物理化学学报 >> 2014, Vol. 30 >> Issue (3): 413-422.doi: 10.3866/PKU.WHXB201401203

理论与计算化学 上一篇    下一篇

扩散模型和凝聚模型耦合作用下胶体凝聚动力学的Monte Carlo模拟研究

熊海灵1,2, 杨志敏3,4, 李航2,3   

  1. 1 西南大学计算机与信息科学学院, 重庆 400715;
    2 西南大学土壤多尺度界面过程与调控重庆市重点实验室, 重庆 400715;
    3 西南大学资源环境学院, 重庆 400715;
    4 西南大学三峡库区生态环境教育部重点实验室, 重庆 400715
  • 收稿日期:2013-11-18 修回日期:2014-01-17 发布日期:2014-02-27
  • 通讯作者: 熊海灵 E-mail:bear@swu.edu.cn,xionghl@swu.edu.cn
  • 基金资助:

    国家自然科学基金(41271292)资助项目

Coupling Effects of Diffusive Model and Sticking Model on Aggregation Kinetics of Colloidal Particles:A Monte Carlo Simulation Study

XIONG Hai-Ling1,2, YANG Zhi-Min3,4, LI Hang2,3   

  1. 1 College of Computer and Information Science, Southwest University, Chongqing 400715, P. R. China;
    2 Chongqing Key Laboratory of Soil Multi-scale Interfacial Process, Southwest University, Chongqing 400715, P. R. China;
    3 College of Resources and Environment, Southwest University, Chongqing 400715, P. R. China;
    4 Key Laboratory of Eco-environments in Three Gorges Reservoir Region (Ministry of Education), Southwest University, Chongqing 400715, P. R. China
  • Received:2013-11-18 Revised:2014-01-17 Published:2014-02-27
  • Contact: XIONG Hai-Ling E-mail:bear@swu.edu.cn,xionghl@swu.edu.cn
  • Supported by:

    The project was supported by the National Natural Science Foundation of China (41271292).

摘要:

以扩散模型(Ds(γ)=D0×sγ)和凝聚模型(Pij(σ)=P0×(i×j)σ)为基础,对胶体体系随时间的演变、团簇大小分布及其标度关系、团簇的重均大小S(t)的变化规律以及模型对最终分形维数的影响四个角度进行了比较研究,发现扩散指数γ<0和凝聚概率指数σ >0对胶体的凝聚动力学过程有相似的影响. 本文在较宽的γσ取值范围内,对胶体的凝聚动力学进行了模拟研究,对慢速凝聚向快速凝聚的转化机理作了定量分析,并进一步分析了在团簇-团簇凝聚(CCA)模型下,得到类似扩散置限凝聚(DLA)模型的凝聚体的物理意义,结果表明:(1) γ >>0代表了体系中团簇或单粒做“定向运动”而非无规则的布朗运动的情况. 这种“定向运动”的推动力可能来自于大团簇产生的强“长程范德华力”、“电场力”等,或来自于体系边界处的外力场的作用. (2) 当σ<<0时,体系成为先快后慢的慢速凝聚,这可能对应大团簇为一排斥中心,即胶体颗粒存在“排斥力场”的现象. (3) 证实了团簇的重均大小在凝聚过程的早期按指数规律增长,而后期按幂函数规律增长的实验现象. 模拟研究还表明,胶体体系的凝聚动力学过程,在σ >0时是一个存在正反馈机制的非线性动力学过程,而在σ<0时则体现出负反馈的特征.

关键词: 扩散模型, 凝聚模型, 扩散指数, 凝聚概率指数, 凝聚动力学, Monte Carlo模拟

Abstract:

The effects of the diffusive (Ds(γ)=D0×sγ) and sticking (Pij(σ)=P0×(i×j)σ) models on the colloidal suspension evolution, cluster-size distribution and scaling, time dependence of weight-averaged cluster size, and the fractal dimensions of aggregates are investigated. Simulations of the aggregation kinetics are carried out for a wide range of diffusivity exponent γ and sticking-probability exponent σ values. γ<0 and σ >0 have similar effects on the colloidal aggregation kinetics. The mechanism of transition from slow to fast aggregation is quantitatively analyzed. The physical significance of a cluster-cluster aggregation model, leading to a diffusion-limited aggregation model, is proposed. γ >>0 corresponds to the directional movement of clusters or primary particles, rather than random Brownian motion. The driving force for this directional movement may be a strong long-range van der Waals force, electric force of the largest cluster, or external force from the boundary. σ<<0 decreases the aggregation velocity of colloidal particles, with the evolution of the colloidal suspension. This may correspond to the largest cluster being a repulsive center, and a repulsive force existing between clusters or primary particles. The simulation confirms particle aggregation involving the weight-averaged size growing exponentially at first, but obeying a power law later. The aggregation kinetics is a positive-feedback nonlinear process as σ >0, but a negative-feedback process as σ<0.

Key words: Diffusive model, Sticking model, Diffusivity exponent, Sticking-probability exponent, Aggregation kinetics, Monte Carlo simulation

MSC2000: 

  • O648