Ordering, dynamics and phase transitions in charged colloids
Introduction
The synthesis of monodisperse spherical polymer latex particles [1] has paved the way for physicists to use aqueous dispersions of latex particles as a model condensed matter system for the study of ordering, dynamics and phase transitions [2], [3], [4]. In order to prevent flocculation and make these suspensions stable, the particles are either coated with a thin layer (∼nm) of polymer (Fig. 1(A)) or by adsorbing polymer chains (Fig. 1(B)). This is known as a steric stabilization. Alternatively, the particles can be made to repel electrostatically by acquiring surface charge (charge stabilization) on the particles (Fig. 1(C)). Sterically stabilized suspensions (e.g. aqueous suspension of polymethyl methacrylate (PMMA) particles) behave almost like hard-sphere suspensions and have been used to study the fluid–solid transition and glass transition [5], [6], [7]. An aqueous suspension of polystyrene particles or colloidal silica constitutes the best example for a charge stabilized suspension [2], [3], [4]. These particles become negatively charged (∼500 charges on a 0.1 μm size particle) leaving an equal number of tiny counter-ions in the medium, making the suspension totally electrically neutral. In addition to the macroions (colloidal particles) and counter-ions, there could be additional ions either due to the added salt (electrolyte) or due to the dissolved ionic impurities (Fig. 1(C)). The small ions (counter-ions and salt ions) screen the dominant Coulomb repulsive interaction between the macroions, hence controlling their concentration helps in tuning the strength as well as the range of the interparticle interaction . In addition, varying the volume fraction, (, where is the number density) of the colloidal particles and the surface charge on the particle also helps to tune .
One of the most fascinating aspects of colloidal dispersions is the appearance of long-range order. For instance, in the case of deionized suspensions of charged particles, the long-range order appears even in extremely dilute dispersions [2], [8], whereas in hard-sphere colloids the crystallization occurs at much higher values of [5]. These structures, commonly known as colloidal crystals, exhibit iridescence (Fig. 2) arising from the Bragg diffraction of visible light [2]. Since the average interparticle distance is of the order of the wavelength of light, static light scattering (SLS) can be used to characterize the structural ordering (Fig. 2). Depending on the volume fraction and the salt concentration , the suspension can undergo disorder–order transitions from fluid state to a highly organized crystal of either body-centered cubic (bcc) or face-centered cubic (fcc) structure [2], [8]. In addition to the crystalline order, these dispersions exhibit ordering similar to those found in atomic liquids and glasses [2], [3], [4]. These features and the striking closeness of the magnitudes of the molar elastic constants [2], [9], latent heat of melting [2], [10] and other thermodynamic parameters of colloidal crystals, with those of atomic solids, allow one to regard colloidal dispersions as the scaled-up version of atomic systems. For instance, a colloidal dispersion with a particle concentration of about 1013 cm−3 has elastic constants of the order of 10 dynes cm−2 [11], whereas in atomic solids with atomic density around 1022 cm−3 the elastic constants have a value around 1012 dynes cm−2. As a result of the small elastic constants, colloidal crystals are extremely fragile and serve as the best example for soft matter systems. Similarly, the latent heat of melting of colloidal crystals, when expressed in units of “per mole” is same as that of atomic solids. The perfect scaling of the magnitudes of the physical properties with particle concentration suggests that the interparticle interaction energy in colloids must be of the same order as the inter-atomic interaction in atomic systems. This has led many scientists to regard these as model systems to simulate condensed matter. In addition to the fundamental importance, colloidal crystals have found many applications such as those in optical Bragg filters [12], optical switches [13], sensors [14] and photonic crystals [15], [16], [17] and templates for the synthesis of novel materials [18], [19].
