Monte Carlo simulation of dendrimers in variable solvent quality

Star Polymers vs. Dendrimers: Studies of the Synthesis Based on Computer Simulations

A generic model was developed for studies of the polymerization process of regular branched macromolecules. Monte Carlo simulations were performed employing the Dynamic Lattice Liquid algorithm to study this process. A core-first methodology was used in a living polymerization of stars with up to 32 arms, and dendrimers consisted of 4-functional segments. The kinetics of the synthesis process for stars with different numbers of branches and dendrimers was compared. The size and structure of star-branched polymers and dendrimers during the synthesis were studied. The influence of the functionality of well-defined cores on the structure and on the dispersity of the system was also examined. The differences in the kinetics in the formation of both architectures, as well as changes to their structures, were described and discussed.

Interface-induced hysteretic volume phase transition of microgels: simulation and experiment

Thermo-responsive microgel particles can exhibit a drastic volume shrinkage upon increasing the solvent temperature. Recently we found that the spreading of poly(N-isopropylacrylamide) (PNiPAm) microgels at a liquid interface under the influence of surface tension hinders the temperature-induced volume phase transition. In addition, we observed a hysteresis behavior upon temperature cycling, i.e. a different evolution in microgel size and shape depending on whether the microgel was initially adsorbed to the interface in expanded or collapsed state. Here, we model the volume phase transition of such microgels at an air/water interface by monomer-resolved Brownian dynamics simulations and compare the observed behavior with experiments. We reproduce the experimentally observed hysteresis in the microgel dimensions upon temperature variation. Our simulations did not observe any hysteresis for microgels dispersed in the bulk liquid, suggesting that it results from the distinct interfacial morphology of the microgel adsorbed at the liquid interface. An initially collapsed microgel brought to the interface and subjected to subsequent swelling and collapsing (resp. cooling and heating) will end up in a larger size than it had in the original collapsed state. Further temperature cycling, however, only shows a much reduced hysteresis, in agreement with our experimental observations. We attribute the hysteretic behavior to a kinetically trapped initial collapsed configuration, which relaxes upon expanding in the swollen state. We find a similar behavior for linear PNiPAm chains adsorbed to an interface. Our combined experimental - simulation investigation provides new insights into the volume phase transition of PNiPAm materials adsorbed to liquid interfaces.

The self-diffusion of polymethylsilsesquioxane (PMSSO) dendrimers in diluted solutions and melts

Recently developed non-functional derivatives of polymethylsilsesquioxane (PMSSO) dendrimers of the first to fifth generation were characterized by 1H, 13C and 29Si NMR spectroscopy. The self-diffusion and NMR relaxation of PMSSO dendrimers in dilute solutions of toluene and melts were investigated in a wide temperature range (-50-80 °C). The hydrodynamic radii of dendrimers were determined from the self-diffusion coefficients measured in diluted solutions according to the Stokes-Einstein equation. The hydrodynamic radius of PMSSO dendrimers as a function of molecular mass follows a power law with the scaling exponent of 0.32 ± 0.02 in the investigated temperature range. The temperature dependences of the self-diffusion coefficients of dendrimers were described by the Arrhenius-type equation. The activation energies of self-diffusion of dendrimers in diluted toluene solutions are identical for different generations while the dependence of activation energy for dendrimers in melts shows a maximum for the third generation (G3) dendrimer. Taking into account the absence of specific interactions in PMSSO dendrimer melts the observed behavior was ascribed to the manifestation of interpenetration of dendrimer molecules. For low generations (G1 and G2) the short length of the branches does not considerably affect the translational diffusion while for higher generations (G4 and G5) the densification of the structure prevents significant interpenetration.

Conformations of poly(propylene imine) dendrimers in an ionic liquid at different pH

The conformational behavior of poly(propylene imine) (PPI) dendrimers at three different solution pH is studied in an ionic liquid (IL) solvent, 1-butyl-3-methylimidazolium chloride ([BMIM]Cl), through molecular dynamics (MD) simulations. The size, shape, density distribution, structure factor, and the scattering intensity are evaluated to probe the conformational transition of dendrimers as a function of pH. The results of the radial atomic and terminal amine group density distribution at low pH indicate a shift in the density towards the periphery of the dendrimers due to the electrostatic repulsion between the charged tertiary amine groups within the dendrimers. The [BMIM] cations are not encapsulated within dendrimers and predominantly reside near the periphery. The extensive back-folding of the outer branches due to the electrostatic repulsion between the solvent cations and the peripheral charged amine groups at neutral and low pH results in a dense compact structure in [BMIM]Cl as compared to that in water, as evident from the results of the structure factor and scattering intensity. The structural analysis in terms of the fractal dimension reveals that the lower generation dendrimers exhibit conformational transition as a function of pH, while the higher generations exhibit a highly compact structure at all solution pH. However, PPI dendrimers at low pH exhibit more free volume as compared to that at high pH, which may be utilized to accommodate specific guest molecules.

