Emory H . Braswell
4026
edimentation Studies of the Aggregation of Methylene Blue ~~r~
H. Braswell
Biochemistry and Biophysics Section, Biological Sciences Group, University of Connecticut, Storrs, Connecticut 06268 (Recc?ivedJanuary 24, 1972) Publication costs assisted by the University of Connecticut Research Foundation
The aggregation of Methylene Blue in aqueous solutions at 30” ‘was studied by means of sedimentation equilibrium techniques. These studies were carried out over a dye concentration range of from ca. to CIZ. M in the presence of NaCl concentrations which were from 7 7 - to 200-fold higher than that of the dye. In the absence of NaCl it was possible to make measurements over a concentration range of‘ from 2 x to ca. 6 x M . The results indicate that (1) a t the lowest concentration studied the dye is 60% ionized; (2) in the presence of a high concentration ratio of NaCl to dye, the dye is not ionized and aggregates by means of a simple ”condensation” type polymerization with ;in equilibrium cons t a t of 600 M - 1 (which corresponds to a dimerization constant of 2400 M-’); (3) in the absence of NaCi the aggregates formed are charged; (4) the reaction goes far beyond pentamer formation; arid ( 5 ) the 6 absorption band is a t a maximum when the quantity of dimer is maximal.
Introduction Upon the addition of certain high molecular weight anionic polymers such as heparin (a chromotrope) to a dilute aqueous solution of certain cationic dyes such as Methylene Blue, there occurs a shift in the wavelength of maximum absorption toward shorter wavelengths. This “metachromatic effect” is easily observed as a change in the color of the solutioin from blue to purple or red. A similar effect can be obscmed as the dye concentration is increased in a solution of the dye alone and is believed to be due to aggregation (“stacking”) of the dye molecule (see, for example, ref 1-81 which presumably is brought about by dispersion forces operating in a direction perpendicular to the plane of the delocalized 7~ electrons.1-3 Metachromasia, therefore, is thought to be due to the facilitated aggregation of the dye molecules which are bound to the chrom0trope.l ,9-11 Bradley and his associate^^^-^^ were able to develop a semiquantitative description of the metachromatic phenomenon by using a statistical approach and by assuming that bound dye molecules only associate with each other to the extent of forming dimers. However he acknowledged that higher stages of aggregation probably exist. In this manner however he was able to clearly delineate the factors involved which contribute to the degree of metachromasia obtained. First, is the innate ability of the dye molecule to “stack” or aggregate with itself. This i s a function of the organic and hence electronic structure of the dye. The second factor involves the spacing of the sites on the chromotrope. This study is limited to the investigation of the mechanism o f the dye-dye association. It must be pointed out that many different types of dye associate, and some show shifts in wavelength of maximum absorption upon association. Of this latter group only some dyes aggregate principally through c electron interaction and show the peculiar metachromatic Lype of absorption maximum shift (see, for example. ref 16). That is, as the dye concentration is increased there appears a second absorption band ( p band) a t shorter wavelengths than that associated with the monomeric dye ( a band), while this latter band decreases in height. Then as the concentration is further inThe Journal of Pbysicai Chemistry, Vol. 76, No. 26, 7972
creased the p band shifts slowly to shorter wavelengths simultaneously decreasing in height while the N band diminishes until it becomes undetectable. Very little is known about the mechanism of aggregation or the number of dye molecules in a metachromatic aggregate. Most attempts to study the effect quantitatively have been limited to considering only dimerization2.436J7 even though many authors note that higher aggregates probably also form.2.4,6.s.17 The role of water in the formation of the aggregates, either as a dielectric sandwiching between the dye molecule^^^^ or as a former of hydrogen bond^,^'.^^ has been found to be of great importance. In a series of a r t i c l e ~ l ~Hillson - ~ ~ and McKay presented (1) G . Scheibe, Angew. Chem., 50, 212 (1937) (2) G . Scheibe, Koiioid Z., 82, 1 (1938) (3) G. Scheibe, Angew. Chem., 52, 631 (1939). (4) E. Rabinowitch and L. F. Epstein, J. Amer. Chem. S o c . . 