- Email: [email protected]
Isotope effect on the coexistence curve and crossover behavior of water+tetrahydrofuran
10 March 2000
Chemical Physics Letters 319 Ž2000. 119–124 www.elsevier.nlrlocatercplett
Isotope effect on the coexistence curve and crossover behavior of water q tetrahydrofuran Alla Oleinikova, Hermann Weingartner ¨
)
Physikalische Chemie II, Ruhr-UniÕersitat ¨ Bochum, D-44780 Bochum, Germany Received 20 September 1999; in final form 6 January 2000
Abstract Liquid–liquid coexistence curves of the system Žtetrahydrofuranq water. and the pseudo-binary system Žtetrahydrofuran q deuterated tetrahydrofuranq heavy water. were measured in the reduced temperature range 3 = 10y5 - t - 7 = 10y2 from their lower critical points. The composition of the deuterated system was adjusted to get the critical temperature close to that of the normal binary mixtures. This ensures that the effect of the upper consolute temperatures is the same in both cases, thus facilitating data interpretation. The refractive index and the Lorentz–Lorenz function were chosen as composition variables for analyzing the order parameter. For t - 10y3 both mixtures exhibit pure Ising behavior. The leading critical amplitude increases in the deuterated mixture. The crossover behavior is found to be sensitive to changes in deuteration. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction It is well established that the critical behavior of binary nonelectrolyte mixtures near their liquid– liquid consolute points is universal and maps onto that of the three-dimensional Ising model. However, the range of the pure Ising-like criticality is usually rather narrow w1x. Further away from the critical point, the various properties do not only depend on the distance from critical point, but also become increasingly influenced by details of the molecular structure and of interparticle interactions. This problem of crossover from universal asymptotic to substance-specific behavior is of special importance for complex fluids such as ionic mixtures w2,3x, polymer ) Corresponding author. Fax: q49-234-3214-293; e-mail: [email protected]
systems w4x or micellar solutions w5x. Recent experimental studies of critical behavior of aqueous nonelectrolyte solutions showed that the presence of ionic impurities leads to a shrinkage of the asymptotic region for the critical isotherm w6x, susceptibility w7x, coexistence curve w5x and viscosity w8x. Crossover theories proposed recently w4,7x attribute these changes to the competition between the correlation length of the critical fluctuations and some characteristic length of the supramolecular structures that participate in the demixing process. Crossover processes are present, of course, in simpler systems as well, albeit more difficult to detect. In seeking for traces of crossover in near-critical nonelectrolyte mixtures, we report here on subtle experiments, enabled by peculiar properties of the system tetrahydrofuranq water. This mixture has a closed-loop phase diagram w9x with lower and upper
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 0 8 6 - 5
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A. OleinikoÕa, H. Weingartnerr Chemical Physics Letters 319 (2000) 119–124 ¨
consolute points near 344 and 410 K, respectively. Deuteration of the compounds changes the immiscibility loop in opposite directions: The gap expands, when water is replaced by heavy water ŽD 2 O., but shrinks when tetrahydrofuran ŽTHF. is replaced by its fully deuterated homologue ŽTHFd . w10,11x. This enables the design of isotopically related systems with almost equal lower Žand presumably also upper. solution temperatures, such as THF q H 2 O and the pseudo-binary system THF q THFd q D 2 O. Then, any difference in the shape of the coexistence curves must result from different crossover behavior.
2. Experimental We used THF ŽBaker, purity ) 99.0%., THFd ŽDeutero, Kastellaun, Germany, 2 D content ) 99.5 at%., D 2 O ŽMerck, 2 D content ) 99.9 at%. and bidistilled and deionized water. The critical mixtures were prepared by weight in the rectangular prisms that were subsequently used in the experiments. To reduce the gravity effect, the height of the fluid did not exceed 1 cm in both cases. After cooling down to 08C, the samples were degassed by pumping for a few seconds, and were sealed. For a THF q H 2 O mixture of composition x 1 s 0.227, where x 1 is the mole fraction of THF, the meniscus appeared in the middle of the cell and the average value of the refractive index of two coexisting phases at the critical temperature coincided with the refractive index in the one-phase region. Thus, this mixture was exactly critical. In the deuterated sample the mole fraction of total tetrahydrofuran ŽTHF q THFd . in the mixture THF q THFd q D 2 O was x s 0.216. The mole fraction of THFd in the mixture THF q THFd Ži.e. the degree of deuteration of THF,. was 0.269. The critical composition of the deuterated sample is not necessarily identical to that of the normal sample. From the equal-volume condition, we concluded that the fraction of THF was very slightly below the critical value, but with the limited amount of substance, no better adjustment could be obtained. The coexistence curves were determined by measuring the refractive indices of the upper and lower liquid phases by the minimum beam deflection method. The displacement of a laser beam transmit-
ted through each phase was measured at 3.24 m from the vertical axis of the cell support. The cell was immersed in a thermostat ŽLauda, type P. filled with a mineral oil. The temperature stability of the oil bath was "Ž3–4. mK near the critical temperature and decreased to "Ž10–15. mK at 80–958C. The temperature was measured by means of a calibrated thermometer ŽHeraeus Sensor. with an accuracy of "0.3 mK. A second rectangle prism filled with water was used for determining the refractive index of the mineral oil simultaneously with the coexistence curve measurements. The relative accuracy of the refractive index data is 2 = 10y5 . More details of the measuring procedure will be given elsewhere w12x. We measured 112 and 120 data points for THF q H 2 O and THF q THFd q D 2 O, respectively, at reduced temperatures t s <ŽT y Tc .rTc < in the range 3 = 10y5 - t - 7 = 10y2 . The critical temperature was determined from the appearance of the spinodal decomposition ring in the forward scattered light, when heating the cell by 1 mK per minute. For both mixtures a comparatively large change of Tc was observed during the measurements, possibly resulting from uncontrollable traces of peroxides, known to form in THF. Generally, Tc increased with time in the coexistence region ŽT ) 344 K., but was almost constant if the cell was kept at ambient temperature. Because even a small drift of Tc is known to distort crossover behavior of the coexistence curve w13x, Tc was redetermined frequently over the entire period of the experiments Žnear 40 days. and its time dependence was interpolated for each measured data point. Tabular sets of the primary data, together with the interpolated critical temperatures, can be obtained from the authors. From data fits to the scaling equation described below, we found the most appropriate values of Tc to be 3–7 mK lower than those determined from the appearance of the spinodal ring.
