Formation of a Particle-Fixed Monolith for Capillary Electrochromatography and an Investigation of Intracolumn Broadening in Liquid Chromatography Karyn Mae Usher

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2005 Formation of a Particle-Fixed Monolith for Capillary Electrochromatography and an Investigation of Intracolumn Broadening in Liquid Chromatography Karyn Mae Usher

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THE FLORIDA STATE UNIVERSITY

COLLEGE OF ARTS AND SCIENCES

FORMATION OF A PARTICLE-FIXED MONOLITH FOR CAPILLARY

ELECTROCHROMATOGRAPHY AND AN INVESTIGATION OF

INTRACOLUMN BROADENING IN LIQUID CHROMATOGRAPHY

KARYN MAE USHER

A Dissertation Submitted to the Department of Chemistry and Biochemistry in partial fulfillment of the requirements for the degree of Doctor of Philosophy

Degree Awarded: Summer Semester 2005 The members of the committee approve the dissertation of Karyn Mae Usher defended on July 7, 2005.

______John G. Dorsey Professor Directing Dissertation

______Mark A. Riley Outside Committee Member

______William T. Cooper Committee Member

______Susan E. Latturner Committee Member

Approved:

______Naresh S. Dalal, Chair, Department of Chemistry and Biochemistry

The Office of Graduate Studies has verified and approved the above named committee members.

This dissertation is dedicated to my dear parents, my husband and son, Hassan and Hussein, and my brothers.

iii

ACKNOWLEDGEMENTS

I would like to thank my advisor, Dr. John G. Dorsey, for his guidance during my graduate years at Florida State University. I would also like to thank him for the supportive atmosphere that he tried to maintain within our group. It is because of his love of chemistry, particularly of the separation sciences, that I became interested in this particular field of chemistry. I would also like to thank him for being a good example of the type of instructor I would like to become. I would like to thank my parents, Rizzeria and Victor, for their love and support throughout the years. They taught me the values that have helped me to become the individual that I am today. They also taught me the importance of an education and did everything possible to help me to attain the best education possible. Special thanks to my mother for going above and beyond to help me when my son was born, and to my father for supporting her decision to do so. I would also like to thank my brothers, Victor and Alex, for being there for me whenever I needed them. Thank you to my husband, Hassan, for his love and support during my graduate career. Thanks for all the lists of things to do that you prepared so that I wouldn’t forget to do anything important. I would like to thank my son, Hussein, for his unconditional love, and for always making me feel needed and wanted. I also want to thank Hussein for making every day of my life better than the day before. Thank you to Hassan’s parents, Awatef and Hussein, and to Amir, Shadi, and Liliane for welcoming me into their family and for their love and support over the last four years. I would like to thank Kate and Pete for starting me going in the right direction in the lab, and for being great friends to me. I’d like to thank Kim and Rayna for their friendship and for all the support they offered me throughout the years. Thanks

iv to Wei, Matt, Kallol, Dave, Luxsana, Pete, Van, Kristen and Jill for their friendship and suggestions to help me with my research. Thanks to Stephanie and Sydana, for their help proofreading presentations and the good times we had in the office we shared. I’d like to thank Jason for always being willing to answer my many questions. I’d like to thank Paul for letting me share any instrument that he was using, and for helping me to fix any instrument that I wanted to use. I’d like to thank Carolyn for being my ally in the lab, and for all the great discussions we had. I’d also like to thank her for being a great friend during the five years we spent at Florida State University. I’d like to thank Joe for putting up with me when we taught 1045 recitation together. Wayne, thanks for “agreeing” that my way is always better. Also thanks to Geoff, Lori and Jennie for their friendship during the time we spent at Florida State University. I’d also like to thank Dana for all her help with Hussein and also Ursula for always babysitting Hussein when I really need the help and Bobby for computer tech support. I would like to thank my graduate committee members, Dr. Cooper, Dr. Latturner, and Dr. Riley for their time and guidance. Also, thanks to Dr. Schlenoff, Dr. Stiegman, and Dr. Striegel for their time and guidance. Thank you to the entire faculty, staff, and student body of Florida State University for making the years that I have spent here enjoyable. I want to thank the Department of Chemistry and Biochemistry and the Congress of Graduate Students for giving me generous graduate assistantships and travel support. Thanks to all the support staff in the Department of Chemistry and Biochemistry for their help.

TABLE OF CONTENTS

LIST OF TABLES x

LIST OF FIGURES xii

LIST OF ABBREVIATIONS, SYMBOLS, AND THEIR MEANINGS xix

ABSTRACT xxi

1. CHROMATOGRAPHY: DEFINITION, SIGNIFICANCE AND

APPLICATIONS 1

1.1 Chromatography 1

1.2 Reversed Phase Liquid Chromatography 2

1.3 Capillary Electrochromatography 4

1.4 Flow Through the Chromatographic System 6

1.5 Silica: The Most Commonly Used Support 9

1.6 Band Broadening 10

2. MONOLITHIC COLUMNS FOR USE IN CAPILLARY

ELECTROCHROMATOGRAPHY 14

2.1 Introduction 14

2.1.1 Monolithic Columns 14

2.1.2 Common Problems Associated with Performing

CEC Experiments 15

vi 2.1.3 Monoliths Used in Capillary Electrochromatography 16

2.1.4 Scanning Electron Microscope images of different

types of monoliths 18

2.1.5 Particle Fixed Monoliths and Their Advantages 21

2.2 Experimental 22

2.2.1 Chemicals 22

2.2.2 Materials 22

2.2.3 Instrumentation 23

2.3 Capillary Electrochromatography 24

2.4 Silica and Tris Buffers 27

2.5 Using pH Changes to Achieve Monolith Formation 30

2.6 Characterization of Monolith Using Fluorescence 32

2.7 Characterization of Monolith Using Scanning Electron

Microscopy 38

2.8 Conclusion 39

3. CHROMATOGRAPHIC ISOLATION OF BAND BROADENING

CONTRIBUTIONS 44

3.1 Introduction 44

3.2 Previous Efforts to Isolate the Contributions to Band Broadening 46

3.2.1 Using Published Equations 46

3.2.2 Horvath and Lin: Band Spreading of Unsorbed Solutes 47

3.2.3 Groh and Halász: Band Broadening in Interstitial Regions 47

3.2.4 Knox and Scott: Study of B and C terms in HPLC 48

vii 3.2.5 Magnico and Martin: Dispersion in Interstitial Space 49

3.3 Chromatographic Isolation 50

3.4 Sources of Band Broadening Experienced by Different Solutes 51

3.5 Choosing a Non-Retained Analyte 52

3.6 Choosing Retained Analytes 53

3.7 Choosing the Appropriate Mobile Phase 53

3.8 Experimental Conditions 54

3.8.1 Chemicals 54

3.8.2 Column 55

3.8.3 Instrumentation 55

3.9 Importance of Subtracting the Extracolumn Variance 58

4. INVESTIGATION OF RESISTANCE TO MASS TRANSFER IN

REVERSED PHASE LIQUID CHROMATOGRAPHY 65

4.1 Band Dispersion in the Mobile Zone 65

4.2 Experimental 66

4.3 Comparison of Plate Height Data for Retained and

Non-retained Solutes 67

4.4 Subtraction of Uracil 69

4.5 Measurement of the Diffusion Coefficient in the Mobile Phase 73

4.6 Changes in the Slope after Subtracting Uracil 75

4.7 Changes in Reduced Plate Height after Subtracting Uracil 82

5. MODELING CHROMATOGRAPHIC DISPERSION:

A COMPARISON OF POPULAR EQUATIONS 86

viii 5.1 Popular Equations Used to Model Chromatographic Dispersion 86

5.1.1 van Deemter Equation 86

5.1.2 Horvath and Lin Equation 90

5.1.3 Giddings Equation 92

5.1.4 Knox Equation 92

5.2 A Previous Study that Compared Plate Height Equations 95

5.3 Experimental 95

5.4 Comparison of Four Popular Equations 96

5.4.1 Curve Fitting: A Visual Inspection 96

5.4.2 Dependence of Fit on k’ 97

5.4.3 Comparison of the Fit of the Individual Equations to

data for 5 solutes 99

6. CONCLUSIONS 104

6.1 Chromatographic Isolation 104

6.2 Investigation of the Resistance to Mass Transfer in

the Mobile Phase 105

6.3 Using Equations to Model Chromatographic Data 105

6.4 Importance 106

APPENDIX A 108 APPENDIX B 114 APPENDIX C 120 APPENDIX D 141 REFERENCES 146 BIOGRAPHICAL SKETCH 155

LIST OF TABLES

TABLE 1. MIXING TABLE FOR TRIS BUFFER SHOWING THE NECESSARY WEIGHT IN GRAMS NEEDED TO MAKE UP ONE LITER OF 0.05 M SOLUTION, AND THE PH FOR EACH OF 67 THESE SOLUTIONS AT THREE TEMPERATURES, 5 °C, 25 °C, AND 37 °C. 29

TABLE 2. RESULTS OF PRESSURE STUDIES FOR FIVE PACKED CAPILLARIES THAT UNDERWENT THE PH EXPERIMENT. THE BUFFER USED WAS THE THIRD ENTRY IN TABLE 1, MADE WITH 6.61 G/L OF TRIZMA HCL AND 0.97 G/L OF TRIZMA BASE. CAPILLARY A AND B WERE NOT SUBJECTED TO HIGHER PRESSURE THAN THOSE RECORDED ALTHOUGH NO STATIONARY PHASE HAD BEEN LOST. CAPILLARY C WAS NOT TESTED FOR ELECTROOSMOTIC FLOW BECAUSE IT BROKE WHEN PLACED IN THE DETECTOR CELL. 32

TABLE 3. INFORMATION ABOUT THE CONDITIONS USED, AND THE PEAK OBTAINED WHEN MEASURING THE EXTRACOLUMN VARIANCE 59

TABLE 4. EFFECTIVE DIFFUSION COEFFICIENTS IN THE 60/40 ACN/H20 MOBILE PHASE AT 25°C. THESE VALUES WERE CALCULATED FROM VARIANCES FOR EACH SOLUTE USING THE ARIS-TAYLOR DISPERSION EQUATION. 75

TABLE 5. THE SLOPES CALCULATED USING THE LAST SIX POINTS IN THE PLATE HEIGHT CURVE CORRESPONDING TO REDUCED VELOCITIES GREATER THAN 16. NOTE THAT WHEN LONGER RETAINED MOLECULES ARE USED, THE SLOPE GENERALLY INCREASES; HOWEVER, WHEN THE MOBILE PHASE STRENGTH IS CHANGED AND AN ANALYTE IS LONGER RETAINED, THE SLOPE DECREASES. 79

TABLE 6. THE SLOPES CALCULATED USING THE LAST SIX POINTS IN THE PLATE HEIGHT CURVE CORRESPONDING TO REDUCED VELOCITIES GREATER THAN 16 AFTER URACIL HAS BEEN SUBTRACTED. NOTE THAT AS THE MOLECULES ARE LONGER RETAINED, THE SLOPE INCREASES. THIS IS INDEPENDENT OF THE REASON FOR THE CHANGE IN RETENTION (DIFFERENT MOLECULE OR DIFFERENT MOBILE PHASE STRENGTH). 79

TABLE 7. THE CHANGE IN THE SLOPE OF THE PLATE HEIGHT CURVE FOR REDUCED VELOCITIES ABOVE 16 AFTER THE VARIANCE ASSOCIATED WITH URACIL IS SUBTRACTED. NOTE THAT THE CHANGE IN THE SLOPE IS GENERALLY DECREASING AS THE SOLUTES ARE RETAINED LONGER, INDEPENDENT OF THE REASON FOR THE CHANGE IN RETENTION (DIFFERENT MOLECULE OR DIFFERENT MOBILE PHASE STRENGTH). 80

TABLE 8. THE REDUCED PLATE HEIGHT CALCULATED USING THE DATA FROM THE CHROMATOGRAM OBTAINED AT A FLOW RATE OF 2.5 ML/MIN. A SINGLE FLOWRATE HAD TO BE CHOSEN IN ORDER TO REPRESENT THE DATA IN A SIMPLE TABULAR FORM. 83

x TABLE 9. THE REDUCED PLATE HEIGHT CALCULATED USING THE DATA FROM THE CHROMATOGRAM OBTAINED AT A FLOW RATE OF 2.5 ML/MIN AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED. 83

TABLE 10. THE CHANGE IN THE REDUCED PLATE HEIGHT CALCULATED FROM THE CHROMATOGRAM OBTAINED AT A FLOW RATE OF 2.5 ML/MIN WHEN THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED. 84

2 TABLE 11. R VALUES FROM THE FIT OF PLATE HEIGHT DATA FOR EACH SOLUTE TO THE VAN DEEMTER EQUATION IN 60% ACN. VALUES IN ROW LABELED “SYSTEM” ARE BASED ON TOTAL PEAK VARIANCE INCLUDING EXTRACOLUMN VARIANCE. VALUES IN ROW LABELED “COLUMN” HAVE THE EXTRACOLUMN VARIANCE SUBTRACTED. 104

2 TABLE 12. R VALUES FROM THE FIT OF PLATE HEIGHT DATA FOR EACH SOLUTE TO THE VAN DEEMTER EQUATION IN 90% ACN. VALUES IN ROW LABELED “SYSTEM” ARE BASED ON TOTAL PEAK VARIANCE INCLUDING EXTRACOLUMN VARIANCE. VALUES IN ROW LABELED “COLUMN” HAVE THE EXTRACOLUMN VARIANCE SUBTRACTED. 104

TABLE 13. TABLE OF THE FIT VALUES OBTAINED FROM THE LEAST SQUARES FIT OF THE PLATE HEIGHT DATA COLLECTED FOR BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE IN 60%, 70%, 80% AND 90% ACN IN WATER TO THE VAN DEEMTER EQUATION. 143

TABLE 14. TABLE OF THE FIT VALUES OBTAINED FROM THE LEAST SQUARES FIT OF THE PLATE HEIGHT DATA COLLECTED FOR BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE IN 60%, 70%, 80% AND 90% ACN IN WATER TO THE GIDDINGS EQUATION. 144

TABLE 15. TABLE OF THE FIT VALUES OBTAINED FROM THE LEAST SQUARES FIT OF THE PLATE HEIGHT DATA COLLECTED FOR BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE IN 60%, 70%, 80% AND 90% ACN IN WATER TO THE KNOX EQUATION. 145

TABLE 16. TABLE OF THE FIT VALUES OBTAINED FROM THE LEAST SQUARES FIT OF THE PLATE HEIGHT DATA COLLECTED FOR BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE IN 60%, 70%, 80% AND 90% ACN IN WATER TO THE HORVATH AND LIN EQUATION. 146

LIST OF FIGURES

FIGURE 1. THIS SCHEMATIC DIAGRAM SHOWS THE EQUIPMENT NECESSARY FOR PERFORMING CAPILLARY ELECTROCHROMATOGRAPHY EXPERIMENTS. THE EQUIPMENT IS QUITE SIMPLE, WITH THE SIMPLEST SYSTEM CONTAINING A VOLTAGE SOURCE, SOLVENT RESERVOIRS, A DETECTOR AND THE CAPILLARY COLUMN. 5

FIGURE 2. REPRESENTATION OF THE ELECTRICAL DOUBLE LAYERS PRESENT IN CAPILLARY ELECTROCHROMATOGRAPHY. WHEN THE CAPILLARY IS PACKED, THERE ARE TWO AREAS WHERE THE ELECTRICAL DOUBLE LAYER CAN FORM, AT THE INNER SURFACE OF THE CAPILLARY, AND AROUND THE CHARGED STATIONARY PHASE 18 PARTICLES. 8

FIGURE 3. DIAGRAM SHOWING THE DIFFERENT FLOW PROFILES IN A PACKED COLUMN USING PRESSURE DRIVEN FLOW AND ELECTROOSMOTIC FLOW. WHEN PRESSURE DRIVEN FLOW IS USED, THE FLOW PROFILE IS PARABOLIC WHICH CAN LEAD TO BROADENING OF THE SOLUTE MOLECULES. WHEN ELECTROOSMOTIC FLOW IS USED, THE FLOW IS FLATTER, WHICH ALLOWS FOR BETTER SEPARATION 18 EFFICIENCIES TO BE OBSERVED. 8

FIGURE 4. SCANNING ELECTRON MICROSCOPE IMAGE OF 5 μM SPHERICAL SILICA PARTICLES PACKED INSIDE A 50 μM POLYIMIDE COATED GLASS CAPILLARY. 9

FIGURE 5. FABRICATION PROCESS USED TO PREPARE POLYMER MONOLITHS BY SVEC AND 41 COWORKERS IN 2000. 17

FIGURE 6. FABRICATION PROCESS USED TO PREPARE SOL-GEL MONOLITHS. THIS PROCESS INVOLVES USING ONLY LIQUIDS AS STARTING MATERIALS. 17

42 FIGURE 7. SEM IMAGE OF POLYMER MONOLITHS BY (A) HORVATH AND COWORKERS AND 43 (B) SVEC AND COWORKERS IN 1999. NOTE THE BULBOUS APPEARANCE OF THE MONOLITH. 18

FIGURE 8. SEM OF SOL GEL MONOLITHIC COLUMNS BY NAKANISHI AND COWORKERS IN 2000 SHOWING THEIR POROUS STRUCTURE WITH THROUGH PORES AND SILICA 44 SKELETONS. NOTE THAT THE SHAPE OF THIS MONOLITH VARIES GREATLY FROM THE POLYMER MONOLITH. 19

45 FIGURE 9. SEM IMAGE OF A SILICA ZEROGEL COLUMN PREPARED BY FIELDS IN 1996. NOTE THAT THE STRUCTURE OF THIS MONOLITH IS NOT AS REGULAR AS THE POLYMER MONOLITHS AND SOL GEL MONOLITHS SHOWN ABOVE. THIS MONOLITH IS, HOWEVER, MORE POROUS THAN THE OTHERS. 19

FIGURE 10. SEM IMAGE OF A SOL GEL COLUMN FILLED WITH ODS PARTICLES OF 3μM IN 46 DIAMETER THAT WAS PREPARED BY ZARE AND COWORKERS IN 1998. 20

xii 40 FIGURE 11. SEM IMAGE OF A SINTERED MONOLITH BY HORVATH AND COWORKERS IN 1998. THIS MONOLITH WAS PREPARED FROM A CAPILLARY COLUMN PACKED WITH 5μM PARTICLES. 20

FIGURE 12. GRAPH OF THE RESULTANT PH VS. TEMPERATURE FOR A TRIS BUFFER MADE WITH 4.88 G/L 0.05 M TRIS HCL AND 2.30 G/L 0.05 M TRIS BASE. THE PH OF THE TRIS BUFFER BECOMES LOWER AS THE TEMPERATURE IS INCREASED. THIS IS A GRAPH OF THE PH VS. TEMPERATURE FOR ENTRY NUMBER SEVEN IN TABLE 1. 28

FIGURE 13. DIAGRAM OF THE CONFOCAL FLUORESCENCE MICROSCOPE USED FOR IMAGING PACKED CAPILLARIES. THE LASER USED IS A COHERENT DPSS 532 FREQUENCY DOUBLED ND:YAG LASER. FOR THIS EXPERIMENT, IT WAS FOCUSED INTO THE SAMPLE AT A DEPTH OF 100Å. TWO SPCM CD2801 SINGLE PHOTON AVALANCHE DIODE DETECTORS THAT WERE SEPARATED BY A DISTANCE OF 570 NM WERE USED TO DETECT THE FLUORESCENCE. DIAGRAM COURTESY OF THE WESTON RESEARCH GROUP. 34

FIGURE 14. FLUORESCENCE IMAGE OF CAPILLARY COLUMN PACKED WITH 5 μM BARE SILICA PARTICLES AND IMAGED USING RHODAMINE B FLUORESCENT DYE. ALTHOUGH THE IMAGE IS NOT EXTREMELY SHARP, THE SPHERICAL SILICA PARTICLES CAN BE SEEN INSIDE THE CAPILLARY TUBE. THE LOWER RIGHT OF THE CAPILLARY IS DARK BECAUSE THE STATIONARY PHASE PARTICLES IN THIS AREA FELL OUT WHEN THE CAPILLARY WAS FRACTURED. 35

FIGURE 15. HERE IS A TWO DIMENSIONAL REPRESENTATION OF THE APPARENT CROSS SECTIONAL AREA OF THE SILICA PARTICLES DEPENDENT ON THE DEPTH AT WHICH THE FLUORESCENCE MEASUREMENT IS MADE. IF THE CONFOCAL MICROSCOPE IS SET TO A DEPTH THAT IS NEAR THE CENTER OF THE PARTICLE, THE PARTICLE APPEARS LARGER THAN IF IT IS FOCUSING NEAR THE TOP OR BOTTOM OF THE PARTICLE. 36

FIGURE 16. FLUORESCENCE IMAGE OF A DIFFERENT SEGMENT OF THE PREVIOUSLY SHOWN PACKED CAPILLARY AFTER IT WAS SUBJECTED TO THE PH EXPERIMENT. IN THIS IMAGE, IT IS OBVIOUS THAT THERE HAVE BEEN SOME CHANGES TO THE SILICA PARTICLES. THEY NO LONGER APPEAR SPHERICAL, AND THEY APPEAR TO BE LARGER THAN IN THE PREVIOUS IMAGE. 37

FIGURE 17. DIAGRAM OF SCANNING ELECTRON MICROSCOPE USED TO IMAGE THE CUT SURFACE OF PACKED CAPILLARIES. 41

FIGURE 18. SEM IMAGE OF A 75 μM CAPILLARY PACKED WITH 5 μM BARE SILICA STATIONARY PHASE PARTICLES. THIS IS NOT THE SAME CAPILLARY THAT WAS SHOWN IN THE FLUORESCENCE STUDIES; HOWEVER, A DARK AREA, WHERE SILICA HAS FALLEN OUT OF THE FRACTURED CAPILLARY, IS ALSO SEEN. 42

FIGURE 19. SEM IMAGE OF THE PACKED CAPILLARY SHOWN IN FIGURE 13 AFTER THE PH EXPERIMENT HAS BEEN PERFORMED. THIS IS ANOTHER SEGMENT OF THE SAME CAPILLARY THAT WAS SHOWN IN THE PREVIOUS IMAGE AFTER IT HAS UNDERGONE THE PH EXPERIMENT. THERE ARE MANY OBVIOUS DIFFERENCES. THERE ARE NO AREAS WHERE SILICA HAS FALLEN OUT. THE PARTICLES ARE NO LONGER SPHERICAL, AND THEY ARE MUCH LARGER. IT IS NOT OBVIOUS WHETHER OR NOT THE PARTICLES ARE ATTACHED TO ONE ANOTHER OR THE CAPILLARY WALL, BUT SINCE NO STATIONARY PHASE PARTICLES HAVE FALLEN OUT, THIS IS LIKELY. 43

FIGURE 20. GRAPH OF PEAK OBTAINED WHEN MEASURING THE EXTRACOLUMN VARIANCE OF THE CHROMATOGRAPHIC SYSTEM. 59

xiii FIGURE 21. PICTURE SHOWING THE ZERO DEAD VOLUME UNION USED TO REPLACE THE CHROMATOGRAPHIC COLUMN IN ORDER TO MEASURE THE EXTRACOLUMN VARIANCE. 62

FIGURE 22. GRAPH OF THE EXTRACOLUMN VARIANCE FOR THE LIQUID CHROMATOGRAPHY SYSTEM USED FOR THIS STUDY. 62

FIGURE 23. GRAPH SHOWING THE DATA WITH AND WITHOUT THE EXTRACOLUMN VARIANCE SUBTRACTED. THE POINTS REPRESENT THE TOTAL VARIANCE (COLUMN AND EXTRACOLUMN VARIANCE) AND THE LOWER CURVE REPRESENTS THE COLUMN VARIANCE (EXTRACOLUMN VARIANCE SUBTRACTED). THE K’ FOR BENZENE AT THESE MOBILE PHASE STRENGTHS IS AS FOLLOWS: 70% ACN, K’=1.4; 80% ACN, K’=0.9; AND 90% ACN, K’=0.5 64

FIGURE 24. GRAPH OF REDUCED PLATE HEIGHT VS. REDUCED VELOCITY FOR URACIL. NOTE THAT AS DISCUSSED IN SECTION 4.3, THE CURVE IS NOT SMOOTH. SOLID LINES WERE PLACED ON THE GRAPH TO GUIDE THE EYE AND ARE NOT MEANT TO IMPLY CONTINUITY BETWEEN DATA POINTS. 68

