Cryoporometry and Relaxometry

NMR cryoporometry method was developed (Overloop and Van Gerven 1993, Strange et al. 1993, Akporiaye et al. 1994) on the basis of the thermodynamic theory of the phase transition in materials in confined space pioneered by J.W. Gibbs, J. Thomson, and W. Thomson. According to Gibbs-Thomson equation for the melting point depression, A7j , for a small isolated spherical crystal of diameter x in its own liquid can be written as (Jackson and McKenna 1990) 

TJyX) is the melting temperature of ice crystallite of diameter x is the bulk melting temperature p is the density of solid 

Oji is the surface energy of solid-liquid interface is the bulk enthalpy of fusion 

If we assume that the interactions between the pore walls and crystal and liquid located there have a weak influence on the phase transition that Equation 1.45 can be interpreted as the dependence between the pore size (x) and melting temperature of ice in this pore. However, a more accurate equation should include the contact angle q (which is commonly assumed to be 0° in the liquid-vapor [Kelvin] case and 180° in the solid-liquid [Gibbs-Thomson] case), that is, cos( p) as a parameter describing interactions in the system vapor-Uquid-solid in pores (Mitchell et al. 2008)  

A is a normalization factor depending on the values of units used in Equation 1.52 

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The interfacial behavior of water/organics (Franks 2000, Chaplin 2011), which can be very important on practical applications of porous materials as adsorbents, catalysts, etc., can be investigated by using both NMR cryoporometry and relaxometry techniques and TSDC method for deeper understanding of structurization of liquids confined in pores of ordered mesoporous silicas. Here, we will analyze results of a study of (i) the structural characteristics of synthesized ordered mesoporous silicas MCM-41, MCM-48, and SBA-15 by XRD, adsorption, and FTIR methods to explain the difference in their adsorption characteristics with respect to polar (water), weakly polar (chloroform), and nonpolar (benzene) adsorbates (ii) the relationships between these characteristics and the behavior of adsorbed pure water and its mixtures with benzene or chloroform-c over a wide... 

Valckenborg, R., Pel, L., and Kopinga, K. 2001. Cryoporometry and relaxometry of water in sUica-gels. Magn. Reson. Imag. 19 (2001) 489-491. 

Thus, different versions of NMR and TSDC cryoporometry (as well as DSC thermoporometry (Landry 2005), vide infra) and relaxometry allow one to obtain the structural characteristics not only for powders but also for strongly hydrated systems that is of importance for biomaterials, cells, and other bio-objects, which can be studied in the native state. In other words, these methods are nondestructive methods. 

FIGURE 1.206 Comparison of the pore (voids between nanoparticles) size distributions calculated using four methods (1) NMR cryoporometry and (2) NMR relaxometry, (3) and (4) TSDC cryoporometry (aqueous suspensions at Cj, qq=3-1 wt%), and (5) PSD calculated using the nitrogen adsorption isotherm (SCV/SCR model, see Section 1.1.1). 

The H NMR cryoporometry method can be used to measure broad pore sizes (Figure 1.239) if octamethylcyclotetrasiloxane is used as an adsorbate (Ono et al. 2009). Three very different methods such as the nitrogen adsorption, the H NMR cryoporometry, and the mercury porosimetry give the PSDs, which are mutually complementary. These results confirm that organic molecules are better probe compounds than water for the structural characterization of macroporous materials with NMR cryoporometry or relaxometry. 

A maximum comprehensive study of any object is the best way to obtain maximum reliable information. For instance, a combination of NMR cryoporometry or relaxometry (or DSC thermoporometry) with nitrogen (or argon) and water (or another compound nsed as a cryoporometry/ relaxometry probe) adsorption, SAXS (Gun ko et al. 2011a), FTIR (Shen and Ostroverkhov 2006, Gun ko et al. 2009d), DRS (Buchner 2008), TSDC (Gun ko et al. 2007i), and CLSM (Savina et al. 

Figure 1.206 shows the PSD (or UWCSD) calculated using the NMR and TSDC cryoporometry methods, NMR relaxometry (aqueous suspensions), and nitrogen adsorption method. 

Krutyeva et al. (2009) used combined NMR cryoporometry, relaxometry, and diffusometry to characterize porous carbon materials. They studied two carbon molecular sieves (CMS Takeda 4A... 

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