Dynamic Template for Assembling Nanoparticles into Highly

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Dynamic Template for Assembling Nanoparticles into Highly Ordered Two-Dimensional Arrays of Different Structures Mahmoud A. Mahmoud* Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States S Supporting Information *

ABSTRACT: The proper assembly of nanoparticles can enhance their properties and improve their applicability. Likewise, imprudent assembly can damage the unique properties of the nanomaterials. Accordingly, finding robust techniques for making ordered assemblies of nanoparticles is a hot topic in materials science research. In this work, the Langmuir−Blodgett (LB) technique was used to assemble polyethylene glycol (PEG)-functionalized gold nanocubes (AuNCs) into highly packed two-dimensional (2D) arrays with different structures. This technique is based on creating polymeric micelles within the AuNC monolayer, which drives the nanocubes to assemble into a highly packed structure even at low LB surface pressures. Interestingly, the micelles could be made more diffuse by changing the LB trough surface pressure, which allowed for tuning the width and the structure of the AuNC 2D arrays. The areas occupied by the micelles appeared as voids that separated the AuNC arrays and prevented the formation of a uniform monolayer of AuNCs. The polymer micelles were therefore able to act as dynamic soft templates, and the separation distances between individual nanocubes as well as the 2D array structure were controlled by changing the chain length of the PEG functionalization on the surface of the nanocubes. Theoretical calculations of the attractive and repulsive forces and the balance between them presented a good prediction for the optimum separation distance between the AuNCs inside the 2D arrays.

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INTRODUCTION In the last few decades, nanoparticles of different chemical compositions, shapes, sizes, and structures have been prepared.1−4 These nanoparticles have been proven to possess unique optical,5,6 electrical,7 catalytic,8 mechanical,9 and photonic properties. For applications of such materials, it is often desirable to assemble them into 1-, 2-, or 3-dimensional (D) assemblies to enhance single-particle properties or create new, emergent properties. Two approaches have commonly been used to assemble the nanostructures into desired assemblies, which involve either the self-assembly10 (no force is applied) or guided assembly11 (requires external energy or forces). The Langmuir−Blodgett (LB) technique combines the 2D self-assembling and guided assembling techniques simultaneously.12 In the LB technique, the nanoparticles are allowed to self-assemble and distribute on the water−air interface, but the self-assembled nanoparticles are guided to organize by a mechanical force resulting from decreasing the surface area that the nanoparticles are occupying.13,14 Magnetic fields are also useful in assembling and aligning magnetic nanoparticles, e.g., assembling of cobalt nanoparticles into rings due to the magnetic dipolar interactions.15 Capillary forces can also form between neighboring nanoparticles while the solvent is evaporating, resulting in adhesion (e.g., gold nanorods are aligned into a parallel assembly after solvent removal).16 This capillary force has been proven to depend on the nanorod © XXXX American Chemical Society

concentration, capping material concentration, nanorod size distribution, the ionic strength of the solution, and the solvent evaporation rate.16 In this study, a new strategy based on the LB technique is introduced to assemble polyethylene glycol (PEG)-functionalized gold nanocubes into highly packed 2D arrays that possess different structures. The structure and the width of these 2D arrays are controlled by changing the applied surface pressure of the LB trough. However, circular voids with micron-sized surface areas, which are filled with polymeric micelles, are observed throughout the 2D nanoparticle arrays. These small micelles can diffuse through the 2D arrays and change their width and the structure upon application of an external surface pressure. These micelle voids behave as soft dynamic templates that change the structure of the arrays upon application of a surface pressure. This templating method can allow the formation of new, highly novel structures and assemblies. For instance, the highly packed AuNC assemblies discussed here are expected to generate huge plasmonic electromagnetic field enhancements, which are useful in many applications such as surface-enhanced Raman scattering (SERS)17 and nanolensing.18 The presence of the voids can be used to separate the Received: August 29, 2014 Revised: November 3, 2014

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Figure 1. (A) Photograph showing the Langmuir−Blodgett (LB) trough coated with a gold nanocube monolayer (red portion in the left side of the trough). The mechanical barrier located in the center of the trough controls the surface area occupied by the nanocubes. The surface pressure of the monolayer is measured by the Wilhelmy plate attached to the pressure sensor at the back of the trough. During the transfer of the LB film to the surface of the silicon substrate, the substrate is fixed vertically by tweezers connected with the mechanical dipper in the middle of the left side of the trough. (B) LB isotherm for the gold nanocube monolayer dispersed on the top of the water sublayer of the trough. AuNCs are functionalized with long-chain polyethylene glycol polymer (Mn = 6k) (black curve) and short-chain polymer (Mn = 2k) (red curve). Although the two isotherms have three different phases (gaseous, liquid condensed, and solid), it is clear that the phase transitions in the case of the shorter-chain polymer are much smoother than those in the case of the long-chain polymer. The green and blue circles in the curves are the surface pressures measured during the transfer of the 2D arrays to the surface of the substrate.

