Binding mechanisms in dendrimer-surfactant complexes.

Molecular dynamics simulations were employed to investigate the impact of interactions between dendritic polyeclectrolytes and amphiphilic surfactants on the supramolecular complex formation. We recognize two crucial parameters that govern association of surfactants within dendrimers: surfactant hydrophobicity, ε^{*}, and dendrimer generation, G. We find that depending on the values of ε^{*} and G encapsulation of surfactants by dendrimers is either noncooperative or cooperative. The noncooperative binding is characterized by absorption of surfactants as unimers, whereas in cooperative binding absorption of unimers is followed by aggregate formation through hydrophobic attractions between the surfactant tails. Our results provide guidelines for controlled encapsulation of guest molecules in dendrimer-based guest-host complexes.

Spatial segregation of mixed-sized counterions in dendritic polyelectrolytes.

Langevin dynamics simulations are utilized to study the structure of a dendritic polyelectrolyte embedded in two component mixtures comprised of conventional (small) and bulky counterions. We vary two parameters that trigger conformational properties of the dendrimer: the reduced Bjerrum length, [Formula: see text], which controls the strength of electrostatic interactions and the number fraction of the bulky counterions, [Formula: see text], which impacts on their steric repulsion. We find that the interplay between the electrostatic and the counterion excluded volume interactions affects the swelling behavior of the molecule. As compared to its neutral counterpart, for weak electrostatic couplings the charged dendrimer exists in swollen conformations whose size remains unaffected by [Formula: see text]. For intermediate couplings, the absorption of counterions into the pervaded volume of the dendrimer starts to influence its conformation. Here, the swelling factor exhibits a maximum which can be shifted by increasing [Formula: see text]. For strong electrostatic couplings the dendrimer deswells correspondingly to [Formula: see text]. In this regime a spatial separation of the counterions into core-shell microstructures is observed. The core of the dendrimer cage is preferentially occupied by the conventional ions, whereas its periphery contains the bulky counterions.

Charged Dendrimers with Finite-Size Counterions.

We report on the structure of dendritic polyelectrolytes accompanied by counterions in a good, salt-free, implicit solvent using Langevin dynamics simulations and a Flory-type approach. Our focus is on the modification of charged dendrimer conformations via the strength of electrostatic interactions and the counterion excluded volume. We study the effects caused by charges by varying the reduced Bjerrum length, λB*, between the extremes of weak and strong electrostatic interactions. The counterion excluded volume was controlled by the size of ions. We investigate counterions ranging from conventional ones, with the size comparable to the monomer size, to bulky ions. Our results indicate that, as compared to neutral dendrimers, dendritic polyelectrolytes exist in swollen conformations, and the degree of swelling changes non-monotonically with increasing λB*. For weak electrostatic couplings, counterion density within dendrimers is minor and their radius of gyration subtly exceeds the size of neutral dendrimers. For intermediate electrostatic couplings, Coulomb attraction between opposite charges promotes absorption of ions into dendrimers' pervaded volume and counterion condensation on charged monomers. As a result, counterion density inside dendrimers abruptly increases and the ionic size starts to play a crucial role. In this regime, we observe that swelling of dendrimers reaches its maximum and is more pronounced for bulky counterions. For strong electrostatic couplings, complete condensation of conventional counterions proceeds, whereas for bulky ions condensation remains partial. In this regime, dendrimers deswell. In particular, in the presence of conventional ions, dendrimers collapse into globules, while, for bulky counterions, deswelling is suppressed.

Dendritic polyelectrolytes as seen by the Poisson-Boltzmann-Flory theory.

