Comparison of salt titration and potentiometric titration

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Jan 4, 2012 - tion of ST-pH0 as the zero point of charge, a calculation procedure (STPT method) ... Key Words: salt titration, potentiometric titration, ZPC, pH0.
Soil Science and Plant Nutrition

ISSN: 0038-0768 (Print) 1747-0765 (Online) Journal homepage: http://www.tandfonline.com/loi/tssp20

Comparison of salt titration and potentiometric titration methods for the determination of Zero Point of Charge (ZPC) Katsutoshi Sakurai , Yohichi Ohdate & Kazutake Kyuma To cite this article: Katsutoshi Sakurai , Yohichi Ohdate & Kazutake Kyuma (1988) Comparison of salt titration and potentiometric titration methods for the determination of Zero Point of Charge (ZPC), Soil Science and Plant Nutrition, 34:2, 171-182, DOI: 10.1080/00380768.1988.10415671 To link to this article: http://dx.doi.org/10.1080/00380768.1988.10415671

Published online: 04 Jan 2012.

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Date: 29 January 2016, At: 10:38

Soil Sci. Plant Nutr., 34 (2), 171-182, 1988

COMPARISON OF SALT TITRATION A N D POTENTIOMETRIC TITRATION METHODS FOR THE DETERMINATION OF ZERO POINT OF CHARGE (ZPC) Katsutoshi SAKURAI, Yohichi

OHDATE,* a n d

K a z u t a k e KYUMA

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Faculty of Agriculture, Kyoto University, Sakyo-ku, Kyoto, 606 Japan Received June 4, 1987 The salt titration (ST) method was evaluated as a method to determine ZPC in comparison with the potentiometric titration (PT) method for 26 soils with variable charge clays, i.e., Oxisols and Ultisols from Thailand and Andisols from Japan. In addition to the determination of ST-pH0 as the zero point of charge, a calculation procedure (STPT method) was adopted here in order to acquire more information from the titration curve. Furthermore, for the purpose of cross-checking of ZPC determined by the PT method, the ST procedure was successively applied to the samples analyzed by the PT method (PTST method). The soil to solution ratios of 1 : 10 to 1 : 5 gave almost an identical ST-pH0 value for every soil. The values of both ST-pH0 and PT-ZPC ranged from 4.7 to 6.3 for the Andisols, while for the Oxisols and Ultisols, they were always below 4.2. The difference between the values of ST-pH0 and PT-ZPC was only slight for the Andisols, whereas it was sometimes large (0.4 pH unit) for the Oxisols and Ultisols. Nevertheless, it was concluded that the ST method with its modification (STPT) was comparable to or even better than the PT method for the soil characterization work due to its convenience and simplicity. Key Words: salt titration, potentiometric titration, ZPC, pH0.

One of the most i m p o r t a n t characteristics of soils d o m i n a t e d by variable charge clays is the Z P C (zero p o i n t of charge) or pH0 (pH naught), at which the value of the net charge of' the variable charge c o m p o n e n t is zero. E v a l u a t i o n of the Z P C value of soils enables to predict the soil response to the changes in s u r r o u n d i n g conditions, e.g., fertilizer application in the field. To estimate ZPC, the i o n a d s o r p t i o n m e t h o d advocated by SCHOrIELD (1949) has been used by m a n y scientists with partial modifications (VAN RAIJ a n d PEECH 1972; ILTON MORRAIS et al. 1976; I~AVERDIERE a n d WEAVER 1977; UEHARA a n d GILLMAN 1981; WADA a n d OKAMURA 1983). I n this method, Z P N C (zero p o i n t of net charge) corresponds to the p o i n t at which anions a n d cations are retained in equal a m o u n t s by the soil, a n d Z P C to the p o i n t at which the balance of the adsorbed a m o u n t of cations a n d anions would n o t change regardless of the c o n c e n t r a t i o n of the s u p p o r t i n g * Present address:

Takara Shuzo Co., Ltd., Nakagyo-ku, Kyeto, 604 Japan. 171

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172

K. SAKURAI, Y. OHDATE, and K. KYUMA

electrolyte. The potentiometric titration (PT) method is also widely used for the determination of ZPC of soils (VAN RAIJ and PEECl~ 1972; LAVERDIERE and WEAVER 1977; PAI~:Eg et al. 1979; UEHARA 1979; UEHARA and GILLNAN 1980, 1981). ZPC corresponds to the point at which equal amounts of H § and O H - (potential-determining ions of soils, PDI) are adsorbed by the soil regardless of the salt concentration. Although these two methods are well established, they are too laborious and time-consuming to enable a high reproducibility, hence the difficulty of using them on a routine basis. UEHARA (1979) suggested the use of the ApH value, which is the difference between the pH measured in 1 N KC1 (pHKcl) and that measured in water, for a rough estimation of variable charge characteristics, i.e., when the ApH value ranges between - 0 . 5 and +0.5, soils would be dominated by components with a highly variable nature. KENG (1974) showed that statistically pH0 could be estimated as the sum of the values of pHKcl and ApH. The salt titration (ST) method was devised by KINNIBURGH e t a / . (1975), and modified by others (GILLMAN and BELL 1976; GILLMAN and UEHARA 1980; UEHARA and GILLMAN 1981). This method is a simplification of the PT method with respect to ZPC. In spite of its ready applicability, the data obtained by this method have so far been relatively scarce probably due to the paucity of the information obtained from the titration curve. In this paper, the ST method is examined in comparison with the PT method, with emphasis placed on zero point of charge and the interpretation of the titration curve. THEORY According to the Gouy-Chapman theory (cf. Eq. (1)), the surface charge density of a variable charge clay is determined, among others, by the potential-determining ions, or H + and OH-, and the electrolyte concentration. ao =(2nslcT/T:). sin 17{1.15. z-(pH0 - pH)]

(1)

where a0 is the surface charge density (esu/cm=), n is the counter ion concentration in the equilibrium solution (ion/cma), s is the dielectric constant (esu2/dyn-cm2), k is the Boltzmann constant (erg/deg), T is the absolute temperature, z is the counter ion valence, pH0 is the zero point of charge, and pH is the pH value of the surrounding solution. The ST method is based on this principle. In case the clay surface has already a net negative charge, the charge becomes more negative upon the addition of salt due to the deprotonation of the surface hydroxyl groups. The release of hydrogen ions to the soil solution results in the decrease of the suspension pH. Conversely the suspension pH rises upon the addition of electrolytes for a positively charged surface. When the net surface charge of the clay is zero, the pH of the solution is not influenced by

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Salt Titration and Potentiometric Titration Methods

173

the addition of electrolytes. This p H value which is the zero point of charge, is designated in this paper as "ST-pH0." In the PT method, the sample is titrated with H + and O H - at three or four electrolyte concentrations, and by running blank titrations the amount of H + or O H adsorbed over a range of p H values and salt concentrations can be calculated. Z P C corresponds to the point at which titration curves at different salt concentrations intersect, i.e., the point at which the salt concentration does not exert any effect. This point is designated as " P T - Z P C " in this paper. The PT method is also based on the same principle as that represented in Eq. (1). In this experiment, for the purpose of cross-checking of the " P T - Z P C " values, the ST procedure was also applied to the samples analyzed by the PT method ("PTST method") and the estimated pH0 value was designated as "PTST-pH0." Furthermore, in order to obtain more information on the ST method, the a m o u n t of H + adsorbed was calculated by running blank titrations before and after salt addition in the ST procedure. This step was designated as the STPT method, which enabled to determine the amount of H + adsorbed in water and in the suspension after salt addition, and also to determine " S T P T - Z P C " as an intersect of the titration curves. The STPT method can be considered as a form of potentiometric titration at a very low salt concentration. Therefore, the development of a surface charge both in water and in an equilibrium solution after the addition of NaC1 and subsequent shaking for 3 h in the ST method, could conveniently be compared with the PT method in terms of the process for the construction of the titration curve and determination of ZPC. When the designation " Z P C " without any specification is used in this text, it refers to the zero point of charge as a general term, including "ST-pH0," " S T P T - Z P C , " "PTZPC," and "PTST-pH0." ap is the remaining charge at ZPC, as defined originally by UEHARA and GILLMAN (1980), and it is expressed as the amount of H + or O H - adsorbed at ZPC, where H + and O H - are balanced on the variable charge components. A positive value for ap implies the adsorption of H + on the remaining negative surface charge, whereas a negative value for ap corresponds to O H - adsorption onto the positively charged site. Thus, the sign of a~ indicates whether soil particles have a net negative or positive charge at ZPC. It was assumed that a permanent charge alone contributed to the value of ap. LAVERDIEREand WEAVER (1977) also reported that the value of ap (expressed in their paper as a,) increased in proportion to the amount of montmorillonite added as a source of permanent negative charge. In addition to the permanent charge on clay mineral surfaces, part of organic functional groups may contribute to the value of a~ if the acidity is high. Thus, both organic and mineral components that are capable of adsorbing H + at ZPC contribute to the value of ap. Since the range of the value of a~ as well as of ZPC is a characteristic value o f variable charge soil, both of these may be estimated at the same time.

