Aem Lect6
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Aem Lect6 Presentation Transcript

  • 1. BET equation Assumption for BET(Brunauer, Emmett and Teller) method - Gas adsorption at the flat and uniform surface - no lateral interaction between the absorbed molecules - multi-layer adsorption is possible • • • ••••• Advanced Electronic Ceramics I (2004) BET equation 1 Advanced Electronic Ceramics I (2004)
  • 2. BET equation 2 Advanced Electronic Ceramics I (2004) BET equation 3 Advanced Electronic Ceramics I (2004)
  • 3. BET equation 4 Advanced Electronic Ceramics I (2004) BET equation 5 Advanced Electronic Ceramics I (2004)
  • 4. BET equation 6 Advanced Electronic Ceramics I (2004) BET equation 7 Advanced Electronic Ceramics I (2004)
  • 5. BET equation 8 V = Volume of gas adsorbed at pressure P Vm = Volume of gas which could cover the entire adsorbing surface with a monomolecular layer Po = Saturation pressure of the gas, i.e. the pressure of the gas in equilibrium with bulk liquid at the temperature of the measurement. P/Po = relative pressure Advanced Electronic Ceramics I (2004) BET analysis Advanced Electronic Ceramics I (2004)
  • 6. BET analysis V = Volume of gas adsorbed at pressure P Vm = Volume of gas which could cover the entire adsorbing surface with a Typical range monomolecular layer Po = Saturation pressure of the gas, i.e. the 1 pressure of the gas in equilibrium with bulk liquid at the temperature of the 2 measurement. Single point BET Advanced Electronic Ceramics I (2004) Validity and limit of BET analysis Assumptions (And limit) 1. Gas adsorbs on the flat, uniform surface of the solid with a uniform heat of adsorption Non-uniform surface due to surface steps, cracks, edges, vacancies and other defects (thereby, non-uniform adsorption energy) 2. No interaction between the adsorbed molecules. Adsorbed molecules can interact with each other 3. From the 2nd layer, gas adsorb either on the remain the remaining free surface or on top of the already adsorbed layer. 4. The adsorption of the 2nd and subsequent layers occurs with a same heat of adsorption (= the energy of evaporation) The heat of adsorption is likely to change gradually as additional layers build up rather than in a single step. 5. There is no limit to the number of layers which can adsorb. Advanced Electronic Ceramics I (2004)
  • 7. BET analysis Why multi-point adsorption at constant temperature? In order to eliminate the changes in pressure from small changes in temperature. (using the regression of multi points of data) A small temperature fluctuation changes the saturation vapor pressure considerably. Ex) 0.1K increase changes the saturation pressure of nitrogen from approx. 760 mm Hg to 800 mm Hg. Argon or Krypton as an absorbent can be used for more sensitive measurement when the surface area of the sample is very low. http://www.micromeritics.com/sa_gemini_at.html Advanced Electronic Ceramics I (2004) BET equipment Surface Area: Specific: 0.01 m2/g and higher Total: 0.1 m2 and higher, +- 0.03 m2 Pore Volume: 4 x 10-6 cm3/g and higher - Fully automatic operation - High speed operation - Multi-point analysis automatically http://www.micromeritics.com/sa_gemini_at.html Advanced Electronic Ceramics I (2004)
  • 8. BET equipment Each pressure point completely equilibrates before the next point is taken. The Gemini has, as illustrated in Figure 1 (below), two gas reservoirs (A) which are filled with equal volumes of the desired adsorptive, usually nitrogen. From the reservoirs, gas is dosed into the sample and balance tubes. A transducer (B) on the sample side monitors for the target pressure. As the sample adsorbs gas, the pressure would tend to decrease in the sample tube were it not that transducer (B) causes a fast response servo valve (C) to hold the pressure constant. Transducer (D) located between the sample and balance tubes detects any pressure difference between the two tubes and causes another servo valve (E) to balance the pressures in both tubes. A third pressure transducer (F) monitors the pressure between the two reservoirs to determine the amount of gas that is adsorbed on the sample. http://www.micromeritics.com/sa_gemini_at.html Advanced Electronic Ceramics I (2004) Scherrer equation λ : wavelength 0.9λ t : crystallite size B : broadening at half t= of the peak height B cosθB angular width of 2θ θB : Bragg angle λ = 1.5Å d=1Å θ = 49o t = 1mm B=2x10-7 rad (10-5deg) t=500Å B=4x10-3 rad (0.2 deg) B. D. Cullity, Elements of X-ray Diffraction Advanced Electronic Ceramics I (2004)
  • 9. Comparison Information Sedimentation Laser Microscopy BET Scherrer (Photo-sedi.) Diffraction (SEM) equation (X-ray sedi.) (TEM) 0.02-50 µm 0.01-50 µm > 0.0005 µm ~0.001 µm size range no limit particle primary + primary + primary primary + primary secondary secondary secondary dispersion Yes Yes usually no no no medium Main convenient sub-micrometer direct actual crystallite advantage detection information contribution size (size & morphology) of surface Main cannot know cannot know disadvantage the real particle the real particle small number sizes when the sizes when the of observation dispersion is dispersion is tends to lead not good not good error in estimation Advanced Electronic Ceramics I (2004)