Mean-Field Theory Prediction of the Phase Behavior and Phase

Langmuir 2003, 19, 4483-4492

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Mean-Field Theory Prediction of the Phase Behavior and Phase Structure of Alkyl-Propoxy-Ethoxylate “Graded” Surfactants in Water: Temperature and Electrolyte Effects Nadezhda P. Shusharina,† Sudhakar Balijepalli,‡ Henri J. M. Gruenbauer,§ and Paschalis Alexandridis*,† Department of Chemical Engineering, University at Buffalo, The State University of New York, Buffalo, New York 14260-4200, New Product & Mathematical Modeling Group, Corporate R&D, The Dow Chemical Company, Midland, Michigan 48674, and New Business Development, Dow Benelux N.V., 4530 AA Terneuzen, The Netherlands Received July 17, 2002. In Final Form: January 30, 2003 A mean-field lattice theory is used to predict electrolyte effects on the temperature-concentration phase behavior and structure of an alkyl-propoxy-ethoxylate surfactant in water. The salt ions are treated as charged species interacting with surfactant segments and water via adjustable Flory-Huggins χ-parameters. The surfactant undergoes thermotropic (rather than lyotropic) transitions with a reversal in curvature (from water continuous to alkyl continuous) upon an increase in temperature. This is attributed to the “graded” nature of the surfactant interactions with water, which originates from the fact that the propoxy and ethoxy groups become progressively more hydrophobic as the temperature increases. The addition of NaCl is found to sharpen the thermotropic phase transitions and to shift them to lower temperatures compared to the salt-free case. The electrolyte effects on the macroscopic phase behavior are reflected in the microscopic information provided by the model on the species volume fraction profiles in the selfassembled domain, the distributions of ends and block junctions, and the domain spacing. The parameters that describe the interactions between the different species are obtained from simple experiments, and thus this theoretical framework can be useful in capturing the effects of various electrolytes on nonionic surfactant phase behavior.

Introduction Nonionic surfactants are commonly used in aqueous systems for household and industrial applications. The use of nonionic surfactants is often desirable because their critical micelle concentration (cmc) is lower than that of ionic surfactants in aqueous solutions. The addition of electrolytes into water can be a valuable tool to increase the efficiency of detergents containing nonionic surfactants. It is known from early works (see refs 1 and 2 and references therein) that added electrolytes affect the surface tension and the cmc. Moreover, observations of adverse interactions of natural soaps with divalent salts present in groundwater gave the push for the development of synthetic surfactants,3 salts are used to tune the properties of microemulsions,4 and it is common to use salt solutions as buffers in pharmaceutical formulations.5-7 * Corresponding author. Fax: (716) 645-3822. E-mail: palexand@ eng.buffalo.edu. † The State University of New York, Buffalo. ‡ Dow Chemical Co. § Dow Benelux N.V. (1) Collins, K. D.; Washabaugh, M. W. The Hofmeister Effect and the Behaviour of Water at Interfaces. Q. Rev. Biophys. 1985, 4, 323422. (2) Cacace, M. G.; Landau, E. M.; Ramsden, J. J. The Hofmeister Series: Salt and Solvent Effects on Interfacial Phenomena. Q. Rev. Biophys. 1997, 30, 241-277. (3) Stokes, R. J.; Evans, D. F. Fundamentals of Interfacial Engineering; Wiley-VCH: New York, 1997. (4) Kabalnov, A.; Olsson, U.; Wennerstro¨m, H. Salt Effects on Nonionic Microemulsions are Driven by Adsorption/Depletion at the Surfactant Monolayer. J. Phys. Chem. 1995, 99, 6220-6230. (5) Schott, H.; Han, S. K. Effect of Inorganic Additives on Solutions of Nonionic Surfactants II. J. Pharm. Sci. 1975, 64, 658-664. (6) Schott, H.; Han, S. K. Effect of Inorganic Additives on Solutions of Nonionic Surfactants III: CMC’s and Surface Properties. J. Pharm. Sci. 1976, 65, 975-978.

It is a general experimental observation that the ability of salt ions to change aqueous solution properties of polar and apolar solutes follows the phenomenologically established Hofmeister series1 SO42 - ≈ HPO42- > F- > Cl> Br- > I- > SCN-; that is, an addition of anions on the left-hand side of the Hofmeister series decreases the solubility (and correspondingly decreases the critical micelle concentration; “salting-out” phenomenon), whereas an addition of anions on the right-hand side increases the solubility (increases the critical micelle concentration; “salting-in” phenomenon) of hydrophobic solutes in water. The effect of the cation type is usually smaller than that of the anion. The salt effects have been the subject of a number of experimental investigations.1,2,5-23 Many experimental (7) Schott, H.; Royce, A. E. Effect of Inorganic Additives on Solutions of Nonionic Surfactants VI: Further Cloud Point Relations. J. Pharm. Sci. 1984, 73, 793-799. (8) Laughlin, R. G. The Aqueous Phase Behavior of Surfactants; Academic Press: San Diego, CA, 1994. (9) Iwanaga, T.; Suzuki, M.; Kunieda, H. Effect of Added Salts or Polyols on the Liquid Crystalline Structures of Polyoxyethylene-Type Nonionic Surfactants. Langmuir 1998, 14, 5775-5781. (10) Rodriguez, C.; Kunieda, H. Effect of Electrolytes on Discontinuous Cubic Phases. Langmuir 2000, 16, 8263-8269. (11) Versluis, P.; van de Pas, J. C.; Mellema, J. Influence of Salt Concentration and Surfactant Concentration on the Microstructure and Rheology of Lamellar Liquid Crystalline Phases. Langmuir 2001, 17, 4825-4835. (12) Bahadur, P.; Li, P.; Almgren, M.; Brown, W. Effect of Potassium Fluoride on the Micellar Behavior of Pluronic F-68 in Aqueous Solution. Langmuir 1992, 8, 1903-1907. (13) Jain, N. J.; Aswal, V. K.; Goyal, P. S.; Bahadur, P. Micellar Structure of an Ethylene Oxide-Propylene Oxide Block Copolymer: A Small-Angle Neutron Scattering Study. J. Phys. Chem. B 1998, 102, 8452-8458. (14) Jain, N. J.; Aswal, V. K.; Goyal, P. S.; Bahadur, P. Salt Induced Micellization and Micelle Structures of PEO/PPO/PEO Block Copolymers in Aqueous Solution. Colloids Surf., A 2000, 173, 85-94.

