Apparent Molar Volume of Adsorbed-State Sodium Dodecyl Sulfate on

Department of Colloid Chemistry, Eo¨tvo¨s University, P.O. Box 32,. H1518 Budapest 112, Hungary. H. Høiland. Department of Chemistry, University of...
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Langmuir 1998, 14, 5539-5545

5539

Apparent Molar Volume of Adsorbed-State Sodium Dodecyl Sulfate on the Polystyrene/Water Interface G. Horva´th-Szabo´* Department of Colloid Chemistry, Eo¨ tvo¨ s University, P.O. Box 32, H1518 Budapest 112, Hungary

H. Høiland Department of Chemistry, University of Bergen, Alle´ gaten 41, N5007 Bergen, Norway Received February 13, 1998. In Final Form: June 30, 1998 A model is proposed to describe the molar volume changes of adsorbed materials on solid/liquid or liquid/liquid interfaces. The model divides the volume of a two-phase system into three subvolumes: two of them are for the homogeneous phases with volumes calculated from the partial molar volumes of the components in the phases and the third volume arises as the difference between the volume of the real system and the joint volume of the calculated phase volumes. It is shown that this third volume can be further separated into two parts: one of them is always present and resulting from the interaction of the two phases and the other originates from the inhomogeneous distribution of an adsorbing component in the interfacial range of the two phases. High-precision liquid density measurements have also been performed on systems containing sodium dodecyl sulfate (SDDS) dissolved both in water and in polystyrene dispersions with a water medium. From these measurements the apparent molar volume of the SDDS was calculated both in water and in a mixed solvent which in this special case is the dispergated particles with the water medium. This adsorption model is used for the interpretation of the data on the basis of which the apparent molar volume of SDDS in the adsorbed state on the polystyrene/water interface has been obtained as a function of the equilibrium concentration of SDDS in the bulk water. The resulted apparent molar volume function of SDDS in the adsorbed state is interpretable by different types of hydrophobic interactions.

Introduction By using the notion of the dividing surface, Gibbs introduced the first surface-thermodynamic description of heterogeneous systems.1 Although his ideas have been reconsidered,2-6 its essence still has remained valid.7-10 Although there have also been proposed models containing interfacial phase, phases, or monolayer assumptions, their success was limited since either they were inconsistent with the Gibbs adsorption equation11-13 or needed some additional information about the local structures of the interfacial layers13-15 which is generally not available. For didactical reasons an algebraic alternative model was also constructed by Goodrich.3 This alternative of the dividing surface treatment is basically suitable for in* To whom correspondence may be addressed. E-mail: [email protected]. (1) Gibbs, J. W. The Collected Works; Yale University Press: New Haven, 1948. (2) Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D. H. Surface Tension and Adsorption; Longmans: London, 1966. (3) Goodrich, F. C. In Surface and Colloid Science; Matijevic, E., Ed.; Wiley: New York, 1969; Vol. 1, p 1. (4) Schay, G. In Surface and Colloid Science; Matijevic, E., Ed.; Wiley: New York, 1969; Vol. 2, p 155. (5) Guggenheim, E. A. Trans. Faraday Soc. 1940, 36, 397. (6) To´th, J. J. Colloid Interface Sci. 1997, 191, 449. (7) Lyklema, J. Fundamentals of Interface and Colloid Science; Academic Press: London, 1995; Vol. 1, 2. (8) Chattoraj, D. K.; Birdi, K. S. Adsorption and the Gibbs Surface Excess; Plenum Press: New York, 1984. (9) Everett, D. H. Colloids Surf. A 1993, 71, 205. (10) Schay, G. J. Colloid Interface Sci. 1971, 35, 254. (11) Everett, D. H. In Adsorption from Solution; Ottewill, R. H., Ed.; Academic Press: London,1983; p 2. (12) Defay, R.; Prigogine, I. Trans. Faraday Soc. 1950, 46, 199. (13) Murakami, T.; Ono, S.; Tamura, M.; Kurata. M. J. Phys Soc. Jpn. 1960, 6, 309. (14) Lane, J. E. Austral. J. Chem. 1968, 21, 827. (15) Altenberger, A. R.; Stecki, J. Chem. Phys. Lett. 1970, 5, 29.

