J. CHEM. SOC. FARADAY TRANS., 1994, 90(5), 733-738 Enthalpies of Mixing a Non-ionic Surfactant with Water at 303.15 K studied by Calorimetry Kristian Weckstrom, Kirsi Hann and darl B. Rosenholm Department of Physical Chemistry, Abo Akademi University, Porthansgatan 3-5,20500Turku, Finland The enthalpy of mixing n-octyl penta(oxyethy1ene glycol) (C,E,) with water has been studied at 303.15 K by titration and mixing calorimetry. In the region of the critical micelle concentration (c.m.c.), when liquid surfactant is added to water, a sudden endothermic shift is observed in the differential enthalpy of mixing of C&. The variation of the differential enthalpy with composition in this region gives information on the average size of the non-ionic micelles. Using the mass-action law model, an aggregation number of 41 was obtained for the micel- les.The value is lower than those obtained from recent spectroscopic studies. The thermodynamic quantities of micelle formation of C,E,, and of C&, in water have been obtained. For binary mixtures the enthalpy of mixing was exothermic for all compositions. The apparent and partial molar enthalpies of mixing of the surfactant and the partial molar enthalpies of the water have been calculated. Beyond the c.m.c. the partial molar enthalpies of the two components vary regularly with the composition. A highly variable temperaturexomposition (T, cCE)phase behaviour is shown by the binary systems of n-alkyl oxyethylene oligomeric amphiphiles of the type CH,(CH,), -(OCH,CH,),OH (abbreviated to C,E,), and water.' In the two-component (T, cCE)phase diagrams there are isotropic micellar or liquid phases, two-phase areas and several meso- phase areas.When the hydrocarbon part of the amphiphile is large (n > 8), the liquid-crystalline phases usually occupy extended areas in the phase diagram. However, C,E, amphi-philes with n < 9 (m= 1-6) often have a liquid phase for a wide composition range. At certain temperatures the two components are mutually miscible. The extent to which such C,E, species induce enhanced mixing of oil and water to a thermodynamically stable multicomponent microemulsion has been studied,'., e.g. the influence of temperature, the properties of the oil and the presence of electrolyte on the phase behaviour.The tendency of several types of amphiphiles to aggregate in water depends on the size of the hydrocarbon art.^.^ When n 2 5 micelles begin to form in the solution at a c.m.c., pro- vided the conditions promote the formation of stable struc- tures.'g6 According to extensive spectroscopic studies, the aggregation number of C,E, micelles in water is usually between 20 and 300.7-9 The value depends on the surfactant structure, the amount of surfactant, the temperature differ- ence from the lower consolution boundary (lcb) and, e.g., the presence of electrolyte in the water. In the micelle, the hydro- carbon parts of the solute molecules collectively form the non-polar region, i.e. the core.8 Both the solvent and the oxy- ethylene parts of the surfactants are absent from the micelle core, as indicated by results from solubilization studies.'O.' ' The oxyethylene part interacts mainly through hydrogen bonds with the water."-'4 A recent study by Alami et al., showed that the division of the solution into non-polar regions and surrounding polar continuum exists up to ca. 50 wt.% of surfactant (C,E,, ClOE6 of ClOE,) in water. From thermodynamic measurements information can be obtained on the state of the surfactant and water in binary mixtures, and on the interaction between the two species, e.g. studied the C,E4-water system at 283.15-313.15 K, and they presented the partial molar enthalpies of the two com- ponents over a rather narrow composition range.For the C,E,-water system there is a large amount of spectroscopic data on the ~ize,',~.'~ andstru~ture~.~ the mutual interacti~n'~,~~ of the micelles as a function of tem-perature and composition. The (T,cCE)phase behaviour is well kno~n,'~.'