Anal. Chem. 2008, 80, 1829-1832
Size-Based Characterization by the Coupling of Capillary Electrophoresis to Taylor Dispersion Analysis Thomas Le Saux† and Herve´ Cottet*,‡
Ecole Normale Supe´ rieure (UMR 8640 CNRS, Universite´ Pierre et Marie Curie Paris 6), 24 rue Lhomond, 75231 Paris Cedex 05, France, and Institut des Biomole´ cules Max Mousseron (UMR 5247 CNRS, Universite´ de Montpellier 1- Universite´ de Montpellier 2), 2, place Euge` ne Bataillon CC 017, 34095 Montpellier Cedex 5, France
In this work, a new methodology is presented for performing capillary electrophoresis (CE) coupled to Taylor dispersion analysis (TDA). The CE step allows the separation of the different compounds of the injected mixture, while the diffusion coefficient related to each sample zone can be derived from the subsequent TDA step. TDA is an absolute and straightforward nonseparative method allowing the determination of the diffusion coefficient (or hydrodynamic radius) from the peak dispersion obtained in an open tube under Poiseuille laminar flow conditions. With a mass concentration sensitive detector, the hydrodynamic radius derived from TDA is a weight average value calculated upon all the molecules present in the sample zone. Since CE can be hardly coupled to light scattering detection for technical reasons (low volumes, short detection path length), TDA represents an interesting alternative for the size characterization, without calibration, of sample mixtures using CE-based separation techniques. The coupling of CE to TDA can be implemented on a commercial CE apparatus. Taylor dispersion analysis (TDA) is a simple, absolute, and rapid method for determining average diffusion coefficient D (or hydrodynamic radius Rh). TDA is based on the dispersion of a solute plug in an open tube under Poiseuille laminar flow conditions.1,2 Due to the parabolic velocity profile, the band dispersion is directly related to the molecular diffusion that redistributes the molecules over the cross section of the tube.1 TDA is applicable on (macro)molecules of virtually any molar mass. Different groups reported the use of TDA for the measurement of diffusion coefficients in either gaseous3 or liquid phases.4-6 TDA was also applied for the size characterization of macromolecules.7-12 Barooah et al. measured the diffusion coefficient of polystyrene in cyclohexane7 and in dioxane,8 at infinite * To whom correspondence should be addressed. Tel: +33 4 6714 3427. Fax: +33 4 6763 1046. E-mail:
[email protected]. † Universite´ Pierre et Marie Curie. ‡ Universite´ de Montpellier. (1) Taylor, G. Proc. R. Soc. London A 1953, 219, 186-203. (2) Aris, R. Proc. R. Soc. London A 1956, 235, 67-77. (3) Giddings, J. C.; Seager, S. L. J. Chem. Phys. 1960, 33, 1579-1580. (4) Ouano, A. C. Ind. Eng. Chem. Fundam. 1972, 11, 268-271. (5) Pratt, K. C.; Wakeham, W. A. Proc. R. Soc. London A 1974, 393-406. (6) Grushka, E.; Kikta, E. J. J. Phys. Chem. 1974, 78, 2297-2301. 10.1021/ac702257k CCC: $40.75 Published on Web 02/02/2008
© 2008 American Chemical Society
dilution. Boyle et al.9 determined diffusion coefficients of pauciand polydisperse poly(styrene sulfonate) samples. Mes et al.10 reported a comparison of different methods (including TDA) for the determination of diffusion coefficients of synthetic polymers (styrene acrylonitrile copolymers). The Leaist group reported the use of TDA for the characterization of poly(ethylene glycol) mixtures.11,12 Bello at al. applied TDA for the measurement of protein and amino acid diffusion coeffcients.13 TDA was also used for the characterization of hyperbranched synthetic polypeptides (namely, dendrigraft poly(L-lysine)).14 Recently, we demonstrated that, for a polydisperse sample, TDA leads to the weight average hydrodynamic radius in the case of a mass concentration sensitive detector.15 Correction from instrumental contributions (injection, pressure ramp) has been studied in detail.16,17 Since TDA is an absolute method, no calibration is required and the knowledge of the sample concentration is not needed. In essence, TDA is a very simple and straightforward method. Capillary zone electrophoresis instrumentation, which allows the detection at a given location inside the column, was shown to be particularly well suited for performing TDA.13-16 In this work, we found it interesting to demonstrate the possibility to achieve TDA after a capillary electrophoresis (CE) separation for the analysis of mixtures. For that, the different compounds constituting the mixtures are first separated by CE. TDA is then performed online, in the same capillary, allowing the