troducing the notion of the surface excess volume, which has been done by G. Schay.9 He, however, took it for zero,10 accepting the generally applied convention. In our opinion this convention is not imperative. Let us consider the volume and the volume changes in a twophase system. Here, the dividing surface separates homogeneous phases with properties equivalent to the properties of the real system far away from the interface. As to S/L phases Gibbs’s model implicitly assumes that the local density function of the liquid has a form which finally results in a liquid phase of the same volume as the liquid phase in the model. Or, expressing the same thing mathematically, the following equation must be true:

1 V

∫V

F(x) dV ) 1 F

where V is the volume of the liquid phase, F is the bulk density of the liquid, and F(x) is the local density of the liquid. But, since no information supporting this relation has turned up, it is advisable to look for some other model description not containing this assumption. There is another reason, too, forcing us to find an alternative model. The volume change of the system in the function of the amounts of adsorbed moles cannot be calculated on the basis of the dividing surface model, since in it the volumes of the adsorbed moles are not taken into consideration. One of the reasons for this has been that the volume change during the adsorption was not an experimentally measurable quantity because of its very small value below the uncertainty of the measurements. This situation, however, has been changed in 1996 when some data were published on the volume change of

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adsorption by using a specially developed dilatometer.16 Although this experiment made it possible to get the first information about the volume change in question, this method is still very time-consuming and it still needs a homemade instrument. In the present article we have been trying to solve the above-outlined problems: (i) to propose an alternative model (without using the local concentration distributions) for the S/L adsorption phenomena, making it possible both to include a finite volume of the adsorbed moles in the volume of the system and to calculate the volume change of the system during the adsorption process; (ii) to suggest a new experimental method for measuring the molar volume of adsorbed materials and to present some experimental data to show both the realizability of the method and the applicability of the model. Theory The determination of the partial molar volume of one of the components in a two-component system is wellknown and is based on the following definitions and equations:

V2 )

( ) ∂V ∂n2

(1) T,P,n1

V - n1V*1 V2,φ ) n2

(2)

( )

V2 ) V2,φ + m2

∂V2,φ ∂m2

(3)

T,P

where V2 and V2,φ are the partial and the apparent molar volumes of the second component, respectively, V/1 is the molar volume of component 1, m2 is the molality of the solution, and the other notations have their usual meanings. In the case of a ternary system any two components of the three can be considered as a mixed solvent with an average molar weight. All relations listed here for binary systems can be used where m is the number of moles of solute per kilogram of the mixed solvent.17 For example, the equation equivalent with eq 2 is

V3,φ(1+2) )

V(1+2+3) - V(1+2) n3

(4)

where V(1+2+3) is the volume of the three-component system, V(1+2) is the volume of components 1 and 2 in the mixed state, n3 is the moles of the third component in the (1+2) is the apparent molar volume volume V(1+2+3), and V3,φ of component 3 in the mixed solvent (1+2). Besides this, for our further discussion and for our special case, the following agreements will be used to describe the properties of a system containing dispergated particles, too: the first component will represent the dispergated particles the second component the medium, and the third component the solute. Since, in this paper, the strict differentiation among the models used is essential, it is worthwhile to devote a few sentences to the description of models in Figure 1: (a) In the first column of the figure the schematics of the real (16) Yamaguchi, N.; Hashitani, T.; Okazaki, M.; Takeda, T. J. Colloid Interface Sci. 1996, 183, 280. (17) Desnoyess, R. M. In Surfactant Science Series; Zana, R., Ed.; Marcel Dekker: New York, 1986; Vol. 22, p 1.