3. Results and data evaluation In extended scaling, the temperature dependence of the order parameter, D p, is described by a Wegner series of the form w1x D p s B0t b Ž 1 q B1t D q B2t 2 D q . . . . ,
Ž 1.
A. OleinikoÕa, H. Weingartnerr Chemical Physics Letters 319 (2000) 119–124 ¨
Fig. 1. Coexistence curves of THFqH 2 O Žopen symbols. and THFqTHFd qD 2 O Žsolid symbols. represented by the normalized refractive index n1, 2 r n c as a function of the reduced temperature t s ŽT-Tc .r Tc . For details see text.
with the theoretical critical exponent b s 0.3258 of the Ising model, and the exponent D s 0.51 of the correction terms w14x. The leading amplitude, B0 , and the amplitudes Bi of the correction terms are nonuniversal quantities. In binary liquids the composition difference of the coexisting phases is the accepted order parameter, but composition can be measured in different ways. Although the asymptotic behavior is not affected by the choice of the order parameter, nonuniversal quantities, such as the size of the asymptotic range and of the crossover region, may do so. In such a situation, that order parameter which provides the most symmetric coexistence curve is usually preferred w1x. Usually, the volume fraction, w , provides the widest asymptotic range for most of neutral w1,15x and ionic w3,16x binary mixtures. For systems with large excess volumes, the effect of the excess volume has to be included in a rigorous definition of the volume fraction by using partial molar volumes instead of molar volumes. Such data are presently not available for the isotopically substituted systems. As in similar cases w1x, we have alternatively analyzed the data using the refractive index n and the Lorentz–Lorenz function f s Ž n2 y 1.rŽ n 2 q 2. as the variables defining the order parameters D n s Ž n1 y n 2 .r2 n c , and D f s Ž f 1 y f 2 .r2 f c , respectively, where n1 and n 2 are the measured refractive indices of the two coexisting phases. The critical value of the refractive index, n c , in these expressions has
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been determined by extrapolation of the mean diameters ² n: s Ž n1 q n 2 .r2 or ² f : s Ž f 1 q f 2 .r2. The two coexistence curves, corrected for shifts of Tc , are shown in Fig. 1. The coexistence curve of the ternary mixture THF q THFd q D 2 O is wider than that of the binary mixture. We have checked that this also holds true in any other reasonable representation of the data as, for example, in terms of volume, mass and molar fractions, ignoring excess volumes. Fig. 2 shows a double-logarithmic plot of the temperature dependencies of the order parameter, D f, for two mixtures. Pure Ising behavior is observed in a rather wide temperature range, as shown by straight lines for both mixtures. It can also be seen from Fig. 2 that the leading amplitude, B0 , is
Fig. 2. Double-logarithmic plot of the order parameter D f defined in the text vs. the reduced temperature t : THFqH 2 O Žsquares., THFqTHFd qD 2 O Žcircles.. Fits to the simple scaling law D f s B0t b with b fixed at its theoretical value Ž0.3258. are shown as straight lines. The amplitudes are B0 s 0.08869 for THFqTHFd qD 2 O and B0 s 0.07939 for THFqH 2 O. The increase of the leading amplitude by 10% in the deuterated mixture is obvious.
