Structure of Mixed-Monolayer-Protected Nanoparticles in Aqueous

Article pubs.acs.org/JPCC

Structure of Mixed-Monolayer-Protected Nanoparticles in Aqueous Salt Solution from Atomistic Molecular Dynamics Simulations Reid C. Van Lehn and Alfredo Alexander-Katz* Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States S Supporting Information *

ABSTRACT: Gold nanoparticles (AuNPs) protected by a grafted ligand monolayer are commonly used for applications in biosensing, bioimaging, and drug delivery, in part because of the ability to tune surface properties by modifying the composition of the protecting ligands. If the surface monolayer contains multiple distinct ligand species, the AuNPs are referred to as mixed-monolayer-protected particles. A typical mixed monolayer consists of two linear alkanethiol ligands, with one ligand species end-functionalized to confer aqueous solubility. However, the inclusion of multiple ligand species raises questions of how the nanoscale morphology and the relative lengths of the two ligands can affect properties, considerations that are unnecessary for single-component monolayers. In this work, we use atomistic molecular dynamics simulations to model the structure of mixed-monolayer-protected AuNPs in aqueous salt solution under typical biological conditions. We focus on identifying changes in the monolayer structure as a function of the diameter of the AuNP core, the morphology of the protecting ligands, and the relative ligand length, complementing existing studies of homogeneous monolayers. Our results show that increasing the particle diameter strongly inhibits ligand fluctuations, consistent with a reduction in free volume associated with higher-curvature substrates. We also show that, in aqueous solution, particles with striped, mixed, and random morphologies exhibit similar behaviors, as ligand fluctuations mask any influence of the grafting positions. Finally, our simulations indicate that long hydrophobic ligands always deform to allow shorter hydrophilic ligands to access water, leading to a significant distortion of the interface if the hydrophobic ligands are much longer than the hydrophilic ones. Our results thus provide new physical insight into the structure of mixed-monolayer-protected particles under typical biological conditions and can be used to guide the experimental design of new classes of AuNPs for biological applications.

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and uncharged ligand species,15−17 and create zwitterionic surfaces by incorporating ligands of opposing charge.18,19 Including multiple species also raises the possibility of microphase separation of the two ligand species, leading to questions considering the role of nanoscale morphology in determining surface properties. For example, one extreme of separation behavior in binary monolayers would be the formation of Janus particles from the complete demixing of the two ligand species into distinct macrophases on the particle surface,20,21 creating bifunctional particles that have been utilized in various applications.22−24 Recently, nanoscale striped morphologies have been reported for binary alkanethiol monolayer-protected AuNPs, where the two ligand components spontaneously form alternating ribbonlike domains.16,25−28 Theoretical approaches have proposed that stripe formation is related to the relative length difference of the two alkanethiol ligands,29−31 adding another parameter for tuning AuNP surface properties. Such nanoscale morphology can have significant consequences for particle behavior, as the striped particles were shown to nondisruptively penetrate

INTRODUCTION Gold nanoparticles (AuNPs) with core diameters on the order of 1−10 nm have emerged as a powerful class of materials for a variety of applications. AuNPs have found particular use in biological applications such as biosensing,1−3 imaging,4−6 and targeted cellular interactions.7,8 The utility of AuNPs is enhanced by the ability to tune AuNP surface properties by grafting a ligand monolayer to the surface such that the physicochemical properties of the surface are controlled by the structure and chemistry of the protecting ligands, not the gold substrate itself. Significant work has focused on the development of monolayer-protected particles for the biological applications mentioned, as well as to improve the biocompatibility of AuNPs, inhibit AuNP aggregation, prevent protein adsorption, and induce favorable interactions with biological membranes.8−11 The toolbox for modifying the surface properties of monolayer-protected particles can be further expanded by simultaneously grafting multiple ligand species to the AuNP surface to form a mixed-ligand monolayer. Incorporating multiple ligand species can be used to induce preferential interactions between specific ligands for self-assembly applications,12−14 tune the surface charge density by mixing charged © 2013 American Chemical Society

Received: August 21, 2013 Published: September 9, 2013 20104

dx.doi.org/10.1021/jp406035e | J. Phys. Chem. C 2013, 117, 20104−20115

The Journal of Physical Chemistry C

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Figure 1. Schematic illustrating different features of the simulation system. All simulations were conducted in 150 mM salt solution at 310 K and 1 bar to represent typical biological conditions. AuNP surfaces were grafted with a mixture of two components: (1) purely hydrophobic alkanethiol ligands and (2) alkanethiol ligands end-functionalized with anionic sulfonate end groups. Although the numbers of carbon atoms in the ligand backbones were varied in some simulations, for most simulations, the ligands represented the molecules 11-mercapto-1-undecanesulfonate (MUS) and 1-octanethiol (OT) as drawn, with 11 carbons in the backbone of the hydrophilic component and 8 carbons in the backbone of the hydrocarbon component. Three nanoscale morphologies corresponding to (a) mixed, (b) striped, and (c) random surfaces were simulated with ligands drawn in their initial, all-trans conformations extending radially from the surface. Hydrophilic (red) and hydrophobic (silver) ligands are partially drawn as surfaces to more clearly illustrate the difference between the nanoscale domains.

