Concurrent Aggregation andDeposition of TiO2 Nanoparticles ina Sandy Porous MediaN A T A L I A S O L O V I T C H , * , †

J E R O M E L A B I L L E , † J E R O M E R O S E , †

P E R R I N E C H A U R A N D , †

D A N I E L B O R S C H N E C K , †

M A R K R . W I E S N E R , ‡ A N DJ E A N - Y V E S B O T T E R O †

CEREGE, UMR 6635 CNRS/Aix Marseille University,Europole Mediterraneen de l′Arbois, 13545 Aix-en-Provence,Cedex 04, France. GDRI- ICEINT, and Department of Civiland Environmental Engineering, Duke University, PO Box90287, Durham, North Carolina 27708-0287

Received January 18, 2010. Revised manuscript receivedMay 11, 2010. Accepted May 25, 2010.

The possibility of simultaneous particle aggregation anddeposition in a porous medium was examined for the case ofTiO2 nanoparticles(NPs).Whilepotential forparticleaggregationis typically assumed to be negligible in porous media due tofavored interactions with porous media surfaces (collectors),we show that nanoscale particle dimensions may favoraggregation kinetics, thus altering the transport and retentionof these materials in saturated porous media. When surfacechemistry favors nanoparticle-nanoparticle attachment (Rpp)over nanoparticle-collector attachment (Rpc), the rate of particleaggregation within pores may be comparable to that ofdeposition at ratios of collector to nanoparticle surface areasas high as 40. Aggregation of NPs in the porous mediaenhances NP deposition, however aggregates that are notremoved will sample a smaller portion of the available porenetwork within the column due to size exclusion.

IntroductionManufactured nanoparticles, varying in diameter from 1 to100 nm, are widely and increasingly used in commercialnanomaterials due to novel properties that can improve thefunctionality of a range of commercial products. Normal useand aging of nanomaterials, accidental release, or inap-propriate disposal, are among the potential sources of thenanoparticles to the environment (1-4).

The transport of nanoparticles or nanomaterial residuesin porous media is of interest due to both potential forintroduction of nanoparticles to aquifers and the need tounderstand the removal capabilities of engineered filters inwater and wastewater treatment.

Nanoparticle deposition and mobility in porous media isstrongly dependent not only on pore size and organization,but also on the physicochemical parameters of solutionchemistry (ionic strength, pH, presence of natural organicmatter), nanoparticle surface properties, and flow rate. Thoseparameters that affect the interactions between the nano-particles and the solid media, also control particle aggrega-

tion, which may subsequently influence the balance betweenfree migration of particles and deposition (5-17).

While Thomas Camp first proposed that particles mayflocculate in the pore spaces of filters (18), relatively littleconsideration has been given to the potential for simulta-neous aggregation and deposition in porous media sincedeposition is often assumed to dominate aggregation. Indeed,when viewed as competing parallel reactions dependent onparticle volume fraction, aggregation in the pore space offilters is predicted to occur at much slower rates thandeposition since the volume fraction of the porous mediumis typically an order of magnitude larger than the suspendedparticle volume fraction. However, from the perspective ofsurface area concentrations, nanoscale particles, even atmoderate mass concentrations, present large surface areasfor particle-particle contacts (aggregation). For example, theparticle surface area of a 50 mg L-1 suspension of 30 nmnanoparticles with a specific density of 4, and filling a 350µm pore is only a factor of 0.2 times smaller than the surfacearea within the pore (considered as a sphere). This ratioincreases to a value of unity for a particle diameter of 6 nm.In column studies (12), high concentrations (1-6 g L-1) of20 nm nanoparticles of nanoscale zerovalent iron appear tofavor aggregation within the porous medium, while aggrega-tion was largely absent at a lower concentration (30 mg L-1).Thus, simultaneous consideration of aggregation and depo-sition would appear to be warranted for nanoparticlesuspensions.

