INTRODUCTION
Potassium is one of the most important plant nutrients in soils and has thus been studied extensively. Although, the distribution of K^{+} forms differs from soil to soil as a function of the dominant soil minerals present, total soil K^{+} reserves are generally large. It is believed that the soils of arid and semiarid regions contain sufficient exchange K^{+} (exchange with NH_{4}^{+} acetate) and K^{+}bearing minerals able to release enough K^{+} to meet crop requirements.
Adsorption and desorption are most important chemical processes in soils and
soil constituents. Desorption kinetics of K^{+} have been determined
by using different extraction methods. In calcareous soils, Ca^{2+}
is the most common cation replacing interlayer K^{+}. The K^{+}
in the interlayer of illite can be exchanged by hydrated cations such as Ca^{2+}
and NH_{4}^{+} (Zhau and Huang, 2007; Scott,
1968). In addition, the presence of NH_{4}^{+} cation of
fertilizer (Mustscher, 1995) and Ca^{2+} in irrigation
water and of soil minerals able to release K^{+}.
Natural clinoptilolite zeolite has a threedimensional crystal structure and
its typical unit cell formula (Tehrani and Salari, 2005;
Rezaei and Movahedi Naeini, 2009). Their cation exchange
capacities is high and have a remarkable tendency for adsorption of cations
within their crystalline network which are plant available through an exchange
reaction by roots. Allen and Ming (1995) proved zeolites
released ions slowly. Processing and optimum application of this mineral in
Iran, sporadic explorations in areas such Semnan have led to valuable zeolite
resources of the eight documented reports regarding zeolite rich areas in Iran
(Rezaei et al., 2008; Rezaei
and Movahedi Naeini, 2009). Coexisted cations such as Na^{+}, K^{+},
Ca^{2+}, NH_{4}^{+} and Mg^{2+} are typically
presented with K^{+} and NH_{4}^{+}, the presence of
these competing cations could affect K^{+} desorption on clinoptilolite
(Cooney et al., 1999; Weatherley
and Miladinovic, 2004). Their selectivity of ionexchange on clinoptilolite
was determined in an order of K^{+}>NH_{4}^{+}>Na^{+}
>Ca^{2+}>Mg^{2+} (Guo et al.,
2008). Although, different potassium exchange capacities under the influence
of those competing cations have been measured by the above named researchers,
so far little information is available for the investigations of desorption
behaviors of K^{+} on natural zeolite and incorporation with loess soil.
In Golestan Province (Pardis Estate) with loess soil with prevailing illite
clay, exchangeable K^{+} is not always a reliable measurement of plant
availability. This region soils can’t supply K to plant growth despite they
are containing 270580 mg kg^{1} exchangeable K^{+} (exchange
with NH_{4}^{+} acetate) (Rezaei and Movahedi
Naeini, 2008, 2009). The available K^{+}
status after fertilizer application is also dependent upon the K^{+}
sorption and desorption capacity of soil. An alternative approach to soil testing
is to consider K^{+} extractable and release rate of K^{+} simultaneously
to improve fertilizer application.
No earlier reports on the rate constants for potassium adsorption or desorption by natural zeolite, soil and their incorporation were found (especially in Iran), hence, comparisons with a similar work was not possible. However, the comprehensive comparison and screening of kinetic models for effects of NH_{4}^{+} and Ca^{2+} concentration on K^{+} desorption on loess soils, clinoptilolite zeolite and the consequent alterations with zeolite additions in Golestan Province loess soils were not documented yet. This study has the following objectives:
• 
To investigate the K^{+} desorption kinetics with
NH_{4}^{+} and Ca^{2+} on zeolite and loess soil
with prevailing illite clay 
• 
To determine the effects of zeolit on desorption kinetics
of K^{+} on the incorpation of loess soil 
• 
To apply five kinetic models on K^{+} desorption 
MATERIALS AND METHODS
Zeolite and soil: The natural zeolite used in experiments was sourced
from North of Semnan Province, Iran. Composition of the natural clinoptilolite
used in this study was almost over 80% clinoptilolite and the remainder consisted
of bantonite (Rezaei and Movahedi Naeini, 2009).
