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Register a new userStructure and interaction of flexible dendrimers in concentrated solution
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We study the influence of mutual interaction on the conformation of flexible poly(propyleneamine) dendrimers of fourth generation in concentrated solution. Mixtures of dendrimers with protonated and deuterated end groups are investigated by small-angle neutron scattering up to volume fractions of 0.23. This value is in the range of the overlap concentration of the dendrimers. The contrast between the solute and the solvent was varied by using mixtures of protonated and deuterated solvents. This allows us to investigate the partial structure factors of the deuterated dendrimers in detail. An analysis of the measured scattering intensities reveals that the shape of the flexible dendrimers is practically independent of the concentration in contrast to the pronounced conformational changes of flexible linear polymers.
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Using small-angle neutron scattering and liquid integral equation theory, we relate the structure factor of flexible dendrimers of 4th generation to their average shape. The shape is measured as a radial density profile of monomers belonging to a single dendrimer. From that, we derive an effective interaction of Gaussian form between pairs of dendrimers and compute the structure factor using the hypernetted chain approximation. Excellent agreement with the corresponding experimental results is obtained, without the use of adjustable parameters. The present analysis thus strongly supports the previous finding that flexible dendrimers of low generation present fluctuating structures akin to star polymers.
Flexible barriers are increasingly used for the protection from debris flow in mountainous terrain due to their low cost and environmental impact. However, a numerical tool for rational design of such structures is still missing. In this work, a hybrid computational framework is presented, using a total Lagrangian formulation of the Finite Element Method (FEM) to represent a flexible barrier. The actions exerted on the structure by a debris flow are obtained from simultaneous simulations of the flow of a fluid-grain mixture, using two conveniently coupled solvers: the Discrete Element Method (DEM) governs the motion of the grains, while the free-surface non-Newtonian fluid phase is solved using the Lattice-Boltzmann Method (LBM). Simulations on realistic geometries show the dependence of the momentum transfer on the barrier on the composition of the debris flow, challenging typical assumptions made during the design process today. In particular, we demonstrate that both grains and fluid contribute in a non-negligible way to the momentum transfer. Moreover, we show how the flexibility of the barrier reduces its vulnerability to structural collapse, and how the stress is distributed on its fabric, highlighting potential weak points.
The transient response of model hard sphere glasses is examined during the application of steady rate start-up shear using Brownian Dynamics (BD) simulations, experimental rheology and confocal microscopy. With increasing strain the glass initially exhibits an almost linear elastic stress increase, a stress peak at the yield point and then reaches a constant steady state. The stress overshoot has a non-monotonic dependence with Peclet number, Pe, and volume fraction, {phi}, determined by the available free volume and a competition between structural relaxation and shear advection. Examination of the structural properties under shear revealed an increasing anisotropic radial distribution function, g(r), mostly in the velocity - gradient (xy) plane, which decreases after the stress peak with considerable anisotropy remaining in the steady-state. Low rates minimally distort the structure, while high rates show distortion with signatures of transient elongation. As a mechanism of storing energy, particles are trapped within a cage distorted more than Brownian relaxation allows, while at larger strains, stresses are relaxed as particles are forced out of the cage due to advection. Even in the steady state, intermediate super diffusion is observed at high rates and is a signature of the continuous breaking and reformation of cages under shear.
Compact and extended dendrimers are two important classes of dendritic polymers. The impact of the underlying structure of compact dendrimers on dynamical processes has been much studied, yet the relation between the dynamical and structural properties of extended dendrimers remains not well understood. In this paper, we study the trapping problem in extended dendrimers with generation-dependent segment lengths, which is different from that of compact dendrimers where the length of the linear segments is fixed. We first consider a particular case that the deep trap is located at the central node, and derive an exact formula for the average trapping time (ATT) defined as the average of the source-to-trap mean first passage time over all starting points. Then, using the obtained result we deduce a closed-form expression for the ATT to an arbitrary trap node, based on which we further obtain an explicit solution to the ATT corresponding to the trapping issue with the trap uniformly distributed in the polymer systems. We show that the trap location has a substantial influence on the trapping efficiency measured by the ATT, which increases with the shortest distance from the trap to the central node, a phenomenon similar to that for compact dendrimers. In contrast to this resemblance, the leading terms of ATTs for the three trapping problems differ drastically between extended and compact dendrimers, with the trapping processes in the extended dendrimers being less efficient than in compact dendrimers.
In the absence of coalescence, coarsening of emulsions (and foams) is controlled by molecular diffusion of dispersed phase between droplets/bubbles. Studies of dilute emulsions have shown how the osmotic pressure of a trapped species within droplets can ``osmotically stabilise the emulsion. Webster and Cates (Langmuir, 1998, 14, 2068-2079) gave rigorous criteria for osmotic stabilisation of mono- and polydisperse emulsions, in the dilute regime. We consider here whether analogous criteria exist for the osmotic stabilisation of mono- and polydisperse concentrated emulsions and foams, and suggest that the pressure differences driving coarsening are small compared to the mean Laplace pressure. An exact calculation confirms this for a monodisperse 2D model, finding a bubbles pressure as P_i = P + Pi + P_i^G, with P, Pi the atmospheric and osmotic pressures, and P_i^G a ``geometric pressure that reduces to the Laplace pressure only for a spherical bubble. For Princens 2D emulsion model, P_i^G is only 5% larger in the dry limit than the dilute limit. We conclude that osmotic stabilisation of dense systems typically requires a pressure of trapped molecules in each droplet that is comparable to the Laplace pressures the same droplets would have if spherical, as opposed to the much larger Laplace pressures present in the system. We study coarsening of foams and concentrated emulsions when there is insufficient of the trapped species present. Rate-limiting mechanisms are considered, their applicability and associated droplet growth rates discussed. In a concentrated foam or emulsion, a finite yield threshold for droplet rearrangement may be enough to prevent coarsening of the remainder.
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