Origin of Order in Alkyl Thiol-Stabilized Nanoparticle Packings

Abstract

The self-assembly of colloidal nanoparticles into regular, crystalline lattices requires the transition from a dispersed fluid state to close-packed solid state of the particles. In charge-stabilized suspensions such a transition leads to the formation of irregular packings. In this chapter we describe a mechanism that allows sterically stabilized nanoparticles to form regular packings. The main requirement is a high mobility of the particles in the agglomerate, allowing them to diffuse and to reach crystalline lattice sites. Mobility is provided in the suspensions used here by a fluid lubricant ligand layer between the particles. This makes the crystalline agglomeration a function of the melting point of the ligand layer of the particles.

Reprinted excerpt with permission from T. Geyer, P. Born, and T. Kraus. Phys. Rev. Lett. 109, 128302 (2012). Copyright 2013 by the American Physical Society. The original article is available online: http://link.aps.org/doi/10.1103/PhysRevLett.109.128302

Appendix

1.1 Mobility Measurements Using Light Scattering

Dynamic light scattering as presented in the appendix of Chap. 4 is an ideal method to gain information on the motion of particles. The method averages a great number of particles in suspension, is non-destructive and applicable in-situ. However, when applied to the diffusion of particles on agglomerate surfaces, three problems arise. First, a typical assumption in the evaluation of dynamic light scattering data is that every photon experiences only a single scattering event, as is the case in dilute suspensions but not in agglomerates. Second, light scattering probes length scales on the order of the wavelength of light. In surface diffusion particle mobility may be very low and displacements over hundreds of nanometer may take very long or never occur. Finally, the diffusion process may be non-ergodic, becuase not all particles experience the same particle film surface morphology and consequently the same mobility. The measurement thus depends on the volume of the sample probed during the measurement.

To make dynamic light scattering applicable to dense particle suspensions, the evaluation of the scattered light signal has been extended to account for multiple scattering in the suspension by a technique termed diffusing wave spectroscopy (DWS) [52]. It is assumed that the photons diffuse through the sample. The autocorrelation (Eq. 4.17) thus turns into a product of the $i$ independent correlation functions of $i$ scattering events in the sample averaged over scattering vector $q$ so as to reflect the average scattering event in the path:

$$\begin{aligned} C(q, \tau )^{i} = \left\langle n(q, t) n(q, t + \tau ) \right\rangle ^{i}_{q}. \end{aligned}$$

(5.1)

This diffusing wave approach enables evaluation of data gained from samples with high concentrations. Contributions by small rearrangements of particles accumulate due to the multiple scattering of a photon and the method becomes sensitive even to motion on scales much smaller than the wavelength of the incident light. However, the method only partially solves the problem of non-ergodic samples: more particles are probed compared to conventional DLS, but the probed sample volume is still limited to the illuminated volume. Also, fast processes such as dust particles diffusing in the pathway of the illuminating laser beam or air bubbles in the thermostating solvent bath overlay the autocorrelation of slow particle surface diffusion, creating problems determining the contribution of the particles.

A method developed to render DLS applicable to non-ergodic samples and minimize unwanted contributions of dust and bubbles is echoed dynamic light scattering (eDLS) [53]. In this method, the sample is rotated at a constant velocity while recording the scattered light. After each rotation the detector ‘sees’ the same sample volume again. The autocorrelation of the scattered light thus exhibits peaks termed ‘echoes’ in correlation at every integer multiple of the rotation period. A slow decay in correlation due to particle rearrangement causes a decay of the envelope of the peaks. Processes with correlation times shorter than the rotation period of the cuvette are not detected. With little additional computational work to filter the envelope of the peaks, this method allows suppression of dust contributions to the autocorrelation and multiplies the probed volume to gain an ensemble average of the sample. Imperfections in the rotation are shown to cause a broadening of the peaks, but for fluctuations in angular speed and wobbling of the cuvette about a fixed mean the envelope reproduces the slow decay due to particle rearrangements.

Combined, DWS and eDLS should provide the tools to measure particle mobilities on particle agglomerate surfaces. However, two problems of sample preparation arise. The agglomerates have to be fixed such that settling or diffusion of the agglomerates in suspension do not cause a decay of the autocorrelation. The limited penetration of light into metals ensures a sensitivity of the scattered light signal to surface diffusion of particles rather than bulk diffusion, but hinders transmission measurement on bulk particle agglomerate sediments as used in conventional DWS measurements. Sample preparation thus has to ensure an exposure of particle agglomerate surfaces to the incident laser light in a geometry suited to cause multiple scattering between surfaces.

We approached this problems as described in Sect. 5.2.3. A slurry of alkyl thiol-stabilized gold nanoparticles was produced in the DLS cuvette, from which the solvent was rapidly evaporated under constant rotation of the cuvette. This procedure lead to macroscopically homogeneous golden particle films on the inner side of the cuvette (Fig. 5.7). On a microscopic scale, the particles agglomerated to form sponge-like structures (Fig. 5.8). We assume that light enters the pores and is trapped, i.e. scattered multiple times prior to leaving the sample, allowing to detect small rearrangements.

Fig. 5.7

Macroscopic appearance of the particle films inside the DLS-cuvettes used for mobility measurements in the solid phase

Fig. 5.8

Microscopic appearance of the particle films used for mobility measurements in the solid phase

The echoed signal was produced by rotation of the cuvette. The scattered light was detected at an angle of 145$^{\circ }$. The autocorrelation of the signal and the envelope to the correlation peaks was computed using our own Matlab [54]-algorithm. An exponential decay was fit to the envelope using Origin [55]. For calculation of diffusion coefficients the value of the transport mean free path of the photons, $l^{*}$, and the thickness of the sample that the photons have traveled through, $L$, is needed [52]. These values are presently unknown; thus only the decay constants as a measure of the mobility are presented.