concentration polarization and nonequilibrium electroosmotic slip in hierarchical monolithic...

Ivo Nischang1

Alexandra Höltzel2

Andreas Seidel-Morgenstern1, 3

Ulrich Tallarek2

1Institut für Verfahrenstechnik,Otto-von-Guericke-Universität,Magdeburg, Germany

2Fachbereich Chemie,Philipps-Universität,Marburg, Germany

3Max Planck Institutfür Dynamik komplexertechnischer Systeme,Magdeburg, Germany

Received September 30, 2007Revised November 26, 2007Accepted November 26, 2007

Research Article

Concentration polarization andnonequilibrium electroosmotic slip inhierarchical monolithic structures

This article illustrates the appearance and electrohydrodynamic consequences of con-centration polarization (CP) in hierarchically structured monolithic fixed beds used as sta-tionary phases in CEC and related electrical-field-assisted separation techniques. Subject ofthe investigation are silica-based monoliths in capillary format with a bimodal pore sizedistribution. Ion-permselectivity in the intraskeleton pore space together with diffusive andelectrokinetic transport induces depleted and enriched CP zones at the anodic and cathodicinterfaces, respectively, of the cation-selective mesoporous skeleton. The extent of electrical-field-induced CP is shown to be governed by the fluid phase ionic strength, which tunes theion-permselectivity of the mesoporous monolith skeleton via local electrical double layeroverlap, and by the applied electrical field strength, which determines local transport. Theanalysis of quantitative confocal laser scanning microscopy data, resolving CP on the localskeleton scale, indicates that at sufficiently high field strength a transition from intraskele-ton to interskeleton boundary-layer-dominated transport of charged species occurs. Thistransition is correlated to the onset of macroscopically measured, nonlinear EOF velocities,whose occurrence is explained in the framework of a nonequilibrium electroosmotic slip. Itis shown that the onset of nonlinear electrokinetics in the system can be tuned by propertiesof the BGE, particularly buffer pH, which modulates the pH-dependent surface chargedensity and consequently the ion-permselective skeleton’s charge selectivity. Finally, the CPdynamics of monolithic and particulate fixed beds are compared, and the observed differ-ences are related to the specific morphologies of the two hierarchical fixed bed structures.

Keywords:

Concentration polarization / Electrochromatography / Ion-permselectivity /Monoliths / Nonlinear electroosmotic flow DOI 10.1002/elps.200700727

1140 Electrophoresis 2008, 29, 1140–1151

1 Introduction

The recent development of rigid, organic-polymer-, or silica-based monolithic structures has contributed to many techno-logical processes in the engineering and life sciences. Mono-lithic fixed beds are employed as solid-phase supports forsynthesis, reaction, digestion, and separation, particularlychromatography [1–7]. Monolithic stationary phases as chro-matographic beds can be prepared in capillary columns andmicrofluidic devices, providing a promising alternative to

packed particulate beds, because particles are increasinglydifficult to handle and retain in such small dimensions [8]. Anadditional advantage of monoliths is the possibility of chemi-cal anchoring to the confining container or column wall, thuseliminating the need for retaining frits. Due to their ease ofpreparation organic-polymer-based monoliths have gainedincreasing popularity [2], though relatively little is knownabout their morphology and associated structure-transportrelations [9]. Silica-based monoliths on the other hand arebetter characterized. Their structure consists of micrometer-sized sponge-like-interconnected silica skeletons containingnanometer-sized mesopores, with micrometer-sized macro-pores outside the skeleton (also called throughpores) trans-ecting the whole bed [6]. A cross-sectional segment of a silicamonolith in capillary format is shown in Fig. 1. The prepara-tion of this type of monolith has been reviewed in [10, 11].Compared to conventional particulate fixed beds employed inLC and CEC, monolithic materials combine specific surfacearea (adsorption capacity), permeability (throughput), andmass transfer (separation efficiency) in a unique manner [5].

Correspondence: Professor Ulrich Tallarek, Fachbereich Chemie,Philipps-Universität Marburg, Hans-Meerwein-Strasse, D-35032Marburg, GermanyE-mail: [email protected]: 149-(0)6421-28-22124

Abbreviations: CDL, convective-diffusion boundary layer; CLSM,confocal laser scanning microscopy; CP, concentration polariza-tion; EDL, electrical double layer; SCR, space charge region

© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.electrophoresis-journal.com

Electrophoresis 2008, 29, 1140–1151 CE and CEC 1141

Figure 1. (a) SEM image of a section of the 100 mm id silica-basedmonolithic capillary column employed in this work. (b) Electrical-field-induced CP in the electrolyte solution (of bulk concentrationc0) around a cation-permselective, curved geometry approxi-mated by locally flat interfaces.

Electrokinetic transport issues play a key role in severalanalytical and technological areas, particularly in microfluidicand lab-on-a-chip devices [12–28]. In the classical description,the EOFalong a charged solid–liquid interface is generated bythe interaction of the local tangential component of an appliedelectrical field with the mobile space charge of the primary,i.e., quasi-equilibrium, electrical double layer (EDL) at the re-spective solid–liquid interface [12, 14]. Central properties ofthe primary EDL depend on static electrolyte (fluid phaseionic strength) and material characteristics (surface chargedensity), but not on the resulting electrohydrodynamics in asystem. In isothermal systems with a locally thin EDL thatremains unaffected by the applied electrical field concerningits charge density and spatial dimension (thin-EDL-limit), theEOF velocity ueo exhibits a linear response to the applied elec-trical field strength (Eext) resulting in field-independent mo-bilities (meo = ueo/Eext). This behavior has been verified foropen channel systems [20] as well as packed beds of non-porous particles [29, 30].