Figure 1. Comparison of the real system with the models used. Model I is used for the calculation of the apparent molar volumes of the third component. Model II is used for the interpretation of the apparent molar volume of the third component in the adsorbed state. The numbers 1, 2, and 3 mark the solid, liquid, and surfactant components, respectively. In the real system, the local values of the apparent molar volumes of the components are dependent on the distance X, while in model II the homogeneity of phases are applied (see detailed description in the manuscript).

systemsor more preciselyour surmise about the structure of the real systemscan be seen. In the first rectangle the PS particles (1) and the water medium (2) are presented. After the third component is added, which is a surfaceactive material, its local concentration will be higher in the interfacial region of PS/water than in the bulk of the water (second rectangle). In the third rectangle a sketch of the apparent molar volume functions are represented according to which all functions change in the interfacial range. (b) In the second column the same system is considered from a phenomenological point-of-view; therefore, there is no structural description of the system here and the states of this system are characterized by global quantities (e.g., by the average densities of the mixtures in the first and second rectangles). (c) In the third column our model representation of the system can be seen according to the system’s volume, consisting of three subvolumes, in two-phase systems: (i) that of the homogeneous liquid, (ii) that of the homogeneous solid, and (iii) that of a volume originating from the interaction of the two phases (see the first circle). This description is similar to that of Gibbs’ in the respect that the phases are homogeneous, but it is also different from it inasmuch as, in addition to the volumes of the two phases, a nonzero third volume is also introduced. This volume in our treatment can be identified as the surface excess volume of Gibbs’ treatment. After the third component is added, the solid and liquid phases will still keep their homogeneity and the third component will also be present both in the liquid phase and in a part of the above-mentioned surface excess volume (second circle). The truth is that the whole structural description of our model (last rectangle in the third column of Figure 1) was constructed with the aim to make both the apparent molar volumes in the solid and in the liquid phases constant as well as the apparent molar volume of component 3 in that part of the surface excess volume in which it is present. Thus, our working program, as suggested by this paper, will be the following: we measure the properties of a real system with techniques by which we are able to detect only the average properties of the system (e.g., its average density, average concentration, etc.); having obtained the

Adsorbed State SDDS on the PS/Water Interface

Langmuir, Vol. 14, No. 19, 1998 5541

average values, our measurements will become a constituent part of the phenomenological description (see point b above), and the apparent molar volumes will also become calculable on the basis of this description. The interpretation of the results will, however, be based on the structural model (last rectangle in third column). The system containing only components 1 and 2 will be regarded as a mixed solvent with average molar mass:

n1M1 + n2M2 M(1+2) ) n1 + n2

)

n3 kg of mixed solvent (1+2)

)

1000n3 n2(1 + k)M(1+2)

n1 n2

(6)

)

; VI3 ) T,P,n3,k

( ) ∂VI ∂n3

VL ) nL2 VL2 (mL3 ) + nL3 VL3 (mL3 )

(8)

VS ) n1V/,S 1

(9) (10)

where mL3 is the molality of the third component in the VL

(11)

T,P,n1,k

By applying the Appendix to express the partial molar volume of the second component with the apparent and the partial molar volumes of the third component in eq 8 we get

(12)

According to the Appendix, by expressing the partial molar volume of the mixed solvent with its molar volume, and with the apparent and partial molar volumes of the third component, eq 10 has the following form: /,I I + n3V3,φ (mI3) VI ) (n1 + n2)V(1+2)

(7)

is the ratio of the moles of components 1 and 2. The volume of the model II system contains three subvolumes (Figure 1): the volume of the solid component VS, the volume of the liquid component VL, and a third certain volume V∆ connected with the interactions of the components of our real system inside the range of action of the interface forces. The model systems I and II are constructed at the same T and P as our real system to satisfy the following conditions: II I (i) nIi ) nII i ) ni, i ) 1, 2, and 3, where ni , ni , and ni are the moles of the ith component in model II, in model I, and in the real system, respectively. (ii) VI ) VII ) V, where VI, VII, and V are the total volumes of models I, II, and the real system, respectively. (iii) VII ) VS + VL + V∆. (iv) VS is the volume of the solid phase containing ni moles. (v) VL and VS are homogeneous. L ∆ L ∆ (vi) nII 3 ) n3 + n3 where n3 and n3 are the moles of L ∆ component 3 in the V and V volumes, respectively. L L (vii) nII 2 ) n2 , where n2 is the number of moles of component 2 in the VL volume. (viii) The partial molar volume of the first component VS1 in volume VS is constant (therefore, the molar volume of this component V/,S is also constant) at the given 1 morphology of the dispersed phase and in contact with the second component. (ix) The concentrations of the components in VL are equal to the concentrations of the components in our real system far away from the interface (i.e., the so-called equilibrium concentrations in the usual adsorption experiments). The volumes of both of the models I and II can be expressed by the partial molar volumes at a fixed molar ratio k:

I (mI3) + n3VI3(mI3) VI ) (n1 + n2)V(1+2)

(

∂VI ∂(n1+n2)

L (mL3 ) VL ) nL2 V/2 + nL3 V3,φ

where

k)

I V(1+2) )

(5)

from which the molality of the third component in the three-component system according to model I’s phenomenological description in Figure 1 is

mI3

volume, mI3 is the molality of the third component in the I system (mol of n3/kg of mixed solvent (1+2)), and VL2 and VL3 are the partial molar volumes of components 2 and 3, respectively, in the VL volume of model II. Furthermore, the definitions of the molar volumes used in eq 10 are given as follows:

(13)

According to conditions ii and iii and from eqs 9, 12, and 13: I I L L L V∆ ) ∆I,II 1,2 + n3V3,φ (m3) - n3 V3,φ(m3 )

(14)

/,I /,S /,L where ∆I,II 1,2 ) (n1 + n2)V(1+2) - n1V1 - n2V2 . I,II The ∆1,2 is nothing else but the volume change when n1 and n2 moles are mixed together or, with other words, the volume change arises from the interaction of the adsorbent and the medium at the fixed molar ratio k, and the unchanged morphology of the adsorbent. It is clear that ∆I,II 1,2 is independent of the presence of component 3, while the rest of the right side of eq 14 is a certain volume connected with the presence of the excess of the third component at the interface. By the analogy of the definition of apparent molar volumes in three-component systems (eq 4), we can calculate the apparent molar volume of component 3, in volume V∆

∆ ) V3,φ

V∆(1,2,3 comp. present) - V∆(1,2 comp. present) n∆3 (15) since, however,

V∆(1,2 comp. present) ) ∆I,II 1,2

(16)

the following equation is valid: ∆ ) V3,φ

1 L [n VI (mI3) - nL3 V3,φ (mL3 )] ∆ 3 3,φ n3

(17)

After some rearrangements:

1 I ∆ L V3,φ (mL3 ) ) (V3,φ (mI3) - (1 - P)V3,φ (mL3 )) (18) P where P ) n∆3 /n3 is the portion of the adsorbed molecules of component 3, which is the function of mL3 . The two independent variables (mI3,mL3 ) in eq 18 are bound to-

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Horva´ th-Szabo´ and Høiland

gether, since

mI3 ) mL3

1 - W1 1-P

(19)

