The thermal conductivity bridge and flow circuits shown in below 2 figures are capable of producing a full-scale signal (1.0 mV) when 0.01 cm3 of nitrogen are desorbed into a 30% nitrogen and helium mixture. To achieve stable operating conditions at this sensitivity, the thermal conductivity block requires some time to equilibrate thermally and the system must be purged of any contaminants.

thermal conductivity bridge electronic circuit

flow diagram for a continuous flow system

A desorbed volume of 0.001 cm3, using nitrogen as the adsorbate, will correspond to about 0.0028 m2 (28 cm2) of surface area if a single adsorbed layer were formed. An equivalent statement is that 0.0028 m2 is the surface area, measured by the single point method, on a sample which gives a high C value, if 0.001 cm3 were desorbed. Assuming that a signal 20% of full scale is sufficient to give reasonable accuracy for integration, then the lower limit for surface area measurement using hot wire detection is about 0.0006 m2 or 6 cm2. With the use of thermistor detectors, the lower limit would be still smaller.

Long before these extremely small areas can be measured with nitrogen, the phenomenon of thermal diffusion obscures the signals and imposes a higher lower limit. Thermal diffusion results from the tendency of a gas mixture to separate when exposed to a changing temperature gradient. The sample cell is immersed partially into liquid nitrogen. Hence, when the gas mixture enters and leaves the sample cell it encounters a very sharp thermal gradient. This gradient exists along the arm of the tube for ca. 2 cm above and below the liquid level, and consequently gases will tend to separate. The extent of separation is proportional to the temperature gradient, the difference in the molecular weights of the two gases and their relative concentrations. The heavier gas tends to settle to the bottom of the cell and as its concentration builds up, a steady state is soon achieved and then the concentration of gas entering and leaving the cell is the same as it was initially. The build up of the heavier gas is only a fraction of a percent and even as low as a few parts per million. Therefore, it does not affect the quantities adsorbed in any measurable way.

However, when the bath is removed and the cell warms up the steady state is disturbed and the slight excess of heavier gas generates a signal followed by a signal due to the excess of lighter gas held up in the "in" arm of the cell. These signals are observed as a negative signal before or after the desorption signal and can generate errors in the integration of the desorption signal. This effect begins to manifest itself with nitrogen and helium mixtures when the total area in the cell is approximately 0.1 - 0.3 m2.

In a static mixture of gases, the amount of thermal diffusion is a function of the time rate of change of the temperature gradient, the gas concentration, and the difference in masses of the molecules. In a flowing gas mixture, in the presence of adsorption, it is difficult to assess the exact amount of thermal diffusion. Lowell and Karp measured the effect of thermal diffusion on surface areas using the continuous flow method. Below figure illustrates a fully developed anomalous desorption signal caused by thermal diffusion. As a result of the positive and negative nature of the signal, accurate integration of the true desorption peak is not possible.

signal shape from desorption of a small volume of nitrogen

Below table 1 shows the results of measuring the surface area of various quantities of zinc oxide using a conventional sample cell, below figure (a). When the same sample was analyzed using a micro cell, below figure (b), the results obtained were considerably improved, as shown in table 2.

Table 1: data obtained using conventional cell (measured using the single-point BET surface area method with 20% N2 in He).

sample cells design (a) & (b)

table 2: data obtained using U-tube cell

The onset of thermal diffusion depends on the gas concentrations, the sample surface area, the rate at which the sample cools to bath temperature, and the packing efficiency of the powder. In many instances, using a conventional sample cell, surface areas less than 0.1 m2 can be accurately measured on well-packed samples that exhibit small interparticle void volume. The use of the micro cell (b) is predicated on the latter of these observations. Presumably, by decreasing the available volume into which the denser gas can settle, the effects of thermal diffusion can be minimized. Although small sample quantities are used with the micro cell, thermal conductivity detectors are sufficiently sensitive to give ample signal.

Attempts to increase the size of nitrogen adsorption or desorption signals, by using larger sample cells, results in enhanced thermal diffusion signals due to the increased void volume into which the helium can settle. However, when krypton is used, no thermal diffusion effect is detectable in any of the sample cells.

The adsorption signals using krypton-helium mixtures are broad and shallow because the adsorption rate is limited by the low vapor pressure of krypton. The desorption signals are sharp and comparable to those obtained with nitrogen, since the rate of desorption is governed by the rate of heat transfer into the powder bed.

With krypton, the ability to use larger samples of low area powders facilitates measuring low surface areas because larger signals are generated in the absence of thermal diffusion. Also, as is true for nitrogen, krypton measurements do not require void volume evaluations or nonideality corrections, nor is thermal transpiration a factor as in the volumetric measurements.