(395ai) Adsorption Isotherms At Different Temperatures May Intersect

By 
Dana Abouelnasr and Kevin F. Loughlin, Department of Chemical Engineering , American University of
Sharjah, PO Box 26666, University City, Sharjah UAE. email:
dabouelnasr@aus.edu & kloughlin@aus.edu: (971) (6) 515-2982; FAX: (971) (6) 515-2979         

ABSTRACT

Common sense dictates that adsorption isotherms for
a given adsorbent-adsorbate system and at different temperatures should never intersect. 
Although this must be true for isotherms represented graphically as the
loading, q, vs. pressure or vs. ln P, this might not be true when they are
presented as θ vs. ln P.  For example, isotherms for n butane on 5A
zeolite clearly demonstrate this phenomenon.  This work uses the Gaussian
isotherm model to illustrate why this crossing may occur. 

The Gaussian model transforms a type I adsorption
isotherm into a straight line with slope equal to the standard deviation of the
isotherm, σ_e.  For two isotherms to never intersect, their
linear representations must be parallel (i.e., σ_e must be the
same for both isotherms).  A comparison of σ_e for several
isotherms indicates that this is not always true. 

The isotherm standard deviation can be found through
a linear regression fit using the Gaussian model.  It can also be estimated in
a relative fashion by eye, by comparing the range of ln P covered by each
isotherm; the larger the range, the larger the standard deviation.  This is
illustrated in Figure 1, in which θ vs. ln P is displayed for two
different standard deviations. 

Figure
1: The effect of increasing standard deviation on isotherm width. 

For example, the isotherms for the adsorption of
several n alkanes onto 5A zeolite were collected from literature and assessed
for consistency between studies.  The resulting isotherms come from several different
studies, and are remarkably consistent.  These isotherms are shown in Figure 2,
taken from our earlier work.

Figure
2:  Isotherms for several n alkanes on 5A zeolite.  Reduced temperatures for a
few isotherms are displayed as values on the graph. Isotherms are taken from
literature data.

The isotherms at low subcritical temperatures cover
a much wider range over ln P than isotherms at higher subcritical temperatures
or those at supercritical temperatures.  This indicates that σ_e
is large at low temperatures, and decreases as the temperature increases in the
subcritical range.  Since σ_e varies, then the slopes of the
linearized isotherms must also vary, dictating that the lines must intersect. 
This also appears in the more conventional representation of the isotherms as θ
vs. ln P, as is displayed in Figure 3 for n butane on 5A zeolite. 

Figure
3:  Intersecting isotherms for n butane.  Reduced temperatures for a few
isotherms are displayed as values on the graph. Isotherms are taken from
literature data.

The intersection between subcritical and
supercritical isotherms is readily apparent in Figure 3.  The reason for the
intersection can be observed to be the difference in the width of the isotherms
(or the standard deviation).  Therefore, adsorption isotherms can intersect
when presented as θ vs. P or ln P.

KEYWORDS: separations, supercritical,
subcritical, 5A zeolite, n alkanes, isotherms