Effect of Temperature on the Thermodynamic Properties, Kinetic

Ooma, B. LC-GC, 1996, 4, 306−324. There is no corresponding record for this reference. (22). Antia, F.; Horváth, Cs. J. Chromatogr. 1988, 435, 1−...
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Anal. Chem. 1997, 69, 837-843

Effect of Temperature on the Thermodynamic Properties, Kinetic Performance, and Stability of Polybutadiene-Coated Zirconia Jianwei Li and Peter W. Carr*

Department of Chemistry, University of Minnesota, Kolthoff and Smith Halls, 207 Pleasant Street, SE, Minneapolis, Minnesota 55455

This article describes the results of a study of the effect of temperature on the performance of a reversed-phase material prepared by coating polybutadiene (PBD) on porous zirconia. We examined the effect of temperature on retention, efficiency, and stability of this phase. The thermodynamic properties were evaluated via the separation of alkylbenzenes and a set of tricyclic antidepressant drugs at different temperatures, while the intrinsic kinetic performance of the PBD phase at elevated temperatures was examined by using alkylbenzenes as probe solutes. Moreover, the thermal stability was determined by measuring the drift in k′ while continuously pumping a mobile phase at 100 °C. We found that enthalpy changes were between -2 and -4 kcal/mol and that changes in selectivity varied with the type of solute. High temperatures improved the column efficiency by 30%, mainly by accelerating the solute diffusion rate in the stationary phase. Finally, the PBD-coated zirconia phase was very stable at a temperature of 100 °C for at least 7000 column volumes. In developing and validating a HPLC method, the most common approach is to optimize the mobile phase composition after an appropriate column has been selected.1 Although column temperature is also a potential variable, its importance in method development has been slighted.2,3 This is due mainly to the fact that capacity factors can be easily adjusted by altering the mobile phase, and temperature generally has only a small effect on the selectivity of small molecules.3,4 More importantly, the thermal stability of many silica-based columns is limited (often less than 60 °C), so one cannot vary the temperature over a wide enough range to be really interesting.5 This situation, however, is changing gradually because some newer silica-based phases are remarkably thermally stable.6-8 For example, Hancock et al.9,10 optimized the separation of peptide (1) Snyder, L. R.; Glajch, J. L.; Kirkland, J. J. Practical HPLC Method Development; Wiley-Interscience: New York, 1988. (2) Chen, H.; Horva´th, Cs. J. Chromatogr. 1995, 705, 3-20. (3) Colin, H.; Diez-masa, J. C.; Guiochon, G.; Czajkowska, T.; Miedziak, I. J. Chromatogr. 1978, 167, 41-65. (4) Kikta, E. J.; Grushka, E. Anal. Chem. 1976, 48, 1098-1104. (5) Nugent, K. D.; Burton, W. G.; Slattery, T. K.; Johnson, B. F.; Snyder, L. R. J. Chromatogr. 1988, 443, 381-397. (6) Kirkland, J. J.; Dilkes, C. H.; Henderson, J. E. LC-C, 1993, 11, 290-297. (7) Chen, H.; Horva´th, Cs. Anal. Methods. Instrum. 1993, 1 (4), 213-222. (8) Boyes, B. E.; Kirkland, J. J. Peptide Res. 1993, 6, 249-258. (9) Hancock, W. S.; Chloupek, R. C.; Kirkland, J. J.; Snyder, L. R. J. Chromatogr. 1994, 686, 31-43. S0003-2700(96)00854-2 CCC: $14.00

