F. Aguilera-Granja

Polymer statistics: II. New simulation of polymers in solution☆

Abstract A new method of simulating the equilibrium shape of linear polymers in solution is presented, based on the analytical output of the statistical mechanical treatment of polymers using the pair approximation of the cluster variation method (CVM). The reported simulation has the following features: it can form a simulation of the equilibrium state of a polymer system by one sweep of the field; therefore it is fast, even if the size of the system is large. Although the average length of polymers in the system is specified by a parameter in the CVM calculation, the analytical output describes a system composed of different-length polymers. The average end-to-end distance is measured as a function of the length l, and gives the length dependence lv with v=0.52 for the phase separation case and 0.59 for the athermal case. The result indicates the capability of the simulation to distinguish between the different configurations taken by the polymers under different solvent conditions.

Polymer statistics: I. Phase separation in polymer solutions: A new statistical treatment

A new statistical mechanics treatment of polymer systems is presented, built on the lattice model as used by Flory and Huggins, but using the pair approximation of the cluster variation method (CVM). The present paper is the first of a series, and shows how the new method compares with the most common theories in the polymer field. Phase separation diagrams are qualitatively similar to those of Flory. A noticeable difference is that our result for χc deviates from the value 12 proposed by Flory for any coordination number z. We also calculate the osmotic pressure for the polymer solution using our approximation and some comparison with Flory (F), Flory-Huggins (FH), Bawendi-Freed (BF) theories and the Monte Carlo (MC) simulations are done for the a thermal case. The qualitative agreement between our results and the FH results and the MC results supports the reliability of the present treatment.

Polymer statistics. IV: Simulation of adsorption of polymers and polyelectrolytes on surfaces

Abstract Simulation of bulk polymer configurations introduced in paper II of this series is extended to both neutral polymers and polyelectrolytes adsorbed on a substrate. The simulation is based on the analytical output of the equilibrium calculations of the cluster variational method (CVM) described in the preceding paper. The polymers described in the simulation are polydisperse. In the simulations, we measure the following quantities: the distribution of the adsorbed polymers on the surface as a function of the polymer length (molecular weight), the end-to-end distance, the maximum height, the average thickness of adsorbed polymers, the area covered by adsorbed segments, the fraction of segments in trains, tails and loops, and the probabilities that the adsorbed linear polymers show zero, one and two tails. Noteworthy results are: (1) long polymers are adsorbed more frequently than short ones, and (ii) adsorbed polyelectrolytes are flat on the surface, and hence practically no loops appear in them.

Polymer statistics: III. Polymer adsorption on a solid surface

Abstract The statistical mechanics for neutral polymers and polyelectrolytes adsorbed on a flat surface is presented. Polymer segments are placed at simple cubic lattice points. The pair approximation of the cluster variational method modified to take into account chemical bonding within a polymer is used. The theoretical technique is a generalization of the one presented in paper I of the series. We calculate the density profile, thickness of the adsorbed polymer layer, and related properties. For the case of polyelectrolyte adsorption, the surface is either neutral or positively charged while the polyelectrolyte segments are negatively charged. It is noteworthy that the density profile of polyelectrolytes shows a depression close to the surface, reflecting Coulomb repulsion among charged segments. The effect of the strength of the van der Waals type interaction (between the surface and the polymer segments on the plane next to the surface), and of the polymer-solvent interaction are studied.

Polymer statistics. V: Simulation of polyelectrolytes adsorbed on negative surface

Abstract We study the geometrical properties of negative-charged linear polyelectrolytes adsorbed on a negative surface (NONS) by using the recently developed simulation method based on the cluster variation method (CVM). This new method has the advantage of the analytical calculation which is based on the equilibrium conditions. At the same time, we can get geometrical information that pure analytical calculations cannot give. Using our simulation method, we find that short chains are preferentially adsorbed, and that the average length of the adsorbed chain is smaller than the average in the solution. The NONS has long tails extending into the solution and a very small area touching the surface. We report the molecular weight (i.e. the length) dependence of the end-to-end distance, the distribution of those which are adsorbed, the layer thickness, the fractions of train, tail and loop, and the average number of tails. The results of this simulation show good qualitative agreement with recent experiments on the adsorption of polyelectrolytes on negative-charged mica surfaces.

Order parameters in anisotropic two-dimensional ±J Ising lattices

We modify the usual isotropic ±J Ising spin glass model introducing stronger interactions by a factor of f (anisotropy factor) along one of the axis. We begin by considering the situation in which concentration of ferromagnetic (F) and antiferromagnetic (AF) interactions are the same, where we study the modification that such axial anisotropy has on the density of states of the system, with particular attention on the modification of the ground level. Splits and merges of levels, as well as decreases and increases of degeneracy are observed for particular values of f. Site order parameters q and p, as well as unfrustrated portion of the lattice h increase substantially in the presence of anisotropy. However, these parameters tend to decrease somewhat for rational values of f which happen to be the same for which merges were noticed. Finally, we study the effect of the variation of relative concentration of F vs. AF bonds on these properties. It is found that far from the equal concentration case order parameters increase even further. All of this indicates that simulation of a spin-glass behavior by this simple system is favored under the introduction of anisotropic interactions.

The Pair Approximation of the Cluster Variation Method as Applied to bcc Alloys

The phase diagram of the order-disorder transformation in binary alloys A x B 1−x with bcc structure is calculated using the pair approximation of the Cluster Variational Method (CVM). Nearest (NN) and next-nearest neighbor (NNN) interactions are considered. Two types of pairs are taken into account: short pairs for the NN and long pairs for the NNN. The results of our calculation are compared with the CVM tetrahedron approximation and Monte Carlo Simulations (MCS)

Adsorption of Statistical Copolymers on Surfaces --A Simulation Based on the Cluster Variational Method--

The conformations adopted by random copolymers of two components adsorbed on a flat surface are studied here by the use of a simulation technique. The model used here assumes that the two copolymer components have different interactions with the surface. The change in the physical and geometrical properties is studied as a function of the interactions with the surface. The configuration of the adsorbed copolymers depends strongly on the interactions with the surface. The behavior of the copolymers shows some similarities with homopolymer, but also some differences are shown. The results shown here can be regarded as a guideline for controlling some specific configurations adopted by the adsorbed copolymers on colloid particles.