Article pubs.acs.org/ac
Fluorescence-Correlation Spectroscopy Study of Molecular Transport within Reversed-Phase Chromatographic Particles Compared to Planar Model Surfaces Justin Cooper and Joel M. Harris* Department of Chemistry, University of Utah, 315 South 1400 East, Salt Lake City, Utah 84112-0805, United States S Supporting Information *
ABSTRACT: Reversed-phase liquid chromatography (RPLC) is a widely used technique for molecular separations. Stationary-phase materials for RPLC generally consist of porous silica-gel particles functionalized with n-alkane ligands. Understanding motions of molecules within the interior of these particles is important for developing efficient chromatographic materials and separations. To characterize these dynamics, time-resolved spectroscopic methods (photobleach recovery, fluorescence correlation, single-molecule imaging) have been adapted to measure molecular diffusion rates, typically at n-alkane-modified planar silica surfaces, which serve as models of chromatographic interfaces. A question arising from these studies is how dynamics of molecules on a planar surface relate to motions of molecules within the interior of a porous chromatographic particle. In this paper, imaging-fluorescencecorrelation spectroscopy is used to measure diffusion rates of a fluorescent probe molecule 1,1′-dioctadecyl-3,3,3′3′tetramethylindocarbocyanine perchlorate (DiI) within authentic RPLC porous silica particles and compared with its diffusion at a planar C18-modified surface. The results show that surface diffusion on the planar C18 substrate is much faster than the diffusion rate of the probe molecule through a chromatographic particle. Surface diffusion within porous particles, however, is governed by molecular trajectories along the tortuous contours of the interior surface of the particles. By accounting for the greater surface area that a molecule must explore to diffuse macroscopic distances through the particle, the molecular-scale diffusion rates on the two surfaces can be compared, and they are virtually identical. These results provide support for the relevance of surface-diffusion measurements made on planar model surfaces to the dynamic behavior of molecules on the internal surfaces of porous chromatographic particles.
A
the stationary-phase surface is the major contributor to transport of molecules within the porous particles.3 Characterizing the transport of molecules in chromatographic media has represented a measurement challenge because most of the surface area in chromatographic porous silica particles resides within the particle. Thus, most of the chemical interactions and transport processes responsible for chromatographic retention and band broadening take place inside the particles, making direct observation of the molecular dynamics difficult. Intraparticle diffusion rates have been inferred from chromatographic-based measurements. Techniques such as frontal analysis of breakthrough curves,4,5 the shallow bed method,6,7 and the pulse-response method combined with moment analysis8−10 have been used to determine mass transfer rate coefficients within various porous chromatographic media, with particular attention given to the surface diffusion component. These techniques rely on analysis of elution profile broadening to infer the contributions of
pplications of chemistry at liquid/solid interfaces, including catalysis, selective adsorption, chromatographic separations, and environmental remediation, depend on the transport rates of molecules at or near the interface, including adsorption/desorption kinetics and lateral diffusion across the surface. Most of these applications employ high surface area, porous materials, so that interfacial phenomena dominate the chemistry and the high surface area provides the large capacities for adsorption, reaction, or catalysis. In chromatographic separations, for example, molecules are retained on porous, particulate supports1 that exhibit specific surface areas on the order of 102 m2/g and surface-area-to-pore-volume ratios of ∼5 × 108 m−1, corresponding to pore diameters of ∼10 nm. Solute retention is governed by interactions with the stationary phase relative to the mobile phase, where the retention equilibrium depends on rates of adsorption and desorption to and from the stationary phase.2 The efficiency of separations is degraded by band spreading, which is dominated in liquid-phase separations by the rates of molecular transport to and from the stationaryphase surface, the majority of which (>99%) resides within the particle interior.2 For strongly retained species, where solute adsorption to the surface is favored, diffusion of molecules on © 2014 American Chemical Society
Received: August 29, 2014 Accepted: October 30, 2014 Published: October 30, 2014 11766
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In this work, we attempt to reconcile the rates of surface diffusion measured on a planar model of a reversed-phase chromatographic surface with diffusion rates of the same probe molecule measured within commercial C18-derivatized chromatographic silica particles. We employ a methodology that combines fast fluorescence imaging with fluorescence-correlation spectroscopy (imaging-FCS), where a small region of a CCD camera chip that can be sampled at a high frame rate provides a fast fluorescence intensity time trace that is autocorrelated to yield dynamic information. This methodology was developed previously for measuring diffusion coefficients in a faster time regime than available to single-molecule tracking,1,28,29 and the acquisition speed of this methodology was recently harnessed to measure the faster lateral diffusion rates observed on planar surfaces.30 Unlike traditional FCS with a single-element detector, imaging-FCS allows electronic control of the probed region, so that the diffusion coefficient can be readily determined from the variation in the autocorrelation relaxation rate with the area of the probed region.30 In the present study, imaging-FCS is used to measure the diffusion coefficient of the fluorescent probe 1,1′dioctadecyl-3,3,3′3′-tetramethylindocarbocyanine perchlorate (DiI) diffusing within the porous network of a reversed-phase chromatographic silica particle and compared with the diffusion coefficients of DiI measured at a planar model of a reversedphase chromatographic interface consisting of a C18-modified glass coverslip. By correcting the porous particle dynamics for the effective surface area explored by the probe molecule as it diffuses laterally in the fluorescence image, the results indicate that fundamental diffusion rates on the two surfaces on the molecular scale are very similar. The results support the use of planar substrates as models for chromatographic interfaces to gain understanding of the interfacial dynamics that influence chromatographic retention behavior.
