In this work shape characteristics for the polymer macromolecules of different architecture are investigated via dissipative particle dynamic.
As a first step in our study we consider shape characteristics of the mesoscopic continuous (off-lattice) model of a linear polymer chain in a good solvent. In order to test the universality properties of the model. We have shown that effective average size and shape characteristics of the mesoscopic polymer chain in a good solvent show universal and scaling type of behavior for the chain length N≥10. Besides that the analysis of the probability distributions for the end-to-end distance and for the radius of gyration was carried out. In the former case known des Cloiseaux-de Gennes analytical asymptotics have been reproduced and in the latter case an analytical expressions, based on the application of the well known Lhuillier form and generalized version of the double Gaussian form for symmetric distribution, have been proposed.
Further, the methods developed and tested above have been used to study the shape properties of the polymers of more complicated topology: star-like polymers of different functionality. In particular the effects of the solvent quality on the polymer shape were studied. Five different versions of the star polymer models have been studied: one model homogeneous polymer star and four versions of heterogeneous models. The effects of the solvent quality on the shape characteristics of the course-grained versions of the models of homogeneous and heterogeneous star polymers, using dissipative particle dynamics, has been analysed. We found an interesting effect that, upon the change of solvent properties, the asphericity of a homogeneous star reaches its maximum value when the solvent is near θ-point. The effect is explained by the interplay between the enthalpic and entropic contributions to the free energy.
We analyzed the set of properties, which allow to characterize the impact of local crowdedness caused by structure of f-branched star polymer on the peculiarities of spatial extension of single arm. To this end, we consider the characteristics, specific to an individual arm within the star, such as the average center-end distance, the average squared gyration radius and the asphericity of an individual arm within a star. The corresponding universal ratios pe(f), pg(f) and pa(f), are introduced, to compare these values directly with that of a freely suspended linear chain of the same molecular weight. Our results, obtained using dissipative particle dynamics, are in a good agreement with results, generated using Monte Carlo and molecular dynamic simulations. Results obtained show that dissipative particle dynamics describes adequately the excluded volume effect in the case of dense star with a relatively large number of arms.
Finally, we have studied the effect of the molecular architecture of amphiphilic star polymers on the shape of aggregates they form in water. Both solute and solvent are considered at a coarse-grained level by means of dissipative particle dynamics simulations. Four molecular architectures have been examined: (a) four disjoint linear diblocks, (b) asymmetric miktoarm polymer, (c) diblock star 1 (hydrophilic parts pointing outwards) and (d) diblock star 2 (hydrophilic parts next to a central bead), all of the same composition and molecular weight. Aggregation is started from a closely packed bunch of Na molecules immersed into water. In the equilibrium state a single aggregate is formed and its shape characteristics are studied at different values of Na. For all cases, the same general sequence of shapes is found with an increase of the aggregation number, namely: spherical micelle, aspherical micelle and a spherical vesicle. The “phase boundaries” between these are found to depend on the details of the molecular architecture. For the case (a)–(c), the transformation between a spherical and aspherical micelle occurs gradually, whereas the transition from an aspherical micelle into a spherical vesicle is in a form of a sharp transition. In the case (b), aspherical micelle is less stable and transition to a vesicle occurs at a lower aggregation number. The case (d) is characterized by gradual transitions between all the shapes. Histograms for the probability distributions of the shape descriptor are relatively narrow for both spherical micelle and spherical vesicle regimes, but become wider next to the micelle-vesicle transition, indicating that a broad range of shapes are possible.
