Polymer Brush Data Processor

Christopher Kemper Ober Lab Group, Department of Materials Science and Engineering, Cornell University

Cory Bethrant, CCMR REU, Howard University

Atomic Force Microscopy (AFM) images can take up to 24 hours to retrieve data from a single sample manually. This is because the process requires multiple programs as well as multiple processes. To save the human labor and make analysis consistent without human error, a C++ based program was created to conduct automated data processing. Compared to manual processing, final automated data processing could reach 99.5% precision and the time for analysis could be reduced to less than 2 hours.

IntroductionData Processing can be very time-consuming, even in modern research; many times taking more time than actual research. In this case, AFM images had to have a cross-section collected and normalized. Then the user would have to extract, using Gwydion software, the detailed information like height and width of the cross-section from raw data. Finally, the user exports the image as an Origin-friendly file in order to calculate the integral of the cross-section. Using Origin, the area of the cross-section is calculated. This process has to be repeated twice for each scan to be processed, and usually two scans are taken of the same line. This results in a large, cumbersome process that can take up to an entire day to complete.

The program allows a user to batch collect, the height, width and area of a cross-section. This reduces manual processing down to only collecting a cross-section and normalizing it. The rest is automated. The resulting process length was reduced down to somewhere between one and two hours.

The main limitation, is that the AFM image cross-section has to be relatively clean (But some noise is filtered out).

AlgorithmThe program begins by prompting the user for the number of files that the user desires to be processed. Then it prompts for a custom sensitivity, which manually allows the user to pick if desired results aren’t achieved at default settings. The user then submits the sample name for batch execution. Then the user inputs the names of the desired lines to be processed.

The program then proceeds to allocate dynamic memory for the following:

i. slopepositiveFLAG – Indicator of whether a datasets slope is positive

ii. slopenegativeFLAG – Indicator of whether a datasets slope is negative

iii. x – Contains all x-coordinates

iv. y – Contains all y-coordinates

v. slope – Contains the slope of each dataset

Cory E. Bethrant

vi. firstDery – Contains the first derivative of each dataset with respect to y

vii. secDery – Contains the second derivative of each dataset with respect to y

viii. filename – Contains all filenames

The program then proceeds to import the data and process it. It begins by determining the slope of each dataset. Then the first derivative and second derivative of each dataset is calculated. Then the dataset is flagged as positive, negative or neither.

Data chunks of 5 are created and used to calculate a slightly longer-term data trend. The program then loops through points from the left to the right lowering the triggering slope through each iteration of the loop. Then once the program finds the point in the middle of the left border, the Program begins a scan in the left direction to find the beginning of the border. That position is then saved. The process is repeated on the right border in the opposite direction (Figure 1.1). Once the bounds of the cross-section are known it’s relatively simple for the program to calculate everything else. The baseline is an average of the two borders y-position. This is subtracted from the max y-position within the bounds to calculate the height. Then the left border x-position is subtracted from the right border to calculate the width. The program then uses numerical approximation to find the area under the curve. The information is then output to an Excel file for easy creation of a chart.

Figure 1.1 Demonstrates Program Accuracy

PerformanceAs long as the left and right border is calculated correctly, everything else will always be correct. Because of this fact, the program checks for bound-related errors such as:

i. A left-bound and right-border that is zero (No border detected).

ii. A height that is negative (Baseline incorrect due to noise).

iii. Integral that is negative or zero (Incorrect Baseline and border incorrect due to noise or no border being detected).

If any of these errors are detected scans are performed again with different sensitivity parameters. If the program still cannot process the data taking a new cross-section being sure to remove significant noise will always solve the issue.

The program has a completion time of 2 seconds per cross-section which is significantly faster than manually calculating those values. The data is also automatically placed in an Excel spreadsheet, eliminating another extra process.

The program can work with any amount of data from a single sample at once. Processing multiple samples at once can be easily added but the time savings is not significant because cross sections still have to be created the same way.

