Thermodynamic investigation of the systems poly(ethylene glycol) + sodium pentane-1-sulfonate + water and poly(vinyl pyrrolidone) + sodium pentane-1-sulfonate + water

Journal of Colloid and Interface Science 346 (2010) 107–117

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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis

Thermodynamic investigation of the systems poly(ethylene glycol) + sodium pentane-1-sulfonate + water and poly(vinyl pyrrolidone) + sodium pentane-1-sulfonate + water Rahmat Sadeghi *, Mehdi Ziaii Department of Chemistry, University of Kurdistan, Sanandaj, Iran

a r t i c l e

i n f o

Article history: Received 17 November 2009 Accepted 13 February 2010 Available online 19 February 2010 Keywords: Sodium pentane-1-sulfonate Poly(ethylene glycol) Poly(vinyl pyrrolidone) Volumetric Compressibility Vapor–liquid equilibria Micellization

a b s t r a c t Thermodynamic properties for aqueous solutions containing sodium pentane-1-sulfonate (C5SO3Na) in the absence and presence of poly(ethyleneglycol) (PEG) or poly(vinylpyrrolidone) (PVP) determined as a function of surfactant concentration from the density, sound velocity, viscosity, conductivity and vapor–liquid equilibria data, are reported here. Densities and sound velocities, allowing for the determination of apparent molar volumes and compressibilities, were measured at 288.15–313.15 K. Changes in the apparent molar properties upon micellization were derived using a pseudo-phase-transition approach and the infinite dilution apparent molar volumes and compressibilities of the monomer and micellar state of C5SO3Na in the investigated solutions were determined. The values of the infinite dilution apparent molar properties of micellar states of C5SO3Na in aqueous polymer solutions are larger than those in pure water. Vapor–liquid equilibrium data such as water activity, vapor pressure, osmotic coefficient, activity coefficient and Gibbs free energies were obtained through isopiestic method at 298.15 K. The variations of the critical micelle concentration (CMC) of C5SO3Na in water and in aqueous PEG and PVP solutions with temperature were obtained and a comparison between the CMC of C5SO3Na obtained from different thermodynamic properties was also made. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction For the understanding of interactions in liquids, the thermodynamic and transport properties such as the activity and osmotic coefficients, enthalpy, volume and compressibility changes on dilution, electrical conductivity, viscosity, transport numbers, etc., are of great interest. These properties are indispensable to test various theories and models of surfactant solutions [1–3]. However, in colloidal chemistry, these thermodynamic properties especially vapor–liquid equilibrium data seem to be rarely determined experimentally, in contrast to electrolyte solution chemistry or biology [4]. For the long-chain ionic surfactants which have the low critical micelle concentration (CMC) values (dilute micellar solutions) and in this case activities can be taken equal to concentration, the value of the free energy of micellization of the surfactant, DGmic , can be determined by using the relationship [5]

DGmic ¼ RTð1 þ bÞ ln CMC;

ð1Þ

where R and T have their usual meaning, and b is the fraction of charges of micellized univalent surfactant ions neutralized by * Corresponding author. Fax: +98 871 6660075. E-mail addresses: [email protected], [email protected] (R. Sadeghi). 0021-9797/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2010.02.034

micelle-bound univalent counterions. However, for the short-chain surfactants which have the high CMC values (concentrated micellar solutions) activities cannot be taken equal to concentration and therefore this procedure cannot be used for the determination of DGmic . In fact, in the case of short-chain surfactants, there are no methods reported in the literature for the calculation of Gibbs free energy of micellization. In this work, based on the experimental water activity data a new manner is presented for the calculation of the free energy of micellization of the investigated short-chain surfactant. For the first time the isopiestic method is used for the studying of thermodynamics of micelle formation of surfactant sodium pentane-1-sulfonate in water and in aqueous solutions of poly(ethyleneglycol) and poly(vinylpyrrolidone). Water activity calculated from this method is an important and key thermodynamic property, because, it is closely related with the other thermodynamic properties and in thermodynamic modeling for separation methods, it is the essential variable. The polymer–surfactant interactions are interesting from a fundamental as well as from a practical point of view. These complex mixtures have important properties for a wide range of industrial application fields such as floatation processes, foaming control, detergency, and enhanced oil recovery [6]. Although interactions between ionic surfactants and nonionic water soluble polymers have been extensively studied during the last decades, but the

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subject is not clearly understood. Among all the mixed polymer– surfactant systems, sodium alkyl sulfates [CH3–(CH2)n1–SO4Na], especially sodium dodecyl sulfate (C12SO4Na), are the most used anionic surfactants. Sodium alkane-1-sulfonates [CH3–(CH2)n1– SO3Na] are one of the most important class of anionic surfactants which can form micelles in aqueous solution and also may interact with water soluble polymers such as poly(ethylene glycol) (PEG) or poly(vinyl pyrrolidone) (PVP) in aqueous solution. Despite the great interest in sodium alkane-1-sulfonates, few physicochemical studies of the monomers and the micelles can be found in the literature [7,8–19]. Also, among all the mixed polymer–surfactant systems, only a few investigations involved sodium alkane-1-sulfonates [15,19–24]. This work is, thus, mainly focused on (i) the study of the thermodynamic properties of monomer and micellar state of sodium pentane-1-sulfonate (C5SO3Na) in water, with especial emphasis on the solute–solute and solute–solvent interactions and (ii) the physicochemical characterization of the C5SO3Na monomers and micelles in aqueous solutions of PEG or PVP. This work, because of the extensive and accurate experimental and theoretical studies closes a gap of information on sodium alkane-1-sulfonates. In order to study the effect of PEG, PVP and temperature on the apparent molar volume, isentropic compressibility, viscosity and vapor–liquid equilibria behavior of the monomer and micellar state of C5SO3Na and therefore make a thorough analysis of the interactions between C5SO3Na and nonionic water soluble polymers, the apparent molar volume and isentropic compressibility of C5SO3Na in water and in aqueous solutions of PEG or PVP were determined at different temperatures from the accurate measurements of density and ultrasonic velocity. The viscosity of these solutions was determined at different temperatures below and above the micellar composition range. Water activities of binary aqueous C5SO3Na solutions and ternary aqueous C5SO3Na + PEG and C5SO3Na + PVP solutions were determined through isopiestic method at 298.15 K. From these data the variation of the critical micelle concentration (CMC) in pure water and in aqueous PEG or PVP solutions with temperature was obtained and a comparison between the CMC of C5SO3Na obtained from different investigated thermodynamic properties was made. 2. Materials and methods 2.1. Materials C5SO3Na (purity >99%), PEG, PVP and NaCl (purity >99.5%) were obtained from Merck and were used without further purification. PEG had a nominal molecular weight of 6000 and the manufacturer has characterized this polymer with charge/lot number S35317 203. PVP had a nominal molecular weight of 10,000 and the manufacturer has characterized this polymer as polyvidon 25 with lot number k34372143 516. The double distilled, deionized water was used for the preparation of the solutions. 2.2. Osmotic coefficient measurements The isopiestic apparatus used for determination of water activity in the ternary water + PEG (or PVP) + C5SO3Na solutions consisted of eight-leg manifold attached to round-bottom flasks. Two flasks contained the standard pure NaCl solutions, one flask contained the pure PEG (or PVP) solution, one flask contained the pure surfactant solution, three flasks contained the PEG (or PVP) + surfactant solutions and the central flask was used as a water reservoir. Similarly, the isopiestic apparatus used for determination of water activity in the binary water + C5SO3Na solutions consisted of five-leg manifold attached to round-bottom flasks and the

