擴散限制反應系統中球形載體上部分覆蓋活化體之分佈計算

Simulation of a sphere partially covered with active patches suspending in a dilute solution for diffusion-limited processes

林恪宇(Ke-Yu Lin)

指導教授 ： 吳瑞璋

中原大學/工學院/化學工程研究所/碩士(2018年)

https://doi.org/10.6840/cycu201800415

摘要

本篇研究利用加速布朗運動模擬並應用首次通過時間理論，於部份活化之單一球型載體，排列不同分佈狀態的活性綴片，透過釋放微小反應粒子經擴散作用，到達球型載體表面，並與球型載體表面之活性綴片，觸發擴散限制反應，以討論反應過程之正規化總反應速率常數kp/kf。
將分佈於部份活化之單一球型載體之活性綴片，以定量的形式由0至1，從最緊密至最鬆散的排列，定義無因次的分離指數Is，表達活性綴片分佈的特徵。經研究發現，以綴片間平均距離所計算並且量化的分離指數Is，其綴片間平均距離分佈，在綴片分離指數Is=0與Is=1以外的情況下，因綴片排列的多樣性，綴片間距離分佈有極大的落差，在計算對應的綴片間平均距離時，建議以Isg幾何平均數作為綴片的分離指數。
對於正規化總反應速率常數的結果發現，在固定綴片覆蓋率fcover下，正規化總反應速率常數與分離指數顯示出高度正相關性。另外將正規化總反應速率常數變化的靈敏度(正規化總反應速率常數對於分離指數作圖之斜率)與綴片覆蓋率作圖，其正規化總反應速率常數的變化受綴片覆蓋率與綴片尺寸影響。該變化隨綴片覆蓋率增加而提升，於fcover= 0.1~0.2時產生極大值，且最大變化出現時的綴片覆蓋率，隨綴片尺寸上升而上升。變化的極大值隨著綴片尺寸的增加而下降。

關鍵字

隨機漫步 ； 首次通過時間 ； 加速布朗動力 ； 擴散限制反應 ； 反應速率常數 ； 幾何平均 ； 算術平均

並列摘要

The normalized overall rate constant, kp/kf for diffusion-limited processes in a spheres, partially covered with active patches in diversity distribution states, is studied with the sped-up Brownian dynamic simulations. Separation index Is, is defined to quantify the characteristics of patch distribution on the sphere surfaces, with values of 0 ~ 1 corresponding to the states of the most compact and loose patch distributions, respectively. In addition, the separation index by geometric mean statistics is conclude to have a compatibity in diffusion-limited processes, it has a level deviation the deviation from different patches distribution than the arithmetic mean statistics .
The normalized overall rate constant is found to strongly correlate in a positive and linear relationship with the separation index at fixed patch coverage, fcover.
The slopes of the kp/kf vs Is lines, a measurement of the state of the distributed patches, are found to depend on patch coverages and patch sizes. The slopes exhibit the maximum value within patch coverage 0.1~0.2, but decreases as patch size increasing.

並列關鍵字

Random Walk ； First-Passage Time ； Sped-up Brownian Dynamic ； diffusion limited ； Overall Rate Constant ； Geometric mean ； Arithmetic mean

參考文獻

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