By William Kung
This monograph represents an extension of the author's unique PhD thesis and features a extra thorough dialogue at the innovations and arithmetic at the back of his study works at the foam version, as utilized to learning problems with part balance and elasticity for numerous non-closed packed buildings present in fuzzy and colloidal crystals, in addition to on a renormalization-group research in regards to the serious habit of loop polymers upon which topological constraints are imposed. the typical thread in the back of those study works is their demonstration of the significance and effectiveness of using geometrical and topological suggestions for modeling and realizing delicate structures present process section transitions.
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Extra info for Geometry and Phase Transitions in Colloids and Polymers
Presumably, we would average over the total spins inside the block to obtain the same mean value for the eﬀective spin σ = i σi , as a function of some new distance scale y = cx. In terms of these mean values of total eﬀective spin per block, we can correspondingly ascribe a new eﬀective interaction J between neighboring spin blocks σ . Consequently, there must also exists a new temperature scale T in this new description using spin blocks corresponding to the physics describing the same physical system of spins at lattice sites at the original temperature T .
These experimental systems consisted typically of aqueous suspension of uniform, charged-polystyrene spheres with variable salt concentration, the latter being a control parameter for the degree of screening of the underlying electrostatic Coulomb interaction. For prototypical colloidal systems with short-range interactions, we consider colloids of the fuzzy kind. Fuzzy systems are made of molecules with long, ﬂexible alkyl chains attached to centers of rigid, aromatic rings. The interparticle potential for these systems may be approximated fairly well by a simple hardcore dressed with a repulsive short-range interaction of ﬁnite strength.
Previously, many experimental studies provided a wealth of data in regard to the stability of various phases, notably the disordered phase, the face-centered cubic phase (FCC) and the body-centered cubic phase (BCC). These experimental systems consisted typically of aqueous suspension of uniform, charged-polystyrene spheres with variable salt concentration, the latter being a control parameter for the degree of screening of the underlying electrostatic Coulomb interaction. For prototypical colloidal systems with short-range interactions, we consider colloids of the fuzzy kind.
Geometry and Phase Transitions in Colloids and Polymers by William Kung