particle diameters permits the ligand end groups to fluctuate to minimize electrostatic repulsion independent of the exact grafting locations of the different ligand components. In contrast, increasing the particle diameter and increasing the length of the hydrophobic component both act to decrease the available free volume, inhibiting ligand fluctuations and effectively confining the ligands from steric interactions with adjacent neighbors. Our results indicate that surface composition and particle size are thus the most important tuning parameters to consider in designing mixed-monolayer-protected particles for use in biological applications.

into cells whereas similar particles with mixed rather than striped morphologies were unable to penetrate.32,33 Similar examples of other systems containing different mixed monolayer compositions and exhibiting phase separation on the surface have also demonstrated unusual surface properties possibly related to the morphology.34−37 However, although several studies have focused on understanding the formation of nanoscale morphology, it is less clear how the structure of the monolayer depends on the ligand properties in an aqueous environment where the surface structure could be dominated by ligand fluctuations rather than by the actual positions of the ligand grafting points. In this work, we develop an atomistic model of mixedmonolayer-protected AuNPs in aqueous solution under typical biological conditions. The monolayer consists of a binary mixture of purely hydrophobic alkanethiol ligands and anionic, end-functionalized alkanethiol ligands, mimicking the experimental system described previously.25,26 Previous atomistic studies of monolayer-protected AuNPs have explored the role of ligand fluctuations in spontaneous domain formation,38,39 the effect of morphology on the surrounding water density in mixed-monolayer-protected particles,40,41 electrostatically mediated ridge formation on faceted nanoparticles,42 and most recently the importance of considering the electrostatic properties and water interactions of small AuNPs.43,44 We expand on these studies by exploring the effects that the particle size, surface morphology, and relative lengths of the two ligand species have on the structure of the monolayer in aqueous salt solution. We show that modifying the nanoscale morphology has little effect on the overall structure of the monolayer because of the flexibility of the alkane backbones of the protecting ligands. The free volume associated with the small

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SIMULATION METHODS The system under consideration consists of a single monolayerprotected gold nanoparticle (AuNP) in aqueous salt solution. For all simulations, the salt composition was fixed at a physiological concentration of 150 mM plus sufficient counterions to neutralize the system. Two different ligand species were grafted to the AuNP surface: “hydrophobic” alkanethiol ligands composed of an alkane backbone and sulfur head group and “hydrophilic” alkanethiol ligands composed of an alkane backbone, sulfur head group, and anionic sulfonate end group. The lengths of the two backbones were varied in different simulations, with the typical system consisting of hydrophilic ligands with 11 carbons in the alkane backbone to mimic 11-mercapto-1-undecanesulfonate (MUS) and hydrophobic ligands with 8 carbons in the alkane backbone to mimic 1-octanethiol (OT), motivated by compositions used experimentally.16,25,26,32,33 Striped, mixed, and random morphologies were represented by positioning the grafting points of the two different ligand species according to a previously developed lattice model modified for a spherical substrate.45 The striped 20105



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motifs,60−62 but because the focus of this study is the role of the ligand monolayer itself, the simple treatment of the gold interface simplified the system significantly. Similarly, the gold surface and grafted sulfur atoms were not assigned partial charges, as previous simulations have shown that the cumulative charge approaches zero at the gold surface.43 The fixed bonding constraints between the sulfur atoms and gold shell ensured that the grafting points retained the same positions throughout the entire simulation, allowing the effect of morphology to be studied without considering ligand rearrangement. Periodic boundary conditions were used with a rhombic dodecahedral box geometry to minimize the overall system volume given the approximately spherical symmetry of the system. The box was sized such that there was a distance of 1.2 nm from the box wall to the closest ligand on the NP in the initial, all-trans state. This distance is 1.5 times the Debye screening length of the aqueous 150 mM electrolyte solution and was chosen so that the minimum distance between periodic images of the AuNP would always be 3 times the Debye length to eliminate possible electrostatic interactions. In practice, this distance was closer to 4−5 times the Debye length after the ligands relaxed during equilibration. Electrostatic interactions were calculated using the particle−mesh Ewald (PME) summation method, with a real-space cutoff of 1.0 nm, a grid spacing of 0.16 nm, and fourth-order interpolation. The van der Waals and neighbor-list cutoffs were also both set to 1.0 nm, mimicking the approach used for the simulation of lipid bilayers with the PME method and the GROMOS 54a7 parameter set.63 For all simulations, the temperature was set to 310 K, and the reference pressure was set to 1 bar to mimic biological conditions. The temperature was controlled by a velocityrescaling thermostat with a coupling time constant of 0.1 ps. The pressure was first equilibrated using a Berendsen barostat and then controlled with a Parrinello−Rahman barostat with a time constant of 2.0 ps and an isothermal compressibility of 4.5 × 10−5 bar−1. The simulation time step was set to 2.0 fs. All bonds were constrained using the LINCS algorithm64 with the exception of water molecules, which were constrained using SETTLE.65 Simulations were first equilibrated in the NVT ensemble for 2 ns and then in the NPT ensemble with the Berendsen barostat for 2 ns, before a further 16 ns of equilibration in the NPT ensemble with the Parrinello− Rahman barostat. Data for analysis were then generated over 100-ns production runs. All simulations were performed using GROMACS version 4.6.1, the latest stable release at the time this work was performed.66 A summary of the simulation parameters for different systems considered in this work can be found in Table S1 of the Supporting Information. Data analysis was performed upon conclusion of the simulations using a combination of default GROMACS analysis tools and analysis tools developed in-house. The radial electrostatic potential of the system was calculated following the approach of Heikkilä et al.43 by applying Gauss’ law with a spherical Gaussian surface of radius r to obtain the electric field as