precipitation (centrifugation at 8000 rpm for 10 min in 15 mL plastic tubes) and redispersed in DI water. Finally, the AuNCs were dispersed in 20 mL of DI water and 0.2 mL of 5 mM thiolated polyethylene glycol (PEG-SH) of average molecular weight (Mn) of either 2000 or 6000 were added. The resulting solution was stirred for 8 h, and the excess PEG-SH was removed by two-fold centrifugation at 6000 rpm for 10 min in 1.7 mL centrifugation tubes followed by the redispersion of the precipitated particles in DI water. The precipitate of the twofold centrifugation was then dispersed in 8 mL of methanol and centrifuged at 6000 rpm for 10 min. After methanol cleaning, the precipitated AuNCs were redispersed in 2 mL of chloroform. A Nima 611D trough with a DI water sublayer was used to assemble the AuNC monolayers; the surface pressure was measured by a Wilhelmy plate attached to a D1L75 model pressure sensor. Using a microsyringe, 2 mL of AuNCs dispersed in chloroform was sprayed over the water sublayer of the trough, and the LB film was allowed to dry for 30 min. Finally, the reading of the surface pressure sensor was adjusted to zero when the trough was opened at one end. Figure 1A shows a photograph of the LB trough after coating with the AuNC monolayer (red portion in the left side of the trough). The AuNC monolayer was transferred to the surface of a silicon wafer substrate (cleaned with piranha solution 30% H2O2 and 70% H2SO4 volume ratio) at different surface pressures by the vertical dip coating technique using an LB mechanical dipper programmed to raise at a speed of 2 mm/ min. A Zeiss Ultra60 was used for the scanning transmission electron microscopy imaging. A JEOL 100C transmission electron microscope (TEM) was used to image as-synthesized AuNCs. Figure S1 in the Supporting Information shows the TEM image of the AuNCs before functionalization with PEG as well as the size distribution analysis of the AuNCs. A Veeco AFM II Dimension 3100 was used for AFM imaging. A Renishaw Invia Raman microscope was used to collect the micro-Raman measurements from different spots in the sample. ImageJ was used for the statistical analysis of the SEM images of the 2D AuNC arrays. A Zetasizer Nano ZS (Malvern) was

AuNC 2D arrays, preventing them from forming a uniform monolayer. The micelles are characterized by atomic force microscopy (AFM) and scanning electron microscopy (SEM) imaging techniques after transferring them onto the surface of a silicon substrate. Raman spectroscopy was used to characterize the composition of the micelles. It was discovered that the individual separation distance between the nanocubes inside the 2D arrays is governed by the chain length of the polymers functionalized with the surface of the nanocubes. The behavior of the micelles in packing the nanocubes tightly into 2D arrays and in changing the structure of the arrays upon increasing the surface pressure of the LB trough is also studied theoretically. The balance between the attraction forces that brings the nanocubes together and the repulsion force pushing the nanocubes away from each other gave an acceptable prediction of the experimental results.

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EXPERIMENTAL METHODS Gold nanocubes (AuNCs) were prepared by the seed-mediated approach as reported earlier,19 but scaling up the volume of the growth solution required modification of the concentration of the reagents. No change was made to the synthetic procedure of the seed nanoparticles.19 The seed solution was prepared as follows: 0.283 g of cetyltrimethylammonium bromide (CTAB, Sigma-Aldrich) was dissolved in 5 mL of deionized water (DI) and mixed with 2.75 mL of 0.909 mM hydrogen tetrachloroaurate trihydrate aqueous solution (HAuCl4·3H2O, SigmaAldrich). Under stirring, 600 μL of an ice cold 0.01 M sodium borohydride (Sigma-Aldrich) solution was added, and the stirring was continued for 2 min. One hour after initial seed synthesis, 0.35 mL of 10-fold diluted seed solution was allowed to grow in the growth solution, which was prepared by mixing CTAB solution (2.916 g dissolved in 400 mL of DI water) with HAuCl4·3H2O solution (0.0394 g dissolved in 143 mL of DI water) followed by adding 7 mL (1 M) of ascorbic acid (SigmaAldrich). The growth process was completed after 4 h. To prepare AuNC solution for Langmuir−Blodgett films, 200 mL of AuNCs was cleaned from excess CTAB by two-fold B

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used to measure the ζ-potential of the gold nanocubes functionalized with PEG when dispersed in water.

