Nanoscopic surface patterns of diblock copolymer thin films

The surface topography of thin diblock copolymer films is studied by atomic force microscopy (AFM). With AFM an island-to-ribbon transition is observed for symmetric polystyrene-b-poly (4-vinylpyridine) (PS-b-P4VP) on mica with increasing solution concentration. Our study also demonstrates how the formation of the pattern strongly depends on the copolymer composition based on the volume fraction. The substrate and solvent used both have great effects on the morphology of the thin films. Only by using highly polar substrate (mica), can we gain regular pattern. The reason why the regular islands cannot be obtained with symmetric PS-b-P4VP on graphite is also explained. On mica using nonselective and selective solvents, a rather regular pattern can be obtained. The difference is only in the solution concentration for forming regular patterns.     

Photon channelling in foams

Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of ɛ.     

Block copolymer adsorption from a homopolymer melt to an amine-terminated surface

Using neutron reflectometry, the adsorption of diblock copolymers from a neutral polystyrene (PS) matrix is studied as a function of substrate type and non-adsorbing block degree of polymerization. The block copolymer is poly(deutero styrene)-block-poly(methyl methacrylate) and the substrates are silicon oxide, SiO_x, and SiO_x functionalized with (3-aminopropyl)triethoxysilane (APTES). We have determined the equilibrium volume fraction-depth profiles for such films, and compared them with volume fraction profiles generated by self-consistent mean-field (SCMF) theory and find good agreement between the experimental and theoretical data. SCMF calculations show that the segmental interaction energy between PS matrix chains and APTES is two orders of magnitude stronger than that between PS and SiO_x.     

A model of Barchan dunes including lateral shear stress

Barchan dunes are found where sand availability is low and wind direction quite constant. The two dimensional shear stress of the wind field and the sand movement by saltation and avalanches over a barchan dune are simulated. The model with one dimensional shear stress is extended including surface diffusion and lateral shear stress. The resulting final shape is compared to the results of the model with a one dimensional shear stress and confirmed by comparison to measurements. We found agreement and improvements with respect to the model with one dimensional shear stress. Additionally, a characteristic edge at the center of the windward side is discovered which is also observed for big barchans. Diffusion effects reduce this effect for small dunes.     

Global symmetry breaking in the nonconserved order parameter system during phase ordering

We study global symmetry breaking in the 2D system of scalar nonconserved order parameter following a quench to zero temperature. We show that the instant of time when the symmetry is broken and the final morphology is chosen corresponds to the saturation of the order parameter inside the domains. There are three possible final morphologies: the positive and negative order parameter final morphology, and the state of the coexisting positive and negative order parameter subsystems with a flat interface between them. We find also that each type of the final morphology constitutes about 1/3 of all cases, what agrees with the results obtained recently by Spirin et al. [Phys. Rev. E 65, 016119 (2001)]. Our results are pertinent for the two dimensional systems, but we suspect that there is also a way to apply similar arguments for the three dimensional ones.     

The role of heat-conducting walls in the measurement of heat and mass transport in transient grating experiments

We present a two-dimensional model to account for the role of heat-conducting walls in the measurement of heat transport and Soret-effect-driven mass transport in transient holographic grating experiments. Heat diffusion into the walls leads to non-exponential decay of the temperature grating. Under certain experimental conditions it can be approximated by an exponential function and assigned an apparent thermal diffusivity D_{th, app} < D_{th, s}, where D_th,s is the true thermal diffusivity of the sample. The ratio D_{th, app}/D_{th, s} depends on only three dimensionless parameters, d /l_s, κ_s/κ_w, and D_{th, s}/D_{th, w}. d is the grating period, l_s the sample thickness, κ_s and κ_w the thermal conductivities of sample and wall, respectively, and D_th,w the thermal diffusivity of the wall. If at least two measurements are performed at different d /l_s, both D_th,s and κ_s can be determined. Instead of costly solving PDEs, D_th,s can be obtained by finding the zero of an analytic function. For thin samples and large grating periods, heat conduction into the walls plays a predominant role and the concentration grating in binary mixtures is no longer one-dimensional. Nevertheless, the normalized heterodyne diffraction efficiency of the concentration grating remains unaffected and the true thermal and collective diffusion coefficient and the correct Soret coefficient are still obtained from a simple one-dimensional model.     

Polymer-assisted complexing controlled orientation growth of ZnO nanorods

The growth of the oriented zinc oxide (ZnO) nanorods on silicon substrates based on a simple novel chemical transformation and thermal hydrolysis by using polyvinyl alcohol (PVA) as self-assembling complex polymer was introduced in this paper. All the polymers were removed after chemical oxidation and only the carbonized grid backbones remained that confines the ZnO nanorod’s diameter and enhance the absorption and diffusion of ZnO at the tips of the nanorods during growth. The ZnO nanorods are investigated by FTIR, XRD and FE-SEM. The results indicated that these nanorods have fine hexagonal wurtzite crystal structure and their diameter varies from 20 to 90 nm and the length up to about 1 μm. A polymer-localized ZnO growth model is proposed, which well explains the growth behavior of ZnO nanorods.This revised version was published online in August 2005 with a corrected issue number.     

Fabrication of copper oxide nanofluid using submerged arc nanoparticle synthesis system (SANSS)

The optimal parameters are found for preparing nanofluid in our submerged arc nanoparticle synthesis system (SANSS) using a copper electrode. A suspended copper oxide nanofluid is thus produced at the current of 8.5–10 A, voltage of 220 V, pulse duration of 12 μs, and dielectric liquid temperature of 2°C. The CuO nanoparticle are characterized by transmission electron microscopy (TEM), field emission scanning electron microscope (FESEM), X-ray diffraction (XRD), electron diffraction pattern (SAD) and electron spectroscopy for chemical analysis (ESCA). The equality volume spherical diameter of the obtained copper oxide particle is 49.1 nm, regular shape and narrow size distribution.This revised version was published online in August 2005 with a corrected issue number.     

The Singularity of Kontsevich’s Solution for QH<Superscript>*</Superscript>(CP<Superscript>2</Superscript>)

In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP². Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99.