Measuring Grafting Density of Nanoparticles (PDF)

Article pubs.acs.org/ac...

Article pubs.acs.org/ac Measuring the Grafting Density of Nanoparticles in Solution by Analytical Ultracentrifugation and Total Organic Carbon Analysis Denise N. Benoit, Huiguang Zhu, Michael H. Lilierose, Raymond A. Verm, Naushaba Ali, Adam N. Morrison, John D. Fortner, Carolina Avendano, and Vicki L. Colvin* Department of Chemistry, Rice University, Houston, Texas 77005, United States * S Supporting Information ABSTRACT: Many of the solution phase properties of See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. nanoparticles, such as their colloidal stability and hydro- dynamic diameter, are governed by the number of stabilizing groups bound to the particle surface (i.e., grafting density). Here, we show how two techniques, analytical ultra- Downloaded via BROCK UNIV on October 21, 2024 at 15:17:20 (UTC). centrifugation (AUC) and total organic carbon analysis (TOC), can be applied separately to the measurement of this parameter. AUC directly measures the density of nanoparticle−polymer conjugates while TOC provides the total carbon content of its aqueous dispersions. When these techniques are applied to model gold nanoparticles capped with thiolated poly(ethylene glycol), the measured grafting densities across a range of polymer chain lengths, polymer concentrations, and nanoparticle diameters agree to within 20%. Moreover, the measured grafting densities correlate well with the polymer content determined by thermogravimetric analysis of solid conjugate samples. Using these tools, we examine the particle core diameter, polymer chain length, and polymer solution concentration dependence of nanoparticle grafting densities in a gold nanoparticle−poly(ethylene glycol) conjugate system. T he number of bound polymers per unit surface area (i.e., the grafting density) is a critical feature to consider when designing nanoparticles for biological or environmental consideration of the physical size of the free polymer and the known available particle surface area.4,9,14 Alternatively, grafting density can be experimentally derived from thermogravimetric applications. This parameter directly affects the hydrodynamic analysis (TGA) of the carbon content in a solid nanoparticle− diameter and colloidal stability of nanoparticles, factors that are polymer sample. TGA is a general and widely used tool for crucial to biological and environmental applications.1−13 Liu et quantitative analysis of polymer grafting densities. Conven- al., for example, found that 10 nm gold particles which were tional instrumentation however requires large volumes of only partially capped with polymer aggregated in dilute salt solution to be evaporated in order to provide sufficient quantity solution; however, by increasing the grafting density to 50 (i.e., milligrams) of dried sample for analysis.7,9,15−18 Advances chains/particle, samples stable in 1 M NaCl could be readily in TGA instrumentation, such as the implementation of quartz achieved.1 Biodistribution studies of poly(ethylene glycol) crystal microbalances, can reduce the required sample weight (PEG)-coated nanocapsules found a strong correlation between substantially.18 For some polymers, spectroscopic methods circulation time and polymer surface coverages.2,3 Fully capped such as X-ray photoelectron spectroscopy (XPS) or nuclear materials, for example, had longer blood circulation times and magnetic resonance spectroscopy (NMR) can be effective in reduced clearance by the liver, spleen, and kidneys as compared the measurement of surface coverage.11,19−21 Alternatively, to materials with 20% less surface-bound polymer.3 Surface fluorescence methods can be applied to either detect labeled coverage and grafting density also influence a nanoparticle’s polymers or the displacement of surface quenched fluoro- transport through environmental matrixes such as soil and phores.22,23 Such approaches however can be highly specific to water. For example, only 1% of uncoated iron oxide a particular polymer capping agent and less effective in the nanoparticles were found in the effluent of a 30 cm long analysis of systems with low coverage, owing to signal sand column; however, greater than 50% were detected when interference arising from the core of the nanoparticles under the same samples were fully capped with poly(acrylic