Modification of the micro-interface adsorption model on particles with fractal theory-Langmuir, Freundlich and surface complexation adsorption model
颗粒物微界面吸附模型的分形修正——朗格缪尔(Langmuir)、弗伦德利希(Freundlich)和表面络合模型

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.