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Register a new userPhonon Spectra, Nearest Neighbors, and Mechanical Stability of Disordered Colloidal Clusters with Attractive Interactions
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We investigate the influence of morphology and size on the vibrational properties of disordered clusters of colloidal particles with attractive interactions. From measurements of displacement correlations between particles in each cluster, we extract vibrational properties of the corresponding shadow glassy cluster, with the same geometric configuration and interactions as the source cluster but without damping. Spectral features of the vibrational modes are found to depend strongly on the average number of nearest neighbors, $bar{NN}$, but only weakly on the number of particles in each glassy cluster. In particular, the median phonon frequency, $omega_{med}$, is essentially constant for $bar{NN}$ $<2$ and then grows linearly with $bar{NN}$ for $bar{NN}$ $>2$. This behavior parallels concurrent observations about local isostatic structures, which are absent in clusters with $bar{NN}$ $<2$ and then grow linearly in number for $bar{NN}$$>2$. Thus, cluster vibrational properties appear to be strongly connected to cluster mechanical stability (i.e., fraction of locally isostatic regions), and the scaling of $omega_{med}$ with $bar{NN}$ is reminiscent of the behavior of packings of spheres with repulsive interactions at the jamming transition. Simulations of random networks of springs corroborate observations and suggest that connections between phonon spectra and nearest neighbor number are generic to disordered networks.
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We investigate thermodynamic and structural properties of colloidal dumbbells in the framework provided by the Reference Interaction Site Model (RISM) theory of molecular fluids and Monte Carlo simulations. We consider two different models: in the first one we set identical square-well attractions on the two tangent spheres composing the molecule (SW-SW model); in the second scheme, one of square-well interactions is switched off (HS-SW model). Appreciable differences emerge between the physical properties of the two models. Specifically, the $k to 0$ behavior of SW-SW structure factors $S(k)$ points to the presence of a gas-liquid coexistence, as confirmed by subsequent fluid phase equilibria calculations. Conversely, the HS-SW $S(k)$ develops a low-$k$ peak, signaling the presence of aggregates; such a process destabilizes the gas-liquid phase separation, promoting at low temperatures the formation of a cluster phase, whose structure depends on the system density. We further investigate such differences by studying the phase behavior of a series of intermediate models, obtained from the original SW-SW by progressively reducing the depth of one square-well interaction. RISM structural predictions positively reproduce the simulation data, including the rise of $S(k to 0$) in the SW-SW model and the low-$k$ peak in the HS-SW structure factor. As for the phase behavior, RISM agrees with Monte Carlo simulations in predicting a gas-liquid coexistence for the SW-SW model (though the critical parameters appears overestimated by the theory) and its progressive disappearance moving toward the HS-SW model.
We study the existence and stability of multibreathers in Klein-Gordon chains with interactions that are not restricted to nearest neighbors. We provide a general framework where such long range effects can be taken into consideration for arbitrarily varying (as a function of the node distance) linear couplings between arbitrary sets of neighbors in the chain. By examining special case examples such as three-site breathers with next-nearest-neighbors, we find {it crucial} modifications to the nearest-neighbor picture of one-dimensional oscillators being excited either in- or anti-phase. Configurations with nontrivial phase profiles, arise, as well as spontaneous symmetry breaking (pitchfork) bifurcations, when these states emerge from (or collide with) the ones with standard (0 or $pi$) phase difference profiles. Similar bifurcations, both of the supercritical and of the subcritical type emerge when examining four-site breathers with either next-nearest-neighbor or even interactions with the three-nearest one-dimensional neighbors. The latter setting can be thought of as a prototype for the two-dimensional building block, namely a square of lattice nodes, which is also examined. Our analytical predictions are found to be in very good agreement with numerical results.
Using Langevin dynamics simulations, we investigate the influence of polymer-pore interactions on the dynamics of biopolymer translocation through nanopores. We find that an attractive interaction can significantly change the translocation dynamics. This can be understood by examining the three components of the total translocation time $tau approx tau_1+tau_2+tau_3$ corresponding to the initial filling of the pore, transfer of polymer from the textit{cis} side to the textit{trans} side, and emptying of the pore, respectively. We find that the dynamics for the last process of emptying of the pore changes from non-activated to activated in nature as the strength of the attractive interaction increases, and $tau_3$ becomes the dominant contribution to the total translocation time for strong attraction. This leads to a new dependence of $tau$ as a function of driving force and chain length. Our results are in good agreement with recent experimental findings, and provide a possible explanation for the different scaling behavior observed in solid state nanopores {it vs.} that for the natural $alpha$-hemolysin channel.
We investigate the elastic and yielding properties of two dimensional defect-free mono-crystals made of highly monodisperse droplets. Crystals are compressed between two parallel boundaries of which one acts as a force sensor. As the available space between boundaries is reduced, the crystal goes through successive row-reduction transitions. For small compression forces, the crystal responds elastically until a critical force is reached and the assembly fractures in a single catastrophic global event. Correspondingly there is a peak in the force measurement associated with each row-reduction. The elastic properties of ideal mono-crystal samples are fully captured by a simple analytical model consisting of an assembly of individual capillary springs. The yielding properties of the crystal are captured with a minimal bond breaking model.
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