~,~~ including the curve for the c.m.c.,Ig and the effect of several third components on the binary system has been studied.I4 There is a large micellar phase in the binary-phase diagram; two critical points {[T,,c,(CE)] and [T,, c,(CE)]} determine the temperature range suitable for calorimetry: the value of the lcb is 332.5 K,14 and T, of the hexagonal phase is ca. 280 K.22 The extension of the phases shown by the C,E,-water system provides an opportunity to study the interactions leading to micelle for- mation, due to the high c.m.c., and to the complete mutual miscibility.For the long-chain surfactant systems the exten- sion of the liquid-crystalline phases up to high temperatures (ca. 310-350 K) prevents the study of the latter.' The polar interactions determine the enthalpy of mixing and also the stability of the micellar solution, and thus the area of the micellar phase in the (T, cCE)diagram. By using suitable models, valuable information is obtained on the micellar structure as well as on the equilibrium conditions, at the c.~.c.~.'~Results from the above binary system can aid the understanding of the more complex systems containing an amphiphile of the type C,E, .293,14 We have investigated the excess enthalpic properties of the C,E,-water system at 303.15 K by calorimetric methods.We have also studied the variation of the surface tension of the solution with composition in the c.m.c. region. The titration- calorimetry method was used in the c.m.c. region, which gives the excess differential enthalpy of mixing. When analysing the enthalpy data, the micelles were considered to be mono-disperse and with a defined aggregation number. The mass- action law was used to describe micelle formation. The fitting of the model to the calorimetric data by least- squares gave the thermodynamic quantities of micelle forma- tion, the c.m.c. and the aggregation number. For thethe various excess properties of mixing can be determi~~ed.~,'~ There are only a few reported studies on C,E,-water systems.composition range beyond the c.m.c., mixing calorimetry Clunie et all6 and Shinoda17 have studied the Cl,E6-water gave the excess heat of mixing. From the data, the apparent system at 298.15 K. The integral heat of mixing and the enthalpies of C8E, in the mixtures were obtained. Using well partial molal enthalpies of the two components over a broad known relationships, we also obtained the partial molar enth- composition range were reported. Andersson and Olofsson l8 alpies of C,E, and water in the mixtures. The excess enthal- pic properties vary smoothly over the whole composition range, indicating regular changes in the intercomponent interactions. Experimental The surfactant C,E5 was used as received from Bachem Fein- chemikalien AG (CH-4416 Bubendorf, Switzerland), which has high monodispersity with respect to both the alkyl chain length and the oxyethylene chain length, comparatively high purity (98.5 wt.%) and chemical ~tabi1ity.l~ The molecular weight of C8E5is 350.5 g mol-'.At 298.15 K the density of the pure liquid surfactant is 1.0081 g cmP3.l9 Other physical data on C,E5 can be found in ref. 19. The water used in the various experiments was freshly distilled; conductivity <1.2 x iz-' cm-' and surface tension =71.0 mN m-' (303.15 K). In the composition range of C8E5in water corresponding to the c.m.c., a calorimeter similar to the microcalorimeter TAM 2277-205 (Thermometric AB, Jarfalla, Sweden) with a 25 cm3 stainless-steel reaction vessel was used.23 The liquid surfactant was introduced to the sample cell from a gas-tight syringe (Hamilton Bonaduz AG, CH-7402, Bonaduz) through a thin stainless-steel capillary tube with an inner diameter of 0.15 mm.The end of the tube was positioned below the surface of the liquid in the cell. The solution was stirred using a constant stirring speed of 200 rpm with a turbine stirrer. Injection of the pure surfactant was accomplished by means of a microprocessor-controlled motor-driven syringe. The injection rate was 6 mm3 min-'. An experimental series con- sisted of the consecutive addition of small aliquots (10.12 