© 1997 American Chemical Society

and protein samples by varying both the mobile phase composition and temperature on “sterically protected” C8 and C18 columns. They found that temperature greatly affected selectivity. Horva´th et al.2,7,11 used pellicular stationary phases to separate proteins at temperatures up to 120 °C. Moreover, the number of complex separation modes such as chiral recognition,12-18 complexation,19 protein interactions,2,7,11 and macrocycle mediation20 applied in new generation columns is growing steadily. These new separation mechanisms are often influenced by temperature to a much larger extent than is reversed-phase chromatography of small solutes.21 Thus, it is now recognized that temperature is an important tool to optimize chromatographic parameters such as retention, efficiency, and selectivity, particularly for large solutes.2,21,22 The trend toward using smaller particles and high flow rates for ultrafast separation will further increase the demand for control at elevated column temperatures to reduce back pressure and to enhance efficiency.21 Finally, the miniaturization of column dimensions will enable faster thermal equilibration, creating new opportunities for selectivity and retention control based on temperature programming.2,21 The effect of temperature in reversed-phase liquid chromatography (RPLC) has been investigated both theoretically and experimentally.3,7,22-27 First, elevated temperatures in most cases will reduce the analysis time because the exothermic enthalpy changes associated with transfer of solutes from the mobile to stationary phases dominate the retention process in most chromatographic systems .22,28 Second, a change in temperature can have a pronounced effect on the efficiency of a separation2,8,22 (10) Chloupek, R. C.; Hancock, W. S.; Marchylo, B. A.; Kirkland, J. J.; Boyes, B. E.; Snyder, L. R. J. Chromatogr. 1994, 686, 45-59. (11) Kalghatgi, K.; Horva´th, Cs. J. Chromatogr. 1988, 443, 343-353. (12) Pirkle, W. H.; Burke, J. A. J. Chromatogr. 1991, 557, 173-185. (13) Takagi, T.; Suzuki, T. J. Chromatogr. 1992, 625, 163-168. (14) Labl, M.; Fang, S.; Hruby, K. J. J. Chromatogr. 1991, 586, 145-148. (15) Herderson, D. E.; Mello, J. A. J. Chromatogr. 1990, 499, 79-88. (16) Sander, L. C.; Craft, N. E. Anal. Chem. 1990, 62, 1545-1547. (17) Sentell, K. B.; Herderson, A. N. Anal. Chim. Acta 1991, 246, 136-149. (18) Paesen, K.; Goetz, J. F. J. Chromatogr. 1978, 157, 185-196. (19) Smith, R. G.; Drake, P. A.; Lamb, J. D. J. Chromatogr. 1991, 546, 139-149. (20) Kura, G.; Kitamura, E; Baba, Y. J. Chromatogr. 1993, 628, 241-246. (21) Ooma, B. LC-GC, 1996, 4, 306-324. (22) Antia, F.; Horva´th, Cs. J. Chromatogr. 1988, 435, 1-15. (23) Melander, W. R.; Campbell, D. E.; Horva´th, Cs. J. Chromatogr. 1978, 158, 215-225. (24) Robbat, A.; Liu, T. Y. J. Chromatogr. 1990, 513, 117-135. (25) Melander, W. R.; Chen, B. K.; Horva´th, Cs. J. Chromatogr. 1979, 185, 99109. (26) Vigh, G.; Varga-Puchony, Z. V. J. Chromatogr. 1980, 196, 1-9. (27) Chmielowiec, J.; Sawatzky, B. J. Chromatogr. Sci. 1979, 17, 245-252. (28) Kenkelem, L. V.; Lewitus, A. J.; Kana, T.; Craft, N. E. Mar. Ecol.: Prog. Ser. 1994, 114 (3), 303-313.

Analytical Chemistry, Vol. 69, No. 5, March 1, 1997 837

because an increase in temperature will reduce viscosity and increase diffusion rates, thereby enhancing the mass transfer rate. Third, the change in retention with temperature is often different for various analytes, and temperature can have a marked effect on the selectivity of a chromatographic separation.12-14,19,20,29-33 Furthermore, the effects of temperature in RPLC on retention time, selectivity, and efficiency are more prominent for large solutes such as proteins than for small solutes.22 Column stability at elevated temperatures over extended periods is a prerequisite for practical high-temperature HPLC. Although a few manufacturers offer thermally stable columns,6-8 most silica-based columns are unstable at high temperatures, which limits the application of temperature for optimization. This situation becomes worse when these columns are operated in acidic or basic conditions. However, due to their very high thermal stability, we believe that zirconia-based reversed-phase materials offer a significant advantage over conventional bonded phases in optimization of RPLC method development, i.e., the exceptional thermal stability of PBD-coated zirconia enables chromatographers to add another dimension to RPLC method development by varying both the mobile phase composition and the temperature. Accordingly, it is the purpose of this paper to evaluate the effect of temperature on the chromatographic selectivity, column efficiency, and thermal stability of PBD-coated zirconia. THEORETICAL SECTION Thermodynamics. It is well known in RPLC that the capacity factor (k′) for a homologous series of solutes is linearly related to the carbon number:34

ln kn′ ) ln k0 + ln RCH2nCH2

(1)

where RCH2 is the hydrophobic selectivity, defined as k′n+1/k′n, nCH2 is the number of methylene groups, and k′0 is the capacity factor of the functional group that defines the series. The dependence of k′ on temperature is given by the van't Hoff equation:34

∂ ln kn′ )∂(1/T)

∆Hn0 R

(2)

where ∆Hn0 is the enthalpy change associated with the transfer of a solute from the mobile to the stationary phase, R is the gas constant, and T is the absolute temperature. Equation 2 allows us to determine the enthalpy change associated with the solute. By differentiating eq 1 with respect to 1/T and substituting eq 2, the change in enthalpy of a homologous series is related to the carbon number:34

series. The change in the selectivity, RT, between two adjacent solutes with temperature is given by3

[

]

0 T - T0 δ(∆HCH2 ) RT ) exp RT0 TT0 R

(4)

where T0 is the reference temperature and RT0 is the selectivity at the reference temperature. Kinetics. When the reduced velocity of the mobile phase, ν (≡µedp/Dm, where µe is the interstitial velocity, Dm is the diffusion coefficient in the free mobile phase, and dp is the particle diameter) is smaller than 100, the reduced height equivalent to a theoretical plate (HETP) (h ≡ HETP/dp) is related to ν through the dimensionless Knox equation:35

h)

