Ali Abou-Hassan

Jean-François Dufrêche

Olivier Sandre

Guillaume Mériguet

Olivier Bernard

Valérie Cabuil

Fluorescence confocal laser scanning microscopy for pH mapping in a coaxial flow microreactor: application in the synthesis of superparamagnetic nanoparticles

The application of fluorescence confocal laser scanning microscopy (CLSM) to quantify three dimensional pH gradients in a coaxial flow microreactor is described. The methodoloy consits in utilizing a micromolar concentration of the common dye fluorescein, which fluorescence in solution strongly increases above pH 6.2, in order to map the pH changes in the central jet stream where an acid-base reaction proceeds. The experimental fluorescence profiles determined by CLSM, have been comprared to models by solving the underlying mass transport equations using the finite element method. The fluorescence profiles were found to be highly sensitive to both the initial bulk solution pH and the applied volumetric rate ratio (α ) of the outer stream to the inner stream. The simulated pH gradients have been compared for different α leading to an optimal value for the preparation of superparamagnetic nanoparticles.

Introduction

In the past decade, the synthesis of superparamagnetic iron oxide nanoparticles has been intensively developed for fundamental scientific interest and also for many technologies. Superparamagnetic iron oxides are used for magnetic storage media, [START_REF] Sun | [END_REF] hyperthermia, 2 biosensing applications, 3 targeted drug delivery, 4 and as contrast agents in magnetic resonance imaging (MRI). 5 The properties of the finely devided magnetic materials closely depend on the size of the particles and their state of dispersion or aggregation. In the case of quantum dots where the monodispersity of diameters is crucial for the fluorecence properties, microfluidics has been proposed to control the conditions of synthesis more accurately than in the bulk. 6 Since then, microfluidic reactors have been designed to produce nanoparticles of a wide number of materials. 7 Among these, superparamagnetic iron oxide nanoparticles have been prepared for the first time by our group in a coaxial flow microreactor that achieves small diffusion distances and fast mixing times. 8 Later on, the setup was improved by separating a nucleation reactor and an aging channel in order to synthesize antiferromagnetic ferrihydrite nanolaths. 9 Microfluidic offers several advantages over batch reactors for controlling the synthesis and the growth of nanoparticles. For example, stationnary concentration or temperature gradients can be tuned during the synthesis of nanoparticles in order to improve their monodispersity. [10][START_REF] Ehrfeld | Microreactors: New Technology for Modern Chemistry[END_REF][START_REF] Cottam | [END_REF] We have focused our attention on building up pH gradients in a microfluidic mixer because pH is a parameter of uppermost importance during the synthesis of nanoparticles by coprecipitation reactions of precursor salts and it remains also a key parameter for their properties (e.g. charge) and their stability in the final colloidal solution. Based on some assumptions, this paper reports experimental and theoretical studies of pH gradients in the coaxial microreactor for nanoparticles synthesis. Several methods probe concentration gradients locally by utilizing the optical properties of either generated or 60 consumed species. These techniques include interferometry 13 and spectroscopic approaches such as Raman spectroscopy 14 and confocal resonance Raman microscopy. 15 Several other techniques based on light absorption rather than refractive index as spatially resolved absorbance electrochemistry 14 and 65 micro X-rays absorption spectroscopy 16 have been used to provide informations on local scale concentration gradients. High-resolution nuclear magnetic resonance imaging and electrochemical techniques have recently proven particularly powerful for observing concentration gradients at both 70 electrode surfaces and liquid/liquid interfaces. 17 Optical imaging by fluorescence has found particular application in the vizualization of pH gradients. Compared to conventional fluorescence microscopy, confocal laser scanning microscopy (CLSM) reduces out of focus blur that would otherwise result from light being collected both above and below the focal plane of the objective. CLSM allows direct, noninvasive, serial optical sectioning of objects and profiling of multilayer structures. [START_REF] Sheppard | Confocal Laser Scanning Microscopy[END_REF] This paper attempts to address the pH gradients in the coaxial flows microreactor, which will be an important parameter in further experimentation for nanoparticles synthesis. The systems considered herein are the chemical reaction between the hydrochoric acid flowing in the inner focalised flow and the alkaline solution of tetamethylamonium hydroxide flowing in the outer flow. In our study, fluorescein is used as a probe to map the pH gradients. Experimental CLSM results are compared to numerical simulations of the spatial distribution of the fluorecein concentration and of pH in both the inner jet and the surrounding stream. Fluorescein is a well-known pH sensitive dye. Its molecular structure becomes progressively deprotonated when pH increases, as shown on Fig. 2. The only fluorescent species is the di-anion F -2 and in a much lower extend the mono-anion F -1 . As the pH rises in an aqueous solution, the fluorescence signal increases starting at pH~5 and saturating at a maximum value above pH~7. To verify the pH dependence of the signal, a stock solution of disodium fluorescein was prepared and diluted at 6 µ M in different pH-buffered solutions. The solutions were perfused in both the inner and outer capillaries and the corresponding fluorence images were 35 captured with the CLSM at the median plane of the channel (i. e. far from the walls which produce an artifact due to possible adsorption of fluorescein onto PDMS). The images appeared uniform across a 300 µ m x 300 µ m view field. By averaging the intensity over this constant area, we built the calibration plot on Fig. 2.(b). The major intensity change occurs between pH 5 and 7, the slow increase between pH 8 and 11 (far above the last pKa of fluorescein) being ascrible to a possible interference with the buffers. These results are in good agreement with cited work. [START_REF] Margulies | [END_REF]20 injected with an outer voulumetric rate flow Q out .

