Anal. Chem. 1992, 64, 479-484
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Effect of Temperature on Separation Efficiency for High-speed Size Exclusion Chromatography Curtiss N. Remt a n d Robert E. Synovec* University of Washington, Center for Process Analytical Chemistry, Seattle, Washington 98195
Theoretlcai relationships for sire exclusion chromatography (SEC) separation etficiency as a function of temperature are presented for the high-speed separation regime. The hlghspeed regime is experimentally determined via asymptotic behavlor of a plot of the height equivalent to a theoretlcai plate ( H ) divided by the linear flow velocity ( v ) versus the linear fbw velocity for polystyrene plymers and toluene used as test mlxtures. A ilnear flow velocity of 10 mm/s was necessary lo meet the requirement of a high-speed separation using a slicabased c ~ k m with n 5-m,&A packing matdal In a l m m X 250mm mlcrobore column. Separation efflciency and analysls time are investigated as a function of temperature at constant pressure. Separatlon effkiency was found to be 4-6 times better at 150 O C than at room temperature. Fwlhemwre, analysis tlme was reduced by a factor of 4 due to the reduced vlsccodty of the high-temperature mobile phase, resulting In a 30-8 SEC separation of polystyrene polymers. Implications of turbulence to high-speed high-temperature separations are discussed. SFC-llke behavior for toluene was observed at 150 OC, even though the phase change to a supercrltical fiuld occurs at 237 OC for methylene chloride as the mobile phase. Implications of SFC-like behavior to small molecule separations are discussed.
INTRODUCTION Size exclusion chromatography (SEC) is commonly used to determine the molecular weight distributions of synthetic macromolecules.' Typically, size exclusion chromatography is performed a t room temperature, thereby simplifying separation hardware requirements? There are, however, a large number of SEC separations which must be performed at high temperature due to limited solubility of the macromolecules at room With the advent of high-temperature (HT) SEC, numerous studies have been conducted to determine the effect of elevated temperatures on many chromatographic parameters including polymer configuration,l retention volume,3 molecular weight calibration ~ I T O B , ~ -solvent ~ and polymer degradation,"and column efficiency as a function of separation t e m p e r a t ~ r e . ~ gEven ~ - ~ though experimental observations relating elevated separation temperature to increased separation efficiency for SEC have been known for many years, little attention has been placed on theoretically predicting and experimentally exploiting the benefits of reduced analysis time and/or increased separation efficiency for high-temperature SEC. Theoretical relationships for separation efficiency, analysis time, and separation temperature are developed in this work on the basis of accepted SEC theory, molecular diffusion, and viscometric properties of macromolecules and the mobile phase, respectively, where high-temperature high-speed SEC (HT-HS-SEC) separation +Presentaddress: ALPKEM Corp., 9445 S.W.Ridder Road, Suite 310, Wilsonville, OR 97070. 0003-2700/92/0364-0479$03.00/0
efficiency and analysis time are the focus of the investigations presented in this paper. Historically, analysis time has been slow for polymer-based columns where low volumetric flow rates were necessary to avoid compreasion of the polymer packing materials. The need for reliable process analysis and control in the polymer industry has focused considerable attention on acquiring chemical and physical information provided by HPLC and SEC-related techniques.l The shift toward real-time (on-line) analysis of the feed stream, intermediate, and finished products has placed an additional burden on the timeliness of information provided by SEC, commonly seen as a reliable, yet slow technique. The scientific literature haa been replete with theoretical relations used to optimize analysis time and separation efficiency for HPLC and SEC.8p9 With the introduction of uniform, wide-pore, silica-based SEC columns, it has been possible to expand the range of SEC to include high-~peed'"~separations with a total separation time of only a few seconds. Recently, theoretical relationships for hightemperature separation of macromolecules were presented which clearly outline the benefits and limitations for both porous and pellicular packing materials used in HPLCm4 In the work presented for this paper, theoretical expressions for column plate height versus separation temperature for SEC are developed. A simplified expression for HT-SEC is presented which conforms to high-speed SEC conditions. Furthermore, predictions of analysis time for high-temperature SEC are presented. Experimental identification of the high-speed SEC regime is presented along with van Deemter plots for polystyrene standards, showing a substantial reduction of plate height a t elevated temperatures. The effect of elevated temperature on the separation time and pressure drop are investigated at constant plate height. Experimental evidence for a substantial change in the diffusion coefficient of the polystyrene test analytes is given. The effect of turbulence on the separation plate height is discussed. Implications to small molecule separation and detection are discussed with reference to SFC-like behavior.