Orientational Relaxation of Poly(propylene imine) Dendrimers at Different pH

The dilute solution dynamics of poly(propylene imine) (PPI) dendrimers is investigated at three different solution pH through molecular dynamics (MD) simulations. The dynamics of PPI dendrimers is characterized by both global and local relaxations that occur at different time and length scales. While the global dynamics may be described in terms of rotational diffusion, the local motion may be characterized through orientational relaxation dynamics measured in terms of the time autocorrelation function (ACF), second-order orientational ACF, and the spin-lattice relaxation rate. The global motion of dendrimers decreases with an increase in the size from high pH to low pH with increasing generations of growth. The results reveal that the segments at low pH relax faster than those at high pH, and the local mobility of the segments near the periphery is higher than the core segments. This observation is also evident from the spectral density and spin-lattice relaxation rate. High values of the spectral density at higher frequencies imply higher segmental mobility of the dendrimer at low pH relative to that at high pH. A shift in the maximum of the spin-lattice relaxation rate toward lower frequencies with decreasing generations indicates the dependence of local mobility on the topological distance of the segment from the periphery at all pH conditions.

Modeling Lower Critical Solution Temperature Behavior of Associating Dendrimers Using Density Functional Theory

We study the phase behavior of associating dendrimers in explicit solvents using classical density functional theory. The existence of association enables uptake of solvent inside the dendrimer even for unfavorable Lennard-Jones interaction between the solvent and dendrimer. Depending on the distributions of associating sites, the dendrimer conformation can be either dense-core or dense-shell. The conformation of the associating dendrimer is greatly affected by the temperature. Due to the interplay between association interaction and Lennard-Jones attractions, we find the lower critical solution temperature (LCST) behavior of dendrimer conformation and study how it changes as the dendrimer size or solvent size changes. The dendrimer in our study displays no LCST behavior at low generations, and it has a maximum LCST at G4. Moreover, increasing the solvent chain length decreases the LCST. For solvents with self-association, the competition between solvent-solvent association and solvent-dendrimer association also tends to reduce the LCST. Qualitatively consistent with experiments, our results provide insight into the molecular mechanism of the LCST behavior of associating dendrimers.

Effect of pH on Size and Internal Structure of Poly(propylene imine) Dendrimers: A Molecular Dynamics Simulation Study

The behavior of poly(propylene imine) dendrimers at three different solution pH is investigated through molecular dynamics (MD) simulations in explicit solvent. MD simulations provide an insight into the conformational properties of dendrimers via the evaluation of their size, shape, radial density distribution, static structure factor, and scattering intensity. The size of the dendrimer increases from high solution pH to low pH. The internal structure of the dendrimer is quantified in terms of the radial atomic density profile and the terminal amine group density distribution. While the radial atomic density distribution shifts away from the core of the dendrimer with decreasing pH, a significant degree of back-folding of the outer generations is observed at high pH for higher generations of growth. Results from the structure factor and scattering intensity indicate two types of conformational transitions: (i) as a function of the solution pH, where the dendrimer evolves from an expanded structure at low pH to a highly compact one at high pH (except for higher generations), and (ii) with increasing generations, where the open structure of the dendrimer at lower generations transforms to a compact structure at higher generations at both high and low pH, characterized by a change in the fractal dimension.

Density functional study of dendrimer molecules in solvents of varying quality

Modified inhomogeneous statistical associating fluid theory (iSAFT) density functional theory is extended to dendrimer molecules in solvents of varying quality. The detailed structures of isolated dendrimers in implicit solvent are calculated and have a semi-quantitative agreement with simulation results available in the literature. The dendrimers form dense-core structures under all conditions, while their radius of gyration follows different scaling laws. Factors that affect the quality of the solvent are systematically studied in the explicit solvent case. It is found that the solvent size, density, chemical affinity and temperature all play a role in determining a solvent to be good or poor. New molecular dynamics simulations are performed to validate the iSAFT results. Our results provide insight into the phase behavior of dendrimer solutions as well as guidance in practical applications.

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.