acid).4 consideration.9 In the majority of the aforementioned studies, investigators We herein separately apply two techniques, analytical estimated “partial” or “full” surface coverage from the amount ultracentrifugation (AUC) and total organic carbon analysis of polymer employed to functionalize the nanoparticle surface. (TOC), to measure the grafting density of gold nanoparticle− Seldom are the number of polymers bound to a particle surface (i.e., the surface coverage) directly measured. One common Received: July 13, 2012 estimate for surface coverage that is applicable only to saturated Accepted: September 11, 2012 systems relies on a geometric argument that includes a Published: September 12, 2012 © 2012 American Chemical Society 9238 dx.doi.org/10.1021/ac301980a | Anal. Chem. 2012, 84, 9238−9245 Analytical Chemistry Article poly(ethylene glycol) conjugates. Both approaches are well distributions using the ls-g*(s) analysis model with parameters suited to the general problem of analyzing inorganic nano- set for the best fit and minimum residuals for each sample.29 particle surfaces in solution. The results of each method agreed Thermogravimetric Analysis (TGA). TGA was performed well for conjugate samples with nanoparticle diameters, using TA Instruments Q-600 Simultaneous TGA/DSC. polymer ligand molecular weights (MWt), and solution Approximately 10 mL of gold or PEGylated gold nanoparticle concentrations of capping polymer in the ranges of 8−11 nm, samples (∼9.0 nM) were concentrated to a volume of 100 μL 1000−20 000 g/mol, and 8.5 nm−8.5 μM, respectively. Over and then dried in the TGA furnace prior to analysis. Each this wide range of conditions, the grafting densities measured sample was first dried at 100 °C for 60 min to remove excess from AUC and TOC varied by less than 20%. The carbon water and then held at 140 °C for 60 min to remove residual content determined by the TGA of dried sample residues water. The analysis was performed under a flow of 100 mL/min validated the measured solution phase grafting densities. As an air while the change in mass was determined every 0.1 °C over example, we applied these tools and evaluated how the grafting a temperature range of 150−1200 °C. A stepwise isotherm density of partially coated and fully coated nanoparticles in method, which is designed to hold the temperature constant solution correlated with their aggregation behavior in salt when the rate of weight loss is greater than 1 wt %/min and solution. For nanoparticles with complete surface coverage, we steadily ramp at 5 °C/min at all other temperatures, was additionally demonstrate how the grafting densities depend on employed during evaluation. The organic component of the the molecular weight of the polymer capping agent and to a sample was found from the percent mass loss over the lesser extent on the diameter of the gold nanocrystal core. temperature range of 150−500 °C, which for the gold MATERIALS AND METHODS Nanoparticle Preparation. Citrate stabilized gold colloids nanoparticles was entirely attributed to the decomposition of surface-bound polymer. A pure PEG sample, analyzed for comparison, displayed a derivative peak at 229 °C (fwhm, 65 (5, 10, 15, and 20 nm) purchased from Ted Pella were used as °C) and 96.5% mass loss between 150 and 500 °C. received or surface-modified with thiol-functionalized methyl- Total Organic Carbon (TOC). A Shimadzu TOC-VWP was poly(ethylene glycol) (mPEG-SH) of 1, 2, 5, 10, or 20 K MWt also used to determine the carbon content of the nanoparticle purchased fresh from Creative BioChem and stored under inert conjugates. The samples were run on a total nonpurgeable gas. mPEG-SH may degrade under a variety of circumstances organic carbon (NPOC) assay with triplicate 50 μL injection and, for these reasons, great care was taken to use materials volumes. Following injection, the NPOC assay pretreats the within one to two weeks of preparation.24−26 All surface-coated sample with acid to remove and measure all inorganic carbon. gold samples were saturated with excess mPEG-SH, as The sample is then oxidized and analyzed to determine the described below, unless otherwise stated. For example, 10 nm remaining carbon content, which is again attributed to the gold particles at a particle concentration of 9.0 × 10−9 M were polymer capping agent of the conjugates. Each sample was added to