Autonomous Brownian gyrators: A study on gyrating characteristics.

We study the nonequilibrium steady-state (NESS) dynamics of two-dimensional Brownian gyrators under harmonic and nonharmonic potentials via computer simulations and analyses based on the Fokker-Planck equation, while our nonharmonic cases feature a double-well potential and an isotropic quartic potential. In particular, we report two simple methods that can help understand gyrating patterns. For harmonic potentials, we use the Fokker-Planck equation to survey the NESS dynamical characteristics; i.e., the NESS currents gyrate along the equiprobability contours and the stationary point of flow coincides with the potential minimum. As a contrast, the NESS results in our nonharmonic potentials show that these properties are largely absent, as the gyrating patterns are very distinct from those of corresponding probability distributions. Furthermore, we observe a critical case of the double-well potential, where the harmonic contribution to the gyrating pattern becomes absent, and the NESS currents do not circulate about the equiprobability contours near the potential minima even at low temperatures.

Stable iridium(iv) complexes supported by tetradentate salen ligands. Synthesis, structures and reactivity.

A series of trans-dichloroiridium(iv)-salen complexes were synthesized and structurally characterized by spectroscopic means and X-ray crystal structures. These Ir(iv) complexes are able to catalyze intramolecular C-H amination of aryl azides. The catalytic amination was drastically accelerated under microwave-assisted conditions, and possibly involves Ir-imido intermediates as supported by high-resolution ESI-MS analysis.

Rubik's cube: an energy perspective.

What if we played the Rubik's cube game by simple intuition? We would rotate the cube, probably in the hope of getting a more organized pattern in each next step. Yet frustration occurs easily, and we soon find ourselves trapped as the game progresses no further. Played in this completely strategy-less style, the entire problem of the Rubik's cube game can be compared to that of complex chemical reactions such as protein folding, only with less guidance in the searching process. In this work we look into this random-searching process by means of thermodynamics and compare the game's dynamics with that of a faithful stochastic model constructed from the statistical energy landscape theory (SELT). This comparison reveals the peculiar nature of SELT, which relies on the random energy approximation and often chops up energy correlations among nearby configurations. Our observation provides a general insight for the use of SELT in the studies of these frustrated systems.

A cell-model study on counterion fluctuations in macroionic systems: effect of non-extensiveness in entropy.

Rigorously speaking, entropy is slightly non-extensive, and this non-extensiveness, which characterizes the degree of fluctuations, can contribute to effective interactions between mesoscopic objects. In this paper, we consider a pair of macroions, each accompanied by 1000 counterions, and with a cell-model description we demonstrate that the slow variation of non-extensiveness in counterion entropy over macroionic distance leads to an effective long-range attraction between the macroions. With the aid of Monte Carlo simulation and a Bragg-Williams theory including counterion number fluctuations, we find the depth of attraction in free energy to be approximately 0.2k(B)T. The observation in our cell-model study provides an insight for further understanding of effective interactions in real macroionic systems.

Polarization of ions under geometric confinement in the strong-interacting regime: a two-ring model study.

We study the polarization and electrostatic interactions of an ionic system under geometric confinement in the strong-interacting regime. The geometric confinement is introduced via a simple two-ring model, where ions of each species are confined on a ring, respectively. The observed polarization curve exhibits staircase transitions in the low-temperature regime, due to the crossover between energy local minima. We examine the criterion for the validity of the linear response theory and introduce a simple two-state picture that illustrates the signatures of the crossover phenomena.

Studies on electrostatic interactions of colloidal particles in two dimensions: a modeling approach.

We study the effective electrostatic interactions between a pair of charged colloidal particles without salt ions while the system is confined in two dimensions. In particular, we use a simplified model to elucidate the effects of rotational fluctuations in counterion distribution. The results exhibit effective colloidal attractions under appropriate conditions. Meanwhile, long-range repulsions persist over most of our studied cases. The repulsive forces arise from the fact that in two dimensions, the charged colloids cannot be perfectly screened by counterions, as the residual quadrupole moments contribute to the repulsions at longer range. By applying multiple expansions, we find that the attractive forces observed at short range are mainly contributed by electrostatic interactions among higher-order electric moments. We argue that the scenario for attractive interactions discussed in this work is applicable to systems of charged nanoparticles or colloidal solutions with macroions.

Phase behavior of polyelectrolyte solutions with salt.

We have computed the phase diagrams of solutions of flexible polyelectrolyte chains with added simple electrolytes. The calculations are based on our recent theory [M. Muthukumar, Macromolecules 35, 9142 (2002)], which accounts for conformational fluctuations of chains, charge density correlations arising from dissolved ions, hydrophobic interaction between polymer backbone and solvent, and translational entropy of all species in the system. The theory is at the mean field level and recovers the results of the restricted primitive model with the Debye-Huckel description for solutions of simple electrolytes without any polymer chains and those of the Flory-Huggins and scaling theories for uncharged polymers in the absence of charges or electrolytes. In constructing the phase diagrams, the chemical potential of each of the species is maintained to be the same in the coexisting phases and at the same time each phase being electrically neutral (Donnan equilibrium). Comparisons are made with a more constrained situation where the chemical potentials of the independent components are maintained to be the same in the coexisting phases. Our calculations predict several rich phenomena. Even for the salt-free solutions, two critical phenomena (corresponding to the Flory-Huggins-type and the restricted-primitive-model-type critical points) are predicted. The coupling between these two leads to two critical end points and triple points. In the presence of salt, the valency of electrolyte ions is found to influence drastically the phase diagrams. Specifically, the predicted liquid-liquid phase transitions in certain temperature ranges is reminiscent of the re-entrant-precipitation phenomenon observed experimentally for polyelectrolytes condensed with trivalent salts.

Diffusion dynamics, moments, and distribution of first-passage time on the protein-folding energy landscape, with applications to single molecules.

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We found that the first passage-time (FPT) distribution undergoes a dynamic transition at a temperature below which the FPT distribution develops a power-law tail, a signature of the intermittent nonexponential kinetic phenomena for the folding dynamics. Possible applications to single-molecule dynamics experiments are discussed.