The Effect of Flow Rate on High Performance Liquid Chromatography Column Re-equilibration after Gradient Elution

Transcription

1 The Effect of Flow Rate on High Performance Liquid Chromatography Column Re-equilibration after Gradient Elution A Thesis Submitted to the Faculty of Drexel University by Michael Robert Fletcher in partial fulfillment of the requirements for the degree of Master of Science in Chemistry November 2016

2 Copyright 2016 Michael Robert Fletcher. All Rights Reserved ii

3 Acknowledgements I would like to express my sincere gratitude to my advisor Prof. Joe P. Foley for the continuous support of my M.S. study and related research, for his patience, motivation, and knowledge. His guidance helped me to become a better scientist and chemist, and tremendously in the writing of this thesis. Besides my advisor, I would like to thank the rest of my thesis committee (Dr. Lynn Penn and Dr. Lee Hoffman) for taking the time to review my studies and for their support. Finally, I would like to thank my family: my parents and my brother and sisters for supporting me spiritually throughout the writing of this thesis and my life in general. iii

4 Table of Contents ABSTRACT.v LIST OF FIGURES..vii LIST OF TABLES ix CHAPTER 1: INTRODUCTION..1 Background...1 Literature Review.. 2 Goals of this Study...6 CHAPTER 2: EXPERIMENTAL....9 Materials...9 Chromatographic System and Analytes...10 Measurement of Dwell Volume of Chromatographic System...10 Measurement of Column Void Volumes..11 Column Re-equilibration Method.11 Determination of Re-equilibration Point..12 CHAPTER 3: RESULTS AND DISCUSSION...13 Modeling of Relationship between Flow Rate and Column Re-equilibration..14 Methanol Results...15 Acetonitrile Results...15 Effect of Particle Size 19 Effect of Bonded Phase Ligand.22 Comparison Between Different C 18 Columns...22 CHAPTER 4: FUTURE WORK...25 CHAPTER 5: CONCLUSION LIST OF REFERENCES...26 iv

5 Abstract The Effect of Flow Rate on High Performance Liquid Chromatography Column Re-equilibration after Gradient Elution Michael R. Fletcher Advisor: Joe P. Foley, Ph.D. In traditional high-performance liquid chromatography (HPLC), column re-equilibration between gradient elution runs is necessary to prepare a column for subsequent experiments. This process replaces the final mobile phase in the column with the mobile phase employed at the start of the run. The replacement of mobile phase occurs in four regions within the column: (i) between the particles (inter-particle); (ii) within the pores of the particles (intra-particle); (iii) in the interfacial region between the mobile phase and stationary phase; and (iv) in the space between the bonded phase ligands. Column re-equilibration, which we hypothesize is limited by the rate of diffusion within the pores and in the interfacial region, traditionally consumes a large quantity of mobile phase due to the high flow rates commonly employed during the reequilibration process. An alternative approach to column re-equilibration after gradient elution is presented, in which solvent consumption is minimized by substantially reducing the flow rate during column re-equilibration, thus allowing more time for new mobile phase to diffuse into the pores and interfacial region while consuming less solvent. The effect of flow rate on reequilibration time and solvent consumption is studied using a variety of column sizes and stationary phase composition. In addition, the effect of the solvent identity (acetonitrile vs. methanol) and the magnitude of the change in mobile phase composition on the re-equilibration time are also evaluated. The volume of mobile phase needed for re-equilibration is shown to be proportional to the flow rate employed during the re-equilibration process, verifying that a reduction in solvent consumption can be achieved by lowering the flow rate. In addition, the v

6 time necessary for re-equilibration is shown to be influenced by two terms: one that is flow rate dependent, and the other that is flow rate independent. vi

7 List of Figures 1. Effect of re-equilibration volume on the retention time of acetophenone. 2. Effect of flow rate on the number of column volumes of solvent required for reequilibration of various columns. Methanol/water %B data. 3. Effect of flow rate on the number of column volumes of solvent required for reequilibration of various columns. Acetonitrile/water %B data. 4. Number of column volumes of solvent required for re-equilibration versus flow rate, showing the effect of particle diameter for various columns. Methanol: water %B data. a. Flow rate in milliliters per minute b. Flow rate in column volumes per minute c. Flow rate in log of column volumes per minute. 5. Time for re-equilibration versus flow rate, showing effect of particle diameter for various comparable columns. Re-equilibration was conducted after gradient elution. Methanol: water %B data. a. Flow rate in milliliters per minute b. Flow rate in column volumes per minute c. Flow rate in log of column volumes per minute. 6. Column volumes for re-equilibration versus flow rate, showing effect of bonded phase ligand after gradient elution for comparable columns. Methanol: water %B data. a. Flow rate in milliliters per minute b. Flow rate in column volumes per minute c. Flow rate in log of column volumes per minute. vii

