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In an open dewar the cryogenic coolant such as liquid nitrogen and/or argon will evaporate, and will therefore change the level of cryogen around the sample cell stem and consequently the cold zone and warm zone volumes. Therefore, it is crucial that the specific position of the cryogen level on the sample cell stem is kept constant during the measurement. It should be maintained - unless otherwise compensated - at least 20 mm above the sample and constant to within at least 1-2 mm. This can be achieved by moving the dewar up, using a thermistor (sensor) coolant level control, a porous sleeve that surrounds the sample tube stem (to maintain the cryogen level by capillary action), or by periodic replenishing of the cryogen.
For maximum accuracy, the calibrated volumes and the manifold should be maintained at constant temperature, or alternatively, the temperature may be closely monitored, i.e., the actual manifold temperature need to be taken into account in the calculations of the adsorbed amount. The sorption isothenn is measured as a function of pressure until the saturation pressure Po of the bulk fluid is achieved. The term Po is defined as the saturated equilibrium vapor pressure exhibited by the pure adsorptive contained in the sample cell when immersed in the coolant (e.g., liquid nitrogen or argon).
The thickness of an adsorbed (liquid-like) film, as well the pressure where pore filling and pore condensation occurs in a pore of given width, is related to the difference in chemical potential of the adsorbate (Ua) and the chemical potential of the bulk liquid (Uo) at the same temperature (i.e., the temperature at which the adsorption experiment is perfonned). This chemical potential difference can be related to the pressures P and Po of the vapor in equilibrium with the adsorbed film and the saturated liquid, respectively , where R is the universal gas constant and T is the temperature. Hence, the adsorbed amount is measured as a function of the ratio P/Po and the accurate monitoring of the saturation pressure is crucial in order to ensure the highest accuracy and precision for pore size and surface area analysis.
The saturation vapor pressure depends on temperature. This is illustrated in the schematic phase diagram in below figure. The vapor pressure line, which defines the temperatures and pressures where vapor and liquid are in coexistence, tenninates in the critical point. The relationship between saturation pressure and temperature is given by the Clausius-Clapeyron equation: , where is the heat associated with the gas-liquid phase transition (heat of evaporation) and is the difference of molar volumes between coexisting vapor and liquid. For temperatures far below the critical temperature, corresponds to the molar volume of the vapor and, for relatively small temperature intervals, one can consider to be constant. Based on these assumptions the Clausius-Clapeyron equation can then be written as Thus, the saturation pressure increases exponentially with temperature. For instance, an increase of ca. 0.2 K results in a saturation pressure increase of ca. 20 torr for nitrogen at a temperature around 77 K.
Schematic phase diagram of a fluid. The vapor pressure line, which defines the temperatures and pressures where gas and liquid are in coexistence, terminates at C, the critical point. Tr is the triple point.
When adsorption isothenns are measured at the liquid nitrogen (77.35 K at 760 torr) or liquid argon (87.27 K at 760 torr), the coolant is usually held in a dewar flask. The system is open to atmosphere and the temperature of the liquid therefore depends on both the ambient pressure and the presence of impurities in the liquid, which tends to elevate the boiling point. Depending upon the amount of dissolved impurities, such as water vapor, oxygen and other atmospheric gases, the pure liquid nitrogen contained in the Po cell therefore exists at a slightly elevated temperature (ca. 0.1 - 0.2 K), which results in a saturation pressure increase of ca. 10- 20 torr. Hence, in order to perform an accurate pore size analysis, Po should be measured with the highest resolution possible. In fact an error in Po of ca. 5 torr at a relative pressure of 0.95 will lead to an error of 10% in the calculated pore size. Preferably, Po should be directly measured by condensing nitrogen in a dedicated saturation pressure cell contained in the coolant and connected directly to a dedicated, high precision pressure transducer. However, the effect of using an incorrect saturation pressure for a surface area calculation is reduced by the nature of the BET plot, since both the ordinate and abscissa will deviate in the same direction, leaving the slope nearly constant. For example, in the case of a BET C constant of 100, a slope of 1000 and an intercept of 10, an error of 15 torr in a total of 760 torr will produce less than 1 % error in surface area. Hence, in this case a direct measurement of the saturation pressure is not necessarily required; very often a value for the saturation pressure is estimated since, in the case of nitrogen adsorption at liquid nitrogen temperature, the real saturation pressure corresponds closely with ambient pressure. The effect of impurities in the liquid nitrogen bath on Po are often taken into account by adding 10 torr to ambient pressure, which will give the corrected saturated pressure to within 5 torr.
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