Full analysis --- Pore size distributions

More information can be extracted when the data are deconvoluted from the experimental resolution and the backscattering component and separate lifetimes are extracted with PATFIT to obtain the experimental resolution function and MELT to obtain lifetime distributions as shown in Fig 7.19 for the case of 23% and 80% porogen load. The probabilities were scaled to the peak value for the component at 0.5 ns and are enhanced by factors of 10 and 200 for lifetimes larger than 2 ns and 7 ns respectively. 

The 2 dominant components are due to the annihilation of positrons in the sample MSSQ material independent of pores ( 0.5 ns) para-positronium (-0.1 ns). Ortho-positronium annihilations in the MSSQ cage structure occur with a -4 ns lifetime. Lifetimes of 10 ns and greater are due to positronium in pores and tend to increase with increasing porogen load. Open porosity is associated with a lifetime of -100 ns (80% case, dashed line). 

The positron lifetime hovers around 0.5 ns ( ). All other lifetimes are due to positronium. The para-positronium (o) with nominally 0.125 ns and the smallest ortho positronium lifetime (A) of about 3.6 ns originate the cages inherent to MSSQ. This result agrees well with measurements on thick samples published earlier by Li et al. [23] The remaining three larger lifetimes originate from positronium in small (B) and large (7) closed pores and pores, connect to channels which link to the surface (Q open porosity). 

1 1 ortho positronium small pores J a large pores 

The lifetime of the small and large pores components increase linear with porogen load to 18 ns and 45 ns respectively at 40% porogen load and then level off or decline somewhat. Their intensities evolve in opposite directions the small pores (B) signal decreases, while large pores (7) 

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The experimental permeation results could be consistently described using Eqs. (9.43b) and (9.47) for Langmuir and Henry sorption respectively as shown by de Lange in a full analysis of sorption, permeation and separation results of five different gases [63]. This description requires knowledge of adsorption isotherms which could be measured only on unsupported membranes. To use these data for calculation of the permeation of supported membranes requires the assumption of equal pore characteristics in both cases. As discussed by de Lange et al. this is probably not correct in the case of silica layers. Based on sorption data a microporosity of about 30% and a pore size distribution with a peak at 0.5 nm is found. Analysis of permeation data point to a pore diameter of = 0.4 nm and a considerably smaller porosity. Table 9.7 summarises the sorption data. H2 and CH4 have relatively low (isosteric) adsorption heats (cf ) while CO2 and isobutane strongly adsorb. 

Despite its restricted applicahihty. Equation 5.5 has been used to quantify the pore size distributions in modern PTL materials (see the next section). An abbreviated version of the general mathematical description is included here to illustrate the limitations of the reported expressions, and the care needed to apply them. The full mathematical analysis is available from intermediate texts on differential geometry (Struik, 1961 Patrikalakis et al., 2010) and summaries are available from speciahzed monographs (Langbein, 2002 Finn, 2002b, 2006), and reports in the public domain (Concus and Finn, 1991,1995). 

To determine the surface area and pore size distribution by gas adsorption/desoiption measurements, nitrogen is most commonly used as the adsorbate, since liquid nitrogen is readily available and inexpensive. Total smface area can be determined from the isotherm between 0.05 and 0.3 relative partial pressme, at which point a complete monolayer has been formed on the sample surface. At higher partial pressures, the pores start to be filled by capillary condensation. From an analysis of the shape of the full isotherm, the distribution of pore sizes and total pore volume can be determined. The adsorption process is generally taken as completely reversible, but imder some conditions the isotherm may exhibit a different shape in desorption, as compared to absorption. This is called hysteresis. Sometimes, hysteresis data can be used to determine the structure and size of pores in the absorbent. Determinations of pore size distribution using adsorption/desorption isotherms are described in previous Porosity measurement chapter. 

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