IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 19 (2007) 113102 (25pp) doi:10.1088/0953-8984/19/11/113102 TOPICAL REVIEW Confocal microscopy of colloids V Prasad, D Semwogerere and Eric R Weeks Department of Physics, Emory University, Atlanta, GA 30322, USA E-mail: [email protected] Received 5 September 2006, in final form 5 January 2007 Published 27 February 2007 Online at stacks.iop.org/JPhysCM/19/113102 Abstract Colloids have increasingly been used to characterize or mimic many aspects of atomic and molecular systems. With confocal microscopy these colloidal particles can be tracked spatially in three dimensions with great precision over large time scales. This review discusses equilibrium phases such as crystals and liquids, and non-equilibrium phases such as glasses and gels. The phases that form depend strongly on the type of particle interaction that dominates. Hard-sphere-like colloids are the simplest, and interactions such as the attractive depletion force and electrostatic repulsion result in more non-trivial phases which can better model molecular materials. Furthermore, shearing or otherwise externally forcing these colloids while under microscopic observation helps connect the microscopic particle dynamics to the macroscopic flow behaviour. Finally, directions of future research in this field are discussed. (Some figures in this article are in colour only in the electronic version) Contents 1. Introduction 2 2. Properties of colloids 3 2.1. Hard spheres and their phase behaviour 3 2.2. Attractive and repulsive interactions 4 3. Comparison of techniques to study colloidal suspensions 5 4. How a confocal microscope works 7 4.1. Resolution 8 4.2. Scanning speed 9 5. Observations of hard-sphere colloids 10 5.1. Hard-sphere colloidal crystals 10 5.2. Hard-sphere colloidal glasses 11 5.3. Ageing in colloidal glasses 13 5.4. Systems under shear 13 0953-8984/07/113102+25$30.00 © 2007 IOP Publishing Ltd Printed in the UK 1 J. Phys.: Condens. Matter 19 (2007) 113102 Topical Review 6. Observations of interacting systems 15 6.1. Colloidal gels 15 6.2. Attractive glasses 16 6.3. Liquid–liquid or liquid–solid coexistence 17 6.4. Ionic systems 17 6.5. Anisotropic systems 19 7. New directions 19 Acknowledgments 20 References 20 1. Introduction Optical microscopy is widely used in many systems where the domain of interest lies in the submicrometre to micrometre range. These include biological systems such as cells or tissue as well as areas of ‘soft’ physics such as complex fluids and colloidal dispersions, the main focus of this review. Since the important length scales are of the order of the wavelength of visible light, microscopy provides a powerful tool to obtain real-space and real-time information about the complex mechanisms that govern these systems [1]. The ease of sample preparation at room temperature and atmospheric pressure (as opposed to, say, low temperature or low pressure conditions for electron microscopy) also makes optical microscopy a convenient technique. Nevertheless, certain problems exist for complex many-body systems that interact with light; the most prominent one being multiple scattering. Visualization deep within the sample is difficult for an optically dense sample such as a biological tissue or a concentrated colloidal dispersion, as the light that enters the sample undergoes many scattering events resulting in blurriness of the image. This problem was first faced by Marvin Minsky in the 1950s as he tried to visualize the way nerve cells were connected in the human nervous system [2]. His solution was two-fold: first, point by point illumination of the sample to minimize aberrant rays of scattered light from regions outside the image plane of interest; and second, a pinhole aperture in the image plane on the other side of the objective, to reject out-of-focus light. This prototype for the first confocal microscope used a carbon-arc lamp as the light source and a translating stage to visualize each point of the sample. Subsequent improvements utilize a laser and scan the laser beam rather than translating the sample. These two improvements enabled confocal microscopy to become a powerful tool for many scientific fields [3–5]; details of these improvements, as well as advances in the speed and resolution of confocal imaging, are described in later sections of this review. The use of confocal microscopy in colloidal systems is a relatively recent development, in part driven by the discovery that monodisperse colloids could mimic many of the phases seen in atomic systems [6]. While these observations were performed by bulk techniques such as light scattering, further information about the microscopic details of these systems required visualization in concentrated dispersions. One of the first studies to look at colloids with a confocal microscope was by Yoshida et al in 1991 [7] who looked deep within a sample of charged polystyrene latex colloids and observed hexagonal ordering of the spheres. van Blaaderen and Wiltzius [8] extended the capability of confocal microscopy to denser systems, imaging spheres with packing fractions of ∼60% to observe structure in the so-called colloidal glass phase. Such a high density of particles required a significant advance in image- analysis algorithms; the positions of thousands of particles separated by distances slightly larger than their diameter had to be located to high accuracy. Once this was achieved almost any micrometre-sized colloidal system could be studied by confocal microscopy. 