Elastic properties, structures and phase transitions in model colloids

Abstract

The nature of the melting transition for a system of hard discs with translational degrees of freedom in two spatial dimensions has been analysed by a combination of computer simulation methods and a finite size scaling technique. The behaviour of the system is consistent with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.The structural and elastic properties of binary colloidal mixtures in two and three spatial dimensions are discussed as well as those of colloidal systems with quenched point impurities.Hard and soft discs in external periodic (light-) fields show rich phase diagrams including freezing and melting transitions when the density of the system is varied. Monte Carlo simulations for detailed finite size scaling analysis of various thermodynamic quantities like the order parameter, its cumulants, etc, have been used in order to map the phase diagram of the system for various values of the density and the amplitude of the external potential. For hard discs we find clear indication of a reentrant liquid phase over a significant region of the parameter space. The simulations therefore show that the system of hard discs behaves in a fashion similar to charge stabilized colloids which are known to undergo an initial freezing, followed by a remelting transition as the amplitude of the imposed modulating field produced by crossed laser beams is steadily increased. Detailed analysis of the simulation data shows several features consistent with a recent dislocation unbinding theory of laser induced melting. The differences and similarities of systems with soft potentials (DLVO, 1/r 12 , 1/r 6 ) and the relation to experimental data is analysed.

Freezing of a soft-core fluid in a one-dimensional potential: Predictions based on a pressure-balance equation

“…Using Eqs. (12), (15), and (16), the required potential amplitude V 0 to enforce the relocation of particles from L s to L c (thus causing an increase fromρ toρ eff ) within our prediction occurs at…”

“…However, here we are working with the integrated form [Eq. (12)], where the impact of the approximation is less obvious.…”

“…On the other hand, one could interpret Eq. (12) in the sense of the mean value theorem for integrals 73 . To this end we note that both integrals appearing in Eq.…”

“…Provided that the wavelength of the light field is commensurate with the mean particle distance, the modulated liquid (characterized by 1D symmetry breaking) appearing at low potential amplitudes freezes into a structure with quasi-long range positional order in both directions. This observation inspired a considerable amount of investigations by theory [5][6][7][8][9][10][11][12][13][14] , computer simulations 7,11,[13][14][15][16][17][18][19][20][21][22][23] and experiments [24][25][26][27] . Major points of discussion concerned the order of the LIF freezing transition, as well as the origin of the re-entrant melting experimentally observed at high laser intensities 25 .…”

Field-induced ordering phenomena and non-local elastic compliance in two-dimensional colloidal crystals

“…rather has C 33 (bulk) ∼ 2C 33 (n), which implies a vanishing shear modulus. The elastic constants could be determined directly from an analysis of the configurations of the particles applying the method of Sengupta et al [51,52]. Particularly remarkably the increase of strip thickness (or number n of rows in the strip, respectively) does not cause any visible approach to bulk behaviour.…”