ALFREDHOLTZER AND MARILYN F. EMERSON
26
n the Utility of the Concept of Water Structure in the Rationalization
of the Properties of Aqueous Solutions of Proteins and Small Molecules1
by Alfred Holtzer and Marilyn F. Emerson Department of Chemistry, Washington Unhersity, St. Louis, Missouri 68180
(Received March ?I 1068)
It is demonstrated for several cases chosen from the literature that arguments based upon the concept of water structure are sufficiently ambiguous so that the change, in a given physical property, that accompanies dissolution of a solute in watcr can always be “explained,” whether that change is positive or negative. The number of examples and the range of physical properties discussed are sufficiently great to arouse suspicion that such arguments are almost always equivocal and that, therefore, rationalizations of most) experimental data on this basis are devoid of content.
Introduction I n 1945, Frank and Evans2 postulated the formation of hydrogen-bonded, quasi-crystalline structures of water molecules around isolated, nonpolar molecules in aqueous solution. This hypothesis, they argued, suc0) and cessfully explains the unusual enthalpy ( A H entropy ( A S < 0) effects associated with the transfer of a nonpolar solute from a hydrocarbon environment (at some low solute mole fraction) to water (at the same low solute mole fraction). They termed these regions of greater crystallinity “icebergs,” but emphasized that the structure of these icebergs need not be the same as that in ordinary ice nor the same for all icebergs. It has been suggested3 that the volume changes accompanying such solute transfer provide evidence that the icebergs are indeed quite different in structure from ordinary ice. The transfer of nonpolar substances from hydrocarbons t o water at 25” is accompanied by a decrease in volume, whereas the formation of ordinary ice from water results in a volume increase. All these enthalpy, entropy, and volume effects become less extraordinary as the temperature is increased. Thus, at temperatures above SO”, hydrocarbons in water begin to behave more like hydrocarbons in nonpolar solvents. Frank and Evans attributed this to the melting of the icelilie structures with increasing temperature. The particular relevance of the Frank-Evans idea to protein and polypeptide chemistry has been clearly pointed out by I i a ~ z m a n n . ~Kauzmann recognized not only that the tendency of nonpolar side chains to adhere to one another in aqueous solution (ie., the formation of hydrophobic bonds) should be an important factor in the stabilization of particular conformations of polypeptide chains but also that the molecular events in the process could be specified in much more detail by using the Frank-Evans approach. On this basis, he concluded that formation of hydrophobic bonds in proteins is attended by the melting of icebergs The Journal of Phgsical Chemistry
and therefore that these bonds are stabilized by solvent entropy effects, since the transfer of a nonpolar group from water to the (nonpolar) interior of the protein molecule should show AG < 0, though it is endothermic (AH > 0). As evidence has accumulated that hydrophobic interactions do, indeed, contribute appreciably to the maintenance of the native conformation of a protein Inolecule,4--6 interest in the molecular rationalization of these interactions on the basis of solvent structural effects has, of course, also increased.’ This interest is understandable, since even a rough, strictly qualitative, picture of the molecular events involved would be quite helpful in dealing with a variety of problems of protein chemistry. For example, it would be extremely useful in predicting the influence of a particular additive upon a protein in solution. There is convincing evidence that many protein denaturants owe their action, a t least in large part, to hydrophobic eff e ~ t s . ~ ,With * an unequivocal picture of the underlying molecular processes, it would be possible to deduce from the physical properties of aqueous solutions of a given additive whether solvent structure has been broken or formed. Knowledge oi the effects upon proteins of substances of lcnozon influence on water structure could then lead to an estimate of the efficacy of the additive as a denaturant and, perhaps in some cases, to a rough idea of what portions of the protein molecule it might affect most. (1) This investigation was supported by Research Grant RG-5488 from the Division of General Medical Sciences, Public Health Service. (2) H. S. Frank and M. W. Evans, J . Chern. Phys., 13, 507 (1945). (3) W. Kauzmann, Advan. Protein Chem., 14, 1 (1959). (4) C. Tanford, J. D . Hauenstein, and D. B. Rands, J . Amer. Chem. Soc., 77, 6409 (1955). (5) J. C. Kendrew, G. Bodo, H. M. Dintzis, R. G. Parrish, H. Wykhoff, and D . C. Phillips, Nature, 181, 662 (1958). (6) C . Tanford, J , Amer. Chem. Soc,, 84, 4240 (1962). (7) G. Nemethy and H. A. Scheraga, J . Phys. Chem., 66, 1773 (1962). (8) D. F. Waugh, Adran. Protein Chem., 9, 325 (1954).