morphology is defined by alternating lines of each ligand species, the mixed morphology consists of a “checkerboard”like arrangement of the two species subject to the constraints of the spherical topology and 1:1 surface composition, and the random morphology is a completely random distribution of the two species. Figure 1 shows the chemical structures of the MUS and OT ligands and schematically depicts the different surface morphologies considered in this work. The recent GROMOS 54a7 united-atom force field,46 an update of the popular GROMOS 53a6 parameter set,47 was used to model the AuNP and the surrounding solution. The GROMOS force field was chosen because of the similarity between the alkanethiol ligands modeled here and the general structure of lipids. GROMOS 54a7 has been shown to accurately reproduce lipid-bilayer properties in a variety of different lipid species48 and thus seems appropriate for the similar ligands modeled here. Furthermore, using this force field leaves open the possibility of exploring the interactions between lipid bilayers and monolayer-protected AuNPs without mixing force fields, a goal for future research. The water molecules were represented by the SPC model to match the parametrization of GROMOS. The parametrization for the sulfonate head groups was adapted from similar sulfonate groups studied by Hinner et al.;49 however, the partial charges were taken from ab initio simulations conducted for ionic liquids.50 The GROMOS 54a7 force field lacks parameters for gold, so some modifications were necessary to accurately model the system. Gold−hydrocarbon Lennard-Jones parameters were adapted from a reparameterization of the Hautman−Klein model for self-assembled aklanethiol monolayers,51 which has been successfully used to reproduce the tilt angles of ligands in planar self-assembled monolayers and is thus appropriate for studies of monolayer structure.51,52 The Hautman−Klein model originally modeled the gold surface as a perfect plane, but later modifications by Tupper and Brenner53 and Mahaffy et al.54 replaced the planar representation with discrete atoms that interact with the alkanethiol hydrocarbons through a typical Lennard-Jones 12−6 potential appropriate for use with the GROMOS force field. All other Lennard-Jones interactions were obtained using the values for gold presented in the UFF force field,55 although, in practice, only gold−hydrocarbon interactions were relevant because of the steric barrier posed by the protecting monolayer. The gold−sulfur−carbon bond angle and gold−sulfur−carbon−carbon dihedral angle at the AuNP interface were left unrestricted as in the Hautman−Klein model. This combination of force-field parameters is commonly found in the self-assembled-monolayer literature and is suitable for this study.38,56,57 The gold surface itself was approximated as a rigid, hollow, perfectly spherical shell with constraints placed on neighboring gold atoms to maintain the rigidity of the spherical shell during simulations. The mass of the missing gold atoms in the hollow interior was redistributed to the surface gold atoms. Sulfur head groups and attached ligands were uniformly distributed on the gold surface with an area of 21.6 Å2 per ligand. Although this grafting density could be a function of surface area,57,58 we assumed that it is invariant for all particle sizes studied here. Sulfur atoms were connected to the gold surface through rigid constraints to maintain the perfectly spherical geometry. The simple spherical approximation might not be accurate for faceted small AuNPs,59 and the structure of the interface does not take into account other possible gold−sulfur binding

E(r ) =

Q enc 4πε0r 2

(1)

where Qenc is the cumulative charge enclosed within the spherical shell and ε0 is the dielectric permittivity. The electrostatic potential, Ψ(r), is then simply expressed as 20106