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works have been dedicated to the qualitative and quantitative examination of salt effects on micellar properties5-8 and phase behavior9-11 of nonionic ethoxylated surfactants in aqueous solutions. It has been found that changes in cmc and micellar size depend on the type of electrolyte and are a function of the electrolyte concentration. In the papers,9,10 the phase behavior of nonionic surfactants C12(EO)7 and C12(EO)25 in aqueous solution with added salts (NaCl, Na2SO4, and NaSCN) has been considered. It has been observed that the two-phase region between ordered phases and the isotropic solution is very narrow for all salts. In the presence of NaCl and Na2SO4, the temperature boundaries between the disordered phase and the normal hexagonal phase, H1, for surfactant C12(EO)7 or the cubic phase, I1, for surfactant C12(EO)25 have been found to shift toward lower temperatures. Moreover, the temperature stability range of the cubic phase dramatically decreases, inducing a transition from I1 to H1. Studies of salt-induced effects in Pluronic (or Poloxamer) poly(ethylene oxide)poly(propylene oxide)-poly(ethylene oxide) ((EO)m(PO)n(EO)m) block copolymer aqueous solutions have shown the same trends as in nonionic surfactant systems; a shift of the cloud point (macroscopic phase separation) when salt is added has also been reported.12-20 Recently, molecular dynamic simulations have been performed to study the salt effects in aqueous solutions.24,25 In particular, the effect of ion concentration on the structure and dynamic properties of aqueous solutions of NaCl and KCl has been examined in ref 24. From an analysis of the single-particle, pair, and collective dynamical properties, significant structural changes in ion and water molecule distributions have been found as the ion concentration is increased. A quantification of saltingin and salting-out effects in aqueous solutions of nonpolar solutes has been done in ref 25. It has been shown that the hydration of hydrophobic solutes depends strongly on the size of salt ions: small highly charged ions (kosmotropes) interact unfavorably with hydrophobic solutes in

water, and, in contrast, large weakly charged ions (chaotropes) associate with hydrophobic solutes. Several phenomenological theoretical models have been proposed to explain experimental observations of salt effects on polymer and surfactant aqueous solutions.4,26,27 A model of the hydration shell surrounding the ions has been discussed in ref 26. This approach is based on an assumption of enhanced polarization of water in the closest vicinity of ions and repulsion of the hydrated ions from regions rich with poly(ethylene oxide) (PEO) molecules which are surrounded by less polarized water. Other authors4 proposed an explanation of the salt effects on the phase behavior based on interfacial partitioning: the salt ions adsorb at or are depleted from the surfactant monolayer, thus affecting the phase equilibrium. In ref 27, a theoretical model developed for the micellization of nonionic alkyl-ethoxylate surfactants has been extended to treat the salt effects. A quantitative analysis has been done by fitting the model parameters to experimental data. It was shown that the salt influences the micellization primarily because of a decreased solubility of the alkyl surfactant tails in the aqueous electrolyte solution. In recent years, a mean-field lattice theory has been found successful in describing the micellization and lyotropic liquid crystal formation in aqueous (EO)m(PO)n(EO)m systems.28-33 In the present study, based on the same approach, we incorporate salt ions as individual charged species to predict salt effects on the phase behavior in water of a surfactant containing ethylene segments, propylene oxide segments, and ethylene oxide segments ((C)k(PO)n(EO)m). The triblock architecture of this surfactant is expected to lead to an increased interaction spectrum, that is, a more complex hydrophilic/hydrophobic balance between the parts of the molecule that range from the very hydrophobic (C)k-block to the hydrophilic (EO)mblock through the moderately hydrophobic (PO)n-block. Such surfactants with “graded” triblock composition are found useful in industrial applications.34-38 Nonyl phenyl-

(15) Desai, P. R.; Jain, N. J.; Sharma, R. K.; Bahadur, P. Effect of Additives on the Micellization of PEO/PPO/PEO Block Copolymer F127 in Aqueous Solution. Colloids Surf., A 2001, 178, 57-69. (16) Alexandridis, P.; Holzwarth, J. F. Differential Scanning Calorimetry Investigation of the Effect of Salts on Aqueous Solution Properties of an Amphiphilic Block Copolymer (Poloxamer). Langmuir 1997, 13, 6074-6082. (17) Pandit, N.; Trygstad, T.; Croy, S.; Bohorquez, M.; Koch, C. Effect of Salts on the Micellization, Clouding, and Solubilization Behavior of Pluronic F127 Solutions. J. Colloid Interface Sci. 2000, 222, 213-220. (18) Mao, G.; Sukumaran, S.; Beaucage, G.; Saboungi, M.-L.; Thiyagarajan, P. PEO-PPO-PEO Block Copolymer Micelles in Aqueous Electrolyte Solutions: Effect of Carbonate Anions and Temperature on the Micellar Structure and Interaction. Macromolecules 2001, 34, 552558. (19) Anderson, B. C.; Cox, S. M.; Ambardekar, A. V.; Mallapragada, S. K. The Effect of Salts on the Micellization Temperature of Aqueous Poly(ethylene oxide-b-poly(propylene oxide)-b-poly(ethylene oxide) Solutions and the Dissolution Rate and Water Diffusion Coefficient in their Corresponding Gels. J. Pharm. Sci. 2002, 91, 180-188. (20) Su, Y.-l.; Liu, H.-z.; Wang, J.; Chen, J.-y. Study of Salt Effects on the Micellization of PEO-PPO-PEO Block Copolymer in Aqueous Solution by FTIR Spectroscopy. Langmuir 2002, 18, 865-871. (21) Aquan-Yuen, M.; Mackay, D.; Shiu, W. Y. Solubility of Hexane, Phenanthrene, Chlorobenzene, and p-Dichlorobenzene in Aqueous Electrolyte Solutions. J. Chem. Eng. Data 1979, 24, 30-34. (22) Xie, W.-H.; Shiu, W.-Y.; Mackay, D. A Review of the Effect of Salts on the Solubility of Organic Compounds in Seawater. Mar. Environ. Res. 1997, 44, 429-444. (23) Segatin, N.; Klofutar, C. Salting-Out of Some Alkyl Acetates in Aqueous Sodium Chloride Solutions. Monatsh. Chem. 2000, 131, 131144. (24) Chowdhuri, S.; Chandra, A. Molecular Dynamic Simulations of Aqueous NaCl and KCl Solutions: Effects of Ion Concentration on the Single-Particle, Pair, and Collective Dynamical Properties of Ions and Water Molecules. J. Chem. Phys. 2001, 115, 3732-3741. (25) Kalra, A.; Tugcu, N.; Cramer, S. M.; Garde, S. Salting-In and Salting-Out of Hydrophobic Solutes in Aqueous Salt Solutions. J. Phys. Chem. B 2001, 105, 6380-6386.