In hierarchically structured materials with a bimodalpore size distribution, e.g., as represented by the silica-basedmonolithic fixed beds (cf. Fig. 1), the transport properties forcharged species are significantly different in the two struc-tural domains (mesoporous skeleton and macropore space

outside the skeleton in Fig. 1). The mean macropore size(micrometer-range) is much larger than the primary EDLthickness (,10 nm for typical buffer concentrations), result-ing in a quasi-electroneutral interskeleton macropore space,while the mesopore size inside the skeleton (nanometer-scale) is comparable to the EDL thickness. Consequently, theEDL extends over the whole mesopore fluid (a situation thatis sometimes referred to as EDL overlap), rendering themesoporous skeleton ion-permselective. In the case of theinvestigated bare silica monolith, the skeleton is cation-selective due to dissociation of surface silanol groups. Themesoporous skeleton enriches counterions and excludes co-ions with respect to the bulk electrolyte in the macropores. Atelectrochemical equilibrium the Donnan potential balancesthe tendency of ionic species to level out the chemicalpotential gradients, i.e., the tendency of the counterions toleave the mesopores of a particle and that of the co-ions toenter them [31].

The classical picture of linear EOF can become sub-stantially modified in monolithic fixed beds by electrical-field-induced concentration polarization (CP) [28, 32]. CPdescribes the formation of concentration gradients ofcharged species, e.g., simple ions of the BGE or solute mole-cules, in the bulk solution adjacent to a charge-selectiveinterface upon the passage of electrical current normal tothat interface [12, 13]. As illustrated in Fig. 1b with a strongelectrolyte solution of univalent ions as a simple example,the concentration (c1) and transport number (z1t1, where t1

denotes the transference number [31]) of the counterion inthe mesoporous cation-selective domain exceeds those of thecoion, while it is quasi-equivalent to the transport number(z2t2) of the coion in the macroporous domain. A depletedCP zone with lower than bulk conductivity exists along theanodic interface and an enriched CP zone with higher thanbulk conductivity along the cathodic interface between liquidin the macropore space (outside the skeleton) and that in thecation-selective mesopore space of the silica skeleton. Thelocal intensity of CP is influenced by the mobile phase ionicstrength (I) and the applied electrical field strength (E) asindicated schematically, e.g., a higher field strength andlower ionic strength stimulate the formation of more intenseenriched and depleted CP zones (Fig. 1b). The favoredtransport of counterions through the intraskeleton mesoporespace by electromigration (and – due to the EDL overlap –only weak electroosmosis) exhibits a relatively strong fieldstrength dependence, while the diffusive flux of counterionicspecies through the depleted CP zone into the mesoporousskeleton depends relatively little on the applied field strengththrough the generated EOF and resulting local thickness ofthis convective-diffusion boundary layer (CDL) [30].

The local enrichment and depletion of electrolyte ionicstrength translates to an increased current density throughthe ion-permselective pore space at increasing field strength.In the underlimiting regime of CP local electroneutrality ispreserved in the depleted CP zone. At increasing fieldstrength and due to the relatively weak dependence of coun-


1142 I. Nischang et al. Electrophoresis 2008, 29, 1140–1151

terionic diffusive flux through the depleted CP zone on theexternal electrical field, a field strength is approached forwhich electrokinetic transport within the monolith skeletonbegins to exceed diffusive charge flux into the skeleton via itsanodic CDL.

This behavior reflecting the transition from intraskeletonto interskeleton boundary-layer-dominated transport in thedepleted CP zone has been identified in a number of appli-cations, e.g., for trans-membrane coupled mass and chargetransport by a macroscopic limiting current density [12, 13,28, 33], and in fixed beds of porous particles by a maximumdecrease (depleted CP zone) or increase (enriched CP zone)of BGE ionic strength at the ion-permselective interfaces ofthe particles [34]. Charge transfer through the depleted CDL,which is diffusion-limited due to the steep and field-depend-ent concentration gradients (cf. Fig. 1b), has been recognizedto modulate the retention of charged analytes in packed bedsof porous adsorbent particles [35]. Charged species have totraverse the field-dependent concentration gradients, whichinfluences their migration and retention dynamics. Reten-tion modulation of charged species occurs in the regimewhere local mass transport transits from intraparticle tointerparticle boundary-layer-dominated behavior [28].

If the electrical field strength is elevated above the valuereflecting the limiting current density, a secondary (non-equilibrium) EDL is generated electrokinetically [33]. Thissecondary EDL consists of a mobile counterionic spacecharge region (SCR) in the adjacent macropore space and animmobile co-ionic SCR of unscreened, fixed surface chargeinside the skeleton or the ion-permselective pore space ingeneral [28]. Fundamental properties of this nonequilibrium,secondary EDL are that both, its local dimension and chargedensity, depend on the local normal component of theapplied electrical field. The local tangential component of theapplied electrical field interacts with the mobile SCR of theelectrical-field-induced secondary EDL to generate nonlinearelectroosmotic slip in the macropore space in a manneranalogous to linear, equilibrium EOF. Nonlinear EOF be-havior in monoliths based on nonequilibrium CP has beenrecognized by a few groups [30, 32, 36, 37] and was shown todepend on the complex morphology of the porous medium,providing an excellent route for tuning morphology-relatedelectrohydrodynamics. Potential drop in the depleted CPzone plays the role of an electrokinetic potential, similar tothe classical zeta-potential at a charged, dielectric solid–liquid interface. This potential (which originates in none-quilibrium CP) depends on a characteristic axial dimensionof the system (e.g., the particle diameter in particulate beds orthe skeleton thickness in monoliths) and the applied fieldstrength [34].

