Emily Liu

pH Responsiveness of polyelectrolyte dendrimers: a dynamical perspective

A combined quasi-elastic neutron scattering (QENS) and high-resolution solution NMR spectroscopy study was conducted to investigate the internal dynamics of aqueous (D2O) G5 PAMAM dendrimer solutions as a function of molecular protonation at room temperature. Localized motion of the dendrimer segments was clearly exhibited in the QENS data analysis while the global, center-of-mass translational diffusion was measured by NMR. Our results unambiguously demonstrate an increased rapidity in local scale (∼ 3 A) motion upon increasing the molecular protonation. This is contrary to an intuitive picture that increased charge stiffens the dendrimer segments thereby inhibiting local motion. These charge-induced changes may be a result of interactions with the surrounding counterions and water molecules as the segments explore additional intra-dendrimer volume made available by slight electrostatic swelling and redistribution of mass in the dendrimer interior. This observation is relevant to development of a microscopic picture of dendrimer-based packages as guest-molecule delivery vehicles because reorganization of the confining dendrimer segments must be a precursor to guest-molecule release.

Effect of counterion valence on the pH responsiveness of polyamidoamine dendrimer structure

An accurate determination of the structure characteristics of protonated generation 5 polyamidoamine dendrimers in aqueous solution has been conducted by analyzing the small angle neutron scattering databased on a statistical mechanics model. In our investigation, the primary focus is to elucidate the effect of counterion valence on the counterion association and its impact on the intramolecular density profile within a dendrimer. In the range of our study for molecular protonation, a strong dependence of the structural properties of charged dendrimers on counterion valence is revealed. Our findings indicate that the association of a large amount of divalent counterions significantly reduces the effective charge of a dendrimer molecule. Surprisingly, no discernible transition of the density distribution profile is observed for the dendrimer charged by D(2)SO(4), as opposed to our previous observation of a pronounced transition in intramolecular density profile for the dendrimer charged by DCl. These findings may be understood from the thermodynamic processes of counterions.

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.

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.

Scattering functions of Platonic solids

The single-particle small-angle scattering properties of five Platonic solids, including the tetrahedron, hexahedron, octahedron, dodecahedron and icosahedron, are systematically investigated. For each given geometry, the Debye spatial autocorrelation function, pair distance distribution function and intraparticle structure factor (form factor) are calculated and compared with the corresponding scattering function of a spherical reference system. From the theoretical models, the empirical relationship between the dodecahedral and icosahedral structural characteristics and those of the equivalent spheres is found. Moreover, the single-particle scattering properties of icosahedral and spherical shells with identical volume are investigated, and the prospect of using different data analysis approaches to explore their structural differences is presented and discussed.

Theoretical studies on the structure of interacting colloidal suspensions by spin-echo small angle neutron scattering

The application of the spin-echo small angle neutron scattering (SESANS) technique for structural characterization of interacting colloidal suspensions is considered in this work. The framework to calculate the theoretical SESANS correlation function is briefly laid out. A general discussion regarding the features of the SESANS correlation functions obtained from different model systems is presented. In comparison with conventional elastic scattering tools operating at the same length scale, our mean-field calculations, based on a monodisperse spherical colloidal system, show that the real-space measurement provided by SESANS presents a powerful probe for studying the intercolloid potential. The reason of this sensitivity is discussed from the standpoint of way, in which how the spatial correlations are manifested in different neutron scattering implementations. This study leads to a better understanding regarding the distinction between SANS and SESANS.

Prospect for characterizing interacting soft colloidal structures using spin-echo small angle neutron scattering

Spin-echo small angle neutron scattering (SESANS) provides a new experimental tool for structural investigation. Due to the action of spin-echo encoding, SESANS measures a spatial correlation function in real space, as opposed to the structure factor S(Q), I(Q), in momentum (Q) space measured by conventional small angle neutron scattering. To establish the usefulness of SESANS in structural characterization, particularly for interacting colloidal suspensions, we have previously conducted a theoretical study of the SESANS correlation functions for model systems consisting of particles with uniform density profiles [X. Li, C.-Y. Shew, Y. Liu, R. Pynn, E. Liu, K. W. Herwig, G. S. Smith, J. L. Robertson, and W.-R. Chen J. Chem. Phys. 132, 174509 (2010)]. Within the same framework, we explore in the present paper the prospect of using SESANS to investigate the structural characteristics of colloidal systems consisting of particles with nonuniform intraparticle mass distribution. As an example, a Gaussian model of interacting soft colloids is used to investigate the manifestation of structural softness in a SESANS measurement. The exploration shows a characteristically different SESANS correlation function for interacting soft colloids, in comparison to that of a uniform hard sphere system. The difference arises from the Abel transform imbedded in the mathematical formalism bridging the SESANS spectra and the spatial autocorrelation function.

Water distributions in polystyrene-block-poly[styrene-g-poly(ethylene oxide)] block grafted copolymer system in aqueous solutions revealed by contrast variation small angle neutron scattering study

We develop an experimental approach to analyze the water distribution around a core-shell micelle formed by polystyrene-block-poly[styrene-g-poly(ethylene oxide (PEO)] block copolymers in aqueous media at a fixed polymeric concentration of 10 mg/ml through contrast variation small angle neutron scattering (SANS) study. Through varying the D(2)O/H(2)O ratio, the scattering contributions from the water molecules and the micellar constituent components can be determined. Based on the commonly used core-shell model, a theoretical coherent scattering cross section incorporating the effect of water penetration is developed and used to analyze the SANS I(Q). We have successfully quantified the intramicellar water distribution and found that the overall micellar hydration level increases with the increase in the molecular weight of hydrophilic PEO side chains. Our work presents a practical experimental means for evaluating the intramacromolecular solvent distributions of general soft matter systems.