B + Aν1/3 + Cν ν

(5)

where the coefficients A, B, and C are related to the packing quality, the axial molecular diffusion, and the efficiency of intraparticulate mass transfer, respectively. Based on the work of Knox and Scott,36 the coefficient B is given as

[

B)2

]

γm + k0γstag Ds + k′γs 1 + k0 Dm

(6)

where γm (≡Dmeff/Dm), γstag (≡Dstageff/Dm), and γs (≡Dseff/Ds) are the obstructive factors in the interstitial mobile phase, in the stagnant mobile phase inside the particles, and in the stationary phase, respectively; Dmeff, Dstageff, and Dseff are the corresponding effective diffusion coefficients, respectively; Ds is the diffusion coefficient in stationary phases; and k0 is the ratio of the intraparticle void space accessible to the solute and the interstitial space in the column. The term k′γsDs/Dm is usually small, and the B coefficient is essentially independent of temperature. However, based on the work of Horva´th and Lin37,38 on band broadening, the C coefficient can be affected by temperature in at least two ways. First, high temperature will improve mass transfer in the stagnant mobile phase inside particles due to the enhanced diffusion; second, elevated temperature will improve the desorption kinetics from stationary phases, as demonstrated below:38

Ckinetic )

2k′Dm (1 + k0)(1 + k′)2 dp2kd

(7)

where δ(∆HCH20) is the enthalpy change per methylene group and ∆H00 is the enthalpy change for the functional group defining the

where Ckinetic is the contribution to the C coefficient (eq 5) from the mass transfer process in the stationary phase per se, and kd is the rate constant for the solute desorption process from the surface. As demonstrated in ref 39, the retention mechanism of nonpolar solutes on PBD phase coated on zirconia is mainly a partition process. Based on the work of Giddings,40,41 a desorption

(29) Papadopoulou-Mourkidou, E. Anal. Chem. 1989, 61, 1149-1151. (30) Liodakis, S.; Pappa, A.; Parissakis, G. J. Chromatogr. Sci. 1989, 27, 149152. (31) Sheikh, S. U.; Touchstone, J. C. J. Chromatogr. 1988, 455, 327-331. (32) Baba, Y.; Yoza, N.; Ohash, S. J. Chromatogr. 1983, 350, 119-125. (33) Sander, L. C.; Wise, S. A. Anal. Chem. 1989, 61, 1749-1754. (34) Grushka, E.; Colin, H.; Guiochon, G. J. Chromatogr. 1982, 248, 325-339.

(35) Knox, J. H. J. Chromatogr. Sci. 1977, 15, 352-384. (36) Knox, J. H.; Scott, H. P. J. Chromatogr. 1983, 282, 297-313. (37) Horva´th, Cs.; Lin H. J. Chromatogr. 1976, 126, 401-420. (38) Horva´th, Cs.; Lin, H. J. Chromatogr. 1978, 149, 43-70. (39) Li., J.; Carr, P. W. Anal. Chem. 1996, 68, 2857-2868. (40) Giddings, J. C. Unified Separation Science; Wiley-Interscience: New York, 1991; Chapter 11, pp 250-268.

0

0

0

∆Hn ) ∆H0 + δ(∆HCH2 )nCH2

838

Analytical Chemistry, Vol. 69, No. 5, March 1, 1997

(3)

