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Determination of the Interaction Enthalpy between Microemulsion Droplets by Isothermal Titration Microcalorimetry Peizhu Zheng,† Yuanming Ma,‡ Xuhong Peng,‡ Tianxiang Yin,† Xueqin An,† and Weiguo Shen*,†,‡ † ‡
School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China ABSTRACT: A new experimental design for the measurement of the real heat of dilution of the microemulsion droplets by isothermal titration microcalorimetry (ITC) has been reported and used to study the interaction enthalpies of the droplets for the system of water/sodium bis(2-ethylhexyl)-sulfosuccinate (AOT)/toluene. The results are in good agreement with those determined from light-scattering experiments.
’ INTRODUCTION A knowledge of the interactions between microemulsion droplets is important not only for an explanation of the phase behaviors of those complex fluids but also for various applications such as drug carriers, cosmetic materials, and microreactors.13 The interactions between microemulsion droplets have been extensively studied in the literature. Hamaker and Vrij4,5 assumed that the interactions between microemulsion droplets resulted essentially from the van der Waals forces between the water cores. Unfortunately, the magnitude of the van der Waals attractive interaction is not sufficient to interpret the experimental results.6 Huang and co-workers3,7 found that an attractive squarewell potential model can be suitably modified to deal properly with the short-ranged interactions in the microemulsion systems resulting mainly from the mutual interpenetration of the surfactant tails. This simple model has been used to calculate the negative interaction energy (ε) through the second virial coefficient (B) determined by light scattering and neutron scattering with the square-well width being 0.3 nm.810 However, this model was unsuccessful at interpreting the second virial coefficients determined for the microemulsion systems where the interaction enthalpy between the droplets was zero or even positive.11,12 Koper et al. proposed a repulsive sticky hard-sphere model13 and an aggregation model14 and related the fraction of aggregates of the droplets and the magnitude of the effective second virial coefficients to the binding free energy of the microemulsion droplets, which consists of an enthalpic part and an entropic part. Lemaire et al.15 proposed a mean-field intermicellar free-energy potential between microemulsion droplets including energetic and entropic contributions, as was suggested for binary polymer solutions.16 Thus, the attraction between two r 2011 American Chemical Society
microemulsion droplets in principle may be driven by enthalpy or/and entropy. It is important to measure the interaction enthalpy between the microemulsion droplets in order to clarify the source that drives two droplets close each other. As Koper et al. pointed out, the interaction enthalpy could be determined by the temperature dependence of the effective second virial coefficient.14 However, more directly, it may be obtained by measuring the heat produced from the dilution of the microemulsion droplets. Such attempts have been made by using isothermal titration microcalorimetry (ITC); unfortunately, the ITC measurements were designed to titrate water into the microemulsion.17,18 The heat measured from such a design should be attributed to the following three contributions: (a) the interaction between water molecules titrated into the ampule and the surfactant molecules in the droplet; (b) a change in the interaction between droplets due to changes in the size and structure of the droplets, namely, a change in the nature of the droplets; (c) a change in the size of the droplets, which yields an increase in the volume occupied by the droplets and consequently the volume fraction of the droplets in the system. Only the third contribution connects directly to the enthalpy of the droplet interactions and is related to the second virial coefficients. Thus, only when the contributions of a and b are negligible may the measured heat in the above design be used for the determination of the dilution enthalpy of the microemulsion droplets and possibly the effective second virial coefficient; however, this is highly unlikely.19 Therefore, a new experimental design for the measurement of the real Received: July 13, 2011 Revised: August 29, 2011 Published: September 13, 2011 12280
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Figure 1. Enthalpy curve of titrating the microemulsion (CAOT = 0.40 M) into toluene.
Figure 2. Calorimetric thermogram for titrations of a microemulsion (CAOT = 0.80 M) into a dilute one (CAOT = 0.08 M).
heat of dilution by ITC is required for an estimation of the interaction between microemulsion droplets. In this letter, we report an ITC experimental design for the measurement of the real heat of dilution of the microemulsion droplets for the system of water/sodium bis(2-ethylhexyl) sulfosuccinate (AOT)/toluene. The dilution enthalpy data are analyzed to give the derivate of the second virial coefficient with respect to temperature and to obtain the second virial coefficient and the interaction energy between droplets by a simple square-well potential model. The results are compared with that determined from the light-scattering experiment that we reported recently.20
which were 2.8 and 2.7 nm, respectively, and consistent with the value of 2.8 nm obtained by static light scattering measurements for dilute microemulsion solutions in our previous work.20 This confirmed that no change in droplet size occurred before and after the titration. A thermogram for these titrations is shown in Figure 2.
