Stability of Superparamagnetic Iron Oxide Nanoparticles at Different

Mar 12, 2012 - The detection of superparamagnetic nanoparticles using NMR logging has the potential to provide enhanced contrast in oil reservoir rock...
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Stability of Superparamagnetic Iron Oxide Nanoparticles at Different pH Values: Experimental and Theoretical Analysis Yoonjee Park,† Ragnhild D. Whitaker,†,⊥ Rikkert J. Nap,§ Jeffrey L. Paulsen,∥ Vidhya Mathiyazhagan,‡ Linda H. Doerrer,‡ Yi-Qiao Song,∥ Martin D. Hürlimann,∥ Igal Szleifer,§ and Joyce Y. Wong*,† †

Department of Biomedical Engineering and ‡Department of Chemistry, Boston University, Boston, Massachusetts 02215, United States § Department of Biomedical Engineering and Chemistry of Life Processes Institute, Northwestern University, Evanston, Illinois 60208, United States ∥ Schlumberger-Doll Research, Cambridge, Massachusetts 02139, United States S Supporting Information *

ABSTRACT: The detection of superparamagnetic nanoparticles using NMR logging has the potential to provide enhanced contrast in oil reservoir rock formations. The stability of the nanoparticles is critical because the NMR relaxivity (R2 ≡ 1/T2) is dependent on the particle size. Here we use a molecular theory to predict and validate experimentally the stability of citric acid-coated/PEGylated iron oxide nanoparticles under different pH conditions (pH 5, 7, 9, 11). The predicted value for the critical surface coverage required to produce a steric barrier of 5kBT for PEGylated nanoparticles (MW 2000) was 0.078 nm−2, which is less than the experimental value of 0.143 nm−2, implying that the nanoparticles should be stable at all pH values. Dynamic light scattering (DLS) measurements showed that the effective diameter did not increase at pH 7 or 9 after 30 days but increased at pH 11. The shifts in NMR relaxivity (from R2 data) at 2 MHz agreed well with the changes in hydrodynamic diameter obtained from DLS data, indicating that the aggregation behavior of the nanoparticles can be easily and quantitatively detected by NMR. The unexpected aggregation at pH 11 is due to the desorption of the surface coating (citric acid or PEG) from the nanoparticle surface not accounted for in the theory. This study shows that the stability of the nanoparticles can be predicted by the theory and detected by NMR quantitatively, which suggests the nanoparticles to be a possible oil-field nanosensor. effect on the signal of the bulk fluid, shortening the relaxation time of its NMR signal decay.4 The quantification of stable nanoparticles is possible because the change in the relaxation rate ΔR2 (reciprocal relaxation times, 1/T2) is proportional to the concentration of nanoparticles.4 Our long-term goal is the use of the nanoparticles as NMR nanosensors in oil fields, where we envision NMR relaxometry directly detecting them either within the formation from the well bore5,6 or in extracted fluid samples at the well site. Ultimately, the successful application of the nanoparticles requires that they be easily detected and stable under high salinity and at typical pH ranges in the reservoir (pH 6.5 to 8.5) and also under basic conditions (pH 11 to 12) required for the hydraulic fracturing of lowpermeability formations. Here, we focus on developing a simple model system in which we can test both theoretically and experimentally the pH effects of particle aggregation. Particle stability is critical because changes such as aggregation or

1. INTRODUCTION With increasing demands for energy, there is great interest in the further extraction of hydrocarbons from mature oil fields. Because of a lack of knowledge about the reservoir properties and the spatial configuration of the remaining oil, 60% of the oil typically remains underground even after secondary and sometimes tertiary attempts to recover the resource.1 Improved reservoir characterization would not only allow for better oil field development but also improve secondary enhanced oil recovery efforts by increasing efficiency and reducing cost. Conventional microelectronic sensors are not able to enter the formation because they are larger than the typical throat size range of conventional reservoir rock (0.03 to 10 μm).2 To overcome these size limitations, the application of nanotechnology, especially nanoparticles, holds great promise. Superparamagnetic iron oxide (SPIO) (Fe3O4) nanoparticles have been used successfully in biomedical applications as contrast agents in magnetic resonance imaging (MRI) because they can be made relatively easily and have excellent nuclear magnetic resonance (NMR) T2 contrast at low concentrations.3 These contrast agents are detected indirectly through their © 2012 American Chemical Society

Received: November 23, 2011 Revised: March 9, 2012 Published: March 12, 2012 6246