The soil samples with a loess origin, obtained from a Typic Calcixerols (Rahmat Abad Series) of silty clay loam texture from the estate of Gorgan University of Agricultural Sciences and Natural Resources at Golestan Province, Iran (approx. 37°45’N, 54°30’E).
Analysis of soil and zeolite: The soil and zeolite samples were air dried
and ground to pass through a 2 mm sieve for laboratory experiments. We added (3.571
g) zeolite per (1000 g) soil (20 t ha
^{1}) zeolite into soil to obtaining
our aims. Samples (soil, zeolit and soil+zeolit) pH and EC were determined using
1:2 soil to water suspension with a glass electrode (
Rhoades,
1996) and particle size was determined by the hydrometer method (
Klute,
1986). Organic matter was determined by dichromate oxidation (
Walkey
and Black, 1934). Cation Exchange Capacity (CEC) of the samples were determined
by the (1 Molar NaOAC), pH 8.2 method (
Chapman, 1965) and
specific surface aria determined with Ethelene glycol monoethyl ether method (
Carter
et al., 1965). The following extraction solution were used for determination
of solution: extraction with a soil water ratio 1:20 for 30 min and exchangeable
form: extraction with (1 M NH
_{4}OAC) solution, pH 7 at a solution ratio
1:20 with an extraction time of 30 min. The semiquantitative mineralogical composition
of the clay fraction treated by Mgsaturation, Mgplus ethyleneglycolsaturation,
Ksaturation and K saturation and heat was determined by
Xray diffraction analysis
and using a Bruker D8 Xray diffractometer using CuKa radiation (40 kV and 30
mA), at a step size of 0.02°2 Theta and a step time of (1 sec) (
Mehra
and Jackson, 1960;
Kittrick and Hope, 1963). Pearson’s
correlations coefficient were used to determine the relationship between K
^{+}
and NH
_{4}^{+} and Ca
^{2+} concentration with the constants
a and b of the best model (to describe the adsorption and desorption of K
^{+})
represent the intercept and the slope of the linear curves.
Kinetics of potassium desorption: Desorption of K^{+} tests
conducted during February 2007 to September 2008 with batch method (Selim
and Archer, 1997; Wilson et al., 2004; Rezaei
and Movahedi Naeini, 2009) by NH_{4}^{+} and Ca^{2+}
solutions in Gorgan University of Agricultural Sciences and Natural Resources
soil laboratory. Kinetics of K^{+} desorption was studied by successive
extraction (Sparks and Libhardt, 1981; LopezPineiro
and Navarro, 1997; Jalali, 2007; Rezaei
and Movahedi Naeeni, 2008, 2009). We weighed 1.0
g of soil, soil+zeolit and zeolite in 50 mL polypropylene centrifuge tubes in
2 repetition and added (10 mL) of with an ionic strength and pH equivalent to
pardis saturated soil paste extract containing NH_{4}^{+} concentrations
(40, 60, 90, 120 and 140 mg L^{1}) from ammonium chloride for NH_{4}^{+}
treatments and Ca^{2+} (0.028, 0.057, 0.085, 0.128 and 0.171 mg L^{1})
from calcium nitrate for Ca^{2+} treatments. We used 10 times (2, 4,
8, 12, 48, 192, 240, 720, 1440 and 1800 h) for two treatments. A few drops of
chloroform were added to the tubes to suppress microbial growth. The centrifuge
tubes were capped and shaken for 1 h in each time at (150 rpm) (Schouwenburg
and Schuffelen, 1963) and room temperature (25±2°C) (Jalali,
2006). At the end of the adsorption times (each time) tubes centrifuged
at 3000 x g for 10 min (Kithome et al., 1998).