CLSM Measurements

The CLSM measurements were taken on the device shown in Fig. 1 mounted on a three-axis piezostage. This device 60 consisted of two syringe infusion pumps (Harvard apparutus, Picoplus) that provide constant flow using various Becton Dickinson syringes of 1, 3 and 30ml capacity. All componenents were interconnected with PTFE tubing (500 µm i.d.) up to the coaxial microreactor. The coaxial jet 65 microreactor consisted of an outer capillary molded in polydimethylsiloxane (PDMS, Sylgard184) of 1.7mm diameter in which a fused silica capillary (Polymicro Technologies Inc) of 150 µm i.d x 350 µm o.d is fixed through the tip of a micropipette (Gilson). The conical shape 70 of the micropipette enables the inner capillary's position to be easily centred in the outer capillary. The length of the reaction zone from the confluence region to the outlet is almost 3 cm. To image the pH gradients in the microchannel, 6 µM fluoresein solution in HCl (pH~0.10) and the alkaline solution 75 of TMAOH 0.172 mol.L -1 were respectively injected in the inner and the outer flows . The volumetric rate flows Q in and Q out were varied by steps in order to achieve different values of the jet diameter and hence to vary the mixing time, a stationnary flow being always reached after a few seconds of 80 transient regime. CLSM images of concentration gradients were acquired using a confocal laser scanning microscope (Leica Tandem Scanner SP5 microscope). The confocal setup is based on a DMI6000 inverted microscope with 5 x objective (0.11 NA), used with 85 a pinhole opened to 1 U.A leading to a theoretical Z resolution of 58µ m. The fluorescent dye was excited using the 488 nm laser line of Argon laser of sufficiently low power such that photobleaching was negligible, and emited fluorescence was captured between 500 to 600 nm. Typical scans were 3.1mm 90 in X dimension, 0.78 mm in Y dimension and 0.4 mm in Z dimension. The images acquired with a camera of 12 bits sensibility range were converted to 32 bits for image analysis using ImageJ NIH software © .

Theory

Modeling of the hydrodynamic and of the mass transport in the microreactor was carried out using a commercial nonlinear solver (FEMLAB by Comsol Inc., version 3.5) to solve iteratively the state equations. Simulations were run on a Mac Pro with 8 GB RAM and 2x3-GHz Quad-Core Intel processors. Since the microchannel in the concentric microreactor has a cylindrical shape with axial symmetry, we examined the flow in the microchannel in cylindrical coordinates (r,θ,z). Here r is 10 the coordinate in the radial direction of the microchannel, θ the coordinate in circumferential direction, and z the coordinate in the flow direction. Besides, the rotational symmetry of the boundary conditions around the central flow axis enables to derive the numerical solutions in the half-plane of a 2D axisymmetric model. The origin of the coordinates was set at the merging point of the inner and the outer flows located on the axis of symmetry (Fig. 3). Please note that we refer to the plane (z,r) in the simulations as the plane (X,Y) in the CLSM images.

The model

The pH distribution in the reactor and the local fluorescein concentration has been predicted by modelling the flow of the 30 various species in the system. The evolution of the concentration C i = C i (r,t) of solute particles i follows the continuity equation

∂ C i ∂ t + div(C i u + j i ) = σ i (1)
u is the hydrodynamic velocity in the channel. It is calculated 35 from the Navier-Stokes equation together with the compressibility condition. For a dilute system, it is identified to the local average velocity of the solvent. σ i is the creation term. It represents the local creation rate of particles due to the chemical reactions. j i is the diffusive flux of species i .

