Thermal Field-Flow Fractionation of Charged Submicrometer Particles

Anal. Chem. 2007, 79, 5284-5296

Thermal Field-Flow Fractionation of Charged Submicrometer Particles in Aqueous Media Luisa Pasti, Sara Agnolet, and Francesco Dondi*

Department of Chemistry, L.A.R.A., University of Ferrara, Via L. Borsari, 46 44100 Ferrara, Italy

Thermal field-flow fractionation (ThFFF) of various types of submicrometer silica particles in aqueous media is experimentally investigated under an extended range of medium ionic strengths with and without the presence of surfactant. The experiments were designed to examine the applicability to submicrometer particles of the theory of charged nanoparticles thermodiffusion recently proposed by Parola and Piazza (Parola, A.; Piazza, R. Eur. Phys. J. E. 2004, 15, 255-263). In particular, the expression for the calibration function in terms of particle radius and channel temperature is derived and experimentally verified. Moreover, retention is expected to be dependent on particle surface potential and charge, and on ionic strength. These dependences are experimentally investigated and the pertinent relationships and correlations derived. The effect of heavy metal adsorption on the silica surface was investigated, and significant ThFFF retention changes were measured. Independent measurements of the zeta potential (ζ-potential) indicated that a decrease in the surface charge of a silica particle is a consequence of heavy metal adsorption, which is, in turn, correlated to the observed decrease in ThFFF retention. Thermal field-flow fractionation (ThFFF) belongs to the FFF family of techniques, where retention occurs as a result of an externally applied thermal gradient, i.e., by thermodiffusion. In the past, ThFFF has been applied to characterization of both dissolved macromolecules and colloidal particles suspended in both aqueous and nonaqueous carriers.2-12 However, extended work has mainly been focused on exploiting the capabilities of * To whom correspondence should be addressed. E-mail: [email protected]. Tel: +39 0532 29115. Fax: +390532240709. (1) Parola, A.; Piazza, R. Eur. Phys. J. E. 2004, 15, 255-263. (2) Giddings, J. C.; Shiundu, P. M.; Semenov, S. N. J. Colloid Interface Sci. 1995, 176, 454-458. (3) Mes, E. P. C.; Tijssen, R.; Kok, Th W. J. Chromatogr., A 2001, 907, 201209. (4) Ragazzetti, A.; Hoyos, M.; Martin, M. Anal. Chem. 2004, 76, 5787-5798. (5) Jeon, S. J.; Schimpf, M. E.; Nyborg, A. Anal. Chem. 1997, 69, 3442-3450. (6) Nguyen, M.; Beckett, R. Anal. Chem. 2004, 76 (8), 2382-2386. (7) Liu, G.; Giddings, J. C. Chromatographia 1992, 34, 483-492. (8) Shiundu, P. M.; Giddings, J. C. J. Chromatogr. 1995, 715, 117-126. (9) Ratanathanawongs, S. K.; Shiundu, P. M.; Giddings, J. C. Colloids Surf. A: Physicochem. Eng. Aspects 1995, 105, 243-250. (10) Mes, E. P. C.; Kok, W. Th.; Tijssen, R. Chromatographia 2001, 53, 697703. (11) Shiundu, P. M.; Munguti, S. M.; Ratanathanawongs Williams, S. K. J. Chromatogr., A 2003, 983, 163-176. (12) Shiundu, P. M.; Williams, K. R. ACS Symp. Ser. 2004, 881 (Chapter 12).

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ThFFF in macromolecule characterization. Such work has led to significant achievements, proving that the capabilities of ThFFF offer specific advantages over those of size exclusion chromatography (SEC):13 (i) ThFFF is a so-called “universal” molecular weight calibration technique because, once the calibration function is available, it does not need to be renewed for a specific separation channel calibration; (ii) it is recommended for ultrahigh molecular weight characterization since shear stresses that can degrade the sample are minimized with respect to SEC; (iii) it can be applied under high-temperature conditions for samples that are particularly difficult to dissolve. On the contrary, to date there have only been a few ThFFF studies of colloidal particles and they do not as yet permit any clear-cut conclusions regarding the effective capability of ThFFF as an analytical technique for colloidal particles. Today there is significant interest in the potential of separation by thermophoresis and as witnessed by the recent increase in the number of articles dealing with the thermodiffusion studies of nanoparticle systems. In these articles, different particles have been studied: biological macromolecules,14 ferrocolloids,15 sodium dodecyl sulfate micelles,16 latex spheres,17-19 and silica particles.19 One reason for the renewed interest in thermophoresis is related to the advances in nanoscience applications. In fact, thermodiffusion is gaining relevance versus other forces that act on colloidal particles (e.g., gravitational force) solely when the colloidal dimension is in the nanoscale dimensional range. The interest in particle thermophoresis is likewise relevant for environmental studies. For instance, colloids are known to be significant in natural waters since metal oxides (Al, Fe, and Si) and clay colloids play a key role in regulating water composition.20 Besides the above-mentioned interest in particle thermophoresis, significant advancements have recently been attained in thermodiffusion theory. Most relevant is the Parola and Piazza thermodiffusion theory (PPTT), which proved that the Soret (13) Giddings, J. C. In Size Exclusion Chromatography; Hunt, J. C., Holding, S., Eds.; Blackie and Son: Glasgow, 1989; pp 191-216. (14) Braun, D.; Libchaber, A. Phys. Biol. 2004, 1, P1-P8. (15) Blumsa, E.; Mezulisa, A.; Buskeb, N.; Maiorov, M. J. Magn. Magn. Mater. 2002, 252, 215-217. (16) Piazza, R.; Guarino, A. Phys. Rev. Lett. 2002, 88 (20), 208302(1-4). (17) Putnam, S. A.; Cahill D. G. Langmuir 2005, 21 (12), 5317-5323. (18) Jancˇa, J.; Berneron, J-F.; Boutin, R. J. Colloid Interface Sci. 2003, 260, 317323. (19) Shiundu, P. M.; Munguti, S. M.; Ratanathanawongs Williams, S. K. J. Chromatogr., A 2003, 984, 67-79. (20) Stumm, W.; Morgan, J. J. Aquatic Chemistry: An Introduction Emphasizing Chemical Equilibria in Natural Waters; John Wiley & Sons: New York, 1981; Chapter 10 10.1021/ac070099t CCC: $37.00

