Universal shape characteristics for the mesoscopic polymer chain via dissipative particle dynamics

Abstract

In this paper we study the shape characteristics of a polymer chain in a good solvent using a mesoscopic level of modelling. The dissipative particle dynamics simulations are performed in 3D space at a range of chain lengths N. The scaling laws for the end-to-end distance and gyration radius are examined first and found to hold for [Formula: see text] yielding a reasonably accurate value for the Flory exponent ν. Within the same interval of chain lengths, the asphericity, prolateness and some other shape characteristics of the chain are found to become independent of N. Their mean values are found to agree reasonably well with the respective theoretical results and lattice Monte Carlo (MC) simulations. We found the probability distribution for a wide range of shape characteristics. For the asphericity and prolateness they are quite broad, resembling in form the results of lattice MC simulations. By means of the analytic fitting of these distributions, the most probable values for the shape characteristics are found to supplement their mean values.

Universal Size and Shape Ratios for Arms in Star‐Branched Polymers: Theory and Mesoscopic Simulations

“…This correlates well with the findings that a linear chain within the DPD enters scaling regime at moderate values of N ∼ 8 − 10. [41] It is also interesting to note that the Daoud-Cotton ansatz provides the result that is very close to our simulations at f > 10, following the discussion in ref. [34] that this ansatz is valid for the case of a rather large number of branches f. Let us now switch to the p A (f ) ratio for a star defined in Equation (3), the results obtained in this study are shown in Figure 3, where they are compared to the simulations by Batoulis and Kremer [23] and the results for the Gaussian model.…”

“…Providing some answers in refs. [40][41][42], here we also show that the method describes adequately the excluded volume effect in the case of dense star with a relatively large number of arms.…”

“…For instance, scaling properties of a linear polymer chain can be reproduced fairly well using chain lengths of 10 ≤ N ≤ 40. [40,41] The simulation length in the current study is 4 × 10 6 DPD steps for each case with the time-step of 0.04 in reduced units, where the first 4 ×…”

“…Then, the mesoscopic dissipative particle dynamics (DPD)-based simulations are undertaken. Earlier, such simulation has been employed for the analysis of the size [40] and shape [41] characteristics of a linear chain, as well as the shape properties of heterostar polymers. [42] The main point of interest is whether or not such simulations, that involve soft interaction potential, can reproduce the effect of branches stretching and swelling upon the increase of their number f. To this end, we compare our findings with available simulation data performed on the lattice models of polymers and the van der Waals potential-based molecular dynamics studies.…”

Statistical physics of complex systems in the world and in Lviv

“…Як виявилося, зокрема й у результатi наших до-слiджень, унiверсальним степеневим законам пiдля-гають й iншi спостережуванi, що описують конформа-цiйнi властивостi полiмерних ланцюгiв та iнших мак-ромолекулярних утворень, складних як за топологiєю (полiмернi сiтки та зiрки), так i за хiмiчним складом (кополiмери та кополiмернi сiтки) [26,27]. Щобiльше, унiверсальною виявляється i форма таких утворень [28]. Деякi нашi результати в цiй дiлянцi, а також ре-зультати дослiдження конформацiйних властивостей полiмерiв у пористому середовищi [29][30][31] наведенi в роздiлах V-VIII.…”