apparatus used for determination of the effect of polymer on the vapor–liquid equilibria of aqueous polymer + surfactant solutions, consisted of nine-leg manifold attached to round-bottom flasks. The apparatus was held in a constant-temperature bath at least 15 days (depend on surfactant concentration) for equilibrium. The temperature was controlled to within ±0.05 K. After equilibrium had been reached, the manifold assembly was removed from the bath, and each flask was weighed with an analytical balance (Sartorius CP124S) with a precision of ±1  104 g. The water activities for the standard aqueous NaCl solutions at different concentrations have been calculated from the correlation of Colin et al. [25]. The uncertainty in the measurement of solvent activity was estimated to be ±2  104. 2.3. Volumetric measurements The density and sound velocity of the mixtures were measured at different temperatures with a digital vibrating-tube analyzer (Anton Paar DSA 5000, Austria) with proportional temperature control that kept the samples at working temperature within ±103 K. The apparatus was calibrated with double distilled deionized, and degassed water, and dry air at atmospheric pressure. Densities and ultrasonic velocities can be measured to ±106 g cm3 and ±102 m s1, respectively, under the most favorable conditions. The uncertainties of density and ultrasonic velocity measurements were ±3  106 g cm3 and ±101 m s1, respectively. 2.4. Viscosity measurements Viscosities were measured with an Ostwald-type viscometer. It was assumed that the dynamic viscosity g was related to the time of flow according to

g ¼ Ldt 

Nd ; t

ð2Þ

where t is the flow time, d is the density of the solution, L and N are constants characteristic of the viscometer. The viscometer constants L and N were determined by a least-squares fit to Eq. (2) of the literature data for viscosity of water [26] and 2-propanol [27] at the respective temperature. The temperature of the water bath was maintained at ±0.01 K. The flow time of investigated solutions was measured with accuracy better than 0.05 s. For each solution the flow time was measured at least three times. The viscosity measurement was reproducible to within ±0.05%. 3. Results and discussion 3.1. Vapor–liquid equilibria measurements For the understanding of interactions in liquids, the activity or osmotic coefficients of the different components are of great interest. They are the most relevant thermodynamic reference data, and they are often the starting point of any modeling. However, in colloidal chemistry, these values seem to be rarely determined experimentally, in contrast to electrolyte solution chemistry or biology. The activity of the solvent, aw, in the reference and in the surfactant solutions must be the same at isopiestic equilibrium and is related to osmotic coefficient, U, as [28]

U¼

1000 ln aw ; mmMw

ð3Þ

where m is the stoichiometric numbers of the solute, m is the molality of solution, and Mw is the molecular weight of the solvent. The isopiestic equilibrium molalities of the solutions of C5SO3Na and the standard solutions of NaCl (Table I of the supporting

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information) enabled the calculation of the osmotic coefficient, U, of the solutions of C5SO3Na by using

m U m ; mm

ln aw ¼ ln

p pw



    Bw  V w p  pw þ ; RT

0.96 0.94 0.92

aw

where m* and m are the sums of the stoichiometric numbers of anions and cations in the reference solution and the solution of C5SO3Na, respectively, m is the molality of the C5SO3Na solution, m* is the molality of the reference standard in isopiestic equilibrium with this solution, and U* is the osmotic coefficient of the isopiestic reference standard, calculated at m*. From the calculated osmotic coefficient data, the activity of water in surfactant solution and the vapor pressure of this solution were determined at isopiestic equilibrium molalities, with the help of Eq. (3) and the following relation:



0.98

ð4Þ

0.86 0.84 0.82

ð5Þ

where Bw is the second virial coefficient of water vapor, V w is the molar volume of liquid water, and pw is the vapor pressure of pure water. The second virial coefficients of water vapor were calculated using the equation provided by Rard and Platford [29]. Molar volumes of liquid water were calculated using density of water [30]. The vapor pressures of pure water were calculated using the equation of state of Saul and Wagner [31]. Experimental data of the osmotic coefficients, water activities and vapor pressures of aqueous C5SO3Na solutions are also given in Table I of the supporting information. The plot of the isopiestic equilibrium molality of surfactant, m, against those of NaCl, m*, exhibits a change in slope at the concentration in which micelles are formed. For the concentrations higher than CMC, the concentration of surfactant which is in equilibrium with a certain concentration of NaCl is larger than those we expect in the absence of formation of micelle. Similarly, once micelles are formed aw and p  pw undergo an abrupt change in concentration dependence. For the concentrations higher than CMC, both of water activity and vapor pressure depression are larger than those we expect in the absence of formation of micelle. In fact, the confinement of a fraction of the counterions to the micellar surface results in an effective loss of ionic charges and therefore the hydration number of monomeric state of surfactant is larger than the hydration number of micellar form of surfactant and therefore micellization lowers the NaCl concentrations required to achieve a certain water activity and therefore for a certain surfactant concentration, both of water activity and vapor pressure depression of micellar solutions of C5SO3Na are larger than those we expect for the monomer solutions of C5SO3Na. In Fig. 1, water activities for some aqueous 1:1 electrolyte (NaCl, NaBr and NaClO4 [32]) solutions have been shown at 298.15 K along with those for C5SO3Na. For 1:1 electrolytes, the data points are smoothly curved and there is no sudden change of slope. For concentrations below the CMC of C5SO3Na, water activities of aqueous C5SO3Na and 1:1 electrolyte solutions have similar values, however for concentrations higher than CMC of C5SO3Na, water activities of aqueous C5SO3Na solutions are larger than those of 1:1 electrolyte solutions, which indicate that by formation of micelles the interactions between water and surfactant become weaker. Similar to the other investigated thermodynamic properties, the values of U (Fig. 2) exhibit a change in slope at the CMC of surfactant. According to the pseudo-phase model [33] for micelle formation, below the CMC the concentrations of the free monomers and counterions are equals to total concentration. However, the concentration of surfactant in monomer form at total concentration higher than CMC is constant and equal to the CMC value. On the basis of this model and using a modified Debye–Hückel type the-

