Stimuli-responsive polymers result inon-demand regulation of properties and functioning of variousnanoscale systems. In particular, they allow stimuli-responsivecontrol of flow rates through membranes and nanofluidic deviceswith submicron channel sizes. They also allow regulation of drugrelease from nanoparticles and nanofibers in response totemperature or pH variation in the surrounding medium. In thepresent work two relevant mathematical models are introduced toaddress precipitation-driven deposition of surface layers ofstimuli-responsive polymers and describe a possible effect ofswelling-shrinkage transition of such polymers on drug release.

We compare dewetting characteristics of a thin nonwetting solid film in theabsence of stress, fortwo models of a wetting potential: the exponential and the algebraic.The exponential model is a one-parameter (r) model, and the algebraic model isa two-parameter (r, m)model, where r is the ratio of the characteristic wetting length to the heightof the unperturbed film,and m is the exponent of h (film height) in a smooth function thatinterpolates the system's surfaceenergy above and below the film-substrate interface at z = 0. The exponentialmodelgives monotonically decreasing (with h) wetting chemical potential, whilethis dependence is monotonic only for the m = 1 case of the algebraic model.Linear stability analysis of the planar equilibrium surface is performed.Simulations of the surface dynamics in the strongly nonlinear regime(large deviations from the planar equilibrium) and for large surface energyanisotropies demonstrate that for any m the film is less prone to dewettingwhen it is governed by the algebraic model. Quasiequilibrium states similar tothe one found in the exponential model [M. Khenner, Phys. Rev. B, 77 (2008), 245445.] exist in the algebraic model as well, and the film morphologies are similar.

We consider the formation of solid drops(“islands”) occurring in the growth of strained solidfilms. Beginning from a detailed model for the growth of an alloy filmthat incorporates the coupling between composition, elastic stress andthe morphology of the free boundary, we develop an asymptoticdescription of the shape and compositional nonuniformity of smallalloy islands grown at small deposition rates. A key feature of theanalysis is a “thin domain” scaling in the island which enablesrecasting the free boundary problem into a set of integrodifferentialequations for the shape and composition profile. Theintegrodifferential system can be decomposed into two parts: one partgives a single integrodifferential equation for the shape analogous tothat obtained for a single-component island determined by Shanahan andSpencer (2002), and the other part gives the composition profile interms of the shape. Thus, the shape of an alloy island is identical tothat of a single-component island with the same system parameters, butwith a nonuniform composition that depends on the stress-compositioncoupling and alloy solution thermodynamics. Finally, we characterizethe structure and magnitude of the compositional nonuniformity andalso interpret our theoretical results in the context of SiGe alloyfilms.

Propagation of chemical waves at very low temperatures, observedexperimentally [V.V. Barelko et al., Advances in Chem. Phys. 74 (1988), 339-384.] at velocities of order  10 cm/s, is due toa very non- standard physical mechanism. The energy liberated bythe chemical reaction induces destruction of the material, therebyfacilitating the reaction, a process very different from standardcombustion. In this work we present recent experimental results and develop anew mathematical model which takes into account mechanical and chemicalprocesses. We carry out numerical simulations and suggest a simplified model inorder to obtain an explicit expression for the wave speed. This modelling allowsus to give a possible explanation of the existence of two modes of propagationobserved experimentally and of the dependence of the speed of propagation on theradiation dose.

The self-organization of porous nanostructures in anodic metal oxideis considered. A mathematical model which incorporates the chemicalreactions at the metal-oxide and oxide-electrolyte interfaces andelastic stress caused by the electrostrictive effects isdeveloped. It is shown through linear stability analysis, that ashort-wave instability exists in certain parameter regimes which canlead to the formation of hexagonally ordered pores observed inanodized aluminum oxide.