The relationship between aggregate size, structure, anddeposition are likely to be complex. While DLVO theory(19-21) predicts decreased attachment to a porous mediumwith larger particle diameter, in some cases, the oppositetrend has been observed (9, 20-22). In yet other studies, noeffect of size was observed (19). Such discrepancies might bedue to nonidealities such as surface roughness on the particlescollectors (porous medium), hydrodynamic interactions,nonhomogeneity of surface charges, dynamics of colloidalinteractions, physical straining or trapping of particles(10, 19-22). Simultaneous aggregation and the depositionof aggregates in porous media further complicate this picture.The transport of particle aggregates will certainly differ fromthat of individual nanoparticles. Indeed the permeability ofporous aggregates decreases drag coefficients compared toequivalent nonporous solid spheres (23). Moreover thehydrodynamic driving of nonporous particles increases whensize decreases, due to weight loss. Both of these tendenciestend to favor further aggregation and deposition of a porousaggregate, compared to the individual nonporous nanopar-ticles constituting it.

In this work we consider the aggregation and depositionof nanoparticles in a porous medium in the context of TiO2

nanoparticles. Among all manufactured nanomaterials, TiO2-based nanomaterials have attracted great attention due totheir photocatalytic, and UV-absorbance properties, withapplications that include photovoltaics, self-cleaning sur-faces, water treatment, and sunscreens. Significant releasesof manufactured TiO2 nanoparticles into aquatic environ-ments have been calculated in modeling work (3) andconfirmed experimentally (24). Moreover, TiO2 has beenrecently classified in the Group 2B of the potentiallycarcinogenic materials (IARC 2006, volume 93) by theInternational Agency For Research On Cancer, which high-lights the need for new evaluation of its safe use.

Only few studies have examined the mobility of TiO2

nanoparticles in porous media (5, 13, 14). They generallyconsidered the effect of aggregation as insignificant. The

* Corresponding author e-mail: solovitch-vella@cerege.fr.† Aix Marseille University.‡ Duke University.

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Published on Web 06/04/2010

dispersion stability of TiO2 nanoparticles in aqueous sus-pensions is mainly governed by solution pH and ionicstrength (13, 25-27, etc.). Here, we focus on the role of theseparameters on the mobility, aggregation and deposition ofTiO2 nanoparticles in a saturated porous medium of sand.

Materials and MethodsCharacterization of the Porous Medium. A silica sand(natural sand of Mios, MI 0.4/0.9, Sibelco, France) was usedas the porous medium for all column experiments. In orderto remove impurities and fine colloidal matter, the com-mercial sand was cleaned thoroughly by successive washingwith HCl (1 M), NaOH (1 M) and Milli-Q water, each repeated10 times. The sand was then oven-dried at 60 °C and storedin a tight container. The grain diameter, measured by laserdiffraction (Mastersizer S, Malvern Instruments), ranged from200 to 1000 µm, with volume-averaged diameter of 650 µm.The specific surface of the sand determined by BET analyses(TRISTAR 3000, Micromeritics) was 0.128 m2 g-1. X-raydiffraction (XRD) analysis (X’pert Pro MPD, Panalytical) ofthe sand revealed that it consisted of quartz with traceamounts of feldspar and mica.

Pore size within the porous media was characterized byscanning electron microscopy in back scattering electron(BSE) mode (SEM, HITACHI S-3000N). Samples for SEMimaging were prepared by filling the porous medium witha polyester resin (resin SS Mecaprex, Presi) and sectioningit in 5 mm slices. The images were binarized so that the blackpixels correspond to the space within pores and the whitepixels correspond to sand grains. For each area examined,a set of 1 pixel distant parallel lines was created andsuperimposed to the images. The line sections correspondingto grain superimposition were measured in length, and thelongest section per pore was recorded. The pore sizedistribution then obtained ranged between less than 1-50µm with an average pore diameter of 350 µm (SupportingInformation (SI) Figure S-1d).

The electric surface potential of the sand (estimated as� potential) was calculated from streaming potential mea-surements (ZetaCad, CAD Instruments, France) for differentconditions of pH and ionic concentration (I), using HCl orNaOH for pH adjustment, and NaCl for I adjustment.

Nanoparticles Characterization. TiO2 aqueous disper-sions were prepared from powdered TiO2 nanoparticles (NPs)(Alfa-Aeser 39953, anatase, 32 nm). The powder was put inwater and acidified at pH 2.5 with HCl. The supernatant wassampled and diluted to concentration of 50 mg L-1, whichconstituted the working TiO2 suspension.

XRD analysis (X’pert Pro MPD, Panalytical) of the productrevealed a pure TiO2 mineral composed largely of anatase withtrace quantities of rutile. The specific surface area of the TiO2

NPs determined by BET analysis (TRISTAR 3000, Micromeritics)was 47.6 m2 g-1, in close agreement with the 32 nm diameterof the primary particles of TiO2 given by the supplier.