0.9 0.88

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-1

m / mol.kg

Fig. 1. Plot of water activity data, aw, against molality of solute, m, at 298.15 K: s, C5SO3Na + H2O; d, NaCl + H2O [32]; N, NaBr + H2O [32]; h, NaClO4 + H2O [32]; —, calculated by Eq. (6); . . .. . ., supposed monomer solution.

0.98 0.93 0.88 0.83

Φ

U¼

1

0.78 0.73 0.68 0.63 0.58

0

0.5

1 0.5

m

1.5 0.5

2

2.5

-0.5

/ mol .kg

Fig. 2. Plot of osmotic coefficient data, U, against surfactant molality, m, for C5SO3Na + H2O system at 298.15 K: s, experimental; —, calculated by Eq. (6).

ory, we can obtain the following equations for the dependence of the experimental osmotic coefficient of surfactant solutions on the molality of surfactant below and above CMC:

U¼1

pffiffiffiffiffi 3 X AU m pffiffiffiffiffi þ Ai miþ0:5 ; 1 þ 1:2 m i¼0

U¼1

pffiffiffiffiffiffiffiffiffiffiffi 3 X AU CMC pffiffiffiffiffiffiffiffiffiffiffi þ Ai ðCMCÞiþ0:5 1 þ 1:2 CMC i¼0

þ

6 X

Ai ðm  CMCÞi2:5 ;

m 6 CMC;

m P CMC;

ð6aÞ

ð6bÞ

i¼4

where AU is the Debye–Hückel constant equal to 0.392 for aqueous solutions at 298.15 K. The coefficients Ai in Eq. (6) were obtained by the method of least-squares as 0.1580146 (i = 0), 0 (i = 1), 0.0792359 (i = 2), 0.0828934 (i = 3), 0.3288549 (i = 4), 0.1353613 (i = 5) and 0.0166162 (i = 6).

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Fig. 3 shows that the water activity coefficient is constant up to the CMC and at concentrations higher than the CMC, the values of the water activity coefficient slightly increase as a result of the micelle formation. For concentrations higher than the CMC, cwi1 (positive deviations from ideal-solution behavior) which indicates that the solvent–solvent interactions are more favorable than the micelle–solvent interactions. The experimental osmotic coefficients are related to the mean molal activity coefficients, c±, at molality m0 by the relation [28]

ln c ¼ U0  1 þ

Z

m0

U1 m

0

dm;

ð7Þ

0

0

where U is the osmotic coefficient of the solution at molality m . For aqueous C5SO3Na solutions, c±h1 (negative deviations from idealsolution behavior) and decreased along with an increase in the surfactant concentration. The following relation was used to obtain the mole fraction ðxÞ mean ionic activity coefficient, c from the molal mean ionic activity coefficient c±:

  M w tm ðxÞ ln c ¼ ln c þ ln 1 þ : 1000

ð8Þ

The activity coefficient data, which had been converted to mole fraction scale, were used to calculate the molar excess Gibbs free energy (Gex) and the molar Gibbs free energy change due to mixing (DGmix ) of aqueous surfactant solutions, and the values are shown in Fig. I of the supporting information. The molar excess Gibbs free energy and the molar Gibbs free energy change due to mixing are negative and decrease with increase in concentration of the surfactant. As expected, the excess free energies for the solutions are less negative than DGmix , indicating the importance of enthalpy and entropy effects in these solutions. For dilute micellar solutions the values of the CMC of 1:1 conventional ionic surfactants in aqueous solution have widely used to determine the free energy of micellization of the surfactant using the Eq. (1) [5]. In fact for deriving Eq. (1) it has been assumed dilute micellar solutions (low CMC value and surfactant concentration very close, although larger, than the CMC) and in this manner, activities are taken equal to concentrations and intermicellar interactions are neglected. For the short-chain surfactants which have the high CMC values, the activities cannot be taken equal to con-

centration and therefore this procedure cannot be used for the determination of DGmic . From Fig. 4 it can be seen that the plots of water activity and mole fraction based surfactant activity against surfactant molality is linear for the surfactant molality smaller than CMC and the concentration dependence of these properties exhibit a change in slope at the concentration in which micelles are formed. The dotted lines in Fig. 4 show the activities of components in the supposed monomer solutions. For m > CMC, the free energy of transfer of xw moles of water and xs (=1  xw) moles of surfactant from the supposed monomer and DGmic can be solutions to the real micellar solutions, DGmic w s obtained as:

 mic  mon DGmic ; w ¼ xw lw  lw  mic  mon ; DGmic ¼ x l  l s s s s

ð9aÞ ð9bÞ

where x and l are the mole fraction and chemical potential, respectively and subscripts w and s stand for water and surfactant, respecand lmon are chemical potential of component i in the tively. lmic i i micellar and supposed monomer solutions, respectively. If we assume the similar standard state in the micellar and supposed monomer solutions we have

amic w ðT; P; mÞ ; amon w ðT; P; mÞ

ð10aÞ

amic s ðT; P; mÞ : amon ðT; P; mÞ s

ð10bÞ

DGmic w ¼ xw RT ln DGmic ¼ xs RT ln s

The calculated values of the free energy of micellization are shown in Fig. 5. The positive values of DGmic w indicate that the water molecules in the supposed monomer solutions are more stable than that in the real micellar solutions. However, the negative valindicate that surfactant ions in the micellar solutions ues of DGmic s are more stable than those in the supposed monomer solutions. Another way for the definition of Gibbs free energy of micelle formation can be calculated from the mass-action model for micellization. According to this model, in the case of long chain 1:1 conventional ionic surfactants which have low CMC values and therefore the activity can be taken equal to concentration, the standard Gibbs free energy of micelle formation at the CMC (DGmic ), can be obtained from the Eq. (1) [5]. For the surfactant 1.2

