Article pubs.acs.org/Langmuir
Size-Controlled Polyelectrolyte Complexes: Direct Measurement of the Balance of Forces Involved in the Triggered Collapse of Layer-byLayer Assembled Nanocapsules Patrick Kékicheff,*,† Grégory F. Schneider,†,‡ and Gero Decher*,†,§,∥ †
CNRS Institut Charles Sadron, 23 rue du Loess, F-67034 Strasbourg Cedex 2, France Faculté de Chimie, Université de Strasbourg, 1 rue Blaise Pascal, F-67008 Strasbourg, France ∥ International Center for Frontier Research in Chemistry, 8 allée Gaspard Monge, F-67083 Strasbourg, France §
S Supporting Information *
ABSTRACT: Polyelectrolyte multilayers composed of poly(allylamine hydrochloride) and poly(styrene sulfonate) were assembled on 13 nm gold nanoparticles and characterized by Transmission Electron Microscopy and Atomic Force Microscopy. The direct measurement of the interactions at the molecular level using a Surface Force Apparatus revealed that the colloidal stability of such coated particles in aqueous media is brought about concomitantly by electrostatic and steric repulsive interactions. The cyanide induced dissolution of the gold cores yields either hollow nanocapsules or collapsed nanospheres, two species which are very difficult to distinguish. In contrast to the established micron sized hollow capsules, the dissolution of the nanosized gold cores may induce a substantial swelling of the polyelectrolyte complex into the central void as induced by the temporary local increase of the ionic strength. At least three layer pairs are required to maintain the structural integrity of the polyelectrolyte shells to yield hollow nanospheres. At about three layer pairs, thin nanocapsules are mechanically compressible and may collapse on themselves following mechanical stimulation to form even smaller spherical polyelectrolyte complex particles that retain the small polydispersity of the gold cores. Thus, the templating of polyelectrolyte shells around, e.g., gold nanoparticles followed by the dissolution of the respective cores constitutes a new method for the synthesis of extremely small polyelectrolyte complex particles with very low polydispersity.
1. INTRODUCTION The interaction between oppositely charged polyelectrolytes and/or colloids is important in nature (DNA compaction, sedimentation, ...) and also for many applications (e.g., paper making, flocculation, gene delivery, polyelectrolyte multilayers, ...) and has stimulated scientific interest for more than 60 years. The formation of polyelectrolyte complexes (PECs) in aqueous media and the concepts of polyelectrolyte complexation have recently been reviewed.1 In the most simple view, PECs have a “ladder-type” or “scrambled egg” structure,2 they are typically polydisperse, and many PECs tend to grow with time, especially at elevated ionic strength. Complexes of strongly interacting polyelectrolytes are often cumbersome to prepare reproducibly since the mixing conditions strongly influence the composition of the complex (stoichiometry) and also its size and polydispersity. There are no methods available yet to prepare small and almost monodiperse polyelectrolyte complexes. The so-called layer-by-layer (LbL) assembly method of polyanions and polycations was introduced in the early 1990s3 and has since become a powerful tool for preparing multimaterial thin films. Here oppositely charged species are consecutively adsorbed at interfaces, leading to the deposition of nanostructured films with up to hundreds of layers. Initially © XXXX American Chemical Society
the LbL process was used for preparation of functional planar films for applications in various domains such as biosensing, catalysis, separation membranes,4 antireflection coatings, and optical devices.5 Later it was shown that multilayer films can also be assembled on nonplanar surfaces, namely, on microparticles, first demonstrated by Mallouk et al. in 19956 and then brought to a sheer explosion by Möhwald and his team a few years later.7,8 In particular, since 1998, the LbL technique has been extended for the decoration of shaped materials with the design of highly tunable microcapsules7−19 as possible advantages of polyelectrolyte capsules are the absence of hazardous procedures and the use of simple building blocks along with the possibility to introduce a high degree of multifunctionality within their shells. For micrometer-sized particles with LbL shells, it is well established that the shells do not collapse upon the dissolution of the particle cores if sufficiently thick, and the mechanical properties of such polyelectrolyte microcapsules have already been investigated.7−9,20,21 At the nanoscale (see the paragraph below), it Received: May 24, 2013 Revised: July 22, 2013
A
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polyelectrolyte complexes whose size depends on the particle size and the number of layers and whose polydispersity depends on the polydispersity of the NPs, which is much better than the polydispersitiy of PECs prepared by classic mixing, to be easily obtained.