The surface charge of the NPs dispersed as a function ofpH and I was measured by electrophoretic mobility mea-surements (Nanosizer NanoZ, Malvern Instruments). Themeasurement were done at pH varying from 3 to 9 in purewater using HCl (1M) or NaOH (1M) additions, or at pH 8with I varying from 10-4 to 1 M (NaCl).

The size distribution of the nanoparticles dispersed inMilli-Q water ranged from 30 to 300 nm with an averagediameter of 150 nm (DLS, BI-200SM-CrossCor, BrookhavenInstrument Corporation, U.S.) (SI Figure S-2). This indicatesthe presence of many stable aggregates of the primarynanoparticles. In order to determine aggregation kinetics ofNPs, the time-resolved size was measured as a function ofsalt concentration at pH 8 and at pH 5. I ranged from 10-3

to 1 M NaCl. For each ionic strength, the extent of aggregation

was measured every 2 min, starting at time 0 of salt addition,and continuing up to 5 h.

Sand/Nanoparticles Interactions in Batch Conditions.The affinity of TiO2 NPs for the sand surface vs pH and I wasmeasured in batch conditions via sorption experiments. Ina series of PTFE bottles, 20 mL of the TiO2 suspension (50mg L-1) were prepared. The value of pH was adjusted from3 to 10 with I ) 1 mM NaCl, using HCl or NaOH additions.Also, I was adjusted from 10-3 to 5 × 10-1 M NaCl at a constantpH value of 8. In each case, 5 g of sand were added into thebottle, and pH was readjusted as needed. The correspondingsurface area ratio of sand/nanoparticles stands between 64/4.9 at the minimum if we consider the nanoparticles asindividually dispersed at the 32 nm diameter, and 64/1 atthe maximum if we consider them as spherical and nonporous clusters of 150 nm diameter. In all cases, this ratioavoids possible saturation of the sand surface by the adsorbednanoparticles. The prepared suspensions were kept mixedon a roller during 48 h, and then allowed to settle for 10 mn.The amount of TiO2 NPs that remained in suspension (notattached to sand) ([TiO2]free) was quantified by ICP-AES(Ultima-C, Jobin Yvon Horiba) as well as the initial con-centration of the NP suspension ([TiO2]ini). The concentrationof TiO2 NPs attached to the sand ([TiO2]sorbed) was obtainedby subtracting [TiO2]free from [TiO2]ini.

Column Experiments. The column experiments werecarried out in plexiglass columns 7 cm in length and 4.7 cmin diameter. The method of column experiments is fullydescribed in the SI.

The effects of I and pH on TiO2 NPs retention wereinvestigated over a range of I from 10-3 to 10-1 M NaCl andpH from 3.5 to 8. The experiments with variable I wereconducted under constant pH buffered at pH 8 using 10-3

M NaHCO3. This pH was selected to assess the effects of I,since it minimizes the deposition of TiO2 NPs in the columndue to repulsive interactions with the sand (see discussionsection). The Darcy velocity in column experiments was 0.002cm h-1, a value typical of groundwater flow in many systems.When conditions of pH or I favored the aggregation of TiO2

NPs during the experiment, the NP suspension was main-tained in ultrasonic bath prior to injection in order to delaysignificant aggregation beyond injection time. In all cases,the size distribution of the NPs in the eluted solution wasmeasured just at the column exit.

Determination of Attachment Efficiency (r). The fractionof particle collisions, with each other or with a sand grain,that result in particle attachment is referred to as theattachment efficiency. The attachment efficiency betweenNPs and collectors in particle-sand grain interactions (Rpc)was calculated using colloid filtration theory (28), whereasthe attachment efficiencies between NPs (Rpp) were deter-mined from the slopes of plots of aggregate size as a functionof time (29). The calculations for both attachment efficienciesare described in detail in the SI.

Determination of Total Interaction Energy. Accordingto the classical Derjaguin-Landau-Verwey-Overbeek(DLVO) theory, the interaction energy between two surfacesis mainly determined by the balance between van der Waalsattraction and electrical double layer repulsion. The interac-tion energy (Φtotal) between NPs and sand grains wasconsidered as that occurring between two spherical doublelayers ((30), see SI).