8 7. Time for re-equilibration versus flow rate showing effect of bonded phase ligand for various comparable columns. Re-equilibration was conducted after gradient elution. Methanol:water %B data. a. Flow rate in milliliters per minute b. Flow rate in column volumes per minute c. Flow rate in log of column volumes per minute. 8. Column volumes to re-equilibration versus flow rate, showing variation among comparable C 18 columns. Re-equilibration was conducted after gradient elution. Methanol:water %B data. a. Flow rate in milliliters per minute b. Flow rate in column volumes per minute 9. Time required for re-equilibration versus flow rate showing variation among comparable. C 18 columns. Re-equilibration was conducted after gradient elution. Methanol:water %B data. a. Flow rate in milliliters per minute b. Flow rate in column volumes per minute c. Flow rate in log of column volumes per minute. viii

9 List of Tables 1. HPLC columns evaluated for column re-equilibration studies..p.9 ix

10 Chapter 1: Introduction Frequently during chemical analysis of a sample mixture, the complexity and/or number of components present greatly reduce the chances of successfully measuring an analyte of interest. In these situations, a separation of the components of a sample is accomplished prior to their detection. Various analytical techniques exist to achieve this separation, the most commonly employed being high performance liquid chromatography (HPLC). HPLC is a form of chromatography that uses pumps to pass a pressurized liquid and sample mixture through a column filled with a solid absorbent material. The sample components interact differently with the absorbent material, which results in their differing flow rates and separation. The affinity of each analyte for the stationary phase relative to the mobile phase (due to differences in intermolecular interactions) determines the analyte s retention time, i.e., the time at which the analyte will elute from the column and be detected. There exist two main modes of elution during HPLC analysis, isocratic, where the mobile phase strength is constant throughout the analysis, and gradient, where the percentage of the organic component of the mobile phase is increased during the analysis. Gradient elution is normally preferred when analyzing samples containing analytes with a large range of polarities. In traditional high-performance liquid chromatography (HPLC), column re-equilibration (CR) between subsequent runs is necessary when the mobile phase conditions are changed. This is most commonly performed after a gradient elution analysis to prepare the column for subsequent experiments. During the process of gradient elution, the mobile phase strength, or percentage of organic modifier, is increased relative to the start of the run. This results in stationary phase composition changes during the run, as the bonded stationary phase chains undergo varying solvation depending on the mobile phase strength. The CR process, which

11 entails flushing the system with a volume of the starting mobile phase, replaces the final mobile phase in the column with the mobile phase employed at the start of the run. The replacement of mobile phase occurs in four regions within the column: (i.) between the particles (interparticle or interstitial); (ii.) within the pores of the particles (intraparticle); (iii.) in the interfacial region between the mobile phase and stationary phase; and (iv.) between the bonded chains of the stationary phase. A column must be fully re-equilibrated prior to subsequent gradient analysis runs in order to achieve consistent retention times of eluting compounds. Full re-equilibration is most important for early eluting compounds, as their retention factors are most strongly affected by differences in the starting mobile phase composition. Incomplete column re-equilibration results in lower precision and shorter retention times compared with full re-equilibration. The rule of thumb for the amount of solvent required to re-equilibrate a column in RPLC has been traditionally quoted as 5-10 column volumes, where one column volume is equal to the void volume of the column employed for the analysis. While this rule of thumb is commonly followed in routine analyses, a number of research groups 1-10 have published studies evaluating the CR process and have identified contributing factors important to understanding the amount of time and number of column volumes of solvent necessary for full re-equilibration. There have been various studies 1-10 done with the aim of elucidating the column reequilibration process and the most influential factors. In 1983, Frenze and Horvath were the first to document relevant factors 3. They used Langmuir isotherm parameters to predict the most effective way to re-equilibrate HPLC columns. They concluded that using a series of multicomponent mobile phases was less effective than re-equilibrating with a one-component mobile phase. Another study by Cole and Dorsey 1 documented the use of mobile phase modifiers to 2