© 2007 American Chemical Society Published on Web 06/13/2007

coefficient (see in the following) of charged nanoparticles in aqueous media depends on the particle radius and on the square of its surface potential.1 Since it is known that, in ThFFF, retention is proportional to the Soret coefficient,21,24 these results can be potentially transferred to ThFFF. These achievements thus open new opportunities for ThFFF both as an analytical and a physicochemical characterization technique in a field that it is as “hot” as the current one. It should be recalled that the theory developed by Giddings et al.2 to model ThFFF retention of metal particles predicts that surface potential distribution plays an important role in the thermodiffusion process. Both PPTT and Giddings’ theory assume that when a thermal gradient is applied, a force is generated by the interaction of the anisotropic thermal gradient (applied along one dimension) with the colloid interface field force having spherical symmetry (under the hypothesis of spherical colloidal particles). In both theories, the generated force is the only thing responsible for thermophoretic motion. The main difference is that in PPTT the interaction between particle surface potential and ionic aqueous solution composition is analytically derived, whereas in Giddings’ theoretical handling, a general expression of thermophoretic velocity depending on only one kind of ion or molecule was obtained. As an analytical technique for charged particle characterization, from PPTT we know that ThFFF retention is driven by both colloidal particle size and by the surface potential. The latter depends on specific particle/solution interactions, which are, in turn, related to the chemical composition of both particle and solution. ThFFF can thus be potentially employed to characterize colloidal particles not only on the basis of their sizesas do, for example, sedimentation FFF or flow FFFsbut also on the basis of their chemical surface composition and physicochemical features, e.g., ζ-potential/electrophoretic mobility, surface charge, and adsorptive properties. Moreover, the well-known capability of FFF techniques in exploiting phoretic processes22 can be useful in exploiting the process of thermophoresis itself, i.e., for physicochemical studies. With reference to this general point, one must recall that mass transport in a temperature gradient is characterized by the thermodiffusion coefficient DT or by the Soret coefficient, which is the ratio of DT to the diffusion coefficient D, ST ) DT/D. These parameters can be evaluated by FFF techniques. In particular, the advantage of FFF in physicochemical studies is that it requires a minimum-sized sample and offers great flexibility in exploring the conditions of the medium (ionic strength, pH, carrier composition, temperature).23 The role of the particle chemical composition on thermal diffusion has been experimentally evaluated and theoretically interpreted using ThFFF for polymers24 and suspended particles.1,18 As regards the behavior in aqueous media, most of the experiments were performed in diluted solutions of FL-70,5,8,12 a commercial product made up of a mixture of surfactants and other (21) Schimpf, M. E.; Semenov, S. N. J. Phys. Chem. B 2000, 104 (42), 99359942. (22) Schimpf, M. In Field-Flow Fractionation Handbook; Schimpf, M., Caldwell, K., Giddings, J. C., Eds.; Wiley-Interscience: New York, 2000; pp 239-256. (23) Dondi, F.; Martin, M. In Field-Flow Fractionation Handbook; Schimpf, M., Caldwell, K., Giddings, J. C., Eds.; Wiley-Interscience: New York, 2000; pp 103-132. (24) Schimpf, M. E.; Semenov, S. N. J. Phys. Chem. B 2001, 105 (12), 22852290.

chemicals.25 For example, a systematic study of how the chemical composition of the colloidal system (particle in a given medium) affects particle surface, solvent ionic strength, pH, and buffer composition has been performed in FL-70.5 However, the role FL70 plays in determining colloidal stability is rather obscure, and consequently, the conclusions that can be drawn from these studies regarding the various aspects of the thermophoretic behavior and retention mechanisms of ThFFF are necessary limited. The aim of this work is to exploit the ThFFF technique in the analysis of submicrometer particle suspensions in an aqueous carrier in light of PPTT.1 In particular, the ThFFF of various types of submicrometer silica particles in an aqueous medium of controlled ionic strength will be investigated as a function of the applied temperature gradient. Qualitative and quantitative effects of specific adsorption processes on the silica particle surface will be exploited. This study has a dual purpose: (i) to explore new opportunities for colloidal separation by ThFFF and (ii) to exploit the capabilities of the ThFFF technique itself in investigating the thermophoretic process of charged colloidal species in aqueous media. THEORY Fundamentals of Thermophoresis. In ThFFF, the driving force for separation is the thermodiffusion process.26 The thermophoretic velocity is proportional to the temperature gradient, dT/dx, along the cross section of the separation channel:

u ) DT (dT/dx)

(1)

where DT is the thermal diffusion coefficient. If diffusion in combination with thermophoresis is considered, one has

J ) - D∇c - cDT∇T

(2)

where J (mol cm-2 s-1) is the flux, D (cm2 s-1) the diffusion coefficient, DT (cm2 s-1 K-1) the thermal diffusion coefficient, T the temperature, and c the concentration. ∇ is the symbol for the pertinent gradient. In the steady-state condition, i.e., for J ) 0, by assuming that the thermal gradient is applied along the x direction, from eq 2 one gets

dc dT ) - cST dx dx

(3)

ST ) DT/D

(4)

where

is the Soret coefficient. A phoretic velocity u is associated with a viscous force Fγ exerted by the medium: (25) http://www2.siri.org/msds/f2/cgk/cgkst.html. (26) Giddings, J. C. Science 1993, 260, 1456-1465.

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u ) Fγ/γ

(5)

where γ is the friction coefficient, which is related to the ordinary diffusion coefficient by the Stokes-Einstein equation:27

γD ) kBT

(6)

where kB is the Boltzmann constant. A generalized force, responsible for the observed effect, can be associated with the phoretic velocity. In the present case, one will have the thermophoretic force FT. Under constant u conditions, FT and Fy balance each other out,27 i.e.

FT ) Fy

(7)

By combining eqs 1 and 5-7, one obtains

FT ) kBTST (dT/dx)

1 ST(dT/dx)w

1 |ST|(dT/dx)w

(9a)

(9b)

With ThFFF alone it is thus not possible to determine the sign of the Soret coefficient, e.g., whether the thermophoresis is positives with migration toward the hot wallsor negative in the opposite case. Equations 9a and 9b hold true in an infinitesimal layer thickness, dx, located at value x and vertical coordinate (0 e x e (27) Giddings, J. C. In Unified Separation Science; Wiley: New York, 1991. (28) Martin, M.; Van, Batten, C.; Hoyos, M. Anal. Chem. 1997, 69, 1339-1346.

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()

(10)

which gives a precise meaning to λ. The fundamental retention parameter employed in FFF is the retention ratio, R, a dimensionless parameter defined27 as the ratio of the average cross-sectional mean velocity of the analyte and the cross-sectional average of the carrier liquid velocity. In ThFFF, R is related to λ as

(8)

Due to the channel symmetry, eq 9 refers to the absolute values of ST:

λ)

1 x dc )- d c λ w

R(λ, ν) )

Equation 8 states that the ratio between the force (FT) induced by the thermal gradient (dT/dx) and the thermal energy (kBT) is proportional to the thermal gradient applied itself, and the proportionality constant is the Soret coefficient. Equation 8 relates the Soret coefficent to FT: thus, eq 8 makes it possible to evaluate ST once the force is known. ThFFF Theory. The ThFFF separation system is made up of a flat ribbon-like channel, free of any packing material, obtained by placing a trimming spacer between two flat bars kept at different temperatures: TH (at the upper wall) and TC (at the lower wall),28 with ∆T ) TH - TC. The thickness of the spacer defines the channel thickness w. Inside the channel, the flow of solvent carrier follows a distorted, parabolic flow profile because of the changing values of the carrier properties along the channel thickness (density, F; viscosity, η; thermal conductivity, kc). In the channel cross section, the thermodiffusion process pushes the analyte toward the so-called accumulation wall, usually the cold wall; the combination of the flow profile and thermodiffusion produces the fractionation. In ThFFF, the λ parameter is defined as27

λ)

w). The temperature does not change significantly within this dx layer located in the x position; moreover, here D and DT or FT (see eqs 4 and 8) are constants and referred to this temperature value. The λ parameter associated with eqs 9 expresses the relative concentration change induced by the thermal gradient:28