A. OleinikoÕa, H. Weingartnerr Chemical Physics Letters 319 (2000) 119–124 ¨
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Fig. 3. Deviations from pure scaling law behavior for THFqH 2 O Žcircles. and THFqTHFd qD 2 O Žsquares. using the temperature variables: Ža. t and Žb. t ) . For details see text. Ža. B0 s 0.07939 ŽTHFqH 2 O., B0 s 0.08869 ŽTHFqTHFd qD 2 O.; Žb. B0 s 0.14538 ŽTHFqH 2 O., B0 s 0.16416 ŽTHFqTHFd qD 2 O..
higher for the deuterated mixture THF q THFd q D 2 O than for THF q H 2 O. A similar trend with deuteration of one component was observed for the mixtures isobutyric acid q water w17,18x, ethyl-am-
monium nitrate q octanol w19x and some other systems. The ranges of asymptotic behavior are compared in Fig. 3a by plotting the quantity D frŽ B0t b . which is unity for pure Ising-like behavior. Evidently, the asymptotic range of THF q THFd q D 2 O is somewhat smaller than that of THF q H 2 O. In a largescale plot, such as Fig. 3, the effect may seem marginal, but its presence is confirmed on a quantitative level by fits of the full data sets. Results for these fits are presented in Table 1: The amplitude, B1 , of the first Wegner correction in Eq. Ž1., is more negative for THF q THFd q D 2 O than for the normal system. For mixtures with closed-loop phase diagrams, the presence of a second critical point at the upper consolute critical temperature, T U , should be taken into account. This critical point is ; 66 K away from the lower consolute point, and one expects a marginal contribution in the asymptotic range, and possibly also in the range, where the first correction terms apply. Its effect will, however, become important when analyzing crossover behavior further away from the critical point. We therefore use the redefined temperature variable w20x
t )s
ž
T y Tc Tc
/ž
TU y T TU
/
Ž 2.
instead of t itself. For our calculations we estimated the upper critical solution temperatures w11x to be T U s 410.2 K for THF q H 2 O and TU s 409.2 K for THF q THFd q D 2 O. Results of fits to Eq. Ž1. with t s t ) are presented in Table 1. Use of t ) yields
Table 1 Values of the amplitudes obtained by fitting the order parameters D n and D f to Eq. Ž1. using two temperature variables t and t ) The values of the critical exponents b s 0.3258 and D s 0.51 were imposed. The standard deviations s n s 3 = 10y5 and sf s 1 = 10y4 were used for fitting of D n and D f, respectively Fit No.
Mixture
Order parameter
Temperature variable
B0
B1
B2
B3
x2
1 2 3 4 5 6 7 8
THF q H 2 O THF q THFd q D 2 O THF q H 2 O THF q THFd q D 2 O THF q H 2 O THF q THFd q D 2 O THF q H 2 O THF q THFd q D 2 O
Dn Dn Df Df Dn Dn Df Df
t t t t t) t) t) t)
0.0235 " 0.0001 0.0261 " 0.0008 0.0794 " 0.0003 0.0887 " 0.0003 0.0431 " 0.0002 0.0482 " 0.0001 0.1454 " 0.0007 0.1642 " 0.0005
y0.187 " 0.13 y0.328 " 0.08 y0.179 " 0.13 y0.330 " 0.08 y2.363 " 0.42 y3.091 " 0.27 y2.289 " 0.42 y3.063 " 0.27
y1.72 " 1.07 y1.67 " 0.69 y1.63 " 1.07 y1.47 " 0.70 68.5 " 11 78.4 " 7 67.2 " 11 78.5 " 7
y7.24 " 2.6 y5.71 " 1.6 y7.36 " 2.6 y6.09 " 1.6 y813.7 " 80 y867.4 " 53 y795.3 " 80 y858.3 " 52
1.22 0.86 1.39 1.00 1.10 0.66 1.25 0.76
A. OleinikoÕa, H. Weingartnerr Chemical Physics Letters 319 (2000) 119–124 ¨
Fig. 4. Residuals from the fits D fexp to Eq. Ž1. using two temperature variables, t Ža. and t ) Žb., for THFqTHFd qD 2 O. The parameters of the fits are given in Table 1 Žfits 4 and 8.. The standard deviation is sf s1=10y4 .
distinctly better fits of the data than obtained with t itself. Fig. 3 shows that in the latter case the shrinkage of the asymptotic range in the deuterated mixture is even more pronounced. We checked that the uncertainties in the estimation of the upper critical solution temperatures Ž"18C. do not change this result. Fig. 4 shows the residuals from the fits of the data for THF q THFd q D 2 O to Eq. Ž1. with three correction-to-scaling terms using reduced temperature t ŽTable 1, fit 4. and the redefined temperature t ) Žsee Table 1, fit 8..
4. Conclusions Deuteration of THF leads to a shrinking of the miscibility gap in THF q H 2 O, while deuteration of water increases the gap. It is well-known that hydrogen bonding in pure D 2 O is stronger than in pure H 2 O, which changes some physical properties to a considerable amount w21x. It is also known that this change in the properties of water affects miscibility gaps with organic solvents, which may even lead to an appearence of an immiscibility loop with D 2 O which in H 2 O is absent w22x. More spectacular, because not expected and difficult to explain, is the shrinkage of the gap upon deuteration of THF. Little is known of the change of physical properties of pure THF upon deuteration.