12 quicken the CR process, and found that the addition of 3% 1-propanol to the mobile phase reduced the re-equilibration time by up to 78%. They hypothesized this was due to the selective solvation of the stationary phase chains by 1-propanol. In 1992 Patthy 5 studied the re-equilibration process as it pertains to reversed phase ionpairing chromatography (RP-IPC). He used five pairing ions of different sizes (and absorption kinetics), each at two different concentrations, and three different gradient slope factors. The efficiency of re-equilibration was studied in terms of the speed of re-equilibration. Patthy concluded that 1-3 column volumes of the starting solvent can be sufficient for re-equilibration between gradient runs, at least for obtaining reproducible retention times in gradient RP-IPC. The re-equilibration of ionized compounds on reversed phase columns with mobile phase buffers was first studied by the Marchand group 4. They ultimately concluded that the mobile phase required under these circumstances can vary significantly based on the specific components and is not very predictable. However, they did conclude the speed on reequilibration was not affected by the flow rate, which suggests they were observing a diffusionlimited scenario at the flow rates they employed. In 2005 Carr et al., expanded on previous studies, and was the first to distinguish between re-equilibration that results in run-to-run reproducibility and full re-equilibration 7-8. They concluded that in general for neutral compounds on reversed phase columns, statistical repeatability of an analyte s retention time occurs within 2 column volumes, whereas full reequilibration of the column s inner composition can require more than 20 column volumes. In addition to the common situation of neutral compounds and unmodified mobile phases, the Carr group also studied the influence of multiple factors on the speed of full re-equilibration. They tested the effect of adding organic modifiers to the mobile phase, as well as the effect of particle 3

13 pore size, initial mobile phase composition, initial mobile phase identity (methanol or acetonitrile), column temperature, and flow rate. In their conclusion, the group stated that full equilibration appears to be more thermodynamically limited than kinetically controlled because the temperature of the re-equilibration solvent (40 C vs 80 C) did not affect the rate of reequilibration, but a flow rate of 3.0 ml/min decreased the re-equilibration time and volume of mobile phase required for CR in comparison to a flow rate of 1.0 ml/min. However, their analysis did not take into account the rate of mass transfer (an increase in rate increases the kinetic energy of the fluid) when examining the effect of flow rate (1.0 ml/min vs 3.0 ml/min) on the re-equilibration process, and therefore the conclusion that re-equilibration is controlled by a thermodynamic process alone is questionable. Also, they only studied one set of conditions (acetonitrile as the mobile phase and a C 18 reversed phase column) when measuring the effect of flow rate, which suggests that more studies are required before such a generalization can be considered acceptable. Carr group studies expanded on the work of Dorsey et al. 1 and concluded that the addition of 6% n-propanol further decreases the re-equilibration time in comparison with 3% n-propanol; they stated that this was either because a higher n-propanol concentration displaces the organic solvent from the stationary phase more efficiently or that the amount of organic solvent during the gradient was not able to completely remove the higher concentration of n-propanol in the stationary phase. In addition, they concluded that the speed of equilibration decreases with increasing alkyl chain length of the alcohol, most likely due to the increased hydrophobicity of the stationary phase in comparison with the mobile phase used for re-equilibration. They also examined the influence of initial mobile phase identity (acetonitrile vs. methanol), but did not take viscosity of the mobile phase into account when drawing conclusions. The Carr group felt 4

14 that negating viscosity as a possible factor was justified since changes in viscosity and backpressure were small between these two mixtures. However, the viscosity of methanol/water versus acetonitrile mixtures can vary as much as 2.5 fold depending on the exact composition in question, suggesting that the dismissal of viscosity when analyzing their data was premature. Coym and Roe 6 further examined the effect of mobile phase modifier and temperature on gradient re-equilibration by varying the stationary phase between a C 18 phase, a polar endcapped C 18 phase, and an alkyl phase with a polar embedded group. They determined that for the C 18 and polar endcapped C 18 phases, at any given temperature, the re-equilibration volume required was lower when methanol was utilized compared to acetonitrile. In addition, for both C 18 phases, significant reductions in re-equilibration volume were observed when the temperature was increased from 10 to 50 C. However, when the stationary phase with the polar embedded group was considered, neither temperature nor choice of organic modifier had any effect on the reequilibration process. In 2011, VanMiddlesworth and Dorsey 9 examined if the type of particle used affected the CR process by comparing the re-equilibration time of three superficially porous columns and one fully porous column. The re-equilibration volumes for all four columns studied were similar, and less than three column volumes of conditioning solvent were required for each. Due to the similarities between the fully porous and superficially porous re-equilibration volumes, no conclusions could be made with regard to the affect of the particle type. However, it was claimed that the limiting variable with column equilibration is not desorption of organic modifier from the stationary phase, but rather the pressure required to force the aqueous phase into the pores. 5

