The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordi...The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.展开更多
Atom economy of the process of rare earth separation by using fluoride was discussed in this paper.We compared the atomic economic characters between the processes of vitriolic composite salt and fluoride,then stated ...Atom economy of the process of rare earth separation by using fluoride was discussed in this paper.We compared the atomic economic characters between the processes of vitriolic composite salt and fluoride,then stated that changing present rare earth producing process by green chemistry and technology transformation was the best way to make our rare earth manufacture prosperous.展开更多
以氯甲基化交联聚苯乙烯树脂(CMCPS)为载体和大分子引发剂,溴化亚铜/2,2'-联吡啶为催化剂体系,采用了表面引发原子转移自由基聚合技术(SI-ATRP),将丙烯酰胺接枝到CMCPS树脂表面,制得了新型聚丙烯酰胺树脂(PAM-CMCPS),并且用元素分...以氯甲基化交联聚苯乙烯树脂(CMCPS)为载体和大分子引发剂,溴化亚铜/2,2'-联吡啶为催化剂体系,采用了表面引发原子转移自由基聚合技术(SI-ATRP),将丙烯酰胺接枝到CMCPS树脂表面,制得了新型聚丙烯酰胺树脂(PAM-CMCPS),并且用元素分析、扫描电镜和红外光谱对其进行了表征。考察了此树脂对2,4-二氯苯氧乙酸的吸附性能、动力学和热力学参数。结果表明,此树脂对2,4-二氯苯氧乙酸的吸附量随溶液初始浓度和温度的升高而增加,当初始浓度为8 mmol/L时吸附效果最佳,树脂的静态饱和吸附容量为111.0 mg/g,Langmuir和Freundlich方程都呈现良好的拟合度。热力学平衡方程计算得ΔG<0,ΔH=268.2 k J/mol,ΔS>0,表明此吸附过程是一个自发、吸热、熵增加的过程。动力学研究表明,准二级动力学方程能较好拟合动力学实验结果,该过程符合准二级动力学模型。此PAM-CMCPS树脂应用于柑橘样品中2,4-二氯苯氧乙酸的吸附,取得了较满意的结果。展开更多
文摘The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.
基金supported by Climate Change Response Project (NRF-2019M1A2A2065612)Brainlink Project (NRF-2022H1D3A3A01081140) funded by the Ministry of Science and ICT of Korea via National Research Foundation+1 种基金by research funds from Hanhwa Solutions Chemicals (2.220990.01) and UNIST (1.190013.01)supported by the Institute for Basic Science (IBS-R019-D1)。
文摘Atom economy of the process of rare earth separation by using fluoride was discussed in this paper.We compared the atomic economic characters between the processes of vitriolic composite salt and fluoride,then stated that changing present rare earth producing process by green chemistry and technology transformation was the best way to make our rare earth manufacture prosperous.
文摘以氯甲基化交联聚苯乙烯树脂(CMCPS)为载体和大分子引发剂,溴化亚铜/2,2'-联吡啶为催化剂体系,采用了表面引发原子转移自由基聚合技术(SI-ATRP),将丙烯酰胺接枝到CMCPS树脂表面,制得了新型聚丙烯酰胺树脂(PAM-CMCPS),并且用元素分析、扫描电镜和红外光谱对其进行了表征。考察了此树脂对2,4-二氯苯氧乙酸的吸附性能、动力学和热力学参数。结果表明,此树脂对2,4-二氯苯氧乙酸的吸附量随溶液初始浓度和温度的升高而增加,当初始浓度为8 mmol/L时吸附效果最佳,树脂的静态饱和吸附容量为111.0 mg/g,Langmuir和Freundlich方程都呈现良好的拟合度。热力学平衡方程计算得ΔG<0,ΔH=268.2 k J/mol,ΔS>0,表明此吸附过程是一个自发、吸热、熵增加的过程。动力学研究表明,准二级动力学方程能较好拟合动力学实验结果,该过程符合准二级动力学模型。此PAM-CMCPS树脂应用于柑橘样品中2,4-二氯苯氧乙酸的吸附,取得了较满意的结果。
