Multiple structural transitions in Langmuir monolayers of charged soft-shell nanoparticles

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1 Supplementary information for: Multiple structural transitions in Langmuir monolayers of charged softshell nanoparticles A. S. ElTawargy a,b, D. Stock c, M. Gallei c, W. A. Ramadan b, M. A. Shams ElDin b, G. Reiter a, R. Reiter a a. Physikalisches Institut, Fakultät für Mathematik und Physik, AlbertLudwigsUniversität, Freiburg, 79104, Germany. b. Department of Physics, Faculty of Science, Damietta University, Damietta, 34517, Egypt. c. ErnstBerlInstitut für Technische und Makromolekulare Chemie, Technische Universität Darmstadt, Darmstadt, 64287, Germany. in memoriam of David Stock S1. Interaction forces between like charged colloidal particles at nonpolar fluidpolar fluid interface Likecharged colloidal nanoparticles repel each other and form a stable dispersion. When deposited at low areal density onto a nonpolar fluidpolar fluid interface, e.g. airwater, these particles try to separate as far as possible from each other, due to longrange electrostatic repulsive forces. Given that they have a sufficiently high charge, they will form a hexagonal arrangement. However, when spreading higher amounts of such particles, they may even form ordered, close packed or less densely packed, aggregates on a water surface. Such ordered aggregates often coexist with regions of randomly distributed particles of low areal density. To generate such domains of ordered particles, we require an attractive force between likecharged colloidal nanoparticles [18]. At first glance, this may appear to be a paradoxical phenomenon because the electrostatic repulsive force between particles increases with decreasing distance. An attractive 1

2 (capillary) force between likecharged particles at a fluidfluid interface is reported to result from distortion of the interface when the curved interfaces (menisci) generated by these particles start to overlap [911]. For the origin of such distorted (curved) interfaces, various interpretations were presented. A planar fluidfluid interface may become deformed by gravity, provided that the particles are of appropriate size, i.e., weight [3, 12]. Such deformations may also be caused when the surface of the particles is rough [13] or when thermal fluctuations are suppressed between two particles in close proximity [14, 15]. For large, (e.g., microsized) particles, their weight might be sufficient to deform an airwater interface and they can float on water surface due to the interplay between gravity, buoyancy and surface tension (capillary) effects [12, 16, 17]. However, the weight of colloidal nanoparticles with diameters of ca. 250 nm is of the order of N and thus too small to distort fluidfluid interfaces [18, 19]. Furthermore, in the case of nanoparticles, effects of surface roughness and thermal fluctuations are also too small to induce significant surface deformations [3]. However, the concept of dipolar character model of the nanoparticles at fluidfluid interfaces is capable to explain the generation of a strong attractive force between likecharged nanoparticles at such interfaces. Due to the high ratio of dielectric constants of water and air (ca. 80), this capillary attraction is stronger for airwater interfaces than for other interfaces like, for example, oil and water (see sec. (S11)) [36]. S11. The concept of the dipolar character model According to the dipolar character model, a charged colloidal particle, which is floating at a fluidfluid interface, for example between a polar and a nonpolar medium, can be represented as an electric dipole [3]. A significant dipole moment can be induced in the particles by the difference in dielectric constants ε of the two interfacing media (ε = 1 for air, ε 80 for water, or ε 40 for oils). Possible screening effects of charges on the particle surface, which might occur, for example, in a fluid containing salt ions, can also be taken into account within such a description. This dipole is oriented normal to the fluidfluid interface. Accordingly, the value of the electrostatic energy density of a particle in air is roughly 80 times higher than in water. In other words, when electric field lines cross the airwater interface, they are reduced to about 1/80 of their strength in air, see figure (S1), causing an electrical stress which pushes the particle into the water phase. As a result, the airwater interface becomes deformed, causing a variation in the curvature 2

