Determination of the critical micelle concentration (cmc) with the integrated concentration model

The following curve fitting examples are based on the integrated "APN" model for the concentration of surfactants near the cmc. This model provides a framework for the determination of the critical micelle concentration (cmc) of surfactants from data obtained from a variety of techniques.

Origin Data Analysis Software

We provide ready to use fitting functions for Origin Data Analysis Software (OriginLab Corporation, Northampton, MA 01060, USA) as compressed zip-archive. The functions were tested with Origin 8.5, 9.1, 2015. The functions also serve as examples for other data analysis packages.

We describe briefly the main code of each of the functions in the document APNModel_Description.pdf.

Description: APNModel_Origin_V2_1c.pdf (V2.1b, pdf-file, 450kb)

Origin-Fit functions: APN_Origin_V2_1 (V2.1, zip archive, 34kb)

Example Origin project: APNModelFunctions_Origin_Example (V2.1, zip archive, 89kb) (Fit of electrical conductivity data of SDS)

The APN-model functions can be easily implemented in typical data analysis software and can be directly fitted to experimental data in order to obtain physical parameters, and especially the cmc itself.

Microsoft Excel

We provide the APN-Model as VBA functions (macros) for Microsoft Excel. The functions were tested with Excel 2010 and 2016.

All functions can be used for nonlinear fitting (Solver) and for calculations in columns or other functions.

Description: APNModel_Excel_Manual_V2_1.pdf (V2.1b, pdf-file, 570kb)

Functions and Examples: APNModel_Excel_V2_1.zip (V2.1b, zip archive, 790kb) (Fit of electrical conductivity and surface tension data of SDS)

Python solution using scipy

Python can be used for nonlinear curve fits of the model functions to experimental data.

Example of a simple nonlinear curve fit with Python to conductivity data.

Ipython notebook.  Python. pdf-version.

Launch as azure notebook (make a copy to your library in order to be able to make edits to the notebook)

Equations for software code:

Relative total surfactant concentration:

 s0 = cS0/cmc;

Concentration of monomeric surfactant [S₁] as function of total surfactant concentration [S]₀ :

 cS1=cmc*(1-(A/2)*(sqrt(2/Pi)*r*exp(-(s0-1)^2/(2*r*r))+(s0-1)*(erf((s0-1)/(sqrt(2)*r))-1))); 

Constant A :

 A=2/(1+sqrt(2/Pi)*r*exp(-1/(2*r*r))+erf(1/sqrt(2)/r));

Licence

Fitting-Functions for the APNModel by Wajih Al-Soufi  are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.