ON THE UTILITYOF
THE
CONCEPT OF WATERSTRUCTURE
This is an obviously desirable goal, and the present tone of the literature suggests that great progress toward its attainment is being made. Recent publications on protein solutions, or on the physical properties of aqueous solutions of small molecules, often contain numerous (usually rather positive) statements about the role of water structure. Unfortunately, the qualitative arguments put forward by different authors often have led to quite contradictory conclusions; indeed, in many cases, even a single given argument is sufficiently indeterminate as to be capable of producing several, contradictory conclusions. It is our contention that, in fact, the position has been little advanced since the work of Frank and Evans2 and Kauzmann3 and that the widespread practice of invoking changes in water structure to rationalize experimental data can only serve to perpetuate the illusion that some real understanding exists. The illusion is soon dispelled when prediction, rather than rationalization, is attempted. It is our view that one cannot, in general, examine the bulk physical properties of an aqueous solution of a nonelectrolyte and determine unambiguously whether the solute is “structure forming” or “structure breaking” (if, indeed, the terms mean anything definite at all). If this is true, then a large number of authors have been led into error. By examining in detail a few rather typical statements from the literature, i t will be shown how easy it is to be misled, apparently by the pictorial simplicity of the iceberg model, into drawing an unwarranted conclusion. The reader, of course, may feel that the particular statements selected are atypical; we urge, therefore, that he search the recent literature for more. Careful examination along the lines suggested below will reveal, we are confident, one or more characteristic errors: (1) the particular physical properties to be interpreted are selected so that a self-consistent physical picture emerges; i e . , “bothersome” facts are ignored, or ( 2 ) a given physical property is interpreted sufficiently superficially, usually by improper or arbitrary subtraction of structure-independent factors, so that the answer becomes determinate (but its accuracy indeterminate), or (3) words suggesting quantitation (e.g., “appreciable”) are used to describe an effect (in spite of the absence of any proper quantitative evaluation) and then are taken literally. Before we proceed, a word is in order about those parts of the iceberg idea that we consider acceptable, a t least for the sake of argument. I n brief, we agree that the correct interpretation of enthalpies and entropies of transfer of simple, nonpolar substances from hydrocarbons to water is that icebergs form, in the Frank-Evans sense, about the nonpolar materials in the aqueous environment. However, it should be emphasized that this is an interpretation of, not a rigorous deduction fsom, the data. Indeed, the idea only follows from the experimental observations if it is assumed that, in
27
water, the effects of solvent rearrangement dominate the enthalpies and entropies. There are numerous other molecular contributions, of course, but they are assumed t o be less important. It must be recognized, however, that domination of the enthalpy and entropy by a particular interaction does not necessarily mean that it dominates some other, arbitrarily chosen, property. Let us now consider some of the ideas that have emerged from the original proposal.
The Properties of D209 The interpretation of bulk properties in terms of the “flickering-cluster” concept has led t o the inference that D20 is more highly structured than H 2 0 at the same temperature.‘O No conclusion in the field would appear to be more strongly supported by the facts: the temperature of maximum density, the freezing and boiling point, the enthalpy and entropy of vaporization, and, perhaps most striking of all, the viscosity of D20 are all higher than the corresponding values for H20. I n some cases, the differences are small (e.y., 4% in the case of the entropy of vaporization), in some large (25% in the case of viscosity), but all are in the direction indicating a greater structure for D2O. However, there is always one omission in this context, the dielectric constant. The omission is startling, because the large dielectric constant, of H 2 0 is customarily, and very convincingly, cited as evidence for the existence of extensive regions of cooperative structure in this 1iq~id.ll-l~I n an electric field, these regions can be polarized (by a mechanism that has not yet been clarified) so that a relatively large dipole moment is induced in the field direction.l4,l5 Now let us consider, rather superficially, what should happen to the dielectric constant when D2O is substituted for H20. The molecular dipole moments in the gas phase of H20and D20are identical;lB the electronic polarizability of the DzO molecule is a bit greater (by about 5 % ) ; and the geometry and spacings of the molecular arrangements in the solid phases are virtually identical. The picture we have, then, is that in each (9) The authors are grateful to Professor Walter Kauzmann for his counsel; before we had his advice this section was considerably less cogent than the reader finds it. Needless to say, any guilt that remains is our own. (10) For a summary of the relevant properties of Ha0 and Da0, see G. Nemethy and H . A. Scheraga, J . Chem. Phys., 41, 680 (1964). (11) W. M.Latimer and W. H. Rodebush, J . Amer. Chem. Soc., 42, 1419 (1920). (12) J. Edsall and J. Wyman, “Biophysical Chemistry,” Academic Press, New York, N. Y., 1958, Chapter 2. (13) L. Pauling, “The Nature of the Chemical Bond,” Cornel1 University Press, Ithaca, N. Y., 1960, Chapter 12. (14) C. P. Smyth, “Dielectric Behavior and Structure,” McGrawHill Book Co., Inc., New York, N. Y., 1955. (15) J. L. Kavanau, ’Water and Water-Solute Interactions,” Holden-Day Inc., San Francisco, Calif., 1964. (16) For a summary of the relevant properties of HzO and DaO, see I. Kirshenbaum, “Physical Properties and Analysis of Heavy Water,” McGraw-Hill Book Co., Inc., New York, N. Y., 1951, and ref 10. Volume 73, Number 1 January 1969
