
Research Article


Effect of Different Factors on Diffusion Characteristics of Potassium in Alluvial Soils of Eastern Indo Gangetic Plain 

Sourov Chatterjee
and
Debjani Ghosh



ABSTRACT

To understand the transport behaviour of potassium as influenced by different factors, the tracer diffusion (D_{a}) and porous diffusion (D_{p}) coefficients of potassium were studied in three alluvial soils of varying potassium content and mineralogical composition. Diffusion coefficients were increased with increase in moisture content (θ), temperature (T), bulk density (d) and tracer:bckground ratio (R). The D_{a} and D_{p} values were significantly higher when NaCl was taken as background electrolyte than for CaCl_{2}. Soil with higher exchangeable K and illite content recorded higher D_{a} and D_{p }values. The energy of activation (E_{a}) decreased significantly with increase in bulk density and the Arrhenius frequency factor (A) and entropy factor of diffusion (σ) were found to significantly decrease with increasing tracer component. Exchangeable K, nonexchangeable K and illitic fraction of the clay minerals was found most relevant factor predicting the diffusion coefficients of potassium in the alluvial soils.





Received: March 03, 2014;
Accepted: June 09, 2014;
Published: August 07, 2014


INTRODUCTION Management of potassium has become very important in sustaining or increasing crop yield. Proper potassium management requires thorough understanding of soil potassium behaviour and the various potassium inputs and outputs of cropping systems. It is well known that the availability of potassium to plants depends not only on the size of the available pool in soil but also on the transport of potassium from soil solution to the root zone and from the root zone into plant roots. The rate of solute movement in soil has a direct relationship with the soil fertility status and diffusion coefficients of the nutrient ion provide the information for that solute movement (Olsen and Kemper, 1968). Diffusion accounts for more than 90% of potassium moving to the plant roots, depending on the initial potassium concentration in the soil solution (Nye, 1972) and can contribute from 7296% of the total potassium uptake (Oliveira et al., 2004). Such diffusion coefficient of potassium may be successfully utilized to predict the plant uptake of the same from soil. The tracerdiffusion may be defined as diffusion of a single component present in very small concentration, in a large excess of the other components; in others words, the tracercomponent is subjected to a concentration gradient of its own (Sanyal, 1980). This tracer diffusion coefficient is influenced by different factors like, tracer:background ratio (R), background electrolyte (E), volumetric soilwater content (θ), bulk density (d) and temperature (T) (Mani and Sanyal, 1995; Dhar and Sanyal, 2002). The soil potassium mobility increases with soil moisture content and had a positive correlation with effective diffusion coefficient (D_{e}) (Zeng and Brown, 2000) which suggest that more K^{+} can diffuse to plant roots at sufficient soil moisture. The diffusion coefficient is also related with the exchangeable form of potassium and soils with higher exchangeable potassium content having higher diffusion coefficients (Wani and Datta, 2007; Benipal et al., 2006). Deb et al. (1983) obtained the highest diffusion coefficient of Zn at a particular bulk density, irrespective of the variations in soil characteristics. The temperature effect may be attributed to a higher probability of the diffusing entities, being more readily able to overrole the activation energy hill at a higher temperature due to concomitant larger kinetic energy content of the diffusing ions (Mani and Sanyal, 1995). However, there is lack of detail information on diffusion characteristics of potassium and its relation with different forms in a particular soil type viz., alluvial soils. Thus, the objective of this investigation was to study the effect of different factors like bulk density, temperature, moisture content background electrolyte, tracer:background ratio on apparent and porous tracerdiffusion coefficient of potassium in alluvial soils widely varying in characteristics with respect to potassium status and mineralogical composition. The relationship between the apparent selfdiffusion coefficient of potassium and the corresponding energy of activation (E_{a}), Arrhenius frequency factor (A) and the entropy factor of diffusion (σ) was also studied to understand the mechanism of diffusion in terms of thermodynamic suitability. In addition to study the semiquantitative assessment of the clay mineralogical makeup of the given soils to ascertain the latter’s ability to release potassium towards supporting the diffusion process under study. Finally to develop a prediction relationship of diffusion of potassium with different forms and different compositions of clay minerals to probe the transport behaviour of potassium in a particular domain which may help for efficient management of added fertilizer for plant uptake.