surface diffusion to the intraparticle transport kinetics within the column. Fluorescence microscopy techniques are uniquely suited to measuring interfacial kinetics, where the high quantum yield of fluorescent probes and the sensitivity of detectors have pushed detection to the single-molecule limit. This technique has been employed to determine adsorption−desorption and surfacediffusion rates of molecules at planar models of reversed-phase chromatographic interfaces, typically alkyl-chain modified fused silica surfaces in contact with varying solvent conditions. Fluorescence-recovery-after-patterned-photobleaching (FRAPP) has been used to measure the lateral diffusion coefficients of rubrene and acridine orange at interfaces of nalkyl chains bound to a planar silica substrate at varying ligand bonding densities, chain lengths, and overlying solution conditions.11−13 Fluorescence correlation spectroscopy combined with a total-internal-reflection illumination (TIR-FCS) to measure the adsorption and desorption rates of rhodamine 6G at a C18-modified planar fused-silica surface under varying solvent conditions.14,15 FCS in a confocal illumination/ detection geometry has been used at an interface to measure the surface diffusion rates of 1,1′-dioctadecyl-3,3,3′3′-tetramethylindocarbocyanine perchlorate (DiI) hydrophobic fluorescent probe molecules at C18-modified silica surface.16,17 These studies represent experiments done on model, planar nalkylsilane-modified fused silica substrates, which are intended to mimic the interface existing within porous reversed-phase chromatographic silica. Although planar silica substrates produce a reasonable model for the interfacial chemistry of porous silica particles, these model substrates represent a simpler geometry for molecular transport compared to porous particles, the pore structure of which should significantly influence surface diffusion results. Thin sol−gel films have been deposited on fused-silica substrates to produce a porous structure that is suited to study via fluorescence microscopy. These porous thin films have been studied with fluorescencecorrelation spectroscopy and single-molecule fluorescence imaging to investigate the influence of their pore structure and chemical interactions on molecular transport.18−23 The pore structure and surface chemistry of silica sol−gel films,24 however, differ significantly from silica xerogels used as chromatographic media, because the latter are sintered at high temperature to collapse the micropores and then subjected to hydrothermal treatment1,25 to increase their average pore diameter, tighten the pore-size distribution, and hydrolyze surface siloxane bonds to provide silanols for anchoring stationary-phase ligands. Recently, fluorescence microscopy techniques have been adapted to measure molecular dynamics within actual reversedphase chromatographic particles. Scanning confocal microscopy combined with FCS has been used to measure the time-scale of strong adsorption events within octadecylsilyl (C18)−silica gel under RPLC conditions.26 More recently, fluorescence imaging of single-molecule trajectories was used to measure analyte residence times, diffusion coefficients, and heterogeneous transport characteristics within commercial RPLC particles.27 As the body of literature concerning fluorescence microscopy studies of RPLC interfaces now includes both studies on planar models of chromatographic surfaces and within authentic chromatographic particles, comparison of results for the two systems could lead to an understanding of the influence of the differing transport geometries on measured transport rates.