FIGURE 25. GRAPH OF REDUCED PLATE HEIGHT VS. REDUCED VELOCITY FOR TOLUENE. NOTE THAT THIS GRAPH, LIKE THE GRAPH OF REDUCED PLATE HEIGHT FOR URACIL, IS ALSO NOT SMOOTH. SOLID LINES WERE PLACED ON THE GRAPH TO GUIDE THE EYE AND ARE NOT MEANT TO IMPLY CONTINUITY BETWEEN DATA POINTS. 68

FIGURE 26. GRAPH OF REDUCED PLATE HEIGHT VS. REDUCED VELOCITY FOR TOLUENE. THIS GRAPH SHOWS THE UNEVENNESS OF THE CURVE AS DESCRIBED PREVIOUSLY. SOLID LINES WERE PLACED ON THE GRAPH TO GUIDE THE EYE AND ARE NOT MEANT TO IMPLY CONTINUITY BETWEEN DATA POINTS. 70

FIGURE 27. GRAPH OF REMAINING REDUCED PLATE HEIGHT VS. REDUCED VELOCITY FOR TOLUENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED. NOTE THAT THE SUBTRACTION PERFORMED HAS SMOOTHED THE CURVES GREATLY. THE SIGNIFICANCE OF THIS IS DISCUSSED IN THE FOLLOWING SECTIONS. SOLID LINES WERE PLACED ON THE GRAPH TO GUIDE THE EYE AND ARE NOT MEANT TO IMPLY CONTINUITY BETWEEN DATA POINTS. 70

FIGURE 28. GRAPH OF REDUCED PLATE HEIGHT VS REDUCED VELOCITY FOR BENZENE (REDUCED VELOCITIES GREATER THAN 16). NOTE THAT THE LINES ARE CONVERGING AND IN SOME CASES HAVE INTERSECTED WITH ONE ANOTHER. 77

FIGURE 29. GRAPH OF REDUCED PLATE HEIGHT VS. REDUCED VELOCITY FOR BENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL HAS BEEN SUBTRACTED. NOTE THAT THE SLOPES OF THE LINES HAVE CHANGED GREATLY, AND THE LOWEST LINE CORRESPONDING TO THE STRONGEST MOBILE PHASE COMPOSITION IS DIVERGING FROM THE OTHER LINES. ALSO NOTE THAT THE TREND LINES APPEAR TO BETTER FIT THE DATA POINTS. 77

FIGURE 30. GRAPH OF REDUCED PLATE HEIGHT VS. REDUCED VELOCITY FOR BUTYLBENZENE (REDUCED VELOCITIES GREATER THAN 16). NOTE THAT THE LINES ARE CONVERGING AND INTERSECTING ONE ANOTHER. 78

FIGURE 31. GRAPH OF REDUCED PLATE HEIGHT VS. REDUCED VELOCITY FOR BUTYLBENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL HAS BEEN SUBTRACTED. NOTE THAT ALTHOUGH THE UPPER THREE LINES ARE STILL CONVERGING THEY ARE NO LONGER OVERLAPPING, AND THE LOWER LINE, CORRESPONDING TO THE

xiv STRONGEST MOBILE PHASE COMPOSITION IS ACTUALLY DIVERGING FROM THE OTHER LINES. 78

FIGURE 32. CONTRIBUTIONS TO PLATE HEIGHT AS DESCRIBED BY VAN DEEMTER AND COWORKERS IN 1956. THE REGION OF THE GRAPH CORRESPONDING TO LOW LINEAR VELOCITIES IS DOMINATED BY MOLECULAR DIFFUSION, WHEREAS THE REGION OF THE GRAPH CORRESPONDING TO HIGH LINEAR VELOCITIES IS DOMINATED BY RESISTANCE TO MASS TRANSFER IN THE STATIONARY PHASE. THE CONTRIBUTION TO PLATE HEIGHT FROM EDDY DISPERSION IS SHOWN TO BE INDEPENDENT OF THE FLOW RATE; THEREFORE, HAVING THE SAME CONTRIBUTION OVER THE ENTIRE RANGE OF REDUCED VELOCITIES. 88

FIGURE 33. MATHEMATICAL FIT OF THE VAN DEEMTER EQUATION TO BENZENE PLATE HEIGHT DATA COLLECTED USING MOBILE PHASES WITH VARYING PERCENT ACETONITRILE. THE EXTRACOLUMN VARIANCE HAS BEEN SUBTRACTED FROM THE TOTAL VARIANCE, SO THIS IS A PLOT OF COLUMN VARIANCE FOR BENZENE. 98

2 FIGURE 34. R VALUES VS. K’ FOR THE FIT OF THE VAN DEEMTER EQUATION TO EACH SOLUTE USING MOBILE PHASES WITH VARYING PERCENT ACN. THE DOTTED LINE SHOWS 2 THE POINT WHERE THE R VALUES BEGIN TO LEVEL OFF FOR ALL THE MOBILE PHASE COMPOSITIONS USED IN THIS STUDY. AT A K’ VALUE OF APPROXIMATELY 2 3, THE R VALUE PEAKS AT ABOUT 0.999 REGARDLESS OF MOBILE PHASE COMPOSITION. THE POINTS ON EACH CURVE REPRESENT THE FIVE RETAINED SOLUTES, BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE GOING FROM LEFT TO RIGHT. 100

FIGURE 35. FIT VALUES CALCULATED WHEN THE DATA COLLECTED FOR EACH SOLUTE WERE FITTED USING FOUR POPULAR PLATE HEIGHT EQUATIONS. ANALYTES: B = BENZENE, T = TOLUENE, E = ETHYLBENZENE, P = PROPYLBENZENE, AND BU = BUTYLBENZENE. 102

FIGURE 36. FIT VALUES CALCULATED WHEN THE DATA COLLECTED FOR EACH SOLUTE WERE FITTED USING FOUR POPULAR PLATE HEIGHT EQUATIONS. ANALYTES: B = BENZENE, T = TOLUENE, E = ETHYLBENZENE, P = PROPYLBENZENE, AND BU = BUTYLBENZENE. 102

FIGURE 37. FIT VALUES CALCULATED WHEN THE DATA COLLECTED FOR EACH SOLUTE WERE FITTED USING FOUR POPULAR PLATE HEIGHT EQUATIONS. ANALYTES: B = BENZENE, T = TOLUENE, E = ETHYLBENZENE, P = PROPYLBENZENE, AND BU = BUTYLBENZENE. 103

FIGURE 38. FIT VALUES CALCULATED WHEN THE DATA COLLECTED FOR EACH SOLUTE WERE FITTED USING FOUR POPULAR PLATE HEIGHT EQUATIONS. ANALYTES: B = BENZENE, T = TOLUENE, E = ETHYLBENZENE, P = PROPYLBENZENE, AND BU = BUTYLBENZENE. 103

FIGURE 39. GRAPH OF THE REDUCED PLATE HEIGHT DATA COLLECTED FOR BENZENE. NOTE THAT NONE OF THE CURVES ARE SMOOTH. 110

FIGURE 40. GRAPH OF THE EFFECTIVE REDUCED PLATE HEIGHT FOR BENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED. NOTE THAT THE CURVES HAVE BEEN VISIBLY SMOOTHED. 110

FIGURE 41. GRAPH OF THE REDUCED PLATE HEIGHT DATA COLLECTED FOR TOLUENE. NOTE THAT NONE OF THE CURVES ARE SMOOTH. 111

xv FIGURE 42. GRAPH OF THE EFFECTIVE REDUCED PLATE HEIGHT FOR TOLUENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED. NOTE THAT THE CURVES HAVE BEEN VISIBLY SMOOTHED. 111

FIGURE 43. GRAPH OF THE REDUCED PLATE HEIGHT DATA COLLECTED FOR ETHYLBENZENE. NOTE THAT NONE OF THE CURVES ARE SMOOTH. 112

FIGURE 44. GRAPH OF THE EFFECTIVE REDUCED PLATE HEIGHT DATA COLLECTED FOR ETHYLBENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED. NOTE THAT THE CURVES HAVE BEEN VISIBLY SMOOTHED. 112

FIGURE 45. GRAPH OF THE REDUCED PLATE HEIGHT DATA COLLECTED FOR PROPYLBENZENE. NOTE THAT THE CURVES ARE FAIRLY SMOOTH. 113

FIGURE 46. GRAPH OF THE EFFECTIVE REDUCED PLATE HEIGHT DATA FOR PROPYLBENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED. THE SMOOTHING EFFECT OF THE SUBTRACTION OF THE VARIANCE ASSOCIATED WITH URACIL IS NO LONGER VISIBLE. 113

FIGURE 47. GRAPH OF THE REDUCED PLATE HEIGHT DATA COLLECTED FOR BUTYLBENZENE. NOTE THAT THE CURVES ARE FAIRLY SMOOTH. 114

FIGURE 48. GRAPH OF THE EFFECTIVE REDUCED PLATE HEIGHT FOR BUTYLBENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED. THE SMOOTHING EFFECT OF THE SUBTRACTION OF THE VARIANCE ASSOCIATED WITH URACIL IS NO LONGER VISIBLE. 114

FIGURE 49. GRAPH OF THE PLATE HEIGHT DATA FOR BENZENE ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 116

FIGURE 50. GRAPH OF THE PLATE HEIGHT DATA FOR BENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 116

FIGURE 51. GRAPH OF THE PLATE HEIGHT DATA FOR TOLUENE ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 117

FIGURE 52. GRAPH OF THE PLATE HEIGHT DATA FOR TOLUENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 117

FIGURE 53. GRAPH OF THE PLATE HEIGHT DATA FOR ETHYLBENZENE ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 118

FIGURE 54. GRAPH OF THE PLATE HEIGHT DATA FOR ETHYLBENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 118

FIGURE 55. GRAPH OF THE PLATE HEIGHT DATA FOR PROPYLBENZENE ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 119

xvi FIGURE 56. GRAPH OF THE PLATE HEIGHT DATA FOR PROPYLBENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 119

FIGURE 57. GRAPH OF THE PLATE HEIGHT DATA FOR BUTYLBENZENE ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 120

FIGURE 58. GRAPH OF THE PLATE HEIGHT DATA FOR BUTYLBENZENE AFTER THE VARIANCE ASSOCIATED WITH URACIL WAS SUBTRACTED ALONG WITH THE VAN DEEMTER FIT WHICH WAS USED TO CALCULATE THE SLOPE OF THE CURVE IN THIS REGION. 120

FIGURE 59. GRAPH OF THE PLATE HEIGHT DATA FOR BENZENE PLOTTED ALONG WITH THE VAN DEEMTER FIT OF THE DATA. 122

FIGURE 60. GRAPH OF THE PLATE HEIGHT DATA FOR TOLUENE PLOTTED ALONG WITH THE VAN DEEMTER FIT OF THE DATA. 123

FIGURE 61. GRAPH OF THE PLATE HEIGHT DATA FOR ETHYLBENZENE PLOTTED ALONG WITH THE VAN DEEMTER FIT OF THE DATA. 124

FIGURE 62. GRAPH OF THE PLATE HEIGHT DATA FOR PROPYLBENZENE PLOTTED ALONG WITH THE VAN DEEMTER FIT OF THE DATA. 125

FIGURE 63. GRAPH OF THE PLATE HEIGHT DATA FOR BUTYLBENZENE PLOTTED ALONG WITH THE VAN DEEMTER FIT OF THE DATA. 126

FIGURE 64. GRAPH OF THE PLATE HEIGHT DATA FOR BENZENE PLOTTED ALONG WITH THE GIDDINGS FIT OF THE DATA. 127

FIGURE 65. GRAPH OF THE PLATE HEIGHT DATA FOR TOLUENE PLOTTED ALONG WITH THE GIDDINGS FIT OF THE DATA. 128

FIGURE 66. GRAPH OF THE PLATE HEIGHT DATA FOR ETHYLBENZENE PLOTTED ALONG WITH THE GIDDINGS FIT OF THE DATA. 129

FIGURE 67. GRAPH OF THE PLATE HEIGHT DATA FOR PROPYLBENZENE PLOTTED ALONG WITH THE GIDDINGS FIT OF THE DATA. 130

FIGURE 68. GRAPH OF THE PLATE HEIGHT DATA FOR BUTYLBENZENE PLOTTED ALONG WITH THE GIDDINGS FIT OF THE DATA. 131

FIGURE 69. GRAPH OF THE PLATE HEIGHT DATA FOR BENZENE PLOTTED ALONG WITH THE KNOX FIT OF THE DATA. 132

FIGURE 70. GRAPH OF THE PLATE HEIGHT DATA FOR TOLUENE PLOTTED ALONG WITH THE KNOX FIT OF THE DATA. 133

FIGURE 71. GRAPH OF THE PLATE HEIGHT DATA FOR ETHYLBENZENE PLOTTED ALONG WITH THE KNOX FIT OF THE DATA. 134

FIGURE 72. GRAPH OF THE PLATE HEIGHT DATA FOR PROPYLBENZENE PLOTTED ALONG WITH THE KNOX FIT OF THE DATA. 135

FIGURE 73. GRAPH OF THE PLATE HEIGHT DATA FOR BUTYLBENZENE PLOTTED ALONG WITH THE KNOX FIT OF THE DATA. 136

xvii FIGURE 74. GRAPH OF THE PLATE HEIGHT DATA FOR BENZENE PLOTTED ALONG WITH THE HORVATH AND LIN FIT OF THE DATA. 137

FIGURE 75. GRAPH OF THE PLATE HEIGHT DATA FOR TOLUENE PLOTTED ALONG WITH THE HORVATH AND LIN FIT OF THE DATA. 138

FIGURE 76. GRAPH OF THE PLATE HEIGHT DATA FOR ETHYLBENZENE PLOTTED ALONG WITH THE HORVATH AND LIN FIT OF THE DATA. 139

FIGURE 77. GRAPH OF THE PLATE HEIGHT DATA FOR PROPYLBENZENE PLOTTED ALONG WITH THE HORVATH AND LIN FIT OF THE DATA. 140

FIGURE 78. GRAPH OF THE PLATE HEIGHT DATA FOR BUTYLBENZENE PLOTTED ALONG WITH THE HORVATH AND LIN FIT OF THE DATA. 141

FIGURE 79. GRAPH OF THE FIT VALUES OBTAINED FROM THE LEAST SQUARES FIT OF THE PLATE HEIGHT DATA TO THE VAN DEEMTER EQUATION. THE FIT VALUES ARE PLOTTED AGAINST THE K’ FOR THE FIVE SOLUTES USED IN THIS STUDY. THE POINTS ON EACH CURVE FROM LEFT TO RIGHT REPRESENT BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE. 143

FIGURE 80. GRAPH OF THE FIT VALUES OBTAINED FROM THE LEAST SQUARES FIT OF THE PLATE HEIGHT DATA TO THE GIDDINGS EQUATION. THE FIT VALUES ARE PLOTTED AGAINST THE K’ FOR THE FIVE SOLUTES USED IN THIS STUDY. THE POINTS ON EACH CURVE FROM LEFT TO RIGHT REPRESENT BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE. 144

FIGURE 81. GRAPH OF THE FIT VALUES OBTAINED FROM THE LEAST SQUARES FIT OF THE PLATE HEIGHT DATA TO THE KNOX EQUATION. THE FIT VALUES ARE PLOTTED AGAINST THE K’ FOR THE FIVE SOLUTES USED IN THIS STUDY. THE POINTS ON EACH CURVE FROM LEFT TO RIGHT REPRESENT BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE. 145

FIGURE 82. GRAPH OF THE FIT VALUES OBTAINED FROM THE LEAST SQUARES FIT OF THE PLATE HEIGHT DATA TO THE HORVATH AND LIN EQUATION. THE FIT VALUES ARE PLOTTED AGAINST THE K’ FOR THE FIVE SOLUTES USED IN THIS STUDY. THE POINTS ON EACH CURVE FROM LEFT TO RIGHT REPRESENT BENZENE, TOLUENE, ETHYLBENZENE, PROPYLBENZENE AND BUTYLBENZENE. 146

xviii LIST OF ABBREVIATIONS, SYMBOLS, AND THEIR MEANINGS

Abbreviations

CE Capillary Electrophoresis CEC Capillary Electrochromatography EMG Exponentially Modified Gaussian EOF Electroosmotic Flow HPLC High Performance Liquid Chromatography RMT Resistance to Mass Transfer RP-HPLC Reversed Phase High Performance Liquid Chromatography SEM Scanning Electron Microscope

Symbols

General

A eddy diffusion term B molecular diffusion term B/A a measure of the peak asymmetry at 10% peak height C resistance to mass transfer term

CM resistance to mass transfer in the mobile phase term

CS resistance to mass transfer in the stationary phase term dt diameter of open tube D diffusion coefficient, D RMT in stagnant layer surrounding particles

DM effective diffusion coefficient in the mobile phase

DS effective diffusion coefficient in the stationary phase dp stationary phase particle diameter d mean distance to emerge from a particle of packing E applied potential E diffusion inside stagnant mobile phase in pores h reduced plate height H plate height

xix HM,D diffusion contribution to the RMT in mobile phase k’ retention factor, ratio of solute in stationary phase to mobile phase k” ratio of solute in stationary zone to mobile zone L length of the column N empirically determined variable (0.2-0.5) N Number of Theoretical Plates Δp pressure drop across the column

2 2 q’ d / d p ⋅ Ds r distance the eluent flows in a given time R2 fit value t time tR retention time u linear velocity ue interstitial velocity uM velocity of a non-retained analyte

V0 void volume w packing factor W width of the peak at the base

W0.1 width of the peak at ten percent peak height

W1/2 width of the peak at half height

Greek

α empirical constant β empirical constant ε porosity of the stationary phase

εo permittivity of a vacuum

εr dielectric constant of the mobile phase η viscosity of the mobile phase σ2 variance ν reduced velocity vee linear velocity of the mobile phase (pressure driven flow)

υeo linear velocity of the mobile phase (EOF) Ψ shape parameter ζ zeta potential

ABSTRACT

The stationary phase used in a chromatography column and the way it is packed inside the column greatly influences the separation in a chromatographic system. In capillary electrochromatography, the column plays an even more vital role than in high performance liquid chromatography, since it acts as both the separation element and where the flow is generated. Traditional capillary electrochromatography columns have problems stemming from use of frits, which cause bubble formation and band broadening. They also suffer from movement of the charged stationary phase particles during separation, leading to spaces in the packed bed known as gapping. It has been suggested that these problems may be overcome by the use of monoliths for capillary electrochromatography experiments. The first part of this dissertation describes the formation of a particle fixed monolith, which uses no frit during the separation, and can be made by adding a few easy steps to the traditional method for making a capillary electrochromatography column by slurry packing.

The second part of the dissertation discusses band broadening in high performance liquid chromatography. High performance liquid chromatography is used in many branches of science and it represents an approximately two billion dollar a year industry. Although this technique has been around for over 30 years, there are still many unanswered questions regarding the fundamental processes that contribute to band broadening in the chromatographic system. In 1956, van Deemter described the band broadening in a chromatographic system with equation [1]. The A term represents eddy diffusion, the B term represents molecular diffusion, the C term represents resistance to mass transfer and u is the mobile phase velocity. Other equations have since been introduced to model efficiency data, and these include the equations of Giddings, Huber and Hulsman, Horvath and Lin, and Knox.

xxi This creates a plight for chromatographers who then need to decide what equation to use since all the equations are based on different theories. All the equations offer similar fits, so it may not seem particularly important which equation one uses. However, if the efficiency data is to be used to try and improve column technology, then the importance of the equation that is chosen becomes evident.

B H = A + + Cu [1] u

By choosing solutes that experience only one or two known types of broadening, it is possible to chromatographically isolate the contributions to band broadening. Such a chromatographic isolation of the band broadening contributions is theoretically better than previously used methods because the experiments would be performed under normal chromatographic conditions. A series of experiments using uracil, benzene, toluene, ethylbenzene, propylbenzene and butylbenzene has been completed, and this data has given additional information about these processes. In the final portion of the dissertation, the four equations mentioned above were used to model plate height data, and the resultant fits were compared. The information presented in this study is useful for chromatographers who need to choose one of the equations to model their data.

xxii

CHAPTER ONE

CHROMATOGRAPHY: DEFINITION, SIGNIFICANCE AND APPLICATIONS

1.1 Chromatography

Chromatography is a separation technique that is used in virtually all branches of science and technology. In 1950, Zechmeister summarized the feelings of scientists of that time by stating that chromatography should be considered a scientific tool, and scientists that utilize that tool should not be referred to as chromatographers.1 Today many scientists focus on chromatography as their main field of research. The title “chromatographer” has gone from a much disliked label to that of a well respected scientist.2 In the chromatographic process, a mixture is introduced into the system that has been chosen for the separation, and as the mixture passes through the system different types of molecules will move at different migration rates, thus effecting a separation. Chromatography is the most widely used of all separation techniques, and this is because of its versatility and its separation power. It is a very powerful method that can analyze even extremely complex mixtures. There are two main categories of chromatography, liquid chromatography and gas chromatography. Within these two categories there are many different modes that can be utilized, and these differ in many features, such as the size of the columns used, the packing materials, or even the pressures and temperatures at which the separation is performed. It is usually possible to find a chromatographic

1 technique that is well suited to whatever analysis needs to be performed, due to the many different types available. There are many things that can be varied when performing chromatographic experiments. These include changing the type of mobile phase, the mechanism of retention, the incoming solute concentration profile, the column and planar procedures, the gradient methods, dimensionality, or even just the physical scale of the column. Each of these changes can be used to enhance the separation from a poor separation to a good separation. Although chromatography is widely used and embraced by scientists involved in many different types of research, there are still many questions about some of the fundamental aspects of this technique. Many of these questions have been investigated previously, but there has been no agreement in the literature about the theory behind many of the fundamental processes. Although everyday it becomes possible to perform more and more difficult separations, each time one of these difficult separations is achieved a more difficult one presents itself. Because of this, there is still a need for scientists to perform fundamental research in this field. Perhaps if the mechanisms behind the separations can be better understood, scientists can decide how to go about improving the technique. By doing so, chromatography can become an even more useful technique.

1.2 Reversed Phase Liquid Chromatography

Liquid chromatography was invented in 1903 by a Russian botanist named Mikhail S. Tswett. He separated the pigments in green leaves using a chalk column. It was not until the 1960’s that more emphasis was placed on developing liquid chromatography as an analytical technique. The chromatographic separation in liquid chromatography takes place in a chromatographic column that is packed with stationary phase particles. The stationary phase is most commonly made up of spherically shaped porous, inert solids. A liquid mobile phase is used to move solutes through the chromatography column, and it is the interaction of the analytes with the stationary phase that effects the separation. During the time that the analyte spends in the column, there

2 are two things that are occurring, the differential migration of the different compounds in the sample that was injected, and the spreading of the molecules of each type of solute as they traverse the column.3 The differential migration refers to the different speeds that different analyte molecules take to travel the length of the column. This is what actually causes the separation. The second effect, the spreading of the molecules of each type of solute, works against the chromatographer, because it results in spreading of the solute band and reduction in column efficiency and resolution. This will be discussed in great detail later. In the late 1960’s, a new type of stationary phase, made of chemically bonded phases, was introduced. Chromatography that was performed using these phases was known as reversed phase chromatography.3 In reversed-phase high performance liquid chromatography (RP-HPLC) a solid support, usually silica, with a hydrophobic, low polarity stationary phase chemically bonded to it is usually used. A liquid mobile phase and high pressures are used to push the mixture through a column packed with the modified solid support towards a detector. The mobile phase is usually a mixture of water with a polar organic solvent such as methanol or acetonitrile. A solvent delivery system, often a reciprocating piston pump with a pressure limit of approximately 6000 PSI, is used to push the pressurized mobile phase of the required composition and flow rate through the chromatography column toward the detector. The pumps typically used for analytical studies are constant volume pumps. The sample is usually introduced into the system via a six port valve injector. The injector has a sample loop that allows for a reproducible volume of the sample to be injected each time. After the sample loop is filled, the valve is turned, and the mobile phase is allowed to flow through the sample loop and push the sample onto the head of the column. The sample is then forced to make its way through the column to the detector. Many different detection systems can be employed, including but not limited to UV detectors, refractive index detectors, fluorescence detectors, electrochemical detectors and mass spectrometers.4 The instrumentation used for liquid chromatography can vary greatly in features and cost depending on the type of separation that is required.5, 6

3 1.3 Capillary Electrochromatography

In 1974 Pretorius described using an electric field applied across a glass chromatographic column in order to perform separations.7 Jorgenson and Lukacs, in 1981, used an electric field imposed across a packed capillary column to perform chromatographic separations, thus expanding on this idea.8 Today, this form of separations is called capillary electrochromatography. This is a mode of chromatography which is a hybrid technique between high performance liquid chromatography (HPLC) and Capillary Electrophoresis (CE). In capillary electrochromatography, the chromatographic separation takes place in a column which consists of a capillary packed with an HPLC packing material. At present, three types of CEC columns are used, open tubular columns, particle-packed column, and monolithic columns, the latter being the newest type of column available. A voltage is imposed across the packed capillary, thus generating electroosmotic flow (EOF) through the capillary. This flow, like the flow in HPLC, moves the mixture through the column and towards the detector. In this case, however, both differential partitioning and electrophoretic migration of the solutes is occurring at the same time, and both lead to the separation in CEC. In CEC charged solutes are separated by electrophoresis, while uncharged solutes are separated due to the interactions that the analytes can have with the stationary phase. For CEC, the column technology is the most important aspect of the separation, and is where most improvements in the technique will have to be made. This is because unlike LC which uses a separate pump to push the mixture through the column, in CEC the column is where both the separation occurs and the flow is generated.9 In CEC, since the flow is maintained by an electric field and not by pressure, the mobile phase velocity is independent of the particle size and the radial flow profile is relatively flat. Because of this, columns can be longer, and they can be packed with smaller particles. Such columns give higher separation efficiencies and higher peak capacity. Over the past 20 years, the interest in capillary electrochromatography has increased rapidly. This technique is seen as a niche technique that can be used in situations where the separation requires much higher column efficiencies and higher peak capacities than are typically achieved in traditional HPLC techniques. Another benefit of

4 using CEC instead of HPLC, when applicable, is that there is less solvent consumption. This is simply a result of the CEC column being very small, usually a coated glass capillary with an inner tube diameter of 50 μm to 75 μm.

