Non-equilibrium morphologies

Crystallization from the melt often leads to a distinct (usually lamellar) structure, with a different periodicity from the melt. Crystallization from solution can lead to non-lamellar crystalline structures, although these may often be trapped non-equilibrium morphologies. In addition to the formation of extended or folded chains, crystallization may also lead to gross orientational changes of chains. For example, chain folding with stems parallel to the lamellar interface has been observed for block copolymers containing poly(ethylene), whilst tilted structures may be formed by other crystalline block copolymers. The kinetics of crystallization have been studied in some detail, and appear to be largely similar to the crystallization dynamics of homopolymers. 

The aim of fusion and controlled solidification of a catalytic material is the generation of a metastable catalytic material. The thermodynamic instability can be caused by a nonequilibrium composition, by a non-equilibrium morphology, or by a combination of both. In the case of the SLP catalysts the desired effect is to avoid the formation of solidification in order to maintain a structureless state of the active material. 

It is an important aspect that block-copolymer micelles are characterized by much longer relaxation times than compared to low molecular surfactants. Non-equilibrium morphologies can easily be obtained in a vitrified state due to the efficient suppression of structural reorganization, because of the corresponding very slow response of the micelles to changes of temperature, solvent and concentration. In the case of a block-ionomer, i.e. a diblock copolymer where one block consists of ionic units, it was observed that micelles which formed in non-polar solution needed weeks to re-equilibrate after dilution of the solvent [226-228]. 

Non-equilibrium morphologies are often frozen in block copolymer samples as a result of the kinetic barriers to reaching equilibrium. This factor is especially critical in the segmented block copolymers, such as those used in polyurethane foams and elastomers [50,51], whose morphologies are seldom able to approach thermodynamic equilibrium. 

Several other machines of this type have been developed since. They all involve intensive mechanical shearing that produces extensive chain scission. Recombination of the free radicals in situ generates sufficient concentration of copolymer, to compatibilize the system. The generated under high stress, non-equilibrium morphology is then locked by quenching. Best performance has been observed for systems with co-continuous morphology. 

Physical compatibilization that generates fine, non-equilibrium morphology, and locks it by nucleated crystallization. The process may take place either in the molten or solid state. 

Another method which is used to increase the kinetic barrier to phase inversion and create more stable non-equilibrium morphologies is to introduce crosslinking in one or in both of the polymer phases [3,9,56,62,63]. Generally, crosslinking... 

O. Shochet, K. Kassner, E. Ben-Jacob, S. G. Lipson, H. Miiller-Krumbhaar. Morphology transitions during non-equilibrium growth I. Study of equilibrium shapes and properties. Physica A 757 136, 1992. 

At r > Tr, the relaxation of a non-equilibrium surface morphology by surface diffusion can be described by Eq. 1 the thermodynamic driving force for smoothing smoothing is the surface stiffness E and the kinetics of the smoothing is determined by the concentration and mobility of the surface point defects that provide the mass transport, e.g. adatoms. At r < Tr, on the other hand, me must consider a more microscopic description of the dynamics that is based on the thermodynamics of the interactions between steps, and the kinetics of step motion [17]. 

In this section, we analyze experiments on the relaxation of non-equilibrium Si(OOl) [12, 25] and Ge(OOl) [24] morphologies to extract values for the step-mobility as a function of temperature. Mobilities derived from the relaxation experiments are compared to more direct measurements of step-mobilities using low energy electron microscopy (LEEM) [26] and STM [27,28]. 

In the context of the morphological evolution of non-equilibrium systems, let us then ask whether the reaction path, when constructed for a system with stable interfaces, can tell us something about the instability of moving boundaries. For this we... 

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