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EXPERIMENTAL SECTION Chemicals and Materials. 1,1′-Dioctadecyl-3,3,3′3′-tetramethylindocarbocyanine perchlorate (DiI) fluorescent dye was purchased from Invitrogen (Carlsbad, CA). Serial dilutions of DiI were made into Omnisolv spectroscopy grade methanol (MeOH) from EMD chemicals (Darmstadt, Germany). Glass coverslips for use as a substrate for derivatization were obtained from VWR International (Radnor, PA). Coverslips were cleaned via UV-ozone cleaning for 25 min on each side. Coverslip cleanliness was verified by a water contact angle of 0°. The coverslips were subsequently silanized using trichloro(octadecyl)silane (C18) followed by trichloro(methyl)silane (C1) obtained from Sigma-Aldrich Corp. (St. Louis, MO). Silanization reactions were conducted in n-heptane. Custom flow cells were constructed using luer lock adapters and tubing from Value Plastics Inc. (Fort Collins, CO) and the silanized glass coverslips. Three micrometer diameter Zorbax octadecylsilyl (ODS) bonded chromatographic media was obtained from Agilent Technologies (Santa Clara, CA). The particles were characterized by nitrogen Brunauer−Emmett−Teller (BET) adsorption measurements by Porous Materials (Ithaca, NY); see the Supporting Information. All aqueous solutions were made using 18 MΩ water, purified using a Barnstead NANOpure II system (Boston, MA). A 10 mM ACS grade sodium chloride solution from Mallinckrodt (Phillipsburg, NJ) was used as a supporting electrolyte in all aqueous solutions. Preparation of Chromatographic Silica Particles for Imaging. Approximately 20 mg of Zorbax 3 μm ODS silica
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was suspended in 10 mL of methanol. A 10−20 μL aliquot of this suspension was added to 10 mL of a 90/10 by volume methanol/water solution and left overnight to equilibrate the interior pore volume. A dilute suspension of chromatographic particles in a 90% MeOH/aqueous solution was pumped into a flow cell constructed over a glass coverslip and was placed on the inverted microscope stage. After several minutes, the particles settled to the glass coverslip, the surface of which had been previously functionalized with a C18−silane by selfassembly,31,32 in order to help immobilized the C18 particles on their surface. Hydrophobic interactions between the ODS particles and the C18-modified glass coverslip fix the particles to the surface and allow for solution flow without detaching the particles from the surface. A 1.0 pM solution of DiI in 90/10 methanol/water by volume was flowed continuously through the cell containing particles at 0.25 mL/min with a syringe pump (Harvard Apparatus PHD 2000). Preparation of Planar Model RPLC Interfaces. Planar analogs of reversed-phase chromatographic materials were prepared by chemically modifying the surfaces of 22 × 22 mm No. 1.5 glass coverslips. C18 modification was accomplished by reaction with 0.5 mM trichloro(octadecyl)silane in n-heptane for 12 h followed by an end-capping step consisting of 0.5 mM trichloro(methyl)silane reacted for 12 h. Following the silanization, coverslips were rinsed in n-heptane and dried in an oven at 120 °C for 1 h to stimulate cross-linking polymerization between adjacent silanes. Dried coverslips were then rinsed with copious amounts of dichloromethane and methanol and stored in methanol until use. The degree of hydrophobic modification was qualitatively characterized by measurement of the water contact angle using the sessile drop method measured with a goniometer. Contact angles for C18/ C1 derivatized coverslips used in experiments fell between 110° and 112°, indicating a high silane surface coverage. Derivatized slides were placed in a flow cell though which a 20 pM DiI solution in 90/10 MeOH/water by volume was flowed at 0.20 mL/min continuously throughout each experiment. Fluorescence Microscopy. Fluorescence images were acquired using an Eclipse TE200 inverted microscope (Nikon Corporation) with 1.49 N.A. Apo-TIRF oil immersion objective lenses (60× and 100×, Nikon). For total-internal-reflection excitation of planar interfaces, the excitation beam was directed into a 60× objective lens and translated off the optical axis until the emerging beam was incident at an angle greater than the critical angle for the glass/aqueous solution interface. Samples were illuminated using the 514.5 nm line from a Lexel Model 95 argon ion laser. The laser light was coupled into a polarization maintaining single-mode optical fiber (Thorlabs) using an aspheric fiber-port collimator/coupler (Thorlabs). Light emerging from the fiber was collimated using a planoconvex achromatic lens and passed through a 514 nm narrow width band-pass filter. The filtered excitation light intensity was measured at ∼20 mW prior to being refocused at the back focal plane of the microscope objective. Fluorescence emission from molecules at the interface was collected back through the 60× objective and passed through a filter cube containing a 532 nm single-edge dichroic beamsplitter and a 585 nm bandpass emission filter. The filtered fluorescence emission was imaged onto an Andor iXonEM+ 897 EMCCD camera. For epiillumination of chromatographic silica particles, the same microscope was employed; however, the focused excitation beam was directed along the optical axis to the center of a 100× objective. This produces a collimated excitation beam into the
sample, producing uniform illumination throughout the particle. The procedure for positioning the focal plane to the center of the particle is previously described.27 Imaging-FCS Data Collection and Processing. Fluorescence correlation spectroscopy is based on examining the fluorescence fluctuations of a system within a given probing region.33 An autocorrelation analysis of the fluorescence time trace reveals the time scale at which fluorescence fluctuation is taking place by calculating the self-similarity of the fluorescence signal at varying time shift, τ (eq 1). The autocorrelation function can be fit to a model that includes parameters relating to the physical processes inducing the fluorescence fluctuations. G(τ ) = lim
