0000000000002886
AUTHOR
A. Cavallo
Unmixing of Polymer Blends Confined in Ultrathin Films: Crossover between Two-Dimensional and Three-Dimensional Behavior
The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16/= N/= 256 effective monomers per chain) and film thicknesses (2/= D/= 19 lattice spacings). Simultaneously, we investigate the geometrical structure of the chains, showing that despite using melt de…
Thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet with long-range interactions via the spectral density method
The thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet, with long-range interactions decaying as $r^{-p}$ and in the presence of an external magnetic field, is investigated by means of the spectral density method in the framework of classical statistical mechanics. We find that long-range order exists at finite temperature for $dd$ with $d>2$, consistently with known theorems. Besides, the related critical temperature is determined and a study of the critical properties is performed.
Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies
It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compres…
Monte Carlo Simulation of a Homopolymer−Copolymer Mixture Interacting with a Surface: Bulk versus Surface Micelles and Brush Formation
Using Monte Carlo simulations of the bond fluctuation model, we study the formation of micelles in a confined mixture of asymmetric AB-diblock copolymers and homopolymers. The composition of the sphere-forming AB-diblock copolymers is fA = 1/8. The mixture is confined into a thin film. The film surfaces attract the minority component of the diblock with strength, eW. To efficiently sample the micelle size distribution and establish equilibrium between the surface and the bulk, we work in the semigrandcanonical ensemble, i.e. at fixed density and fixed chemical potential difference between the two types of chains, choosing a large incompatibility χN ≃ 100 (strong segregation regime). The com…
Polymer mixtures in confined geometries: Model systems to explore phase transitions
While binary (A,B) symmetric polymer mixtures ind = 3 dimensions have an unmixing critical point that belongs to the 3d Ising universality class and crosses over to mean field behavior for very long chains, the critical behavior of mixtures confined into thin film geometry falls in the 2d Ising class irrespective of chain length. The critical temperature always scales linearly with chain length, except for strictly two-dimensional chains confined to a plane, for whichT; c ∝N; 5/8 (this unusual exponent describes the fractal contact line between segregated chains in dense melts in two spatial dimensions, d = 2). When the walls of the thin film are not neutral, but preferentially attract one …
Single chain structure in thin polymer films: Corrections to Flory's and Silberberg's hypotheses
Conformational properties of polymer melts confined between two hard structureless walls are investigated by Monte Carlo simulation of the bond-fluctuation model. Parallel and perpendicular components of chain extension, bond-bond correlation function and structure factor are computed and compared with recent theoretical approaches attempting to go beyond Flory's and Silberberg's hypotheses. We demonstrate that for ultrathin films where the thickness, $H$, is smaller than the excluded volume screening length (blob size), $\xi$, the chain size parallel to the walls diverges logarithmically, $R^2/2N \approx b^2 + c \log(N)$ with $c \sim 1/H$. The corresponding bond-bond correlation function d…
Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach
We explore the low-temperature thermodynamic properties and crossovers of ad-dimensional classical planar Heisenberg ferromagnet in a longitudinal magnetic field close to its field-induced zero-temperature critical point by employing the two-time Green’s function formalism in classical statistical mechanics. By means of a classical Callen-like method for the magnetization and the Tyablikov-like decoupling procedure, we obtain, for anyd, a low-temperature critical scenario which is quite similar to the one found for the quantum counterpart. Remarkably, ford>2the discrimination between the two cases is found to be related to the different values of the shift exponent which governs the beha…
Chain Conformations and Phase Behavior in Confined Polymer Blends
We investigate the chain conformations and phase separation in binary polymer blends. Using large scale semi-grandcanonical Monte Carlo simulations and finite size scaling, we investigate the molecular extension and the intermolecular paircorrelation function in thin films with hard, non-preferentially adsorbing surfaces. The interplay between chain conformations, demixing and the validity of mean field theory is investigated for a large variation of chain lengths 16 ≤ N ≤ 512. Three regimes of film thickness D can be distinguished: (i) For film thicknesses much larger than the unperturbed chain extension R e, bulk behavior is observed, i.e., the critical temperature of demixing T c increas…
Anomalous scaling of the critical temperature of unmixing with chain length for two-dimensional polymer blends
The thermodynamics, structure and the chain configurations of symmetrical polymer mixtures confined into ultrathin films are studied by Monte Carlo simulations of the bond fluctuation model. It is shown that the Flory-Huggins–type scaling of the critical temperature (Tc ~ N) with chain length N in the bulk is replaced by a weaker increase, Tc ~ N1/2, in an ultrathin film, and this is interpreted in terms of geometric arguments. The pair-correlation function g(r) of monomers from different chains exhibits a pronounced correlation hole, and the density of intermolecular contacts zc decreases with N as zc ~ N−1/2.
Formation of Micelles in Homopolymer-Copolymer Mixtures: Quantitative Comparison between Simulations of Long Chains and Self-Consistent Field Calculations
Using Monte Carlo simulations of the bond fluctuation model and self-consistent field calculations, we study the formation of micelles in a mixture of homopolymers and asymmetric AB-diblock copolymers with composition, fA = 1/8. Both types of molecules are fully flexible and have identical length. We work in the semi-grand-canonical ensemble, i.e., we fix the monomer density and incompatibility, χN ≃ 100 (strong segregation regime), and control the composition of the mixture via the exchange chemical potential, δμ ≡ μAB − μB between the copolymers and homopolymers. The Monte Carlo simulation comprises moves that allow homopolymers to mutate into AB-diblock copolymers and vice versa. These m…
The Classical Spectral Density Method at Work: The Heisenberg Ferromagnet
In this article we review a less known unperturbative and powerful many-body method in the framework of classical statistical mechanics and then we show how it works by means of explicit calculations for a nontrivial classical model. The formalism of two-time Green functions in classical statistical mechanics is presented in a form parallel to the well known quantum counterpart, focusing on the spectral properties which involve the important concept of spectral density. Furthermore, the general ingredients of the classical spectral density method (CSDM) are presented with insights for systematic nonperturbative approximations to study conveniently the macroscopic properties of a wide variet…