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Register a new userThermodynamics of nano-cluster phases: a unifying theory
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Nicolas Destainville
Publication date
2008
fields
Physics
and research's language is
English
Authors
Nicolas Destainville
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We propose a unifying, analytical theory accounting for the self-organization of colloidal systems in nano- or micro-cluster phases. We predict the distribution of cluter sizes with respect to interaction parameters and colloid concentration. In particular, we anticipate a proportionality regime where the mean cluster size grows proportionally to the concentration, as observed in several experiments. We emphasize the interest of a predictive theory in soft matter, nano-technologies and biophysics.
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The amount and type of self-entanglement of DNA filaments is significantly affected by spatial confinement, which is ubiquitous in biological systems. Motivated by recent advancements in single DNA molecule experiments based on nanofluidic devices, and by the introduction of algorithms capable of detecting knots in open chains, we investigate numerically the entanglement of linear, open DNA chains confined inside nano-slits. The results regard the abundance, type and length of occurring knots and are compared with recent findings for DNA inside nano-channels. In both cases, the width of the confining region, D, spans the 30nm- 1mu m range and the confined DNA chains are 1 to 4mu m long. It is found that the knotting probability is maximum for slit widths in the 70-100nm range. However, over the considered DNA contour lengths, the maximum incidence of knots remains below 20%, while for channel confinement it tops 50%. Further differences of the entanglement are seen for the average contour length of the knotted region which drops significantly below D ~100nm for channel-confinement, while it stays approximately constant for slit-like confinement. These properties ought to reverberate in different kinetic properties of linear DNA depending on confinement and could be detectable experimentally or exploitable in nano-technological applications.
A scaling theory is developed for diffusion-limited cluster aggregation in a porous medium, where the primary particles and clusters stick irreversibly to the walls of the pore space as well as to each other. Three scaling regimes are predicted, connected by smooth crossovers. The first regime is at low primary particle concentrations where the primary particles stick individually to the walls. The second regime is at intermediate concentrations where clusters grow to a certain size, smaller than the pore size, then stick individually to the walls. The third regime is at high concentrations where the final state is a pore-space-filling network.
Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that energetic rigidity, in which all non-trivial deformations raise the energy of a structure, is a more useful notion of rigidity in practice than two more commonly used rigidity tests: Maxwell-Calladine constraint counting (first-order rigidity) and second-order rigidity. We find that constraint counting robustly predicts energetic rigidity only when the system has no states of self stress. When the system has states of self stress, we show that second-order rigidity can imply energetic rigidity in systems that are not considered rigid based on constraint counting, and is even more reliable than shear modulus. We also show that there may be systems for which neither first nor second-order rigidity imply energetic rigidity. The formalism of energetic rigidity unifies our understanding of mechanical stability and also suggests new avenues for material design.
The non-equilibrium dynamics of condensation phenomena in nano-pores is studied via Monte Carlo simulation of a lattice gas model. Hysteretic behavior of the particle density as a function of the density of a reservoir is obtained for various pore geometries in two and three dimensions. The shape of the hysteresis loops depend on the characteristics of the pore geometry. The evaporation of particles from a pore can be fitted to a stretched exponential decay of the particle density $rho_f(t) sim exp [ -(t/tau)^beta]$. Phase separation dynamics inside the pore is effectively described by a random walk of the non-wetting phases. Domain evolution is significantly slowed down in presence of random wall-particle potential and gives rise to a temperature dependent growth exponent. On the other hand roughness of the pore wall only delays the onset of a pure domain growth.
It is generally believed that the intrinsic properties of glasses are intimately related to potential energy landscapes (PELs). However, little is known about the PELs of glasses below the glass transition temperature (T_g). Taking advantage of lower potential energy barriers in nano systems, we have systematically investigated the dynamics behavior of two nano glasses, Al43 and Al46. Structure transformation is identified in our pure molecular-dynamics simulation far below T_g, which manifests the existence of metabasins in PELs. Surprisingly, we find that the distribution of potential energies shows a paired-Gaussian and long-tailed distribution at temperatures below and approaching T_g, correspondingly the distribution of the {alpha}-relaxation time exhibits an exponential decay. In contrast to the Gaussian distribution of energy in typical liquids and solids, the paired-Gaussian and long-tailed distribution of potential energies, as well as the exponential distribution of the {alpha}-relaxation time, may be considered as the intrinsic feature of a glass or supercooled liquid. The current results are important not only for checking the reliability of various PEL-based models, but also for exploring the microscopic nature of glasses.
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