DETECTION SYSTEM

Packed Capillary

HIGH VOLTAGE SOURCE Mobile Phase Reservoirs

Figure 1. This schematic diagram shows the equipment necessary for performing capillary electrochromatography experiments. The equipment is quite simple, with the simplest system containing a voltage source, solvent reservoirs, a detector and the capillary column.

1.4 Flow Through the Chromatographic System

One major difference between HPLC and CEC is the way the flow is generated. In CEC, the surface of the stationary phase is mainly responsible for generating the flow that drives the separation.3, 10 The stationary phases used should be charged, and so silica-based bonded phases are particularly well suited for such separations. The methods for preparing these stationary phases are well developed, and many different types of functionalities are available. The unreacted silanols that remain after a derivatization reaction is performed are useful for this technique because they allow for the generation of the EOF. Differences in the amount of residual silanols can affect the flow in CEC greatly, and the degree of protonation of the silanols at the pH being used is also an issue. The flow profile in CE is plug-like, and this flow profile minimizes the eddy diffusion contribution to band broadening. This plug-like profile thus increases the efficiency of a separation when compared to a system that uses pressure as the driving force. A pressure driven system would have a flow profile that is parabolic with the linear velocity in the center being the highest. Recent studies have shown that the flow profiles for EOF through packed beds as in CEC may not be exactly plug-like, but the flow profile is still much flatter than that observed in pressure driven systems.11-13 This leads to less axial dispersion of the analyte band, which gives higher efficiencies in CEC than in traditional HPLC. CEC provides highly efficient separations, in relatively short periods of time with low solvent consumption. CEC was given a lot of attention in the mid 1990’s and the number of papers written about the technique grew exponentially. However, due to technical difficulties including difficulties with packing small particles14 and formation of frits15, 16, the further development of this method was slowed. The interest in monolithic columns is helping to once again revive this technique. In electrokinetically driven systems, there is another factor that leads to the increase in efficiency over pressure driven systems. In such systems, the flow has no dependence on the particle size or the column length as shown in Equation 1. In pressure

6 driven systems, the pressure of the system and the particle size and column length are related as shown in Equation 2, the Kozeny Carmen equation.17

Equation 1 (ε ε ζE) υ = or eo η

Equation 2 ε d 22 Δp v = p ee 180()1−ε 2ηLΨ 2

In Equation 1, υeo is the linear velocity of the mobile phase, εr is the

dielectric constant of the mobile phase, εo is the permittivity of a vacuum, ζ is the zeta potential, E is the applied potential, and η is the viscosity of the mobile phase. In

Equation 2, vee is the linear velocity of the mobile phase, ε is the porosity of the stationary

phase, dp is the particle diameter, Δp is the pressure drop across the column, η is the viscosity of the mobile phase, Ψ is the shape parameter, and L is the length of the column. From these equations, one can see that whereas pressure is one of the major limiting factors in HPLC, when using CEC, theoretically much longer columns and much smaller particles can be used. Although not shown by the equations, there are limitations to this. The use of longer columns requires higher voltages for the same applied potential, and using very small particles makes the packed capillaries more difficult to prepare.14

Figure 2. Representation of the electrical double layers present in Capillary Electrochromatography. When the capillary is packed, there are two areas where the electrical double layer can form, at the inner surface of the capillary, and around the charged stationary phase particles.18

Figure 3. Diagram showing the different flow profiles in a packed column using pressure driven flow and electroosmotic flow. When pressure driven flow is used, the flow profile is parabolic which can lead to broadening of the solute molecules. When electroosmotic flow is used, the flow is flatter, which allows for better separation efficiencies to be observed.18

8 1.5 Silica: The Most Commonly Used Support

The solid support most commonly used for stationary phases in liquid chromatography is silica.19-25 The silica used for this purpose usually has the following parameters: 3-10μm particle size, narrow particle size distribution (usually within 10% of the mean)22, 26, 27, 70-300 Å pore size, and surface area of 50-250 m2/g. Silica with these properties is relatively easy to manufacture, and methods producing well controlled and specifically tailored pore morphologies and surface areas are available.28 Another property that makes silica ideal as a stationary phase support is that its surface can be made to readily react with different chemical species that provide the functionality required for different separations. Figure 4 shows a scanning electron microscope image of stationary phase particles. This image is of a 75 μm capillary packed with traditional liquid chromatography stationary phase taken by our laboratory. The stationary phase shown is 5 μm bare silica. Some of the stationary phase is seen outside the column, and that was simply stationary phase that fell out of the column after the frit was removed in order to image the stationary phase particles.

10μm

Figure 4. Scanning Electron Microscope image of 5 μm spherical silica particles packed inside a 50 μm polyimide coated glass capillary.

1.6 Band Broadening

In liquid chromatography, the solutes are injected into the system as a finite band. If a solution containing several different compounds is injected onto the columnm then this injected band will be separated into several bands corresponding to each injected analyte. These analyte bands that are each composed of one type of molecule become broadened as they pass through the column and the connecting tubing. This broadening is due to several different processes that occur as the analytes move through the column, and is one of the limiting factors that must be considered when performing chromatographic separations. The processes that cause this broadening are the following: Eddy diffusion, longitudinal diffusion, mobile phase mass transfer, stagnant mobile phase mass transfer and stationary phase mass transfer. For a more in depth description of these contributions to band broadening please read section 5.1. The broadening of solutes is typically described by the number of theoretical plates for the column (N). The number of theoretical plates is a descriptor of column efficiency, it tells the ability of a given column to provide narrow bands and therefore good separations relative to other columns. The band broadening that an analyte band undergoes is directly proportional to the time that the analyte is retained in the column. The number of theoretical plates (N) is a ratio of the retention time of the peak to the width of the peak. Therefore the narrower the peak, the higher the number of theoretical plates will be. The more theoretical plates a column has, the more efficient it is. Assuming a Gaussian peak, Equation 3 can be used to calculate the number of theoretical plates. In the equation, tR is the retention time of the solute of interest, and W is the width at the base.

Equation 3 2 ⎛ t ⎞ N =16⎜ R ⎟ ⎝W ⎠

10 This equation can be modified to use the width at half height instead of the width of the base. This gives the benefit of not having to determine where the peak begins and ends near the baseline, which can often be ambiguous. The modified equation is given in

Equation 4, where W1/2 means the width at half height.

Equation 4 2 ⎛ ⎞ ⎜ t ⎟ N = 54.5 ⎜ R ⎟ ⎜W1 ⎟ ⎝ 2 ⎠

Because of the band broadening processes discussed earlier, the peaks observed in liquid chromatography are rarely Gaussian and very large errors can result from using these equations for calculating column efficiency.29, 30 Chromatographic peaks can better be approximated by using an exponentially modified Gaussian (EMG) as suggested by Foley and Dorsey in 1983. The equation used to calculate the efficiency values for a peak that can best be approximated as an EMG is given in Equation 5, the Foley-Dorsey equation.31, 32

Equation 5 2 ⎛ t ⎞ 7.41 ⎜ R ⎟ ⎜W ⎟ N = ⎝ 1.0 ⎠ B 25.1 + A

In Equation 5, tR is the retention time of the analyte, W0.1 is the width at ten percent of the peak maximum, B is the width from the center of the peak to the tail end of the peak at ten percent, and A is the width from the front end of the peak to the center of the peak. The B/A value can be used to compare the asymmetry of different peaks. As the value becomes closer to one, the peak is more symmetrical and approaching a Gaussian shape. If the B/A value is less than one, the peak is fronting. In this case, the B/A value must be inverted before calculating the number of theoretical plates using the Foley-Dorsey Equation. This equation is valid for peak with B/A values in the range of 1.01 to 2.76.31

11 The number of theoretical plates is a function of column length, so if columns of different lengths are to be compared, this value needs to be normalized for length. When the number of theoretical plates is normalized for length, the resulting value is called the plate height. The plate height represents the efficiency of a given column per unit length of the column. In order to rate the separating efficiency and therefore the usefulness of HPLC columns, one can calculate this efficiency parameter which can then be used to compare different columns. The plate height in liquid chromatography is analogous to the plate height in distillation theory.33 The plate height describes the separating power of the chromatography column, and the smaller the plate height, the more efficient the column. The plate height is the number of theoretical plates normalized for the length of the column as shown in Equation 6. Because the plate height is independent of column length, chromatographers can use a compound to calculate the plate height of several different columns that have the same size stationary phase particles, and the values obtained can be directly compared to one another.

Equation 6 L H = N

Although 5μm particles are most commonly used, there are many different sizes of stationary phase particles for use in HPLC. The plate height is dependent on the particle size of the stationary phase, and therefore cannot be used to compare columns with different sized stationary phase particles. For this purpose, there is yet another normalization that can be performed in order to compare columns that are packed with different sized particles. To do this, one divides the plate height by the particle diameter as shown in Equation 7. This yields a reduced parameter that Knox introduced as the reduced plate height.34-37 The reduced plate height allows chromatographers to use the efficiency data collected for a single analyte in order to compare columns of different length and packed with different sized stationary phase particles.

Equation 7 H h = d p

In HPLC, it is preferable to have narrow bands in order to obtain better separations. As the bands broaden more and more, the peak capacity of the column is decreased. The peak capacity refers to the number of peaks that can possible be separated, using the chosen conditions, in a certain window of time. If the peak capacity is decreased, it becomes more difficult to perform separations.

CHAPTER TWO

MONOLITHIC COLUMNS FOR USE IN CAPILLARY ELECTROCHROMATOGRAPHY

2.1 Introduction

2.1.1 Monolithic Columns

Although there has been much interest in capillary electrochromatography (CEC) over the last 20 years, there have also been many limitations associated with the technique. Most of the first columns used for capillary electrochromatography were just miniaturized versions of existing HPLC column technology. Over the past ten years, a new type of column technology, monolithic columns, has emerged for both HPLC and capillary electrochromatography. Monolithic columns are being carefully studied and appear to offer many benefits over the traditional stationary phases currently used. This new technology has attracted much attention in the field and promises to make capillary electrochromatography a more viable separation option. A monolith is a single porous solid. The monolithic column being used for capillary electrochromatography utilizes the same coated glass tubing, but instead of being packed with spherical particles, it contains a single porous solid as the separation element. Initially, the monolithic columns for CEC contained swollen hydrophilic polyacrylamide gel, like the capillary columns used for capillary gel electrophoresis. It has since been determined that the mechanism of separation in these monoliths was size

14 exclusion.38 The next type of monoliths to surface in the literature were more hydrophobic monoliths that were covalently attached to the capillary wall.39 These types of monoliths required the use of aqueous buffer/acetonitrile mobile phases, and performed much better that the hydrophilic monoliths. In these columns, the mode of separation was different than in the hydrophilic monolith columns. The use of monoliths for capillary electrochromatography has made it unnecessary to use frits to hold the stationary phase in the column during the separation. This impacts the performance, stability and reproducibility of the capillary columns greatly, because frits can negatively affect these three features of a column. A monolith formed inside the capillary is often attached to the capillary wall, which is an added benefit that makes the column even more stable. Since a monolith forms a continuous bed inside the capillary, this helps to overcome many of the common problems associated with capillary electrochromatography experiments.

2.1.2 Common Problems Associated with Performing CEC Experiments

There two major problems associated with performing CEC experiments with the available column technology. The first one involves the need for frits to retain the stationary phase inside the column. The frits used for this purpose are usually formed in the capillary column, as opposed to frits used in liquid chromatography which are fitted onto the column at each end. The frits in CEC are formed either from the stationary phase material, or from another material such as a sol-gel or a polymer. The retaining frit, once formed, should be highly porous and very rigid, and this is often times difficult to achieve. When frits with these features are made there are often problems with bubble formation, they may cause the efficiency of the column to be lowered9, or they may lead to a decrease in reproducibility of retention times. The second problem involves the movement of the stationary phase particles from their positions in the column by either pressure during flushing, or by the influence of the high electric field. If this occurs, this causes a change in the properties of the column, which leads to irreproducibility of the separation. This movement of stationary phase particles is called gapping. To combat these problems, many researchers have tried using monolithic columns, which use a single porous solid as the separation element. These types of columns are fritless, have

15 high permeability, and are mechanically strong. Since the stationary phase is a porous solid, this eliminates the possibility of gapping. In most cases, monolithic columns also allow for increased throughput and decreased analysis times. Many types of monoliths that are not silica based have been presented in the literature, as have several sol-gel based monoliths. Since the chromatography associated with C18 derivatized silica is fairly well understood, using a traditional liquid chromatography stationary phase as the starting materials for a monolith is an interesting way to approach this idea.

2.1.3 Monoliths Used in Capillary Electrochromatography

As discussed before, monolithic columns have been used to try to overcome some of the major difficulties encountered when performing CEC experiments. The two main types of monolithic columns are organic polymer based monoliths and silica based monoliths. Polymer based monoliths have good pH stability, and are easier to prepare than packed columns. They do have major disadvantages such as problems with shrinkage and swelling, which may result in the reduction of permeability. This would potentially change the properties of the column during use.9 Figure 5 shows a simplified method describing how most polymer based monolithic columns are prepared. Silica based monoliths are made by two main methods, the sol gel method and by converting a traditionally packed column into a monolith. Columns formed by the sol gel method use no particles, just simply a sol gel solution, and are formed in a single step process like that shown in Figure 6. This type of monolith is chromatographically favorable, and very porous. The sol gel is also bonded to the inner walls of the capillary, giving it even more mechanical stability. Another method for making a monolithic column is to make a traditionally packed column by packing silica particles into the column and then using some method of irreversible agglomeration to convert this to a monolithic column. A monolith made by this method is known as a particle fixed monolith. At present, the most common way of producing this type of monolith is by sintering.40 Figures 7 through 11 show the several scanning electron microscope images of different types of monoliths. From these, it can be seen that monoliths made by different techniques can have very different features.

16 Bare Capillary Polymerization Mixture

Filled Capillary

(B ) Polym erization Thermal UV Initiation Initiation

M onolithic Capillary Column

Figure 5. Fabrication process used to prepare polymer monoliths by Svec and coworkers in 2000.41

HO,2 acid, Macropore Mesopore polymer Formation Formation Si(OCH ) 34 Drying and Heat Treatments Aging and starting Ph a se sol Se p a ra t i o n So l v e n t and Gelation Exchange

Su r f a c e Modification

Figure 6. Fabrication Process used to prepare sol-gel monoliths. This process involves using only liquids as starting materials.

17 2.1.4 Scanning Electron Microscope images of different types of monoliths

Figure 7. SEM image of polymer monoliths by (a) Horvath and coworkers42 and (b) Svec and coworkers43 in 1999. Note the bulbous appearance of the monolith.

Figure 8. SEM of sol gel monolithic columns by Nakanishi and coworkers in 2000 showing their porous structure with through pores and silica skeletons.44 Note that the shape of this monolith varies greatly from the polymer monolith.

Figure 9. SEM image of a silica zerogel column prepared by Fields in 1996.45 Note that the structure of this monolith is not as regular as the polymer monoliths and sol gel monoliths shown above. This monolith is, however, more porous than the others.

Figure 10. SEM image of a sol gel column filled with ODS particles of 3μm in diameter that was prepared by Zare and coworkers in 1998.46

Figure 11. SEM image of a sintered monolith by Horvath and coworkers in 1998.40 This monolith was prepared from a capillary column packed with 5μm particles.

2.1.5 Particle Fixed Monoliths and Their Advantages

Particle fixed monoliths have many advantages and disadvantages. Because they are prepared from traditionally packed columns, some typical advantages associated with monoliths are not present. In such a column, it is not expected that the porosity of the column would be greater than that of the traditional column, so this benefit of monolithic columns would not be applicable in this situation. However, there are still benefits to forming a monolithic column that is made by converting a traditionally packed column into a monolith. This type of monolith will have similar properties to the precursor column, but it would be more mechanically stable. This type of treatment prevents gapping, which is the formation of discontinuities in the bed structure due to the particles being dislocated40, and such a column would have the benefit of not having frits. As described earlier, frits are thought to cause many problems in CEC, including but not limited to the level of difficulty in preparation, and the lack of reproducibility. Frits are believed to act as catalysts for bubble formation, and they have an unpredictable influence on electroosmotic flow and band-broadening. At the point where the packed bed meets the frit there is a disturbance in the column bed, and this causes a change in the electroosmotic flow through the capillary. Horvath and coworkers made a particle fixed monolith in 1998 by packing a capillary with 6μm octadecylated particles, using frits during the packing process. Once the column was packed, it was washed with water to remove the packing solvent, then it

was rinsed with 0.1M NaHCO3, followed by water, and finally with acetone. The column

was then purged with N2 to dry it. It was then heated at 120°C for 5 hours, then at 360°C for 10 hours. The columns were then rinsed with acetone a final time. This method removed much of the C18 groups from the particles, so an in situ octadecylation procedure was performed. This was performed using a solution of 20% (v/v) dimethyloctadecylchlorosilane and 10% (v/v) pyridine in toluene. This solution was pumped through the sintered column in an oven at 100°C for six hours.40 An SEM image of this sintered monolith can be seen in Figure 11. In this chapter, the preparation of a particle-fixed monolithic column for capillary electrochromatography will be discussed. By using a buffer that has a large pH

21 temperature coefficient, a capillary column packed with spherical silica particles was converted into a particle fixed monolith. Pressure studies were performed on these columns, to determine the strength of the monolith, and fluorescence and scanning electron microscope images were taken in order to study the monolith.

2.2 Experimental

2.2.1 Chemicals

Tris hydrochloride (Tris[hydroxymethyl]amino-methane hydrochloride) reagent grade, minimum 99.9% by titration from the Sigma Chemical Company and Tris base (Tris[hydroxymethyl]amino-methane) from the Sigma Chemical Company were used to prepare the buffers used for formation of the monolith. The buffer solutions were made using a Tris buffer mixing table. These tables are readily available from many sources and give pH information for a variety of different temperatures. One must be certain to thoroughly desiccate the components before preparing the buffer. If this is done, it is possible to weigh the correct ratio and achieve the predicted pH with an accuracy of ± 0.05. This is of great importance since it has been indicated that certain pH electrodes do not give accurate pH readings when used with tris buffers.47, 48 This error is believed to arise from a reaction between the tris and the reference electrode, and it results in long equilibration times among other things. Acetone used in capillary electrochromatography experiments as a sample component was certified A.C.S. Spectranalyzed and obtained from Fisher Scientific.

2.2.2 Materials

The hollow capillary tubing used to prepare capillary columns for the electrochromatography experiments was purchased from Polymicro Technologies. Three different sizes were used in the experiments. The largest size used was larger in both inner diameter and outer diameter. The inner diameter as indicated by the supplier ranged from 529μm to532 μm from the beginning of the reel to the end of the reel. The

22 outer diameter ranged from 693 nm to 696 nm from the beginning of the reel to the end of the reel. The poly-imide coating thickness ranged from 22 nm to 24 nm. This capillary’s outer diameter was too large to fit in the detector cell, so columns prepared with this tubing could not be tested for electroosmotic flow. Another size of capillary used had an inner diameter ranging from 150 μm - 149 μm over the length of the reel, and an outer diameter ranging from 365 nm – 366 nm over the length of the reel. The coating thickness was 17 nm – 18 nm. The capillary tubing used for the majority of the experiments had an inner diameter of 73 μm as reported by the supplier, an outer diameter of 357 nm, and coating thickness ranging from 18.5 nm to 17.5 nm. All the capillary electrochromatography experiments to determine if the columns could produce electroosmotic flow were performed using this tubing. The silica used was obtained from Stellar Phases, Inc. It was AstroSil™ silica lot number 7-102F3. The pore size (nitrogen, average pore) was 106 Angstroms; the pore volume (nitrogen, single point) was 0.9 mL/gram; the surface area (nitrogen, BET multipoint) was 325 sq. m/gram; the apparent density (tap density) was 0.45 grams/mL; the particles size (microscopic analysis) was 5.0 micrometers, and the particle distribution (dp90/dp10) was 1.5.

2.2.3 Instrumentation

The silica slurries were prepared by mixing the required amount of silica in the slurry solvent of choice, then sonicating them for at least 5 minutes using a Fisher Scientific FS30 ultrasonic cleaner. This helped to evenly distribute the silica particles throughout the slurry mixture. The pump used for packing the capillary columns, filling them with the required solutions and mobile phases, and performing the pressure experiments was an ISCO Model 100DM Syringe Pump along with an ISCO Series D Pump Controller. The pump’s cylinder capacity was 102.93 mL. The UV light source used to prepare the photopolymerized frits was a model UVL-56 Black Ray Lamp with Longwave UV-366 nm, 115 V, 60 Hz, and 0.16 A. The capillary electrochromatography system used for the experiments was made up of an ISCO CV4 Capillary Electrophoresis Absorbance Detector that utilized a deuterium lamp. The wavelength chosen for these experiments was 254 nm. The detector

23 sensitivity was set to 1.0, the rise time was set to 0.40 sec, and the corresponding time constant was 0.18 sec. A Spellman CZE1000R power supply from Spellman High Voltage Electronics Corporation was used to supply the necessary voltages.