mg) of liquid surfactant to the calorimeter vessel, which initially contained pure water (20.00 g).An LKB 10700 batch microcalorimeter was used for com- positions of C,E5 beyond the c.m.c. Inside the calorimeter in a large carefully isolated rotating drum there were two gold cells, a reaction cell and a reference cell, which were necessary to account for the heats of friction at the liquid-liquid and liquid-cell wall, which occurred during the experiments. In each cell there were two liquid compartments, with maximum filling volumes of 2.5 and 4.5 cm3, which were partially divided by a thin wall. Mixing of the contents in the cells occurred during the rotation of the drum. Samples to be mixed were directly transferred by syringes into the cells, and a corresponding amount of liquid was transferred into the reference cell.In order to obtain thermal homogeneity, the system was allowed to equilibrate for 15 min, after which the calorimetric experiment was started by rotating the drum around its rotation axis; 3-4 cycles of +400" were needed to ensure complete mixing. The signal due to the heat effect in the system was amplified, registered and mechanically inte- grated. The system was calibrated by introducing precise amounts of energy into the sample cell, through a resistance located inside the cell. The heat evolved in an experiment was obtained using established procedures. The surface tension of solutions of C,E, in water (303.15 K) was determined as the maximum pull of a platinum-iridium ring through the surface, avoiding however, complete detachment of the ring from the surface, using a ring-tensiometer balance constructed in our department, but similar to the Sigma 70 (KSV Instruments OY, Helsinki, Finland).Before starting measurements, the tensiometer was calibrated with small weights, A small amount of C,E5 was introduced to the precisely known amount (ca. 40 g) of water with a syringe. The solution was allowed to equilibrate with stirring for 15 min. The determination of the force was then carried out. At the lowest solute molalities (mCE< 3 x mol kg -'), the surface tension exhibited clear equilibration- time dependence, exceeding 15 min. In addition, the time was J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 fixed for the start of the series, and was noted at each force determination. At intervals of 2-3 molalities of C&5 the whole cell compartment containing the aqueous solution was weighed.Precise molalities of C8E5 in water could be calcu- lated, since the variation of the solution weight was known as a function of the time. The surface tension was calculated from the observed maximum force, using established pro- cedures. The c.m.c. of C8E5 in water was obtained as the minimum of the curve representing the surface tension.6 Results There is a smooth decrease in surface tension with concentra- tion of C&5 in the solution. The minimum of the curve of surface tension us. ln(mola1ity) of surfactant occurs at mCE= 7.3 x mol kg-' at 303.15 K (Fig. 1) which represents the c.m.c. (see ref. 6). At compositions above the c.m.c.the tension is nearly constant after a small increase. The shallow minimum in the curve probably indicates the presence of surface-active impurities at low (ca. 1 wt.%) amounts in the liquid surfactant.6 The impurities are solubilized in the micel- les as they form. Whether the non-linear variation of the tension below the c.m.c. is due to the presence of the impu- rities in the solution, or to a property of the system remains unclarified. The surface tension results will be examined further in another p~blication.'