’ EXPERIMENTAL SECTION
’ DATA TREATMENT The experimental procedure was designed as follows: a solution in the syringe with the quantity and concentration of the droplet being n2 and F2s (the number of droplets in unit volume), respectively, was continuously titrated into a pure solvent in an ampule to form a dilute solution with a concentration of F2i, and the molar dilution enthalpy (ΔH)/(∑n2i) of the solution is ΔH dB ¼ ΔH2 ðF2s Þ RT 2 F2i dT n2i
Materials. Sodium bis(2-ethylhexyl) sulfosuccinate (AOT) (g99% mass fraction) was obtained from Fluka and dried with P2O5 in a desiccator for 2 weeks before use. Toluene (g99% mass fraction) was obtained from Tianjin Chemical Reagent Company. Twice-distilled water was used in all experiments. Microemulsion Preparation. Microemulsions with a molar ratio ω of water to AOT of 12 and the required concentrations of AOT were prepared by mixing the proper amounts of water, AOT, and toluene. The prepared microemulsions were left to equilibrate for 1 day before measurement. Isothermal Titration Microcalorimetry (ITC). The ITC experiment was carried out using a thermal activity monitor (Thermometric AB, Sweden) at 298.15 K. First, we investigated the concentration range of AOT in which the dissociation of the microemulsion droplets is insignificant for ITC measurements. As shown in Figure 1, the heat of titration increases sharply as the microemulsion is diluted sufficiently but approaches a linear dependence with respect to the AOT concentration when it is larger than about 0.07 M, which indicates that the heat of dissociation of the droplets is negligible. Thus, to prevent the dissociation of the microemulsion droplets titrated into the ampule and the corresponding heat effect, a concentrated microemulsion was titrated into a dilute one to measure a series of heats of mixing for various droplet concentrations. A 2.30 mL microemulsion with an AOT concentration of 0.08 M was placed in the ampule. A Hamilton syringe was used to titrate the microemulsion continuously, with the AOT concentration being 0.80 M in the ampule. The stirring speed in the ampule and the titration speed of the syringe were set at 60 rpm and 0.5 μL 3 s1, respectively. The radii of the microemulsion droplets were measured by dynamic light scattering for both the concentrated microemulsion in the syringe and the diluted microemulsion in the ampule after the titration,
ð1Þ
∑
where ΔH is the sum of the enthalpies of i titrations, ΔH2(F2s) is the molar dilution enthalpy of the droplets for diluting the solution with a concentration of F2s in the syringe to infinite dilution, and F2i and ∑n2i are the concentration of the droplets in the ampule with the same units as F2s and the total quantity of the droplets titrated into the solvent after the ith titration, respectively. To restrain the dissociation of the droplet, in our experimental design a solution in the syringe with a droplet concentration of F2s was continuously titrated into a solution in the ampule with the concentration and quantity of droplets being F20 and n20, respectively. Then " # n2i þ n20 ΔH n20 2 dB ¼ ΔH2 ðF2s Þ RT F2i F dT n2i n2i n2i 20
∑
∑
∑
∑
ð2Þ Taking into account that a microemulsion droplet is constructed of m surfactant molecules and ωm water molecules, we write eq 2 as ΔH ΔH2 ðF2s Þ ¼ m n2i m
∑
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dB " # mn2i þ mn20 m mn20 m dT F F NA 2i m2 mn2i mn2i NA 20
RT 2 NA
∑
∑
∑
ð3Þ
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with NA being Avogadro’s constant. Equation 3 may be rearranged as ΔH ¼ ΔHsurs ðCsurs Þ nsuri dB " # RT 2 NA n þ n n suri sur0 sur0 dT Csuri Csur0 m2 nsuri nsuri
∑
∑
∑
∑
ð4Þ where Csur0 and Csuri are the concentrations (moles per unit volume) of the surfactant in the ampule before the titration starts and in the ampule after the ith titration, respectively; ΔHsurs(Csurs) is the dilution enthalpy per mole of surfactant for diluting the solution with a concentration of Csurs in the syringe to infinite dilution; and nsur0 and ∑nsuri are the surfactant quantities in the ampule before the titration and for the sum of i titrations, respectively. If the volume fraction ϕ2 of the droplets is used as the concentration variable instead of F2, then eq 2 becomes " # dB n þ n ΔH n ϕ 2i 20 20 ¼ ΔH2 ðF2s Þ RT 2 ϕ2i ϕ dT n2i n2i n2i 20
∑
∑
∑
∑
ð5Þ where Bϕ is the dimensionless second virial coefficient. Let ΔHCsur ¼
RT 2 NA
ΔHϕ ¼ RT 2
m2 dBϕ dT
dB dT
ð6Þ ð7Þ
where ΔHCsur is the dilution enthalpy per mole of surfactant for the dilution of the solution with the value of ω being fixed and the concentration of the surfactant being 1 mol per unit volume to infinite dilution and ΔHϕ is the hypothetical molar enthalpy of the droplets for the dilution of the pure droplets to infinite dilution. Thus, the corresponding interaction enthalpies ΔHCsur and ΔHϕ can be determined from experimental ITC data. The uncertainty in the determination of ΔHCsur and ΔHϕ was estimated by repeating the measurement of the same titration routing and was found to be about 14% of the values, which may be attributed mainly to the irreproducible vaporization of the sample during the ITC measurements. Changes in the stirring speed in the ampule from 50 to 90 rpm or the titration speed of the syringe from 0.5 to 0.75 μL 3 s1 resulted in no significant effects on the measurements of ΔHCsur and ΔHϕ as compared to the experimental uncertainties.