MATERIALS AND METHODS Soil samples (00.15 m) were collected from three sites namely Nonaghata Uttarpara (S_{1}), Telegacha (S_{2}) and Moratripur (S_{3}), where ricewheat cropping system was followed from last 15 years located in the hot, humid subtropics at Nadia District of West Bengal, India (22° N and 88° E) which is located at Eastern Indo Gangetic Plain considering the wide variability in their potassium supplying capacity. Some important physicochemical characteristics of the soils were determined following the standard procedure and given in Table 1. Exchangeable K was determined by neutral 1M NH_{4}OAc extractant and nonexchangeable K was determined using boiling 1 M HNO_{3 }for a period of 10 min as stated by Pratt (1965). The clay fractions of the soils were fractionated by the method described by Jackson (1973) and for the interpretation of the minerals present, the clay samples were Casaturated, Caglycolated, Ksaturated and heated to 300 and 550°C. For the semiquantitative estimation of the clay minerals, the methodology proposed by Gjems (1967) was adopted. Diffusion studies were conducted following the Browns’ halfcell technique (Brown et al., 1964). The soil samples were air dried, finely powdered and passed through a 2 mm sieve. Calcium and sodium were used as the background cation for diffusion of K in soils, all having limiting ionic conductance of the same order of magnitude. A bulk amount of soil (600 g) was equilibrated with calcium chloride and sodium chloride solutions separately leading to a cationic concentration in the homoionic soils of 3200 mg kg^{1} with respect to each cation. The soil was mixed thoroughly with the appropriate aqueous salt solution in order to ensure a uniform distribution of Ca^{++} and Na^{+} ions.
Table 1: 
Some important properties of soil in West Bengal 
 This was followed by six cycles of alternate wetting and drying after which the water extractable Ca^{++} and Na^{+} ion concentrations in the treated soils were found to attain constant values. The potassium chloride was added to one half of the calcium and sodiumequilibrated soils to have two different K levels of 100 and 200 mg kg^{1}. Three additional cycles of wetting and drying processes were continued in each treated soil sample for ensuring a uniform distribution of the tracer. For measurement of diffusion coefficient of K, experiments were run marinating two different bulk densities of 0.99 and 1.08 Mg m^{3} for the selected soils. The corresponding amounts of the oven dry soil to be packed in each halfcell (M) was obtained by using the equation: M = V.ρ where, V is the inner volume (m^{3}) of each halfcell and ρ is the required bulk density (Mg m^{3}). The inner volume V is given by: V = πr^{2}h where, r is the inner radius of the halfcell and h is the length of each halfcell. The desired moisture level was maintained by adding water to the surface of the soil. One half of the diffusion cell was packed with only background electrolyte treated soil, while the other half with (background+tracer)equilibrated soil at the desired bulk density and moisture content. The two halfcells were slowly brought together and were held in position by tightening the screws (at four corners) across the supporting pair of bakelite sheets. The cells were covered with polythene sheets and kept inside an incubator at the desired temperature for the requisite period of diffusion (Sanyal and Bhattacharya, 1986). A cellotape seal was used along the periphery where the two halfcells joined each other in order to ensure (water) leakproof condition in course of diffusion. Potassium diffusion experiments were run maintaining two different temperatures, 25 and 35°C for all three soils, in an incubator which allowed temperature fluctuations within ±1°C. On expiry of the diffusion period (six days in the present case), the two halfcells were carefully detached from each other and the soil from each halfcell was thoroughly mixed, from which 5 g soil was extracted with 50 mL of distilled water and the suspension was filtered. The K contents of the filtrates corresponding to soil extracts were determined flame photometrically. The capacity factor (b) was determined by the method described by O’Connor et al. (1971, 1975). One, 2, 3, 4 and 5 g soil containing no extraneous K was taken. The 25 mL of 100 ppm KCl solution was added and was kept for two days to ensure equilibrium and maximum K adsorption by the soil. After shaking for 1 h, the suspensions were centrifuged and total K present in the supernatant was determined flame photometrically. The difference between the initial and the final K contents of the soil solution indicated the amount of K adsorbed by the soil. For each treatment, K adsorbed, expressed as percent of K adsorbed per cm^{3} of soil, was plotted against percent of added K left per cm^{3} of the filtrate. The slope of the curve gave the b factor.