28 liquid there are clusters that are identical in geometric arrangement of their constituent molecules; the only difference in the clusters themselves is that the DzO clusters contain molecules of slightly greater electronic polarizability, which would give them a higher moment in the applied field and lead to a slightly higher dielectric constant for DzO. This effect, however, should be minor-the contribution of electronic distortion to the dielectric constant of water is supposedly small. What is not minor is that the conventional interpretation of the other physical properties insists that in DzO there be more such clusters or that their average size be greater or both. I n either case we would predict that the polarization of these regions, as described above, would lead to a higher dielectric constant for DZO. The experimental result, however, is just the rev e r ~ e . ’ ~The , ~ ~difference, as in many other properties, is very small, but the dielectric constant of DzO is distinctly lower than that of HzO over the entire normal liquid range. Understandably reluctant to give up our earlier, seemingly well-buttressed conclusion that DzO is the more structured liquid, we simply assume that we cannot perform such a superficial analysis of the dielectric constant and expect to be able to make a valid prediction, even a qualitative one. How, then, can we look a t the question? A clue to the problem of the effect of structure in the liquid is available from measurements of the dielectric constants of DzO ice and HzO ice.lg I n the solid form, both substances are essentially completely structured. The experimental finding is that heavy ice has a slightly lower (-2%) dielectric constant. The superficial analysis (as in the previous paragraph), when applied to ice, would predict that the two should be the same. The temptation is strong to call 2% “small” and to hail the agreement between theory and experiment as a kind of triumph of superficiality. However, having eschewed the superficial view because of its failure to yield the correct answer for the liquid, we must rather admit that a difference of 2% means that some other structure-independent effect must contribute to the dielectric constant in such a manner as t o reduce the DzOvalue relative to HzO. What this effect is cannot be specified a t present. However, since the dipole moment of the water molecule in the condensed phase can be considerably larger than that of the isolated molecule (by a factor of about 2 in ice20) and since this increase may very well be sensitive to effects essentially quantum mechanical in nature, such as the amplitudes of zero point motions, it may account for the difference in the two ices. In any event, admitting that such a structure-independent effect is present can serve to remove the liquid anomaly. The important factors are the molecular dipole moment in the liquid and the angular correlation between dipoles.21t22 Since the more structured liquid The Journal of Physical Chemistry
ALFREDHOLTZER AND MARILYK F. EYERSON (presumably DzO) has improved dipole-dipole correlation, its dielectric constant would be increased relative to HzO. However, the structure-independent factor described above (be it the condensed-phase value of the dipole moment or whatever) acts in the opposite direction. Thus the assumption that DzO has more structure than HzO does not lead to a clear prediction of the relative dielectric constants, since it is not known, a priori, which effect, the amount of iceberg or the structure-independent factor, dominates. This resort to nonsuperficiality thus neutralizes the dielectric constant “anomaly.” Unfortunately, nonsuperficiality, once invoked, has insidious effects. The gnawing fear grows that perhaps there are opposing effects that contribute to the other physical properties of HzO and DzO, thus precluding any firm, a priori, prediction of the relative amounts of clusters in the two liquids. A closer look a t the viscosity, for example, confirms this idea. It is natural that suspicion should first fall on the viscosity. The realization that the dielectric constant changes are rather subtle, on a molecular level, and not susceptible t o simple, qualitative arguments immediately directs ones troubled gaze to the viscosity; hydrodynamic problems are notoriously refractory to intuitive analysis. One might begin by inquiring what the ratio of the viscosities (of HzO and D20) would be in the normal course of events, that is, if they were “simple” fluids without spec$fic structure or bothersome intramolecular degrees of freedom. The quantitative theory of viscosity of simple fluids is certainly not at a stage near perfection, but it does seem clear that, ignoring quantum effects, which are probably small for water near room temperature, several factors contribute :23 (a) differences in the molecular masses, (b) differences in moment of inertia, and (c) differences in intermolecular potential. Since the viscosity varies as the square root of the mass, factor a alone accounts for a difference somewhat over 5% out of the 25% total observed. The second factor (b) is rather more difficult to estimate, but since all three of the principal moments of inertia of D20 are about double the corresponding ones for water, an additional 1 or 2% is certainly to be exp e ~ t e d . Finally, ~~ the effects of differences in inter(17) J. Wyman and E. N. Ingalls, J . Amer. Chem. SOC.,60, 1184 (1938). (18) G. A. Vidulich, D. F. Evans, and R. L. Kay, J . Phys. Chem., 71, 656 (1967). (19) R. P. Auty and R. H. Cole, J . Chem. Phys., 20, 1309 (1952). (20) L. Onsager and M. Dupuis in “Electrolytes,” B. Pesce, Ed., Pergamon Press Ltd., New York, N. Y., 1962, p 27. (21) J. G. Kirkwood, J . Chem. Phys., 7, 911 (1939). (22) H. Frohlich, “Theory of Dielectrics,” 2nd ed, Oxford University Press, London, 1958, p 49. (23) S. A. Rice, J. P. Boon, and H. T. Davis in “Simple Dense Fluids,” H. Frisch and Z. Salsburg, Ed., Academic Press, New l-ork, N. Y., 1968.