40

The general expression of the j i 's can be obtained from nonequilibrium thermodynamics. [START_REF] De-Groot | Non-Equilibrium Thermodynamics[END_REF] For a dilute solution cross correlations are negligible and it reduces to the Nernst-Planck expression [START_REF] Turq | Transport, Relaxation and Kinetic Processes in Electrolyte Solutions[END_REF][START_REF] Berne | Dynamic Light Scattering[END_REF] : Since F -2 is the only species that can be followed by CLSM, the following reactions were considered:

j i = -D i gradC i + D i k B T C i Z i eE
80 F 0 F -1 + H + pKa 1 = 4.31 (3)
F -1 F -2 + H + pKa 2 = 6.27

In each point (r,z), the fluorescein mass balance gives:

85 Flu = F 0 + F -1 + F -2 (5)
By introducing the equilibrium constant Ka 1 and Ka 2 the local concentration of the different species F -2 and F -1 can be

F -2 = β x Flu (6) F -1 = β' x F -2 (7)
With

β = 1+ H + K a 1 × K a 2 + H + K a 2 (8) ′ β = H + K a 2 (9)
The term of chemical kinetics is not zero for H + (aq) , OH -

because of the dissociation equilibrium:

OH (aq) -+ H (aq) + H 2 O pK w = 14.00 (10)
For a dilute solution, in the most general case, the resulting σ i term for H + (aq) and OH - (aq) is:

σ H + =σ OH -=σ = f( C i { })(C H +C OH --K w ) (11)
where K w is the water dissociation constant. The term

f C i { } ( )
expresses the kinetics of the reaction. In principle, the evolution of the concentration depends on f C i { } ( ) . However, in our case, the dissociation kinetics is very fast. In particular, it is much faster than the time scale of the experimental measurements in the reactor. Accordingly the resulting evolution of the concentration should not depend on the exact

expression of f C i { }
( ) . This can be shown by eliminating the fast variables, [START_REF] Van Kampen | [END_REF] as it is explained in the appendix. Thus it is practically possible to describe the system by assuming that

f C i { } ( ) is constant: σ = k(C H + C OH --K w ) ( 12
)
If k is chosen to be large enough, the evolution of the concentration does not depend on its value because the system is in the regime where chemical kinetics is a fast variable.

Validation

The model has been solved numerically for the geometry represented in Fig. 3, for different flow rates of the inner and the outer tubes Q in and Q out . In the inner solution, the concentrations of the various species were 0.794 mol.L -1 for H + and Cl -. In the outer solution, they were 0.172 mol.L -1 for OH -and TMA + .

-1.2 10

R s 2 = R 2 1- 1 1/α +1       1/2         (13)
Where R s denotes the inner stream radius when the Poiseuille flow is developped, R the radius of the PDMS capillary and α the volumetric rate ratio ( α = Q out /Q in ). and more noisy. By refining the mesh in that domain it should be possible to obtain the same titration curve as pH H + in the whole concentration range but this requirement overcomes the possibilities of the computer memory. In fact, this noisy domain corresponds to the domain for which OH - concentration is negligible compared to the other concentrations and the pH is driven by the H + concentration. Accordingly, all the simulations were run with k = 10 9 L/(mol.s -1 ) and the pH has been estimated from the H + concentration.

