Molecular dynamics study of charged dendrimers in salt-free solution: effect of counterions

Polyamidoamine dendrimers, being protonated under physiological conditions, represent a promising class of nonviral, nanosized vectors for drug and gene delivery. We performed extensive molecular dynamics simulations of a generic model dendrimer in a salt-free solution with dendrimer's terminal beads positively charged. Solvent molecules as well as counterions were explicitly included as interacting beads. We find that the size of the charged dendrimer depends nonmonotonically on the strength of electrostatic interactions demonstrating a maximum when the Bjerrum length equals the diameter of a bead. Many other structural and dynamic characteristics of charged dendrimers are also found to follow this pattern. We address such a behavior to the interplay between repulsive interactions of the charged terminal beads and their attractive interactions with oppositely charged counterions. The former favors swelling at small Bjerrum lengths and the latter promotes counterion condensation. Thus, counterions can have a dramatic effect on the structure and dynamics of charged dendrimers and, under certain conditions, cannot be treated implicitly.     

Structured water in polyelectrolyte dendrimers: understanding small angle neutron scattering results through atomistic simulation

Based on atomistic molecular dynamics (MD) simulations, the small angle neutron scattering (SANS) intensity behavior of a single generation-4 polyelectrolyte polyamidoamine starburst dendrimer is investigated at different levels of molecular protonation. The SANS form factor, P(Q), and Debye autocorrelation function, γ(r), are calculated from the equilibrium MD trajectory based on a mathematical approach proposed in this work. The consistency found in comparison against previously published experimental findings (W.-R. Chen, L. Porcar, Y. Liu, P. D. Butler, and L. J. Magid, Macromolecules 40, 5887 (2007)) leads to a link between the neutron scattering experiment and MD computation, and fresh perspectives. The simulations enable scattering calculations of not only the hydrocarbons but also the contribution from the scattering length density fluctuations caused by structured, confined water within the dendrimer. Based on our computational results, we explore the validity of using radius of gyration R(G) for microstructure characterization of a polyelectrolyte dendrimer from the scattering perspective.     

Structural investigation of PAMAM dendrimers in aqueous solutions using small-angle neutron scattering: effect of generation

We investigate a series of poly(amidoamine) starburst dendrimers (PAMAM) of different generations in acidic, aqueous solutions using small-angle neutron scattering (SANS). While the overall molecular size is found to be practically unaffected by a pD change, a strong generational dependence of counterion association is revealed. Upon increasing the dendrimer generation, the effective charge obtained from our SANS experiments only shows a small increase in contrast to the nearly exponential increase predicted by a recent atomic simulation. We also find that with the same degree of molecular protonation the specific counterion association, which is defined as the ratio of bound chloride anions to positively charged amines in solutions, is larger for higher-generation PAMAM dendrimer. The associated counterion density also increases upon increasing generation number.     

Simulation Study of the Conformational Properties of Diblock Polyelectrolytes in Salt Solutions

Coarse-grained molecular dynamics simulations are performed to understand the behavior of diblock polyelectrolytes in solutions of divalent salt by studying the conformations of chains over a wide range of salt concentrations. The polymer molecules are modeled as bead spring chains with different charged fractions and the counterions and salt ions are incorporated explicitly. Upon addition of a divalent salt, the salt cations replace the monovalent counterions, and the condensation of divalent salt cations onto the polyelectrolyte increases, and the chains favor to collapse. The condensation of ions changes with the salt concentration and depends on the charged fraction. Also, the degree of collapse at a given salt concentration changes with the increasing valency of the counterion due to the bridging effect. As a quantitative measure of the distribution of counterions around the polyelectrolyte chain, we study the radial distribution function between monomers on different polyelectrolytes and the counterions inside the counterion worm surrounding a polymer chain at different concentrations of the divalent salt. Our simulation results show a strong dependence of salt concentration on the conformational properties of diblock copolymers and indicate that it can tune the self-assembly behaviors of such charged polyelectrolyte block copolymers.     