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exchanged with citric acid. The oleic acid-coated nanoparticles were dissolved in a DCB/DMF mixture, citric acid was added, and the mixture was heated to 100 °C for 24 h. Diethyl ether was added upon cooling the mixture to room temperature in order to precipitate light-brown particles. Finally, citric acidcoated iron oxide nanoparticles (CA Fe NPs) were extracted upon washing with acetone (10 mL) and diethyl ether several times to remove unreacted citric acid. The CA Fe NPs were further functionalized with amineterminated poly(ethylene glycol) (PEG) of varying chain lengths (75, 550, 2000, 5000, and 10 000 Da) following a method used in ref 15. PEG was grafted onto the surface using N-hydroxysuccinimide (NHS) ester and 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC) in pH 9 for 24 h on an agitator at room temperature. For 50 mg of CA Fe NPs in 10 mL of a pH 9 solution, 50 mg of EDC, 60 mg of NHS ester, and 10−5 mol of each PEG (i.e., 100 mg for PEG 10 000 Da) were used. The PEG Fe NPs were obtained after they were dialyzed for 48 h in pH 9 water. 2.3. Characterization of CA Fe NPs and PEG Fe NPs. 2.3.1. TEM. A 400-mesh copper grid, with a carbon-coated Formvar resin, was glow discharged prior to use. The grid was contacted for about 5−10 min with the sample and then blotted with a filter paper. The remaining water was allowed to evaporate. Samples were examined using an FEI/Philips CM100 TEM (FEI Company, Hillsboro, OR) using LaB6 filament at 100 kV. The polydispersity of individual particles, σ, was calculated to be σ = δ/davg × 100%, where δ is the standard deviation and davg is the average diameter of an individual nanoparticle from TEM images. 2.3.2. Elemental Analysis. The Fe NP samples were analyzed at Intertek QTI Laboratory (Whitehouse, NJ) for carbon, nitrogen, and hydrogen content by combustion elemental analysis. Nanoparticle samples in pH 9 water were dried in scintillation vials before being transported to Intertek QTI. The results allowed us to determine quantitatively the nanoparticle surface composition for different PEG molecular weights. 2.3.3. Dynamic Light Scattering (DLS). Measurements were made at a wavelength λ of 659 nm at 25 °C with a Brookhaven 90Plus (Brookhaven Instruments, Holtsville, NY). The Fe NP samples were measured at a concentration of 20 ppm. Three 2 min measurements were made for each sample. 2.3.4. Zeta (ζ) Potential Measurements. The Fe NP solutions were tested at 25 °C with a Brookhaven 90Plus using PALS Zeta Potential Analyzer software. Each measurement consisted of 20 cycles, and 5 measurements were made with each sample. 2.3.5. Quantification of Fe NPs. The number of Fe NPs was analyzed by quantifying the iron (Fe3+) concentration in Fe3O4 nanoparticles (NPs). Iron (Fe3+) in Fe3O4 was reduced to Fe2+ by adding 2 μL of thioglycolic acid (Sigma-Aldrich, St. Louis, MO) to 100 μL of a sample. After 2 h, 200 μL of 10% hydroxyl amine (Sigma-Aldrich), 300 μL of 0.25% phenanthroline (Sigma-Aldrich), 15 μL of 2.5% sodium citrate (Sigma-Aldrich), and DI water up to 1 mL were added, resulting in the [Fe(Phen)3]2+compound. The concentration of Fe2+ was measured by UV−vis absorbance at 510 nm and determined by a calibration curve in parts per million. 2.4. Stability of CA Fe NPs and PEG Fe NPs. 2.4.1. Molecular Theory. The theoretical approach predicts the effective interaction between two nanoparticles that are coated with both citric acid (CA) and poly(ethylene glycol) (PEG)

alterations to the coating will alter or hinder their transport through a porous rock formation. Finally, NMR contrast from the nanoparticles is sensitive not only to their concentration but also to their state, complicating their quantification in any eventual application. In this study, to predict nanoparticle stability, we developed a molecular theory to determine the interactions between SPIO nanoparticles coated with poly(ethylene glycol) (PEG). The molecular theory explicitly incorporates the molecular details of each of the different species in the system treated. Hence, the size, shape, conformation, and charge distribution of every molecule type, which includes the PEG molecules, citric acid, dissolved salts, water, and SPIO nanoparticles, are accounted for.7−10 Also, unlike other models, it does not involve the Derjaguin approximation, which is valid only for the low curvature of a particle.11−15 The predictions of the interaction between the two nanoparticles as a function of the polymer molecular weight, pH, and size of the nanoparticles enable us to gain insight into the stability of the nanoparticles under different conditions. Results from the characterization of the nanoparticles, such as the size and surface coating coverage, were used as inputs for the molecular theory. The theoretical predictions were then compared to the experimental results (dynamic light scattering, TEM, and NMR measurements) in order to validate the theoretical model.

2. METHODOLOGY 2.1. Materials. Iron tri(acetylacetonate) (99.9%), citric acid (CA, 99.5+%), methanol (99.8%), and acetone were purchased from Sigma (St. Louis, MO). Benzyl ether (99%), Nhydroxysuccinimide ester (NHS ester, 98%), oleic acid (OA, 90%), and oleyl amine (OAm, 70%) were purchased from Aldrich (St. Louis, MO). 1,2-Dichlorobenzene (DCB, 99%), N,N′-dimethylformamide (DMF, 99.8%), diethyl ether (99.9%), and hexane (99.9%) were purchased from Acros (Morris Plains, NJ). 1-Ethyl-3-(3-dimethylamino-propyl)carbodiimide hydrochloride (EDC, 97%) was purchased from Fluka. Ethanol (ACS grade) was purchased from Pharmco (Lees Summit, MO). Amino end-functionalized poly(ethylene glycol) (NH2- PEG) with molecular weights of 75, 550, 2000, 5000, and 10 000 Da was purchased from Laysan Bio, Inc. (Arab, AL). Water used for all experiments was distilled with a Myron L Company series 750 (Carlsbad, CA) and had a resistivity of 16 MΩ at 25 °C. 2.2. Synthesis of CA Fe NPs and PEG Fe NPs. Oleic acidcoated iron oxide nanoparticles were first synthesized by a method presented by Sun et al.16 and further modified to yield citric acid-coated iron oxide nanoparticles following a method described in ref 17. Briefly, iron(III) tri(acetylacetonate) [Fe(acac)3] (2 mmol), benzyl ether (40 mL), 1,2-tetradecanediol (10 mmol), oleic acid (6 mmol), and oleylamine (6 mmol) were mixed and stirred magnetically under a flow of nitrogen. The mixture was heated at 2°/min to 100 °C and kept for 45 min, followed by heating to 200 °C at 2°/min and holding for 2 h. Subsequently, the reaction mixture was heated to reflux (∼300 °C) and held for another 30 min to 1 h. The reaction mixture was cooled to room temperature and washed with ethanol, and precipitates were collected using a magnet. The precipitates were dissolved in hexane (10−15 mL) and centrifuged at 3000 rpm for 5 min. The oleic acid-coated iron oxide nanoparticles were stored after the washing step with excess ethanol and after the drying step in a vacuum oven. To obtain water-soluble NPs, oleic acid capping of the NPs was 6247