Cory E. Bethrant

2

Source Code#include <iostream>#include <cmath>#include <fstream>#include <vector>#include <string>#include <algorithm>#include <math.h>#include <new>

using namespace std;

int main(){ // Initialize Variables // int numberoflines = 0; int numberoffiles = 0; int slopeNeutralCount = 0; int slopeNegativeCount = 0; int slopePositiveCount = 0; int rightborderPOSint = 0; int leftborderPOSint = 0; int patternamount = 0; int profileamount = 0; int j = 0; int k = -1; int d = 0; string unitType; string pattern; string sample; string customsensitivity; string brlg = "------------------------------------------------------------"; string br = "-------------------------------------------"; bool rightborder = false; bool onPattern = false; bool patternDone = false; bool TrendNegative = false; bool TrendPositive = false; bool * slopepositiveFLAG; bool * slopenegativeFLAG; string * filename; double * x; double * y; double * slope; double * firstDery; double * secDery; double leftborderPOS = 0.0; double rightborderPOS = 0.0; double baseline = 0.0; double height = 0.0; double width = 0.0; double slopeTotal = 0.0; double slopeAVG = 0.0; double integral = 0.0; double sensitivity = 4;

// Print Copyright Info // cout << brlg << '\n' << "Ober Group Data Processor for Polymer Brushes" << '\n' << "Created by Cory Bethrant on 7/11/16." << '\n' << "Copyright © 2016 Cornell University. All rights reserved." << '\n' << brlg << '\n' << '\n'; // Datafile Amount Prompt // cout << "Please enter the amount of pattern lines you wish to be processed: "; cin >> patternamount; cout << "Please enter the amount of profiles for each pattern line (1/2/4/6/8): ";

cin >> profileamount; if (profileamount > 8){ cout << "Profile Amount is Too High! Please reenter the amount of profiles for each pattern line (Max is 8): "; cin >> profileamount; } numberoffiles = patternamount * profileamount; filename = new string[numberoffiles]; // Sensitivity Prompt // cout << "Would you like a custom sensitivity(Y/N)? (Default is 4)"; cin >> customsensitivity; if (customsensitivity == "y" || customsensitivity == "Y" || customsensitivity == "Yes" || customsensitivity == "YES" || customsensitivity == "yes"){ cout << "Enter custom sensitivity: " << '\n'; cin >> sensitivity; } // Find File Names and Initiate Excel File cout << "Please enter the sample name: "; cin >> sample; for (int w = 0; w < patternamount; w++){ if (w == 0) cout << "Please enter the name of the line you would like to process: "; else cout << "Please enter the name of the next line you would like to process (If you would like to go back just type a b/B): "; cin >> pattern; if (pattern == "b" || pattern == "B"){ w--; w--; } switch (profileamount) { case 1: filename[w] = sample + "_" + pattern + "0000"; break; case 2: filename[(w*2)] = sample + "_" + pattern + "0000"; filename[(w*2)+1] = sample + "_" + pattern + "0001"; break; case 4: filename[(w*4)] = sample + "_" + pattern + "0000"; filename[(w*4)+1] = sample + "_" + pattern + "0000(2)"; filename[(w*4)+2] = sample + "_" + pattern + "0001"; filename[(w*4)+3] = sample + "_" + pattern + "0001(2)"; break; case 6: filename[(w*6)] = sample + "_" + pattern + "0000"; filename[(w*6)+1] = sample + "_" + pattern + "0000(2)"; filename[(w*6)+2] = sample + "_" + pattern + "0000(3)"; filename[(w*6)+3] = sample + "_" + pattern + "0001"; filename[(w*6)+4] = sample + "_" + pattern + "0001(2)"; filename[(w*6)+5] = sample + "_" + pattern + "0001(3)"; break; case 8: filename[(w*8)] = sample + "_" + pattern + "0000"; filename[(w*8)+1] = sample + "_" + pattern + "0000(2)"; filename[(w*8)+2] = sample + "_" + pattern + "0000(3)"; filename[(w*8)+3] = sample + "_" + pattern + "0000(4)"; filename[(w*8)+4] = sample + "_" + pattern + "0001(1)"; filename[(w*8)+5] = sample + "_" + pattern + "0001(2)"; filename[(w*8)+6] = sample + "_" + pattern + "0001(3)"; filename[(w*8)+7] = sample + "_" + pattern + "0001(4)";

