Simulations of Terminally Charged Dendrimers with Flexible Spacer Chains and Explicit Counterions

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.

Characterization of Monte Carlo Dynamic/Kinetic Properties of Local Structure in Bond Fluctuation Model of Polymer System

We report the results of the characterization of local Monte Carlo (MC) dynamics of an equilibrium bond fluctuation model polymer matrix (BFM), in time interval typical for MC simulations of non-linear optical phenomena in host-guest systems. The study contributes to the physical picture of the dynamical aspects of quasi-binary mosaic states characterized previously in the static regime. The polymer dynamics was studied at three temperatures (below, above and close to the glass transition), using time-dependent generalization of the static parameters which characterize local free volume and local mobility of the matrix. Those parameters play the central role in the kinetic MC model of host-guest systems. The analysis was done in terms of the probability distributions of instantaneous and time-averaged local parameters. The main result is the characterization of time scales characteristic of various local structural processes. Slowing down effects close to the glass transition are clearly marked. The approach yields an elegant geometric criterion for the glass transition temperature. A simplified quantitative physical picture of the dynamics of guest molecules dispersed in BFM matrix at low temperatures offers a starting point for stochastic modeling of host-guest systems.

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.

Modeling of Nonlinear Optical Phenomena in Host-Guest Systems Using Bond Fluctuation Monte Carlo Model: A Review

We review the results of Monte Carlo studies of chosen nonlinear optical effects in host-guest systems, using methods based on the bond-fluctuation model (BFM) for a polymer matrix. In particular, we simulate the inscription of various types of diffraction gratings in degenerate two wave mixing (DTWM) experiments (surface relief gratings (SRG), gratings in polymers doped with azo-dye molecules and gratings in biopolymers), poling effects (electric field poling of dipolar molecules and all-optical poling) and photomechanical effect. All these processes are characterized in terms of parameters measured in experiments, such as diffraction efficiency, nonlinear susceptibilities, density profiles or loading parameters. Local free volume in the BFM matrix, characterized by probabilistic distributions and correlation functions, displays a complex mosaic-like structure of scale-free clusters, which are thought to be responsible for heterogeneous dynamics of nonlinear optical processes. The photoinduced dynamics of single azopolymer chains, studied in two and three dimensions, displays complex sub-diffusive, diffusive and super-diffusive dynamical regimes. A directly related mathematical model of SRG inscription, based on the continuous time random walk (CTRW) formalism, is formulated and studied. Theoretical part of the review is devoted to the justification of the a priori assumptions made in the BFM modeling of photoinduced motion of the azo-polymer chains.

Formation of Monolithic Ion-Selective Transport Media Based on "Click" Cross-Linked Hyperbranched Polyglycerol

In the emerging field of organic bioelectronics, conducting polymers and ion-selective membranes are combined to form resistors, diodes, transistors, and circuits that transport and process both electronic and ionic signals. Such bioelectronics concepts have been explored in delivery devices that translate electronic addressing signals into the transport and dispensing of small charged biomolecules at high specificity and spatiotemporal resolution. Manufacturing such "iontronic" devices generally involves classical thin film processing of polyelectrolyte layers and insulators followed by application of electrolytes. This approach makes miniaturization and integration difficult, simply because the ion selective polyelectrolytes swell after completing the manufacturing. To advance such bioelectronics/iontronics and to enable applications where relatively larger molecules can be delivered, it is important to develop a versatile material system in which the charge/size selectivity can be easily tailormade at the same time enabling easy manufacturing of complex and miniaturized structures. Here, we report a one-pot synthesis approach with minimal amount of organic solvent to achieve cationic hyperbranched polyglycerol films for iontronics applications. The hyperbranched structure allows for tunable pre multi-functionalization, which combines available unsaturated groups used in crosslinking along with ionic groups for electrolytic properties, to achieve a one-step process when applied in devices for monolithic membrane gel formation with selective electrophoretic transport of molecules.

