Homogeneous Nucleation Temperatures in Aqueous Mixed Salt

Aug 28, 2007 - The empirical parameter, q0, indicating ionic interaction is related to the ... Further, a linear correlation exists between the q0 par...
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J. Phys. Chem. B 2007, 111, 10985-10991

10985

Homogeneous Nucleation Temperatures in Aqueous Mixed Salt Solutions Anil Kumar† Physical Chemistry DiVision, National Chemical Laboratory, Pune 411 008, India ReceiVed: May 18, 2007; In Final Form: July 24, 2007

This is the first report on the measurement of homogeneous nucleation temperature, TH, in the presence of aqueous mixed salt systems of varying compositions and ionic strengths. The TH,m (TH value in aqueous mixed salt system) data for these systems have been analyzed in terms of a simple empirical equation. The TH,m values in simple aqueous mixed salts like NaCl-KCl can be approximated by linear summation of the products of ionic strength fraction and the TH values of pure salt solutions at the same ionic strength as that of the mixture. The empirical parameter, q0, indicating ionic interaction is related to the viscosity B-coefficients. The TH,m data, though correlated on the basis of the B-coefficients also depends upon the mixing of two ions of like charges. Further, a linear correlation exists between the q0 parameter and self-diffusion coefficient, D0, of the ionic solute. The q0 parameter is also well correlated with the rotational correlation time, τch/τc0 of the ionic species involved in the mixtures. It is possible to compute TH,m for the salt mixtures with no common ions from the knowledge of the TH,m values of the salt mixtures with common ions.

Introduction A study of the low-temperature physical chemistry of aqueous medium can help us in understanding phenomena involved in climate prediction, medicine, agriculture, and biotechnology, etc.1 Homogeneous nucleation temperature, denoted by TH of aqueous solutions, can provide vital information on the supercooling of these solutions. In this connection, we recall the seminal contribution made by the school of Angell, who investigated homogeneous nucleation and glass formation in aqueous salt solutions, including under elevated pressures.2 Angell and Sare examined the role of highly soluble salts in suppressing the nucleation process.2a Highly significant contributions on the accurate determination have also been made by Kanno and his research group.3 It was noted that the TH values for several aqueous alkali chloride and acetate solutions varied linearly with the inverse of the cationic radii involved.3b It was demonstrated that the relationship between TH and ionic radii could be explained on the basis of the orientational difference of water molecules in the hydration spheres between cations and anions and also the structure-making and structure-breaking abilities of ions in the water medium. In the case of weak salts like alkali acetates, their ionization constants played important role in determining the supercooling behavior of aqueous solutions.3e Supercooling of aqueous solutions containing alcohols and ionic solutes has been investigated by designing an accurate experimental setup.3a A recent and systematic study suggested that the TH values for aqueous alcohols, glucose, and fructose could be expressed in terms of additive contributions from each structural unit of a solute.3a Very recently, an attempt has been made to correlate TH and equilibrium melting points depression, Tm, for aqueous solutions using a solute-specific supercooling capacity denoted by λ. The λ parameter has been shown to correlate well with the hydration characteristics and self-diffusion coefficients.4 † E-mail: [email protected]. Tel.: +91 20 25902278. Fax: +91 20 25902636.

