Clearing phase transitions

Other proof was obtained from experiments with artificial membranes in which BHT or its glycoside isolated from Bacillus acidocaldarius led to a condensation of C16 0 and abolished the clear phase transition between the gel-like and the liquid-crystalline phases. Furthermore, it was found that 40 mol-% of BHT completely suppresses this phase transition in phospholipid bilayers. 

The monolayer resulting when amphiphilic molecules are introduced to the water—air interface was traditionally called a two-dimensional gas owing to what were the expected large distances between the molecules. However, it has become quite clear that amphiphiles self-organize at the air—water interface even at relatively low surface pressures (7—10). For example, x-ray diffraction data from a monolayer of heneicosanoic acid spread on a 0.5-mM CaCl2 solution at zero pressure (11) showed that once the barrier starts moving and compresses the molecules, the surface pressure, 7T, increases and the area per molecule, M, decreases. The surface pressure, ie, the force per unit length of the barrier (in N/m) is the difference between CJq, the surface tension of pure water, and O, that of the water covered with a monolayer. Where the total number of molecules and the total area that the monolayer occupies is known, the area per molecules can be calculated and a 7T-M isotherm constmcted. This isotherm (Fig. 2), which describes surface pressure as a function of the area per molecule (3,4), is rich in information on stabiUty of the monolayer at the water—air interface, the reorientation of molecules in the two-dimensional system, phase transitions, and conformational transformations. 

The well defined change in compressibility of the fee alloy at 2.5 GPa clearly indicates the expected behavior of a second-order phase transition. The anomalously high value of the compressibility for the pressure-sensitive fee alloy is demonstrated in the comparison of compressibilities of various ferromagnetic iron alloys in Table 5.1. The fee Ni alloy, as well as the Invar alloy, have compressibilities that are far in excess of the normal values for the... 

Furthermore, one can infer quantitatively from the data in Fig. 13 that the quantum system cannot reach the maximum herringbone ordering even at extremely low temperatures the quantum hbrations depress the saturation value by 10%. In Fig. 13, the order parameter and total energy as obtained from the full quantum simulation are compared with standard approximate theories valid for low and high temperatures. One can clearly see how the quasi classical Feynman-Hibbs curve matches the exact quantum data above 30 K. However, just below the phase transition, this second-order approximation in the quantum fluctuations fails and yields uncontrolled estimates just below the point of failure it gives classical values for the order parameter and the herringbone ordering even vanishes below... 

It is of special interest for many applications to consider adsorption of fiuids in matrices in the framework of models which include electrostatic forces. These systems are relevant, for example, to colloidal chemistry. On the other hand, electrodes made of specially treated carbon particles and impregnated by electrolyte solutions are very promising devices for practical applications. Only a few attempts have been undertaken to solve models with electrostatic forces, those have been restricted, moreover, to ionic fiuids with Coulomb interactions. We would hke to mention in advance that it is clear, at present, how to obtain the structural properties of ionic fiuids adsorbed in disordered charged matrices. Other systems with higher-order multipole interactions have not been studied so far. Thermodynamics of these systems, and, in particular, peculiarities of phase transitions, is the issue which is practically unsolved, in spite of its great importance. This part of our chapter is based on recent works from our laboratory [37,38]. 

However intuitive the edge-of-chaos idea appears to be, one shoidd be aware that it has received a fair amount of criticism in recent years. It is not clear, for example, how to even define complexity in more complicated systems like coevolutionary systems, much less imagine a phase transition between diffen ent complexity regimes. Even Langton s sugge.stion that effective computation within the limited domain of cellular automata can take place only in the transition region has been challenged. ... 

It is clear that systems of hard ellipsoids exhibit an intriguingly simple phase behaviour with some resemblance to that of real nematogens. However, such systems cannot form smectic or columnar phases and in addition the phase transitions are not thermally driven as they are for real mesogens. As we shall see in the following sections the Gay-Berne potential with its anisotropic repulsive and attractive forces is able to overcome both of these limitations. 

The phase transition temperatures (lower critical solution temperature, LCST) of the pol5miers were obtained from the change in the transmittance of their aqueous solutions (Figure 1). The aqueous solution of the obtained pol5uner was prepared and its transmittance at 500 nm was monitored with increase in the ambient temperature. Both of poly-NIPA and poly-NEA showed a sudden decrease in the transmittance at 37.5 and 69.2 °C, respectively. The result shown in Figure 1 clearly suggests the thermosensitivity of the pol5mers, and the obtained LCST values are close to those reported for poly-NIPA (34.8 °C) [8] and poly-NEA (72 °C) [9]. 

The DSC spectra confirm that the fluid phase of the polymerized vesicles remains and the phase transitions are retained with the introduction of the spacer group. As can been seen in Figure 8 of the DSC spectrum of the monomeric lipid, there is a peak around 28°C which corresponds to the phase transition of monomeric lipid. As the result of the presence of the spacer group, a similar phase transition can also be observed clearly in the spectrum of the polymerized lipid as shown in Figure 9, but the transition temperature is increased to 36°C by the presence of the polymer chains. 

From Eq. (6) it clearly can be seen that pressure and temperature are related by the changes in entropy and volume for the phase change. This equation also shows that once temperature is chosen, pressure must be fixed accordingly. It is easy to show that the change in entropy for the phase transition is simply the... 

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