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RESULTS AND DISCUSSION Assembly of Gold Nanocubes into Highly-Packed 2D Arrays with Different Structures. Polymers and long-chain hydrocarbons are commonly used as capping materials in the synthesis of colloidal nanoparticles.1 Assembly of the nanoparticles into 2D or 3D building block structures is governed by a multitude of factors such as the overall van der Waals interaction force between the nanoparticles and the binding affinity among the capping materials,20 the chain length of the capping materials bound to the surface of the nanoparticles,21,22 the shape and the structure of nanoparticles,20 the solvent polarity compared to the polarity of the capping materials (the conformation of the polymer depends on the polarity of both the solvent and the capping materials of the nanoparticles), and the evaporation rate of the solvent during the assembly process, because the solvent molecules between nanoparticles have to be removed during the assembly of the nanoparticles.11,20 Finally, the thermodynamic stability of the assembly and the external energy or force that would be applied to drive the assembly to produce desired structures both need to be considered.11 Assembly of the nanoparticles using a template is one of the successful techniques for organizing the nanoparticles.23 On the basis of the shape and size of the template, the structure of the nanoparticles assembly can be engineered.23,24 LB technique succeeded in assembling various isotropic and anisotropic nanoparticles into 2D arrangements.12,13,25−27 2D arrays of AuNCs functionalized with 6k PEG polymers assembled on the surface of silicon substrate at different LB surface pressures are shown in Figure 2A−F. For more clarification, SEM imaging was conducted for the 2D arrays at higher magnification (see Figure S2 in the Supporting Information). The LB isotherm is given in Figure 1B (relationship between the change in the surface pressure of the LB trough and the surface area that the AuNCs are occupying). As in all traditional LB isotherms, it is clear that the isotherm has three different regions corresponding to different phases: gaseous, liquid condensed, and solid. Two different AuNC monolayer samples were transferred to the surface of silicon substrates from each phase using the vertical dip technique. An interesting observation seen in all samples regardless of surface pressures is that the AuNCs are organized into highly packed 2D structures with surrounding circular voids filled with spherical particles. Both the surface area of the voids and the width of the 2D arrays of the nanocubes are altered depending on the surface pressure. The change of the structure of the 2D arrays of the AuNCs is determined by carrying out a statistical analysis for the surface area of the voids in the SEM images of the AuNC 2D arrays (Figure S3 in the Supporting Information). As expected, the percentage of surface coverage of the AuNCs to the substrate calculated by ImageJ from the SEM images was increased upon increasing the surface pressure and was found to be 18.5, 22.9, 25, 37.1, 49, and 50.5% for arrays prepared at surface pressures of 0, 0.1, 2, 6, 9.5, and 11.5 mN/m, respectively. It is expected that nanoparticles deposited at a surface pressure corresponding to the gaseous phase of the LB isotherm would be arranged randomly, resembling the behavior of gaseous molecules in a container.13 Interestingly, in this experiment, the AuNCs are arranged into a highly packed 2D structure. For the two samples transferred to the substrate from the gaseous phase (SEM images in Figure 2A,B), the surface

Figure 2. SEM images of gold nanocubes functionalized with longchain 6k polyethylene glycol polymers and assembled using the Langmuir−Blodgett technique on the surface of silicon substrates into highly packed 2D arrays with different structures. The structures of the nanocube 2D arrays are controlled by changing the surface pressure of the trough: (A) 0 mN/m, (B) 0.1 mN/m, (C) 2 mN/m, (D) 6 mN/ m, (E) 9.5 mN/m, and (F) 11.5 mN/m. Circular voids filled with small nanospheres and surrounded by highly packed 2D array of gold nanocubes are observed in all the samples. The surface area of the voids and the width of the 2D arrays of the AuNCs depend on the surface pressure measured during the transfer of the nanocubes to the surface of the substrate. The scale bar is 1 μm.

area of the voids is increased while their number is decreased when the surface pressure is increased from 0 to 0.1 mN/m (see Figure S3A,B in the Supporting Information). The majority of the voids in the case of the 2D arrays fabricated at a surface pressure of 0.1 mN/m have surface areas below 1 μm2, but when the surface pressure was increased to 2 mN/m (liquid condensed phase region), the surface coverage was slightly increased and the number of voids with a surface area of 1−2 μm2 was also increased at the expense of the smaller ones (Figure 2C and Figure S3C in the Supporting Information). Despite being transferred to silicon substrates from the same liquid condensed phase, 2D arrays fabricated at surface pressures of 2 and 6 mN/m displayed remarkably different structures (Figure 2D). The surface area of the majority of the voids became larger (surface area ∼2−4 μm2) (Figure S3D in the Supporting Information) and linear cracks started appearing, as shown in Figure 2D. When the surface pressure was increased to reach the solid phase of the LB isotherm (LB surface pressure of 9.5 mN/m), the linear cracks became rare and larger, oblate voids were observed (see Figure 2E and Figure S3E in the Supporting Information). The number of voids also decreased for this increase in surface pressure. Finally, when the surface pressure was increased to 11.5 mN/m, the number of voids was found to decrease along with the surface area of the voids (see Figure 2F and Figure S3F in the Supporting Information). C

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The obtained results raise many questions, which will be answered after further characterization of the arrays. Why are the nanoparticles arranged into highly packed 2D structural arrays surrounding large voids even for samples prepared at low surface pressures? Why does changing the surface pressure during the assembly of the nanoparticles change the width of the 2D Au NC arrays as well as the individual surface area and the structure of the voids? What are the spherical particles filling the voids composed of and what is their role in the nanocube assembly? Ultimately, although the traditional LB isotherm was obtained with the three different phases, the distribution of the AuNCs inside the LB monolayer did not behave as expected compared to previously reported organization in each phase.14 Effect of Chain Length of the AuNC Polymer Functionalization on the Structure of the AuNC 2D Arrays. The chain length, rigidity, or grafting density of the polymer functionalized with the surface of the nanoparticles have been proven to have significant effects on their assembly behavior.28 Short-chain polyvinylpyrrolidone polymers were used to assemble silver nanocubes face-to-face, while long-chain polymers organized them into edge-to-edge conformations inside of a polystyrene thin-film matrix.22 Similarly, the effects of PEG chain length on the structure of the AuNC 2D arrays were investigated. Panels A through F in Figure 3 show the SEM images of 2D arrays of AuNCs functionalized with the

