Sergey V. Lyulin

Molecular dynamics study of charged dendrimers in salt-free solution: Effect of counterions

Polyamidoamine dendrimers, being protonated under physiological conditions, represent a promising class of nonviral, nanosized vectors for drug and gene delivery. We performed extensive molecular dynamics simulations of a generic model dendrimer in a salt-free solution with dendrimers terminal beads positively charged. Solvent molecules as well as counterions were explicitly included as interacting beads. We find that the size of the charged dendrimer depends nonmonotonically on the strength of electrostatic interactions demonstrating a maximum when the Bjerrum length equals the diameter of a bead. Many other structural and dynamic characteristics of charged dendrimers are also found to follow this pattern. We address such a behavior to the interplay between repulsive interactions of the charged terminal beads and their attractive interactions with oppositely charged counterions. The former favors swelling at small Bjerrum lengths and the latter promotes counterion condensation. Thus, counterions can have a dramatic effect on the structure and dynamics of charged dendrimers and, under certain conditions, cannot be treated implicitly.

Molecular-dynamics simulation of polyimide matrix pre-crystallization near the surface of a single-walled carbon nanotube

Polyimide-based composite materials with a single-walled carbon nanotube as filler were studied by means of extensive fully-atomistic molecular-dynamics simulations. Polyimides (PI) were considered based on 1,3-bis-(3′,4-dicarboxyphenoxy)-benzene (dianhydride R) and various types of diamines: 4,4′-bis-(4′′-aminophenoxy)-diphenylsulfone (diamine BAPS) and 4,4′-bis-(4′′-aminophenoxy)-diphenyl (diamine BAPB). The influence of the chemical structure of the polyimides on the microstructure of the composite matrix near the filler surface and away from it was investigated. The formation of subsurface layers close to the nanotube surface was found for all composites considered. In the case of R–BAPB-based composites, the formation of an organized structure was shown that could be the initial stage of the matrix crystallization process observed experimentally. Similar structural features were not observed in the R–BAPS composites. Carbon nanotubes induce the elongation of R–BAPB chains in composites whereas R–BAPS chains become more compact similar to what is observed for EXTEM™ polyimide. It was shown that electrostatic interactions do not influence the microstructure of composites but slow down significantly the dynamics of PI chains in composites.

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/T(1) 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 dendrimers 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.

Effect of the SO2 group in the diamine fragment of polyimides on their structural, thermophysical, and mechanical properties

Experimental and theoretical investigations, including an all-atom computer simulation, are performed for block samples of thermoplastic polyimides, amorphous R-BAPS (based on R dianhydride 1,3-bis(3′,4-dicarboxyphenoxy)benzene and diamine BAPS 4,4′-bis(4″-aminophenoxy)biphenyl sulfone), and crystallizable R-BAPB (based on R dianhydride and diamine BAPB 4,4’-bis(4″-aminophenoxy)biphenyl), which differ in either the presence or absence of the sulfone group in the repeating unit of the polyimide macromolecule. The features of thermophysical, structural, and mechanical properties of R-BAPS and R-BAPB are related to the formation of associates from sulfur and oxygen atoms of the sulfone group that are stabilized by electrostatic interactions.

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.

Effects of topology and size on statics and dynamics of complexes of hyperbranched polymers with linear polyelectrolytes

Brownian dynamics simulations with explicit hydrodynamic interactions have been employed to study generic effects of size and topology in noncovalent (Coulombic-driven) complexes formed by irregular-shaped hyperbranched polymers and linear polyelectrolytes. The behavior of the complexes was explored in detail in terms of static and dynamic properties, both in local and in the entire complex scale. The results were compared to previous studies on perfect dendrimers and other hyperbranched molecules where available. It was found that both molecular weight and structure may impart significant changes to key factors known to be associated with the ability of these systems to take part in relevant nanoscale applications.

Influence of the carbon nanofiller surface curvature on the initiation of crystallization in thermoplastic polymers

Experimental results have shown that graphitizated carbon nanofibers initiate crystallization in R-BAPB polyimides twice as fast as single-wall carbon nanotubes (CNT) leading to the hypothesis that nanofiller curvature influences polyimide crystallization. Therefore, atomistic molecular-dynamics simulations have been performed for R-BAPB in the presence of a flat graphene sheet and the results were compared with those obtained in the presence of a small-radius CNT. The polyimide chain segments tend to lie parallel to the nanofiller surface and this tendency is stronger and the segments are closer to the graphene surface than to the CNT one. Moreover, the density of the polyimide in the near-surface layer is higher for composites filled with graphene than with CNT. This confirms the assumption that the nanofiller surface curvature is indeed a factor influencing the polymer patterning structure, and that a smaller curvature (i.e. flat surface) provides an enhanced initiation of polymer ordering.

Evaluation of the characteristic equilibration times of bulk polyimides via full-atomic computer simulation

The full-atomic computer simulation of bulk plastic polyimides based on dianhydride 1,3-bis(3′,4-dicarboxyphenoxy)benzene and two types of diamines, 4,4′-bis(4″-aminophenoxy)diphenyl sulfone and 4,4′-bis(aminophenoxy)diphenyl oxide, is performed on the microsecond scale via the moleculardynamics method. For the investigated molecules, which consist of eight repeating units, the limiting values of the characteristic sizes of individual polymer chains are established. The limiting sizes obtained via computer simulation are in good agreement with theoretical values calculated in terms of virtual-bond formalism. It is found that the time of sample equilibration for the full-atomic computer simulation of bulk plastic polyimides is ∼1 μs, which agrees in order of magnitude with the displacement time of the center of mass of an individual molecule by a distance equal to its own size.

Influence of the carbon nanotube surface modification on the microstructure of thermoplastic binders

The structural properties of polymer nanocomposites based on thermoplastic polyimides filled with surface-modified carbon nanotubes (CNT) have been studied by means of fully-atomistic molecular-dynamics simulations. The influence of the distribution of functional carboxyl groups over the CNT surface on the polymer-matrix density distribution, and the orientational ordering of polymer chains have been investigated. It was shown that the polymer shifts far away from the nanoparticle surface with increase of the CNT modification degree. The orientational ordering of PI chains was not observed in the case of nanocomposites filled with modified CNTs where carboxyl groups are distributed uniformly on the surface. However, in case of the edge-modified CNTs the polymer can interact with the CNT surface; such edge-modified nanoparticles induce orientational ordering of crystallisable polyimide chains which can be considered as an initial stage of the polymer matrix crystallization.

Local orientational mobility in dendrimers. Theory and computer-aided simulation

The orientational mobility of segments in dendrimers are studied by the method of Brownian dynamics, and the results are analyzed in terms of an earlier proposed analytical theory. The orientational autocorrelation function for the cosine of an angle of segmental rotation in dendrimers of a given generation P 1(t) is controlled by three relaxation processes with the corresponding relaxation times. Characteristic times and the contribution from the above processes to P 1(t) are calculated. The first process refers to the local mobility of a selected segment; the second process, to the rotations of a dendrimer branch, which originates from the selected segment of a given generation; and the third process, to the rotation of a dendrimer macro-molecule as a whole. The proposed approach makes it possible to estimate the relaxation spectrum of a dendrimer by studying the orientational mobility of segments in different generations. The relaxation times can be used to describe various relaxation processes observed by different experimental methods, such as dielectric relaxation, NMR, dynamic birefringence, and polarized luminescence.