The quantity of K^{+} release by soil, soil+zeolite and zeolite was
calculated in the extracted solution.
Kinetic models: Different kinetic models described in Eq.
15, were used to describe K^{+} adsorption and
desorption by the natrul clinoptilolite zeolite, soil and soil+zeolit clinoptilolite.
First order modelln 
(K_{0}–Kt) = b–at 
(1) 
Zero order model 
(K_{0}–K_{t} ) = b–at 
(2) 
Elovich model 
K_{t} = b+a ln t 
(3) 
Parabolic diffusion model 
K_{t}/ K_{0} = b+at^{1/2} 
(4) 
Power fraction modelln 
K_{t} = b+a ln t 
(5) 
where, K_{t} is the amount of cumulative K^{+} desorbed or adsorbed at time t, t the time of adsorb or desorb, K_{0} is the maximum K^{+} adsorbed or desorbed (final equilibrium), a and b are constants.
An important term of these equations is the constant a, which is indicative
of the adsorb and/or desorb rate of K^{+}. These mathematical models
were tested by least square regression analysis to determine which equation
best described K^{+} adsorb and/or desorb by treatments. Coefficients
of determination (r^{2}) were obtained by least square regression of
measured versus predicted values. A relatively high r^{2} and low (SE)
values for the relationship between measured and predicated K^{+} adsorption
or desorption data indicate that the model successfully describe the kinetics
of K^{+} adsorption and desorption by soil, soil+clinoptilolite zeolite
and clinoptilolite zeolite. It should be noted that a high r^{2} value
for a particular kinetic model dos not necessarily mean that this model is the
best (Sparks, 1989). A model also cannot be used to definitivly
determine the mechanisms of K^{+} adsorption or desorption. Standard
errors of the estimate were calculated by:
SE = [Σ(K_{t}–K*)^{2}/n–2
]^{1/2}  (6) 
where, K_{t} and K* represent the measured and predicted K^{+} adsorb and/or desorb, respectively and n is the number of data points evaluated.
RESULTS
Samples properties: The soil was calcareous with large silt and clay
contents (silty clay loam) and zeolite was sandy. The exchangeable form of K
and zeolite was also relatively high in the studied samples. The soil was neutral
to slightly alkaline and low in EC and organic matter. Like soil, zeolite was
alkaline and Low in organic matter but high in EC. Clinoptilolie zeolite increased
CEC, EC exchangeable K^{+} and decrease organic matter, solution K^{+}
and specific surface area in soil+zeolite treatment (Table 1).
The predominate clays in soil were illite, chlorite, smectite. Xray diffraction
spectrum showed the standard peak for clinoptilolite zeolite was identical with
that in the raw sample and that the zeolite was of relatively high purity (over
80%) and clinoptilolie containing bantonit (less than 20%).
The soil sample had adequate K^{+} to supply the needs of cereal crops,
but inputs of K^{+} are required to maintain the availability of K^{+}
and zeolite cantining high exchangeable K^{+} (1983.3 mg kg^{1})
can help to reach that aim. Levels of exchangeable K^{+} reflect (1)
the ability of the soil minerals to weather and release K^{+}, (2) the
management and cropping of the site prior to sampling (Rezaei
and Movahedi Naeini, 2009).
Kinetics of potassium desorption: Potassium desorption was initially
fast (first 192 h, first stage) but continued with low speed (after 192 h) until
the end of the experiment (second stage). Potassium desorption for soil, soil
with zeolite and zeolite was 85.3 to 1496.9, 46.3 to 1380.6 and 14 to 559.9
mg kg^{1}, respectively for all NH_{4}^{+} concentration
(0 to 140 mg L^{1}). The amount of K^{+} desorbed was greatest
in the soil (Fig. 1ac). The natural clinoptilolite
zeolite addition to soil decreased K desorption than soil treatment. The amount
of K desorption increased with increasing NH_{4}^{+} concentration
in initial solution in all treatments. K desorbed amount was over than 60% total
desorption in rapid stag.