a solution of 2.5 × 10−5 M PEG (∼2800 PEG/ prepared by diluting 1 mL of purified nanoparticle solution to a particle), covered, and subsequently stirred for 12 h prior to total volume of 24 mL with Milli-Q 18 MΩ nanopure water. purification. We chose 12 h for equilibration as studies of thiol- Concentration curves ranging from 0.02 to 50 ppm were PEG bound to gold suggests that this time should be enough to prepared from a TOC standard solution (100 ppm) purchased allow for full equilibration.27,28 Samples with unsaturated from Sigma with a resulting R2 value of 0.998. polymer coating were prepared by reducing the polymer Dynamic Light Scattering (DLS). DLS was performed on concentration in solution without change to nanoparticle a Malvern Instruments ZEN-3600 Zetasizer Nano equipped concentration or stirring time. Unbound polymer was then with a HeNe 633 nm laser. Undiluted and as-purified half removed by repeated (three times) centrifugal filtration (100 milliliter samples were analyzed (3 runs/measurement) in MWCO, EMD Millipore) at 4150 rpm for 10 min. TOC was standard small volume disposable cuvettes (Fisher). The used to verify that the cleaning method was sufficient to remove particle size was taken to be the first peak of the volume unbound polymer for each molecular weight. It was found that corrected data, and the standard deviation was determined from ∼80−90% of the initial polymer could be removed in a single triplicate measurements. cleaning step and ∼10% in the second, and then, there was less Flocculation Assay. Flocculation assays were used to than 1% change for each additional round of centrifugation. No determine the critical coagulation concentrations (CCCs) of significant change in the carbon concentration was seen after the gold nanoparticles in sodium chloride and calcium chloride the third centrifugation, so three cleaning steps were chosen for solutions.1 Colorimetric determination of the CCCs were purification. performed by evaluating the optical absorbance at 520 nm for Transmission Electron Microscopy (TEM). To determine nonaggregated and 595 nm for aggregated nanoparticle samples the size of the gold nanoparticle core, a JEM-2100F JEOL field using a SpectroMax brand UV/vis multiwell plate reader over a gun emission transmission electron microscope operating at salt concentration range of 0.01−2.5 M. The CCC for each 200 kV was used. Samples were prepared by drop casting ∼20 sample corresponded to the lowest concentration of salt μL of nanoparticle solution on an ultrathin carbon type-A 400 necessary to induce aggregation. mesh copper grid (Ted Pella). ImagePro software was used to Grafting Density Calculations. TGA Grafting Density. determine the sizes and distribution of over 500 particles. The grafting density (σTGA) was calculated from TGA analysis Analytical Ultracentrifugation (AUC). Sedimentation using eq 1. First, the relative mass of the polymer (wt %shell) velocity AUC experiments were run on a Beckman and the residual mass of the pure gold nanocrystal (wt %core) ProteomeLab XL-A ultracentrifuge equipped with a UV/vis were found from the experimental TGA data at 500 °C. The (monitored at 525 nm) scanning detection system and a AN-60 number of polymer units per total sample was then derived by Ti 4-position rotor. Samples were housed in a 12 mm, charcoal- taking the polymer mass (wt %shell) and dividing by the polymer filled, dual channel, Epon centerpiece with quartz windows. mass per chain (i.e., polymer molecular weight/Avogadro’s SEDFIT was used to find the sedimentation coefficient number). The denominator requires a measure of the total 9239 dx.doi.org/10.1021/ac301980a | Anal. Chem. 2012, 84, 9238−9245 Analytical Chemistry Article Figure 1. Analytical ultracentrifugation (AUC) characterization of nanoparticle conjugates as a function of conjugate size and density. Panels A−D show transmission electron micrographs of four batches of gold nanoparticles (scale bars = 100 nm). Sedimentation coefficient distributions for the four sizes are shown in panels E and F, which show there is an increase in s-value as a function of the particle diameter. A nanoparticle sample of 9.1 nm (B2) coated with PEG of increasing molecular weights, from 1K to 20K, show a decrease in the sedimentation coefficient distributions due to a decrease in the overall particle density (G and H). particle surface