The surface energy of talc

Journal of Colloid and Interface Science 285 (2005) 314–317 www.elsevier.com/locate/jcis

The surface energy of talc Ahmed K. Helmy a,∗ , E.A. Ferreiro a,b , S.G. de Bussetti a a Universidad Nacional del Sur, B8000 Bahía Blanca, Argentina b Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina

Received 23 September 2004; accepted 8 November 2004 Available online 22 December 2004

Abstract The determination of an average value for the surface energy of talc (γ¯S ) via solid–water interfacial interactions is described. It is based on a formula obtained by the combination of the Young equation with a general equation of pair interaction. Important features of the method are (a) the use of the Young equation to determine the range where the value of the surface energy lies and (b) the determination of the mean value within this range using a probability function. The value found is 217.31 mJ m−2 in the range 193.36–257.43 mJ m−2 .  2004 Elsevier Inc. All rights reserved. Keywords: Adsorption of water; Surface energy; Surface tension; Talc

1. Introduction

2. Materials and methods

Talc is used in many industrial preparations such as paint, paper, and cosmetic and pharmaceutical products. Adhesion and other surface interactions determine the quality of the products and are dependent on the surface properties of talc. Hence the many investigations about the surface energy of the material via solid–liquid interactions [1,2, and references therein]. The adoption of approximations in the calculation of surface energies such as the neglect of the surface pressure and the excessive use of the geometric mean approximation (which is known to overestimate the quantities sought) produce unreliable results for the surface energies and related properties of talc and other materials [2,3,5]. In this work an attempt is made to produce an average value for the surface energy of talc via solid–water interfacial interactions using a formula obtained by the combination of the Young equation with the general equation of pair interactions [3,4].

Talc, Mg3 Si4 O10 (OH)2 , was from Longuang Talc Co., Ltd. (Osmanthus brand talc powder of industrial first grade, China), of composition SiO2 , 59%; MgO, 30%; CaO, 1.2%. A sample was washed with water and passed a sieve with a 200-µm screen. After air-drying it was used for the determination of the adsorption isotherm. X-ray diffraction analysis showed the characteristic talc peaks at 3.118 (1), 9.371 (0.28), 4.694 (0.13), and 1.552 Å (0.02) (values between parentheses are peak intensities). The presence of magnesite, dolomite, and chlorite as impurities was detected.

* Corresponding author.

E-mail address: [email protected] (A.K. Helmy). 0021-9797/$ – see front matter  2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.11.022

2.1. Water adsorption isotherm Samples of 5.0 g of talc were air-dried (0.5% humidity), placed in Pyrex glass weighing bottles (diameter 50 mm, height 30 mm), placed in vacuum desiccators with aqueous concentrations of H2 SO4 of different p/p0 values (0.058– 0.37), and maintained at 28 ◦ C. When equilibrium adsorption was reached (constant weight), the quantities of water adsorbed per g of talc were determined by weighing. The vapor adsorption isotherm is shown in Fig. 1a.

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Literature data [2] give Π = 81.10 mJ m−2 at the same p/p0 . A contact angle of 60◦ for talc is reported in many publications [1,2] and was adopted in the present work.

3. Background The determination of the surface energy of a solid via liquid/solid interfacial interactions is based on the formula, [3,4] γS + γ L k= (3) γS − Π − γ L cos θ obtained by combining the Young equation, γS − Π − γSL − γ L cos θ = 0

(4)

with the pair interaction equation [3], γS + γ L − kγSL = 0,

(5)

where k is an interaction parameter, γS , γ L , and γSL are the surface tension of solid and the liquid and the solid/liquid interfacial tension, θ is the contact angle, and Π is the spreading or film pressure, Π = γS − γSV ,

(6)

where γSV is the solid/vapor interfacial tension. Equation (1) can also be written as Fig. 1. (a) Water vapor adsorption, q (mg g−1 ) on talc as a function of p/p0 of the aqueous solution of H2 SO4 (p0 = 23.756 Torr). (b) Water vapor adsorption, q (mmol g−1 ) on talc as a function of ln p (p expressed in dyn cm−2 ). The error bars are 95% confidence interval from averaging, and the line is the corresponding fits.