Figure 2ac show potassium desorption process
at Ca^{2+} concentration treatment in soil, soil+zeolite and zeolite
by passing of time. Like NH_{4}^{+} treatment the desorption
was initially rapid followed by a slower reaction. Potassium desorption for
soil, soil with zeolite and zeolite was 85.3 to 978.0, 46.3 to 889.0 and 14
to 432.21 mg kg^{1}, respectively for all Ca^{2+} concentration
(0 to 0.171 mg L^{1}).
It seems, increasing Ca^{2+} initial concentration increased K desorption
at Ca^{2+} treatment. The amount of K desorbed with natural clinoptilolite
zeolite was less than soil+zeolit and it was less than soil. K desorbed amount
was 60% from total K desorption in first stag (first 192 h) for soil and soil+zeolite
and it was 50% from total K desorption for zeolite.
Table 1: 
Some chemical and physical properties of soil, zeolite and
soil+zeolite 

CEC: Cation exchange capacity, SSA: Specific surface area,
OM: Organic matter, EC: Electrical conductivity 

Fig. 1: 
Cumulative potassium desorbed by (a) soil, (b) soil+zeolit
and (c) zeolite with time at NH_{4}^{+} treatment 
Result showed K desorption in Ca^{2+} treatment for zeolite was very
low. In similar equivalent concentrations of NH_{4}^{+} and
Ca^{2+}, K^{+} desorption in NH_{4}^{+} treatment
greater than Ca^{2+} in zeolite treatment.
The changes in the amount of K^{+} desorption in the loess soil with
prevailing illite clay and soil+zeolite with desorbe time in different treatments
and solution at 25±2°C indicating that the K^{+} desorption
in different Ca^{2+}and NH_{4}^{+} solutions during
the initial period (2192 h) was faster than that in the latter period of over
192 h.

Fig. 2: 
Cumulative potassium desorbed by (a) soil, (b) soil+zeolit
and (c) zeolite with time at Ca^{2+} treatment 
Zhou and Huang (2007) founded the same result like
these result. The K^{+} desorption from the illite of soil and zeolit
apparently did not proceed through a single reaction rate process during the
reaction period (01800 h); the exchange reaction appeared to greatly contribute
to K^{+} desorption in the period of 0192 h in all of treatment (especially
zeolit).
With Ca^{2+} and NH_{4}^{+} treatment, initial K^{+}
and NH_{4}^{+} concentration affected the amount of K^{+}
desorbed by the soil, soil+zeolite and zeolite. Similar observations were made
by Rezaei and Movahedi Naeini (2009) on studied of K^{+}
adsorption and desorption. this biphasic is characteristic of a diffusion control
process and has previously been observed for K^{+} (Martin
and Sparks, 1983) and other similar ion, lik NH_{4}^{+}
(Steffens and Sparks, 1997).
Zhou and Huang (2007) showed that the reactions of
K^{+} release from the illite in Ca(H_{2}PO_{4})_{2}
and NH_{4}H_{2}PO_{4} systems had a similar activation
energy, indicating that these two systems had a similar mechanism for the K^{+}
release and the cation and pH also affected the rate of K^{+} release.
Therefore, the variation in the rates of K desorption in different treatments (Ca^{2+} and NH_{4}^{+}) indicates that the cations (NH_{4}^{+} and Ca^{2+}) affected the rate of K desorption. Comparing K^{+} desorbed from the Ca^{2+} and NH_{4} treatments indicated K^{+} desorption from NH_{4}^{+} treatment was more than K desorption in Ca^{2+} treatment. Rezaie and Movahedi Naeini (2009) suggested no potassium preferential adsorption due to clay edge or inner positioning with bath experiment or K may be located in a truncated diffuse double layer soil.