~ The excess differential enthalpy of mixing of C8E5,HEEE, was determined by introducing small amounts of the liquid surfactant into the aqueous solution. Owing to the relatively high c.m.c. of C,E5 in water, solutions can be obtained with a final molality of monomers clearly below the c.m.c.Eqn. (1) describes the mixing of a known amount of neat surfactant C,E, (CE) with pure water (w) to form an aqueous surfactant solution (aq. I): %E(l) + nw(l) nCE(aq*I) + nw(aq. I) (1) If the enthalpies of the pure components, HI (i = CE or w), at 303.15 K and atmospheric pressure are chosen as references, then: AH(1)= Hg(I)n(I) (2) where AH(1) is the heat of reaction, HE@) represents the molar enthalpy of mixing of the solution (I), and n(1) [=nCE(I)+ nw(I)] is the total amount of substance in solution (I). The contribution of the initial state is equal to zero since HM(i)= +E(l)(H& -&E) + nw(l)(Hw-Kw)= 0. 60 c 50, z E-..A 40 -30 --10 -8 -6 -4 In(rn ,/rnol kg-') Fig.1 Dependence of the surface tension on the natural logarithm of the molality of C,E, in water at 303.15 K J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 When an exceedingly small amount of neat surfactant [n&(1)] is added to the aqueous solution (cf: the experimental section) containing only monomers eqn. (3) and (4) are obtained : &,(I) + ncE(aq. I) + n,(aq. I) +ncE(aq.11) + n,(aq. 11) (3) AH(I1) = HE(II)n(II) -HzI)n(I) (4) The contribution from the added surfactant is equal to zero according to the definition of standard states. Since the amount of water is kept constant in eqn. (3) and the amount of surfactant is very small, the conditions for differential enth- alpy apply (n, is constant): HFE(II) = (dH'/ancE) = AH^/^;^) (5) In eqn.(5) HEE(II)is the partial molar enthalpy of the sur- factant and AHM= AH(I1).The observed differential enthalpy is thus equal to the difference between the partial molar enth- alpy of the monomer in the aqueous solution (11)and that of the monomer in the pure state, i.e. the partial molar enthalpy of mixing in the monomeric state: HzE(II) = HzE(mon). At compositions well above the c.m.c. the added surfactant essentially all dissolves to form micelles. The same formal dis- cussion applies then as for the pre-micellar solutions; the partial molar enthalpy of mixing surfactant with water to form micelles, HvE(mic), is obtained. Provided that both HFE(mon) and HpE(mic) are roughly independent of the C,E, molality (cf:Fig.2), the partial molar enthalpy of micelle for- mation is given by the difference between the values observed above and below the c.m.c.:23 AHcE(mic)= HFE(mic)-HEE(mon) (6) There is narrow region of mCEwhere a rapid increase of HEE is observed. In this transition region a fraction, aCE, of the added surfactant will dissolve in the water as monomers, while the fraction (1 -aCE) will dissolve to form micelles. The formal process in eqn. (3) is now described by [cf: eqn. (5)]: H&(II)= aC-HFE(mon)+ (1 -acJH&(mic) (7) The observed differential enthalpy is considered to be the sum of the contributions due to the monomer and micellar states, respectively. A series of four calorimetric titrations were conducted in the c.m.c.region of C8E,in water, each consisting of 18 injec--20 I I 1 1 I I I I 0 100 200 300 mcE/l0-3 1 0 10 20 30 mcE/l0-3 mol kg-' Fig. 2 Excess differential enthalpies of solution of C,E, in water as a function of the molality at 303.15 K. There are four separate titra- tion series: series 1, triangles; series 2, squares; (with the curve showing the calculated values); series 3, dots; series 4, crosses. The inset shows the differential enthalpies (series 2) and the partial enth- alpies (in kJ mol-') of C,E, at compositions near to the c.m.c. 735 tions of the neat surfactant into the aqueous solution. In the experiments, the pressure (1 atm) and temperature (303.15 K) were held constant.Of the total number of injections 17 were within the pre-micellar region. A linear least-squares fit of the observed HzE values US. mcE (mcE < 8 x low3mol kg-') yields H& = -(41.56 -112.2 mCE) kJ mol-'. The deviation of the individual enthalpy values from the least-squares line is substantial (f0.5 kJ mol- '). Using titration calorimetry, HFE increases slightly with mcE (below the c.m.c.), and the slope of the least-squares line is 112.2 kJ mo1-'. The change in the differential enthalpy as a function of mCEfor the four series is shown in Fig. 2. A large increase in the observed enthalpy begins at a well defined solute molality (8.2 x mol