15 The column re-equilibration process when ionizable analytes and buffers are employed was examined by the Shellinger 7,8 and Grivel 10 groups. They studied the parameters most important to the re-equilibration process, and concluded that in general higher temperatures and higher flow rates reduce the re-equilibration time. Due to the varying and sometimes contradictory conclusions of past column reequilibration studies, a more thorough, systematic study on the re-equilibrium process is warranted. Justification for the study includes the expected savings in the amount of time and solvent materials over repeated gradient separation, as well as the frequency with which this technique would be more commonly employed. Furthermore, it is expected that elucidation of the column re-equilibration mechanism will result in a strategy for achieving shorter reequilibration times (and therefore total analysis times) and/or decrease solvent consumption, resulting in lower costs and increased productivity. In this study, the effect of flow rate on re-equilibration time and solvent consumption is analyzed for a variety of column sizes and stationary phase compositions. Column reequilibration, we hypothesize, is limited by a complex set of kinetic processes primarily due to the slow rate of diffusion within the pores, the interfacial region, and the bonded-phase ligands. This traditionally results in the consumption of a large quantity of mobile phase due to the high flow rates commonly employed during the re-equilibration process. An alternative approach to column re-equilibration after gradient elution is presented, in which solvent consumption is minimized by substantially reducing the flow rate during column re-equilibration, thus allowing more time for new mobile phase in the interstitial region to diffuse into the bulk pore volume, interfacial region, and bonded-phase layer while consuming less solvent. 6

16 This study differs substantially from the previous studies reviewed, both in methodology and scope. In contrast to past studies, the mobile phases employed will contain no wetting agents, and a much larger set of columns will be employed. In addition, a much wider range of flow rates is tested, particularly at the lower end, in order to test specific points of our hypothesis. Based on the physical process of column re-equilibration, we believe it can be broken down into 4 elementary kinetic steps that are distinguishable by their location and timing. Step 1 involves the bulk mobile phase replacement between the stationary phase particles. This replacement is determined by the rate of convection (flow rate) rather than diffusive processes. Step 2 involves the diffusion of the bulk mobile phase into the particle pores. Step 3 involves the replacement of mobile phase within the interfacial region by diffusion of mobile phase within the pores. This mass-transfer process will occur under different conditions than the previous step due to the local diffusion environment. Step 4 occurs when the new mobile phase is replaced within the bonded chains of the stationary phase. This final mass-transfer process via diffusion will also be different than in steps 2 and 3 because of the local diffusion environment. It is important to note the timing of steps 1-4 with respect to each other. Step 2, diffusion of new mobile phase into the pores, cannot begin until a concentration gradient of mobile phase components between the interstitial region and bulk pore volume in the column has been established, i.e., until after step 1 has begun and there is new mobile phase in the interparticle region. Similarly, step 3, diffusion of new mobile phase into the interfacial region, cannot start until new mobile phase is present in the bulk pore volume, i.e., until after step 2 has begun. Likewise, step 4 cannot begin until after step 3 has begun. Finally, each of the steps preceding the final step must continue until step 4 is completed, otherwise there would be a deficiency of 7

17 new mobile phase in the mobile phase regions leading up to the bonded-phase layer. Thus the process of column re-equilibration consists of 4 asynchronous, parallel, kinetic steps. Because mass transfer processes based on convection are typically much faster than those depending on diffusion, diffusional mass-transfer steps 2-4 will be rate-limiting except at very low flow rates. Extending this reasoning to higher flow rates, the volume of mobile phase required for CR (column re-equilibration) at high flow rates will be linearly proportional to the rate of convection (flow rate). Similarly, at the lowest flow rates, the volume of mobile phase required for CR will reach a minimum value that is independent of convection (flow rate). This suggests that above a certain flow rate, the time saved during CR is negligible compared to the increase in solvent use, i.e. a diminishing returns scenario results. 8

18 Chapter 2: Experimental 1.1 Materials HPLC-grade acetonitrile (ACN) was purchased from EMD Millipore Chemicals (Billerica, MA, USA) and HPLC-grade methanol (MeOH) from Sigma Aldrich (St. Louis, MO, USA). Deionized (DI) water was produced in house. Acetophenone and 2-butanone were purchased from Sigma Aldrich (St. Louis, MO, USA). Column specifications are given in Table 1. Table 1: Columns Evaluated Column # for reference Column Producer Product Name Length (mm) Diameter (mm) Particle size (µm) Totally porous? (Y/N) Thickness of porous shell (µm) Pore Size (A) 1 phenylhexyl ACE Ultra N Core 2 C 18 AMT Halo N C 18 AMT Halo N PFP MN EC Nucleodur PFP 5 C 18 MN EC Nucleodur C 18 Gravity 6 C 18 MN EC Nucleodur C 18 Gravity 7 C 8 MN EC Nucleodur C 8 Gravity 8 C 18 Thermo Hypersil Gold 9 C 8 Thermo Hypersil Gold C 8 10 C 18 Thermo Hypersil Gold 11 C 8 Thermo Hypersil 12 PFP Pentafluorophenyl 13 polar endcapped C 18 Thermo Thermo Gold C 8 Hypersil Gold PFP Hypersil Gold Aq Y Y Y Y Y Y Y Y Y Y CN Thermo Hypersil Y 175 Gold 15 C 18 Macmod Titan Y 110 9