The Journal of Physical Chemistry C Ψ(r ) =

∫0

r

E(r′) dr′ = −

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Q enc 4πε0r

2

tendency of the ligands to fold toward the gold surface because of the unfavorable interaction with water, effectively minimizing the solvent-accessible surface area. Similar snapshots of the other systems considered in this work are shown in Figure S1 of the Supporting Information. Radial distribution functions (RDFs) of the same two 2.0-nm particles are shown in Figure 3 to gain more detailed insight into the structure of the AuNP interface. In both plots, RDFs for the gold shell and grafted sulfur head groups for the thiol ligands are not included as the positions of these beads were fixed relative to the gold-shell center of mass during the simulations and thus would generate meaningless peaks. The radius of the gold core was 1.0 nm, so in both plots, the alkanethiol peaks decay to 0 at a distance of about 1.25 nm, corresponding to the radius of the gold core plus the size of the gold−sulfur bond (∼0.23 nm62). The center of mass of the sulfonate end group is assigned a separate plot from the overall MUS ligand density to more clearly identify where the charged end groups reside relative to the interface (labeled as MUS End in the figure). As expected from the relative lengths of the long hydrophilic ligand and the shorter hydrophobic ligand, the peak for the MUS end group is centered at a distance farther from the gold surface than the bulk of the hydrophobic-ligand density in the 1:1 MUS:OT case. Furthermore, the average hydrophobic-ligand density is closer to the gold surface than the average hydrophilic-ligand density because of this length difference. Aside from the addition of this OT curve, the qualitative features of the two systems are largely identical. The broad peaks for the ligands indicate the flexibility of these species, agreeing with the simulation snapshots, and similarly, the enhanced peak for sodium ions near the MUS end groups is consistent with the observed counterion condensation. It is also interesting to note that there is effectively zero water penetration toward the gold surface because of the protecting effect of the hydrophobic-ligand layer. Figure 4 shows the average radial electrostatic potential for the same two AuNPs as in Figure 3. Three regimes of behavior are evident and are denoted by vertical dashed lines corresponding to relevant distances from Figure 3. The black vertical line indicates the distance where the water density is 10% of its bulk value, which is an approximation of the maximum distance that water penetrates toward the gold core. The positive peak in the electrostatic potential at this potential indicates that these water molecules are oriented such that a positive hydrogen atom is closer to the gold surface than the negative oxygen atom. The blue dashed line indicates the peak density of the anionic MUS end groups, which is approximately invariant between the two surface compositions. The anionic groups flip the sign of the electrostatic potential, which then reaches a maximum shortly before the green dashed line that indicates the maximum density of sodium counterions. For distances in excess of the counterion maximum, the potential decays to 0, as expected from Debye−Hückel theory. The overall shapes of the potential are nearly identical between the 1:1 MUS:OT and all-MUS surface compositions, with the major quantitative difference lying in the magnitude of the potential at both the positive and negative peaks. However, the potential decays to 0 over approximately the same length scale (i.e., the Debye length), and thus, measurable zeta potentials are unlikely to differ significantly, as is indeed observed for similar particle compositions.32 Combined with the RDFs in Figure 3, Figure 4 thus indicates that replacing MUS ligands

(2)

Calculating Ψ(r) thus requires an estimate of the cumulative enclosed charge for each r value. To reduce error associated with treating the ions as point charges, the charge was spread over a spherical grid centered on each ion with a Gaussian spread function that decayed to 0 at the distance σ associated with the Lennard-Jones parameters for that atom. Grid points were separated by a distance of 0.01 nm; decreasing the grid separation further did not change the results. Ligand tilt angles were calculated from the dot product of a vector drawn from the center of mass of the gold shell to the grafting sulfur atom and a vector drawn from the grafting sulfur atom to the end of the ligand chain. The chain end was defined as the terminal sulfur atom in the charged sulfonate end groups or the terminal CH3 bead in the hydrophobic ligands. According to this definition, an all-trans ligand oriented radially outward from the gold surface would have a tilt angle of approximately 0°. Tilt angles were computed for each ligand species independently and averaged over all ligands in the monolayer. The root-mean-square fluctuations of ligands in the system, radius of gyration, solvent-accessible surface area, distribution of torsional angles, radial distribution functions, and average number of hydrogen bonds per charged end group were all calculated using default GROMACS analysis tools.66 Additional information on the methods of these calculations are described in the Supporting Information; more detailed information can be found in the GROMACS User Manual, Version 4.6.1.67

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RESULTS AND DISCUSSION Comparison of Mixed and Homogeneous Monolayers. As a first test of system properties, two systems of particles with gold core diameters of 2.0 nm were simulated, the first with a surface composition of all MUS ligands to mimic single-component monolayers found in the literature and the second with a 1:1 MUS:OT composition in a mixed morphology. Example simulation snapshots of these two systems in the final equilibrated state are shown in Figure 2. The snapshots show the fluid nature of the monolayer at 310 K, with no visual indication of domain formation or crystallization in either case. Counterion condensation on the surface is also apparent, as expected (blue beads). The images also show the

Figure 2. Simulation snapshots of AuNPs with gold core diameters of 2.0 nm. The left image shows a particle with an all-MUS surface composition, whereas the right image shows a particle with a 1:1 MUS:OT surface composition. The legend on the right identifies the different atom types in the simulation, with hydrophobic ligands also colored silver to distinguish them on the 1:1 MUS:OT particle. Water and some ions are not shown for clarity. 20107



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Figure 3. Radial distribution functions for 2.0-nm-core-diameter all-MUS and 1:1 MUS:OT AuNPs. Distances are measured relative to the center of mass of the gold shell. The two plots indicate similar features, with the exception of an increase in the counterion density near the surface of the allMUS particle, as expected.