kg-'). Beyond the region of the increase the differential enth- alpy is almost constant. The dependence of the differential enthalpy on the solution composition in the c.m.c.region can be described by the mass-action law However, certain simplifications must be introduced: First, the micelles which appear at the c.m.c. in the solution are assumed to have a fixed aggregation number N. Secondly, the activity coefficients of both the monomer (ys) and the micelle (yM) are fixed at unity. There- fore, the solution is described as being in an equilibrium state between monomers and micelles. The equilibrium constant, K,, depends on the amounts of the two species and on N, and is given by the following relationships : NCE = (CE)N (8) KN = mCE(mic)/CmCE(mon)lN (9) where wE(i) represents the molality of the monomers (i = mon) and micelles (i = mic), respectively.Within the region of mcE where the surfactant added is distributed between the micellar and monomeric state, the equilibrium constant can be expressed in terms of the fraction a of the monomer species : K, = (1 -a)/~aNm& ' (10) In eqn. (10) mCE is the total molality of the surfactant in the solution. For each titration the value of a at the start and at the end is required. Eqn. (10) is solved by varying N, using the Newton-Raphson numerical method. At the chosen value of N, both K, and AHcE(mic) are optimized using a search routine. Thus in eqn. (11) is obtained, and a comparison with the experimental differential enthalpies is carried out. Allowing the partial molar enthalpy of the monomers at the c.m.c.to be constant [HpE(mon, c.m.c.) = -40.73 kJ mol- '3, the fraction @CE is related to the differential enthalpy by com- bining eqn. (6) and (7): H&(II) = (1 -a,--)AH&nic) + HFE(mon, c.m.c.) (11) where HFE(II)and HFE(mon, c.m.c.) are experimental quan- tities. The fit is given in Fig. 2 as the line through the experi- mental points (series 2). The four different series were fitted separately. The results for N and AHcE(mic) for the series 1-4 are: N = 35 (1); 50 (2); 45 (3); 35 (4) and AHcE(mic) = 16.10 (1); 15.75 (2); 15.75 (3); 16.19 kJ mol-' (4).The average value of AH,,(mic) is 15.9 kJ mol-' and the average aggregation number of the micelles is 41. The ~.m.c.~~ is 8.2 x mol kg-'. For the best fits the standard deviation approached the estimated uncertainty cf the calorimetric measurement (0.07-0.1 kJ mol-').The corresponding Gibbs free energy for the transfer of the surfactant from the monomeric state to the micellar state may then be obtained as: AGCE(miC)= -RTN-' In K, (12) Eqn. (12) represents the Gibbs energy relationship of the mass-action law approach.25 If it is assumed (mCE> c.m.c.) J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 C.m.c. values, dissolution enthalpies, enthalpies, free energies and entropies of micelle formation for the surfactants C,E, and C,E, (303.15K) c.m.c. HFE(mon)l H&(mic) AHcE(mic) AGcE(miC)" AGc,(mic)b AS (mi$ AS (mic)b /mol kg-' /kJ mol-/kJ mol-' /kJ mol-' /kJ mol-' /kJ mol-' /J Ks5 mol-' /J Ks5 mol-' C,E, 6.52 x 10-3 -3 1.40 -16.58 14.82 C,E, 8.20 x 10-3 -40.73 -24.83 15.90 a Calculated from eqn.(13). Calculated from eqn. (12). that all monomers are consumed in micelle formation, AGcE(miC) at the c.m.c. (a = 0) is obtained from eqn. (12):26 AGcE(miC)= RT ln(c.m.c.) (13) Eqn. (13) thus corresponds to the pseudo-phase model. The entropy of micelle formation, AScE(mic), is readily obtained through the Gibbs-Helmholz relation and values of these are included in Table 1. The molar enthalpy of mixing C& and water, HE [ct eqn. (l)], was determined over the entire composition range. The calculated enthalpies are listed in Table 2 and shown in Fig. 3. Since CsE, is completely miscible with water at 303.15 K, the mole fraction scale is used.The observed excess solution properties may then be represented as the apparent molar enthalpy of mixing defined as:27 where xCE is the mole fraction of surfactant in the mixture (I). Alternatively, the contribution of C8E5 and water may be represented by the partial