THEORY Efficiency. One measure of liquid chromatographic separation efficiency can be e x p r e d in terms of the plate height, H, which is given by14
H = (1/A
+ l/C,,,u)-l + B / u + C,u + C,
(1)
where A is the multipath term, a measure of the "goodness" of packing, B, the longitudinal diffusion term, a measure of the random diffusion of the analytes in the mobile phase, C , and C,, the resistance to mass transfer in the interstitial and stagnant mobile phase, respectively, u, the interstitial linear flow velocity of the mobile phase, and C, the polydispersity term. Equation 1 is widely accepted for HPLC and is also appropriate for SEC? For macromolecules,the diffwion term, B / v , is negligible at all but very low flow velocities and, with the condition of high-speed (to< 10 s) or superspeed SEC (to < 1s),the A and C, coupled terms are negligible, which allows simplification of eq 1to yield 0 1992 American Chemical Society
480
ANALYTICAL CHEMISTRY, VOL. 64, NO. 5, MARCH 1, 1992
H = C,u
(2)
where the plate height of a separation is described as the product of the rate of mass transfer4 and the linear flow veloci ty. The C, term can be viewed as an additional A term and was eliminated in these studies by the use of narrow dispersion polymer standards,' used as test analytes. For complex samplea which are polydisperse by nature, an increase in efficiency will facilitate identification of individual or groups of components. The effect of temperature on the mass-transfer term, C,, can be in~estigated'~ via
H
0:
d,2v/D,
(3)
where d, is the diameter of the column packing material and D, is the diffusion coefficient of an analyte in the stagnant mobile phase of the SEC packing material. The ratio D,/D, (D, = diffusion in the interstitial mobile phase) is referred to as the tortuosity factor and provides a measure of restricted diffusion in the pores of the SEC packing material. The tortuosity factor has been shown to be independent of linear flow velocity16for LC and, for the following derivations, assumed to be independent of temperature, thereby permitting the use of D, in the Einstein-Stokes equation. With the Einstein-Stokes expre~sion,'~ the relative dependance of D, on temperature can be given as Ds1/Ds2 = Tln2/T2n1 (4)
Dsl/Ds2is the relative diffusion coefficient a t temperatures Tl and T2in Kelvin and nl and n2 are the viscosities of the mobile phase at Tl and T,, respectively. The viscosity of the mobile phase can be represented as4 ni = a exp(@/Ti)
(5)
where (Y and /3 are empirically determined viscosity parameters. Combining eqs 3-5 while holding the packing diameter constant, i.e. utilizing the same column a t two different temperatures, yields H1/& = (47'2 exp(B/TJ)/(v2T1 exp(@/T2)) (6)
Thus,it is possible to predict the reduction of the column plate height for HS-HT-SEC using eq 6. Analysis Time. As an added benefit to HT-SEC, the reduced viscosity allows for a higher linear flow velocity and therefore faster analysis time. Earlier work by Snyder" clearly defined the trade-offs between packing diameter, column length, pressure, and flow rate to obtain a desired resolution in a given analysis time for conventional HPLC. Since the retention volume for SEClaJ9is relatively invariant with flow rate, the analysis time can be evaluated through Darcy's law15 P = $nvL/dP2
(7)
where 6,P, L, and d,2 are held constant, i.e., the same column a t two different temperatures. A decrease in viscosity of the high-temperature mobile phase is offset by an increase in the linear flow velocity to yield constant-pressure conditions. Substituting eq 5 into eq 7 yields W 2= ex~(B/TJ/exp(@/7'1) (8) where t l / t , is the relative analysis time at temperatures Tl and T2,respectively. With the added dimension of temperature in the high-speed and superspeed SEC regime, it is possible through eqs 6 and 8 to balance linear flow velocity, plate height, and temperature to control the analysis time and desired resolution for a separation without the added necessity of changing the column length. In the context of eqs 2 and 6, it is conceivable that an increase in linear flow velocity (faster analysis time) at elevated temperatures could be achieved with no loss in resolution. To predict the potential benefits of increased temperature in SEC, it is first necessary to determine j3 values, given in