Results and Discussion

A series of volumetric ratio values chosen between 400 and 40 was applied, a delay of a few seconds being respected each time before capturing the CLSM images in order to enable the new stationnary flow and concentration profiles to establish in the microreactor. Fig. 6 shows the steady-state 2D fluorescence profile obtained by confocal slicing in the middle of the outlet of the inner capillary where acidified fluorescein solution (6 µM) flows in the centre surrounded by the outer alkaline TMAOH solution upon application of a volumetric ratio α = 400. Since the microreactor is cylindrical, a 3D image can be obtained by rotation of that plane around the axis of symmetry. After "Z-stacking" of the 20 X-Y slices, CLSM cross sections in the X-Z plan at different positions from the tip of the inner capillary show a disk shape fluorescence that mirrors the diffusion profile and the establishement of pH gradients in the central jet. The fluorescence burst in the central jet is due to the deprotonation of fluorescein by the hydroxide ions diffusing towards the center that remain in excess after reaction with H + . The hollow cylindrical shape on the fluorecence image (crosssections (1) and (2) of the central stream) illustrates the transition from a still acidic core (below pH 4) of the stream to a neutralized "skin" near the pKa of 6.2 of fluorescein. It is exactly in this boundary region near the pH equivalence that we expect the coprecipiration of the iron salts in a synthesis experiment with the same hydrodynamic ratio. However, we cannot deduce a pH mapping by inverting directly the images such as Fig. 6 using the calibration cuve intensity vs. pH of Fig. 2(b). From a mathematical point of view, this curve should be sigmoidal, which means that no difference in the fluorescence intensity should exist for pH higher than 7 or repectively lower than 4. This is not verified experimentally, as we see that the curve does not reach perfectly a plateau. Besides, fluorescein diffusion from the inner stream to the 60 outer stream occurs so that pH values deduced from the calibration curve can be underestimated. Please note that we could not perfuse fluoresceine both in the outer and the inner flows as in the calibration experiment, because the inner jet would have appeared as a dark cylinder inside a bright 65 (because alkaline) surrounding stream, so that their interface would have been very difficult to distinguish by CLSM. To avoid all these experimental issues, and in order to reach the true mapping of pH gradients in the micoreactor, we have calculated the spatial distribution of F -2 and pH numerically. 1), ( 2) and ( 3), constructed from a "Z-stack". The Z-stack consisted in 20 slices, which were spaced at 20 µm intervals. 80 After background substraction, the measured fluorescence intensity is directly proportional to the F -2 concentration with a constant of proportionality that we calculated by the following method: at first, we extracted the experimental curves I(r) from different cross-sections at constant z deduced 85 from the stack of images; then we compared them to the numerical simulations of the F -2 concentration field. The experimental fluorescence curves were fitted and the best fit were obtained with I exp = 2.56 x 10 +5 x F -2 + 6.39, where 6.39 value accounts for the background. The right part of the curve (for z ≥ z c ≈ 1000 µm) exhibits a linear decrease of the intensity with increasing z. This observation evidences two regimes : (i) for z ≤ z c ≈ 1000 µm the concentration field is controlled by both the reaction and diffusive processes, so that a sigmoidal intensity curve is observed ; (ii) for z ≥ z c , the system evolves only through a diffusive process, by which the fluorescein molecules diffuse radially thus decreasing the fluorescence intensity locally around the r = 0 axis. The variation in the fluorescence intensity in the first regime is then related to the pH and to the local variations in concentration due to diffusion, while in the second regime, the fluoresence intensity is related to the variation in the local concontration field of the fluorescent dye. To illustrate the good agreement between the CLSM experiment and the model, Fig. 8 compares the 2D fluorescence intensity map of fluorescein represented by a scale from cold (low intensity) to warm colors (high levels).

The symmetry between the experimental part of the image on the left and the calculated one on the right is a clear evidence that the assumptions made to calculate the diffusion of the fluorescein species and the acid-base reaction (paragraph 3.1) are acceptable. 100 µm 100 µm 100 µm Finally, the flow rates ratio α was tuned between 40 and 400 and the corresponding fluorescence profiles along the r = 0 axis were compared on Fig. 10.a. The good matching between the predicted and the experimental intensity curves for several values of α clearly validates our method. decrease of the yield of magnetic nanoparticles due to the precipitation of antiferromagnetic iron hydroxides. These results have been used to produce the stable and colloidal magnetic nanoparticles described in details in our previous work 8 . Fig. 12 shows the Transmission Electron Microscopy 55 of the synthesized magnetic nanopartciles for α = 400.

∂ C i ∂t = -div(C i u) + D i ∆C i + div D i k B T C i Z i eE       ∂C j ∂t = -div(C i u)+ D j ∆C j + div D j k B T C j Z j eE       + g( C i { }) ε (C H + C OH --K w ) 35
To emphasize that we are interested in the behaviour of the slow variables and want to eliminate the fast variables, we adjust the time by setting t = ετ :

∂C i ∂τ = -ε div(C i u)+εD i ∆C i +ε div D i k B T C i Z i eE       40 ∂ C j ∂ τ = -ε div(C j u) +εD j ∆C j + ε div D j k B T C j Z j eE      + g( C i { })(C H + C OH --K w )
It is clear that for small ε the variables C i vary in a slower time than C j . τ corresponds to the fast time scale and t is the slow one. Actually C d = C H + -C OH -is also a slow variable as it can be understood by writing the evolution of the concentration of H and let's require that the various orders of ε vanish 55 separately when the evolution equations are written in the slow time scale:

∂ C s ∂ t = Y s + g( C i { }) 2ε (C s + C d )(C s -C d ) -4K w ( ) ∂ C d ∂ t = Y d
The term of order ε -1 reads

Mathematical demonstration of equation 13

The equation of the inner stream radius can be derived as follow from the flow conservation of incompressible fluids.