1 V - 2λ ) 6λ ν + (1 - 6λν) coth 2λ 〈v〉

(

( ( )

))

(11)

where ν is a computable parameter29 related to the changes that occur in carrier viscosity and thermal conductivity within the channel cross section; it accounts for the distortion in the ideal parabolic flow profile within the channel. The ν parameter roughly expresses the relative changes in the slope of the flow velocity profile at x ) 0. Reference 29 reports full specific handling of the matter. The retention ratio R can be evaluated by the experimental quantity Rexp:

Rexp ) ht 0/thR

(12)

where ht0 and htR are respectively the first moments of an unretained compound and of the analyte peak profile (corrected for the connection dead times). By equating eqs 11 and 12 one has

ht 0 ht R

(

( (2λ1 ) - 2λ)) ) 0

- 6λ ν + (1 - 6λν) coth

(13)

λ can be obtained as the solution of eq 13 provided that ν is computed. The ThFFF λ parameter, determined by solving eq 13, is associated with a well-defined value of x, the so-called equivalent position xeq, where the quantities (D/DT), FT, the local temperature T, and the local gradient (dT/dx) assume well-defined values, (D/DT)eq, Teq, (FT)eq, and (dT/dx)eq, respectively.28 ThFFF Calibration Curves. In this section, the calibration curves for charged particles in an aqueous media are derived in ThFFF. For the sake of comparison, the derivation of the polymer calibration curves is recalled. Equation 9b under linear and constant thermal gradient becomes

λ∆T ) 1/|ST|

(14)

(29) Martin, M. In Advances in Chromatography; Brown, J. C., Grushka, E., Eds.; Marcel Dekker: New York, 1998; Vol. 39, pp 1-138.

In polymer solution, eq 4 is considered, with D expressed by the Mark-Houwink equation.6

D ) aM

b

(16)

By introducing eq 16 into eq 14 and taking the logarithm one obtains

log(λ∆T) ) c0 + c1 logM

d log T r 2 ψ dx 8 s

(18)

where ψs is the surface potential of a particle of radius r and  the carrier dielectric constant. Equation 18 was obtained adopting the Debye-Hu¨ckel (DH) approximation in describing how a charged particle interacts in ionic solutions (eq 18 holds true inside the validity domain of the DH approximation). Consequently, in the case of charged nanoparticles, eq 18 plays the same role as the Mark-Houwink equation and as the assumption that DT is independent of M for the polymer solutions. By substituting eq 18 in eq 8, the expression of the PPTT Soret coefficient is obtained:1

ST ) (r/kBT2)ψs2

(20)

where Zq is the particle charge, Z being the number of charged sites and q the elementary charge unit, and κ is the Debye-Hu¨ckel parameter; i.e., it is the reciprocal of the so-called thickness of the double layer, which can by calculated by31

κ ) (2q2/kBT)1/2 xI

(21)

where I is the ionic strength (I ) 1/2 ∑i cizi2), ci is the concentration of ion i, having valence zi. By substituting eq 19 in eq 14, and after logarithmic transformation, one has the calibration curve for charged colloids:

log(λ∆T) ) c0 + c1 logr + c2 logψs + c3 logT (22a)

(17)

which is the classical calibration curve used for the polymer characterization6,30 that holds true at constant TC value. c0 and c1 are calibration constants related to DT. Alternative forms of eq 17 are reported in the literature.30 It should also be recalled that nonideal solution behavior due to concentration effects can affect the transport diffusion coefficients (eq 2), and thus, in the experimental determination of the calibration curve, care must be taken as regards the amount of the injected sample. In fact, ThFFF is known to be sensitive to overloading effects. For charged particles, the Soret coefficient can be obtained from eq 8 instead of eq 4. In PPTT,1 the expression for the generalized force due to a thermal gradient acting on the charged colloid in an electrolytic medium was obtained:

FT ) -

ψs ) Zq/[r(1 + κr)]

(15)

where a and b are constants that depend on the particular polymer/solvent system and on the temperature, but which are independent of M, the molecular weight of the polymer. DT is assumed to be independent of M. Thus, by combining eqs 14, 4, and 15, one has

ST ) DT/aMb

The surface potential, in turn is given by

(19)

Note that all the terms in eq 19 are positive, and thus, this relationship is not able to evaluate the sign of the thermophoretic effect; moreover, eq 19 holds true in DH approximation domain and thus for small particles of moderate charge. (30) Pasti, L.; Bedani, F.; Contado, C.; Mingozzi, I.; Dondi, F. Anal.Chem. 2004, 76, 6665-6680.

where the theoretical coefficients are c1 ) -1, c2 ) -2, and c3 ) 2 and c0 is the ST value at a given reference state of the system (temperature, etc.). Under the constant ψs hypothesis, see discussion below, one has

log(λ∆T) ) c′0 + c1 logr + c3 logT

ψs constant (22b)

where c′0 ) c0 + c2 log ψs. For ψs and T constant, one has

log(λ∆T) ) c′′0 + c1 logr

ψs, T constant

(22c)

where c′′0 ) c0 + c2 logψS + c3 logT. By using the experimental calibration plots based on eqs 22b and 22c, the relations between λ∆T and r are determined and the knowledge of ψs is prevented. It must be underlined that eqs 22a-c were derived under the assumption that the sole field force acting in the ThFFF process is the thermophoretic one, (i.e. FT). Finally, one should remember that ψs can be, in first approximation, assumed to be related to zeta-potential (ζ):32

ζ ≈ Cψs

(23)

and thus the ζ-potential can be correlated to ST, as is seen when one combines eqs 19 and 23. As previously mentioned (see eqs 18 and 19), PPTT is rigorous in a well-defined domain; however, eqs 22 a-c can be used as starting point to estimate semiempirical ThFFF calibration curves. EXPERIMENTAL SECTION The ThFFF system was a model TF3 Polymer Fractionator (Postnova Analytics GmbH, Landsberg, Germany) described in refs 30 and 33. Channel dimensions were as follows: length 45.6 cm tip-to-tip, width 1.9 cm, and thickness 0.0127 cm obtained from a polyimide sheet, sandwiched between two chrome-plated copper (31) Everett, D. H. In Basic Principles of Colloid Science; Royal Society of Chemistry Paperbacks: London, 1988; Chapters 1-3. (32) Hunter, R. J. Zeta Potential in Colloid Science: Principles and Applications; Academic Press: London, 1988.