T →∞
1 T
T /2
∫−T /2 F(t )F(t + τ)dt
(1)
For the case of diffusion, the autocorrelation function (ACF) can be fit to a model that relates the time dependence of the autocorrelation decay to the diffusion in two dimensions across the probe region33,34 G (τ ) =
A +B 1 + τ /τ1/2
(1/τ1/2) = 4DS /ω 2
(2) (3)
where Ds is the diffusion coefficient and ω2 is the square of the e−2 radius of the probed region determined by convoluting the square, imaged region with the point-spread function, as detailed in recent publications.30,34 The imaging-FCS instrumentation setup and methodology have been recently described. 30 Briefly, the sample is illuminated via epi-illumination or total internal reflection, for silica particles and planar RPLC interfaces, respectively. The FCS probing region is bounded in the axial dimension by the depth-of-field of the objective, in the case of imaging silica particles or by the penetration depth of the evanescent field (∼100 nm), in the case of total-internal-reflection excitation. The lateral dimension is bounded by the active area of the CCD detector, the size and location of which was selected by electronically defining the pixel ranges in the x and y dimensions (see the Supporting Information). The active region of the CCD camera was limited to an 8 × 8 pixel region, and fluorescence intensity time traces were generated by imaging the active region at a high frame rate (917 Hz) in the case of the planar surface, and 25 Hz in the case of intraparticle measurements, and then summing the pixel intensity in each frame. A kinetic series of images of this pixel area was thus acquired, and the total intensity within a defined region in each image corresponds to a point in the fluorescence intensity-time trace (see the Supporting Information), with the time coordinate corresponding to the frame number in the kinetic series multiplied by the inverse of the framing rate (Hz−1). The raw fluorescence time traces were then autocorrelated using an algorithm written in the Matlab (Mathworks) where the time traces were Fourier-transformed, multiplied by their complex conjugate to generate the power spectrum, and then inverse Fourier-transformed to produce an the autocorrelation function. To mitigate noise in the autocorrelation functions, the average of 10 autocorrelations was calculated for each condition by coadding their power spectra and inverse Fouriertransforming the result. Background subtraction was accomplished by averaging 10 autocorrelation functions of a C18/ aqueous solution interface with no fluorescent dye, giving a 11768
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measure of the intensity arising from background fluorescence or Raman scattering. The square root of this blank autocorrelation was then subtracted from the square root of the autocorrelation functions taken under the same experimental conditions, and the result was resquared.14,35
of the autocorrelation, 1/τ1/2, versus the inverse of the squared radius of the probed region, 1/ω2, which produces a linear relationship with a zero intercept (Figure 1B), as predicted by eq 3. The observed diffusion coefficient defining molecular transport of DiI through the particle, calculated from the slope of the line, was found to be Dp = 1.8 ± 0.04 × 10−9 cm2/s. The lack of detectable intercept indicates that there are no fluorescence fluctuations that are independent of the probing region size, and the fluctuations are entirely due to the diffusion of DiI through the probed region.30 Diffusion at a Planar Hydrophobic Interface. Many of the spectroscopic-based studies of molecular transport at chromatographic-like interfaces have been conducted on planar fused silica or glass surfaces that have been functionalized with an n-alkane ligand to serve as a model of reversed-phase interactions found in porous silica particles used in chromatography.11,16,17,36 Even if the chemistries of the two interfaces are identical and the diffusional motions on a molecular scale are the same, long-range molecular diffusion rates measured at a planar surface should differ from those measured within actual chromatographic media due to differences in surface geometries and dimensionality of diffusional trajectories. To elucidate the effect that these differences may have on measured diffusion rates, surface diffusion of DiI was also measured at a C18modified planar interface in equilibrium with a 20 pM DiI in 90/10 MeOH/H2O solution and compared with that measured within reversed-phase porous silica particles. As with the Zorbax particles, the active region of the CCD detector was limited to 8 × 8, 6 × 6, 4 × 4, and 2 × 2 pixel regions, which when convoluted with the point-spread function of the 60× objective, corresponds to squared radii of the probing region ω2 = 1.94, 1.28, 0.84, 0.46 μm2, respectively. Because the diffusional relaxation rates are much faster on the planar surface, the kinetic image series were acquired 37 times faster, at a framing rate of 917 Hz. Time traces of the fluorescence intensities within each pixel region per frame were autocorrelated and fit to eq 2, as above, and the results are plotted in Figure 2A. The relaxation rate versus the inverse of the squared radius of the probed region is linear (Figure 2B), the slope of which corresponds to a diffusion coefficient of DiI on the flat surface, Ds = 6.5(±0.1) × 10−8 cm2/s, which is 36 times faster than the diffusion rate measured within the porous particle. Unlike within-particle diffusion, the dependence of the flat-surface relaxation rate on the inverse of the probed region area exhibits a nonzero intercept. The intercept corresponds to where 1/ω2 in eq 3 is equal to zero, an extrapolation to an infinite probed area. Thus, the intercept reports a relaxation that is independent of area of the probed region and, therefore, independent of diffusion on the surface. With total-internalreflection-excitation, an area-independent relaxation can arise from desorption of the fluorescent probe molecule from the surface followed by diffusion of molecules out of the evanescent wave. The intercept in Figure 2B thus provides a measurement of the desorption rate, kdesorb = 5.5 (±0.4) s−1 or a characteristic desorption time, τ = 1/kdesorb ∼ 182 ms. In contrast, desorption of DiI molecules from the C18 surface within a porous particle does not lead to diffusion into bulk solution because of rapid readsorption to the nearby C18 surface within the small (5 nm radius) pores. The characteristic readsorption time can be estimated by using the diffusion coefficient of DiI in solution, D ∼ 4 × 10−6cm2/s, derived from the Stokes−Einstein equation and the van der Waals radius of DiI,37,38 to predict the collision frequency of DiI with the walls