Implicit solvent coarse-grained model of polyamidoamine dendrimers: Role of generation and pH

Highly branched polymers such as polyamidoamine (PAMAM) dendrimers are promising macromolecules in the realm of nanobiotechnology due to their high surface coverage of tunable functional groups. Modeling efforts of PAMAM can provide structural and morphological properties, but the inclusion of solvents and the exponential growth of atoms with generations make atomistic simulations computationally expensive. We apply an implicit solvent coarse-grained model, called the Dry Martini force field, to PAMAM dendrimers. The reduced number of particles and the absence of a solvent allow the capture of longer spatiotemporal scales. This study characterizes PAMAM dendrimers of generations one through seven in acidic, neutral, and basic pH environments. Comparison with existing literature, both experimental and theoretical, is done using measurements of the radius of gyration, moment of inertia, radial distributions, and scaling exponents. Additionally, ion coordination distributions are studied to provide insight into the effects of interior and exterior protonation on counter ions. This model serves as a starting point for future designs of larger functionalized dendrimers.

End-group distributions of multiple generations of spin-labeled PAMAM dendrimers

Dendrimers are attractive templates to display functional molecular components. Since the behavior of dendrimer systems can depend greatly on the accessibility of these molecular components to the external environment, and on the spatial arrangement of functional groups attached to the dendrimer terminal branches (end-groups), techniques to determine the locations of end-groups are highly desirable. In this report, we describe a method to analyze the EPR spectra of multiple generations of poly(amidoamine) (PAMAM) dendrimers which have spin-labels attached to end-groups in variable percentages of the total number of available sites. The spectra are treated as a convolution of a narrow spin-label spectrum and a variable line broadening function. Trends in the parameters that describe the best-fit line broadening function with spin-label loading reveal the spatial arrangements and homogeneity of spin environments of the labels. We observe a shift in the end-group distribution from generation 3 (G(3)) to G(4) dendrimers that indicates a change in morphology from an open, extended structure to a more dense, compact arrangement.

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.

A theoretical study of conformational properties of dendritic block copolymers of first generation

Conformational properties of a dendritic block copolymer of the first generation are studied by means of an analytic calculation and dimensionality techniques. The polymer can have different functionalities and branch lengths in the interior region and the exterior shell. Three parameters are included in order to describe the intensity of the interactions between the same or different monomeric units. Based on the average end to end distances of the branches effective angles are defined in order to study how the microscopic parameters control the position and activity of the end groups, but also the hollowness in the internal region and the tweezing ability of the external shell of the macromolecule.

Monte Carlo calculations for the intrinsic viscosity of several dendrimer molecules

We have performed Monte Carlo simulations to reproduce the intrinsic viscosity corresponding to different generation of several types of dendrite molecules: polyamidoamine dendrimers with an ethylendiamine core, polypropylene-imine with a diaminobutane core, and monodendrons and tridendrons of polybenzylether. With this end, we have employed coarse-grained idealizations of the molecules constituted by only two beads in each repeat unit (one in a branching or end unit and one intermediate along the repeat unit) and a simple hard-sphere potential between non-neighboring beads. Our goal is to investigate if this simple model is able to provide a reasonable description of some differences between these systems that have been observed experimentally, in particular, the location of the maximum in the intrinsic viscosity as a function of the generation number. Experimental radii of gyration in a given solvent are reproduced by a fit of the hard-sphere potential diameter. Subsequently, intrinsic viscosities are calculated by the variational approach of Fixman, which yields an accurate lower-bound value with an additional hydrodynamic interaction parameter (the friction radius of the beads). The results show a pronounced variation of the maximum location with the value of the friction radius and the structural details that cannot be mimicked with simpler models. The initial conformations for the Monte Carlo procedure are taken from atomistic configurations thermalized by means of a molecular dynamics.

A Monte Carlo study of amphiphilic dendrimers: Spontaneous asymmetry and dendron separation

We study via Monte Carlo simulation the conformation of amphiphilic dendrimers for which terminal monomers (t) and internal monomers (i) interact differently with the solvent (s). Specifically, we have studied g = 3,6 dendrimers as a function of chi(it), chi(is), and chi(ts) (chi is the differential contact energy between the different particles) for parameter values chi(it) = 0, +/-1 and -1 < chi(is), chi(ts) < 1. We have allowed negative chi values in order to model attractive polar interactions (e.g., hydrogen bonding) which are believed to be important in many dendrimer/solvent systems. We find the "phase diagram" of dendrimer conformations to be extremely rich and to be a strong function of g, chi(is), and chi(ts) but only a weak function of chi(it), For chi(is), chi(ts) > 0, we observe dendrimer conformations, such as unimolecular normal micelles and inverted loopy micelles. However, for chi(is) < 0 or chi(ts) < 0, we observe more exotic molecular conformations, for example, the spontaneous development of asymmetry and dendron separation. These properties are analyzed in terms of snapshots as well as more quantitatively in terms of the radii of gyration, radial density profiles, pair-correlation functions, degree of asymmetry, and dendron overlap factor. By exploiting the dramatic conformational changes under different solvent conditions, we suggest the possibility of using amphiphilic dendrimers as stimuli-responsive smart materials.