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bars clamped together. The coolant liquid was tap water. The void volume at room temperature was calculated from the retention time of an unretained solute in the absence of an applied field (sodium benzoate, Fluka Chemie, Buchs, Switzerland) and was 1.08 ( 0.04 mL (30 data points): this value agrees with the geometrical value of 1.05 mL. The carrier flow rates (F) were measured at room temperature (23-25 °C). Carrier flow was generated by a model 420 pump (Kontron Instruments S.p.A.) operating at a flow rate of 0.301 mL min-1. The carrier was MilliQ water (Millipore). The pH values were obtained by addition of KOH (Fluka Chemie) 0.01 M. The ionic strength was modified by using KNO3 (Fluka Chemie). The monodisperse particle standards of silica of nominal radii 50, 100, 150, and 175 nm, silica coated with carboxylic groups (Si-COOH) (nominal radius 100 nm) and polystyrene (PS) of nominal radius 150 nm were provided by the manufacturer (Gerlinder Kisker). A 20-µL loop was used to inject the standards into the ThFFF system by means of a model 7725i Rheodyne (Cotati, CA) valve. The flow was stopped for 30 s after injection with a Valco (Huston, TX) valve to relax the sample inside the channel. The detector was a UV model 106 (Linear Instrument Corp., Reno, NV) used at a fixed wavelength, 254 nm. Data handling of both ThFFF output and ThFFF temperature control were performed by NOVAFFF TF3 Control release 2.0 (Postnova Analytics GmbH, Landsberg, Germany) run on a PC equipped with an I/O acquisition board model NI-6034E (National Instruments, Austin, TX). The maximum of 1200 data points was obtained as a product of data rate and run time. The experimental fractograms and the relative TC and ∆T values were acquired at a data rate of 10 points min-1. The concentration of the particle suspensions injected in the ThFFF system was 0.1% w/v in carrier (injected quantities were 20 µg). The samples were prepared at room temperature and sonicated for 5 min before injection. The solutions for the specific sorption experiments were obtained by adding to the particle dispersions the proper volume of concentrated solution, prepared by dissolving Ni(NO3)2 and Co(NO3)2 (Fluka Chemie) in MilliQ water. In the present work, standard ThFFF operative conditions for ∆T and TC values were chosen, compatible with the employed coolant liquid (tap water). TH e 90 °C was employed in order to prevent sample coagulation. The elemental determinations were performed by electrothermal atomic absorption spectrometry (ETAAS) with a model AAnalist 800 Perkin-Elmer spectrometer, equipped with a THGA graphite furnace (Perkin-Elmer). Pyrolytically graphite-coated tubes were used with an autosampler AS800 (Perkin-Elmer, Italy) injecting 20 µL of sample. Calibration lines were built up by using standard solutions (50, 100, 500, 1000 ppb) freshly prepared by dilution of BDH (Dorset, UK). The 1000 mg L-1 nickel with Milli-Q water acidified with HNO3 was used. The ETAAS instrumental temperatures and hold times (ht) setting were as follows: drying T ) 403 K, ht ) 30 s; ashing 1373 K, ht ) 20 s; atomization 2573 K, ht ) 5 s; and cleanup 2723 K, ht ) 3 s. The nickel absorbance signals was measured at wavelength 232.0 nm by using a slit width of 0.2 nm, during the atomization step. The flow rate of internal gas (Ar) was 250 mL min-1. The electrophoretic mobility of freshly prepared dispersions was determined using laser Doppler electrophoresis, namely, a Zetasizer Nano Series (Malvern Instrument Worcestershire, UK) 5288

Analytical Chemistry, Vol. 79, No. 14, July 15, 2007

instrument. In determining the electrophoretic properties, the particle solutions described above for FFF measurements were diluted 1:100 with a low ionic strength solution (e.g., KNO3 1 mM in Milli-Q water at pH 9). COMPUTATION The computations were performed with Matlab release 5.3 using our own programs. The computation involving the dependence of solvent physical-chemical properties (the coefficients of fluidity (1/η) ) d0 + d1T + d2T2 + d3T3 d0 ) 5.57 cP-1; d1 )1.95 × 10-3 cP-1 K-1; d2 )1.32 × 10-3 cP-1 K-2; d3 ) 3.39 × 10-6 cP-1 K-3; thermal conductivity3 kc,T ) q0 + q1 (T - 298.15), q0 ) 6.07 × 104 erg cm-1 s-1 K-1; q1 ) -10.7 erg cm-1 s-1 K-2) were performed to obtain the ν values for any given TC and ∆T values by using the algorithms reported in the literature.29 Recorded fractograms were used to evaluate the retention time from the peak barycenter. The λ values were obtained from htR, ht0, and ν data, using the routine Matlab FZERO to find the root of a function (see eq 13). RESULTS AND DISCUSSION Equation 19 is the basic expression of the PPTT giving the Soret coefficient value for a charged nanoparticle. Consequently, on the basis of eqs 13, 14, and 19, one can expect ThFFF retention to be dependent on the field strength ∆T, on the particle radius r, and on the particle surface potential ψs in an aqueous medium. More precisely, eqs 22a, b, and c predict a bilogarithmic calibration curve versus r and the channel temperature. In addition, the PPTT should be able to describe the effect the ionic strength has on ThFFF retention, by using eqs 19-21. Moreover, since the Soret coefficient is affected by ψs, ThFFF should detect any physicochemical effect able to modify ψs, e.g., the surface adsorption, as a change in retention and thus interpret it according to the theory. Finally, it is observed that ST is related to the particle charge Zq (see eqs 19 and 20). Consequently, any other measurable chargerelated property of the particle, e.g., the ζ-potential (see eqs 20 and 23), should in turn be correlated to ST. These points were exploited for submicrometer particles where PPTT is not rigorously valid1 (see eqs 18 and 19), and the results are reported below. Effect of Thermal Field. As previously mentioned, the driving force behind ThFFF separation is thermophoresis, which is induced by an applied thermal gradient. Figure 1 reports the fractograms obtained at various ∆T values for particles that differ in both size and composition. It can be seen that the retention time increases as ∆T increases. This behavior agrees with data in the literature obtained with an aqueous carrier modified with FL-70.5 Table 1 reports the retention data of the fractograms of Figure 1. It can be seen that the λ∆T values (related to Soret coefficient by eq 14) are almost constant for PS particles. Significant differences are instead noted for the other particles (i.e., Si and SiCOOH). Clear-cut conclusions regarding the constancy of the λ∆T values, i.e., of the Soret coefficients (see eq 14), are hindered by the limited number of points (three) and by experimental error in determining htR values of retention profiles which, in certain cases, were close to the void time. The low retention ratios observed even at modest thermal gradients (see Figure 1), and thus at moderate force fields (see eq 8), confirm that a thermophoretic separation mechanism is

Figure 2. Fractograms of Si particles of different radius. Carrier: KNO3 3 mM aqueous solution, pH 9; F ) 0.304 mL min-1; TC ) 308 K; ∆T ) 30 K. Table 2. Retention Parameters of Si Particles of Different Radiusa

Figure 1. Elution profiles obtained at various thermal gradients Carrier: KNO3 3 mM aqueous solution pH 9, F ) 0.304 mL min-1. (a) Si particle r ) 150 nm. (b) Si-COOH particle r ) 100 nm. Table 1. ThFFF Retention Data Obtained at Various Thermal Gradients ∆Ta sample PS r ) 150 nm

∆T TC htR (K) (K) (min)

λ

log(λ∆T)

ST (K-1) 1.466 1.543 1.529 1.521

295 298 299 305

0.0682 0.0432 0.0327 0.0263

-0.1732 -0.1822 -0.1839 -0.1821

Si r ) 150 nm

21 30 40

301 9.28 0.0863 308 15.88 0.0464 312 27.07 0.0284

0.2582 0.1436 0.0661

0.5518 0.7184 0.8588

Si-COOH r ) 100 nm

10 20 25 30

299 4.8 313 8.5 314 10.2 316 14.3

0.4363 0.2953 0.2730 0.2159

0.3661 0.5065 0.5333 0.6082

0.2731 0.0987 0.0750 0.0548

a Carrier, KNO 3 mM aqueous solution pH 9, F ) 0.304 mL min-1 3 of PS particle r )150 nm, Si particle r ) 150 nm, and Si-COOH particle r ) 100 nm.