area in the sample, a value defined here to be surface area of a single particle (using the radius found from the surface area per particle (4πr2) multipled by the total TEM) results in a value of the grafting density. number of particles. Nanocrystal number was derived from the [C] nanocrystal mass (wt %core) divided by the nanocrystal mass per σTOC = particle, which corresponded to the product of the density of 2n[NP]4πrcore 2 (2) bulk gold (ρcore = 19.6 g/cm3) and the volume of a single AUC Grafting Density. This method takes a different particle (4/3πr3). Note that the radius of the particle was approach to determining the surface coverage of particles. It measured from TEM and both the surface area and volume relies on the change in density induced by the association of calculations require the assumption that the particle assumes a lower density particles with the very dense gold cores. In effect, spherical shape. particles become less dense as greater polymer capping agent is wt %shell ρ 4 πr 3N bound to their surfaces. This is quantified through measure- wt %core core 3 core A ment of the sedimentation coefficient (s), a value related to σTGA = MW4πrcore 2 (1) particle density (ρp) by eqs 3 and 4. Other parameters that are pertinent to the definition of the sedimentation coefficient TOC Grafting Density. The grafting density (σTOC) was include the solvent viscosity (η) and density (ρs) as well as the calculated from TOC data using eq 2. The nonpurgeable particle’s hydrodynamic diameter (dh). While the first two organic carbon concentrations ([C]), reported in ppm (mg/L) parameters are easily obtained from the solvent itself (note that from a typical TOC analysis, must first be converted to molarity nanoparticle concentrations are too low to impact these (mol/liter) by dividing by the molar mass of carbon (12 g/ values), dh is challenging to measure particularly for nano- mol) and multiplying by 1000 to convert the volume to liters particle systems with unsaturated surface capping. (1000 mL/L). The molarity of carbon is then used to determine polymer concentration by applying the ratio of dh 2(ρp − ρs ) carbons per monomer unit (2 for PEG) and the number of s= 18η (3) monomers (n) in each polymer sample, which is given by the molecular weight divided by the molar mass of a single 18ηs monomer unit (44 g/mol for PEG). To determine the number ρp = + ρs dh 2 (4) of PEG molecules per particle, the molar concentration of nanoparticles in solution ([NP]) must first be acquired; it can The volume of the polymer capping shell (Vshell) is the be determined on the basis of the optical absorbance of the product of the polymer thickness and the nanoparticle surface gold nanoparticle solution.30 The molarity of PEG is then area (4πrcore2). The thickness of the polymer layer corresponds divided by the molarity of the nanoparticles, [PEG]/[NP]. The to the difference between the hydrodynamic radius (rh, from molar ratio of PEG molecules per particle once divided by the DLS) and the core radius (rcore, from TEM). The total density 9240 dx.doi.org/10.1021/ac301980a | Anal. Chem. 2012, 84, 9238−9245 Analytical Chemistry Article Table 1. Method Based on Nanoparticle Densitya S-value (Sv) dh (nm) density (g/cm3) mass-polymer/NP (g) grafting density (PEG/nm2) ligand footprint (nm2) AuNP_B2 586.3 9.9 AuNP_lKPEG 418.1 13.9 4.9 1.37 × 10−18 3.2 0.31 AuNP_2KPEG 337.4 17.5 3.0 1.67 × 10−18 1.9 0.52 AuNP_5KPEG 225.4 25.3 1.6 2.39 × 10−18 1.1 0.90 AuNP_10KPEG 170.2 34.6 1.3 3.51 × 10−18 0.8 1.23 AuNP_20KPEG 138.5 79.9 1.0 9.41 × 10−18 1.1 0.92 a Analytical ultracentrifugation and DLS data. Figure 2. Poly(ethylene) glycol coatings of 2K (red) and 20K (blue) on ∼10 nm gold nanoparticles (A) decrease the density and lower the sedimentation coefficients measured on 400 μL of sample via analytical ultracentrifugation. Carbon present on the AuNP sample is due to the citrate molecules used as a stabilizer by the manufacturer. Polymer addition adds carbon to the sample which raises the carbon concentration found using (B) total organic carbon analysis and (C) thermogravimetric analysis, on 1 and 10 mL of sample, respectively. Each of these measurements can be used to quantify the polymer grafting densities; panel D shows a comparison of the values obtained using each of these techniques (some error bars are not larger than the line). of the