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We have demonstrated that these isotope effects can be exploited by designing two isotopically related mixtures, THF q H 2 O and THF q THFd q D 2 O, with similar lower critical solution temperatures. A comparative scaling-law analysis of the coexistence curve data for the two systems shows that deuteration causes the leading critical amplitude to increase, as already noted by others in cases, where only water was deuterated w17,18x. Our major result is that deuteration also changes the asymptotic range of simple scaling. While, in principle, such a result could be obtained by a Wegner expansion analysis of accurate data for any isotopically related pairs, the adjustment of the immiscibility loops to equal size leads to the same effect of the upper consolute point on the reduced temperature at the lower consolute point. This largely facilitates interpretation of data for the two systems, thus eliminating possible sources of ambiguity in the comparative data analysis of the two systems. In a wider range of reduced temperatures, deviations from Ising-like criticality are often characterized by a crossover temperature, rather than by the Wegner expansion. It remains to see how modern crossover theories w23x explain the data. At a simple level, we recall that the Ginzburg criterion w24x predicts a characteristic crossover temperature t=s AŽ l 0rj 0 . 6 , where l 0 is a characteristic interaction length and j 0 is usually equated with the amplitude of the correlation length of the critical fluctuations. Depending on details of the theory, the prefactor, A, is of the order of 0.01. t= can be related to the Wegner coefficients w24x. Within this concept, the observed shrinkage of the asymptotic range upon deuteration leads to a decrease of the crossover temperature. The two solutions considered here differ primarily in the hydrogen-bonded interactions, so that a change of the length scale, l 0 , can be expected. Modern crossover theory w23x does not necessarily equate this length scale with the characteristic length scale of interactions between single molecules, but considers supramolecular structures as units. Indeed, it has been suggested that in such solutions, not the single molecules but the solute–solvent clusters should be considered as the elementary units of demixing, which would imply a different cluster size w25x. The same structural changes may, however, also affect
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A. OleinikoÕa, H. Weingartnerr Chemical Physics Letters 319 (2000) 119–124 ¨
j 0 . From our experiments such an isotope effect on j 0 is strongly suspected, because the amplitude of the order parameter changes as well. Unless experimental information on j 0 is available from scattering experiments, this issue remains, however, speculative. It remains to be noted that comparatively subtle differences in molecular interactions induced by deuteration seem to affect crossover behavior to a notable degree.
Acknowledgements We are grateful to the Alexander-von-HumboldtStiftung for a fellowship to A.O. permitting to carry out this work. The Fonds der Chemischen Industrie e.V. is thanked for general support.
References w1x S.C. Greer, M.R. Moldover, Annu. Rev. Phys. Chem. 32 Ž1981. 233. w2x T. Narayanan, K.S. Pitzer, J. Chem. Phys. 102 Ž1995. 8118. w3x M. Kleemeier, S. Wiegand, W. Schroer, J. ¨ H. Weingartner, ¨ Chem. Phys. 110 Ž1999. 3085. w4x Yu.B. Melnichenko, M.A. Anisimov, A.A. Povodyrev, G.D. Wignall, J.V. Sengers, W.A. Van Hook, Phys. Rev. Lett. 79 Ž1997. 5266. w5x A. Martin, I. Lopez, F. Monroy, A.G. Casielles, F. Ortega, R.G. Rubio, J. Chem. Phys. 101 Ž1994. 6874.
w6x L.A. Bulavin, A.V. Oleinikova, A.V. Petrovitskij, Int. J. Thermophys. 17 Ž1996. 137. w7x J. Jacob, A. Kumar, M.A. Anisimov, A.A. Povodyrev, J.V. Sengers, Phys. Rev. E 58 Ž1998. 2188. w8x A. Oleinikova, L. Bulavin, V. Pipich, Chem. Phys. Lett. 278 Ž1997. 121. w9x J. Matous, J. Hrncirik, J.P. Novak, J. Sobr, Collect. Czech. Chem. Commun. 35 Ž1970. 1904. w10x P. Lejcek, J. Matous, J.P. Novak, J. Pick, J. Chem. Thermodyn. 7 Ž1975. 927. w11x V. Balevicius, N. Weiden, A. Weiss, Ber. Bunsenges. Phys. Chem. 98 Ž1994. 785. w12x A. Oleinikova, H. Weingartner Žin preparation.. ¨ w13x A. Oleinikova, M. Bonetti, Chem. Phys. Lett. 299 Ž1999. 417. w14x R. Guida, J. Zinn-Justin, J. Phys. A: Math. Gen. 31 Ž1998. 8103. w15x L.A. Bulavin, A. Oleinikova, J.V. Stepanenko, Ukr. Fiz. Zh. 43 Ž1998. 324. w16x M. Bonetti, A. Oleinikova, C. Bervillier, J. Phys. Chem. B 101 Ž1997. 2164. w17x E. Gulari, B. Chu, D. Woermann, J. Chem. Phys. 73 Ž1980. 2480. w18x S. Greer, Ber. Bunsenges. Phys. Chem. 81 Ž1977. 1079. w19x M. Bonetti, P. Calmettes, Int. J. Thermophys. 19 Ž1998. 1555. w20x T. Narayanan, A. Kumar, Phys. Rep. 249 Ž1994. 135. w21x G.S. Kell, in: F. Franks ŽEd.., Water. A Comprehensive Treatise, Vol. 1, Chap. 10, Plenum, New York, 1972, p. 363. w22x G.M. Schneider, in: F. Franks ŽEd.., Water. A Comprehensive Treatise, Vol. 2, Chap. 6, Plenum, New York, 1973, p. 381. w23x M.A. Anisimov, A.A. Povodyrev, J.V. Sengers, Fluid Phase Equil. 158r160 Ž1999. 537. w24x V.L. Ginzburg, Sov. Phys. Solid State 2 Ž1962. 1824. w25x I.V. Brovchenko, A.V. Oleinikova, J. Chem. Phys. 106 Ž1997. 7756.