where W1 is the mass fraction of the dispersion, that is, W1 ) n1M1/(n1M1 + n2M2). All the quantities and functions on the right side of eq 18 are determinable because (a) P ) f(mL3 ) is measurable by means of the usual adsorption experiment; (b) the construction of the model system results in n∆3 ) n3 mL3 (n2M2)/1000; (c) mL3 is calculable from eq 19; (d) W1 is determinable by the measurement of the dried mass of a I L ) f(mI3) and V3,φ ) portion of the dispersion used; (e) V3,φ L f(m3 ) are determinable with density measurements on the systems containing components 1, 2, and 3 and components 2 and 3, respectively. ∆ as the apparent molar volume of We may call V3,φ component 3 in the adsorbed state. It is clear that this quantity cannot be independent of the other components of the system, namely the molar volume of the liquid (providing that the solid is unaltered), since there is an exchange between the solvent and solute molecules during the adsorption in the interfacial range, resulting in ∆ . But it is to be kept exchange-volume properties for V3,φ in mind that this quantity is an artificial construction like the surface excess quantities introduced by Gibbs, and it is not a molar volume in the usual sense. Nevertheless, it still makes it possible to get information about the volume changes during the adsorption, and this binds it together with the interactions and structural changes in the adsorption layer versus the function of the equilibrium concentration of the adsorbed material. Materials and Methods. Sample Preparation. Polystyrene (PS) latex particles were prepared by aqueous emulsion polymerization with a K2S2O8 initiator at 70 °C. The PS sample (code name: PS105) was polymerized by a mixture of sodium dodecylbenzene sulfonate and Triton X-100.18 It was steam-stripped at 100 °C for 4-5 h, then dialyzed against double-distilled water for 1 month, and ion-exchanged using Vanderhoff’s method.19 The dialysis tube (Sigma D 0655) was cleaned before usage according to the instructions of the manufacturer. The particle size was determined by an electron microscope. The diameter was found to be 0.1 µm. The sodium dodecyl sulfate salt (Merck, assay > 99%) (SDDS) used for the molar volume measurements was recrystallized from the mixture of ethanol/benzene (1:1 volume), and then the precipitated surfactant was washed by acetone, dried under vacuum at room temperature, and kept in a desiccator above dried CaSO4. The benzene (assay > 99.5%), ethanol (assay > 99.5%), and acetone (assay > 99.5%) were supplied by Merck. The potassium peroxydisulfate (assay >99%, Merck) was doubly recrystallized from water. The stock dispersions of polystyrene were kept at 5 °C. The mass fraction of the particles in the stock dispersion was determined by drying one portion of the dispersion at 25 °C in a desiccator under reduced pressure using 98% sulfuric acid to remove the evaporated water. The average of three measurements was used for the calculation. The mixed media for the density measurements were prepared by dilution with double-distilled water from the stock dispersions. All the samples including those containing SDDS had been prepared 24 h before the experiments by measuring the masses of the parts with an analytical balance and kept at 25.0 ( 0.1 °C. (18) Szende, G.; Udvarhelyi, K. Int. J. Appl. Radiat. Isot. 1975, 26, 53. (19) Vanderhoff, J. W. Pure Appl. Chem. 1980, 52, 1263.

Density Measurements. An A-PAAR DMA60 instrument with a 602 cell was used for the measurements. The short-term stability (0.5 h) of the thermostating system of the instrument was around (0.003 °C. The reference water values were measured at every half hour during the interval of the density measurements. The reproducibility of the measurements under these circumstances was around (2 × 10-6 g/mL. In the case of samples containing colloidal particles the effect of the viscosity on the measured data was taken into consideration,25 and the corrected densities were used for further calculations. In the case of samples without colloidal particles the viscosity correction was unnecessary. The viscosities were measured with a Ubbelohde viscometer at 25.0 ( 0.1 °C. Measurements of Apparent Molar Volumes. To calculate the apparent molar volume in the system containing SDDS in water, the following equation was used:

V2,φ )

M2 d - d* - 1000 × d dd*m

(20)

where M2 is the molar mass of the solute, d and d* are the densities of the solution and solvent, respectively, and m is the molality. In the case of the determination of the apparent molar volumes in mixed solvents d* is the density of the mixed solvent. Using the colloidal dispersion as the mixed solvent, the solid SDDS should have been dissolved in the dispersion. However, since the SDDS is an electrolyte, aggregations of the charge-stabilized PS particles might occur during this step. To avoid this, first, the SDDS was dissolved in water and then some amount of the stock dispersion of polystyrene was added to the system. The concentrations of the SDDS and PS samples were set to values, which resulted in a series of solutions of the same PS concentration with different SDDS concentrations. Parallel to the preparation of these sample four other samples were prepared simultaneously from water and from the same stock dispersion of PS: two of the four with higher and two with smaller concentrations of PS than the samples from the above series containing SDDS too. The densities of these solutions were measured, and their mass fractions were calculated knowing the mass fraction of the stock dispersion and the masses of the water and stock dispersion used. A linear equation was fitted to the four density/mass-fraction point-pairs. (The linearity of the density vs mass fraction function for PS is found to be strictly valid as in the case of silica dispersions which was investigated recently.20) This made it possible to calculate by interpolating each of the densities of hypothetical PS dispersions, which we ought to have used if solid SDDS had been dissolved, to result finally in the series of samples with the same SDDS and PS contents as it was in our real case. By this interpolation we got the exact density of the hypothetical dispersion which has to be used in eq 20 as the density of the mixed solvent. So the apparent molar volume of the SDDS in the mixed solvent was determined by eq 20. Measurements of the Adsorption Isotherms. The separation of the supernatant liquid from the particles was performed by 1 h centrifugation at 25.0 ( 0.1 °C with 50 000-g acceleration. For this step a MOM-3170 ultracentrifuge with a swing-out rotor was used. The mass fraction of the PS dispersion used was 0.03. Potentiometric titration with tetradecyltrimethylammonium bromide (Aldrich, assay > 99%) solution was used for the determination of the SDDS concentrations in the supernatants. The equivalence points were detected by a surfactant-sensitive (20) Horva´th-Szabo´, G.; Hoiland, H. J. Colloid Interface Sci. 1996, 177, 568. (21) Goddard, E. D.; Higham, E. H.; Stewart J. C. Res. Corresp. 1955, 7, 1. (22) Elworthy, P. H.; Mysels, K. J. J. Colloid Interface Sci. 1966, 21, 331. (23) Vass, Sz.; To¨ro¨k, T.; Ja´kli. Gy.; Berecz, E. J. Phys. Chem. 1989, 93, 6553. (24) Lyklema J. In Adsorption from Solution at the Solid/Liquid Interface, Parfitt, G. D., Rochester, C. H., Ed.; Academic Press: London, 1983. (25) Ashcroft, S. J.; Booker, D. R.; Turner, J. C. R. J. Chem. Soc., Faraday Trans. 1990, 86, 145.