nanoparticle is given by the sum of the volume fraction mshell = ρshell Vshell (7) of the core (Vcore, TEM) multiplied by the density of the core and the volume fraction of the shell multiplied by the density of mshell the shell (eq 5). Given the density of the nanoparticle (eq 2) σAUC = MW·NA 4πrcore 2 (8) and the density of the core, which can be determined theoretically or by AUC analysis of an uncoated particle, eq 5 can be rearranged to solve for the density of the polymer shell RESULTS AND DISCUSSION (eq 6). The mass of polymer therefore corresponds to the In this work, the grafting densities of nanoparticle−polymer product of the volume of the shell and the calculated shell conjugates were derived from measurements of particle density density. The mass is related to the number of polymers per using ultracentrifugation (AUC) as well as from total organic particle, obtained using Avogadro’s number (NA) and the carbon content in solution (TOC). These tools only require known molecular weight. Finally, normalization of the number small volumes of dilute nanoparticle dispersions for analysis of polymer molecules by the available surface area of the and, thus, are ideally suited for laboratory scale sample batches nanoparticle core (4πrcore2) subsequently affords the desired typically required for medical applications, environmental grafting density (σAUC). remediation, or reservoir analysis.5,9,18 Because these methods Vshell V rely on different assumptions to arrive at the particle grafting ρp = ρ + core ρcore Vp shell Vp (5) density, a comparison of their results provides insight into the true value of the grating density as well as the magnitude of the Vpρp − Vcoreρcore methodological systematic error. ρshell = Analytical ultracentrifugation has been developed primarily as Vshell (6) a tool for physical biochemists.31,32 Over the last ten years, 9241 dx.doi.org/10.1021/ac301980a | Anal. Chem. 2012, 84, 9238−9245 Analytical Chemistry Article however, it has found increasing use in nanotechnology for the of this particle was 1.04 ± 0.03 g/cm3, which corresponds to a evaluation of the sizes and size distribution of various polymer mass of 9.41 ± 0.85 × 10−18 g and a grafting density of nanocrystal ensembles such as bioconjugates of gold nano- 1.09 ± 0.03 PEG/nm2. particles. The surface structure and utility of various surfactant Another approach to measuring grafting density relies on coating materials on carbon nanotubes have also been changes in the sample composition, which can be monitored by investigated with this methodology.33−40 AUC finds a total organic carbon (TOC) analysis. This method is in sedimentation coefficient for a given nanoparticle−polymer principle very similar to thermogravimetric analysis; however, sample, which significantly depends on the overall nano- TOC measurements can be performed on as little as 50 μL of particle−polymer density. If the hydrodynamic diameter of the solution phase sample.41 In conventional TOC, phosphoric nanoparticle−polymer conjugate can be accurately measured, acid, an oxidant, and heat are used to catalyze and convert all this density can then be used to determine the nanoparticle carbon present to CO2 which is then quantified. Figure 2B surface coverage. shows that, at equilibrium saturation (i.e., full coverage), the Figure 1 illustrates how the sedimentation coefficients (s- carbon concentration measured by TOC is minimal for the values) of the nanoparticle system bearing saturated surfaces citrate coated gold nanoparticles and increased with addition of varied with nanoparticle size and polymer thickness. Data was a surface coating and with increasing polymer chain length. collected as a function of core nanoparticle size (7.5−25.5 nm, The carbon concentrations of the conjugates acquired from panels A−D) as well as polymer chain length (1 to 20 K MWt, TOC measurements can be readily converted to the desired panels G−H). TEM micrographs provided in Figure 1 show nanoparticle−polymer grafting densities. This first requires an gold particles of 7.5, 11.7, 19.9, and 25.5 nm diameter. AUC accurate measure of nanoparticle concentration, derived here velocity sedimentation experiments run on each of these from the absorbance of the gold nanocrystal solutions.30 The samples displayed increasing sedimentation coefficients (288 ± grafting density is then given by the ratio of