Spatial distribution of intra-molecular water and polymeric components in polyelectrolyte dendrimers revealed by small angle scattering investigations

An experimental scheme using contrast variation small angle neutron scattering technique is developed to investigate the structural characteristics of amine-terminated poly(amidoamine) dendrimers solutions. Using this methodology, we present the dependence of both the intra-dendrimer water and the polymer distribution on molecular protonation, which can be precisely adjusted by tuning the pH of the solution. Assuming spherical symmetry of the spatial arrangement of the constituent components of dendrimer, and that the atomic ratio of hydrogen-to-deuterium for the solvent residing within the cavities of dendrimer is identical to that for the solvent outside the dendrimer, the intra-dendrimer water distribution along the radial direction is determined. Our result clearly reveals an outward relocation of the peripheral groups, as well as enhanced intra-dendrimer hydration, upon increasing the molecular protonation and, therefore, allows the determination of segmental backfolding in a quantitative manner. The connection between these charge-induced structural changes and our recently observed progressively active segmental dynamics is also discussed.     

Correlations and Fluctuations of Charged Colloids as Determined by Anomalous Small‐Angle X‐Ray Scattering

Summary: We performed molecular dynamics simulation of a charged colloidal particle with explicit counterions. Our work provides a direct comparison between simulations and ASAXS‐experiments, offering insight into the counterion distribution of charged colloidal suspensions. We give a detailed constitution of the appearing scattering terms with their physical meaning. It is shown that the cross‐correlation between a macroion and its counterions gives the meanfield approximation of the counterion density even if the counterion system is highly fluctuating. Furthermore, it is shown that cross‐correlations can be negative due to oscillations of the density amplitudes of the macroion and counterions and, therefore, must be distinguished from other scattering contributions. These oscillations become more pronounced if the counterions exhibit a fixed shape and if the size of the macroion and that of the counterion system are different.

Simulation sanpshot of a charged colloid (big central sphere) with counterions (small spheres).     

Counterion Association and Structural Conformation Change of Charged PAMAM Dendrimer in Aqueous Solutions Revealed by Small Angle Neutron Scattering

Our previous study of the structure change of poly(amidoamine) starburst dendrimers (PAMAM) dendrimer of generation 5 (G5) have demonstrated that although the overall molecular size is practically unaffected by increasing DCl concentration, a configurational transformation, from a diffusive density profile to a more uniform density distribution, is clearly observed. In the current paper, the focus is placed on understanding the effect of counterion identity on the inter-molecular structure and the conformational properties by studying the effect due to DBr using small angle neutron scattering (SANS) and integral equation theory. While the overall molecular size is found to be essentially unaffected by the change in the pD of solutions, it is surprising that the intra-molecular configurational transformation is not observed when DBr is used. The overall effective charge of a dendrimer is nearly the same for α < 1, independent of the type of acids. However, when α > 1, the effect of counterion identity becomes significant, the effective charge carried by a charged G5 PAPAM protonated by DBr becomes smaller than that of solutions with DCl. As a consequence, a counterion identity dependence of counterion association is revealed: Under the same level of molecular protonation, the specific counterion association, which is defined as the ratio of bound chloride anions to positively charged amines per molecule, is larger for the G5 PAMAM dendrimer charged by DBr than the one by DCl.     

Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

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.     

Conformational effect on small angle neutron scattering behavior of interacting polyelectrolyte solutions: a perspective of integral equation theory

We present small angle neutron scattering (SANS) measurements of deuterium oxide (D(2)O) solutions of linear and star sodium poly(styrene sulfonate) (NaPSS) as a function of polyelectrolyte concentration. Emphasis is on understanding the dependence of their SANS coherent scattering cross section I(Q) on the molecular architecture of single polyelectrolyte. The key finding is that for a given concentration, star polyelectrolytes exhibit more pronounced characteristic peaks in I(Q), and the position of the first peak occurs at a smaller Q compared to their linear counterparts. Based on a model of integral equation theory, we first compare the SANS experimental I(Q) of salt-free polyelectrolyte solutions with that predicted theoretically. Having seen their satisfactory qualitative agreement, the dependence of counterion association behavior on polyelectrolyte geometry and concentration is further explored. Our predictions reveal that the ionic environment of polyelectrolyte exhibits a strong dependence on polyelectrolyte geometry at lower polyelectrolyte concentration. However, when both linear and star polyelectrolytes exceed their overlap concentrations, the spatial distribution of counterion is found to be essentially insensitive to polyelectrolyte geometry due to the steric effect.     