is however rather difficult to unequivocally distinguish polymer spheres from polymer capsules at diameters of 10−15 nm.22 Although considerably more difficult, polyelectrolyte multilayers were also deposited on nanoparticles (NPs),22−24 a process that was then further enhanced25,26 and which led to very interesting and very small multifunctional nanoscale objects.27,28 Such gold core/polyelectrolyte shell systems were, for example, used to investigate distance-dependent fluorescence quenching of fluorophores by metallic nanocores or as drug delivery systems in cancer therapy. In fact, these investigations underlined that LbL assembly produces similarly layered films on very different surfaces and demonstrated the potential for preparing multifunctional coatings around NPs. In the case of therapeutic NPs, small gold NPs were functionalized with an anticancer drug aimed at reaching tumors passively through the so-called enhanced permeability and retention (EPR) effect. In the case of the accumulation of NPs in the tumor (passive tissue targeting), the NPs extravasate through increased permeability of the tumor vasculature and are retained within the tumor by ineffective lymphatic drainage.29 The pores through which the NPs are intended to leave the blood vessels and enter the tumor tissue have diameters in the range of about 100 nm; it is thus an indispensable prerequisite that any NP (diagnostic or therapeutic) used for the EPR targeting of tumors must be highly stabilized. The aggregation of NPs to dimensions larger than this pore size would completely prevent extravasation. Answering the question of colloidal stability is actually not obvious since sole electrostatic repulsions cannot ensure the stability of a dispersion when the colloid size is no longer in the range of a few micrometers but of nanometers.30 We have therefore investigated how gold NPs coated with polyelectrolyte shells interact in situ by means of the surface force apparatus (SFA) technique, taking advantage of the atomic resolution in surface separation accessible.31 In situ measurements are the only way to access such properties since even a short drying step or exposure to PECs to air would lead to irreversible structural changes. In addition, we have investigated how the force−distance profile determined by the SFA evolves when core/shell NPs become template-free after dissolution of the gold cores. Our work demonstrates that stability depends on a set of prerequisites comprising a minimal number of polyelectrolyte shells required to obtain physicochemically stable nanospheres as individual entities, a robust elastic and plastic behavior of polyelectrolyte shells to avoid the nanocapsules collapsing on themselves upon applied mechanical loads and strains, and a sufficiently large interplay of both electrostatic and steric repulsive interactions between the nanospheres conferred by their LbL coating to ensure a stable colloidal dispersion. For this purpose gold NPs with a shell consisting of five layer pairs of poly(allylamine) (PAH) and poly(styrenesulfonate) (PSS) were adsorbed on mica surfaces and investigated by atomic force microscopy (AFM) and SFA; the latter technique allowed determination of particle−surface and particle−particle interactions as a function of distance. Such measurements were performed prior to and after dissolution of the gold cores. Finally, the empty particles were deformed by defined mechanical stimuli, and the force triggering their collapse was determined. Therefore, at five layer pairs of PAH/PSS and a size of the gold core of 13 nm, the polyelectrolyte shells are indeed empty nanospheres. Note that the templated preparation of polyelectrolyte shells around gold NPs allows
2. EXPERIMENTAL SECTION 2.1. Materials. The citrate-stabilized gold nanocolloids (AuNPs; 13.5 ± 0.5 nm diameter) were prepared and then coated via layer-bylayer assembly3 with a multilayer of alternate charged cationic poly(allylaminehydrochloride) PAH (M̅ w = 15 000 g/mol from Sigma-Aldrich) and anionic poly(sodium-4-styrenesulfonate) PSS (M̅ w = 15 000 g/mol from Polymer Standard Service) polyelectrolytes as described in detail in a previous publication.25 Thus, core/shell nanoparticles with a general structure of AuNP/(PAH/PSS)n (1 < n < 10) were obtained (for n = 5, the outer diameter is about 25 nm, as measured by transmission electron microscopy). To yield empty nanospheres, the gold core was etched by cyanization using potassium cyanide (KCN; 1 mM) as previously described.25 2.2. Procedure. 2.2.1. TEM Imaging. Each of the core/shell samples reported here were first checked with a transmission electron microscope operating at 120 kV (Philips CM12) equipped with a Megaview III Soft Imaging System camera. 