In this paper we present small-angle neutron scattering (SANS) studies on liquidlike ordered binary colloidal suspensions. Using perfluorinated (sigma(PFA) = 162 nm) and polystyrene (sigma(PS) = 79 nm) particles, we prepared samples made of the same colloids as in the preceding paper. All system parameters of the mixtures were as before. Via neutron contrast variation we directly obtained all three partial intensities I(PFA-PFA)(Q), I(PFA-PS)(Q), and I(PS-PS)(Q) and partial structure factors S(PFA-PFA)(Q), S(PFA-PS)(Q), and SPS-PS(Q) The experimental results are compared with theoretical predictions for binary colloidal mixtures, based on the pure repulsive part of the DLVO potential. Within the hypernetted chain (HNC) closure an accurate agreement is achieved. The particle correlation in the mixtures is clarified by means of the partial distribution functions g(ij)(r) and the one-component effective pair potentials U(PFA-PFA)(eff)(r) and U(PS-PS)(eff)(r). From this we deduce for the examined suspensions a partial clustering or local demixing by attractive interaction contributions of depletion origin.

Electrostatically stabilized diluted suspensions of negatively-charged poly(p-bromostyrene) particles have been studied by ultra small angle X-ray scattering (USAXS) and simultaneous osmotic pressure measurements. We investigated the structure and the interparticle interactions as a function of the crystal stiffness controlled by the salinity. By adding monovalent salt (NaCl) or multivalent +1/−5 salt (polyd(T)5), we reduced electrostatic repulsions and finally induced fusion of the colloidal crystal. The osmotic pressure drops and the crystal melts when the salt concentration in the reservoir is higher than 2.10−4 M for NaCl. In the case of a multivalent co-ion, 3.10−3 M polyd(T)5 is enough to reduce the osmotic pressure to zero. Thus, an experimental determination of the pressure versus distance relation allows the detection of less than micromolar amounts of multicharged co-ions. Surprisingly, the Poisson–Boltzmann cell model remains valid even when only a few screening co-ions are present in each unit cell of the colloidal crystal. By calculating the mean square displacement of a particle inside the cage made of nearest neighbours from the eccentric Poisson–Boltzmann Cell model, we have verified that the Lindemann criterion for the crystal–liquid transition is satisfied when the crystal melts due to the addition of monovalent salt.

In this and the following paper we present scattering studies on binary colloidal mixtures made of charge-stabilized polystyrene (PS) and perfluorinated (PFA) particles with diameters sigma=79 and 162 nm, respectively. Both colloidal species were mixed to well-defined compositions. The total concentration was about 9 vol % fraction. By using ultra-small-angle X-ray scattering, we directly obtained the partial scattering intensities of only the PFA particles in liquidlike ordered suspensions. Furthermore, after dividing intensities by the PFA particle form factor P(PFA)(Q), We got the partial structure factor S(PFA-PFA)(Q) Without any additional treatment. The experimental results are compared with theoretical predictions obtained from the pure repulsive DLVO potentials and the hypernetted chain (HNC) integral equation, as applied to charged colloidal mixtures. It is shown that all measured intensities and extracted structure factors are in good agreement with the theoretical results.

Electrostatically stabilized aqueous suspensions of bromopolystyrene particles have been studied by scattering and osmotic pressure measurements. We investigated their structure and the interparticle interactions as a function of the volume fraction at very low salinity of the order of micromole/l. At slow crystallization speed we observe perfect crystals, body centrered cubic crystals by light scattering for volume fractions between 0.04 and 0.7% and face centrered cubic crystals by Ultra Small Angle X-ray Scattering (USAXS) for higher volume fractions (2-12%). After shear the crystal displays other structures. At low volume fractions (0.1-0.3%), some reflexions disappear by light scattering whereas a strong diffuse ''prepeak'' appears before the first Bragg peak for higher concentrations (2-12%) evidenced by USAXS. This ''prepeak'' can be attributed to defects in the crystal. Osmotic pressures have been measured by difference between the hydrostatic pressure in the solution and in the reservoir separated by an hemipermeable membrane. The experimental data are very well reproduced by the Poisson Boltzmann Cell (PBC) theory which shows that the interaction between particles is purely repulsive. No attractive contribution has been experimentally detected. By calculating the mean square displacement of a particle inside its cage from the eccentric PBC model, we have verified that the Lindemann criterion for the existence of crystals (against melting) is satisfied. This study has allowed to determine the equation of state of an electrostatical colloidal crystal and is equivalent to an ultraprecise force/distance measurement between latex particles since the measured forces are of the order of 10(-12) N for distances of the order of 4000 Angstrom.

We investigate the structure and the osmotic pressure versus concentration of a colloidal crystal of charged bromopolystyrene particles of diameter 100 nm. In a concentration range between 2 and 12% volume fraction and in the presence of ion exchange resin which fixes a very low (micromolar) salt concentration, a colloidal crystal is obtained. The packing structure evidenced via Ultra-Small-Angel X-ray scattering (USAXS) are either fcc or fcc in equilibrium with bcc. A strong diffuse band before the first Bragg peak is observed. The Q-values ratio of this diffuse pre-peak to the first Bragg peak is 1.44. Osmotic pressures of these colloidal crystals are measured with different salt contents. Particle structural charge and diameter are known. Assuming screened electrostatic potential is the main repulsive interaction stabilising the system, all measurements can be rationalized using a simple electrostatic model. The melting of the fcc structure occurs with an average displacement from equilibrium position, deduced from the screened electrostatic potential, which is 10% larger than for molecular solids. This type of study of the colloidal crystal osmotic pressure versus distance (in the range 300 nm) is equivalent to an ultraprecise atomic force measurement, since it allows measurements of forces smaller than 10−12 N.

Nous mesurons la pression osmotique de solutions de particules de polystyrène bromé polydisperse en régime dilué (0,5-6,5 % en fraction volumique) correspondant à des distances moyennes entre particules de 150 à 400 nm.

We measure the osmotic pressure of bromopolystyrene particles suspensions in the dilute sol regime (0.5-6.5% in volume fraction) i.e. for average distances between particles in the range between 150 to 400 nm.The osmotic pressure varies linearly with the concentration and is about 400 times higher than the perfect gas pressure due to the particles alone. The explanation is that the main contribution to the osmotic pressure in the absence of salt is due to the (uncondensed) counter-ions. This observation allows an experimental definition of an effective charge.The measured pressures are in agreement with theoretical values determined by the non linearized Poisson-Boltzmann Cell model.Structure factors of these solutions are obtained by light and ultrasmall angle X-ray scattering (USAXS): a strong liquid order is observed. The theoretical curves calculated with the HNC integral equation fit very well this short range order.The effective charge determined by fitting the shape of the observed structure factor is compatible with the value determined directly from the osmotic pressure. Both values are much lower than the effective charge determined by pH and conductivity measurements.