Ionic aggregate structure in ionomer melts: effect of molecular architecture on aggregates and the ionomer peak

We perform a comprehensive set of coarse-grained molecular dynamics simulations of ionomer melts with varying polymer architectures and compare the results to experiments in order to understand ionic aggregation on a molecular level. The model ionomers contain periodically or randomly spaced charged beads, placed either within or pendant to the polymer backbone, with the counterions treated explicitly. The ionic aggregate structure was determined as a function of the spacing of charged beads and also depends on whether the charged beads are in the polymer backbone or pendant to the backbone. The low wavevector ionomer peak in the counterion scattering is observed for all systems, and it is sharpest for ionomers with periodically spaced pendant charged beads with a large spacing between charged beads. Changing to a random or a shorter spacing moves the peak to lower wavevector. We present new experimental X-ray scattering data on Na(+)-neutralized poly(ethylene-co-acrylic acid) ionomers that show the same two trends in the ionomer peak, for similarly structured ionomers. The order within and between aggregates, and how this relates to various models used to fit the ionomer peak, is quantified and discussed.     

Dendrimer building toolkit: Model building and characterization of various dendrimer architectures

We have developed a graphical user interface based dendrimer builder toolkit (DBT) which can be used to generate the dendrimer configuration of desired generation for various dendrimer architectures. The validation of structures generated by this tool was carried out by studying the structural properties of two well known classes of dendrimers: ethylenediamine cored poly(amidoamine) (PAMAM) dendrimer, diaminobutyl cored poly(propylene imine) (PPI) dendrimer. Using full atomistic molecular dynamics (MD) simulation we have calculated the radius of gyration, shape tensor and monomer density distribution for PAMAM and PPI dendrimer at neutral and high pH. A good agreement between the available simulation and experimental (small angle X‐ray and neutron scattering; SAXS, SANS) results and calculated radius of gyration was observed. With this validation we have used DBT to build another new class of nitrogen cored poly(propyl ether imine) dendrimer and study it's structural features using all atomistic MD simulation. DBT is a versatile tool and can be easily used to generate other dendrimer structures with different chemistry and topology. The use of general amber force field to describe the intra‐molecular interactions allows us to integrate this tool easily with the widely used molecular dynamics software AMBER. This makes our tool a very useful utility which can help to facilitate the study of dendrimer interaction with nucleic acids, protein and lipid bilayer for various biological applications. © 2012 Wiley Periodicals, Inc.     

The effect of the counterion on water mobility in reverse micelles studied by molecular dynamics simulations

In this study, mobility and structure of water molecules in Aerosol OT (bis(2-ethylhexyl) sulfosuccinate, AOT) reverse micelles with water content w0 = 5 and Na+, K+, Cs+ counterions have been explored with molecular dynamics (MD) simulations. Using the Faeder/Ladanyi model (J. Phys. Chem. B, 2000, 104, 1033) of the reverse micelle interior, MD simulations were performed to calculate the self-intermediate scattering function, FS(Q,t), for water hydrogen atoms that could be measured in a quasielastic neutron scattering experiment. Separate intermediate scattering functions FRS(Q,t) and FCMS(Q,t) were determined for rotational and translational motion. We find that the decay of FCMS(Q,t) is nonexponential and our analysis of the MD data indicates that this behavior arises from decreased water mobility for molecules close to the interface and from confinement-induced restrictions on the range of translational displacements. Rotational relaxation also exhibits nonexponential decay, which is consistent with relatively rapid restricted rotation and slower rotational relaxation over the full angular range. Rotational relaxation is anisotropic, with the O-H bond short-time rotational mobility considerably higher than that of the molecular dipole. This behavior is related to the decreased density of water-water hydrogen bonds in the vicinity of the interface compared to core or bulk water. We find that the interfacial mobility of water molecules is quite different for the three counterion types, but that the core mobility exhibits weak counterion dependence. Differences in interfacial mobility are strongly correlated with structural features, especially ion-water coordination, and the extent of disruption by the counterions of the water hydrogen bond network.     