63, 69 (1941). (5) S. E. Sheppard and A . L. Geddes, J. Amer. Chem. Soc.. 66, 1995 (1944). (6) S. E. Sheppard and A. L. Geddes, J. Amer. Chem. Soc., 6 6 , 2003 (1944). (7) L. Michaelis and S. Granick. J. Amer. Chem. S o c . . 67, 1212 (1945). (8) T. Vickerstaff and D. R . Lemin, Nature (London). 157, 373 (1946). (9) J . M. W i a m e , J. Amer. Chem. SOC.,69,3146 (1947) (10) B. Sylven, Quart. J. Microscop. Sei.; 95, 327 (1954). (11) M. Schubert and A. Levine, J. Amer. Chem. SOC.,79,4197 (1955). (12) D. F . Bradley and ivl. K. W o l f , Proc. Nat. Acad. Sei. U. S.. 45, 944 (1959). (13) D. F. Sradley and F. Feisenfeid. Nature (London), 185, 1920 (1959). (14) A. L. Stone and D. F. Bradley, J. Amer. Chem. SOC., 83, 3627 (1961). (15) A. L. Stone, L. G . Chiiders. and D.F. Bradley, Biopolymers, 1 , 111 (1963). (16) E. Braswell, J , Phys. Chem.. 72,2477 (1968). (17) M. E. Lamm and D. M . Neville, J r . , J . Phys. Chem., 69, 3872 (1965). (18) G . R . Haugen and E. R. Hardwick, J. Phys. Chem., 67: 725 (1963). (19) P. J. Hilison and R. B. McKay. Trans. Faraday Soc., 61, 374 (1 965). (20) P. J . Hiiison and R. B. McKay, Nafure (London), 210, 297 (1966). (21) R. B. McKay and P. J . Hillson, Trans. f a r a d a y SOC., 61, 1800 (1965). (22) R. B. McKay and P. J . Hillson, Trans. Faraday Soc., 62, 1439 (1966). (23) R. B. McKay, Trans. FaradaySoc., 61, 1785 (1965). (24) R. B. McKay, Nature (London), 218, 296 (1966). (25) R. B. McKay and P. J. t-liiison, Trans. Faraday Soc., 63, 777 (1967).
Aggregation of ~ ~ e t l i yBlue i~~e
4027
evidence to back their belief that the metachromasia of “negligible counterion participation i.n association equilibria a t low ionic strengths.” dyes observed in solvents of low dielect,ric strength was ‘due to strong interactions between dye ions and counterAn equilibrium technique that seems to be especially ions to produce an undissociated dye in which the ions are suited for the study of such aggregating systems is that o f in intimate coritact and are not separated by solvent mol- equilibrium sedimentation. I t has been used extensively ecuhxZ1 In one article they suggest that aggregation probfor the study of multistep equilibria in protein aggregation ably does not occur a t ali in solvents of very low dielectric and other substances (see for representative bibliography strengthz2 even though metachromasia is evident. In a ref 31-41]. A system which beafs ;esemblance t o the later article, they imply that even when the dye is in the aggregation o f metachromatic dyes which was studied by preseiice of a c ~ ~ r ~ ~ r n o tin r o water pe metachromasia occurs van Molde36339involves the association of cytidiFe and pulargely as a result of the interaction of the dye cation with rine. Since tlaese substances have similar molecular the polyanion, resulting in a perturbation of the charge r constants than Methylene weights but b ~ e association distribution of the dye cation.20 Still later, however, they Blue. the feasibility of using sedimentation techniques for concede that dinierizatkm of the dye is an important the study of the aggregation of Methylene Blue seemed cause of metachromasia in water and that this is due to firnly based. the 1;endency of water molecules to self-associate, giving rise to strong hydrophilik bonding between dye m01ecules.~~ Experimental Methods a n d Results Because salt is known to increase dye aggregation, HauThe dye was purified by the method of Bonneau, Faure, gen and E[ard.c;~iclc:~* have suggested that the dye dimeriand J o u s s e t - D ~ b i e n This . ~ ~ method gave a product which zation may take place in the following manner was found to be somewhat purer by chromatographic analysis on Eastman thin layer silica gel chromagram 2D+ -t A- (D2.4)~ sheets (using 9 : ? metbanol:acetic acid) than that puri:La” and Nevilhjz7 however, have found for Acridine fied in the manner used for our previous study.16 That is, Orange that it is impossible to distinguish between this the faint leading spot previously observed was missing or model and the simple dimerization one. extremely faint in the purified dye samples used for this Some progress has been made on determining the destudy. gree of polymerization attainable by the dye. Hillson and The sedimen.tation