With a focus on electrokinetic separation issues in po-rous media, this article intends to probe the local transportdynamics of charged analytes and the macroscopic flowdynamics in a silica-based capillary monolith employingconfocal laser scanning microscopy (CLSM). Based on ear-lier CLSM studies of particulate packed beds [34], this work

is motivated by correlating the locally observed CP dynam-ics in monoliths with the macroscopically resulting (net)EOF. The microscopic analysis of CP by CLSM is realizedemploying refractive index matching of the fluid phase tothe mesoporous silica skeleton. This approach facilitatesobservation of stationary distributions of a variety of fluo-rescent tracers used as indicators for CP under a given setof conditions defined by the morphology and chemistry ofthe monolith, the fluid phase composition, and the appliedfield strength.

2 Materials and methods

2.1 Reagents and materials

Sodium acetate trihydrate (p.a., �99.5%), acetic acid(�99.5%), hydrochloric acid, Tris, ACN, and DMSO (bothspectrophotometric grade) were purchased from Sigma–Aldrich Chemie (Taufkirchen, Germany). Fluorescent tracermolecules Bodipy™ 493/503 (D-3922) and Bodipy™ 492/515disulfonate (D-3238) were from Invitrogen (Karlsruhe, Ger-many), while Rhodamine 6G (Fluka BioChemika) was fromSigma–Aldrich Chemie. Fluorescent nanoparticles with anominal particle diameter of 50 nm and a negatively chargedsurface were purchased from Duke Scientific (Palo Alto, CA,USA). Bare silica monoliths in 100 mm id650 cm cylindricalfused-silica capillaries were received as research samplesfrom Merck KGaA (Darmstadt, Germany). The structure ofthe monoliths is characterized by a bimodal pore size dis-tribution with relatively large interskeleton macropores ofabout 2 mm size (as in Fig. 1a), or smaller ones of 0.9 mmsize, and mesoporous skeleton domains of about 1 mm sizewith a high internal porosity and 13 nm-sized intraskeletonmesopores. Packed beds in 100 mm id cylindrical fused-silicacapillaries were fabricated after a similar protocol describedearlier [30]. A fluid phase consisting of a 90:10 v/v mixture ofDMSO and aqueous sodium acetate buffer (pH 5.0) wasused for refractive index matching to the silica-based mate-rials (porous monolith, particles, and capillary column). Anaqueous stock solution of 0.1 M sodium acetate was preparedusing doubly distilled water from a Milli-Q-Gradient waterpurification system (Millipore, Eschborn, Germany). The pHwas adjusted to pH 5.0 by titration with concentrated aceticacid. Appropriate volumes of this stock solution, MilliQwater, and DMSO were then mixed to yield acetate buffersolutions of the desired ionic strengths in 90:10 v/v DMSO/water. The fluid phase contained 10 mM of either of theaforementioned fluorescent tracer molecules. For electro-osmotic mobility studies, a mobile phase of 80:20 v/v ACN/aqueous Tris buffer (pH 8.3) containing 10 mM Bodipy™ 493/503 was used. The latter mobile phase was prepared by mix-ing appropriate volumes of a 0.1 M Tris buffer stock solution,MilliQ water, and ACN. Tris buffer stock solution was pre-pared from 0.1 M Tris solution (base form) in MilliQ waterand titration to pH 8.3 with concentrated hydrochloric acid.



2.2 Microfluidic device and CLSM studies

Imaging experiments were performed on an Axiovert 100confocal laser scanning microscope (Carl Zeiss AG, Jena,Germany) equipped with two continuous gas lasers (Argonion laser: 488 nm, 25 mW maximum output power; helium-neon ion laser: 543 nm, 1 mW) and a 406oil immersionobjective (NA 1.3). Images were acquired in the xy-plane,perpendicular to the optical axis and parallel to the appliedelectrical field. The principal experimental setup has beendescribed elsewhere [34]. Electrolyte reservoirs (2.5 mL vol-ume) consisted of PEEK material and were equipped with astandard 1/1600 thread to insert and fix the capillaries. Fittingmaterials were purchased from Upchurch Scientific (OakHarbor, WA, USA). High-voltage power supply was realizedusing a 30 kV d.c. power generator (F.u.G. Elektronik,Rosenheim, Germany). Platinum wire electrodes were di-rectly inserted into the electrolyte solutions of each vial. Priorto the measurements the confocal microscope wasgrounded. If not stated otherwise, images were acquired asxy-sections of 115.16 mm6115.16 mm with a resolution of5126512 data points in a slice of thickness 1 mm. Generally,two consecutive scans were averaged for a better S/N. Dataanalysis was accomplished using Image J (Rasband, W. S.,ImageJ, U.S. National Institutes of Health, Bethesda, MD,USA, http://rsb.info.nih.gov//ij/, 1997-2006).