To study the effect of different factors such as soil moisture content (θ), temperature (T), bulkdensity (d), tracer:background cation concentration ratio (R) and background electrolyte (E) on diffusion, a set of 2x2x2x2x2 factorial experiments were conducted. The experimental set consisted of a combination of 32 treatments. The apparent tracerdiffusion coefficient (D_{a}) of K was obtained by using the relationship (Porter et al., 1960):
where, f is the fraction of the tagged ion (K^{+}) which diffuses in time t from the tagged to the untagged halfcell and ‘h’ is the length of each halfcell, f is given by: The D_{P} is related to Da as: D_{p} = D_{α}(b+θ) where, b is the capacity factor and θ is the volumetric moisture content. As θ is generally small in comparison with b (0<θ<1) for the agricultural soils, the approximation was made that: By the method described by De LopezGonzalez and Jenny (1959) and Brown et al. (1968), Ea (energy of activation) was calculated using the following Eq. 4:
where, D_{a }is the apparent tracerdiffusion coefficient, A is the Arrhenious frequency, R is the universal gas constant and T is the absolute temperature of the study, thus: By plotting log D_{a} against 1/T, one obtains E_{a} and A from the slope and the intercept, respectively of the resulting linear plot. Entropy factor of diffusion (σ) (De LopezGonzalez and Jenny, 1959) was calculated from the Eyring’s theory of absolute reaction rate (Atkins, 1982) by using the D_{a} values in the following Eq. 6:
where, e is the base of natural logarithm, k is the Boltzman constant, T is the absolute temperature, h is the Planck’s constant, d is the average distance between adjacent equilibrium positions during diffusion, ΔS^{≠} is the entropy of activation, E_{a} is the energy of activation and R is the universal gas constant. The parameter [d exp (ΔS^{≠}/R)]^{1/2} is designated as the entropy factor of diffusion and has the dimension of length. Statistical analysis: Effect of soil moisture content (θ), bulk density (d), temperature (T), tracer:background ratio (R) and background electrolytes (E) on apparent diffusion coefficient (D_{a}) and porous diffusion coefficient (D_{p}) of K were tested by a 2x2x2x2x2 factorial ANOVA. Ftest and mean comparison by Tukey test (5%) was performed using Proc GLM (SAS, 2013). Multiple regression analysis was determined by SPSS (Chicago, IL.; version 16.0).
RESULTS
The important soil physicochemical properties, different forms of soil potassium and semiquantitative composition of clay fraction of the experimental soil samples have been presented in Table 1. All three soils belong to silty clay loam, although, the clay content varied from 26.535.3%. The distribution of different forms of K in the three soils (Table 1) revealed that the exchangeable K, nonexchangeable K content was highest in Moratripur soil followed by Telegacha and Nonaghata soil.