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molecules and submerged in an aqueous solution of fixed pH and salt concentration of dissociated sodium chloride. From a knowledge of the effective interactions between the two coated NPs, one can determine whether the coated NPs are stable in solution or whether they will tend to aggregate. The coated NP consists of a sphere of radius R with NPEG polymers endtethered to the surface and NCA citric acid molecules. The theoretical approach used in this work is based on a molecular theory that for each molecular species treats the size, shape, charge distribution and conformations explicitly.7,9 We formulate the free energy of the system, and its minimization provides for the probability of each chain conformation and the distribution of all molecular species and their state of charge. Therefore, the spatial arrangement of the PEG chains and the degree of charge of citric acid molecules coating the two interacting NPs as well as the ion and solvent distribution are not imposed but are obtained as an output of the theory for each separation distance D. Namely, for each distance between the two coated NPs, the degree of charge of the citric acid and the molecular organization of the PEG chains coating the NPs and the distribution of the cations, anions, water, protons, and hydroxyl ions are those that minimize the free energy. The free energy of the system is expressed as a function of the polymer probabilities, the density distribution of all molecular species, and the fraction of charged and uncharged groups of the citric acid molecules found on the NPs. The total free energy for two NPs separated at a distance D, F(D), describing the system is F(D) = −TSconf − TSmix + Eelec + Erep + Echem + EvdW + Emag. Here, T is the absolute temperature. Sconf is the conformational entropy of the polymer chains tethered to the two NPs; Smix is the (translational) mixing entropy of the cations, anions, water, protons, and hydroxyl ions; Eelec corresponds to the total electrostatic energy; Erep represents the steric repulsions between all molecular species; Echem is the free energy of the acid−base chemical equilibrium (i.e., the enthalpic and entropic costs associated with charging and uncharging of the citric acid molecules found on the surfaces of the NPs); and EVdW and Emag correspond to van der Waals and magnetic attractions between the two NP cores, respectively. In the Supporting Information (SI), explicit expressions for each term in the freeenergy functional are presented and their meaning and content are discussed. Furthermore, the minimization procedure and technical details of the calculation are presented. The attractive van der Waals and magnetic interactions tend to aggregate the coated NPs whereas the loss of conformation entropy of the PEG chains as the NPs are brought close together and the electrostatics repulsions work to repel the coated NPs. By calculating the total effective interaction between two coated NPs, one can determine whether the coated NPs are stable in solution or whether they will tend to aggregate. The predictions of the molecular theory have been shown to be in excellent quantitative agreement with experimental observations for a large variety of systems relevant to the studies presented here, including the structure and thermodynamics of grafted poly(ethylene glycol) layers7−9 and the effective charge of ligand-modified nanoparticles.10 Therefore, we believe that the predictions presented here are reliable. 2.4.2. Experimental Conditions. The 20 ppm Fe NP dispersions were stored for 30 days in pH 5, 7, 9, and 11 buffer solutions at 25 °C. Ten millimolar phosphate buffer solutions were used. The average hydrodynamic diameter (Dh) and R2(1/T2) relaxivity of the Fe NP dispersions were

measured for 30 days approximately every 3 days, and the results shown are the average of two sets of measurements. TEM images were taken right after the Fe NPs were prepared and 5 days later. 2.4.3. NMR Relaxation Measurements. The NMR response of the nanoparticles (36.7, 25.8, and 27.9 ppm for CA Fe NP, PEG 2K Fe NP, and PEG 5K Fe NP, respectively, as determined in section 2.3.5) at different pH values was monitored for a month. All NMR measurements were performed at a 2 MHz proton frequency with a 15.2 G/cm gradient in the fringe field of a 2T horizontal bore imaging magnet in a 2.5-cm-diameter tuned solenoid coil using a KEA spectrometer and a 2 kW Tomco RF pulse amplifier. This particular selection of the proton resonance frequency and field gradient is similar to that of existing NMR tools used in oil well logging.5,6 We emphasize that these experimental conditions are very different from those of typical NMR spectroscopy applications used for chemical and structural analysis: the magnetic field is several orders of magnitude lower in strength, while the field gradient (spatial variation of the field strength) is several orders of magnitude larger. Thus, neither chemical shift resolution nor the direct detection of trace quantities is possible in well logging, leaving relaxation and diffusion analysis of the bulk fluids as the primary NMR techniques available.5,6 The Fe NPs create a strong shift in the observed transverse relaxation time T2 of the bulk fluid, allowing their detection at low concentrations and small magnetic fields. The T 2 measurements were performed with a standard CPMG sequence.4 This allowed us to monitor the relaxation properties of the particles and examine the effect of particle aggregation on this detection technique in view of eventual field applications. The CPMG sequence repeatedly refocuses the NMR signal (Supporting Information Figure S.3) and is essential to observing the signal in the presence of the short T2* dephasing time arising from the permanent gradient.5,6 A rapid refocusing of the signal is needed to minimize the contribution to signal decay from fluid self-diffusion in the existing gradient.6,18 We monitor the shift in relaxation rates, ΔR2 ≡ 1/T2,[C] − 1/T2,[0] where T2,[C] is the transverse relaxation time at a concentration [C] of the Fe NPs. ΔR2 is proportional to the nanoparticles concentration: ΔR2 = k2[C].9 The proportionality constant k2 is the relaxivity and is sensitive to the aggregation of the nanoparticles. We also performed a simultaneous diffusion measurement with a modified CPMG measurement6,18 (Figure S.3). In this sequence, the first two echo spacings are systematically varied. It is identical to a D−T2 sequence for these NMR oil well logging tools used to correlate the relaxation time, T2, and the apparent self-diffusion constant, D, to identify fluids.18,19 The diffusion measurements are used to confirm that the measured relaxation times are independent of the echo spacing. All sequences used excitation and refocusing pulses of 30 μs duration with an echo spacing of tE = 350 μs. One thousand echoes were collected. The refocusing pulses have double the amplitude of the excitation pulse to produce 90 and 180° pulses, respectively. The D−T2 sequence starts with two echoes with long echo spacings (0.5 to 15.0 ms, 12 values) and is followed by a standard CPMG train using the default echo spacing of tE = 350 μs. T2 values from the CPMG experiment are extracted by a least-squares fit of the decay to an exponential curve. The decay of the modified CPMG undergoes 2D “inversion” for a D−T2 map18 to account for the echo time-dependent diffusion term. In short, the inversion 6248