Table I. Temperature Dependence of Chromatographic Parameters at 150 OC (2) relative to 25 OC (1) liquid
B"
nIm?CP
1-butanol water methanol acetonitrile acetone chlorobenzene toluene hexane methylene chloride
2301 1710 1270 812 743 1126 1042 852 774
0.261 0.158 0.160 0.153 0.152 0.254 0.199 0.130 0.190
n 2 / n I c H21Hld 0.102 0.178 0.284 0.447 0.479 0.327 0.356 0.430 0.464
0.072 0.126 0.200 0.315 0.337 0.231 0.251 0.303 0.327
a Exponential coefficient derived from literature values via eq 5. bCalculatedfrom 150 O C via eq 5 and room-temperature viscosity literature data. 'The ratio n2/nl is also equivalent to P 2 / P , (at conatant t ) and t 2 / t l (at constant P via eq 8). dRatio of plate height at 150 and 25 OC, respectively, calculated via eq 6.
Table I for common HPLC and SEC solvents. The j3 values were calculated from published viscosity data." Also included in Table I are the relative pressure drop, relative viscosity, relative analysis time, and relative plate height of separation a t 25 and 150 "C. For temperatures above the atmospheric boiling point of the solvent, a pressure of 250 psig is sufficient to maintain the solvent in the liquid state. The result of reduced viscosity at elevated temperatures is a reduced pressure drop for a packed column as can be seen in Table I, calculated via eq 7. The reduced pressure drop can minimize the maintenance of the chromatographic equipment, mainly the pump, injector, and column. Alternatively, the reduced pressure drop can be traded for a higher flow rate to reduce analysis time as seen in Table I, via eq 8. A dominant trend in Table I is that the largest change in viscosity is exhibited by liquids with strong intermolecular bonding forces. Liquids with the largest j3 values will experience the largest change in viscosity and, thus, the largest change in analysis time. Similarly, the relative plate height shows a substantial change in separation efficiency with a similar dependence on molecular bonding as exhibited by the relative analysis time. EXPERIMENTAL SECTION An important consideration for HS-HT-SECwas the configuration of the chromatographic separation apparatus and the choice of the detector. Microbore LC is ideal for HS-HT-SEC due to low volumetric flow rates which promote rapid heating and equilibration of the eluent, and therefore, allow the pump and injector to be maintained at room temperature. With the choice of microbore LC bLC), careful attention must be paid to minimize extracolumn band broadening, best served by placing the flow cell in the SEC oven, thereby eliminating exma connecting tubing. An effective method of remotely monitoring the absorbance in a micro flow cell was previously demonstrated via fiber optics and was chosen for use in the following investigation. The dualwavelength detector used for these experiments was described in detail in previous publications,21~22 and therefore, only a brief description of the detector is presented in this work. A schematic of the separation and detection apparatus is shown in Figure 1. The likht source consisted of a 150-Wmediumpressure mercury-xenon lamp with fused-silica collimating and focusing optics to collect and focus the broad-band UV-vislight into a fused-silica optical fiber, 480/500/505 fim core/clad/ polyimide jacket (Fiberguide Industries, Superguide-G, Stirling, NJ). The optical fiber then directed the light to a micro flow cell, 0.5 mm i.d. X 6 mm made in house (1.2-fiL volume),with a similar fiber across the flow cell to collect light transmitted through the flow cell and guide the light to a grating monochromator (American Holographic, Chemspec 100M, Littleton, MA). The spectrum was then dispersed via a grating onto a l-mm X 12-mm continuous position-sensitivedetector (PSD) (Hamamatsu,S1545, Hamamatau City, Japan) with an optical mask applied to select the two spectral regions of interest, 254 and 314 nm with a 10-nm
ANALYTICAL CHEMISTRY, VOL. 64, NO. 5, MARCH 1, l9Q2 481
Flguro 1. High-temperature chromatograph: HgL = mercury-xenon lamp; OF = optical fiber; FC = flow cell; OM = grating monochromator; PSD = position-sensithre detector; sum = sum of chosen spectral regions; diff = difference of chosen spectral regions; PC = personal computer; P = syringe pump; I V = Injection valve; MLC = microbore column; R = pressure restrictor; TC = temperature controller; H = heating enclosure.