Koop et al.5 noted that homogeneous nucleation of ice from supercooled aqueous solutions was independent of the nature of solutes such as salts, glycerol, ethylene glycol, etc. but was dependent on the water activities, aW, of aqueous solutions. Their conclusion was based on the assumptions of the dependence of melting point on the solute concentration and full dissociation of salts in a given situation. Miyata et al. however, demonstrated the TH-aW correlation to be an approximate one.3b In terms of theoretical developments with regard to nucleation phenomena, mention should be made of a report published by Rasmussen,1c who summarized the available theories with quantitative support. The nucleation phenomena is limited by the thermodynamic properties of the phases involved in the transformation process. In their classical work, Rasmussen and Mackenzie showed that a solute depresses the homogeneous nucleation temperature for ice formation in a manner that is proportional to the effect of the solute on equilibrium temperature.6 This was tested for aqueous polyethylene glycol E-9000, polyvinylpyrrolidone, plasdone-C, sucrose, glucose, ethylene glycol, ammonium fluoride, NaCl, KCl, CaCl2, and ammonium chloride. With the use of the emulsion method, these authors demonstrated that a linear relationship existed between TH and equilibrium melting points, Tm of several solutes.1c,6 Accordingly, ∆TH ) λ∆Tm, where λ indicates the dependence of supercooling on the solute. λ is specific to the solute employed in the study. ∆TH and ∆Tm are defined as TH0 - TH and Tm0 Tm, respectively. TH0 and Tm0 are homogeneous nucleation temperature and the melting point of water, respectively. The detailed discussion on TH and Tm is given by Rasmussen in his review article.1c It was later demonstrated on the basis of classical nucleation theory that the TH data for several solutes obtained by the emulsion method could be interpreted in terms of thermodynamic parameters.1g Since the λ parameter can be analyzed in terms of thermodynamics, this parameter can be correlated with the hydration properties of the solutes in question. From the knowledge of the λ parameter, it is possible to understand thermodynamic limitation to undercooling in the liquid to solid transformation.

10.1021/jp073846z CCC: $37.00 © 2007 American Chemical Society Published on Web 08/28/2007

10986 J. Phys. Chem. B, Vol. 111, No. 37, 2007

Kumar

A careful survey of the literature shows that the supercooling behavior has not been investigated in the presence of mixed ions, a situation of practical importance for meteorologists and environmentalists, because of the presence of many ionic solutes in the aqueous phase. In this work, we demonstrate how the supercooling behavior is influenced in the presence of mixed salts. The mixed salt solutions are known to possess nonidealities, which are characterized by interaction coefficients, that should influence the homogeneous nucleation process. We also examine the effect of ionic strength and the composition of the mixtures on the TH data. We also propose to analyze the TH data in aqueous two-salt mixtures. Last, we wish to predict the supercooling behavior induced by a mixture of two salts with uncommon ions from the knowledge of several pairs of two salts with common ions. Experimental Section High-purity methylcyclopentane and methylcyclohexane were procured from M/S Aldrich Chemical Co. LiCl, NaCl, KCl, guanidinium chloride (GnCl), MgCl2, CaCl2, Na2SO4, MgSO4, and tetra-n-alkylammonium salts were procured from M/S Aldrich Chemical Co., recrystallized from water, and vacuumdried prior to their use in making their aqueous solutions. Solutions were prepared in double-deionized water with its specific conductivity less than 0.55 × 10-6 S cm-1. Solutions were prepared on the molal basis. The composition of mixtures at constant ionic strength, I is given by the ionic strength fraction of salt B as yB ) IB/(IA + IB). The ionic strength I of salts and their mixtures is calculated by I ) 0.5 ∑mizi2, where z is ionic charge and i stands for an ion of a salt. Note that the ionic strength fraction of salt A in the mixture of A and B is given by yA ) (1 - yB). We have essentially followed the experimental methodology of Kanno et al.3a This methodology was initially developed by Rasmussen and MacKenzie.6 We used sorbitan tristerate for preparing emulsions. A 1:1 mixture (v/v) of methylcyclopentane and methylcyclohexane was used as a dispersant phase. A Shimadzu-made DSC 50 unit was employed to measure TH data with a cooling rate of 10 K min-1. We calibrated our data with those listed by Miyata et al.3b and Kanno et al.3a for aqueous NaCl and methanol. The TH data thus are accurate to 1.5 K. Each reported TH value in this work is an average of triplicate readings with a precision of (0.5 K. At very high concentration, say at 4 mol kg-1 of salt, the precision was not better than (0.8 K.

Figure 1. TH vs molality plots for aqueous (crossed diamond) GnCl, (x) KCl, (2) (CH3)4NBr, (9) NaCl, (0) LiCl, (3) (C3H7)4NBr, (O) CaCl2, (b) MgCl2, (4) LaCl3, (×) MgSO4. The data for Na2SO4 overlap with those of MgCl2 and hence are not shown for the sake of clarity. The data for tetra-n-alkylammonium chloride are not shown due to clustering of data. TH in water ) -37.6 °C.