short-chain 2k PEG polymers and deposited on the surface of silicon substrates at surface pressures of 0, 0.2, 1, 4, 5.5, and 6.5 mN/m, respectively. The higher magnification SEM images of the arrays are shown in Figure S4A−F in the Supporting Information. The percent surface coverage of the AuNCs on the silicon substrate was found to be 23.9, 26.8, 40.4, 45, 50.8, and 60.6% for samples prepared at surface pressures of 0, 0.2, 1, 4, 5.5, and 6.5 mN/m, respectively (calculated from SEM images in Figure 3A−F). The structure of the AuNC 2D arrays fabricated from the gaseous phase region in the case of AuNCs functionalized with 2k PEG (surface pressure of 0 and 0.2 mN/ m) is found to be different from that of the case of the AuNCs functionalized with the 6k PEG. However, the surface area of the voids for 2D AuNC arrays functionalized with 2k PEG was larger than that observed for 2D AuNC arrays functionalized with 6k PEG, although the number of voids present was lower. The number of small voids in the case of the 2D arrays of AuNCs functionalized with 2k PEG was less than that observed in the case of the 2D arrays of AuNCs functionalized with the 6k PEG (see the statistical analysis in Figure S5A,B in the Supporting Information). When the surface pressure was increased to the liquid condensed phase region, both the surface area of the voids and the width of the 2D AuNC arrays were increased (see Figure S5C,D in the Supporting Information). In the liquid condensed phase region, this structural change with a change in surface pressure occurred for both the 2 and 6k PEG. For the solid region of the LB isotherm, three differences in the structure of the arrays were observed when the 6k PEG functionalization was replaced by 2k PEG: the number of cracks in the arrays increased, the surface areas of the voids increased, and the number of voids decreased (see Figure S5E,F in the Supporting Information). Generally, the chain length of the PEG functionalization had several noteworthy effects on the structure of the 2D AuNC arrays. The number of cracks observed throughout the AuNC arrays functionalized with the short-chain 2k PEG increased as the LB surface pressure was increased. However, cracks were observed in only the 2D AuNC arrays functionalized with 6k PEG at relatively high LB surface pressures. The width of the AuNC arrays was found to increase systematically as the LB surface pressure was increased for the 2k PEG, although systematic changes were not seen for the 6k PEG arrays. Consequently, the width of the arrays in the solid-state region for AuNCs functionalized with 2k PEG was larger than when the AuNCs were functionalized with 6k PEG. Also, the individual AuNCs inside the arrays were more closely packed for the 2k PEG. The average separation distance between neighboring nanocubes calculated by imageJ was 4.2 ± 1.5 nm and more organized for the 2k PEG functionalization compared with that of the 6k PEG, which had an average separation distance of 7.4 ± 2.3 nm (see Figure 4). As noted previously, the number of voids decreased while the surface area of the voids increased for the 2k PEG arrays compared to the voids of the 6k PEG arrays. The phase transitions between phases in the LB isotherm (gaseous, liquid condensed, and solid) for the 2k PEG functionalization were much smoother than that for arrays with 6k PEG (see Figure 1B). Finally, the nanospheres inside the voids for the short-chain 2k PEG arrays were observed to be smaller than those of the long-chain 6k PEG arrays. It is important to mention that the structure of the 2D arrays formed at 0 mN/m seems to play a major role in the formation of other array configurations at higher surface pressures. To confirm this idea, the amount of AuNCs sprayed over the water

Figure 3. SEM images of gold nanocubes functionalized with shortchain polyethylene glycol (Mn = 2000) polymers and assembled by the Langmuir−Blodgett technique on the surface of silicon substrates into highly packed 2D arrays of different structures. The structures of the 2D arrays are controlled by changing the surface pressure of the trough: (A) 0 mN/m, (B) 0.2 mN/m, (C) 1 mN/m, (D) 4 mN/m, (E) 5.5 mN/m, and (F) 6.5 mN/m. The AuNCs are assembled into highly packed 2D arrays structures with circular voids filled with spherical nanoparticles. On increasing the surface pressure of the trough, the surface area of the voids is decreased and the width of the 2D arrays is increased. The scale bar is 1 μm. D

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voids have an approximate disc shape, because their height is 6.3 ± 0.2 nm while their diameter is 46.1 ± 4.5 nm (Figure 5C). This suggests that the voids are free from AuNCs, which are 40.3 ± 3.2 nm in height. The composition of the nanodiscs located inside the voids was characterized by micro-Raman spectroscopy. These nanodiscs were hypothesized to be made of PEG and/or CTAB. In view of this assumption, Raman spectra were collected from the surface of voids and from the surface of the AuNCs (see Figure 6A). Figure 6B shows the bright-field image of the 2D arrays of AuNCs. The Raman spectra of the voids, collected from the area highlighted by the blue circle in the bright-field image, and the AuNCs are compared with the Raman spectra of pure CTAB and pure 6k PEG films cast on silicon substrates. To make the film of pure CTAB and PEG, 0.1 mL of their aqueous solutions with a concentration of 20 mM was drop cast and allowed to dry on the surface of a silicon substrate. The Raman band intensities of the pure film of CTAB were found to be higher than that measured for the pure PEG film although they had the same concentration, suggesting that the Raman cross section of PEG is less than that of CTAB. The Raman bands collected from the surface of the voids for the nanodiscs and from the surface of the AuNCs resemble the Raman bands of both CTAB and PEG. However, the ratio of Raman band intensities of CTAB to that of PEG for the nanodiscs located inside the voids was less than that for the AuNC arrays. The Raman spectrum collected from the surface of arrays was sharp because of the Raman signal enhancement by the AuNCs, while the Raman signal collected from the voids was multiplied by a factor of 100 because of the weak intensity of the Raman signal. The large differences in intensity of the Raman signal measured for the voids and that collected from the surface of the AuNCs arrays confirms the accuracy of the Raman measurement because the surface area of the voids is comparable to the focused laser beam size. A sharp band was also observed at 1350 cm−1 in the case of the Raman spectrum of the AuNC arrays and voids, which is not present in the spectrum of either the pure CTAB or PEG. This new Raman band is assigned to the CH2 wagging mode, which is characteristic for amorphous PEG in its gauche conformation.29 The Raman measurements suggest that the nanodiscs are composed of both CTAB and PEG, and the concentration of CTAB inside the nanodiscs was higher than that on the surface of AuNCs. Although the Raman bands of CTAB are not weak compared with the bands of PEG, the concentration of PEG