Table 11. Polystyrene Polymer and Toluene Constants mol wt 1113000 9OOo
92 (toluene) a
Pe&
MW/M,6
A B C
1.06 1.04 1.00
Identification of peak in Figure 2a,b. *Polydispersity.
spectral band-pass. The protective glass cover was removed from the PSD to allow more sensitive detection in the UV spectral region. The detector was configured to provide low noise absorbance information by performing the analog difference (diff output) of the two spectral regions chosen by the optical mask. The detector waa also configuredto provide the sum of the spectral regions to yield the total light flux impinging on the PSD. A syringe pump (lsco, LC-500, Lincoln,NE)was used to deliver the mobile phase to a microbore injection value (Rheodyne,7125, Cotati, CA) equipped with a 0.5 pL injection disk at the head of mm,Spm,&A-pore, silica-based microbore HPLC a I-mm x m column (Altech,Absorbosphere, Deerfield, IL)followed by a micro flow cell previously described. Lengths (5 cm) of 0.005 in. i.d. X in. 0.d. stainless steel tubing were used to connect the column to the injector and flow cell. A 250 psig preasure restrictor (Upchurch, U-462, Oak Harbor, WA) was placed after the flow cell to eliminate b o i i of the mobile phase at temperatures above its atmospheric boiling point. The flow cell and column were contained in an oven, with temperature control via temperature controller (FIAtron, TC-55, Oconomowoc, WI)with a maximum temperature range to 150 OC. The pump, injector, and pressure restrictor were maintained at room temperature. The mobile phase consisted of HPLC grade methylene chloride (EM Science, Omnisolv, Cherry Hill, NJ). Narrow molecular weight polystyrene standards were used to investigate the effect of temperature on separation efficiency (Polymer Laboratories Inc., Amherst, MA). Polymer molecular weight and polydispersity are presented in Table 11. Reagent grade toluene (EM Science, Omnisolv, Cherry Hill, NJ) was used as a marker for a totally permeating solute. Data collection was facilitated via a laboratory interface (Metra Byte, Dash-16, Tauton, NY) at loo0 point/s and connected to a personal computer (BM-XT h o n k , NY), with a digital boxcar integration performed on the fly. The boxcar integration was performed to meet the minimum requirement of generating at least 20 independent data points for the narrowest peak in the SEC chromatograms at a given flow rate. High molecular weight polystyrene and toluene standards were included in the SEC chromatograms as a measure of the totally excluded pore volume (interstitial volume) and totally permeating pore volume, respectively, both independent of temperature for
this work. Temperature independence was determined by monitoring the volume difference between the totally excluded and totally permeating peaks from 25 to 150 OC. Since the pump is at room temperature, there is a volumetric flow rate increase through the column and detector for separations above room temperature." After correction for the increased volumetric flow rate/density change, the difference between the totally excluded and total permeating volume was found to be independent of temperature, substantiating the change in pore volume to be negligible for this work. The elution time of the totally excluded polystyrene peak was then used as a measure of the interstitial volume, which allowed calculation of the linear flow velocity at the elevated temperatures. The width of the peaks were determined using the average of two different methods. The first method, the tangential drop method, was used which defiies the width at the base, W,= 4u. The second method used the relation u = area/[(peak height)( 2 ~ ) ' / ~ Both ] . methods compared favorably, and the average of the two methods was chosen to minimize any bias in determining peak width.