determination of the diffusion coefficient (or hydrodynamic radius) of each sample zone previously separated by CE. (7) Barooah, A.; Chen, S. H. J. Polym. Sci., Part B: Polym. Phys. 1985, 23, 2457-2468. (8) Barooah, A.; Sun, C. K. J.; Chen, S. H. J. Polym. Sci., Part B: Polym. Phys. 1986, 24, 817-825. (9) Boyle, W. A.; Buchholz, R. F.; Neal, J. A.; McCarthy, J. L. J. Appl. Polym. Sci. 1991, 42, 1969-1977. (10) Mes, E. P. C.; Kok, W. Th.; Poppe, H.; Tijssen, R. J. Polym Sci., Part B: Polym. Phys. 1999, 37, 593-603. (11) Kelly, B.; Leaist, D. G. Phys. Chem. Chem. Phys. 2004, 6, 5523-5530. (12) Callendar, R.; Leaist, D. G. J. Solution Chem. 2006, 35, 353-379. (13) Bello, M. S.; Rezzonico, R.; Righetti, P. G. Science 1994, 266, 773-776. (14) Cottet, H.; Martin, M.; Papillaud, A.; Souaı¨d, E.; Collet, H.; Commeyras, A. Biomacromolecules, 2007, 8, 3235-3243. (15) Cottet, H.; Biron, J.-P.; Martin, M. Anal. Chem. 2007, 79, 9066-9073. (16) Sharma, U.; Gleason, N. J.; Carbeck, J. D. Anal. Chem. 2005, 77, 806813. (17) Alizadeh, A.; De Castro, C. A.; Wakeham, W. A. Int. J. Thermophys. 1980, 1, 243-284.
Analytical Chemistry, Vol. 80, No. 5, March 1, 2008 1829
THEORY Molecules injected in a narrow band at the inlet end of a cylindrical capillary tube move with different velocities depending on their positions in the capillary cross section under laminar flow conditions. The combination of the dispersive velocity profile with the molecular diffusion leads to a specific mechanism of dispersion described by the Taylor-Aris-Golay equation for unretained solutes:10-12
HS )
2 2D dc u + u 96D
(1)
where HS is the height of an equivalent theoretical plate, u is the average velocity of the mobile phase, dc is the capillary diameter, and D is the molecular diffusion coefficient. The plate height HS 2 is related to the elution time tR and the temporal variance σS of the elution peak by
HS ) lσS2/tR2
(2)
where l is the capillary length to the detector. The condition for eq 1 to hold true is that the residence time t of the solute before detection is much longer than the characteristic diffusion time of the solute in the cross section of the capillary:
t . Rc2/2D
(3)
with Rc the internal radius of the capillary tube. Furthermore, it is assumed there is no interaction of the solute with the capillary wall. For determining the diffusion coefficient, it is possible to perform experiments at various carrier velocities. For each velocity, HS is calculated from eq 2. Then D is determined from the slope, S, of the ascending branch of the HS versus u plot as
D ) dc2/96S
(4)
This method allows us to get rid of the flow-independent potential 2 contribution to σS . With typical dimensions used in capillary electrophoresis (dc ) 50 µm, u ∼ 10-3 m s-1), and for D ∼ 10-10 m2 s-1, the first right-hand side term in eq 1 scales as 10-7 m whereas the second scales as 10-3 m. In such conditions, HS is a linear function of u. EXPERIMENTAL SECTION Reagents. Sodium tetraborate (99% purity) and formamide (99% purity) were purchased from Fluka (Saint-Quentin-Fallavier, France). Water used throughout was produced by an Alpha Q system (Millipore, Molsheim, France). The 13-mer DNA (5′TCCTTTGTTTGTG) was purchased from IBA (Go¨ttingen, Germany). Random copolymer (Pol) of acrylamide (90% in mol) and 2-acrylamido-2-methylpropanesulfonate (10% in mol) were synthesized by radical polymerization initiated by potassium persulfate and N,N,N′,N′-tetramethylethylenediamine according to the procedure described by McCormick and Chen.18 The copolymer was purified by precipitation in absolute ethanol. The number average molecular weight of the PAMAMPS was evaluated (number 1830
Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
average molar mass, Mn 3 × 105 g mol-1) by size exclusion chromatography using poly(ethylene oxide) standards for the calibration. Electrolyte and Sample Solutions. The background electrolyte was a 50 mM sodium borate buffer, pH 9.2 (25 mM ionic strength). Stock solutions of 10 g L-1 Pol and 1.96 g L-1 DNA were prepared in the sodium borate buffer. When needed, these solutions were diluted with the background electrolyte to obtain the final sample solutions. Capillary Electrophoresis Instrumentation. Electrophoretic and TDA experiments were performed with a HP3DCE (Agilent Technologies, Waldbronn, Germany) capillary electrophoresis system. This apparatus automatically realizes all the steps including capillary conditioning, sample introduction, voltage, and pressure applications and diode array detection. Migrations and mobilization procedures were performed in bare fused-silica