Adsorbed State SDDS on the PS/Water Interface

Figure 2. Apparent molar volume of the SDDS dissolved in water as plotted against its concentration. A linear equation (dashed line) is fitted upon the data points in the concentration range below the CMC. The dotted line is a part of the hyperbola fitted upon the points measured in the concentration range above the CMC. (See Figure 3) membrane electrode (Metrohm 6.0504.150) with Ag/AgCl reference (Metrohm 6.0724.140) at 25.00 ( 0.01 °C. The surfactant electrode was conditioned before the titration according to the instructions of the manufacturer. Furthermore, one “conditioning” titration was also performed before the titration of the samples using a similar concentration solution as that of the sample. The electrodes were connected to a digital pH meter with 0.1-mV resolution (Radelkis OP-208/1). The amounts of the SDDS were calculated from the inflection points of the titration curves by means of the following procedure: the millivolts versus volume function was differentiated numerically, and then a Gaussian curve was fitted to its points; the mean value of the Gaussian distribution was taken as the inflection point. The reproducibility of the titration at 0.0001 M/L concentration was 1% and at 0.001 M/L concentration it was around 0.01%.

Results and Discussion The measured apparent molar volumes of SDDS are plotted in low and in high concentration ranges in Figures 2 and 3, respectively. A linear equation (apparent molar volume ) A + B × molality) is fitted in Figure 2 upon the measured data with the following parameters A ) 238.15 and B ) 31.75 within the molality range 0-0.009. A rectangular hyperbola (apparent molar volume ) P1 × molality/(P2 + molality)) is fitted upon the measured data in Figure 3 with the following parameters P1 ) 249.82, P2 ) 0.00039 within the molality range 0.009-0.16. The crossing point of the two curves (m ) 0.00815) is in accordance with the CMC values of SDDS in the literature (CMC ) 0.0081 mol/L21 and CMC ) 0.000815 mol/L22). The agreement of the measured molar volumes with those of the data of Vass23 further confirm the reliability of our data of molar volumes. The above-mentioned linear equation is used to describe the dependence of the apparent molar volume on the molality of SDDS in the low concentration range for the L (mL3 ) function further calculations (i.e., it is used as V3,Φ in eq 18).

Langmuir, Vol. 14, No. 19, 1998 5543

Figure 3. Apparent molar volume of the SDDS dissolved in water as plotted against its concentration. The dotted line is a hyperbola fitted upon the points measured in the concentration range above the CMC.

Figure 4. Apparent molar volume of the SDDS dissolved in polystyrene dispersion (mass fraction ) 0.003) with a water medium as plotted against its total concentration in the system. The circles mark the data calculated without the viscosity correction and the squares with the viscosity correction. The solid line represents the curve of the equation fitted upon the points as calculated with the viscosity correction. The dashed line is from Figure 2, representing the apparent molar volume of SDDS in water.