19 1.2. Chromatographic System and Analytes The liquid chromatographic system, an Agilent Series 1290 quaternary UPLC (Agilent Technologies, Santa Clara, CA, USA), consisted of a degasser (G1322A), a column thermostat (G1316A), a quaternary pump (G1312A) able to handle a maximum backpressure of 1200 bar, an autosampler (G1329A), and an ultraviolet-visible diode array detector (DAD) (G1314A) set at 260 nm for the detection of acetophenone and 2-butanone. Prior to analysis of each column, analytes were selected based on the value of their retention factor (k). On a given column, the analyte having a retention factor (k) closest to unity (1.0) after an isocratic separation with a mobile phase having 50% strong solvent (50 %B) was selected. 1.3 Measurement of Dwell Volume of Chromatographic System The dwell volume of a chromatographic system is the volume of tubing from the exit of the solvent pump to the start of the chromatographic column. The dwell volume of the Agilent 1290 UPLC system employed was accomplished by executing a specially-designed gradient elution program without a column from 0 to 100 %B over 10 minutes. Reservoir A contained water and Reservoir B contained 0.02% acetone in water. The signal was monitored at 260 nm as a function of time and then imported into Excel. A regression line was fitted to the linear portion of the signal, and the regression equation was solved for the x-intercept. That value was then multiplied by the flow rate employed during the analysis. Subtraction of that value from the volume of the tubing between the column outlet and the detector yielded the dwell volume of the system. The dwell volume was determined to be 530 µl. 10

20 1.4 Measurement of Column Void Volumes A column volume or CV is the volume of mobile phase within the column at any given instant, i.e., the dead volume V m. CV = V m (volume units) (1.1) In order to determine the CV of each column employed in the analysis, a sample containing a small, unretained compound was injected and eluted with an isocratic mobile phase, i.e., one whose composition is constant throughout the separation. The CV was then determined from the product of the retention time of the unretained compound and the flow rate. All measurements used acetone as the unretained compound, and the eluent strength for the isocratic runs was adjusted as necessary between 50 and 80 %B, depending on the nature of the stationary phase of the column being analyzed. 1.5 Column Re-equilibration Method In order to replicate a typical gradient elution method employed in industry, the method below was employed at varying flow rates: 0.002, 0.005, 0.010, 0.050, 0.100, 0.150, 0.200, 0.250, 0.300, 0.350, and ml/min. 1.) A gradient is run from %B (MeOH or ACN) with a gradient steepness of ) The mobile phase is maintained at 100 %B for 5 additional column volumes. 3.) The mobile phase composition is stepped back to the initial mobile phase (50 %B) and analyte samples are injected at constant intervals of time, sometimes after an initial delay to account for the dwell volume of the system. 11

21 One microliter (1 µl) volumes of acetophenone or 2-butanone were injected into the chromatographic system, and eluted according to the above method using the columns in Table 1. The columns were held at 25 C during the analyses. The mobile phase contained MeOH or ACN in the ratios specified in the text, using on-line solvent mixing. The chromatographic system was controlled and the data were acquired from a computer running Chemstation software (Agilent Technologies, Santa Clara, CA, USA). Measurements were repeated three times for all columns except the Superphenylhexyl column, which was measured once. 1.6 Determination of Re-equilibration Point The number of column volumes required to achieve column re-equilibration is equal to the ratio of the total volume used for re-equilibration (V mp,cr ) to the volume of the column being tested (V m ): CV CR = V mp,cr V m (unitless) (1.2) Immediately after the mobile phase composition is stepped back to 50%B, samples are injected intermittently and the varying retention time of the analyte is recorded. A graph of the analyte retention time versus the number of column volumes of re-equilibration solvent is then constructed (Figure 1). A quadratic equation is then fit to the first five data points past the Halfway point using Microsoft Excel. The first derivative of the quadratic is taken and the volume of mobile phase required for CR is taken as the minimum volume where 0 is within the 95% confidence interval of the slope of the line. The flow rate in column volumes per minute can be defined as F CV = F V m (volume/time) = F (time -1 ) (1.3) (volume) V m The time required for column re-equilibration is denoted as t CR. 12