the surface curvature is increased. For the 8-nm particles, the average tilt angle for both the hydrophilic and hydrophobic ligands is near 30°, similar to the tilt angle calculated for homogeneous monolayers on flat surfaces.51 This analysis might thus indicate that the surface of AuNPs with diameters of ∼10 nm might already have a sufficiently large curvature that the structural properties are similar to those of flat surfaces. The shift in distribution also agrees with previous results showing a similar decrease in the average tilt angle with size for homogeneous monolayers on spherical substrates;38 in the present study, however, the presence of charged end groups and multiple ligand species inhibits the ordering observed for homogeneous alkyl monolayers. The effect of this shift in the average tilt angle is further explored in Figure 6, which shows the correlation between the average root-mean-square fluctuations (RMSFs) per atom along each ligand species and the average tilt angle as a function of particle size. The plot shows that, as the average tilt angle decreases, the spatial fluctuations of the ligand chain similarly decrease. This observation is consistent with a physical picture in which each ligand fluctuates through a cone of free volume confined by steric interactions with adjacent ligand chains.29 Increasing the particle diameter thus inhibits ligand fluctuations as the free volume accessible to each ligand is reduced. This restriction on ligand flexibility with increased particle diameter is also confirmed by the decreasing number of gauche torsional angles along both hydrophilic and hydrophobic ligands with large particle diameters, as shown in Figure S3 of the Supporting Information. The inhibited flexibility of the ligands with increasing size demonstrated here is likely to have a significant effect on surface properties, especially for systems that rely on the flexibility of interfacial ligands to display adaptive or environmentally responsive behavior.68,69 The electrostatic potential as a function of radial distance is plotted on the same axes for all four particle sizes in Figure 7. The same general trends previously reported in Figure 4 are observed; first, a strong positive peak in the potential corresponding to oriented water molecules appears, followed by a large negative peak at the position of the anionic end groups, followed by a gradual decay of the potential to zero at large distances. The major distinction between different sizes is only in the relative magnitudes of the peaks, their widths, and their positions, as would be expected from the change in

Figure 4. Radial electrostatic potential for 2.0-nm-core-diameter allMUS (red line) and 1:1 MUS:OT (black line) AuNPs. The dashed lines indicate relevant positions from the RDFs in Figure 3 to illustrate different regimes of behavior. The black dashed line indicates the radial distance where the water density is 10% of its bulk value, the blue dashed line indicates the distance where the MUS end-group density is maximized, and the green dashed line indicates the distance where the counterion density is maximized. These distances are approximately equivalent for both 1:1 MUS:OT and all-MUS, as shown in Figure 3.

with OT ligands does not significantly alter the structural or electrostatic properties of the interface. Effect of Particle Size on Monolayer Structure. Having verified that the simulation model reproduces previous structural and electrostatic properties obtained for anionic AuNPs,43 we next explore the effect that particle size has on the structure of the protecting monolayer. For a fixed ligand grafting density, increasing the diameter of the particle reduces the amount of free volume accessible to each ligand on the surface, inhibiting ligand fluctuations. Figure 5 shows the average tilt angles of MUS and OT ligands as a function of particle size for core diameters of 2, 4, 6, and 8 nm, all with 1:1 MUS:OT surface compositions. Solid lines show the tilt angle of the hydrophilic MUS ligand, whereas dashed lines indicate the tilt angle of the hydrophobic OT ligand. The figure shows that the tilt-angle distributions for both ligand species shift toward smaller angles as the particle diameter increases, consistent with a reduction in the free volume per ligand as 20108



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Figure 5. Tilt-angle distributions for hydrophilic MUS ligands (solid lines) and hydrophobic OT ligands (dashed lines) for AuNP diameters of 2 nm (black), 4 nm (red), 6 nm (blue), and 8 nm (green). The distributions of both ligand species shift toward smaller tilt angles as the particle diameter is increased.

Figure 6. Correlations between the root-mean-square fluctuations (RMSFs) per atom and the average tilt angles of the two ligand species for particles of different diameters. Identical trends are observed in both quantities for both ligand species as the diameter varies, implying that a decrease in the average ligand tilt angle inhibits ligand fluctuations.

Figure 7. Radial electrostatic potential as a function of distance from the AuNP center for AuNP diameters of 2 nm (black), 4 nm (red), 6 nm (blue), and 8 nm (green). The general shape of the potential is the same, with the magnitudes of the peaks increasing as the number of charged ligands increases for larger particle diameters.

particle diameter. This analysis suggests that the electrostatic properties of all particle sizes considered are similar and that, especially at long distances in excess of the screening length, the electrostatic potentials should be similar. Effect of Nanoscale Morphology on Monolayer Structure. The previous results show the critical role that particle diameter plays in determining the properties of the interface due to the inhibited fluctuations of the grafting ligand layer. Another factor that might influence the properties of the interface is the nanoscale arrangement of the ligands into different morphologies. Previous work has shown that nanoscale morphology can greatly affect interactions with cells,32,33 induce self-assembly,70 and inhibit protein interactions.9,71 To test whether any differences in ligand properties emerge from changing the ligand morphology, we generated striped, mixed, and random morphologies as shown in Figure 1. Note that, in any given physical system, it is likely that a single such morphology would be thermodynamically preferred based on

the ligand properties,13,29,31 but here, we assume that any given arrangement is possible. Table 1 summarizes the results of a series of structural characterizations of 4.0-nm AuNPs with the three different morphologies shown in Figure 1, including three different realizations of a random surface to yield a total of five distinct ligand arrangements. Particles with a diameter of 4.0 nm were chosen because this diameter is close to the typical value used experimentally32 and is sufficiently large that morphology distinctions can be observed experimentally.27 The parameters calculated include the average solvent-accessible surface area (SASA), a measure of the amount of hydrophobic material exposed to solvent; the average number of hydrogen bonds formed; the average tilt angles of the MUS and OT ligands; the root-mean-square fluctuations of each ligand species; and the fractions of gauche dihedral conformations for MUS and OT ligands averaged over the entire chain. Standard deviations are 20109