2.3 Capillary Electrochromatography

In traditional CEC, the column is made by first forming a frit at one end of the capillary. In this research, sol gel frits will primarily be used. The frit is used to retain the stationary phase in the capillary during the packing process. Next, either slurry49-61, electrokinetic62-64, centripetal, or supercritical fluid65, 66 methods are used to pack the capillary with the selected stationary phase. After the capillary is packed past the desired length, it is heated at the desired position to create an outlet frit. The excess stationary phase is then flushed out of the capillary. Finally, a small portion of the polyimide coating of the capillary is burned off to form the detection window. The capillary is then placed in the appropriate cassette for the detector being used and flushed with the solvent of choice. In order to connect the capillary to the pump to flush solvents through it both for packing purposes and for filling the capillary with mobile phase, a ferrule assembly had to be made. For this, a short piece of orange peek tubing, approximately one inch long, of inner diameter 0.020 inch was cut and slipped over the end of the capillary. A universal ferrule and a male nut were slipped over the peek tubing, and tightened into a zero dead volume union. This created a ferrule assembly with a permanently crimped ferrule that could then be slipped on and off the capillary whenever it was needed. Care was taken not to tighten the assembly onto the union too tight, as this would crush the end of the glass capillary, thus restricting flow. Two types of frits were used in this study, a sol-gel frit, and a photopolymerized frit. Both of these frits are made by filling a portion of the capillary with a solution, then allowing it to solidify to form a porous frit. The sol-gel solution was made by mixing 750 μL of Kasil (potassium silicate) (1624) with 118 μL of formamide in a glass vial. Dry capillaries that had been measured and pre-cut to the desired lengths were then

24 dipped into the sol solution, and capillary action pulled some of the solution into the capillary. The end of the capillary that had been dipped in the sol solution was then placed in a steam bath for 30 minutes. After 30 minutes, the capillaries were removed, and they were checked to see if the frit was formed. If a frit had been formed, it would then be trimmed to about 2mm, and connected to the pump using a ferrule assembly. If the frit formed was too long, flow through the capillary would be restricted, and it would become almost impossible to pack the capillary. By trimming the frit to two millimeters, the flow through the capillary was usually adequate for the packing process to be completed. After the frit was trimmed, the capillary was rinsed at 200-600 PSI for about ten minutes with either water or acetonitrile to remove any traces of the solutions used to form the frits. This was done to ensure that the frit was porous and pressure driven flow could be achieved through the capillary. It was also a way of testing the strength of the frit. The frit needs to be porous and strong in order to be useful. If the flow through the capillary was too slow, the frit would be cut off and the procedure repeated after the inside of the capillary had dried. Once the frit has been formed, it is time to pack the column. First, one must decide on the length of column needed in order to perform the separation at hand. In addition to this, one must consider the dimensions of the detector cell that holds the capillary in place during the analysis, as well as the internal size of the entire CEC instrument. The capillary is packed by first creating a frit on the inlet end of the capillary. As described earlier, there are many different ways to form this frit. After the frit was formed, it was trimmed to approximately two millimeters. Next, the stationary phase slurry was formed by placing a small scoop of bare silica in about 20 mL of water or acetonitrile. This mixture was sonicated for at least ten minutes in order to distribute the silica evenly throughout the solution. While the stationary phase slurry was being sonicated, the stationary phase reservoir was cleaned. This reservoir was simply an empty stainless steel liquid chromatography column that had both frits removed. In addition to removing the frits, one of the end fittings was drilled to make the outlet large enough to accommodate the peak tubing being used to connect the column to the reservoir. The end fittings of the reservoir were cleaned by sonicating them for five minutes while they were submerged in methanol, then rinsing

25 them with water. The reservoir itself was cleaned using cotton-tipped sticks dipped in methanol. The reservoir was thoroughly cleaned each time before it was used to pack a capillary. The reservoir would then be assembled, and filled with the stationary phase slurry using a syringe fitted with a plastic male screw on tip. Once filled, the syringe was not removed until the following steps were performed. Once filled, the following steps had to be performed rapidly in order for the packing procedure to go smoothly. The capillary, which was already fitted with the ferrule assembly, was then tightened onto the end fitting on the side of the reservoir that had the larger outlet. Then, the syringe was removed and the reservoir was attached to the syringe pump which was filled with water or acetonitrile. The solvent used was chosen to match the solvent used in the stationary phase slurry. The pump was turned on, in the constant pressure mode, starting at 100 PSI. The reservoir and a portion of the capillary were submerged into the water in the sonic bath, in order to keep the stationary phase suspended in the slurry solvent. The pressure would then gradually be increased until the capillary was packed. The capillary columns were considered packed once they had from 20 cm to 25 cm of packing. The maximum pressure used to pack the capillaries was 6000 PSI, but it was found that in most cases, the higher the pressure used to pack the capillaries the more likely they were to clog, rendering them useless for the temperature experiment. After the capillaries were packed, they were allowed to sit under pressure for several hours, in order to allow for bed consolidation to occur. Once these steps were completed, a glowing nichrome wire, or an apparatus utilizing a nichrome ribbon was used to burn a detection window. This was done by simply marking a spot right after the end of the packed portion of the capillary where the window was desired. The capillary was then slipped into a loop of nichrome wire or a hole in the nichrome ribbon and clipped in place when the mark was lined up with the ribbon or wire. The positive and negative wires for a two prong plug were attached to the nichrome wire or ribbon, and a variable autotransformer was used to provide the power necessary to heat the nichrome wire or ribbon. The heat given off by the glowing nichrome wire or ribbon was used to burn a small segment of the polyimide coating off of the capillary, thus creating a detection window. This detection window is a weak point in the capillary since the coating has been removed and one must be very gentle with

26 capillaries once the detection window has been made. The capillary would then be immediately placed into the detector cell, as this provides some protection against breakage. Once in the detection cell, the capillaries were flushed with pure HPLC grade acetonitrile, until no bubbles were seen coming out of the end which was placed in a vial of acetonitrile. Once this was complete the detection cell was placed in the detector. The equipment used to perform capillary electrochromatography experiments varies greatly from the equipment used for liquid chromatography. An instrument used for capillary electrochromatography can be as simple as consisting of only a voltage source, solvent reservoirs, the column, and a detector. Much more complex integrated systems can also be used, but for these experiments, only a simple instrument was used. Once the capillary has been prepared as described previously, and has been placed in the detector cell, both ends of the capillary are placed in vials filled with the chosen mobile phase. For these experiments, both acetonitrile and water acetonitrile mixtures were used as mobile phases. The voltage applied across the column ranged from 10 kV to 15 kV depending on the experiment. A sample vial was also prepared; this vial contained a solution of the analyte dissolved in the mobile phase. To perform a sample injection, the vial into which the packed portion of the capillary (the inlet end) was submerged was replaced with the sample vial. Then 10 kV was applied for 1-3 seconds depending on how much sample needed to be injected. After the injection was made, the sample vial was replaced with the original vial for the duration of the chromatographic run. The detector used was a capillary electrophoresis absorbance detector.

2.4 Silica and Tris buffers

Silica dissolves at a pH above 7.5. Based on this, it is possible that a monolithic column could be made from a traditionally packed column by changing the pH of a buffer solution in the column. This idea was tested using Tris buffer, which has a large temperature coefficient as shown in Figure 12. Tris is a primary aliphatic amine. The buffer solutions were prepared by mixing the proper amounts of Tris base, Tris(hydroxymethyl)aminomethane, and Tris HCL which is the completely neutralized

27 crystalline salt of Tris as shown in Table 1. Tris base, as supplied, is pure, essentially stable, relatively non-hygroscopic and has a high equivalent weight. As a Tris buffer solution decreases in temperature from 25°C to 5°C, the pH of the solution increases an average of 0.03 pH units per °C. As the same solution increases in temperature from 25°C to 37°C, the pH decreases an average of 0.025 pH units per °C.

Change in pH of Trizma Buffer with Temperature

8 pH 7

6 0 102030405060 Temperature C

Figure 12. Graph of the resultant pH vs. temperature for a Tris buffer made with 4.88 g/L 0.05 M Tris HCl and 2.30 g/L 0.05 M Tris Base. The pH of the Tris buffer becomes lower as the temperature is increased. This is a graph of the pH vs. temperature for entry number seven in Table 1.

Table 1. Mixing table for Tris buffer showing the necessary weight in grams needed to make up one liter of 0.05 M solution, and the pH for each of these solutions at three temperatures, 5 °C, 25 °C, and 37 °C.67

pH at Different Temperatures g/L for 0.05 M Solution 5°C 25°C 37°C Trizma HCL Trizma Base 7.76 7.20 6.91 7.02 0.67 7.89 7.30 7.02 6.85 0.80 7.97 7.40 7.12 6.61 0.97 8.07 7.50 7.22 6.35 1.18 8.26 7.70 7.40 5.72 1.66 8.37 7.80 7.52 5.32 1.97 8.48 7.90 7.62 4.88 2.30 8.58 8.00 7.71 4.44 2.65 8.68 8.10 7.80 4.02 2.97 8.78 8.20 7.91 3.54 3.34 8.88 8.30 8.01 3.07 3.70 8.98 8.40 8.10 2.64 4.03 9.09 8.50 8.22 2.21 4.36 9.18 8.60 8.31 1.83 4.65 9.28 8.70 8.42 1.50 4.90 9.36 8.80 8.51 1.23 5.13 9.47 8.90 8.62 0.96 5.32 9.56 9.00 8.70 0.76 5.47

29 The effects of the change of concentration of the buffer solution on the pH are also documented but these changes were not used in this study. The best way to prepare tris buffers is to use a mixing table such as the one given in table 1.

2.5 Using pH Changes to Achieve Monolith Formation

Capillary columns were made by the traditional method described in section 2.4. Tris buffers were prepared using the amounts given in Table 1. Several different buffers needed to be prepared in order to find the right buffer and the right temperature to form the monolith from the traditionally packed columns. The concept behind this experiment was that by using the Tris buffer to partially dissolve the silica that had been packed into the capillaries and then allowing it to re-gel, the physical properties of the silica would be changed22, and a monolith would be formed. First, buffers that required very low temperatures, below 5°C, to get the pH to a high enough level to begin the partial dissolution of the silica were used (1 to 5 in Table 1). After trying several different compositions, the one that gave the best results based on pressure studies that are explained below was chosen. Next, a composition that gave the required pH values at higher temperatures was chosen (13 in Table 1). Pressure studies again showed that possibly a change had occurred in the silica, but the results from these studies were not as good as the previous ones because the silica was flushed out of the capillaries at a pressure of about 2000 PSI in most cases. It was decided that the best composition was entry three in Table 1 which was made with 6.61 g/L Trizma HCl and 0.97 g/L Trizma base. The results of these studies using this composition are shown in Table 2, and are explained in the next paragraph. All packing and flushing procedures were carried out using an Isco 100DM Syringe pump and a series D pump controller. The buffer experiment and the pressure studies performed involved the following procedures: 1. Form an inlet frit in the empty capillary. 2. Pack the capillary with 5micrometer silica particles using pressures usually only as high as 1000 PSI.

30 3. Flush the capillary with water for several hours, then with the prepared Tris buffer. 4. Once the capillary had been flushed with the buffer for several hours, and I felt certain it was completely filled with buffer and all the water had been removed, I disconnected it from the syringe pump. 5. The capillary was then placed in a water bath at the temperature required to change the buffer’s pH to the desired value. Different capillaries were left for varying amounts of time. 6. Once during the allotted time, the capillary was sonicated for a minute. 7. After the allotted time, the capillary was placed in a warm water bath, and left for 30 minutes. Then it was reconnected to the syringe pump, and the buffer was flushed out with water. 8. The column was filled with water overnight, then the next day the portion of the capillary that had the frit was cut off. It was cut at least one cm past where the frit ended to ensure that the frit was fully removed. 9. Starting with 100 PSI, the pressure was ramped upward in 100 PSI increments until it reached 6000 PSI.

Some of the packed capillaries were able to withstand pressures of up to 6000 PSI with no stationary phase loss, but others would begin to lose stationary phase at lower pressures, mostly around 3000 PSI. Even in these columns, sometimes only small amounts of stationary phase would be lost, for example maybe a half of a centimeter from a column packed over 20 cm. Control experiments were run where all steps of the above procedure were followed except that instead of buffer, water was used for all steps. In these control experiments, the prepared capillaries were emptied of stationary phase at pressures below 500 PSI, and usually the stationary phase started to be lost around 100 PSI. Based on the ability of the capillary columns that underwent the temperature experiment to withstand very high pressures, it is suggested that a monolithic column had actually been formed. The capillaries were tested to determine if electroosmotic flow through the capillaries could be achieved. This was done by filling them with acetonitrile and injecting acetone into the capillary as described in section 2.3.

Table 2. Results of pressure studies for five packed capillaries that underwent the pH experiment. The buffer used was the third entry in Table 1, made with 6.61 g/L of Trizma HCl and 0.97 g/L of Trizma base. Capillary A and B were not subjected to higher pressure than those recorded although no stationary phase had been lost. Capillary C was not tested for electroosmotic flow because it broke when placed in the detector cell.

Capillary Pressure (no sp lost) EOF Flow?

A 3000 PSI NO

B 4000 PSI Yes

C 6000 PSI Not Tested

D 6000 PSI Yes

E 6000 PSI Yes

2.6 Characterization of Monolith Using Fluorescence

Fluorescence spectroscopy was utilized in order to study the change in the size and shape of the silica particles. This type of imaging revealed information about the physical changes taking place when the silica packed in the capillary was subjected to the Tris buffer. In order to do this experiment, a section of capillary about 2.5 cm long was cut from those capillaries that had been packed and subjected to the temperature experiment for varying times. One end of this segment was submerged into Rhodamine B

32 fluorescent dye for 5 seconds. The capillary was then allowed to air dry for 30 minutes, before it was placed into a mount specifically designed for this experiment. This mount held the capillary in a vertical position on the scanning stage so that the full diameter of the capillary was in the path of the detector. The laser, a Coherent DPSS 532 frequency doubled Nd:YAG laser, was focused into the sample at about a depth of 100Å. Two identical detectors, SPCM CD2801 single photon avalanche diode detectors, separated at 570nm were used to detect the fluorescence. A schematic diagram of this confocal fluorescence microscope is shown in Figure 13. Porous and non-porous particles were easily distinguished by this technique, but the image seen was not three-dimensional. Figure 14 shows the fluorescence image of a 75μm glass capillary packed with 5μm bare silica particles. These particles appear different sizes due to the type of fluorescence microscope being used. This microscope is a confocal microscope, this means that it is actually focusing into the capillary and the stationary phase at a chosen depth. Since the particles are not packed in an even row across the diameter of the capillary, the microscope is focusing on each particle at a different depth. Some particles appear larger because the microscope is focusing on them near their centers, where the cross section is larger. Some particles appear smaller because the microscope is focusing near their edges, where the cross section is smaller. This is illustrated in Figure 15. The fluorescence image in Figure 14 shows that the particles are unattached, and that they appear, as expected, to be tightly packed into the capillary column. There is a region, however, where it appears that some of the stationary phase particles have fallen out after the capillary was cut open. This is seen as a dark region on the lower right side of the image. Figure 16. is an image of the same capillary after the temperature experiment has been completed. The appearance of the capillary has changed greatly. In this image, the particles are no longer spherical, but it is not clear whether or not the particles have fused to form a monolith, or simply formed larger particles.

Figure 13. Diagram of the confocal fluorescence microscope used for imaging packed capillaries. The laser used is a Coherent DPSS 532 frequency doubled Nd:YAG laser. For this experiment, it was focused into the sample at a depth of 100Å. Two SPCM CD2801 single photon avalanche diode detectors that were separated by a distance of 570 nm were used to detect the fluorescence. Diagram courtesy of the Weston Research Group.

Figure 14. Fluorescence image of capillary column packed with 5 μm bare silica particles and imaged using Rhodamine B fluorescent dye. Although the image is not extremely sharp, the spherical silica particles can be seen inside the capillary tube. The lower right of the capillary is dark because the stationary phase particles in this area fell out when the capillary was fractured.

Figure 15. Here is a two dimensional representation of the apparent cross sectional area of the silica particles dependent on the depth at which the fluorescence measurement is made. If the confocal microscope is set to a depth that is near the center of the particle, the particle appears larger than if it is focusing near the top or bottom of the particle.

Figure 16. Fluorescence image of a different segment of the previously shown packed capillary after it was subjected to the pH experiment. In this image, it is obvious that there have been some changes to the silica particles. They no longer appear spherical, and they appear to be larger than in the previous image.

2.7 Characterization of Monolith Using Scanning Electron Microscopy

Scanning electron microscopy (SEM) was used to directly observe changes in the silica structure. A schematic diagram of the scanning electron microscope used in this study is shown in Figure 17. The SEM is patterned after a reflecting light microscope, but it yields better resolution at a much higher magnification. The images produced are in black and white because electrons, and not light are used to do the imaging. A virtual source, usually an incandescent tungsten or lanthanum hexaboride electrode is used to produce a stream of monochromatic electrons. The first condenser lens is used to shape the beam and limit the beam’s current. The condenser aperture then eliminates the high- angle electrons from the beam. The electrons are then directed into a tight, thin, coherent beam by the second condenser lens. Another objective aperture helps to further eliminate high-angle electrons. The specimen is placed at the end of the focused electron path. A set of coils then scans the beam in a grid-like fashion over the sample. Reflected and secondary electrons are detected and form a quasi-three-dimensional image on the screen. This entire process must be carried out in-vacuo since the electron would be easily absorbed by air. SEM can show the shape, size and arrangement of particles making up the sample, and detectable features are limited to a few nanometers.22, 68 Packed columns that were to be studied were fractured, dried overnight, and mounted to the SEM puck. Four capillary fragments of approximately 0.5cm in length were placed on the SEM puck at a time. This gave information about the changes that the silica particles underwent after being treated with the Tris buffer. This study utilized a Joel 5900 Scanning Electron Microscope, and a Princeton Gamma-Tech PCT Prism Detector. The total current used was 1nA, at 5kV. The capillaries that were previously imaged using fluorescence spectroscopy were imaged again using the scanning electron microscope. The images obtained vary slightly from the previous images, but this was expected, since the fluorescence microscope used was imaging inside the sample, and the scanning electron microscope simply images the surface. Even with these differences, both types of images suggest similar changes in the

38 silica. In Figure 18 which is the traditionally packed capillary, it is obvious that the stationary phase particles are simply packed against one another, but that nothing is holding them in place. This is the reason why there is a gap in the packing, which is simply an empty space created when some of the stationary phase which is loosely held in place fell out of the column. In this image, the stationary phase particles all appear to be the same size, because it is a surface technique. In Figure 19, the scanning electron microscope image of the packed capillary after the temperature experiment has been completed, it is clear that there have been many changes in the silica. First and most obvious, is that the particles are not longer spherical, they are actually angular, and have obvious edges. In addition to this, the particles are much larger than they previously were. It is still not obvious whether or not the particles are connected to one another, but the fact that there are no obvious gaps in the packing seems to suggest that the particles are actually connected together, forming a silica monolith.

2.8 Conclusion

This chapter discussed the creation of a particle-fixed monolith for use in capillary electrochromatography. The method used was to change the pH of a buffer solution in contact with the spherical silica particles packed inside a capillary column. By manipulating the pH of this buffer, the silica particles could be partially dissolved and then allowed to re-gel. Figures 18 and 19 suggest that this method is a plausible method for converting a traditional capillary electrochromatography column to a monolithic column. The results from the pressure studies given in Table 2 also offer support for this idea. Horvath and coworkers showed that a particle-fixed monolith could be derivatized in situ and that a useful chromatography column could be prepared by this method.40 This suggests that the particle-fixed monolithic columns formed by the use of pH changes could be derivatized by the same method and then used as chromatographic columns. Another use for a monolith prepared by this method would be as a frit for the capillary column. In capillary electrochromatography, the frit is often a cause of bubble

39 formation which interrupts electroosmotic flow through the capillary. It has been suggested that one reason for this is that the frits commonly used for these experiments are made from materials that are different from the stationary phase. It would be plausible to use this technique for the formation of frits because the column could be packed as usual, and then the capillary could be filled with buffer, but only small portions on either end of the capillary would be cooled using a thermocouple. In this way, the column chemistry would be the same as for the traditional column but the frits would be less likely to lead to bubble formation which would interrupt the electroosmotic flow. One technique commonly used for frit formation is the sintering technique. After a capillary is packed, the spot where the frit is desired is marked. This area is then heated to sinter the particles. The temperatures required for the sintering of the frit are high enough that the polyimide coating on the capillary is burned off. This leaves the glass exposed, and is a weak point in the capillary. By using the method of pH changes described in section 2.5, it would be possible to create a frit made with the same material as the stationary phase without removing the protective polyimide coating from the capillary. Since it was shown that this process did not interfere with the electroosmotic flow through the capillary, this seems like a reasonable use for this type of monolith.

Figure 17. Diagram of Scanning Electron Microscope used to image the cut surface of packed capillaries.

Figure 18. SEM image of a 75 μm capillary packed with 5 μm bare silica stationary phase particles. This is not the same capillary that was shown in the fluorescence studies; however, a dark area, where silica has fallen out of the fractured capillary, is also seen.

Figure 19. SEM image of the packed capillary shown in Figure 13 after the pH experiment has been performed. This is another segment of the same capillary that was shown in the previous image after it has undergone the pH experiment. There are many obvious differences. There are no areas where silica has fallen out. The particles are no longer spherical, and they are much larger. It is not obvious whether or not the particles are attached to one another or the capillary wall, but since no stationary phase particles have fallen out, this is likely.

CHAPTER THREE

CHROMATOGRAPHIC ISOLATION OF BAND BROADENING CONTRIBUTIONS

3.1 Introduction

Band broadening in liquid chromatography is generally attributed to three main processes that were introduced by van Deemter and coworkers in 1956.69 In the van Deemter equation, these contributions to band broadening are referred to as the A term, the B term, and the C term. Eddy diffusion (A Term) is the contribution from inhomogeneous packing of the stationary phase, and also accounts for the different flow paths that the analyte molecules can take as they pass through the column. Longitudinal diffusion (B-term) is the diffusion of the analyte molecules along the axis of the flow path. This adds to the broadening of the injected band and is a function of the diffusion coefficient of the analyte molecule and the flow rate of the mobile phase through the column. The third factor that affects the efficiency of the column is the resistance to mass transfer (C Term). This was described by van Deemter and coworkers as involving the solute partitioning between the mobile phase and the stationary phase. The van Deemter equation is the most commonly used equation for fitting chromatographic efficiency data. This equation offers a fairly good fit to most data, and is the equation usually found in undergraduate text books. Since this equation was first derived, other researchers have performed many studies to investigate band broadening in the chromatographic system. The results obtained from these studies are not in total agreement with the conclusions given by van Deemter and coworkers in 1956. As a

44 result, other equations have been introduced to model efficiency data, and these include the equations of Giddings70 , Horvath and Lin71, 72, and Knox73. To learn more about these equations and the theory these equations are based on, please read section 5.1. The goal of researchers that are studying this fundamental aspect of liquid chromatography is to understand band broadening and the way that the processes that contribute to band broadening relate to one another. This topic has been studied in great detail by many scientists with the hope of understanding and deconvoluting the complex set of dispersion processes that occur within the column. Although so much effort has been placed on understanding these processes, there have been many roadblocks that have stood in the way of this type of research. First, there have been so many developments in stationary phase technology that older studies do not seem to be particularly relevant to modern chromatography. In addition, there has been much advancement in available equipment, and even improvements in equations used to model the chromatographic peaks. Today’s researchers have an advantage over previous scientists because they have available to them columns that are packed with newer generation stationary phases, and also improved equipment and data acquisition software that are better able to produce and collect data. However, in addition to these advantages, one of the most important points is that if the equations used to calculate the efficiency data used for these previous studies were incorrect, the error produced would skew the results. The results of this study are arguably the best obtained for a study of this type because the equation that was used to model the chromatographic peaks, the Foley-Dorsey equation, has been shown to better model chromatographic peaks.29, 37 In order to understand how band broadening occurs in the column, it is first necessary to understand each band broadening process individually. Unlike some experiments in which it is easy to hold several variables constant while changing only one variable at a time in order to study a system, this system is very complex to study. The variables that we can change in the instrumental setup in this study are the flow rate and corresponding pressure, the temperature, and the column. It is practically impossible to change just one of the band broadening processes by changing any of these variables. Due to this, the experiments that have been performed over the past fifty years to

45 deconvolute the contributions to band broadening in the chromatographic system have been largely unsuccessful. It has not been possible to isolate the effects of the individual processes contributing to the broadening of the injected solute band. There have been many noble efforts71, 74-76 that have offered much insight into these band broadening processes, but most of these have led to more assumptions and more questions than answers.

3.2 Previous Efforts to Isolate the Contributions to Band Broadening

3.2.1 Using Published Equations

Many researchers have studied band broadening over the years. One very common way that has been used to investigate the different band broadening contributions was to use a published plate height equation to model collected chromatographic data. The data collected for such a study was usually for several retained solutes. This means that the solutes being used are experiencing all three known sources of dispersion, eddy diffusion, molecular diffusion, and resistance to mass transfer. After the data had been fit using the chosen equation, information would be extracted from the fit values in order to describe the contribution from each source of dispersion in the column. At first glance, this may seem to be a valid method for obtaining these values, but there is one major flaw with this method. The problem is that depending on the equation being used the resulting fit values would be different. In order to overcome this problem, one would have to be certain that the equation chosen is the proper model of the dispersion in the column. To date, it is not known which model, if any, is the right one, so this method cannot be validated. There have been other methods used to isolate the contributions to band broadening, but these have not been totally successful. Some of these methods will be described in the following sections.