(26) Florin, E.; Kjellander, R.; Eriksson, J. C. Salt Effects on the Cloud Point of the Poly(ethylene oxide) + Water System. J. Chem. Soc., Faraday Trans. 1 1984, 80, 2889-2910. (27) Carale, T. R.; Pham, Q. T.; Blankschtein, D. Salt Effects on Intramicellar Interactions and Micellization of Nonionic Surfactants in Aqueous Solutions. Langmuir 1994, 10, 109-121. (28) Malmsten, M.; Linse, P.; Zhang, K.-W. Phase Behavior of Aqueous Poly(ethylene oxide)/Poly(propylene oxide) Solutions. Macromolecules 1993, 26, 2905-2910. (29) Linse, P. Micellization of Poly(ethylene oxide)-Poly(propylene oxide) Block Copolymers in Aqueous Solution. Macromolecules 1993, 26, 4437-4449. (30) Linse, P. Phase Behavior of Poly(ethylene oxide)-Poly(propylene oxide) Block Copolymers in Aqueous Solution. J. Phys. Chem. 1993, 97, 13896-13902. (31) Linse, P.; Hatton, T. A. Mean-Field Lattice Calculations of Ethylene Oxide and Propylene Oxide Containing Homopolymers and Triblock Copolymers at the Air/Water Interface. Langmuir 1997, 13, 4066-4078. (32) Noolandi, J.; Shi, A.-C.; Linse, P. Theory of Phase Behavior of Poly(oxyethylene)-Poly(oxypropylene)-Poly(oxypropylene) Triblock Copolymers in Aqueous Solutions. Macromolecules 1996, 29, 59075919. (33) Svensson, M.; Alexandridis, P.; Linse, P. Phase Behavior and Microstructure in Binary Block Copolymer/Selective Solvent Systems: Experiments and Theory. Macromolecules 1999, 32, 637-645. (34) Miano, F.; Bailey, A.; Luckham, P. F.; Tadros, T. F. Adsorption of Nonyl Phenol Propylene-oxide Ethylene-oxide Surfactants on Carbonblack and the Rheology of the Resulting Dispersions. Colloids Surf. 1992, 62, 111-118. (35) Trochetmignard, L.; Taylor, P.; Bognolo, G.; Tadros, T. F. Concentrated Coal-water Suspensions Containing Nonionic Surfactants and Polyelectrolytes. 2. Adsorption of Nonyl Phenyl Propylene-oxide Ethylene-oxide on Coal and the Rheology of the Resulting Suspension. Colloids Surf., A 1995, 95, 37-42. (36) Taugbol, K.; Ly, T. V.; Austad, T. Chemical Flooding of Oilreservoirs. 3. Dissociative Surfactant-polymer Interaction with a Positive Effect on Oil-Recovery. Colloids Surf., A 1995, 103, 83-90.

Phase Behavior and Structure of Surfactants

propoxy-ethoxylate surfactants with long EO-blocks are used for the stabilization of aqueous dispersions.34,35 Surfactants of the type alkyl-propoxy-ethoxy sulfate are also used in enhanced oil recovery applications, where their graded nature offers an advantage in stabilizing oilwater interfaces over alkyl ethoxylates.36-38 In recent work,52 we have investigated the phase behavior of (C)k(PO)n(EO)m surfactants in water in the framework of the lattice self-consistent mean-field lattice approach. In the present paper, we treat the case of an aqueous solution with added low molecular weight salt using interaction parameters obtained from fitting experimental data on simple systems. Our aim is to model the composition-temperature phase diagram focusing on the temperature and salt effects. We also analyze the structure and the size of the domains forming the phases, thus depicting the influence of the external parameters. The mean-field lattice theory is implemented to model the effect of electrolytes on the liquid crystalline phase formation and structure for the first time in this study. Theoretical Modeling Model and Method. The theory that we use in this work is based on a mean-field lattice model initially developed by Scheutjens and Fleer39 for describing polymer adsorption from solution. Further extensions of the original theory have been done in several directions,41-43 but here we focus on one that describes the reduced solubility of EO- and PO-containing polymers in water at elevated temperature (clouding). It is experimentally observed that above a certain temperature a PEO homopolymer aqueous solution separates into two phases, one polymer rich and one polymer poor. To model the lower consolute point in the binary polymer-solvent systems, an approach suggested by Karlstro¨m has been employed.44 This approach states that the conformations of EO- and PO-segments vary with temperature, and different conformations interact unequally with the surroundings. Quantum chemical calculations and a statistical mechanical simulation performed for PEO in the gas phase and in water45 show that the conformations can be divided into two classes or states: one being polar, P, and one (37) Milter, J.; Austad, T. Chemical Flooding of Oil Reservoirs. 7. Oil Expulsion by Spontaneous Imbibition of Brine with and without Surfactant in Mixed-wet, Low Permeability Chalk Material. Colloids Surf., A 1996, 117, 109-115. (38) Minana-Perez, M.; Graciaa, A.; Lachaise, J.; Salager, J.-L. Systems Containing Mixtures of Extended Surfactants and Conventional Nonionics. Phase Behavior and Solubilization in Microemulsion. World Surfactants Congr., 4th 1996, 2, 226-234. (39) Scheutjens, J. M. H. M.; Fleer, G. J. Statistical Theory of the Adsorption of Interacting Chain Molecules. I. Partition Function, Segment Density Distribution and Adsorption Isotherms. J. Phys. Chem. 1979, 83, 1619-1635; (40) Scheutjens, J. M. H. M.; Fleer, G. J. Statistical Theory of the Adsorption of Interacting Chain Molecules. II. Train, Loop, and Tail Size Distribution. J. Phys. Chem. 1980, 84, 178-190. (41) Leermakers, F. A. M.; Scheutjens, J. M. H. M.; Gaylord, R. J. Modelling the Amorphous Phase of a Melt Crystallized, Semicrystalline Polymer: Segment Distribution, Chain Stiffness, and Deformation. Polymer 1984, 25, 1577-1588. (42) Leermakers, F. A. M.; Scheutjens, J. M. H. M. Statistical Thermodynamics of Association Colloids. I. Lipid Bilayer Membranes. J. Chem. Phys. 1988, 89, 3264-3274. (43) Bo¨hmer, M. R.; Evers, O. A.; Scheutjens, J. M. H. M. Weak Polyelectrolytes between Two Surfaces: Adsorption and Stabilization. Macromolecules 1990, 23, 2288-2301. (44) Karlstro¨m, G. A New Model for Upper and Lower Critical Solution Temperatures in Poly(ethylene oxide) Solutions. J. Phys. Chem. 1985, 89, 4962-4964. (45) Anderson, M.; Karlstro¨m, G. Conformational Structure of 1,2Dimethoxyethane in Water and Other Dipolar Solvents, Studied by Quantum Chemical, Reaction Field, and Statistical Mechanical Techniques. J. Phys. Chem. 1985, 89, 4957-4962.

