Langmuir 1991, 7, 2877-2880
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A New Concept “Ideal Organized Solution”: Comparison of Random Mixing Solutions and Ideal Organized Solution K6z6 Shinodat Department of Physical Chemistry, Division of Materials Science and Engineering, Yokohama National University, Tokiwadai, Yokohama 240, Japan Received August 3, 1990. In Final Form: November 8, 1990 In order to clarify “organized solutions”,a comparison among an ideal solution, regular solutions, and organized solutions was carried out, and the differences among these solutions were examined. From the fundamental differencesof the characteristicproperties of randomly mixed solutionsand organizedsolutions (systems),a new concept ‘ideal organized solution”evolved. The ideal solution has earlier been considered to represent ideal cases of all types of solutions, but it is the ideal case of randomly mixed solutions. A new concept “ideal organized solution”, which has not been conceived over the long history of physical science,is indispensableas an idealized model of organized solutions,Le., self-organizedsystems. An ideal mixing solution and ideal organized solution are in direct oppositionin fundamentalrespects. The necessity of two ideal solutions, i.e., ideal mixing solution and ideal organized solution, was elucidated. The new concept of two ideal solutions in chemistry may be as revolutionary as the concept of duality of light in physics.
Introduction Thermodynamic models are powerful organizers of the world in which we live. Idealized models of solutions based on random mixing of components provide physical insights and understanding of a variety of important chemical systems. Ideal dilute solutions, electrolyte solutions, regular solutions, and regular polymer solutions are notable examples. As a group they span an enormous range of variables: solvents ranging from oil to water, solute size varying from the atomic to the polymeric, and intermolecular interactions that encompass Coulombic and London dispersion energies. However, random mixing driven by thermal motion provides a common conceptual basis for formulating tractable thermodynamic mode1s.l There exists an important class of solutions for which there is no idealized thermodynamic model. These solutions are characterized by their ability to self-organize and thus are the exact opposite of randomly mixed solutions. Biologically important examples are aqueous solutions containing amphiphiles, proteins, or nucleic acids.z4 Industrially important examples involve aqueous surfactants and functional polymers or mixtures of oil, water, and surfactant.&ll Organized solutions form microstructures that include micelles, bilayers, vesicles, bicontinuous structures, and helical and folded polymers. They exhibit a wide diversity of properties that cannot be adequately described by random mixing models. They play key roles in many biologicaland industrial processes. tI
am very happy to contribute to Adamson’s Festschrift issue. (1)Shinoda, K. J. Phys. Chem. 1986,89,2429. (2)Lindblom, G.;Larsson, K.; Johansson, L.; Fontell, K.; Forsen, S. J. Am. Chem. SOC.1979,101,5465. (3)Andersson, S.;Hyde, S.T.;Larsson, K.; Lidin, S. Chem. Reo. 1988, 88,221. (4) Lnrsson, K. J. Phys. Chem. 1989,93,7304. (5) Friberg, S.;Larsson, K. Adv. Liq. Cryst. 1976,12,173. (6)Stilbs, P.;Lindman, B. h o g . Colloid Polym. Sci. 1984,69,39. (7)Jonsson, B.; Wennerstrdm, H. J. Phys. Chem. 1987,91,338. (8)Lindman, B.;Stilbs, P. In Microemulsion Systems; Rosano, H. L., Clausse, Marc, Eds.; Marcel Dekker, Inc.: New York, 1987;Chapter 7, DD 129-143. --- ~~(9)Miller, D.D.;Bellare, J. R.; Evans, D. F.; Talmon, Y.; Ninham, B. W. J. Phys. Chem. 1987,91,674. (10)Evans, D. F. Langmuir 1988,4,3. (11)Shinoda, K. Pure Appl. Chem. 1988,60(lo),1493. r r
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In a previous publication, I discussed the important features of organized so1utions.l In this paper, a thermodynamic idealized model for organized solutions is presented and then compared to an idealized solution and the regular solution models. The necessary conditions of an “ideal organized solution” will be proposed.