174

K. SAKURAI, Y. OHDATE, and K. KYUMA

EXPERIMENTAL

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(a)

Salt titration (ST) method.

(1) Place 2 g of soil in each of seven 50 ml glass sample tubes. In order to adjust the p H to span the expected pH0 value, add deionized water first and 0.1 N HC1 or N a O H to obtain a final solution volume of 20 ml. (2) Allow the soil to equilibrate for 4 days, stirring occasionally, and then record the equilibrium pH. Designate this value as pill. (3) Add 0.5 ml of 2 N NaCI solution, shake reciprocally for 3 h, and record the pH. Designate this value as pH2. (4) For each tube, calculate the value of A p H = p H z - p H 1 and plot the value of ApH versus p i l l to determine the point where ApH = 0 . This corresponds to ST-pH0 - - t h e p H value which is indifferent to the salt concentration. (b) S T P T method. Steps (1) to (4) are the same as those for the ST method, and subsequently, (5) Construct titration curves based on the titration with acid or base for water and 0.0485 N NaC1 solution. These are blanks. (6) Calculate H + or O H - adsorbed by subtracting the blank reading from the amount added at the respective pH. (7) Plot H + or O H - adsorbed against the p H for water and 0.0485 N NaC1 solution. The intersection point corresponds to STPT-ZPC.

(c)

Potentiometrie titration (PT) method.

(1) Place 2 g of soil in each of fourteen 50 ml glass sample tubes and arrange them into 2 rows of 7 tubes. (2) Add 10 ml of NaC1 solution, the concentration of which is 0.2 N and 0.02 N for rows 1 and 2 respectively. (3) Designate the middle tube in each row as expected ZPC. (4) Add 0.1 N HC1 or N a O H to the row of the 0.2 N NaC1 aq., and 0.01 N of acid or alkali to that of 0.02 N NaCI. (5) Add deionized water to bring the total volume in each tube to 20 ml. (6) Allow to equilibrate for 4 days, stirring occasionally. (7) Construct titration curves based on the titration with acid or base for each of the 2 electrolyte solutions. These are the blanks. (8) After 4 days record the p H of the suspension (PH0 and calculate the amount of H + or O H - adsorbed by subtracting the blank reading from the amount added at the respective pH. (9) Plot H + or O H - adsorbed against p H for each electrolyte concentration. (10) I f there is a sufficient amount of variable-charge colloid, the curves will intersect. This point corresponds to PT-ZPC.

(d) (1)

Potentiometric titration followed by salt titration (PTST) method. After the p H measurement (pill) in the PT method, add 0.5 ml of a 2 N NaC1

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Salt Titration and Potentiometric Titration Methods

175

solution to the 0.01 N suspension, and 1.0 ml of it to the 0.1 N suspension. (2) Shake for 3 h and record the p H value. Designate this value as pH2. (3) For each tube calculate the value of A p H = p H 2 - p i l l and estimate PTST-pH0 in the same way as in the salt titration method. There were four salt concentration levels in the original PT method corresponding to 1, 0.1, 0.01, and 0.001 N. But in the present study, the highest and the lowest levels were omitted for simplification, and also to exclude possible A1 influence. PT curve in the 1 N salt solution often deviated from the others to the acid side as was observed elsewhere (VAN RAIJ and PEECH 1972; GILLMANand UEHARA 1980). The behavior of the aluminum ion in the process of titration by the two methods will be discussed in a paper to follow. In the PT method, after 4 days the soil suspensions are in equilibrium with a set of P D I and supporting electrolyte. In the ST method, the soil suspension is first equilibrated for 4 days with water and PDI. Then 0.5 ml of 2 N NaCI is added and the solution is shaken for 3 h, bringing the final concentration of the supporting electrolyte to 0.0485 N. The PTST method is equivalent to the ST method with the initial NaC1 concentration of 0.01 and 0.1 N, and the final concentration of 0.0585N and 0.191 ~r, respectively. The initial equilibrium state for each NaC1 concentration is designated as PTST (0.01) and PTST (0.1) in the following discussion. As a species of supporting electrolyte, NaCI aq. was selected for avoiding a specific adsorption of the component ions onto the surface (PARKER et al. 1979). All the p H measurements were carried out consistently by immersing a combination electrode into the upper part of the suspension, and reading the p H after a clear separation, where possible, of the supernatant in order to evaluate the H + activity in the bulk solution. The pH measurement took as long as 2 min, except that the pill measure-