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starts with the matrices (kernels) for the 1D inversions of D and T2 and retains only the largest singular values of their SVD decompositions to create a single matrix relating the acquired data set and the D−T2 map. A Kirchoff (least-squares) regularization is then used to generate a smooth D−T2 map consistent with the acquired data. This is an ill-conditioned inversion problem, and the reader is referred to the following texts for its correct implementation.18,19 2.4.4. FTIR. FTIR experiments were performed in order to examine the surface coating under different pH conditions on a Nicolet 4700 FTIR instrument (Thermo Scientific, West Palm Beach, FL) using a Smart Orbit diamond ATR accessory. Spectra were recorded in the wavenumber interval between 4000 and 400 cm−1. Each nanoparticle dispersion was stored at 25 °C for 7 days and dialyzed in a corresponding pH solution for 2 days. Then the samples were lyophilized and analyzed on the ATR accessory. The background spectrum from air was subtracted from the sample spectrum. Each spectrum was acquired twice, and an average of the two measurements was analyzed.

3. RESULTS 3.1. Characterization of CA Fe NPs and PEG Fe NPs: Size, Surface Charge, and Surface Coverage. The citric acid-coated iron oxide nanoparticles (CA Fe NPs) and the PEGylated iron oxide nanoparticles (PEG Fe NP) were characterized by several methods to determine individual particle sizes, the ensemble particle size distribution, and the surface chemistry. When the NP dispersions were prepared, the pH values were around 7. TEM images showed that the CA Fe NPs and the PEG Fe NPs with 2000 MW PEG (PEG 2K Fe NPs) consisted of iron oxide cores of 6−11 and 5−11 nm in diameter, respectively (Figure 1). The average diameters from the TEM images for CA Fe NPs and PEG 2K Fe NPs were both 8 nm. Polydispersities were 14 and 27%, respectively, indicating that CA Fe NPs were more monodisperse. CA Fe NPs and PEG 2K Fe NPs looked similar in the TEM images because PEG chains are not visible in TEM and the distances between the particles may become small during the preparation of the sample grid when the sample liquid is evaporated. The hydrodynamic effective diameter of CA Fe NPs, measured by dynamic light scattering (DLS), was 60 ± 2 nm, and the size range between 20 and 80% of the total distribution calculated on the basis of the Gaussian distribution was 52−68 nm. The zeta potential value of CA Fe NPs was −8 ± 1 mV. The density of the CA or PEG coatings on the nanoparticles was characterized by CHN combustion analysis (Table 1). According to the results, the number of CA capping molecules on each NP was 4.33 per nm2 and the number of PEG chains grafted to the NPs ranged from 2.19 to 0.0422 per nm2 depending on the molecular weight of the PEG chain. As the PEG molecular weight increases, the number of PEG chains grafted onto the NPs decreases. The values of the size and the surface coverage were used as input for the theory (Theoretical Results on NP Stability section). 3.2. Stability of CA Fe NPs and PEG Fe NPs. 3.2.1. DLS Data and TEM Images. The stability of CA Fe NPs and PEG Fe NPs under different pH conditions was studied over a 1 month period. The average hydrodynamic diameter (Dh) of NP dispersions at four different pH values, as measured by DLS for 30 days, stayed almost the same for all kinds of NP dispersions except at pH 11 (Figure 2). For CA Fe NPs at pH 11, Dh increased from 46 to 170 nm after 30 days, and for PEG 2K Fe

Figure 1. TEM of 1-day-old nanoparticles at pH 7: (A) CA Fe NPs and (B) PEG 2K Fe NPs.