Figure 2. Variation of TH,m as a function of yB in aqueous NaCl-KCl mixtures, (9) I ) 0.5mol kg-1, (0) I ) 1 mol kg-1, (2) I ) 2 mol kg-1, (4) I ) 3 mol kg-1, (b) I ) 4 mol kg-1.

Results and Discussion Before measuring the effect of mixed ionic salts on the TH data, we obtained TH values of many pure salts. There were two reasons for doing this: first to gain confidence in our data and second to have our own data on those pure salts of which we planned to investigate the effect of the salt mixtures under identical conditions. These included NaCl, KCl, MgCl2, CaCl2, LaCl3, MgSO4, Na2SO4, GnCl, and tetra-n-alkylammonium halides such as (CH3)4NCl, (C2H5)4NCl, (C4H9)4NCl, (CH3)4NBr, and (C3H7)4NBr. In Figure 1 are plotted the TH data (see the Supporting Information) as a function of the salt molality. The effect of LiCl, NaCl, and KCl on the supercooling is already discussed by Kanno and co-workers3 and is not repeated here. CaCl2 and MgCl2 offer more supercooling than do the 1:1 salts. Similarly LaCl3 offers much more supercooling than any 1:1 and 2:1 salts do. It has been shown that the TH data are correlated with the viscosity of aqueous salt solutions.2,3 The viscosity of salt solutions when analyzed with the help of the Jones-Dole

Figure 3. TH,m values as a function of yB in aqueous (9) NaCl-CaCl2, (4) NaCl-MgCl2, (×) NaCl-LaCl3, (b) CaCl2-MgCl2; all the data are at I ) 4 mol kg-1.

equation7 offers important information on the ion-water interaction parameter, denoted by the B-coefficient. The sign and magnitude of the B-coefficient indicate the structure-making or structure-breaking abilities of the constituent ions and so of salts. Accordingly, the higher the value of the B-coefficient of a salt, the higher is the supercooling. GnCl is a potent protein denaturant and also a rate-inhibiting salt. Aqueous GnCl is a

Nucleation Temperatures in Mixed Salt Solutions

J. Phys. Chem. B, Vol. 111, No. 37, 2007 10987

TABLE 1: Salt Mixtures Employed to Determine TH,m Values systems NaCl-KCl NaCl-GnCl NaCl-CaCl2 NaCl-MgCl2 NaCl-LaCl3 CaCl2-MgCl2 NaCl-Na2SO4

ionic strength, mol kg-1 0.5, 1, 2, 3, 4 0.5, 1, 2, 3, 4 0.5, 1, 2, 3, 4 0.5, 1, 2, 3, 4 0.5, 1, 2, 3, 4 0.5, 1, 2, 3, 4 1

Na2SO4-MgSO4 1 NaCl-MgSO4 1 MgCl2-Na2SO4 1

systems MgCl2-MgSO4 NaCl-(CH3)4NCl NaCl-(C2H5)4NCl NaCl-(C4H9)4NCl NaCl-(CH3)4NBr NaCl-(C3H7)4NBr (CH3)4NBr-(C3H7)4 NBr NaCl-MgCl2-LaCl3 NaCl-KCl-MgCl2

ionic strength, mol kg-1 1 0.5, 1 0.5, 1 0.5, 1 0.5, 1, 2, 3, 4 0.5, 1, 2, 3, 4 2 1 1

