We present a theoretical study of polymernetworks, 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 f c of the core. The GD’s cover wide classes of macromolecules, such as the “classical” dendrimers (f c =f ), the dendritic wedges (f c =f−1), and the macromolecular stars (f c >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 polymernetworks. 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 M cr , the number of connections between the neighboring DBB’s, increases. This effect may be understood due to the exclusion of the longest DBB relaxation times from the spectrum of the network, given that the additional connections hinder the mobility of the peripheral DBB branches. We expect that such effects may be readily observed through appropriate mechanical experiments.

We investigate the effects of the range of adsorption potential on the equilibrium behavior of a single polymer chain end-attached to a solid surface. The exact analytical theory for ideal lattice chains interacting with a planar surface via a box potential of depth $U$ and width $W$ is presented and compared to continuum model results and to Monte Carlo (MC) simulations using the pruned-enriched Rosenbluth method for self-avoiding chains on a simple cubic lattice. We show that the critical value ${U}_{c}$ corresponding to the adsorption transition scales as ${W}^{$-${}1/$\nu${}}$, where the exponent $$\nu${}=1/2$ for ideal chains and $$\nu${}$\approx${}3/5$ for self-avoiding walks. Lattice corrections for finite $W$ are incorporated in the analytical prediction of the ideal chain theory ${U}_{c}$\approx${}(\frac{{$\pi${}}^{2}}{24}){(W+1/2)}^{$-${}2}$ and in the best-fit equation for the MC simulation data ${U}_{c}=0.585{(W+1/2)}^{$-${}5/3}$. Tail, loop, and train distributions at the critical point are evaluated by MC simulations for $1$\le${}W$\le${}10$ and compared to analytical results for ideal chains and with scaling theory predictions. The behavior of a self-avoiding chain is remarkably close to that of an ideal chain in several aspects. We demonstrate that the bound fraction $$\theta${}$ and the related properties of finite ideal and self-avoiding chains can be presented in a universal reduced form: $$\theta${}(N,U,W)=$\theta${}(N{U}_{c},U/{U}_{c})$. By utilizing precise estimations of the critical points we investigate the chain length dependence of the ratio of the normal and lateral components of the gyration radius. Contrary to common expectations this ratio attains a limiting universal value $$\langle${}{R}_{g$\perp${}}^{2}$\rangle${}/$\langle${}{R}_{g$\parallel${}}^{2}$\rangle${}=0.320\ifmmode\pm\else\textpm\fi{}0.003$ only at $N$\sim${}5000$. Finite-$N$ corrections for this ratio turn out to be of the opposite sign for $W=1$ and for $W$\ge${}2$. We also study the $N$ dependence of the apparent crossover exponent ${$\phi${}}_{\mathrm{eff}}(N)$. Strong corrections to scaling of order ${N}^{$-${}0.5}$ are observed, and the extrapolated value $$\phi${}=0.483\ifmmode\pm\else\textpm\fi{}0.003$ is found for all values of $W$. The strong correction to scaling effects found here explain why for smaller values of $N$, as used in most previous work, misleadingly large values of ${$\phi${}}_{\mathrm{eff}}(N)$ were identified as the asymptotic value for the crossover exponent.

Spin–lattice NMR relaxation rate vs. reversed temperature for terminal and inner CH ₂ groups of n = 2 and 4 generation poly- l -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.