’ RESULTS AND DISCUSSION According eq 4, a plot of (ΔH)/(∑nsuri) versus [(∑nsuri + nsur0)/ (∑nsuri)Csuri (nsur0)/(∑nsuri)Csur0] gives a straight line, which is shown in Figure 3. A least-squares fit gave ΔHCsur = 307 ( 43 J 3 L 3 mol2, which was used together with aggregation number 90 at 298.15 K determined in our previous static light scattering experiment20 to calculate the value of dB/dT by eq 6 from ITC measurements. We obtained dB/dT = 5.6 nm3 3 K1. According the simple square-well potential model proposed by Huang et al.,7 the droplet interaction is expressed in terms of
Figure 3. Plot of (ΔH)/(∑nsuri) vs β = [(∑nsuri + nsur0)/(∑nsuri)Csuri (nsur0)/(∑nsuri)Csur0]. The points represent the experimental results, and the line represents the result of the least-squares fitting.
an interaction potential U(r), which is the work required to bring the two droplets from infinity to a distance r in a given microemulsion solution and has the form 8 > < ∞ðr e σ wÞ UðrÞ ¼ εðσ w < r e σÞ ð8Þ > : 0ðr > σÞ The relationship of the second virial coefficient B and the potential U(r) can be expressed by Z ∞ UðrÞ 1 exp ð9Þ r 2 dr B ¼ 2π kT 0 The integration of eq 9 from r = 0 to r = ∞ gives ( " #) 3 σ ε=kT B ¼ BHS 1 ðe 1Þ 1 σw
ð10Þ
where the second virial coefficient of the hard sphere BHS may be simply calculated by 2/3π(σ w)3.10,21 The differential of eq 10 yields " # 3 dB σ ε ¼ BHS 1 eε=kT 2 ð11Þ dT σw kT with w = 0.3 nm and σ = 2Rh = 5.54 nm determined in our previous static light scattering experiment20 and dB/dT = 5.6 nm3 3 K1 from ITC measurements; the well depth ε was obtained by solving eq 11, which was 1.03 1020 J. Substitution of the value of ε into eq 10 gave the value of B, which was 305 nm3. The value of B measured by light scattering was 497 nm3 at 298.15 K.20 This large difference may be mainly attributed to the invalidation of the square-well potential model and the oversimplification of the expression of the second virial coefficient of the hard sphere. We measured the second virial coefficients at various temperatures in our previous static light scattering experiment,20 which may be related to the free-energy potential between the droplets. This free-energy potential includes the contributions of enthalpy and entropy, and the latter arises from the release of 12282
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (projects 20973061, 21073063 and 21173080) and the Committee of Science and Technology of Shanghai (08jc1408100). ’ REFERENCES
Figure 4. Plot of (ΔH)/(∑n2i) vs βϕ = [(∑n2i + n20)/(∑n2i)ϕ2i (n20)/(∑n2i)ϕ20]. The points represent the experimental results, and the line represents the result of least-squares fitting.
solvent molecules and the changes in configuration and conformation in the droplets during the overlap of the aliphatic interfaces.15 It was also found that the size of the droplets changed slightly with temperature,20 thus the derivative d(B BHS)/dT instead of dB/dT was used to calculate ΔHCsur by eq 6, which yielded ΔHCsur = 362 ( 35 J 3 L 3 mol2. This value is consistent with 307 ( 43 J 3 L 3 mol2 from ITC measurements. According to the CarnahanStarling description of osmotic pressure for a hard sphere,3,6,22,23 the second vivial coefficient Bϕ can be expressed as a function of the volume fraction ϕ of the microemulsion droplets 0 B Bϕ ¼ a@
1 4 aϕ
C AA ð1 aϕÞ þ 2 4
ð12Þ
where a is the volume ratio of hard spheres to droplets, and the contribution of hard spheres is ðBϕ ÞHS ¼
að4 aϕÞ ð1 aϕÞ4
ð13Þ
and the interaction parameter A is expressed in terms of the molar enthalpy ΔHϕ and entropy ΔSϕ of the dilution: ΔHϕ ΔSϕ A ¼ þ 2 RT R
ð14Þ
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Our previous light-scattering experiment gave ΔHϕ and ΔSϕ to be (4.0 ( 0.2) 104 J 3 mol1 and 131 ( 7 J 3 mol1 3 K1, respectively.20 According to eq 5, a plot of (ΔH)/(∑n2i) versus [(∑n2i + n20)/(∑n2i)ϕ2i (n20)/(∑n2i)ϕ20] gives the straight line shown in Figure 4. The ITC data were fit to eq 5 and further by using eq 7 to obtain ΔHϕ, which was (4.6 ( 0.6) 104 J 3 mol1. The difference between the values from the light-scattering experiment and ITC measurement is less than the estimated experimental uncertainty and confirms once again the validity of our experimental design for the determination of the interaction enthalpy between the microemulsion droplets by ITC measurements. 12283
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