RESULTS AND DISCUSSION The issue of analysis time versus temperature is straightforward and is simply based on the reduction of the mobilephase viscosity at elevated temperatures. As indicated by Table I, analysis time should be reduced at elevated temperatures, with the constraint of maintaining constant pressure, i.e. increased flow rate. A room-temperature separation is shown in Figure 2a and one a t 150 "C, offset for clarity. The entire separation at 150 "C is complete before the fist peak elute from the room-temperature separation. This constitute over a factor of 4 reduction in analysis time at 150 OC with a modest increase in separation pressure. Figure 2b is an expanded view of the 150 "C separation, allowing qualitative comparison of the efficiency at room temperature and 150 OC. Clearly, no significant separation efficiency has been sacrificed even though the flow rate is 4 times higher at 150 OC. The reduction in analysis time is relevant for rigid packing material such as silica, yet, however, may not extend to polymer-based SEC packing materials which are more susceptible to compression at high linear flow velocities. With a polymer-based packing material, an increase in temperature will increase ita susceptibility to compression, therefore, negating the utility of increased flow velocities via reduced separation efficiency. Silica packing was chosen to eliminate the detrimental effect of packing compression at high linear flow velocities, thereby facilitating HS-SEC. Increased linear flow velocities increase the magnitude of shear degradation, particularly for high molecular weight species, i.e. greater than lo6. According to a review by Barth and Carlin, shear degradation is proportional to the linear flow velocity and inversely proportional to the mobile-phase viscosity.23 Even though the high-temperature linear flow velocity is larger, the viscosity is lower by the same proportion, resulting in no net change in shear degradation. Further work is necessary to experimentally evaluate the effect of HT-HS-SEC on shear degradation. Having a d d r e a d the effect of temperature on SEC analysis time, next it is of interest to investigate the effect of temperature on separation efficiency. With this goal in mind, it is first appropriate to identify the high-speed regime. Consistent with previous work,1° a plot of H / u versus u, Figure 3, clearly identifies an asymptote region, indicative of the C, term in eqs 1and 2 as the dominant source of chromatographic band broadening. Above 10 mm/s, this flat region provides a well-behaved representation of mass-transfer-limited chromatographic behavior and allows prediction of the effect of temperature on separation efficiency. To evaluate the effect of temperature on the plate height, it is useful to plot H versus u, as shown in Figure 4 which is for four different temperatures, 25,65,105, and 150 OC, and exhibits features characteristic of SEC. As expected, for a
482
ANALYTICAL CHEMISTRY, VOL. 64, NO. 5, MARCH 1, 1992 0.26 0.24
1x v
0.22
.
0.20
0
0.18
A 105C
25C 85c
. -.
0
10
20
30
v (mdsec) Figure 4. van Deemter plot for polystyrene 9000.
d
30
60
90
Table 111. C, Values for Polystyrene 9000
120
T I M E (SEC)
temp,
25 65
d
id
2d
30
T I M E (SEC) Flguro 2. (a, top) High-speed SEC separations of polystyrene standards. Separation conditions for lower trace: temperature = 25 OC, Row rate = 100 s/min, presswe = 4100 psig. Separatbn conditions for upper trace: temperature = 150 OC, flow rate = 400 pL/min, pressure = 5100 psig. Injected concentration for both separations = 20 mg/lO mL methylene chloride. See Table I1 for analyte idenUfication. (b, bottom) Expanded view of 150 OC SEC separation of porvstvrene standards. Separation condltkns: flow rate = 400 Wmin, pressure = 5100 psig; same sample as Figure 2a.
