Crystallization self-generated fields

Schultz JM. Self-generated fields and polymer crystallization. Macromolecules 2012 45 6299-6323. 

The dislocation method of stress analysis is also useful for determining craze stress fields in anisotropic (e.g., oriented) polymers . All one needs here is the stress field of a single dislocation in a single crystal with the same symmetry as the oriented polymer (the text by Hirth and Lothe provides a number of simple cases plus copious references to more complete treatments in the literature) the craze stress field can be generated by superposition of the stress fields of an array of these dislocations of density a(x). Dislocations may also be used to represent the self-stress fields of curvilinear crazes (produced by craze growth in a non-homogeneous stress field for example). Such a method has been developed by Mills... 

The perturbed-cluster approach [701,702] is formulated in the LCAO approximation and is based on the following sequence of steps, [703] a) subdivide the entire defect system into a molecular cluster (C), containing the defect, and an external region (D), the indented crystal b) calculate the wavefunction for the molecular cluster in the field of the indented crystal c) correct the cluster solution in order to allow for the propagation of the wavefunction into the indented crystal while generating the density matrix of the defect system. Steps b and c are repeated to self-consistency. The corrective terms in step c are evaluated by assuming that the density of states projected onto the indented crystal is the same as in the perfect host crystal (fundamental approximation). 

Several different sites and cluster sizes were used to generate a self-consistent model of the crystal. All clusters were embedded in the potential field of the infinite ideal... 

In 1996, Munn extended the microscopic theory of bulk second-harmonic generation from molecular crystals to encompass magnetic dipole and electric quadrupole effects [96] and included all contributions up to second order in the electric field or bilinear in the electric field and the electric field gradient or the magnetic field. This was accomplished by replacing the usual polarization of Refs. 72 and 84 by an effective polarization as well as by defining an effective quadrupole moment. Consequently, the self-consistently evaluated local electric field and electric field gradient were expressed in terms of various molecular response coefficients and lattice multipole tensor sums (up to octupole). In this... 

In fact, the TB solution can be made to correspond very closely to the ab initio reference in Fig. 3 we compare the B3LYP band structure for WO3 with that obtained with a self-consistent TB scheme [85, 86]. In addition to the parameters a-y, the TB calculation employed for generating the band structure of Fig. 3 included crystal-field splitting terms, which however do not modify the M-0 hybridisation pattern. 

The concept for the design of supramolecular liquid crystals and supramolecular polymers has opened new fields in materials and polymer science, which are ever expanding. New stable and dynamic structures are generated by self-organization of these materials. Related functional polymeric materials such as dendrimers [140-143], block copolymers [144], polymer blends [145,146], rotaxanes [147-149], anisotropic gels [150-152], metallo-supramolecular polymers [153,154], nanoobjects [155,156] as well as supramolecular polymers are also obtained by self-assembly of multicomponents through noncovalent interactions. 

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