29
O N THE UTILITY O F THE CONCEPT O F WATER STRUCTURE
molecular potential must be accounted for. Since the Lennard-Jones parameters for DzO have not been determined, we must rely on analogy: in the case of CH,-CD,, this factor augments the viscosity of the isotopic species by another 1% or Consequently, considering only factors not related to the specific structure of the liquid, more than one-third of the observed difference can be explained. In fact, the theory is sufficiently inexact23that one cannot say for sure that these factors do not account for all the difference. Even if me assume that the remaining (- 150j0) difference is real, however, it surely is explainable if all hydrogen bonds (not only the nice linear ones found in ice and textbooks) formed by DzO are simply slightly stronger than their H 2 0 counterparts, i.e., if DzO molecules are slightly stickier. This specific interaction is not included in factor c, which was derived only for intermoleecular potentials characteristic of simple fluids. I n any event, the augmented “stickiness” of DzO obviously is not necessarily productive of clusters in the Frank-Wen sense, arid the viscosity difference seems clearly explainable without their presence. As far as we know, a continuum model would produce a viscosity increase that is enough to make up the remaining difference between the results of simple fluid theory and experiment, if there is, in reality, such a difference, Indeed, the hydrodynamic effect of Franl-Wen clusters is moot. Their influence on the viscosity mould depend not only on their volume fraction but also on their ability to act, in part, as obstacles more or less penetrable by (nonhydrogeri bonded) “solvent.” One could envision such clusters in DzO being more rigid than those in HzO, and thus remaining relatively impenetrable, while the HzO clusters are hydrodynamically more penetrable by “solvent.” It is a well-known result of the theory of viscosity that such partially penet,rable obstacles can produce a higher viscosity than impenetrable ones. Thus it is conceivable that an increase in (Frank-Wen-type) structure might decrease the viscosity if it is accompanied by a decrease in penetrability of the clusters sufficient to off set their lesser volume concentration. Thus a superficial consideration of the physical properties of HzO and DzO leads to satisfactory explanations of all of them in terms of the relative amounts of clusters in the two liquids; all, that is, except the dielectric constant. I n order to account for the experimental dielectric properties, a more penetrating analysis has to be made, the result being that an experimental result in either direction can be ‘(explained” but no prediction made. However, when a similar, but still qualitative, analysis of other properties is attempted, the result is often that either experimental result can be rationalized. The existence of more clusters in DzO, for example, does not necessarily require a higher viscosity. We wish to make it perfectly clear that we believe that DzO is more sti~.~ctured than H20, although not necessarily in the Frank-Wen sense. We merely wish to
emphasize that even in this simplest, best established case, qualitative arguments based on the flickeringcluster concept are not unambiguous.
