Thin pattern formation

As shown in Fig. 21, in this case, the entire system is composed of an open vessel with a flat bottom, containing a thin layer of liquid. Steady heat conduction from the flat bottom to the upper hquid/air interface is maintained by heating the bottom constantly. Then as the temperature of the heat plate is increased, after the critical temperature is passed, the liquid suddenly starts to move to form steady convection cells. Therefore in this case, the critical temperature is assumed to be a bifurcation point. The important point is the existence of the standard state defined by the nonzero heat flux without any fluctuations. Below the critical temperature, even though some disturbances cause the liquid to fluctuate, the fluctuations receive only small energy from the heat flux, so that they cannot develop, and continuously decay to zero. Above the critical temperature, on the other hand, the energy received by the fluctuations increases steeply, so that they grow with time this is the origin of the convection cell. From this example, it can be said that the pattern formation requires both a certain nonzero flux and complementary fluctuations of physical quantities. 

This equation has been derived as a model amplitude equation in several contexts, from the flow of thin fluid films down an inclined plane to the development of instabilities on flame fronts and pattern formation in reaction-diffusion systems we will not discuss here the validity of the K-S as a model of the above physicochemical processes (see (5) and references therein). Extensive theoretical and numerical work on several versions of the K-S has been performed by many researchers (2). One of the main reasons is the rich patterns of dynamic behavior and transitions that this model exhibits even in one spatial dimension. This makes it a testing ground for methods and algorithms for the study and analysis of complex dynamics. Another reason is the recent theory of Inertial Manifolds, through which it can be shown that the K-S is strictly equivalent to a low dimensional dynamical system (a set of Ordinary Differentia Equations) (6). The dimension of this set of course varies as the parameter a varies. This implies that the various bifurcations of the solutions of the K-S as well as the chaotic dynamics associated with them can be predicted by low-dimensional sets of ODEs. It is interesting that the Inertial Manifold Theory provides an algorithmic approach for the construction of this set of ODEs. 

Fig. 6 Illustration of surface energy effects on the self-assembly of thin films of volume symmetric diblock copolymer (a). Sections b and c show surface-parallel block domains orientation that occur when one block preferentially wets the substrate. Symmetric wetting (b) occurs when the substrate and free surface favor interactions with one block B, which is more hydrophobic. Asymmetric wetting (c) occurs when blocks A and B are favored by the substrate and free surface, respectively. For some systems, a neutral substrate surface energy, which favors neither block, results in a self-assembled domains oriented perpendicular to the film plane (d). Lo is the equilibrium length-scale of pattern formation in the diblock system...

Smith AP, Douglas JF, Meredith JC, Amis EJ, Karim A (2001) Combinatorial study of surface pattern formation in thin block copolymer films. Phys Rev Lett 87 015503... 

In addition, patterns created by surface instabilities can be used to pattern polymer films with a lateral resolution down to 100 nm [7]. Here, I summarize various possible approaches that show how instabilities that may take place during the manufacture of thin films can be harnessed to replicate surface patterns in a controlled fashion. Two different approaches are reviewed, together with possible applications (a) patterns that are formed by the demixing of a multi-component blend and (b) pattern formation by capillary instabilities. 

A. Sharma and R. Khanna, Pattern formation in unstable thin liquid films, Phys. Rev. Lett. 81, 3463-3466 (1998). 

When adsorbed (from ambient air), water molecules might act as plasticizers and alter the dynamics of polymers. Moreover, water has a strong dipole moment and, consequently, dielectric active relaxation processes, which could partially occlude significant parts of the dielectric spectra of interest. Special attention to this effect has to be paid when the dynamics of thin polymer films is investigated, for example in relation to phenomena like the glass transition, dewetting, pattern formation, surface mobility etc. 

The deformation of the sample geometry during the pattern formation, while no changes are detected in a pure nitrogen atmosphere, suggests that thin PS films exhibit an enhanced mobility in ambient air. To prove this, several experimental techniques were employed. 

Figure 3.29 Diffraction pattern formation from a thin foil specimen in a TEM. The surface of Ewald sphere intersects the elongated diffraction spots. An elongated spot reflects the diffraction intensity distribution along the transmitted beam direction.

J. R. Dutcher, K. Dalnoki-Veress, B. G. Nickel, and C. B. Roth, Instabilities in thin polymer films From pattern formation to rupture. Macromol. Symp. 159, 143 (2000). 

A. Serghei, H. Huth, M. Schellenberger, C. Schick, and F. Kremer, Pattern formation in thin polystyrene films induced by an enhanced mobility in ambient air. Phys. Rev. E 71, 061801... 

Soft lithography The pattern-transfer element is formed by pouring a liquid polymer onto a master made from silicon. This replica can be used as a stamp to transfer chemical ink, such as a solution of alkanethiol, to a surface. Spin-coating Thin film formation by deposition of a solution onto a solid, which is then rotated at a speed of several thousand revolutions per minute. 

Reconstructed clean metal surfaces may thus be interesting templates. However, their given structure does not provide the experimentalist with a control on the nature and physical dimensions of the nanostructure. This implies that these surfaces can be suitable candidates for the investigation of the basic properties of templates on an atomic scale but are less interesting in terms of appHcations. To overcome this limitation systems are needed for which the pattern formation by self-organization can to some extent be controlled by the experimentaUst. This leads us to two promising systems stepped metal surfaces and thin films on metal surfaces. 

Abstract Some aspects of self-assembly of quantum dots in thin solid films are considered. Nonlinear evolution equations describing the dynamics of the fihn instability that results in various surface nanostructures are analyzed. Two instability mechanisms are considered the one associated with the epitaxial stress and the other caused by the surface-energy anisotropy. It is shown that wetting interactions between the film and the substrate transform the instability spectrum from the long- to the short-wave type, thus yielding the possibility of the formation of spatiaUy-regular, stable arrays of quantum dots that do not coarsen in time. Pattern formation is analyzed by means of ampbtude equations near the insta-bibty threshold and by numerical solution of the strongly nonlinear evolution equations in the small-slope approximation. 

Keywords Quantum dots, self-assembly, thin solid films, pattern formation, instabilities... 

Here, we will discuss physical aspects of structure formation in thin polymer films induced by microphase ordering in diblock copolymers, pattern formation in crystallizable polymer films, as well as the interplay between both. 

Pattern Formation by Rim Instability in Dewetting Polymer Thin Films... 

Gutmann, J.S., Muller-Buschbaum, P., Stamm, M. Complex pattern formation by phase separation of polymer blends in thin films. Faraday Discuss. 112, 285-297 (1999)... 

Mukherjee, R., Sharma, A., Steiner, U. Surface instability and pattern formation in thin polymer films. In del Campo, A., Arzt, E. (eds.) Generating Micro- and Nanopattems on Polymeric Materials. Wiley-VCH, Weinheim (2011)... 

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