Figure 4. SEM images of 2D arrays of AuNCs functionalized with PEG polymers of different chain lengths: (A) long-chain 6k PEGfunctionalized arrays fabricated at a surface pressure of 11.5 mN/m and (B) short-chain 2k PEG-functionalized arrays fabricated at a surface pressure of 6.5 mN/m. The 2D arrays of AuNCs functionalized with the short-chain polymer are more organized than those functionalized with the long-chain polymer, and the separation distance between the neighboring cubes in the case of the 2k polymer is 4.2 ± 1.5 nm, while for 6k PEG the distance is 7.4 ± 2.3 nm.

surface was lowered to half its original value; interestingly, the 2D arrays assembled into strips instead of the regular network structure that was usually obtained. Figure S6A−B in the Supporting Information shows the SEM image of 2D arrays of AuNCs functionalized with 6k PEG when the amount of the initial AuNCs used in making the LB film was lowered to half the original amount. The arrays were transferred to the surface of silicon substrate while the surface area that the AuNCs were occupying was 440 cm2. However, when the surface pressure was increased, the network arrays were obtained instead of strips. The effect of increasing the concentration of the PEG on the structure of the AuNCs 2D arrays assembly was also examined, and the concentration of PEG functionalized with the AuNCs was doubled. 2D arrays of curved short stripes were obtained, as seen in Figure S6C−D in the Supporting Information. When the surface pressure was increased, the network arrays were obtained, in addition to large empty zones. Characterization of the Voids Located between the AuNC 2D Arrays. AFM imaging was used to provide more clarification on the topography of the AuNC 2D arrays, especially on the height of the spherical particles that occupy the voids. Figure 5 shows AFM images of the 2D arrays of AuNCs functionalized with the 6k PEG and fabricated at an LB surface pressure of 11.5 mN/m (the SEM image of these arrays is shown in Figure 2F). It is confirmed from the lowmagnification AFM image in Figure 5A that the AuNCs are arranged into 2D, monolayer structures. The AFM image in Figure 5B shows that the polymer nanoparticles inside the

Figure 5. AFM images of 2D AuNC arrays functionalized with 6k PEG and fabricated at a surface pressure of 11.5 mN/m. (A) The lowmagnification image confirms the 2D structure of the AuNC arrays. (B) The medium magnification image shows that circular voids are filled with nanodiscs with a height lower than the height of the AuNCs. Panel C presents a high-magnification image of the voids. E

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Figure 6. (A) Micro-Raman spectra for the 2D AuNC arrays functionalized with 6k PEG and assembled on the surface of a silicon substrate collected from the surface of AuNC arrays (green) and circular voids (blue). The spectrum collected from the void areas and the surface of the AuNCs are a combination of the Raman spectra recorded for the pure CTAB (red) and pure PEG (black). However, the ratio between the intensity of the PEG bands to the intensity of the CTAB bands for the spectrum collected from the voids is higher than that collected from the surface of the AuNCs. This suggests that the concentration of CTAB in the disc particles present in the voids is less than that on the surface of the AuNCs.31 (B) Bright-field image of the 2D arrays of AuNCs after white light excitation. The Raman spectrum of the voids was collected from the area inside the blue circle in the image.

surface charge on the AuNCs, the charge on the PEG molecules functionalized with the surface of the AuNCs, the repulsion force between the polymer chains, and the interaction of the PEG-functionalized AuNCs with the surface of the water sublayer. The values of the interaction potential energy were calculated for a pair of gold nanocubes placed face-to-face at different interparticle separation distances (Figure 7A).

both in the nanodiscs and on the surface of AuNCs is higher than that of CTAB because of the effect of Raman cross section. The Raman results suggest that the small nanodiscs are composed of both PEG and CTAB. After the exchange of CTAB with PEG and multiple cleanings of the nanoparticles, it is evident that some CTAB remains on the surface of the AuNCs and in the solution, which is capable of forming disc nanoparticles with the free PEG molecules.30 Mechanism of Assembly of the AuNCs into Highly Packed 2D Arrays. AuNCs functionalized with PEG and dispersed in water, methanol, and chloroform showed great stability even after multiple precipitations by centrifugation and redispersion in these solvents. The net electrostatic surface potential of the AuNCs functionalized with both 2 and 6k PEG was measured by ζ-potential when dispersed in water. The value of the ζ-potential was found to be −31 ± 4 and −37 ± 6 mV for AuNCs functionalized with 2 and 6k PEG, respectively. These large negative ζ-potential values facilitate the stability of the nanocubes when dispersed in a water medium and suggest a low concentration of CTAB, which has a positive potential. The stability of AuNCs was also experimentally confirmed from the optical measurement when dispersed in the water, methanol, and chloroform solvents because no peak was observed corresponding to the aggregation of the AuNCs. To understand the mechanisms behind the arrangement of the AuNCs into highly packed 2D arrays even at low surface pressures, the attractive forces acting to assemble the nanocubes and the repulsion forces that attempt to keep them separated were assigned and calculated. The calculation of the overall interaction potential energy makes it possible to predict whether the nanoparticle assembly is thermodynamically favorable and also allows the determination of an approximate value of the optimum separation distance between individual nanocubes, with the optimum distance being the distance that minimizes the potential energy of the nanocube system.32 For simplification, the calculation was carried out for a pair of nanocubes functionalized with PEG and assembled as a LB film on the surface of a water sublayer. The interaction potential energy for this system is governed by the following factors: the