0.1 0

1

micellar solution

-0.1 micellization

0.8

supposed monomer solution

-0.3 -0.4

a

ln(γw ), ln(γ±)

-0.2

micellar solution

monomer solution

0.6

-0.5 -0.6

0.4

-0.7 supposed monomer solution

0.2

-0.8

micellization

-0.9 -1

0 0

0.5

1 0.5

m

1.5 0.5

/ mol .kg

2

2.5

-0.5

Fig. 3. Variation of water activity coefficient, lnðcw Þ, and mean molal activity coefficients, lnðc Þ, as a function of square root of surfactant molality, m0.5, for C5SO3Na + H2O system at 298.15 K: s, lnðcw Þ; d, lnðc Þ.

micellar solution

0

1

2

m / mol.kg

3

4

5

-1

Fig. 4. Variation of activity of water, aw, and mole fraction based surfactant activity, as, as a function of surfactant molality, m, for C5SO3Na + H2O system at 298.15 K: s, aw; d, as; —, calculated by Eq. (6); . . .. . ., supposed monomer solution.

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0.25

300

0.2

100 0.15 0

mp

ΔG mic / J.mol

-1

200

0.1

-100

0.05

-200

-300

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-1

0

0

m / mol.kg

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

ms

Fig. 5. Variation of the free energy of micellization, DGmic , as a function of surfactant mic molality, m, for C5SO3Na + H2O system at 298.15 K: s, DGmic w ; d, DGs ; 4, mic DGmic w þ DGs .

Fig. 6. Plot of molality of polymer, mp, against molality of surfactant, ms, for constant water activity curves of C5SO3Na + PEG or PVP + H2O system at 298.15 K: filled symbols, C5SO3Na + PEG + H2O; empty symbols, C5SO3Na + PVP + H2O; N and 4, 0.9077; d and s, 0.9416; j and h, 0.9632;  and e, 0.9720; . . .. . ., Zdanovskii linearity calculated by Eq. (12).

C5SO3Na which have a high CMC value, the activity coefficient cannot be neglected and Eq. (1) can be written as

DGmic ¼ RTð1 þ bÞ ln xCMC cðxÞ CMC ; ðxÞ

ð11Þ

where cCMC is the mole fraction mean ionic activity coefficient at the CMC. The b values were calculated as b = (1  a), where a provides an estimate for the degree of counterion dissociation which can be estimated from the ratio of slopes of the linear segments above and below CMC in the experimental specific conductivity, j, vs. molarity of surfactant, C s , plot as shown in Fig. II of the supporting information. The values of a and DGmic for C5SO3Na + water system at 298.15 K were obtained as 0.482 and 16.06 kJ mol1, respectively. It is apparent that the gradual increase of the surfactant concentration leads to two readily distinguishable linear dependencies in the specific conductivity. In the low concentration domain the rise of j is due to the growing number of free C5 SO 3 and Na+ ions, whereas the break in the plot originates from the onset of micellization. Above the CMC the augmentation of the specific conductivity has a smaller slope because of two reasons [34,35]: (i) the confinement of a fraction of the counterions to the micellar surface results in an effective loss of ionic charges and (ii) the micelles can contribute to the charge transport to a lesser extent than the free ions owing to their lower mobility. In this work, the isopiestic equilibrium weight fractions of different C5SO3Na(s) + PEG (p) + H2O (w) and C5SO3Na(s) + PVP (p) + H2O (w) solutions were also obtained at 298.15 K. Table II of the supporting information reports the water activities of C5SO3Na + PEG + H2O and C5SO3Na + PVP + H2O systems at 298.15 K. Table III of supporting information shows the different ternary aqueous C5SO3Na + PEG and C5SO3Na + PVP solutions which have a constant water activity at 298.15 K (obtained from the isopiestic apparatus consisted of nineleg manifold attached to round-bottom flasks). The lines of constant water activity or vapor pressure of C5SO3Na + PEG + H2O and C5SO3Na + PVP + H2O systems at 298.15 K respectively are plotted in Figs. III and IV of the supporting information. In Fig. 6, comparison between the lines of constant water activity or vapor pressure for C5SO3Na + PEG + H2O and C5SO3Na + PVP + H2O systems has been made. In fact points on the each line in these figures have a constant water activity or chemical potential and thus these points are in equilibrium. The constant water activity lines exhibit a change in

slope at the concentration in which micelles are formed. In other words, for surfactant concentrations higher than CMC, the constant water activity lines have a concave slope, but for concentrations below the CMC, the constant water activity lines have a convex slope. The slopes of the constant water activity lines for C5SO3Na + PVP + H2O system are larger than those for C5SO3Na + PEG + H2O system. The isopiestic equilibrium mass fractions of binary aqueous C5SO3Na, PEG and PVP solutions follow the order PVP > PEG > C5SO3Na at 298.15 K. Fig. 6 also shows that, the concentration of polymer in ternary systems with a same concentration of surfactant and water activity, follow the same order with the binary polymer solution. In fact the results show that for a binary aqueous polymer solution, at a certain polymer concentration, PEG depresses water activity (and vapor pressure) more than PVP. If we assume that depression of water activity of a ternary C5SO3Na + polymer + H2O system is the sum of two contributions, water activity depression by polymer and water activity depression by surfactant, we may expect that for a certain concentration, water activity of a ternary C5SO3Na + PVP + H2O system to be larger than those of C5SO3Na + PEG + H2O system. The linear isopiestic relation [36,37] for multicomponent solutions can be written as

X mi ¼ 1; m0i i

  mi aw ¼ constant and 0 6 0 6 1 ; mi

ð12Þ

where mi is the molality of component i (polymer and surfactant) in the ternary solutions and m0i is the molality of component i in the binary solution of equal aw. Eq. (12) was proposed empirically by Zdanovskii [36] for ternary aqueous electrolyte solutions under isopiestic equilibrium, while this equation was first derived by Stokes and Robinson [37] for aqueous nonelectrolyte solutions in their semi-ideal hydration model. The semi-ideality means that solute– solute interactions can be neglected and the solute–solvent interactions can be simply described by a hydration number. In fact the thermodynamic behavior of the mixed solution conforming to Eq. (12) is as simple as that of an ideal solution, that is, the constituent binary solution mixed ideally under isopiestic equilibrium. Tests of