 Fig. 1: 
Relationship between absorbed K and concentration of K in equilibrium solution of soils 
The distribution of different minerals in the clay fraction of the soils was presented in the Table 1 and Xray diffractograms of the clay fraction of the soils was presented in Fig. 2. The result showed that all the soils were dominant in illite followed by smectite. Sekhon et al. (1992) also found that illite was the dominant clay mineral in the alluvial soils of West Bengal. The apparent tracerdiffusion coefficient of K(D_{a}) in Ca and Nasaturated background (E_{1} and E_{2}) soils have been expressed as logarithmic functions of the inverse absolute temperatures of study (297 and 308°K) in Fig. 3 and 4, corresponding to two different bulk densities maintained. The corresponding porous diffusion coefficient (D_{p}) values were obtained by multiplying D_{a} values with the capacity factor of the soil (b), which was obtained from the slope of the plots (Fig. 1). The effect of different factors like soil moisture content (θ), bulk density (d), temperature (T), tracer:background ratio (R) and background electrolytes (E) on apparent diffusion coefficient (D_{a}) and porous diffusion coefficient (D_{p}) of K in the studied soils was presented in Table 2. The results reveals that with decrease in water content from 100% of water holding capacity to 85% water holding capacity, there was significant (p<0.05) fall in D_{a} and D_{p} values (Table 2 and Fig. 3). Upon increasing the bulk density from 0.991.08 Mg m^{3}, the diffusion coefficient values significantly (p<0.05) increased (Table 2 and Fig. 4). It has been observed that with increase of tracer: background ratio from 1:32 to 1:16, the D_{a} and D_{p} values (Table 2) significantly (p<0.05) increased in all the soils. For all the soils, the D_{p} values (and also the D_{a} values) were significantly (p<0.05) higher (Table 2) when NaCl was taken as background electrolyte than for CaCl_{2}. This increase may possibly be related to the difficulty of K^{+} to replace Ca^{++} compared to Na^{+} in the exchange sites. The probability levels of 2x2x2x2x2 factorial ANOVA of different factors and their interaction effect on D_{a} and D_{P} of K in the studied soils were presented in Table 3. All the factors have significant effect (p<0.001) on D_{a} and D_{p} of K in the studied soils. The interaction effects of different factors were significant (p<0.05) for most of the cases except for the dxTxE and θxdxTxE.
The energy of activation (E_{a}) and Arrhenius frequency factor (A) under different treatments in all the three soils were computed from the slope and the intercept of the plots log D_{a} against T^{1} and presented in Table 4.

Fig. 2(ac): 
Xray diffractograms of the clayfraction of the three soil, (a) Nonaghata (S_{1}), (b)
Telegacha (S_{2}) and (c) Moratripur (S_{3}) 

Fig. 3(ac): 
Relationship between logarithm of apparent tracerdiffusion coefficient (D _{a}) of potassium and reciprocal of absolute temperature (T ^{1}) at 100% water holding capacity moisture content and at a bulk density of 0.99 Mg m ^{3}, (a) Nonaghata Uttarpara (S _{1}), (b) Telegacha (S _{2}) and (c) Moratripur (S _{3}) 
The entropy factor of diffusion (θ) for the given treatments was computed from D_{a} and E_{a} values by using the Eq. 6.

Fig. 4(ac): 
Relationship between logarithm of apparent tracerdiffusion coefficient (D _{a}) of potassium and reciprocal of absolute temperature (T ^{1}) at 100% water holding capacity, moisture content and at a bulk of 1.08 Mg m ^{3}, (a) Nonaghta Uttarpara (S _{1}), (b) Telegacha (S _{2}) and (c) Moratripur (S _{3}) 
The energy of activation (E_{a}) decreased significantly (p<0.05) with increase in bulk density (Table 4). The Arrhenius frequency factor (A) and entropy factor of diffusion (θ) were found to significantly decrease in the given soils with increasing tracer component (Table 4).
