Name: Elizabeth Caldwell, Peter Book, Aaron Harrison
Professor Name: Dr. Levine
Course #: STAT 512
Due Date: March 7, 2013
Assignment: Final Project Proposal
Problem Description
The force with which individual particles adhere to a surface is of interest to the pharmaceutical,
microelectronic, and food industries. Herein we propose to determine the influence of an organic
solvent on the magnitude of adhesion between an atomic force microscopy (AFM) silicon nitride
cantilever. To determine whether or not the adhesion is affected by the addition of organic solvent to
the particle, we will need to include other variables that are inherent in the experimental process, such
as tip radius of curvature and tip location. Due to the proprietary nature of the materials in use, the
powders with 0, 2, 5 and 10 wt. % of solvent, S, will be referred to as Powder A, B, C, and D, respectively.
The pull-off (adhesion) force between a silicon nitride AFM probe and a particle was determined by
measuring the amount of deflection of the cantilever while it was pulled out of contact. This deflection
distance was then multiplied by the spring constant of the cantilever, resulting in the adhesion force in
nN. For each powder type, the cantilever was brought into contact with the surface and 100 pull-off
forces were measured at the initial spot of contact. Then the cantilever was moved 1 micron in the x
direction and another 100 forces were recorded. Next, the cantilever was moved 1 micron in the y
direction for another 100 forces. Finally, the cantilever was moved 1 micron in the –x direction for the
final 100 pull-off forces. The final result is 400 data points at one location divided into 4 spots. Two
more locations were chosen, usually on different particles, and 400 data points were recorded at each
location. All in all, there are 1200 data points for each powder. The temperature and relative humidity
were recorded at each spot and the radius of curvature of the silicon nitride tip was determined before
and after the experiments for each powder. Since the overall adhesion depends significantly on the true
area of interaction between the particle and the tip, the variables of interest in our study are the tip
radius, surface location, spot, amount of S in the particle, and for completeness, the temperature and
the relative humidity.
By taking into account all of the variables in the experiment, we hope to be able to determine whether
or not there is a statistically significant dependence of the force on the composition of the particle. If
there is not, then we hope to determine what other variables are affecting the overall adhesion so that
better force experiments may be designed for future studies.
Preliminary Analysis
An excerpt of the data is presented in the following table:
Tip ROC (nm) Location Spot Temp C Humidity Solvent wt. % Force (nN)
13
1
1
24.83
14.91
5
38.487
13
1
1
24.83
14.91
5
38.634
13
1
2
24.56
14.95
5
35.439
13
1
2
24.56
14.95
5
34.731
13
1
3
24.49
15
5
37.242
13
1
3
24.49
15
5
36.637
13
1
4
24.57
14.93
5
18.426
13
1
4
24.57
14.93
5
18.759
13
2
1
24.73
14.93
5
34.133
13
2
1
24.73
14.93
5
35.65
13
2
2
24.69
14.86
5
29.224
13
2
2
24.69
14.86
5
29.043
13
3
1
24.68
14.93
5
40.154
13
3
1
24.68
14.93
5
40.239
13
3
2
24.65
14.93
5
18.643
13
3
2
24.65
14.93
5
18.827
13
4
1
24.69
14.98
5
17.548
13
4
1
24.69
14.98
5
17.327
13
4
2
24.67
14.95
5
65.687
13
4
2
24.67
14.95
5
65.823
13
4
3
24.61
15.07
5
19.351
13
4
3
24.61
15.07
5
19.708
13
4
4
24.56
15.07
5
33.235
13
4
4
24.56
15.07
5
33.207
21
1
1
24.4
8.47
2
24.308
21
1
1
24.4
8.47
2
23.689
21
1
2
24.27
8.39
2
19.3
21
1
2
24.27
8.39
2
19.693
21
1
3
24.2
8.39
2
22.405
21
1
3
24.2
8.39
2
22.412
21
1
4
24.19
8.38
2
21.147
21
1
4
24.19
8.38
2
21.897
21
2
1
24.06
8.46
2
30.224
21
2
1
24.06
8.46
2
31.118
21
2
2
24.14
8.45
2
49.154
21
2
2
24.14
8.45
2
50.336
21
2
3
24.14
8.47
2
54.487
21
2
3
24.14
8.47
2
54.194
21
2
4
24
8.5
2
56.789
21
21
21
21
21
21
21
21
21
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
2
3
3
3
3
3
3
3
3
1
1
1
1
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
1
1
2
2
3
3
4
4
1
1
2
2
1
1
2
2
3
3
4
4
1
1
2
2
3
3
4
4
1
1
2
2
3
3
4
4
24
24.07
24.07
24.03
24.03
23.97
23.97
24.02
24.02
23.13
23.13
23.22
23.22
24.03
24.03
23.93
23.93
23.55
23.55
23.25
23.25
23.37
23.37
23.34
23.34
23.7
23.7
24.15
24.15
23.88
23.88
23.49
23.49
23.27
23.27
23.16
23.16
8.5
8.6
8.6
8.55
8.55
8.59
8.59
8.56
8.56
11.26
11.26
11.23
11.23
10.5
10.5
10.66
10.66
10.81
10.81
10.83
10.83
10.52
10.52
10.52
10.52
10.33
10.33
10.05
10.05
10.07
10.07
10.26
10.26
10.33
10.33
10.55
10.55
2
2
2
2
2
2
2
2
2
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
56.464
31.146
31.298
35.074
35.044
18.483
18.314
11.093
11.343
62.128
61.913
42.924
42.272
87.819
87.529
35.217
35.187
29.807
30.083
29.545
29.526
17.259
17.155
34.374
34.603
37.666
37.816
34.144
34.377
20.316
19.364
54.442
54.024
39.386
40.261
46.405
47.566
Preliminary Plans of Analysis
For our data sets we would like to run several multiple regression tests to determine the relationship
between the force and the composition of the different powders. After we create a model for our data
and run an ANOVA table, we would create an F-test to conclude if any of our explanatory variables help
us model the response. Aside from an F-test we can also run a multiple regression correlation test and a
scatter plot matrix to further see the possible relationships. If the data is inconclusive, we either add or
remove variables based on Type I SS and Type II SS which will show if any are cancelling each other out.