Q in Q out 0 R s R
Outer capillary

V (r) Q in Q out 0 R s R
Outer capillary V (r) After the entrance length the Poiseuille flow is fully developed:

              - = 2 0 ) ( 1 R r v v r
(1)

∫ = ⇒ = = R tot tot R Q v R v dr r v Q 0 2 0 2 0 2 2 ) ( π π (2) ∫ - = = s R s s in R R v R v dr r v Q 0 2 4 0 2 0 2 ) ( π π (3)

Fig. 1

 1 Fig. 1 Coaxial flow device studied in this paper. The inset shows an 55

Fig. 2

 2 Fig. 2 (a) Chemical structures of fluorescein based on different pH.20

Fig. 3

 3 Fig.3Meshes used in the modelling of the coaxial flow microreactor. rin is the inner radius of the inner capillary (75 µm), rw is the outer radius of the inner capillary (175µm) and rmax is the radius of the PDMS capillary (0.85 mm). The model is solved with 24000 elements and the density of25

  and Z i respectively the diffusion coefficient and the charge number of species i. e is the elementary charge, k B is Boltzmann's constant and T is the temperature. The local electric field E depends on the concentrations of the ions C i (r,t) . It can be calculated either from the Henderson 50 approximation, which supposes the local electroneutrality condition, or from the Poisson equation. The time scale of the electrostatic relaxation in the system corresponds to the Debye time, which is equal to a few picoseconds. It is much smaller than the time scale of the experiments. Consequently, at any 55 time the charge distribution has the time to relax and the local electroneutrality condition Z i C i i ∑ = 0 is valid. The electric field E is chosen to satisfy this condition (Henderson field). The various solute species i are H + (aq) , OH - (aq) , Cl -, TMA + and the fluorescein. Diffusion coefficients were estimated from 60 the value at infinite dilution: D H + = 9.2 x 10 -9 , D Cl -= 2.03 x 10 -9 , D OH -= 5.28 x 10 -9 , D TMA + = 2 x 10 -9 m 2 .s -1 . To simulate the different fluorescein species during the acidbase reaction between HCl and TMAOH we made the following assumptions: (i) fluorescein is diluted in the 65 hydrochloric acid, so no need to account for its charge. Convection diffusion equation with no chemical reaction can be solved to calculate the local concentration map of the total fluorescein denoted Flu; (ii) Fluorescein is diluted compared to H + concentration in the acidified fluorescein solution and 70 can not interfer during the acid base-reaction; (iii) The different ionic species of the fluorescein have the same diffusion coefficient D ≈ 0.2 x 10 -9 m 2 .s -1 . After calculating the local pH in the microreactor, the convection diffusion equation was solved for the fluorescein 75 dye. Since the acid-base reactions are virtually instantaneous, it can be assumed that chemical equilibriums are locally achieved for the different fluorescein species.

0

  18100 | J. Phys. Chem. C 2009, 113, No. 42 Abou-Hassan et al, authormanuscript calculated:

Fig. 4 (

 4 Fig. 4 (a) z velocity; (b) r velocity at different positions from the point of confluence in the microreactor showing the hydrodynamic transition till a laminar Poiseuille profile is established.45

Fig. 5

 5 Fig. 5 pH curves obtained from pHH + =-log[H + ] (red curves) and from pHOH -= 14+log[OH -] (green curves) when k is increased from 1 to 10 7 L/(mol.s -1 ) (curves 1) and for k = 10 8 and 10 9 L/(mol.s -1 ) (curves 2) for a volumetric rate flow ratio α = 400 and Zmax= 1100 µm65

70Fig

  Fig.6 (a) CLSM image of the acid-base reaction in presence of 6 µM75

  90

Fig. 7

 7 Fig.7 Radial (a, b, c) and longitudinal at r = 0 (d) cross sections of the fluorescence intensity as measured experimentally ( ) and calculated numerically (lines) for different positions z = 440; 770 and 1575 µm from the point of confluence.