Table 2: 
Effect of soil moisture content (θ), bulk density (d), temperature (T), tracer:background ratio (R) and background electrolytes (E) on apparent diffusion coefficient (D_{a}) and porous diffusion coefficient (D_{P}) of K in Nonaghata Uttarpara (S_{1}), Telegacha (S_{2}) and Moratripur soil (S_{3}) 
 Means followed by same lowercase letters in columns do not differ by Tukey's Studentized Range (HSD) test for diffusion at (p<0.05, n = 96), θ_{1} and θ_{2}: 100 and 85% moisture content of the water holding capacity of the soil, d_{1} and d_{2}: Bulk density of the soil maintained at 0.99 and 1.08 Mg m^{3}, respectively, T_{1} and T_{2}: Temperature of 297 (±1)and 308 (±1)°K maintained during the corresponding diffusion experiment, R_{1} and R_{2}: Tracer:background electrolyte of 1:32 and 1:16, respectively, E_{1} and E_{2}: Casaturated and Na saturated background electrolyte, respectively 
Table 3: 
Probability levels of 2^{5} factorial ANOVA using soil moisture content (θ), bulk density (d), temperature (T), tracer:background ratio (R) and background electrolytes (E) as independent factor and their interaction on apparent diffusion coefficient (D_{a}) and porous diffusion coefficient (D_{P}) of K in Nonaghata Uttarpara (S_{1}), Telegacha (S_{2}) and Moratripur (S_{3}) soil 
 **, *Significant at 0.01 and 0.05 probability levels, respectively, CV: Coefficient of variation, df: Degrees of freedom, Rep: Replication, θ: Soil moisture content, d: Bulk density of the soil, T: Temperature maintained during the corresponding diffusion experiment, R: Tracer:background ratio, E: Background electrolytes, NS: Non significant 
Table 4: 
Effect of bulk density (d), temperature (T), tracer:background ratio (R) and background electrolytes (E) on Energy of activation (E_{a}), Arrhenius frequency factor (A) and Entropy factor of diffusion (θ) at 100% water holding capacity; probability levels of 2^{3} factorial ANOVA using bulk density (d), tracer : background ratio (R) and background electrolytes (E) as independent factor and their interaction on Apparent Diffusion Coefficient (D_{a}) of K in Nonaghata Uttarpara (S_{1}), Telegacha (S_{2}) and Moratripur soil (S_{3}) 
 **, *Significant at 0.01 and 0.05 probability levels, respectively. CV: Coefficient of variation. Means followed by same lowercase letters in columns do not differ by Tukey’s Studentized Range (HSD) Test for Diffusion at (p<0.05, n = 9 6), d_{1} and d_{2}: Bulk density of the soil maintained at 0.99 and 1.08 Mg m^{3}, R_{1} and R_{2}: Tracer:background electrolyte of 1:32 and 1:16, respectively; E_{1} and E_{2}: Casaturated and Nasaturated background electrolyte, respectively 
Table 5: 
Regression equation relating apparent diffusion coefficient (D_{a}) and porous diffusion coefficient (D_{p}) of K with different forms of potassium and different fractions of clay minerals 
 **, *Significant at the 0.01 and 0.05 probability levels, respectively, SE: Standard error of estimate, R^{2}: Regression coefficients for the fitted data  Results of multiple regression equations for the apparent (D_{a}) and tracer diffusion coefficient (D_{P}) drawn with different forms of K and different fractions of clay are presented in Table 5. The regression equations revealed that exchangeable K (denoted by X_{2}) and illite (denoted by Y_{3}) fraction of the clay contributed significantly toward variability in diffusion coefficient of K (both D_{a} and D_{P}) as evidenced from the magnitude of coefficient of X_{2} and Y_{3} than other coefficients. However, the standardized coefficient of beta values was highest in X_{2 }(i.e., exchangeable K) for D_{a} and X_{3} (i.e., nonexchangeable K) for D_{p}. DISCUSSION The data presented in Table 1 revealed that the soil of Moratripur has showed highest clay content (35.3%) and hence the highest cation exchange capacity as well as exchangeable bases. The clay fraction of Moratripur soil was dominatend by micaceous minerals for which the exchangeable and nonexchangeable K content was highest of the above said soil (Table 1). The decrease of D_{a} and D_{p} values due to decrease in soil moisture may be due to the fact that as the soil water content decreases, the crosssectional area available for diffusion becomes smaller and the path length increases with the viscosity and negative adsorption becoming more important as the water films decreases in thickness (Paul et al., 1998). The results are in satisfactory agreement with the observations made by Mani and Sanyal (1996) and Dhar and Sanyal (2002) on K. It may be mentioned here that b, the capacity factor values at different moisture levels, were taken to be same as the present method did not permit the determination of b value at different moisture levels, notwithstanding though the observation of Olsen and Kemper (1968) that with increasing soil moisture content, b value increases. The higher bulkdensity causes the diffusion path to become less tortuous. Such decrease in tortuosity at higher compaction or higher bulkdensity is resulted from effective destruction of air pockets by which the crumbs get pressed more readily into contact, thereby, reducing the tortuosity of the diffusion path (Meisheri and Deb, 1986).
