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The non-stationary case of the Maxwell-Garnett theory: growth of nanomaterials (2D gold flakes) in solution
Nanoscale Advances ( IF 4.6 ) Pub Date : 2019/12/04 , DOI: 10.1039/c9na00636b
Prakash Natarajan 1 , Awad Shalabny 1 , Sumesh Sadhujan 1 , Ahmad Idilbi 1 , Muhammad Y Bashouti 1, 2
Affiliation  

The solution-based growth mechanism is a common process for nanomaterials. The Maxwell-Garnett theory (for light–matter interactions) describes the solution growth in an effective medium, homogenized by a mean electromagnetic field, which applies when materials are in a stationary phase. However, the charge transitions (inter- and intra-transitions) during the growth of nanomaterials lead to a non-stationary phase and are associated with time-dependent permittivity constant transitions (for nanomaterials). Therefore, time-independence in the standard Maxwell-Garnett theory is lost, resulting in time dependence, εi(t). This becomes important when the optical spectrum of a solution needs to be deconvoluted at different reaction times since each peak represents a specific charge/energy transfer with a specific permittivity constant. Based on this, we developed a time-resolved deconvolution approach, f(t) ∝ εi(t), which led us to identify the transitions (inter- and intra-transitions) with their dominated growth regimes. Two gold ion peaks were precisely measured (322 nm and 367 nm) for the inter-transition, and three different polyaniline oxidation states (PAOS) for the intra-transition, including A (372 nm), B (680 nm), and C (530 nm). In the initial reaction time regime (0–90 min), the permittivity constant of gold was found to be highly dependent on time, i.e. fEεi(t), since charge transfer takes place from the PAOS to gold ions (i.e. inter-transition leads to a reduction reaction). In the second time regime (90–180 min), the permittivity constant of gold changes as the material deforms from 3D to 2D (fSε3D–2D), i.e. intra-transition (combined with thermal reduction). Our approach provides a new framework for the time-dependent modelling of (an)isotropic solutions of other nanomaterials and their syntheses.

中文翻译:


麦克斯韦-加内特理论的非平稳情况:纳米材料(二维金片)在溶液中的生长



基于溶液的生长机制是纳米材料的常见过程。麦克斯韦-加内特理论(用于光与物质相互作用)描述了有效介质中溶液的生长,通过平均电磁场均匀化,该理论适用于材料处于静止相的情况。然而,纳米材料生长过程中的电荷跃迁(内部跃迁和内部跃迁)会导致非稳态相,并与时间相关的介电常数跃迁(对于纳米材料)相关。因此,标准麦克斯韦-加内特理论中的时间无关性消失,导致时间依赖性ε ( t )。当溶液的光谱需要在不同的反应时间进行解卷积时,这一点变得很重要,因为每个峰代表具有特定介电常数的特定电荷/能量转移。基于此,我们开发了一种时间分辨反卷积方法f ( t ) ∝ ε ( t ),该方法使我们能够识别转变(内部和内部转变)及其主导的增长机制。精确测量了内部跃迁的两个金离子峰(322 nm 和 367 nm),以及内部跃迁的三种不同的聚苯胺氧化态 (PAOS),包括 A (372 nm)、B (680 nm) 和 C (530 纳米)。在初始反应时间范围(0-90 分钟)中,金的介电常数被发现高度依赖于时间,即 f Eε ( t ),因为电荷从 PAOS 转移到金离子(-转变导致还原反应)。 在第二个时间范围(90–180 分钟)中,金的介电常数随着材料从 3D 变形到 2D ( f Sε 3D–2D ) 发生变化,内部转变(与热还原相结合)。我们的方法为其他纳米材料及其合成的(非)各向同性解决方案的时间相关建模提供了新的框架。
更新日期:2020-03-19
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