Self-assembly theoretical models

In contrast to static properties, where LP and GM reveal generally the same behavior as that of conventional polymers, due to the self-assembling nature of the breakdown process the transport properties of GM are much more complex. Like conventional polymers, these materials are highly viscoelastic [73,74] and their novel rheology has been intensively studied recently, both experimentally [75,76] and theoretically [11,31,77-79]. A theoretical model... 

The distinctive properties of densely tethered chains were first noted by Alexander [7] in 1977. His theoretical analysis concerned the end-adsorption of terminally functionalized polymers on a flat surface. Further elaboration by de Gennes [8] and by Cantor [9] stressed the utility of tethered chains to the description of self-assembled block copolymers. The next important step was taken by Daoud and Cotton [10] in 1982 in a model for star polymers. This model generalizes the... 

To address this issue, several researchers have developed models of chiral self-assembly. In this section, we review these models. We begin with models based on nonchiral mechanisms and argue that they all have limitations in identifying a mechanism to select a particular tubule radius. We then discuss models based on the elastic properties of chiral membranes and argue that they provide a plausible approach to understanding the formation of tubules and helical ribbons. Most of this discussion was previously presented in our recent theoretical review article.139... 

A detailed justification of the surfactant parameter approach is still the subject of theoretical investigations, and we will return to several issues below. We mention that the surfactant parameter approach is consistent with the fluid mosaic model of Singer and Nicolson. It tells us that the self-assembly of amphiphiles is driven by the strong segregation of water and hydrocarbon chains, and that packing effects dominate the self-assembly process. 

Fig. 1 Phase diagram of self-assembled structures in AB diblock copolymer melt, predicted by self-consistent mean field theory [31] and confirmed experimentally [33]. The MesoDyn simulations [34, 35] demonstrate morphologies that are predicted theoretically and observed experimentally in thin films of cylinder-forming block copolymers under surface fields or thickness constraints dis disordered phase with no distinct morphology, C perpendicular-oriented and Cy parallel-oriented cylinders, L lamella, PS polystyrene, PL hexagonally perforated lamella phase. Dots with related labels within the areal of the cylinder phase indicate the bulk parameters of the model AB and ABA block copolymers discussed in this work (Table 1). Reprinted from [36], with permission. Copyright 2008 American Chemical Society...

Nolte et al. found that an amphiphilic block copolymer 83 composed of a hydrophobic tail of poly(styrene) and a hydrophilic head group of a charged, right-handed helical poly(isocyanide), which is referred to as a superamphiphile , self-assembles in a hierarchical fashion in water to form left-handed superhelices (Fig. 34) [ 158]. They suggest that this type of copolymer will serve as an experimental model for the theoretical study of the packing of helices due to their versatility and easy accessibility. 

Early theoretical models on the feasibility of stochastic mirror symmetry breaking at prebiotic conditions have been successfully realized under laboratory conditions, particularly in studies in crystal and surface science, asymmetric auto catalysis and polymer chemistry. The first step, common in all these scenarios, is the self-assembly of non-chiral or chiral molecules to form diastereoisomeric supramolecular architectures that display different physico-chemical properties. 

To do so, it is necessary to consider all the possible self-assembled species present in the medium. A convenient way to handle such a complex system is to use a theoretical model involving equilibrium constants between the different species. Determination of the equilibrium constants then makes it possible to compute the average molar mass at any concentration. For ex-... 

Sayle et al. (2008) also developed (Figure 9) a route exploiting the classical atomistic simulation to make combined studies of theoretical and experimental works. A typical selected system is ceria. Since the pair potential model based on electrostatic interaction and Buckingham short range presentations are often adequate to describe the fluorite structure of ceria, Sayle et al. explored the application of such models in nano-sized particles. A series of works have been reported on the assembly behaviors of nano-building blocks into complex nanostructures, including the ceria nanoparticles self assembly in ice mold (Karakoti... 

Because of the interaction of the two complicated and not well-understood fields, turbulent flow and non-Newtonian fluids, understanding of DR mechanism(s) is still quite limited. Cates and coworkers (for example, Refs. " ) and a number of other investigators have done theoretical studies of the dynamics of self-assemblies of worm-like micelles. Because these so-called living polymers are subject to reversible scission and recombination, their relaxation behavior differs from reptating polymer chains. An additional form of stress relaxation is provided by continuous breaking and repair of the micellar chains. Thus, stress relaxation in micellar networks occurs through a combination of reptation and breaking. For rapid scission kinetics, linear viscoelastic (Maxwell) behavior is predicted and is observed for some surfactant systems at low frequencies. In many cationic surfactant systems, however, the observed behavior in Cole-Cole plots does not fit the Maxwell model. 

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