Table 1. Description of the soil samples. Pedon

Location

K1

Seta, Otsu-cho, Kikuchi county, Kumamoto Pref. Kodonbaru, Uenmra, Kuma county, Kumamoto Pref.

K4 AOJ T5 T6 9 T7

Kuroishi, Kubokawa-cho, Takaoka county, Kochi Pref. Amphoe Muang, Nakhon Ratchasima province, Thailand Amphoe Chok Chai, Nakhon Ratchasima provilace, Thailand Amphoe Pak Chong, Nakhon Ratchasima province, Thailand

T6E in Table 2 was taken from a pedon adjacent to T6.

Characteristics Volcanic ash soils Volcanicash soils (K41) Weathered pumice "imogo" (K42) Fan deposits (K43, K44, K45) Weathered pumice "Akaonji" Yasothon series Ultisol Cbok Chai series Oxisol Pak Chong series UItisol

0 r~

o ~

4.34 3.83 3.82

I

5.18 5.03 4.90

I

0-12 12-53 53-137

I I I I i

0.62 7.25 7.05

47.0 37. 6 52.0 52.6 51.9 40.4 8.7 8.9 11.0 26. 5 26. 2 56.6 65.3 69.1 57.7 73.4 73. 3 78.8 74. 0

219 325 161 139 139 351 12 7 11 22 28 69 83 94 94 114 183 205 197

4.02 0.51 0.56 0.68 1. 73 1. 87 8.37 8.74 9.44 9.66 12.25 8.92 9.01 9. 11

0.27 0.27 0.29

0.28 0.21 0.23 0.24 0.28

0.08 0.05 0.03 0.09 0.10

14.43

11. 44 13.39 7.99 4.81 4.82

4.66 4.63 5.72 5.27 5.28

54. 5 38. 1 43. 5 64.8 61. 9 49. 5 45. 9

C%)

A,A'~Ch,M

A,A'~M

Ht>Ch,M Ht>Ch,M

A,A'~Ch,M

A,A'~Ch,M

A,A'~Ch,M

Clay mineral b

Vt-Ch>M,Kt,Gp Vt-Ch,M,Kt M>Kt>Vt-Ch

A,A',lm~M,Qz

A,A'~M

Kt~Ch

Kt Kt Kt Kt Kt>M

Kt~Qz

Kt~Qz

Kt~Qz

Kt>Qz Kt>Qz

A,A',Im

I

Kt~Ch

Kt~Ch

~A~

O. 3

1.2 0.4

0.3 0.6

0.36 0.32 2. 72 2.65 1. 76

0.29 0.50 0.57 1. 58 2. 15

0.07

0.31 0.0 O. 55 O. 52 0.45

(m'/g)

C/~)

Clay a

143 301 318 273 321 324 431

SSA

Fed

10. 13 5.92 17.69 7.49 21. 08 10.07 12.5911.63 11.95 11.19 18.40 10.19 22.64 11. 08

(%)

Alo

g

I I

,,4.~

[.-, [.-,

;>-

.~o'

~=~

~d

a Clay content of fraction less than 0.5 mm. b A, Allophane; 1m, Imogolite; A', Allophane-like materials; Ch, Chlorite; Vt, Vermiculite; Vt-Ch, Vt Ch intergradient mineral; M, Mica; Gp, Gibbsite; Kt, Kaolinite; Ht, Halloysite; Qz, quartz.