available surface 7, 617 ± 15, 1697 ± 35, and 3359 ± 87 Sv) with increasing core area (per volume) to the number of PEG molecules derived diameter (Figure 1E). This trend is captured quantitatively in from the carbon concentration and the PEG molecular weight Figure 1F which illustrates the expected cubed dependence of (see TOC grafting density calculation provided in the Materials sedimentation coefficient on core diameter, given its relation- and Methods). To illustrate, consider a 9.0 nM solution of 2 K ship to diameter and density in eq 3. Figure 1G illustrates that MWt PEG-gold (9.1 nm core) with a measured carbon the addition of a polymer capping to the surface of a 9.1 nm concentration of 9.4 ± 0.3 ppm. From eq 2, the corresponding batch of gold nanoparticles resulted in a decrease in their grafting density is 2.46 ± 0.03 PEG/nm2. The most significant sedimentation coefficient. Figure 1H shows this relationship source of systematic error associated with the TOC method graphically as the sedimentation coefficient is plotted as a originates from the assumption that all measured carbon is function of surface-bound polymer molecular weight over a derived from surface associated polymers. Careful sample range of 1−20 K. Longer capping polymers evidently exhibited purification ensures that carbon contamination is minimized; greater effect on nanoparticle sedimentation. however, it should be expected that this method will generally The sensitivity of the sedimentation coefficient on the overestimate the carbon concentration at the nanoparticle− nanoparticle core size and the surface-bound polymer chain polymer interface. length derives from its relationship to both hydrodynamic To validate both the ultracentrifugation and TOC methods, diameter and overall conjugate density (see eq 3 above).34 By we applied thermogravimetric analysis to powders derived from considering the hydrodynamic diameter (dh) determined from the nanoparticle solutions. This technique measures the total DLS along with known solution parameters such as solvent quantity of carbon in the solid phase as opposed to the liquid density and viscosity, the nanoparticle−polymer density can be phase. Figure 2C shows that the percent mass loss between 150 readily obtained from eq 4. This data is reported in Table 1, and 500 °C increases with increasing PEG molecular weight. which highlights that the nanoparticle−polymer conjugates had The TGA-acquired weight percent of the carbonaceous a lower density than bulk gold due to the presence of the material (polymer) and the core diameter of the particle organic capping groups. If the volume of the polymer shell is determined from TEM can then be used to determine the calculated from the hydrodynamic data, it is then possible to polymer grafting densities (see TGA grafting density calculate the net mass of the polymer layer and thereby arrive at calculation included in the Materials and Methods). For the the number of surface-bound polymers. 2 K PEG-coated 8.5 nm gold, 20.8% of the sample weight was To demonstrate how the grafting density can be extrapolated attributed to capping polymer, and therefore, this system from AUC analysis, consider the 2 and 20 K PEG-coated gold possessed a grafting density of 2.3 PEG/nm2. In contrast, the nanoparticle samples (see AUC grafting density calculation polymer component of the 20 K PEG-coated gold conjugate provided in the Materials and Methods). The core particle made up 47.0 ± 0.8% of the sample weight and, thus, a diameter selected here is 9.1 nm which possesses a resulting grafting density of 0.8 PEG/nm2. TGA, like TOC, is sedimentation coefficient of 586 ± 19 Sv and hydrodynamic sensitive to organic contamination in the samples. However, diameter of 9.9 nm. The slight increase in hydrodynamic with carefully purification, this error can be minimized and the diameter is attributed to the presence of citrate capping agents largest systematic error in TGA stems from the possibility that and solvent interactions at the particle surface. The 2 K PEG- some carbonaceous materials will not be fully combusted, coated sample shown in Figure 2A had a polymer shell leaving behind graphitic soot, which subsequently contributes thickness of 4.2 ± 0.4 nm (85.9% of the total volume). Using to the apparent weight of the inorganic fraction. an overall particle density of 3.0 ± 0.3 g/cm3, this