2.2. Calculations To obtain the spreading pressure Π , the amount adsorbed q (mmol g−1 ) was plotted against ln p (Fig. 1b) and Π was obtained by graphical integration according to the Gibbs equation, ln
pΓ

Π = RT

Γ d(ln p),

(1)

ln p=0

where R is the gas constant, T is the absolute temperature, Γ is the amount adsorbed per m2 , and pΓ is the pressure corresponding to the monolayer adsorption (ln pΓ = 8.97718). The area of the graph was found equivalent to 1.00487 mmol g−1 . The adsorption maximum of vapor was 7.145 mg H2 O g−1 obtained at p/p0 = 0.25. This amount gives a surface area (A) of A = 4.182 [m2 mg−1 ] × 7.145 [mg g−1 ] = 29.88 m2 g−1 . Thus  Π = (8.314 × 103 mJ mol−1 K−1 )(301 K)  ×(1.00487 × 10−3 mol g−1 ) 29.88 m2 g−1 = 84.16 mJ m−2 .

(2)

1+x (7) , 1 − mx where x = γ L /γS and m = (γ L cos θ + Π)/γ L . Equations (3) and (7) contain two unknowns, γS and k, and an extra exact relation is necessary for a complete solution to be obtained. Since this is yet to be found, we turn our attention to the range where γS lies. This, however, can be obtained using the Young equation subject to two conditions: k=

(1) γ L < γSL < γS [4,6], √ (2) γSL
γS γ L [7,8]. Hence the lower limit of the range for γS is given by the Young equation for γSL = γ L , and the upper limit is given √ for γ = γS γ L . Thus γS − γ L = γ L cos θ + Π , and γS − √ SL √ γ L γS − (γ L cos θ + Π) = 0, respectively. For Π = 84.16 mJ m−2 , θ = 60◦ , and γ L = 72.8 mJ m−2 the range for γS is 193.36–257.43 mJ m−2 . It is clear therefore that γS for talc lies in this range. Knowing the range where γS lies makes possible the calculation of some average value (γ¯S ) for this range. The mean value x¯ (x¯ = γ L /γ¯S ), can be calculated using the formula [9] (see Appendix A)  x2 dk x1 x dx dx , x¯ = (8) k(x2 ) − k(x1 ) where x2 and x1 are the limit values of x in the range where the surface energy lies.

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4. Results and discussion

or

To obtain the mean value (x) ¯ in the range fixed by the Young equation, we first differentiate Eq. (7) with respect to x:

γSV < γSL + γ L cos θ.

1+m dk = . dx (1 − mx)2

(9)

Hence Eq. (8) can be written as  x2 x(1+m) x1 (1−mx)2 dx x¯ = . k(x2 ) − k(x1 ) Integration gives  (1+m)  ln(1 − mx) + 2 x¯ = m k2 − k1

1 (1−mx)

(10) x2 x1

.

(11)