0
10
20
30
v (mdsec) Flgure 3. High-speed limit for polystyrene 9000. Region above 10 mm/s chosen as the high-speed (mass-transfer-limited) regime for eq 2.
given separation temperature, the plate height increased with linear flow velocity. There are however, anomalies in the van Deemter plots manifested as a nonlinear relation a t higher linear flow velocities. Common explanations for the nonlinear behavior, such as coupling between the A and C, terms and
O C
C, a
0.0488 0.0313
temp,
105 150
O C
C,,
8
0.0105 0.0075
influence of the C, term and B term, would all produce downward curvature at lower linear flow velocities and approach linear behavior at high linear flow velocities, contrary to the data presented in Figure 4,and therefore, are not good candidates to explain the curvature of the van Deemter plots. The retention volume of the probe polystyrene in the SEC regime was relatively invariant of flow rate and temperature and therefore does not suggest introduction of secondary separation mechanisms.' Similar downward curvature has been seen and attributed to the introduction of turbulence in the column at high linear flow v e l o c i t i e ~ . ~A~ -significant ~~ benefit of turbulent flow would be the increase of convective diffusion, thereby reducing the magnitude of C, and C,. Under laminar flow conditions, mass transport perpendicularto the local interstitial fluid flow path is primarily due to molecular diffusion, which gives rise to nonequilibrium conditions of analyte concentration in the stagnant and bulk mobile phase. Turbulent flow increases mass transfer of the analytes via convective mechanisms instead of only diffusion mechanisms, thereby minimizing nonequilibrium conditions experienced for laminar As predicted by eq 6, the higher temperature separations yielded a smaller H value, or more efficient separation for the same flow velocity. The curvature of the H versus u plots in Figure 4 for the high-speed regime indicates eq 2 is only an approximation yet, however, should provide reasonable predictive power. Qualitatively, it is clear from Figure 4 that the higher temperature separations are more efficient; however, it is of interest to quantitatively evaluate the predictive power of eq 6. Selection of a silica-based column allowed separations with column pressures approaching 500 psig to achieve high linear flow velocities; however, the large viscosity differences between 25 and 150 "C resulted in a wide range of maximum flow rates. Since it was not possible to operate the chromatograph above 5 mm/s at 25 OC,it was not possible to make a direct comparison between plate height at 25 and 150 "C in the high-speed regime. Alternatively, the slope of the H versus u curves, Table 111, can be used to compare predicted separation efficiency. The slopes were calculated using the linear portion of the curve at lower linear flow velocities. Even though the slopes were not measured in the asymptotic region of Figure 4,the linear relation of H versus u allows reasonable estimation of the C, term. Comparison of the plate heights at the respective temperatures, 25 and 150 "C, can then be accomplished via eq 2 to yield a factor of 6 lower plate height at 150 "C. A steeper slope at the lower temperatures indicated a larger C,
ANALYTICAL CHEMISTRY, VOL. 64, NO. 5, MARCH 1, 1992
1 0.04 -
483
I
0.06
U'u'
0
X
mc mc
A 106 C
0.04
A 160 C
".""
,
10
0
20
0.03
30
0
v (mdsec) Figwe 5. mshgpeed limit for toluene. Region above 10 mm/s chosen as the high-speed (mass-transfer-llmited)regime.
25 65
OC
e,,
8
0.00509 0.003 25
temp,
20
30
O C
105 150
c,,
Flgure 8. van Deemter plot for toluene.