acting. This can be expressed in terms of a thermophoretic force acting on the particles and by comparing it to the gravitational force. From the experimental data, it is possible to evaluate ST (see eq 14), and thus, using eq 8, it is possible to obtain FT. For a particle having a radius of 50 nm, under conditions of T ) 300 K, ST ) 0.2 K-1, w ) 0.0127 cm, ∆T ) 25 K, ∆T/w ) 1968 K cm-1, one obtains FT ) 2 × 10-11 dyn. The gravitational force is given by

FG ) (4/3)πr3 ∆FG

∆T (K)

TC (K)

htR (min)

λ

ST (K-1)

50 100 150 175 50 100 150 175 50 100 150 175

20 20 21 21 30 30 30 30 40 40 40 41

301 301 301 301 308 308 308 308 314 314 312 314

5.15 5.81 9.28 10.47 6.02 9.31 15.88 17.32 8.44 14.78 27.07 28.06

0.2522 0.1433 0.0863 0.0725 0.1415 0.0772 0.0464 0.0389 0.0903 0.0476 0.0284 0.0265

0.1914 0.3388 0.5518 0.6587 0.2240 0.4331 0.7184 0.8472 0.2767 0.5180 0.8588 0.8867

a Carrier, aqueous solution KNO 3 mM, pH 9, F ) 0.304 mL min-1, 3 TC ) 308 K ∆T ) 30 K.

10 15 20 25

11.41 17.37 24.56 31.62

r (nm)

(24)

where ∆F is the differential density between the carrier and the particle and G the acceleration gravity. For ∆F ) 1.5 g cm-1 (silica particle in an aqueous media), and G ) 1000 cm s-2, one obtains FG ) 7.8 × 10-13 dyn. It is evident that, in this case, the thermophoretic force is predominant and the observed retention is related to this force. Instead, for particles greater than 50 nm, e.g., r ) 175 nm and under moderate ∆T values, e.g., for ∆T ) 30 K (as it is the case of the last fractogram of Figure 2). one has FT ) 8.7 × 10-11 dyn and FG ) 3.3 × 10-11 dyn, which is still lower than FT component, even if not negligible with respect to it. To decompose the two component forces would require specific experimental design, changing channel orientation. This investigation was not followed in this first work. In any case, relevance of the point will be considered in the following. Effect of Particle Radius. The effect particle radius has on retention was evaluated by using standards of known nominal size. Si particles in aqueous solution of KNO3 3 mM, pH 9, were employed. The resulting fractograms obtained at ∆T ) 30 K and TC ) 308 K are shown in Figure 2, and the retention parameters reported in Table 2. It can be observed that retention increases as particle diameter increases. To model the radius retention, it was assumed that all Si particles have the same ψs values, (see below) and that the sole acting force is the thermophoretic one (eqs 14 and 18) or, more precisely that FT . FG. Consequently, eq 22c was employed. Analytical Chemistry, Vol. 79, No. 14, July 15, 2007

5289

Table 3. Calibration Coefficients Estimated from the Data Reported in Table 2a ∆T

eq

c′′0(22c) or c′0(22b)

c1

20 30 40

22c 22c 22c

2.32 ( 0.11 2.31 ( 0.14 2.38 ( 0.12

-0.97 ( 0.058 -0.96 ( 0.062 -1.0 ( 0.061

λ∆T(-FG)

20 30 40

22c 22c 22c

0.7 ( 0.55 2.0 ( 0.15 2.0 ( 0.12

-0.00 ( 0.27 -0.78 ( 0.065 -0.83 ( 0.061

λ∆T(+ FG)

20 30 40

22c 22c 22c

3.1 ( 0.25 2.9 ( 0.14 2.6 ( 0.12

-1.38 ( 0.12 -1.33 ( 0.062 -1.17 ( 0.065

30-40 30-40 30-40

22b (T ) Tav) 22b (T ) TH) 22b (T ) TC)

9.41 ( 0.21 8.97 ( 0.28 9.66 ( 0.23

-0.98 ( 0.091 -1.0 ( 0.11 -0.98 ( 0.097

experimentalλ∆T

experimentalλ∆T

a

c3

-2.8 ( 0.68 -2.6 ( 0.73 -2.9 ( 0.71

Experimental λ∆T data were increased or decreased by the effect of FG and reported as λ∆T(-FG) and λ∆T(+ FG), respectively (see text).

The eq 22c linear fit regression parameters for the experimental retention data versus particle nominal radius are given in Table 3 and shown in Figure 3a. For all exploited thermal gradients, the slopes of the regression line fall within the confidence interval of -1 (95% of probability), as predicted by eq 22c. According to eq 19, the Soret coefficient can be assumed proportional to the particle radius provided the surface potential of the particle is constant. This last assumption (i.e., ψs ) constant) requires two hypotheses: that (1) the surface charge density (σ) is constant and (2) the ionic strength of the solution is sufficiently high (i.e., term κr > 1). In fact, under such conditions, from eq 20 one can write

ψs )

Zq 4σπr2 4σπ ) ≈ κ r(1 + κr) r(1 + κr)

(25)

remembering that 4πr2 is the particle surface, assumed spherical, and that σ ) Zq/4πr2 is the surface charge. The experimental verification of the above, in reference to the first hypothesis, requires specific measurements. However, the validity of this hypothesis is assured by the manufacturer and it was thus accepted. On the contrary, the second hypothesis (i.e., term κr > 1) can easily be verifiable at a given electrolyte concentration, by using eq 21: for 3 mM KNO3 at T ) 300 K, for a particle having a radius of 100 nm, one has κr ) 18, e.g., the approximation error if (1 + κr) ≈ κr is assumed to be ∼5%. The relevance of the above-mentioned hypothesis of FT . FG with respect the observed correlation between log λ∆T data versus log r (eq 22c) must be checked in order to be sure that what observed is to be correctly interpreted according to PPTT. A simulation procedure was followed, which consisted of computing theoretical λ∆T data free of a FG contribution, by remembering also that one does not know a priori the relative signs of FG and of FT. Consequently, experimental λ∆T data were increased or decreased by the effect of FG (eq 24), by using eqs 8 and 14, and by assuming dT/dx ) ∆T/w. These new sets of λ∆T data were reprocessed according to eq 22c and the results reported under λ∆T(-FG) and λ∆T(+ FG), respectively, in Table 3. One can verify 5290