The Relationship of Icebergs to Ice9 As a second example, we might quote an argument that was mentioned above concerning the nature of the icebergs, as revealed by volume changesS3 This argument on the volume change accompanying transfer of a nonpolar molecule from a hydrocarbon to water (a volume change which is negative) makes the tacit assumption that the formation of the iceberg dominates the volume change (as i t does the enthalpy and entropy); since the sign of the experimental volume change, and thus the sign of the volume change on iceberg formation, is opposite to that for the formation of (real) ice from liquid water, it is concluded that the icebergs do not have a true icelike structure. However, a different interpretation i s possible. It is often suggested that nonpolar solutes dissolve interstitially in water, a t least so far as they are able, i.e., so as to break as few normal water-water hydrogen bonds as possible. If this were the only factor involved, a negative volume change on transfer of the nonpolar molecule from a hydrocarbon to water would result. If, in addition, however, some truly icelilte structure formed about the solute in water, this would tend t o make the volume change positive. The observed, negative volume change could then result by domination of the former effect over the latter. Since there is a t present no way of assessing the relative contributions of these two effects, the argument offered here, while it cannot refute the earlier one, would seem to be of equal force. It is also obvious that the lack of a quantitative measure of these individual effects makes any such argument indeterminate; not even the sign of the volume change follows uniquely from the idea of water structure. At this point, it is hard to avoid the impression that there is a strong semantic component to the disagreement between the two arguments. Nuch depends on the interpretation to be placed on the phrase “true icelike structure.” If we interpret this very strictly, i.e., if we require that dissolution of a nonpolar molecule in water be precisely like embedding the molecule in a single ice crystal, then the logic of the earlier argument (of ref 3) acquires strength but at the expense of content. It is true that small, nonpolar molecules are not very soluble in ice, which is rich in interstitial spaces. Therefore, such solutes evidently cannot fit into a single ice crystal without displacing some water molecules, an effect which should surely serve to increase the volume, contrary to the observation. Hence, that the iceberg is not a small, completely undistorted ice crystal seems indisputable, but, of course, it is rarely thought of in such literal terms anyway. On the other hand, if the strictness of interpretation is relaxed to allow some disVolume 78, Number 1 January 1969
ALFREDHOLTZER AND MARILYN I?. EMERSON tortion of the ice structure near the solute particle (a situation covered in the preceding paragraph by the phrase “so far as they are able”), then the argument of the last paragraph acquires relative force and the situation becomes ambiguous. How much freedom is to be alIowed in distorting the structure locally while still calling i t truly icelike? Obviously, this is a matter of taste rather than substance. It does, however, emphasize precisely the point we are trying to make, namely, how very difficult it is to use the flickering-cluster model in malting even qualitative deductions that are at once nontrivial and unambiguous. The model seems to become less distinct the more closely it is examined.
conclusion, unfortunately, is as irrelevant as i t is incontestable, because it contains no information about the nature of the structure formed when a urea molecule interacts with water. Perhaps urea molecules participate in the regular water clusters; perhaps a new type of cluster is formed; perhaps hydrogen bonding, while it exists, is less regular in the solution and there is a net cluster disruption. None of these possibilities is inconsistent with high solubility, which requires only that the net free energy of dissolution be strongly negative, a result that could be achieved by any of the molecular routes described. Since no one knows, or can estimate, the contribution to the free energy of these various molecular events, no one can decide which of the many molecular models is correct. I n fact, it may well be Influence of Solutes on Water Structure that different mechanisms are involved for different solutes. Sucrose is also very soluble in water, yet it Finally, we consider a recent paper that purports to delineate the changes in solvent structure that accomhas spectacularly less effect on proteins and on the hydrophobic bonds in micelles25~2~ than does urea. pany dissolution of urea in water.24 It goes without (a) Heat Capacity. The infinite-dilution partial saying that this problem is central to our interest in molal heat capacity of urea is “very close” to that of assessing the efficacy of protein denaturants. Furtherpure, solid urea, which, i t is argued, “shows that a simmore, the entire paper is devoted to a discussion of this ilar environment exists in the solid state and in aqueous one problem. The rcsult, however, far from being desolutions.” finitive or convincing, provides instead a multitude of The superficiality of this analysis can be seen by conexamples of the kind of reasoning we are examining. sidering the following statement, cooked up by ourWe do not wish to risk misstating the arguments in selves, which uses identical logic and, as the reader can questions, and we therefore suggest that the reader obreadily verify by consulting ref 24, almost identical tain a copy of the paper and examine each of the statewording. “The molal heat capacity of water (which is ments carefully as we