Micro X-ray Fluorescence Spectroscopy (µ-XRF) Imagesof Retained TiO2 in the Column. Columns containing retainedTiO2 after the deposition experiments were frozen and cut inlongitudinal slices of 0.5 cm thickness. Laboratory-based microX-ray fluorescence (µ-XRF) measurements were done on thesamples that were kept frozen using a Peltier cooled sampleholder. Measurements were carried out on a HORIBA XGT-7000 microscope equipped with an X-ray guide tube producing

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a finely focused and high-intensity beam with a 10 µm spotsize. The results of µ-XRF analyses presented in this paperconcern the experiment realized at pH 6, I ) 10-3 M, Darcyvelocity ) 0.002 cm s-1, and with an average diameter of TiO2

NP aggregates in injected suspension of 2 µm.

Results and DiscussionSalt-Induced Aggregation. When I ) 10-3 M, TiO2 NPs werevery stable both at pH 5 and pH 8, showing very little further

aggregation over a period of some 250 min. When I increased,charge screening virtually eliminates repulsive interactionsoriginating from diffuse layer repulsions between nanopar-ticles, enabling aggregation of the TiO2 suspension. Thisoccurred at a lower NaCl concentration at pH 5 than at pH8. The corresponding critical coagulation concentrations(CCC) fall in the ranges 10-3 - 10-2 M and 10-2 - 4 × 10-2

M respectively (Figures 1a and b). Moreover, the aggregationrate measured at pH 5 was always higher than that obtained

FIGURE 1. Aggregation kinetics of TiO2 nanoparticles (50 mg L-1) for different NaCl concentrations (I) at pH 5 (a) and pH 8 (b); ZetaPotential of sand and TiO2 nanoparticles vs pH in Milli-Q water (c) and vs ionic concentration at pH 8 (d).

FIGURE 2. Fraction of TiO2 NPs adsorbed to the sand in batch experiments vs pH and ionic concentration (a). Open symbolsrepresent the fraction of TiO2 settled down due to the aggregation in the absence of sand, no settling was observed for I ) 10-3 Mand 10-2 M. Breakthrough curves of TiO2 nanoparticles for different ionic concentrations (b) and for different pH (d). C/C0 is a ratio ofthe TiO2 concentrations in the effluent to the influent of the column, V/Vp is the ratio of the eluted volume to total pore volume of thecolumn. TiO2 injection starts at time 0, and ends at v. C0 ) 50 mg l-1, pH 8, Darcy velocity ) 0.002 cm s-1. Size distribution of TiO2nanoparticles in initial injected, and of aggregates eluted from the column (pH 8, I ) 4 × 10-2 M) (c).

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at pH 8 and maximum in both cases at I ) 1 M. Consideringthe aggregation regime at pH 5 and I ) 1 M as diffusionlimited, its corresponding maximum aggregation rate wasused in eq 2 (see SI) to calculate the lower attachmentefficiencies (Rpp) corresponding to other conditions. WhenpH 8, Rpp ) 0.58; 0.36 and 0.02 with I ) 1, 10-1 and 10-2 M,respectively.

Surface Charges of Nanoparticles and Sand. The �potential of the NPs ranged from +35 to -40 mV with pHfrom 3 to 9. The isoelectric point of the nanoparticles (IEPTiO2)was determined to be at pH 5.5 (Figure 1c). This value issimilar to those reported elsewhere for larger TiO2 particles(13, 31-33). Moreover, it is the causality of the faster NPaggregation observed at pH 5 compared to pH 8 (Figures 1aand b), since the lower surface charge at pH 5 favorscoagulation. At pH 8, the negative � potential of the TiO2 NPsdecreased from -40 to -13 mV when I increased from 10-4

to 1 M (Figure 1d).The sand � potential remained negative in all the pH and

I ranges studied, varying from -30 to -60 mV with pH from3 to 9 (Figure 1c), and from -55 to -45 mV for I from 10-4

to 10-2 M at pH 8 (Figure 3d), which is typical for silica (34).Batch Attachment Experiments. Figure 2a presents the

ratio of TiO2 attached to the sand for various values of pHat I ) 10-3 M, and for various ionic concentrations at pH 8.At pH 3.5, most of the TiO2 NPs were attached to the sandsurface, reflecting the charge attraction between positivelycharged NPs and negatively charged sand grains. In contrast,at pH > 6.7, no significant attachment occurred for I ) 10-3

M. However, increasing I enabled significant TiO2 attachmentat pH 8, ranging from 20 to 95% for I ) 10-2 to 5 × 10-1 M.This enabled us to define a critical salt concentration favoringattachment, CSCbatch, between 10-3 and 10-2 M NaCl atpH 8.

