Dynamics of complexation of a charged dendrimer by linear polyelectrolyte: Computer modelling

Brownian-dynamics simulations have been performed for complexes formed by a charged dendrimer and a long oppositely charged linear polyelectrolyte when overcharging phenomenon is always observed. After a complex formation the orientational mobility of the individual dendrimer bonds, the fluctuations of the dendrimer size, and the dendrimer rotational diffusion have been simulated. Corresponding relaxation times do not depend on the linear-chain length in a complex and are close to those for a single neutral dendrimer. At the same time fluctuations of the size of a complex are completely defined by the corresponding fluctuations of a linear polyelectrolyte size. Adsorbed polyelectrolyte practically does not feel the rotation of a dendrimer; simulated complexes may be considered as nuts with light core (dendrimer) and heavy shell (adsorbed linear polymer); the electrostatic contacts between dendrimer and oppositely charged linear polymer are easily broken due to the very fast dendrimer-size fluctuations

Conformational effects in non-stoichiometric complexes of two hyperbranched molecules with a linear polyelectrolyte

We report results from Brownian dynamics computer simulations of systems comprised by two terminally charged hyperbranched molecules preferentially branched in the periphery, with an oppositely charged linear chain of varying length. Comparison of the findings from the present study to stoichiometric counterparts and to analogous dendrimer-based complexes, reveal that the presence of the second hyperbranched molecule incurs significant changes in the conformational characteristics of both components of the complex. Instead of step-like changes in the average size and shape of the hyperbranched component that were noted in the previously studied stoichiometric systems, a rather smooth change is observed upon increase of the length of the linear component. In addition, a markedly different behavior is also noticed in the conformational characteristics of the linear chain when compared to that in similar dendrimer-based systems. The above findings are consistent with the higher degree of deformability of the peripherally branched molecules which allow appropriate rearrangements in shape in order to accommodate the favorable Coulombic interactions between the two components of the complex. This behavior offers new insight towards the design of more efficient hyperbranched-based systems which can take advantage of the multifunctionality and the structural properties of the highly branched polymer components

Orientational mobility and relaxation spectra of dendrimers : theory and computer simulation

The developed theory of the orientational mobility of individual segments of a perfectly branched dendrimer is used to calculate the relaxation spectrum of a dendrimer. Frequency dependences of NMR relaxation 1/T1 and of the nuclear Overhauser effect have been theoretically calculated from the Brownian dynamics simulation data. The dendrimer segmental orientational mobility is governed by three main relaxation processes: (i) the rotation of the dendrimer as a whole, (ii) the rotation of the dendrimer's branch originated from a given segment, and (iii) the local reorientation of the segment. The internal orientational mobility of an individual dendrimer segment depends only on the topological distance between this segment and the terminal shell of the dendrimer. Characteristic relaxation times of all processes and their contributions to the segmental mobility have been calculated. The influence of the number of generations and the number of the generation shell on the relaxation times has been studied. The correlation between the characteristic times and the calculated relaxation spectrum of the dendrimer has been established

Linker formation in an overcharged complex of two dendrimers and linear polyelectrolyte

The complexes formed by two dendrimers with charged terminal groups and oppositely charged long linear polyelectrolyte (LPE) have been studied using Brownian dynamics simulations. The structural properties of the complexes and their dependence on the LPE chain length were investigated. It was observed that dendrimers in the considered complexes are sufficiently overcharged; i.e., the number of adsorbed LPE monomers is larger than required for the neutralization. The degree of overcharging increases with the increase of the LPE length and is accompanied by the linker appearance until saturation in overcharging is reached. Nonmonotonic dependence of the linker size on the LPE length was observed. To describe the structural properties of the complexes formed by two macroions and a polyelectrolyte chain, the correlation theory has been developed

Charge inversion of dendrimers in complexes with linear polyelectrolytes in the solutions with low pH

Complexes of fully ionized third-generation dendrimers with oppositely charged linear polyelectrolyte chains are studied by the Brownian dynamics method. A freely jointed model of a dendrimer and a linear chain is used. Electrostatic interactions are considered within the Debye-Hückel approximation with the Debye radius exceeding the dimensions of a dendrimer. In these systems, the phenomenon of charge inversion is observed, and the degree of "overcharging" is higher as compared with that taking place in analogous complexes formed by dendrimers in which only terminal groups are charged. The dependence of the amount of chain units adsorbed on a dendrimer on the polyelectrolyte chain length is nonmonotnic and agrees qualitatively with the predictions of the theory proposed by Nguyen and Shklovskii for a complex composed of a spherical macroion with an oppositely charged linear chain. This nonmonotonic character also manifests itself for certain other structural characteristics of the complexes. Upon the formation of a complex, a chain is shown to penetrate deeply into a dendrimer

Coarse-grained molecular-dynamics simulations of nanoparticle diffusion in polymer nanocomposites