2.2.2. Force Measurement Procedures. Force−distance profiles were measured at 25.000 ± 0.004 °C with a homemade device based on the initial version of the Tabor−Israelachvili SFA.31 This instrument allows the force F between two mica surfaces (of mean radius of curvature R) to be measured to within 5 nN as a function of the determined surface separation D, which can be measured to a typical accuracy of 0.2 nm, using an optical-interference technique (fringes of equal chromatic order32). Normalized force F/R corresponds to the free energy E per unit area of two equivalent flat surfaces as related by the Derjaguin approximation (F/R = 2πE).33 The freshly cleaved mica sheets used in the SFA were first coated by with a thin layer of cationic PAH (from Sigma-Aldrich, MW = 70 000) to reverse the native negative charge of mica34 to a positive charge. Then the negatively charged core/shell NPs were adsorbed from aqueous dispersions onto the PAH-functionalized mica surfaces (see the Supporting Information). Thin films of template-free nanocapsules were obtained by immersing the adsorbed gold core/shell NPs onto mica in a KCN solution at 1 g/L for a couple of hours. After being extensively rinsed in pure water, the silica disks were mounted back in the SFA chamber for force measurement. Two experimental configurations were built for investigations of the interactions: a symmetric configuration where each mica sheet is covered by a single layer of irreversibly adsorbed NPs and an asymmetric configuration where only one surface is covered with adsorbed NPs whereas the opposite surface is a sole bare PAH-coated mica. This asymmetric configuration is of advantage as it allows in particular measurement of the adhesion energy of the adsorbed NPs with the PAH-coated mica surface. 2.2.3. AFM Imaging. The adsorbed layer of NPs on the mica surfaces was imaged with a Nanoscope IV (Digital Instruments, Inc., Santa Barbara, CA.) using microfabricated silicon AFM tips (cantilevers with a spring constant of 0.01 N/m) in the tapping mode in a liquid cell. Similar surface features were noted for images acquired over any scan size, indicating that no desorption of NPs occurred over periods of days. The mica surfaces used after completion of the SFA measurements were also observed under water in the tapping mode for comparison. As similar surface features for the same solution conditions were obtained, we concluded that the surface force measurements did not induce desorption of the adsorbed NPs over a period of days provided not too large loads were applied during force measurements. 2.2.4. Image Processing. From the original and global AFM image (1024 × 768 pixel size), the useful image (512 × 512 pixel size) of the structure was extracted and converted into a black and white image. The digitized image was analyzed with Visilog image analysis software (Noesis, France) following an edge detection procedure to determine B
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the number of NPs and their position. Several techniques were combined, such as filtering (background correction and Gaussian smoothing for removing detail and noise), edge detection methods (Laplacian of Gaussian and zero-crossing operators), and adaptative threshold to locate the boundary (or edge) of each domain considered as “particles” or “cells”.35−37 The cells at the edges of the binary image were removed, and the cells with hole(s) were filled for the determination of the area of the cell. Particles lying with the specific region of interest (ROI) in the AFM digital image were analyzed to extract their dimensions (area, perimeter, diametral variations, and shape factor) and to determine their positions within the ROI (x and y centroid coordinates). To characterize the 2D distribution of particles, the pair correlation function (PCF), g(r), also known as the radial distribution function, was used. It represents the averaged probability of finding the center of a particle at a given distance r from the center of another particle normalized to the uniform probability at large distances.38 It is given by
g (r ) =
1 Np
N
∑ i=1
ni(r ) ρπ(δr 2 + 2r δr )
(1)
where Np denotes the number of particles under consideration, ρ is the average particle number density, and ni(r) is the number of particles that lie within an annular ring, δr, of radius r from an arbitrary origin. The quantity π(δr2 + 2r δr) represents the sampling area for a particular radial distance r. In this work, the 2D PCF calculations were performed from eq 1 using Plugin’s Image J software with δr = 1 nm and rmax = 460 nm. The g(r) function was plotted using eq 1 by analyzing coordinates of about 1000 particles.