proceed. Briefly stated, the supindicative of the environment of the water molecule in position is that hydrocarbons dissolve interstitially in the pure liquid) is of the order of 18 callmol deg, which aqueous solution-the more stable the interstices in a is far from that of the solid (-10 cal/mol deg). This particular aqueous solvent, the better solvent i t is for shows that a dissimilar environment exists in the solid hydrocarbons. I t is concluded that a urea molecule state and in the pure liquid. As it is known that in the can enter into the normal clusters of water molecules solid the water molecule is hydrogen bonded, this must without distorting them appreciably and that the not be true in the liquid. Thus, water is an unstruccluster is (with its interstices) slightly stabilized by its tured liquid.” presence, thus accounting for the hydrophobic bondThe fallacy is easy to spot: i t lies in using a vague breaking power of urea. Five physical properties of word like “dissimilar” and then acting as though i t aqueous urea solutions are cited in support of this conmeans “completely different from.” I n the statement tention. Let us examine the argument in each case. from ref 24 the word “similar” is used and then tacitly (1) Solubility. Since the argument here consists of converted to “exactly the same.” Even if the equality only two sentences, we can state it in full. “It is a wellof heat capacities zce1.e evidence that the environment of known fact that urea has an extremely high solubility a urea molecuIe is “similar” in the solid and in aqueous in water (about 20 m a t 25’). The ease of mixing urea solution, we must then ask: “Similar in what respect?” with water means that urea is able to compete with The question, alas, cannot be answered, since it is not water molecules for the hydrogen bonds.” This argupossible to take as given a particular molecular arrangement has not been well put, Clearly, the absolute magment in solution and show just how “similar” it has to nitude of the solubility can tell us nothing. Tetrabe to the solid in order to get heat capacities that agree methylurea (a liquid), for example, is miscible in all proto the correct degree of approximation. I n other portions with water; solid NIX’-dimethylurea (“which, no one knows how sensitive the heat capacity would not be able to enter into cluster f o r m a t i ~ n ” ~ ~ ) words, , for another, is as soluble as urea. The point is that urea is known to be strongly hydrogen bonded in the (24) M. Abu-Hamdiyyah, J . Phys. Chem., 69, 2720 (1965). solid state. It is thus reasonable to conclude, from its (25) M. F. Emerson, Ph.D. Thesis, Washington University, St. large solubility in water, that a strong, attractive ureaLouis, Mo., 1966. water interaction must exist-strong, that is, compared (26) M. F. Emerson and A. Holtzer, J . Phgs. Chem., 71, 3320 with the interaction of water with hydrocarbons. This (1967). The Journal of Physical Chemistry
ON THE UTILITYOF
THE
COSCEPTOF WATERSTRUCTURE
may be to postulated changes in the structure of the solution. More important, however, is the possibility that the agreement is fortuitous. We might just as well have suggested, for example, that this argument about the (constant-pressure) heat capacity (temperature derivative of the enthalpy) hold for the enthalpy as well; i.e., one could, with equal justice, argue that if the environments are similar, the enthalpies should be too. I n fact, of course, they are quite different, dissolution of urea in water being so spectacularly endothermic that the solvent often freezes when the process is carried out. Closer examination of all the heat capacity data confirms this suspicion; the agreement, in fact, exists only for room temperature. I n the same reference cited in ref 24 for these dataz7the reader’s attention is explicitly called to the slight variation of the heat capacity of solid urea with temperature compared with the pronounced temperature coefficient of the infinite dilution partial molal heat capacity of urea in water. The difference between the two is only about 15yoa t 25” (this is apparently the definitionin ref 24 of “very close”) but becomes about 100% a t 2 ” . The agreement a t room temperature is quite obviously fortuitous. One might add that i t is easy to find examples of other compounds for which the two heat capacities happen to agree at room temperature. For sucrose, for example, the agreement is, percentagewise, better than for urea.28 Yet, a molecule of molecular weight over 300 can scarcely be thought of as able to “enter” clusters of water molecules with “only slight” distortion. (3) Viscosity. The argument here is that an increase (decrease) in viscosity upon addition of solute to water indicates that the solute is structure forming (breaking) ; urea increases the viscosity of water slightly, confirming the notion of the structure forming tendency of this solute. This argument is inexcusably superficial; in fact, two of the references given in ref 24 refute it.293O If spherical particles (solute molecules) are inserted into a structureless solvent, the suspension will have a higher viscosity than that of the pure solvent because of the distortion of the solvent flow lines by the solute particles. A quantitative and definitive theory of this effect was first presented by Einstein31 who found that, a t infinite dilution
where 7 and 70 are the viscosities of the solution and solvent, respectively, c h is the concentration of the hydrodynamic solute particle, i.e., of the spheres (in grams per cubic centimeter of solution) ; and uh is the specific volume of the spheres (in cubic centimeter per gram). Thus a spherical particle, when introduced into a structureless solvent, would increase the viscosity, and such
31