Fig. 7

 7 Fig. 7 shows the experimental and predicted fluorescence intensities profiles for α = 400 at different positions in the channel and the good agreement between the theoretical and experimental curves. Besides, the left part of the longitudinal cross-section of Fig 7.d (for z ≤ zc ≈ 1000 µ m) can be fitted by a sigmoidal shape, which is coherent with a regular increase of pH according to the calibration curve of Fig 2.b. The right part of the curve (for z ≥ z c ≈ 1000 µm) exhibits a linear decrease of the intensity with increasing z. This

Fig. 8

 8 Fig. 8 Comparison of the experimental and predicted fluorescence 40

Fig. 9

 9 Fig. 9 Comparison in the X-Y plane between (a) CLSM image of the fluorescein and (b) the theoretical pH profiles in the central stream for α =400.

Fig. 10 (

 10 Fig. 10 (a) Evolution of the experimental fluorescence profiles ( ) when α = 40; 80 and 400 along the symmetry axis (r = 0). The lines represent the predicted fluorescence intensities calculated for each case from the simulated F -2 concentrations, (b) Simulated pH profiles along the symmetry axis (r = 0) for α = 40; 80 and 400 As fluorescein is just a pH reporter dye, these curves can be interpreted from the results of the pH calculations (Fig. 10.b). As expected, the shape of the pH curves are typically of a

Fig. 12 TEM

 12 Fig. 12 TEM image of magnetite nanoparticles prepared by coprecipitation of iron(II) and iron(III) salts by addition of TMAOH for α 60

  0 + C d )(C s 0 -C d ) -4K w ( )This equation corresponds to the local chemical equilibrium(C s 0 +C d )(C s 0 -C d ) = 4K w 65 It determines C s 0 as a function of C d . Substitution of C s = C s 0 (C d ) inthe equation of evolution for C d and the C i s gives the evolution of the slow variables. At that level of approximation, the fast variable C s follows instantaneously the slow variable in order to satisfy the chemical equilibrium. 70 Furthermore, the evolution of the slow variables does not depend on the kinetic term g C i { } ( ) /ε .

Figure 1 .

 1 Figure 1. Schematic representation of the Poiseuille flow developed in the channel. R s is the inner stream radius. R is the PDMS radius (0.85 mm). Q in is the inner stream rate flow and Q out is the outer stream rate flow.

Figure 2 .

 2 Figure2. This curve shows the variation of the inner jet stream when α is varied. Three domains are observed on this curve: 1/ for 0 ≤ α ≤ 50; 2/ for 50 ≤ α ≤ 200 and 3/ α > 200. We studied 3 cases in our simulations, from each domain: α = 40; 80 and 400.

  For the CLSM pH-mapping

	45
		measurements, 6 µM fluoresein sodium solution acidified in
		hydrochloric acid (pH~0.10 ) was injected in the inner flow
		with a volumetric rate flow Q in . For the nanopartciles
		synthesis experiments, the inner solution was replaced by a
	50	mixture of iron salts solution of a total concentration c = 10 -2
		mol.L -1 with 0.5 as molar ratio Fe(II)/Fe(III) prepared by
		mixing FeCl 3 and "fresh' FeCl 2 .4H 2 O salts in diluted and
		degased hydrochloric acid (pH ~ 0.10). The outer flow in the
		two	experiments	was	an	alkaline	solution	of
	55	tetramethylammonium (TMAOH, 0.172 mol.L -1 ) which was

  s and Y d are two terms, which depend on u and on the various local concentrations. They are directly obtained from 50 the preceding equations. Consequently C s is the only fast variable since it is the only one that does not become constant for ε → 0 . Let's substitute for C s a power series in ε

	∂C s ∂τ	= εY s +	g( C i { }) 2	(C s +C d )(C s -C d ) -4K w (	)
			∂C d ∂τ	= εY d
			C s = C s 0 +εC s 1 +K

+ (aq) and OH - (aq) in terms of C d and C s = C H + +C OH -. Y

J. Phys. Chem. C 2009, 113, No. 42 | 18099

Acknowledgments

We thank Virginie Georget from the cellular imaging facility for the CLSM images (UPMC, IFR 83), Karine Gisclon, Rokia El-Mais and Thomas Boudier (UPMC, IFR 83) for fruitful discussions regarding image analysis.

Appendix

The fact that the chemical kinetics is fast can be modelled by replacing

( ) /ε with ε a small parameter. We shall derive the evolution of the system in the limit ε → 0 .