structure-breaker, implying that it disturbs the orientation of water molecules and is also hydrophobic in nature. Our TH data on GnCl show that its effect on supercooling is quite weak. KCl, another weak structure-breaker, also has shown a similar type of behavior. The TH data in the presence of (CH3)4NCl, (C2H5)4NCl, and (C4H9)4NCl could not be collected above 1 mol kg-1, as we noted some precipitation above this concentration. (CH3)4NCl, (C2H5)4NCl, and (C4H9)4NCl are the hydrophobic salts with the (CH3)4 group imparting least and the (C4H9)4 group maximum hydrophobicity. The TH values in 1 mol kg-1 solutions of (C4H9)4NCl, (C2H5)4NCl, and (CH3)4NCl are -72, -66, and -63.4 °C, respectively. It seems that the increased hydrophobicity of ionic solute offers more supercooling than the one with less hydrophobicity. Further, their B-coefficients are large and also follow the similar order of (C4H9)4NCl (B ) 2.73 cm3 mol-1) > (C2H5)4NCl (B ) 0.373 cm3 mol-1) > (CH3)4NCl (B ) 0.113 cm3 mol-1)8 corresponding to the supercooling behavior. The relative magnitude of supercooling behavior in these salts, however, does not seem to follow the numerical ratio of B-coefficients of these salts. Our data in aqueous (CH3)4NBr and (C3H7)4NBr could be measured up to 5 mol kg-1 and were in excellent agreement with the reported values4 measured up to 2 mol kg-1. Again, (C3H7)4NBr offered higher supercooling than (CH3)4NBr at a given salt concentration. The supercooling imparted by Na2SO4 is nearly similar to that offered by MgCl2. In the case of MgSO4, which offers high supercooling, the measurements could not be made at high molalities due to its restricted solubility in water. Again, the TH values in the presence of Na2SO4 and MgSO4 follow the order of the viscosity B-coefficients. This point will not discussed in detail here, as many other workers have already deliberated on this issue.3,4 The mixed salt systems used in the determination of TH,m (TH value in the mixed salt system) are listed in Table 1. We examined the TH,m values in the NaCl-KCl mixtures at different yB values at I ) 0.5, 1, 2, 3, and 4 mol kg-1. The results are shown in Figure 2. The TH,m values vary linearly with yB from low to high ionic strengths. Further, at any yB value, the TH,m values also vary linearly with ionic strength. Normally, in the mixture of NaCl and KCl, the interactions between Na+ and K+ in addition to those in between Na+ and Cl- and K+ and Cl- can be present. The linearity of the curves shown above suggests that the like charge interactions between Na+ and K+ are negligible. We then decided to see how the TH,m values were influenced when the experiments were carried out in the mixtures of NaCl with CaCl2, MgCl2, and LaCl3. Some of the results are depicted in Figure 3. The TH,m versus yB plots in Figure 3 belong to I ) 4 mol kg-1 for the mixtures of NaCl with CaCl2, MgCl2, and LaCl3.In the mixed NaClCaCl2 system, the supercooling is a linear function of yB in the mixtures of low ionic strengths, say I ) 1 mol kg-1. The

behavior becomes more prominent and nonlinear at I ) 2, 3, and 4 mol kg-1. The mixtures of NaCl with MgCl2 and LaCl3 display similar behavior. A closer examination of the results show that at a given ionic strength, the supercooling decreases sharply upon addition of a small amount of CaCl2, MgCl2, or LaCl3. It seems that the increase in the supercooling in the NaClrich mixtures depends upon the cationic charge in addition to the viscosity B-coefficients of the salts used as component to form mixtures. The supercooling did not change appreciably in the presence of CaCl2-MgCl2 even at I ) 4 mol kg-1. It suggests that the interactions between Ca2+ and Mg2+ are not significant in these mixtures. With regard to the role of ionic interactions, we recall the specific ion interaction theory developed by Pitzer.9,10 The Pitzer theory, a combination of long- and short-range interactions, considers the interactions between two ions of opposite charges and also between two ions of like charges. The interactions between two cations of like charges are characterized by a binary interaction term called θ and those between any two cations with an anion (also one cation with two anions) by a ternary interaction term denoted by ψ. The Pitzer equations accurately describe equilibrium thermodynamic properties of aqueous single and mixed salt solutions, including under elevated temperatures and pressures.11 The analysis of activity coefficient and aW data by the Pitzer equations suggests the θ and ψ parameters to be negligible in the case of NaCl-KCl suggesting an absence of Na+-K+ and Na+-K+-Cl- interactions. However significant θ and ψ parameters have been noted in aqueous mixtures of NaCl with CaCl2 and MgCl2. The interactions between Na+ and Ca2+ or Mg2+ are the examples of asymmetric mixing and can have significant bearing on the solution properties. Considering the significant interactions between Na+ and La3+, the effect of NaCl-LaCl3 should have been larger on the TH,m values particularly at high ionic strengths. However, our repeated experiments did not yield any different results. The curves drawn in Figure 3, however, show the same pattern of the TH,m-yB plots independent of charge types. The activity coefficient data of aqueous CaCl2-MgCl2 show small values of θ at high ionic strengths showing a weak parabola in Figure 3 for this system. NaCl is a hydrophilic salt, whereas many guanidinium salts such as GnCl, GnBr, GnNO3, GnClO4, and CH3COOGn are the hydrophobic ones. Out of these guanidinium salts, GnCl has been used to delineate the origin of forces responsible for the rate enhancement of Diels-Alder reactions12 and to understand their opposing roles in protein denaturation.13 The mixtures of NaCl-GnCl have also been used to probe the role of water medium in carrying out Diels-Alder reactions.14 In the recent past, we have estimated isopiestic osmotic coefficients and calculated the aW values and other thermodynamic properties of aqueous mixtures containing hydrophilic and hydrophobic salts, including tetra-n-alkylammonium halides.15-18 Other properties investigated were densities, speed of sound, surface tension, and viscosities at various ionic strengths. The study was carried out to determine ionic interactions using the excess free energy, ∆mGE, volume, ∆mVE, and compressibility of mixing, ∆mKE. These excess properties of mixing displayed both the negative and positive signs that were attributed to the mixing of hydrophilic and hydrophobic ions. It was shown that the θ and ψ interaction terms played an important role in the accurate representation of the osmotic coefficients, activity coefficients, volumes, and compressibilities of the mixtures. Considering the importance of ionic interactions in this ionic mixture, we measured the supercooling behavior in the presence of NaCl-