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Table 1. Comparison of Morphologies for 4.0-nm AuNPs with 1:1 MUS:OT Compositions SASA (nm2) no. of H-bonds MUS tilt (deg) OT tilt (deg) MUS RMSF (nm) OT RMSF (nm) MUS fraction gauche OT fraction. gauche

mixed

stripes

random 1

random 2

random 3

183.35 ± 3.89 744.1 ± 12.3 47.05 ± 13.91 44.72 ± 15.31 0.697 ± 0.019 0.376 ± 0.010 0.322 ± 0.050 0.313 ± 0.037

183.22 ± 3.93 743.7 ± 12.3 47.12 ± 13.83 44.63 ± 15.54 0.683 ± 0.032 0.375 ± 0.011 0.322 ± 0.049 0.317 ± 0.037

183.83 ± 4.02 744.0 ± 12.3 46.91 ± 14.07 44.54 ± 15.60 0.687 ± 0.026 0.375 ± 0.012 0.321 ± 0.048 0.316 ± 0.037

183.53 ± 3.88 744.0 ± 12.3 47.19 ± 13.99 44.02 ± 15.73 0.683 ± 0.031 0.371 ± 0.011 0.321 ± 0.049 0.315 ± 0.037

183.62 ± 3.95 743.9 ± 12.3 47.31 ± 13.97 44.27 ± 15.60 0.688 ± 0.030 0.372 ± 0.011 0.322 ± 0.050 0.315 ± 0.037

particle types into similar instantaneous morphologies independent of the location of grafting points, qualitatively agreeing with the snapshots in Figure S1 (Supporting Information). These results, combined with the similarity of the average structural quantities in Table 1, indicate that nanoscale morphological changes have minimal discernible effect on the properties of the AuNPs in solution over even the short nanosecond time scales studied here. Effect of Relative Ligand Length on Monolayer Properties. Having established the effects of particle diameter and morphology on the structural characteristics of the surface monolayer, we next explore the effect of changing the relative lengths of the two ligand species. This system feature is particularly important given the variety of ligand compositions reported in the literature, including both the case where the hydrophilic ligand species is longer than the hydrophobic one16,32 and the opposite case where the hydrophobic ligand is longer than the hydrophilic one.25,26,40,72 To explore the effect of varying ligand lengths, we fixed the length of the hydrophilic ligand while increasing the length of the hydrophobic ligand. Ligand length is denoted by the number of CH2 or CH3 groups in the ligand backbone, so that the MUS:OT composition discussed so far would be described as an 11:8 composition. The ligand compositions tested can be described with this nomenclature as 11:8, 11:11, 11:14, and 11:17. All particle diameters were fixed at 4.0 nm with mixed morphologies. Figure 9 shows tilt-angle distributions of the hydrophilic and hydrophobic ligands as a function of increasing hydrophobicligand length in analogy to Figure 5. When particle size was increased, the previous results in Figure 5 showed that the tiltangle distributions of both ligand species shifted to smaller values, consistent with increasing steric confinement as the surface curvature grew. For increasing hydrophobic-ligand length, however, the hydrophilic-ligand tilt angle shifts to smaller values, whereas the hydrophobic-ligand tilt angle shifts to larger values. Again, in analogy with the previous results for varying AuNP diameter, these results show that increasing the hydrophobic-ligand length effectively confines the hydrophilic ligands. This confinement effect is further confirmed by comparing the root-mean-square fluctuations with the average tilt angle. Figure S8 (Supporting Information) shows that these two quantities are again highly correlated, implying that an increase in hydrophobic-ligand length inhibits hydrophilicligand fluctuations while enhancing the fluctuations of the longer hydrophobic ligands. The reason for this shift in tilt angle can be observed in Figure 10, which shows simulation snapshots of 11:8 particles and 11:17 particles, the two opposing extremes of ligand length tested here. In all snapshots, hydrophilic end groups are red, hydrophilic ligand chains are cyan, hydrophobic ligands are silver, and the first solvation shell of water is shown in blue. For

reported for each measurement. For each of these measurements, the five different ligand arrangements showed effectively identical values, indicating no ability to distinguish the nanoscale morphology on average. These results again make sense given the small diameter of the AuNP core, allowing extensive ligand fluctuations that ultimately define the structural properties of the interface more than the positions of the actual grafting points. The similarity in measurable structural characteristics is indicative of the tendency for charged head groups to maximize their separation due to electrostatic interactions, whereas the hydrophobic backbones avoid water exposure. These driving forces lead to similar structural characteristics independent of grafting positions. To further demonstrate the similarity among the three types of morphologies in aqueous solution, the relative positions of the charged ligand end groups were compared using end-groupto-end-group radial distribution functions with three curves corresponding to mixed, striped, and random morphologies shown in Figure 8. All three curves show very similar behaviors,