Molecular-dynamics simulations have emerged as an effective tool to characterize polymer systems. Molecular level effects (even on microsecond time scales) are nowadays well reproduced by atomistically detailed models. Beyond this, further insights into the properties of the polymer system at a mesoscopic level can be gained by resorting to simulations based on appropriate coarse-grained models. However, reducing the number of degrees of freedom during the coarse-graining procedure may have a significant impact on atomistic level effects. A common example is the overall enhancement of the diffusive motion of polymer chains in coarse-grained simulations, which arises from the reduced friction of the coarse-grained beads. In the present work we investigate this well-known effect and study how the diffusive properties of the nanoparticle are affected by the coarse-graining procedure. To this end, we apply iterative Boltzmann inversion to develop two coarse-grained models of a nanocomposite based on the thermoplastic polyimide R-BAPB, containing a single fullerene C60 nanoparticle. By changing the size and, correspondingly, the total number of coarse-grained beads in each polymer chain, we can control the effect of chemical detalization on various phenomena. We exploit this idea to study the influence of the degree of detalization of polymer chains on their structural properties as well as on the diffusive properties of the fullerene nanoparticle, whose detalization is kept fixed. Although the structural properties of the coarse-grained systems are in good agreement with those of the fully atomistic system, the nanoparticle diffusion is significantly affected by the local chain structure. In particular, we find that the coarse-graining of the polymer chains on the length scale of the nanoparticle size leads to a full suppression of the subdiffusive regime observed in the fully atomistic system

Energetic and conformational aspects of dendrimer overcharging by linear polyelectrolytes

Extensive Brownian dynamics simulations of conformational changes accompanying the overcharging of a dendrimer by an oppositely charged long linear polyelectrolyte (LPE) have been carried out. The simulated results have been compared with the predictions of the Nguen and Shklovskii correlation theory [Physica A 293, 324 (2001)] for impenetrable charged spherical macroion. Dendrimer overcharging is caused by the spatial correlations between the "excess" of the LPE charges adsorbed onto its surface. The simulated LPE-length dependence of the corresponding "correlation" energy is in agreement with the theoretical predictions. Maximum of the LPE adsorption occurs at some critical LPE length N, and the first order phase transition from completely coiled conformation to the conformation with released tails takes place. The phase transition is accompanied by the drastic increase in the relative fluctuations of the polyelectrolyte size. Upon increasing the linear-chain length above N, the one-long-tail conformation becomes energetically preferable; the exchange time between the long-tail conformation and the short-tail conformation is very large

Dynamics of Complexation of a Charged Dendrimer by Linear Polyelectrolyte: Computer Modelling

Brownian-dynamics simulations have been performed for complexes formed by a charged dendrimer and a long oppositely charged linear polyelectrolyte when overcharging phenomenon is always observed. After a complex formation the orientational mobility of the individual dendrimer bonds, the fluctuations of the dendrimer size, and the dendrimer rotational diffusion have been simulated. Corresponding relaxation times do not depend on the linear-chain length in a complex and are close to those for a single neutral dendrimer. At the same time fluctuations of the size of a complex are completely defined by the corresponding fluctuations of a linear polyelectrolyte size. Adsorbed polyelectrolyte practically does not feel the rotation of a dendrimer; simulated complexes may be considered as nuts with light core (dendrimer) and heavy shell (adsorbed linear polymer); the electrostatic contacts between dendrimer and oppositely charged linear polymer are easily broken due to the very fast dendrimer-size fluctuations

Microsecond atomic-scale molecular dynamics simulations of polyimides

We employ microsecond atomic-scale molecular dynamics simulations to get insight into the structural and thermal properties of heat-resistant bulk polyimides. As electrostatic interactions are essential for the polyimides considered, we propose a two-step equilibration protocol that includes long (microsecond-scale) MD simulations of polymer melt with partial atomic charges switched off, followed by relatively short runs (100 ns) of the polymer system with full electrostatics. We demonstrate that macroscopic characteristics of a polyimide sample (such as the glass transition temperature and density) are not particularly sensitive to the degree of equilibration. However, great caution should be paid when local structural characteristics are considered: proper equilibration of the local polymer structure (monitored through the radius of gyration and the end-to-end distance of individual chains) is found to require simulations on a microsecond time scale. Finally, we found a dramatic impact of electrostatic interactions on the properties of the bulk polyimides considered: when intra- and intermolecular dipole–dipole interactions come into play we witness compaction of individual polymer coils and eventually an increase in the glass transition temperature and polymer density

Structural effects in overcharging in complexes of hyperbranched polymers with linear polyelectrolytes

New insight is provided by a combined theoretical and simulational approach regarding the effects of structural characteristics of the constituents, on the overcharging phenomena in complexes formed by hyperbranched polymers with linear polyelectrolytes