studies were performed at 30” in a McKaylg found, irsing polarographic methods, that the Spinco, Model E, analytical ultracentrifuge using a Spindegree of aggregation of ethylene Blue a t high conceneo photoelectric scanner (with moriochromator) to detect :rations was about 3 , BraswelP using spectral techniques dye concentration changes across the cell. due to absorpand studying dye concentrations far higher than those tion. The wavelength of light chosen depended largely on !studied previuusly found that a limiting aggregation numthe cell thickness-dye concentration combination studied. ber of 3 described the data qualitatively a t moderately It was found that observation near 406 m p obeyed Beer’s high concentrations h t poorly st the highest concentraLaw over the widest concentration range and, since this tions, Vapor pressure osmometry data presented in the was near the wavelength of least absorption, was the same paper indiciited a limiting aggregation number of 3. v~avelength chosen most often a t high dye concentration. In addition Braswdi16 obtained an equilibrium constant At ]low dye concentration, however, there was not enough for both the dimerization and. trimerization steps o f the absorpGion for accurate concentration measurement hence reaction. The latter value was 1.5 times the former (3000 other wavelengths (principally 366 and 436 mp) were us. 2000 M - I ) . . The third unit is therefore easier to add used. Corrections for deviation from Beer’s Law were than the second, indicating a second nearest neighbor efata gathered from spectral studies performed fect. with a Gary 14 spectrophotometer. U!tracentrifuge. cells Recently a series of lay Mukerjee and Ghosh varying in thickness from 3 to 0.004 cm were used. Aicast new light on the problem. They pointed out that thnugh double sector cell operation o f the scanner was most methods of studying the dye reaction involved the possible for the larger celi sizes, for the smaller single secdetermination of an additional parameter, e.g., for absorption spectrophotometry the molar extinction coeffiP. Mukerjee and A. K. Ghcsh. .I, Amer. Cheni. S ~ C . 9, 2 , 6433 (1 9 7 0 ) , cient for each species, as well as the equilibrium constant A, K . Ghosh and P. Mukerjee, J. Amer. Chem. Soc., 92, 6408 for each association step. Therefore they developed an (1970). A. K . Ghcsh and P. Vukerjee, J. Amer. Chem. Soc.. 92, 64.13 equilibrium method which they called the “isoextraction (1970). technique .” This techrrique is essentially a sensitive way A. K . Ghosh, J. Amer. Chem. SOC.,92,6415 (1970) of determining the monomer concentration as EL function P. Viukerjee and A. K . Ghosh, J , Amer. Chem. SOC., 9 2 , 6419 (1970). of the total dye concentration by means o f the extractabilE. 1.Adams, Jr., and H. Fujita, “Ultracentriftigal Analysis in Theory ity of the moriomeric dye--salt into an organic phase. By and Experimen1,”Academic Press, New York N Y , , 1963. p 119. E. T. Adams, .!I., Proc. Nat. Acad. Sci. U.S . , 51 (31, 509 (1964) means of i t they miere able to show that the aggregation of E. T Adams, Jr., and J. W. Williams, J. A m e r . Chem. Soc., 86, Methylene Blue goes a t least as far as the pentamer stage 3454 (1964). anci in agreement with Braswell16 have found that the E. T. Adams, Jr., and D. L. Filmer. Biochem!s:ry, 5, 2971 (1966). E. T. Adams, Jr., Biochemistry. 6 , 1864 (1967) equilibrium constant associated with the addition of the K . E. van Holde and G . P.Rossetti, Biochemis:ry. 6 , 2189 (1967) third dye unit !,s about 1.5 times greater than that for the M. Derechin, Biochemistry, 3, 3253 (1968). dimerization step. They Fxther show that as the associa0.E. Roark and D. A . Yphantis, Ann. N . Y Acad. Sci., 164, 245 (1969). tion proceeds beyond trimerization the equilibrium conK . E. var Holde, G. P, Rossetti, and F?. D. Dyson, Ann. N. Y. stants gradually decrease. The well-known increase of dye Acad. Sci., 164, 279 (1969) N R. Langerman and I . M. Kiotz, Biochemistry, 8, 4746 ( 1969), aggregation caused by the presence of salt was felt by P. J. Trotter a i d D. A. Yphantis, d. Phys. Chem., 74: 1399 (1970). these authors to be in “rough accord with that expected R. Bonneau, 2 . Faure. and J. Joussot-Dubie?, Taianta, 14, 121 from changes in activity coefficients” and that there is (1967). The Journal of Physical Chemistry, Vol. 76, No. 26, 1972
Emory H. Braswell
402