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126

-1

124

3

Eq. (12) were made for the experimental constant water activity lines of investigated systems below and above the micellar composition range. As shown in Fig. 6 the results do not agree well with this linear relation for the investigated systems in the surfactant concentrations both below and above the CMC. In the surfactant concentrations below and above the CMC, the experimental constant water activity lines respectively have positive and negative deviations from Zdanovskii linearity. This behavior shows that in the polymer–surfactant mixtures there are considerable solute–solute (surfactant–polymer) interactions and the constituent binary polymer and surfactant solutions mix non-ideally under isopiestic equilibrium. Table IV of the of supporting information shows that the vapor pressure depression for a ternary aqueous C5SO3Na + PEG (or PVP) system is more than the sum of those for the corresponding binary solutions. In the aqueous solutions, hydration of segments of PEG (or PVP) will result in a reduction in the free water content and consequently in an increase in the effective concentration of the surfactant. Similarly, ionic species of surfactant in the aqueous solutions are hydrated and this hydration will result in an increase in the effective concentration of the polymer. Thus, it can be expected that the vapor pressure depression for an aqueous C5SO3Na + PEG (or PVP) system to be more than the sum of those for corresponding binary solutions and this behavior for PVP solutions is larger than those for PEG solutions.

φV / cm .mol

112

122

120

118

116

114

0

0.5

1

1.5

2

2.5

3

3.5

-1

m / mol.kg

Fig. 7. Apparent molar volume, /V , isotherms of C5SO3Na in water and in aqueous solutions of 2 wt.% PVP as a function of molality of C5SO3Na, m: s, C5SO3Na in water at 288.15 K; 4, C5SO3Na in water at 298.15 K; }, C57SO3Na in water at 308.15 K; d, C5SO3Na in aqueous solutions of 2 wt.% PVP at 288.15 K; N, C5SO3Na in aqueous solutions of 2 wt.% PVP at 298.15 K; , C5SO3Na in aqueous solutions of 2 wt.% PVP at 308.15 K. The solid and dotted lines show the results of the fitting of the experimental data to Eq. (16a).

3.2. Volumetric measurements Two important thermodynamic parameters characterizing the physical state of the micelle is apparent molar volume, /V , and adiabatic compressibilities, /K , which can be obtained from density and sound velocity measurements given in Table V of the supporting information by means of the following equations:

M 1000ðd  d0 Þ ;  d mdd0 M js 1000ðdjs0  d0 js Þ ; /K ¼  mdd0 d

/V ¼

ð13Þ ð14Þ

where d is the density of a solution of molality m, M is the molecular weight of the surfactant, d0 is the density of the solvent. js0 and js are isentropic compressibility of the solvent and solution, respectively. Isentropic compressibility js (MPa)1 is calculate from sound velocity, u, and density data as

js ¼

1000 2

du

ð15Þ

:

Fig. 7 shows that the apparent molar volumes slightly depend on concentration up to the CMC and at concentrations higher than the CMC, the value of the apparent molar volume increases as a result of the micelle formation, until a constant value is reached. Increasing the apparent molar volume upon micellization can result from the contribution of three different processes [38]: (i) the liberation of structured water around the hydrocarbon tail, (ii) the electrostatic repulsion between the head groups of the surfactant, (iii) the release of water molecules from the counterion upon binding to the micelles. The experimental apparent molar volume data in the region of concentration above and below the CMC were analyzed in the framework of a pseudo-phase-transition model for micelle formation [33,39–41]. The values of the apparent molar volume, /V , have been fitted to the following equations:

/V ¼ /V;f þ Av m0:5 þ bV m;

m 6 CMC;

CMC /V ¼ /V;m  ð/V;m  /V;cmc Þ ; m

m P CMC;

ð16aÞ ð16bÞ

where /V,f, /V,m and /V,cmc respectively are the apparent molar volume of surfactant in the monomer state at infinite dilution, the apparent molar volume of surfactant in the micellar phase and the apparent molar volume of surfactant in the CMC. By assuming the solutions of surfactant behave like those of 1:1 electrolytes in the preaggregation region, where AV is the Pitzer–Debye–Hückel limiting slope (AV values for aqueous solutions of 1:1 electrolytes at different temperatures were taken from the literature [42]) and bV is an adjustable parameter related to the pair interactions and equivalent to the second virial coefficient, which indicates the deviation from the limiting law due to the nonelectrostatic solute–solute interactions [43]. The values of AV for aqueous solutions taken from reference [42] were also used for the aqueous dilute PEG or PVP solutions (2 wt.%). The values of /V,f, /V,m, /V,cmc, bV and CMC which have been determined by fitting the concentration dependencies of uV using Eq. (16), are given in Table 1. The values of /V,f, /V,m and /V,cmc for all systems investigated in this work increase by increasing temperature. Although, the infinite dilution apparent molar volume of the monomer state of C5SO3Na, /V,f, in pure water is almost same as with those in investigated aqueous polymer solutions, however, the values of /V,m and /V,cmc in the aqueous polymer solutions are larger than those in pure water. The change in the volume upon micellization, which can be obtained by D/V;m ¼ /V;m  /V;cmc , for the all systems investigated in this work decrease by increasing temperature and at each temperature the values of D/V;m for C5SO3Na in aqueous PVP solutions are larger than those in aqueous PEG solution which, in turn, are larger than those in pure water. The results of sound velocity measurements at different temperatures for C5SO3Na in water and in aqueous solutions of PEG or PVP show a very clear change in the slopes of the two straight lines to which experimental u values can be fit in the pre- and postmicellar ranges. The intersection of these straight lines affords the value of the CMC of the system. The more important behavior of the plots of sound velocity against molality of surfactant is the intersection of sound velocities isotherms. This phenomenon has also been observed in aqueous water soluble polymers [44–46], electrolyte [47], and ionic liquid [48,49] solutions.

