Percolation model of hyperbranched polymerization

Computer simulations of the step-growth homopolymerization of an AB₂ monomer have been carried out on a square lattice. No rearrangements of units were made between reaction events. Instead, the capture radius, i.e., the maximum distance between the randomly selected unit and its reaction partner was changed. The reaction was considered as controlled either by diffusion and local concentration fluctuations or by the law of mass action (classical limit). The size distribution of polymer species and the extent of cyclization reactions in the polymerization are discussed.     

Optimization of parallel implementation of UNRES package for coarse-grained simulations to treat large proteins

We report major algorithmic improvements of the UNRES package for physics-based coarse-grained simulations of proteins. These include (i) introduction of interaction lists to optimize computations, (ii) transforming the inertia matrix to a pentadiagonal form to reduce computing and memory requirements, (iii) removing explicit angles and dihedral angles from energy expressions and recoding the most time-consuming energy/force terms to minimize the number of operations and to improve numerical stability, (iv) using OpenMP to parallelize those sections of the code for which distributed-memory parallelization involves unfavorable computing/communication time ratio, and (v) careful memory management to minimize simultaneous access of distant memory sections. The new code enables us to run molecular dynamics simulations of protein systems with size exceeding 100,000 amino-acid residues, reaching over 1 ns/day (1 μs/day in all-atom timescale) with 24 cores for proteins of this size. Parallel performance of the code and comparison of its performance with that of AMBER, GROMACS and MARTINI 3 is presented.     

Extremely asymmetric sawtooth potential in the ratchet theory

We present a review of analytical approaches involved in developing the ratchet theory, which are based on the model of extremely asymmetric sawtooth potential. Analytical expressions are given for the average velocity of ratchets which operate in various motion modes, namely, motion induced by dichotomous half-period shifts of potential profiles, adiabatic and high-temperature modes, and motion induced by small fluctuations of an arbitrary type. The presence of jumps in the periodic extremely asymmetric sawtooth potential profile leads to a number of features of the obtained solutions which follow from the competition of the reverse sliding time tending to infinity with high fluctuation frequencies. The resulting dependences of the average velocity on the ratchet parameters clearly demonstrate that the motion direction can be controlled by tuning the frequency and temperature. The heuristic value of the presented models for controlling nanoparticle transport is discussed.     

A three parameter kinetic model of formation of linear polyurethane from 2,4‐toluenediisocyanate and butane‐1,4‐diol

A model of linear isothermal polymerization of two bi‐functional monomers, one of which has alike functional groups of different reactivities, is presented. The model has been applied to the polymerization of 2,4‐toluenediisocyanate (TDI)^a and butane‐1,4‐diol carried out in solution at 86 or 101°C. The rate constant K of the reaction between an isocyanate group in position 4 of TDI and a hydroxy group, the ratio κ of reactivities of groups in position 4 relative to that in position 2, and the ratio k_φ of reactivities of an isocyanate group in the monomer relative to that at the end of an oligomer chain, have been evaluated from experimental data to be 6.51·10^–4 dm³·mol^–1·s^–1, 1.47, and 1.55 at 86°C, and 17.2·10^–4 dm³·mol^–1·s^–1, 1.55, and 1.62 at 101°C, respectively.