3 Results and discussion

3.1 CLSM studies

Figure 2 probes the sensitivity of a variety of fluorescent tra-cer molecules for CP in a bare silica capillary monolith withinterskeleton macropores and intraskeleton cation-selectivemesopores (cf. Fig. 1). The electroneutral tracer serves asreference (Fig. 2a). An electroneutral tracer is not involved incoupled mass and charge transport and also insensitive toany electrostatics and BGE ionic strength differences in thesystem. As illustrated by the series of CLSM images andselected intensity profiles for the co-ionic fluorescent tracer,the externally applied field strength (Eext) sensitively influ-ences the development of CP in the monolith. While theimage contrast in Fig. 2b (left image) without applied fieldcompared to Fig. 2a (left image) originates from Donnan-exclusion of the co-ionic tracer from the intraskeleton meso-pore space due to EDL overlap at relatively low ionic strength,CP develops if Eext is superimposed (Fig. 2b, right image).This is evident from the “mountains” and “valleys” in fluo-rescence intensity reflecting enriched and depleted CP zoneswith increased and decreased BGE concentration, respec-tively, which demonstrate the systematic change in the equi-librium distribution of ionic species in the interconnectedpore space. It can be also anticipated that – compared to thedimensions of the equilibrium (primary) EDL – the CDLsdue to electrical-field-induced CP have a considerably larger

size. As a consequence of the continuous monolith matrixthe CDLs smear along the ion-permselective skeleton’s ca-thodic and anodic interfaces.

Figure 2c shows CLSM images from experiments withpolystyrene-based nanoparticles with a nominal diameter of50 nm. These nanoparticles have a fluorescent core and anegatively charged surface. The image contrast atEext = 0 kV/m (left image, Fig. 2c) originates from size-exclu-sion of the tracer from the intraskeleton mesopore spacewith a mean pore size of 13 nm. Upon application of Eext weobserve the development of enriched and depleted CP zones(right image in Fig. 2c and related profile). These CP zonesare sharper than observed for the small co-ionic tracer (rightimage, Fig. 2b) because the nanoparticles are completelysize-excluded from the mesoporous skeleton and accumulatelocally while the electrical field (which penetrates theintraskeleton pore space) drives these negatively chargedparticles against the cathodic interfaces of the monolithskeleton. In contrast, a nonideal ion-permselectivity allowsthe much smaller co-ionic tracer in Fig. 2b to partly penetratethe mesopore space.

Compared with co-ionic tracer, a counterionic tracer(Fig. 2d) shows strong adsorption to the oppositely chargedsurface and is in average enriched in the intraparticle porespace. In addition to this intraskeleton enrichment at elec-trochemical equilibrium an applied field imparts an increas-ing current density through the mesoporous skeleton withincreasing Eext (right image, Fig. 2d). In the regime wherethe intraskeleton transport properties are determined by thedynamics inside the skeleton, because enough counterionscan still be supplied through the adjoining depleted CP zone,it results in an increasing current density, which togetherwith the diffusive backflux from the enriched CP zone at thecathodic interface in average increases the intraskeletoncounterionic tracer concentration.

Figures 3 and 4 study the development of CP at increas-ing electrical field strength for the co-ionic (Fig. 3) andcounterionic tracer (Fig. 4). CP probed by the co-ionic traceris like “a landscape of mountains and valleys” in electrolyteconcentration. Although intensity and extension of the CPzones vary slightly in the images, a similar evolution of eachCP zone with increasing Eext is apparent. Scanning the con-focal plane up and down the sample revealed increasing anddecreasing intensity of the spots at a certain field strength,implying that the confocal volume with a slice thickness of1 mm does not probe every CP zone at is maximum intensity.In this respect it should also be recognized that the pore-levelprofile of EOF in fixed beds of spherical particles and mono-liths, even in the thin-EDL-limit, may obscure the shape andarchitecture of the CP zones. It is not uniform and it is acomplex function of the local distribution of velocities causedby the complex morphology of the porous medium [27, 29,30]. Thus, local flow maldistributions and monolith archi-tecture influence the thickness of the CDL and in turn mod-ulate transport properties in the CP zones via their effectivespatial dimensions. Even though the detailed behavior



Figure 2. CP dynamics in a silica capillary monolith (100 mm id) with cation-selective skeleton in dependence of the applied electrical fieldstrength (Eext) as probed by (a) Bodipy™ 493/593 as electroneutral tracer, (b) Bodipy™ 492/515 disulfonate as co-ionic tracer, (c) polystyrenenanoparticles (50 nm) with a negatively charged surface as co-ionic and size-excluded tracer, and (d) Rhodamine 6G as counterionic tracerin a fluid phase of 90:10 v/v DMSO/aqueous sodium acetate buffer (pH 5.0) with an effective ionic strength of 0.1 mM. Axial profiles (coaxialto the direction of Eext and the resulting macroscopic EOF) were taken along the dashed lines indicated in the images and normalized withrespect to their mean intensity at Eext = 0 kV/m.

appears barely accessible by our experimental equipment,the development of electrical-field-induced CP clearly scaleswith an increasing applied electrical field strength, whichcorrespondingly increases local electrical field strength in thehierarchical monolithic material with the differing normaland tangential field components. Also the shape of the an-odic depleted and cathodic enriched CP zones with respect toEext compared to objects of much simpler planar or spherical

symmetry [28, 33, 34] is expected to be influenced by thebranching of the sponge-like structure as schematically il-lustrated in Fig. 3. The enriched CP zone of a vertical branch(with respect to flow direction) feeds electrolyte concentra-tion to the depleted CP zones of another branch, directlydiverting the skeleton further downstream. This is mostpronounced when the branching is directly located behindan enriched CP zone and/or the monolithic structure