Table 1. Elemental Analysis Results for CA Fe NPs and PEG Fe NPs and Calculation of the Number of Capping Molecules on Each Nanoparticle capping molecules CA PEG PEG PEG PEG PEG

75 550 2K 5K 10K

% carbon 4.6 1.1 1.69 2.07 2 3.06

weight of capping in 1 mg (mg) 1.23 2.29 3.45 3.90 3.67 5.64

× × × × × ×

10−1 10−2 10−2 10−2 10−2 10−2

capping molecules per NP 2.02 9.92 2.07 6.46 2.43 1.91

× × × × × ×

103 102 102 101 101 101

molecules/ nm2 4.33 2.19 4.58 1.42 5.37 4.22

× × × × × ×

100 100 10−1 10−1 10−2 10−2

NPs and PEG 5K Fe NPs, it increased from 64 to 830 nm and from 56 to 930 nm, respectively. PEG-coated Fe NPs showed a more rapid increase in size and larger aggregates than did CA Fe NPs at pH 11. The effect of the PEG MW in this study was not significant between PEG 2K and PEG 5K for all pH values. TEM images show aggregates of CA Fe NPs and PEG 2K Fe NPs at pH 11 when observed 5 days after the dispersions were prepared (Figure 3). The aggregates of the 5-day-old CA Fe NPs at pH 11 varied in size and shape, with the size varying from 50 to 200 nm. Particle fusion or degradation was barely observed, showing individual particle diameters from 5 to 11 6249

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Figure 2. Average hydrodynamic diameters of (A) CA Fe NPs, (B) PEG 2K NPs, and (C) PEG 5K NPs at the four different pH values measured by DLS: 5, 7, 9, and 11.

nm in the aggregates. Aggregates from PEG 2K Fe NPs at pH 11 were larger but less dense than the aggregates from CA Fe NPs. These observations from TEM images agreed well with the DLS results. The analysis of the aggregation mechanism will be further discussed in the Quantitative Comparison: Extracting Dh from R2 Data section 3.2.2. NMR Relaxivity (1/T2) Data. The aggregated form of the NPs dephases the spins of the surrounding protons of water molecules more efficiently than do individual NPs present in the dispersed state.20 The effect was observed when the T2 relaxivity (1/T2 = R2) was measured for 30 days for CA Fe NPs, PEG 2K Fe NPs, and PEG 5K Fe NPs, with the same conditions as in the DLS stability study (DLS Data and TEM Images section) such as pH and concentration (Figure 4). As the average hydrodynamic diameter increases, the R2 value also increases. For freshly prepared particles, the relaxivity values of PEG Fe NPs are approximately ∼0.4 s−1 ppm−1 and are generally greater than those of CA Fe NPs by ∼0.1 s−1 ppm−1. A likely explanation of the effect of the PEG coating on T2 can be explained if the NPs are coated with a dilute polymer matrix that allows water to diffuse into the NP coating.21 As detailed later in the Quantitative Comparison: Extracting Dh from R2 Data section, the relaxation rate is proportional to the time that the individual fluid molecules stay within the vicinity of the nanoparticles. The coating increases this time and hence the relaxivity by slowing down the diffusive motion of the water within the polymer matrix. This effect has been intentionally used to increase the relaxivity of particles in ref 21. 3.2.3. Theoretical Results on NP Stability. We investigated NP−NP interactions as a function of pH, salt concentration, and NP surface functionalization. Subsequently, the behavior of the NP−NP interactions was studied for many conditions: different NP radii and number and length of PEG chains. The

Figure 3. TEM images of (A) 5-day-old CA Fe NPs and (B) 5-day-old PEG 2K Fe NPs at pH 11.

results of these calculations were summarized in a stability diagram that provides guidelines for the rational design of the polymer-coated nanoparticles. 3.2.3.1. Effect of pH on the Stability. The interaction between PEG 2K NPs at different pH values with different salt concentrations was predicted within the framework of the molecular theory as outlined in the theory section (section 2.4.1 and Supporting Information) (Figure 5). The system corresponds to the experimental NP system of the Fe NP covered with PEG 2K. The NP core has a radius of R = 5 nm, and the surface coverage of PEG and citric acid units is σPEG = 0.142 nm−2 and σCA = 4.33 nm−2, respectively. The Hamaker constant A = 4.0 × 10−19 J and the magnetic saturation M = 4.46 × 105 Am−1 were used.22,23 Figure 5A,B corresponds respectively to pH 5 and 7. With increasing pH and decreasing salt concentration, the interaction free energy increases. At low pH, there is almost no effect of changing the salt concentration upon the interaction between the two tethered NPs because NPs with citric acid units at low pH values have a very small amount of charge and hence the system behaves like a neutral system. With increasing pH, the size and range of the repulsions increase. Likewise, the repulsions increase in size 6250

