The use of nanoparticles as building blocks for the self-assembly of functional materials has been rapidly increasing in recent years. In particular, two-dimensional materials can be effectively selfassembled at liquid interfaces thanks to particle localization and mobility at the interface in combination with tailoring of specific interactions. Many recent advances have been made in the understanding of the adsorption and assembly at liquid interfaces of small hydrophobic nanoparticles stabilized by short-chain rigid dispersants but the corresponding studies on core-shell nanoparticles sterically stabilized by extended hydrophilic polymer brushes are presently missing. Such particles offer significant advantages in terms of fabrication of functional, responsive and bio-compatible materials. We present here a combination of experimental and numerical data together with an intuitive and simple model aimed at elucidating the mechanisms governing the adsorption of iron oxide nanparticles (5-10 nm) stabilized by low molecular weight poly(ethylene glycol) (1.5-10 kDa). We show that the adsorption dynamics and the structure of the final assembly depend on the free energy of the particles at the interface and discuss the thermodynamics of the adsorption in terms of the polymer solubility in each phase.

We give a compact non-technical presentation of two basic principles for reducing the description of nonequilibrium systems based on the quasi-equilibrium approximation. These two principles are: construction of invariant manifolds for the dissipative microscopic dynamics, and coarse-graining for the entropy-conserving microscopic dynamics. Two new results are presented: first, an application of the invariance principle to hybridization of micro-macro integration schemes is introduced, and is illustrated with non-linear dumbbell models; second, Ehrenfest's coarse-graining is extended to general quasi-equilibrium approximations, which gives the simplest way to derive dissipative equations from the Liouville equation in the short memory approximation. © 2001 Elsevier Science B.V. All rights reserved.Keywords: Non-equilibrium thermodynamics; Quasi-equilibrium approximation; Invariant manifold; Coarse-graining Quasi-equilibrium approximations and their place in the problem of transition from microscopic to macroscopic variables Most of the works on non-equilibrium thermodynamics deal with corrections to quasi-equilibrium approximations or with applications of these approximations (with or without corrections).This viewpoint is not only possible but it proves very efficient for the construction of a variety of useful models, approximations and equations, as well as methods to solve them.

We give evidence of a clear structural signature of the glass transition, in terms of a static correlation length with the same dependence on the system size, which is typical of critical phenomena. Our approach is to introduce an external, static perturbation to extract the structural information from the system's response. In particular, we consider the transformation behavior of the local minima of the underlying potential energy landscape (inherent structures), under a static deformation. The finite-size scaling analysis of our numerical results indicate that the correlation length diverges at a temperature Tc, below the temperatures where the system can be equilibrated. Our numerical results are consistent with random first order theory, which predicts such a divergence with a critical exponent ν=2/3 at the Kauzmann temperature, where the extrapolated configurational entropy vanishes.

Embedding magnetic nanoparticles into soft host media offers the opportunity to externally control material properties via a magnetic field. Choosing a hydrogel as the host medium allows modification of not only the elastic properties, but also the degree of swelling of the gel and the shape changes of the sample. Hydrogels where magnetic nanoparticles serve as the only crosslinking reagent of the network are a promising new class of such stimuli-responsive gels. The well-defined magnetomechanical coupling present in these materials should allow for a better understanding and optimization of field-induced changes.

The quasi-equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions are obtained from the maximum entropy principle, how macroscopic and constitutive equations are derived therefrom and how these constitutive equations can be implemented numerically. In addition, a measure for the accuracy of the quasi-equilibrium approximation is proposed that can be evaluated while integrating the constitutive equations. In the example considered, it is confirmed that the accuracy of the approximation is increased by including more macroscopic variables. In steady elongational flow, it is found that more macroscopic variables need to be included above the coil-stretch transition to achieve the same accuracy as below.