to control retention behavior for reversed-phase and normal-phase separations; however an increase in temperature would also increase the separation
Table IV. C, Values for Toluene temp,
10
v (mdsec)
8
0.002 28 0.001 97
value and therefore a larger plate height for a given flow rate. The plate height values reported for Figure 4, Table 111, are representative of values for SEC8which tend to be larger than reversed-phase separation due to restricted diffusion of the high molecular weight polymers, particularly when the hydrodynamic radius of the polymer approaches a significant fraction of the pore volume. The A term was relatively indpendent of temperature with an average value of 0.150 mm and standard deviation of 0.035 mm. A more direct comparison of the measured plate height data can be achieved by selecting a plate height a t 20 mm/s for the 150 "C separation and comparing the linear flow velocity required to produce the same plate height a t 25 "C. Since the plate heights are nearly equal, the ratio of the linear flow velocities yields the ratio of the C, terms at the two temperatures via eq 2. Using this approach in conjunction with eq 3, a 4-fold change in C, would be necessary to account for the same plate height a t the maximum flow rates at 25 and 150 "C, similar to the result of the slope method of determining the C, term. This is in reasonable agreement with a value of H J H , obtained from Table I; however, the downward curvature of the van Deemter plots has compromised the accuracy of the linear prediction yet benefited the improvement in efficiency at higher temperature and higher linear flow velocity. So far the discussion has centered around macromolecules; however the issue of temperature effects on separation efficiency for small molecules is of interest and can be addressed via investigation of the chromatographic behavior of toluene versus separation temperature. Again, a plot of H / u versus u is useful for determine the range of the C, term dominated regime, as shown in Figure 5. The region above 10 mm/s shows an asymptoticrelationship. A plot of H versus u, Figure 6, shows a feature not seen in the polymer separations: the relatively large influence of a B term at 150 "C similar to what is seen for SFC even though methylene chloride does not attain a supercritical fluid state until 237 0C.20With the large increase in D, at 150 "C it is reasonable to see the increased influence of a B term at low flow rates for toluene due to its small size and therefore large diffusion coefficient. Futhermore, the slopes of the H versus u curves for toluene decrease with increasing t e m p e r a t ~ r eas , ~ given in Table IV, similar to the macromolecule behavior. The A term was relatively independent of temperature with an average value of 0.0352 mm and standard deviation of 0.0016 mm. The role of temperature in small-molecule separations has primarily been demonstrated via thermal gradient separations mainly used
CONCLUSIONS The effect of column turbulence could further enhance the utility of high-speed HT-SEC. The trend in LC has been toward smaller particle size packing material, which is more difficult to uniformly pack into columns and typically exhibits a larger particle size distribution and pore size distribution, thereby offsetting some of the benefits of the smaller packing material. Alternatively, larger packing material is easier to pack columns and ie available with more uniform particle and pore size distribution; however, the plate height is larger (less efficient) where the A term is proportional to d, and the C, term is proportional to dp2. With the condition that analysis time is the chromatographic parameter to be optimized, the incorporation of HT and high linear flow velocitiea would have several distinct advantages not offered by manipulation of other chromatographic parameters. First, H T would allow higher linear flow Velocities for a faster analyeistime. Second, H T analysis would reduce the plate height by reducing the mass-transfer limitation via increased diffusion coefficients. Third, as a result of the increased flow rate due to larger particle diameter and of the H T separation conditions, the introduction of turbulence could further reduce the A and C terms via the previous discussion. In fact, it has been shown that at very high linear flow velocities, the plate height reaches a maximum and actually decreases with increasing flow rate beyond the maximum.25 It is obvious from the data presented that the simple mass transfer limit model does not completely account for the change in plate height versus temperature; however, the model does provide reasonable predictive power for the effect of temperature on high-speed HT-SEC separations. Futhermore it has been shown for HT-SEC with rigid packing material, the analysis was completed in one-fourth the time with only a 25% increase in pressure and with no appreciable loss in separation efficiency. This is of particular interest for SEC chromatographicseparations which typically suffer from poor efficiency and/or long analysis time. Registry No. HO(CH&&H3,71-36-3;HzO,7732-185;HOMe, 67-56-1;H,CCN, 75-05-8; H&C(O)CH3,67-64-1;ClPh, 10890-7; MePh, 108-88-3; H3C(CH2)4CH3, 110-54-3; Cl2CHZ,75-09-2; polystyrene (homopolymer),9003-53-6.
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RECEIVED for review June 24,1991. Revised manuscript received November 25, 1991. Accepted November 27, 1991.