process in a partition mechanism involves getting the solute molecules from the interior of the stationary phase to the surface where they can escape. Thus, kd is proportional to the diffusion coefficient (Ds) of the solute in the stationary phase. An increase in temperature will improve the diffusional rate in the stationary phase (and increase kd) and, therefore, decrease the C coefficient if the mass transfer resistance in the stationary phase is the dominant process. The effect of temperature on the A coefficient is uncertain;36-38,40,41 however, high temperature should improve the laminar flow and lateral mixing of molecules among different flow channels. Thus, elevated temperature might improve the A term, although the improvement may not be significant. EXPERIMENTAL SECTION PBD-Coated Zirconia Particles and Columns. The PBDcoated zirconia particles used in this study were the same as those used in previous investigations.39,42 Thus, the preparation, physical characterization, and packing of PBD-coated zirconia particles have been detailed elsewhere.39 The carbon loads used in this study were 2.7, 3.1, and 5.6 (% w/w), respectively, and the column dimensions used were all 100 mm × 4.6 mm i.d. Reagents. All reagents used were obtained from commercial sources and were reagent grade or better, unless noted below. The organic solvents used in liquid chromatography were ChromAR HPLC grade acetonitrile (ACN) and methanol (MeOH) (Mallinckrodt Chemical Co., Paris, KY 40361). DI water was filtered through a 0.45 µm filter (Gelman Sciences Inc., Ann Arbor, MI) and then boiled to remove carbon dioxide before use. All solvents were filtered a second time with a 0.45 µm filtration disk. Solutes used in this study were benzene, toluene, ethylbenzene, n-propylbenzene, n-butylbenzene, n-pentylbenzene, 1-phenylnonane, 1-phenylundecane, 1-phenyltridecane, 1-phenylpentadecane, lidocaine, amitriptyline, tryptamine, nortriptyline, quinidine, and norephedrine (Aldrich Chemical Co., Milwaukee, WI). Deuterium oxide (D2O) and acetonitrile (CD3CN) (CIL Cambridge Isotope Laboratories, Woburn, MA) were used to determine the column void volumes. Chromatographic Apparatus. All chromatographic experiments were carried out on a fully automated Hewlett Packard 1090 liquid chromatography with an autosampler, a temperature controller, a UV detector, and a computer-based Chemstation (Hewlett Packard, Wilmington, DE). The chromatographic apparatus was used to carry out chromatographic and diffusion coefficients measurements. Chromatographic Conditions. Separation of Alkylbenzenes: A 5.6% (w/w) carbon column was used to carry out chromatographic measurements on solutes of a homologous series of alkylbenzenes (benzene to n-pentylbenzene) at a mobile phase composition of 40% (v/v) ACN. The temperatures used were 40, 60, 80, and 100 °C. Solute concentrations were 1-2 mg/mL, the injection volume was usually 2 µL, the flow rate was 1 mL/min, and the detection wavelength was set at 260 nm. Separation of Tricyclic Antidepressant Drugs. A column of 5.6% (w/w) carbon was used to separate pharmaceutical antidepressants. The solutes included lidocaine, amitriptyline, tryptamine, nortriptyline, quinidine, and norephedrine. Solute concentrations (41) Giddings, J. C. Dynamics of Chromatography, Part I: Principles and Theory; Marcel Dekker: New York, 1965; Chapters 11 and 12. (42) Li, J; Carr, P. W. Anal. Chem., submitted.

Table 1. Experimental Conditions for the Flow Studya T (°C) 25

65

100

mobile phase

solute

85% ACN 1-phenylnonane 1-phenylundecane 1-phenyltridecane 1-phenylpentadecane 78% ACN 1-phenylnonane 1-phenylundecane 1-phenyltridecane 1-phenylpentadecane 32% ACN 1-phenylnonane 1-phenylundecane 1-phenyltridecane 1-phenylpentadecane

k′

diffusion coefficientb (Dm × 105 cm2/s)

1.1 1.9 3.4 6.3 1.1 1.9 3.3 5.9 1.2 2.2 3.8 6.7

1.39 1.28 1.19 1.14 2.25 2.14 2.00 1.93 1.61 1.42 1.41 1.31

a Other conditions: solute concentrations were about 2 mg/mL, the injection volume was usually 2 µL, the flow rate was varied from 0.1 to 4 mL/min; and the detection wavelength was set at 260 nm. b Determined by the open tube method.42

were about 1 mg/mL and, the injection volume was 1 µL. The flow rate was 1.0 mL/min, and detection was set at 254 nm. The mobile phase included 40% (v/v) ACN and 60% (v/v) water containing 20 mM NH4F (Mallinckrodt) and 50 mM tris(hydroxymethyl)aminomethane (TRIS) and adjusted to pH ) 10 by addition of sodium hydroxide (Fisher Scientific Inc., Fair Lawn, NJ). Column Efficiency. To examine the effect of temperature on column efficiency, we collected data (h vs ν) on a column of 3.1% (w/w) carbon at three temperatures. The mobile phase compositions were different at each temperature to adjust the capacity factors of all solutes to be in a similar range (between 0 and 10). Table 1 shows the experimental conditions used in the study. It is noted that the particles were relatively small (2.5 µm), so we used some less viscous mobile phases (high concentrations of ACN) in our experiments to reduce the column back pressure. Therefore, sufficient retention was obtained by using relatively large hydrophobic alkylbenzenes as solutes. Column Stability. The stability of the PBD-coated zirconia was examined using a column of 2.7% (w/w) carbon at a temperature of 100 °C at a flow rate of 2 mL/min. The mobile phase was 50% (v/v) MeOH, and the solutes used were ethylbenzene, npropylbenzene, and n-butylbenzene. Solute concentrations were 1-2 mg/mL, the injection volume was usually 1 µL, and the detection wavelength was set at 254 nm. An injection was made every 30 min. Finally, all solutes were dissolved in pure ACN (Mallinckrodt), and all data acquisition was made at 0.16 s/point. The column dead volumes were determined by injecting isotopic components (CD3CN and D2O) of the mobile phases, as proposed by Knox and Kaliszan.43 Diffusion coefficients of solutes used in the flow study were measured by the open tube method, as detailed elsewhere.42 Computation of Reduced Plate Height and Velocity. Each chromatogram generated by the HP Chemstation was a binary file. All the binary files obtained for the kinetic measurement were converted to ASCII formats. We then used PeakFit (Jandel Scientific Inc., San Rafael, CA) to compute the peak width (W) at half-height. If there were not enough points for very narrow peaks, we fitted the peaks with appropriate mathematical models (43) Knox, J. H.; Kaliszan, R. J. Chromatogr. 1985, 349, 211-234.