Figure 8. Hydrophilic sulfonate end-group-to-end-group RDFs for mixed, striped, and random morphologies. Two local maxima appear, indicating preferred end-group separations that are nearly identical for all three morphologies. The similarity of all three curves indicates that no morphological distinction appears during the simulation run.

each exhibiting two local maxima corresponding to preferred end-group separations. These peaks are consistent with the charged sulfonate groups uniformly distributing to minimize electrostatic repulsion, leading to preferred end-group separations rather than a continuous distribution of possible separations. The inability to differentiate between the different morphologies again indicates that ligand fluctuations drive all 20110



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Figure 9. Tilt-angle distributions for hydrophilic and hydrophobic ligands with varying hydrophobic-ligand lengths. Different sets of ligand compositions have the same color, with hydrophilic-ligand tilt angles shown as solid lines and hydrophobic-ligand tilt angles shown as dashed lines. Increasing the length of the hydrophobic ligand shifts the distribution of the hydrophilic ligand toward smaller tilt angles, whereas the distribution for the hydrophobic ligand shifts toward larger tilt angles.

Figure 10. Snapshots illustrating the bending of long hydrophobic ligands to permit access of hydrophilic end groups to the aqueous interface. The two rows compare identical 4.0-nm particles with mixed surface compositions, but with hydrophobic-ligand lengths of (A) 8 and (B) 17 carbons. The first column shows the starting all-trans conformation to indicate the extent of the difference in ligand lengths. Hydrophobic ligands are drawn in silver. The second two columns show two different views of the final equilibrated particles, with the first solvation shell of each end group drawn in blue. Comparison of these images shows that MUS end groups always access water because of the need for ion solvation; as a result, the longer 17carbon ligands must bend significantly to avoid water exposure and not disrupt the water solvation shells. The deformation is apparent in the segments of the ligands that lie nearly parallel to the MUS−water interface, which are not observed for the shorter hydrophobic ligand. The observations are further confirmed by radial distribution functions showing that the hydrophobic-ligand density is always closer to the AuNP surface than the MUS end-group density, leading to a prominent increase in the hydrophobic density around 3.0 nm in the 17-carbon case that is due to the bending of the ligands.

the 11:8 case (top row), the images show that, when the hydrophilic ligands are longer, they extend toward the water layer and are solvated as expected, with hydrophobic ligands shielded from the aqueous interface by the longer hydrophilic layers. For the 11:17 case (bottom row), the all-trans conformations of the hydrophobic ligands are now significantly longer than the hydrophilic ligand species. However, the strong driving force for solvation of the ionic end groups, coupled with

the poor solubility of the hydrophobic groups, leads the hydrophobic ligands to “bend” to avoid the aqueous interface. A comparison of the 11:8 and 11:17 systems in the second column of images clearly shows that the positions of the aqueous interface are effectively the same for the two cases and the solvation shells of the hydrophilic ligands are similar. The third column shows the bending of the silver hydrophobic ligands to accommodate the solvation of the hydrophilic end 20111



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understand the effects of the gold particle diameter, nanoscale morphology, and relative ligand lengths on the structure of the monolayer at 310 K and 1 bar, typical biological conditions. Our results first showed that a surface composition consisting of a 1:1 ratio of hydrophilic/hydrophobic ligands has properties similar to those of a homogeneous all-MUS surface, with only small differences in the electrostatic potential and distribution of counterions consistent with a reduction in the number of charged species in the protecting monolayer. We next showed that changing the size of the particle diameter has a similarly expected result on the electrostatic potential, effectively just increasing the magnitude of the peaks in the potential, which again reflects the increase in the number of charged species. However, increasing the size also leads to a decrease in the tilt angles of both ligand species because of the greater steric barriers to ligand fluctuations arising from the decrease in free volume per ligand with increasing substrate curvature. This decrease in tilt angle thus implies that the surface of larger particles is less fluidlike than that of smaller particles where ligands are subject to much larger fluctuations. In contrast to the changes in structure observed for changing particle diameter, changes in the nanoscale morphology of the ligands had no effect on structural characteristics because of the tendency of hydrophilic end groups to always take the same relative positions with respect to each other. The nanoscale morphology was thus inconsequential, in part because of the ability of these ligands to fluctuate to obtain favorable positions in aqueous solution. Finally, we showed that changes in the relative lengths of the hydrophilic and hydrophobic ligand species could lead to significant bending of the hydrophobic ligands to prevent exposure of hydrophobic material to the aqueous interface and ensure that the hydrophilic end groups were always solvated by water. This bending was especially prevalent when the hydrophobic ligands were much longer than the hydrophilic ligands, leading to confinement of the hydrophilic ligands as a result of the increase in the density of surrounding neighbors from the bent hydrophobic ligands. This extreme bending behavior could impose a severe entropic penalty on the hydrophobic ligands that could affect particle solubility or short-range interactions with other molecules. However, even under conditions such that the hydrophobic ligands were longer than the hydrophilic ones, our results still showed that no distinction in the three nanoscale morphologies can be observed because the hydrophilic ligands always have access to the aqueous interface and will thus distribute themselves approximately uniformly across the surface to minimize electrostatic effects. The trends obtained from our simulations thus indicate that, when considering the properties of mixed-monolayer-protected AuNPs in solution, the particle size and choice of relative ligand lengths can have significant effects on the system properties but changes in the relative position of the grafted ligands have minimal effect. However, we must emphasize that, by construction, the sizes of the ligand domains considered for the three different morphologies were on the order of only a few angstroms to match experimental observations;32 it is likely that AuNPs with macrophase-separated domains, such as Janus particles, would demonstrate more significant differences, as has been shown previously.40 Similarly, we considered only structural properties in an aqueous environment and cannot say whether changes in nanoscale morphology modify interactions with biological molecules, as has been previously observed. Nonetheless, our results are important in establishing