G3-G9 dendritic polyelectrolytes accompanied by counterions are investigated using the Poisson-Boltzmann-Flory theory. Within this approach we solve numerically the Poisson-Boltzmann equation for the mean electrostatic potential and minimize the Poisson-Boltzmann-Flory free energy with respect to the size of the molecules. Such a scheme enables us to inspect the conformational and electrostatic properties of the dendrimers in equilibrium based on their response to varying the dendrimer generation. The calculations indicate that the G3-G6 dendrimers exist in the polyelectrolyte regime where absorption of counterions into the volume of the molecules is minor. Trapping of ions in the interior region becomes significant for the G7-G9 dendrimers and signals the emergence of the osmotic regime. We find that the behavior of the dendritic polyelectrolytes corresponds with the degree of ion trapping. In particular, in both regimes the polyelectrolytes are swollen as compared to their neutral counterparts and the expansion factor is maximal at the crossover generation G7.

Dendritic polyelectrolytes revisited through the Poisson-Boltzmann-Flory theory and the Debye-Hückel approximation.

The properties of a dendritic polyelectrolyte in equilibrium with a reservoir of monovalent salts are investigated using the cell model and the Poisson-Boltzmann-Flory theory. Within this approach we use the Debye-Hückel approximation to solve the Poisson-Boltzmann equation and minimize the semi-grand potential of the system with respect to the size of the molecule which enables us to inspect its conformations as well as the electric field, the ionic density profile, the overall charge density, the effective charge of the dendrimer and the osmotic pressure based on their response to the salt concentration and the dendrimer charge. The model predicts pronounced trapping of salt ions, a local charge neutrality and a zero electric field in the volume of the molecule as well as oscillations of the density profiles and the electric field in the vicinity of the dendrimer-bulk interface. As a result of ion trapping and screening of Coulomb interactions monovalent salts are found to have a minor effect on the size of the dendrimer. Specifically, the dendrimer exists in slightly swollen states as compared to the neutral molecule which indicates that the conformational properties of the polyelectrolyte depend weakly on monovalent salts. These observations harmonise with the equilibrium behavior of the dendrimer pressure, the internal pressure and the bulk pressure, respectively.

Dendrimer solutions: a Monte Carlo study.

We study the conformational properties of dendrimers with flexible spacers in solutions over a wide range of concentrations from dilute solutions to melts. By combining large scale computer simulations using the bond fluctuation model with scaling arguments we identify the semi-dilute regime of dendrimers which is controlled by the concentration behavior of the linear spacers. Associated with this observation we find that the decrease in the size of flexible dendrimers is accompanied by increasing interpenetration between the molecules with increasing concentration of the solution. In the melt state we show that the size of individual dendrimers follows the scaling prediction for isolated dendrimers at the θ-point rather than that of collapsed dendrimers. The pair correlation functions between the centers of dendrimers indicate that for short spacers dendrimer solutions retain the morphological characteristics of simple liquids. For long spacers the functions reveal high penetration of neighboring dendrimers in the melt state. Our studies show that flexible dendrimers in solution can be understood with arguments similar to those of linear polymers. The role of generation is to influence the particular form of the crossover-function.

Adsorption of branched and dendritic polymers onto flat surfaces: a Monte Carlo study.

Using Monte Carlo simulations based on the bond fluctuation model we study the adsorption of starburst dendrimers with flexible spacers onto a flat surface. The calculations are performed for various generation number G and spacer length S in a wide range of the reduced temperature τ as the measure of the interaction strength between the monomers and the surface. Our simulations indicate a two-step adsorption scenario. Below the critical point of adsorption, τc, a weakly adsorbed state of the dendrimer is found. Here, the dendrimer retains its shape but sticks to the surface by adsorbed spacers. By lowering the temperature below a spacer-length dependent value, τ*(S) < τc, a step-like transition into a strongly adsorbed state takes place. In the flatly adsorbed state the shape of the dendrimer is well described by a mean field model of a dendrimer in two dimensions. We also performed simulations of star-polymers which display a simple crossover-behavior in full analogy to linear chains. By analyzing the order parameter of the adsorption transition, we determine the critical point of adsorption of the dendrimers which is located close to the critical point of adsorption for star-polymers. While the order parameter for the adsorbed spacers displays a critical crossover scaling, the overall order parameter, which combines both critical and discontinuous transition effects, does not display simple scaling. The step-like transition from the weak into the strong adsorbed regime is confirmed by analyzing the shape-anisotropy of the dendrimers. We present a mean-field model based on the concept of spacer adsorption which predicts a discontinuous transition of dendrimers due to an excluded volume barrier. The latter results from an increased density of the dendrimer in the flatly adsorbed state which has to be overcome before this state is thermodynamically stable.

