Equilibrium Thin-Film Physics

Even after thermal annealing, the morphology of a BC thin film may be different from that of the bulk BC microstmcture. In thin films, the phase behavior is complicated by different effects originating from the film thickness, and interactions between the polymer/substrate and polymer/air interface. Film thickness can be controlled by varying the concentration of the polymer solution and rotational velocity of the substrate during the spin-coating process. In the 

Most of the current theoretical research of symmetric boundary conditions has been done on lamellar diblock films. Various techniques have been used to determine the influence of film thickness on morphology. Turner used a scaling analysis to study symmetric versus antisymmetric lamellae as a function of film thickness and surface potential (Turner, 1992). Walton and coworkers used this same scaling analysis to study vertically oriented lamellae relative to the substrate (Walton et al, 1994). It was found that this arrangement relaxes the entropic penalty imposed on the chains. Comparing the surface and interfacial energies associated with lamellar orientation, it was determined that domain orientation is film-thickness dependent and for neutral surface energies vertical-oriented lamellae are stable for all film thicknesses (Walton et al, 1994). 

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It can be shown, (Gibbs, Scientific Papers, I. J. J. Thomson, Applications of Dynamics to Physics and Chemistry), that a chemical equilibrium can be modified by the action of capillary forces. Thus, a state of equilibrium in solution may conceivably be modified if the latter is in the form of thin films, such as soap bubbles. Since, according to Freundlich (Kapillarchemie, 116), there is at present no direct evidence of the existence of such modification (which would no doubt be exceedingly, though possibly measurably, small) we shall not enter any further into the matter here. 

Diffusion in general, not only in the case of thin films, is a thermodynamically irreversible self-driven process. It is best defined in simple terms, such as the tendency of two gases to mix when separated by a porous partition. It drives toward an equilibrium maximum-entropy state of a system. It does so by eliminating concentration gradients of, for example, impurity atoms or vacancies in a solid or between physically connected thin films. In the case of two gases separated by a porous partition, it leads eventually to perfect mixing of the two. 

Fig. 8 Polymer volume fraction (j) = ho//t,w, where ho is the thickness of the polymer film after spin-coating and hsw is the thickness of a swollen film, measured by in situ spectroscopic ellip-sometry as a function of (a) the relative solvent vapor pressure for thin films of homopolymers PS, PB, and SBS block copolymer. Reprinted from [49], with permission. Copyright 2004 American Institute of Physics, (b) Polymer volume fraction as a function of the swelling time for PS- >-P2VP (SV) block copolymer and for homopolymers PS and P2VP at p/po = 1.0 [118]. The equilibrium degree of swelling indicates that toluene is a selective solvent for the PS block, and that SV block copolymer shows asymmetric swelling under toluene vapor. Reproduced by permission of The Royal Society of Chemistry (RSC) [118]...

Although saturated vapours can be reproduced precisely in the laboratory the application of equilibrium vapour pressures to the prediction of field volatilization rates are fraught with difficulties. The pesticide may interact with other spray components to change the physical characteristics of the deposits. As pointed out by Hartley (4) a pesticide which can exist in a supercooled state (eg. impure DDT in thin films) will be more volatile and more soluble than if it is crystalline. As a rough approximation a crystalline substance becomes one-third to one-fourth as volatile as the supercooled liquid for each... 

Stability and formation of thin films has become an important issue of current activities in physics [276-279], If the film thickness is below the bulk equilibrium... 

The following five chapters deal with problems associated with solid phases, in some cases involving surface and interfacial problems. In Chapter 14, Steele presents a review of physical adsorption investigated by MD techniques. Jiang and Belak describe in Chapter 15 the simulated behavior of thin films confined between walls under the effect of shear. Chapter 16 contains a review by Benjamin of the MD equilibrium and non-equilibrium simulations applied to the study of chemical reactions at interfaces. Chapter 17 by Alper and Politzer presents simulations of solid copper, and methodological differences of these simulations compared to those in the liquid phase are presented. In Chapter 18 Gelten, van Santen, and Jansen discuss the application of a dynamic Monte Carlo method for the treatment of chemical reactions on surfaces with emphasis on catalysis problems. Khakhar in... 

For small curvatures, Eq. (6.15) shows that the curvature energy of a thin film is characterized by the three parameters k, k, and cq. The qualitative behavior of any system, including such properties such as the equilibrium shape, magnitude of thermal fluctuations, and any phase transitions, can of course be calculated as a function of these constants. However, the physics of the system can be radically different depending on the physical parameters e.g., a change in cq can induce shape changes in the system. It is thus of interest to relate the bending elastic moduli and the spontaneous curvature to the physics of the particular system of interest. This section first shows how these parameters are related to the pressure distribution in the membrane and then presents a simple but instructive microscopic model that relates k, and Co to more molecular properties. 

The widespread application of thin films can be understood for several reasons. First, only small quantities of material are necessary for the enhancement of such physical parameters as hardness, mechanical and adhesive. strength, wear and chemical resistance, etc. Second, optimum property-performance combinations can be achieved which could not be obtained for the substrate bulk material alone. Last, surface films can be prepared in metasiable stales with unusual combinations of properties not achievable in equilibrium bulk-phase materials. 

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