3 dependent local Laplace pressure. Thus, a lateral capillary attractive force between neighboring particles will be generated. Depending on the induced deformation of the interface, the range of capillary attraction may be much larger than the range of van der Waals (vdw) forces. Such capillary attraction may occur between nanoparticles in a Langmuir layer. However, when the distances between colloidal particles gets small (e.g., a few nanometers), attraction due to vdw forces between these particles may overrule capillary attraction and become the dominant force of interaction [17, 2022]. In this case, particles begin to get in repulsive steric contact and start to form aggregates or grow ordered clusters of closepacked particles [2022]. The competition between attractive and repulsive forces may cause a minimum in the interaction potential as a function of separation distance between the particles, similar as discussed in the DerjaguinLandauVerwayOverbeck (DLVO) theory [21], see red curve in figure (S2). Assuming that the depth of this minimum is shallow (e.g., of the order of thermal energy kt), such domains of aggregated particles will be dissolved when the areal density of particles is decreased as it is the case for the expansion of Langmuir layers. Repulsive electrostatic forces between sufficiently charged particles may favor such reversible behavior [23]. Electrostatic repulsive force Electric field lines in air Air ε a /ε a = 1 Interface Colloidal particle Electric field lines in water Water ε w /ε a ~ 80 Lateral capillary attractive force Figure (S1): Schematic representation of the dipolar character, shown for two colloidal particles at an airwater interface. εa and εw are dielectric permittivities of air and water, respectively. 3

4 Repulsion Energy U(r) Attraction Electrostatic Aggregation Steric barrier vdw Capillary d r U total (r) Interparticle distance (r) Figure (S2): Schematic of the qualitative interaction energy vs. interparticle distance curves for two interacting CIS particles. Tables (S1a and S1b): Values of area per particle, surface pressure and elapsed time (from the beginning of compression) corresponding to images shown in figures 5 and 7, respectively. (a) 2 μl Compression Expansion Image A (µm) 2 Π (mn/m) Time (sec) i ii iii iv v (b) 5 μl Compression Expansion Image A (µm) 2 Π (mn/m) Time (sec) i ii iii iv v

5 S2. A discussion on the structure (and possible changes) of transferred monolayers Based on the following points, we conclude that the observed structures of the transferred monolayers are representative for the ordering (and aggregation) of CIS nanoparticles on the water surface: 1 BAM images (although they are of low resolution) reflect that particles are forming domains of sizes of several microns. The inhomogeneities in the observed intensities of the BAM images clearly exclude that nanoparticles are evenly distributed, even at rather large areas per particles (see figure (2)). 2 The transfer of monolayers was performed at the same area per nanoparticle using both horizontal and vertical transferring methods i.e. LangmuirSchaefer and Langmuir Blodgett, respectively. Despite differences in how water evaporated, both methods gave similar morphologies. 3 Right after transferring the monolayer when visible amounts of water were still present at the substrate (i.e., evaporation was not yet completed), we already observed similar closepacked aggregates, see figure (S3). Thus, capillary forces (due to dewetting in the course of water evaporation) were not responsible for the formation of such aggregates. Figure (S3): Right after the transfer of the monolayer, closepacked aggregates exist already underneath a layer of water. 4 In a control experiment after the transfer, we immersed transferred monolayers for a few minutes in water. After immersion and drying of the sample, we did not observe any noticeable rearrangement. Thus, the transferred nanoparticles were strongly adsorbed at the substrates. 5 Furthermore, when adding a droplet of acetone onto a transferred film, we observed changes in its interference color without any noticeable change in the shape of the ordered domains of nanoparticles on the substrate. This reconfirms that particles were strongly adsorbed to the substrate. The change in color resulted from swelling of the outer soft shells of polymers, see figure (S4). 5

6 (a) (b) (c) Figure (S4): (a) The optical microscopy image shows a part of a domain of closepacked CIS nanoparticles. (b) The same domain after adding a droplet of acetone, which caused swelling of polymer chains, causing a change of the interference color. (c) After reevaporation of acetone, almost the same color as was observed initially (suggesting a rather similar arrangement of nanoparticles). 6 For large areas per nanoparticles (e.g., right after spreading the smaller volume of 2 µl of dispersion), the nanoparticles were separated evenly at a mean distance of several micrometers (i.e., some tenfold of the diameter of the nanoparticles) over the whole sample. We did not observe any aggregation or agglomeration of nanoparticles, which may have been the result of the transfer process or dewetting caused by evaporation of water. 6

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