Lower values of K^{+} desorption amount could be due to exchange of
K^{+} by Ca^{2+} on surface site of clay structure in the Ca^{2+}K^{+}
system (Ca^{2+} treatment). Once K^{+} is exchanged on these
sites, further exchange of K^{+} by Ca^{2+} would be slower,
as the size of hydrate Ca^{2+} (4.3A°) is larger than hydrate K^{+}
(3.3A°) (Rao et al., 1999). But at the NH_{4}^{+}K^{+}Ca^{2+}
system (NH_{4} treatment), the size of hydrate NH_{4}^{+}
(2.9A°) is close hydrate K^{+}. Martin and Sparks
(1983) indicated that wedge zones would selectivity screen out the Ca^{2+}
ion because of its larger size.
For most cases of this study, the desorption of potassium on all treatments didn’t finish to 1800 h in the experimental condition. In stage 2 of Ca^{2+} treatment the slop of K^{+} release mort than NH_{4}^{+} treatment. In zeolite in second stage the rate of K^{+} desorption was more than initial stage. This result shows that zeolite release K^{+} slowly. The higher desorption kinetics for potassium by various NH_{4}^{+} in zeolite is of significant importance to apply fertilizer and zeolite for supplay potassium and other nutrients.
Application of data to kinetic models
Desorption process: Different kinetic models were used to describe
K^{+} desorped in soil, soil+zeolit and zeolite. The desorption data
in NH_{4}^{+} treatment and all of concentration were found
to conform to the elovich model on soil, soil with zeolit and zeolite, other
models were also tested but did not fit the data and therefore are not discussed.
Table 2 shows the coefficients of determination (r^{2}),
Standard Errors (SE) and parameters (a and b) of Elovich model for soil, soil
with zeolit and zeolite. The coefficients of determination ranged 0.6400.768,
0.6490.801 and 0.8090.949 for soil, soil+zeolit and zeolite, respectively.
In all of treatments, Standard Errors (SE) of Elovich model increased with increasing
initial NH_{4}^{+} concentration (increasing trended).
In Ca^{2+} treatment the Elovich, zero order and power function models
describe the K desorption with soil and soil+zeolite (Table 3).
The Power function, zero order and first order models describe the K desorption
with zeolit in Ca^{2+} treatment and all of concentration. Table
4 shows parameters of those models. Increasing initial Ca^{2+} and
NH_{4}^{+} concentration increased parameters (slop and intercept)
of describing models on soil, soil+zeolite and zeolite (Table
3, 4).
Table 2: 
Parameters coefficient of determination (r^{2}) and
standard error of the estimate (SE) of the Elovich model, the best model
to describe of K^{+} desorption kinetics in soil, soil+zeolite and
zeolit, at NH_{4}^{+} treatment 

a: Slop, b: Intercept 
Table 3: 
Parameters coefficient of determination (r^{2}) and
standard error of the estimate (SE) of the power fraction, Elovich and zero
order models, the best models to describe of K^{+} desorption kinetics
in soil and soil+zeolit, at Ca^{2+} treatment 

a: Slop, b: Intercept. *a: mg kg^{1}, *b: mg/kg/h 
Table 4: 
Parameters coefficient of determination (r^{2}) and
standard error of the estimate (SE) of the zero order, power function and
first order the best models to describe of K^{+} desorption kinetics
in zeolite, at Ca^{2+} treatment 

a: Slop, b: Intercept. *For power fraction zero order and
first order models. *a: mg kg^{1}, *b: mg/kg/h 
Zeolite decreased these parameters on corporation
with soil. In Ca^{2+} treatment the trend of slop values of zero order and first
order was less than 1 mg/kg/h (Table 4).
