Agustín E. González

Viscosity of ionomer gels

Abstract We study the viscosity behaviour of metal sulphonate- (or metal carboxylate-) containing ionomers in solution with non-polar solvents; at relatively low polymer concentration these ionomer solutions show an unusually large thickening behaviour, due to the association of the metallic groups. By regarding the ionomer system as a polymer solution with transient crosslinks, an expression is derived from the viscosity of the sulphonated polymer in terms of the viscosity of the corresponding non-sulphonated polymer and the average number of crosslinks associated with any chain.

Concentration effects on two- and three-dimensional colloidal aggregation

By means of extensive numerical simulations of diffusion-limited colloidal aggregation in two and three dimensions, we have found the concentration dependence of the structural and dynamical quantities. Both on- and off-lattice simulations were used in 2D to check the independence of our results on the simulational algorithms and on the space structure. The range in concentration studied spanned two-and-a-half orders of magnitude, in both dimensionalities. In two dimensions, it was found that the cluster fractal dimension difference from the zero-concentration value shows a linear increase with the concentration, while this increase is of a square root type for the three-dimensional case. For the exponent z, defining the increase of the weight-average cluster size as a function of time, the difference from the zero-concentration value in three dimensions is again of a square root type increase with concentration, while in two dimensions this increase goes as the 0.6 power of the concentration. We give arguments for the drastic change in the power laws for the case of the fractal dimension, when going from two to three dimensions, and for the small change for the case of the kinetic exponent z. We also present the master curves for the scaling of the cluster size distribution and their dependence on concentration, in both dimensionalities.

Evidence of ionic aggregates in some ampholytic polymers by transmission electron microscopy

Transmission electron microscopy observations were conducted on some zwitterionic polymers. Our observations were concentrated on the morphology of the solid state of poly (4-vinyl pyridine-sulfopropyl bctaines), with different degrees of quaternization. Among the morphological features, a microstructure arising from aggregated regions in the range of 50 to 200 A is observed. Quite striking is the fact that this structure is absent in the micrographs for the base polymer, indicating that the aggregates are due to the interactions of the ion pairs of the polyzwitterions, as in the ionomer case. It is also found that the density of the aggregates increases when we increase the zwitterionic content of the copolymers.

Colloidal aggregation in the presence of a gravitational field

We present the results of a computational model for colloidal aggregation that considers the Brownian motion, sedimentation and deposition experienced by the colloidal particles and clusters. Among our results, we find that for intermediate strengths of downward gravitational drift, the aggregation crosses over from diffusion-limited colloidal aggregation to another type of aggregation with a higher cluster fractal dimension, Df. We also get a critical gelation concentration that is higher by several orders of magnitude than for the non-drifting case. We also found a speeding up followed by a slowing down of the aggregation rate and an algebraically decaying cluster size distribution. As the drift strength becomes much higher, the new fractal dimension is reduced due to the anisotropy of the clusters, becoming more elongated along the vertical direction. We finally present the scaling shown by the cluster size distribution for all the drift strengths studied.

On the Concentration Dependence of the Cluster Fractal Dimension in Colloidal Aggregation

We have undertaken the task to calculate, by means of extensive numerical simulations and by different procedures, the cluster fractal dimension (d) of colloidal aggregates at different initial colloid concentrations. Our first approach consists in obtaining d from the slope of the log-log plots of the radius of gyration versus size of all the clusters formed during the aggregation time. In this way, for diffusion-limited colloidal aggregation, we have found a square root type of increase of the fractal dimension with concentration, from its zero-concentration value: d = d0f + a φβ, with d0f = 1.80 ± 0.01, a = 0.91 ± 0.03 and β = 0.51 ± 0.02, and where φ is the volume fraction of the colloidal particles. In our second procedure, we get the d via the particle-particle correlation function gcluster(r) and the structure function Scluster(q) of individual clusters. We first show that the stretched exponential law gcluster(r) = Ard −3e−(r/ξ) gives an excellent fit to the cutoff of the g(r). Here, A, a and ξ are parameters characteristic of each of the clusters. From the corresponding fits we then obtain the cluster fractal dimension. In the case of the structure function Scluster (q), using its Fourier transform relation with gcluster(r) and introducing the stretched exponential law, it is exhibited that at high q values it presents a length scale for which it is linear in a log-log plot versus q, and the value of the d extracted from this plot coincides with the d of the stretched exponential law. The concentration dependence of this new estimate of d, using the correlation functions for individual clusters, agrees perfectly well with that from the radius of gyration versus size. It is however shown that the structure factor S(q) of the whole system (related to the normalized scattering intensity) is not the correct function to use when trying to obtain a cluster fractal dimension in concentrated suspensions. The log-log plot of S(q) vs. q proportions a value higher than the true value. Nevertheless, it is also shown that the true value can be obtained from the initial slope of the particle-particle correlation function g(r), of the whole system. A recipe is given on how to obtain approximately this g(r) from a knowledge of the S(q), up to a certain maximum q value.

Search for universality in the computer simulations of reaction limited colloid aggregation. I : Sticking probability effects

Abstract The dynamics of reaction limited colloid aggregation is studied via simulations to compare the results with the experimental ones, which a growing number of researchers agree to be universal. Sticking probabilities ten times smaller than before are reached, obtaining the universal results only at the beginning of the aggregation.

Growth laws and spinodal decomposition type of scaling in fractal aggregation of colloids

By means of extensive numerical simulations we have studied the time evolution and the scaling properties of the structure factor S(q,t) of diffusion-limited (DLCA) and reaction-limited (RLCA) colloid aggregation in three dimensions. We found that in DLCA S(q, t) scales in a similar way as in the spinodal decomposition process. The exponents a′ and a″ that relate the position and the height of the maximum of S(q, t) versus time, respectively, were however found to be different from those corresponding to the spinodal decomposition exponents. Unlike in the DLCA case, the S(q, t) for RLCA neither shows a pronounced maximum for the earlier times nor presents scaling. Nonetheless, the earlier broad peak eventually stretches and becomes higher than in DLCA.

Universality of “four-coordinated” correlated percolation and random percolation

Abstract We consider a site-correlated percolation problem, recently introduced in connection with the anomalous properties of liquid water. Within a position-space renormalization group approach, this problem is shown to belong to the same universality class as random percolation.

On Casimir pressure, the Lorentz force and black body radiation

It is shown that the Casimir attraction, including the temperature dependence, between two metallic plates can be derived from the Lorentz force acting on the surfaces of the plates. The force per unit area acting on a surface turns out to be a pressure, i.e. directed toward the bulk of the metal, and infinite in magnitude for a perfect conductor. The Casimir formula for the attraction between the plates can be obtained when we consider the pressure acting on the other side of the plates. It is then concluded that any conductor, at least in the shape of a plate, experiences a compression; the better the conductor, the greater that compression is. It is also noticed that there should be a repulsion between two semi-infinite metallic slabs separated by a planar gap. The relation of these results to the Lifshitz general theory of attraction between solids is also discussed.

Colloidal Aggregation with a Drift: A computer simulation

Preliminary results of an aggregation model that takes into account both the Brownian motion as well as the gravitational drift experienced by the colloidal particles and clusters is presented. It is shown that for high strengths of the drift the system crosses over to a regime different from diffusion-limited colloid aggregation, for which there is an increase of the fractal dimension, a speeding up of the aggregation rate and a widening of the cluster size distribution, becoming algebraically decaying with an exponent τ.