3. RESULTS The combination of the different techniques used in this study allows us to answer three main questions: First, do the nanocapsule polyelectrolyte shells keep their physicochemical stability and structure upon the dissolution of the solid cores? Second, which interactions ensure the colloidal stability of the dispersion? Third, to what extent do the nanocapsules resist collapsing when applying mechanical strains? By addressing these questions along this route, we show that template-free nanocapsules made of polyelectrolyte multilayer shells is a promising perspective in the field of engineering nanoparticlebased drug carriers. 3.1. Physicochemical Stability of the Polyelectrolyte Shells. Our previous work has shown that core/shell NPs can be fabricated by a multilayer consecutive deposition of alternate charged cationic and anionic polyelectrolytes onto the 13.5 nm citrate-stabilized gold nanoparticles (AuNPs).25 Aqueous colloidal dispersions of AuNP/(PAH/PSS)n were obtained for different assemblies of pair layer numbers (1 < n < 10). In particular for n = 5 pairs, the colloidal dispersion is stable over more than three months: it contains almost singlets (outer diameter of about 25 nm) and very few clusters, as revealed by TEM (Figure 1). As the goal of this work is to study to what extent stable colloidal dispersions of nanocapsules may be obtained from these core/shell NPs, the first question to address is the stability of the shell when the core solid is destroyed. When investigating the stability of the polyelectrolyte shells as a function of the number of polyelectrolyte layers, we found that at least three layer pairs of (PAH/PSS)n (n = 3) are needed to detect, after cyanide etching, any nano-objects by TEM. This result indicates that at least three layer pairs of PAH/PSS (i.e., at least a total of six layers) are required to form shells with enough strength to prevent the destruction of the nanocapsule during etching. The value of three layer pairs is very close to the one found for micrometer-sized polyelectrolyte capsules.7,8
Figure 1. Morphological distribution of gold core/shell nanoparticles bearing 10 layers (e.g., Au/(PAH/PSS)5) as seen by TEM at two different magnifications (a, b). The statistical distribution of core/shell structures indicates that the bulk aqueous dispersion (5000 particles were sampled) is mostly composed of singlets (c).
For n > 3, the comparison of TEM micrographs of the core/ shell NPs before and after the etching step (Figure 2) revealed no major variations in diameter, suggesting that the inner core (initially filled with the gold NP) is hollow. One can infer from TEM imaging that the hollow core is visible for some species, since the core appears with higher contrast, possibly due to the accumulation of uranyl acetate (the staining agent) or the reaction product of gold with cyanide (AuCN2−) in the center or at the inner interface between the cavity and the multilayer shell. This enhanced darkness extends over a larger area for NPs with thicker shells (e.g., the inner spot is larger for n = 10 than it is for n = 6; it never exceeds, however, 8 nm in diameter for particles with the larger shell presented here). The quantitative analysis of the ratios a/b of the core/shell NP diameters before and after the dissolution of the gold core (Figure 2) decreasingly converges to 1.0 as the number of layers in the shell increases (at least for n = 5, 6, 8, 9, and 10; other ratios, for other values of n, are written in parentheses). This shows that under high vacuum conditions (e.g., ∼10−10 Torr, which is the typical vacuum inside a TEM microscope) the template-free nanospheres shrink by about 20% for five pairs of layers and by about 10% for ten pairs of layers as C
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Figure 2. TEM micrographs of typical core/shell nanoparticles of the general structure AuNP/(PAH/PSS)n before (top) and after (bottom) cyanide etching. The value of n is indicated in each micrograph. The values below the images refer to the ratio of particle diameters before and after dissolution of the gold cores.