Analytical Chemistry, Vol. 69, No. 5, March 1, 1997

839

Figure 2. van’t Hoff plots for retention of alkylbenzenes. See Figure 1 for experimental conditions. Symbols: 9, benzene; b toluene; 2, ethylbenzene; 1, n-propylbenzene; (, n-butylbenzene; +, n-pentylbenzene. Table 2. Enthalpy of Transfer and Related Thermodynamic Data for Alkylbenzenesa

Figure 1. Chromatograms showing the separation of alkylbenzenes on PBD-coated zirconia at four temperatures. Experimental conditions: mobile phase, 40% (v/v) ACN; flow rate, 1 mL/min. Peaks: 1, benzene; 2, toluene; 3, ethylbenzene; 4, n-propylbenzene; 5, nbutylbenzene; 6, n-pentylbenzene.

provided with the software and then evaluated the peak width (W1/2) at half-height. The plate count (N) of each peak was computed by

( )

N ) 5.54

tr W1/2

2

(8)

where tr is the retention time. The reduced velocity was computed as

ν)

dp F 2 D 60 eπR m

(9)

where F is the flow rate (mL/min), e is the external porosity (0.38 for our columns), R is the radius of the column (0.23 cm), and Dm is the diffusion coefficient. Finally, the data were fitted to the Knox equation via Origin software (MicroCal Software Inc., Northampton, MA) to evaluate the A, B, and C coefficients. The B coefficients were also independently determined by a linearization method.42 RESULTS AND DISCUSSION Effect of Temperature on Absolute Retention. To investigate the effect of temperature on the absolute retention on PBD840

Analytical Chemistry, Vol. 69, No. 5, March 1, 1997

solute

intercept ln(k′)0

∆H0 (kcal/mol)

SDb

benzene toluene ethylbenzene n-propylbenzene n-butylbenzene n-pentylbenzene

-2.81 ( 0.05 -2.72 ( 0.05 -2.70 ( 0.08 -2.75 ( 0.11 -2.84 ( 0.16 -2.94 ( 0.20

-2.07 ( 0.04 -2.38 ( 0.05 -2.72 ( 0.06 -3.13 ( 0.08 -3.57 ( 0.11 -4.00 ( 0.14

0.01 0.01 0.01 0.01 0.02 0.03

a Enthalpy change associated with transfer of a solute was determined by the slope of ln(k′) against 1/T. The slope is -∆H/R (R is the gas constant). b Average standard deviation of the fit.

coated zirconia, we carried out a separation of a mixture of alkylbenzenes at four different temperatures with 40% ACN in the mobile phase. Figure 1 shows the chromatograms. It is obvious that, as the temperature is increased from 40 to 100 °C, the analysis time decreases significantly from 35 to 13 min at virtually no cost in chromatographic resolution. The decrease in analysis time will save organic solvent and time. In addition, the viscosity of the mobile phase becomes smaller at these elevated temperatures, leading to reduced column back pressures. The pressure drops were about 130 and 65 bar at 40 and 100 °C, respectively. It is also evident that the peaks are higher at high temperatures, resulting in improved S/N ratios. Figure 2 shows the relationship between ln(k′) and 1/T for the homologous series of alkylbenzenes. The slope of each plot is the enthalpy change associated with the transfer of a solute from the mobile to stationary phase. Table 2 shows the measured ∆H0 for the solutes used in Figure 1. We can see from Table 2 that the enthalpy changes range from -2 to -4 kcal/mol. These values are typical and comparable to the enthalpy changes found on conventional bonded phases.26,34 Thus, it is concluded that PBD-coated zirconia and conventional bonded phases behave similarly toward hydrophobic solutes. This conclusion is supported by other thermodynamic studies including retention studies39 and the study of linear solvation energy relationships.44 Effect of Temperature on the Selectivity of PBD-Coated Zirconia. To evaluate the selectivity of the PBD-coated zirconia phase, we computed the enthalpy change associated with a methylene group because it is related to the hydrophobic selectiv(44) Li, J.; Carr, P. W. Anal. Chim. Acta, in press.