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Figure 1. Two-dimensional illustration of a spherical lattice or a perpendicular cut of a cylindrical lattice with an assembly formed by four A3B2C3 triblock copolymer molecules. The hydrophobic segments (filled circles) form the central part of the assembly, whereas the more hydrophilic segments (connected open and dot-centered circles) form the outer layer of the assembly. Anions and cations are also shown (unconnected open circles). Note the small number of unfavorable contacts between the hydrophobic segments and the solvent (unfilled lattice cells).

being less polar or apolar, AP. The internal energy of the polar states is lower, but their degeneration is low; the apolar states have higher internal energy but are more degenerated. Since poly(propylene oxide) (PPO) displays inverse temperature behavior similar to that of PEO, this formalism is also applied to PO-segments. An extension of the mean-field lattice theory for the case where polymer segments may possess internal degrees of freedom (states) has been reported in refs 46 and 47. More recently, the theory has been applied for predicting composition-temperature phase diagrams for (EO)m(PO)n(EO)m block copolymers in selective solvents.32,33 The free energies of the disordered micellar-free solution and different ordered phases as a function of the composition and temperature are used for determination of the phase boundaries. Each ordered phase has a structure unit, which is in the following referred to as a domain, of a certain symmetry. A complete theoretical background of the lattice model is presented in ref 47. Here we briefly describe the model adapted for our present study, and for more details the reader is referred to the original publications.39,46,47 In the framework of the lattice description, space is divided into layers, i ) 1, 2, ... M; spherical, cylindrical, or planar, depending on the domain geometry. Each layer is further divided into lattice cells. Each cell is filled with one of the system species (see Figure 1). The lattice is scaled with a polymer segment size a, so all the lengths are measured in a units. To obtain real length units, we have used a ) 4 Å for the length of a lattice cell, which has previously been shown to give reasonable agreement with experimental data.29 Since we deal with a periodic system, we apply reflective boundary conditions at the periphery of the spherical and cylindrical lattice, that is, φA,i)M+1 ) φA,i)M, and also φA,i)0 ) φA,i)1 for the planar lattice, for all species A. (46) Bjo¨rling, M.; Linse, P.; Karlstro¨m, G. Distribution of Segments for Terminally Attached Poly(ethylene oxide) Chains. J. Phys. Chem. 1990, 94, 471-481. (47) Linse, P.; Bjo¨rling, M. Lattice Theory for Multicomponent Mixtures of Copolymers with Internal Degrees of Freedom in Heterogeneous Systems. Macromolecules 1991, 24, 6700-6711.

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The Helmholtz free energy, A, of a multicomponent system with internal degrees of freedom includes three contributions:

Ω + β(U - U*) β(A - A*) ) β(Aint - A/int) - ln Ω*

(1)

where β ) 1/kBT, kB being the Boltzmann constant, and T the absolute temperature. Aint and U are the internal free energy and interaction energy, respectively, while ln(Ω/Ω*) is the mixing conformational entropy. The quantities marked with an asterisk correspond to ones for the reference pure amorphous system. For a homogeneous mixture of the components, the three contributions to the Helmholtz free energy are given by the following equations:

βAint )

nxrAx∑PAB ∑x ∑ A B ln

βU )

1 2

Ω Ω*

)-

∑x

[

]

PAB

βUAB + ln

gAB

nxrx

nx ln

(2)

(3)

L

∑x ∑ ∑∑∑nxrAxPABχBB′PA′B′φA′ A A′ B B′

(4)

Here rAx denotes the number of segments of type A (C, PO, EO, water, Na, and Cl) in component x ((C)k(PO)n(EO)m, water, Na, and Cl), rx the total number of segments in component x (k + n + m or 1), nx the total number of molecules of type x, L the total number of lattice sites, φA the volume fraction of species A, and χBB′ the FloryHuggins interaction parameter between species A in state B and species A′ in state B′. PAB is the fraction of species A in state B. UAB and gAB are the internal energy and degeneration factor, respectively, of state B of species A; in the case of EO or PO, these quantities describe the equilibrium between the polar and apolar states. In a system with segregated components, a heterogeneity of species density is introduced in one direction, radial in the case of a spherical or cylindrical lattice and in the z-direction in the case of a planar lattice. Within each layer, the Bragg-Williams approximation of random mixing is applied, and thus all sites in a layer are equivalent. Density distribution profiles are obtained as a function of layer number. In line with the random mixing approximation, the charged species (salt ions) interact with an electrostatic potential of mean force, Ψi, which depends only on layer number i. The potential of mean force is related to the charge density through Poisson’s equation:

0r∇2Ψi ) -Fi

(5)

where 0r is the dielectric permittivity of the medium, ∇2 is the Laplacian, and Fi ) ∑AqAφAi is the charge density in layer i (qA is the charge of species A, and φAi is the volume fraction of species A in layer i). The relative dielectric permittivity, r ) 80, is assumed to be constant throughout the solution. For a heterogeneous system, the three contributions in eq 1 are written as follows:

βAint )

[

]

PABi

nAi∑PABi βUAB + ln ∑i ∑ g A B

AB

(6)

ln

Ω Ω*

)-

nxcrx

∑x ∑c nxc ln ω

(7)

xc

where nxc is the number of chains of component x in conformation c. wxc is related to the degeneration of a conformation c of component x, and it is given by eq A.1.2 in ref 47.

βU )

1M

∑i Li∑ ∑∑∑φAiPABiχBB′〈PA′B′iφA′i〉 + A A′ B B′

2

1M

∑i LiFiΨi

2

(8)

where Li is the number of lattice sites in the layer i, A and A′ run over all species, and B and B′ run over all states. 〈xi〉 ≡ ∑i′Mλii′xi′, where λii′ is the fraction of nearest-neighbor sites in the same layer, i′ ) i, or in adjacent layers, i′ ) i ( 1 (the values of λ are dependent on the lattice topology). In our case of only nearest-neighbor interactions, the sum over i′ contains at most three terms. M is the total number of the layers in the system corresponding to the domain size. At a given temperature and system composition, the size of the domain is optimized. In the calculations, we use the difference between the free energy of a heterogeneous system of a certain structure given by the sum of contributions (6), (7), and (8) and the free energy of a homogeneous system given by the sum of (2), (3), and (4). The free energy difference curves are obtained as a function of polymer volume fraction at a given temperature. Five ordered phases have been considered in this work: normal (“oil-in-water”) cubic phase (ordered array of spherical micelles), I1, normal hexagonal phase (ordered array of cylindrical micelles), H1, lamellar phase, LR, reverse (“water-in-oil”) hexagonal phase, H2, and reverse cubic (discrete) phase, I2. In the temperature range 280-380 K of interest here, only four of them, shown schematically in Figure 2, are found to be stable. The disordered phase L in our model is defined as a homogeneous mixture of surfactant and water. Other disordered structures, such as micellar solutions, with spherical and/ or cylindrical micelles, either normal or reverse, and twophase regions with disordered water-rich and surfactantrich phases have not been considered in the framework of the approach used here, because our present focus is on the formation and structure of the ordered phases. To construct a phase diagram, the phase boundaries have to be evaluated. For each temperature, two-phase regions can be determined by using the double tangent method (see Figure 1 in ref 33). Our calculations show that throughout the whole temperature range considered here, two-phase regions are narrow. For simplicity, they are neglected, and we defined the location of a phase transition from the crossing of the free energy curves. The calculations were performed using the program POLYMER.48 Interaction Parameters. The considered surfactant molecule has the chemical structure (C)14(PO)12(EO)17, and it is modeled as a triblock copolymer with 7 (-CH2-CH2-) segments, denoted as 2C, 12 (-CH(CH3)-CH2-O-) segments, denoted as PO, and 17 (-CH2-CH2-O-) segments, denoted as EO. The considered two-component (triblock copolymer/water) or four-component (triblock copolymer/water/NaCl) systems consist of four or six (48) Linse, P. POLYMER, Version 2.8.2; Lund University, Sweden, 1990.