Figure 3. Assembly of AuNP(PAH/PSS)5 on PAH-coated mica substrates (a−c) and after cyanide etching (a′−c′). Original AFM height mode images obtained in tapping mode in water (a, a′). Binary pictures after the edge detection procedure (b, b′). Position of each singlet NP compared to that in the original picture (c, c′). Scale bars represent 500 nm. The maximum z range is 30 nm.
D
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desorption when the free particles are removed from the bulk.40 This is actually the case in the system investigated here, as will be demonstrated by direct force measurement (see section 3.2.2). 3.2.1. Morphology of the Layer As Seen with AFM. Figure 3a shows a typical image (3 × 3 μm, taken in tapping mode in the liquid cell of the atomic force microscope) of the adsorbed layer built after immersion of a PAH-coated mica sheet in the AuNP/(PAH/PSS)5 dispersion overnight. Similar surface features were noted for images acquired over larger scan sizes. The layer appears homogeneous over the whole substrate although with an incomplete surface coverage by the adsorbed NPs. The height profile indicates the adsorbed film is comprised of NPs packed in a single layer, as the substrate underneath is clearly visible in the areas where no adsorption has occurred. The images reveal NPs adsorbed mostly as individual particles, although a few aggregates are present (see the typical histograms of the frequency of the different crosssection areas of adsorbed NPs in Figure 4a). These clusters generally lie flat on the substrate and are often surrounded by noncovered areas as if these clusters had attracted their neighboring NPs by displacing them laterally. However, a few clusters may appear as bumps (height 30−50 nm) sticking out of the monolayer, as seen in some rare spots of the covered substrate (not more than one cluster per about 10 μm2). The origin of these clusters is likely due to the fact that the dispersion, although macroscopically stable, already contains a few clusters of aggregated particles in bulk as revealed by TEM (doublets, 7. These results are consistent with the short-range ordering of NPs on a coated mica surface for distances close to
compared to the corresponding core/shell particle in which the cores were not removed. This indicates that thicker shells are more robust and more resistant to shrinking. Physicochemical changes in the shell further than shrinking after dissolution of the cores were also observed by AFM (parts a and a′, respectively, of Figure 3; etching was performed outside the AFM chamber to avoid sample drying). The analysis of the height profile revealed an average height of ∼22.3 nm for AuNP/(PAH/PSS)5 whose core was still present, while the average height was only ∼13.2 nm after the core dissolution. This result means that the force exerted by the tip of the atomic force microscope possibly contributes to compression force high enough for the nanocapsule to shrink in height. The size and the morphology of the NPs were also inferred from the image analysis (Figure 3). They confirm the ∼20% decrease in diameter observed by TEM for the singlet template-free NPs. At this stage of analysis, we could believe from those results (i) that the shrinking is also accompanied by an increase in the density of the nanosphere resulting from a denser packing of the polyelectrolytes to condense in the given volume (the ratio a′/b′ of the apparent diameters of individual NPs as measured by AFM before and after the dissolution of the gold core is similar to that observed with TEM; e.g., a/b ≈ a′/b′ ≈ 1.2), and thus that the dissolution of the template yields empty nanospheres that are not hollow, or (ii) that the nanospheres are so compressible that they appear not hollow under the even low applied load of the AFM tip upon imaging while they are hollow in the absence of an applied force. The SFA technique is therefore called for to clarify the latter hypothesis. 3.2. Building and Morphology of a Layer of Adsorbed Nanoparticles. In this work the native surface chemistry of the colloidal state is maintained by investigating surfaces supporting a layer of NPs adsorbed from solution. The experiments, performed entirely within the liquid chamber of the atomic force microscope (for imaging) and of the SFA (for direct measurement of the interactions), prevent the shell of the nanospheres from experiencing any environment outside its native aqueous state. This preserves the structure of the polyelectrolyte multilayers, which would otherwise collapse in the usual drying and washing processes. As the probability of adhesion is governed by collision efficiency between the substrate and particles, solution conditions, such as pH, ionic strength, incubation time, and volume fraction in particles, govern the morphology of the adsorbed layer. Its structural properties result from the subtle interplay of the interactions between the particles with the substrate and of the interactions between particles. To not affect the structure of the polyelectrolyte multilayers ensheathing the nanospheres, the pH and ionic strength were preferred not to be varied and hence to be kept at the values encountered in the bulk dispersion. Therefore, the study was limited to the variation of two parameters: incubation time and volume fraction in particles. Typically, as pointed out by Iler,39 for small particles with specific areas of several hundred square meters per gram, sol concentrations of less than Φ = 0.005 must be applied. To respect this criterion, we used dispersions containing about 6 nmol/L or a volume fraction in particles Φ = 3 × 10−5. As mentioned before, this sol is a stable dispersion of independent particles charged negatively with very few clusters occurring in bulk at these dilute solutions (Figure 1). The last requirement is that the adsorption energy should be relatively high (at least several kBT per particle) to avoid a rapid E
