrogen. Silicon particles as well as dust from the cyclones and fi lters were collected, weighed, and analyzed with respect to particle size distribution by sieving or by Fraunhofer diffraction, morphology and composition. Selectivities and mass balances were calculated on basis of the amount of silicon deposited and the total silane fl ow during one experiment. The conversion of silane was calculated on the basis of the silane molar fraction at the reactor inlet and outlet as (Kojima et al., 1989):x Si i outSiH inS X SiH )iH /,4(4H in ,SiH4,iH 4H i =−n S x x x Si SiH out ut,)4H o 1(+(2)The term (1+x ) considers the volume change during the out ) cSiH4,out reaction. The error in the mass balance amounted to less than 3% in all the experiments. Concerning the reproducibility of the experiments some runs were performed under the same conditions. The results are shown in Figure 4. For the three runs, a conversion of about 80 % was achieved. The selectivity to CVD-reaction amounted in all the cases about 95 – 96% of the converted silane.ResultsAn overview of the operation range covered by this work is given in Figure 5. Experimental data published in the open literatureFigure 2.Schematic drawing of the lab-scale fl uidized bed reactor employed for investigations.Figure 3.Profi les of temperatures and molar fractions of silane and nitrogen during a run (p = 110 kPa, = total T = 923 K, = bed D = 430 µm, = Pseed g u /u = 5-4, = mf m Si,0 = 0.9 kg).were gained using small particles, up to ~ 300 µm. However, in industrial reactors large particles with an average diameter in the range of 1000 µm are fl uidized. By using larger particles and other conditions, representative for technical reactors, a reliable data basis for scale-up considerations was established. In following data on particle growth and morphology, stability of fl uidization and reactor performance will be reported.Particle Growth Rate and Main Product DistributionLong time experiments were performed as a proof of principle for the production of granular polysilicon. The analysis of the experimental results was focused on the elucidation of the rate of the particle growth and on the analysis of the change of particle morphology with its growth. The experiments were performed in a batch mode applying N 2 as diluting gas. After each experiment, the particles and dust were removed from the reactor, fi lter and cyclone. A representative part of a bed was separated and a starting mass of 0.8 kg was refi lled into the reactor as seed particles for the next experiment. After each experiment, the particle size distribution was determined. The temperature in the bed amounted to 923 K and mole fraction of silane was varied between 1% and 10%. The average molar fraction amounted to 9%. In a total time on stream of 42 h particles grew from a mean particle diameter of 350 up to 900 µm (see Figure 6). However, the particle size distribution did not change with time on stream. This effect indicates that the chemical vapor deposition occurs equally on all particles in the parameter range investigated. Since there is no accumulation of dust, it can be concluded that silicon seed particles and the deposited layer are mechanically stable. Furthermore, dust generated due to the homogeneous reactions is elutriated from the bed. Against this background a self-seeding process will not be possible, at least not in the range of reaction conditions investigated. On the other hand, there is no accumulation of larger particles which could indicate building of agglomerates. This conclusion was also confi rmed by the visual analysis of the bed content and large size fractions. The similar dependency of the particle size distribution on the time on stream was also obtained during experiments performed in hydrogen rich atmosphere.Figure 4.Results about reproducibility of experiments (p = 115 kPa,= total T = 923 K, = bed D = 415 – 450 µm, = Pseed x SiH4 = 4 – 6 %;g u /u = 6 – 4, = mf m Si,0 = 0.6 kg).Figure parison of the operation range of this work with litera-ture data.Figure parison of particle growth rates in an I.D. = 0.05 (thiswork) m and an I.D: = 0.15 m reactor (Rohatgi, 1986 b). Conditions:Rohatgi (1986 b): H 2; 923 K; 7-20 % SiH 4. This work: N 2; 923 K; 1-10 % SiH 4 and H 2; 953 K°C; 10-20 % SiH 4Figure 6.Cumulative particle size distribution as a function of total time on stream during long time batch experiments (N 2; m Si,0 = 0.6 – 0.8 kg; x SiH4= 1 – 10 %; bed bed T = 923 K).From the change of the average particle diameter