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Figure 3. Cloud point of Pluronic F127 (EO)99(PO)65(EO)99 block copolymer (1 wt %) in aqueous salt solution as a function of NaCl molar concentration. Experimental data are from Desai et al. (ref 15) (filled circles); calculated data are from the model (open circles).

Figure 2. Schematic illustration of different modes of selforganization of (C)5(PO)5(EO)7 in water. Filled circles represent C-segments, open triangles represent PO-segments, and open circles represent EO-segments. Lyotropic liquid crystalline (ordered) phases are denoted as follows: (a) normal hexagonal, H1, (b) lamellar, LR, (c) reverse hexagonal, H2, and (d) reverse micellar cubic, I2.

species, respectively, referred to as 2C-segments of alkyl block, PO-segments of poly(propylene oxide) block, EOsegments of poly(ethylene oxide) block, W solvent (water)

molecules, Na positively charged ions, and Cl negatively charged ions. In the model, two states, polar P and apolar AP, are considered for each of the ethylene oxide and propylene oxide segments in order to account for the reverse temperature dependence of the solubility of PEO and PPO in water. The alkyl segments have a single state. Na and Cl ions are monovalently charged, that is, carry +|e| and -|e| charge, respectively. In the framework of the mean-field approach, all species experience a potential of mean force. The contributions to the potential of mean force considered in the theory are those arising from (i) hard core interactions, (ii) shortrange nearest-neighbor interactions described by FloryHuggins χ-parameters, and, when salt ions are present in the system, (iii) long-range electrostatic interactions. The calculations for the model require a knowledge of the interaction χ-parameters between all pairs of species in different states. Parameters that describe the 10 binary interactions in a system containing PO, EO, and W as well as the internal energy and degeneration of polar and apolar states were taken from previous works.28,44,47 The binary interactions of the alkyl segment, 2C, with W and with PO- and EO-segments in both polar and apolar states were taken from our previous work.52 As was previously reported,12-17 the addition of low molecular weight salt into an aqueous (EO)m(PO)n(EO)m block copolymer solution leads to a change of the cloud point. To obtain W/ion, EO/ion, PO/ion, and ion/ion χ-parameters, cloud point determination data for (EO)m(PO)n(EO)m/water/salt systems can be used. We made a fitting of the model to macroscopic phase separation (cloud point) data, reported in ref 15, of dilute (1 wt %) Pluronic F127, which has a molecular structure (EO)99(PO)65(EO)99, in aqueous NaCl solution in the salt concentration range 0-2 M. As a first approximation, we consider the Na/Cl interactions to be athermal, and the EO/Na and PO/Na interactions to be equal to the EO/Cl and PO/Cl interactions. The fitting results are presented in Figure 3. The calculated coexisting curve is qualitatively correct; that is, the slope is the same as for the experimental curve within an error smaller than 2%. The cloud point in saltfree 1 wt % aqueous solution of Pluronic F127 is obtained from the model using the interaction parameters obtained by fitting the model to the experimental phase diagrams of PEO or/and PPO homopolymers in water.29 The temperature shift of +9% that appeared in the salt-free diagram29 is retained in the present fitting.

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Figure 4. Solubility of hexane in aqueous NaCl solution, S, relative to the hexane solubility in pure water, S0, as a function of salt molar concentration. Experimental data are from AquanYuen et al. (ref 21) (filled circles); calculated data are from the model (open circles). Table 1. Interaction Parameters (RTχA,A′) of the Theoretical Model (Energy in kJ mol-1) EO-P W 0.6508a EO-P EO-AP PO-P PO-AP 2C Na

EO-AP PO-P PO-AP 5.568a 1.266a

1.7b 1.8c 0.5c

8.5b 3.0c -2.0c 1.4b

2C

Na

Cl

11.0d 1.8f 2.33f 3.0e 1.0f 1.0f 0.0e 12.0f 12.0f 0.0e 3.99f 3.99f 0.0e 12.0f 12.0f 6.8g 12.96g 0.0f

a From the fit to the experimental PEO/water phase diagram (ref 44). b From the fit to the experimental PPO/water phase diagram (ref 47). c From the fit to the experimental PEO/PPO/water phase diagram (ref 28). d From the fit of the (C)14(PO)12(EO)17/ water phase diagram (ref 52). e As a first approximation (ref 52). f From the fit to the experimental cloud point measurements for Pluronic F127 in aqueous NaCl solution (ref 15). g From the fit to the experimental solubility measurements for hexane in aqueous NaCl solution (ref 21).

To evaluate the 2C/ion interaction parameters, model calculations were performed for the system hexane/water/ NaCl in order to fit the experimental data for the solubility of hexane as a function of salt concentration in aqueous electrolyte solution.21 In the model, the solubility is defined as the highest volume fraction of hexane (with tolerance 10-4) at which the system remains unseparated, that is, a one-phase system has a lower free energy than a twophase system. The results of the linear fitting are presented in Figure 4 as a plot of S/S0 versus molar concentration of NaCl, where S and S0 are the solubilities of hexane in aqueous salt solution and in pure water, respectively. The qualitative behavior of the calculated curve is correct, and the slope is approximated with an error of 5%. All interaction χ-parameters used in this work are compiled in Table 1. The interactions of all species with the salt ions Na+ and Cl- are obtained for the first time in the present study by fitting to the experimental data as outlined above. Results and Discussion Phase Diagrams. In this section, we present the calculated binary phase diagram of (2C)7(PO)12(EO)17 in water in coordinates of surfactant volume fractiontemperature. To study the effect of salt addition, we present also the calculated pseudobinary phase diagram