an increase is therefore not necessarily an indication of any perturbation of solvent structure whatever. A more sophisticated analysis of the problem has been attempted,30but, we believe also without success. I n ref 30 deviations of the observed viscosity from Einstein behavior are interpreted in terms of the solvent structural effect; ie., a value of [77]/2.5uh that is greater than unity supposedly indicates the formation of solvent structure, and a value less than unity supposedly indicates the disruption of structure. I n spite of this refinement, however, analysis of the viscosity cannot yield the required information, as the following discussion will show. Clearly, several assumptions are involved here. I n using the Einstein formulation, it must be assumed that the solute molecule is spherical. Since the solute molecules in question are small and since the theory of the viscosity of ellipsoids demonstrates that the viscosity increment varies rather slowly with axial ratio for nearspheres, this assumption is probably not seriously in error. However, it is now necessary to insert a numerical value for 2)h, the specific volume of the spheres. For this, the reciprocal of the density of the pure solute is ~ s e d , ~beO it solid or liquid. The second assumption, then, is that a solute particle occupies the same volume in solution as it, does when pure; this is, in general, wrong, and one can only hope the effect is not large. Even accepting the assumptions, however, it can be shown that deviations from Einstein behavior can be caused by factors other than the formation or breakage of (cooperative) solvent structure, and therefore such deviations cannot be interpreted uniquely in terms of changes in such structure. Einstein’s theory applies to the kinetic unit in solution, and this may consist of more than just, a solute molecule. A less superficial use of the Einstein relation thus might be as follows. First we must note that if the hydrodynamic particle is solvated, then the quantity 7 s p / ~ his not experimentally accessible. The analogous quantity that can be measured is, of course, vSp/c, where c is the mass of dry solute contained in 1 ml of solution. If the kinetic unit is a solvated solute molecule binding w g of solvent/g of (dry) solute, then ch
=
c(1
+ w)
(2)
Furthermore, the specific volume of the kinetic unit is given by (27) E. J. Cohn and J. T. Edsall. “Proteins. Amino Acids and Peptides as Ions and Dipolar Ions,” Reinhold Publishing Corp., Kew York, N. Y., 1943, p 171. (28) Reference 27, p 169. (29) R. W. Gurney, “Ionic Processes in Solution,” McGraw-Hill Book Co., Inc., Kew York, N. Y., 1953, Chapter 9. (30) J. A. Rupley, J . Phys. C‘hem., 68, 2002 (1964). (31) A. Einstein, Ann. Phys., 19, 289 (1906); “Investigations o n the Theory of Brownian Movement,” Dover Publications, Inc., New York, K, Y . , 1956.
Volume 78, Number 1
January 1989
32
ALFREDHOLTZER AND MARILYN F. EMERSON
v+-
W
(3) where v is the volume of 1 g of dry solute part,icles and Pb is the density of bound solvent. Again, the experimentally accessible quantity is rather U, the increase in volume of solution upon addition of 1 g of dry solute. This quantity is g =
v
+
-
z>
(4)
i.e., fl represents the sum of the increase of the volume of solution due to the displacement of solvent by solute particles and the change in solvent volume suffered by bound solvent. Eliminating v between eq 3 and 4, we find 21+-
w
Using eq 2 and 5 in eq 1, we obtain
Since [V I and z? are operational quantities, eq 6 suggests [71/2.58 as the significant quantity, i.e., that 8 should have been used in ref 30 instead of the reciprocal of the density of pure solute. Unfortunately, this more complete interpretation is difficult to implement in any practical way that would allow conclusions to be drawn about water structure. Values of [~7]/2.%greater than unity could signify deviations from Einstein’s equation caused by a net structure formation in the surrounding solvent, since this would lead to an increased local solvent viscosity, in violation of one of the Einstein assumptions. However, since eq 6 shows that [~]/2.58is simply l (zo/Op,), it could also mean that the solute particle simply carries some solvent with it ( i e . , that t u > O), a situation quite distinct from the cooperative structure formation considered hitherto. I n fact, beyond the solvation layer, cooperative structure might be bolcen, the experimental observation reflecting both effects. The occurence of a value of [r]/Z.% that is greater than unity thus does not have a unique structural interpretation, because of the possibility of solvationeven if we assume the solute particles are spherical in shape. Since, from a simple solvation viewpoint, zu < 0 would seem to be senseless, it might appear that an experimental value of [ ~ ] / 2 . 5 0that is less than unity would be more susceptible to interpretation in terms of solvent structure. Unfortunately, closer examination, as we shall see, does not bear this out. I n deriving Einstein’s equation, it must be assumed
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The Journal of Physical Chemistry
