Measurement of Frictional Forces Using Nano-R™ SPM

c) Do you want to refine the offset? (yes = 1)

(1) Type 0 or hit ENTER if offset value is correct.

(2) If you type the number incorrectly or wish to modify the offset, type 1 at this prompt. Then repeat process as in b2, according to the offset that you now see in the plot.

d) Perform lateral calibration using this image? (yes = 1) Type 1

e) Normal and lateral forces will remain in volts for lateral calibration routine. Pull_off_force_V =-2.2084 Your image should contain 2 sloped features/facets parallel to the edge of the image.
image_size =512 (pixels) and scan_size_nm =100 (nm) Specify facet 1. See plot for (lateral offset) image (rotate the image for a top view.) Input the range of pixels to include (smallest value first.) Select the first edge (integer between 1 and image pixel size):

(1) A window will appear showing in 3D the trace minus retrace friction image. Rotate the image using the rotate tool to see the image as 2D with colors giving the 3rd dimension.

(2) The colors should show you the friction image captured on the faceted surface. You should have two facets visible. Make sure you know which region the tip is going up on during the trace (this is the UP
slope) and which the tip is going down on during the trace (DOWN slope).

(3) Also the edges of n. Note the pixel numbers that enclose this region.

(5) Type in the corresponding pixel numbers to eliminate data before the first edge facet. For example, if there are about 20 pixels of unwanted data on the edge, then type 20 at first prompt.

f) Select the second edge (integer between 1 and image pixel size):

(1) Again determine what pixel number you would like to cut the facet off at.

(2) For example, if the data are good from pixel 20 to pixel 190, type 190.

g) Do you want to revise this region? (yes = 1)

(1) This prompt allows you to go back and fix things is you made an error in choosing the region.

(2) With this prompt will appear the region you have chosen, with the graph axes modified so that the beginning edge starts at pixel 1.

(3) If you hit ENTER or type anything but 1, the program will continue.

(4) If you type 1, care needs to be taken to redo the region. You will either need to remember what you think it should be in relation to the original pixel numbers, or you can type 1 and 512 to see the original image with its original numbers, and then redo the region once more.

h) Calculated lateral offset and halfwidth from each of the two sloped features. The program will output a text file with the name results.txt. This will have the space-delimited data in 5 columns and a row of data for every line of the image (512 for this example), where the columns are:
Deflection[V] Halfwidth(1)[V] LatOffset(1)[V] Halfwidth(2)[V]LatOffset(2)[V].
These columns are cantilever deflection, friction loop halfwidth on facet 1, friction loop lateral offset on facet 1, friction loop halfwidth on facet 2, and friction loop lateral offset on facet 2, respectively. This file will be created in the same folder as the original file.

4. Repeat process (step 3) for additional friction calibration files.

5. Using the output file from friction_v_load.m, plot deflection versus the other variables. Determine the slopes of each of these curves. Use Ogletree et. al. RSI (1996) to determine the lateral sensitivity factor of the cantilever/AFM system for the experiment. This will be S (non dim.).

D. Analyzing F versus L Data

1. Once the normal stiffness and normal and lateral sensitivities have been calculated, you are ready to analyze data to create fully calibrated F versus L plots. You may also go ahead an analyze F versus L data without the calibration numbers.

2. Run friction_v_load.m on actual F versus L experiment files for your sample.

a) Follow steps in C1,2,3a-c

b) Perform lateral calibration using this image? (yes = 1) Type 0 or hit ENTER.

c) Enter the normal force calibration in nN/V (none = 1 or return):

(1) Enter the value of the spring constant of the cantilever in N/m and multiply it by the normal sensitivity of the cantilever in nm/V. Enter this value at this prompt. You may multiply the numbers together at the prompt if you like.

(2) For example, if the normal spring constant of the lever is 0.05 N/m and the normal sensitivity is 100nm/V, then you can either type in 5 or 0.05*100.

(3) If the normal calibration is unknown, type 1 or hit ENTER at the prompt.

d) pull_off_force_V = -2.2084

(1) The pull-off force is measured automatically and given in either nN or V, depending on if the normal forces were calibrated or not.

e) Eliminate edges from friction trace and retrace? (yes = 1)

(1) Hit ENTER or type 0 if you do not wish to perform this operation. Note that this will need to be performed on most images, unless the scan size is so large that these edge regions can be ignored. Skip to part f).

(2) Type 1 if you wish the analysis of the image to take place on the sliding region of the images. This means that at the edges, where the tip initially sticks before sliding, will be eliminated from the analysis.

(a) Calculating friction force (or energy dissipation) from region to be specified as follows:
image_size = 512 (in pixels)
scan_size_nm = 100 (nm)
See plot for trace-retrace image. Note: rotate the image for a top view. Input the range of pixels to include (smallest value first.) Select the first edge (>=1):

(i) A window will appear showing in 3D the trace minus retrace friction image. Rotate the image using the rotate tool to see the image as 2D with colors giving the 3rd dimension.

(ii) At the beginning and end of the image, the friction trace minus retrace values will be slightly smaller than the rest of the image. We want to eliminate these regions because this is where the tip has not yet begun sliding. Note the pixel numbers where this region begins.

(iii) Type in the corresponding pixel number to eliminate the first edge. For example if there are about 20 pixels of unwanted data along the edge, then type 20 at the first prompt.

(b) Select the second edge (>=1):

(i) Note the pixel numbers where the sliding region of the image begins.

(ii) Type in the pixel number corresponding to eliminate the second edge of the image. For example if there are about 20 pixels of unwanted data along the edge, then type 490 at this prompt.

(c) Do you want to change the region? (yes = 1)

(i) The modified image will appear with this prompt. Rotate the image again using the rotate tool to see if the edge regions have been eliminated.

(ii) If the edges have successfully been eliminated, type 0 or hit ENTER.

(iii) If the edges have not been completely eliminated, type 1. You will either need to remember what you think it should be in relation to the original pixel numbers, or you can type 1 and 512 to see the original image with its original numbers, and then redo the region once more.

f) Choose friction or energy dissipation (energy = 1): Type 0 or hit ENTER.

g) Enter the lateral calibration factor in nN/V (none = 1 or return):

(1) Enter the value of the lateral calibration factor of the cantilever in nN/V. Use the value of S determined in C6 and multiply it by the normal calibration factor of the cantilever in nN/V. Enter this value at this prompt. You may multiply the numbers together at the prompt if you like.

(2) For example, if the normal spring constant of the lever is 0.05 N/m, the normal sensitivity is 100nm/V, and S=10, then you can either type in 50 or 0.05*100*10.

(3) If the lateral calibration is unknown, type 1 or hit ENTER at the prompt.

h) The program will output a text file with the name results.txt. This will have the space-delimited data in 2 columns: load data for every line (512 for this example) and friction data (trace-retrace) for every line. This file will be created in the same folder as the original file.

3. Repeat process (step 2) for additional friction calibration files.

III. Plotting Friction Data

A. Now the data is ready to be plotted in a software analysis program such as KaleidaGraph or Origin.

B. When the data are plotted you may notice some stray data points clustered around 0 nN applied load. These stray points are due to a false frictional signal measured while the tip is out of contact with the surface. From this plot, eliminate all the data points within the out-of-contact region of the curve. Then replot the FvL curve and you will have eliminated these stray points.