Figure 5. Binary phase diagram in coordinates of surfactant volume fraction-temperature for the system (a) (2C)7(PO)12(EO)17/water; (b) (2C)7(PO)12(EO)17/water/NaCl at salt concentration (with respect to water) ms ) 1 M; (c) (2C)7(PO)12(EO)17/ water/NaCl at salt concentration (with respect to water) ms ) 2 M. The notation is the same as in Figure 2 with the addition that L refers to the disordered phase.

in the same coordinates, considering that the effective solvent is a stock solution of salt in water. The (2C)7(PO)12(EO)17/water phase diagram in the temperature range T ) 280-380 K exhibits four ordered phases: hexagonal H1, lamellar LR, reverse hexagonal H2, and reverse cubic phase I2, as well as a disordered phase L (see Figure 5a). The most striking feature of the phase diagram presented in Figure 5a is temperature-induced transitions between different ordered phases (thermotropic phase behavior). Within surfactant volume fractions ranging from very low to φsurfactant ≈ 0.6, as the temperature is increased, successive phase transitions take place from the hexagonal phase to the lamellar phase, the reverse hexagonal phase, the reverse cubic phase, and the disordered phase. In addition to the thermotropic behavior, in the temperature range T ) 280-300 K an increase of


the surfactant volume fraction causes a transition from the hexagonal phase to the lamellar phase (lyotropic phase behavior). Let us now examine the influence of added salt on the phase behavior of (2C)7(PO)12(EO)17 in water. Figure 5b shows the (2C)7(PO)12(EO)17/water/NaCl phase diagram at the salt concentration ms ) 1 M (note that the molar concentration is defined with respect to water; i.e., the surfactant is dissolved in a stock aqueous solution of NaCl). This phase diagram exhibits only two ordered phases: normal hexagonal and reverse hexagonal. The transition between them occurs at increasing temperature. At T < 310 K and φsurfactant > 0.6, the transition can also be caused by increased surfactant volume fraction. In comparison with the salt-free phase diagram (Figure 5a), the phase diagram in the presence of NaCl exhibits a more extended region of H1 phase and the disordered phase L shifts to lower temperatures. These two trends become more pronounced in the phase diagram for the (2C)7(PO)12(EO)17/ water/NaCl system at the salt concentration ms ) 2 M, which is presented in Figure 5c. In refs 9 and 10, it is reported that the temperature of melting of the ordered phase decreases when NaCl or Na2SO4 is added in the C12EOm/water system. The disappearance of the lamellar phase and the direct transition from the normal water-continuous hexagonal phase to the reverse, surfactant-continuous, hexagonal phase are the main features of the phase diagram for the system in the presence of salt. Our calculations indicate (results are not presented here) that even at a very low concentration of NaCl (ms ) 0.01 M) and at fixed temperature T ) 280 K the transition H1 f H2 occurs; however, the free energies of the LR and the H2 phases are only slightly distinguished in the vicinity of the transition from the H1 phase. From such observations, we can conclude that the temperature stability range of the lamellar phase is very narrow and it is not detected in the modeling with the presently used temperature step that equals 1 K (see also Electrolyte Effects). Species Volume Fraction Profiles. In addition to the phase behavior, other important features predicted from the theory are the volume fraction profiles for the species 2C, PO, EO, and W and salt ions Na and Cl. Figure 6 compares the volume fraction profiles for the systems (2C)7(PO)12(EO)17/water and (2C)7(PO)12(EO)17/water/NaCl at salt concentration ms ) 2 M. Profiles in the normal hexagonal (Figure 6a) and reverse hexagonal (Figure 6b) phases are shown for φsurfactant ) 0.6. The temperature is fixed at T ) 290 K for the normal phase and T ) 320 K for the reverse phase. In the normal hexagonal phase, the interior of the cylinder is filled mostly with 2C-segments. φ2C drops fast from a maximum value, whereas φPO increases with the distance from the center and reaches its maximum at a distance where φ2C has decreased significantly. The concentration of EO-segments is very low in the center of the cylinder and exhibits a maximum far away from it. From such profiles, one can conclude that the domain has a “triple-layer” structure, with a 2C-rich center, a POrich intermediate layer, and an EO-rich periphery. In the center of the domain, φ2C + φPO ≈ 1; therefore, no water or EO-segments penetrate the region where 2C- and POsegments are located. As salt is added (dotted curves), the domain spacing increases, 2C- and PO-segments mix more in the interior, and the interface between PO- and EOlayers becomes more sharp (cf. crossings of PO and EO profiles). The salt ions are depleted from the hydrophobic core made of 2C- and PO-segments and are located in the

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Figure 6. 2C, PO, EO, and Na, Cl volume fraction profiles in the (a) normal hexagonal phase at T ) 290 K and (b) reverse hexagonal phase at T ) 320 K for the (2C)7(PO)12(EO)17/water system (solid curves) and for the (2C)7(PO)12(EO)17/water/NaCl system at ms ) 2 M (dotted curves) at the surfactant volume fraction φsurfactant ) 0.6.

water-rich part of the domain, which contains a considerable amount of the EO-segments. The volume fraction profiles for the reverse hexagonal phase are shown in Figure 6b. The interior of the cylindrical assembly is filled with water, and maxima of φPO and φC are located at the periphery of the cylindrical domain. EO-segments form a layer outside the water core. The same trends as for the normal hexagonal phase are observed for the reverse hexagonal phase when electrolyte is added. The salt ions are dissolved in the water-rich domain interior and are partially located in the EO-rich layer. The hydrophobic periphery consisting of 2C- and PO-segments is essentially salt-free. The volume fraction profiles presented in Figure 7 illustrate the effect of temperature on segment segregation in normal (Figure 7a) and reverse (Figure 7b) hexagonal phases in the aqueous electrolyte solution. Similarly to the salt effect, a raise of the temperature causes an increase in the domain size. The segregation of 2C- and POsegments in the hydrophobic part of the domain becomes less distinct, because the difference in the segment hydrophobicity decreases. As temperature is increased, the EO-water separation becomes stronger and salt ions are depleted more from the 2C-PO region. Finally, the effect of surfactant concentration on the species volume fraction profiles is examined in Figure 8 where the profiles are given for φsurfactant ) 0.2 and 0.8 at the same temperature in the normal hexagonal phase in the presence of salt. At higher surfactant content, the amount of solvent (water + salt) per surfactant molecule is smaller, and thus the solvophilic part of the assembly is less swollen creating a smaller domain. From Figure 8,

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Figure 9. Free 2C-end and EO-end and 2C-PO junction and PO-EO junction distributions in the normal hexagonal phase for the (2C)7(PO)12(EO)17/water system (solid curves) and for the (2C)7(PO)12(EO)17/water/NaCl system at ms ) 2 M (dotted curves). T ) 290 K, and φsurfactant ) 0.4.