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RESULTS AND DISCUSSION Measuring Diffusion within Chromatographic Silica Particles. Although planar models of chromatographic interfaces are convenient for spectroscopic imaging, a planar sample represents a significantly different surface geometry than chromatographic media, which are generally high surface-area, porous silica-gel particles. To compare measured diffusion rates of molecules in these two different geometries, imaging-FCS is used first to observe diffusion of DiI within Zorbax ODS 3 μm chromatographic particles. Kinetic image series were collected at a framing rate of 25 Hz and 100× magnification, and the size of the probing region was varied to be 8 × 8, 6 × 6, 4 × 4, and 2 × 2 pixels. Convolution of the sampled area with the pointspread function (see above)34 determines values of squared radii of the probing region correspond to ω2 = 0.68, 0.46, 0.28, and 0.17 μm2, respectively. The time-dependent fluorescence intensities from each probing region were autocorrelated, and the results were fit to eq 2 and plotted in Figure 1A. The diffusion coefficient was determined by plotting the decay rate
Figure 1. (A) Normalized autocorrelation functions for molecules diffusing within a 3 μm chromatographic particle for varying probe region sizes fit to eq 2. (B) Plot of 1/τ versus 1/ω2, fit to eq 3. 11769
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of-field) was NT = 90 ± 3, determined from the amplitudes of the autocorrelation functions, accounting for the molecular statistics and fluorescence yield variations that are the origins of the intensity fluctuations (see the Supporting Information). This value represents the total number of molecules, NT = Ns + Nm, on the stationary-phase surface, Ns, and the intraparticle mobile phase, Nm. The number of molecules in the intraparticle mobile phase can be estimated from the solution concentration of DiI, the void fraction of the particle (from BET data), and the probed volume (given by the probed area and depth-offield). For 1 pM DiI in solution, the number of molecules in the intraparticle pore volume within an 8 × 8 pixel probed area is very small, Nm = 5.4 × 10−4 molecules. Nm is a negligible fraction (6 ppm) of NT so that Ns ∼ NT. These values of Nm and Ns correspond to a capacity factor k′ = Ns/Nm ∼ 1.7 × 105, which is within a factor 2 of the value of k′ predicted from desorption and adsorption rates and the surface-area-to-volume ratio in the porous RPLC material, discussed above. Under these very high retention conditions, analyte molecules within a particle spend effectively all (99.999%) of their time adsorbed to the stationary-phase surface, thus diffusion within mobile phase can be neglected. This situation allows direct comparison of measured intraparticle surface diffusion coefficients with surface diffusion coefficients at planar interfaces. The apparent diffusion rate of DiI measured within the chromatographic silica particles was measured above (Figure 1B) to be 1.8 ± 0.4 × 10−9 cm2/s, which is approximately 36 times slower than DiI diffusion at the planar surface. From Einstein’s relation for diffusion in two dimensions (eq 3),33,39 the time constant for diffusional relaxation is proportional to the area explored by the molecule within the probed region. For molecules diffusing at a planar surface, the area over which they diffuse is defined simply by the probed region (convoluted with the point spread function). For molecules diffusing on the interior surfaces of a porous particle, however, the surface area explored by the molecule during its trajectory is much larger than the projection of the motion onto a two-dimensional image acquired by the microscope. Diffusing molecules adsorbed to the interior surfaces of the particle must follow the contours of a high surface-area, porous network, sampling a much greater area than is projected in two dimensions on the CCD camera. The diffusion rate measured by the camera, however, reports the rate at which molecules move into and out of the particle on a macroscopic distance scale.27 This is an important diffusional rate to characterize, because it predicts the residence times of moving molecules as they diffuse over macroscopic (μm) distances into and out of the particle;27 it is the diffusional rate that governs resistance-to-mass-transfer in chromatographic separations.40 This macroscopic diffusional rate is not, however, the rate at which molecules diffuse with respect to the local interior surfaces of the particle on a molecular scale. To determine the rate of diffusion with respect to the interior pore surfaces, one must know of the surface area explored by molecules while traversing the probing region in two dimensions, which can be estimated from the volume and corresponding internal surface area. Silica xerogels used as chromatographic media are prepared from aggregation of small silica colloidal particles followed by sintering at high temperature and hydrothermal treatment1,25 to increase their average pore diameter and tighten the pore-size distribution. The resulting structure provides a uniform, well connected, threedimensional pore network (see SEM images in the Supporting
Figure 2. (A) Normalized autocorrelation functions for molecules diffusing at a planar chromatographic interface for varying probe region sizes fit to eq 2. (B) Plot of 1/τ versus 1/ω2, fit to eq 3.