Determination of Formation Constants for ,8-Cyclodextrin Complexes of Anthracene and Pyrene Using Reversed-Phase Liquid Chromatography Vincent C. Anigbogu: Arsenio Muiioz de la Peiia,*Thilivhali T. Ndou, and Isiah M. Warner* Department of Chemistry, Emory Uniuersity, Atlanta, Georgia 30322
The stolchlometry and apparent formatlon constants of anthracene and pyrene 8-cyclodextrln (B-CD) complexes were determlned by use of llquld chromatography. These values were measured In moblle-phase mlxtures of methanol-water and In the same mixtures modlfled wlth 1% v/v fed-butyl alcohol or cyclopentanol. The results show that anthracene forms a 1:l complex wlth 8-CD, and the apparent forrnatlon constant ( K , ) values In mobile-phase mlxtures of 55 % v/v, 60% v/v, and 65% v/v methanol-water are 373, 242, and 136 M-', respectlvely. Modlflcatlon of the moblle-phase mixtures wlth 1% v/v fed-butyl alcohol or cyclopentanol produced a sllght decrease In the anthracene K , values. Pyrene exhibited prohlbltlvely long retantbn t h s In the 55 % v/v methanol-45 % v/v water mixture and also showed llttle lnteractlon with 8-CD In 60 % v/v and 65 % v/v methanolwater mixtures. However, a remarkable change in capachy factor was observed for pyrene In the presence of 1 % v/v fed-butyl alcohol or cyclopentanol. A stokhlometrlc ratlo of 2 1 and apparent formatbn constant values of 1.88 X lo7 and 2.96 X 10' M-* were detennlned for the 8-CDpyrene In 54% v/v methanol-45 % v/v mobHe phase mMures contalnlng 1% v/v cyckpentand and 1% v/v ferf-butyl alcohol, respecthrely. The lmpllcatlon of 8-CDpyrene:alcohol ternary complex formation and analytkal chemistry applkatlons of the concomltant effects are dlscussed.
INTRODUCTION Cyclodextrins(CDs) are naturally occurring, torus-shaped, cyclic oligosaccharides made of six,seven, or eight glucose units (a-,p-, or y-CDs) joined by 1-4 LY linkages.' They readily form *Author for correspondence. 'Present address: Department of Chemistry, Austin Peay State University, Clarksville, TN 37044. Present address: Department of Analytical Chemistry, University of Extremadura, Badajoz 06071, Spain.
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0003-2700/92/0364-0484$03.00/0
stable inclusion complexes with a variety of organic and inorganic molecules and ions. Unlike other types of organized media such as micelles, CDs exhibit a broad range of desirable properties such as (1) no critical concentration needed to include guest molecules, (2) stability over a wide range of pHs, (3) resistivity to light, (4) little or no absorption in the UV region, ( 5 ) nontoxicity, and (6) nonfoaming solution when purged. The 0-CD inclusion phenomena have been extensively characterized. Notwithstanding their limited solubility in water (1.85 g/100 mL) compared to the other two naturally occurring systems,viz.a-CD and y-CD, BCDs have been used in pharmaceutics to improve solubility, dissolution rate, stability, and bioavailability of therapeutic compounds.24 It has also found extensive application in improving molecular luminescence measurement^.^ Chromatographic studies have mostly centered on the improved resolution of However, whether the interest is in the use of CDs as potential drug carriers, as a means of isolating an analyte from a quenching environment, or to improve chromatographic resolution of isomers, knowledge of the stoichiometries and formation constants of p-CD:guest complexes and the effect of the environment (bulk solvent) on these values is germane to the development of such uses for j3-CDs. Many methods have been used to determine the association constants of 0-CD:guest complexes including UV-vis absorption,+12 NMR, spectrometry12 potentiometry,12 liquid chr~matography,'~-'~ and fluorescence measurement^.'^-^^ Much of the studies of the stoichiometry and apparent formation constants for the complexes of a-CD, o-CD, and y-CD under different experimentalconditionshave been done using spectroscopic methods such as fluorescence and absorbance measurements. Although spectroscopic techniques such as the fluorescence vibronic band ratio method are sensitive and rapid for studies of the p-CD inclusion mechanisms, pyrene is, unfortunately, only one of a few molecules that exhibit such a phenomenon. Furthermore, for some compounds, signifcant inclusion into the p-CD cavity is not necessarily accompanied by significant spectral changes. These limit the scope of the applicability of some spectroscopic techniques. Liquid 0 1992 American Chemical Society
