C - Lublin

Q V (pH)/N t = α(pH) =
n
∑
i=
1
n
αi(K i , pH s ) N i /N t = ∑ αi(K i , pH s ) f(K i ), (4)
where N t is the total amount of surface groups and f(K i )=N i /N t is a fraction of i-th
groups. Using condensation approximation (Nederlof et al. 1993) the f(K i ) values
are:
f(K i ) = 1/N t ∆ Q V (pH)/∆K i ; K i = [H + s ], (5)
and in logarithmic scale:
f(pK i ) = 1/N t ∆ Q V (pH)/∆pK i ; pK i = pH s . (6)
The distribution function of surface dissociation constants, i.e. f(K i ) vs. K i dependence,
can be calculated knowing both surface protons activity (pH s ) and N t
values. Soil components, as well as plant root surfaces may have different shapes
and different charges thus may vary in surface potential values. For pH s (and K i )
calculations, basing on the diffuse double layer theory, a single potential value
spread uniformly over all surfaces of the same shape is a common assumption,
which seems not to be valid in the case of soils and plants. Also, there still exist
much controversies on the application of the DDL theory to surface chemistry (Mc
Bride, 1997). Therefore, the surface proton activity is replaced by the solution activity
and N t is taken as N max = maximal value of (N susp -N sol ) measured within the
experimental window and, instead of the intrinsic, the distribution functions of
apparent surface dissociation constants, K app , are determined:
f (pK app,i ) = 1/N max ∆Q V (pH)/∆pK app ; pK app = pH. (7)
The average value of pK app , pK app,av , is calculated as:
n
pK app,av = ∑ pKi,app f i (pK app ), (8)
i=1
which is direct measure of the average energy of the proton binding.
Having the variable charge vs. pH dependence one can find the relation of actual
surface charge, Q A , vs. pH. To do this the Q V (pH) curves are shifted against y-
axis to meet the actual charge value at any pH e.g. a cation exchange capacity of
the studied solid, estimated at the same ionic strength, at which the titration is performed.
One should select a higher pH value to diminish eventual occurrence of
positive surface charge that is not determined during the CEC measurements.
i=1
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