• 关键词：分形修正  微界面吸附  吸附模型(朗格缪尔、弗伦德利希、表面络合模型)

• 基金项目：国家自然科学基金资助项目(50178009)

• 赵旭
• 北京林业大学资源与环境学院环境科学学科, 北京 100083

• 王毅力
• 北京林业大学资源与环境学院环境科学学科, 北京 100083

• 郭瑾珑
• 国家环境保护总局, 北京 100035

• 韩海荣
• 北京林业大学资源与环境学院环境科学学科, 北京 100083

• 解明曙
• 北京林业大学资源与环境学院环境科学学科, 北京 100083

• 摘要：运用分形理论修正了颗粒物微界面吸附模型,建立了朗格缪尔(Langmuir)、弗伦德利希(Freundlich)和表面络合模型的分形吸附等温线方程式.其中,朗格缪尔(Langmuir)吸附等温线的分形表达式为:#=#mCe1pmP(bm+Ce1pm),指数m与颗粒物表面分维Ds的关系如下:mWaOsP2-1WrOs-2;表面络合模型的分形表达式为:#=#mCe(xpn)P(b(xpn)+C(npx),而且lgb=lg(kakb)+pH,指数xn与颗粒物表面分维Ds的关系如下:xpn WaOsP2-1 WrOs-2;相应的弗伦德利希(Freundlich)吸附等温线的分形形式分别为:#=(#mPbm)Ce1pm,#=(#mPb(xpn))C(npx)通过对文献中的数据的模拟初步讨论了分形模型的适用性,结果表明,它们具有更接近于实际的描述微界面吸附过程的能力,通过lg(xn)=lgk′+(Ds-2)lgr0计算出土壤颗粒和尾矿砂颗粒的表面分形维数分别为242和272.

• Abstract：The fractal geometry theory was used to modify micro-interface adsorption models, and the fractal adsorption isotherm equations on Langmuir, Freundlich and Surface complexation models were built. The fractal expression of the Langmuir adsorption isotherm was #=#mCe1pmP(bm+Ce1pm). In the equation, # and #m were adsorption capacity and saturation adsorption capacity respectively, Ce was the equilibrium concentration, and the power-law item of bm could correlate with the interaction affinity and space between micro-interfaces. The exponent m in the equation had such relations with the surface fractal dimension Ds of particles, cross-section area a0 or radius r0 of absorbate as WaOsP2-1WrOs-2. The surface fractal dimension Ds of particles could give structure information on the absorbent irregular surface. The higher value of Ds indicated the more rough and irregular surface structure, and the more adsorption space on the particle surface. Similarly, the surface complexation fractal model could be expressed as the following equation: #=#mCe(xpn)P(b(xpn)+C(npx), relating the parameter b to pHaslgb=lg(kakb)+pH, where kaP/kb was the ratio of the adsorption reaction rate constant to the desorption one, and also the exponent item of Pxn had relations with the surface fractal dimension Ds of particles, cross section area a0 or radius r0 of absorbate, as which Pxn was directly proportional to the a0 to the power of DsP2-1 or to the r0 to the power of Ds-2 (WaOsP2-1WrOs-2). At this time, the surface fractal dimension Ds indicated the distribution of the surface active spots.

• Key words：fractal modification  micro-interface adsorption  adsorption model (Langmuir, Freundlich and Surface complexation model)

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