Equilibrium self-assembly of colloids with distinct interaction sites: Thermodynamics, percolation, and cluster distribution functions

We calculate the equilibrium thermodynamic properties, percolation threshold, and cluster distribution functions for a model of associating colloids, which consists of hard spherical particles having on their surfaces three short-ranged attractive sites (sticky spots) of two different types, A and B. The thermodynamic properties are calculated using Wertheim's perturbation theory of associating fluids. This also allows us to find the onset of self-assembly, which can be quantified by the maxima of the specific heat at constant volume. The percolation threshold is derived, under the no-loop assumption, for the correlated bond model: In all cases it is two percolated phases that become identical at a critical point, when one exists. Finally, the cluster size distributions are calculated by mapping the model onto an effective model, characterized by a-state-dependent-functionality (f) over bar and unique bonding probability (p) over bar. The mapping is based on the asymptotic limit of the cluster distributions functions of the generic model and the effective parameters are defined through the requirement that the equilibrium cluster distributions of the true and effective models have the same number-averaged and weight-averaged sizes at all densities and temperatures. We also study the model numerically in the case where BB interactions are missing. In this limit, AB bonds either provide branching between A-chains (Y-junctions) if epsilon(AB)/epsilon(AA) is small, or drive the formation of a hyperbranched polymer if epsilon(AB)/epsilon(AA) is large. We find that the theoretical predictions describe quite accurately the numerical data, especially in the region where Y-junctions are present. There is fairly good agreement between theoretical and numerical results both for the thermodynamic (number of bonds and phase coexistence) and the connectivity properties of the model (cluster size distributions and percolation locus).

Percolation of colloids with distinct interaction sites

We generalize the Flory-Stockmayer theory of percolation to a model of associating (patchy) colloids, which consists of hard spherical particles, having on their surfaces f short-ranged-attractive sites of m different types. These sites can form bonds between particles and thus promote self-assembly. It is shown that the percolation threshold is given in terms of the eigenvalues of a m x m matrix, which describes the recursive relations for the number of bonded particles on the ith level of a cluster with no loops; percolation occurs when the largest of these eigenvalues equals unity. Expressions for the probability that a particle is not bonded to the giant cluster, for the average cluster size and the average size of a cluster to which a randomly chosen particle belongs, are also derived. Explicit results for these quantities are computed for the case f = 3 and m = 2. We show how these structural properties are related to the thermodynamics of the associating system by regarding bond formation as a (equilibrium) chemical reaction. This solution of the percolation problem, combined with Wertheim's thermodynamic first-order perturbation theory, allows the investigation of the interplay between phase behavior and cluster formation for general models of patchy colloids.

From unthinned continent to ocean: The deep structure of the West Iberia passive continental margin at 38 degrees N

