Stable and metastable hard-sphere crystals in fundamental measure theory

Mechanical relaxation of functionalized carbosilane dendrimer melts

Functionalizing the internal structure of classical dendrimers is a new way of tailoring their properties. Using atomistic molecular dynamics simulations, we investigate the rheological behavior of functionalized dendrimer (FD) melts obtained by modifying the branching of carbosilane dendrimers (CSD). The time (relaxation modulus G(t)) and frequency (storage G' and loss G'' moduli) dependencies of the dynamic modulus are obtained. Fourth generation FD melts present a region where G' > G''. In contrast, their non-functionalized counterparts (i.e., classical dendrimers with regular branching) do not show such a region. The comparative analysis of FD and CSD suggests that the internal densification due to functionalization prevents the penetration of branches and causes FD to behave like colloidal particles in a crowded environment. Since CSD have no special interactions, we expect that this effect will be common for other dendrimer macromolecules.

Density-functional theory study of the body-centered-cubic and cI16 hard-sphere crystals

The properties of the body-centered-cubic (bcc) solid phase of hard spheres are challenging to compute because of its lack of mechanical and thermodynamic stability, yet this structure remains of interest for theoretical and practical reasons. Density-functional theory (DFT) studies of the bcc hard-sphere solid, using the most accurate functionals from fundamental measure theory, have yielded results with unphysical behaviors in structural and thermodynamic properties. We recently reported [Warshavsky et al., J. Chem. Phys. 148, 024502 (2018)] a Monte Carlo (MC) simulation study of hard spheres initiated in a bcc structure. We observed that such systems, even under constant-volume and single-occupancy-cell constraints, rapidly evolved into either a crystalline state with the cI16 structure or one of a few amorphous states. With these observations in mind, we revisited the DFT calculations of the bcc hard-sphere system by allowing for a bcc-to-cI16 structural transformation. Specifically, the free energy functional was minimized with respect to a density profile having two scalar parameters: the traditional alpha parameter characterizing the width of the Gaussian density distribution around each lattice site and a geometric parameter characterizing the bcc-to-cI16 structural transition. The numerical solutions were physically reasonable across the entire density range. At all densities above ρ_bσ³ = 1.0, a cI16 structure had lower free energy than the corresponding perfect bcc structure. The degree of lattice distortion from bcc to cI16 increased with density up to the close-packing limit. Finally, the predicted values of the structural and thermodynamic properties were in excellent agreement with those extracted from our previous MC simulations.

Investigation of Melts of Polybutylcarbosilane Dendrimers by 1H NMR Spectroscopy

Melts of polybutylcarbosilane (PBC) dendrimers from third (G3) up to sixth (G6) generations are investigated by ¹H NMR spectroscopy in a wide temperature range up to 493 K. At room temperature, NMR spectra of G3-G5 dendrimers exhibit resolved, solution-like spectra (“liquid” phase). In contrast, the spectrum of the G6 dendrimer is characterized by a single unresolved broad line at whole temperature range, which supports the presence of an anomalous phase state of G6 at temperatures higher than glass transition temperature. For the first time, an unexpected transition of G5 dendrimer from a molecular liquid state to an anomalous state/phase upon temperature increase has been detected using NMR data. Specifically, an additional wide background line appears in the G5 spectrum above 473 K, and this line corresponds to a G5 state characterized by restricted molecular mobility, i.e., a state similar to the “anomalous” phase of G6 melt. The fraction of the G5 dendrimers in “anomalous” phase at 493 K is approximately 40%. Analysis of the spectral shapes suggests that changes in the G5 dendrimers are reversible with temperature.

A fundamental measure density functional for fluid and crystal phases of the Asakura-Oosawa model

We investigate a density functional for the Asakura-Oosawa model of colloid-polymer mixtures, describing both fluid and crystal phases. It is derived by linearizing the two-component fundamental-measure hard sphere tensor functional in the second (polymer) component. We discuss the formulation of an effective density functional for colloids only. For small polymer-colloid size ratios the effective, polymer-induced potential between colloids is short-range attractive and of two-body form but we show that the effective density functional is not equivalent to standard mean-field approaches where attractions are taken into account by terms second order in the colloid density. We calculate numerically free energies and phase diagrams in good agreement with available simulations, furthermore we discuss the colloid and polymer distributions in the crystal and determine equilibrium vacancy concentrations. Numerical results reveal a fairly strong sensitivity to the specific type of underlying fundamental measure hard sphere functional which could aid further development of fundamental measure theory.