Figure 7. Schematic diagram of AuNCs (red) functionalized with PEG (blue): (A) van der Waals forces between a pair of AuNCs separated by a distance of L, with the length of the stretched PEG normalized to l; (B) AuNCs functionalized with PEG, which is arranged into brush structures with Flory radius (h), grafting density (Γ), and Kuhn length (b); and (C) depletion force generated between a pair of AuNCs due to the diffusion of micelles made of PEG−CTAB from the area between them.

The movement of the positive and negative charges within the nanocubes and the PEG generates a van der Waals (vdW) attractive force. Generally, the vdW force between the AuNCs is attractive, but because of the interaction of the polymer chains bound to the surface of AuNCs with the molecules of the solvent, the vdW force between the nanocubes becomes repulsive and allows the nanocubes to be stable in water.33 When AuNCs in chloroform are sprayed over the water sublayer of the LB trough, the solvent will evaporate F

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Figure 8. Potential energy diagram calculated for a pair of 40 nm gold nanocubes placed at different separation distances. The black curve is for the van der Waals attractive potential energy, which is expressed as a negative value; the red curve represents the change in the value of the steric potential energy as a function of separation distance and has a positive value; and the depletion potential generated by the osmotic pressure of the micelles is shown in blue with negative values. The overall potential energy of the nanocube system as a function of the separation distance between the nanocube pair is represented by the green curve. The most stable separation distance is obtained at the minimum value of the potential energy, which is (A) 4−5 nm for AuNC pairs functionalized with 2k PEG and (B) 7−9 nm for AuNC pairs functionalized with 6k PEG.

nanocubes. The potential energy of the steric repulsion (US) between a pair of AuNCs is calculated as a function of the separation distance between them from eq 2

immediately and the vdW force between the AuNCs becomes attractive instead. For any pair of gold nanocubes placed side-by-side, vdW forces are expected to be generated between the following: the gold surfaces of the nanocubes, the PEG functionalized with one cube and the gold surface of the other nanocube, the PEG polymer chains functionalized with the two nanocubes, and the gold surface of the nanocubes and the polymer bound to it with the surface of water sublayer (solvation force). The vdW potential energy (UvdW) for each vdW force was calculated using the Hamaker integral approximation in eq 134 UvdW =

−Aa 24L

π 3akT Γh3 ⎡ 9 1 3 ⎢⎣ −ln μ − (1 − μ) + (1 − μ ) 2 5 3 6Nb ⎤ 1 − (1 − μ6 )⎥ ⎦ 30

US =

(2)

where h ∼ N(Γb5)1/3, μ = L/2h, and b is the Kuhn length for PEG (1.1 nm);22 Γ is 0.1 chain/nm2 for both 2 and 6k PEG and N is the number of Kuhn segments, which is simply the length of the stretched polymer divided by the Kuhn length, b;38 T is the absolute temperature, and K is the Boltzmann constant (1.38 × 10−23 J·K−1). The schematic in Figure 7B clearly represents these constants. The steric repulsion potential energy curve of a pair of AuNCs functionalized with 2k PEG and 6k PEG and calculated at different separation distances is shown in Figure 7 A and B. The steric repulsion potential energy has a positive value while the vdW is negative; the value of UvdW seems to be much smaller than US, suggesting that the attraction force does not balance the repulsion force, which disagrees with the experimental observation that the AuNCs are arranged into a highly packed structure. Therefore, an additional attractive force must be acting to balance the strong, steric repulsion force. As observed from the SEM and AFM images, polymer nanoparticles with a disc shape formed inside the voids between the nanocube arrays. On the basis of the Raman measurements, these disc-shaped nanoparticles are composed of a PEG and CTAB mixture. Israelachvili39 showed that in bulk solutions, surfactants self-assemble into aggregate micelles; however, when sprayed on the top of a water surface, two-dimensional surface micelle aggregates with disc structures will be obtained. In fact, PEG and CTAB are capable of forming such aggregates.40 Although all characterization of the PEG− CTAB particles was carried out after drying, based on the experimental results and literature the disc PEG−CTAB nanoparticles were originally micelles inside the AuNC solution. During and after spraying the AuNCs over the surface of the water sublayer of the LB trough, the interparticle