that the spheres are “wet,” Le., that the contact layer of solvent moves with the same velocity as the surface of the spheres. For macroscopic bodies immersed in a fluid, this assumption is undeniably but for a single solute molecule surrounded by solvent particles that are comparable with it in dimensions, it is, in general, false. In other words, i t seems clear that there could be some “slip” at the surface of contact of the kinetic unit (centered around the solute molecule) and the solvent. Clearly, this would reduce the viscous drag and consequently the coefficient of viscosity would be smaller. For solute molecules that are approximately the same size as the solvent moleculcs we cannot expcct the “no-slip” condition to hold rigorously; so the measured viscosity may be less than that for Einstein spheres, i e . , we might find [773/2.38 < 1. Indeed, one would expect Einstein’s theory to work for colloidal particles, i.e., for spheres much larger than a solvent molecule, but not for anything else. Thus, as before, it is not possible to draw conclusions about water structure from the change in the property in question (in this case the viscosity) as solute is added. (4) Dielectric Consta?at. The argument in ref 24 is that the molar dielectric increment of urea Ae/Ac is positive ( = 2.72) and that this is caused not by the high dipole moment of urea (4.56 D) but by its influence in increasing solvent structure. As evidence for the latter, i t is claimed that S,N’-dimethylurea “which would not be able to enter into cluster formation” has a larger dipole moment (4.8 D) than urea and yet a dielectric increment of zero. I n this case, the argument is apparently based on a simple mistake; the wrong value of Aq‘Ac seems to have been transcribed. I n fact, the source cited in ref 2433 gives a value of Ae/Ac = 3 (not zero) for N,S’-dimethylurea. This value is about the same as that for urea, as is the dipole moment. When we consider the above data and add to them the fact that N,X-dimethylurea has a dipole moment! of 4.7 D and Ae/Ac 0 and that both methanol and acetamide (each with a healthy dipole moment and both described in ref 24 (via Frank and Wen34)as “...able to enter clusters with only slight distortion...”) actually lower the dielectric constant of water, i t is apparent that both the dipole moment and the structural influence of a solute will be important and that, without a way of calculating the first, the second cannot be estimated from the data. (5) Ideality of Urea Solutiolzs in Watev. This argument is typical; if the reader will consult it in the originalz4it will be seen that the phrase “nearly ideal”
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(32) R. P. Feynman, It. B. Leighton, and AT. Sands, “The Feynnlan Lectures on Physics,” Addison-Wesley Publishing Co., Inc., Itending, Mass., 1964, Chapter 41. (33) J. Wyman, Chem. Rev., 19, 213 (1936). (34) H. S. Frank and W.Y . Wen, Disctrssious Faraday Soc., 24, 133 (1957).
ON THE UTILITYOF
THE
CONCEPTOF WATERSTRUCTURE
is applied to solutions of urea in water and then made to mean “truly ideal” and thus to rule out urea-urea association in solution, thus setting the stage for the thesis that a urea molecule can enter water clusters almost unnoticed. In fact, however, the amount of “nonideality” produced depends on the association constant and may be “large” or “small.” Thus, while urea-water soIutions are, indeed, more nearly ideal than hydrocarbon-water solutions, they are not nearly “nearly ideal” enough to rule out some urea-urea association. I n fact, the thermodynamic properties of these solutions have been interpreted quantitatively in terms of exactly such interactions.3j The latter inlerpretation is quite self-consistent, but, of course, so may be many another model. However, the existence of some associative urea-urea interaction, even if it could be proven, would not give any definitive information about the influence of isolated urea molecules on mater structure. Under the circumstances, it is not surprising that when a prediction is attempted (that the alkyl-substi; tuted ureas, because of their decreased ability to hydrogen bond with water, will not be able to participate in cluster formation as easily and, in fact, will, themselves, use up the available interstices and thus will not be as effective as urea in breaking hydrophobic bondsz4),it is precisely opposite to the experimental result.26r26 Indeed, one would expect such predictions to be right in about 50% of the cases, since the predictions are of the form: “A should affect the system more than B,” and the argument leading to the prediction, is, in fact, indeterminate. It would seem, then, that aqueous solutions are too complex to be interpreted molecularly in the facile mariner that has become rather common. It is note-
33
worthy, however, that we have raised no fundamental difficulties that were not envisioned by Frank and Evans, who stated the following in their comments about icebergs: “It is not implied that the structure is exactly icelike, nor is it necessarily the same in every case when the word iceberg is used.”2 With this to fall back on, however, it is clear that a qualitative explanation can readily be supplied for any experimental result simply by postulating a suitable kind of iceberg.36 Unfortunately, since no experimental methods, except, possibly definitive X-ray or neutron diffraction, can give such specific structural information, the “explanation” cannot be tested by experiment, can lead to no unique prediction, and therefore can convey no more information than was obtained by doing the experiment in the first place. Water is structural, all right, but knowing that doesn’t seem to help. The situation mould appear to be bad enough without the curiously assured, yet essentially sterile, invocations of water structure that seem to be proliferating so boundlessly in the literature.
Acknozcledyrnent. The authors wish to thank Professor Walter Kauzmann of Princeton University for a thoughtful and informative review of the manuscript. We also wish to thank Professor Joseph Kurz of Washington University for several stimulating discussions. (35) J. A, Schellman, Compt. Rend, Tvaa. Lab. Carlsberg Sbr Chim.. 2 9 , 223 (1555).
(36) “Another thing I must point out is that you cannot prove a vague theory wrong.” (R. Feynman, “The Character of Physical Law,” The Massachusetts Institute of Technology Press, Cambridge, Mass., 1965, p 158.)
Volume 78, Number 1 Januarg 1968