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the acid−base equilibrium toward its uncharged state. The first option reduces the translational entropy of the counterions, whereas the free-energy penalty in shifting the acid−base equilibrium toward its uncharged state involves the free energy of reaction for weak carboxylic acid groups of the citric acid molecule (pKa = 5): the latter is less costly than counterion confinement. Consequently, with decreasing salt concentration the fraction of charged acid groups decreases. The packing of the acid molecules onto a nanosized particle significantly alters both the quantitative and qualitative behavior of the acid molecules. The presence of the PEG chains also influences the degree of charging. With an increasing number of polymer chains, the penalty of confining counterions increases because of the increase in the excluded volume interaction. However, in the present case the amount of polymer is relatively small compared to the number of citric acid units, hence this effect is relatively unimportant. More details on the description of the effect of pH and salt for the case of tethered weak polyelectrolyte layers and nanoparticles coated with ionizable surfactants can be found in refs 9, 24, and 25. 3.2.3.2. Stability Diagram. We explored quantitative aspects of the NP stability, which was defined as how many PEG molecules (surface coverage) are needed to coat the NP and prevent a solution of PEG-coated nanoparticles from aggregating. We computed the critical PEG surface coverage σ* required to set up a steric barrier that will prevent aggregation. The barrier height for stability was chosen to be 5kBT. The results are presented in Figure 6, showing the critical surface coverage as a function of the NP core radius and polymer length. NPs having a surface coverage of PEG exceeding the critical surface coverage (σ > σ*) (i.e., above the surface/curves presented) will be stable against aggregation whereas for NPs having a surface coverage that is less than the critical coverage (σ < σ*) the NP solution will be unstable. With increasing polymer length, fewer PEG chains are required for stabilization because with increasing polymer length and surface coverage the steric repulsion increases (Supporting Information). With increasing NP core size, the required surface coverage decreases and starts to approach asymptotic values for larger NPs as the effect of curvature diminishes. The left graph in Figure 6 clearly illustrates the functional dependence of the critical surface coverage. However, it is difficult, on the scale of the graph, to read the actual values of the critical surface coverage. For this purpose, we also present the right graph in Figure 6, which shows the critical surface coverage as a function of the NP core radius for various polymer chain lengths.

Figure 4. T2 relaxivity (R2) of (A) CA Fe NPs, (B) PEG 2K NPs, and (C) PEG 5K NPs at 2 MHz under the four pH conditions: 5, 7, 9, and 11.

and range with decreasing salt concentration. When the NPs become charged, the electrostatic interactions increase. It is also important to point out the quantitative effect of the electrostatic interactions. The repulsions between the NPs increase by a factor of almost 2 when the pH is changed from 3 to 7. For low pH, the acid−base equilibrium of the surface acid is shifted toward its uncharged state. Increasing the pH leads to a shift in the acid−base equilibrium toward the charged state (i.e., an increase in the fraction of charged acid units). It is important to emphasize that the molecular theory does not assume a priori the nanoparticle charge. Instead, it predicts the charge state for each condition and as a function of the separation distance between nanoparticles, as discussed next. The effect of the salt concentration can be explained as follows. With decreasing salt concentration, the electrostatic repulsions between the citric acid units on the surface of the NP increase, as the charges become less shielded. The system can respond in two ways to compensate for these large, energetically unfavorable repulsions. The system either (1) recruits extra counterions from the bulk solution or (2) shifts

Figure 5. The free energy of two interacting NPs as a function of the surface-to-surface separation of the NPs for different salt concentrations at (A) pH 5 and (B) pH 7. R = 5 nm, σPEG2K = 0.142 nm−2, and σCA = 4.33 nm−2. 6251

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Figure 6. Stability diagram. (Left) Critical surface coverage as a function of the radius of the NP core (R) and the PEG chain length (N). (Right) Critical surface coverage as a function of the radius of the NP core for different PEG lengths. The red line on the surface of the left graph delineates the critical surface coverage for NPs coated with PEG 2K.

Here we considered the situation where the NP does not have any acid groups (i.e., the charge stability does not assist the steric repulsion in stabilizing the NP solution, which is different from that in the previous section, Effect of pH on the Stability). Consequently, the critical surface coverage presented in Figure 6 corresponds to the worst possible scenario. Note also that the critical surface coverage depends on the strength of the van der Waals and magnetic attractions, whose strength is characterized by the Hamaker constant (A = 4.0 × 10−19 J) and the magnetic saturation (M = 4.46 × 105 A m−1), respectively. Note that for the values of A and M the van der Waals interactions dominate the magnetic interactions. It should also be noted that the Hamaker constant is chosen to be relatively large so as to provide the upper bound for the critical surface coverage of the PEG chains coating the NPs.

4. INTERPRETATION AND DISCUSSION 4.1. Comparison of Experiment and Theory. 4.1.1. Moderate−Low-pH Conditions. The moderate conditions correspond to the well-bore conditions from pH 6.5 to 8.5. In the stability diagram from theory (Figure 6), the comparison with the experimental systems indicated that the PEG-coated nanoparticles have sufficient surface coverage for the solution of NPs to be stable. For example, the experimental NP coated with PEG2K was σPEG2K = 0.142 nm−2, whereas the theoretical critical surface coverage is σ*PEG2K = 0.078 nm−2 for R = 5 nm. Moreover, Figure 5 shows that, for the experimental NP coated with PEG 2K, the height of the steric barrier has values ranging from 45kBT to 70kBT with increasing pH from 5 to 7. The barrier height is well above our stability criteria of 5kBT. Hence these NPs should remain stable under these conditions. Smaller NPs with radii of R = 3 and 4 nm have a critical surface coverage of σ*PEG2K = 0.106 and 0.087 nm−2, respectively, which is still lower than the experimentally measured value. Therefore, under the moderate−low-pH conditions, the experimental results are in agreement with the theoretical predictions. 4.1.2. High-pH Condition. Under higher pH conditions, the DLS results indicated NP aggregation, whereas the theory suggested that the NP solution should become increasingly stable as the barrier height increases at higher pH. FTIR spectra of 7-day-old CA Fe NPs and PEG 2K Fe NPs at pH 9 and 11 were collected to examine the surface coatings (Figure 7). CA Fe NPs at pH 9 showed distinctive peaks at 1593 and 1362 cm−1, which are typical of carbonyl stretches in carboxyl groups,

