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Journal ArticleDOI

A colloidal model system with an interaction tunable from hard sphere to soft and dipolar

TL;DR: This work demonstrates a charge- and sterically stabilized colloidal suspension—poly(methyl methacrylate) spheres in a mixture of cycloheptyl (or cyclohexyl) bromide and decalin—where both the repulsive range and the anisotropy of the interparticle interaction potential can be controlled.
Abstract: Monodisperse colloidal suspensions of micrometre-sized spheres are playing an increasingly important role as model systems to study, in real space, a variety of phenomena in condensed matter physics—such as glass transitions and crystal nucleation1,2,3,4. But to date, no quantitative real-space studies have been performed on crystal melting, or have investigated systems with long-range repulsive potentials. Here we demonstrate a charge- and sterically stabilized colloidal suspension—poly(methyl methacrylate) spheres in a mixture of cycloheptyl (or cyclohexyl) bromide and decalin—where both the repulsive range and the anisotropy of the interparticle interaction potential can be controlled. This combination of two independent tuning parameters gives rise to a rich phase behaviour, with several unusual colloidal (liquid) crystalline phases, which we explore in real space by confocal microscopy. The softness of the interaction is tuned in this colloidal suspension by varying the solvent salt concentration; the anisotropic (dipolar) contribution to the interaction potential can be independently controlled with an external electric field ranging from a small perturbation to the point where it completely determines the phase behaviour. We also demonstrate that the electric field can be used as a pseudo-thermodynamic temperature switch to enable real-space studies of melting transitions. We expect studies of this colloidal model system to contribute to our understanding of, for example, electro- and magneto-rheological fluids.
Citations
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Journal ArticleDOI
TL;DR: This work argues for a conceptual framework for these new building blocks based on anisotropy attributes and discusses the prognosis for future progress in exploiting an isotropy for materials design and assembly.
Abstract: A revolution in novel nanoparticles and colloidal building blocks has been enabled by recent breakthroughs in particle synthesis These new particles are poised to become the ‘atoms’ and ‘molecules’ of tomorrow’s materials if they can be successfully assembled into useful structures Here, we discuss the recent progress made in the synthesis of nanocrystals and colloidal particles and draw analogies between these new particulate building blocks and better-studied molecules and supramolecular objects We argue for a conceptual framework for these new building blocks based on anisotropy attributes and discuss the prognosis for future progress in exploiting anisotropy for materials design and assembly

2,558 citations

Journal ArticleDOI
20 Jan 2011-Nature
TL;DR: This paper shows how colloidal spheres can be induced to self-assemble into a complex predetermined colloidal crystal—in this case a colloidal kagome lattice—through decoration of their surfaces with a simple pattern of hydrophobic domains, and encodes the target supracolloidal architecture.
Abstract: A challenging goal in materials chemistry and physics is spontaneously to form intended superstructures from designed building blocks. In fields such as crystal engineering and the design of porous materials, this typically involves building blocks of organic molecules, sometimes operating together with metallic ions or clusters. The translation of such ideas to nanoparticles and colloidal-sized building blocks would potentially open doors to new materials and new properties, but the pathways to achieve this goal are still undetermined. Here we show how colloidal spheres can be induced to self-assemble into a complex predetermined colloidal crystal-in this case a colloidal kagome lattice-through decoration of their surfaces with a simple pattern of hydrophobic domains. The building blocks are simple micrometre-sized spheres with interactions (electrostatic repulsion in the middle, hydrophobic attraction at the poles, which we call 'triblock Janus') that are also simple, but the self-assembly of the spheres into an open kagome structure contrasts with previously known close-packed periodic arrangements of spheres. This open network is of interest for several theoretical reasons. With a view to possible enhanced functionality, the resulting lattice structure possesses two families of pores, one that is hydrophobic on the rims of the pores and another that is hydrophilic. This strategy of 'convergent' self-assembly from easily fabricated colloidal building blocks encodes the target supracolloidal architecture, not in localized attractive spots but instead in large redundantly attractive regions, and can be extended to form other supracolloidal networks.

1,125 citations

Journal ArticleDOI
25 Nov 2004-Nature
TL;DR: It is demonstrated that in both model systems, a combination of short-range attraction and long-range repulsion results in the formation of small equilibrium clusters, which is relevant for nucleation processes during protein crystallization, protein or DNA self-assembly.
Abstract: Controlling interparticle interactions, aggregation and cluster formation is of central importance in a number of areas, ranging from cluster formation in various disease processes to protein crystallography and the production of photonic crystals. Recent developments in the description of the interaction of colloidal particles with short-range attractive potentials have led to interesting findings including metastable liquid-liquid phase separation and the formation of dynamically arrested states (such as the existence of attractive and repulsive glasses, and transient gels). The emerging glass paradigm has been successfully applied to complex soft-matter systems, such as colloid-polymer systems and concentrated protein solutions. However, intriguing problems like the frequent occurrence of cluster phases remain. Here we report small-angle scattering and confocal microscopy investigations of two model systems: protein solutions and colloid-polymer mixtures. We demonstrate that in both systems, a combination of short-range attraction and long-range repulsion results in the formation of small equilibrium clusters. We discuss the relevance of this finding for nucleation processes during protein crystallization, protein or DNA self-assembly and the previously observed formation of cluster and gel phases in colloidal suspensions.

967 citations

Journal ArticleDOI
08 Sep 2005-Nature
TL;DR: The electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with the approach to controlling opposite-charge interactions facilitating the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications.
Abstract: Colloidal suspensions are widely used to study processes such as melting, freezing1,2,3 and glass transitions4,5. This is because they display the same phase behaviour as atoms or molecules, with the nano- to micrometre size of the colloidal particles making it possible to observe them directly in real space3,4. Another attractive feature is that different types of colloidal interactions, such as long-range repulsive1,3, short-range attractive5, hard-sphere-like2,3,4 and dipolar3, can be realized and give rise to equilibrium phases. However, spherically symmetric, long-range attractions (that is, ionic interactions) have so far always resulted in irreversible colloidal aggregation6. Here we show that the electrostatic interaction between oppositely charged particles can be tuned such that large ionic colloidal crystals form readily, with our theory and simulations confirming the stability of these structures. We find that in contrast to atomic systems, the stoichiometry of our colloidal crystals is not dictated by charge neutrality; this allows us to obtain a remarkable diversity of new binary structures. An external electric field melts the crystals, confirming that the constituent particles are indeed oppositely charged. Colloidal model systems can thus be used to study the phase behaviour of ionic species. We also expect that our approach to controlling opposite-charge interactions will facilitate the production of binary crystals of micrometre-sized particles, which could find use as advanced materials for photonic applications7.

915 citations

Journal ArticleDOI
TL;DR: Some important parameters related to crystal nucleation and growth/dissolution including the supersaturation/undersaturation, pH, ionic strength and the ratio of calcium to phosphate activities are discussed.
Abstract: Calcium orthophosphates are the main mineral constituents of bones and teeth, and there is great interest in understanding the physical mechanisms that underlie their growth, dissolution, and phase stability. By definition, all calcium orthophosphates consist of three major chemical elements: calcium (oxidation state +2), phosphorus (oxidation state +5), and oxygen (oxidation state −2).1 The orthophosphate group (PO43−) is structurally different from meta (PO3−), pyro (P2O74−), and poly (PO3)nn−. In this review, only calcium orthophosphates will be discussed. The chemical composition of many calcium orthophosphates includes hydrogen, either as an acidic orthophosphate anion such as HPO42− or H2PO4−, and/or incorporated water as in dicalcium phosphate dihydrate (CaHPO4 · 2H2O).1 Most calcium orthophosphates are sparingly soluble in water, but all dissolve in acids; the calcium to phosphate molar ratios (Ca/P) and the solubilities are important parameters to distinguish between the phases (Table 1) with crystallographic data summarized in Table 2. In general, the lower the Ca/P ratio, the more acidic and soluble the calcium phosphate phase.2 It is now generally recognized that the crystallization of many calcium phosphates involves the formation of metastable precursor phases that subsequently dissolve as the precipitation reactions proceed. Thus, complex intermediate phases can participate in the crystallization process. Moreover, the in vivo presence of small peptides, proteins, and inorganic additives other than calcium and phosphate has a considerable influence on crystallization, making it difficult to predict the possible phases that may form.3 Studies of apatite mineral formation are complicated by the possibility of forming several calcium phosphate phases. The least soluble, hydroxyapatite (HAP), is preferentially formed under neutral or basic conditions. In more acidic solutions, phases such as brushite (DCPD) and octacalcium phosphate (OCP) are often encountered. Even under ideal HAP precipitation conditions, the precipitates are generally nonstoichiometric, suggesting the formation of calcium-deficient apatites. Both DCPD and OCP have been implicated as possible precursors to the formation of apatite. This may occur by the initial precipitation of DCPD and/or OCP followed by transformation to a more apatitic phase. Although DCPD and OCP are often detected during in vitro crystallization, in vivo studies of bone formation rarely show the presence of these acidic calcium phosphate phases. In the latter case, the situation is more complicated, since a large number of ions and molecules are present that can be incorporated into the crystal lattice or adsorbed at the crystallite surfaces. In biological apatite, DCPD and OCP are usually detected only during pathological calcification, where the pH is often relatively low. In normal in vivo calcifications, these phases have not been found, suggesting the involvement of other precursors or the formation of an initial amorphous calcium phosphate phase (ACP) followed by transformation to apatite. Table 1 Ca/P Molar Ratios, Chemical Formulas, and Solubilitiesa of Some Calcium Orthophosphate Minerals1,3,4 Table 2 Crystallographic Data of Calcium Orthophosphates1,4,5 In this review, we will discuss some important parameters related to crystal nucleation and growth/dissolution including the supersaturation/undersaturation, pH, ionic strength and the ratio of calcium to phosphate activities (Table 3). We then focus on the dynamics of crystallization/dissolution in the presence of additive molecules pertinent to biogenic calcium phosphate minerals. Table 3 Crystal Growth Controls and Their Effect on the Bulk Solution and the Crystal Surfaces6 2. Biologically Related Calcium Phosphate Phases 2.1. Structure, Composition, and Phase Stability 2.1.1. Amorphous Calcium Phosphate (ACP) During the synthesis of HAP crystals through the interaction of calcium and phosphate ions in neutral to basic solution, a precursor amorphous phase is formed that is structurally and chemically distinct from HAP.7 However, calculations have shown that the phase consisted of individual or groups of HAP unit cells.8 Chemical analysis of the precursor phase indicated this noncrystalline phase to be a hydrated calcium phosphate (Ca3(PO4)2 · xH2O) with a Ca/P ratio 1.50,8 consisting of roughly spherical Ca9(PO4)6 “Posner’s clusters” (PC) close-packed to form larger spherical particles with water in the interstices.9 PCs appeared to be energetically favored in comparison to alternative candidates including Ca3(PO4)2 and Ca6(PO4)4 clusters.10 The structure of PCs in isolated form is notably different from that in a HAP environment.11 In particular, the chirality feature of PCs found in the HAP environment is suggested to disappear in an isolated form and in aqueous solution. The reconsideration of PCs as possible components in the actual structural model of ACP resulted from the cluster growth model of the HAP crystal.12 Ab initio calculations confirmed that stable isomers exist on the [Ca3(PO4)2]3 potential energy surface (PES).12,13 These isomers correspond to compact arrangements, i.e., arrangements in which the Ca and PO4 are disposed closely together. Their geometries are compatible with the terms “roughly spherical” used in Posner’s hypothesis. The calculations performed on the monomer and dimer PES revealed that the relative energies of the different isomers are governed by a specific bonding pattern in which a calcium atom interacts with two PO43− groups, forming four CaO bonds.12,13 The compact isomers on the trimer PES are energetically favored in comparison to monomer or dimer isomers. This is rationalized by the appearance of a specific bonding pattern for the trimer case in which a calcium forms six CaO bonds with six different PO4 groups. This type of bonding in encountered in HAP.13 It is now generally agreed that, both in vitro and in vivo, precipitation reactions at sufficiently high supersaturation and pH result in the initial formation of an amorphous calcium phosphate with a molar calcium/phosphate ratio of about 1.18–2.50. The chemical composition of ACP is strongly dependent on the solution pH: ACP phases with Ca/P ratios in the range of 1.18:1 precipitated at pH 6.6 to 1.53:1 at pH 11.7 and even as high as 2.5:1.4 Two amorphous calcium phosphates, ACP1 and ACP2, have been reported with the same composition, but differing in morphology and solubility.14,15 The formation of ACP precipitate with little long-range order tends to consist of aggregates of primary nuclei (roughly spherical clusters) with composition Ca9(PO4)65 dependent on the conditions of formation. It hydrolyzes almost instantaneously to more stable phases. These amorphous clusters served as seeds during HAP crystallization via a stepwise assembly process12 and were presumed to pack randomly with respect to each other,16 forming large 300–800 A spheres. Recent experimental studies found that ACP has definite local atomic microcrystalline order rather than a random network structure. NMR of thoroughly dried ACP suggests that the tightly held water resides in the interstices between clusters,17 but these are probably not of intrinsic importance in the structure of ACP. It is well-known that ACP contains 10–20% by weight of tightly bound water, which is removed by vacuum drying at elevated temperature.9 However, drying does not alter the calcium and phosphorus atomic arrangement. The side band intensities of dried ACP suggest that its chemical shift anisotropy is similar to or identical with that of normal ACP.17 ACP has an apatitic short-range structure, but with a crystal size so small that it appears to be amorphous by X-ray analysis. This is supported by extended X-ray absorption fine structure (EXAFS) on biogenic and synthetic ACP samples.18–20 The CaP amorphous phase transforms to HAP microcrystalline in the presence of water. The lifetime of the metastable amorphous precursor in aqueous solution was reported to be a function of the presence of additive molecules and ions, pH, ionic strength, and temperature.21 The transformation kinetics from ACP to HAP, which can be described by a ”first-order” rate law, is a function only of the pH of the mediating solution at constant temperature. The solution-mediated transformation depends upon the conditions which regulate both the dissolution of ACP and the formation of the early HAP nuclei.22 Tropp et al. used 31P NMR to demonstrate that the strength of ACP side bands is due to a characteristic structural distortion of unprotonated phosphate and not to a mixture of protonated and unprotonated phosphates,17 suggesting that ACP could contain substantial amounts of protonated phosphate not in the form of any known phase of calcium phosphate crystals. Yin and Stott suggested that, in the transformation from ACP to HAP, ACP need only dissociate into clusters rather than undergo complete ionic solvation. The cluster with C1 symmetry is the most stable isomer in vacuum. The interaction of Posner’s cluster with sodium ions and especially with protons leads to a considerable stability increase, and surprisingly, the cluster with six protons and six OH− recovers the C3 symmetry and similar atomic arrangement that it has as a structural unit in the HAP crystal. This may be a key factor in the transformation from ACP to HAP crystal.23 In general, ACP is a highly unstable phase that hydrolyzes almost instantaneously to more stable phases. In the presence of other ions and macromolecules or under in vivo conditions, ACP may persist for appreciable periods3 and retain the amporphous state under some specific experimental conditions.24

779 citations

References
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Journal ArticleDOI
TL;DR: This work presents a scheme of a quantum repeater that connects a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity.
Abstract: In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. Our scheme tolerates general errors on the percent level, it works with a polynomial overhead in time and a logarithmic overhead in the number of particles that need to be controlled locally.

2,787 citations

Journal ArticleDOI
01 Mar 1986-Nature
TL;DR: In this paper, a detailed study of the phase diagram of suspensions of colloidal spheres which interact through a steep repulsive potential is presented. But it is not a detailed analysis of the colloidal glass phase.
Abstract: Suspensions of spherical colloidal particles in a liquid show a fascinating variety of phase behaviour which can mimic that of simple atomic liquids and solids. ‘Colloidal fluids’1–4, in which there are significant short-range correlations between the positions of neighbouring particles, and ‘colloidal crystals’5–7, which have long-range spatial order, have been investigated extensively. We report here a detailed study of the phase diagram of suspensions of colloidal spheres which interact through a steep repulsive potential. With increasing particle concentration we observed a progression from colloidal fluid, to fluid and crystal phases in coexistence, to fully crystallized samples. At the highest concentrations we obtained very viscous samples in which full crystallization had not occurred after several months and in which the particles appeared to be arranged as an amorphous ‘colloidal glass’. The empirical phase diagram can be reproduced reasonably well by an effective hard-sphere model. The observation of the colloidal glass phase is interesting both in itself and because of possible relevance to the manufacture of high-strength ceramics8.

1,881 citations

Journal ArticleDOI
23 Oct 1997-Nature
TL;DR: The preparation of a material that changes colour in response to a chemical signal by means of a change in diffraction (rather than absorption) properties is reported, anticipating that this strategy can be used to prepare ‘intelligent’ materials responsive to a wide range of analytes, including viruses.
Abstract: Chemical sensors respond to the presence of a specific analyte in a variety of ways. One of the most convenient is a change in optical properties, and in particular a visually perceptible colour change. Here we report the preparation of a material that changes colour in response to a chemical signal by means of a change in diffraction (rather than absorption) properties. Our material is a crystalline colloidal array of polymer spheres (roughly 100 nm diameter) polymerized within a hydrogel that swells and shrinks reversibly in the presence of certain analytes (here metal ions and glucose). The crystalline colloidal array diffracts light at (visible) wavelengths determined by the lattice spacing, which gives rise to an intense colour. The hydrogel contains either a molecular-recognition group that binds the analyte selectively (crown ethers for metal ions), or a molecular-recognition agent that reacts with the analyte selectively. These recognition events cause the gel to swell owing to an increased osmotic pressure, which increases the mean separation between the colloidal spheres and so shifts the Bragg peak of the diffracted light to longer wavelengths. We anticipate that this strategy can be used to prepare 'intelligent' materials responsive to a wide range of analytes, including viruses.

1,861 citations

Journal ArticleDOI
TL;DR: This work gives the conditions for high fringe visibility and particle collection efficiency as required for a Bell test and subcoherence-time monitoring of the idlers provides a noninteractive quantum measurement entangling and preselecting the independent signals without touching them.
Abstract: Using independent sources one can realize an ``event-ready'' Bell--Einstein-Podolsky-Rosen experiment in which one can measure directly the probabilities of the various outcomes including nondetection of both particles. Our proposal involves two parametric down-converters. Subcoherence-time monitoring of the idlers provides a noninteractive quantum measurement entangling and preselecting the independent signals without touching them. We give the conditions for high fringe visibility and particle collection efficiency as required for a Bell test.

1,636 citations

Journal ArticleDOI
25 Nov 1999-Nature
TL;DR: It is shown that single quantum bit operations, Bell-basis measurements and certain entangled quantum states such as Greenberger–Horne–Zeilinger (GHZ) states are sufficient to construct a universal quantum computer.
Abstract: Algorithms such as quantum factoring1 and quantum search2 illustrate the great theoretical promise of quantum computers; but the practical implementation of such devices will require careful consideration of the minimum resource requirements, together with the development of procedures to overcome inevitable residual imperfections in physical systems3,4,5 Many designs have been proposed, but none allow a large quantum computer to be built in the near future6 Moreover, the known protocols for constructing reliable quantum computers from unreliable components can be complicated, often requiring many operations to produce a desired transformation3,4,5,7,8 Here we show how a single technique—a generalization of quantum teleportation9—reduces resource requirements for quantum computers and unifies known protocols for fault-tolerant quantum computation We show that single quantum bit (qubit) operations, Bell-basis measurements and certain entangled quantum states such as Greenberger–Horne–Zeilinger (GHZ) states10—all of which are within the reach of current technology—are sufficient to construct a universal quantum computer We also present systematic constructions for an infinite class of reliable quantum gates that make the design of fault-tolerant quantum computers much more straightforward and methodical

1,604 citations