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different length scales in the packing with laminar flow. 10 Inaddition to the convective mechanism of exchange, the time scaleof lateral diffusion between the slow and fast stream paths largelygoverns the actual extent of band spreading. 10,11 Velocity extremeswithin and (on any time and length scale) between differentchannels in the packing may be absolutely minimized withelectroosmotic flow, resulting in a much smaller eddy dispersioncontribution. An improvement in efficiency by a factor of almost2 over CHPLC has been demonstrated experimentally for CECwhen carried out with the same column. 12 It was concluded thatonly axial diffusion constitutes the ultimate limitation to performancein CEC when achieved with nanoparticles.Due to the high efficiencies that may be obtained withelectrokinetically driven fluid flows in open tubes 13 (CE) andpacked capillaries 5 (CEC), any factor influencing fluid dispersionunder these hydrodynamic conditions should be well characterizedand under control. The actual profile of the EOF and itsstability have a large effect in improving the resolution andefficiency and certainly belong to the most important aspectscontrolling reproducibility. 14 Temperature effects may constitutea further source of difficulties.The goal of our work is the development of an experimentalapproach toward the intrinsic fluid dynamics of capillary electroseparationtechniques. In this first article, we report about a qualitativeand quantitative characterization of pressure- and electrokineticallydriven flows through open and packed capillaries. Thediscrimination is based on the respective fluid flow field and axialdispersion behavior which are both directly measured overdiscrete temporal and spatial domains by pulsed field gradientnuclear magnetic resonance (PFG-NMR). 15-17 A setup has beendevised that allows measurements in capillary columns to beperformed with a 0.5-T ( 1 H 20.35 MHz) electromagnet. Due to itsopen access, the presented NMR configuration offers a mostflexible and convenient implementation of the CE, CHPLC, andCEC equipment, and the approach holds great promise for afundamental study of many hydrodynamic aspects within theseopen tube and packed bed segments.EXPERIMENTAL SECTIONNMR Hardware Configuration. The schematics of the setupis shown in Figure 1. 1 H 20.35-MHz PFG-NMR measurementswere made on a 0.5-T NMR spectrometer with open access,consisting of a SMIS console (Surrey Medical Imaging Systems,Guildford, U.K.), an iron core magnet (Bruker, Karlsruhe,Germany), and a 45-mm-i.d. actively shielded gradient system(Doty Scientific, Columbia, OH) capable of producing pulsedmagnetic field gradients of up to 0.5 T/m in the direction of thecolumn axis (y-direction). The solenoidal radio frequency (rf) coil 18(10) Giddings, J. C. Dynamics of Chromatography, Part I: Principles and Theory;Marcel Dekker: New York, 1965.(11) Tallarek, U.; Bayer, E.; Guiochon, G. J. Am. Chem. Soc. 1998, 120, 1494-1505.(12) Knox, J. H.; Grant, I. H. Chromatographia 1991, 32, 317-328.(13) Gaš, B.; Štědrý, M.; Kenndler, E. Electrophoresis 1997, 18, 2123-2133.(14) Rathore, A. S.; Horváth, Cs. Anal. Chem. 1998, 70, 3069-3077.(15) Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1987, 19, 1-45.(16) Kärger, J.; Pfeifer, H.; Heink, W. Adv. Magn. Reson. 1988, 12, 1-89.(17) Callaghan, P. T. Principles of Nuclear Magnetic Resonance Microscopy;Clarendon Press: Oxford, U.K., 1993.(18) Hoult, D. I.; Richards, R. E. J. Magn. Reson. 1976, 24, 71-85.was directly wound on a 35-mm-long, 1.57-mm-o.d. (381-µm- i.d.)PEEK tubing sleeve, which accommodates the 360-µm-o.d. (openor packed) capillary columns and which can be properly fixedwithin the setup (Figure 1a). For this purpose, a 300-µm-o.d.varnished copper wire was used in combination with a 200-µmdiameterNylon strandsthe latter keeping constant the distancebetween individual turns of the copper wiresto obtain a regular,∼11-mm-long solenoid (22 closely wound turns of the coppernylonpair). The gradient system including the rf coil assemblycan be rotated by 90° (i.e., from the y- into the x-direction, Figure1a). This horizontal configuration was used for all CE experimentsto prevent any pressure-driven flow component in the capillarydue to gravity.PFG-NMR Background. With this technique, the quantitativemeasurement of nuclear spin (hence, molecular) displacementsover an adjustable time ∆ relies on motion encoding by a pair ofidentical magnetic field gradients of amplitude (and direction) g. 19These are applied (pulsed) for a short time δ at the beginningand the end of this period ∆, respectively. The PFG-NMRtime domain may cover a range for ∆ from a few millisecondsup to a few seconds. Thus, several parameters of the involvedfluid dynamics, e.g., dispersion in the axial and transversedirection 20-22 or the stagnant mobile-phase mass transfer, 23 canbe studied in packed beds over any discrete evolution time withinthis range. For a PFG-NMR experiment in the narrow gradientpulse approximation (δ , ∆), 24 the echo signal amplitude andphase E ∆ (g) depend on the nuclear spin self-correlation function,P s (r/r 0 ,∆), which is the conditional probability that a spin initiallyat r 0 has migrated to r over time ∆E ∆ (g) ) ∫F(r 0 ) ∫P s (r/r 0 ,∆) exp[iγδg‚(r - r 0 )] dr dr 0(1)Here, F(r 0 ) denotes the normalized density of the initial spinpositions, γ is the magnetogyric ratio of the nucleus considered(e.g., 1 H), and as usual, i 2 )-1. Introducing the concept of thedynamic displacement R (with R ) r - r 0 ) and defining anaveraged propagator P av (R,∆) as the ensemble-averaged probabilitythat any molecule will move a net distance R over time∆, 25 we obtainE ∆ (q) ) ∫P av (R,∆) exp(i2πq‚R) dR (2)The signal is acquired in the q-space (with 2πq ) γδg) which isthe space reciprocal to the dynamic (i.e., net) displacement R. 26The key feature of eq 2 is that it bears a direct Fourier relationbetween the normalized echo signal, E ∆ (q), and the averaged(19) Callaghan, P. T. Aust. J. Phys. 1984, 37, 359-387.(20) Tallarek, U.; Albert, K.; Bayer, E.; Guiochon, G. AIChE J. 1996, 42, 3041-3054.(21) Seymour, J. D.; Callaghan, P. T. AIChE J. 1997, 43, 2096-2111.(22) Stapf, S.; Packer, K. J.; Graham, R. G.; Thovert, J.-F.; Adler, P. M. Phys. Rev.E 1998, 58, 6206-6221.(23) Tallarek, U.; van Dusschoten, D.; Van As, H.; Guiochon, G.; Bayer, E. Angew.Chem., Int. Ed. Engl. 1998, 37, 1882-1885; Angew. Chem. 1998, 110,1983-1986.(24) Stejskal, E. O.; Tanner, J. E. J. Chem. Phys. 1965, 42, 288-292.(25) Kärger, J.; Heink, W. J. Magn. Reson. 1983, 51, 1-7.(26) Callaghan, P. T.; Eccles, C. D.; Xia, Y. J. Phys. E: Sci. Instrum. 1988, 21,820-822.Analytical Chemistry, Vol. 72, No. 10, May 15, 2000 2293