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R. Sadeghi, M. Ziaii / Journal of Colloid and Interface Science 346 (2010) 107–117 Table 1 The values of /V,f, /V,m, /V,cmc, bV and CMC for C5SO3Na in aqueous PEG or PVP solutions at different temperatures. T (K)

/V,f (cm3 mol1)

/V,m (cm3 mol1)

/V,cmc (cm3 mol1)

bV (cm3 kg mol2)

CMC (mol kg1)

C5SO3Na in water 288.15 293.15 298.15 303.15 308.15 313.15

115.1865 116.1691 117.0529 117.8479 118.5992 119.299

124.6841 125.3799 126.0373 126.6574 127.2502 127.8136

117.0182 118.0411 118.9929 119.894 120.7417 121.5443

0.0170 0.0474 0.0588 0.0429 0.0409 0.0390

1.1655 1.1558 1.1471 1.1407 1.1349 1.1296

C5SO3Na in aqueous solutions of 2 wt.% PEG 288.15 115.0609 293.15 116.0675 298.15 116.9568 303.15 117.7873 308.15 118.5572 313.15 119.2898

126.1466 126.7655 127.3594 127.9297 128.4802 129.0114

117.7196 118.7472 119.7341 120.6422 121.5076 122.3258

0.4950 0.4502 0.4527 0.4373 0.4274 0.4044

1.3482 1.3415 1.3408 1.3386 1.3394 1.3405

C5SO3Na in aqueous solutions of 2 wt.% PVP 288.15 115.2592 293.15 116.2443 298.15 117.1435 303.15 117.9449 308.15 118.7121 313.15 119.4406

126.0992 126.7096 127.2986 127.8657 128.4133 128.943

117.5343 118.5742 119.5445 120.4632 121.3225 122.0832

0.2121 0.1905 0.1759 0.1888 0.1777 0.1237

1.3459 1.3400 1.3356 1.3348 1.3342 1.3243

In Fig. 8, the temperature and concentration dependence of js have been given for C5SO3Na in aqueous solutions of 2 wt.% PVP. The similar behavior was obtained for the other systems investigated in this work. The plots show two linear segments with the intersection at the CMC. The linear regions may be assigned to monomeric and micellar forms. For the monomeric state of surfactant, the adiabatic compressibility of C5SO3Na solutions decreases with increasing surfactant concentration. However, for the micellar form of the surfactant, the adiabatic compressibility of C5SO3Na solution is almost independent of surfactant concentration. In fact, the values of js show a shallow minimum and this minimum shifts to lower surfactant concentration as the temperature is increased. In aqueous electrolyte solutions the isentropic compressibility is the sum of two contributions, js (solvent intrinsic) and js (solute intrinsic). For the concentrations below the CMC, the js (solvent intrinsic) is the dominant contribution to the total value of js . Therefore we may conclude that the compressibility of a dilute 4.6

4.2

4

4

10 κs / (MPa)

-1

4.4

3.8

3.6

3.4

0

0.5

1

1.5

2

2.5

3

3.5

-1

m / mol.kg

Fig. 8. Isentropic compressibility, js , isotherms of C5SO3Na in aqueous solutions of 2 wt.% PVP as a function of molality of C5SO3Na, m: e, 288.15 K; , 293.15 K; s, 303.15 K; 4, 308.15 K; h, 313.15 K; , 318.15 K.

surfactant solution (with concentration below CMC) is mainly due to the effect of pressure on the bulk (unhydrated) water molecules. As the concentration of the surfactant increases and a large portion of the water molecule are electrostricted, the amount of bulk water decreases causing the compressibility to decrease. For the surfactant concentrations higher than the CMC, as the concentration of the surfactant increases, decreasing of compressibility of solutions because of decreasing of the amount of bulk water is offset by increasing the number of micelles in the solution and therefore the isentropic compressibility of solutions becomes independent of concentration. It has been shown [50,51] that for electrolytes with large hydration numbers, such as MgSO4 and Na2SO4, the concentration dependence of js is more negative than electrolytes such as NaCl with small hydration numbers. In fact the hydration number of monomeric state of surfactant is larger than the hydration number of micellar form of surfactant and therefore as can be seen from Fig. 8, for m < CMC concentration region, the concentration dependence of js is more negative than those for the m > CMC concentration region. The compressibility of pure water decreases with temperature to a minimum js value near 337.15 K and then increases gradually [48]. For all systems investigated, the all compressibility isotherm pairs intersect each other at a certain surfactant concentration and the converging concentration shifts to lower surfactant concentration as sum of two temperatures increase. For low surfactant concentration, the measured values of js decrease with the increase in temperature which is completely opposite to that for high surfactant concentrations. In fact for temperature range investigated in this work (288.15–313.15 K), djs (solute intrinsic)/dT > 0 and djs (solvent intrinsic)/dT < 0. The js (solvent intrinsic) is the dominant contribution to the total value of js from pure solvent up to the converging concentration, and beyond that js (solute intrinsic) is the substantial contribution. The results show that the converging concentration for solution of C5SO3Na in pure water is larger than those for aqueous PVP solutions which, in turn, is larger than those for aqueous PEG solutions. In Fig. III of supporting information, the converging surfactant molalities have been plotted against sum of temperatures of two isentropic compressibility isotherms which intersect each other for different systems investigated in this work. The dependence of the isentropic compressibility of surfactant solutions, js , on the concentration of surfactant Cs (mol L1) below

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and above CMC can be expressed by the following two corresponding equations [52,53]:

 s1  js0 Þ/V;f C s ; 1000ðjs  js0 Þ ¼ ðj

C s 6 CMC;

ð17aÞ

 s1  js0 Þ/V;f CMC þ ðj  sm  js0 Þ/V;m ðC s  CMCÞ; 1000ðjs  js0 Þ ¼ ðj C s P CMC;

ð17bÞ

 s1 and j  sm respectively are the isentropic compressibilwhere js0 , j ity of solvent and the apparent isentropic compressibilities of sur s1 , factant in the monomeric and micellar states. The values of j j sm and CMC which have been determined by fitting the concentration dependencies of js using (17), are given in Table IV of the supporting information. Fig. 9 depicts the effect of C5SO3Na concentration on its apparent molar isentropic compressibility in water and in aqueous solutions of 2 wt.%. PEG at different temperatures. Previous studies of /K have shown (a) that this quantity is large and negative for ionic compounds in water, (b) positive for mainly hydrophobic solutes, and (c) intermediate, small, and negative, for uncharged hydrophilic solutes such as sugars [54,55]. The negative values of /K (loss of compressibility of the medium) indicate that the water molecules surrounding the surfactant molecules would present greater resistance to compression than the bulk. On the other hand, the positive values of /K indicate that the water molecules around the C5SO3Na molecules are more compressible than the water molecules in the bulk solution. Fig. 9 shows that in dilute solution, /K increases with m until the CMC and at concentrations higher than the CMC, the value of the apparent molar isentropic compressibility increases as a result of the micelle formation. The negative values of /K for low concentration of surfactant are attributed to the strong attractive interactions due to the hydration of ions. By increasing concentration of surfactant and micelle formation, because of the release of water molecules from the counterion upon binding to the micelles, some water molecules are released into the bulk, thereby making the medium more compressible. The values of /K of C5SO3Na in aqueous polymer solutions are larger than those in pure water and also the apparent molar