Attachment of Nanoparticles in Porous Media. Resultsfrom column experiments are presented as breakthroughcurves of TiO2 concentration in the effluent normalized bythe influent concentration (C/C0) as a function of elutedvolume normalized by total pore volume of the column(V/Vp).

When I < CCC (4 × 10-2 M at pH 8) the results from TiO2

salt-induced aggregation experiments suggest that aggrega-tion in the column should be negligible (Rpp ) 0.02) and thatthe retention of NPs in the column reflects interactionsbetween relatively stable NPs and the porous medium (Figure2b). The affinity of these NPs to the sand is relatively weak,with approximately 5% or less being retained in the columncorresponding to an attachment efficiency Rpc ) 0.01 or lessas calculated by eq 1 (see SI). (Note that the particleconcentration in the effluent continues to rise from porevolumes 1.5-3). This small retention is characterized by alonger delay for the nanoparticles to reach the plateauconcentration C/C0)1, compared to the conservative tracer.It may be due to a transitory step during which a certainproportion of NPs deposits onto micas minerals present astrace, or is retained in the small pores by straining effect.

When I g CCC (4 × 10-2 M), the retention of NPs in thecolumn was significant, and increased with I, reaching 65%for I ) 10-1 M (Figure 2b). Moreover, the plateau of thebreakthrough curves displayed a continuous slow decrease,characteristic of an increasing deposition. This could be dueto particle aggregation. Indeed, in addition to the high ionicconcentration favoring attachment of the NPs to collectors(Table 1), porous aggregates exhibit low drag coefficients(23) and may therefore deposit more easily.

Association of NPs with sand grains in column (5% forI ) 10-2 M, 65% for I ) 10-1 M) remained lower than in thebatch experiments (20 and 85% respectively) and the ratioof initial NP surface area to sand grain surface area wassimilar. The higher relative velocities present in the batchexperiments (e.g., mixing plus a Stokes settling velocity inthe batch experiments for sand grains of 32 cm h-1 comparedwith simple creeping flow with a Darcy velocity of 0.002 cmh-1 in the column experiments) implies more energeticcollisions between NPs and sand grains that may have beensufficient to overcome potential energy barriers and produceattachment. Moreover, in column, the NPs are mostlytransported along streamlines that do not result in contactwith sand grains.

The particle-particle attachment efficiency of 0.36 forTiO2 NPs alone in a solution at pH 8 and I ) 10-1 M isconsiderably higher than the corresponding particle-sandgrain attachment efficiencies calculated from column data.

TABLE 1. Collision Efficiency (r, Eq 1) and Interaction Energy(Φtotal, Eq 3) between TiO2 NPs and between TiO2 NPs andPorous Mediaa

experimentalconditions

r of TiO2NPs in

porous media

Φtotal TiO2-sandinteractions

at 2 nm

Φtotal TiO2-TiO2interactions

at 2 nm

pH 8, I ) 10-1 M 22.1 –2.5pH 8, I ) 4 × 10–2 M 70.6 –0.7pH 8, I ) 10–2 M 0.01 129.6 44.5pH 8, I ) 10–3 M 0.01 208.5 77.7pH 6, I ) 10–3 M 52.4 –11pH 3.6, I ) 10–3 M 0.98 –400 67.2

a Unit of energy is kT. 1kT)4.11 × 10–21 J.

FIGURE 3. Distribution of Ti (Kr line) and Si (Kr line) in frizzed column slice (256 px2 image, 1 px ) 20 µm, total counting time of9000 s). Column experimental conditions: pH 6, I ) 10-3 M, Darcy velocity ) 0.002 cm s-1

, average size of injected TiO2 aggregatesis 2 µm.