Ali Abou Hassan

Olivier Sandre

Valérie Cabuil

Patrick Tabeling

Synthesis of iron oxide nanoparticles in a microfluidic device: preliminary results in a coaxial flow millichannel

has been designed to study the synthesis of iron oxide nanoparticles in a millichannel. The flow rate of the different reagents has been adjusted all over the experiments so that magnetic and stable colloidal iron oxide particles with a size less than 7 nm have been prepared continuously.

Miniaturization of chemical reactions and the development of "lab on a chip" (LOC) technology has gained significant importance in the recent years. 1 One predicts indeed that small dimensions of vessels lowers the diffusion times of chemical species, so that mass transport is improved in microstructured reactors. 2 Scaling down reactors dimensions is proposed as an opportunity to improve size and composition control in the field of materials synthesis. 3 Local variations in reaction conditions such as concentration and temperature are minimized and therefore control of both nucleation and 20 particle growth can be used to improve monodispersity in nanoparticles synthesis. 4 As an example, the synthesis of iron oxides nanoparticles has attracted much attention motivated by their wide range of applications. Colloidal iron oxides are used as single bitelements in high density magnetic data storage arrays, 5 ionic ferrofluids, 6 and in the biomedical field for example as contrast enhancement agents for Magnetic Resonance Imaging, 7 or for hyperthermia, 8 etc… Because the properties of these nanocrystals strongly depend on their dimension, the 30 synthesis of monodisperse nanoparticles is one of the most challenging problems. 4 At the beginning of the 1950's V. K. Lamer proposed a mechanism based on a nucleation-growth process to describe the synthesis of nanoparticles. 5,6 Since then, various chemical synthetic strategies have been reported to obtain monodisperse nanoparticles with different shapes. 10 Recently, several groups designed microreactors and reported the improvement of inorganic and metallic nanoparticles synthesis. However the synthesis of inorganic materials has been focused on Quantum Dots as CdS 11 or CdSe 12 , silica, 13 titania, 14 and titania/silica core-shell colloidal nanoparticles. 15 There has been until now no reported study of the synthesis in microchannels of colloidal iron oxide nanoparticles from the following alakaline coprecipitation reaction:

Fe 2+ (aq) + 2 Fe 3+ (aq) + 8OH - (aq) → Fe 3 O 4(s) + 4H 2 O (l)
For this purpose, we designed a 3D millifluidic device performing the mixing of two coaxial flows of miscible fluids (Fig. 1), one containing the iron "precursor salts", the other a strong base. The length of the capillary from the confluence into the channel through two syringes actuated automatically (Harvard apparatus), the iron "precursors" solution was pumped into the inner capillary and the TMAOH base into the outer capillary of the channel. TMAOH was chosen prior to any other base as the TMA + cations afford enhanced stability of colloidal oxide dispersion. 16 The volumetric rate flows of both solutions (respectively Q in and Q out ) were ajusted to avoid any turbulent vortex in the capillary. 17 Owing to the laminar regime in the channel, mixing is controlled by the diffusion of species. 18 The diffusion of iron complexes in aqueous solution is much slower than the diffusion of hydroxide ions OH -and of the protons H + . The diffusion coefficient (D) is almost 1x10 -9 m 2 /s for a single iron complex as [Fe(OH 2 ) 6 ] 2/3+ 19, 20 compared to D~5.3x10 -9 m 2 /s for OH -and D~9.31x10 -9 m 2 / for H + 21 at 25°C in diluted solutions. Thus, the diffusion of iron complexes from the central acidic stream into the peripheral TMAOH stream flow is disregarded. On the contrary, the fast diffusion of H + and OH -leads to the prediction that the pH varies continuously from acidic in the central flow to basic at 20 the periphery, the pH gradient being progressively smoothed out when moving towards the outlet of the channel. The coprecipitation reaction will therefore be likely confined in the neutral region near the channel centre. The excess of TMAOH will allow the dispersion of the particles after their synthesis, and avoid their adsorption onto the walls. The particles will be collected at the outlet without any problem of plugging. In order to stabilize the inner flow of iron solution before initiating the hydrolysis, we injected at first a HCl solution of same pH~0.4 in the outer stream. The outer flow is then switched to TMAOH solution. A few seconds after the outlet (time across the PTFE tubing), the reaction was "quenched" by fast solvant extraction to prevent any ageing of the nanoparticles in the aqueous solution. In practical, the collection vial containing a cationic surfactant didodecyl-35 dimethyl ammonium bromide (C 26 H 56 BrN, DDAB, C=0.02M) in cyclohexane was stirred at around 200 rpm with a glass helix stirrer. [START_REF] Mériguet | [END_REF] A stable colloidal suspension of nanoparticles coated by DDAB is obtained in the cyclohexane phase. Samples for Transmission Electron Microscopy (TEM) were prepared by placing a single drop of the resulting 45 suspension onto a 200 mesh holey carbon-coated copper grid (SPI) which was then allowed to dry in air. The suspensions obtained by Fe(II)/Fe(III) coprecipitation were also analysed by Vibrating Sample Magnetometry (VSM). As the flow of TMAOH was fixed (Q out =400 µ l/min) and the 50 volumetric flow of the iron precursors mixture was increased (10 < Q in < 100 µ l/min), colour changed from brown to black, characteristic of magnetite Fe 3 O 4 . The suspensions obtained in cyclohexane are always stable. However, Dynamic Light Scattering (DLS) measurements of the aqueous solutions 55 showed that the colloidal suspension exhibits the lowest hydrodynamice size (d H =120 nm) for a ratio Q out /Q in ~4. TEM observation of the colloidal suspension in cyclohexane indicated that the nanoparticles produced in the channel are fairly spherical with an average size around 7 nm. The 60 evidence of their cristallinity is provided by the electron microdiffraction pattern in the inset of Fig. 2, which shows the presence of the maghemite phase γ-Fe 2 O 3 . Although suspensions obtained in cyclohexane are stable in zero magnetic field. They sediment in the presence of a 65 magnetic field gradient (for example on a strong permanent magnet), which suggests a magnetic character. This observation agrees with the VSM measurement on a stable unquenched (aqueous) suspension: the magnetization curve (Fig. 3 value about 2.6x10 +5 A/m usually obtained for nanoparticles of approximatively the same sizes prepared with the standard large scale synthesis. [START_REF] Gazeau | COMSOL Multiphysicss simulations and focusing defocusing images[END_REF] Therefore we can deduce that compared to classical ones, nanoparticles prepared within few seconds in a millifluidic channel exhibit only a small decrease of ordering of their magnetic moments.