Analytical Chemistry, Vol. 79, No. 14, July 15, 2007

that the c1 values referred to λ∆T, λ∆T(-FG), and λ∆T(+ FG) for the cases of ∆T ) 40 K and ∆T ) 30 K are statistically equal by considering that the t value in this case is 4.3 (two degrees of freedom, 95% of probability). Moreover, they are not different from the expected PPTT theoretical value of -1. Instead, the correlation fails in the case of ∆T ) 20 K, since c1 drops to zero or increases to -1.38 (see Table 3) when the FG component is considered: in this case, one cannot say that FG can be neglected with respect to FT. The conclusion is that, for thermal fields strong enough to ensure the condition of FT . FG, the PPTT predicted dependence of the Soret coefficient on particle diameter expressed by eq 19 is experimentally confirmed. Effect of Temperature. The effect of temperature on the retention can be seen by considering the calibration plots obtained at various thermal gradients (see Figure 3a) as well as the retention data for a given particle, eluted under temperature conditions where the condition of FT . FG is respected, i.e., for ∆T ) 40 K and ∆T ) 30 K. The linear bilogarithmic dependence of λ∆T on r is confirmed for these two temperature values, with slope values statistically not different from -1 (see Table 3). This means that the PPTT expected linear dependence of the Soret coefficient versus r is confirmed (see eqs 14, 19, and 22c). The obtained calibration lines (see Table 3) differ in both applied thermal gradient (∆T) and cold wall temperature (TC). Since, from the ThFFF experiment, one does not know the sign of the Soret coefficient a priori, i.e., whether the particle accumulates at the hot or cold channel wall, in order to take into account the effect of temperature on retention, the average channel temperature (Tav) was employed:

Tav ) (TC + TH)/2

(26)

and by assuming ψs constant for all the Si particles as discussed above. A multilinear regression (MLR)34 of the λ∆T data (∆T ) 40 K and ∆T ) 30 K) in Table 3 versus both particle radius and Tav (33) Pasti, L.; Ventosa, E.; Mingozzi, I.; Dondi, F. J. Sep. Sci. 2006, 29 (8), 10881101.

Figure 4. Fractograms of Si particles (r ) 100 nm) obtained at different TC values. Carrier: KNO3 3 mM aqueous solution, pH 9, F ) 0.304 mL min-1, ∆T ) 30 K.

Figure 3. ThFFF calibration line for Si particles. Carrier: KNO3 3 mM aqueous solution, pH 9, F ) 0.304 mL min-1. (a) log(λ∆T) vs log(r) at various TC and ∆T. (b) log(λ∆T) predicted by the logarithm model (see eq 34) vs the experimental values.

was performed (see Figure 3b). The regression parameters are reported in Table 3. The estimated c3 parameter has a negative value, which means that λ∆T decreases (or Soret coefficient increases) as temperature increases. This finding is in contrast with the theoretical expression of the Soret coefficient (see eq 19), which establishes an inverse proportionality between Soret coefficient and the square of the temperature. The negative slope value could be explained by the fact that the Soret coefficient is negative, which as mentioned above (see eq 9b) cannot be verified here. Moreover, in recent studies a negative Soret coefficient was observed for silica colloids.31 For what concerns the magnitude of the slope coefficient (λ∆T vs Tav), in all the examined cases, it is quite different from the theoretical value (i.e., 2). From a statistical point of view, it can be said that the c3 coefficient error (see Table 3) is quite large and that the MLR regression coefficient is poor. This may be due to the fact that the exploited temperature range is very limited (only 10 K). Moreover, on a logarithmic scale, this range is even smaller and this hinders any clear-cut conclusion regarding the congruence between experimental findings and PPTT. To better understand the effect of the temperature, MLR of the λ∆T data in Table 3 versus both particle radius and TC and TH (instead of Tav see eq 22c), respectively, was performed. The different regression coefficients are reported in Table 3, and it was verified by the t-test34 that the estimated regression coefficients are not each other statistically different, at 95% of probability. In the literature,5,19 there are other works in which ThFFF retention was found either to decrease or to increase as the cold (34) Massart, D. L.; Vandeginste, B. M. G.; Deming, S. N.; Michotte, Y.; Kaufman, L. Chemometrics: a Textbook. Elsevier: Amsterdam, 1990; pp 301-303.

Figure 5. (a) Fractograms of Si particles (r ) 100 nm) at TC ) 308 K and ∆T ) 30 K obtained at various ionic strengths. Carrier: KNO3 at different concentrations in aqueous solution, pH 9, F ) 0.304 mL min-1. (b) Fractograms of Si-COOH particles (r ) 100 nm) at TC ) 306 K and ∆T ) 28 K obtained at various ionic strengths. Carrier: KNO3 at different concentrations aqueous solution, pH 9, F ) 0.304 mL min-1.

wall temperature increases, depending on the physicochemical particle/carrier interactions. This phenomenon was interpreted on the basis of the magnitude of particle surface tension. In particular, when the surface tension is high, retention increases with TC, whereas for systems of low interfacial tension, a decrease in retention is observed.5 In order to further confirm our observation, the particle was eluted at different TC while keeping particle diameter and applied field constant. The fractograms reported in Figure 4 again show an increase in the retention with TC. It should be recalled that eq 19 is an approximated relationship between the Soret coefficient and temperature, in fact, it does not elucidate the effect temperature has on both dielectric constant () and Analytical Chemistry, Vol. 79, No. 14, July 15, 2007

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Table 4. Instrumental Parameters and Retention Data of Si and Si-COOH Particlesa KNO3 (mM)

∆T (K)

TC (K)

htR (min)

λ

ST (K-1)

Si

0.3 0.5 0.5 1 1 1.5 1.5 3 3

30 30 30 30 30 30 30 30 30

314 315 315 314 314 315 315 313 313

5.47 6.91 6.89 7.34 7.38 8.56 8.48 9.02 9.12

0.1348 0.1025 0.1028 0.0935 0.0937 0.0845 0.0843 0.0796 0.0797

0.2473 0.3252 0.3243 0.3565 0.3557 0.3945 0.3954 0.4188 0.4182

Si-COOH

0.5 0.5 1 1.5 3 3

28 28 28 28 28 28

312 313 313 312 312 312

7.61 7.59 8.21 8.83 9.34 9.21

0.0991 0.0994 0.0898 0.0821 0.0765 0.0779

0.3604 0.3593 0.4124 0.4511 0.4668 0.4584

sample

a

Elution details are reported in Figure 5a and b.

double layer thickness (see eq 21). Moreover, hydrodynamic effects can play an important role on submicrometer particles. To clearly state the role of temperature on colloids thermodiffusion additional investigations are required, which go beyond the scope of the present study. Effect of Ionic Strength. The effect of the ionic strength on ThFFF retention was previously investigated by Schimpf,5 using PS particles in aqueous media. In this study, an increase in retention was observed with increased ionic strength. Recently, a more systematic study devoted to the effect ionic strength has on ThFFF was performed by Shiundu.19 However, in most of these experiments, the employed aqueous carrier contained FL-70. As previously mentioned, FL-70 is a technical mixture detergent made up of glycols, surfactants, ethylenediamminotetracetic acid (EDTA),25 and its role on the surface chemistry of silica seems to be quite complex: silica particles can adsorb surfactant molecules and this can partially change the chemical behavior of the surface.35 For this reason, some silica particle retention experiments were performed in an aqueous medium without any surfactant. The obtained fractograms are reported in Figure 5a. In the salt concentration range explored, retention increases as ionic strength increases (see Table 4), in agreement with the cited studies.5,19 To exploit these observations, the PPTT theory was employed. By combining eqs 19 and 20 and under condition of constant Zq value, of one obtains

ST )

(Zq)2 rkBT

2

(

)

1 1 ) sl 2 (1 + κr) (1 + κr)2

(27)

where sl is the slope of the plot ST versus (1 + κr)-2. To check if this relationship can be applied in the studies of silica submicrometer particles, the dependence of the experimental ST versus (1 + κr)2 was investigated (see Figure 6a). The observed linear trend confirms the dependence of thermophoresis on the square (35) Portet, F.; Desbe´ne, P. L.; Treiner, C., C. J. Colloid Interface Sci. 1997, 194, 379-391.