Figure 3. Plot of the enthalpy change against the number of methylene units. The enthalpy changes were taken from Table 2. Conditions same as in Figure 1. Table 3. Enthalpy of Transfer for a Methylene Groupa homologous series

mobile phase

stationary phase

δ(∆HCH2) (kcal/mol)

alkylbenzeneb alkylbenzenec alkylbenzenec n-alkanolsd n-alkanols-DNPHsd 2-n-alkanols-DNPHsd

40% ACN 90% MeOH 80% MeOH 78.2% MeOH 80% MeOH 80% MeOH

PBD-zirconia Hypersil C-18 Hypersil C-18 MicroPak CH-10 Nucleosil C-18 Nucleosil C-18

-0.39 -0.27 -0.41 -0.44 -0.42 -0.40

a Determined by the slope of eq 3. b Obtained for PBD-zirconia phase. c Taken from ref 34. d Taken from ref 26.

ity through eq 4. Figure 3 illustrates the changes in enthalpy from Table 2 against the number of methylene groups. Based on eq 3, the slope of Figure 3 is the enthalpy change for a methylene group. The measured δ(∆HCH20) value on PBD-coated zirconia is about -0.39 kcal/mol when the mobile phase is 40% ACN. This value is also similar to those observed on conventional bonded phases (see Table 3). In a previous paper, we reported on the selectivity of PBD-coated zirconia39 and found that the hydrophobic selectivity of the PBD phase was similar to that of conventional bonded phases. The data here support our previous conclusion. The δ(∆HCH20) values allow us to compute the effect of temperature on selectivity based on eq 4. If we choose 30 °C as the reference temperature, the selectivity change with temperature is given by

RT 198 - 0.65 ≈ exp R30°C T

(

)

(10)

Equation 10 predicts that with 40% ACN in the mobile phase, an increase in temperature by 10 °C will decrease the selectivity by about 2%. When we increase the temperature to 100 °C, the selectivity will decrease by 12%. The results here demonstrate that, for very similar solutes such as alkylbenzenes, the selectivity at elevated temperatures tends to decrease. However, the decrease is not significant and can be easily compensated for by a slight change in the mobile phase composition while maintaining the advantage of operation at high temperatures. It is important to point out that the change in selectivity with temperature also depends on the mobile phase composition.39 As more ACN is added to the mobile phase, we should see even less dependence of selectivity on temperature, and vice versa.

Figure 4. Chromatograms showing the separation of therapeutic tricyclic antidepressants on PBD-coated zirconia. Solutes: 1, lidocaine; 2, quinidine; 3, norephedrine; 4, tryptamine; 5, amitriptyline; 6, nortriptyline.

The change in selectivity upon a change in temperature depends on the retention process.9,12 If the retention mechanism for some solutes in a mixture includes more than one process, a temperature change is expected to effectively change the selectivity. Figure 4 demonstrates a significant improvement in the selectivity of the common tricyclic antidepressants at three different temperatures. It is obvious in Figure 4 that the analysis time was decreased from 7 min at 40 °C to less than 4 min at 100 °C. Peaks at 100 °C become significantly narrower than those at 40 °C. More importantly, peaks of tryptamine, quinidine, and norephedrine are merged at 40 °C, but become very well resolved at 100 °C. This example suggests that a temperature increase can sometimes have a significant beneficial effect on selectivity. In a subsequent study, we will focus on the effect of temperature on the selectivity on PBD-coated zirconia in practical HPLC method development. Resolution is expected to change in a way that parallels the selectivity because, as will be shown below, the optimum column efficiency really does not increase significantly at elevated temperatures. Based on the general resolution equation, at constant efficiency a change in resolution is mainly affected by changes in selectivity. Effect of Temperature on the Column Kinetic Performance. The kinetic performance of PBD-coated zirconia was evaluated at elevated temperatures. Some results are given in Figure 5 as plots of the reduced plate height against reduced velocity. In this experiment, we are interested in the improvement in overall column efficiency and the mass transfer resistances. Table 4 presents the coefficients of the Knox equation as obtained by fitting the data of Figure 5. Analytical Chemistry, Vol. 69, No. 5, March 1, 1997

841

Table 4. Summary of Knox Coefficientsa Knox coefficientsb T (°C)

solute

k′

A

B

Bc

C

χ2 d

25e

1-phenylnonane 1-phenylundecane 1-phenyltridecane 1-phenylpentadecane average 1-phenylnonane 1-phenylundecane 1-phenyltridecane 1-phenylpentadecane average 1-phenylnonane 1-phenylundecane 1-phenyltridecane 1-phenylpentadecane average

1.0 1.9 3.4 6.3

2.6 ( 0.0 2.5 ( 0.1 2.8 ( 0.1 2.9 ( 0.1 2.7 2.0 ( 0.1 2.0 ( 0.1 2.1 ( 0.2 2.3 ( 0.2 2.1 1.8 ( 0.1 1.7 ( 0.1 1.8 ( 0.2 2.0 ( 0.2 1.8

2 2 2 2 2 3.2 ( 0.1 3.3 ( 0.1 3.5 ( 0.1 3.8 ( 0.2 3.4 6.8 ( 0.1 7.8 ( 0.2 7.8 ( 0.2 8.0 ( 0.3 7.6