o~ -0.84 -1. 20 -1. 08

I

Ap B21t B22t

I

4.51 4.53 3.98 3.99 4.01

I

A

T71 T72 T73

~§ [

5.56 5.39 4.46 4.42 4.99

I

0-10/14 14/10-36 36-86 86-156 85-156

I

O. 5

1.5 0.9

-1. 05 -0.86 -0.48 -0.43 -0.98

~ I

Al B2lt B22t B23t B23t

I

A A ~ A

T61 T62 T63 T64 T6E

0.4 0.4 0.2 0.2 0.2

-0.99 -0.87 -1. 01 -0.94 -1. 11

0-14 5.12 4.13 14-34 5.00 4.13 34-62 4.95 3.94 62-1154.863.90 115-200 4.95 3.84

I

Al A3 Bl B21t B22t

I

T51 T52 T53 T54 T55

1.5

-0.20

6.10

6.30

I

50-100

i

X ~

C

I

A

AOJ

17.3 2.0 10.0 3.0 2.9

-1. 18 -0.09 -0.85 -0.74 -0.70

4.79 5.64 4.72 4.74 4.80

5.97 5.73 5.57 5.48 5.50

I

0-25 25-50 50-70 70-120 120+

I

Al llBI JUA1 IIlB2 lIIB3

0-22 22-51 51-78 78-102 102-125 125-170 170-240 0.03 0.10 0.07 O. 14 0.07 0.03 0.0

(meq/l00 g)

(%)

6. 1 3.2 4.0 5.5 3.3 4. 7 2.4

I

-0.50 -0.25 -0.31 -0.74 -0.44 -0.46 -0.32

5. 12 5.78 5.73 5.27 5.46 5.50 5.75

5.62 6.03 6.04 6.01 5.90 5.96 6.07

ex. Al

T-C

XXX~XX

K41 K42 K43 K44 K45

0

pHNa

LlpH

d~ P T , in the case of ZPC; ST> PTST (0.01)>PTST STPT-ZPC>PTST

(0.1), i n t h e c a s e o f p H o ;

(0.01)-pH0>PT-ZPC>PTST

(0.1)-pHo f o r b o t h

and ST-pH0= ZPC

a n d pH0.

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Salt Titration and Potentiometric Titration Methods

181

This general order corresponded to the increase in the final concentration of the supporting electrolyte from 0.0485 N for ST (water) to 0.191 N for PTST (0.1). The difference between the value of ST-pH0 and PT-ZPC or PTST (0.1)-pH 0 was as large as 0.42 for T73 and 0.37 for T64. Although the Thai soils are characterized by a certain enrichment of crystalline Fe oxides (hematite) that may affect the ZPC value, the dissolution of A1 in the course of titration may have played a more important role. Since the amount of ex.A1 was high for T64 (2.65 meq/100 g), and very high for T73 (7.05 meq/100 g), equilibration at a high salt concentration and at a low p H should have resulted in A1 solubilization, and subsequent hydrolysis leading to H + release (JAaDINE et al. 1985). Thus the H + adsorption from the equilibrating solution may have been underestimated, and ZPC as a crossing point may have shifted to the more acid range due to the increased solubilization of A1 at the higher salt concentration adopted in the PT or PTST procedure. On the contrary, ZPC variations in the Andisols were small, reflecting the absence of ex.A1 (see Table 2). Generally, a soil sample with a low ZPC tended to exhibit a large value for av, whereas in a sample with a high ZPC a small a~ value was recorded. This relationship applied to both Andisols and Ultisols/Oxisols, and suggested that the p H (1 : 10) of variable charge soils should be close to ZPC when the content of organic matter and permanent charge clay is low (K12, K42, AOJ). The magnitude of the ap value recorded by the PT method was generally larger than that by the STPT method. Dissolution of Al from the permanent charge site on the clay surfaces may also affect the magnitude of the ap value. The effect of dissolved A1 on Z P C and the magnitude of the ap value should be studied in more detail. In the ST method, some authors proposed the use of a salt concentration ranging from 0.0015 to 0.005 N for the initial equilibration to simulate the actual level of the soil solution concentrations in strongly weathered soils (KINNIBURGHet al. 1975; GILLMANand UEHARA 1980; UEHARAand GILLMAN 1980). In the current PTST procedure, the initial salt concentration of 0.1 N, and in some cases, even of 0.01 N, was not appropriate for inducing a measurable change in the potential upon further addition of salt for certain soils and clays, e.g., soils with a sandy texture (T51) and/or with a low content of variable charge components. For this reason, although an initial concentration as high as 0.01 N was appropriate for most of the sample soils, equilibration in deionized water was more suitable in spite of the lower potential stability of the suspension. Conclusions

The ST method combined with the calculation of P D I adsorption (STPT method) was comparable to the PT method for the determination of ZPC. The change in the surface charge density was usually sufficiently large to measure the response to salt addition. In the STPT method, it was also possible to determine the value of ap as a measure of permanent charge at ZPC. Fluctuations of the values of ZPC and ap determined by the ST and/or STPT method generally fell within 0.1 p H unit and 0.2 meq/100 g, respectively.

