This application imports ASCII files, which have two columns of data: column 1 is the z position and column 2 is the deflection value, separated by a space. Data format is float, possible with an exponent excluding units. One typical line may look like: 1.023e-9 234.7e-9.
So, the units of the data are "m".
If your data, have differents, e.g. they are scaled in nanometers, you can use the xscaling or yscaling for correcting this, e.g. by using a scaling factor of 1e-9.
If the orientation of data is different then the example data, because your instrument uses a different definition for the sign of height or deflection data, you may use a scaling factor of "-1" to correct this. The data should look like below.
The file should include approach and retract part of the data as a continuous sequence of data as they are recorded by the AFM. So the z data will look like a triangular wave.
Using the Application
The application will analyze the force curve in a region of interest determined by delta1 and delta2. It will calculate the slope and try to fit a Hertz model to the data within this range. During the procedure it will display the part of the force curve of interest (approach or retract), the force versus indentation calculated from the data on a linear and a log-log scale, the application will also add theoretical curves based on results of the fit.
Every time you change a relevant parameter of the fit, it will redo the procedure, so the DoFit button is mostly obsolete.
If you type in a Young modulus value it will calculate a simulated force curve and force versus indentation curve based on this value
Understanding the application
The details of the fit procedure have been documented in the following book chapter (Radmacher, M., Studying the mechanics of cellular processes by atomic force microscopy, in Cell Mechanics, Y.-l. Wang and D.E. Discher, Editors. 2007, Academic Press. p. 347-372.).
The procedure is summarized briefly here:
Subtracting Deflection Offset
Since the laser spot is usually not perfectly centred on the laser diode, there will be a deflection value other than zero when the cantilever is off the surface. The application averages the first 10% of the data points, assuming they are off the surface and subtracts this value. The Raw Force Data panel shows approach and retract curves before offset subtraction.
The Force Data to Analyse panel shows either approach or retract curve after offset subtraction.
The parameters delta1 and delta2 define the range of deflection values, which are included in the analysis. Delta1 may become as small as zero. The analysis range is depicted by two green horizontal lines in the Force Data to Analyze panel and in the Force vs Indentation panel, where the deltas have been converted to the corresponding force values.
The analysis range is used for calculating the slope as well as for the Hertz fit.
The Hertz fit is implemented using a so called Levenberg Marquardt algorithm. In short, χ2 (the difference between the fit function and the data points) is minimized by varying the fit parameters. The Levenberg Marquard algorithm does this minimization in an optimized way since in addition to the fit function the derivatives of the fit function with respect to the fit parameters are used to obtain a fast and stable optimization. However the algorithm can only work reasonably, when start values sufficiently close to the expected results are provided.
The Fit Process Step by Step
1. Subtract deflection offset by averaging first 10% of data to be analysed
2. Use threshold value to determine a first guess of the contact point
3. On basis of this first guess for a contact point the force and indentation values at the two data points, where the deflection corresponds to delta1 or delta2. The fit function is inverted for these two value pairs to obtain a new guess for the contact point and the elastic modulus.
4. These two values are the starting point for the Levenberg Marquard algorithm, which will result in new values for E and δ0.
5. On the basis of this new contact point δ0 the indentation is calculated again and the Levenberg Marquard algorithm is started a second time.
6. The results of this second round are the final results
7. In addition to the numerical values, a theoretical force vs. indentation curve and a theoretical force curve are calculated and displayed at the corresponding panels.
We have tested both applets in the following configuration:
Mac OS X 10.7, 10.8, 10.9
Windows XP, Windows 7
Ubuntu Linux 10.04, 12.04
Since the applet loads data from your system, you need to grant them the necessary privileges and change the certificate.
This requires to include our website on the Java exception list and then accept the certificate.
Java Exception List
In order to do so, you have to set the appropiate exemption in the second tab of the Java Control Panel. If you feel uncomfortable with this procedure, you may download the source code and run it locally. We have used Eclipes for development.