the determination of parameters of Multi-Step Adsorption Isotherm by Sequential Simplex optimization

Tolner László

Department for Soil Science and Agricultural Chemistry, Szent István University
Pater Karoly street
, H-2103 Gödöllő, Hungary
(phone: +36-30-581-0327; fax: +36-28-522-081)

Abstract. The nutrient and toxic compounds can be adsorbed on the surface of soil colloids. Investigating the adsorption of some pesticide compounds, instead of the simply asymptotic Langmuir isotherm multi-step isotherms can be obtained. In these cases a new layer is formed after the surface saturation, however, this mechanism can be described by using a new Langmuir-type isotherm. The adsorption of some compounds led to three superposition steps. The mathematical form is a nonlinear function with 8 parameters. The parameters were determined by a robust, direct optimum searching subroutine carried out by Visual basic macro made in Excel spreadsheet program which uses a simplex stepping procedure. The aim of the optimization is to minimize the residual sum of squares between measured and calculated values. The aim function can be calculated for any parameter series in the adequate dimension number. During the iteration the residual sum of squares decreases step by step, while the differences will be negligible.

Keywords: Regression; Model; Adsorption; Pesticide; Soil