Phase transitions condensation

In bacteria, a family of molecules with a striking chemical similarity to cholesterol, the hopanoids, insert into the membrane hemilayer and stabilize membrane structure (figure 7.28 bacteriohopanetetrol). The effects of these prokaryotic cholesterol analogs are similar to those of cholesterol they broaden the gel-fluid phase transition, condense the bilayer, and reduce bilayer permeability. Contents of hopanoids in bacterial membranes may rise with acclimation temperature (Poralla et ah, 1984). 

Notice that the phase transitions—condensation at point B and evaporation at point D—take place at boundaries on the phase diagram the system cannot move off these boundaries until the transitions are complete. 

During phase transition (condensation), under the action of capillary forces, the liquid is collected between two rhombic surfaces forming a channel (Fig. 16b) with curved surface Rj (curvature radius of the liquid along channel Rj is infinite). 

Liquid films There exists a certain degree of cooperative interaction between the film-forming molecules. Two types have been observed liquid expanded and liquid condensed films. The first type can be characterized by high compressibility, the absence of islands, and they show a first-order liquid-gas phase transition. Condensed films are formed by compressing expanded films. 

It is seen that the phase transition (condensation) in the monolayer is accompanied by a significant decrease of the slope of the surface pressure isotherm. In contrast to the model based on Frumkin s equation and Maxwell s construction (see Fig. 2.19), the dependence of n on 0 in the phase coexistence region does not generally have a horizontal line, except for very small 6 values. 

Comparison of cases 2 and 3 shows that the basic growth of drops in the throttle is caused by phase transitions (condensation). 

The three general states of monolayers are illustrated in the pressure-area isotherm in Fig. IV-16. A low-pressure gas phase, G, condenses to a liquid phase termed the /i uid-expanded (LE or L ) phase by Adam [183] and Harkins [9]. One or more of several more dense, liquid-condensed phase (LC) exist at higher pressures and lower temperatures. A solid phase (S) exists at high pressures and densities. We briefly describe these phases and their characteristic features and transitions several useful articles provide a more detailed description [184-187]. 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

It has long been known from statistical mechanical theory that a Bose-Einstein ideal gas, which at low temperatures would show condensation of molecules into die ground translational state (a condensation in momentum space rather than in position space), should show a third-order phase transition at the temperature at which this condensation starts. Nonnal helium ( He) is a Bose-Einstein substance, but is far from ideal at low temperatures, and the very real forces between molecules make the >L-transition to He II very different from that predicted for a Bose-Einstein gas. 

Ddnweg B 1996 Simulation of phase transitions critical phenomena Monte Carlo and Molecular Dynamics of Condensed Matter Systems vol 49, ed K Binder and G Ciccotti (Bologna Italian Physical Society) pp 215-54... 

Fluorine is a pale yellow gas that condenses to a yellowish orange Hquid at — 188°C, sohdifies to a yellow soHd at —220°C, and turns white in a phase transition at —228° C. Fluorine has a strong odor that is easily detectable at concentrations as low as 20 ppb. The odor resembles that of the other halogens and is comparable to strong o2one (qv). 

It was estabhshed ia 1945 that monolayers of saturated fatty acids have quite compHcated phase diagrams (13). However, the observation of the different phases has become possible only much more recendy owiag to improvements ia experimental optical techniques such as duorescence, polarized duorescence, and Brewster angle microscopies, and x-ray methods usiag synchrotron radiation, etc. Thus, it has become well accepted that Hpid monolayer stmctures are not merely soHd, Hquid expanded, Hquid condensed, etc, but that a faidy large number of phases and mesophases exist, as a variety of phase transitions between them (14,15). 

Ross, M., A Review of Some Recent Theoretical Calculations of Phase Transitions and Comparisions with Experimental Results, in Shock Waves in Condensed Matter—1983 (edited by Asay, J.R., Graham, R.A., and Straub, G.K.), North-Holland Physics, Amsterdam, 1984, pp. 19-26. 

From Eq. (33) it follows that, in the case of very large homogeneous domains, even very small heterogeneity effects should completely destroy any phase transition connected with the adsorbate condensation. This result is quite consistent with the theoretical predictions stemming from the random field Ising model [40,41]. 

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... 

Simulations of monolayers have focused on internal phase transitions, e.g., between the expanded phase and the condensed phases, between different tilted phases, etc. These phenomena cannot be reproduced by models with purely repulsive interactions. Therefore, Haas et al. [148,149] represent the amphiphiles as stiff Lennard-Jones chains, with one end (the head bead) confined to move in a plane. In later versions of the model [150-152], the head bead interactions differ from those of the tail beads they are taken to be purely repulsive, and the head size is variable. 

A.I. Kolesnikov, A.M. Balagurov, I.O. Bashkin, V.K. Fedotov, V.Yu. Malyshev, G.M. Mironova, E.G. Ponyatovsky, A Real-Time Neutron Diffraction Study of Phase Transitions in the Ti-D System after High Pressure Treatment, J. Phys. Condensed Matter 5 5045 (1993). 

The uncertainties in the condensed-phase thermodynamic functions arise from (1) the possible existence of a solid-solid phase transition in the temperature range 2160 to 2370 K and (2) the uncertainty in the estimated value of the liquid heat capacity which is on the order of 40%. While these uncertainties affect the partial pressures of plutonium oxides by a factor of 10 at 4000 K, they are not limiting because, at that temperature, the total pressure is due essentially entirely to O2 and 0. 

Charvolin J (1989) In Riste T, Sherrington D (eds) Phase transitions in soft condensed matter. Plenum Press, New York, p95... 

In 1990, Schroder and Schwarz reported that gas-phase FeO" " directly converts methane to methanol under thermal conditions [21]. The reaction is efficient, occuring at 20% of the collision rate, and is quite selective, producing methanol 40% of the time (FeOH+ + CH3 is the other major product). More recent experiments have shown that NiO and PtO also convert methane to methanol with good efficiency and selectivity [134]. Reactions of gas-phase transition metal oxides with methane thus provide a simple model system for the direct conversion of methane to methanol. These systems capture the essential chemistry, but do not have complicating contributions from solvent molecules, ligands, or multiple metal sites that are present in condensed-phase systems. 

Soderlind, P. (2002) Comment on Theoretical prediction of phase transition in gold . Physical Review B -Condensed Matter, 66,176201-1—176201-2. 

Although we have explained Bose-Einstein condensation as a characteristic of an ideal or nearly ideal gas, i.e., a system of non-interacting or weakly interacting particles, systems of strongly interacting bosons also undergo similar transitions. Eiquid helium-4, as an example, has a phase transition at 2.18 K and below that temperature exhibits very unusual behavior. The properties of helium-4 at and near this phase transition correlate with those of an ideal Bose-Einstein gas at and near its condensation temperature. Although the actual behavior of helium-4 is due to a combination of the effects of quantum statistics and interparticle forces, its qualitative behavior is related to Bose-Einstein condensation. 

Verdugo, P. Polymer Gel Phase Transition in Condensation-Decondensation of Secretory Products, VoL 110, pp. 145-156,... 

Feng H, Zhong W, Punkosdy G et al 1999 CUL-2 is required for the Gl-to-S-phase transition and mitotic chromosome condensation in Caenorhabditis elegans. Nat Cell Biol 1 486-492 Hedgecock EM, White TG 1985 Polyploid tissue in the nematode Caenorhabditiselegans. Dev Biol 107 128-133... 

---