Chemical Physics Letters 319 Ž2000. 119–124 www.elsevier.nlrlocatercplett
Isotope effect on the coexistence curve and crossover behavior of water q tetrahydrofuran Alla Oleinikova, Hermann Weingartner ¨
)
Physikalische Chemie II, Ruhr-UniÕersitat ¨ Bochum, D-44780 Bochum, Germany Received 20 September 1999; in final form 6 January 2000
Abstract Liquid–liquid coexistence curves of the system Žtetrahydrofuranq water. and the pseudo-binary system Žtetrahydrofuran q deuterated tetrahydrofuranq heavy water. were measured in the reduced temperature range 3 = 10y5 - t - 7 = 10y2 from their lower critical points. The composition of the deuterated system was adjusted to get the critical temperature close to that of the normal binary mixtures. This ensures that the effect of the upper consolute temperatures is the same in both cases, thus facilitating data interpretation. The refractive index and the Lorentz–Lorenz function were chosen as composition variables for analyzing the order parameter. For t - 10y3 both mixtures exhibit pure Ising behavior. The leading critical amplitude increases in the deuterated mixture. The crossover behavior is found to be sensitive to changes in deuteration. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction It is well established that the critical behavior of binary nonelectrolyte mixtures near their liquid– liquid consolute points is universal and maps onto that of the three-dimensional Ising model. However, the range of the pure Ising-like criticality is usually rather narrow w1x. Further away from the critical point, the various properties do not only depend on the distance from critical point, but also become increasingly influenced by details of the molecular structure and of interparticle interactions. This problem of crossover from universal asymptotic to substance-specific behavior is of special importance for complex fluids such as ionic mixtures w2,3x, polymer ) Corresponding author. Fax: q49-234-3214-293; e-mail: [email protected]
systems w4x or micellar solutions w5x. Recent experimental studies of critical behavior of aqueous nonelectrolyte solutions showed that the presence of ionic impurities leads to a shrinkage of the asymptotic region for the critical isotherm w6x, susceptibility w7x, coexistence curve w5x and viscosity w8x. Crossover theories proposed recently w4,7x attribute these changes to the competition between the correlation length of the critical fluctuations and some characteristic length of the supramolecular structures that participate in the demixing process. Crossover processes are present, of course, in simpler systems as well, albeit more difficult to detect. In seeking for traces of crossover in near-critical nonelectrolyte mixtures, we report here on subtle experiments, enabled by peculiar properties of the system tetrahydrofuranq water. This mixture has a closed-loop phase diagram w9x with lower and upper
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 0 8 6 - 5
120
A. OleinikoÕa, H. Weingartnerr Chemical Physics Letters 319 (2000) 119–124 ¨
consolute points near 344 and 410 K, respectively. Deuteration of the compounds changes the immiscibility loop in opposite directions: The gap expands, when water is replaced by heavy water ŽD 2 O., but shrinks when tetrahydrofuran ŽTHF. is replaced by its fully deuterated homologue ŽTHFd . w10,11x. This enables the design of isotopically related systems with almost equal lower Žand presumably also upper. solution temperatures, such as THF q H 2 O and the pseudo-binary system THF q THFd q D 2 O. Then, any difference in the shape of the coexistence curves must result from different crossover behavior.
2. Experimental We used THF ŽBaker, purity ) 99.0%., THFd ŽDeutero, Kastellaun, Germany, 2 D content ) 99.5 at%., D 2 O ŽMerck, 2 D content ) 99.9 at%. and bidistilled and deionized water. The critical mixtures were prepared by weight in the rectangular prisms that were subsequently used in the experiments. To reduce the gravity effect, the height of the fluid did not exceed 1 cm in both cases. After cooling down to 08C, the samples were degassed by pumping for a few seconds, and were sealed. For a THF q H 2 O mixture of composition x 1 s 0.227, where x 1 is the mole fraction of THF, the meniscus appeared in the middle of the cell and the average value of the refractive index of two coexisting phases at the critical temperature coincided with the refractive index in the one-phase region. Thus, this mixture was exactly critical. In the deuterated sample the mole fraction of total tetrahydrofuran ŽTHF q THFd . in the mixture THF q THFd q D 2 O was x s 0.216. The mole fraction of THFd in the mixture THF q THFd Ži.e. the degree of deuteration of THF,. was 0.269. The critical composition of the deuterated sample is not necessarily identical to that of the normal sample. From the equal-volume condition, we concluded that the fraction of THF was very slightly below the critical value, but with the limited amount of substance, no better adjustment could be obtained. The coexistence curves were determined by measuring the refractive indices of the upper and lower liquid phases by the minimum beam deflection method. The displacement of a laser beam transmit-
ted through each phase was measured at 3.24 m from the vertical axis of the cell support. The cell was immersed in a thermostat ŽLauda, type P. filled with a mineral oil. The temperature stability of the oil bath was "Ž3–4. mK near the critical temperature and decreased to "Ž10–15. mK at 80–958C. The temperature was measured by means of a calibrated thermometer ŽHeraeus Sensor. with an accuracy of "0.3 mK. A second rectangle prism filled with water was used for determining the refractive index of the mineral oil simultaneously with the coexistence curve measurements. The relative accuracy of the refractive index data is 2 = 10y5 . More details of the measuring procedure will be given elsewhere w12x. We measured 112 and 120 data points for THF q H 2 O and THF q THFd q D 2 O, respectively, at reduced temperatures t s <ŽT y Tc .rTc < in the range 3 = 10y5 - t - 7 = 10y2 . The critical temperature was determined from the appearance of the spinodal decomposition ring in the forward scattered light, when heating the cell by 1 mK per minute. For both mixtures a comparatively large change of Tc was observed during the measurements, possibly resulting from uncontrollable traces of peroxides, known to form in THF. Generally, Tc increased with time in the coexistence region ŽT ) 344 K., but was almost constant if the cell was kept at ambient temperature. Because even a small drift of Tc is known to distort crossover behavior of the coexistence curve w13x, Tc was redetermined frequently over the entire period of the experiments Žnear 40 days. and its time dependence was interpolated for each measured data point. Tabular sets of the primary data, together with the interpolated critical temperatures, can be obtained from the authors. From data fits to the scaling equation described below, we found the most appropriate values of Tc to be 3–7 mK lower than those determined from the appearance of the spinodal ring.