46 3.2.2 Horvath and Lin: Band Spreading of Unsorbed Solutes

In 1976 Horvath and Lin published a paper discussing the band broadening of unsorbed solutes in liquid chromatography.71 This paper was published after equations by van Deemter,69 Giddings,70 and Knox,77 were published. Horvath and Lin felt the need for a simple theory that was based on measurable parameters, a requirement that the other theories did not meet. In order to achieve this, they used a column packed with 48.5 μm impervious glass beads. By doing so, they were able to eliminate any resistance to mass transfer into the stationary phase, and also eliminate any resistance to mass transfer into the stagnant mobile phase that would be found in any pores. Since these contributions to band broadening were eliminated, the corresponding terms in the Horvath and Lin equation, Equation 8, could also be removed. This meant that only the first two terms of the Horvath and Lin equation were necessary to model the collected data. This was essentially the first instance that I have found in the literature where researchers tried to isolate the contributions to band broadening by experimental methods such as changing the solutes used. In their conclusions, it was obvious that the fit obtained was not particularly good, but according to Horvath and Lin, their method yielded a better fit than the fits obtained in the previously published papers.

Equation 8 2 1 B 3 H = + + Due + Eue 1 1 ue + 1 A 3 Cue

3.2.3 Groh and Halász: Band Broadening in Interstitial Regions

Groh and Halász performed experiments to study the interstitial band broadening occurring in columns packed with silica based stationary phases.74 They used a pore- filling method where the pores of the column were filled with water, a polar solvent that is impenetrable to the samples they chose to use. The band broadening measured when the stationary phase pores were filled with water was a measure of the interstitial band

47 broadening. The columns were then flushed with organic solvent in order to remove the water from the pores, and the band broadening was measured again. This measurement gave the total band broadening in the column. By performing a simple subtraction of the two measurements, the contribution to band broadening from the pores could be ascertained. By this method, they found that the reduced interstitial band broadening measured was at least a factor of two lower than previously reported. By accurately controlling the water content of the mobile phase, the pores can be either fully filled or partially filled. For these experiments Groh and Halász performed experiments with the pores either fully filled or empty. When the pores were filled, the band broadening measured was ten times less than when the pores were empty. Some of the columns tested did not yield useable results, because 20% to 90% of the water filling the pores was washed out of the pores during the experiment. They reported that this was possibly because of erosion by eddies at the entrance to the pores. This could be important in HPLC in isocratic mode when using binary or ternary mobile phases of widely different polarities, when one component is enriched in the pores. Their results suggest that the enrichment could be a function of particle size, pore size, and flow rate which could cause changes in retention over time even after equilibration.

3.2.4 Knox and Scott: Study of B and C terms in HPLC

In 1983 Knox and Scott attempted to obtain values for the C term of the van Deemter Equation.75 They also tried to separate the mobile zone and stationary zone dispersion processes. In the experimental procedures it was stated that all the measurements were made using standard HPLC components that had only minor modifications. However, one of these so called minor modifications was that silica particles of diameter up to 540μm were used. This is actually a major modification, since any change in the packing of the column can greatly affect the dispersion processes occurring in the column. Knox and Scott attempted to separate these processes by first measuring the diffusion coefficient in the mobile phase using the open tube method, 75 and the effective diffusion coefficient in the mobile phase using the arrested elution method developed by

48 Horne, Knox and McLaren.78 Next they attempted to measure the C values, corresponding to the contribution to plate height due to resistance to mass transfer, at high reduced velocities of elution using particles with diameters ranging from 50μm to 540μm. Knox and Scott reported that the peaks obtained were non-Gaussian, and therefore they had to perform additional experiments in order to determine Vm and Vo. They concluded that the basic theories of dispersion that had been previously published were quantitatively and qualitatively correct, but that their equations for the B and C terms better recognized the contributions from different rates of diffusion in different regions of the packed column. They also concluded that further studies needed to be performed to be able to separate the mobile zone and stationary zone dispersion processes, but that equipment of the highest quality coupled with computer data acquisition was necessary to do so properly.75

3.2.5 Magnico and Martin: Dispersion in Interstitial Space

In 1990 Magnico and Martin investigated the dispersion that occurs in the interstitial space of a packed column by using large impenetrable particles.76 Their experiment was designed to minimize all sources of broadening other than the broadening due to the fluid moving through the column. They tried to reduce the effects of all the sources of dispersion except longitudinal diffusion, which they stated could not be reduced. In order to achieve the conditions necessary to perform such an experiment, they used sieved, impervious, spherical particles, very low pressure drops, and non-retained solutes. By using impervious particles, they eliminated particle permeation, which should have allowed them to calculate the correct dependence of the flow rate in the coupling equations used to describe column efficiency. They also used a dry packing procedure that was supposed to provide as regular a packing inside the column as possible. This procedure involved using a vibrating distributor that was to induce “a constant flow of particles falling onto a short column that was filled with 5mm glass beads”.76 The stationary phase passes through the glass beads and falls into a set of parallel 2.5 mm I.D. tubes which keep the stationary phase particles flowing

49 homogeneously. At the same time the column is being moved downward to ensure that the particles all travel the same distance before settling into the packed bed. In addition to this, the column is being simultaneously rotated along its axis to avoid radial stratification. Magnico and Martin concluded that the dispersion of a non-retained solute was properly fitted by the Giddings coupling equation, but that this dispersion deviated from the behavior predicted by both the Horvath and Lin equation and the Huber equation. They believed the reason their experiments allowed them to distinguish between the equations whereas many other HPLC experiments previously performed have not was because of the care they took in assuring that the column was well packed.76

3.3 Chromatographic Isolation

After reviewing the different methods that have previously been used for isolating the contributions to band broadening, it was decided that the best way to do this would be by choosing solutes that experience different sources of broadening in the chromatographic column and collect plate height data using these solutes. After this was completed, the data could be mathematically manipulated in order to isolate the contributions from each source. This is similar to the method used by Horvath and Lin in 1976, except that they chose to manipulate the chromatographic column used, and only used non-retained solutes.71 Chromatographic isolation, as will be described in the following sections, appears to be a better alternative, since conventional columns will be used in the study. The reason this is very important is that dispersion in the column is very dependent on the conditions under which experiments are being performed. The type of stationary phase used in the column will have a great effect on the observed band broadening. Changes in the size of the particles, the stationary phase material and the stationary phase support can have a large influence on the band broadening contributions being studied.

50 3.4 Sources of Band Broadening Experienced by Different Solutes

The premise behind chromatographic isolation is to use carefully chosen solutes that experience different sources of band broadening in order to learn more about each individual type of broadening. In order to choose the solutes, it is important to understand what types of solutes will experience different types of band broadening. Once a suitable class of molecules has been identified, one can consider the mobile phase choice, the type of column being used, and the type of detector in order to determine the specific solute that will be used for each measurement. There are some sources of band broadening that will be experienced by any solute that enters the column. For example, eddy diffusion is experienced by any analyte molecule that travels through the column towards the detector. In addition to eddy diffusion, all analyte molecules will experience molecular diffusion as they move through the column. The magnitude of this diffusion, however, will be different for different molecules. Besides these sources of dispersion that all solutes experience, there are other sources of dispersion that different types of molecules may or may not experience. Retained solutes will experience every source of band broadening in the column. This is because in addition to the eddy diffusion and molecular diffusion, they will also experience resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. This is true because these analytes are sampling the areas of stagnant mobile phase and also partitioning into the stationary phase as they travel through the column. On the other hand, non-retained solutes experience eddy diffusion, molecular diffusion and resistance to mass transfer in the mobile phase since they too sample the areas of stagnant mobile phase, but they will not experience resistance to mass transfer in the stationary phase because they do not partition into the stationary phase. It is now clear that we have two distinct groups of solutes to choose from, and that now specific molecules from each of those groups must be chosen as the analytes of interest. It appears that choosing solutes from both the retained and non-retained category would be wise since the behavior exhibited by these solutes should be different and will give information about the amount of broadening that is attributable to each different band broadening process.

3.5 Choosing a Non-retained Analyte

There are two categories of non-retained solutes; excluded non-retained analytes and non-excluded non-retained analytes. An excluded non-retained analyte is a solute that does not penetrate the stationary phase particles. Therefore they are excluded from the particle’s pore space and are only able to sample the interstitial space in the column. A non-excluded non-retained analyte is an analyte that passes through the column without being retained. If a sufficiently small non-retained analyte is used, the entire intraparticulate region is sampled, and if a sufficiently large non-retained analyte is used that cannot sample any of the intraparticulate region, it will be an excluded non-retained analyte. For a more detailed description of this, please read section 5.1.2. One organic compound that is commonly used to measure void volumes in liquid chromatography is uracil. Uracil is a small organic molecule that should sample all the areas in the column that are filled with mobile phase, therefore it is not a non-excluded analyte. It is believed that uracil is non-retained, so it should not enter the stationary phase, but it will enter and sample the pore volume. For this study, uracil appears to be a suitable analyte to use for the non-retained molecule. In contrast to uracil, inorganic salts, such as sodium nitrate, sample different amounts of the pore volume or are totally excluded from the pore volume by a phenomenon known as Donnan Exclusion. The degree of exclusion depends on the conditions under which the sample is injected. This is often seen as a problem to chromatographers, but work done in collaboration with Carolyn Simmons has shown that the Donnan Exclusion of inorganic salts can be manipulated and used for chromatographic isolation. The results offer a great deal of interesting information about the stagnant mobile phase region of the column.

52 3.6 Choosing Retained Analytes

A retained analyte, as discussed in section 3.4, will experience every type of broadening that occurs in the chromatographic column. This type of analyte will experience dispersion due to eddy diffusion (A term), molecular diffusion (B term), and

both resistance to mass transfer in the stationary phase (Cs term) and resistance to mass transfer in the mobile phase (Cm term). There are many compounds that would be retained on the C18 column used in this study. Because of this, it was important to decide what type of information was of most interest for this study before choosing the analytes that were to be used. It was decided that the study would focus on the investigation of resistance to mass transfer both in the mobile phase and the stationary phase. In order to obtain information about the resistance to mass transfer in the stationary phase it was necessary to use molecules that spent different amounts of times in the stationary phase. It would also be useful if the difference in the retention factor for the molecule could be correlated to something in the structure of the molecule. It was decided that a homologous series would give the information that was required, and the one chosen included the following molecules: benzene, toluene, ethylbenzene, propylbenzene, and butylbenzene.

3.7 Choosing the Appropriate Mobile Phase

In section 3.6 it was mentioned that one purpose of this study was to investigate the resistance to mass transfer in the stationary phase. By using a homologous series, where the addition of a CH2 group causes the analyte to spend more time in the stationary phase, the effect of the resistance to mass transfer can be studied. However, although for the members of the homologous series chosen, the increase in molecular weight is not too large, each molecule used could possibly experience slightly different broadening in the column. In order to approach this problem by a different route, it is possible to change the retention factor of an individual analyte by changing the mobile phase composition.

53 The components of the binary mobile phase used in this study were acetonitrile and water. It was decided that in order to investigate the resistance to mass transfer in the stationary phase, four different compositions of the acetonitrile/water mixture would be used. The chosen compositions were the following: 60% ACN, 70% ACN, 80% ACN, and 90% ACN in water. These mobile phase mixtures were prepared by volume.

3.8 Experimental Conditions

3.8.1 Chemicals

All aqueous solutions and mixed mobile phases were prepared using deionized water that was filtered using a Barnstead NANOpure II water purification system. This system incorporated three filters: a macroporous and organic removal filter; an ultra pure mixed bed filter / deionizer; and an organic removal (scavenger) filter. The acetonitrile used for the preparation of mobile phases and samples was HPLC grade with a UV cutoff of 190 nm obtained from Fisher Scientific. All mobile phase components were filtered, using a high pressure filter, before mixing to allow for efficient pump and detector operation.79-82 Oxygen in the mobile phase can cause reduced detector sensitivity and poor baseline stability in UV detectors. For these reasons, all mobile phases were helium-sparged prior to filling the pump. All samples were prepared in appropriate volumes of the mobile phase being used for each experiment. Sample components included uracil, 98% from Aldrich; benzene from Fisher Scientific (certified A.C.S Spectranalyzed); toluene, HPLC grade, UV cutoff 286 nm from Fisher Scientific; ethylbenzene, 99% from the Aldrich Chemical Company, Inc.; propylbenzene, 98% from the Aldrich Chemical company, Inc.; and butylbenzene, 99+% from the Aldrich Chemical Company, Inc.

54 3.8.2 Column

The column used in this study was a traditional Zorbax C18 column, the same one used in the previous study. This column was a 15cm x 4.6mm column packed with 5μm spherical silica particles that had been derivatized with C18 groups. This column had a 70 Å pore diameter. The extracolumn variance was subtracted using the method described in section 3.9. The part number was 883952-702, the serial number was USG0014021, and the lot number was B02011.

3.8.3 Instrumentation

In liquid chromatography, a pressurized liquid is used as the mobile phase. In order to achieve the conditions necessary for a liquid chromatography experiment, the equipment used is typically more complex than the capillary electrochromatography system described in section 2.3. The system used for liquid chromatography traditionally includes a pump, an injector, a column, a temperature controller, and a detector. There are many different options to choose from for each of these components. A typical pump used for HPLC would be a constant flow-rate pump. There are many different types of pumps that can be used, and these include reciprocating piston pumps, and positive displacement pumps.3 For most purposes, the reciprocating piston pumps are satisfactory, and these are the most commonly used pumps for liquid chromatography. For the experiments performed to study the broadening contributions in this technique, it was decided that a positive displacement, or syringe pump, should be used. These types of pumps provide flow that is relatively independent of the column back pressure and the solvent viscosity similar to reciprocating piston pumps. Syringe pumps also provide more constant flow. The pump used in this experiment was a screw-driven type pump, which allowed for the mobile phase to be pushed through the column in a pulse-free action, unlike what is common when using a piston pump. Pressure pulses from the pump could possibly have interfered with some of the studies that were being performed. Pump performance has a large effect on the reproducibility of analyte retention times and the baseline stability of the detector.5, 83, 84 Because of this, the choice of pumps is very

55 important. The pump used in this study was an ISCO model 100DM syringe pump with a cylinder volume of 102.93 mL along with an ISCO series D pump controller. The major disadvantage to using the syringe pump was that the cylinder volume was quite small, so it had to be refilled often, which necessitated re-equilibration of the column. The detector used in the liquid chromatography system was a Spectroflow model 757 absorbance detector with an LH-4 D2 cartridge lamp from Sonntek. This detection system was a UV absorbance detector with the following specifications: a 1180 gr/mm grating double beam monochromator, 5 nm bandwidth, less than 0.2% stray light, and a matched silicon photodiode photodetector. The flow cell had an 8 mm path length, with a flow cell volume of 12 μL. The detector rise time was always set at 0.1 sec, which corresponded to an effective time constant RC filter equivalent value of 0.045. If a slower rise time was selected, a small negative dip would show up after the tail end of each peak. The detector sensitivity was set to 0.1 AUFS. The light source was a Deuterium lamp with a usable range of 190 nm to 380 nm. The detector wavelength was set at 254 nm for these experiments. At this wavelength, the mobile phase gave an absorbance of about 37 mV, and our largest peak gave an absorbance of about 85 mV. Using this wavelength allowed us to use samples with a low enough concentration that they were in the linear range of the concentration vs. absorbance isotherm. A Beckman model 506 microprocessor-controlled modular automatic liquid sampling unit designed for use in HPLC was the autosampler used for these experiments. This was a stand alone autosampler that utilized a stainless steel Rheodyne model 7010 sample injection valve made for use in HPLC. This type of injection valve allows for the samples to be reproducibly introduced into a pressurized column without much interruption of the flow through the column. This autosampler had a remote signal that allowed the data acquisition software to automatically start collecting data when the injection was made. The data collection system used was TotalChrome v6.2.1. Scientific Data Analysis Software (SDAS) v1.1 was used for all curve fitting. All connective tubing was factory precut stainless steel tubing, except for the tubing from the pump to the injector, which was PEEK tubing. It was decided that the stainless steel tubing be used instead of PEEK tubing because the peak shape for the extracolumn volume measurements was not very reproducible when using PEEK tubing

56 if any of the connections had to be disconnected and reconnected. Also, the stainless steel tubing gave better B/A values than those seen when using the PEEK tubing. The stainless steel tubing used was 316 stainless steel capillary tubing with an inner diameter of 0.010 inches. As supplied from the manufacturer, these lengths of tubing were cut using a special cutoff machine, then each end was machine polished, followed by de- burring of the inside and outside edges. Finally the tubing was ultrasonicated, passivated, and washed. This provided square, burr-free ends that allow for zero dead volume connections. All the connections were made with this precut stainless steel tubing that was 10 cm long. The injection loop was also made of a precut piece of stainless steel tubing with this same inner diameter but of length 30 cm. The inner diameter was chosen to match the inner diameter of the flow path through the injection valves which were 0.01 inches in diameter, as suggested by the valve manufacturer. This allowed for less mixing and flow disturbances. The nominal injection volume was 15 μL. The extracolumn volume was minimized by using the shortest lengths of tubing possible for our system. The importance of minimizing the extracolumn volume will be discussed in section 3.9. The temperature of the chromatography column was kept at 30.0°C throughout the experiments. The cooling system used for this purpose was an Isotemp Refrigerated Circulator, model 4100, from Fisher scientific attached to a water jacket that surrounded the column. The water jacket and the tubing leading from the water bath to the water jacket were covered with insulating material. The chromatographic column needed to be equilibrated at each flow rate, and whenever the pump was refilled. It was found that flushing the column with 20 mL was sufficient for column equilibration. At very low flow rates, the system pressure was very low and it was necessary to use a back pressure regulator that was attached to the outlet of the detector. This was simply a flow restrictor made of a chosen length of capillary with 75 μm inner diameter fitted into a ferrule assembly as described previously for packing capillary columns. At very low flow rates, 0.1 mL/min and 0.2 mL/min it was necessary to use the back pressure regulator even when the chromatographic column was included in the system. When performing experiments to get the extracolumn volume at each flow rate, two back

57 pressure regulators were utilized. A long one, 17.7 cm, was used for the low flow rates (0.1 mL/min to 0.5 mL/min) and a shorter one, 4.8 cm, was used for the higher flow rates (0.6 mL/min to 1.5 mL/min). At flow rates higher than 1.5 mL/min, no back pressure regulator was required. The LC columns, when supplied, were stored in 85/15 methanol/water. After being used, they were always stored in 100 % acetonitrile. When it was required that the column be tested, it would be tested using a mobile phase of composition 85/15 methanol/water, so the resulting chromatograms could be compared to the literature that was supplied with the column. Several precautions were taken in sample preparation. All the samples were prepared in approximately 20 mL aliquots of the mobile phase. This was done to avoid having refractive index peaks on our chromatograms. Such disturbances could interfere with the uracil measurements, since they would be almost superimposed. Once an appropriate concentration for each component was found, all the samples made using that component were prepared so that the peak absorbance related to that component was on the same order of magnitude for all samples.

3.9 Importance of Subtracting the Extracolumn Variance

In Liquid Chromatography significant broadening occurs outside the column. This is described as the extracolumn broadening, and can greatly affect the data that is collected.85 This broadening occurs in the connecting tubing and fittings used in the system, the column frits, the detector cell and the injector. In liquid chromatography, the magnitude of the extracolumn band broadening is often underestimated and ignored.86 Many previous studies did not subtract the extracolumn variance and that was one reason why it has been difficult to choose the correct plate height equation.87 The purpose of the experiments described here is to study chromatographic band broadening; therefore, only intracolumn broadening is of interest. Because of this, it is important to measure the extracolumn broadening and subtract it from the total broadening. A graph of a peak obtained when measuring the extracolumn variance is given in Figure 20, and information about the peak obtained and the conditions used are given in Table 3.

58 tR

W A B 0.1

02468101214

Time (s)

Figure 20. Graph of peak obtained when measuring the extracolumn variance of the chromatographic system.

Table 3. Information about the conditions used, and the peak obtained when measuring the extracolumn variance

File Name ECV-21 March076.rst Solute Uracil

Mobile Phase Composition 60% ACN-40% H20 Flow Rate 1.0 mL/min Time (s) 4.5 s B/A 1.72 Foley Plates 20 Peak Width at 10% (s) 3.75 s

59 I have chosen three of the known methods of measuring extracolumn variance to discuss here. I will include the procedure and some limitations of these methods, and finally the reasons for using the method that was chosen. The first and simplest method is to remove the column from the chromatographic system and replace it by a low dead volume union. Once this has been done, the variance due to the dispersion in the extracolumn regions can be measured.88, 89 The problem with this method is that when the column is removed, the variance due to the column fittings and the frits is not measured. In addition to this, the variance due to the union used to replace the column is not a part of the system variance. Even more important than this, the dispersion due to the difference in the diameter of the column and the connecting tubing is not measured. This is believed to be a major contributor to peak dispersion. In addition to these problems, the injection profile may be changed by the absence of back pressure on the system and the effects due to the rise time of the detector may become disproportionately large.86 The second method that is sometimes used is to replace the column by a capillary tube and then measure the variance of the system. The variance due to the capillary tube can be calculated using Equation 9 and then subtracted from the total variance for the system.90 This method can also be modified by using capillaries of different length to measure the corresponding variances, then extrapolating from a graph of total variance plotted against capillary length in order to calculate the expected variance when a capillary of “zero” length is used in place of the column.91 This method has all the same shortfalls as the previous method except that it does not add the variance of a union to the measurement. It does, however add the variance of the fittings used to secure the capillary in place. The third method used to subtract the extracolumn variance is known as the linear extrapolation method. This method uses the idea that the variances due to the column and the extracolumn effects are independent and therefore additive. In this method, components with different retention times are injected into the column and a graph of total variance against (1+k’)2 is plotted. This graph is then extrapolated to a k’ of zero, and this value should be the extracolumn variance.88, 90, 92, 93 This method does not have the same shortfalls that the two previous methods have, however it also is not a perfect

60 method. The main problem is that it only works when very strict conditions are satisfied. Two of the necessary conditions which are difficult to satisfy are that the solutes should have the same diffusion coefficients in the stationary phase and mobile phase, and that they should have the same plate heights. 86 The method used in this study was to remove the column from the chromatographic system and join the tubing from both sides of the column using a zero dead volume union. Next, the sample of interest was injected and the variance of the observed peak was calculated using Equation 9.31 This was done for all the solutes used, and the results were similar, leading to the conclusion that the contribution of extracolumn broadening to the total broadening for each solute is the same. This was done at all the flow rates used for this study, and at least three replicate measurements were collected for each flow rate. In addition to this, the pressure of the system was measured and when necessary a back pressure regulator set to the appropriate pressure was used.

Equation 9 2 2 W 1.0 σ = 2 ⎛ B ⎞ ⎛ B ⎞ .1 764⎜ ⎟ − 15.11 ⎜ ⎟ + 28 ⎝ A ⎠ ⎝ A ⎠

Variances for independent processes are additive, so the intracolumn dispersion and the measured extracolumn dispersion which are independent of one another can easily be separated. The extracolumn variance can simply be subtracted from the total variance in order to calculate the column variance. Although this process should give data that only includes intracolumn dispersion, as discussed previously, some of the extracolumn dispersion is not accounted for by this method. These variances that are not taken into account are the dispersion due to the column frits and the column fittings. This extracolumn dispersion was not accounted for because both of these contributors to peak dispersion were removed when the column was replaced by the zero dead volume union as shown in Figure 21. A plot of the measured extracolumn variance is shown in Figure 22.

Figure 21. Picture showing the zero dead volume union used to replace the chromatographic column in order to measure the extracolumn variance.

Extra-Column Variance 80 70 60 ) 2 50 40 ECV (s ECV

2 30 σ 20 10 0 0 0.5 1 1.5 2 2.5 3 F (mL/min)

Figure 22. Graph of the extracolumn variance for the liquid chromatography system used for this study.

Equation 10

2 2 2 σ Total = σ Column +σ Extra−column

Equation 11

2 2 2 σ Column = σ Total −σ Extra−column

Equation 12

σ 2 = σ 2 +σ 2 +σ 2 +σ 2 Column A B Cs CM

Figure 23 shows the plate height data collected for benzene, and highlights the difference that is seen in the data when the extracolumn variance has been subtracted. As the graph shows, when the plate height corresponding to the total variance is plotted, the overall plate height becomes lower as the percent acetonitrile in the mobile phase is decreased. However, when the plate height corresponding to the column variance is plotted, the overall plate height decreases as the percent acetonitrile in the mobile phase is increased. This obvious difference in the trends illustrates how important it is to subtract the extracolumn variance from the overall variance when one is interested in studying only the broadening occurring in the column.