of a 5 nm radius pore,39 fc ∼ 1 × 108 s−1. The previously measured rate of DiI adsorption to a planar C18 surface,30 kads= 0.13 ± 0.01 cm/s, corresponds to adsorption efficiency of 0.0045 per collision, which when multiplied by the pore-wall collision frequency, predicts a reabsorption rate of DiI to the surface of a 5 nm radius pore of ∼5 × 105 s−1, or readsorption time of ∼2 μs, much faster than the time resolution of this experiment. Thus, unlike the results acquired at a planar surface, desorption of DiI within a porous particle does not lead to a measurable relaxation because the desorbed DiI does not escape the field of view, but is quickly readsorbed by the surrounding C18 surface, where it can continue diffusing on the interior C18 surfaces of the porous particle. Comparing Diffusion Rates at Porous-Particle- versus Planar-Surfaces. A significant issue with understanding intraparticle molecular transport is that it can involve both diffusion of the solute adsorbed to the pore-wall surfaces and solution diffusion through the mobile phase within the particle.3 The measured diffusion rate represents the average of the two diffusional processes weighted by the fraction of time spent by the analyte in each phase. The fraction of time an analyte spends adsorbed to the surface is estimated from the capacity factor, k′, defined as the ratio of the number of analyte molecules in the stationary phase to those in the mobile phase, Ns/Nm. The total number of molecules within the probed volume of the particle (8 × 8 pixel probed area times the depth11770
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coefficient of DiI measured on the interior surface of a particle and that observed on a planar model surface is reassuring, indicating that the interfacial dynamics of molecules measured on planar surface models can indeed be comparable to those occurring within reversed-phase chromatographic silica, where only a 32% difference in surface diffusion coefficient is observed between the authentic particle and the model surface. This small difference could arise from differences in the bound C18 ligand density or conformations. It has been shown on planar model surfaces that increased reversed-phase ligand density results in faster solute diffusion rates, due to a more homogeneous and continuous bonded phase on the high density surfaces.13 An additional contribution to faster apparent surface diffusion rates within the particles compared to the planar surface could be due to the smaller surface area sampled by the DiI probe molecules compared to N2 molecules used in the BET isotherm measurement of the specific surface area of the chromatographic particles. This would increase the apparent diffusion coefficient calculated for DiI using the larger N2-BET derived surface area. Regardless of the origins of the small difference in surface diffusion rates, however, it is clear that taking into account the larger surface area explored by a solute in the case of diffusion within porous particles and scaling the apparent diffusion coefficient accordingly are key to comparing surface diffusion within porous chromatographic media to those measured on planar surfaces.