3. Results and data evaluation In extended scaling, the temperature dependence of the order parameter, D p, is described by a Wegner series of the form w1x D p s B0t b Ž 1 q B1t D q B2t 2 D q . . . . ,
Ž 1.
A. OleinikoÕa, H. Weingartnerr Chemical Physics Letters 319 (2000) 119–124 ¨
Fig. 1. Coexistence curves of THFqH 2 O Žopen symbols. and THFqTHFd qD 2 O Žsolid symbols. represented by the normalized refractive index n1, 2 r n c as a function of the reduced temperature t s ŽT-Tc .r Tc . For details see text.
with the theoretical critical exponent b s 0.3258 of the Ising model, and the exponent D s 0.51 of the correction terms w14x. The leading amplitude, B0 , and the amplitudes Bi of the correction terms are nonuniversal quantities. In binary liquids the composition difference of the coexisting phases is the accepted order parameter, but composition can be measured in different ways. Although the asymptotic behavior is not affected by the choice of the order parameter, nonuniversal quantities, such as the size of the asymptotic range and of the crossover region, may do so. In such a situation, that order parameter which provides the most symmetric coexistence curve is usually preferred w1x. Usually, the volume fraction, w , provides the widest asymptotic range for most of neutral w1,15x and ionic w3,16x binary mixtures. For systems with large excess volumes, the effect of the excess volume has to be included in a rigorous definition of the volume fraction by using partial molar volumes instead of molar volumes. Such data are presently not available for the isotopically substituted systems. As in similar cases w1x, we have alternatively analyzed the data using the refractive index n and the Lorentz–Lorenz function f s Ž n2 y 1.rŽ n 2 q 2. as the variables defining the order parameters D n s Ž n1 y n 2 .r2 n c , and D f s Ž f 1 y f 2 .r2 f c , respectively, where n1 and n 2 are the measured refractive indices of the two coexisting phases. The critical value of the refractive index, n c , in these expressions has
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been determined by extrapolation of the mean diameters ² n: s Ž n1 q n 2 .r2 or ² f : s Ž f 1 q f 2 .r2. The two coexistence curves, corrected for shifts of Tc , are shown in Fig. 1. The coexistence curve of the ternary mixture THF q THFd q D 2 O is wider than that of the binary mixture. We have checked that this also holds true in any other reasonable representation of the data as, for example, in terms of volume, mass and molar fractions, ignoring excess volumes. Fig. 2 shows a double-logarithmic plot of the temperature dependencies of the order parameter, D f, for two mixtures. Pure Ising behavior is observed in a rather wide temperature range, as shown by straight lines for both mixtures. It can also be seen from Fig. 2 that the leading amplitude, B0 , is
Fig. 2. Double-logarithmic plot of the order parameter D f defined in the text vs. the reduced temperature t : THFqH 2 O Žsquares., THFqTHFd qD 2 O Žcircles.. Fits to the simple scaling law D f s B0t b with b fixed at its theoretical value Ž0.3258. are shown as straight lines. The amplitudes are B0 s 0.08869 for THFqTHFd qD 2 O and B0 s 0.07939 for THFqH 2 O. The increase of the leading amplitude by 10% in the deuterated mixture is obvious.