Figure 7. 2C, PO, EO, and Na, Cl volume fraction profiles in the (a) normal hexagonal phase at T ) 280 K (solid curves) and T ) 310 K (dotted curves) and (b) reverse hexagonal phase at T ) 280 K (solid curves) and T ) 330 K (dotted curves) for the (2C)7(PO)12(EO)17/water/NaCl system at ms ) 2 M. The surfactant volume fraction φsurfactant is 0.4 for the normal hexagonal and 0.8 for the reverse hexagonal phase.

Figure 8. 2C, PO, EO, and Na, Cl volume fraction profiles in the normal hexagonal phase at T ) 280 K for the (2C)7(PO)12(EO)17/water/NaCl system at ms ) 2 M for φsurfactant ) 0.2 (solid curves) and 0.8 (dotted curves).

one can also see that at φsurfactant ) 0.2 the surfactant segments are more separated, resulting in a more pronounced triple-layer structure: the segment profiles shown by solid curves are more segregated, and thus the intermediate PO-rich layer is more distinguished. Moreover, it is necessary to underline that the addition of electrolyte and the increase of the surfactant concentration (decreasing amount of solvent) act in opposite ways: the presence of salt increases the domain size because of

worsening the quality of the effective solvent and corresponding increased surfactant/water segregation; as the surfactant content increases, the domain size decreases because the solvophilic parts shrink (see also ref 50). Block End and Junction Distributions. The lattice theory also provides volume fraction profiles of segments of a given rank, so we can obtain the distributions of both chain ends and of the two block junctions of the triblock copolymer. Figure 9 shows the end and junction distributions for (2C)7(PO)12(EO)17 in water and in water/NaCl solution at NaCl concentration ms ) 2 M in the normal hexagonal phase. The 2C-end distribution closely follows the distribution of all 2C-segments (cf. Figure 9 and Figure 7a), indicating that the alkyl chains are not stretched in the interior of the assembly. The distribution of EO-ends is broad without a well-pronounced maximum; therefore the EO-blocks are not stretched in the corona. From the 2C-PO junction distribution, one can conclude that at these conditions the 2C- and PO-segments are segregated slightly in the hydrophobic part of the domain. The distribution of the PO-EO junction has a maximum located outside the 2C/PO core. When salt is added, the maximum becomes sharper indicating stronger segregation of PO- and EO-segments (sharpening of the PO-EO interface, see Figure 6a). This segregation is caused by the different interaction of the polar state of PO and EO with salt (at a given temperature, T ) 290 K, most of the segments are in the polar state). As one can see from Table 1, RTχEO-P,salt ) 1.0 kJ mol-1 but RTχPO-P,salt ) 3.99 kJ mol-1; thus the segments interact differently with the solvent (water + salt), and as a result they mix less. The addition of salt, therefore, causes a segregation of the solvophobic part of the domain consisting of 2C and PO from the solvophilic part consisting of EO. Domain Spacing. Small-angle neutron and X-ray scattering measurements are often used to characterize ordered phases.49-51 The magnitude of the principal (49) Alexandridis, P.; Olsson, U.; Lindman, B. A Record Nine Different Phases (Four Cubic, Two Hexagonal, and One Lamellar Lyotropic Liquid Crystalline, and Two Micellar Solutions) in a Ternary Isothermal System of an Amphiphilic Block Copolymer and Selective Solvents (Water and Oil). Langmuir 1998, 14, 2627-2638. (50) Alexandridis, P.; Ivanova, R.; Lindman, B. Effect of Glycols on the Self-Assembly of Amphiphilic Block Copolymers in Water. II. Glycol Location in the Microstructure. Langmuir 2000, 16, 3676-3689. (51) Holmqvist, P.; Alexandridis, P.; Lindman, B. Modification of the Microstructure in Block Copolymer-Water-“Oil” Systems by Varying the Copolymer Composition and the “Oil” Type: A Small-Angle X-ray Scattering and Deuterium NMR Investigation. J. Phys. Chem. B 1998, 102, 1149-1158. (52) Shusharina, N. P.; Alexandridis, P.; Linse, P.; Balijepalli, S.; Gruenbauer, H. J. M. Phase Behavior and Structure of ABC Triblock Copolymers Dissolved in Selective Solvent. Eur. Phys. J. E, in press.


Figure 10. Domain spacing plotted as a function of surfactant volume fraction in double logarithmic scale: (a) for the system (2C)7(PO)12(EO)17/water in the different ordered phases and at correspondingly different temperatures (indicated in the figure); (b) in the normal hexagonal phase at T ) 290 K with no salt added (solid line) and with added salt at ms ) 1 M (dashed line) and ms ) 2 M (dotted line); (c) the same as in (b) but for the reverse hexagonal phase at T ) 320 K.

scattering vector provides a measure of the domain spacing. Here, we obtain such information from the theory. Figure 10 displays the calculated domain spacing in the ordered phases of (2C)7(PO)12(EO)17 in water (Figure 10a) and in aqueous salt solution (Figure 10b,c) as a function of surfactant volume fraction at fixed temperature. The increase in the domain spacing when temperature is increased is clearly seen from Figure 10a (cf. also the profiles in Figure 7). The domain size within a given ordered phase decreases with increasing surfactant concentration (cf. Figure 7a,b and Figure 8). The reverse and lamellar phases exhibit a stronger φsurfactant dependence than the normal phase. In the normal hexagonal phase at φsurfactant > 0.55, the size of the domain becomes bigger than in the lamellar phase at the same surfactant content. From Figure 10b,c, one can note only a slight variation of the domain spacing when NaCl is added. However, several subtle features can be observed. With addition of salt, the φsurfactant dependence of the domain size becomes weaker, that is, a decreased amount of better solvent shrinks the domain faster. Moreover, the effect of addition of salt on the domain size is stronger in the normal hexagonal phase than in the reverse hexagonal phase (see also the volume fraction profiles in Figure 6). This can be explained by the fact that the hydrophobic part of the domain is larger in the reverse structure so that a