63 Benzene

8 7 6 5

h 4 3 2 1 0 0 5 10 15 20 25 30 ν

70% ACN 80% ACN 90% ACN

Figure 23. Graph showing the data with and without the extracolumn variance subtracted. The points represent the total variance (column and extracolumn variance) and the lower curve represents the column variance (extracolumn variance subtracted). The k’ for benzene at these mobile phase strengths is as follows: 70% ACN, k’=1.4; 80% ACN, k’=0.9; and 90% ACN, k’=0.5

CHAPTER FOUR

INVESTIGATION OF RESISTANCE TO MASS TRANSFER IN REVERSED PHASE LIQUID CHROMATOGRAPHY

4.1 Band Dispersion in the Mobile Zone

Although it has been suggested that there are two distinct regions in the column where dispersion occurs, the mobile zone and the static zone, there is not absolute agreement in the literature about how to separate the contributions to dispersion arising from these regions. The van Deemter equation suggests that broadening occurring in the stagnant zone is dependent on the flow velocity, but that broadening occurring in the mobile zone from eddy diffusion is independent of the flow velocity. However, a paper published by Knox in 2002 gave a different view.94 Knox argued that broadening occurring in both the stagnant and the mobile zones has significant velocity dependences. He wrote that the A term dispersion likely has a strong dependence on the mobile phase velocity, unlike what is suggested by the van Deemter equation. He also concludes that unlike what is widely accepted, the C term dispersion is not due solely to the slow equilibration within the static zone. He suggests that a large part of the dispersion due to resistance to mass transfer is actually a consequence of mobile zone processes. From this, he suggests that it is possible to improve column performance using the stationary phase technology that is available today. If, however, this view is wrong, and the dispersion associated with the C term is due mostly to slow equilibration within the static

65 zone, then there is not much improvement that can be made to chromatographic columns using the current stationary phase technology.94

4.2 Experimental

The liquid chromatograph used is the one described in Chapter 3 section 3.8. The detector wavelength was set to 254 nm, the detector rise time was set to 0.1 s. The column was temperature controlled at 30°C ± 0.5°C. When the diffusion coefficients were measured, the open tubing was also temperature controlled at 30°C ± 0.5°C. The column used in this study was the Zorbax C18 column described in section 3.8.2. This column was a 15cm x 4.6mm column packed with 5μm spherical silica particles that had been derivatized with C18 groups. This column had a 70 Å pore diameter. The extracolumn variance was subtracted using the method described in section 3.9. The part number was 883952-702, the serial number was USG0014021, and the lot number was B02011. The extracolumn variance was subtracted using the method described in Chapter 3 section 3.9. The mobile phase compositions used were 60%, 70%, 80%, and 90% acetonitrile in water. The non-retained solute used was uracil; the retained solutes used were benzene, toluene, ethylbenzene, propylbenzene, and butylbenzene. The samples were made up with multiple components in each sample. Two samples were prepared for the mobile phase composed of 60% acetonitrile. The first contained uracil, toluene and ethylbenzene, and the second contained uracil, benzene, propylbenzene and butylbenzene. Three samples were prepared for the mobile phase composed of 70% acetonitrile. The first contained uracil and benzene, the second contained uracil, toluene and ethylbenzene, and the third contained uracil, propylbenzene and butylbenzene. Two samples were prepared for the mobile phase composed of 80% acetonitrile. The first contained uracil and benzene, and the second contained uracil, toluene, ethylbenzene, propylbenzene and butylbenzene. Two samples were also prepared for the mobile phase composed of 90% acetonitrile. The first contained uracil, benzene and ethylbenzene, and the second contained uracil, toluene, propylbenzene and butylbenzene. All the samples

66 were prepared using the sample and mobile phase components and methods described in section 3.8.1.

4.3 Comparison of Plate Height Data for Retained and Non-retained Solutes

After the chromatograms were collected for both the non-retained specie (uracil) and the retained species (benzene, toluene, ethylbenzene, propylbenzene, and butylbenzene) and the extracolumn variance was subtracted, the reduced plate height was calculated using Equation 7. One noticeable feature of all the graphs is that none of the curves were smooth. The plots were the typical shape of a graph of reduced plate height vs. reduced velocity, but none of them were as smooth as expected (see Figures 24 and 25). This could be attributed to irreproducibility issues in the individual measurements, so it was important to include error bars on the graphs. Because the curve was not smooth, one would expect that once the graphs were plotted with the error bars, the error bars would be somewhat large, suggesting that the lack of smoothness was due to plotting the averages of the calculated plate heights and not having shown all the data points. However, when the error bars were added to the graph, it was seen that they were not large and did not make the curve appear any smoother. Since this was seen for both the non-retained compound and all the retained species, it was necessary to figure out why the curve was not smooth. Was it random, or if it was due to some process that all the solutes were being exposed to as they passed through the column? If a meaningful mathematical process could be performed that resulted in the smoothing of the curves, this could help to determine the cause. In order to do this, it was decided that the variance of the non-retained species, uracil, would be subtracted from the variance for each retained species. This subtraction would only be meaningful if it resulted in a smoothing of the reduced plate height curves for each of the retained species. After performing the subtraction, it should be possible to determine if whether the cause is random, based on the plot of the reduced plate height corresponding to the remaining variance for each retained solute vs. the reduced velocity.

Uracil

4.5

3.5 h 3

2.5

1.5 0 5 10 15 20 25 30 ν

Figure 24. Graph of reduced plate height vs. reduced velocity for uracil. Note that as discussed in section 4.3, the curve is not smooth. Solid lines were placed on the graph to guide the eye and are not meant to imply continuity between data points.

60% ACN 70% ACN 80% ACN 90% ACN

Toluene

4.5

3.5 h 3

2.5

1.5 0 5 10 15 20 25 30 ν

Figure 25. Graph of reduced plate height vs. reduced velocity for toluene. Note that this graph, like the graph of reduced plate height for uracil, is also not smooth. Solid lines were placed on the graph to guide the eye and are not meant to imply continuity between data points.

4.4 Subtraction of Uracil

It was decided that to investigate the cause of the unevenness of the curves, the uracil data for each mobile phase composition would be subtracted from the data for all of the retained species in that mobile phase composition. This was done by taking the average value of the calculated variances for each of the retained solutes and subtracting the corresponding average value of the calculated variances for the uracil peak. Uracil was a component of every sample that was prepared and used, resulting in an enormous amount of uracil data having been collected and available for use. Because uracil was present in every chromatographic run, it was possible to investigate what was causing the unevenness in the curves shown in Figures 24 and 25. Was this due to a phenomenon associated with each individual injection or was it due to broadening processes that were seen by all the solutes that were injected? After performing the subtraction, the remaining variance for each retained solute was used to calculate the corresponding reduced plate height value. A graph was then generated for each of the retained solutes by plotting the reduced plate height values against the corresponding reduced velocities. The curves resulting from this subtraction were much smoother than the originals. Although this was true for all the retained solutes used in this study, the results were most obvious for the less retained solutes since the graphs of the data for these solutes had been the least smooth. This suggests that the cause is not random, but actually a result of a process that all the solutes are exposed to independent of their retention in the column. If the cause had been random, then subtracting the variances should not have smoothed the curves. The plots of the plate height data for all the solutes with and without the variance associated with uracil subtracted can be found in Appendix A.

69 Toluene

4.5

3.5 h 3

2.5

1.5 0 5 10 15 20 25 30 ν

Figure 26. Graph of reduced plate height vs. reduced velocity for toluene. This graph shows the unevenness of the curve as described previously. Solid lines were placed on the graph to guide the eye and are not meant to imply continuity between data points.

60% ACN 70% ACN 80% ACN 90% ACN

Toluene after Uracil Subtracted

4 3.5 3 2.5 h 2 1.5 1 0.5 0 2 4 6 8 101214161820222426283032 ν

Figure 27. Graph of remaining reduced plate height vs. reduced velocity for toluene after the variance associated with uracil was subtracted. Note that the subtraction performed has smoothed the curves greatly. The significance of this is discussed in the following sections. Solid lines were placed on the graph to guide the eye and are not meant to imply continuity between data points.

70 As mentioned previously, uracil was a component of every sample prepared, so the values used for the uracil variance were averages of numerous injections. Because the data used for uracil at each flow rate and in each mobile phase composition was collected over several different days, it is even more reasonable to believe the argument that the cause of the unevenness was not random. The uracil data included uracil that was injected with different samples as well as uracil that was injected alone. The only thing that was the same for the uracil samples at each given mobile phase composition was the mobile phase composition itself. Figures 26 and 27 illustrate that after the variance associated with uracil was subtracted from the variance for toluene that the curves were smoother that they had been prior to the subtraction. This suggests that every time uracil was injected onto the column in a particular mobile phase composition it had the same behavior. It is also noteworthy that the uracil data showed that when the mobile phase composition was changed the behavior of the uracil was different, and performing the subtraction using uracil data for a mobile phase composition that did not match that of the retained compound did not smooth the curves. In order to understand the significance of this mathematical operation, it was important to understand which of the band broadening processes were causing dispersion in each of the solutes being studied. Uracil, being a non-retained solute, does not experience all of the dispersion that the retained solutes experience. The extracolumn variance was discussed in section 3.9, and the measured extracolumn variance has been subtracted from each data set. However, the method chosen for measuring the extracolumn variance in this study did not allow for the measurement of the variance due to the column fittings and the frits. Therefore, it was not possible to subtract the variance due to these extracolumn components although this would have been desirable. Because of this, the plate height curves for both the retained and non-retained solutes include these sources of extracolumn broadening. In addition to this, all the solutes, both the retained and the non-retained, also experience broadening due to eddy diffusion, molecular diffusion, and resistance to mass transfer in the mobile phase. However, only the retained solutes experience broadening due to resistance to mass transfer in the stationary phase.

71 The broadening due to the frits and the column fittings should be the same for both retained and non-retained compounds. The subtraction performed should therefore have removed all the remaining contributions to band broadening from extracolumn dispersion. The contribution to the variance of the solutes due to eddy dispersion as the solutes move through the column should also be the same for the retained and non- retained solutes, so this contribution was also subtracted. On the other hand, the molecular diffusion is different for each of these molecules, so when the variance associated with the uracil is subtracted it does not subtract the molecular diffusion of the retained solute. This is one aspect of the subtraction that is not desirable. In effect, the subtraction has removed the variance due to molecular diffusion for the uracil molecule from the variance associated with the retained compound. Since the two molecules are not related, this does not give any useful information. However, the contribution to band broadening from molecular diffusion becomes negligible after a reduced velocity of about sixteen. Because of this, for the rest of this study only data corresponding to reduced velocities higher than sixteen will be considered. By doing this, it is possible to subtract the variance associated with uracil from the variance associated with each retained compound without this negative effect. In the portion of the data being used, corresponding to reduced velocities higher than sixteen, the only variances that remain for the retained solutes after the subtraction are due to resistance to mass transfer in both the stationary phase and the mobile phase. It is known that the resistance to mass transfer in the stationary phase is different for each of the solutes used in this study. Furthermore, since uracil is non-retained, the variance associated with the uracil peak does not have any contribution from resistance to mass transfer in the stationary phase. On the other hand, all the solutes, whether retained or non-retained, experience broadening due to the resistance to mass transfer in the mobile phase. At this point it was uncertain whether the dispersion associated with this process was the same for the six solutes chosen in this study. If the resistance to mass transfer in the mobile phase was the same for all the solutes used in this study, both retained and non-retained, performing this subtraction is actually subtracting out the resistance to mass transfer in the mobile phase. This would mean that the remaining variance would only be due to resistance to mass transfer in the stationary phase. It is very important to know

72 whether or not the solutes used in the experiment all experienced the same resistance to mass transfer in the mobile phase, and this information is necessary in order to determine what the variance remaining after this mathematical operation was performed represents.

4.5 Measurement of the Diffusion Coefficient in the Mobile Phase

The contribution to the total plate height from resistance to mass transfer in the 4 mobile phase, HM,D, is described by Equation 13. In this equation, w is an empirical packing factor that corrects for radial diffusion. The values for this factor can range from 0.02 to 5. This equation shows that the contribution to plate height from the resistance to mass transfer in the mobile phase is inversely related to the diffusion coefficient in the mobile phase (Dm). The significance of this information is the following: if the diffusion coefficients for all the solutes used in this study, both retained and non-retained, are the same in the mobile phase being used, then the resistance to mass transfer in the mobile phase for these solutes should be similar. As stated previously, this would mean that after subtracting the variance associated with the uracil, the variance remaining for the retained compound would be due solely to the resistance to mass transfer in the stationary phase.

Equation 13

2 wud p H ,DM = DM

When measuring the diffusion coefficient for this purpose, it is actually the effective diffusion coefficient in the mobile phase that is important. There are several different methods that can be used to measure this value. The method by which the diffusion coefficient in the mobile phase was measured for this study was to replace the chromatographic column with a known length of tubing of known inner diameter. The tubing used was 130.3 cm in length, and 0.02 inch in diameter. All six solutes were injected, and the variance for the observed peaks was then calculated after the solutes

73 passed through this open tube. This type of flow measurement correlates the width of the peak after it passes through an open tube to the effective diffusion coefficient in the mobile phase. It was very important to correct the data for the extracolumn variance and the extracolumn volume to make the calculation more accurate. Equation 14 was used to calculate the diffusion coefficient in the mobile phase from the value obtained for the variances.95 The data shown in Table 4 was collected using a straight tube of 130.3 cm at 26.0°C. The values calculated for the diffusion coefficients were corroborated by data collected using a coiled tube that was thermostatted at 30.0°C. The data collected from the experiment with the straight tube was reported in preference to the data collected using the coiled tube because of several rigid constraints that had to be satisfied for the experiments to be valid.96

Equation 14

2 2 (dt L) σ z = 96D tRM

Effective diffusion coefficients for all the solutes in the mobile phase were calculated from these variances. The diffusion coefficients for the different solutes are given in Table 4. The average value for the diffusion coefficients was 1.40 x 10-5 cm2/s. The values calculated for the effective diffusion coefficients for all the solutes were within 8.5 % RSD of the average value. Because these values are within 8.5% RSD of the average value, the effect of the difference in these values when used to calculate the resistance to mass transfer in the mobile phase will be negligible. This suggests that the resistance to mass transfer in the mobile phase would be similar, and that the variance remaining after the subtraction of the variance associated with uracil as previously described was solely due to resistance to mass transfer in the stationary phase. The values calculated for the diffusion coefficient in 60/40 ACN/H20 are comparable to those measured by Li and Carr in 1997. They measured the value of the effective diffusion coefficients for toluene and butylbenzene to be 1.71 x 10-5 cm2/s and 1.19 x 10-5 cm2/s respectively. 96

Table 4. Effective diffusion coefficients in the 60/40 ACN/H20 mobile phase at 25°C. These values were calculated from variances for each solute using the Aris-Taylor dispersion equation.

-5 2 Solute DM (x 10 cm /s) Uracil 1.26 Benzene 1.57 Toluene 1.49 Ethylbenzene 1.41 Propylbenzene 1.36 Butylbenzene 1.31

4.6 Changes in the Slope after Subtracting Uracil

After the variance associated with uracil was subtracted from the variance for each of the retained solutes, there were visible changes in the plots of the resulting reduced plate height data. One of the most obvious changes, and perhaps one of the most important observations, was that the slopes associated with the portions of the curves corresponding to reduced velocities greater that sixteen were greatly changed (see Figures 28-31). In order to point out the importance of this change, recall the van Deemter equation and the graph of the overall plate height. In this model, and in the other models discussed, the portion of the graph corresponding to reduced velocities greater than sixteen is dominated by the contribution to overall plate height by the resistance to mass transfer. In the original van Deemter equation, this corresponds to the

75 resistance to mass transfer in the stationary phase, but in the modified van Deemter equation, it corresponds to the resistance to mass transfer in both the stationary phase and the mobile phase. Any changes seen in the slopes of the curves in this region would correspond to changes in the resistance to mass transfer in either the mobile phase or the stationary phase. As discussed in sections 4.4 and 4.5, the data collected suggests that when the variance associated with uracil was subtracted from the variances for the retained solutes, one of the contributions to band broadening that was removed was the resistance to mass transfer in the mobile phase. If this is correct, then it would be expected that the slopes of the curves in this region would change. The change in the slope that would be observed would be expected to be larger for the less retained compounds than for longer retained compounds. The reason for this is that for the less retained compounds the resistance to mass transfer in the mobile phase would comprise a larger portion of the total resistance to mass transfer than it would for the more retained compounds. As the compounds are retained longer, the resistance to mass transfer in the stationary phase becomes a greater and greater contributor to the overall plate height, finally overshadowing the constant contribution from resistance to mass transfer in the mobile phase. The slopes for the portion of the curves corresponding to a reduced velocity greater than sixteen were calculated as follows. First, the entire range of data points for each solute was used to generate a fitted curve using the van Deemter equation and the Giddings equation. The y values from the fitted curve that correspond to each flow rate used in the experiment were calculated. From these y values, those corresponding to reduced velocities greater than sixteen were then chosen. These values were used to calculate a trend line using the linear trend line function in the graphing utility of Microsoft Excel. The slopes for each of the curves were obtained from the equations for the calculated trend lines. This was done for each solute using the data before and after the uracil was subtracted from the column data. In this manner, it was possible to calculate the change in the slope due to the subtraction of the variance associated with the uracil. Plots of the plate height data for all the solutes corresponding to reduced velocities greater than 16 can be found in Appendix B.

76 Toluene

3.5

2.5

h 2

1.5

0.5 16 18 20 22 24 26 28 30 ν

Figure 28. Graph of reduced plate height vs reduced velocity for benzene (reduced velocities greater than 16). Note that the lines are converging and in some cases have intersected with one another.

60% ACN 70% ACN 80% ACN 90% ACN

Toluene with Uracil Subtracted

3.5

2.5

h 2

1.5

0.5 16 18 20 22 24 26 28 30 ν

Figure 29. Graph of reduced plate height vs. reduced velocity for benzene after the variance associated with uracil has been subtracted. Note that the slopes of the lines have changed greatly, and the lowest line corresponding to the strongest mobile phase composition is diverging from the other lines. Also note that the trend lines appear to better fit the data points.

77 Butylbenzene

3.5 3.3 3.1 2.9

h 2.7 2.5 2.3 2.1 1.9 16 18 20 22 24 26 28 30 ν

Figure 30. Graph of reduced plate height vs. reduced velocity for butylbenzene (reduced velocities greater than 16). Note that the lines are converging and intersecting one another.

60% ACN 70% ACN 80% ACN 90% ACN

Butylbenzene with uracil subtracted

3.5 3.3 3.1 2.9

h 2.7 2.5 2.3 2.1 1.9 16 18 20 22 24 26 28 30 ν

Figure 31. Graph of reduced plate height vs. reduced velocity for butylbenzene after the variance associated with uracil has been subtracted. Note that although the upper three lines are still converging they are no longer overlapping, and the lower line, corresponding to the strongest mobile phase composition is actually diverging from the other lines.

78 Table 5. The slopes calculated using the last six points in the plate height curve corresponding to reduced velocities greater than 16. Note that when longer retained molecules are used, the slope generally increases; however, when the mobile phase strength is changed and an analyte is longer retained, the slope decreases.

% ACN Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

60 0.0536 0.0532 0.0506 0.0547 0.0555

70 0.0542 0.0566 0.0614 0.0616 0.0586

80 0.0593 0.0643 0.0628 0.0660 0.0690

90 0.0609 0.0611 0.0683 0.0707 0.0706

Table 6. The slopes calculated using the last six points in the plate height curve corresponding to reduced velocities greater than 16 after uracil has been subtracted. Note that as the molecules are longer retained, the slope increases. This is independent of the reason for the change in retention (different molecule or different mobile phase strength).

% ACN Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

60 0.0474 0.0519 0.0491 0.0540 0.0552

70 0.0407 0.0485 0.0565 0.0591 0.0574

80 0.0321 0.0454 0.0496 0.0580 0.0643

90 0.0181 0.0272 0.0414 0.0512 0.0571

79 Table 7. The change in the slope of the plate height curve for reduced velocities above 16 after the variance associated with uracil is subtracted. Note that the change in the slope is generally decreasing as the solutes are retained longer, independent of the reason for the change in retention (different molecule or different mobile phase strength).

% ACN Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

60 0.0062 0.0013 0.0015 0.0007 0.0003

70 0.0135 0.0081 0.0049 0.0025 0.0012

80 0.0272 0.0189 0.0132 0.0080 0.0047

90 0.0428 0.0339 0.0269 0.0195 0.0135

The values for the slopes are given in Tables 5 and 6. The calculated values for the change in the slope are given in Table 7. These are the values for the change in the slope determined using the van Deemter fits. The values calculated using the Giddings fits were different only in the fourth decimal place, and only in some instances. The values shown in Table 7 are in agreement with the previous suggestion that the mathematical operation performed was removing the contribution due to resistance to mass transfer in the mobile phase. Looking at the data in Table 7 one can see that there is a change in the slope for all the curves in the region of interest. Even more important than that, however, is that the change in the slope is progressively smaller for each solute starting from the least retained solute, benzene, and moving across to the longest retained

80 solute, butylbenzene. As stated previously, this indicates that the subtraction of the variances removed some of the contribution to band broadening that was due to resistance to mass transfer, either in the mobile phase or the stationary phase. However, it is likely that it is the contribution to band broadening due to resistance to mass transfer in the mobile phase that has been subtracted. To make certain that this is the proper conclusion, presented here is a review of the mathematical operation that was performed. The variance associated with uracil was subtracted from the variances associated with each retained solute. Uracil is a non- retained molecule, therefore it has only a contribution to band broadening due to resistance to mass transfer in the mobile phase, but no contribution due to resistance to mass transfer in the stationary phase. The reason for this is that it does not partition into the stationary phase. All the other solutes are retained, and therefore they have a contribution to band broadening due to both the resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. Each of these solutes, both the retained and the non-retained solutes, have the same contribution to resistance to mass transfer in the mobile phase, and this was removed when the variance associated with uracil was subtracted. Each of the retained solutes, however, have a different contribution to band broadening due to resistance to mass transfer in the stationary phase, the magnitude of which is dependent on the retention of the solute in the column. The longer a solute is retained in the column, the larger the contribution due to resistance to mass transfer in the stationary phase. The significance of this observation is that if a subtraction of the variance associated with the uracil causes a change in the slope of the plate height curve for each retained solute, then this subtraction is removing a portion of the resistance to mass transfer term. Since the portion removed corresponds to the resistance to mass transfer in the mobile phase, and is a constant value, then it is expected that this subtraction will have a greater effect on the less retained compounds. This is what is illustrated by the data.

81 4.7 Changes in Reduced Plate Height after Subtracting Uracil

When the subtraction of the variances was performed, the overall plate height was reduced. This is an obvious result of this mathematical operation, but there is some interesting information that can be obtained from looking at the magnitude of the change in reduced plate height. The calculated values for the reduced plate height before and after the subtraction was performed are given in Tables 8 and 9. Table 10 shows the change in the reduced plate height after the subtraction of the variance associated with uracil. Previously it was shown that subtracting this variance was removing dispersion due to the column fittings, the two frits, eddy dispersion, and resistance to mass transfer in the mobile phase. All the dispersion due to other sources of extracolumn variance has already been subtracted, so this process has removed all remaining contributions due to extracolumn variance. The variance that corresponds to the subtracted reduced plate height can then be calculated and this tells us the expected variance for a column that exhibits no dispersion due to eddy diffusion and resistance to mass transfer in the mobile phase. These tables only include values for the reduced plate heights corresponding to data collected at the flow rate 2.5 mL/min. The data for each of the other flow rates from 1.75 mL/min to 3.0 mL/min (corresponding to the reduced velocities above 16) show similar results. The values in Tables 7 and 8 can be used to calculate the corresponding number of theoretical plates that would be added to the current calculated value if it was possible to make a column that exhibited no dispersion due to eddy diffusion and resistance to mass transfer in the mobile phase. Using the values corresponding to the largest change in reduced plate height, an increase of 60,000 plates is calculated, but using those corresponding to the smallest change in reduced plate height only an increase of 1000 plates is calculated. Rather than stating that this would be the number of theoretical plate increase expected from a better designed column, it is reasonable to say that this shows that there is room for improvement in the overall efficiency of columns using the current stationary phase technology. A large increase in the plate count would be beneficial for analytical columns, but for preparatory scale chromatography, even a more modest increase of 1000 plates would prove beneficial.

82 Table 8. The reduced plate height calculated using the data from the chromatogram obtained at a flow rate of 2.5 mL/min. A single flowrate had to be chosen in order to represent the data in a simple tabular form.

% ACN Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

60 2.80 2.88 2.92 2.96 3.02

70 2.60 2.70 2.84 2.95 3.03

80 2.36 2.74 2.83 2.94 3.02

90 2.23 2.57 2.63 2.79 2.92

Table 9. The reduced plate height calculated using the data from the chromatogram obtained at a flow rate of 2.5 mL/min after the variance associated with uracil was subtracted.