0

-0.02

-0.04

-0.06

-0.08

/K ¼ /K;f þ AK m0:5 þ bK m;

m 6 CMC;

CMC /K ¼ /K;m  ð/K;m  /K;cmc Þ ; m

m P CMC;

0

0.5

1

1.5

2

2.5

3

3.5

ð18aÞ ð18bÞ

where /K;f , /K;m and /K;cmc respectively are the apparent molar isentropic compressibility of surfactant in the monomer state at infinite dilution, the apparent molar isentropic compressibility of surfactant in the micellar phase and the apparent molar isentropic compressibility of surfactant in the CMC, bK is an empirical parameter and AK is the Debye–Huckel slope for the apparent molar isentropic compressibility and taken from the Ref. [42]. It has been assumed that for aqueous PEG or PVP solutions the AK have similar values with those of aqueous solutions. The values of /K;f , /K;m , /K;cmc , bK and CMC which have been determined by fitting the concentration dependencies of /K using Eq. (18), are given in Table 2. The values of /K;f , /K;m and /K;cmc for all systems investigated in this work increase by increasing temperature and their values in the aqueous polymer solutions are larger than those in pure water. As can be seen from Fig. 10, the change in the isentropic compressibility upon micellization, which can be obtained by D/K;m ¼ /K;m  /K;cmc , for the all systems investigated in this work decrease by increasing temperature and at each temperature the values of D/K;m for C5SO3Na in water are larger than those in aqueous PVP solutions which, in turn, are larger than those in aqueous PEG solution. 3.3. Viscosity measurements The viscosity measurements for aqueous solutions of C5SO3Na were made in presence and absence of PEG and PVP at 293.15, 298.15, 303.15 and 308.15 K. Experimental data of viscosity for the investigated systems are given in Table VII of the supporting information. Based on the semi-empirical Jones–Dole equation and pseudophase model [33] for micelle formation, we can obtain the following equation for viscosity of surfactant solutions:

g 2 0:5 2 ¼ 1 þ Af C 0:5 s;f þ Bf C s;f þ Df C s;f þ Am C s;m þ Bm C s;m þ Dm C s;m ; gw

3

-1

φK / cm .mol . MPa

-1

0.02

isentropic compressibility of the C5SO3Na increases by increasing temperature. By differentiating Eq. (16) with respect to pressure, we obtain the following equation for the apparent molar isentropic compressibility:

ð19Þ

where gw is the viscosity of solvent. The A-coefficient (also called Falkenhagen coefficient), reflecting solute–solute interactions, is usually small. The constant B is the so called viscosity B-coefficients and is attributed to the solute–solvent interactions. The constant D has to be attributed both to solute–solvent interactions and to solute–solute interactions. Denoting the molar concentration of the solution by Cs, we can put: Cs,f = Cs and Cs,m = 0 at Cs < CMC and Cs,f = CMC and Cs,m = Cs  CMC at Cs > CMC. The values of coefficients of Eq. (19) for the solutions investigated in this work have been summarized in Table VIII of the supporting information. The positive B-coefficients suggest kosmotropes (structure-making), while negative B-coefficients indicate chaotropes (structure-breaking) for weakly hydrated solutes.

-1

m / mol.kg

Fig. 9. Apparent molar isentropic compressibility, /K , isotherms of C5SO3Na in water and in aqueous solutions of 2 wt.% PEG as a function of molality of C5SO3Na, m: s, C5SO3Na in water at 288.15 K; 4, C5SO3Na in water at 298.15 K; }, C57SO3Na in water at 308.15 K; d, C5SO3Na in aqueous solutions of 2 wt.% PEG at 288.15 K; N, C5SO3Na in aqueous solutions of 2 wt.% PEG at 298.15 K; , C5SO3Na in aqueous solutions of 2 wt.% PEG at 308.15 K. The solid and dotted lines show the results of the fitting of the experimental data to Eq. (18).

4. Conclusions The micellization behavior of the anionic surfactant C5SO3Na in water and in aqueous PEG or PVP solutions has been investigated by vapor–liquid equilibria, volumetric, compressibility, conductivity and viscosity measurements over the temperature range of 288.15–313.15 K.

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R. Sadeghi, M. Ziaii / Journal of Colloid and Interface Science 346 (2010) 107–117 Table 2 The values of /K,f, /K,m, /K,cmc, bK and CMC for C5SO3Na in aqueous PEG or PVP solutions at different temperatures. /K,f (cm3 mol1 MPa1)

/K,m (cm3 mol1 MPa1)

/K,cmc (cm3 mol1 MPa1)

bK (cm3 kg mol2 MPa1)

CMC (mol kg1)

C5SO3Na in water 288.15 0.0721 293.15 0.0626 298.15 0.0540 303.15 0.0467 308.15 0.0403 313.15 0.0347

0.0283 0.0305 0.0326 0.0346 0.0365 0.0383

0.0396 0.0325 0.0265 0.0208 0.0156 0.0106

0.0292 0.0276 0.0260 0.0250 0.0243 0.0240

1.2309 1.2264 1.2200 1.2209 1.2256 1.2373

C5SO3Na in aqueous solutions of 2 wt.% PEG 288.15 0.0690 293.15 0.0593 298.15 0.0513 303.15 0.0443 308.15 0.0378 313.15 0.0326

0.0326 0.0345 0.0365 0.0383 0.0402 0.0420

0.0313 0.0254 0.0195 0.0138 0.0087 0.0028

0.0305 0.0283 0.0269 0.0260 0.0251 0.0250

1.3526 1.3392 1.3442 1.3578 1.3727 1.4318

C5SO3Na in aqueous solutions of 2 wt.% PVP 288.15 0.0699 293.15 0.0596 298.15 0.0513 303.15 0.0442 308.15 0.0367 313.15 0.0322

0.0326 0.0345 0.0365 0.0385 0.0404 0.0422

0.0329 0.0271 0.0210 0.0153 0.0109 0.0055

0.0300 0.0273 0.0259 0.0249 0.0231 0.0235

1.3531 1.3350 1.3406 1.3531 1.3475 1.3875

T (K)

0.07

Table 3 Comparison between the CMC (mol kg1) of C5SO3Na in water at 298.15 K obtained from different thermodynamic properties.