Cory E. Bethrant

3

break; } } ofstream MyExcelFile; MyExcelFile.open("Output.csv"); MyExcelFile << "Pattern Line, Width, Height, Integral" << endl; // Begin Data Proccess // cout << "Press Enter to begin processing data..." << '\n' << '\n'; cin.get(); // Find size of datafile // while (d < numberoffiles){ ifstream f(filename[d]); string line; for (int i = 0; getline(f, line); i++){ numberoflines = i; } cout << "Filename: " << filename[d] << '\n'; cout << "Length of Gwyddion data file: " << numberoflines << '\n' << '\n'; f.clear(); f.seekg(0); // Allocate memory // slopepositiveFLAG = new bool[numberoflines]; slopenegativeFLAG = new bool[numberoflines]; x = new double[numberoflines]; y = new double[numberoflines]; slope = new double[numberoflines]; firstDery = new double[numberoflines]; secDery = new double[numberoflines]; if (slopepositiveFLAG == nullptr || slopenegativeFLAG == nullptr || slope == nullptr || firstDery == nullptr || secDery == nullptr || x == nullptr || y == nullptr){ cout << "Error: memory could not be allocated" << '\n' << "Program Terminated. Email Cory Bethrant @ cory.bethrant@gmail." << '\n' << '\n' << "Press Enter to Close Program."<<'\n'; delete[] filename; delete[] x; delete[] y; delete[] slope; delete[] firstDery; delete[] secDery; delete[] slopepositiveFLAG; delete[] slopenegativeFLAG; cin.get(); return 0; } else // Unit type determination based on filename string // unitType = "m"; // Import Data // for (int i = 0; i <= numberoflines; i++){ f >> x[i] >> y[i]; } for (int i = 0; i < numberoflines; i++){ // Perform Calculations // slopepositiveFLAG[i] = false; slopenegativeFLAG[i] = false; slope[i] = ((y[i+1]-y[i])/(x[i+1]-x[i])); slopeTotal += slope[i]; slopeAVG = slopeTotal / 5; if ((i+1) % 5 == 0){

// Calculate Data Chunk Information // slopeAVG = (slopeTotal/(i+1)); slopeTotal = 0; } // Print Current Data Set Values and Set Flags // cout << "Data Set " << i+1 << '\n' << "x1: " << x[i] << unitType << '\t' << "y1: " << y[i] << unitType << '\n' << "x2: " << x[i+1] << unitType << '\t' << "y2: " << y[i+1] << unitType << '\n'; if (x[i+1] == y[i+1] && x[i] == y[i]){ cout << "The two data points are the same." << '\n' << '\n'; } else if ((y[i+1]-y[i])==0){ cout << "The slope of Data Set " << i+1 << " is Undefined." << '\n' << '\n'; } else if (slope[i] > 0.03){ cout << "The slope of Data Set " << i+1 << " is Positive." << '\n'; slopepositiveFLAG[i] = true; cout << "The slope of Data Set " << i+1 << " equals: " << slope[i]<< '\n' << '\n'; } else if (slope[i] < -0.03){ cout << "The slope of Data Set " << i+1 << " is Negative." << '\n'; slopenegativeFLAG[i] = true; cout << "The slope of Data Set " << i+1 << " equals: " << slope[i]<< '\n' << '\n'; } else { cout << "The slope of Data Set " << i+1 << " is Neutral." << '\n'; slopepositiveFLAG[i] = false; slopenegativeFLAG[i] = false; cout << "The slope of Data Set " << i+1 << " equals: " << slope[i]<< '\n' << '\n'; } // Determine if Pattern Border Has Been Reached // if (slope[i] > sensitivity && onPattern == false && patternDone == false){ cout << "Left Pattern Border Reached." << '\n' << '\n'; for (int f = 1; f < numberoflines; f++){ if (slopepositiveFLAG[i-f] == false && slopepositiveFLAG[i-f-1] == false){ break; } if (slopepositiveFLAG[i-f] == true){ j++; } } leftborderPOS = x[i-j-1]; leftborderPOSint = i - j - 1; onPattern = true; slopePositiveCount = 0; slopeNegativeCount = 0; slopeNeutralCount = 0; j = 0; }