% ACN Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

60 2.46 2.71 2.83 2.92 3.00

70 1.97 2.33 2.61 2.83 2.97

80 1.22 1.95 2.28 2.61 2.82

90 0.40 1.14 1.49 1.97 2.35

83 Table 10. The change in the reduced plate height calculated from the chromatogram obtained at a flow rate of 2.5 mL/min when the variance associated with uracil was subtracted.

% ACN Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene

60 0.34 0.17 0.09 0.04 0.02

70 0.63 0.37 0.23 0.12 0.06

80 1.14 0.79 0.55 0.33 0.20

90 1.83 1.43 1.14 0.82 0.57

There have been many theoretical studies suggesting that by changing either the shape of the packing or the way the column is packed, the efficiency of the column could be greatly improved.97-106 These computational studies suggest that by using differently designed stationary phase supports the dispersion due to eddy diffusion and resistance to mass transfer in the mobile phase can be drastically reduced, thereby allowing much higher efficiencies in HPLC. From their calculations, reduced plate heights of 1 are possible by such a restructuring of the column. It is suggested that the increase in efficiency is due mostly to having a more homogenous structure for the stationary phase. One of these studies was by Billen and coworkers in 2005.98 In this paper, a set of two- dimensional particles in a two dimensional geometry was used to represent the three- dimensional packed bed of a chromatographic column. In this study, the particles are not allowed to touch each other, which differs from an actual three-dimensional packed bed. However, this was justified because in a packed bed, the particles are only in contact at isolated points. The dispersion in the column was simulated using a commercially

84 available software, Fluent v6.1.22, along with several additional routines that were prepared specifically for this study. Plots of the simulated dispersion showed that when the particles were homogenously packed, the computed velocity magnitude fields were evenly spread across the column, and all flow-through pores were equally permeated. This means that an injected solute band would not be greatly broadened, since the velocity paths are all similar. For the simulation of packing with short scale randomness, there are a few flow paths that are preferential over the others, and because of this, solute molecules that are in these flow paths move through the column faster. This leads to great band broadening, since some solute molecules travel through the column faster than others. In clustered packing, similarly, there are a few preferential flow paths. However, in the clustered packing, these preferential flow paths are better connected than in the case with the short scale randomness. Also, since the clustered case offers larger spaces between some of the particles, the preferential flow paths can transport a larger flow rate than in the other cases. This leads to excessive band broadening, as the solute molecules in the wide flow paths move very far ahead of those in the narrower flow paths. This further supports the idea that the dispersion in the chromatographic column can be reduced by restructuring the column packing in order to make it more homogenous.

CHAPTER FIVE

MODELING CHROMATOGRAPHIC DISPERSION: A COMPARISON OF POPULAR EQUATIONS

5.1 Popular Equations Used to Model Chromatographic Dispersion

5.1.1 van Deemter Equation

The van Deemter equation69 was formulated in 1956. This equation was used to describe the contributions to band broadening in chromatography. In the original version of this equation three independent contributions to band broadening were described. These contributions were the A term, which described eddy diffusion, the B term, which described molecular diffusion, and the C term, which described the resistance to mass transfer in the stationary phase. The variances due to these processes were then added to give the van Deemter equation, with H being the total plate height associated with the specific chromatographic column being used. Eddy diffusion, the A term, describes the contribution to band broadening that results from inhomogeneous packing of the stationary phase bed. The eddy diffusion term was used to describe the broadening associated with the different paths that an analyte could take through the chromatographic column. There are many different paths available to each analyte, each with a different length. This leads to broadening of the injected solute band because different molecules of the same analyte elute from the column at slightly different times. The different paths also have different flow velocities, also leading to additional broadening. The molecular diffusion term, the B term, describes the diffusion of the injected analyte molecules along the axis of the flow path as they move through the column. This diffusion adds to the broadening of the injected band and is a function of the diffusion coefficient of the analyte molecule and the flow

86 rate of the mobile phase through the column. This type of band broadening is particularly important at low flow rates since the analytes have a much longer time to diffuse inside the column. The Einstein equation, Equation 15, is used to describe this type of diffusion. The resistance to mass transfer term, the C term, in the original van Deemter equation was specifically used to describe resistance to mass transfer in the stationary phase. This resistance to mass transfer in the stationary phase was described by van Deemter and coworkers as involving the solute moving between the mobile phase and the stationary phase.

Equation 15

σ 2 = 2Dt

These three band broadening processes are independent of one another and therefore their variances are additive. The van Deemter equation, shown in Equation 16, was the model that van Deemter and coworkers arrived at to model these dispersion processes. Figure 32 is a graphic description of the individual broadening processes and their sum. Until about 1961 this equation was believed to accurately represent the peak dispersion that occurred in a packed chromatographic column.

Equation 16 B H = A + + Cu u

The van Deemter equation is still the most commonly used equation for fitting chromatographic efficiency data and is the equation most often found in undergraduate text books. The equation offers a good fit to most chromatographic data. After several years, it was found that there was another possible contributor to band broadening, the resistance to mass transfer (RMT) in the mobile phase. In order to account for this source of broadening, the C term was further divided into two terms, the CM term and the CS term. The CS term involves the solute moving between the mobile phase and the stationary phase, and the CM term involves the solute moving between the mobile phase and the stagnant mobile phase.

Column Plate Height vs. Mobile Phase Velocity

0.8

0.7

0.6 Htot H0.5 0.4 C

0.3

0.2 H (plate height) H (plate A 0.1 B 0 012345678 u (linearu velocity)

Figure 32. Contributions to plate height as described by van Deemter and coworkers in 1956. The region of the graph corresponding to low linear velocities is dominated by molecular diffusion, whereas the region of the graph corresponding to high linear velocities is dominated by resistance to mass transfer in the stationary phase. The contribution to plate height from Eddy Dispersion is shown to be independent of the flow rate; therefore, having the same contribution over the entire range of reduced velocities.

A – Flow Pattern: “Eddy Dispersion” B – Molecular Diffusion: σ2 = 2Dt C – Stationary Phase Mass Transfer

H = A + B/u + Cu

88 The van Deemter equation was modified to include both these terms, simply by making the CS and CM terms additive, giving Equation 17. There are two areas of stagnant mobile phase found within the packed bed. The first area of stagnant mobile phase is inside the pores of the stationary phase. Here, there are areas of mobile phase that may be adsorbed onto the stationary phase and are not continuously flushed through the column along with the rest of the mobile phase. Another area of stagnant mobile phase occurs in the tiny crevices where one stationary phase particle comes in contact with another one.

Equation 17 B H = A + + (C + C )u u s M

Around 1961, other scientists began to question the validity of this equation, and therefore ventured to come up with other equations to describe the dispersion. Many of these scientists agreed that van Deemter had identified the important contributors to band broadening, but there was discord as to how those factors should be combined and what the overall equation describing the band broadening processes in a chromatographic column should look like. Some of the other equations that have been introduced to model efficiency data include those of Giddings70 , Horvath and Lin71, 72, and Knox73. All of these equations are based on different theories, but they can all be used to fit efficiency data. This creates a plight for chromatographers who then need to decide which equation to use. Since all the equations offer similar fits, it may not seem particularly important which equation one uses. However, if the efficiency data is to be used to try to improve column technology, then the importance of the equation that is chosen becomes evident. In 2002, John Knox addressed this issue when he stated that if it is believed that the C term is due only to the RMT in the stationary zone, then the associated plate height contribution cannot be lessened. However, if C depends strongly on mobile zone

89 processes, then there can be much improvement to the separations possible using current stationary phases.94 In order to determine whether or not improvements in the separations can be achieved using currently available stationary phases, one must be using an equation that not only fits the data, but actually models the processes occurring in the column.

5.1.2 Horvath and Lin Equation

In 1976, Horvath and Lin studied the band spreading of non-retained analytes in liquid chromatography.71 They offer a good explanation of the different velocities that can be measured by using different types of analytes in liquid chromatography. This is very important in order to understand the data collected using different solutes. Horvath and Lin described several new terms in their equation in order to better fit the chromatographic data. The interstitial velocity (ue) is the hold-up time of an excluded non-retained analyte. An excluded analyte is an analyte that does not permeate the particles of the stationary phase. The interstitial velocity therefore corresponds to the velocity in the area between the particles. This can be measured using an analyte with a sufficiently high molecular weight that is excluded from the pores. The chromatographic velocity (u) is the hold-up time of a non-retained analyte that is able to sample the entire pore space of the stationary phase particles in addition to the interstitial space in the column. This can be measured using a non-retained analyte that is on the molecular dimensions of the solvent. A third velocity that can be measured is the velocity of a non- retained analyte (uM). This is the velocity of a solute as it passes through the column without being retained by the stationary phase. Analytes of different sizes will give different velocities depending on how much of the intraparticulate fluid space they are able to sample. If the chosen analyte is large enough, the measured velocity will be equal to the interstitial velocity, and if it is small enough the measured velocity will be the chromatographic velocity. Horvath and Lin then continued to describe what they call the “Interstitial Stagnant Fluid Model”. This model is used to describe the situation where a liquid is flowing through a packed bed at low Reynold’s numbers. Horvath and Lin suggested that there is a relatively large stagnant layer that surrounds the stationary phase particles.

90 The justification for this is that the typical conditions used in liquid chromatography allow for a thick hydrodynamic boundary layer at the surface of the particles.107 There are also cusp regions where the stationary phase particles are in contact with each other. In these areas the flow channels become very narrow and finally disappear, meaning that the particles would be surrounded by a stagnant layer. The areas where the particles contact each other would have an even larger stagnant region than the layer surrounding the particles. In order to reach the stationary phase surface, solutes would have to diffuse through these stagnant areas, leading to increased band broadening. Although this is an additional source of band broadening, it was stated that since this stagnant area occupied some of the interstitial space in the column, the broadening from eddy diffusion would be minimized. This leads to a coupling term which is also seen in the Giddings equation which is described in the next section. The Horvath and Lin equation is given in Equation 18.

Equation 18

2 1 B 3 H = + + Due + Eue 1 1 ue + 1 A 3 Cue

In Equation 18, the coupling of the broadening due to the stagnant layer surrounding the particles and the eddy diffusion is described by the first term (A and C). The second term (B) describes the broadening due to molecular diffusion. The third term (D) describes the broadening due to resistance to mass transfer in the stagnant layer for particles that sample the intraparticulate space. The final term (E) describes the diffusion as an analyte moves through the stagnant mobile phase inside the stationary phase pores.71

91 5.1.3 Giddings Equation

In 1965, Giddings reported a new equation to describe the dispersion taking place in a packed chromatographic column. He disagreed with van Deemter’s equation because it suggested that there was a finite contribution to dispersion that was independent of the solute diffusivity, in the limit of no mobile phase velocity. That is, that even when there is no mobile phase flow through the column, there is still a contribution from eddy diffusion. Since eddy diffusion describes the flow of the analyte along different paths in the column, Giddings believed it was unreasonable for this term to contribute to dispersion when there is no flow. The Giddings equation70 reduces to the van Deemter equation when u >> E, and when u << E the first term in the equation reduces to almost zero, thereby removing the contribution from eddy diffusion when the mobile phase flow rate is zero. This equation is given in Equation 19.

Equation 19

A B H = + + Cu E u 1+ u

5.1.4 Knox Equation

Knox and coworkers also published an empirical equation to model the reduced plate height73. The reduced plate height (h), as mentioned before, normalizes the plate height (H) for the particle size, so that plate height data for columns with particles of different sizes can be compared. In order to decide on the constants used for this equation, he used a curve fitting procedure, making the equation empirical. For his study, he chose to use data from nine geometrically similar columns that had a ratio of length to particle diameter equal to 20,000. Knox assumed that the columns were all equally well packed, and introduced the concept of “efficient use of pressure drop”.73 Because of his use of this concept, it was more useful to use the reduced plate height to model the data he collected.

92 Knox approached the problem of modeling the three types of dispersion by looking at them separately because each type contributed independent variances that were additive. When he attempted to model eddy diffusion he was unable to come up with a suitable theoretical equation. He did, however, find empirically that the contribution to plate height from this type of dispersion is well modeled by Equation 20. In this equation, α and β are constants and n has an empirically determined value between 0.2 and 0.5. He further simplified this equation to the popular version which is given in Equation 21.

Equation 20

⎡ − n ⎤ h = /1 ⎜⎛α + βν ⎟⎞ n < l ( flow) ⎣⎢ ⎝ ⎠⎦⎥

Equation 21

1 3 h( flow) = Aν

The dispersion of the band due to axial molecular diffusion is given by the Einstein equation as previously shown in equation 15. He was able to further simplify this equation to represent the plate height contribution due to axial diffusion by equation 22.

Equation 22

B h = ()axial diffusion ν

Knox realized that the amount of dispersion that occurred due to resistance to mass transfer was a function of the distance the individual molecules were able to travel during the time it takes for one of them to partition out of the stationary phase and back into the mobile phase. This is shown by Equation 23. He also realized that because this involved a moving band it was dependent on k”, and he included this in his equation for

93 the plate height contribution due to resistance to mass transfer shown in Equation 24. He was further able to simplify this into the simpler model given in Equation 25.

Equation 23

r / d p = (q' Dm / Ds )ν

Equation 24

2 h()mass transfer = kq 1/("'[ + k )" ](Dm / Ds )ν

Equation 25

h()mass transfer = Cv

Once Knox had developed equations for modeling these processes individually, the equations were combined to give Equation 26, the Knox equation73. This equation can be used to fit reduced plate height curves, and can give useful qualitative information about a column. Although this equation is useful for obtaining information about the quality of a column, it is empirical, and therefore not useful for deciding how to improve columns.

Equation 26

1 B h = Aν 3 + + Cν ν

5.2 A Previous Study that Compared Plate Height Equations

Mulholland and coworkers published a paper in 2004, where they compared four band broadening equations by fitting plate height data collected for methylparaben and propylparaben using these equations.108 They used the van Deemter equation, the Knox equation, the Golay-Guichon equation, and a new empirical equation that accounts for curvature at high reduced velocities which the paper suggests is quite common. They measured plate height at flow rates ranging from 0.1 mL/min to 2 mL/min. Their data shows curvature in the region between 1 mL/min and 2 mL/min, so the last equation discussed in their paper, which accounted for curvature in this region, was the only one that fit well. Their data displayed heteroscedacity at the higher flow rates, and this was the region where the first three equations did not fit well. By comparison with the data discussed in chapter 5 of this dissertation, their data was quite different. The data discussed in chapter 5 did not have curvature at high flow rates, and was fitted quite well by the van Deemter equation, which was the equation that gave the worst fit in the study by Mulholland and coworkers. In their conclusions, they stated that they are not certain if the curvature seen in their data is due to intracolumn broadening or extracolumn broadening. They also did not state their extracolumn volume in the experimental section, so it is impossible to know whether they took precautions to minimize the extracolumn broadening or not. Because of this, and the fact that they did not mention what equation was used to calculate the plate heights, I do not feel that the conclusions stated in this paper are valid, and a more complete study needs to be performed to compare the available plate height equations.

5.3 Experimental

The chromatographic system used for this study is described in detail in section 3.8. The chromatographic system includes an ISCO 100DM syringe pump, a

95 Spectroflow 757 UV/Vis detector, and a Beckman 506 Autosampler. The detector wavelength used was 254 nm, the rise time was set to 0.1 s, and the column was temperature controlled at 30.0°C ± 0.5°C. The data collection system used was

TotalChrome v6.2.1. The column used in this study was a traditional Zorbax C18 column, the same one used in the previous study. This column was a 15cm x 4.6mm column packed with 5μm spherical silica particles that had been derivatized with C18 groups. This column had a 70 Å pore diameter. The extracolumn variance was subtracted using the method described in section 3.9. The part number was 883952-702, the serial number was USG0014021, and the lot number was B02011. The mobile phase compositions used were 60%, 70%, 80%, and 90% acetonitrile in water. The retained solutes were benzene, toluene, ethylbenzene, propylbenzene, and butylbenzene, and uracil was used as a void marker. All the samples were prepared using the sample and mobile phase components and methods described in section 3.8.1. The flow rates in mL/min that were used in this study were as follows: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, and 3. These flow rates corresponded to reduced velocities of 1-30. The Foley-Dorsey equation31, 32 was used for all efficiency calculations as described previously. Scientific Data Analysis Software (SDAS) v1.1 was used for all curve fitting.

5.4 Comparison of Four Popular Equations

5.4.1 Curve Fitting: A Visual Inspection

Data were collected using five solutes that exhibited different retention on the chosen column in order to compare the four equations described in the previous sections. Four mobile phase compositions were used ranging from 60% acetonitrile in water to 90% acetonitrile in water. The data collected in this study for benzene using the four different mobile phase compositions is represented by Figure 33. This data was fit with the van Deemter equation in order to study how well this equation models the data. From a visual inspection, it appears that the equation models the data very well. The data points appear to fall very close to the fitted line, and one would expect that the R2 values

96 would be very close to one for each of the four sets of data. When the fit values are calculated, they vary from 0.998 for benzene in 60% ACN to 0.992 for benzene in 90% ACN. For this type of study, an acceptable fit value would be 0.998 or above. From this simple experiment, it is obvious that the van Deemter equation gives a good enough fit for modeling chromatographic data for graphing purposes. However, if the data is to be used for estimating plate height contributions or in order to get information about the column being used, the usefulness of the information would be dependent on the conditions under which the experiment was performed. Similar results were seen for the all five of the solutes used in this study, and a sample of the graphs showing this can be found in appendix C. Because there are several different equations that have been published, it seems that a systematic study of these equations could reveal information that would be very useful for chromatographers.

5.4.2 Dependence of Fit on k’

One way to measure how well an equation models collected data is to perform a fit of the model to the data. The fit value (R2) represents how similar the actual data and the fitted curve are. A fit value of unity means that the data and the fitted curve are identical. As the fit value gets further from unity, the data and the fitted curve are becoming less and less similar. Figure 34 is a graph of the R2 fit values for the van Deemter equation fitted to the data collected for each of the five solutes vs. the k’ for that solute in a particular mobile phase composition. Upon studying this graph, it becomes obvious that when the k’ value for the solute is low the van Deemter equation gives a poor fit to the data. However, as the k’ value gets higher, the fit value approaches one and the equation is shown to model the data very well. The lowest fit value calculated was approximately 0.992, and the fit values seem to level off between 0.998 and 1.000.

Benzene

8 7 6 5

h 4 3 2 1 0 0 5 10 15 20 25 30 ν

60% ACN 70% ACN 80% ACN 90% ACN

Figure 33. Mathematical fit of the van Deemter equation to benzene plate height data collected using mobile phases with varying percent acetonitrile. The extracolumn variance has been subtracted from the total variance, so this is a plot of the column variance for benzene.

98 The dotted line in Figure 34 shows the point at which the fit values seem to level off at values above 0.998. This occurs for all the solutes when they have a k’ value that is higher than three. This is independent of the mobile phase composition that is being used. For any solute and any mobile phase composition, the van Deemter equation provides an adequate model for the data when the k’ value of the solute of interest is three or more. This suggests that if one would like to use the van Deemter equation to model chromatographic plate height data, it is important that the solute being used has at least a k’ of three under the conditions being used. As discussed earlier, if the k’ value is less than three, the equation still gives a visually pleasing model of the data, but any information taken from the fitted curve would not truly represent the data. The other three equations used in this study gave similar results, and the graphs of these results can be seen in appendix D.

5.4.3 Comparison of the Fit of the Individual Equations to data for 5 solutes

When a least square analysis was performed to compare the model generated by each equation to the actual chromatographic data, the results are difficult to interpret. From Figures 35 through 38, it is obvious that the Horvath and Lin equation always gives the best fit. However, this is expected since this equation has the most variables, and mathematically, the more variables present in the equation the better the fit will be. However, when the collected data were modeled, the fit values show that all the equations reasonably model the data. Because of this, it is important to decide if there is any benefit to using one equation over another. Of all the equations studied, the van Deemter and Knox equations are the simplest to use and have the least variables. The Knox equation, as shown in Figures 35 through 38, does not fit the data as well as the other three equations in most cases. For this reason, it is not suggested that the Knox equation given in equation 26 be the first choice used to model chromatographic data. Instead, the van Deemter equation would be the best choice, since it is the easiest to manipulate and gives a reasonable fit in all cases studied. Although the Horvath and Lin equation fits best, it is very difficult to manipulate and the difference in the fit values is very small when compared to the other equations, not making it worth the difficulty associated with using it.

2 FitFit Value Value vs. Rvs. Retention vsCapacity k’ FactorFactor 1.000 0.999 0.998 0.997 0.996 2

R 0.995 0.994 0.993 0.992 0.991 02468101214 k’

60% ACN 70% ACN 80% ACN 90% ACN

Figure 34. R2 values vs. k’ for the fit of the van Deemter equation to each solute using mobile phases with varying percent ACN. The dotted line shows the point where the R2 values begin to level off for all the mobile phase compositions used in this study. At a k’ value of approximately 3, the R2 value peaks at about 0.999 regardless of mobile phase composition. The points on each curve represent the five retained solutes, benzene, toluene, ethylbenzene, propylbenzene and butylbenzene going from left to right.

100

Tables 11 and 12 show the fit values obtained when the plate height data for each solute in a mobile phase of 60% ACN and 90% ACN were fitted to the van Deemter equation. The tables include fit values for data that was plotted without subtracting the extracolumn variance and for data that had the extracolumn variance subtracted. The fit values in Table 11 show that there is not much difference in the fit of the van Deemter equation to the plate height data for any of the solutes whether or not the extracolumn variance has been subtracted. This suggests that if one is interested in using this equation to fit data it is not important to subtract the extracolumn variance, and any information obtained from the coefficients is representative of dispersion that is occurring in the column. This would be beneficial to chromatographers because measuring extracolumn variance is a time consuming process. However, Table 12 shows that for the data acquired for the solutes in 90% ACN, the fit values show a larger change dependent on whether or not the extracolumn variance has been subtracted. The fit values increase when the extracolumn variance is subtracted. A closer look at Table 12 reveals that the magnitude of the increase in the fit values when the extracolumn variance is subtracted depends on the solute being studied. This supports the discussion in section 5.3.2 and 5.3.3 where it was stated that the fit value depends on the length of time the solute is retained in the column. This explains why the percent change in the fit values decreases as the solute becomes longer retained. It is therefore best to use longer retained solutes for plate height analysis although this will increase the length of the experiment. It has been suggested that if the extracolumn volume is less than 10 % of the peak volume that the contribution due to extracolumn variance is negligible.4

101 60% ACN / 40% H2O 1.000 0.999 0.998 0.997 0.996 2

R 0.995 0.994 0.993 0.992 0.991 B24591 T E P Bu5 Solutesk'

Figure 35. Fit values calculated when the data collected for each solute were fitted using four popular plate height equations. Analytes: B = Benzene, T = Toluene, E = Ethylbenzene, P = Propylbenzene, and Bu = Butylbenzene.

Van Deemter Giddings Knox Horvath & Lin

70% ACN / 30% H2O 1.000 0.999 0.998 0.997 0.996 2

R 0.995 0.994 0.993 0.992 0.991 B24591 T E P Bu5 Solutesk'

Figure 36. Fit values calculated when the data collected for each solute were fitted using four popular plate height equations. Analytes: B = Benzene, T = Toluene, E = Ethylbenzene, P = Propylbenzene, and Bu = Butylbenzene.

102 80% ACN / 20% H2O 1.000 0.999 0.998 0.997 0.996 2

R 0.995 0.994 0.993 0.992 0.991 B24591 T E P Bu5 k' Solutes

Figure 37. Fit values calculated when the data collected for each solute were fitted using four popular plate height equations. Analytes: B = Benzene, T = Toluene, E = Ethylbenzene, P = Propylbenzene, and Bu = Butylbenzene.

Van Deemter Giddings Knox Horvath & Lin

90% ACN / 10% H2O 1.000 0.999 0.998 0.997 0.996 2

R 0.995 0.994 0.993 0.992 0.991 B24591 T E P Bu5 Solutesk'

Figure 38. Fit values calculated when the data collected for each solute were fitted using four popular plate height equations. Analytes: B = Benzene, T = Toluene, E = Ethylbenzene, P = Propylbenzene, and Bu = Butylbenzene.

103

Table 11. R2 values from the fit of plate height data for each solute to the van Deemter equation in 60% ACN. Values in row labeled “System” are based on total peak variance including extracolumn variance. Values in row labeled “Column” have the extracolumn variance subtracted.

Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene Column 0.9983 0.9992 0.9986 0.9995 0.9993 System 0.9984 0.9983 0.9983 0.9995 0.9993 % Change 0.008 0.095 0.022 0.001 0.001

Table 12. R2 values from the fit of plate height data for each solute to the van Deemter equation in 90% ACN. Values in row labeled “System” are based on total peak variance including extracolumn variance. Values in row labeled “Column” have the extracolumn variance subtracted.

Benzene Toluene Ethylbenzene Propylbenzene Butylbenzene Column 0.9919 0.9939 0.9962 0.9985 0.9987 System 0.9881 0.9896 0.9934 0.9959 0.9967 % Change 0.386 0.439 0.281 0.258 0.203

104

CHAPTER SIX

CONCLUSIONS

6.1 Chromatographic Isolation

The work discussed in chapter 3 outlined a novel way to measure the individual contributions to band broadening in a chromatographic column. This method of chromatographic isolation appears to be a plausible method for investigating the different mechanisms of dispersion in the column. The most important aspect of this technique is choosing the right analytes for the study. It is very important to take into account all the sources of broadening that an analyte will experience as it traverses the column. It is also very important to subtract any extracolumn variance from the total variance in order to ensure that dispersion occurring outside the column does not skew the results of the study. Chromatographic isolation is unique in that it allows for the investigation of the dispersion in the column to be performed using typical experimental conditions. This is important because much of the dispersion occurring in the chromatographic column is highly dependent on the conditions of the experiment. Changing experimental variables such as flow rate, temperature, stationary phase particle size, or mobile phase can have a large effect on the dispersion in the column.

105 6.2 Investigation of Resistance to Mass Transfer in the Mobile Phase

By choosing solutes that experience different known sources of broadening, it was possible to deconvolute the resistance to mass transfer terms in the mobile phase and the stationary phase. It was shown that the effective diffusion coefficients in the mobile phase for the six solutes used in this study were within 8.5% RSD. Equation 13 shows that because the diffusion coefficients are similar, the resistance to mass transfer in the mobile phase would be approximately the same for the six solutes. This allowed the subtraction of the variance due to the non-retained compound in order to isolate the contribution to plate height from the resistance to mass transfer in the stationary phase. When the variance associated with the non-retained compound was subtracted this simulated the effect of removing the contribution to plate height due to eddy diffusion and resistance to mass transfer in the mobile phase. When this subtraction was performed, the number of theoretical plates was increased by as much as 60,000 plates for less retained compounds. Longer retained compounds showed a more modest increase in the number of theoretical plates; just 1000 plates. Stating these values is not to suggest that the efficiency can definitely be improved this much, but merely suggests that there is room for improvement if the column structure could be improved.

6. 3 Using Equations to Model Chromatographic Data

There are several published equations that can be used to model chromatographic data. Each of these equations is based on a different theory, and it has been difficult for chromatographers to choose which equation best models chromatographic data. This systematic study has shown that all four of the equations model the data fairly well, meaning that by a visual inspection it is difficult to tell which equations fit better than others. This makes the decision of what equation to use even more difficult. If the curve fitting is performed simply to guide the reader’s eyes when looking at the graph then the equation that is chosen is of little importance. However, if information about the column is desired the choice of which equation to use is important.

106 There is another very important conclusion that can be drawn from the results of this study. Although it is well documented that extracolumn broadening occurs, many chromatographers ignore this fact. This can be extremely costly when one is analyzing chromatographic data. It is very important to subtract the extracolumn variance from the variance of the chromatographic peak in order to prevent the results from being skewed. For longer retained solutes the effect of the extracolumn variance is not as noticeable but for less retained solutes the extracolumn variance is a major contributor to total variance, and can greatly influence the data. The data presented in Tables 11 and 12 show that it is better to use longer retained solutes for plate height analysis even if the extracolumn variance will be subtracted. From the fit results of this study it can be concluded that the van Deemter equation is adequate for modeling chromatographic data. This equation is the easiest to manipulate, and when a fit is performed between the model generated using the van Deemter equation and the chromatographic data, the fit value obtained is comparable to the fit values obtained when using models generated by the other equations. As expected, the Horvath and Lin equation did give a slightly better fit for all the data that was modeled, but the difficulty associated with using this equation due to the large number of variables present is more than the improvement in fit is worth.

6.4 Importance

Although high performance liquid chromatography has been one of the most widely used analytical techniques for many years, much of the fundamental principles of how the technique works are still not fully understood. Investigations of fundamental aspects of high performance liquid chromatography may not seem glamorous, but research in this area is very important if the field is to continue to gain momentum and continue as one of the most widespread analytical techniques. The information that is obtained in fundamental studies such as the ones described in this dissertation help to reveal the mysteries behind how the technique works and these details may lead other scientists to become interested in further studying the fundamental aspects of the

107 technique. In this way, it is hopeful that future scientists will be able to fully understand the way the technique works in order to unlock its full potential.

6.5 Remaining Critical Issues

There are many more issues that need to be investigated before a thorough understanding of the band broadening processes that occur inside the chromatographic column can be achieved. This study has only begun to uncover the intricacies of the way that chromatography works. The method detailed in chapter 3, chromatographic isolation, can be used in intricately designed experiments in order to obtain enough information about the other dispersion processes to be able to truly understand this system. Another study that could yield critical information is one that investigates the volume of the stagnant layer of mobile phase that is surrounding the stationary phase particles. This can most likely be done by several sets of experiments using different mobile phase compositions, while changing the temperature of the column. In addition to this, many different types of chromatographic columns exist, so it would be necessary to study different types of columns, for example reversed phase HPLC columns made of different stationary phases and columns made for other modes of chromatography such as ion exchange, size exclusion chromatography etc. In addition to this, several sets of solutes would need to be chosen to study each type of dispersion, as one cannot assume that all compounds will act in the same manner. By performing experiments using several different sets of compounds, it would be possible to understand whether there can be one general equation that can describe the chromatographic system, or if several equations need to be available for the use of chromatographers depending on what type of solute they are interested in separating. Once this has been completed, the information collected will be helpful to scientists trying to redesign chromatographic columns. The information will make it possible for scientists to know exactly which types of dispersion are major contributors to overall peak dispersion, and therefore allow them to focus their work on the factors that can offer the greatest improvement for chromatographic separations.

108 APPENDIX A

Graphs of the reduced plate height vs. reduced velocity for the five solutes used in this experiment; benzene, toluene, ethylbenzene, propylbenzene and butylbenzene. The graphs on the upper half of the pages (Figures 39, 41, 43, 45 and 47) illustrate that the curves corresponding to the measured reduced plate heights are not smooth. The graphs of the reduced plate heights for the least retained solutes are the least smooth, and as the solutes become longer retained, the graphs become smoother. The graphs on the lower half of the pages (Figures 40, 42, 44, 46 and 48) are plots of the effective reduced plate heights calculated after the variance associated with the non-retained solute, uracil, was subtracted. These graphs are visibly smoother than the graphs of the measured reduced plate height found on the upper halves of the pages. The solid lines on the graphs are meant to guide the eye, and are not meant to imply continuity of the curves between the points.

109 Plate Height Data for Benzene

8 7 6 5

h 4 3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 ν

Figure 39. Graph of the reduced plate height data collected for benzene. Note that none of the curves are smooth.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Benzene with Uracil Subtracted

h 4

0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 ฀ν

Figure 40. Graph of the effective reduced plate height for benzene after the variance associated with uracil was subtracted. Note that the curves have been visibly smoothed.

110 Plate Height Data for Toluene

8 7 6 5

h 4 3 2 1 0 0 2 4 6 8 1012141618202224262830 ν

Figure 41. Graph of the reduced plate height data collected for toluene. Note that none of the curves are smooth.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Toluene with Uracil Subtracted 8 7 6 5

h 4 3 2 1 0 02468101214161820222426283032 ν

Figure 42. Graph of the effective reduced plate height for toluene after the variance associated with uracil was subtracted. Note that the curves have been visibly smoothed.

111 Plate Height Data for Ethylbenzene

8 7 6 5

h 4 3 2 1 0 0 2 4 6 8 1012141618202224262830 ν

Figure 43. Graph of the reduced plate height data collected for ethylbenzene. Note that none of the curves are smooth.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Ethylbenzene with uracil subtracted

8 7 6 5

h 4 3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 ν

Figure 44. Graph of the effective reduced plate height data collected for ethylbenzene after the variance associated with uracil was subtracted. Note that the curves have been visibly smoothed.

112 Plate Height Data for Propylbenzene

10 9 8 7 6 h 5 4 3 2 1 0 5 10 15 20 25 30 ν

Figure 45. Graph of the reduced plate height data collected for propylbenzene. Note that the curves are fairly smooth.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Propylbenzene with Uracil Subtracted

10 9 8 7 6 h 5 4 3 2 1 0 2 4 6 8 1012141618202224262830 ν

Figure 46. Graph of the effective reduced plate height data for propylbenzene after the variance associated with uracil was subtracted. The smoothing effect of the subtraction of the variance associated with uracil is no longer visible.

113 Plate Height Data for Butylbenzene

h 6

0 0 2 4 6 8 1012141618202224262830 ν

Figure 47. Graph of the reduced plate height data collected for butylbenzene. Note that the curves are fairly smooth.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Butylbenzene with Uracil subtracted

h 6

0 0 2 4 6 8 1012141618202224262830 ν∠

Figure 48. Graph of the effective reduced plate height for butylbenzene after the variance associated with uracil was subtracted. The smoothing effect of the subtraction of the variance associated with uracil is no longer visible.

114 APPENDIX B

The graphs on the following five pages (Figures 49-58) are expanded versions of the graphs shown in Appendix A, arranged in the same order. These graphs are plotted to show only portions corresponding to reduced velocities greater than 16, where the main contributors to the reduced plate height would be the resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase. The point of these plots is to show the change in the slope when the variance associated with uracil is subtracted from the column variance for each solute.

115 Plate Height Data for Benzene with van Deemter Fits

4 3.5 3 2.5

h 2 1.5 1 0.5 0 16 18 20 22 24 26 28 30 ν

Figure 49. Graph of the plate height data for benzene along with the van Deemter fit which was used to calculate the slope of the curve in this region.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Benzene with Uracil Subtracted

4 3.5 3 2.5

h 2 1.5 1 0.5 0 16 18 20 22 24 26 28 30 ν

Figure 50. Graph of the plate height data for benzene after the variance associated with uracil was subtracted along with the van Deemter fit which was used to calculate the slope of the curve in this region.

116 Plate Height Data for Toluene with van Deemter Fits

3.5

2.5

h 2

1.5

0.5 16 18 20 22 24 26 28 30 ν

Figure 51. Graph of the plate height data for toluene along with the van Deemter fit which was used to calculate the slope of the curve in this region.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Toluene with Uracil Subtracted 3.5

2.5

h 2

1.5

0.5 16 18 20 22 24 26 28 30 32 ν

Figure 52. Graph of the plate height data for toluene after the variance associated with uracil was subtracted along with the van Deemter fit which was used to calculate the slope of the curve in this region.

117 Plate Height Data for Ethylbenzene with van Deemter Fit 4.0

3.5

3.0

h 2.5

2.0

1.5

1.0 16 18 20 22 24 26 28 30 ν

Figure 53. Graph of the plate height data for ethylbenzene along with the van Deemter fit which was used to calculate the slope of the curve in this region.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Ethylbenzene with uracil subtracted

4.0

3.5

3.0

h 2.5

2.0

1.5

1.0 16 18 20 22 24 26 28 30 ν

Figure 54. Graph of the plate height data for ethylbenzene after the variance associated with uracil was subtracted along with the van Deemter fit which was used to calculate the slope of the curve in this region.

118 Plate Height Data for Propylbenzene with van Deemter Fit

3.5

3.0

h 2.5

2.0

1.5 16 18 20 22 24 26 28 30 ν

Figure 55. Graph of the plate height data for propylbenzene along with the van Deemter fit which was used to calculate the slope of the curve in this region.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Propylbenzene with Uracil Subtracted

3.5

3.0

h 2.5

2.0

1.5 16 18 20 22 24 26 28 30 ν

Figure 56. Graph of the plate height data for propylbenzene after the variance associated with uracil was subtracted along with the van Deemter fit which was used to calculate the slope of the curve in this region.

119 Plate Height Data for Butylbenzene with van Deemter Fit 4.0

3.5

3.0

h 2.5

2.0

1.5

1.0 16 18 20 22 24 26 28 30 ν

Figure 57. Graph of the plate height data for butylbenzene along with the van Deemter fit which was used to calculate the slope of the curve in this region.

60% ACN 70% ACN 80% ACN 90% ACN

Plate Height Data for Butylbenzene with Uracil subtracted

4.0

3.5

3.0

h 2.5

2.0

1.5

1.0 16 18 20 22 24 26 28 30 ν

Figure 58. Graph of the plate height data for butylbenzene after the variance associated with uracil was subtracted along with the van Deemter fit which was used to calculate the slope of the curve in this region.

120 APPENDIX C

Graphs of the reduced plate height data vs. the reduced velocity for the five solutes used in this experiment; benzene, toluene, ethylbenzene, propylbenzene and butylbenzene. These curves have been modeled using four popular plate height equations. The models have been plotted as solid curves alongside the data to show how well each model fits the data. Figures 59-63 shows the data for the five solutes alongside the van Deemter models. Figures 64-68 show the data for the five solutes alongside the Giddings models. Figures 69-73 show the data for the solutes alongside the Knox models. Figures 74-78 show the data for the five solutes alongside the Horvath and Lin models.

121 Deemter fitofthedata. Figure 59.Graphoftheplateheightdata

Plate Height Data for Benzene with van Deemter Fit

5 122

h 4 forbenzene plotted alongwith thevan 3

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Deemter fitofthedata. Figure 60.Graphoftheplateheight data

Plate Height Data for Toluene with van Deemter Fits

7.5

6.5

5.5 123 h

fortolueneplottedalongwith thevan 4.5

3.5

2.5

1.5 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

van Deemter fitof thedata. Figure 61.Graphofthe plateheightdata

Plate Height Data for Ethylbenzene with van Deemter Fit

5 124

h 4 for ethylbenzeneplotted alongwith the 3

0 0 5 10 15 20 25 30 ν

60%ACN 70% ACN 80% ACN 90% ACN

van Deemter fitof thedata. Figure 62.Graphoftheplateheightdatafor propylbenzene plottedalongwith the

Plate Height Data for Propylbenzene with van Deemter Fits

7.5

6.5

5.5 125

h 4.5

3.5

2.5

1.5 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

van Deemter fitof thedata. Figure 63.Graphoftheplateheightdata

Plate Height Data for Butylbenzene with van Deemter Fit 12

h 6 126 forbutylbenzeneplottedalongwith the

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Giddings fitofthedata. Figure 64.Graphoftheplateheightda

Plate Height Data for Benzene with Giddings Fit

5 127

h 4 ta forbenzene plottedalongwith the 3

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Giddings fitofthedata. Figure 65.Graphoftheplateheightdata fortolueneplottedalongwith the

Plate Height Data for Toluene with Giddings Fit

7.5

6.5

5.5 128 h 4.5

3.5

2.5

1.5 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Giddings fitofthedata. Figure 66.Graphoftheplateheightdata

Plate Height Data for Ethylbenzene with Giddings Fit

5 129

h 4 for ethylbenzeneplotted alongwith the 3

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Giddings fitofthedata. Figure 67.Graphoftheplateheightdatafor propylbenzene plottedalongwith the

Plate Height Data for Propylbenzene with Giddings Fit

7.5

6.5

5.5 130

h 4.5

3.5

2.5

1.5 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Giddings fitofthedata. Figure 68.Graphoftheplateheightdata

Plate Height Data for Butylbenzene with Giddings Fit 12

h 6 131 forbutylbenzeneplottedalongwith the 4

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

fit of thedata. Figure 69.Graphoftheplateheightdata

Plate Height Data for Benzene with Knox Fit

5 132

h 4 for benzene plottedalongwith theKnox 3

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

of thedata. Figure 70.Graphoftheplateheightdatafo

Plate Height Data for Toluene with Knox Fit

7.5

6.5

5.5 133 h

r tolueneplottedalongwiththeKnoxfit 4.5

3.5

2.5

1.5 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Knox fitof thedata. Figure 71.Graphoftheplateheightdata

Plate Height Data for Ethylbenzene with Knox Fit

5 134

h 4 for ethylbenzeneplotted alongwith the 3

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Knox fitof thedata. Figure 72.Graphoftheplateheightdatafor propylbenzene plottedalongwith the

Plate Height Data for Propylbenzene with Knox Fit

7.5

6.5

5.5 135

h 4.5

3.5

2.5

1.5 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Knox fitof thedata. Figure 73.Graphoftheplateheightdata

Plate Height Data for Butylbenzene with Knox Fit 12

h 6 136 forbutylbenzeneplottedalongwith the 4

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Horvath and Linfitofthedata. Figure 74.Graphoftheplateheightda

Plate Height Data for Benzene with Horvath and Lin Fit

5 137

h 4 ta forbenzene plottedalongwith the 3

0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Horvath and Linfitofthedata. Figure 75.Graphoftheplateheightdata fortolueneplottedalongwith the

Plate Height Data for Toluene with Horvath and Lin Fit

7.5

6.5

5.5 138 h 4.5

3.5

2.5

1.5 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Horvath and Linfitofthedata. Figure 76.Graphoftheplateheightdata

Plate Height Data for Ethylbenzene with Horvath and Lin Fit

5 139

h 4 for ethylbenzeneplotted alongwith the 3

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Horvath and Linfitofthedata. Figure 77.Graphoftheplateheightdatafor propylbenzene plottedalongwith the

Plate Height Data for Propylbenzene with Horvath and Lin Fit

7.5

6.5

5.5 140

h 4.5

3.5

2.5

1.5 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

Horvath and Linfitofthedata. Figure 78.Graphoftheplateheightdata

Plate Height Data for Butylbenzene with Horvath and Lin Fit 12

h 6 141 forbutylbenzeneplottedalongwith the 4

0 0 5 10 15 20 25 30

60%ACN 70% ACN 80% ACN 90% ACN

APPENDIX D

Figures 79-82 are graphs of the fit values obtained from the least square fits of the plate height data to the four chosen plate height equations, the van Deemter equation, the Giddings equation, the Knox equation and the Horvath and Lin equation. The fit values are plotted vs. the value for the retention factor of the solute under the specific conditions. The points on each curve correspond to the five solutes from left to right in the following order: benzene, toluene, ethylbenzene, propylbenzene and butylbenzene. The dotted line on each graph corresponds to the point at which the R2 values for the curves appear to reach a value of about 0.998. This occurs at about a retention factor of three for each of the graphs. Tables 13-16 give the fit values for the compounds in the four mobile phases for the four equations.

142 vanvan Deemter Equation Equation FitFit ValueValues vs. vs. RetentionCapacity Factor Factor

1.000 0.999 0.998 0.997

2 0.996

R 0.995 0.994 0.993 0.992 0.991 0 2 4 6 8 10121416 k'

60% ACN 70% ACN 80% ACN 90% ACN

Figure 79. Graph of the fit values obtained from the least squares fit of the plate height data to the van Deemter equation. The fit values are plotted against the k’ for the five solutes used in this study. The points on each curve from left to right represent benzene, toluene, ethylbenzene, propylbenzene and butylbenzene.

Table 13. Table of the fit values obtained from the least squares fit of the plate height data collected for benzene, toluene, ethylbenzene, propylbenzene and butylbenzene in 60%, 70%, 80% and 90% ACN in water to the van Deemter equation.

Compound 60% ACN 70% ACN 80% ACN 90% ACN Benzene 0.9983 0.9953 0.9954 0.9919 Toluene 0.9992 0.9984 0.9966 0.9939 Ethylbenzene 0.9986 0.9983 0.9975 0.9962 Propylbenzene 0.9995 0.9992 0.9977 0.9985 Butylbenzene 0.9993 0.9994 0.9988 0.9987

143 GiddingsGiddings Equation Equation FitFit Value Values vs. vs. Retention Capacity Factor

1.001 1.000 0.999 0.998 0.997 2 0.996 R 0.995 0.994 0.993 0.992 0.991 0 2 4 6 8 10 12 14 16 k'

60% ACN 70% ACN 80% ACN 90% ACN

Figure 80. Graph of the fit values obtained from the least squares fit of the plate height data to the Giddings equation. The fit values are plotted against the k’ for the five solutes used in this study. The points on each curve from left to right represent benzene, toluene, ethylbenzene, propylbenzene and butylbenzene.

Table 14. Table of the fit values obtained from the least squares fit of the plate height data collected for benzene, toluene, ethylbenzene, propylbenzene and butylbenzene in 60%, 70%, 80% and 90% ACN in water to the Giddings equation.

Compound 60% ACN 70% ACN 80% ACN 90% ACN Benzene 0.9983 0.9953 0.9954 0.9919 Toluene 0.9992 0.9984 0.9966 0.9939 Ethylbenzene 0.9986 0.9985 0.9980 0.9962 Propylbenzene 0.9998 0.9996 0.9984 0.9985 Butylbenzene 0.9994 0.9994 0.9992 0.9987

144 KnoxKnox Equation Equation FitFit Value Values vs. vs. Retention Capacity Factor

1.001 1.000 0.999 0.998 0.997 2 0.996 R 0.995 0.994 0.993 0.992 0.991 0 2 4 6 8 10121416 k'

60% ACN 70% ACN 80% ACN 90% ACN

Figure 81. Graph of the fit values obtained from the least squares fit of the plate height data to the Knox equation. The fit values are plotted against the k’ for the five solutes used in this study. The points on each curve from left to right represent benzene, toluene, ethylbenzene, propylbenzene and butylbenzene.

Table 15. Table of the fit values obtained from the least squares fit of the plate height data collected for benzene, toluene, ethylbenzene, propylbenzene and butylbenzene in 60%, 70%, 80% and 90% ACN in water to the Knox equation.

Compound 60% ACN 70% ACN 80% ACN 90% ACN Benzene 0.9983 0.9932 0.9951 0.9914 Toluene 0.9983 0.9977 0.9956 0.9930 Ethylbenzene 0.9982 0.9989 0.9980 0.9956 Propylbenzene 0.9998 0.9995 0.9986 0.9975 Butylbenzene 0.9992 0.9986 0.9995 0.9985

145 HorvathHorvath and and Lin Lin EquationEquation FitFit Value Values vs. vs. Retention Capacity Factor

1.001 1.000 0.999 0.998 0.997 2 0.996 R 0.995 0.994 0.993 0.992 0.991 0 2 4 6 8 10121416 k'

60% ACN 70% ACN 80% ACN 90% ACN

Figure 82. Graph of the fit values obtained from the least squares fit of the plate height data to the Horvath and Lin equation. The fit values are plotted against the k’ for the five solutes used in this study. The points on each curve from left to right represent benzene, toluene, ethylbenzene, propylbenzene and butylbenzene.

Table 16. Table of the fit values obtained from the least squares fit of the plate height data collected for benzene, toluene, ethylbenzene, propylbenzene and butylbenzene in 60%, 70%, 80% and 90% ACN in water to the Horvath and Lin equation.

Compound 60% ACN 70% ACN 80% ACN 90% ACN Benzene 0.9987 0.9957 0.9954 0.9923 Toluene 0.9993 0.9985 0.9968 0.9941 Ethylbenzene 0.9987 0.9990 0.9981 0.9963 Propylbenzene 0.9998 0.9996 0.9986 0.9985 Butylbenzene 0.9994 0.9994 0.9996 0.9990

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BIOGRAPHICAL SKETCH

Karyn M. Usher was born in Belize City, Belize in 1979 to Victor and Rizzeria Usher. She grew up in Belize City and attended Saint Catherine Elementary School and then graduated from high school at Saint Catherine Academy in 1995. She then attended Saint John’s College, Junior College and received an A.S. in 1997. After completing this degree, she moved to Tallahassee to attend Florida State University. She received her B.S. in Chemistry in the Summer of 1999. In the Fall of 2000 she enrolled in graduate school at Florida State University, majoring in Analytical Chemistry. There she joined the research group of Dr. John G. Dorsey and performed research in his group, studying the fundamental aspects of chromatography until the Summer of 2005. The research she performed during her graduate career at Florida State University resulted in her giving two oral presentations and two posters at scientific conferences, being invited to give two technical seminars, and being second author on four oral presentations and posters. In the summer of 2001 she married Hassan H. Rmaile and their son, Hussein, was born in the summer of 2003. She successfully defended her dissertation in the summer of 2005, and will be starting as a tenure track assistant professor at West Chester University of Pennsylvania in the fall of 2005.

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