Figure 3. CP dynamics in andaround the cation-selectivemonolithic skeleton in depend-ence of the applied electricalfield strength (Eext) as probed bythe co-ionic tracer (Bodipy™ 492/515 disulfonate) in a fluid phaseof 90:10 v/v DMSO/aqueoussodium acetate buffer (pH 5.0)with an effective ionic strengthof 0.1 mM. Normalized axialprofiles show the enriched anddepleted CP zones along theposition indicated by the dashedline in the images. The sche-matic illustrates an extinguish-ing interaction between en-riched and depleted CP zones.The dashed box in the profilediagram refers to the regionindicated by the white arrow inthe left image from which thedata for Fig. 5 were extracted.

becomes denser: the feeding of electrolyte concentrationfrom the enriched CP zone of the upstream branch into thedepleted CP zone of the downstream branch can renderimpossible the local observation of the depleted CP zone atthe downstream branch when the branches actually comecloser. This fact also may partly explain the axial inhomo-geneity of the profiles with varying local amplitude along theprofiles. Nevertheless enriched CP zones (smearing alongthe skeleton) are complemented by their counterpart in formof a depleted CP zone (also smearing along the skeleton).Consequently, depleted and enriched CP zones are shiftedradially up- or downward, depending on where electricalfield lines enter and/or leave the ion-permselective skeletonand the local flow dynamics.

CP as probed by the counterionic tracer produces differ-ent images (Fig. 4). The image contrast stems from theintraskeleton enrichment at Eext = 0 kV/m which intensifieswith increasing Eext (CP). Neither distinctive CP zonesaround the mesoporous skeleton nor any slope characteriz-ing the backward diffusion from the enriched CP zone canbe detected in the profiles in Fig. 4 due to the small spatialdimensions involved. For the same reason, CP zones probedby a counterionic tracer could not be resolved in earlierinvestigations of electrical-field-induced CP in dense parti-culate systems [34], where packed beds of porous adsorbentparticles with the relatively small diameters typical for CECwere employed. The manifestation of CP as an increase ofintraskeleton (pore-level) counterion concentration resultsfrom the increasing current density through the mesoporouspore space and the diffusive backflux. At a certain electricalfield strength, the intraskeleton counterion concentrationapproaches saturation (plateau regime), a situation that –

similarly as for the co-ionic tracer – indicates limiting currentdensities on the local skeleton scale. This dependence of CPon Eext (at constant mobile phase ionic strength) thus reflectsthe transition from intraskeleton to boundary-layer-domi-nated interskeleton transport behavior, where the realizationof higher currents appears impossible.

Figure 5 depicts the local enrichment and depletion ofthe BGE as a function of Eext based on experiments with theco-ionic tracer (Fig. 3). The respective intensities were takenat the position indicated by the arrow in Fig. 3. The BGEconcentration is monotonically increasing in the enrichedCP zone and decreasing in the depleted CP zone withincreasing Eext and approaches asymptotic values above acritical electrical field strength (plateau regime). The electro-lyte concentrations in enriched and depleted CP zones areinherently related. A maximum enrichment in the CP zonetherefore translates to a maximum depletion in the depletedCP zone, so that the concentration in the enriched CP zonecannot be increased further. The value of the critical electricalfield strength is influenced by the actual ion-permselectivityof the mesopore space and actual (electro-)hydrodynamicconvection through the material which determines the localthickness of the CDL. In the plateau regime electrokinetictransport through the monolith skeleton locally exceeds dif-fusion-limited transport through the depleted CP zone; thus,in this plateau regime (here at Eext .80–90 kV/m) chargetransport through the skeleton is determined locally by thetransport behavior in the adjoining anodic CDL (depleted CPzone). In other words, with increasing field strength, i.e.,while the electrical current through the mesoporous skeletonincreases and ionic concentration in the depleted CP zonedecreases towards zero (Fig. 1b), a transition occurs from



Figure 4. CP dynamics in andaround the cation-selectivemonolithic skeleton in depend-ence of the applied electricalfield strength (Eext) as probed bythe counterionic tracer (Rhoda-mine 6G) in a fluid phase of90:10 v/v DMSO/aqueoussodium acetate buffer (pH 5.0)with an effective ionic strengthof 0.1 mM. Axial profiles weretaken along the dashed lines inthe images and normalized withrespect to their mean intensityat Eext = 0 kV/m.

Figure 5. Dependence of the co-ionic tracer intensity on Eext inthe stationary, enriched and depleted CP zones at the region ofinterest (see dashed box and arrow in Fig. 3). Experimentaldetails as in Fig. 3.

intraskeleton electrokinetic to interskeleton boundary-layer-dominated transport behavior on the local skeleton scale ofthe monolith.