capillaries (Polymicro, Phoenix, AZ), 50.2 µm i.d. × 40 cm (31.5 cm to the detector, respectively) as detailed in the figure captions. Cross section of the capillary was imaged with a CCD camera mounted on phase-contrast DMIL inverted microscope (Leica) equipped with 20× and 60× objectives. After pixel scaling calibration, the inner diameter of the capillary was measured with ImageJ software freely available from the NIH website.19 The temperature of the capillary cartridge was set at 25 °C. Detection of the analytes was performed by UV absorbance at 214 and 260 nm. Sample solutions were injected hydrodynamically as indicated in the figure captions. Prior to the experiments, the capillary was conditioned by percolation of background buffer for 3 min. Data were processed by the Agilent Chemstation, PeakFit (SPSS version 4.11, evaluation version, Chicago, IL) and Microcal Origin 4.0 softwares. Method I (residual minimization) was used for peak fitting as no hidden peaks are expected. RESULTS AND DISCUSSION To demonstrate the feasibility of coupling TDA to CE, a twocomponent mixture was considered. The first component was a 10% charged synthetic polyelectrolyte (Pol) containing 90% (in mol) of acrylamide and 10% sodium 2-(acrylamido)-2-methylpropanesulfonate. The second component was a 13-mer DNA. As depicted in Figure 1, the mixture was injected hydrodynamically in the capillary (step 1). After injection, positive voltage was applied (step 2) for separating the two components by CE. Since the separation was performed in a fused-silica capillary in alkaline conditions (50 mM borate buffer, pH 9.2), solutes migrate in counterelectroosmotic mode. As a consequence, the copolymer with 10% charge rate had a higher apparent velocity than the DNA. Once the two sample zones were separated, the voltage was stopped and a marker (formamide) was injected (step 3). The injection of the marker was important for allowing the determination of the position of the sample zones in the capillary at the end of the CE step. Although not strictly required, small molecules should be preferred for the marker in order to observe a narrow final band. Finally, TDA analysis was performed online in the same capillary (step 4) by displacing the whole content of the capillary to the detector upon application of pressure. (18) Mc Cormick, L.; Chen G. S, J. Polym. Sci. Polym. Chem. Ed, 1982, 20, 817-838. (19) http://rsb.info.nih.gov/ij/index.html.
of 50 mbar. Upon effects of the Taylor dispersion, the peaks corresponding to the solutes are widened and merge partially. From the detection time tM of the marker injected in step 3, it is possible to get the linear velocity during the TDA step according to
u)
Figure 1. Schematic representation of the different experimental steps allowing the coupling of CE to TDA. Step 1: the mixture is hydrodynamically injected into the capillary. Step 2: CE separation step by application of a constant voltage. Step 3: injection of a marker. Step 4: mobilization by pressure for TDA.
l tramp tinj Pinj tM + 2 2 Pmob
(5)
where tramp (6 s) is the duration of the pressure ramp for the mobilization step, tinj is the injection time of the marker (step 3), Pinj is the injection pressure, and Pmob is the mobilization pressure. The height equivalent to a theoretical plate relative to each sample zone depends on the capillary length lS traveled by each solute during TDA (step 4), on the temporal peak variance, and on the average detection time following eq 6:
HS ) lSσS2/tS2
(6)
Since the linear velocity is the same for all the solutes and the neutral marker M, Hs can then be expressed as
HS )
uσS2 ) tS
1 × σS2 tramp tinj Pinj + tM t 2 2 Pmob S
(
)
(7)
2
Figure 2. UV traces obtained by CE separation of DNA and Pol mixture in zone mode (A) and by the coupling of CE with TDA following the methodology described in Figure 1 (B). Experimental conditions: bare silica capillary, 50 µm i.d. × 40 cm (31.5 cm to the detector). BGE: 50 mM sodium borate buffer, pH 9.2. Temperature: 25 °C. Detection by UV absorbance at 214 and 260 nm. Neutral marker: formamide, 0.03% (v/v) in BGE. Sample: 7.5 g L-1 Pol and 0.98 g L-1 DNA in BGE. Peak identification: electroosmotic flow (EOF); formamide marker (Fo); copolymer (Pol); 13-mer DNA (DNA). (A) Injection: neutral marker (30 mbar, 2 s), BGE (30 mbar, 2 s), sample (30 mbar, 2 s), BGE (30 mbar, 2 s). Applied voltage: 20 kV. Current intensity: 22.6 µA. (B) Sample injection (step 1): 30 mbar, 2 s. CE separation (step 2): BGE, 20 kV, 60 s. Marker injection (step 3): 30 mbar, 2 s. Pressure mobilization (step 4): 50 mbar with 6-s linear ramp.