molar enthalpies of mixing. These can be obtained in the following way:27 H:E = Ht + (1 -XcEXdH3dXcE) (15) H! = H,M -x,,(dH3dx,,) = (HE -xCE H&)/( 1 -xCE) (16) In eqn. (15) and (16) xCEis the mole-fraction of C,E, in the binary mixture. First, the variation of the enthalpy of mixing with composition (Fig. 3) is described by suitable functions. If Table 2 Excess molar enthalpies of mixing C,E, and water, partial enthalpies and apparent enthalpies of C,E, (303.15 K) 0.002 16 -0.0475 -26.32 0.0094 -21.99 0.00221 -0.0489 -26.30 0.0092 -22.13 0.00229 -0.0529 -26.28 0.0073 -23.10 0.004 19 -0.0943 -25.71 0.014 -22.50 0.00427 -0.0982 -25.69 0.011 -23.01 0.00450 -0.104 -25.62 0.011 -23.20 0.00476 -0.111 -25.54 0.011 -23.34 0.00721 -0.161 -24.82 0.019 -22.27 0.00795 -0.172 -24.60 0.024 -21.64 0.0147 -0.319 -22.72 0.015 -21.72 0.0151 -0.287 -22.57 0.055 -18.99 0.0248 -0.542 -20.14 -0.044 -21.86 0.0485 -0.977 -14.98 -0.26 -20.15 0.0926 -1.494 -8.25 -0.80 -16.13 0.155 -1.679 -3.29 -1.38 -10.83 0.209 -1.754 -1.84 -1.80 -8.39 0.279 -1.753 -1.22 -1.95 -6.28 0.332 -1.690 -0.81 -2.12 -5.09 0.408 -1.572 -0.61 -2.23 -3.85 0.484 -1.399 -0.37 -2.36 -2.89 0.624 -1.058 -0.096 -2.65 -1.69 0.664 -0.998 -0.097 -2.78 -1.50 0.775 -0.706 -0.050 -2.97 -0.91 0.840 -0.500 -0.027 -2.98 -0.59 0.903 -0.313 -0.030 -2.95 -0.35 -12.68 90.7 -12.11 -11.25 92.4 89.6 the entire composition range is represented by two partially overlapping ranges, a standard fourth-order polynomial func- tion can be used.The derivatives in eqn. (15) and (16) were calculated by least-squares fitting the polynomial functions to two sets of enthalpies of mixing, covering the following com- positions: 0.002 < xCE< 0.33 and 0.16 < xCE< 0.91, respec-tively. The curve in Fig. 3 shows the enthalpy obtained from the two polynomial functions. The results for H& and HE are given in Table 2. They are shown graphically in Fig. 4(a)and (b).HE is shown to be positive at values of xCE close to zero in the inset of Fig.qb). The values of partial molar enthalpy of C8E, determined by the two calorimetric methods are similar close to the c.m.c. This is shown in the inset of Fig. 2. From the extrapolation of HE to xCE = 1, we estimate that HE = -2.9 kJ mol-I. Discussion By titration calorimetry enthalpic information can be obtained on both the monomeric and the micellar states of the non-ionic amphiphile in water. At least for C,E, sur-factants with n = 8-12, it is possible to carry out precise experiments below the c.m.c. Olofsson23~28*29 has reported the differential enthalpies in the c.m.c. region at 298.15 K for the surfactants C,E, and CI2Em, rn = 5, 6 or 8. In the mono- meric state the hydrophilic and hydrophobic parts of the molecule are expected to be in full contact with the solvent.The nearly linear variation of ln(c.m.c.) with the length of the hydrocarbon chain indicates an extensive incorporation of the non-polar part in the water structure.6 The oxyethylene part interacts very exothermically with water, whereas it appears that the interaction of the hydrocarbon part with water is endothermic. The observed differential enthalpy of the monomer, H&(mon), is thus a function of the lengths of 0.0 -0.4 1 -0.8 ? 75 -1.2 z -1.6 I#I,I.I.-2.0 0.0 0.2 0.4 0.6 0.8 1 .Q XCE Fig. 3 Excess molar enthalpies of mixing of C,E, and water as a function of the mole fraction of surfactant at 303.15 K. The curve was obtained by fitting two polynomial functions to the experimental values.J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0 --10 7Y 3 a (a) l,l,I,j,-30 0.0 0.2 0.4 0.6 0.8 1.0 XCE I”’”’’’’I 0 -1 r I 3, -2 5% \ t -4’ ” ’ ’ ’1 ‘ 1 ’ I 0.0 0.2 0.4 0.6 0.8 1.0 XCE Fig. 4 Partial molar enthalpies of the components as a function of the mole fraction of surfactant in the mixtures: (a) C,E, (apparent molar enthalpies represented by open circles), (b)water. The inset in (b)shows the partial molar enthalpies of water when xCE< 0.05. both parts. An almost linear decrease of this quantity occurs as a function of m, for a constant size of the non-polar part of CI2E, at 298.15 