corresponds In this study, TGA provided a measure of polymer surface to a polymer mass of 1.7 ± 0.2 × 10−18 g and a grafting density coverage that was in reasonable agreement; i.e., within 24% of of 1.9 ± 0.2 PEG/nm2. In contrast, the conjugate system the values determined from both AUC and TOC analyses prepared with a longer chain PEG had a coating thickness of (Figure 2D and Table 2). The TGA-determined surface 35.4 ± 0.5 nm (99.9% of the total volume). The overall density coverage of the nanoparticle−polymer (2 K) conjugate was 9242 dx.doi.org/10.1021/ac301980a | Anal. Chem. 2012, 84, 9238−9245 Analytical Chemistry Article Table 2. Nanoparticle Grafting Density (PEG/nm2) exchange processes for fully coated particles indicate this is Determined by Three Methodsa sufficient time to reach equilibrium.27,28 Still, it may be possible that if the dynamics are much slower for the undersaturated TOC AUC TGA surfaces, then the data at the lower PEG treatment σ σ σ concentrations may reflect slower surface exchange rather AuNP_2KPEG 2.46 ± 0.03 1.93 ± 0.17 2.25 ± 0.01 than a true equilibrium state. For our purposes, the trend allows AuNP_20KPEG 1.22 ± 0.02 1.09 ± 0.03 0.76 ± 0.04 us to illustrate that both measurements can detect changes in a The errors provided reflect the standard deviation of the replicate grafting density with less than a 10% increase in polymer error in triplicate measurements of the same sample. concentration. The intersection of linear fits for the increase and plateau region of the respective samples was used to 2.2 PEG/nm2, which was greater than the AUC value of 1.9 determine saturation of the surface of 8.2 nm gold nano- PEG/nm2 and less than the TOC value of 2.5 PEG/nm2. The particles at a solution concentration of 9.0 nM, requiring longest polymer studied, with a MWt of 20 K, afforded concentrations of 4 and 3 μM PEG for 2 and 20 K PEG, conjugates with a grafting density of 0.8 PEG/nm2 as measured respectively. These saturation concentrations corresponded to by TGA which was less than both of the values obtained by surface coverages of 500 and 370 PEG/particle, respectively. TOC and AUC analyses (1.2 and 1.1 PEG/nm2, respectively). As an indirect measure of the extent of particle surface Interestingly, TGA measured carbon content consistently lower capping, the critical coagulation behavior of the conjugates was than the solution TOC methods. We attribute this to the also evaluated. The minimum NaCl or CaCl2 concentration systematic errors associated with TGA already discussed above. that results in particle aggregation is known as the critical Also notable in Figure 2 was the consistent agreement coagulation concentration (CCC).1 This analysis assumes that between the grafting densities measured by AUC and TOC dispersions consisting of particles with saturated surface methods. The differences were most pronounced for the capping will remain colloidally stable irrespective of the salt conjugates that contained shorter polymer chains as capping concentration of the dispersion solution.1 Figure 3 compares groups. For instance, AUC analysis of conjugates prepared with the colloidal stability data for particles with surface coverages 2 K PEG yielded a grafting density of 1.9 PEG/nm2 as opposed independently evaluated using TOC or AUC. The data to the 2.5 PEG/nm2 measured from TOC. The grafting demonstrates that even partially capped nanoparticles were densities for the conjugates that contained longer PEG chains resistant to aggregation in NaCl solutions. For example, (i.e., MWt = 20 K) were within 0.2 PEG/nm2 (1.0 to 1.2 PEG/ samples treated with polymer concentrations of 2.1 μM 2 K nm2). Table 3 shows ∼10 nm gold nanoparticles individually PEG and 0.9 μM 20 K PEG (corresponding to grafting densities of 300 and 100 PEG/particle, respectively) were not Table 3. Grafting Density by TOC and AUC for Five yet fully saturated. However, these particles were resistant to Molecular Weight Polymer Coatings on ∼10 nm Gold aggregation as indicated by the flocculation assays. The Zeta Particlesa potential measurements of these partially capped samples revealed that their surface charge was fully neutralized at average of the two TOC AUC methods polymer concentrations of 1.3 μM (150 PEG/particle) 2 K sample σ σ σ PEG and 0.6 μM (75 PEG/particle) 20 K PEG. These data illustrate that inferring the extent of nanoparticle