Organized Solutions The necessary and sufficient conditions for idealized organized solutions are as follows: (1) Low Solute Solubility. When the solute dissolves, it forms a randomly mixed solution, but with a very low monomer solubility, i.e.
x p = 0 (> 0 (2) Molecules possessing large lyophobic group(s) such as lecithin or proteins in water satisify this condition. Since the iceberg formation of water molecules surrounding a solute molecule markedly depress the enthalpy and entropy of solution of solute, the apparent partial molar enthalpy and entropy of solution is usually small or negative around room temperature.12 Because of the very low solute solubility (Xpt = 0), the activity of the solvent a t the saturation concentration remains close to 1 However, the activity of the solvated solute increases very rapidly as shown in Figure IC and the activity coefficient is very large
Addition of solute above the saturation concentration results in a self-organized solution (system) that can be viewed as a solvated pseudophase or phase in equilibrium (12)Shinoda, K.J . Phys. Chem. 1977,81,1300.
0 1991 American Chemical Society
2878 Langmuir, Vol. 7, No. 12, 1991
Shinoda
x2
Figure 1. Change of activity of second component with the mole fraction in ideal solution (a),regular solution (b), and organized solution (c). 12c
100
so
0
H2O
Y c
0.2
0.4
0.6
0.5
I
mole frocfion C,,E,
I 60
a,
E
2 40
20
rigure
I. ivieiung poinc ueyreuaion aue w nyaracion, pnase
diagram of L-dipalmitoylphosphatidylcholine-H20system (ref 13).
with a solvent phase saturated with solute. Hence, the organized solution, which is usually two-phase system, is opposite to the ideal mixing solution. (2) Swelling of Solvent by Solute Phase. A second condition is that the solute phase swells by dissolving a large amount of solvent Xl**t= 1 (>0.9)
(5)
In order to satisfy this condition, the solute molecules must possess a reasonably strong lyophilic group(& Thus, conditions 1 and 2 require that the solute molecules contain both large lyophobic and lyophilic moieties. ( 3 ) Solute in a Liquid or Liquid Crystalline State. The third condition is that the solute phase be in the liquid or liquid crystalline state. The relative activity of solute (relative to the solvated solute phase in the liquid state) should be =l a2 = 1or =1
-.
,
(6)
(4) High Molecular or Aggregate Weight of Solute Species. Since the driving force for random mixing is mainly translational motion of the molecules, the fourth necessary condition for organization is high molecular or aggregate weight of organized species as well as strong attractive force in or between solute molecules. Some of the manifestations of conditions 1,2,3, and 4 are summarized below.
0 Hz 0
Weight
I .o c H O (CHzCH 20) H
Fraction 12
25
6
Figure 3. Water activity as a function of mole fraction (umer, ref181 and weight fraction(lower,ref 19)for H~O-CI~H~~O(C'H~CH20)eH at 25 "C. (1') As a consequence of hydrated solid formation due to lyophilichead groups,the melting point of the anhydrous solute is dramatically depressed and the solvated solute is usually in the liquid or liquid crystalline state.' The phase diagram for a pure lecithin-water system shown in Figure 2 illustrates this point.13J4 Since the lecithin in biological membranes consists of a mixture of saturated, shorter chain, and unsaturated homologues,whose melting point is depressed below 0 O C . (2') The Gibbs molar free energy of mixing of the solvated solute aggregate with solvent is very small or zero. This is an important property of organized solutions. A small but positive free energy of mixing corresponds to a positive interfacial tension between the solvated solute phase (organized phase) and the solvent phase, and the system remains as two phases. The lecithin-water system in which the aggregationnumber is effectively infinite is an example. Y12 = 0 (7) A negative free energy of mixing correspond to a negative interfacial tension. As it decreases to zero, the interfacial
(13)Kodama, M. Thermochim. Acta 1986,109,81. (14)Kodama, M.; Seki, S. Prog. Colloid Polym. Sci. 1983, 68, 158.