10988 J. Phys. Chem. B, Vol. 111, No. 37, 2007

Figure 4. TH,m-yB plots obtained in aqueous NaCl-GnCl system; for symbols see Figure 2.

GnCl (Figure 4). An addition of GnCl at higher ionic strengths decreases the supercooling effect, and this effect is less pronounced in lower ionic strengths (I ) 0.5 and 1 mol kg-1). A sharp decrease in supercooling was noted in the GnCl-rich solutions. This is in contrast to the results obtained for the mixtures of NaCl with KCl, CaCl2, MgCl2, and LaCl3. Also note the contrast in the shapes of plots given in Figures 3 and 4. The decrease in supercooling in the GnCl-rich mixtures may be attributed to the structure-breaking tendency of Gn+ , which dominates due to its higher concentration over that of the structure-making ability of Na+. Our studies have shown the θ term to be significant at high ionic strengths. The θ terms obtained during the analysis of the NaCl-CaCl2, -MgCl2, and -LaCl3 systems are opposite in sign to that obtained in the case of NaCl-GnCl mixtures.11,15 This indicates that the mixing effects in the NaCl-GnCl mixtures are opposite to those noted in the mixtures of NaCl with CaCl2, MgCl2, and LaCl3. In this connection, we also wish to restate the fact, which has been discussed in the original work of Kanno and coworkers3 and of Kimizuka and Suzuki4 that the orientation of water molecules around an ion plays a pivotal role in the supercooling process. We planned to test this in the mixtures of LiCl (a structure-maker, BLi+ ) 0.146 cm3 mol-1, BCl- ) -0.007 cm3 mol-1) with LiClO4 (BClO4- ) -0.046 cm3 mol-1, a structure-breaker). We carried out experiments in several compositions and ionic strengths of these salts to determine whether it was possible to locate a mixture composition that will offer TH,m close to that one would get in water alone. The TH values for 1 mol kg-1 of LiCl and LiClO4 are -43.3 and -40.2 °C, respectively. The only mixture containing 0.7 mol kg-1 of LiCl with 1.2 mol kg-1 of LiClO4 offered -39.4 °C, which was not very close to that obtained in water alone (-37.6 °C). We have noted in our work14,15 that such a compensation of structure-making and breaking abilities of ions takes place in the mixture of NaCl with GnCl. This neutralization of forces was tested for carrying out a cycloaddition reaction to demonstrate that the rate of such a reaction in a specific composition of NaCl-GnCl was approximately equal to that obtained in pure water. NaCl was noted to enhance the rate of the reaction, whereas GnCl inhibited it. The variations in rates were attributed to the structure-making and structure-breaking abilities of ions in addition to the salting phenomena. However, when we measured in TH,m in several compositions of the NaClGnCl mixtures, we could not obtain the TH value obtained in water. This suggests that the structure-making and structurebreaking effects are not neutralized in any composition of salt mixtures. It seems that the structure-altering abilities of ions are not the sole force to determine the supercooling behavior.