5292 Analytical Chemistry, Vol. 79, No. 14, July 15, 2007

Figure 6. Experimental data (9) and regression line (solid line) of ST vs (1 + κr)-2. (a) Si particle data obtained from fractograms in Figure 5a); (b) Si-COOH particle data obtained from fractograms of Figure 5b).

of the double layer thickness. The negative slope is difficult to interpret since both eq 9b and eq 19 refer to absolute Soret coefficient values and to small particle dimensions (cf. note at eqs 9b and 19). Nonetheless, in recent studies, a negative Soret coefficient and an absolute values of the Soret coefficient increases versus ionic strength were observed, for silica colloids in an aqueous media.36 The ST linearity versus (1 + κr)-2 exploited here, based on PPTT, was also checked with the data plotted in Figure 5b of ref 19 and the results were similar, i.e., a linear trend with negative slope value. Consequently, the observed negative dependence of ST with ionic strength observed in these experiments cannot thus be explained in the light of the PPTT and assuming at the same time a constancy of Zq (see eq 34b). In order to further exploit this finding, the retention behavior of silica chemically modified with carboxylate groups (referred to as Si-COOH) versus the carrier salt concentration was studied following the same procedure (see Figure 5b). Figure 5b shows that the fractograms have the same qualitative trend as those of Si. Statistical analysis of ST values versus (1 + κr)-2 reported in Figure 6b proved that a linear dependence of first order well represents the trend, again confirming a linear dependence of thermophoresis on the square of the double layer thickness. By comparing the regression coefficients for Si and Si-COOH particles (see Figure 6), it can be seen that the slope of the SiCOOH plot is higher than that of Si, the difference being at the limit of the statistical significance. Consequently, thermophoresis data for charged particles at different ionic strengths can be useful in discriminating and quantifying surface/colloid interaction. (36) Rusconi, R.; Isa, L.; Piazza, R. J. Opt. Soc. Am. B 2004, 21, 605-617.

Table 5. Ni Concentrations in ThFFF Eluted Fractions Obtained by ETAAS

Si-Ni

fraction

elution time range (min)

rel UV signal (%)

vol (mL)

concn (ppb)

1 2 3

3.0-4.1 4.1-5.6 5.6-6.8

16 56 28

0.33 0.45 0.35

128 870 370

Effect of Specific Adsorption. Heavy metals are known to be specifically adsorbed onto silica surfaces and thus to modify the surface charge of the silica particles under given ionic strength condition.32 Specific adsorption of heavy metals on silica depends on many factors. The ion type plays the most important role, but adsorption parametersssuch as pH, ionic strength, solution composition, and solid to liquid ratio (i.e., the ratio between the number of active sites on the particle surface and the number of solution ions)salso significantly affect the magnitude of absorption, as extensively studied by Kosmulski.37,38 Quantitative study of specific sorption interactions by ThFFF is beyond the aim of the present work since we are mainly concerned with the methodological aspects of thermophoresis in colloid analysis performed with ThFFF. To accomplish this task, only a limited set of metal ions (namely, Ni and Co) at different concentrations were considered and the choice of the sorption conditions was based on the data in the literature.37,38 To verify the sorption of metal ion on Si particle during ThFFF elution, some fractions of the peaks eluted from ThFFF were collected and submitted to ETAAS analysis. As mentioned above, these analyses were performed to qualitatively verify the effective distribution of ions onto particles. Full characterization of the overall process of thermal fractionation of Si particles carrying adsorbed species or development of an optimized hyphenation or coupling technique to obtain highquality quantitative data is instead beyond the aim of the present paper. For such a limited investigation, three fractions for Si particle (r ) 100 nm) with 10-3 M Ni2+ eluted from ThFFF were collected and ETAAS analyzed. The metal ions contents of the fractions are reported in Table 5. It can be seen that the metal ion is found in all the fractions and the maximum concentration corresponds to the peak maximums; this gives indication of the stability of the sorption process in the ThFFF elution condition. Heavy metal concentration effects on retention can be seen in Figure 7, which reports the fractograms of silica particles (r ) 100 nm) obtained under different medium conditions and at different Co2+ (Figure 7a, b) and Ni2+ (Figure 7c) ion concentrations. In the case of Co2+ adsorption, the elution profiles in 1 mM KNO3 are only slightly different from each other (see Figure 7a), the differences being magnified in FL-70 + 1 mM KNO3 aqueous solution (see Figure 7b). In particular, in this latter, the elution profile changes as the concentration change from 10-10 to 10-6 M Co2+, with no change being found if the Co2+ concentration is increased further. By comparing Figure 7a and b, it can be also observed that, for a given metal ion concentration, the elution order in FL-70 is opposite what is found in water; this finding may support the hypothesis that a drastic change in the particle surface (37) Kosmulski, M.; Eriksson, P.; Gustafsson, J.; Rosenholm, J. B. J. Colloid Interface Sci. 1999, 220, 28-132. (38) Kosmulski, M. J. Colloid Interface Sci. 1997, 190, 212-223.

Figure 7. (a) Fractograms of Si particles with Co2+ adsorption under different Co(NO3)2 concentrations: TC ) 308 K; ∆T ) 30 K; carrier, KNO3 1 mM aqueous solution; F ) 0.304 mL min-1. (b) Fractograms of Si particles with Co2+ adsorption under different Co(NO3)2 concentrations: TC ) 308 K; ∆T ) 30 K; carrier, FL-70 0.2% KNO3 1 mM aqueous solution; F ) 0.304 mL min-1. (c) Fractograms of Si particles with Ni2+ adsorption under different Ni(NO3)2 concentrations: TC ) 308 K; ∆T ) 30 K; carrier: FL-70 0.2% 1 mM aqueous solution; F ) 0.304 mL min-1.

characteristic takes place due surfactant adsorption. The same procedure was applied to select Ni concentration (see Figure 7c). It seems that at concentrations higher than 5 × 10-4 M Ni2+ the fractogram does not change. On the basis of the experimental results, the concentration of Co2+ and Ni2+ to be used in the further investigation was set at 5 × 10-6 and 5 × 10-4 M, respectively. Moreover, to avoid the effects of FL-70, KNO3 solutions were employed as the carrier. The influence heavy metal has on Si particles is shown in Figure 8 and in Table 6. One can see that, under the selected experimental conditions, retention decreases in the following order: Si, Si-Co, Si-Ni. This behavior appears to be correlated to the suppression of the silica surface potential due to heavy metal Analytical Chemistry, Vol. 79, No. 14, July 15, 2007

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Table 7. ζ-Potential (Two Replicates) of Si, Si-Ni, and Si-Co Particles (r ) 100 nm) ζ-potential (mV)

electrophoretic mobility (cm/V s)

conducibility (mS/cm)