(1)

where A is the Hamaker coefficient, with its value depending on both the composition of the material and the surrounding medium; L the separation distance between the two gold nanocubes; and a half the edge length of the nanocube. The value of the overall UvdW is the summation of the values of all possible vdW forces, the calculation details of which can be found in the Supporting Information. Panels A and B in Figure 8 show the vdW potential energy as a function of the separation distance between a pair of AuNCs functionalized with 2k PEG and 6k PEG, respectively. The vdW potential energy is found to decrease as the separation distance is increased for AuNCs functionalized with either 2 or 6k PEG and becomes very small when the distance exceeds 10 nm for 2k PEG and 20 nm for 6k PEG. PEG functionalized on the surface of AuNCs can be arranged into either brush or mushroom regimes, depending on the grafting density (distance between each neighboring polymer chains) and the Flory radius (an estimated size of the polymer coil) of the polymer. However, the brush structure is favored when the value of the Flory radius (h) is greater than twice the value of the grafting density (Γ).35,36 Figure 7B shows the schematic diagram of a single AuNC coated with PEG arranged into a brush structure, with h and Γ are represented in the Figure. For both the 2 and 6k PEG functionalizations, the polymers are arranged into brush structures around the nanocubes.37 Because of this brush structure of the polymer, steric repulsion force will be generated between the two G

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polymer chains per micelle (which is ∼50 based on the size of the dry micelles measured from AFM images and the size of the polymer chains). Figure 8 shows the UD values of a pair of AuNCs calculated for different separation distances when functionalized with 2k PEG (Figure 8A) and when functionalized with 6k PEG (Figure 8B). The overall potential energy of a pair of AuNCs was calculated from eq 4:

chloroform will evaporate and the micelles between the nanocubes will deplete and exert an osmotic pressure41 on the AuNCs, driving them to assemble and balancing the strong repulsion force between the PEG brushes. After the diffusion of the micelles, they will assemble into surface micelles with disc structures on top of the water sublayer. The micelle formation and the role of their diffusion on the assembly of AuNCs into highly packed arrays were confirmed by two previously mentioned experiments. First, when the amount of AuNCs used in making the LB film was reduced to half the original concentration, highly packed long strip arrays were obtained which were separated by large distances (Figure S6A,B in the Supporting Information). This will not occur without the diffusion of said micelles generating a vacuum that fills with neighboring AuNCs. It is useful in this case to differentiate between assembling the AuNCs on the surface of a solid substrate and on the surface of water. The water sublayer organizes the AuNCs into a monolayer unlike the solid substrate where multiple layers are possible. Upon assembling the nanoparticles on the top of a solid substrate, capillary forces are usually generated as a result of the solvent dewetting effect (Marangoni effect) which has proven to have a great impact on the assembly of nanostructures in the case of substrate assembly.42 Whereas for the LB assembling of AuNCs, the particles were dispersed in chloroform which evaporates during spraying, causing the nanoparticles to stick on the water’s surface. Second, when the concentration of the PEG was doubled, the AuNCs were assembled into highly packed arrays of short, curved strips (Figure S6C in the Supporting Information). Upon increasing the surface pressure, the free PEG accumulated together and the AuNCs arranged into a network structure (Figure S6D in the Supporting Information). If AuNCs can assemble without the assistance of diffused micelles due solely to PEG−PEG interactions, in principle, the free PEG should have the same possibility of assembling on the surface of AuNCs and preventing the formation of highly packed AuNC arrays. Moreover, the accumulation of the free polymer away from the areas of AuNC arrays further illuminates how PEG interacts with the AuNCs. Figure 7C shows a pair of AuNCs arranged face-to-face; the PEG micelles diffuse from the gap between the two cubes and apply an osmotic pressure, driving the cubes to assemble. The depletion of these micelles generates a depletion potential (UD).43,44 This depletion potential energy was calculated for a pair of AuNCs as a function of the interparticle separation distance when functionalized with 2k PEG and 6k PEG using eq 3: UD = −

⎤ πP ⎡ 1 2 ⎢ (d − L) (6a + 2d + L)⎥⎥ 4 ⎢3

UTotal = UvdW + UD + US

(4)

The minimum overall potential energy was obtained at separation distances of 4−5 nm and 7−9 nm for the AuNCs functionalized with 2k PEG and 6k PEG, respectively. The separation distance between the nanocubes was close to the values obtained from the SEM image in Figure 4, which is 4.2 ± 1.5 nm in case of 2k PEG and 7.4 ± 2.3 nm for 6k PEG. It is important to note that the deep area in the potential energy curve for the AuNCs functionalized with the 6k PEG is not sharp as in the case of the AuNCs functionalized with the 2k PEG. This suggests that the AuNCs functionalized with 6k PEG can be stabilized at different potential separation distances inside the 2D arrays, causing a decrease in the organization of the AuNCs inside the arrays. The above calculations were carried out assuming that the barrier of the LB trough was not used (no external surface pressure was applied by the LB barrier). It is useful to study the change in the structure potential energy curve of the AuNC 2D arrays when the monolayer is compressed by the LB barrier. For the 2D arrays of AuNCs functionalized with 6k PEG, the potential energies applied on each nanocube are 0.073, 3.398, 15.173, 42.537, and 65.397 (× 10−18 J) when the surface pressure of the LB trough is increased to 0.1, 2, 6, 9.5, and 11.5 mN/m, respectively (Supporting Information). The potential energy per gold nanocube functionalized with 2k PEG is 0.134, 1.289, 12.916, 24.974, and 32.933 (× 10−18 J) for applied surface pressure of 0.2, 1, 4, 5.5, and 6.5 mN/m, respectively. The potential energy of a pair of gold nanocubes located inside the AuNC 2D arrays and dispersed on the surface of the LB trough after applying different surface pressures is shown in Figure S7 in the Supporting Information. The values of the potential energy per nanocube are added to the total potential energy−distance curve. It is clear that the applied pressure by the LB trough does not affect the separation distance corresponding to the minimum potential energy but does increase the negative value of the minimum potential energy. These calculations accorded well with what was observed in the SEM images, as no change in the separation distance between the nanocubes inside the 2D arrays was observed by increasing the surface pressure. The large negative value of the potential energy of the nanocube system gives the 2D arrays more stability and enhances the likelihood of their assembly. This leads to an aforementioned increase in the width of the 2D arrays upon increasing the surface pressure. Remarkably, an increase in the negative value of the minimum potential energy is observed for the three samples fabricated at the highest applied surface pressures (one from the liquid condensed phase and two from the solid phase) for either AuNCs functionalized with 2k PEG or 6k PEG. This large increase in the negative value of the potential energy supports the formation of a thick array width, but the change is much steeper in the case of AuNCs functionalized with 2k PEG, which agrees well with the observations in Figures 2 and 3. Because of the assembly of a large numbers of AuNCs into the 2D arrays, a geometrical strain is generated. In the case of AuNCs functionalized with 6k