therange of particle growth rates can be estimated. The particle growth rate varied between 1 and 27 µm•h -1 depending on the reaction conditions (see Figure 7). This agrees well with the growth rates reported by Rohatgi (1986 b). The increase of the growth rate with time on stream is related to the experimental procedure. Since the mass of the bed was reduced to the initial value after each several hours, the effective surface of solids available for CVD decreased. Similar production rates (about 0.1 kg/h) increase the growth rate with time on stream. Assuming conservatively that the average growth rate amounts to 20 µm/h, a total time on stream of about 40 hours will be necessary to convert seed particles with the initial diameter of 100 µm to the fi nal product particles with 900 µm diameter. Fluidizing properties depend not only on the particle diameter but are also infl uenced by the particle shape. Against this background optimum hydrodynamic conditions can depend on the method of preparation of seed particles. The fi nal shape of the particles in the bed is very insensitive to the form of seed particles (see Figure 8a, b, c). Fresh seed particles are covered on the whole surface with silicon layer. The surface of the deposited layer is rough. The sharp edges on the seed particles caused by grinding are replaced by round and broad ones. (see Figure 8c). With time particles become more and more spherical. The fi nal product is free fl owing and dense. Further results concerning the particle properties are reported in the following section. Not all dust particles are incorporated into grains in the bed. Some of the dust formed was elutriated from the bed and collected in the cyclone and fi lter. The diameter of the dust particles varied between 1 and 20 µm and the average diameter amounted to about 8 µm (see Figure 9). The microscopic analysis (Figure 10c, d) revealed that the dust particles form soft agglomerates of primary particles. These dust agglomerates can be partly separated by ultra sonic treatment. Moreover part of dust was deposited on the walls of the reactor in the separation zone. The dust deposits on the walls had powder-like properties and could easily removed from the wall by a brush.Morphology of Silicon-ParticlesThe morphology of the surface of Si deposited on seed particles and of dust collected in the cyclone was investigated using Scanning Electron Microscopy (SEM) and microscopic investigations of cross-section of particles. In order to elucidate the effect of the gas composition in the pyrolysis reactor Si-particles deposited in nitrogen and hydrogen atmosphere were analyzed. For the cross-section microscopic investigations the particles were mounted in resin, etched with a HF/HNO 3solution (1:9) and polished.Figure 8.Change of particle shape with increasing time on stream (N 2; m ,Si 0 0.6 – 0.8 kg; x SiH4 = 1 – 10 %; bed bed T = 923 K).Figure9.Particle size distribution of the dust elutriated from the reactor (N 2; m Si,0 = 0.6 – 0.8 kg; x SiH4 = 1 – 10 %;T = 923 K).= bed Figure 11.Micro graph of particles (N 2; m Si,0 = 0.6 – 0.8 kg; x SiH4: 1 – 10 %; bed T : 923 K).Figure10.Particle surface after silane decomposition in nitrogen at normal pressure, two different scales (D = 415 µm, = P ,Seed bed bed T = 923 K, <P SiH4> = 147 hPa, g u = 0.33 – 0.36 m/s, τ = 1.4 – 2.2 s). b) Particle surface after silane decomposition in hydrogen at normal pressure, two different scales (D = 415 µm, = P ,Seed T = 923 K, < = bed P SiH4> = 52 kPa, g u = 0.66 – 0.61 m/s, τ = 1.0 – 1.1 s). c) Surface of dust particles after silane decomposition in nitrogen and d) in hydrogen, experimental conditions as decribed above.Cross-section of particles illustrates the history of the particle growth (see Figure 11 a and b). A distinct discontinuity occurs at the seed/grown-shells contact. None of the seed structure propagates into the deposited material. Also a discontinuity occurs at the grown shells contact, what indicates that the particle surface suffers modifi cations between runs, maybe oxidation, which infl uence the further deposition phenomena. The shells of new material appear not as monolith as the seed particles, but they are also not porous. The dust particles are responsible for the rough surface of the grains. Dust is cemented into grains by means of CVD. The cross-section of the fi nal particles confi rms that scavenging of the fi ne Si-dust signifi cantly contributes to the particle growth, witch agrees with the observations of Rohatgi, 