22 Chapter 3: Results and Discussion Figure 1: Retention time of acetophenone versus number of column volumes of re-equilibration solvent. A gradient was run from % MeOH with a gradient steepness of 0.3, followed by a 5-column volume hold and then an immediate step back to 50% MeOH. Injections were then made every ~0.5 CV of solvent passed through the column and the varying retention time was recorded. Column conditions: ACE Superphenylhexyl 5 cm x 3 mm x 3.0 µm, column and mobile phase temperature = 25 ⁰C. Flow rate = ml/min. A plot of the retention time of acetophenone as a function of re-equilibration volume of the new mobile phase passed through the column at the time of injection is shown in Figure 1. Since re-equilibration of the column cannot begin until the starting mobile phase travels from the point at which the individual mobile phase components are mixed to the column, negative column volume values are used to designate the dwell volume remaining at the time of injection. The dwell volume was determined to be 530 µl, or about 4-5 column volumes for a typical column of length 50 mm and inner diameter of 2.1 mm. A sigmoidal curve is observed for the retention time of an analyte as a function of the re-equilibration volume passed through the column at the time of injection. The number of column volumes of solvent required for reequilibration is determined by fitting a quadratic equation to the first five data points past the inflection point of the curve and solving for the point where the value 0 is within the 95% confidence interval of the slope of the line. In most cases three measurements of the CR volume were made at a given flow rate. This process was then repeated for each additional flow rate. 13

23 Figure 2: Column volumes of solvent required for re-equilibration versus flow rate for various columns. Methanol/water %B data Figure 3: Column volumes of solvent required for re-equilibration versus flow rate for various columns. Acetonitrile/water %B data. 14

24 Plots of the number of column volumes of starting mobile phase required for reequilibration as a function of the mobile phase flow rate for various columns is shown in Figures 2 (methanol:water) and 3 (acetonitrile:water). A gradient was run from 50% to 100 %B using either methanol or acetonitrile as the strong solvent, held at 100 %B for five column volumes, and then returned to the starting mobile phase. An average of three trials is plotted for each column; a positive linear trend is observed for each column studied. Regardless of the flow rate employed, the number of column volumes of solvent required for re-equilibration was five or less for the large majority of columns studied. This suggests the 5-10 column volume rule of thumb for the amount of mobile phase required for column re-equilibration is overstated for RPLC when neutral analytes are analyzed. At all flow rates other than those of a very low magnitude, the flow-rate dependence of the number of column volumes required to achieve column re-equilibration, can be described as CV CR = mf CV + b (1.4) Since the dependent variable CV CR is unitless, the y-intercept b must also be unitless and the unit for the slope m is the multiplicative inverse of the unit for F CV (time -1 ), i.e., time 1. The time required for column re-equilibration can be expressed as ( t CR = CV CR )V m F = CV CR F CV (1.5) Substitution of equation 1.4 into equation 1.5 yields t CR = mf CV + b = m + b (1.6) F CV F CV This expression suggests that the time needed for column re-equilibration is determined by two terms. The first term, m, is flow rate independent. We hypothesize the magnitude of m, the 15

25 slope, results from the efficiency of diffusion of the mobile phase into the intraparticle, interfacial, and bonded-phase regions of the stationary phase. The second, bv c /F, is flow-rate dependent, which is attributed to the rate of replacement of the bulk mobile phase in the interparticle region. Since the time needed for re-equilibration is influenced by two terms, one which is flow-rate dependent and another which is flow-rate independent, increasing the flow rate during the re-equilibration process will not proportionately decrease the time needed for full re-equilibration. To minimize the time required for column re-equilibration, the flow rate can be increased to minimize (eliminate) the second term on the right hand side of equation 1.6. t CR,minimum = lim F m + b F CV = m (1.7) At increasing flow rates, the time required for re-equilibration of a given column asymptotically approaches a value which is equal to the slope of its regression line in Figure 2. This shows that there is a tradeoff between the amount of solvent used for re-equilibration and the time for reequilibration, and there are diminishing returns corresponding to the amount of time saved at high flow rates, while the volume of solvent needed increases linearly. The minimum time required for re-equilibration for the majority of columns studied was approximately one minute. Consistent with our hypothesis, this suggests that column re-equilibration can be performed more efficiently (using less mobile phase) if the flow rate is lowered to an optimal level for the re-equilibration process. 16

26 a.) b.) c.) Figure 4: Number of column volumes of solvent required for re-equlibration versus flow rate, showing the effect of particle diameter for various columns. Methanol:water %B data. a.)flow rate in milliliters per minute b.)flow rate in column volumes per minute. c.) flow rate in log of column volumes per minute. Columns measured are reported in the figure legend. 17

27 a.) b.) c.) Figure 5: Time for re-equilibration versus flow rate, showing effect of particle diameter for various comparable columns. Re-equilibration was conducted after gradient elution. Methanol:water %B data. a.) flow rate in milliliters per minute b.)flow rate in column volumes per minute. c.) flow rate in log (column volumes per minute). Columns measured are reported in the figure legend. 18

