Crystallization-Driven Structure Formation

There is also the special case where two crystallizable units are incorporated into a statistical copolymer. If the two units are structurally similar, in some cases these copolymers can be isodimorphic and show a high degree of crystallinity over the entire range of copolymer compositions. The abrupt transition between the two limiting crystal structures, each characteristic of one of the homopolymers, occurs at a composition that corresponds to a minimum in both melting temperature and heat of fusion. 

In order to better quantify the crystallization and melting behavior in copolymers, various models, both empirical and theoretical, have been proposed. The first copolymer melting model was proposed by Flory. Although it correctly describes the equilibrium crystallization/melting behavior in copolymers in the limit of complete counit exclusion, it lacks quantitative accuracy in predicting experimentally accessible copolymer crystallization data. Subsequent models attempt to incorporate crystals of finite thickness and/or allow 

Besides its effects on morphology, comonomer sequence distribution also affects copolymer crystallization kinetics. In statistical copolymers, due to the broad distribution of crystaUizable sequence lengths, bimodal melting endotherms are typically observed. In block copolymers, the dynamics of crystallization have features characteristic of both homopolymer crystallization and microphase separation in amorphous block copolymers. In addition, the presence of order in the melt, even if the segregation strength is weak, hinders the development of the equihbrium spacing in the block copolymer solid-state structure. 

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The sterically crowded ligand (106) forms a very rare square-planar Co complex, as shown by an X-ray crystal structure, and a spin triplet (paramagnetic) ground state was also identified in the solid state. The Co complex of (107) catalyzes the epoxidation of norbomene with t-BuOOH or Phi as terminal oxidant, catalysis driven by formation of t-BuOO radicals employing a Co redox process. 

Recently, new interesting phenomena that control the mode of packing of polymers have been found, and it has been shown that the basic principles of polymer crystallography are, in some cases, violated. In particular, (1) an atactic polymer can crystallize this is, for instance, the case of polyacrylonitrile [107] (2) in a crystalline polymer the chains can be nonparallel for instance, the structure of the yform of iPP is characterized by the packing of nearly perpendicular chains [108, 109] (3) the principle of entropy-driven phase formation may be violated and the high local symmetry of the chains is lost in the limit-ordered crystkhne lattice of polymers (symmetry breaking). 

Since the solid-state structure formed in block copolymers with homogeneous melts is driven by crystallization, the kinetics of lamellar-scale structure formation might be expected to parallel those of crystallization at the unit-cell level. In the same poly(ethylene-6-(ethylene- / -propylene)) diblock copolymer system, the time evolution of the copolymer crystallinity calculated based on the observed SAXS peaks, as illustrated in Figure 11.16, overlaps with that calculated based on the WAXS data. Since SAXS measures the development of diblock copolymer microstructure on the tens-of-nanometers scale, while WAXS measures polyethylene crystallization on the angstrom scale, the observation that the SAXS data track the WAXS data indicates that the formation of the lamellar microstructure in these diblock copolymers is indeed driven by crystallization, rather than by microphase separation between chemically incompatible blocks [115]. 

Interpreting the process of structure formation of a small system of LJ particles as a conformational transition, it is particularly interesting to consider the structural behavior at the surface as it is for these system sizes more relevant than the bulk effects. In the thermodynamic limit, of course, the phase transition will be driven mainly by the crystal formation in the bulk (fee structure in the case of LJ particles). However, the systems we are going to study in this chapter are so small that the general aspects of nucleation transitions for very large systems are not valid anymore. The crystallization of small systems depends extremely on the precise system size - a lesson that has already been taught in Section 5.2 -and this is due to surface effects. 

It is noteworthy that prior to the advent of scanning probe microscopy electrochemically driven reconstruction phenomena had been identified and studied using traditional macroscopic electrochemical measurements [210,211], However, STM studies have provided insight as to the various atomistic processes involved in the phase transition between the reconstructed and unreconstructed state and promise to provide an understanding of the macroscopically observed kinetics. An excellent example is provided by the structural evolution of the Au(lOO) surface as a function of potential and sample history [210,211,216-223], Flame annealing of a freshly elec-tropolished surface results in the thermally induced formation of a dense hexagonal close-packed reconstructed phase referred to as Au(100)-(hex). For carefully annealed crystals a single domain of the reconstructed phase... 

The dissolution of salt in water (2) is endothermic (AH > 0)—i. e., the liquid cools. Nevertheless, the process still occurs spontaneously, since the degree of order in the system decreases. The Na"" and Cl ions are initially rigidly fixed in a crystal lattice. In solution, they move about independently and in random directions through the fluid. The decrease in order (AS > 0) leads to a negative -T AS term, which compensates for the positive AH term and results in a negative AG term overall. Processes of this type are described as being entropy-driven. The folding of proteins (see p. 74) and the formation of ordered lipid structures in water (see p. 28) are also mainly entropy-driven. 

This conformation resembles that determined by X-ray single-crystal structure analysis. Apart from a close interaction of the -system of the amide groups with the para-substituted aryl moieties, no further n-n interactions are observed. The template-assisted catenane formation is on this account mainly driven by hydrogen-bonding, and n-n interactions are of minor importance only. 

Note that the low-temperature structure is neither a quasicrystal nor an icosahedral glass. Given the molecular symmetry, one might have predicted the latter, whereas icosahedral quasicrystals require two distinct structural units to satisfy space filling. While the precise energetic requirements for crystal versus icosahedral glass formation are not understood, it seems likely that the structural order at low T is driven both by a preference for close packing and,by local orientational order. 

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