Cory E. Bethrant

4

if (slope[i] < -sensitivity && onPattern == true && patternDone == false && rightborder == false){ cout << "Right Pattern Border Reached." << '\n' << '\n'; rightborder = true; rightborderPOS = x[i]; patternDone = true; slopePositiveCount = 0; slopeNegativeCount = 0; slopeNeutralCount = 0; } if (onPattern == true && rightborder == true){ if (slopenegativeFLAG[i] == true){ ; } else { onPattern = false; rightborderPOS = 0; rightborderPOS = x[i]; rightborderPOSint = i; k = -1; } } // Calculate Derivatives // double t = 10^-7; firstDery[i] = ( 4.0 / 3.0 * (y[i + 1] - y[i - 1]) / (2.0 * t) - 1.0 / 3.0 * (y[i + 2] - y[i - 2]) / (4.0 * t) ); secDery[i] = ( 4.0 / 3.0 * (firstDery[i + 1] - firstDery[i - 1]) / (2.0 * t) - 1.0 / 3.0 * (firstDery[i + 2] - firstDery[i - 2]) / (4.0 * t) ); // Print Derivative Information // if (i < 2 || i > numberoflines - 2){ cout << "First Derivative can't be calculated currently. " << '\n'; } else { cout << "First Derivative is: " << firstDery[i] << '\n'; } if (i < 4 || i > numberoflines - 4){ cout << "Second Derivative can't be calculated currently. " << '\n' << '\n' << '\n'; } else { cout << "Second Derivative is: " << secDery[i] << '\n' << '\n' << '\n' ; } // Determine Data Trend for Data Chunk // if ((i+1) % 5 == 0 && slopeAVG > 0.5 && i > 0){ cout << br << '\n' << "Data Trend for last 5 points is Positive." << '\n' << "Average Slope: " << slopeAVG << '\n' << br << '\n' << '\n'; TrendPositive = true; if (slopeAVG > 0.5){ slopePositiveCount++ ; if (slopeAVG > 2){ slopePositiveCount = 3; } } else if (slopeAVG < -0.5){ slopeNegativeCount++ ; if (slopeAVG > 2){ slopeNegativeCount = 3; } }

else { slopeNeutralCount++ ; if (slopeAVG > 2){ slopeNeutralCount = 3; } } slopeAVG = 0; } else if ((i+1) % 5 == 0 && slopeAVG < -0.5 && i > 0) { cout << br << '\n' << "Data Trend for last 5 points is Negative." << '\n' << "Average Slope: " << slopeAVG << '\n' << br << '\n' << '\n'; slopeTotal = 0; TrendNegative = true; if (slopeAVG > 0.5){ slopePositiveCount++ ; if (slopeAVG > 2){ slopePositiveCount = 3; } } else if (slopeAVG < -0.5){ slopeNegativeCount++ ; if (slopeAVG < -2){ slopeNegativeCount = 3; } } else { slopeNeutralCount++ ; if (slopeAVG > 2){ slopeNeutralCount = 3; } } slopeAVG = 0; } else if ((i+1)% 5 == 0 && i > 0){ cout << br << '\n' << "Data Trend for last 5 points is Neutral." << '\n' << "Average Slope: " << slopeAVG << '\n' << br << '\n' << '\n'; slopeTotal = 0; if (slopeAVG > 0.5){ slopePositiveCount++ ; if (slopeAVG > 2){ slopePositiveCount = 3; } } else if (slopeAVG < -0.5){ slopeNegativeCount++ ; if (slopeAVG > 2){ slopeNegativeCount = 3; } } else { slopeNeutralCount++ ; if (slopeAVG > 2){ slopeNeutralCount = 3; } } slopeAVG = 0; } } double max = 0; for(int i = leftborderPOSint; i < rightborderPOSint; i++){ if(y[i] > max) max = y[i]; // End of Data Loop // } baseline = (y[leftborderPOSint] + y[rightborderPOSint])/2; // Find Integral //