28 In order to understand more fully which column characteristics influence the reequilibration process, columns were compared that differ in composition by one component. The influence of particle size was studied by comparing two fully porous C 18 columns, a Macherey-Nagel 5 cm x 2.0 mm i.d. x 5.0 µm particle diameter and Macherey-Nagel 5 cm x 2.0 mm i.d. x 1.8 µm particle diameter, and two superficially porous C 18 columns, a Halo 5cm x 2.1mm i.d. x 5.0(0.6) µm particle diameter and Halo 5cm x 2.1mm i.d. x 2.7(0.5) µm particle diameter (Figure 4a-c, Figure 5a-c). For the Macherey-Nagel columns (Figure 4a-c), at every flow rate tested, the column having the larger particle size (5.0 µm) required more column volumes of solvent for re-equilibration than did the column having the smaller particle size (1.8 µm). In addition, the slope of least squares regression line fitted to the 5.0 µm particle size data is larger than the slope of the regression line fit to the 1.8 µm particle size data. A similar trend is noted when comparing the superficially porous Halo columns (Figure 4a-c). At every flow rate tested, the larger 5.0 µm particle size column required more column volumes of solvent for re-equilibration than did the 2.7 µm particle size column. In addition, the slope of least squares regression line fitted to the 5.0 µm particle size data is larger than the slope of the regression line fitted to the 2.7 µm particle size data. It is important to note that when comparing the Halo columns, both the particle size and depth of the porous shell is larger for the 5.0 µm column (0.6 µm) than for the 2.7 µm column (0.5 µm). Since the slopes of the regression lines fitted to the data are reflective of the flow rate independent contribution to the reequilibration process, we attribute these differences to the fact that longer times are required for diffusion of the mobile phase into larger diameter particles compared with the times required for smaller diameter particles. According to the above equation, this would also suggest that 19

29 columns with larger particles require a longer minimum time for their re-equilibration compared with similar columns with smaller particles (Figure 5a-c). a.) b.) c.) Figure 6: Column volumes for re-equilibration versus flow rate showing effect of bonded phase ligand after gradient elution for comparable columns. Methanol:water %B data. a.)flow rate in milliliters per minute b.) flow rate in column volumes per minute c.) flow rate in log of column volumes per minute. Columns measured are reported in the figure legend. 20

30 a.) b.) c.) Figure 7: Time for re-equilibration versus flow rate showing effect of bonded phase ligand for various comparable columns. Re-equilibration was conducted after gradient elution. Methanol:water %B data. a.) flow rate in milliliters per minute. b.) flow rate in column volumes per minute. c.) flow rate in log of column volumes per minute. Columns measured are reported in the figure legend. 21

31 Another characteristic important to consider when analyzing the re-equilibration process is the identity of the phase bonded to the silica particles. This was evaluated by comparing three Hypersil GOLD columns, a C 18 5 cm x 3.0 mm x 3.0 µm, C 8 5 cm x 3.0 mm x 3.0 µm, and PFP 5 cm x 3.0 mm x 3.0 µm, which have the same pore size (175 A) and similar bonding densities (Figure 6a-c). For every flow rate tested, the C 18 column required a larger number of column volumes of solvent than the C 8 column did, which in turn required more column volumes than the PFP column. This trend is attributed to the differences in the ease of re-equilibration of the interface between the bonded phase and mobile phase. The stationary phase polarities in order from the least to most polar are C 18, C 8, and PFP respectively. When stepped back to a more polar mobile phase, 50:50 organic:water compared to 100% organic, some of the organic solvent molecules must diffuse from between the bonded chains of the stationary phase as well as from the interfacial region into the bulk solution to be replaced by water molecules. The exact proportion may differ from the proportion in the bulk solution due to typical preference of the C 18 phase or organic solvent. Due to the greater diffusional distance for a given bonding density and comparable extensions of the bonded phase ligands, it should take more time for the new mobile phase components to reach an equilibrium distribution in a C 18 versus a C 8 bonded layer. It is proposed that this faster re-equilibration rate between the C 8 and C 18 stationary phases is because the PFP phase is composed of a more polar group oriented towards the bulk solution. During the re-equilibration process the PFP groups are preferentially solvated by the H 2 O molecules, resulting in a less viscous interfacial and bonded chain region. The lower viscosity of these regions results in faster diffusion of the solvent molecules and therefore faster re-equilibration. Comparison of the re-equilibration times of the three columns (Figure 7a-c) shows a similar trend due to the similarities in the column volumes 22

