Andrzej Sikorski

Bio: Andrzej Sikorski is an academic researcher from University of Warsaw. The author has contributed to research in topics: Monte Carlo method & Excluded volume. The author has an hindex of 17, co-authored 104 publications receiving 850 citations.

Monte Carlo study of the dynamics of star-branched polymers

Abstract: A uniform star-branched polymer model with f = 3 arms based on a simple cubic lattice was studied by means of the dynamic Monte Carlo method. The model chain is athermal with excluded-volume interactions and it is flexible. A new type of local micromodification was introduced to make the branching point movable. Static properties of the star polymer are in accordance with other theoretical predictions and experimental evidence. Scaling of the self diffusion constant and the terminal relaxation times is close to those of the Rouse theory and to simulation results of linear chains.

Computer Simulation of Adsorbed Polymer Chains with a Different Molecular Architecture

Abstract: Simulations of simple models of polymer chains were carried out by the means of the dynamic Monte Carlo method. The model chains were confined to a simple cubic lattice. Three different chain architectures were studied: linear, star-branched and ring chains. The polymer model chain interacted with an impenetrable surface with a simple contact attractive potential. It was found that size parameters of all these polymers obey scaling laws. The temperatures of the transitions from weakly to strongly adsorbed chain were determined. It was shown for weakly adsorbed chains that ring polymers are always ca. 50% more adsorbed than linear and star-branched ones. The properties of adsorbed linear and star-branched polymers are very similar in the length of chain and the strength of adsorption studied. Strongly adsorbed ring polymers are still more adsorbed but differences between all kinds of chains become less pronounced.

Monte Carlo simulations of star-branched polymers confined between two walls

Abstract: The properties of simplified lattice models of confined branched polymers were studied by the Monte Carlo method. Model chains were located between two parallel impenetrable surfaces. The distance between surfaces, as well as the chain length, were varied. The model chains consisted of f=3 branches of equal length (star-branched polymers) and were based on a simple cubic lattice. The model was athermal and the excluded volume was introduced. Monte Carlo sampling algorithm using local chain micromodifications was applied. Both static and dynamic properties of the system were investigated. The differences between star-branched chains and linear ones which were trapped between walls were discussed. The behavior of static properties made it possible to construct a universal curve presenting the effect of surface-to-surface distance on chain dimensions. The possible explanation of the shape of this curve was given. The changes of dynamic properties were discussed in the context of possible chain’s mechanism of...

Dynamics of polymer chains in confined space. A computer simulation study

Abstract: We studied the properties of simple models of star-branched polymer chains confined in a slit. The chains were constructed of united atoms (segments) and were restricted to vertices of a simple cubic lattice. We modeled good solvent conditions and thus the chains interacted with the excluded volume only. The macromolecules were put between two parallel and impenetrable surfaces and the surfaces were attractive for polymer segments. The properties of the model chains were determined by means of Monte Carlo simulations with a sampling algorithm based on chain's local changes of conformation. The differences and similarities in the structure for different adsorption regimes and the size of the slit were shown and discussed. The dependence of the short- and long-time scale dynamic behavior of chains on these factors was determined.

Structure of Adsorbed Polymer Chains: A Monte Carlo Study

Abstract: The structure of adsorbed polymer chains was studied using simplified lattice models. The model chains were adsorbed on an impenetrable surface with an attractive potential. The dynamic Monte Carlo simulations based in the Metropolis scheme were carried out using these models. The influence of the internal chain architecture (linear, star-branched and ring chains) and the degree of adsorption on the chain's structure was studied. It was shown that for weakly adsorbed chain regime the ring polymers which exhibit an almost twice as high degree of adsorption compared to linear and star chains have a higher number of adsorbed parts of chain (trains). But the length of such train remains almost the same for all types of a polymer chain. Star-branched chains exhibit a slightly different change in number and the mean length of trains, loops and tails with the temperature and the chain total length compared to two other types of chain.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

The nature of folded states of globular proteins.

Abstract: We suggest, using dynamical simulations of a simple heteropolymer modelling the alpha-carbon sequence in a protein, that generically the folded states of globular proteins correspond to statistically well-defined metastable states. This hypothesis, called the metastability hypothesis, states that there are several free energy minima separated by barriers of various heights such that the folded conformations of a polypeptide chain in each of the minima have similar structural characteristics but have different energies from one another. The calculated structural characteristics, such as bond angle and dihedral angle distribution functions, are assumed to arise from only those configurations belonging to a given minimum. The validity of this hypothesis is illustrated by simulations of a continuum model of a heteropolymer whose low temperature state is a well-defined beta-barrel structure. The simulations were done using a molecular dynamics algorithm (referred to as the "noisy" molecular dynamics method) containing both friction and noise terms. It is shown that for this model there are several distinct metastable minima in which the structural features are similar. Several new methods of analyzing fluctuations in structures belonging to two distinct minima are introduced. The most notable one is a dynamic measure of compactness that can in principle provide the time required for maximal compactness to be achieved. The analysis shows that for a given metastable state in which the protein has a well-defined folded structure the transition to a state of higher compactness occurs very slowly, lending credence to the notion that the system encounters a late barrier in the process of folding to the most compact structure. The examination of the fluctuations in the structures near the unfolding----folding transition temperature indicates that the transition state for the unfolding to folding process occurs closer to the folded state.