Si

-61.7 ( 6.5 -71.6 ( 6.4

-4.7 ( 0.5 -5.6 ( 0.5

0.121 0.141

Si-Ni

-34.3 ( 6.4 -36.5 ( 6.4

-2.7 ( 0.5 -2.9 ( 0.5

0.163 0.159

Si-Co

-50.8 ( 6.3 -47.5 ( 6.3

-4.0 ( 0.5 -3.7 ( 0.5

0.131 0.139

sample

Figure 8. Fractograms of Si, Si-Co, and Si-Ni particles at TC ) 308 K and ∆T ) 30 K, obtained at various ionic strengths. Carrier: KNO3 at different concentrations in aqueous solution, pH 9, F ) 0.304 mL min-1. (a) KNO3 0.1 mM; (b) KNO3 1 mM; and (c) KNO3 6 mM. Table 6. Instrumental Parameters and Retention Data of Si-Ni and Si-Co Particlesa KNO3 (mM)

∆T (K)

TC (K)

htR (min)

λ

ST (K-1)

Si-Ni

0.1 1 3

30 30 30

314 313 313

5.44 5.84 5.91

0.1635 0.1451 0.1424

0.2039 0.2297 0.2341

Si-Co

0.1 1 3 3

35 35 35 30

318 319 319 312

6.73 8.50 8.82 7.42

0.1150 0.0842 0.0804 0.1103

0.2484 0.3393 0.3554 0.3077

sample

a

Elution details are reported in Figure 8a-c.

adsorption, this effect being higher for nickel than for cobalt ions.37 The effect ionic strength has on heavy metal-Si particle can be seen by comparing Figure 8a-c. Retention increases as the ionic strength increases, and in such manner that the Si-Ni and Si5294

Analytical Chemistry, Vol. 79, No. 14, July 15, 2007

Co particles behave as the Si and Si-COOH particles. This behavior was further exploited through the regression line of ST versus 1/(1 + κr)2 (see eq 27). From the regression parameters of Si-Ni (ST ) (0.23 ( 0.013) - (0.60 ( 0.091) 1/(1 + κr)2) and Si-Co (ST ) (0.35 ( 0.018) - (2.0 ( 0.22) 1/(1 + κr)2) particles, it can be seen how differently these particles behave versus the Si and Si-COOH particles (cf. data of Figure 6). Such evidence calls for further investigation of the effect particle charge and ionic strength have on ST as mentioned above. Surface Charge/ζ-Potential versus ST Correlation. Table 7 reports ζ-potential of the Si, Si-Ni, and Si-Co of 100-nm radius values, under selected metal concentrations. One can see that the absolute ζ-potential values decrease in the following sequence, Si, Si-Co, and Si- Ni; i.e., they exhibit the same trend as ThFFF retention. Owing to the structure of eq 27, the square root sl slope values, sl1/2 (see Table 7), were correlated to the ζ-potential as shown in Figure 9a. Again both sl1/2 and ζ-potential values increase in the order Si, Si-Co, andSi-Ni as illustrated in Figure 9a. Moreover, despite of the low number of points, the correlation is quite good. The observed linear relationships can be explained by considering that both ζ-potential and sl1/2 are related to the surface charge of the particle and that the absolute value of the surface charge decreases when specific adsorption occurs.37 Consequently, for a given particle type, ThFFF is able to identify absorption phenomena provided this phenomenon has a significant effect on the ζ-potential. Note also that this cannot be simply extended to different types of particles since we must always remember that, according to the PPTT, the driving factor is ψs (see eq 19) and that the proportionality constant of the latter quantity versus ζ-potential (see eq 23) may be different for different particle types. In the practice, one can conceive a ThFFF calibration plot as a function of log ζ, but only for a given particle class type. The above-described success in correlating ST obtained from ThFFF with the PPTT prompted us to check the ability of the same PPTT to predict thermophoretic behavior also besides the rigorous applicability limits of the theory. A rigorous computation of surface charge density was here avoided since, in the case of specific sorption, this requires a discussion lying beyond the aim of the present paper. Instead, by combining eqs 19 and 23, and by assuming C ) 1 in eq 23, one obtains the following approximate relationship:

S/T ≈ (r/kBT2)ζ2

(28)

Figure 9. (a) Experimental data (9) and regression line (solid line) of ζ-potential vs the slope of the lines for ST vs (1 + κr)-2 obtained for Si, Si-Co, and Si-Ni particles. (b) Experimentally determined ST vs S/T computed according to eq 28, of Si, Si-Co, and Si-Ni particles ∆T ) 30 K; carrier, KNO3 3 mM aqueous solution.

where the use of the symbol S/T underlines the introduced strong assumptions and approximations. Figure 9b reports the plot of S/T versus ST (calculated from eq 14). One can see that there is a good correlation between the corresponding values, but the regression coefficients are quite far from the assumed values of unitary slope and null intercept. This is most likely due to the number of uncertainties and approximations made for both S/T, as above-mentioned, as well as for ST calculated from eq 14. For example, as far as the ST measurement is concerned, a constant thermal gradient was assumed and in some cases one has uncertainties in the λ determinations close to the void time. It is worth noting that the agreement in the high ST domain is better than in the lower ST domain. We observe that the former values refer to the Si particle and the latter to the Si-Co and Si-Ni particles. For these two classes of particles, the ζ-potential measurement can be critical because of the required dilution procedure (see under Experimental Section). Especially in the case of Si-Co and Si-Ni particles, dilution can affect the adsorption extent. Nonetheless, S/T values obtained by eq 28 can be considered at least a starting point for evaluating Soret coefficients and choosing the ThFFF operative conditions. These findings, based on only three cases, stimulate further exploitations, which lie beyond of the scope of this exploratory work. CONCLUSIONS ThFFF is able to characterize charged colloidal particles in aqueous media. The first attempt to interpret by PPTT the ThFFF

separation mechanisms for charged colloids in aqueous solution on the basis of colloidal system properties is achieved. Quantitative evaluation of the thermophoretic force and of the major factors affecting the separation induced by a thermal field are given. In particular, the PPTT linear dependence of the Soret coefficient on particle radius was confirmed under conditions where thermophoretic force prevails with respect to the gravitational one. Instead, explanation of the observed dependence of the Soret coefficient on ionic strength appears not straightforward since it requires knowledge of either the surface charge or the surface potential. Good, but not yet full quantitative agreement between PPTT and experiments were found with reference to the correlation between ST data and ζ-potential, confirming thus the role of the surface potential as the driving force of the observed thermophoretic effects. The present exploratory work points out that there are several aspects which call for further investigation, e.g., the explanation of observed retention differences between the different particles (Si; SiCOOH; Si-Ni; Si-Co) and the role of the particle surface potential. Likewise, direct application of ThFFF to the study of other samples (e.g., environmental colloids, metallic particles, and their behavior with pH and ionic strength) also requires further investigation. Nonetheless ThFFFsamong other established FFF subtechniques such as FlFFF and SdFFFspromises to furnish specific analytical characterization not only on the basis of the hydrodynamic volume and specific mass given, respectively, by FlFFF and SdFFF but also of the particle surface properties. Analytical Chemistry, Vol. 79, No. 14, July 15, 2007

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ACKNOWLEDGMENT This work has been supported by the objective 2 (2000/06) L.A.R.A. Project (FE120) and by the Italian University and Scientific Research Ministry (Grant 2005039537_005). We thank Achille de Battisti for useful discussions. We also thank Antonella

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Pagnoni for her assistance in ETAAS measurements and Rita Cortesi for her assistance in electrophoretic measurements. Received for review January 17, 2007. Accepted May 3, 2007. AC070099T