Figure 7. Representative FTIR spectra, displaced vertically for clarity, of 7-day-old CA Fe NPs and PEG 2K Fe NPs at pH 9 and 11. (1) CA Fe NPs at pH 9, (2) CA Fe NPs at pH 11, (3) PEG 2K Fe NPs at pH 9, and (4) PEG 2K Fe NPs at pH 11.

and at 1068 cm−1, which is consistent with hydroxyl groups.17 PEG Fe NPs at pH 9 showed PEG peaks at 2970 cm−1 from CH2 groups, at 1373 cm−1 from C−O−C ether vibrations, and at 1215−1230 and 1041 cm−1 from C−O−C ether stretches.26 The spectrum of CA Fe NPs at pH 11 did not show any peaks from the carboxylic acid group, which were shown in the spectrum of CA Fe NPs at pH 9. Also, the peaks of PEG and CA were not observed in the spectrum of PEG 2K Fe NPs at pH 11, which indicates the coating desorbed from surface. In the theoretical predictions, it was assumed that the PEG coating is tethered to the NP irreversibly at any pH value. When the PEG polymers dissociate from the NPs at higher pH and the surface coverage drops below the critical surface coverage, the NP solution will become unstable. Thus, the apparent discrepancy between theory and experiment at pH 11 can be explained by the desorption of the surface coating at this pH, which was not considered in the theory. 4.2. Quantification of the Stability from DLS Data Using Stability Ratio W. The dispersion stability was also evaluated quantitatively with the stability ratio W from DLS data. The kinetic rate constant of the Smoluchowski slow coagulation equation is ks = kf/W, where kf = 8kBT/3η is Smoluchowski’s fast coagulation rate constant, kB is the 6252

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Table 2. Stability Ratios W and t1/2 from the DLS Data in Figure 2 CA Fe NPs pH 5 7 9 11

W infinite infinite infinite 4.74 × 105

PEG 2K Fe NPs t1/2 (day)

W

infinite infinite infinite 5.5

5.93 × 10 2.12 × 107 infinite 9.70 × 104 5

PEG 5K Fe NPs t1/2 (day)

W

8.4 250 infinite 1.4

× × × ×

5.30 1.23 3.96 8.97

t1/2 (day) 5

10 107 106 104

7.5 175 56 1.3

Figure 8. Predicted hydrodynamic diameter of NPs extracted from R2 at pH 11: (A) CA Fe NPs and (B) PEG Fe NPs. Open dots represent DLS data.

Boltzmann constant, T is the absolute temperature, and η is the viscosity of the aqueous phase.27 For two spherical noncoalescing particles in contact, a relation between Rh(t) from DLS and ks or W for Rayleigh-sized particles was derived by Vaccaro and Morbidelli.28 Its asymptotic form for ksN0t ≪ 1 is R̅ h(t ) ≈ 1 + 0.55ksN0t R S0

characterized by the weak dephasing regime, where the interaction of the immediately surrounding fluid molecules with the nanoparticles is weak relative to the characteristic frequency of the motion of the bulk fluid molecules around the nanoparticle.4 Specifically, Δω−1 ≫ τD, where Δω is the frequency shift at the particle surface and τD is the characteristic time for water molecules to diffuse past a particle.4 In addition, the refocusing/echo time for the CPMG sequence is much longer than the diffusion timescale, tE ≫ τD, placing the relaxation process in the motional averaging (MA) regime, where the experimental refocusing time (tE) is far too long relative to the interaction of the fluid and nanoparticles (τD) to have a significant effect on the relaxation mechanism. In the MA regime, 1/T2 increases linearly with concentration, and the shift is unaffected by the timing of the echo pulses.4,30 Both of these properties were confirmed over the course of the stability test. For the particle concentrations considered (0−30 ppm), the dependence of R2 was observed to be linear with concentration, and no echo time dependence for R2 was observed in our control D−T2 measurements when varying the initial echo times. Both of these observations confirm that the relaxation induced by these nanoparticles is well within the MA regime. Approximating the particles and their aggregates as solid spheres, in the MA regime, we find that the relaxation has the following dependence31

(1)

where RS0 is the initial radius, here taken to be equal to the value at 1 h after sample preparation.29 By plotting the data in the form of [(Rh(t)/RS0) − 1] versus t, the value of ks or of W is obtained from the initial slope, which is normally determined from curve fitting. The stability ratio W values of the dispersions of CA Fe NPs at pH 5, 7, and 9 were infinite because the slopes of ks were flat (Table 2). The values of PEG 2K and PEG 5K Fe NPs at pH 5, 7, and 9 ranged from 5.3 × 105 to infinite, which indicates a measure of significant dispersion stability.27 In addition, these values show the stability as a function of pH qualitatively, which is in good agreement with the theoretical results. However, the W values of PEG 2K and PEG 5K at pH 11 are less than 105, implying that the dispersions are not stable. The W values for PEG 2K and PEG 5K were not significantly different. The half-life time t1/2 = (kfN0/W)−1, which is the time required to reduce N0 by 50% by aggregation, was also calculated and ranged from days to infinite. Even though the DLS and NMR results demonstrated good stability of both CA Fe NPs and PEG Fe NPs in pH 5 solution, the values of t1/2 indicated that the NPs at pH 7 and 9 were much more stable (Table 2). 4.3. Quantitative Comparison: Extracting Dh from R2 Data. The detection of SPIO NPs with NMR is through their effect on the signal of the bulk fluid. This interaction is a function of not only the magnetization of the NPs and their aggregates but also the relative motion of the bulk fluid’s molecules. Thus, depending on the specifics of the particles and the experimental settings, effects such as an experimental echo time dependence on relaxivity or aggregation changing the particle’s relaxivity are possible.4,30,31 For SPIO NPs, this interaction between the bulk fluid and the NPs is usually