The apparent molar volume data of SDDS measured in polystyrene dispersions are plotted against molality in Figure 4. The mass fraction of the dispersion at these measurements was 0.0031. The circles mark the data withoutswhile the squares mark them withsthe viscosity correction.25 According to our measurements, it is un-

5544 Langmuir, Vol. 14, No. 19, 1998

Figure 5. Adsorption isotherm of SDDS on the polystyrene/ water interface. The amount of adsorbed moles is per 1 g of polystyrene.

necessary to use the viscosity correction at molality 0.003 and above, since the viscosity value of the dispersion of the used concentration becomes very close to that of the water. It shows that the increased viscosity of our electrostatically stabilized dispersion was caused by the electroviscous effect which was broken down by the SDDS, acting here not only as an adsorbed surfactant but also as an electrolyte. The following equation was fitted by us to the apparent molar volume data with viscosity correction: Apparent molar volume ) P1/XP2 + P3/XP4, where X is the molality of SDDS in the PS dispersion, P1 ) 8.943 × 10-7, P2 ) 2.184, P3 ) 247.9, and P4 ) 0.01503. This I (mI) function in eq 18. To function was used as the V3,Φ illustrate the deviation of the apparent molar volumes in water and in PS dispersion, the linear curve of the apparent molar volume of SDDS in water from Figure 2 was also plotted against molality with a dashed line in Figure 4. To preclude the possibility of the effect of impurities on the measured apparent molar volumes in PS dispersions, some samples of SDDS solution were also prepared by using the centrifugally separated supernatant liquid of the PS dispersion as the solvent. The calculated molar volumes of SDDS in these solutions were the same as those of the SDDS molar volumes in water, canceling out the possibility of impurities. The adsorbed amount of SDDS was per 1 g of PS at the calculation of the adsorption isotherm. In Figure 5 the following equation was used in order to describe the concentration dependence of adsorption: adsorbed moles of SDDS ) P1 + P2 × X(1/2) + P3 × X, where X is the equilibrium molality of SDDS in the medium at the PS dispersion: P1 ) -1.991 × 10-7, P2 ) 5.858 × 10-4, and P3 ) -1.654 × 10-4. From this curve the P function was calculated and plotted in Figure 6. Since, from the results of the above-described measureL I (mL3 ), V3,Φ (mI3), and P ments and calculations, the V3,Φ functions are known, it has become possible to calculate ∆ (mL3 ) function (i.e., the apparent molar volume of the V3,Φ SDDS in the adsorbed state as a function of the equilibrium concentration of SDDS (Figure 7), which was originally the target of our whole investigation.

Horva´ th-Szabo´ and Høiland

Figure 6. Fraction of (adsorbed moles)/(total moles) of SDDS vs its equilibrium concentration.

Figure 7. Apparent molar volume of the SDDS in the adsorbed state (solid line) at the PS/water interface as plotted against its equilibrium concentration. The dashed line marks the apparent molar volume of SDDS in water.

Furthermore, since the SDDS dissociates in the solution, some more considerations become necessary to understand this result. The measured apparent molar volumes of SDDS in the bulk water are the result of the two individual molar volumes of its ions. The meaning of the measured apparent molar volume of a dissociable material in the adsorbed state, however, does not have such simple properties, and therefore we have to know which types of its ions are in the adsorbed state. This is a nonsimply question discussed by Lyklema.24 The analytical technique used for the determination of the adsorbed amount of the SDDS gave the moles of the DDS ions which belong to the PS particles, either on the surface of particles or in

