| 研究課題/領域番号 |
26800220
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| 研究機関 | 東北大学 |
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研究代表者 |
PACKWOOD Daniel 東北大学, 原子分子材料科学高等研究機構, 助教 (40640884)
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| 研究期間 (年度) |
2014-04-01 – 2016-03-31
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| キーワード | Charge transport / Organic crystal / Organic semiconductor / Lithium ion battery / Stochastic model / Random walk |
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| 研究実績の概要 |
Charge transport in organic crystals has properties that are difficult to explain with conventional charge transport theories: near room temperature, a) the mobility of charge carriers decreases with temperature, and b) charge carriers are relatively localised. During H26, we investigated these properties from the point-of-view of a stochastic tight-binding model, in which the electronic coupling between molecules is stochastic. This captures the strong phonon-electron coupling in organic crystals. We performed a mathematical analysis on this model (one-dimensional case) to identify the key paths that charge carriers take when they move through the crystal. It was found that charge transport takes place predominantly through paths with highly correlated stochastic modulation (highly correlated phonon motion). Based on this result, we explained properties (a) and (b) as follows. The correlation of the phonon motion decays with temperature, which explains (a). On the other hand, correlated phonon motion cannot persist far in space, which explains (b). This new type of ‘correlation-assisted charge transport’ regime lies between band-type transport and hopping-type transport, and is expected to be a basis for a unified model of charge transport in organic crystals in the future.
Publication:
D. M. Packwood et al. Charge Transport in Organic Crystals: Critical Role of Correlated Fluctuations Unveiled by Analysis of Feynman Diagrams. Journal of Chemical Physics 142, 2015, 144503
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
The first goal for this research is to identify which paths are of greatest important to charge transport in organic crystals. This has been achieved for the case of a one-dimensional crystal (see above). We have started to develop a Monte Carlo method to analyse the case of a three-dimensional, face-centered cubic lattice with realistic assumptions. In this method, the paths are mapped onto the lattice polymer model from statistical physics, and then the paths are sampled by simulating this polymer. However, it is still unclear how we can calculate the ‘importance’ of each path from this sample.
The second goal is to identify paths that make the dominant contribution to lithium ion transport in metal oxides such as LixCoO2 and LiFePO4. Over FY2014 we studied multiple random walks on a finite hexagonal lattice, where at time 0 the random walks have a non-equilibrium distribution. This is a model for lithium ion intercalation inside of LixCoO2 crystals. Then, we projected the time evolution of the entire multi-body system onto a single random walk on another lattice (this lattice is called the ‘Markov kernel’), and analyzed the Markov kernel by looking for the regions (subgraphs) of the Markov kernel which have small ‘Cheeger constants’. The Cheeger constant measures how much ‘difficult’ it is for a random walk to escape from a subgraph, and appears to be related to an entropy barrier to the intercalation process. Early calculations suggest that localised rearrangements of neighboring lithium ions during the intercalation process have high entropy barriers.
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| 今後の研究の推進方策 |
For the organic crystal part of this research, we must find a method for calculating the importance of the charge transport paths sampled by the Monte Carlo method outlined above. In the physics literature, a similar technique called ‘diagrammatic Monte Carlo’ has been used (e.g., Prokofev and Svistunov, Phys. Rev. B. 77, 020408, 2008). Over 2015, I will study this method carefully and see if it can be adapted to the current problem, however I expect that new mathematical developments of this method will be necessary. This will be carried out over 2015. After these developments, we expect that pathways with highly correlated phonon motion will play the dominant role for charge transport in 3D crystals as well.
For the lithium ion transport part of this research, we must improve our method for identifying subgraphs of the Markov kernel with small Cheeger constants. Actually, it may not be possible to perform this task well, because the Markov kernel is very complicated and it is difficult to identify subgraphs from it. We will instead collect a sample of subgraphs form the Markov kernel, and then predict the structure of subgraphs with very small Cheeger constant by using statistical techniques. To do this, I will first fit a sample of subgraphs and Cheeger constants with a kernel regression model. If this technique yield a poor fit to the data or makes unreasonable predictions, other approaches will be considered.
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| 次年度使用額が生じた理由 |
アメリカで開催されたAPS Meetingに参加する予定でしたが、科研費の計画書作成の段階でAPS Meetingの日程が発表されておらず、国内での会議と同時期のため参加できなかった為。
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| 次年度使用額の使用計画 |
並列計算機のためのハードウェア（InfiniBandコネクタ）: 50,000円
国内出張：（筑波、東京） 70,000円×2回
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