Ideal Organized Solution
Langmuir, Vol. 7, No. 12, 1991 2879
Table I. Comparison of Ideal Solution, Regular Solution, and Ideal Organized Solutions solubility of "solute"
ideal solution soluble (each other)
solubility of "solvent"
molecular volume change of activity with concn
regular solution X p t = a2 exp(-VZ&zB'/RT)
ideal organized solution
Xlsat= a1 exp(-V1$$B'/RT) two-phase region is useless solute may be liquid, gas, or solid Vl = vz a1 = x1 a2 = Xp
VI VZ a1 = XI exp(V1q@B'/RT) a2 = XZexp(V~b1~B'/RT)
Xzsat = 0 ( 106 (below sat.) aazlaxz = N X@ (above sat.) aal/aXz = -k/X1iV = 0 (above sat.)
= 0, hEm = 0 ( X p = 0) A&(organized) = 0 (above sat.) AS1 = -R In XI = 0 (XI = 1) AS2 = -R/N In XZ= 0 ( N = m or large) A&
$qC=
1, @zc = small (CO.01)
large provided X p t = 0 small or 0 (although X p t = 0) Key: Xi, mole fraction of ith component; XzSat,saturation concentration of singly dispersed solute, 2; az, relative activity of solute, az(1iquid) = 1, az(so1id) = fzS/f2' = pz8/p2',adgas) = f z g / f i ' = p28/p2';fz, fuga+ of 2nd component; Vi, molar volume of ith component; bi, volume fraction of ith component; B', interchange energy per unit volume; N, average aggregation number; hEi, partial molar energy of ith component; AE", total energy of mixing. interfacial tension
area between two phases increases and the aggregation number decreases from infinite to a finite value and a micellar solution is obtained. In this case the activity of the solute very gradually increases with concentration as expected from the thermodynamics of small systems.15J6 These phenomena are illustrated by a nonionic surfactant solution above and below the cloud point at its critical composition.17 (3') Another important characteristic of an organized solution is that its solvent activity remains almost constant (or constant in the case of two phases coexisting)and nearly equal to unity up to the high solute weight fraction. For example, in the C ~ ~ H ~ ~ O ( C H ~ C system, H Z O ) the ~ Hrelative activity of water is practically 1.0 (>0.998) up to 38 w t % surfactant (Figure 3 lower), but the upper figure plotted on the mole fraction of anhydrous surfactant may be misleading for the present d i s c u s ~ i o n , ~because ~J~ a hydrated solute retains about 15 water molecules. (4') The importance of the liquid (crystalline) state can be seen by comparing its properties with that of the corresponding hydrated (crystalline) solid. If the saturated solvent is in equilibrium with hydrated solid solute phase, then its monomer solubility is significantly smaller than that in its supercooled liquid state. This simply reflects the fact that the relative activity of hydrated solid is far less than 1 in liquid state. The relation is given as d In a,"/dT = AHzf/RP
This difference is simply a reflection of the very large enthalpy of fusion associated with large complex amphiphilic molecules or proteins. Hence, functional molecules in the solid state are virtually useless, Le., they cannot form organized solutions. Surfactants below their Krafft point, i.e., soap precipitated in hard water serves as an example. In fact the melting point of most hydrated biological molecules occurs below physiological temperatures. The melting point of hydrated natural lecithin is below 0 "C.