Cory E. Bethrant

5

integral = 0.0; for(int i = leftborderPOSint; i <= rightborderPOSint; i++){ integral += ((((y[i]+y[i+1])/2)-baseline)*(x[i+1]-x[i])); } // Final Calculations // height = max - baseline; width = rightborderPOS - leftborderPOS; // Error Catching (If error is detected line is rescanned with lower sensitivity) // if (width <=0 || integral <= 0 || height <= 0 || leftborderPOSint <= 0){ patternDone = false; rightborder = false; onPattern = false; patternDone = false; TrendNegative = false; TrendPositive = false; leftborderPOS = 0.0; rightborderPOS = 0.0; baseline = 0.0; height = 0.0; width = 0.0; slopeTotal = 0.0; slopeAVG = 0.0; integral = 0.0; rightborderPOSint = 0; leftborderPOSint = 0; j = 0; k = -1; for(int q = 2; q < numberoflines; q++){ for(int v = 1; (width <=0 || integral <= 0 || height <= 0 || leftborderPOSint <= 0) && v < (sensitivity / .0001); v++){ if (slope[q] > (sensitivity - (v * .0001)) && onPattern == false && patternDone == false){ for (int f = 1; f < numberoflines; f++){ if (slopepositiveFLAG[q-f] == false){ break; } if (slopepositiveFLAG[q-f] == true){ j++; } leftborderPOS = x[q-j-1]; leftborderPOSint = q - j - 1; onPattern = true; slopePositiveCount = 0; slopeNegativeCount = 0; slopeNeutralCount = 0; j = 0; } } } } for(int q = numberoflines-2; q >= 0; q--){ for(int v = 1; (width <=0 || integral <= 0 || height <= 0 || rightborderPOS == 0) && v < (sensitivity / .0001); v++){ k = -1; slopePositiveCount = 0; slopeNegativeCount = 0; slopeNeutralCount = 0; if (slope[q] < -(sensitivity - (v * .0001)) && onPattern == true && patternDone == false && rightborder == false){ rightborder = true; rightborderPOS = x[q]; if (onPattern == true && rightborder == true){ if (slopenegativeFLAG[q] == true){ ; } else { onPattern = false; patternDone = true; rightborderPOS = 0; rightborderPOS = x[q]; rightborderPOSint = q;

k = -1; } } rightborderPOS = 0; rightborderPOS = x[q]; rightborderPOSint = q; k = -1; slopePositiveCount = 0; slopeNegativeCount = 0; slopeNeutralCount = 0; } for(int i = leftborderPOSint; i < rightborderPOSint; i++){ if(y[i] > max) max = y[i]; // End of Data Loop // } } baseline = (y[leftborderPOSint] + y[rightborderPOSint])/2; if (leftborderPOSint == 0){ leftborderPOSint = 1; } // Find Integral // for(int i = leftborderPOSint; i <= rightborderPOSint; i++){ integral += ((((y[i]+y[i+1])/2)-baseline)*(x[i+1]-x[i])); } // Final Calculations // height = max - baseline; width = rightborderPOS - leftborderPOS; } } // Find Integral // integral = 0.0; for(int i = leftborderPOSint; i <= rightborderPOSint; i++){ integral += ((((y[i]+y[i+1])/2)-baseline)*(x[i+1]-x[i])); } // Output // cout << brlg << '\n' << "Final Statistics for Pattern: " << filename[d] << '\n' << "Left Border: x = " << leftborderPOS << unitType << '\n' << "Right Border: x = " << rightborderPOS << unitType << '\n' << '\n' << "Baseline Value: y = " << baseline << unitType <<'\n' << "Max: y = " << max << unitType << '\n' << "Width: x = " << width << unitType << '\n' << "Height: y = " << height << unitType << '\n' << "Integral of Pattern is: " << integral << unitType << '\n' << '\n'; // Output Data to Excel File // MyExcelFile << filename[d] << "," << width << "," << height << "," << integral << endl; // Reset Loop // patternDone = false; rightborder = false; onPattern = false; patternDone = false; TrendNegative = false; TrendPositive = false; leftborderPOS = 0.0; rightborderPOS = 0.0; baseline = 0.0; height = 0.0; width = 0.0; slopeTotal = 0.0; slopeAVG = 0.0; integral = 0.0; numberoflines = 0; slopeNeutralCount = 0; slopeNegativeCount = 0; slopePositiveCount = 0; rightborderPOSint = 0;

Cory E. Bethrant

6

leftborderPOSint = 0; j = 0; k = -1; f.clear(); f.seekg(0); f.close(); d++; } MyExcelFile.close(); // Delete All Dynamically Allocated Memory // delete[] filename; cout << "Thanks for using this program :)" << '\n' << '\n' << "Press Enter to Close..."; cin.get(); return 0; }

ConclusionSince each cross-section can be processed within 2 seconds, the time savings gained by automating this process will increase over time. The program will allow more research to be completed and less human error to occur.

AcknowledgmentsI would like to thank Wei-Liang Chen, Dr. Christopher Ober, and the Ober lab for their help and support with this project. This work was supported in part by the Cornell Center for Materials Research with funding from the Research Experience for Undergraduates program (DMR-1460428 and DMR-1120296) and the NSF PREM program (DMR-1205608). This work made use of the Cornell Center for Materials Research Shared Facilities which are supported through the NSF MRSEC program (DMR-1120296).

Cory E. Bethrant

7