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This is a rather personal review of the problem of self-avoiding walks and polygons. After defining the problem, and outlining what is known rigorously and what is merely conjectured, I highlight the major outstanding problems. I then give…
We study the adsorption of polymer chains on a fluctuating surface. Physical examples are provided by polymer adsorption at the rough interface between two non-miscible liquids, or on a membrane. In a mean-field approach, we find that the…
We study self-avoiding walks on the square lattice restricted to a square box of side $L$ weighted by a length fugacity without restriction of their end points. This models a confined polymer in dilute solution. The model admits a phase…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is used to study polymer growth near a $D$-dimensional attractive hyperspherical boundary. The…
We consider a directed random walk model of a random heterogeneous polymer in the proximity of an interface separating two selective solvents. This model exhibits a localization/delocalization transition. A positive value of the free energy…
Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…
We investigate the phase behavior of symmetric AB diblock copolymers confined into a thin film. The film boundaries are parallel, impenetrable and attract the A component of the diblock copolymer. Using a self-consistent field technique…
We consider a model mixture of hard colloidal spheres and non-adsorbing polymer chains in a theta solvent. The polymer component is modelled as a polydisperse mixture of effective spheres, mutually noninteracting but excluded from the…
We present several ordering mechanisms in diblock copolymers. For temperatures above the order-disorder temperature and in the weak segregation regime, a linear response theory is presented which gives the polymer density in the vicinity of…
A lattice model of the directed self-avoiding walk is used to estimate the possibility on the formation of an infinitely long linear semi-flexible copolymer chain. The copolymer chain is assumed to composed of four different types of the…
We investigate the mechanism of chain exchange in diblock copolymer micelles using two distinct yet complementary simulation techniques. First, enhanced sampling method is combined with coarse-grained molecular dynamics to compute a…
Isoporous membranes made from diblock copolymers have numerous applications, including water treatment and protein separation, and are successfully produced at a laboratory scale under controlled conditions. However, achieving optimal…
This paper reports the force spectroscopy analysis of a polymer that translocates from one side of a membrane to the other side through an extended pore, pulled by a cantilever that moves with constant velocity against the damping and the…
We analyze the localized phase of a general model of a directed polymer in the proximity of an interface that separates two solvents. Each monomer unit carries a charge, $\omega_n$, that determines the type (attractive or repulsive) and the…
The behavior of polyampholytes near a charged planar surface is studied by means of Monte Carlo simulations. The investigated polyampholytes are overall electrically neutral and made up of oppositely charged units (called blocks) that are…
We analyze the unbinding transition for a two dimensional lattice polymer in which the constituent strands are mutually avoiding random walks. At low temperatures the strands are bound and form a single self-avoiding walk. We show that…
In this paper we study a model describing a copolymer in a micro-emulsion. The copolymer consists of a random concatenation of hydrophobic and hydrophilic monomers, the micro-emulsion consists of large blocks of oil and water arranged in a…
Nanocomposite materials made of block copolymer and nanoparticles display properties which can be different from the purely polymeric matrix. The resulting material is a crossover of the original properties of the block copolymer and the…
We investigate neighbor-avoiding walks on the simple cubic lattice in the presence of an adsorbing surface. This class of lattice paths has been less studied using Monte Carlo simulations. Our investigation follows on from our previous…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…