Charge and hydration structure of dendritic polyelectrolytes: molecular simulations of polyglycerol sulphate

Macromolecules based on dendritic or hyperbranched polyelectrolytes have been emerging as high potential candidates for biomedical applications. Here we study the charge and solvation structure of dendritic polyglycerol sulphate (dPGS) of generations 0 to 3 in aqueous sodium chloride solution by explicit-solvent molecular dynamics computer simulations. We characterize dPGS by calculating several important properties such as relevant dPGS radii, molecular distributions, the solvent accessible surface area, and the partial molecular volume. In particular, as the dPGS exhibits high charge renormalization effects, we address the challenges of how to obtain a well-defined effective charge and surface potential of dPGS for practical applications. We compare implicit- and explicit-solvent approaches in our all-atom simulations with the coarse-grained simulations from our previous work. We find consistent values for the effective electrostatic size (i.e., the location of the effective charge of a Debye-Hückel sphere) within all the approaches, deviating at most by the size of a water molecule. Finally, the excess chemical potential of water insertion into dPGS and its thermodynamic signature are presented and rationalized.

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.

Dendritic polyelectrolytes as seen by the Poisson–Boltzmann–Flory theory

The conformational and electrostatic properties of dendritic polyelectrolytes accompanied by counterions are investigated using the Poisson–Boltzmann–Flory theory.

Computer Simulation Studies on the pH-Responsive Self-Assembly of Amphiphilic Carboxy-Terminated Polyester Dendrimers in Aqueous Solution

This paper investigates the pH-responsive self-assembly of an amphiphilic carboxyl-terminated polyester dendrimer, H20-COOH, in aqueous solution using the dissipative particle dynamics method. The electrostatic interactions were described by introducing the explicit interaction between the smeared charges on ionized polymer beads and the counterions. The results show that the self-assemblies could change from unimolecular micelles, microphase-separated small micelles, wormlike micelles, sheetlike micelles, and small vesicles to large vesicles with the decrease in the degree of ionization (α) of carboxylic acid groups. In addition, the detailed self-assembly mechanisms and the molecular packing models have also been disclosed for each self-assembly stages. Interestingly, the wormlike micelles are found to change from linear to branched when α decreases from 0.182 to 0.109. The current work might serve as a comprehensive understanding on the effect of carboxylic acid groups on the self-assembly behaviors of dendritic polymers.

Beware of phosphate: evidence of specific dendrimer–phosphate interactions

G5 PAMAM dendrimers interact with phosphate ions by forming H-bonds with tertiary amino groups in neutral medium.

Molecular dynamics simulation studies of hyperbranched polyglycerols and their encapsulation behaviors of small drug molecules

Computer simulation could disclose more details about the conformations of HPGs and their encapsulation behaviors of guest molecules.

From vesicles to micelles: microphase separation of amphiphilic dendrimer copolymers in a selective solvent

The microphase separation of amphiphilic dendrimer copolymers in a selective solvent with different excluded volume effects (αS) is investigated using three-dimensional real space self-consistent field theory. The morphological transition of disorder-to-order and order-to-order is observed by systematically regulating the excluded volume effect parameter, interaction parameter of block species, and the spacer length of the second generation of the dendrimer. The ordered segregates of the dendrimer solution are observed with a stronger excluded volume effect due to the strong depletion effect of solvent on the dendrimer. The relative magnitude between hydrophobic block B and hydrophilic block C is very important for microphase separation: when they are equal (NB = NC), a structural shift from vesicles to micelles has been found upon increasing the interaction parameter, and the region of disordered morphology is controlled by the interfacial free energy (Uint); when NB > NC, the vesicular morphologies overwhelmingly appear in the ordered region and then NC increases to close to NB, and the ordered aggregates take a shift from vesicles to micelles. Furthermore, the amphiphilic block C of the dendrimer is intended to enlarge to NC > NB, the micellar morphology is dominant in the ordered regime with a stronger excluded volume effect, which contributes to the decrease in the hydrophobic block repulsion that is affected by the decrease in the entropic free energy (-TS). The knowledge obtained from the microphase separation of dendrimer solution induced by the excluded volume effect of selective solvent is full of referential significance in understanding the morphological transition from vesicles to micelles for the amphiphile in the field of soft matter.