3

aw

U

c±

j

u

/V

js

/K

g

1.035

1.051

0.953

0.947

1.053

1.147

1.085

1.220

1.533

0.06

-1

ΔφK,m / cm .mol . MPa

-1

0.065

0.055

0.05

0.045

0.04 285

290

295

300

305

310

315

T /K Fig. 10. Plot of the change in the isentropic compressibility upon micellization, D/K;m , against temperature, T, for C5SO3Na: s, in water; 4, in aqueous solutions of 2 wt.% PEG; d, in aqueous solutions of 2 wt.% PVP.

Although the concentration dependence of the all investigated thermodynamic properties exhibit a change in slope at the concentration in which micelles are formed, however, among the investigated thermodynamic properties, the concentration dependence of vapor–liquid equilibria properties such as water activity and osmotic coefficient exhibits a more distinct change. The obtained values of CMC for C5SO3Na, (which is a short-chain anionic surfactant and forms a small micelle in aqueous solutions) in pure water and in aqueous PEG or PVP solution strongly depend on the type of the used thermodynamic property. The CMC obtained from the vapor–liquid equilibria, conductivity, j, sound velocity, u, and isentropic compressibility, js , have similar values which are smaller than those obtained from the apparent molar volume, /V , apparent molar isentropic compressibility, /K , and viscosity, g (Table 3). In most cases the U-shaped temperature dependence of CMC has been observed. The concentration dependence of the thermodynamic properties of long-chain anionic surfactants in aqueous polymer solutions

shows two break-points: the first slope change is due to the onset of the formation of surfactant–polymer aggregates (critical aggregation concentration, CAC), whereas the second slope change occurs at the surfactant molality at which free micelles form (CMC) [56]. However, the plots of thermodynamic properties of C5SO3Na + PEG (and PVP) + H2O systems (similar to those of C5SO3Na + H2O system) as a function of the surfactant concentration show only one break-point corresponding to the onset of surfactant micellization, which occurs at the CMC. In the presence of polymer, the C5SO3Na micellization occurs at a molality slightly different from the CMC value in binary system and there is no distinct effect between PVP and PEG. Overall, although in the systems investigated in this work no clear evidence can be detected for surfactant–polymer cluster formation, however, investigated thermodynamic properties of C5SO3Na in water and in aqueous polymer solutions show that the polymer–surfactant interactions cannot be neglected in these systems. The isopiestic measurements show that the concentration of surfactant which is in equilibrium with a certain concentration of NaCl, PEG or PVP is larger than those we expect in the absence of formation of micelle and at the same concentration, the water activity and vapor pressure depression for real surfactant solution are larger than those we expect for the monomer solutions of C5SO3Na. The excess and mixing Gibbs free energy calculated from the vapor–liquid equilibria properties are negative and decrease with increase in concentration of the surfactant. The standard Gibbs free energy of micelle formation for C5SO3Na + water system at 298.15 K calculated from the mass-action model for micellization was obtained as 16.06 kJ mol1. The slopes of the constant water activity lines for C5SO3Na + PVP + H2O system are larger than those for C5SO3Na + PEG + H2O system and for both ternary systems, the experimental constant water activity lines show positive and negative deviations from Zdanovskii linearity respectively in the surfactant concentrations below and above the CMC. Positive deviations from the semiideality behavior in the monomeric region show that the surfactant

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monomers randomly associate with the polymer chain through the some hydrophobic interaction between the surfactant tail and the polymer backbone and these interactions induce dehydration of polymer and surfactant and therefore the concentrations of polymer and surfactant in a ternary mixture which is in equilibrium with a certain binary surfactant or polymer solution are larger than those we expect on the basis of Zdanovskii linearity. Also the high-charge density on the alkylsulfonate headgroup favors its ion–dipole interaction with the N–C@O group of the pyrrolidone rings of PVP. Furthermore it has been known that [24], because of the electronegative potential on the PEG chain, the electrostatic interaction between the ether oxygen group (–CH2CH2O–) and the electropositive counterions, such as Na+, results in a partially positive charge transferring to the ether oxygen group and therefore this positive charge favors the ion–dipole interaction between the headgroup of C5SO3Na and the PEG chain. From the ratio of the water activity of real micellar solution and those of the corresponding supposed monomer solution with the same concentration, the free energies of transfer of water from the supposed monomer solutions to the real micellar solutions, DGmic w , were calculated. Similarly, the free energies of transfer of surfactant from the supposed monomer solutions to the real micellar solutions, DGmic s , were also calculated. Water molecules in the supposed monomer solutions are more stable than that in the real indicate micellar solutions. However, the negative values of DGmic s that surfactant ions in the micellar solutions are more stable than those in the supposed monomer solutions and therefore the behavior of surfactant is the deriving force for the micelle formation. The were large and negative so that although the calcuvalues of DGmic s lated DGmic w values are positive but the calculated free energies of þ DGmic micellization (DGmic s w ) have negative values. Increasing the chemical potential of water upon micellization indicate that the surfactant–water interactions in the supposed monomer solutions are stronger than those in the corresponding real micellar solutions. From the volumetric data measured in this work, it was found that although the molar volumes of the monomer state of C5SO3Na in pure water is almost same as with those in the investigated aqueous polymer solutions, however, the molar volumes of the micellar state of C5SO3Na in aqueous polymer solutions are larger than those in pure water. The change in the volume upon micellization, D/V;m , decrease by increasing temperature and at each temperature the values of D/V;m for C5SO3Na in aqueous PVP solutions are larger than those in aqueous PEG solution which, in turn, are larger than those in pure water. For the all systems investigated in this work the values of D/K;m , decrease by increasing temperature and at each temperature the values of D/K;m for C5SO3Na in water are larger than those in aqueous PVP solutions which, in turn, are larger than those in aqueous PEG solution. Each pair of isentropic compressibility isotherms cross each other at a certain surfactant concentration and the intersection point shifts to lower surfactant concentration as the sum of temperatures of two isotherms increases and also the converging concentrations for investigated systems follow the order C5SO3Na + H2O > C5SO3Na + PVP + H2O > C5SO3Na + PEG + H2O. For surfactant concentration below the converging concentration, the values of js decrease with the increase in temperature which is completely opposite to that for high surfactant concentrations. The plots of js  js0 versus the surfactant molality show that, decrease in concentration dependence of js  js0 upon micellization for aqueous PEG solutions is larger than those for aqueous PVP solutions, which, in turn, is larger than those for aqueous solutions. The values of the apparent molar isentropic compressibility of both monomer and micellar states of C5SO3Na in aqueous polymer solutions are larger than those in pure water.

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