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Fig. 3. Deviations from pure scaling law behavior for THFqH 2 O Žcircles. and THFqTHFd qD 2 O Žsquares. using the temperature variables: Ža. t and Žb. t ) . For details see text. Ža. B0 s 0.07939 ŽTHFqH 2 O., B0 s 0.08869 ŽTHFqTHFd qD 2 O.; Žb. B0 s 0.14538 ŽTHFqH 2 O., B0 s 0.16416 ŽTHFqTHFd qD 2 O..
higher for the deuterated mixture THF q THFd q D 2 O than for THF q H 2 O. A similar trend with deuteration of one component was observed for the mixtures isobutyric acid q water w17,18x, ethyl-am-
monium nitrate q octanol w19x and some other systems. The ranges of asymptotic behavior are compared in Fig. 3a by plotting the quantity D frŽ B0t b . which is unity for pure Ising-like behavior. Evidently, the asymptotic range of THF q THFd q D 2 O is somewhat smaller than that of THF q H 2 O. In a largescale plot, such as Fig. 3, the effect may seem marginal, but its presence is confirmed on a quantitative level by fits of the full data sets. Results for these fits are presented in Table 1: The amplitude, B1 , of the first Wegner correction in Eq. Ž1., is more negative for THF q THFd q D 2 O than for the normal system. For mixtures with closed-loop phase diagrams, the presence of a second critical point at the upper consolute critical temperature, T U , should be taken into account. This critical point is ; 66 K away from the lower consolute point, and one expects a marginal contribution in the asymptotic range, and possibly also in the range, where the first correction terms apply. Its effect will, however, become important when analyzing crossover behavior further away from the critical point. We therefore use the redefined temperature variable w20x
t )s
ž
T y Tc Tc
/ž
TU y T TU
/
Ž 2.
instead of t itself. For our calculations we estimated the upper critical solution temperatures w11x to be T U s 410.2 K for THF q H 2 O and TU s 409.2 K for THF q THFd q D 2 O. Results of fits to Eq. Ž1. with t s t ) are presented in Table 1. Use of t ) yields
Table 1 Values of the amplitudes obtained by fitting the order parameters D n and D f to Eq. Ž1. using two temperature variables t and t ) The values of the critical exponents b s 0.3258 and D s 0.51 were imposed. The standard deviations s n s 3 = 10y5 and sf s 1 = 10y4 were used for fitting of D n and D f, respectively Fit No.
Mixture
Order parameter
Temperature variable
B0
B1
B2
B3
x2
1 2 3 4 5 6 7 8
THF q H 2 O THF q THFd q D 2 O THF q H 2 O THF q THFd q D 2 O THF q H 2 O THF q THFd q D 2 O THF q H 2 O THF q THFd q D 2 O
Dn Dn Df Df Dn Dn Df Df
t t t t t) t) t) t)
0.0235 " 0.0001 0.0261 " 0.0008 0.0794 " 0.0003 0.0887 " 0.0003 0.0431 " 0.0002 0.0482 " 0.0001 0.1454 " 0.0007 0.1642 " 0.0005
y0.187 " 0.13 y0.328 " 0.08 y0.179 " 0.13 y0.330 " 0.08 y2.363 " 0.42 y3.091 " 0.27 y2.289 " 0.42 y3.063 " 0.27
y1.72 " 1.07 y1.67 " 0.69 y1.63 " 1.07 y1.47 " 0.70 68.5 " 11 78.4 " 7 67.2 " 11 78.5 " 7
y7.24 " 2.6 y5.71 " 1.6 y7.36 " 2.6 y6.09 " 1.6 y813.7 " 80 y867.4 " 53 y795.3 " 80 y858.3 " 52
1.22 0.86 1.39 1.00 1.10 0.66 1.25 0.76
A. OleinikoÕa, H. Weingartnerr Chemical Physics Letters 319 (2000) 119–124 ¨
Fig. 4. Residuals from the fits D fexp to Eq. Ž1. using two temperature variables, t Ža. and t ) Žb., for THFqTHFd qD 2 O. The parameters of the fits are given in Table 1 Žfits 4 and 8.. The standard deviation is sf s1=10y4 .
distinctly better fits of the data than obtained with t itself. Fig. 3 shows that in the latter case the shrinkage of the asymptotic range in the deuterated mixture is even more pronounced. We checked that the uncertainties in the estimation of the upper critical solution temperatures Ž"18C. do not change this result. Fig. 4 shows the residuals from the fits of the data for THF q THFd q D 2 O to Eq. Ž1. with three correction-to-scaling terms using reduced temperature t ŽTable 1, fit 4. and the redefined temperature t ) Žsee Table 1, fit 8..
4. Conclusions Deuteration of THF leads to a shrinking of the miscibility gap in THF q H 2 O, while deuteration of water increases the gap. It is well-known that hydrogen bonding in pure D 2 O is stronger than in pure H 2 O, which changes some physical properties to a considerable amount w21x. It is also known that this change in the properties of water affects miscibility gaps with organic solvents, which may even lead to an appearence of an immiscibility loop with D 2 O which in H 2 O is absent w22x. More spectacular, because not expected and difficult to explain, is the shrinkage of the gap upon deuteration of THF. Little is known of the change of physical properties of pure THF upon deuteration.
