Denis A. Markelov

Dynamics of dendrimer-based polymer networks

We present a theoretical study of polymer networks, formed by connecting dendritic building blocks (DBB’s). We concentrate on the Rouse dynamics of such networks and perform our study in two steps, considering first single generalized dendrimers (GD’s) and then networks formed by such DBB’s. In GD’s the functionality f of the inner branching points may differ from the functionality fc of the core. The GD’s cover wide classes of macromolecules, such as the “classical” dendrimers (fc=f ), the dendritic wedges (fc=f−1), and the macromolecular stars (fc>2, f=2). Here we present a systematic, analytic way which allows us to treat the dynamics of individual GD’s. Then, using a general approach based on regular lattices formed by identical cells (meshes) we study the dynamics of GD-based polymer networks. Using analytical and numerical methods we determine the storage and loss moduli, G′(ω) and G″(ω). In this way we find that the intradendrimer relaxation domain of G′(ω) becomes narrower when Mcr, the number of ...

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.

Are structural properties of dendrimers sensitive to the symmetry of branching? Computer simulation of lysine dendrimers.

Poly-L-lysine (PLL) dendrimers are promising systems for biomedical applications due to their biocompatibility. These dendrimers have a specific topology: two spacers of different lengths come out of each branching point and thus the branching is asymmetric. Because of this asymmetry terminal groups are located at branches of different lengths, unlike dendrimers with a symmetric branching. This paper presents the results of the first systematic molecular dynamics simulation of such asymmetric PLL dendrimers. It is shown that PLL dendrimers are porous molecules with all terminal groups equally accessible to water. We have found that in spite of an asymmetry of branching the general structural characteristics of PLL dendrimers are rather similar to those of dendrimers with symmetric branching. We have also found that the structural characteristics of PLL dendrimers obey the general laws for dendrimers and that their electrostatic properties agree with the predictions of a general analytic theory.

NMR relaxation of the orientation of single segments in semiflexible dendrimers

We study the orientational properties of labeled segments in semiflexible dendrimers making use of the viscoelastic approach of Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)]. We focus on the segmental orientational autocorrelation functions (ACFs), which are fundamental for the frequency-dependent spin-lattice relaxation times T1(ω). We show that semiflexibility leads to an increase of the contribution of large-scale motions to the ACF. This fact influences the position of the maxima of the [1/T1]-functions. Thus, going from outer to inner segments, the maxima shift to lower frequencies. Remarkably, this feature is not obtained in the classical bead-spring model of flexible dendrimers, although many experiments on dendrimers manifest such a behavior.

NMR Studies of Carbosilane Dendrimer with Terminal Mesogenic Groups

The 4-generation carbosilane dendrimer with terminal cyanobiphenyl mesogenic groups in dilute solution of CDCl(3) was investigated using (1)H NMR technique. The spectrum was obtained and the relaxation time, T(1), was measured in the temperature range 320-225 K. For the first time, the extrema of T(1) values were achieved for majority of the dendrimer functional groups. The values of activation energies of the dendrimer functional groups were obtained. The relaxation data for outer and inner methyl groups show that the dendrimer investigated has dense corona and hollow core. This structure is formed because the mesogenic groups do not allow terminal segments to penetrate into the dendrimer, that is, the backfolding effect is absent. The NMR spectral and relaxation data give evidence for changing conformation of the dendrimer internal segments with decreasing temperature. This reorganization is most likely connected with a change of dendrimer size. We suppose that our experimental results will provide additional information for understanding principles of dendrimer nanocontainer operation. NMR can possibly be a tool for indicating the encapsulation effect as well as the dendrimer effective size.

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.

Mathematical simulation of lysine dendrimers: Temperature dependences

The mathematical simulation of second- and fourth-generation lysine dendrimers is performed via the molecular-dynamics method. Temperature dependences of primary structural characteristics are obtained. It is shown that the sizes and atomic distributions of these dendrimers are weakly temperature-dependent. Together with the structural properties, the local mobility of CH2 groups in the dendrimers is investigated via the molecular-dynamics method and NMR spectroscopy. It is shown that the orientational mobility of internal groups of the lysine dendrimers is lower than that of terminal groups, in agreement with the data available for flexible-chain dendrimers. Changes in correlation times with temperature are well described by the Arrhenius dependence. At the same time, the orientational mobility of internal groups in the lysine dendrimers depends on the generation number. This behavior is different from that of flexible-chain dendrimers, in which the mobility of internal groups is the same for dendrimers of different generations.

Average relaxation time of internal spectrum for carbosilane dendrimers: Nuclear magnetic resonance studies

A new theoretical description of the interior mobility of carbosilane dendrimers has been tested. Experiments were conducted using measurements of the (1)H NMR spin-lattice relaxation time, T(1H), of two-, three- and four-generation carbosilane dendrimers with three different types of terminal groups in dilute chloroform solutions. Temperature dependences of the NMR relaxation rate, 1/T(1H), were obtained for the internal CH(2)-groups of the dendrimers in the range of 1/T(1H) maximum, allowing us to directly evaluate the average time of the internal spectrum for each dendrimer. It was found that the temperature of 1/T(1H) maximum is practically independent of the number of generations, G; therefore, the theoretical prediction was confirmed experimentally. In addition, the average time of the internal spectrum of carbosilane dendrimers was found to be near 0.2 ns at room temperature, and this value correlates well with the values previously obtained for other dendrimer structures using other experimental techniques.

Temperature dependence of the structure of a carbosilane dendrimer with terminal cyanobiphenyl groups: Molecular-dynamics simulation

The molecular-dynamics simulation of the structure and molecular mobility of an individual macromolecule of a fourth-generation carbosilane dendrimer with terminal cyanobiphenyl groups in a highly diluted chloroform solution in the range 213–323 K is performed. Upon a change in temperature, the dendrimer undergoes structural rearrangement that depends on the ability of terminal segments to penetrate into the dendrimer. At temperatures close to the boiling point of the solvent, aliphatic spacers of terminal segments can penetrate deep into the dendrimer. As temperature decreases, the terminal segments are grouped only on the surface of the molecule; this leads to a 45% increase in the number of solvent molecules in the treelike part of the macromolecule. These results make it possible to give a new interpretation of temperature effects previously observed in NMR experiments for dilute solutions of these macromolecules.

Local orientational mobility in regular hyperbranched polymers

We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation forms of the complex dielectric susceptibility. We show that the dynamic behavior of single segments depends on their remoteness from the periphery rather than on the size of the whole macromolecule. Remarkably, the dynamics of the core segments (which are most remote from the periphery) shows a scaling behavior that differs from the dynamics obtained after structural average. We analyze the most relevant processes of single segment motion and provide an analytic approximation for the corresponding relaxation times. Furthermore, we describe an iterative method to calculate the orientational dynamics in the case of very large macromolecular sizes.