Kumar

Figure 5. TH,m vs yB plots for NaCl-(CH3)4NBr at I ) 0.5, 1, 2, 3, and 4 mol kg-1. For symbols see Figure 2. (B) (CH3)4NBr-(C3H7)4NBr at I ) 2 mol kg-1.

Other properties that influence the TH,m data in addition to the B-coefficients need to be probed for developing better understanding of supercooling phenomena. We also turned our attention to the mixtures of NaCl with (CH3)4NBr. Tetra-n-alkylammonium halides like (CH3)4NBr, (C4H9)4NBr, etc. are known to form clathrates and have been widely used to probe hydrophobic hydration.8 The variation in the TH,m values with yB at different ionic strengths for these mixtures is shown in Figure 5. We note that the higher is the ionic strength, the higher is the supercooling. The mixing of (CH3)4N+ with Na+ gives rise to significant θ terms as evident from the analysis of aW data of these mixtures.19 The recent experimental work showed (C3H7)4NBr to offer higher supercooling than (CH3)4NBr. However, when we examined the TH,m data of a mixture of (CH3)4NBr-(C3H7)4NBr (a mixture of a weak structure-maker with a strong structure-maker), we noted a sharp decrease in the TH,m values at yB ≈ 0.6. It suggests that the (C3H7)4N+-rich mixture dominates through its strong structure-making ability over that of (CH3)4N+. The difference in relative tightening of the water molecules around these cations can explain the supercooling behavior. We also measured TH,m data in the mixed salts containing NaCl with tetra-n-alkylammonium chloride at I ) 0.5 and 1 mol kg-1. The supercooling behavior in the presence of these mixtures is similar to the one noted in the case of mixing of NaCl with tetra-n-alkylammonium bromide. The TH,m data in the presence of ionic mixtures can be analyzed in a simple manner. If we consider only the interactions between pairs of cation and anion of a salt to be dominant in the mixed ionic systems, we can conveniently write

TH,m )

∑yJTH,J0

(1)

where TH,m is the TH value obtained experimentally in the presence of the mixtures of two salts, whereas TH,J0 is the TH value in the presence of a single constituent salt, J, at the same ionic strength as that of the mixture. Equation 1 implies that TH,m is linear with respect to yB at a specific ionic strength. Equation 1 is analogous to a classical Young’s rule,20 which describes that equilibrium excess thermodynamic properties are zero resulting out of mixing two salt solutions at the same ionic strength as that of a mixture is zero. The Young’s rule is therefore applicable to estimate the properties of ideal mixtures. This equation is not obeyed in systems in which binary interactions between two ions with like charges or/and ternary

Nucleation Temperatures in Mixed Salt Solutions

J. Phys. Chem. B, Vol. 111, No. 37, 2007 10989

TABLE 2: Adjustable Parameters of Eq 3 for Fitting the TH,m Data in Various Salt Mixtures at I ) 1 mol kg-1 a mixtures

q0/°C

mixtures

q0/°C

NaCl-KCl NaCl-CaCl2 NaCl-LaCl3 NaCl-Na2SO4 NaCl-MgSO4 MgCl2-MgSO4 NaCl-(C2H5)4NCl (CH3)4NBr-(C3H7)4NBr I ) 2 mol kg-1 NaCl-(C3H7)4NBr

0 2.02 2.89 -4.40 -9.12 -7.72 5.4 28.6

NaCl-GnCl NaCl-MgCl2 CaCl2-MgCl2 Na2SO4-MgSO4 MgCl2-Na2SO4 NaCl-(CH3)4NCl NaCl-(C4H9)4NCl NaCl-(CH3)4NBr

-6.33 2.00 0 -7.84 -3.76 2.88 12 2.91

a

6.72

Figure 6. Correlation between the q0 parameter of eq 3 and the viscosity B-coefficients for various salts used for preparing their mixtures with NaCl. See text for the significance of the arrow.