the molecular weight were obtained a t a given dye concentration regardless of speed, it was felt that the effect of pressure on aggregation, due to a change in the partiai molar volume of the dye upon aggregation, could be ignored. Specific volumes were determined picnometrically on aqueous Methylene Blue solutions ranging from 5 x M to approximate saturation (ea. 0.06 M ) . The values of over this concentration range were found to be from 0.762 to 0.745. Unfortunately it was not possible with this technique to measure specific volumes a t lower concentrations.
Log
c,.
Figure 1. Apparent weight average molecular weight of Methylene
Blue as a function of concentration. Thickened lines represent continuous data over 3 range of concentration; points represent discrete data. Upper lirie represents data obtained in the presence of NaCl (NaCI:tfye ratio = 200/1 to 77/1); lower line represents data obtained in the absence of NaCI.
tor cells, solvent ba.lancing was performed by centrifuging the solution cell with an identical cell containing solvent. The smallest (:el: (ea. 0.604 cm) was formed by simply placing a red polyth.ene gasket between two sapphire windows and tightening the cell to an average torque of 140 in. Ib. The sample or solvent was measured out with a microsyringe on the window before assembling the cell. Since the thickness of the cell was amazingly reproducible (10%) the solution column which formed as soon as the centrifuge was rotating a t a few thousand rpm was approximately the d.esired height. With solution columns of 3-mm centrifugation. a t 48 or 56 krpni for 6 hr was enough to obtain practical equilibrium. For solution columns of 6 mm 24 hr of sedimentation was required. At low dye concentration the concentration gradient formed was small (1.2-2.0) and generally a plot of In concentration us. X2 yielded a lin'e with little or no curvature. I t was found necessary to include 0.5% sucrose in solutions of low dyeplus-salt concentration (c0.01 M ] in order to provide a density gradient large enough to stabilize the system and eliminate turbulance. Spectral studies indicated that this concentration o f suc!:ose had no effect on the aggregation of the dye a t low concentration. At high dye concentration or in the presence of NaC1 considerably Larger gradients were formed, the largest having a concentration ratio of almost fourfold. The results obtained from these studies are shown in Figure 1. The data from each single experiment a t low dye concentration or short column height or both are shown as single points. At high dye concentration with long columns the data are shown as a thickened line over the concentration range of the experiment. The graph of the effect of NaCl on the molecular weight of the dye ends a t a dye concenM due toathe insolubility of trat,ion of abotit 1.2 x the dye a t a NaCI concentration of 0.1 M.Since the molecular weights obtained were found to be approximately a t a maximum when the salt concentration is about 100 times the dye concentration, the concentration of salt included in a n experiment, is from 77 to 200 times that of the dye concentration used. The effect of pressure was determined by making equilibrium runs a t different speeds. Since the same values for The Journal of Physical C!iemistry, Yo!. 76, No. 26, 1972
Discussion Although it is not yet possible to assign a unique model to the aggregation of Methylene Blue, the data presented in the figure considerably reduce the number of possibilities. At low dye concentration it can be seen that the weight average molecular weight of the dye in the absence of salt is ca. 260 a t a dye concentration of 10-5 M.If every dye molecule had one charge on it under these conditions it would yield an apparent molecular weight of 3 2 0 / ( 2 i. I) or 160. An apparent molecular weight of 260 indicates that the dye is only ionized ea. 6070 under these conditions. In the presence of salt the molecular weight a t this concentration rises to ea. 330, using = 0.75. It is known by spectrophotometry studies that there is no significant aggregation a t this dye concentration.16 Since there is no detectable change in spectrum upon addition of 0.002 M NaCl (NaC1 t'o dye concentration ratio 200:1)43 indicating that this ].eve1 of salt does not cause aggregation, it seems reasonable to conclude that the addition of this quantity of NaCl suppresses the ionization of the dye. If the dye is assumed to be a t low concentration (monomeric, concentration-dependent berms omitted, and p = 1) and to be singly charged, the following relation should (R'P/w2rG,,,)(dCoo/dr) = M D ~ , ( I VDc!,
