Transitions phase separation

Type of movement Photoisomerization H-aggregation Phase transition Phase separation Mass transportation... 

The phase behaviour of phospholipid monolayers at electrolyte/gas interfaces is studied by fluorescence microscopy. At the LE/LC phase transition, phase separation leads to a WignerH ype lattice structure. The observations are quantified using digital image processing. The results show that the phase transition comprises three different regimes. 

The polymer-based miscible systems can be either intermolecular mixtures, for instance polymer solutions and blends, or intramolecular mixtures, such as block copolymers, star-shape multi-arm copolymers, grafted copolymers, random copolymers, and gradient copolymers with a composition gradient from one chain end to the other. Polymer-based miscible systems can phase separate into segregated phases with stable interfaces, or crystallize into crystalline ordered phases. In other words, there are two types of phase transitions, phase separation and crystallization. Under proper thermodynamic conditions, two phase transitions may occur simultaneously. The interplay of these two transitions will dictate the final morphology of the system. In the following, we will choose polymer solutions as typical examples to introduce the polymer-based miscible systems. 

Loss of stability and phase transitions (phase separation)... 

Chapter 4 is devoted to one dimensional (1-D) systems. Although none of the models treated here represents a real system, the study of 1-D models is very useful in gaining insight into various phenomena that do occur in reality, such as the helix-coil transition, phase separation, and the temperature of maximum density of liquid water. These are all real phenomena which may be mimicked by extremely simple and artificial models. The main reward of studying these models comes from their solvability. Section 7.1 treats the helix-coil transition theory as a classic example of the application of the 1-D techniques to solve a problem that arises in physical biochemistry. In reality, however, the helix-coil transition occurs in aqueous solution. The solvent might affect the process to the extent that the vacuum theory may not be relevant to the actual process taking place in aqueous solution. (This aspect of the problem is deferred to Chapter 8.)... 

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

Much later, experiments on model colloids revealed tliat tire addition of polymer may eitlier induce a gas-liquid type phase separation or a fluid-solid transition [94, 95, 96 and 97]. Using perturbation tlieories, tliese observations could be accounted for quite well [97, 98]. 

Elastomeric Modified Adhesives. The major characteristic of the resins discussed above is that after cure, or after polymerization, they are extremely brittie. Thus, the utility of unmodified common resins as stmctural adhesives would be very limited. Eor highly cross-linked resin systems to be usehil stmctural adhesives, they have to be modified to ensure fracture resistance. Modification can be effected by the addition of an elastomer which is soluble within the cross-linked resin. Modification of a cross-linked resin in this fashion generally decreases the glass-transition temperature but increases the resin dexibiUty, and thus increases the fracture resistance of the cured adhesive. Recendy, stmctural adhesives have been modified by elastomers which are soluble within the uncured stmctural adhesive, but then phase separate during the cure to form a two-phase system. The matrix properties are mosdy retained the glass-transition temperature is only moderately affected by the presence of the elastomer, yet the fracture resistance is substantially improved. 

Another example of phase transitions in two-dimensional systems with purely repulsive interaction is a system of hard discs (of diameter d) with particles of type A and particles of type B in volume V and interaction potential U U ri2) = oo for < 4,51 and zero otherwise, is the distance of two particles, j l, A, B] are their species and = d B = d, AB = d A- A/2). The total number of particles N = N A- Nb and the total volume V is fixed and thus the average density p = p d = Nd /V. Due to the additional repulsion between A and B type particles one can expect a phase separation into an -rich and a 5-rich fluid phase for large values of A > Ac. In a Gibbs ensemble Monte Carlo (GEMC) [192] simulation a system is simulated in two boxes with periodic boundary conditions, particles can be exchanged between the boxes and the volume of both boxes can... 

Another interesting version of the MM model considers a variable excluded-volume interaction between same species particles [92]. In the absence of interactions the system is mapped on the standard MM model which has a first-order IPT between A- and B-saturated phases. On increasing the strength of the interaction the first-order transition line, observed for weak interactions, terminates at a tricritical point where two second-order transitions meet. These transitions, which separate the A-saturated, reactive, and B-saturated phases, belong to the same universality class as directed percolation, as follows from the value of critical exponents calculated by means of time-dependent Monte Carlo simulations and series expansions [92]. 

Models of a second type (Sec. IV) restrict themselves to a few very basic ingredients, e.g., the repulsion between oil and water and the orientation of the amphiphiles. They are less versatile than chain models and have to be specified in view of the particular problem one has in mind. On the other hand, they allow an efficient study of structures on intermediate length and time scales, while still establishing a connection with microscopic properties of the materials. Hence, they bridge between the microscopic approaches and the more phenomenological treatments which will be described below. Various microscopic models of this type have been constructed and used to study phase transitions in the bulk of amphiphihc systems, internal phase transitions in monolayers and bilayers, interfacial properties, and dynamical aspects such as the kinetics of phase separation between water and oil in the presence of amphiphiles. 

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