The q ) 0 is within experimental error. 1

interactions between two cations and one anion or one cation and two anions play significant role. If either binary or ternary or both types of interactions are important, one can write

TH,m )

∑yJTH,J0 + ∂TH,m

(2)

where ∂TH,m, the correction or nonideality term, is defined as the difference between the measured TH,m and the second term on the right-hand side of eq 2. The ∂TH,m can be fitted to the equation of the form

∂TH,m ) yB(1- yB)[q0 + q1(1 - 2yB)]

(3)

where q0 and q1 are the adjustable parameters indicating ionic interactions. The analysis of data show that the ∂TH,m versus yB plots in many mixtures are symmetric parabola within experimental error. If the ∂TH,m versus yB plots are symmetric parabola, the q0 parameter, a binary interaction term, will be the only significant ion interaction term. The q1 parameter represents skew in such plots and indicates the presence of ternary interactions. Out of the systems studied by us, NaCl-KCl is the only mixture for which random ∂TH,m values are observed. This clearly indicates the interactions between Na+ and K+ are negligible, and the interactions between opposite charged ions alone govern the homogeneous nucleation temperatures up to high ionic strength. A mixture of CaCl2-MgCl2 also showed small values of ∂TH,m except at I ) 4 mol kg-1. However, the situation is different in the cases of other mixtures, where we noted that the values of ∂TH,m with respect to yB showed clear parabola. Equation 3 was fitted to evaluate q0 and q1 parameters as required. These parameters, for example, at I ) 1 mol kg-1, are listed in Table 2. The q0 parameter is a function of the radii of ions present in the mixtures. This is clear from the examples of the mixing of 1:1 salt with 2:1 and 3:1 types of salts. Similarly, the mixtures containing SO42- offer negative q0 values. However, q0 values are large in some mixtures of NaCl with tetra-n-alkylammonium halides. These q0 values increase with the ionic radii of tetra-n-alkylammonium cations. The above given simple treatment of the TH,m data shows that a single interaction parameter can describe the effect of mixed ions on the supercooling phenomena to within an average standard deviation of 1.3 °C. It is interesting to note that the q0 parameters obtained for the mixtures containing NaCl as a common salt were linearly correlated with the viscosity B-coefficients of the salts with which the mixtures were prepared. The B-coefficients for these salts were taken from the literature.8 The plot is shown in Figure 6.

Figure 7. q0 vs D0 plot for aqueous mixtures containing NaCl.

The mixture data for GnCl with NaCl as indicated by an arrow in Figure 6 was scattered from the linear correlation given by

q0 ) -0.45 + 9.876B

with correlation coefficient r ) 0.849, N ) 9

Without the point of GnCl, the correlation is

q0 ) 0.99 + 8.052B

with correlation coefficient r ) 0.925, N ) 8

The above correlation indicates a possibility that even the mixed salt effect on supercooling may be interpreted in terms of the viscosity B-coefficients, as has been reported in the past.3,4 Kimizuka and Suzuki have demonstrated a linear relationship between the solute-specific supercooling capacity parameter, λ, with the self-diffusion coefficients, D0, of many solutes with intent to clarify the dependence of λ on the hydrodynamic size and shape of the solute molecule.4 We decided to test the validity of such a correlation in the case of mixtures. In Figure 7 we plot the q0 parameters against the D0 values of different salts employed in forming mixtures with NaCl. An examination of this plot shows that a linear relationship with r ) 0.921 is applicable even in the case of aqueous mixed salt systems. However, the fit in the mixed salts did not significantly improve with the plotting of the q0 parameter with log D0 as was reported by the authors.4 Another important property, which has been shown to correlate well with λ, is the rotational correlation time, τch/τc0, of the solutes. Our plot of the q0 parameters against τch/τc0 values for different salts forming mixtures with NaCl is shown in Figure 8. The plot is linear with r ) 0.921 for several mixtures. Unfortunately, we are unable to delineate these linear plots further in the case of mixed salts due to complex nature of the q0 parameters, the information on which we plan to gather in due course of time.

10990 J. Phys. Chem. B, Vol. 111, No. 37, 2007

Kumar

Figure 8. Correlation of q0 parameter with τch/τc0 for aqueous mixtures containing NaCl.