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We have demonstrated that these isotope effects can be exploited by designing two isotopically related mixtures, THF q H 2 O and THF q THFd q D 2 O, with similar lower critical solution temperatures. A comparative scaling-law analysis of the coexistence curve data for the two systems shows that deuteration causes the leading critical amplitude to increase, as already noted by others in cases, where only water was deuterated w17,18x. Our major result is that deuteration also changes the asymptotic range of simple scaling. While, in principle, such a result could be obtained by a Wegner expansion analysis of accurate data for any isotopically related pairs, the adjustment of the immiscibility loops to equal size leads to the same effect of the upper consolute point on the reduced temperature at the lower consolute point. This largely facilitates interpretation of data for the two systems, thus eliminating possible sources of ambiguity in the comparative data analysis of the two systems. In a wider range of reduced temperatures, deviations from Ising-like criticality are often characterized by a crossover temperature, rather than by the Wegner expansion. It remains to see how modern crossover theories w23x explain the data. At a simple level, we recall that the Ginzburg criterion w24x predicts a characteristic crossover temperature t=s AŽ l 0rj 0 . 6 , where l 0 is a characteristic interaction length and j 0 is usually equated with the amplitude of the correlation length of the critical fluctuations. Depending on details of the theory, the prefactor, A, is of the order of 0.01. t= can be related to the Wegner coefficients w24x. Within this concept, the observed shrinkage of the asymptotic range upon deuteration leads to a decrease of the crossover temperature. The two solutions considered here differ primarily in the hydrogen-bonded interactions, so that a change of the length scale, l 0 , can be expected. Modern crossover theory w23x does not necessarily equate this length scale with the characteristic length scale of interactions between single molecules, but considers supramolecular structures as units. Indeed, it has been suggested that in such solutions, not the single molecules but the solute–solvent clusters should be considered as the elementary units of demixing, which would imply a different cluster size w25x. The same structural changes may, however, also affect
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j 0 . From our experiments such an isotope effect on j 0 is strongly suspected, because the amplitude of the order parameter changes as well. Unless experimental information on j 0 is available from scattering experiments, this issue remains, however, speculative. It remains to be noted that comparatively subtle differences in molecular interactions induced by deuteration seem to affect crossover behavior to a notable degree.
Acknowledgements We are grateful to the Alexander-von-HumboldtStiftung for a fellowship to A.O. permitting to carry out this work. The Fonds der Chemischen Industrie e.V. is thanked for general support.
References w1x S.C. Greer, M.R. Moldover, Annu. Rev. Phys. Chem. 32 Ž1981. 233. w2x T. Narayanan, K.S. Pitzer, J. Chem. Phys. 102 Ž1995. 8118. w3x M. Kleemeier, S. Wiegand, W. Schroer, J. ¨ H. Weingartner, ¨ Chem. Phys. 110 Ž1999. 3085. w4x Yu.B. Melnichenko, M.A. Anisimov, A.A. Povodyrev, G.D. Wignall, J.V. Sengers, W.A. Van Hook, Phys. Rev. Lett. 79 Ž1997. 5266. w5x A. Martin, I. Lopez, F. Monroy, A.G. Casielles, F. Ortega, R.G. Rubio, J. Chem. Phys. 101 Ž1994. 6874.
w6x L.A. Bulavin, A.V. Oleinikova, A.V. Petrovitskij, Int. J. Thermophys. 17 Ž1996. 137. w7x J. Jacob, A. Kumar, M.A. Anisimov, A.A. Povodyrev, J.V. Sengers, Phys. Rev. E 58 Ž1998. 2188. w8x A. Oleinikova, L. Bulavin, V. Pipich, Chem. Phys. Lett. 278 Ž1997. 121. w9x J. Matous, J. Hrncirik, J.P. Novak, J. Sobr, Collect. Czech. Chem. Commun. 35 Ž1970. 1904. w10x P. Lejcek, J. Matous, J.P. Novak, J. Pick, J. Chem. Thermodyn. 7 Ž1975. 927. w11x V. Balevicius, N. Weiden, A. Weiss, Ber. Bunsenges. Phys. Chem. 98 Ž1994. 785. w12x A. Oleinikova, H. Weingartner Žin preparation.. ¨ w13x A. Oleinikova, M. Bonetti, Chem. Phys. Lett. 299 Ž1999. 417. w14x R. Guida, J. Zinn-Justin, J. Phys. A: Math. Gen. 31 Ž1998. 8103. w15x L.A. Bulavin, A. Oleinikova, J.V. Stepanenko, Ukr. Fiz. Zh. 43 Ž1998. 324. w16x M. Bonetti, A. Oleinikova, C. Bervillier, J. Phys. Chem. B 101 Ž1997. 2164. w17x E. Gulari, B. Chu, D. Woermann, J. Chem. Phys. 73 Ž1980. 2480. w18x S. Greer, Ber. Bunsenges. Phys. Chem. 81 Ž1977. 1079. w19x M. Bonetti, P. Calmettes, Int. J. Thermophys. 19 Ž1998. 1555. w20x T. Narayanan, A. Kumar, Phys. Rep. 249 Ž1994. 135. w21x G.S. Kell, in: F. Franks ŽEd.., Water. A Comprehensive Treatise, Vol. 1, Chap. 10, Plenum, New York, 1972, p. 363. w22x G.M. Schneider, in: F. Franks ŽEd.., Water. A Comprehensive Treatise, Vol. 2, Chap. 6, Plenum, New York, 1973, p. 381. w23x M.A. Anisimov, A.A. Povodyrev, J.V. Sengers, Fluid Phase Equil. 158r160 Ž1999. 537. w24x V.L. Ginzburg, Sov. Phys. Solid State 2 Ž1962. 1824. w25x I.V. Brovchenko, A.V. Oleinikova, J. Chem. Phys. 106 Ž1997. 7756.