Region, coexistence

The free energy of a monolayer domain in the coexistence region of a phase transition can be described as a balance between the dipolar electrostatic energy and the line tension between the two phases. Following the development of McConnell [168], a monolayer having n circular noninteracting domains of radius R has a free energy... 

Experimentally, tire hard-sphere phase transition was observed using non-aqueous polymer lattices [79, 80]. Samples are prepared, brought into the fluid state by tumbling and tlien left to stand. Depending on particle size and concentration, colloidal crystals tlien fonn on a time scale from minutes to days. Experimentally, tliere is always some uncertainty in the actual volume fraction. Often tire concentrations are tlierefore rescaled so freezing occurs at ( )p = 0.49. The widtli of tire coexistence region agrees well witli simulations [Jd, 80]. 

Another interesting class of phase transitions is that of internal transitions within amphiphilic monolayers or bilayers. In particular, monolayers of amphiphiles at the air/water interface (Langmuir monolayers) have been intensively studied in the past as experimentally fairly accessible model systems [16,17]. A schematic phase diagram for long chain fatty acids, alcohols, or lipids is shown in Fig. 4. On increasing the area per molecule, one observes two distinct coexistence regions between fluid phases a transition from a highly diluted, gas -like phase into a more condensed liquid expanded phase, and a second transition into an even denser... 

At the temperature of the critical isotherm (71 = 304.19 K for C02), the coexistence region has collapsed to a single point and represents a point of inflection in the isotherm. From calculus we know that at an inflection point, the first and second derivatives are equal to zero so that... 

The primary classical method of study of Langmuir monolayers is clearly that of recording H-A isotherms. Another classical method applied to the study of Langmuir monolayers is the measurement of surface potential [8,9], which is sensitive to changes in the orientation and density of the molecular dipoles of the monolayer. In addition, surface potential fluctuations were clearly observed in the coexistence region of palmitic acid [35]. 

C, 0.25 nm molecule in the coexistence region between the liquid-expanded and the liquid-condensed (L2) phases (b) BAM image of stearic acid at 22°C, 0.60 nm molecule in the coexistence region between the gas (G) and the hquid-condensed (L2) phases. In each of these images, the polarizer angle has been set to 60°. The subphase is milh-Q water acidified to pH 1.8 with HCl. The scale bar in the lower left of each image is 450 p,m. 

As discussed above, lipid membranes are dynamic structures with heterogeneous structure involving different lipid domains. The coexistence of different kinds of domains implies that boundaries must exist. The appearance of leaky interfacial regions, or defects, has been suggested to play a role in abrupt changes in solute permeabilities in the two-phase coexistence regions [91,92]. 

On the basis of the concept described above, we propose a model for the homogeneous crystallization mechanism of one component polymers, which is schematically shown in Fig. 31. When the crystallization temperature is in the coexistence region above the binodal temperature Tb, crystal nucleation occurs directly from the melt, which is the well-known mechanism of polymer crystal nucleation. However, the rate of crystallization from the coexistence region is considered to be extremely slow, resulting in single crystals in the melt matrix. Crystallization at a greater rate always involves phase separation the quench below Tb causes phase separations. The most popular case... 

The determination of the character and location of phase transitions has been an active area of research from the early days of computer simulation, all the way back to the 1953 Metropolis et al. [59] MC paper. Within a two-phase coexistence region, small systems simulated under periodic boundary conditions show regions of apparent thermodynamic instability [60] simulations in the presence of an explicit interface eliminate this at some cost in system size and equilibration time. The determination of precise coexistence boundaries was usually done indirectly, through the... 

Fig.66 Phase diagrams of a symmetric (peo = 0.51, Mn = 2700, Mw/Mn = 1.10) and b asymmetric (0peo = 0.32, Mn = 2100, Mw/Mn = 1.14) PEO-fc-PEP block copolymers blended with epoxy resin. Phase transitions which originate from swelling of PEO chains with epoxy and/or curing agent are drawn as single lines, without implication that there are no coexistence regions. From [197]. Copyright 2001 Wiley...

Fig. 13 Phase diagram of PS310-PAA52 in dioxane/water mixtures (A). Shaded regions between sphere and rod phases and between rod and vesicle phases correspond to coexistence regions. Reversibility of vesicle formation and growth process for PS300-PAA44 as function of THF/dioxane composition of nonselective solvent (B). Reprinted with permission from [239]. Copyright (2002) American Association for the Advancement of Science...

Figure 5.1 shows that the pressure ceases to monotonically increase. The break point in the curve corresponds to a transition in the structural order. Instead of all the particles being distributed in a relatively disordered configuration, regions of the box begin to order in an fee structure. The lower bound occurs when 49.4% of the volume is particles. This coexistence region extends along the plateau until at a critical volume the system is entirely composed of particles with an fee order where the particles occupy 54.5% of the box volume. This is the... 

Figure 5. Regions of stability of isotropic and anisotropic solutions of 150 bp DNA, calculated according to Stigter 22L) The light band corresponds to the coexistence region for fully charged DNA, the dark band to DNA with 76% of charge neutralized by counterion condensation. The salt/DNA concentration regions where the gelation and ordinary-extraordinary transitions were studied are indicated by brackets.

Figure 5.23 Pressure composition isotherms for critical temperature 7. The construction of the hydrogen absorption in atypical metal (left). The van t Hoff plot is shown on the right. The slope of solid solution (a-phase), the hydride phase the line is equal to the enthalpy of formation (p-phase) and the region ofthe coexistence ofthe divided by the gas constant and the intercept with two phases. The coexistence region is the axis is equal to the entropy of formation...

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