1986 a and b. In Figure 9 a to d SEM-pictures of the surface of silicon particles and of dust are shown. As already indicated by the analysis of the cuts of the fi nal product obtained in the nitrogen-atmosphere, the surface consists of fi ne, spherically-shaped primary particles which seem to be scavenged by the surface of the bed particles (see also Figure 11a). These primary particles exhibit a diameter of 80 to 300 nm, predominately 150 nm. Areas up to 600 nm wide can be seen where the primary particles seem to be cemented together by CVD-silicon. It has to be mentioned that no evidence was found by BET measurements that the particles are porous. In contrast, the surface of silicon particles grown in a hydrogen atmosphere (see Figure 10b) is considerably different from the material obtained under similar conditions but with nitrogen as diluting gas. The surface is much smoother. Sphere-shaped primary particles can be also recognized, but they are embedded in silicon which is deposited on the surface. The average diameter of these primary particles, determined from the SEM-pictures, was in the range of 80-200 nm, predominately about .120 nm. The dust particles formed seem also to be formed of spherical primary particles, exhibiting a slightly higher average diameter for the dust obtained in nitrogen (30 – 300 nm) thanin hydrogen (50 – 250 nm) (see Figure 10c and d). The very fi ne structure of the dust explains the low density and higher surface area of the silicon-dust. As already observed for the primary particle diameter in hydrogen, the average diameter of the primary dust particles formed in hydrogen rich atmosphere appears to be a little bit smaller resulting in a fi ner structure of the dust particle. It was found in further SEM-investigations (not shown here) that the morphology of the surface of Si-granules as shown in the fi gures for experiments in nitrogen and hydrogen above is nearly not infl uenced by changes in the hydrodynamics, e.g. change of gas velocity, particle size or the molar fraction of silane. A large change of the particle morphology was observed when the temperature was varied. With increasing reaction temperature, the surface obtained after deposition of silane in a hydrogen atmosphere becomes more and more similar to the surface obtained in nitrogen. It has to be pointed out that the dust production for those experiments at a higher temperature was higher than normal. The possibility that much more dust was scavenged by larger particles when more dust was produced in the bed can also contribute to the rougher surface of the particle.Agglomeration and Defl uidisation PhenomenaThe primary criterion for the selection of the optimum reaction conditions and reactor design is the necessity to assure a stable fl uidization. As the main problems agglomeration of particles in the bed, deposition of silicon on the reactor wall and on capillaries inside the reactor, deposition of silicon in the gas distributor and plugging of the holes in the gas distributor were identifi ed.Deposits and AgglomeratesFigure 12 shows photographs of the typical agglomeration phenomena. Silicon is deposited on the reactor wall and on internals, e.g. on the capillary used for pressure measurements. These deposits were especially intensive in the lower part of the reactor. Cooling of the elements immersed in the fl uidized bed limits application of contact thermometers for measurements of temperature in the bed. The Si-deposits are tight and upon cooling down the Si-deposits crack to smaller pieces caused by the different thermal expansion coeffi cients of silicon and steel. On the other hand, the experiments show that signifi cant deposition on the reactor walls occurs infl uencing life time of the reactor. This effect limits application of materials with quite different coeffi cients of thermal expansion compared to the silicon as inliner. The selectivity to deposits was close to the one predicted from the particle growth rate corrected by the ratio of the wall area to the total surface of the silicon particles in the bed (see Table 1).Figure12.Deposition of Si on a capillary (1) and different forms of agglomeration (2-4).Table parison of the ratio of the reactor wall surface to the total surface available for deposition and selectivity to wall-deposits as determined in the reactor (all values determined at the end of the experiment). D p , µm Expanded S / wall S Dep,exp, %Height, m (Swall+SSi)367 1.01 2.1 1.6 373 1.00 2.0 0.3 417 1.15 2.3 3.0 4601.152.54.0。