物理化学学报 >> 1994, Vol. 10 >> Issue (03): 241-246.doi: 10.3866/PKU.WHXB19940310

研究论文 上一篇    下一篇

胶束形成的分形研究

李后强, 赵华明   

  1. 四川大学物理系,化学系,成都 610064
  • 收稿日期:1992-08-26 修回日期:1993-02-11 发布日期:1994-03-15
  • 通讯作者: 李后强

Fractal Studies on Micellar Formation

Li Hou-Qiang, Zhao Hua-Ming   

  1. Department of Physics, Sichuan University, Chengdu 610064; Department of Chemistry, Sichuan University, Chengdu 610064
  • Received:1992-08-26 Revised:1993-02-11 Published:1994-03-15
  • Contact: Li Hou-Qaing

摘要:

提出了测定胶束质量分维的两种新方法即粘度法和GPC-LALLS联机法,随后从动态光散射数据计算了离子型胶束SDS的分维,这些实验数值之间能互相印证.建立了放束形成过程的Laplace分形理论,计算得分维D=1.54(二级),作高级计算的分维D=1.67与前面实测值基本相符,另外,从唯象理论角度,讨论了胶束的多重分形及其热力学行为,发现有两个相变点β_c=-4和β_c=-1.并认为这两个转折分别对应着单分子<=>分形胶束<=>经典胶束结构之间的转变.

关键词: 胶束, 分形, 多重分形, 相变

Abstract:

The Mark-Houwink equation [η]=KW~α is used to determine the mass fractal dimensions of Ancelles. Here [η] being intrinsic viscosity, M beging molecular weight of micellar cluster. K, α, constants. The viscosity exponent α=(3/D-1), and the fractal dimension D may be obtained by ln[η]-InM plot, e.g. D=1.73 for Brij 35 in water and D=1.68, 1.62 for polyepichlorohydrin in tetrahydrofuran (THE) and cyclohexanone.
To determine with easy the fractal dimensions of micelles and macromolecules, a new approach, dubbed GPC-LALLS (gel permeation chromatography coupled with LALLS), has been work out by us, and the value of fractal dimension for polyepichloropydrin in THF obtained by GPC-LALLS is 1.667. The results indicate that the micellar clusters resemble the DLA. According to the Laplace fractal approach. The theoretical values of fractal dimensions of micellar clusters are obtained as D=1.54 (second order). D=1.67 (higer order) in agreement with computer simulation. In the same time. the multifractal spectrum f(α)-α of micelles are obtained and f_(max)(α)=1.75.
The multifractal thermodymics is employed to study the formation and transition of micelle. The partition function is defined as Z(β.L)=Σ_αC_αΣ_iP~β_(i,α) where C_α is the weight of configuration α. P_i, α is the growth probability of site i of configuration α, L is the system size, and β is the parameter measuring the heterogeneity of surfactant aggregation. Thereby two transition points, β_c=-4. β_c=1, for micelle aare found and set β_c=-4 corresponds the transition between surfactants and fractal micelles. and β_c=-1, the transition between fractal micelles and Euclidean structures (i.e. spherical, cylindrical, layer micelles etc.). These transitions correspond to the Brigg (5-5 nm). Porod (5-20 nm) and Guinier (20-100 nm).

Key words: Micelles, Fractals, Multifractals, Phase transition