- 1/2MNac1(1 _- VNac,)
vDe,
where MDclarid MNaeIare the formula weights and and V,,,, are the specific volumes of the dye chloride and salt, 'respectively. The left-hand term is experimentally determined and the symbols have the usua! meanings. According to the definition of components used, the iefthand side of the equation is identical with M1(4- y.,), where M,\ is the apparent molecular weight, = (UDc, - l/aUNaC1)/MA,and U represents the respective molar volumes. Performing this caiculation yields predicted M values of 291 for Mzi and 0.79 for V.\. The data a t yielded respective values of 314 and 0.74. Since the observed molecul.ar weight is close to that, expected when no charge is present (320) it is reasonable to treat data a t higher concentrations as un-ionized also, therefore VDc, (0.75) was used for all calculations. This results: a t a dye M , in the value for iW,\of 330 (inconcentration of stead of 314) which was mentioned previously. The fact that the dye is not charged at high salt to dye concentration ratios simplifies the theoretical treatment considerably since one does not have to apply polyelectrolyte theory to the results. If one assumes that the dye in the presence of a high salt to dye concentration ratio is un-ionized throughout the dye concentration range and that the dye can undergo
vA
(43) Data to be published In the future. (44) C. Tanfcrd. "Physical Chemistry of Macromolecules. York, N. Y . . 1961, pp267-269.
'
Wiley, New
B condensation type of infinite polymerization wherein each dye molecule contributes two aggregation sites, one can write the following splations
n(dyej Ft (dye),
or 2js1tes) Fi bond
K = [bonds]/[sitesI2
and
P = reactec §ltes/tQ&alsjtes = [bonds]/C, where P IS the probability of a site havipg reacted (the degree of reaction) and C. is the original dye concentration in molesjiiter o i dye monomer units. I t then follows that
est concentration used in this study, and since the effect of this amount of salt on the polymerization as observed by ~ p e c t r o ~ h o t Q m e t(as r y will be shown in a future publication43) is equivalent to increasing the dye concentration by a t most 30% it is ciear that the latter cause is more important. Therefore it is clearly t h e effect of charge QE the dye molecules which suppresses the observed molecular weights. That this effect is iaot enormous though can be seen in the only 60% ionization observed in hf dye solutions in the absence of salt. It might be expected that this degree of dissociation would decrease as the molecule growst SO that a t high degrees of polymerization one would expect QE rhe average there to bme Less than one charge for every two subunits in the chain. The maxinziini weight average d e c u l . a . r weight found in the absence of salt is approximately 1450, This is lower than the true uncharged molecular weight by a factor which could be estimated from the following equation. PLL4 = n M 1 / ( Z 4- 1) = nM1/(na 1) where Z is the charge per chain, n is the number of monomers in $he aggregate, M I the moiecuirar weight of the uncharged monomer, oi the degree of ionization, and M A the apparent molec~dar weigh.t. It can be shown from the equation that the maximum value that CY can have for MA = 1450 when the molecules are of infinite size ( n = m ) is 0.22. If we assume that the value of a is 0, then the maximum value of the true molecular weight woiild be 11650 (01: n 4.5). More insight can be achieved if one felt confident that the equilibrium constanr obtained a t high salt and OW dye c:oncentration applied also a t high dye and low salt concentrations. The limit.ed justification for this has already been presented as resting on the fact that the highest concer?trati.cns of NaCk used for these stcdies insia by an amounu equivalent to that if the dye concent,sation had been increased by a maximum. of only 30%' Pbirthei. the fair agreement between the PT found in salt uio, sedimentation M-' for dimerization) with that found S Of S ~ e c t r o ~ h Q t Q (%co ~ ~ t r k-') y iendS stronger credence to this belief. Use of the value (600 M - I ) f~0;ulCiIzere for K (for a condensa$iorz-type polymerization) leads