182

K. SAKURAI, Y. OHDATE, and K. K Y U M A

T h u s , it is c o n c l u d e d t h a t the S T m e t h o d is m o r e s u i t a b l e t h a n t h e P T m e t h o d f o r r o u t i n e soil analysis, b e c a u s e it is less l a b o r i o u s a n d r e q u i r e s a s m a l l e r a m o u n t o f soil.

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REFERENCES CARTER, D.L,, HEILMAN, M.D., and GONZALEZ, C.L. 1965: Ethylene glycol monoethyl ether for determining surface area of silicate minerals. Soil Sci., 100, 356-360 GILLMAN, G.P. and BELL, L.C. 1976: Surface charge characteristics of six weathered soils from tropical North Queensland. Aust. J. Soil Res., 14, 351-360 GILLMAN,G.P. and UEHARA,G. 1980: Charge characteristics of soils with variable and permanent charge minerals; IL Experimental. Sail Sci. Soc. Am. J., 44, 252-255 ILTON MORRAIS, F., PAGE, A.L., and LUND, L.J. 1976: The effect of pH, salt concentration and nature of electrolytes on the charge characteristics of Brazilian tropical soils. Soil Sci. Soc. Am. J., 40, 521-527 JARDINE, P.M., ZELAZNY,L.W., and PARKER,J.C. 1985: Mechanisms of aluminum adsorption on clay minerals and peat. Soil Sci. Soc. Am. J., 49, 862-867 KENG, J.C.W. 1974: Surface chemistry of some constant potential soil colloids. M.S. Thesis. University of Hawaii, Honolulu, Hawaii (cited from UEHARA,1979) KINNmURGH, D.G., SVERS, J.K., and JACKSON, M.L. 1975: Specific adsorption of trace amounts of Ca and Sr by hydrous oxides of Fe and AI. Soil Sci. Soc. Am. Prec., 39, 464-470 LAVERDIERE,M.R. and WEAVER, R.M. 1977: Charge characteristics of spodic horizons. Soil Sci. Soc. Am. J., 41, 505-510 PARKER, J.C., ZELAZNY,I.W., SAMPATH,S., and HARRIS, W.G. 1979: A critical evaluation of the extension of ZPC theory to soil systems. Soil Sci. Soc. Am. 3"., 43, 668-674 SCHOFIELD,R.K. 1949: Calculation of surface areas of clays from measurements of negative adsorption. Trans. Br. Ceramic Sac., 48, 207-213 UEHARA,G. 1979: Mineralo-chemical properties of Oxisols. In Proceedings of Second International Soil Classification Workshop. Part I: Malaysia, p. 45-60. Soil Survey Division, Land Development Dept. Bangkok, Thailand. UEHARA, G. and GILLMAN, G.P. 1980: Charge characteristics of soils with variable and permanent charge minerals; I. Theory. Soil Sci. Soc. Am. J., 44, 250-252 UEHARA, G. and GILLMAN,G.P. 1981: Analytical Methods. In "The Mineralogy, Chemistry, and Physics of Tropical Soils with Variable Charge Clays, Chapter 6, p. 137-152. Westview Tropical Agriculture Series, No. 4. Westview Press, Boulder, Colorado VAN RAIJ, B. and PEECH, M. 1972: Electrochemical properties of some Oxisols and Alfisols of the tropics. Soil Sci. Soc. Am. Prec., 36, 587-593 WADA,K. and OKAMURA,Y. 1983 : Net charge characteristics of Dystrandept B and theoretical prediction. Soil Sci. Soc. Am. J., 43, 902-905 YOSHINAGA, N., EGASHIRA, K., and NAKAI, S. 1984: A method for particle-size analysis of Andepts. J. Sac. Soil Sci. Plant Nutr., 55, 248-256 (in Japanese)