Information); the internal pore structure of chromatographic silica has been characterized by small angle neutron scattering,41 which shows that the pore structure permeates the particle in three dimensions with distances between scattering surfaces comparable to pore diameters measured via mercury porosimetry. Intraparticle molecular transport measured in single-molecule trajectories is consistent with these results, where spatial distributions and residence times of molecules within the particle are well modeled by a randomwalk in three dimensions,27 where radial displacements, r, in each dimension on distance scales larger than the 10 nm pore structure are independent and equivalent, where r = (2Dpt)1/2. From eq 3, τ1/2 is the characteristic time for molecules with an apparent diffusion coefficient in the particle, Dp, to diffuse laterally across a probed region of macroscopic area, Ap = ω2. Thus, in a given time of τ1/2, molecules executing a threedimensional random-walk would also undergo a random displacement in the z-dimension of rz = (2Dpτ1/2)1/2, which, in turn, defines a volume, Vp = Aprz, that molecules explore during the time τ1/2. The total interior surface area over which molecules diffuse, Si, contained within the volume Aprz is given by
Si = ρA przSspec
(4)
where ρ is the mass density of the chromatographic particles, calculated from the density of fused silica and the specific pore volume from BET measurements (see the Supporting Information) and Sspec is the specific surface area, also from BET measurements. Note that detectable radial displacement in the z-direction, rz, has an upper bound given by half the depth of field, DOF/2, which limits Si at the longest relaxation times. Using this concept to estimate the interior surface area, Si, explored by a DiI molecule within the porous chromatographic particle for a given probed area, Ap, one can plot of the relaxation rate, 1/τ1/2, versus 1/Si, which is shown in Figure 3. The slope of this plot is 4 times the interior surface diffusion coefficient, Di = 8.6 (±0.2) × 10−8 cm2/s, which is only 32% faster than the DiI diffusion coefficient measured at the planar C18 model surface. The close agreement between the diffusion
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CONCLUSIONS In this work, a comparison is made between solute transport and retention made within authentic reversed-phase chromatographic silica particles and C18-modified planar surfaces used as models for reversed-phase chromatographic interfaces. Historically, spectroscopic-based studies of solute transport and retention at chromatographic interfaces has been conducted on planar models due to their ease in being adapted to fluorescence microscopy measurements. However, C18-modified planar substrates can differ from actual chromatographic porous silica gel in both surface chemistry and transport geometry. Imaging-FCS was used to measure diffusion coefficients of the fluorescent probe DiI within actual reversed-phase chromatographic silica particles and at C18modifed planar substrates under conditions where diffusion on the C18 surface dominates the motions of the probe molecule. The surface diffusion coefficient of DiI with respect to the interior surface of the particle was calculated by accounting for the volume and internal surface area that molecules explore during the characteristic diffusion time obtained from the autocorrelation analysis. The interior surface diffusion rate thus determined was found to be within 32% of that measured on the planar model reversed-phase surfaces. These results provide support for the relevance of surface-diffusion measurements made on planar model surfaces to the dynamic behavior of molecules on the internal surfaces of porous chromatographic particles. The results also shed light on the effect that the pore network has on surface diffusion into and out of porous particles, generating a surface-diffusion analogue to a tortuosity factor,41 which is commonly used to compare solution-phase molecular diffusion within pores to diffusion in free solution. Although molecules may diffuse with nearly the same rate along the surface on a molecular scale, the pore surfaces within the particle are tortuous and extend into three dimensions; the greater surface area that must be explored produces a slower
Figure 3. Plot of the inverse decay constant versus the inverse total interior surface area contained within the volume explored by molecules diffusing within a particle during a time of τ1/2, with a linear fit having no intercept. 11771
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Analytical Chemistry
Article
