Outline 1 Phase Transitions Theories

The present article attempts to clarify the nature of the discontinuous transition of gels. First, in Sect. 2 we give an outline of the fundamental aspect of the volume phase transition on the basis of the Flory-Rehner theory of gels, with special attention to how the discontinuous transition comes about within the phenomenological treatment Then, in Sect 3 previous experimental results... 

First, we will describe briefly the biology of secretory cells in general and goblet cells in particular. Next, we will outline our earlier studies on the conformation of mudn networks using dynamic laser scattering. Short discussions on the Donnan swelling properties of the mucin network will bring us to the application of the theory of polymer gel phase transition to explain condensation and decondensation in secretion. 

The new non-equilibrium thermodynamic theory of heterogeneous polymer systems [37] is aimed at giving a basis for an integrated description for the dynamics of dispersion and blending processes, structure formation, phase transition and critical phenomena. Our new concept is derived from these more general non-equilibrium thermodynamics and has been worked out on the basis of experiments mainly with conductive systems, plus some orienting and critical examples with non-con-ductive systems [72d]. The principal ideas of the new general non-equilibrium thermodynamical theory of multiphase polymer systems can be outlined as follows. 

The discussion of a positive feedback as the deciding point of excitation models leads us directly to a class of models in which a cooperative mechanism from statistical physics is applied to nerve excitation. This cooperative mechanism is the Ising model it is frequently used to describe phase transitions in solids and liquids and its application to nerve excitation is very suggestive. The first one who worked out an excitation theory on the basis of the Ising model was ADAM (1968 1970). Meanwhile, a number of variations of this idea has been proposed by BLUMEN-THAL, CHANGEUX, LEFEVER (1970), HILL, CHEN (1971), BASS, MOORE (1973), KARREMANN (1973), GOTOH (1975). Since the basic idea is the same in all these theories, let us restrict ourselves to a brief outline of Adam s model. 

In this chapter, intermolecular forces that are the basis of self-assembly are considered in Section 1.2. Section 1.3 outlines common features of structural ordering in soft materials. Section 1.4 deals similarly with general considerations concerning the dynamics of macromolecules and colloids. Section 1.5 focuses on phase transitions along with theories that describe them, and the associated definition of a suitable order parameter is introduced in Section 1.6. Scaling laws are defined in Section 1.7. Polydispersity in particle size is an important characteristic of soft materials and is described in Section 1.8. Section 1.9 details the primary experimental tools for studying soft matter and Section 1.10 summarizes the essential features of appropriate computer simulation methods. 

In this section we consider a general model that has broad applicability to phase transitions in soft materials the Landau theory, which is based on an expansion of the free energy in a power series of an order parameter. The Landau theory describes the ordering at the mesoscopic, not molecular, level. Molecular mean field theories include the Maier-Saupe model, discussed in detail in Section 5.5.2. This describes the orientation of an arbitrary molecule surrounded by all others (Fig. 1.5), which set up an average anisotropic interaction potential, which is the mean field in this case. In polymer physics, the Flory-Huggins theory is a powerful mean field model for a polymer-solvent or polymer-polymer mixture. It is outlined in Section 2.5.6. 

In recent years, studies of solutions of polymer blends and of copolymers have aroused a substantial theoretical and experimental interest. This is motivated by both numerous applications and more fundamental issues concerning the usefulness of the scaling and universality concepts to describe the thermodynamic properties and the phase transitions in these systems. In this lecture, chain interactions in dilute and semidilute solutions are reviewed and it is discussed how and when the interactions between chemically different monomers lead to a macroscopic phase separation in the case of ternary polymer A-polymer B- solvent systems and to a mesophase formation in diblock-copolymer solutions. The important conclusion is that due to both the overall monomer concentration fluctuations (excluded volume effects) and the composition fluctuations, the classical Flory theory often fails. This requires the use of the renormalization method and of scaling concepts to give a correct description of the phase diagrams and the critical phenomena observed in these complex systems. We give only here a brief outline, a complete review has been published elsewhere, ... 

Unimolecular gas phase studies try to isolate reacting molecules from their environment. Insofar as this is successful, gas phase studies provide the most unambiguous data on the intramolecular forces which control reaction rates and pathways. The energetic and conformational requirements of transition state species are of paramount interest, and with the stringent limitations placed on the data by modern reaction rate theories, the results may be critically examined and meaningfully evaluated. A critical survey of the data leading to the rejection of some and a selection of the best parameters in others, has been one of our primary concerns. Transition state theory has been assumed, and the methods and criteria employed in the calculations are based on this theory. They are outlined very briefly for each... 

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal enviromnent to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment. 

The theory and implementation of a novel computational method capable of looking at large transition-state shape-selective systems is outlined. It is then applied to the alkylation reaction of toluene in the gas phase as well as in zeolites MFI, MOR and BEA. Alkylating agents from the series methyl, ethyl, /50-propyl and /er/-butyl are employed to investigate the size and shape effects of the confinement. 

Although our own research has outlined a complete new theoretical concept, there is still a great need to invest further research into the fundamentals of blend technology, such as dispersion, interfacial phenomena, conductivity breakthrough at the critical concentration, electron transport phenomena in blends, and others. It is not the purpose of this section to review these aspects in greater depth than in Section 1.1 and Section 1.2. In the context of this handbook, it should be sufficient to summarize the basis of any successful OM (PAni) blend with another (insulating and moldable or otherwise process-able) polymer is a dispersion of OM (here PAni, which is present as the dispersed phase) and a complex dissipative structure formation under nonequilibrium thermodynamic conditions (for an overview, see Ref [50] for the thermodynamic theory itself, see Ref [15], for detailed discussions, cf Refs. [63,64]). Dispersion itself leads to the drastic insulator-to-metal transition by changing the crystal structure in the nanoparticles (see Section 1.1). 

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