The crustal and lithospheric mantle structure at the south segment of the west Iberian margin was investigated along a 370 km long seismic transect. The transect goes from unthinned continental crust onshore to oceanic crust, crossing the ocean-continent transition (OCT) zone. The wide-angle data set includes recordings from 6 OBSs and 2 inland seismic stations. Kinematic and dynamic modeling provided a 2D velocity model that proved to be consistent with the modeled free-air anomaly data. The interpretation of coincident multi-channel near-vertical and wide-angle reflection data sets allowed the identification of four main crustal domains: (i) continental (east of 9.4 degrees W); (ii) continental thinning (9.4 degrees W-9.7 degrees W): (iii) transitional (9.7 degrees W-similar to 10.5 degrees W); and (iv) oceanic (west of similar to 10.5 degrees W). In the continental domain the complete crustal section of slightly thinned continental crust is present. The upper (UCC, 5.1-6.0 km/s) and the lower continental crust (LCC, 6.9-7.2 km/s) are seismically reflective and have intermediate to low P-wave velocity gradients. The middle continental crust (MCC, 6.35-6.45 km/s) is generally unreflective with low velocity gradient. The main thinning of the continental crust occurs in the thinning domain by attenuation of the UCC and the LCC. Major thinning of the MCC starts to the west of the LCC pinchout point, where it rests directly upon the mantle. In the thinning domain the Moho slope is at least 13 degrees and the continental crust thickness decreases seaward from 22 to 11 km over a similar to 35 km distance, stretched by a factor of 1.5 to 3. In the oceanic domain a two-layer high-gradient igneous crust (5.3-6.0 km/s; 6.5-7.4 km/s) was modeled. The intra-crustal interface correlates with prominent mid-basement, 10-15 km long reflections in the multi-channel seismic profile. Strong secondary reflected PmP phases require a first order discontinuity at the Moho. The sedimentary cover can be as thick as 5 km and the igneous crustal thickness varies from 4 to 11 km in the west, where the profile reaches the Madeira-Tore Rise. In the transitional domain the crust has a complex structure that varies both horizontally and vertically. Beneath the continental slope it includes exhumed continental crust (6.15-6.45 km/s). Strong diffractions were modeled to originate at the lower interface of this layer. The western segment of this transitional domain is highly reflective at all levels, probably due to dykes and sills, according to the high apparent susceptibility and density modeled at this location. Sub-Moho mantle velocity is found to be 8.0 km/s, but velocities smaller than 8.0 km/s confined to short segments are not excluded by the data. Strong P-wave wide-angle reflections are modeled to originate at depth of 20 km within the lithospheric mantle, under the eastern segment of the oceanic domain, or even deeper at the transitional domain, suggesting a layered structure for the lithospheric mantle. Both interface depths and velocities of the continental section are in good agreement to the conjugate Newfoundland margin. A similar to 40 km wide OCT having a geophysical signature distinct from the OCT to the north favors a two pulse continental breakup.

Magma flow, exsolution processes and rock metasomatism in the Great Messejana-Plasencia dyke (Iberian Peninsula)

Magma flow in dykes is still not well understood; some reported magnetic fabrics are contradictory and the potential effects of exsolution and metasomatism processes on the magnetic properties are issues open to debate. Therefore, a long dyke made of segments with different thickness, which record distinct degrees of metasomatism, the Messejana-Plasencia dyke (MPD), was studied. Oriented dolerite samples were collected along several cross-sections and characterized by means of microscopy and magnetic analyses. The results obtained show that the effects of metasomatism on rock mineralogy are important, and that the metasomatic processes can greatly influence anisotropy degree and mean susceptibility only when rocks are strongly affected by metasomatism. Petrography, scanning electron microscopy (SEM) and bulk magnetic analyses show a high-temperature oxidation-exsolution event, experienced by the very early Ti-spinels, during the early stages of magma cooling, which was mostly observed in central domains of the thick dyke segments. Exsolution reduced the grain size of the magnetic carrier (multidomain to single domain transformation), thus producing composite fabrics involving inverse fabrics. These are likely responsible for a significant number of the 'abnormal' fabrics, which make the interpretation of magma flow much more complex. By choosing to use only the 'normal' fabric for magma flow determination, we have reduced by 50 per cent the number of relevant sites. In these sites, the imbrication angle of the magnetic foliation relative to dyke wall strongly suggests flow with end-members indicating vertical-dominated flow (seven sites) and horizontal-dominated flow (three sites).

Phase diagrams of binary mixtures of patchy colloids with distinct numbers and types of patches: Theempty fluid regime

We investigate the effect of distinct bonding energies on the onset of criticality of low functionality fluid mixtures. We focus on mixtures ofparticles with two and three patches as this includes the mixture where "empty" fluids were originally reported. In addition to the number of patches, thespecies differ in the type of patches or bonding sites. For simplicity, we consider that the patches on each species are identical: one species has threepatches of type A and the other has two patches of type B. We have found a rich phase behavior with closed miscibility gaps, liquid-liquid demixing, and negative azeotropes. Liquid-liquid demixing was found to pre-empt the "empty" fluid regime, of these mixtures, when the AB bonds are weaker than the AA or BB bonds. By contrast, mixtures in this class exhibit "empty" fluid behavior when the AB bonds are stronger than at least one of the other two. Mixtureswith bonding energies epsilon(BB) = epsilon(AB) and epsilon(AA) < epsilon(BB), were found to exhibit an unusual negative azeotrope. (C) 2011 American Institute of Physics. [doi:10.1063/1.3561396]