For an investigation of the ionic strength dependence ofCP in the monolith initial laser and detector settings of themicroscope were optimized to include the brightest region ofthe images, i.e., the enriched CP zones at the lowest investi-gated ionic strength (0.1 mM) and Eext = 53 kV/m (Fig. 6).The column was subsequently equilibrated with fluid phaseof higher ionic strength until a steady state was achieved. Allimages were acquired under identical laser and detector set-tings. Intensities were taken from the region indicated by thewhite arrow in the upper-left image of Fig. 6 and normalizedwith respect to the average value at Eext = 0 kV/m, displayingthe relative extent of electrical-field-induced CP. Both, withand without electrical field, a decrease in image contrast withincreasing ionic strength is observed. For Eext = 0 kV/m thisresults from an increase of the intraskeleton coion con-centration due to a decrease of the skeleton’s cation-selectiv-ity. At Eext = 53 kV/m the decrease in image contrast atincreasing ionic strength corresponds to an attenuation ofCP as a direct consequence of the decreasing cation-selectiv-ity of the skeleton. In other words, as the ionic strength isincreased and EDL overlap in the mesopore space reduced(Fig. 1b), the CP phenomenon is attenuated because thetransport numbers for co-ionic species inside the monolithskeleton increase, while those for counterions decrease cor-respondingly (Fig. 6). Thus, as the mesopore space becomesless ion-permselective, the CP zones are less intense, whichis shown in Fig. 6b for a selected enriched and depleted CP



Figure 6. Ionic strength dependence of the co-ion distribution in ahierarchical monolithic structure at an external electrical field ofEext = 53 kV/m. The fluid phase was 90:10 v/v DMSO/aqueoussodium acetate buffer (pH 5.0) at varying effective ionic strengths.

zone. The investigated ionic strength range translates to an EDLoverlap ranging from rintra/lD = 0.268 (rintra denotes the meanintraskeleton pore radius and lD the Debye screening length)for 0.1 mM effective ionic strength to rintra/lD = 2.68 for 10 mMeffective ionic strength, representing an order of magnitude forthis characteristic ratio. The ionic strength region at which CPdevelops may be partly reflected by the intraskeleton surfacecharge density of the material. It should be remembered that themean intraskeleton pore radius (rintra < 6.5 nm) of the mono-lith is in the same order of magnitude as the EDLthickness. Thelatter can be modulated by the BGE ionic strength, while therespective extent of ion-permselectivity is a direct consequenceof the intraskeleton surface charge density.

3.2 Electrohydrodynamics

Electroosmotic mobilities (meo) in fixed beds of porous adsorb-ent particles are basically composed of different contribu-tions [27], including (i) normal or conventional EDL behaviorat the particle’s external surface, (ii) intraparticle volumetricEOF, and (iii) the porosity of a particle. As an additional fac-tor the intraparticle EDL overlap influences the ion-perms-electivity of a particle or alternatively the skeleton of amonolith (cf. Fig. 1) which, in turn, determines the intensityof CP and a CP-based nonequilibrium EOF at higher fieldstrengths. In this respect, we have to expound on the mono-lith’s unique morphology. Due to the continuous skeleton,extended CP zones (which are less confined than in a packedbed of discrete particles) penetrate the monolith like a spiderweb (Fig. 3). Compared to the size of the charge-selectivedomains, macropores in a monolith have larger lateral andaxial dimensions than the interparticle pores in a random-close packing of mesoporous particles. The continuous,relatively thin skeleton also provides an axial length dimen-sion which may, in turn, also stimulate a nonlinear or none-quilibrium electrokinetics. On the other hand it has beenshown that the achievable intraskeleton classical EOF hasonly limited relevance for the electrokinetic transport in themonolith, especially in view of separation efficiency [30].

Monitoring electrohydrodynamic features with the elec-troneutral Bodipy tracer by measuring the average EOF ve-locity ueo and expressing it via meo in the ionic strength rangefrom 0.1 to 10 mM revealed an increasing deviation of meo

from linearity at elevated electrical field strengths. This indi-cates a significant contribution of nonequilibrium electro-osmotic slip (Fig. 7a) to the overall EOF dynamics. Thelocally varying intensity of electrical-field-induced CP alongthe curved ion-permselective skeleton, where the transportdynamics of counterionic species changes from intraskele-ton to interskeleton boundary-layer-dominated behaviorcharacterizing the transition to nonequilibrium CP (Fig. 4),results macroscopically in a nonlinear ueo behavior. Depend-ing on the intensity of nonequilibrium CP, i.e., the actualpotential drop in the developed mobile SCR as part of thedepleted CP zone, nonlinear contributions to the overall EOFcan thus significantly modify the classical picture of linearelectroosmotic slip velocities. This is illustrated in Fig. 7a fora bare silica monolith with bimodal pore size distributionand the same mobile phase conditions as employed in ourCLSM imaging experiments. At relatively low applied elec-trical field strength (Eext ,20 kV/m) the electroosmotic mo-bilities tend towards the classical, field-independent behav-ior. Increasing ionic strength reduces the shear plane poten-tial at the skeleton’s external surface and subsequently leadsto a reduction of meo with increasing ionic strength (Fig. 7a).At elevated field strengths a nonlinear contribution becomesapparent originating from nonequilibrium electroosmoticslip and resulting in field-dependent mobilities. This non-linear contribution starts for the lowest employed ionicstrength 0.1 mM at Eext = 40 kV/m. For higher ionic



Figure 7. Double logarithmic plot of the electroosmotic mobility(meo = ueo/Eext) measured in a bare silica monolith as a function ofEext with a mobile phase of (a) 90:10 v/v DMSO/sodium acetatebuffer (pH 5.0), ionic strength as indicated; and (b) 80:20 v/v ACN/Tris-HCl buffer (pH 8.3), concentration as indicated. For compar-ison, electroosmotic mobility data of a silica monolith with0.9 mm macropore size and of a packed bed of porous silica par-ticles (with a mean particle diameter, dp, of 2.5 mm), all containedin 100 mm id identical capillary columns, have been included toaddress morphology aspects of the resulting electrohydro-dynamics.

strengths the critical field strength increases to values barelyattainable under the present experimental conditions, whichis not surprising considering the attenuation of electrical-field-induced CP at higher ionic strength (Fig. 6). For allinvestigated ionic strengths it can be summarized that theinitially field-independent behavior of the electroosmoticmobilities is at higher field strengths increasingly dominatedby nonequilibrium electroosmotic slip locally generated atthe skeleton’s surface and increasingly contributing to theoverall average velocities in the monolithic structure. Thisnonlinear contribution can be well correlated to the asymp-totic value of CP (see Fig. 5), which reflects the local transi-tion from equilibrium to nonequilibrium CP.