(3)

In this equation, d is the diameter of the polymer micelles and is found to be 31 and 88.9 nm for the 2k PEG and 6k PEG, respectively, as calculated from the Stokes−Einstein equation. The diameter of the micelles is much larger than that observed in the AFM because of their dry state. For the d calculations, the specific values of the viscosity and diffusion coefficient of PEG were obtained as reported earlier40 at the concentration of PEG used. P is the osmotic pressure generated by the micelles, which can be calculated from (P = nRT), where R is the universal gas constant (8.31 J·K−1·mol−1), n the number of micelles, where n is the ratio between the concentration of PEG and the number of aggregations. The concentration of PEG is 0.5 mM, and the number of aggregations is the number of H

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concentration of PEG was doubled (Figure S6); potential energy curve of a pair of AuNCs placed at different separation distances and calculated at different applied LB surface pressures (Figure S7). This material is available free of charge via the Internet at http://pubs.acs.org.

PEG, the relatively large separation distance between the nanocubes of 7.4 ± 2.3 nm can easily relax the local geometric strains (the nanocubes in the arrays can easily be twisted). But for the 2D arrays of AuNCs functionalized with 2k PEG, the small separation distance (4.2 ± 1.5 nm) between the highly packed nanocubes leads to the generation of linear cracks that relax the geometrical strain.

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Corresponding Author

CONCLUSIONS A new Langmuir−Blodgett-based strategy has been introduced to guide gold nanocubes to assemble into highly packed 2D arrays with different structures, with polymeric micelles present throughout the nanocube monolayer. The micelles are composed of the free leftover CTAB molecules used during the synthesis of the gold nanocubes and the PEG molecules used during the ligand exchange. The micelles act as a dynamic soft template that applies force on the nanocubes, guiding them to assemble into highly packed structures even at low Langmuir−Blodgett surface pressures. Upon increasing the surface pressure, the micelles diffuse and change the structure of the 2D gold nanocube arrays. The structure of the 2D gold nanocubes arrays is controlled by changing not only the Langmuir−Blodgett surface pressure but also the chain length of the polymers functionalized with the nanocube surfaces. When the short-chain polymers are functionalized with the surface of the nanocubes, the organization of the nanocubes inside the arrays is better than that in the case of using longchain polymers. The high organization of the nanocubes functionalized with the short-chain polymers results from the small separation distance between the nanocubes and the generation of linear cracks throughout the arrays that relax the geometrical strain. The geometrical strain resulted from the variation of particle size of the AuNCs as well as shape imperfections of individual AuNCs. Theoretical calculations provided a satisfactory description for the mechanisms behind the high packing of the gold nanocube 2D arrays, especially for low surface pressures of the Langmuir−Blodgett trough. The theoretical reasoning was based on the calculations of the potential energy of the attraction and repulsion forces affecting the nanocubes at different separation distances. The most effective force was the depletion force of the small polymer− CTAB micelles, which was able to balance the strong repulsion force between the polymer brushes. These micelles were observed in AFM images, and their composition was obtained from Raman measurements. These calculations ultimately gave insight into why the structure of the 2D arrays was altered upon changing the surface pressure of the trough.

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AUTHOR INFORMATION

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award # DE-FG02 09ER46604.

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REFERENCES

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ASSOCIATED CONTENT

* Supporting Information S

TEM image of the AuNCs before functionalization with PEG as well as the size distribution analysis (Figure S1); highermagnification SEM images of 2D arrays of gold nanocubes functionalized with 6k PEG with different structures (Figure S2); statistical calculations of the surface area of the voids located throughout the AuNC 2D arrays functionalized with 6k PEG (Figure S3); higher-magnification SEM images of AuNC 2D arrays functionalized with 6k PEG with different structures (Figure S4); statistical calculations of the surface area of the voids located throughout the 2D arrays of AuNCs functionalized with 2k PEG (Figure S5); SEM image of 2D arrays of gold nanocubes functionalized with 6k PEG when the amount of initial AuNCs was lowered by half and when the I

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