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worsening of the solvent leads to a deswelling of an effectively smaller domain part. Temperature Effects. The basic temperature effect, that is, temperature-induced phase transitions between ordered phases in the (2C)7(PO)12(EO)17/water system, can be explained within the two-state model formalism implemented here for describing the EO and PO interactions with water.46,47 The model allows the polymer segments to adopt an equilibrium state distribution that depends on the temperature and the polymer concentration. The fraction of apolar states of PO- and EO-segments increases with increasing temperature and with increasing polymer concentration in an aqueous solution (see ref 52). This leads to a shift of the hydrophilic/hydrophobic balance toward increased hydrophobicity of both PO- and EOsegments. Moreover, the set of interaction χ-parameters used here (see Table 1) is a key for understanding features of the phase behavior. The 2C/water interaction reflects the highly hydrophobic nature of the alkyl block and results in its location in the water-free part of the structural domain. The interaction between 2C- and POsegments is athermal, whether PO-segments adopt a polar or an apolar state. The interaction between a 2C-segment and an EO-segment in the apolar state is athermal (RTχ2C,EO-AP ) 0), whereas it is repulsive when the EOsegment is in the polar state (RTχ2C,EO-P ) 3 kJ mol-1). Therefore, at elevated temperature the part of the surfactant that interacts favorably with water decreases, effectively shifting the surfactant composition toward one that exhibits a larger hydrophobic part, thus making reverse structures more preferable. At the same time, the segregation between 2C- and EO-blocks becomes weaker and, therefore, concentration-induced (lyotropic) phase transitions vanish. At high surfactant concentrations, the fraction of apolar states increases; thus the effect of the effective renormalization of surfactant composition toward the larger hydrophobic part is more pronounced, and as a result, no high-curvature normal phases are observed there. The mainly thermotropic phase behavior of (2C)7(PO)12(EO)17 in water is different from that found for (EO)m(PO)n(EO)m block copolymers which exhibit mainly lyotropic phase behavior in aqueous solution.32,33,53 From the modeling point of view, the difference can be explained as follows. In the (EO)m(PO)n(EO)m/water system, an increase of temperature causes a shift of the state distribution toward apolar states for both PO- and EO-segments. The fraction of apolar states increases for the two segment types proportionally;52 thus no significant change in the hydrophilic/hydrophobic balance between the blocks occurs. On the contrary, the graded structure of the (2C)7(PO)12(EO)17 molecule and the given set of interaction parameters results in a difference in hydrophobicity between the alkyl block from one side and the PO- and EO-blocks from the other. The increased fraction of apolar states of PO- and EO-segments with increasing temperature causes an effective renormalization of the molecular composition, thus rendering the hydrophobic part effectively longer compared to the hydrophilic part. Electrolyte Effects. In the presence of NaCl, the phase behavior of (2C)7(PO)12(EO)17 in water exhibits the following features: (i) The disordered phase, L, shifts toward lower temperatures; that is, the ordered lyotropic liquid crystalline structures become less stable. (ii) The phase (53) Alexandridis, P.; Zhou, D.; Khan, A. Lyotropic Liquid Crystallinity in Amphiphilic Block Copolymers: Temperature Effects on Phase Behavior and structure of Poly(ethylene oxide)-b-Poly(propylene oxide)b-Poly(ethylene oxide) Copolymers of Different Compositions. Langmuir 1996, 12, 2690-2700.

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transitions become sharper, so that the lamellar phase is unfavorable and a direct transition from the normal to the reverse hexagonal structure occurs. The origin of such effects can be explained in terms of the species interactions (see Table 1). The interaction of all surfactant species with salt species is repulsive, and it is stronger than the interaction of salt with water molecules. Therefore, a partial exchange of water by salt ions renders the solvent, which is a mixture of water and salt, effectively worse for the surfactant segments, even if only a small amount of salt is added. At the same time, the polar and apolar states of both EO- and PO-segments interact differently with the salt species. Specifically, the interaction between the apolar states and the salt ions is much more repulsive than the interaction between the polar states and the salt ions. As the temperature is increased, the population of the apolar states grows, and thus the EO- and POsegments become more hydrophobic. In the presence of salt, a worsening of the effective solvent (water + salt) for EO- and PO-segments develops faster (in terms of temperature dependence), and this is reflected in a faster effective renormalization of the surfactant composition toward an effective increase of the solvophobic part. An increase of the temperature tends to favor the appearance of the reverse phases, and as a result, the system passes through the lamellar phase in an indistinguishably narrow temperature range. Conclusions The mean-field formalism used in the paper allows us to predict the effects of temperature and addition of electrolyte on the phase behavior and phase structure of alkyl-propoxy-ethoxylate surfactants in water. The parameters of interaction of 2C, PO, EO, and water with Na and Cl are evaluated by fitting the model to experimental data obtained for simple systems (hexane/water, Pluronic F127/water/NaCl). The availability of these data allows the use of the theoretical framework presented here so as to capture the effects of various electrolytes on nonionic surfactant phase behavior. The key features of the theoretical prediction of the composition-temperature phase behavior are (i) thermotropic phase behavior which dominates over lyotropic phase behavior; (ii) decrease of the temperature-range stability of ordered phases when electrolyte is added; (iii) disappearance of the lamellar phase when electrolyte is added, resulting in a direct normal hexagonal-reverse hexagonal phase transition. The explanation for such behavior is based on the graded interaction of the solvent

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with the parts of the surfactant molecule. Pure water becomes an effectively worse solvent for the EO- and POsegments as the temperature is increased because of the increasing population of the apolar states. The addition of NaCl increases the solvophobicity of all polymer segments in general, and of the apolar states in particular. A combination of temperature and salt effects results in sharpening the thermotropic phase transitions. The structural characteristics provided by the theory (species volume fraction profiles, chain end and junction distributions) allow us to describe the phase-forming domains and to analyze the temperature and electrolyte effects. Spherical, cylindrical, or planar domains have a triple-layer structure. The layers are rich with 2C-, PO-, and EO-segments, respectively. In the normal hexagonal phase, the hydrophobic solvent-free 2C/PO core is separated from the hydrophilic solvated EO-corona; in the reverse phases, the center of the domain is filled with water and EO-segments while 2C- and PO-segments are at the periphery. The calculated volume fraction profiles show that the salt ions are located in the EO-rich solvated layer. The blocks forming the domains are not stretched. Both an increase of the temperature and the addition of salt lead to an increase of the domain size. Both change in temperature and addition of salt cause an effective shift in the solvophobic-solvophilic balance of the graded surfactant in water. The location of the POblock of intermediate polarity between the solvophobic 2C-block and the solvophilic EO-block makes it possible to “tune” the surfactant composition by means of temperature or added salt. Different structures from welldefined triple layers to double layers of different composition (2C + PO/EO or 2C/PO + EO) and different phases can be observed when the temperature or salt concentration is varied. An increase of temperature causes a renormalization of the surfactant composition toward the longer solvophobic part, thus resulting in the phase transitions into reverse structures. The same trend takes place upon an addition of salt since the interaction of salt with the apolar states is much more repulsive than that with polar states (see Table 1). The temperature effects on both phase behavior and structure are more pronounced in the presence of salt. Acknowledgment. P.A. acknowledges The Dow Chemical Company for a grant that funded this research. We thank Professor P. Linse for helpful discussions and comments on the manuscript. LA026257N

Mean-Field Theory Prediction of the Phase Behavior and Phase

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