Monte Carlo simulations of charged dendrimer-linear polyelectrolyte complexes and explicit counterions.

We study complexes composed of one dendrimer of generation G = 4 (G4 dendrimer) with N(t) = 32 charged terminal groups and an oppositely charged linear polyelectrolyte accompanied by neutralizing counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. In our study both the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature τ and the chain length N(ch) as the main simulation parameters. Our calculations indicate that there exist three temperature ranges that determine the behavior of such complexes. At τ(complex) stable charged dendrimer-linear polyelectrolyte complexes are formed first, which are subsequently accompanied by selective counterion localization within the complex interior at τ(loc) ≤ τ(complex), and counterion condensation as temperature is further decreased below τ(cond) < τ(loc). In particular, we observe that condensation takes place exclusively on the excess charges in the complex and thus no condensation is observed at the compensation point (N(ch) = N(t)), irrespective of τ. For N(ch) ≠ N(t) the complex is overally charged. Furthermore, we discuss the size and structure of the dendrimer and the linear polyelectrolyte within the complex, as well as spatial distributions of monomers and counterions. Conformations of the chain in the bound state are analysed in terms of loops, trains, and tails.

Adsorption of random copolymers from a melt onto a solid surface: Monte Carlo studies.

We study the behavior of random AB-copolymer melts near a selective surface. We consider the case where the copolymers do not display phase segregation behavior in the bulk but the surface is strongly selective for the A-component and the probability of finding an A-monomer along the chain is p<<1. Using self-consistent field theory and scaling arguments, we discuss some aspects of conformational rearrangements and composition selection in the surface layer. For strong selectivity we discuss the formation of a polydisperse brush on the surface. Next, we consider selection mechanisms of chains and sequences of A-species in the surface layer. We used the bond-fluctuation method to simulate copolymer melts at different values of the surface selectivity. Several aspects of the surface layer are analyzed, such as the composition profiles, chemical composition of chains on the surface, chain extension, and dynamics. We find evidence for conformational rearrangements in the surface layer according to the polydisperse brush model, as well as enrichment of A-monomers in the adosorbed chains, stretching of chains in the direction perpendicular to the surface, and selection of multiple A-sequences. Slight but systematic variation of the properties of surface layer at long simulation times indicates that selection processes require very long time scales as expected from theoretical arguments.

Adsorption of random copolymers by a selective layer: Monte Carlo studies.

We use scaling arguments and computer simulations to investigate the adsorption of symmetric AB-random copolymers (RC) from a diluted solution onto a selective ABA layer. Depending on the ratio between the layer thickness and the size of excess blobs, d/xi, three regimes of RC adsorption are predicted. For large values of the layer thickness RC adsorption can be understood as adsorption on two selective interfaces where sequences of RC chains form bridges. When the layer thickness is of the order of xi, excess blobs are trapped in the layer and localize the copolymer chain strongly. If the layer thickness is very small a weak adsorption scenario is predicted where large loops are formed outside the layer. Our simulations using the bond fluctuation model are in good agreement with the scaling predictions. We show that chain properties display non-monotonous behavior with respect to the layer thickness with optimal values for d approximately xi. In particular, we discuss simulation results for density profiles, statistics of bridges, loops and tails formed by the adsorbed chains, as well as for the adsorption order parameter and free energy.