For x1 = 0.2828, x2 = 0.3765, k1 = 2.4127, k2 = 3.6559, and m = 1.656, x¯ = 0.3350, corresponding to γ¯S = 217.31 mJ m−2 and k = 2.9984. Published values of γS vary from 30 to more than 300 mJ m−2 [1,10]. The small values are too small to be true since they are lower than the values of the surface pressure. That a solid surface energy can never be less than the surface pressure is a thermodynamic fact that follows from Eq. (6) in combination with the Gibbs equation (1). Relatively high values of the spreading pressures are found in the literature [2,11–13] up to 296 mJ m−2 for clays. The reason for obtaining such values resides probably in the values of the surface areas of the materials, since these properties are expressed per unit area. The surface areas for clays determined by N2 adsorption are usually much lower than those determined by water vapor adsorption or other molecules [14]. Hence the smaller the determined area the higher the value of the property. Another important factor affecting the values of surface energy of solids is the contact angle. The contact angle in the Young equation is obviously that at equilibrium, and not that extrapolated to zero time [15]. Differences of 10◦ or more between advancing and receding angles are reported for talc [2]. The relatively high value of the surface pressure of talc reported here and in other publications [1,2,11,12] throws some doubt on the relatively large value of 60◦ for the water/talc contact angle, taking into consideration also the similarity of the value of surface energy of talc to those of other minerals reported to have low or zero contact angles with water [16,17]. It is perhaps of interest to end this discussion by stating that the determination of the surface energy of solids via solid–liquid interfacial interactions depends on the fact that these interactions are described by the Young equation. Some solid–liquid interactions do not conform to the requirements of the Young equation, as for example when γSV > γSL + γ L cos θ

(12)

(13)

These inequalities have been discussed by Gibbs [18], who stated that the interfacial discontinuities are difficult to realize between the phases when Eq. (11) or (12) is valid. Experimental observations in this laboratory have indicated that the inequality (11) is valid for the system montmorillonite/EGME (ethylene glycol monoethyl ether). Thus for γS = 205.1 mJ m−2 , θ = 61◦ , γ L = 28.3 mJ m−2 , Π = 36.38 mJ m−2 , and γSL = 76.19 mJ m−2 the latter value is √ calculated from the geometric mean ( γS γ L ), even knowing that the geometric mean overestimates γSL [7,8]. The above values give the inequality (11) as 168 > 76.19 + 13.72, thus indicating that the montmorillonite/EGME interactions cannot be described by the Young equation. On the other hand, the inequality (12) could be true when cos θ is negative (i.e., θ ≈ 100◦ ) and/or γSV and γ L are of similar magnitudes. For example [19], for the polystyrene/water system θ = 92◦ , γS = 33, and γ L = 72.8 mJ m−2 the inequality (12) is 33 < 49 − 2.5. For the polycarbonate/water system θ = 60◦ , γS = 45 mJ m−2 the inequality (12) is 45 < 57.2 + 36.4. For the polypropylene/water system θ = 104◦ , γS = 32 the inequality (11) is 32 > 48.26 − 17.61. The literature is full of similar results.

5. Conclusion An average value for the surface energy of talc is obtained by determining the range where the value lies and calculating the mean value within this range. The value found is 217.31 mJ m−2 .

Acknowledgments The authors thank Dr. Amina Helmi (Faculty of Mathematics and Natural Sciences, Groningen University, the Netherlands) for the mathematical treatment of the interval average. We are grateful to Dr. A.T. Hubbard for improving the English of the text. The present work was financed by the Secretaría General de Ciencia y Técnica (Research Group Project, Expte. No. 1805/01; Res. CSU-488/03), Universidad Nacional del Sur, Argentina.

Appendix A. The mean value of the surface energy in a given interval The mean value of the surface energy x¯ (x¯ = γ L /γ¯S ) in the interval x1 < x¯ < x2 is obtained by first assuming that k is a random variable uniformly distributed over the interval

A.K. Helmy et al. / Journal of Colloid and Interface Science 285 (2005) 314–317

(kmin , kmax ). This is the simplest assumption we can make, and a priori, there seem to be no constraints that would make one value of k more likely over any other. In this case the distribution function of k is f (k) = 1/(kmax − kmin ).

(A.1)

Since k and x are related through Eq. (7) it is possible to derive the probability distribution of x over the interval [x(kmax ), x(kmin )]. The distribution h(x) has to satisfy h(x) dx = f (k) dk, and therefore   h(x) = f k(x) |dk/dx|.

(A.2)

The mean value x in the interval is given by the integral [9]
x2   dxxh(x) .

(A.3)

x1

Hence from (A.1), (A.2), and (A.3) we get  x2 x¯ =

x1

x(dk/dx) dx

(kmax − kmin )

.

(A.4)

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