Transition collapse pressure

Transition Collapse Pressure Formula. The minimum collapse pressure for the plastic to elastic transition zone P. is calculated by... 

The factors F and G and applicable D/t range for the transition collapse pressure formula are shown in Tables 4-152 and 4-151, respectively. 

Fig. 8. Surface-area/surface-pressure isotherms for spreading 1,5, and mixtures of 1 + 5 at 0.2,0.4, 0.6, and 0.8 mole fractions of 1 on aqueous S.O mM NaCl. Areas (A,) and pressures (iq) associated with the transition to a compressed state were taken by projecting the intersection of straight lines drawn to the appropriate sections of the isotherm to the surface-area and surface-pressure axes. The collapse pressure (nc) and collapse area (Ac) were taken by treating that transition, similarly. The insert shows an expansion of the isotherms between 20-40 mN/m. Temperature = 24.0 + 0.5 °C [116]...

The last phase transition is to the solid state, where molecules have both positional and orientational order. If further pressure is applied on the monolayer, it collapses, owing to mechanical instability and a sharp decrease in the pressure is observed. This collapse-pressure depends on the temperature, the pH of the subphase, and the speed with which the barrier is moved. 

Odd-even alternations have not been directly observed in k[A) curves, at least not in the G, LE and LC state. However, Sims and Zografi ), who systematically studied the pressure loss as a function of time upon keeping the film at constant A below the collapse pressure for the CjgCOOH- C20COOH series, found differences in film stability between odd and even-fatty acids. The odd-numbered ones were more resilient against pressure loss. On the other hand, up to the transition pressure, at any rate of compression there is a gradual increase of this pressure with the chain length ). 

The multiple reflection IR spectra are identical for films transferred above or below the plateau pressure (Figure 8). The surface entropies corresponding to the plateau pressure of —0.15 erg/cm2 K and the value of AH of transition (monomolecular film — b imolecular film), calculated at about 70 ergs/cm2, agree well with the corresponding values necessary for the a form to pass from the mono- to the bilayer (30, 31), Therefore, the plateau represents collapse, and the isotherm curves at pressures greater than the collapse pressure pertain to films which are not homogeneous monolayers. 

The equilibrium spreading pressure (ESP) of monolayers from polar lipids has the same value as the plateau pressure defining the transition between the form with liquid chains and that with crystalline chains. Above the chain melting temperature the ESP value is the same as the collapse pressure of the monolayer phase with liquid chains. 

There is a transition point at the 11- 4 isotherm from a monolayer with crystalline chain in a tilted arrangement to a monolayer with vertical (and crystalline) chains. The monolayer phase with vertical chains is unstable which is not surprising as no stable crystal form exists with vertical chains. At variations in compression rate (Table 8.14) this transition pressure is constant whereas the collapse pressure is reduced with decreasing compression rate. The equilibrium spreading pressure of these fatty acids is equal to the transition pressure in Table 8.14. As discussed in Section 8.4 the reduction in surface tension, when crystalline fatty acids are present, is equal to the equilibrium spreading pressure. 

The surface pressure (7i )-area (A) isotherms for pure CiiCONH-j6-CD and its mixed monolayers with DPPC are illustrated in Fig. 4, and those for pure PEO-lipid (12,13) and its monolayers with DMPC are shown in Fig. 5. From Fig. 4 it is apparent that while at all studied surface concentrations of CnCONH-j8-CD the two components behave independently of each other, as indicated by the location of all isotherms of mixed films falling between those corresponding to pure components, their collapse pressures gradually increased with the increase in the DPPC surface concentration. From Fig. 4 it is also apparent that the presence of CuCONH-j9-CD led to the disappearance of the liquid-expanded (LE) to the liquid-condensed (LC) phase transition characteristic of pure DPPC. 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

As the him is compressed, a transition to a solid him is observed, which collapses at higher surface pressure. The II versus A isotherms, below the transition temperatures, show the liquid to solid phase transition. These solid hlms have been also called condensed films. They are observed in such systems where the molecules adhere to each other through van der Waals forces very strongly. The Tl-A isotherm shows generally no change in II at high A, while at a rather low A value, a sudden... 

The Mott-like transition, a central concept for the description of the actinide metal series, causes the sudden increase of the atomic volumes, encountered when between Pu and Am (Fig. 3). All other properties indicate the onset of a 5f localized behaviour at Am (see Part V) the 5 f pressure, which had contained to smaller values the equilibrium interactinide distance, suddenly gives in, with the withdrawal of the 5f s within the atomic core. The occurrence of such a transition within a series characterized by an unsaturated shell, is a unique phenomenon of the actinide series. In lanthanides, it does not occur except perhaps under pressure in cerium metal the approaching of cerium atoms induces suddenly the itineracy of 4f orbitals and a sudden volume collapse - see Chap. C. Neither it occurs in d-transition metal series, where the atomic volumes have an almost parabolic behaviour when plotted vs. Z (see Fig. 3 and Chap. C). The current... 

The much weaker collapse encountered experimentally in the non-isostructural transition of americium might perhaps be associated with the fact that the 5f are already (slightly) bonding in this metal in its low pressure modification. As seen in Fig. 2, AV/V increases the more the 5f are localized. 

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