K. It is known that HzE(mon) for a specific surfactant varies significantly with temperature, and values for the partial molar heat capacity have been reported.23 The heat capacity should also be a composite of the heat capac- ities of the two parts of the molecule, which can show quite distinct values and variations with the temperature.In the micelles the strength of the interaction of the oxy- ethylene part of the molecule with water is slightly reduced, resulting in an endothermic enthalpy shift for the micellar state, compared to the monomeric state. This occurs despite the probably exothermic contribution of removing the non- polar part from the water structure into the inside of the micelle. The H&(mic) values also decrease nearly linearly with m,but with a smaller gradient than those of the mono- meric state. Interestingly, the HFE(mic) value for C,E4 falls on the same line as the values for the three C,,E, surfactants.Eventually, the micelle palisade of the different surfactants exhibits certain common properties, which give the regular variation of the partial enthalpy with the length of the polar part. The enthalpy of micelle formation is simply the enthal- pic difference between the two states. When the mass-action law model was used to analyse the differential enthalpy values of C,E, in the c.m.c. region, we assumed that the aggregation number of the micelles and the equilibrium constant do not vary as did Andersson and Olofsson in an earlier study of C,E4 in water.23 For C,E,, the variation of HFEwith mCEis very similar to that of C,E4.The four series of differential enthalpies of C,E, are close to each other as shown in Fig. 2. The break point of HFEdefines the c.m.c.; mCE = 8.2 x mol kg-’, and the value is nearly the same as that obtained from surface tension experi- ments (7.3 x mol kg-’). With the surfactants C8E, (rn = 4 or 5), the endothermic shift with increasing surfactant molality is not very It is therefore possible to deter- mine the average aggregation number of the micelles. The calculated excess enthalpy curves using the values obtained from the model correspond closely to the experimental values.23 Table 1 shows the thermodynamic data for the two sur- factants C,E, (m = 4 or 5) at 303.15 K.The enthalpic values for C,E, were calculated from the available data at 298.15 K, and the heat ~apacities.~~The dissolution enthalpies AH&(mon) and AH&(mic) are included in the table. A com-parison of the results for C,E4 and C,E, reveals the differ- ences in the thermodynamic properties. The dissolution enthalpies both below and above the c.m.c. are, as expected,29 more exothermic for the surfactant with the larger polar part. The calculated enthalpy of micelle forma- tion is slightly larger (1.1 kJ mol-’) for C,E,. As shown in Table 1, the Gibbs energy and the c.m.c. of the two sur-factants both increase slightly when m changes from 4 to 5. Much larger variations of the values are observed when the polar part is kept constant, and the properties are monitored as a function of the length of the non-polar part.6 The calcu- lated entropies of micelle formation for the two surfactants C8E, are almost equal.The present view is that this entropy is mainly determined by the size of hydrocarbon part.28 However, if the oxyethylene part is dehydrated on incorpor- ation of the monomer in the micelle, as mentioned above, this should also contribute to the observed entropy. It appears that the monomeric state and the micellar state of the two surfactants are very similar, since the entropy values coincide. The Gibbs energy and the entropy depend partly (cf:Table 1) on the relationship used [eqn. (12) or (13)]. The value obtained for the aggregation number of the C8E, micelles in water, N = 41, corresponds reasonably well with the value previously deduced from static neutron scat- tering,’ N = 80 (7 wt.% C,EJ at 303.15 K.Binana-Limbele et al.’ also obtained a value of N = 80 (1.7 wt.