2 J. Phys.: Condens. Matter 19 (2007) 113102 Topical Review Advances in imaging and particle-tracking have led to rapid advances in our understanding of colloidal phenomena, and confocal microscopy is currently a tool in the laboratories of many research groups. In subsequent sections we discuss the details of how confocal microscopes function and some of the interesting physics governing colloidal systems that can be captured with this technique. 2. Properties of colloids 2.1. Hard spheres and their phase behaviour Colloids have been used as models for atomic and molecular systems as they demonstrate many of the phases observed in such systems. The simplest model system is the hard- sphere system [9–13] in which the colloids are non-interacting at all separations beyond their radius and infinitely repulsive on contact. The sole control parameter that determines the phase behaviour of hard-sphere colloids is the sphere volume fraction φ, a non-dimensional quantity related to the number density n (φ = (4π/3)a3n with particle radius a). Here we discuss only the simple monodisperse case, although other parameters that could be considered include polydispersity, the aspect ratio of ellipsoids, etc. The size of the sphere is not a control parameter for ideal hard spheres, but for colloidal suspensions it can strongly affect sedimentation or even the overall dynamics of the sphere. In the case of sedimentation this is because gravitational energy is still significant at the colloidal length scale when compared to thermal fluctuations. Balancing this energy with kBT gives a gravitational height h = kBT/Fg, 3 where the gravitational force on a sphere of radius a is Fg = (4/3)πa ρg (ρ is the density difference between the colloid and the surrounding fluid). The gravitational height can be varied by many orders of magnitude, either by going to a low gravity environment, such as in space [14], or a high gravity one, by mismatching the density of the colloid and solvent [15–17]. For most systems it is desirable to have h larger than the sample chamber height as gravitational effects can then be neglected (for example, h = 1mmfora ∼ 0.5 μmandρ = 1kgm−3). The other effect of size arises due to diffusion; larger particles diffuse more slowly than smaller particles. This can be quantified by the diffusion coefficient D = kBT/6πηa which determines how fast a sphere diffuses in a fluid solvent of viscosity η. The time scale for a particle to 2 diffuse a distance equal to its own radius is τB = a /6D; this sets the dynamic time scale of the colloidal system in question (for a micrometre-sized particle in water τB is of the order of seconds). In a dilute system (φ → 0) the spheres are disordered and generally far from each other like a dilute gas. As the volume fraction increases from the dilute limit spheres remain in a disordered state. Denser states have spatial correlations between the positions of the spheres and thus these states are more analogous to liquids than to gases, although this distinction is somewhat arbitrary. The maximum amorphous packing is φ ≈ 0.64 [18–21], often termed RCP for ‘random close packing’ (see figure 1). If the hard-sphere system is allowed to equilibrate as the volume fraction is increased, however, the system undergoes an entropy driven phase transition to a crystalline state [6]. This transition starts at φ = 0.494 with a coexistence region up to φ = 0.545. States with 0.494 <φ<0.545 have crystalline domains (φ = 0.545) coexisting with liquid regions (φ = 0.494) (see figure 1). This phase persists from φ = 0.545 to 0.740, the maximal packing a 3D system of monodisperse spheres can obtain. In addition to these equilibrium phases colloidal systems can also exhibit non-equilibrium behaviour. For example, at φ = 0.58 the crystallization of the colloids can be arrested by the appearance of a metastable, kinetically trapped state known as a glass that persists until 3 J. Phys.: Condens. Matter 19 (2007) 113102 Topical Review Figure 1. Phase diagram of hard spheres, where the control parameter is the volume fraction φ. random close packing. (It is now believed that this requires some slight polydispersity to occur, ∼5% [22, 23].) The glass is characterized by a large increase in the viscosity of the system [24] despite no perceptible change in structure [8].