After we have shown the correlation of electrical-field-induced CP with the macroscopically observable electro-hydrodynamics (Figs. 3–5 and 7a), the influence of mobilephase pH and BGE buffer composition was investigated. The90:10 v/v DMSO/aqueous buffer system was used in ourCLSM studies for the necessary refractive index matching, buta more common fluid phase for chromatographic purposes[30, 32] is a mixture of ACN and aqueous buffer (Fig. 7b). Inchoosing a solvent system that can be used as hydro-organicBGE, the necessity of achieving significant EOF for trans-porting bulk fluid in open channel systems or packed beds hasto be considered [38, 39]. Suitable solvents usually possesssufficient relative permittivity (er) and low viscosity (Zf ). Theeffect of er and Zf on meo for linear (equilibrium) EOF andnonlinear (nonequilibrium) EOF for a given system isexpressed by meo ? er/Zf [33, 39]. Neglecting in a first approx-imation other physicochemical effects, two solvent systemsmay be compared by this relation. Electroosmotic mobilitiesderived from experiments using a fluid phase of 80:20 v/vACN/aqueous buffer with a viscosity of Zf = 1.01 mPa?s andrelative permittivity of er = 42.8 (er/Zf = 42.4) are generallyhigher (Fig. 7b) than mobilities obtained with a fluid phase of90:10 v/v DMSO/aqueous buffer with a viscosity ofZf = 2.6 mPa?s and er = 49.6 (er/Zf = 19) (Fig. 7a).

However, there are also other factors that contribute tothe higher electroosmotic mobilities observed with the ACN/aqueous buffer system. For the ACN system a Tris buffer atpH 8.3 was used compared to the sodium acetate buffer atpH 5 in the DMSO system. At higher buffer pH there is anincreased surface electrical potential due to a higher degreeof dissociation of silanol groups, resulting in a higher surfacecharge density in the primary EDL at the skeleton’s externalsurface and consequently higher net EOF velocities. Further,a higher degree of silanol group dissociation in the intra-skeleton pore space increases the ion-permselectivity andthus decreases the critical electrical field strength at whichnonequilibrium electroosmotic slip starts to influence theoverall electrohydrodynamics. For the ACN system with0.1 mM effective Tris buffer concentration nonlinearity isobserved starting around Eext = 20 kV/m (Fig. 7b), an elec-trical field strength range where for the DMSO/sodium ace-tate buffer system of equal ionic strength meo still displays theclassical, field-independent behavior (Fig. 7a).



3.3 Morphology

Finally, addressing morphology aspects, a monolith withthe same base chemistry and comparable skeleton thick-ness, but smaller macropore size (dmacro ,0.9 mm) hasbeen studied (Fig. 7b). In this monolith the resultingnonequilibrium electrokinetics are clearly attenuated, be-cause the CP zones have less space to develop freely dueto extinguishing interaction of adjacent and neighboredCP zones. This not only indicates that relatively largemacropores (above 1.5 mm) are a bona fide route for high-speed nonlinear flow characteristics [30, 32] in mono-lithic structures, but also addresses the attenuated non-linear electrohydrodynamics in a packed bed of smallporous adsorbent particles (data included in Fig. 7b),where extinguishing interactions of the enriched anddepleted CP zones attenuate the manifestation of elec-trical-field-induced CP and consequently the resultingnonequilibrium electrokinetics [34]. It appears that thenonlinearity can be tuned in packed beds by artificiallydiluting the particles, thereby decreasing interference ofneighbored or adjacent CP zones by artificially increasingthe interparticle pore dimensions and thus bed porosity.Such an architecture would mimic a monolithic structurewith larger macropore dimensions. The schematic inFig. 7 illustrates the architecture of two monoliths (dmacro

,2 mm vs. 0.9 mm) and how the introduction of larger

macropores in a monolith, while keeping the skeletonthickness similar, relates to an artificially diluted spherepacking.

The influence of macropore or interparticle pore sizeon CP has been corroborated by the CLSM imagingexperiments (Fig. 8). All images in Fig. 8 were acquiredunder identical microscope settings (slice thickness: 1 mm),and intensities were normalized with respect to the averageintensity at Eext = 0 kV/m, displaying the relative extent ofelectrical-field-induced CP. Monolithic architecture favorsthe occurrence of nonlinearity not only because the con-tinuous skeleton allows the development of relativelyextended CP zones (less confined than in a bed of discreteparticles), but also because the thin, extended skeletonoffers larger axial length dimensions compared to the sizeof the charge-selective domains than random-close pack-ings of spherical porous particles. Even if it would be pos-sible to artificially dilute the particles in a packing (i.e., byremoving them from each other by a distance of the orderof the particle radius), the resulting arrangement wouldstill display discontinuous features. An extended, con-tinuous skeleton and relatively large macropores are themorphological aspects of the monolithic structure that de-crease extinguishing interactions between adjacent andneighbored, enriched and depleted CP zones (Fig. 8) andenable the realization of nonlinear EOF at moderate fieldstrengths (Fig. 7b).

