Dynamics of internally functionalized dendrimers

Influence of the Chemical Structure on the Mechanical Relaxation of Dendrimers

The rheological properties of macromolecules represent one of the fundamental features of polymer systems which expand the possibilities of using and developing new materials based on them. In this work, we studied the shear-stress relaxation of the second generation PAMAM and PPI dendrimer melts by atomistic molecular dynamics simulation. The time dependences of relaxation modulus G(t) and the frequency dependences of the storage G'(ω) and loss G″(ω) moduli were obtained. The results were compared with the similar dependences for the polycarbosilane (PCS) dendrimer of the same generation. The chemical structure of the dendrimer segments has been found to strongly influence their mechanical relaxation. In particular, it has been shown that hydrogen bonding in PAMAM dendrimers leads to an entanglement of macromolecules and the region is observed where G'(ω) > G″(ω). This slows down the mechanical relaxation and rotational diffusion of macromolecules. We believe that our comprehensive research contributes to the systematization of knowledge about the rheological properties of dendrimers.

Mechanical relaxation of functionalized carbosilane dendrimer melts

Functionalizing the internal structure of classical dendrimers is a new way of tailoring their properties. Using atomistic molecular dynamics simulations, we investigate the rheological behavior of functionalized dendrimer (FD) melts obtained by modifying the branching of carbosilane dendrimers (CSD). The time (relaxation modulus G(t)) and frequency (storage G' and loss G'' moduli) dependencies of the dynamic modulus are obtained. Fourth generation FD melts present a region where G' > G''. In contrast, their non-functionalized counterparts (i.e., classical dendrimers with regular branching) do not show such a region. The comparative analysis of FD and CSD suggests that the internal densification due to functionalization prevents the penetration of branches and causes FD to behave like colloidal particles in a crowded environment. Since CSD have no special interactions, we expect that this effect will be common for other dendrimer macromolecules.

Comparison of Structure and Local Dynamics of Two Peptide Dendrimers with the Same Backbone but with Different Side Groups in Their Spacers

In this paper, we perform computer simulation of two lysine-based dendrimers with Lys-2Lys and Lys-2Gly repeating units. These dendrimers were recently studied experimentally by NMR (Sci. Reports, 2018, 8, 8916) and tested as carriers for gene delivery (Bioorg. Chem., 2020, 95, 103504). Simulation was performed by molecular dynamics method in a wide range of temperatures. We have shown that the Lys-2Lys dendrimer has a larger size but smaller fluctuations as well as lower internal density in comparison with the Lys-2Gly dendrimer. The Lys-2Lys dendrimer has larger charge but counterions form more ion pairs with its NH 3 + groups and reduce the bare charge and zeta potential of the first dendrimer more strongly. It was demonstrated that these differences between dendrimers are due to the lower flexibility and the larger charge (+2) of each 2Lys spacers in comparison with 2Gly ones. The terminal CH 2 groups in both dendrimers move faster than the inner CH 2 groups. The calculated temperature dependencies of the spin-lattice relaxation times of these groups for both dendrimers are in a good agreement with the experimental results obtained by NMR.

Lysine-based dendrimer with double arginine residues

Due to their well-defined structure, multivalency, biocompatibility, and low toxicity, lysine dendrimers can be used as safe and efficient nanocarriers for drug and gene delivery. One useful strategy for improving the gene delivery properties of dendrimers is modification with arginine amino acid (Arg) residues. Incorporation of Arg residues could be favorable for the enhancement in transfection efficiency of lysine based dendrimers. In this work, we have synthesized a new second-generation poly-l-lysine dendrimer with repeating units containing two linear Arg residues between neighboring lysine branching points (Lys-2Arg dendrimer) and studied its physicochemical properties. We confirmed the structure of Lys-2Arg dendrimer using various one- and two-dimensional ¹H and ¹³C NMR spectroscopy methods. Comparison of T_1H relaxation data for Lys-2Arg and Lys-2Lys dendrimers showed that the replacement of double Lys residues with double Arg residues resulted in a sharp decrease in the mobility of methylene groups in side segments and in the main chain of ε-Lys inner segments. We suggest that this unexpected effect is caused by a guanidine–guanidine pairing effect in water, which leads to entanglements between dendrimer branches.

A new poly-l-lysine dendrimer with arginine residues was synthesized and its structure and physical–chemical properties were analyzed by NMR spectroscopy.

Dynamics of a Polymer Network Modeled by a Fractal Cactus

In this paper, we focus on the relaxation dynamics of a polymer network modeled by a fractal cactus. We perform our study in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. By performing real-space renormalization transformations, we determine analytically the whole eigenvalue spectrum of the connectivity matrix, thereby rendering possible the analysis of the Rouse-dynamics at very large generations of the structure. The evaluation of the structural and dynamical properties of the fractal network in the Rouse type-approach reveals that they obey scaling and the dynamics is governed by the value of spectral dimension. In the Zimm-type approach, the relaxation quantities show a strong dependence on the strength of the hydrodynamic interaction. For low and medium hydrodynamic interactions, the relaxation quantities do not obey power law behavior, while for slightly larger interactions they do. Under strong hydrodynamic interactions, the storage modulus does not follow power law behavior and the average displacement of the monomer is very low. Remarkably, the theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results from the literature.