Adsorbed State SDDS on the PS/Water Interface

their ion atmospheres. Some (not necessarily equivalent) amounts of sodium ions are also in the interfacial range in exchange equilibrium with the hydrogen counterions (the PS have negative surface charge) when the DDS ions are on the surface of the particles and vice versa. Therefore, the calculated apparent molar volume of adsorbed SDDS contains some amount of the molar volumes of “adsorbed” sodium and hydrogen ions as well. The sodium/hydrogen ratio is unambiguously determined by the model and the experimental conditions; therefore, the calculated adsorbed molar volumes also have welldefined values. To separate the adsorbed molar volumes of SDDS into individual adsorbed molar volumes of DDS, Na, and H ions, supplementary experiments are necessary. Fortunately, in our case the contribution of the H/Na ion exchange process to the measured molar volumes of SDDS at the polystyrene/water interface is negligible, since our experiments have shown that the measured apparent molar volumes of sodium chloride in the same PS dispersion (without SDDS) are the same as those of the sodium chloride in water within the experimental error. This supports our assumption that the DDS present in the interfacial range is responsible for the measured molar volume changes. The apparent molar volume of SDDS in the bulk was also plotted in Figure 7 (dashed line). There is a remarkable difference between this function and that of the molar volume function of the adsorbed SDDS. Although the clear understanding of this deviation and the detailed structural description of the effect needs further investigations, it is clear that some change had to occur either in the structure of DDS or in that of the exchanged water during the adsorption process, and it is very probable that the hydrophobic interaction is also included in this phenomenon. What follows is one of the possible interpretations of the measured apparent molar volume function of the adsorbed SDDS: the curve is a result of two types of hydrophobic interaction: (i) an interaction between DDS and some adsorption site on the PS surface; (ii) an interaction among the adsorbed SDDS molecules. Since from Figure 3 it can be seen that the molar volumes of SDDS in the associated state have higher values than those of the SDDS in the nonassociated form and since, furthermore, it is well-known that the driving force of micellization is the hydrophobic interaction, it is very probable that the hydrophobic interaction generally results in an increase of the molar volume function of the SDDS. One part of this increase is obviously the released water from the surrounding space of the headgroups of DDS. This water is in an electrostriced form having a smaller molar volume than bulk water. During the adsorption the headgroups become partially dehydrateds like in the case of micellizationsresulting in an overall increase in the partial molar volume of DDS during the adsorption. On the basis of this, in case i as a result of the hydrophobic interaction the molar volume of SDDS is higher when it is adsorbed onto the surface of PS than it is in the solution. Regarding case ii the hydrophobic interaction among the adsorbed SDDS molecules increases with increasing surface covering. This is a lateral hydrophobic interaction among the DDS (the appearance of “surface-micelles” are also possible before the CMC); therefore, the molar volume function is also increasing with increasing equilibrium concentration. The form of the apparent molar volume function of SDDS is the result of the linear superposition of effects discussed in (i) and (ii).

Langmuir, Vol. 14, No. 19, 1998 5545

Conclusion There is a contradiction on one hand between the condition of the homogeneity of phases in space up to the Gibbs dividing surface and on the other hand, between the condition of the generally accepted zero value of the surface excess volume in the usual description of either S/L or L/L adsorption based on the usage of surface excess quantities. When a nonzero surface excess volume is allowed, it becomes possible to develop another type of adsorption description, on the basis of which the apparent molar volume of the adsorbed material is interpretable. Our experimental results show that this model is usable and the apparent molar volumes of the adsorbed materials are measurable. The resulting apparent molar volume function of SDDS in the adsorbed state is interpretable by different types of hydrophobic interactions. Now we are working on a detailed theoretical explanation of the consequences of the nonzero surface excess volume condition in the surface thermodynamics. Acknowledgment. Financial support from OTKA project T025878 is acknowledged. Appendix The following equation is valid for a homogeneous phase with two components according to the Gibbs-Duhem equation:

0 ) n1 dV1 + n2 dV2

(T, P constant)

(A1)

where V1 and n1 are the partial molar volume and the number of moles of the first component in the phase, respectively. Introducing the molality m of component 1:

m1 )

1000n1 M2n2

(A2)

using it in the integrated form of eq A1:

M

) 2 dV2 ) ∫VV(m(m)0) 1000 2

2

1

1

) m1 dV1 ∫VV(m(m)0) 1

1

1

1

(A3)

After some rearrangements of this equation we obtain:

V2(m1) ) V/2 -

M2 [m V (m ) 1000 1 1 1

∫0m V1(m1) dm1] 1

(A4)

By the application of eq 3 we get

V2(m1) ) V/2 -

n1 [V (m ) - V1,φ(m1)] n2 1 1

(A5)

where V/2 is the molar volume of the pure second component. LA980182Z