R2 =

⎛4⎞ 2 ⎜ ⎟V (Δω) τ D ⎝9⎠

(2)

where V is the volume fraction of the particles and τD = r2/D is the diffusion correlation time, a function of the diffusion constant, D, and the sphere radius, r. For a quantitative comparison of the DLS and R2 data, a simple relaxivity model for nanoparticle aggregation suggested in refs 4 and 31 was applied. The size of an aggregate is approximated by its radius of gyration rG, which is the rootmean-square distance of the nanoparticles to the center of mass. The aggregates are assumed to be fractal in the sense that their size follows a power law dependence of a fractal 6253

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dimension, df ≠ 3 for the number of particles, n, in the aggregate. rG ∝ n1/ d f

ments showed that the 1/T2(R2) values scale with the particle aggregate size as a power law. This allows the extraction of the hydrodynamic diameter of the aggregates from the R2 data. The combination with T1 measurements that are sensitive to different particle properties could potentially allow us to quantify the NP concentration in the presence of aggregation. Their quantification with NMR in the presence of aggregation and other particle behaviors such as core degradation and adsorption is the subject of future work. NMR quantification with only T2 measurements requires a knowledge of the aggregation state and stable particles. Alternatively, additional measurements such as T1 with different sensitivities to particle properties could enable their quantification robustly in the presence of decay. Establishing the behavior of the system for many conditions will enable us to provide guidelines for the rational design of the NPs. An experimental determination of the stability of NPs at different pH values and predictions from the theory can therefore be used to determine the characteristics of NPs used in the enhanced characterization of reservoir rock, such as the size, surface coverage, and surface charge.

(3)

For eq 2, Δω = ( /3)μ0γM where μ0 is the free space magnetic permeability, γ is the proton gyromagnetic ratio, and M is the particle magnetization. M is roughly proportional to ρ, the density of an aggregate, which is the number of particles, n, per volume defined by rG. Therefore, from eq 2 the relationship between R2 and rG scales as 1

⎛ n ⎞2 R 2 ∝ ⎜ 3 ⎟ rG 2 ∝ rG 2d f − 4 ⎝ rG ⎠

(4)

where we use the substitution τD = Assuming that the effective hydrodynamic radius is equal (or proportional) to rG, which is reasonable,32 we obtained the predicted hydrodynamic diameters by fitting the R2 data at pH 11 to eq 4 (Figure 8). Power law fits of R2 to DLS diameters linearly interpolated the two nearest R2 values to the time of the DLS measurement before fitting. The extracted Dh shows quite good agreement with the DLS data. Thus, the quantitative measurement of SPIO NP aggregation with NMR is possible using the relaxivity model for the fractal aggregation analysis. However, the fractal dimension of the aggregates can depend on the particles type and possibly the decay conditions. The fractal dimensions obtained from the R2 data fitting for CA Fe NPs and PEG Fe NPs aggregating at pH 11 were 2.3 and 2.1, respectively. Typical values from other theoretical and experimental work for df are between 1.75 and 2.3.33 Molecular dynamics simulations and TEM studies both indicate that df is mechanism-dependent. When df =1.8, the aggregation is in the diffusion-limited regime, and when df = 2.1−2.5, it is in a reaction-limited regime.32,34 The TEM images of the CA Fe NPs and PEG Fe NPs in Figure 3 appear to be between the diffusion and reaction-limited types of clusters seen in prior outside work (Figure 2 of ref 32) for df = 1.8 and 2.5. Likewise, the df values extracted from the DLS and NMR data (df = 2.1 and 2.3) are between the two values of 1.8 and 2.5. This is consistent with the interpretation of the varying power law relation of the NMR R2 response on Dh arising from the formation of fractal aggregates. The fractal dimensions of the NPs suggest the NP aggregation mechanism for each kind of particle and enable us to perform quantitative analysis of NP aggregation using NMR and DLS, with the advantage of analyzing the particles directly in solution, which is not possible using TEM. rG2/D.

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ASSOCIATED CONTENT

S Supporting Information *

Free-energy functional for NP−NP interactions. Numerical methodology. The chain model. Theoretical results. Effects of molecular weight and surface coverage and the NP core size. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel: 617-353-2374. Fax: 617-353-6766. E-mail: jywong@bu. edu. Present Address ⊥

Department of Pharmacy, University of Tromsoe, 9037 Tromsoe, Norway.

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported in part by the Advanced Energy Consortium. We thank Mrs. Debby Sherman for advice and help with the electron microscopy images and the BU CORE Facility for DLS and FTIR. We also thank the Boston University UROP program for the partial funding of V.M..

■

5. CONCLUSIONS Complementary techniques of DLS, TEM, and NMR were used to analyze the SPIO NP stability quantitatively at different pH values and to compare it with molecular theory predictions. The critical surface coverage needed to produce a steric barrier was 0.078 nm−2 (less than the experimental value of 0.143 nm−2), and this implies that nanoparticles should be stable at all pH values. Under moderate- and low-pH conditions, both the theory and experiment showed that the NPs are stable. The disagreement between theory and experiment at high pH was resolved by confirming, using FTIR, that surface coating desorption occurs at high pH. The unstable coating at pH 11 caused NP aggregation, which indicates that different types of coatings may be needed in order to employ these NPs during hydraulic fracturing in oil fields. The NMR relaxivity measure-

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