to a. waBue of 0.913 for P~ This means that a t this c o n c e ~ ~ the ~ a dye ~ ~has ~ na weight average *molecular weight of 7037. Since the apparent weight a.verage moiecular weight is 1.450, one can conclcdc that there is, on the average, about 3.85 charges ((7037/14580) - 1) for every 22 dye units (7037/320) or an average ionization of about 0.18. Because of the small reaction-pmmoting effect of the salt one rfius~,regard these calculated values of the molecular weight and the extent of ionization as a bit h.igh. TWO concltlsions can therefore be arrived a t from the data taken without the presence of salt. Fir& is that the degree of ionization decreases from 60% ai low dye concentrations to a value close to 18% a t high concermatlon. The j ~ nis that, there are aggregates present a t high dye concentrations that are most certainly far iarger thani pentamer in sine. This then pros7ides some justificai;~~~ at tion for applying ;an ihfinite p o ~ y n ~ e r i z amcchanjsm low dye concc12tration, and does not rule out the possibiiity of s01mi.e larger limiting a'ggrega.tion number such as might be expzcted in the case of micelle formation. This cannot be determined until stud.ies car! be made in the presence of high concentrations of a salt, which does not cause precipitation and preferably d w ~not l affect the de-
-+
and
where M , i s the observed weight average molecular weight is the molecular weight of the un-ionized monomer kind (320). It was found that eq 1 and 2 fitted the experimental data obtained from experiments performed in the presence of high salt to dye concentration ratios when K was approximately equal to 600 M - I . This value is equivalent t~ a dimerization constant of 2400 - - l In ~ an earlier pubiication,l$ by assuming a stepwise aggregation, an equilibrium constant of dimerization of 2000 M - l and that of the next step (dime.r to trimer) of 3000 211-* were found in the absence of salt. The ecguivalent value of 2400 found in the current study may be partiaily reflecting the value of the equilibrium constant of the dimer-trimer step, or it may be higher than the dimerization constant because of the smali reaction-promoting effect of salt a t the higher dye and salt conceritrations (see below) An observation of interest is that the weight average mo!ecular weight obtained i 3 the presence of salt attains a M. value of 640 a t a dye concentration of ca. 3.4 x This should correspond to a number average molecular weight of 480 and a degree o f polymerization of 0.333 for the assumed aggregation model and equilibrium constants. I t can be shown that, for an infinite condensation type of aggregation, a t a degree of polymerization of 0.333 the concentration of dimer is a t a maximum. We have J ~ in this region of dye concentration, previously S ~ Q X that the abscrption peak is a t its a n a x i m ~ m . ~Sicce 6 this peak has t r a d i t b n d y been associated with the absorption of the dimer it i s felt that this is further indicative evid e m e that the foregoing conclus;ons regarding aggregation mechanism are not, in great eTror. In fact this observation provides support for thc identification of the 3/' band with dye dimers. In the srtuation where salt was absent, the apparent molecular weights are lower than those determined in the presence of salt a t all dye concentrations where comparisor!. was possible. 'The increasing divergence of the data taken in the preserice of salt from that in the absence of salt may be due to either or both of two factors. Either the NaGi strongly increases the degree of polymerization, or an increasingiy larger charge per moiecule developing on the aggregated dye in the absence of salt, reduces the observed mQlec\nlar weight. Since 0.1 M salt was the high~
The Journei of Physical Chemistry Voi 76, No. 26, 1972
Michel bucas
4030
g e e of polymerization of the dye. Such studies are now in progress. No treatment of nonideality effects a t high dye and low salt concentration has been attempted in this study, for not enough is known about the charged nature of the dye. Our current investigations a t high salt concentration should help elucidate this situation. However, it was felt that nonideaiity could be ignored in the case of dye conM in the presence of salt. The centrations below 1 x excellent agreement of the simple aggregation model with
the data bears out this contention.