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Calculated attachment efficiencies for the column rangedfrom 0.04 (data taken at one pore volume) to 0.09 (two porevolumes). The conditions of increasing retention over timeviolate the assumptions embedded in eq 1 (see SI), but leadto an upper bound on particle-sand attachment efficiencythat is nonetheless lower than that for particle-particlecollisions. Moreover, the interaction energy calculatedbetween NPs is less repulsive than that between NP andsand at pH 8, thereby facilitating NP aggregation (Table 1).The greater affinity of NPs for one another compared withNP-collector attachment (Rpp > Rpc), even at higher ratio ofcollector surface to NP surface (about 40) suggests that therate of particle aggregation within pores was likely compa-rable to that of deposition in altering NP concentrationsthrough the column.

A hydraulic shock associated with the stoppage of NPfeed produced a burst of NPs in the column effluent at V/Vp

) 2.3 for the case of I ) 10-1 M (Figure 2b). Subsequentclearance of NPs from the column pore water in this case,as in the case of I ) 4 × 10-2 M, was more rapid than in thecases where aggregation may not have been favored. In thesecases, the average size of TiO2 NP aggregates eluted from thecolumn was much larger than that in the influent solution(Figure 2c) indicating aggregation in the column.

The influence of pH on the NP retention in the columnwas studied in the range from 3 to 8 (Figure 2d). The retentionof NPs in the column was nearly complete at pH 3.6 (99%)where collectors and NPs presented opposite surface charges.This observation is consistent with the observations of NPattachment to sand grains in the suspended batch system.In contrast, retention at pH 8 where particles and collectorsurfaces were both negatively charged was only 5%. Thesesvalues yield calculated attachment efficiencies (eq 1) of 0.98and 0.01 respectively and are in agreement with totalinteraction energies that were calculated to be highlyattractive or repulsive (beyond the primary minimumdistance) (Table 1). At pH 6, a high retention of TiO2 wasmeasured in the column (78%) corresponding to a muchreduced energy barrier as calculated by DLVO. The clearanceof NP from the pore volume in the column at pH 6 was alsomuch more rapid than at pH 8. Micro X-ray fluorescencespectroscopy (µ-XRF) images of retained TiO2 in the columnunder these conditions of pH and ionic concentrationrevealed the presence of TiO2 in large deposits, roughly80-120 µm in diameter and randomly distributed throughoutthe porous media (Figure 3). The more favorable NP-NPattachment efficiency implies that previously deposited TiO2

particles and aggregates will be preferential sites for sub-sequent deposition, leading to these larger patchy deposits.

A more rapid clearance of NPs in the pore space of thecolumn coincides with conditions that favor NP aggregationand is attributed to two phenomena. First, aggregationenhances NP deposition as it produces objects that are lesssubject to hydrodynamic retardation that otherwise occurswhen streamlines are compressed as particles approachsurfaces. Second, those aggregates that are not removed willsample a smaller portion of the available pore network withinthe column due to size exclusion. Therefore, those aggregatesthat do not attach to the sand will be more rapidly clearedfrom the column.

In an environmental context like aquifers, this may havesubstantial consequences since it appears that nanoparticletransfer is not only driven by their interaction with the porousmedium. Indeed, according to their mutual interactions,aggregating nanoparticles will deposit in a higher extent inpore spaces, but will also migrate more rapidly throughpreferential pathways toward farther end points. Suchaggregation effect stands even more determining in realenvironment, where industrial functionalization of themanufactured nanoparticles or interaction with natural

organic matter often induce new surface properties anddispersion behavior, which strongly alter their potentialexposure and hazard (35, 36).

AcknowledgmentsThis work was founded by French National Agency ofResearch (grant number: PNano ANR-07-NANO-035) and isbased in part upon work supported by the National ScienceFoundation and the Environmental Protection Agency underNSF Cooperative Agreement Number EF-0830093, Centerfor the Environmental Implications of NanoTechnology(CEINT). We gratefully thank Dr. L. Cary for the surfacecharacterisation of the sand and NPs by BET analyses, Dr.S. Sczeknect for her help in measuring the pore sizedistribution in the porous media, and Dr. A. Masion for fruit-ful discussions.

Supporting Information AvailableSize distribution (a) of the dispersed sand; X-ray diffractionpattern (b), SEM image (c) and pore size distribution (d) ofthe sand packed as the porous media (Figure S1). X-raydiffraction pattern (a) and size distribution (DLS) (b) of theTiO2 nanoparticles dispersed in aqueous suspension (FigureS2). Column experiments. Determination of attachmentefficiency (R). Determination of Total Interaction Energy.This material is available free of charge via the Internet athttp://pubs.acs.org.

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