Figure 8. Comparison of the co-ion distribution in the hierarchical structure of a silica monolith (skeleton thickness ,1 mm, dmacro ,2 mm; cf.Fig. 1a) with that in a packed bed of porous silica particles (mean particle diameter: 2.5 mm, dmacro ,0.7 mm) with and without applied elec-trical field. The fluid phase was 90:10 v/v DMSO/sodium acetate buffer (pH 5.0) at an effective ionic strength of 0.1 mM.



4 Concluding remarks

This work has analyzed the local CP dynamics in fixed bedsof cation-selective monolithic structures with respect to themacroscopic EOF dynamics, particularly in view of a con-tribution of CP-based nonequilibrium electroosmotic slipand specifically addressing morphological aspects for thedeveloping nonequilibrium or nonlinear electrokinetics. CPwas visualized by CLSM employing refractive index match-ing of the fluid phase to the mesoporous silica skeleton of themonoliths (Figs. 2–6). The electrical-field-dependence of theCP pattern (Figs. 3 and 4) demonstrates that a limiting cur-rent density is approached on the local skeleton scale atincreasing Eext (Fig. 5). At low electrical field strengths, thecurrent through the skeleton (in varying degrees accom-plished by the counterions, depending on ionic strength) iscontrolled by the intraskeleton transport characteristics,while it is governed by the behavior in the depleted CP zone(anodic CDL) towards the limiting current regime at higherfield strengths. The presented CLSM images reveal that theCP pattern in a monolith with a continuous skeleton is sig-nificantly modulated and less discrete than observed for par-ticulate beds (discontinuous stationary phase) or single po-rous particles, penetrating the whole material like a spiderweb. A connection of the developing CP with evolving non-linear dynamics became accessible through macroscopicallymeasurable EOF velocities (Fig. 7), which could be well cor-related to the optical imaging data. A limiting boundary-layer-dominated mass transport regime characterized by thedevelopment of nonequilibrium space charges is manifestedin a nonlinear or nonequilibrium EOF. While the local ionconcentrations in the depleted and enriched CP zonesapproach asymptotic behavior (Fig. 5), e.g., ionic concentra-tion in the depleted CP zone is reduced towards zero atincreasing field strength, we observe the onset of a signifi-cantly nonlinear contribution to the overall EOF dynamics(Fig. 7a) in the same monolithic structure. In the frameworkof nonequilibrium CP this suggests that a secondary EDL iselectrokinetically induced by the applied field, consisting of amobile SCR in the depleted CP zone and an immobile SCRin the adjacent pore space of the skeleton.

It has been shown that nonequilibrium electroosmosisbased on this secondary EDL shows fundamental electro-hydrodynamical features and is a result of the mutual inter-play of a variety of parameters, including pore space mor-phology (Fig. 7b) and applied field strength (Fig. 7), but alsofactors modulating the charge selectivity on the local skele-ton scale, e.g., the intraskeleton pore size and surface chargedensity (Fig. 7), and the fluid phase ionic strength (Figs. 6and 7a). In contrast to the primary EDL dimensions the CPzones around the skeleton are considerably larger (Fig. 3)and additionally smear along the skeleton.

The silica-based monoliths used in this work are aninteresting alternative to random-close sphere packingswhere the interparticle (void space) dimensions are inher-ently related to the particle diameter. Silica monoliths are

manufactured by a two-step process, resulting in bimodalpore size distributions and morphologies different fromthose of particulate beds. The monolithic structures resem-ble particulate systems in which ion-permselective sphereswould be relatively loosely placed in space. We have observedthat decreasing the macropore space in a monolith results inthe attenuation of CP and nonlinearity (Fig. 7b) [30]. Thus,nonequilibrium electroosmotic slip and CP, which are basedon the ion-permselectivity of the thin, but axially extendingmonolithic skeleton, develop better in the interskeletonmacropores than in the interstitial pores of dense packings ofion-permselective particles (Fig. 8). This includes a reducedextinguishing interaction of neighbored CP zones in themonoliths.

With respect to these investigations it is undoubtful thatthe migration and retention behavior and also zone disper-sion of charged analytes with respect to electroneutral ana-lytes in porous media employed in electrical-field-assistedchromatographic techniques can be principally correlated tothe development and manifestation of CP. The transitionfrom intraskeleton to interskeleton boundary-layer-domi-nated transport behavior is experienced by charged analytes,which have to traverse the CP zones and thus the field-de-pendent conductivity gradients resulting from local ionicstrength differences [28, 35]. This roller coaster ride throughconductivity “mountains” and “valleys” not only influenceslocal transport dynamics, but possibly also zone propagation(stacking/destacking) observed on the macroscopic scale. Weare currently working on resolving these and related issuesmore quantitatively which still puzzle chromatographersstrongly.

We thank Dr. Dieter Lubda from Merck KGaA (Darmstadt,Germany) for the preparation of the capillary monoliths and Dr.Gerard Rozing from Agilent Technologies GmbH (Waldbronn,Germany) for the loan of a HP3DCE instrument. This work wasfinancially supported by the Deutsche ForschungsgemeinschaftDFG under grants TA 268/1-2 and TA 268/2-1.

The authors have declared no conflict of interest.

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