The conformational behavior of a single, intrinsically flexible, weakly charged polyelectrolyte chain in poor solvent is analyzed by extensive computer simulations combining Monte Carlo and molecular dynamics techniques. After determining the ϑ point for the charge-free case, we focus on the weak screening limit, corresponding to low salt concentration in the solution. We study the dependence on both the solvent strength, characterized by the relative deviation from the ϑ point, τ, and the fraction of charged monomers in the chain, which is effectively tuned by varying the Coulomb interaction parameter. The conformations are discussed in terms of global properties (such as the end-to-end distance, the inertia tensor components, etc.) and functions revealing more detailed information, such as the density distribution around the center of mass and the structure factor. For chains in the ϑ regime our data confirm the picture of a string of electrostatic blobs. For poorer solvents (up to τ = 0.4) we observe, upon increasing the intrachain Coulomb repulsion, a splitting of the spherical globule into a dumbbell-type structure, accompanied by a sharp increase in the chain's gyration radius. For sufficiently large τ, a further splitting is observed as well. Such a “necklace globule” (a sequence of transitions) had been predicted by Dobrynin, Rubinstein and Obukhov (Macromolecules 1996, 29, 2974), with a nontrivial scaling of the gyration radius with chain length and interaction parameters, which is confirmed by our data. By means of a scaling analysis, we argue that the transitions can be interpreted as thermodynamic first-order phase transformations, when taking the appropriate thermodynamic limit, which implies a scaling of the electrostatic coupling with inverse chain length.

Dynamic properties of dilute solutions of neutral and charged dendrimers with explicit excluded-volume, electrostatic, and hydrodynamic interactions have been investigated by Brownian dynamics simulation. Three different types of motions in dendrimers up to g = 5 generations have been considered:  the motion of a dendrimer as a whole; the size and shape fluctuations (pulsations); the local reorientations of the individual monomers. The influence of the excluded-volume, electrostatic, and hydrodynamic interactions on these motions has been studied. The characteristic relaxation times have been compared with the theoretical predictions of the Rouse and Zimm models. The self-diffusion of a dendrimer can be described with the help of the preaveraged Zimm approach, and a dendrimer may be considered as an impenetrable sphere with the hydrodynamic radius R h. For both neutral and charged dendrimers the hydrodynamic radius is smaller than the gyration radius R g. The dynamics of the size fluctuations for a dendrimer with rigid spacers differs significantly from the theoretical predictions for a dendrimer with flexible spacers. The relaxation of these fluctuations is weakly sensitive to the presence of the hydrodynamic interactions, and the behavior of a dendrimer is close to that of an elastic body in a viscous medium. The local orientational mobility of individual monomers is significantly influenced by the ionization of the terminal groups.

Brownian dynamics computer simulations have been carried out of complexes formed by charged dendrimers and oppositely charged linear polymer chains of different degree of polymerization N ch. Bead−rod freely jointed models in the Debye−Hückel approximation without hydrodynamic interactions have been considered. Mean-square radii of gyration together with the radial density distribution functions have been calculated separately for a complex, a dendrimer, and a linear chain in a complex. The mean-square radius of gyration, the different monomer radial distribution functions, and the static structure factor for a dendrimer in a complex with long enough chains are very close to those for a single neutral dendrimer. The monomers of the linear chains with N ch equal to the number of the dendrimer's terminal charged groups are located very close to these terminal groups. For longer chains the total number of the chain monomers adsorbed onto a dendrimer exceeds the number that is necessary for a dendrimer neutralization, and the overcharging phenomenon is observed. Comparison with predictions of the correlation theory has been carried out.

Conformational properties of neutral and charged dendrimers in dilute solutions of different quality have been investigated by a mean-field analytical approach and by Brownian dynamics (BD) computer simulation for systems up to generation six. Radial monomer distribution and mass distribution functions, radii of gyration, and structure factors have been studied as functions of solvent quality, effective charge of the terminal groups, and Debye screening radius. For high-generation dendrimers BD simulations show that the dendrimers hardly fluctuate. Swelling of both neutral and charged dendrimers is reasonably described by a generalized Flory mean-field theory in which the two-body virial term is replaced by the sum of the excluded-volume and two-body attraction terms. A non-Gaussian term taking into account the finite extensibility of spacers and a Coulomb term in the form of the Debye-Hu ¨ckel approximation have been included as well. The θ-point for a single dendrimer molecule is defined as the characteristic energy of the excluded-volume interactions when the linear expansion factor R is equal to unity. In contrast to linear polymers, the θ-point defined in such way is different from that calculated as the characteristic energy when scaling relation for a good-solvent conditions stops to be valid. Dendritic terminal groups are distributed through the whole volume of the molecule, but the maximum of this distribution is shifted toward the periphery with increase of Debye screening radius and effective charge of a terminal group. It is shown that fractal dimension of a neutral dendrimer depends on both its generation number and spacer length.

Document VersionPublisher's PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. 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: ͑i͒ the rotation of the dendrimer as a whole, ͑ii͒ the rotation of the dendrimer's branch originated from a given segment, and ͑iii͒ 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.

NMR relaxation experiments are widely used to investigate the local orientation mobility in dendrimers. In particular, the NMR method allows one to measure the spin-lattice relaxation rate, 1/T1, which is connected with the orientational autocorrelation function (ACF) of NMR active groups. We calculate the temperature (Θ) and frequency (ω) dependences of the spin-lattice NMR relaxation rates for segments and NMR active CH2 groups in poly-L-lysine (PLL) dendrimers in water, on the basis of full-atomic molecular dynamics simulations. It is shown that the position of the maximum of 1/T1(ω) depends on the location of the segments inside the dendrimer. This dependence of the maximum is explained by the restricted flexibility of the dendrimer. Such behavior has been predicted recently by the analytical theory based on the semiflexible viscoelastic model. The simulated temperature dependences of 1/T1 for terminal and inner groups in PLL dendrimers of n = 2 and n = 4 generations dissolved in water are in good agreement with the NMR experimental data, which have been obtained for these systems previously by us. It is shown that in the case of PLL dendrimers, the traditional procedure of the interpretation of NMR experimental data - when smaller values of 1/T1 correspond to higher orientation mobility - is applicable to the whole accessible frequency interval only for the terminal groups. For the inner groups, this procedure is valid only at low frequencies.

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.

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