groups. This strong bending behavior thus explains the large average hydrophobic tilt angle evident in Figure 9. The confinement of the hydrophilic ligands is similarly explained by the increased local density in the monolayer necessitated by ligand bending, leading to inhibited fluctuations and hence a decreased tilt angle. Further evidence of the bending effect is shown in the two radial distribution functions, which indicate that the hydrophobic ligands are confined closer to the AuNP surface than the MUS ligands, leading to a large increase in the RDF for the 11:17 case because of the increased amount of hydrophobic material within this layer. The plots also show that the peak for the MUS end group shifts to slightly farther distances in the 11:17 case, consistent with the decrease in hydrophilic tilt angle observed in Figure 9. Figure S6 (Supporting Information) demonstrates that this enhancement of hydrophobic density at a position close to the gold surface is consistent for all ligand lengths studied. Figure S7 (Supporting Information) further demonstrates the increase of gauche dihedrals along the hydrophobic chains, again supporting the observation of enhanced ligand bending. The observation of bending forced by the necessity of solvating hydrophilic end groups and avoiding the exposure of hydrophobic ligands to water implies that the hydrophobic ligands must incur a significant conformational entropic penalty under aqueous conditions. This entropic penalty could lead to changes in the solubility of the particles, but it could also affect interactions with other biological molecules or processes that depend on ligand deformation.69 It is also important to note that the long-range electrostatic interactions associated with the AuNP are largely identical independent of hydrophobic-ligand length because the bending process allows water to access the hydrophilic end groups, leading to similar radial electrostatic potential profiles (Figure S9, Supporting Information) and hydrogen-bonding numbers (Table S4, Supporting Information) as the ligand length is increased. Thus, it is likely that the long-range interactions between all particle types are similar, but the entropic penalty incurred by the bending of long hydrophobic ligands could lead to modified short-range interactions in which the hydrophobic ligands might play an important role. Finally, despite the inhibited ligand fluctuations, as shown in Figure S8 (Supporting Information), there is still no observed difference in the end-group-to-end-group RDFs between mixed, striped, and random morphologies when the relative ligand lengths are flipped, as shown in Figure S5 (Supporting Information). Furthermore, similar structural quantities are recorded for all three morphologies, as shown in Table S3 (Supporting Information), agreeing with the same behavior demonstrated in Table 1. These results again suggest that, in aqueous solution, there is no practical distinction between grafting the two ligand species in mixed, striped, or random morphologies, as electrostatic interactions between the charged end groups will lead to the same distribution of end groups independent of ligand grafting points.

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CONCLUSIONS In this work, we used molecular dynamics simulations to explore the structure of mixed-monolayer-protected gold nanoparticles in 150 mM aqueous salt solution. Monolayers were composed of a binary mixture of hydrophilic endfunctionalized alkanethiol ligands and hydrophobic alkanethiol ligands, yielding an amphiphilic surface characteristic of mixedmonolayer-protected particles found in the literature. Simulations were performed on a series of simulation systems to 20112



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that particular care for considering the exact morphology of the particle surface might not be necessary for many applications given the structural similarities between the resulting monolayers. We expect that the physical insight gained from our work will be useful in guiding the design of particle surfaces for biological interactions, especially when these interactions depend on ligand fluctuations or other structural features of the particle interface.

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ASSOCIATED CONTENT

S Supporting Information *

Additional simulation snapshots, tables summarizing relevant data, several figures mentioned in the text, and additional simulation methods. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS R.C.V. is supported in part by a National Science Foundation Graduate Research Fellowship. R.C.V. and A.A.-K. also acknowledge support from the MRSEC Program of the National Science Foundation under Award DMR-0819762. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant OCI-1053575. Some of the computations in this work were run on the Odyssey cluster supported by the FAS Sciences Division Research Computing Group. The authors also thank J. Aragones, J. Q. Lin, and R. Carney for helpful discussions.

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REFERENCES

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Nanoparticles into Bilayer Structures via Adaptive Surface Chemistry. J. Am. Chem. Soc. 2013, 135, 590−593.

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Structure of Mixed-Monolayer-Protected Nanoparticles in Aqueous

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