Acknowledgments. The author is indebted to Professor Geoffrey A. Gilbert of The University, Birmingham, U. K., for his hospitality and help while the author was there on sabbatical, and also for his interesting suggestion that this charged aggregating system has striking similarities with that of the starch-(Is-), complex. Credit is also due to Jeffrey Lary for his expert technical work in obtaining the data a t the University of Connecticut.
f a !Hard-Sphere Solute on Water Structure Michel Lucas DBpartement de Genie Radioactif, 92260 Fontenay-aux-Hoses, France
(Received April 10, 7972)
Publication costs assisted by the Commissariat a l'Energie Atomique
Equations were derived by Pierotti yielding the thermodynamic properties of solutions of a hard-sphere solute in water a t infinite dilution. A possible interpretation of these equations is that a hard-sphere solute enhances the bonds between water molecules a t temperatures below 4" and lessens these bonds at higher temperatures. Such a solute also increases the water temperature of maximum density. Calculated thermodynamic properties of hard-sphere solutes in water are very similar to those of real nonpolar gasel; with the same size. It follows then that the experimental entropies of solution, increase in the water temperature of maximum density by a solute, heat capacity changes, and solute molal volume in water, cannot be taken as evidences for water structure promotion by nonpolar solutes a t temperatures higher than 4". Finally some measurements of the enthalpies of transfer of tetraalkylammonium bromzdt?s from H28 to I D 2 0 a t 51" suggest that these cations also enhance the water structure a t low temperature and lessen it a t higher temperatures.
T i e solubility of nonpolar gases in water is the subject of considerable interest since a difference exists between the solubility of gaE,es in water and in organic so1vents.l This difference is manifest in the large negative heats, negai ive entropiei,, and positive molal heat capacities of solution of gases inlo water.2 Frank and Evans3 ascribed this difference to the formation of an ordered, more hydrogen bonded than pure water, structure around the solute. In grder to account for this effect, Nemethyl and Scheraga4 developed a statistical thermodynamic theory of water. Howevea. this model has been criticized, since the difference in density between the water cluster molec u b s and other water molecules assumed in the model is not in agreement with results of small angle X-ray scatt e r i ~ ~ On g . ~the other hand, the solubility of gases in water was treated with very good success by Pierotti.2 He has divided the process of solution of nonpolar gas in water into two steps. First a cavity has to be made in the solvent to accornodate the solute particle. Its diameter is exactly the hard-sphere diameter of the gas particle. The scaleld particle theory allows the computation of the free energy involved in this step. The second step is t o considPr the interaction5 of the solute with the solvent molecules The Journal of Physical Chemistry, Vol. 76, No. 26, 7972
through dispersion forces. The first step only needs t o be considered if the solute is a hard sphere not interacting with the solvent. From the thermodynamic equations computed by Pierotti, the possible influence of a hardsphere solute on the water structure may be derived. The comparison between the thermodynamic properties of real nonpolar solutes and of hard-sphere solutes of the same size may help to determine which thermodynamic properties yield evidence for water structure promotion by the real solute. First let us consider some equations of interest for the discussion. From ref 2 , the internal energy change on dissolving 1mol of a hard-sphere solute a t infinite dilution is AU-aRP[f(y)
+ 11
(1)
where CY is the thermal expansion coefficient of water a t constant pressure and f(y) a function of the solvent and (1) ( a ) D. D. Eley, Trans. Farada)/Soc., 35, 1281 (1939); (b) ibid., 35, ,1242 (1939). (2) R. A . Pierotti, J. Phys. Chem., 69, 281 (1955). (3) H. S. Frank and M.W. Evans, J. Chem, Phys.. 13,507 (1945). (4) G. Nemethy and H. A . Scheraga, J. Chem. Phys., 36, 3382, 3401 (1962). ( 5 ) A . H. Narten and H. A. Levy, Science, 165,447 (1969).