surface AuNP_lKPEG 3.62 ± 0.37 4.61 ± 1.69 4.12 ± 0.70 coverage based on its stability in monovalent salt solutions or AuNP_2KPEG 2.42 ± 0.91 2.59 ± 0.58 2.50 ± 0.12 from its zeta potential can be misleading. AuNP_5KPEG 2.07 ± 1.26 1.46 ± 0.31 1.77 ± 0.43 In contrast, when CaCl2 was employed as salt, much higher AuNP_10KPEG 1.39 ± 0.68 1.02 ± 0.18 1.21 ± 0.27 polymer grafting densities were required to achieve colloidal AuNP 20KPEG 1.19 ± 0.36 0.93 ± 0.14 1.06 ± 0.18 a stability (Figure 3). For example, 2.6 μM PEG (i.e., 300 PEG/ The errors provided reflect the standard deviation between particle) treatments were not sufficient to stabilize the measurements of four batches. The column on the right is the average conjugates against aggregation. Only particles with the highest grafting density between the two methods and their agreement. grafting densities were stable in CaCl2 solutions. Thus, measuring flocculation in a divalent salt solution is a capped with five different molecular weight polymers within a significantly better approach for indirectly evaluating the extent range of 1−20 K were found to have average grafting densities of surface capping in a nanoparticle−polymer conjugate system. that deviated by less than 22% between methods. Overall, the We also used these tools to study how the capping polymer agreement between the two methods was on average 20%, chains packed in conjugates with complete surface coverage. As which is about four times the typical random error found in shown above, the grafting density of nanoparticle−polymer replicate studies using each technique alone. conjugates is sensitive to the polymer molecular weight as well Applications for Grafting Density Measurements. An as the curvature of the gold nanocrystal. Figure 4a shows how advantage of both the AUC and TOC methods is that they are the grafting density of five polymers, with molecular weights sufficiently sensitive to analyze conjugates with incomplete ranging from 1 to 20 K, varied for four different gold polymer surface coverage. We exploited this capability to nanocrystal diameters, ranging from 8 to 11 nm. As expected, examine how the grafting densities varied as the nanocrystals the grafting densities decreased with increasing polymer were exposed to increasing amounts of capping polymer. Figure molecular weight for all nanoparticle diameters tested (Table 3 shows the systematic increase and eventual plateau in grafting 3).27,28,42 For 1K PEG on the 9.1 nm particles, the grafting densities as the polymer concentration was varied from 8.5 nM density of 4.6 PEG/nm2 matches well with the ideal packing of to 8.5 μM for 2 and 20 K PEG-SH-coated gold nanoparticles. helical PEG molecules with a cross-sectional area of 0.213 nm2 We note that samples were allowed to equilibrate for 12 h (4.7 PEG/nm2) expected from literature.27 Also, as the before measurement, and studies of these dynamic surface diameter of the core increased from 8 to 11 nm, a 9243 dx.doi.org/10.1021/ac301980a | Anal. Chem. 2012, 84, 9238−9245 Analytical Chemistry Article Figure 3. Polymer grafting densities increase upon the addition of (A) 2 K or (B) 20 K PEG to a solution of ∼10 nm gold nanoparticles (red dotted lines are added to guide the eye). Critical coagulation concentration (CCC) of (C) 2 K and (D) 20 K PEG-capped particles in sodium chloride (open squares) and calcium chloride (closed circles) solutions show that increased polymer concentrations improve the colloidal stability. Neither of the PEG coatings prevents nanoparticle aggregation in CaCl2 solutions below surface saturation. corresponding increase in grafting density from 2.5 to 6.5 PEG/ nm2 (Figure 4B) exceeded the expected coverage for a monolayer of PEG in a helical conformation and suggests the polymers are further extended or additional material interca- lated within the coating. This trend was only seen where the height of the polymer was equal to or less than the radius of the particle.43 The diameter dependence likely arises from the improved ability for short polymers to pack and optimize their interchain interactions on flatter surfaces of larger particles.44 This work presents two options for solution-based assays that can easily and reproducibly measure the polymer grafting densities of nanoparticle−polymer dispersions. Both AUC and TOC require liquid samples and use less than 1 mL (