We have demonstrated that aqueous dispersions of superparamagnetic iron oxides nanoparticles can be prepared on chip in a millichannel reactor by providing a cylindrical geometry of the device and the use of TMAOH as alcaline

  50

Fig. 1

 1 Fig. 1 Coaxial flows device operating under laminar regime. The inset image shows the outlet of the inner capillary with the solution of iron +II and iron +III flowing into the stream of TMAOH alkaline solution. region to the outlet is 3cm. A (poly) tetrafluoroethylene (PTFE) tube (500µ m ID and 10cm long) leading to a sample 55

Fig. 2

 2 Fig. 2 TEM image of nanoparticles prepared in the channel (for flow rates Qin = 100 µl/min and Qout =400 µl/min). The inset shows the electron microdiffraction pattern with the Miller indices of γ-Fe2O3

Fig. 3

 3 Fig. 3 Magnetisation curve of a stable suspension in water of nanoparticles produced in the millifluidic device. The inset curves represent the fitting Log-normal laws for the numbers distribution (solid 80

10 reagent.

 10 These results open the way to other experiments such as online fonctionnalization, online detection and structural measurements of the nanoparticles. A further miniaturization of the channels would enhance the time resolution and enable kinetic studies of the coprecipitation mechanism.AknowlegdmentsWe would like to thank Dr. Hervé Willaime from "Microfluidics, MEMS & Nanostructures" (MMN) laboratory 20 at ESPCI, France and Dr. Caroline Derec, from "Matières et Systèmes Complexes" (MSC) laboratory at Univ Paris 07, France for their very fruitful discussions at the beginning of this work . We thank also Patricia Beaunier from the Service de Microscopie Electronique de Paris 6 for TEM images. 25 Notes and references a Laboratoire Liquides Ioniques et Interfaces Chargées (LI2C), UMR7612 UPMC Univ Paris 06 / CNRS / ESPCI, Université Pierre et Marie Curie, 4 place Jussieu, case 51 75252 Paris cedex 5, France. Fax: +33 (1) 30 44273228; Tel: +33 (1) 44273166; E-mail: abouhas@ccr.jussieu.fr b Laboratoire "Microfluidics, MEMS & Nanostructures" (MMN), UMR7083 CNRS / ESPCI, Ecole Supérieure de Physique et de Chimie Industrielles de Paris, 10 rue Vauquelin 75231 Paris cedex 5, France