Capillary critical point

Evans and his co-workers (1986) have shown that a statistical mechanical treatment may be used to derive the Kelvin equation. This approach, which was designed to avoid the difficulties associated with the exact form of the meniscus, led to a new mathematical description of the effect of confining a fluid in pores of different size and shape on its liquid-gas coexistence curve. An equation of the same mathematical form as Equation (7.10) was obtained, provided that the undersaturation was not too great, i.e. that pjp° was not too low. It was shown that this simple equation becomes less accurate as rK is reduced and is no longer applicable beyond a capillary critical point . At a lower rK or higher T, the two-phase relation fails because of the existence of only one stable fluid configuration in the pore. 

Fig. 54. Schematic phase diagrams for wetting and capillary condensation in the plane of variables temperature and chemical potential difference, (a) Refers to a case in which the semi-infinite system at gas-liquid condensation (ftaKX — d = 0) undergoes a second-order wetting transition at T = 7V The dash-dotted curves show the first-order (gas-liquid) capillary condensation at p = jt(I), T) which ends at a capillary critical point T v, for two choices of the thickness D. For all finite D the wetting transition then is rounded off. (b), (c) refer to a case where a first-order wetting transition exists, which means that ps remains finite as T - T and there jumps discontinuous towards infinity. Then for /iaKX - /i > 0 a transition may occur during which the thickness of the layer condensed at the wall(s) jumps from a small value to a larger value ( prewelting ). For thick capillaries, this transition also exists (c) but not for thin capillaries because then /Jcnn - (D,T) simply is loo large.

Capillary condensation occurs when a fluid is confined within nanopores. It is analoguous to the usual gas-liquid transition but displaced towards lower pressure because of confinement. In fact, capillary condensation concerns pores large enough so that the transition can occur due to cooperative interactions between adsorbed molecules. In contrast, such a phenomenon is not expected in micropores of a few angstroms. The status of capillary condensation in nanoporous adsorbents as being or not a first order transition is still the subject of intense research. Theoretical works for slit pores have demonstrated the existence of a true first order transition with a so-called capillary critical point characterized by a critical temperature of the confined fluid T that is lower that of the bulk. In a pioneering work on the criticality of... 

K. Morishige, H. Fujii, M. Uga, D. Kinakawa, Capillary critical point of argon, nitrogen, oxygen, ethylene, and carbon dioxide in MCM-41, Langmuir 13 (1997) 3494-3498. 

In Fig. 6 are displayed the selectivity versus the bulk pressure p for different bulk mole fractions for a fixed pore size, H 3.05nm. For a solution with high concentration of methane, (e.g., yj = 0.9 at this temperature), the isotherm passes through a maximum and levels off as the pressure increases. This type of S-p isotherm is typical for a fluid at supercritical conditions (we note that the capillary critical point depends on the bulk mole fraction). For results at low concentration of methane (e.g., y i = 0.1 at this temperature), however, the isotherm exhibits a second maximum. This type of isotherm seems to occur when the temperature is near the capillary critical point. 

The result shown in Fig. 6 is for a rather large pore. For the y values indicated above, the bulk critical temperatures are 301, 262, and 206 K, respectively. The corresponding capillary critical points are shifted to lower values as the pore size is decreased [3]. We therefore expect that at a smaller H value, e.g., 1.0 nm, S-p isotherms for T = 296 K will fall into the first type discussed above for most y i values. 

In Fig. 15 we show similar results, but for = 10. Part (a) displays some examples of the adsorption isotherms at three temperatures. The highest temperature, T = 1.27, is the critical temperature for this system. At any T > 0.7 the layering transition is not observed, always the condensation in the pore is via an instantaneous filling of the entire pore. Part (b) shows the density profiles at T = 1. The transition from gas to hquid occurs at p/, = 0.004 15. Before the capillary condensation point, only a thin film adjacent to a pore wall is formed. The capillary condensation is now competing with wetting. 

Fluids in narrow pores adsorption, capillary condensation and critical points,... 

Beyond its critical point, a substance can no longer be condensed to a liquid, no matter how great the pressure. As pressure increases, however, the fluid density approaches that of a liquid. Because solubility is closely related to density, the solvating strength of the fluid assumes liquid-like characteristics. Its diffusivity and viscosity, however, remain. SFC can use the widest range of detectors available to any chromatographic technique. As a result, capillary SFC has already demonstrated a great potential in application to water, environmental and other areas of analysis. 

GC-type capillary columns and conventional packed HPLC columns may be used. Modified GC and HPLC instmmentation is used respectively, such that the eluent can be maintained above the critical point throughout the chromatographic system. One of the advantages of SFC is that many of the detectors from both GC and HPLC are compatible. Hence SFC-FID is common, giving the near universality of FID when analysing compounds that are not amenable to GC. 

The NLDFT predicts the critical point for capillary condensation phase transition (capillary critical pore size) at ca. 2 nm, which is approximately the minimum pore size in which capillary condensation is experimentally observed [21,27], However, the theory fails to predict the disappearance of the hysteresis loop for pores smaller than ca. 4 nm (hysteresis critical point) [20,15], It should be noted that the theory of Broekhoff and de Boer fails to predict both critical points unless some additional semi-empirical corrections are made [16]... 

Supercritical fluid chromatography (SFC) is a column chromatographic technique in which a supercritical fluid is used as a mobile phase. A supercritical fluid is a gas or liquid brought to a temperature and a pressure above its critical point. The first report of SFC dates back to 1962 when Kesper et al. [1] used supercritical fluid chlorofluorocarbons as a mobile phase for the separation of metal porphyrins. It was not until the early 1980s that an important breakthrough of the technique occurred. This was the introduction of capillary SFC and the availability of commercial instrumentation. These became major factors in the recent rise in popularity of SFC. According to the latest estimation, approximately 100 SFC articles are published in major journals every year. 

In stage 2 the pores are emptied. Though the capillary pressure is at its highest level, at the critical point the network may not be compressed further, and the pore liquid evaporates. Liquid is transported through films that cover partially empty pores and evaporates at the surface. The capillary forces reduce consequently. 

Melt fracture occurs when the rate of shear exceeds a critical value for the melt concerned at a particular temperature (that is, the critical shear rate ). There is a corresponding critical shear stress and the relevant point on the flow curve (or the shear rate-shear stress diagram) is known as the critical point. It is believed that it is reached in the die entry region (that is, where material is being funnelled from the die reservoir into the capillary of a capillary rheometer)—which, in an extruder, corresponds with the point at which melt moves into the die parallel portion of the die. Some further complicating effects may occur at the wall of the die. 

Critical point. The gel matrix reaches a point where it can no longer shrink to release the solvent necessary to reduce the capillary pressure. At this point the liquid meniscus enters the matrix and drying from within the film begins. This is when a crack is most likely to appear in the material, especially those produced with alkoxides, where the M—O—M network is stiff. Cracking occurs more with thicker films than with thin films. 

However, the influence of the attraction, exerted by the pore wall on the adsorptive, also plays a role and in more detailed interpretations, this should be taken into account. An illustration that liquids in capillaries may behave differently from their bulk counterpart is given in fig. 1.39. With increasing temperature, the hysteresis loops become thinner, disappearing completely at T=0.94 Tprif, i.e. the critical point of liquid in pores is lower than that of bulk liquid. 

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