Experimentally, the sample variance σS was calculated by fitting the experimental UV traces with Gaussian curves. HS values were next plotted as a function of u for the two solutes (see Figure 3). Two lines were obtained with the y-intercepts corresponding to the contributions of CE dispersion and of the injection to the H values. The diffusion coefficients of the solutes were derived from the slopes of these lines using eq 4. The experimental D values are reported in Table 1 and were compared to the values obtained for each compound by direct TDA (without CE separation). Very good agreement was obtained between these values demonstrating the interest of the CE-TDA methodology for the size-based characterization of mixtures. It is worth noting that the condition expressed by eq 3 is verified since the characteristic diffusion times are respectively 23 s for the copolymer (Pol) and 2 s for the DNA fragment. As a general rule, for solutes with diffusion coefficients ranked between 10-9 and 10-11 m2 s-1 and on a 50µm-i.d. capillary, mobilizing velocities equal or higher than 5 × 10-4 m s-1 are required for being in the ascending branch of the HS versus u plot. On a 30 cm (effective length) × 50 µm i.d. capillary and for the same range of diffusion coefficients, eq 3 is verified as long as the mobilizing velocity is lower than 2 × 10-3 m s-1. For solutes with diffusion coefficients below 10-11 m2 s-1, capillaries with lower internal diameter would be preferred.
Figure 2A displays the CE separation obtained for the twocomponent mixture at 214 and 260 nm. As expected from the charge ratio of the two polymers, resolution of the separation is very high (R ) 9.6). Figure 2B gives an example of the UV traces obtained by performing the coupling of TDA to CE, following the four steps described in Figure 1 and using a mobilization pressure
CONCLUSION This work demonstrates the possibility to couple CE to TDA. This new methodology has the advantage of combining the high separation performances of CE to the simplicity of TDA, allowing the absolute determination of the diffusion coefficient (or hydrodynamic radius) of each sample zone. Knowing the difficulty of Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
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Figure 3. HS ) f(u) plots obtained from the CE-TDA experiment for the two components of the mixture. Other conditions as in Figure 2. Table 1. Diffusion Coefficients (m2 s-1) Obtained by CE-TDA or by TDA D (m2 s-1) CE-TDA 214 nm copolymer (Pol) DNA (13 bases) a
10-11 (
0.22a
1.37 1.60 10-10 ( 0.13a
260 nm
D (m2 s-1) TDA
1.61 10-10 ( 0.15a
1.37 10-11 ( 0.20a 1.63 10-10 ( 0.13a
All 95% confidence interval.
getting a reliable hydrodynamic radius in the case of polydisperse samples by dynamic light scattering measurements, there is no doubt that this simple methodology should facilitate the analysis of real complex samples in the field of synthetic polymers, biopolymers, colloı¨ds, latexes, quantum dots, and other particles, as far as the CE step allows separating the solutes into individual zones. Compared to the classical size exclusion chromatography coupled to a refractive index, light scattering, and viscosimetry detections, this methodology is fundamentally different. First, the separation technique is complementary to chromatography since it is based on electrophoretic properties. Next, the separation medium is much more open, without any stationary phase. It is thus much more adapted for the analysis of charged or polycharged (macro)molecules by limiting undesirable interaction with the stationary phase. The method and the instrumentation are simpler; the methodology can be performed on a CE commercial apparatus using minute amounts of sample. Moreover, it does not require the determination of the increment of refractive index with concentration. Regarding the detection issue, CE-TDA can be
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Analytical Chemistry, Vol. 80, No. 5, March 1, 2008
performed with all detectors commonly used for CE analysis such as UV absorbance, fluorescence, contactless conductivity, and mass spectrometry. ACKNOWLEDGMENT H.C. gratefully acknowledges the support from the French National Research Agency (ACI jeunes chercheurs 4093). The authors thank Pr. P. Gareil (ENSCP, Paris) for access to capillary electrophoresis instrument; Dr. D. Baigl (ENS, Paris) for access to DMIL microscope; and Dr. M. Martin for fruitful discussions. SUPPORTING INFORMATION AVAILABLE Figure S-1 provides a microscopic picture of the capillary cross section. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review December 13, 2007. AC702257K
November
1,
2007.
Accepted