A higher concentration of the background electrolyte may have hindered the effective passage of K from the tagged to the untagged soil (Phillips and Brown, 1964) for which with the increase of tracer:background ratio the D_{a} and D_{p} values increased significantly. The Moratripur soil which had greater exchangeable K, nonexchangeable K and illite content than other two soils was found to possess higher D_{a }and D_{p }values. The decrease of E_{a} due to increase of bulk density (Table 4) may be attributed due to the facilitated K diffusion at a higher bulk density as discussed earlier. While with increasing the tracer:background ratio, the E_{a} values decreased significantly (p<0.05) for Nonaghata and Telegacha soil in contrast with Moratripur soil where, higher background concentration made the diffusion of potassium thermodynamically unfavourable as evidenced with the increase in E_{a} values. Significantly (p<0.05) lower E_{a} values were observed when Na was taken as background electrolyte which again reflecting the fact of ease of replacement of Na from the exchange site as compared to Ca^{+2} ion by K. The Arrhenius frequency factor (A) defines the probability of ion interaction which includes the frequency of oscillations that an ion undergoes at a given exchange site (Brown et al., 1968). The lower values of ‘A’ may be explained by lower probability of ionexchange preceding diffusion (Mani and Sanyal, 1995).
The multiple regression equations for D_{a} and D_{p} with different forms of K suggested that exchangeable K appeared to be the most relevant form for apparent tracer diffusion coefficient (D_{a}) of K in alluvial soils while, nonexchangeable K is most relevant for porous diffusion coefficient (D_{P}) of K. For both the D_{a} and D_{p}, standardized coefficient of beta values were found maximum for illite fraction of the clay minerals. In illite mineral, the most of the exchangeable ions are in interlayer positions. However, when ion like potassium diffusing into the illite dominant soil, it may diffuse preferentially on the external surfaces rather the interlayer positions. Indeed, the main factor influencing the diffusion coefficient is the interlayer spacing of the clay mineral (Nye, 1980). In the present study, the alluvial soils having dominance of weathered illitic type of minerals characterized by sufficiently fast release of potassium from wedge zones of (2:1) type of minerals and thus appeared to be the most relevant for describing the diffusion coefficient.
CONCLUSION The different factors studied for their role in K diffusion have significant influence on diffusion of K in soil. It was evidenced that with the increase in moisture content, temperature, bulk density and tracer:background ratio there was a significant increase in both apparent and tracer diffusion coefficient. The interaction effects of different factors of K diffusion was found significant (p<0.05) in most of the cases except for the interaction of bulk density, temperature and electrolyte together (dxTxE) and moisture content with the earlier ones (θxdxTxE). It can be concluded that the diffusion coefficients of potassium in these alluvial soils can be predicted in terms of exchangeable K and nonexchangeable K (for D_{a} and D_{P}, respectively) and also in terms of the proportion of illitic minerals of the clay. Prediction of such diffusion coefficients of K may be successfully utilized to estimate the plant uptake of K from soil and also to understand the transport behaviour of K from bulk soil phase to crop root and hence its dynamics. ACKNOWLEDGMENT The authors are thankful to Prof. S. K. Sanyal, The ExVice Chancellor, Bidhan Chandra Krishi Viswavidyalaya, Kalyani, West Bengal for his guidance and valuable suggestions received during this study. The authors also thankfully acknowledge the National Bureau of Soil Survey and Land Use Planning, Nagpur, India for providing the instrument facilities to obtain xray diffractograms of clay minerals.

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