2.0 ( 0.1 2.1 ( 0.3 1.8 ( 0.4 1.6 ( 0.5 1.9 2.6 ( 0.0 2.6 ( 0.1 2.7 ( 0.1 2.8 ( 0.2 2.6 6.1 ( 0.2 7.0 ( 0.2 7.1 ( 0.4 6.9 ( 0.4 6.8

0.07 ( 0.01 0.07 ( 0.01 0.08 ( 0.01 0.08 ( 0.01 0.08 0.00 ( 0.02 0.00 ( 0.03 0.00 ( 0.04 0.00 ( 0.05 0.00 0.00 ( 0.02 0.00 ( 0.02 0.00 ( 0.01 0.00 ( 0.03 0.00

0.01 0.01 0.04 0.09

65

100

1.1 1.9 3.3 5.9 1.2 2.2 3.8 6.7

0.03 0.06 0.11 0.21 0.03 0.07 0.14 0.20

a See Table 1 for experimental conditions. b The standard deviations of the coefficients are also given. c Obtained by a linearization method.42 Chi-squared of the fit. e Data obtained at this temperature are difficult to fit to the Knox equation but can be fitted very well to the Van Deemter equation (A′ + B/ν + Cν). To be consistent with other temperatures, the A coefficients of the Knox equation are estimated by A′/ν1/3 at the high-velocity region, where B/ν is ignored.

d

Figure 5. Effect of temperature on column efficiency. The symbols are experimental data, and the dotted lines are fits to the Knox equation. Note the mobile phase compositions are different at the three temperatures (see Table 1). Symbols/solutes: 9, 1-phenylnonane; b, 1-phenylundecane; 2, 1-phenyltridecane; 1, 1-phenylpentadecane.

We observe from Figure 5 that, at 25 °C (mobile phase 85% ACN), the optimum reduced plate height (hmin) was 5.5 for 1-phenylnonane, but it decreased to about 4 (improved by 30%) at 65 °C (mobile phase 78% ACN) and 4.5 at 100 °C (mobile phase 32% ACN). The slight increase in hmin at 100 °C may be due to the effect of a mismatch in temperature of mobile phase entering the column and the column temperature.45 Another possibility is 842

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that, due to the change in the mobile phase composition (and accordingly the viscosity) from 78% ACN at 65 °C to 32% ACN at 100 °C (see Table 1), the diffusivities of solutes at 100 °C are actually slower than those at 65 °C. Thus, the efficiency of mass transfer in the stagnant mobile phase should be poorer at 100 °C than that at 65 °C, which could result in a slight increase in hmin. Furthermore, the contribution of the axial molecular diffusion at elevated temperatures is more significant. Overall, Figure 5 demonstrates that the optimum column efficiency is improved when the column is operated at elevated temperatures. Moreover, this trend holds true for other well-retained solutes. The optimum reduced velocity (νopt) at which the highest column efficiency is realized is about 2, 4, and 7 at 25, 65, and 100 °C, respectively. The move of hmin toward high reduced velocity at elevated temperatures clearly indicates that high temperature improves the mass transfer resistances.2,22 This conclusion is supported by the data in Table 4. The C coefficient at 25 °C is about 0.08 on average; however, it is nearly zero at 65 and 100 °C. This point is obvious even if we do not fit the data to the Knox equation. The finite slope of the reduced plate height at the high-velocity region is clear at 25 °C, but it becomes nearly zero at the higher temperatures. The improvement in the mass transfer resistances at elevated temperature is most likely due to both the enhanced diffusion inside the stagnant mobile phase and the increase in the stationary phase desorption rate constant controlled by the stationary phase diffusion.2,21,22,40,41 The diffusion coefficients at 65 °C are significantly larger (by a factor of 1.6) than those at 25 °C (see Table 1); thus, the improved mass transfer resistances at 65 °C relative to those at 25 °C must be due to the increased diffusion both inside the stagnant mobile phase and in the stationary phase. However, little change is seen in the measured diffusion between 25 and 100 °C due to the fact that we simultaneously changed the mobile phase composition to a more viscous medium. Accordingly, the significant improvement in the mass transfer resistances at 100 °C relative to those at 25 °C is probably due (45) Abboh, S.; Achener, P.; Simpson, R.; Klink, F. J. Chromatogr. 1981, 218, 123-135.