Comparison of a n Ideal Solution, Regular Solutions, and Idealized Organized Solutions The thermodynamic relationships defining an ideal (mixing) solution, regular solutions, and idealized organized solutions are compared in Table I. In the thermodynamic definition of an ideal solution, V I = V Zand the enthalpy and volume change of mixing are zero over all mole fractions. Accordingly, the activity equals the mole fraction over the entire composition range as shown in Figure l a a2 = f2If2" = x2 = P2IP2O aa,/ax, = 1, aa2/ax2= 1
(11) where a2 is the relative activity of component 2 in an ideal solution relative to pure liquid 2. The partial molal entropy of mixing is
AS2 = -R In X,
and In a; = -AH24Tf- T)/RTTf Where a28 is the relative activity of hydrated solute in solid state at T, AHzf is the enthalpy of fusion of hydrated solute, and T , the melting point of hydrated solute. (15)Hill, T.L.Thermodynamics of Small Systems; Benjamin: New York, 1963 (Vol. 1) and 1964 (Vol. 2). (16)Hall, D. G.; Pethica, B. In Non-ionic Surfactants; Schick, M. J., Ed.; Marcel Dekker, Inc.: New York, 1967;Chapter 16.
(17)Fig. 3 in Ref. 1. (18)Clunie, J. S.;Goodman, J. F.; Symons, P. C. Trans. Faraday SOC. 1969,65, 287. (19)Shinoda, K.J. Colloid Interface Sci. 1971,34, 278.
(12) and the partial molal Gibbs free energy of mixing is AG2 = R T In X,
In the thermodynamic definition of regular solution, there is a positive enthalpy of mixing AE, = V,@J:B' and AE, = V2@JI2B'
(14 where B' is the interchange energy per unit volume. The volume change of mixing is usually neglected. Completely random mixing is assumed and data agree reasonably well with theory. In the case when the enthalpy of mixing is large, the mutual solubility is correspondingly small, and
Shinoda
2880 Langmuir, Vol. 7, No. 12, 1991 the assumption of random mixing is still adequate. Namely AS2 = -R In X ,
(15)
The Gibbs free energy of solution is AG2 = R T In ( p , / p Z o )= R T In X ,
+ V2&2B’
(16)
The change of activity of component 2 p 2 / p Z o= a2 = x 2 ~XPW,@J,~B’IRT)
(17)
is shown in Figure lb. In the case when 41 i= 1 and 42 = 0 p 2 = X g 2 0 exp(V@’lRT)
(18)
PI = X,P,O
(19)
and
which corresponds to Henry’s law and Raoult’s law in an ideal dilute solution. The comparisons given in Table I and in Figure 1provide a clear demarcation between solutions that can be modeled by using the random mixing concept and those that require the self-organizing concept. Just as the wave and particle properties of light, the properties of random mixing solution and organized solution are opposite. The duality of light came from the difference in actions (topic in physics), whereas the opposite properties in solutions resulted from the difference in molecules (topic in chemistry). The former was interpreted by quantum mechanics, but it took much longer time to recognize the characteristics of organized solutions and to conceive the ideal
organized solution concept. Two ideal solutions in chemistry will be as revolutionary as the concept of duality in physics. Conclusions Random mixing solutions and organized solutions are entirely different in many respects. An ideal (mixing) solution is the ideal case of randomly mixed solutions but not organized solutions. There is a need to introduce a new concept “ideal organized solution” as an ideal case of an organized solution. If the solute satisfies the necessary and sufficient conditions for organization, it will be selforganized from the beginning, i.e., since it was synthesized by DNA. The biological organization maintains ita selforganized structure over a thousand years. And the entropy will remain constant without metabolism. Classical thermodynamics will well-explain self-organized systems. I would like to quote Albert Einstein’s saying20“Atheory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced that, it will never be overthrown, within the framework of applicability of its basic concepta.”
Acknowledgment. I gratefully acknowledgeProfessors D. Fennel1 Evans and Stig E. Friberg for their kind discussions and revisions of the manuscripts. (20) Einstein,A. Autobiographisches. In Albert Eimtein: PhilosopherScientist, 1st ed.;Schilpp, P. A., Ed.; Tudor Publishing Co.: New York, 1949.