DISCUSSION
According to results the Elovich model was the best model to describe desorption
data for potassium, for soil and zeolite amended soil and zeolite in Ca^{2+}
and NH_{4}^{+} treatments. Successful presentation of the Elovich
equation for nonexchangeable K^{+} release from soils has been reported
by Jalali (2006, 2007). Aharoni
et al. (1991) and Aharoni and Sparks (1991)
have noted that a conformity of experimental data to Elovich equation indicated
by a relatively high r^{2} value during an entire excrement could suggest
a heterogeneous diffusion process. The slops of the Elovich model for the desorption
processes for all Ca^{2+} and NH_{4}^{+} suggesting
heterogeneous diffusion (Aharoni and Sparks, 1991;
Kithome et al., 1998; Rezai and Movahedi Naeini, 2009).
Since, both power function and parabolic diffusion models describe the rate process
and then the latter may also represent slow diffusion of K
^{+} from mica
interlayer positions (
Havlin et al., 1985). The
power function described slow diffusion desorption of K
^{+} by the natural
clinoptilolite zeolite on Ca
^{2+} and NH
_{4} treatments.
The cumulative K^{+} desorption was fitted to the first order model
in zeolite at Ca^{2+} treatment. Successful description of K^{+}
release by the first order model was previously reported by Dhillon
and Dhillon (1990). This was expected since several mass action rate processes
may have been occurring independently the possibility of multiple first order
reactions corresponding multiple independent retention sites in the zeolit mineral,
similar to the multiple reactions suggested by Kithom et al. (1998) and
Jardin and Sparks (1984) was not justified by the data.
Since, the zeroorder and firstorder rate equations were virtually the same
in fitting the data of K release. The zeroorder rate equation described the
data quite well as shown by the SE and r^{2} values. The results indicate
that the K release, which was induced by Ca^{2+}, apparently followed
the same rate process in the reaction period of 21800 h.
The results shown a significant positive correlation between ammonium concentration
and potassium desorption coefficient rate of Elovich with zeolite treatment
(p = 0.05, 0.88), a non significant positive correlation for soil (p = 0.11,
0.78) and also mixture of soil and zeolite (p = 0.8, 0.83). The Increasing correlation
(mixture of soil and zeolite toward soil) suggested the effect of ammonium concentration
and zeolite addition on potassium desorption in soil by passing of time. Also,
the results of this study shown significant positive correlation between calcium
concentration and potassium desorption coefficient rate of Elovich model with
soil treatment (p = 0.014, 0.94) and the mixture of soil and zeolite (p = 0.003,
0.98) and also zero order for zeolit (p = 0.008, 0.96).
CONCLUSIONS
Arid and semiarid region soils generally contain large quantities of exchangeable and nonexchangeable K^{+}. Increasing of Ca^{2+} and NH_{4}^{+} concentration increased rate of K^{+} desorption in soil, zeolite and their incorporation and zeolite decreased desorption rate by incorption with soil. Result shows that zeolite release K^{+} slowly.
The power function, zero order and first order models suggested that the process of K desorption by all of treatments in Ca^{2+} was controlled as slow diffusion and mass action. A good fit with Elovich, suggests diffusion as the principle mechanism at least for the later stages of K^{+} desorption kinetic of the studied elements (soil, soil+zeolit and zeolite). Intercept increased with zeolite incorporation in NH_{4}^{+} treatment and some of concentration in Ca^{2+} treatment which might suggest increased potassium availability in soils with limited diffusion to the bulk solution due to a truncated double layer.
In this study, although (a) the rate constant and (b) intercept for potassium expressed differently between two treatments, one fact should be notified that desorb rates of potassium on Ca^{2+} treatment less than NH_{4}^{+} treatment occurred on soil, soil+zeolite and zeolite. The Increasing correlation between ammonium and potassium desorbed (mixture of soil and zeolite toward soil) suggested the effect of ammonium concentration and zeolite addition on potassium desorption in soil by passing of time.
ACKNOWLEDGMENTS
The authors thank Mohamad Zaman Alaodin and Mohamad Ajami for their technical. This research was funded by Gorgan University of Agriculture Science and Natural Research (Iran).