Figure 6. Effect of mobile phase volumes on the stability of PBDcoated zirconia. See Experimental Section for conditions. Solutes/ symbols: 0, ethylbenzene; O, n-propylbenzene; 4, n-butylbenzene.

mainly to the increased diffusional rate in the stationary phase. The improvement in the molecular diffusion rate in the stationary phase at 100 °C may reflect the fact that solute molecules and segments of the polymer stationary phase both become more motile at high temperature. These results also confirm our separate finding that the diffusional rate of solutes in the material is very slow for PBD-coated zirconia phase, particularly at high carbon loads.42 It is also obvious from Figure 5 and Table 4 that, as the temperature increases, the B coefficient also increases (see Table 4). For example, the average B coefficient by the linearization method is about 1.9 at 25 °C; however, it is about 2.6 and 6.7 at 65 and 100 °C, respectively. Although it is not expected from eq 6 that the B coefficient should increase with temperature for the dimensionless Knox equation, the large B coefficients at high temperatures are not due to either the errors in the measured diffusion coefficients or the goodness-of-fits (the fits of Knox equation in the low-velocity region are very good at 65 and 100 °C). Moreover, there is basically no dependence of B on the capacity factor at high temperatures (see Table 4); thus, the large B coefficients at high temperatures cannot be due to the contribution of the longitudinal molecular diffusion in the PBD stationary phase.46 We also found large B terms in a separate study42 and attributed them to column wall effects.47 The very large B coefficients at 100 °C seem to confirm our conclusion. We need to point out that, no matter what the actual B coefficients are, their contributions at high velocity are insignificant and have no effects on the A and C coefficients; therefore, our conclusions (the effects of temperature on A and C coefficients) are still justified. The change in the A coefficient with temperatures in Table 4 is obvious but not significant within experimental errors. For example, the averaged A coefficient at 25 °C is about 2.7; however, it becomes 2.1 and 1.8 at 65 and 100 °C, respectively. The (46) Stout R. W.; Pestetano, J. J.; Snyder, L. R. J. Chromatogr. 1983, 282, 263286. (47) Knox, J. H.; Laird, G. R.; Raven, P. A. J. Chromatogr. 1976, 122, 129-145. (48) Nawrochi, J.; Rigneym M. P.; McMormick, A.; Carr, P. W. J. Chromatogr. 1993, 657, 229-282. (49) Rigney, M. P.; Weber, T. P.; Carr, P. W. J. Chromatogr. 1989, 484, 273281. (50) Rigney, M. P.; Funkenbusch, E. F.; Carr, P. W. J. Chromatogr. 1990, 499, 291-304.

decrease in the A coefficient is about 30% from 25 to 65 °C, which is consistent with the improved hopt. The small decrease in A coefficients at elevated temperatures could be due to an increase in the radial diffusion of solutes in the mobile phase, thereby opposing flow-induced dispersion. Thermal Stability of PBD-Coated Zirconia. To take full advantage of the beneficial effect of high temperature in RPLC, it is necessary to understand the thermal stability of the phase. Because zirconia has high acid-base and thermal stabilities,48 the present PBD-coated zirconia phase is expected to exhibit similar properties. Rigney et al.49,50 evaluated the alkaline and thermal stabilities of the phase by exposing PBD-zirconia columns to methanol-0.1 M sodium hydroxide (50:50) at a temperature of 50 °C and found no indication of instability upon exposure to 30 000 column volumes of the alkaline mobile phase. Furthermore, they exposed PBD-coated zirconia columns to a mobile phase of 1 M sodium hydroxide at 100 °C for more than 3 h, and there was no evidence of degradation. To further evaluate the thermal stability of PBD-coated zirconia phase, Figure 6 illustrates the results of a stability test on a 2.7% carbon PBD phase evaluated at a temperature of 100 °C. Except for a slight initial decrease in k′, there is no further decrease in k′ up to 7000 column volumes of mobile phase. The stable k′ means that there is no further change in the stationary phase. We note in Figure 6 that each discontinuity corresponds to the time at which the mobile phase reservoirs were refilled. We intentionally stopped the test at 7000 column volumes; we believe that PBDcoated zirconia is very stable at 100 °C. Accordingly, the excellent thermal stability of PBD-coated zirconia relative to silica-based columns allows us to do HPLC method development at elevated temperatures, so as to take full advantage of the effects of temperature on the retention, selectivity, and efficiency. We will report in a subsequent study on the practical chromatographic separations on the zirconia-based phase. CONCLUSIONS In this paper, we examined the effects of temperature on the thermodynamic properties, kinetic performance, and thermal stability of PBD-coated zirconia. We found that the thermodynamic properties of the PBD phase are comparable to those found on conventional bonded phases. The change in selectivity at elevated temperatures for small solutes can be very significant, depending on the type of solute. In addition, high temperature can improve the column efficiency by 30%, mainly by increasing the diffusional rate in the stationary phase. More importantly, the use of high temperature greatly decreases the C term and then allows the use of higher linear velocity, thereby enabling a decrease in analysis time. Finally, the zirconia-based PBD phases are very stable at temperatures of 100 °C for at least 7000 column volumes. ACKNOWLEDGMENT The authors acknowledge the financial support by Grant GM 45988-05 from the National Institutes of Health. Received for review August 21, 1996. Accepted December 2, 1996.X AC960854V X

Abstract published in Advance ACS Abstracts, February 1, 1997.

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