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repulsion from those particles already adsorbed, the Brownian movement ensures that the remaining exposed PAH-coated mica areas become coated eventually. This is because the magnitude of the electrical double layer interaction is not strong enough to resist the kinetic energy generated by the Brownian movement (see also the discussion in section 4). This explains why the average distance between adjacent adsorbed particles is about 3 times their diameter. Furthermore, any restriction of directions of the particles could have led to a rough film. This does not occur because the contact between NPs is not adhesive. The reason why the adsorption does not go beyond a single monolayer is quite trivial. As will be shown in the following section, two adsorbed AuNP/(PAH/PSS)5 layers are not mutually adhesive in water and they even repel free NPs in the bulk. Although NPs are kinetically allowed to approach and contact the external polyelectrolyte PSS/aqueous solution interface of the already adsorbed particles in the layer from time to time, they are bounced back to the bulk since they cannot attach. Hence, the monolayer is the final state of adsorption. As a result the building mechanism of the layer appears to be very simple: The NPs are almost free to diffuse toward the surface. Once having reached the PAH-coated mica, they will adhere to the substrate with a high probability. Once in contact with the wall, the NPs are not able to migrate from their initial point of contact as they stick strongly due to their large adhesion (see section 3.2.2). This explains why there is no propagation of any lateral long-range order (no formation of a 2D lattice along the wall): the layer is amorphous. This large adhesion also explains why the morphology of the adsorbed layer remains stable even after washing: the particles do not desorb (provided the layer does not experience any strong mechanical shearing). In conclusion, the final state of adsorption is that of a film, relatively smooth and flat, homogeneous and amorphous, almost dense although incomplete, comprised of irreversibly adsorbed NPs. The absence of desorption over long periods and over removal of the solid cores is possible only if the energy of adsorption per particle is at least several kBT. A quantitative estimate can be extracted from the third kind of experiment described in the next section. 3.2.2. Building of the Layer As Seen with a Surface Force Apparatus. The present results show that the surface force apparatus allows insight into the structure of the adsorbed layer and its organization as a whole. Furthermore, by setting an asymmetric configuration where a PAH-coated mica surface with adsorbed AuNP/(PAH/PSS)5 is opposite a sole PAHcoated mica, one can directly measure the adhesion energy of the adsorbed NPs with the PAH-coated mica substrate. Such opposite surfaces attract from large separations, indicating the charges of the two walls have opposite signs. In other words, despite a non-close-packing coverage of the substrate by the adsorbed core/shell particles, there is a charge reversal of the PAH-coated mica surface from positive to negative. Upon approach, due to the mechanical instability of the device, the two surfaces jump into the next mechanically stable position, which is located at about 30 nm (Figure 5). The force−distance regime turns out to be repulsive when the surface separation is decreased. At last, after a range of a few nanometers, a large steric repulsion is experienced upon further compression. Comparison with the bare mica contact position gives the extent of adsorption to the mica surfaces, since the primary minimum observed for adhesive mica in air or in water can no
Figure 4. (a, top) Size distributions of the adsorbed nanoparticles on PAH-coated mica substrate before (solid bars) and after (empty bars) cyanide etching. To compare the size distributions of singlet and aggregated NPs, the surface area occupied by the particles is normalized by the mean surface area calculated from the statistical size analysis of the NPs appearing as singlets in the AFM image (Figure 3; solid core/shell NP and template-free NP, respectively). (b, middle; c, bottom) Pair correlation function g(r/σ) corresponding to singlet NP assemblies on PAH-coated mica substrates before (b) and after (c) cyanide etching. The distance is normalized by the NP diameter σ (mean value calculated from the statistical analysis of the NPs appearing as singlets in the AFM images).