NMR studies of excluded volume interactions in peptide dendrimers

Peptide dendrimers are good candidates for diverse biomedical applications due to their biocompatibility and low toxicity. The local orientational mobility of groups with different radial localization inside dendrimers is important characteristic for drug and gene delivery, synthesis of nanoparticles, and other specific purposes. In this paper we focus on the validation of two theoretical assumptions for dendrimers: (i) independence of NMR relaxations on excluded volume effects and (ii) similarity of mobilities of side and terminal segments of dendrimers. For this purpose we study 1H NMR spin-lattice relaxation time, T1H, of two similar peptide dendrimers of the second generation, with and without side fragments in their inner segments. Temperature dependences of 1/T1H in the temperature range from 283 to 343 K were measured for inner and terminal groups of the dendrimers dissolved in deuterated water. We have shown that the 1/T1H temperature dependences of inner groups for both dendrimers (with and without side fragments) practically coincide despite different densities of atoms inside these dendrimers. This result confirms the first theoretical assumption. The second assumption is confirmed by the 1/T1H temperature dependences of terminal groups which are similar for both dendrimers.

Dynamics of networks in a viscoelastic and active environment

We investigate the dynamics of fractals and other networks in a viscoelastic and active environment. The viscoelastic dynamics is modeled based on the generalized Langevin equation, where the activity is introduced to it by means of the exponentially correlated noise. The intramolecular interactions are taken into account by the bead-spring picture. The microscopic connectivity (studied in the form of Vicsek fractals, of dual Sierpiński gaskets, of NT_D trees, and of a family of deterministic small-world networks) reveals itself in the multiscale monomeric dynamics, which shows vastly different behaviors in the active and passive baths. In particular, the dynamics under active forces leads to a swelling that is characterized through power laws which are not present in the passive case. In all cases, the dynamics reflects the broad scaling behavior of the density of states and not necessarily the maximal relaxation time of the structures in a passive bath, as it is exemplified on the NT_D trees.

Dynamics of a Complex Multilayer Polymer Network: Mechanical Relaxation and Energy Transfer

In this paper, we focus on the mechanical relaxation of a multilayer polymer network built by connecting identical layers that have, as underlying topologies, the dual Sierpinski gasket and the regular dendrimer. Additionally, we analyze the dynamics of dipolar energy transfer over a system of chromophores arranged in the form of a multilayer network. Both dynamical processes are studied in the framework of the generalized Gaussian structure (GSS) model. We develop a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multilayer network can be determined iteratively, thereby rendering possible the analysis of the dynamics of networks consisting of a large number of layers. This fact allows us to study in detail the crossover from layer-like behavior to chain-like behavior. Remarkably, we highlight the existence of two bulk-like behaviors. The theoretical findings with respect to the decomposition of the intermediate domain of the relaxation quantities, as well as the chain-like behavior, are well supported by experimental results.

Marginally compact fractal trees with semiflexibility

We study marginally compact macromolecular trees that are created by means of two different fractal generators. In doing so, we assume Gaussian statistics for the vectors connecting nodes of the trees. Moreover, we introduce bond-bond correlations that make the trees locally semiflexible. The symmetry of the structures allows an iterative construction of full sets of eigenmodes (notwithstanding the additional interactions that are present due to semiflexibility constraints), enabling us to get physical insights about the trees' behavior and to consider larger structures. Due to the local stiffness, the self-contact density gets drastically reduced.

Investigation of Melts of Polybutylcarbosilane Dendrimers by 1H NMR Spectroscopy

Melts of polybutylcarbosilane (PBC) dendrimers from third (G3) up to sixth (G6) generations are investigated by ¹H NMR spectroscopy in a wide temperature range up to 493 K. At room temperature, NMR spectra of G3-G5 dendrimers exhibit resolved, solution-like spectra (“liquid” phase). In contrast, the spectrum of the G6 dendrimer is characterized by a single unresolved broad line at whole temperature range, which supports the presence of an anomalous phase state of G6 at temperatures higher than glass transition temperature. For the first time, an unexpected transition of G5 dendrimer from a molecular liquid state to an anomalous state/phase upon temperature increase has been detected using NMR data. Specifically, an additional wide background line appears in the G5 spectrum above 473 K, and this line corresponds to a G5 state characterized by restricted molecular mobility, i.e., a state similar to the “anomalous” phase of G6 melt. The fraction of the G5 dendrimers in “anomalous” phase at 493 K is approximately 40%. Analysis of the spectral shapes suggests that changes in the G5 dendrimers are reversible with temperature.

Dynamics of a Polymer Network Based on Dual Sierpinski Gasket and Dendrimer: A Theoretical Approach

In this paper we focus on the relaxation dynamics of a multihierarchical polymer network built through the replication of the dual Sierpinski gasket in the form of a regular dendrimer. The relaxation dynamics of this multihierarchical structure is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, we show a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multihierarchical structure can be determined iteratively, thereby rendering possible the analysis of the Rouse-dynamics at very large generations. Remarkably, the general picture that emerges from both approaches, even though we have a mixed growth algorithm and the monomers interactions are taken into account specifically to the adopted approach, is that the multihierarchical structure preserves the individual relaxation behaviors of its constituent components. The theoretical findings with respect to the splitting of the intermediate domain of the relaxation quantities are well supported by experimental results.

Marginally compact hyperbranched polymer trees

Assuming Gaussian chain statistics along the chain contour, we generate by means of a proper fractal generator hyperbranched polymer trees which are marginally compact. Static and dynamical properties, such as the radial intrachain pair density distribution ρ_pair(r) or the shear-stress relaxation modulus G(t), are investigated theoretically and by means of computer simulations. We emphasize that albeit the self-contact density diverges logarithmically with the total mass N, this effect becomes rapidly irrelevant with increasing spacer length S. In addition to this it is seen that the standard Rouse analysis must necessarily become inappropriate for compact objects for which the relaxation time τ_p of mode p must scale as τ_p ∼ (N/p)^5/3 rather than the usual square power law for linear chains.