32 of the C 18, C 8, and PFP columns (314, 329, and 321 µl respectively. Columns with a greater viscosity in their interfacial and bonded phased regions take more time to re-equilibrate than those that are less viscous. The C 18 column requires the longest amount of time for reequilibration, followed by the C 8 and then the PFP column; however these differences diminish as the flow rate is increased. a.) b.) Figure 8: Column volumns to re-equilibration versus flow rate, showing variation among comparable C 18 columns. Re-equilibration was conducted after gradient elution. Methanol:water %B data. a.) flow rate in milliliters per minute b.) flow rate in log of column volumes per minute. Columns measured are reported in the figure legend. 23

33 a.) b.) c.) Figure 9: Time required for re-equilibration versus flow rate showing variation among comparable C 18 columns. Re-equilibration was conducted after gradient elution. Methanol:water %B data. a.)flow rate in milliliters per minute b.) flow rate in column volumes per minute c.) flow rate in log of column volumes per minute. Columns measured are reported in the figure legend. 24

34 Experiments were also conducted to compare four fully porous C 18 columns, a Hypersil GOLD C cm x 3.0 mm i.d. x 3.0 mm, a Macherey-Nagel Nucleodur C cm x 2.0 mm i.d. x 5.0 mm, a Macherey-Nagel Nucleodur C cm x 2.0 mm i.d. x 5.0 µm, and a Supelco Titan C cm x 2.1 mm i.d. x 5.0 µm (Figure 8a-c). The exact reasons for the differences in the number of column volumes of mobile phase required for re-equilibration between these columns cannot be attributed to a single variable, as they differ in particle size, pore size, pore morphology, and bonding density. However, Figure 8a-c does illustrate the variation in column volumes required for re-equilibration of C 18 columns in general. This difference was up to one column volume for the columns studied, which at commonly utilized flow rates could amount to 1-2 minutes per run. For applications requiring repeat analyses, the savings in time can be quite substantial. Chapter 4: Future Work There exist other column and mobile phase characteristics, which are thought to affect the re-equilibration process, and were not evaluated here. The magnitude of the change in mobile phase composition is thought to have a major contribution to the re-equilibration process, as well as the identity of the strong solvent used (methanol vs. acetonitrile vs. tetrahydrofuran). These organic solvents, when mixed with water in different proportions have different viscosities and viscosity curves, which in turn will affect the rate of diffusion of the mobile phase and therefore the re-equilibration process. Other parameters such as pore size, pore morphology, and bonding density are also thought to influence the re-equilibration process and can be evaluated in future studies. 25

35 Chapter 5: Conclusion In conclusion, this research has shown that the HPLC column re-equilibration process is influenced by the flow rate of the mobile phase employed. Column characteristics such as particle size and the identity of the bonded phase also influenced the rate of re-equilibration. In addition, the time for re-equilibration is influenced by two terms: one that is flow rate dependent, and one that is flow rate independent. By manipulating the factors involved in the reequilibration process, it can be possible to achieve substantial reductions in analysis time and organic solvent consumption. 26

36 References 1. Cole, L. A. and J. G. Dorsey (1990). "Reduction of reequilibration time following gradient elution reversed-phase liquid chromatography." Analytical Chemistry62(1): Coym, J. W. and B. W. Roe (2007). "Effect of temperature on gradient reequilibration in reversed-phase liquid chromatography." J. Chromatogr. A1154(1-2): Frenz, J. and Horvath, C. (1983). "Movement of Components in Reversed-Phase Chromatography.3. Regeneration Policies in Liquid-Chromatography." J.Chromatogr. A282(Dec): Marchand, D. H.,Williams, L.A., Dolan, J.W., Snyder, L.R. (2003). "Slow equilibration of reversed-phase columns for the separation of ionized solutes." J. Chromatogr. A1015(1-2): Patthy, M. (1992). "Gradient elution with shorter equilibration times in reversed-phase ion-pair chromatography." J.Chromatogr. A592(1 2): Coym, J. W., Roe, B. W. (2007) Effect of temperature on gradient reequilibration in reversed-phase liquid chromatography J. Chromatogr. A1154: Schellinger, A. P., Stoll, D.R., Carr, P.W. (2005). "High speed gradient elution reversedphase liquid chromatography." J. Chromatogr. A1064(2): Schellinger, A. P., Stoll, D. R., Carr P. W. (2008) High speed gradient elution reversed phase liquid chromatography of bases in buffered eluents. Part II. Full equilibrium. J.Chromatogr. A1192: Van Middlesworth, B. J. and J. G. Dorsey (2011). "Reequilibration time of superficially porous silica based columns in gradient elution reversed phase liquid chromatography." J. Chromatogr. A1218(40): Grivel, C., Rocca, J., Guillarme, D., Veuthey, J., Heinisch, S. (2010) Selection of suitable operating conditions to minimize the gradient equilibration time in the separation of drugs by Ultra-High-Pressure Liquid Chromatography with volatile (mass spectrometry-compatible) buffers. J. Chromatogr. A1217: