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) [1][2][3][4][5][6][7] The emerging glass paradigm has been success-fully applied to complex soft-matter systems, such as colloid-polymer systemss and concentrated protein solutions 9 . However, intriguing problems like the frequent occurrence of cluster phases remain 10-13 . Here we report small-angle scattering and confocal microscopy investigations of two model systems: pro-tein solutions and colloid-polymer mixtures. We demonstrate that in both systems, a combination of shortrange attraction and long-range repulsion results in the formation of small equili-brium 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 suspension [12][13][14][15][16][17] .A number of globular proteins have been shown to exhibit the major characteristics of colloids that interact via a short-range attractive potential. At high ionic strength, where the salt screens electrostatic repulsions, these short-range attractions increasingly dominate with decreasing temperature. This leads to a metastable liquid-liquid phase separation and related critical phenomena [18][19][20] . In agreement with predictions from modecoupling theory 9 , there is also-evidence for a glass or gel transition at low-particle volume fractions and high interparticle attractions. Such a scenario obviously affects the ability to form the high quality crystals required for protein crystallography 15 .Using two apparently quite different model systems, we demonstrate the generality of this emerging description of the effect of a short-range attraction combined with either a hard or soft repulsion on the phase behaviour of a wide range of colloidal suspensions.We first investigated solutions of the globular protein lysozyme (molecular mass 14.4 kDa, radius R m ≈1.7 nm) [17][18][19] .Using small-angle X-ray (SAXS) and neutron (SANS) scattering, we studied spatial correlations in concentrated solutions at low ionic strength, where the long-range repulsive electrostatic potential is only weakly screened. We then compared these findings with confocal microscopy results using colloid-polymer mixtures, a popular model system with easily tunable interactions. Here we used spherical colloidal particles interacting with a long-range repulsion resulting from a modest charge 21 and a short-range attraction induced by a polymer-mediated 'depletion ...

We studied clustering and gelation in low-volume-fraction () hard-sphere colloids, some with charge, with added non-adsorbing polymers. The range of the effective ‘depletion’ attraction induced by the polymers between the particles is of the particles’ diameter. The effects of density mismatch between the particles and the solvent and unscreened charges on the particles were investigated. The onset of aggregation and gelation in a neutral, density-matched system is discussed in terms of mode-coupling theory (MCT) and a recent ‘renormalized’ version of MCT respectively. Gravity causes sedimentation of growing clusters and shifts the gelation boundary. In the charged and density-matched system, a ‘cluster phase’ in which finite-size aggregates ‘coexisted’ with monomers occurred before gelation. Its origins remain unclear.

To understand the non-equilibrium behavior of colloidal particles with short-range attraction, we studied salt-induced aggregation of lysozyme. Optical microscopy revealed four regimes: bicontinuous texture, 'beads', large aggregates, and transient gelation. The interaction of a metastable liquid-liquid binodal and an ergodic to non-ergodic transition boundary inside the equilibrium crystallization region can explain our findings.

Glycerol is widely used as an additive to stabilize proteins in aqueous solution. We have studied the effect of up to 40 wt % glycerol on the crystallization of lysozyme from brine. As the glycerol concentration increased, progressively larger amounts of salt were needed to crystallize the protein. Like previous authors, we interpret this as evidence for glycerol changing the interaction between lysozyme molecules. We quantitatively model the interprotein interaction using a Derjaguin-Landau-Verwey-Overbeek potential. We find that the effect of glycerol can be entirely accounted for by the way it modifies the dielectric constant and refractive index of the solvent. Quantifying the interprotein interaction by the second virial coefficient, B(2), we find a universal crystallization boundary for all glycerol concentrations.