The crystalline order of colloidal particles can be destroyed by the application of very small stresses; crystallized suspensions are easily shear-melted by simply tumbling the container. Furthermore, re-crystallization of the shear-melted metastable colloidal fluid is sufficiently slow (several minutes to hours) to allow the measurement of structure and dynamics during the crystallization process. Similarly, these fluid-like suspensions can be concentrated (density quench) to form a dense long-lived amorphous, non-ergodic phase [20], [21]. The dynamics in colloidal liquids, colloidal glasses and colloidal crystals span across a timescale of microseconds to several minutes. This timescale can be covered using dynamic light scattering (DLS) [22], [23], digital video microscopy [24], confocal microscopy [6], [7], [25], [26] and fluorescence recovery after photo-bleaching (FRAP) techniques [27], [28]. Recent studies in charged colloids using these techniques are presented in this paper.
The parameters, which influence structural ordering and drive the phase transitions are particle volume fraction , osmotic pressure , effective surface charge density , salt concentration and polydispersities of size and charge. A number of studies on colloidal dispersions in external fields such as laser optical fields, shear, electric and magnetic fields and geometrical confinement have been reported. A special issue covering this subject [29], is published recently, hence it is not discussed here. In this paper we present light scattering and confocal microscopy studies on ordering, dynamics and phase transitions in bulk charged colloidal suspensions. Recent observations such as gas–solid coexistence in highly charged colloids [30], [31], a reentrant order–disorder transition as a function of [32], [33], gas–liquid condensation [34], [35], [36] and existence of stable voids [37] suggest the existence of a long-range attraction between like-charged particles. These puzzling observations in bulk suspensions as well as measurements of attractive interaction in the effective pair-potential of confined charged colloidal particles [38], [39], [40], [41] have raised a debate about the origin of the long-range attraction and its existence in the of like charged colloids under confinement free conditions. Apart from reviewing the experimental and theoretical results, we present direct evidence for long-range attraction and existence of an attractive term in the of like-charged colloids [42]. The need for further theoretical and experimental studies on the interparticle interaction and also on the dynamics and phase behavior of charged colloids is highlighted.
Section snippets
Structural ordering and phase diagrams
Aqueous suspensions of polystyrene particles or silica particles are examples of charged colloidal systems [2]. A typical charged colloidal system, shown schematically in Fig. 1(C) consists of charged colloidal particles (macroions) and counter-ions. In a polar medium like water, the colloidal particles acquire a negative charge due to the dissociation of end groups (e.g,–KSO4) and the cations (K+) liberated into the medium are known as counter-ions. Similarly in the case of silica particles,
Phase transitions in inhomogeneous charged colloids
As mentioned earlier, the interparticle interaction in charge stabilized suspensions can be tailored by varying the volume fraction , salt concentration , and charge density on the particle . Though bulk suspensions of low charge density particles remained homogeneous under deionized conditions, at relatively high salt concentration, dilute suspensions showed phase separation analogous to vapor–liquid condensation in atomic systems. Though dilute suspensions of relatively high
Measurements of the effective pair-potential
The above mentioned observations (gas–liquid, gas–solid and reentrant transitions) in charged colloids and the inadequacy of DLVO theory in describing the observed phase separation phenomenon in charged colloids has renewed interest in reexamining the effective pair-potential in charged colloids experimentally [38], [39], [40], [41], [42], [43], [44], [45], [46], [87] as well as theoretically [88].
Under dilute conditions the pair-correlation function is related to by
Conclusions
Charge stabilized colloidal systems offer enormous tunability in interparticle interaction to study the ordering, dynamics and phase transitions at ambient conditions. The melting and freezing is studied by varying the salt concentration and the volume fraction, which are shown to be analogous to temperature and pressure in atomic systems. Charged colloids can serve as an ideal model condensed matter system to study crystallization and glass transition under pressure. It is shown that spatially
Acknowledgements
The authors wish to thank Dr. P.S. Mohanty and Dr. J. Yamanaka for fruitful collaboration. We also thank Dr. B. Purniah for helpful discussions and careful reading of the manuscript.
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