their diameter: the packing is jammed disordered, and no longrange 2D order is propagated. Images observed after overnight immersion (such as Figure 3) are very similar to those after a few hours, indicating a surface saturation at long times. A full surface coverage of the PAH-coated mica sheet is nevertheless never reached. The formation of an incomplete packed monolayer is probably related to the low ionic strength of the dispersion (no added salt, pH ≈ 5.7), where the electrostatic repulsions between NPs are screened only beyond a separation of more than 100 nm (as evidenced by the direct force measurements; see section 3.3). Although the free NPs in solution experience a long-range F
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presence of an adsorbed mixed layer of thickness d ≈ σNP on the surface. The adsorbed amount of nanoparticles can be extracted, since the dielectric constant in the direction perpendicular to a planar array of spheres with dielectric constant εNP, diameter σNP ≈ 25 nm, and center-to-center separation L, immersed in a water medium of dielectric constant εw = 1.3332, is equivalent to that perpendicular to a slab of thickness σNP and dielectric constant44 ⎡ Δ − 9.0338 ⎢ ε = εw ⎢ σ ⎢⎣ Δ − 9.0338 2NP L 2εw + εNP Δ= εw − εσNP
3
⎤ ⎥ 2 ⎥ NP 2 ⎥ ⎦
( σ2L ) 3 ( ) + πσ2L NP
where
(2)
With the estimate 1.72 of the refractive index of a pure gold core/shell nanoparticle AuNP/(PAH/PSS)5, as inferred from the knowledge of the refractive index of pure gold (n = 0.37457 + i2.6371)45 and that measured for PAH/PSS multilayers (≈1.48),46 the measured refractive index of the adsorbed nanospheres film (n = 1.52 ± 0.04; the large error bars reflect the range of measured values for independent experiments) indicates an incomplete coverage of the mica surface: σNP/L ≈ 0.44. This value is in agreement with the analysis of the AFM images (section 3.2.1). A similar analysis could in principle be carried out to infer insight into the internal structure of the template-free NPs after the etching reaction has been processed: After dissolution of the gold cores the question of interest is to know if the nanospheres are hollow with a core filled ultimately with water or if their shells comprised of polyelectrolyte multilayers have collapsed on themselves, filling out the empty internal space. Actually, a measurement of the refractive index of the adsorbed film at contact yields a too low sensitivity to make a conclusion (we recall that the error bar in the refractive index profile measured with an SFA monotonically increases as the surface separation decreases43). A single analysis of the multiple-beam interferometry cannot yield the desired information if it is carried out at only one given surface separation. We have therefore developed a novel approach to extract the information that will be presented in a forthcoming paper. In short, the analysis calls for a full measurement of the whole refractive index profile as a function of the separation, encompassing a range from large separations down to contact. The analysis of these data shows that these template-free particles are hollow: their core is mostly water. No change in both the force curve and the refractive index measurements was ever observed over periods of up to two days whether the NPs possess a solid gold core or are templatefree. This indicates that the film, once built on the mica surfaces, is not in equilibrium between adsorbed and free NPs, since such an equilibrium would imply a gradual decrease of the adsorbed amount with time as the adsorbed NP monolayer under investigation (total area of