(15) Hansen, R. L.; Harris, J. M. Anal. Chem. 1998, 70, 4247−4256. (16) Swinton, D. J.; Wirth, M. J. Anal. Chem. 2000, 72, 3725−3730. (17) Wirth, M. J.; Swinton, D. J.; Ludes, M. D. J. Phys. Chem. B 2003, 107, 6258−6268. (18) McCain, K. S.; Harris, J. M. Anal. Chem. 2003, 75, 3616−3624. (19) McCain, K. S.; Hanley, D. C.; Harris, J. M. Anal. Chem. 2003, 75, 4351−4359. (20) Fu, Y.; Ye, F.; Sanders, W. G.; Collinson, M. M.; Higgins, D. A. J. Phys. Chem. B 2006, 110, 9164−9170. (21) Ye, F.; Higgins, D. A.; Collinson, M. M. J. Phys. Chem. C 2007, 111, 6772−6780. (22) Ye, F.; Collinson, M. M.; Higgins, D. A. Phys. Chem. Chem. Phys. 2009, 11, 66−82. (23) Kirkeminde, A. W.; Torres, T.; Ito, T.; Higgins, D. A. J. Phys. Chem. B 2011, 115, 12736−12743. (24) Brinker, C. J.; Scherer, G. W. Sol-Gel Science: The Physics and Chemistry of Sol-Gel Processing; Academic Press: Boston, 1990. (25) Unger, K. K. Porous Silica: Its Properties and Use as Support in Column Liquid Chromatography; Elsevier Science: Amsterdam, 1979. (26) Zhong, Z.; Lowry, M.; Wang, G.; Geng, L. Anal. Chem. 2005, 77, 2303−2310. (27) Cooper, J. T.; Peterson, E. M.; Harris, J. M. Anal. Chem. 2013, 85, 9363−9370. (28) Burkhardt, M.; Schwille, P. Opt. Express 2006, 14, 5013−5020. (29) Kannan, B.; Har, J. Y.; Liu, P.; Maruyama, I.; Ding, J. L.; Wohland, T. Anal. Chem. 2006, 78, 3444−3451. (30) Cooper, J. T.; Harris, J. M. Anal. Chem. 2014, 86, 7618−7626. (31) Wirth, M. J.; Fatunmbi, H. O. Anal. Chem. 1992, 64, 2783− 2786. (32) Olson, L. G.; Lo, Y.-S.; Beebe; Harris, J. M. Anal. Chem. 2001, 73, 4268−4276. (33) Elson, E. L.; Magde, D. Biopolymers 1974, 13, 1−27. (34) Boening, D.; Groemer, T. W.; Klingauf, J. Opt. Express 2010, 18, 13516−13528. (35) Koppel, D. E. Phys. Rev. A 1974, 10, 1938−1945. (36) Wirth, M. J.; Ludes, M. D.; Swinton, D. J. Anal. Chem. 1999, 71, 3911−3917. (37) Hashimoto, F.; Tsukahara, S.; Watarai, H. Langmuir 2003, 19, 4197−4204. (38) Barton, A. F. M. CRC Handbook of Solubility Parameters and Other Cohesion Parameters, 2nd ed.; CRC Press: Boca Raton, FL, 1991. (39) Berg, H. C. Random Walks in Biology; Princeton University Press: Princeton, 1993. (40) Miyabe, K.; Guiochon, G. J. Sep. Sci. 2003, 26, 155−173. (41) Barrande, M.; Bouchet, R.; Denoyel, R. Anal. Chem. 2007, 79, 9115−9121.
effective diffusion rate through the particles over longer distance scales. To better understand the role of intraparticle surface structure on molecular diffusion rates, it would be interesting to examine how this rate changes with pore diameter. As the pore diameter increases, the surface-area-to-volume ratio within the particle decreases, and molecules diffusing within the particle would need to explore less surface area for a given distance traveled, and the intraparticle diffusion coefficient should increase, as predicted by eq 3. Additionally, in the large pore diameter case, the intraparticle capacity factor would decrease and molecules would spend more time in free solution following a desorption event, prior to readsorption and intraparticle diffusion would contain contributions due to both surface and solution diffusion.3 The contributions of each diffusional component would be weighted by the amount of time spent in each phase, which depends on retention of molecules in the stationary phase. Thus, changes in mobilephase composition would also govern the relative contributions of surface- and solution-diffusion diffusion, where, in the limit of minimal surface retention, the intraparticle diffusion coefficient should approach free-solution diffusion rates, modified by the tortuosity factor41 of the porous silica material.
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ASSOCIATED CONTENT
* Supporting Information S
C18 particle characterization, quantifying DiI molecules within porous chromatographic particles, examples of raw data, and movie. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*J. M. Harris. E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was supported in part by the U.S. Department of Energy under Grant DE-FG03-93ER14333. Additional support from Agilent Technologies in the form of a University Relations Grant is gratefully acknowledged.
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REFERENCES
(1) Sankaran, J.; Bag, N.; Kraut, R. S.; Wohland, T. Anal. Chem. 2013, 85, 3948−3954. (2) Giddings, J. C. Unified Separation Science; Wiley: New York, 1991. (3) Miyabe, K.; Guiochon, G. J. Chromatogr. A 2010, 1217, 1713− 1734. (4) Guan-Sajonz, H.; Sajonz, P.; Zhong, G.; Guiochon, G. Biotechnol. Prog. 1996, 12, 380−386. (5) Miyabe, K.; Guiochon, G. J. Chromatogr. A 2000, 890, 211−223. (6) Gowanlock, D.; Bailey, R.; Cantwell, F. F. J. Chromatogr. A 1996, 726, 1−23. (7) Li, J.; Cantwell, F. F. J. Chromatogr. A 1996, 726, 37−44. (8) Gritti, F.; Guiochon, G. Anal. Chem. 2006, 78, 5329−5347. (9) Miyabe, K.; Guiochon, G. J. Phys. Chem. B 1999, 103, 11086− 11097. (10) Miyabe, K.; Guiochon, G. J. Chromatogr. A 2002, 961, 23−33. (11) Zulli, S. L.; Kovaleski, J. M.; Zhu, X. R.; Harris, J. M.; Wirth, M. J. Anal. Chem. 1994, 66, 1708−1712. (12) Hansen, R. L.; Harris, J. M. Anal. Chem. 1995, 67, 492−498. (13) Hansen, R. L.; Harris, J. M. Anal. Chem. 1996, 68, 2879−2884. (14) Hansen, R. L.; Harris, J. M. Anal. Chem. 1998, 70, 2565−2575. 11772
dx.doi.org/10.1021/ac503250a | Anal. Chem. 2014, 86, 11766−11772