% C,E,) at 303.15 K in a fluorescence quenching study on this sur-factant. An exact comparison of the values from calorimetry and from static neutron scattering is not possible, since the first value is at the c.m.c. and the latter value is at higher concentration. However, both neutron scattering and fluores- cence quenching indicate only small variations of the micelle size as a function of surfactant concentration (1.7-10 wt.%) at 303.15 K. Although the aggregation number calculated from calorimetry is lower than that from the other data, the result gives further support to the concept of small spherical C8E, (rn = 4 or 5) micelles.In the calorimetric study on C8E4 in water, Andersson and 010fsson~~ observed that N depends on the temperature: at 298.15 K, N = 23 and at 313.15 K, N = 17. The value at the lower temperature differs signifi- cantly from the value of N reported by Frindi et aL3’ [N = 147 at 298.15 K (1.5 wt.% C,E,)]. Thus at a fixed tem- perature calorimetry gives a lower aggregation number for the C,E4 than for the C8E, micelles. The excess enthalpies of mixing C,E, and water obtained in this study are shown in Table 2 and in Fig. 3. The minimum of the Hr us. xCEcurve is located at xCE(min) = 0.225 and Ht(min) = -1755 J mol-’. On both sides of the 738 minimum, the enthalpy of mixing increases smoothly.It approaches zero when the composition approaches either one of the pure liquid states (xi = 1, i = CE or w). Similar trends for enthalpies of mixing were observed for ethylene glycol, polyethylene glycol (PEG) oligomers or polymers, and water (298.15 K),15*'8731 and with 2-butoxyethanol and water (298.15 K).32 At HE(min), the mole fraction of solute in the mixture depends on the degree of polymerisation of the mol- ecule, e.g. for the PEG oligomers in water. The dependence is quite weak, x,,,(min) varies between ca. 0.2 and 0.35. The similarity of curves for enthalpies of mixing of the PEG oli- gomers and the present surfactant indicates, in our opinion, that for these binary systems the variation of the excess enth- alpy is mainly determined by the interaction between oxy- ethylene glycol and water, i.e.the hydrocarbon parts of the surfactants avoid contact with the polar regions. For the PEG 400-water binary system, the calorimetric experiments established that HE(min) increases with increasing tem-perature.', The endothermic shift of H!(min) is nearly 50% when the temperature changes from 278.15 to 353.18 K. The oligomeric state is clearly determined by the average inter- action between solute and water, and the interaction becomes weaker with increasing temperature. The partial molar enthalpies for both C,E, and water, Hy (i = CE or w), are shown in Fig. 4. For the partial enthalpy of C,E,, an increase is seen from the fairly exothermic value of -26.3 kJ mol-' at concentrations near to the c.m.c., to nearly zero at the highest concentration of CBE,.There is a good overlap of the partial enthalpies with the differential enthalpies. For 0.001 < xCE< 0.25, the change of HEE with the composition is especially significant. In this region, the partial enthalpy is dominated by the interaction between the micelles and water. At higher values of xCE,a much slower variation of HEE with the composition is observed. The average surroundings of added surfactant molecules increas- ingly resembles those in the neat surfactant. A similar varia- tion of Hy (i = solute) with xCEhas been found for the PEG 400-water and C,E,-water systems.18 The partial molar enthalpy of water in the C,E,-water mixtures decreases regu- larly from values close to zero at the c.m.c., to = -2.9 kJ mol-' at xCE= 1.A shallow endothermic maximum of Ht occurs close to the c.m.c., which is typical for hydrophobic semi-polar solutes in water. The infinite dilution value of Ht indicates highly polar surroundings of the water molecules in the solution. This can be deduced by comparing the value obtained with the Htvalues observed for binary mixtures of alcohols, with different chain lengths, and water.33 Only minor variations of Ht are observed for 0.6 < xCE< 1. 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