Charged dendrimers in trivalent salt solutions under the action of DC electric fields

The structural properties and electrophoretic mobility of charged dendrimers in 3:1 electrolyte solutions subjected to direct current electric fields are studied using molecular dynamics simulations. The simulated dendrimer size is studied in zero fields and found to scale as R(g) ∼ N(0.29). The dendrimers exhibit shape distortions when the applied electric field is larger than some critical value, which scales with the number of dendrimer monomers as E(z,crit) ∼ N(0.39(6)). Families of curves, such as the curves of the square of radius of gyration, the asphericity, the degree of prolateness, and the electrophoretic mobility of dendrimers, are shown to collapse to single, master curves in electric fields through appropriate scaling. This reflects the fractal characteristics of these systems. The density profile of the surface monomers and salt cations reveals two pronounced combination effects between the polarization of dendrimer complexes and stripping-off of the condensed salt cations from the dendrimer surface.

Deswelling and Electrolyte Dissipation in Free Diffusion of Charged PAMAM Dendrimers

The diffusion coefficient of charged PAMAM dendrimers was measured by fluorescence correlation spectroscopy in aqueous solution at submicromolar concentrations. The solution pH was varied for conditions ranging from a fully charged to neutral charge dendrimer to infer about electrostatic swelling in the dilute regime. The diffusion coefficient of generation G4 increases by as much as 20% between high and low charge conditions due to the combined effects of polyelectrolyte deswelling and loss of electrolyte dissipation. By taking into account the electrolyte dissipation in the friction factor, we have found that the observed deswelling corresponds to a change of hydrodynamic radius between 7-13% for generation G4 and about 12% for generation G7. Simulations of molecular dynamics of dendrimer G4 show that counterion uptake by the dendrimer structure upon full protonation induces a 16% increase of its radius of gyration. The change in dendrimer size is slightly larger than that previously reported from neutron scattering techniques, thereby suggesting that electrostatic swelling is more pronounced at dilute dendrimer concentration and low ionic strength. It is confirmed that even higher generations, which have more congested molecular structures, can experience some degree of conformational change in response to a change of the dendrimer charge density.

Theoretical and computational studies of dendrimers as delivery vectors

It is a great challenge for nanomedicine to develop novel dendrimers with maximum therapeutic potential and minimum side-effects for drug and gene delivery. As delivery vectors, dendrimers must overcome lots of barriers before delivering the bio-agents to the target in the cell. Extensive experimental investigations have been carried out to elucidate the physical and chemical properties of dendrimers and explore their behaviors when interacting with biomolecules, such as gene materials, proteins, and lipid membranes. As a supplement of the experimental techniques, it has been proved that computer simulations could facilitate the progress in understanding the delivery process of bioactive molecules. The structures of dendrimers in dilute solutions have been intensively investigated by monomer-resolved simulations, coarse-grained simulations, and atom-resolved simulations. Atomistic simulations have manifested that the hydrophobic interactions, hydrogen-bond interactions, and electrostatic attraction play critical roles in the formation of dendrimer-drug complexes. Multiscale simulations and statistical field theories have uncovered some physical mechanisms involved in the dendrimer-based gene delivery systems. This review will focus on the current status and perspective of theoretical and computational contributions in this field in recent years. (275 references).

Structural response of polyelectrolyte dendrimer towards molecular protonation: the inconsistency revealed by SANS and NMR

Polyamidoamine (PAMAM) dendrimers and their charged state in deuterium oxide have been investigated with proton pulsed field gradient diffusion nuclear magnetic resonance (PFG-NMR) and small-angle neutron scattering (SANS) techniques. NMR measurements suggest that significant variation of the hydrodynamic radius, calculated by the Stokes-Einstein relation with appropriate surface conditions, is observed upon increasing the molecular protonation. However, a comparative SANS experiment indicates little dependence of the dendrimer global size, in terms of its radius of gyration, on molecular protonation. The inconsistency indicates the necessity of incorporating the effect of molecular interface modification and molecular porosity provided by dressed counterions, when dynamical measurements are used for the determination of the structural characteristics of ionic soft colloids even in dilute suspensions.

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.