Anomalous mixing behavior of polyisobutylene/polypropylene blends: molecular dynamics simulation study

The unusual mixing behavior of polyisobutylene (PIB) with head-to-head (hhPP) and head-to-tail polypropylene (PP) is studied using large-scale molecular dynamics (MD). The heats of mixing and Flory chi parameters were computed from MD simulations of both blends using a united atom model. The chi parameters from the simulations were estimated from the structure factors using the random phase approximation in analogy with neutron scattering (SANS) experiments. MD simulations for syndiotactic hhPP/PIB predicted a lower critical solution temperature with a chi parameter in very good agreement with SANS experiments on the atactic hhPP/PIB blend. MD simulations also predicted that the isotactic PP/PIB blend was immiscible at high molecular weight in qualitative agreement with cloud point measurements on atactic PP/PIB.     

Molecular dynamics simulations of dendritic polyelectrolytes with flexible spacers in salt free solution

We present the results of molecular dynamics simulations of dendritic polyelectrolytes in dilute salt-free solutions. The dendritic polyelectrolytes are modeled as an ensemble of regular-branched bead-spring chains of neutral and charged Lennard-Jones particles with explicit counterions. A wide range of molecular variables of the dendritic polyelectrolytes such as generation number, spacer length, and charge density were considered in the simulations. The effect of dendrimer size on relaxation time, the conformation of spacers, and the size dependence of the dendrimer on molecular variables are discussed and compared with a Flory type theory. The osmotic coefficients of the dilute dendritic polyelectrolyte solutions, as well as the profiles of monomers and counterions, are calculated directly from the simulations. Our simulation results show that the inner spacers of the dendrimers are extensively stretched, and the size dependence on the molecular weight deviates from the scaling prediction that assumes a Gaussian elasticity of the spacer.     

Electrostatically-driven Ordering in Model Dendrimer Polyelectrolytes: Effects of Concentration

In this study we extend our previous work in the self-organization of dendrimer polyelectrolytes (Macromolecules, 2008 , 41, 225) by examining the effects of dendrimer concentration and/or total volume fraction in the ordering process and the resulting structure, in the arrangement of counterions and dendrimer beads and in the diffusive motion of dendrimers at different strengths of Coulombic interactions. It is found that as long as the total volume fraction remains low (i.e. no jamming phenomena intervene) the symmetry of the resulted cubic phases is unaltered. At a higher volume fraction and at the strong electrostatic regime a kinetic arrest of the dendrimer molecules much in analogy to a colloidal glass-like transition is observed, inhibiting thus the ordering process. Changes in the strength of electrostatic interactions and dendrimer concentration induces a systematic variation of the counterion - counterion and the counterion - charged-dendrimer-bead spatial arrangement. These findings are in qualitative agreement with previous studies in systems with very different structural details of the considered solutes, indicating a more general behaviour in charged macroion/counterion solutions.     

Explicit water molecular dynamics study of the mobility of halide ions in presence of ionene oligocations

We present explicit water molecular dynamics simulations of solutions of aliphatic 3,3- and 6,6-ionene oligocations neutralized with (i) fluoride, chloride, bromide, or iodide counterions, respectively, or (ii) with a 1:1 mixture of chloride and bromide anions in presence of a low molecular weight salt at 298 K. The SPC/E model was used to describe water molecules. Results of the simulation are presented in form of the pair distribution functions between various atoms on the ionene oligoion and counterions in solution. In addition, we were interested in the dynamics of counterions around model ionenes. We showed that counterions residing in the vicinity of the oligoion exchange rapidly with those in the bulk solution, with the frequency depending on the nature of the counterion and on the charge density of the oligoion. We calculated the average residence times of the various counterion species to the oligoions and proposed the model which divides the counterions into "free" and "bound" and calculated the fraction of "free" counterions. In the second part of the study, we investigated interaction of the sodium chloride and sodium bromide, being simultaneously present in the solution, with differently charged ionenes in water. The selectivity effect was clearly observed: bromide ions tend to replace chloride ions in the immediate vicinity of the ionene oligoions. Simulation results are discussed in light of our recent measurements of thermodynamic and transport properties of aqueous ionene solutions.     