The analysis of TH,m data for the mixtures in terms of λ is cumbersome task owing to the difficulty in computing binary interactions at such a low temperature. The data are not yet available to present a clear picture of such a correlation in mixed salts. We analyzed our data on mixtures with a view to checking the combined effect of ions and salts on the TH,m values. Let us take four two-salt mixtures with a common ion. It is possible to prepare a mixture of two salts with no common ion using these four salt mixtures. For example, the four two-electrolyte mixtures with common ion prepared from M, N, X, and Y (M and N ) cations; X and Y ) anions) can give the salt pairs as MY-NY, MY-MX, MX-NX, and NX-NY. We can also prepare two two-salt solutions of MX-NY and MY-NX. We now address the question of whether it is possible to predict the TH,m data in MX-NY and MY-NX from the knowledge of the similar data collected in MY-NY, MY-MX, MX-NX, and NX-NY at a fixed composition and at the same ionic strength. In this connection, we recall one of the Young’s rules, known as Young cross square rule (YCSR)20 used by a large number of workers to investigate the excess chemical potentials and other properties of the mixtures.11,17 The YCSR suggests that the sum of the ∆mGE values for the four two-electrolyte mixtures with common ion prepared from M, N, X, and Y equals to the sum of ∆mGE of those two pairs having no common ions. Accordingly we make use of an equation analogous to YCSR to compute the ∂TH,m values as

∂TH,m(MX-MY) + ∂TH,m(MY-NY) + ∂TH,m(NX-NY) + ∂TH,m(MX-NX) ) ∂TH,m(MX-NY) + ∂TH,m(MY-NX)

(4)

Note that accurate calculation of ∂TH,m will yield correct values of TH,m. In the present case of our example, we write

∂TH,m(NaCl-MgCl2) + ∂TH,m(MgCl2-MgSO4) + ∂TH,m(Na2SO4-MgSO4) + ∂TH,m(NaCl-Na2SO4) ) ∂TH,m(NaCl-MgSO4) + ∂TH,m(MgCl2-Na2SO4)

(5)

Use of eq 5 requires the ∂TH,m values for MgCl2-MgSO4, Na2SO4-MgSO4, NaCl-Na2SO4, NaCl-MgSO4, and MgCl2Na2SO4. The TH,m data for several of these systems are plotted in Figures 3 and 9. Application of eq 5 to our systems is demonstrated in Table 3, where we list ∂TH,m values for the

Figure 9. TH,m vs yB plots for (0) MgCl2-MgSO4, (b) Na2SO4MgSO4, (2) NaCl-Na2SO4, (3) MgCl2-Na2SO4, (O) NaCl-MgSO4; all the data are at I ) 1 mol kg-1.

Figure 10. Three-dimensional display of the TH,m distribution with respect to yA and yB in the NaCl (A)-MgCl2 (B)-LaCl3 (C) mixtures at I ) 1 mol kg-1.

TABLE 3: Application of the YCSR Type of Method to Calculate DTH,m at yB ) 0.5 and I ) 1 mol kg-1 mixture

∂TH,m/°C

mixture

∂TH,m/°C

MgCl2-MgSO4 Na2SO4-MgSO4 NaCl-Na2SO4 NaCl-MgCl2 sum

-1.93 -1.96 -1.10 2.00 -2.99

MgCl2- Na2SO4 NaCl-MgSO4

-0.94 -2.28 -3.22

constituent pairs. We verified the above methodology at yB ) 0.5 and I ) 1 mol kg-1. As seen in Table 3, the sum of ∂TH,m for the salt mixtures with a common ion is -2.99 °C, which is close to that (-3.22 °C) obtained for the salt mixtures with uncommon ions. The success of the above proposed method indicates that it is possible to predict the supercooling arising out of the effect of the salt mixture with uncommon ions using the knowledge of the combined effects created by those salt mixtures with a common ion. Further, we have also seen that many of these mixtures are characterized by the presence of binary mixing term that we have calculated by a simple difference method. It seems that the YCSR is obeyed in those systems, where binary interactions are present. We also note that the above mixtures for which YCSR is tested are composed of both structuremaking and structure-breaking ions. At last, we studied the effect of mixed ionic system containing Na+, Mg2+, La3+, and Cl- species at a total ionic strength of 1 mol kg-1. These data collected within the solubility limits are plotted in the form of a three-dimensional diagram in Figure 10. Sufficient care was taken to ensure to prepare the mixtures

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