Micropore Area and Volume by the t-Plot Method
The t-plot allows one to determine the micropore volume and micropore area from a gas sorption isotherm without the need to measure the low pressure micropore-filling portion of the isotherm. The t-method is applied to the range of multi-layer adsorption and can be applied to isotherms from instruments such as the NOVA series and QUADRASORB evo that do not have the low pressure transducers or the turbomolecular pump.
A wide variety of industrially important materials, such as zeolite catalysts and carbon blacks, include a substantial quantity of micropores (pores smaller than 2 nm) and larger mesopores (pores 2-50 nm). Micropore size distributions, volume, and area can be directly accessed through measurement of an N2 (77 K) or Ar (87 K) isotherm starting at low relative pressures (P/P0 < 10-5 ). Measurements at these pressures require the use of low pressure transducers and a turbomolecular pump vacuum, which can be costly additions to an instrument. And, while the tmethod developed by deBoer can be applied in instruments which do have a turbomolecular pump and low pressure transducer (such as the Anton Paar Autosorb iQ-MP and –XR), its advantage is in the ability to indirectly measure the contributions of micropores to the total pore volume and surface area without the need for a low pressure transducer or turbomolecular pump, (such as on the NOVA series of instruments). Also note that micropore measurements starting at low relative pressures may take longer than 24 hours to complete, while the limited range for the tplot calculation can be measured in only a few hours.
Using the t-method, adsorption data can be plotted as a t-curve: the volume of nitrogen adsorbed vs. t, the statistical thickness of an adsorbed layer on a nonporous reference surface at a corresponding relative pressure. The t values can be calculated from the relative pressures used in obtaining the adsorption data from the equation proposed initially by deBoer or equations based on carbon black, depending on the material you are analyzing.
Examples of the two possible resulting t-plots are shown in Figure 1. In the case of a meso-, macro-, or non-porous material (i.e., no micropores), extrapolation of the t-plot to the y-axis will result in a line through the origin (or, sometimes slightly negative). In this case, the calculated micropore volume and area will be zero. When micropores are present, the t-plot will exhibit a positive intercept. The intercept of the t-plot, when converted to liquid volume, gives the micropore volume.
- J.H. deBoer, B.C. Lippens, B.G. Linsen, J.C.P. Broekhoff, A. van den Heuvel, T.V. Osinga. J. Colloid Interface Sci., 1966, 21, 405-414
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