Self-doping of molecular quantum-dot cellular automata: mixed valence zwitterions

Molecular quantum-dot cellular automata (QCA) is a promising paradigm for realizing molecular electronics. In molecular QCA, binary information is encoded in the distribution of intramolecular charge, and Coulomb interactions between neighboring molecules combine to create long-range correlations in charge distribution that can be exploited for signal transfer and computation. Appropriate mixed-valence species are promising candidates for single-molecule device operation. A complication arises because many mixed-valence compounds are ions and the associated counterions can potentially disrupt the correct flow of information through the circuit. We suggest a self-doping mechanism which incorporates the counterion covalently into the structure of a neutral molecular cell, thus producing a zwitterionic mixed-valence complex. The counterion is located at the geometrical center of the QCA molecule and bound to the working dots via covalent bonds, thus avoiding counterion effects that bias the system toward one binary information state or the other. We investigate the feasibility of using multiply charged anion (MCA) boron clusters, specifically closo-borate dianion, as building blocks. A first principle calculation shows that neutral, bistable, and switchable QCA molecules are possible. The self-doping mechanism is confirmed by molecular orbital analysis, which shows that MCA counterions can be stabilized by the electrostatic interaction between negatively charged counterions and positively charged working dots.     

抗衡离子对硫酸盐表面活性剂气/液界面性质影响的分子动力学模拟

采用全原子分子动力学方法研究了抗衡离子为第一主族离子(Li⁺、Na⁺、K⁺、Rb⁺和Cs⁺)的十二烷基硫酸盐表面活性剂的气/液界面性质. 通过分析体系中各组分的密度分布曲线, 考察表面活性剂单分子层在界面的聚集形态, 并利用径向分布函数分析了表面活性剂极性头基与抗衡离子间的相互作用. 研究结果表明: 随着抗衡离子半径的增大, 不同体系的界面水层厚度依次增加, 表面活性剂极性头基与抗衡离子形成的Stern和扩散层厚度也相应增加. 但表面活性剂吸附层的抗衡离子缔合度以及体系表面张力却随抗衡离子半径的增大而减小. 研究表明抗衡离子的差异对十二烷基硫酸盐表面活性剂气/液界面性质有很大影响.     

Solvent quality changes the structure of G8 PAMAM dendrimer, a disagreement with some experimental interpretations

We have performed approximately 20-40 ns of molecular dynamics (MD) simulations for the generation 8 PAMAM dendrimer in explicit water under varying pH conditions to study the structure of the dendrimer (approximately 156,738 atoms at low pH). This is the first report of such a long MD simulation of a larger generation PAMAM dendrimer including the effect of salt and counterions with explicit water molecules. We find that changing the pH from a high value (approximately 12) to a low value (approximately 3) changes the radius of gyration from Rg = 37.8 to 43.1 A (increasing by 13%). We also find significant back-folding of the primary amines and a large amount of water penetration inside the polymer. The increase in size with decrease in pH is consistent with our earlier studies on G3-G6 and agrees with the Monte Carlo theory by Welch and Muthukumar of G8 (Macromolecules, 1998, 31, 5892) and the experiments on G5 and G8 PAMAM dendrimer by Topp et al. (Macromolecules, 1999, 32, 7232). However, these results disagree dramatically with the interpretations of SANS experiments of G8 PAMAM dendrimers by Nisato et al. (Macromolecules, 2000, 33, 4172) who observe no change in the size of the dendrimer with variations of solution pH and ionic strength. We assume that the disagreement might arise from neglecting nonspherical shape, penetration of water and ions into the core, and aggregation, all of which might depend on pH.