J. Phys. Chem. B 2001, 105, 5419-5426
5419
Effect of Hydrophilic- and Hydrophobic-Chain Lengths on the Phase Behavior of A-B-type Silicone Surfactants in Water Hironobu Kunieda,*,† Md. Hemayet Uddin,† Makiko Horii,† Haruhiko Furukawa,‡ and Asao Harashima‡ Graduate School of Engineering, Yokohama National UniVersity, Tokiwadai 79-5, Hodogaya-ku, Yokohama 240-8501, Japan, and Dow Corning Toray Silicone Co. Ltd., Chigusa-Kaigan 2-2, Ichihara 299-01, Japan ReceiVed: September 16, 2000; In Final Form: March 12, 2001
The phase behavior of a long hydrophobic chain A-B-type silicone surfactant, Me3SiO-(Me2SiO)m-2-Me2SiCH2CH2CH2-O-(CH2CH2O)nH (Sim C3EOn), in water was investigated by phase study and small-angle X-ray scattering (SAXS). The types of liquid crystals or self-organized structures are highly dependent on both EO-chain (n) and poly(dimethylsiloxane)-chain (m) lengths or the volume ratio of the EO chain to the total surfactant, nVEO/VS, which is related to the classical Griffin’s HLB value. Reverse discontinuous cubic phase (I2) for Si14C3EO7.8 and Si25C3EO7.8,12.2,15.8, reverse hexagonal phase (H2) for Si14C3EO12, lamellar (LR) phase for Si14C3EO15.8 and Si25C3EO51.6, and hexagonal (H1) and discontinuous cubic (I1) phases for Si5.8C3EO36.6,51.6 are formed. Hence, both hydrophobic and hydrophilic chains affect the surfactant layer curvature, but in an opposite way. On the other hand, the effective cross-sectional area per surfactant at the hydrophobic surface of self-organized structures, aS, increases with increasing m (or n) at constant n (or m). aS is related to the amphiphilicity of surfactant (surfactant size). Since the surfactant layer curvature changes from positive to negative with increasing m at constant n, the leff/lmax decreases with m, where leff is the effective hydrophobicchain length and lmax is the length of the chain in its fully extended form. Namely, the entropy loss of a long hydrophobic chain would be largely increased when it is stretched, and thus, long hydrophobic chain tends to be in a shrunk-bulky state. This causes the expansion of aS and the change in the surfactant layer curvature from positive to negative. In a similar mechanism, aS increases with increasing the EO-chain length, n, but the surfactant layer curvature changes from negative to positive.
Introduction Hydrophilic surfactants form a normal-type self-organized structure or liquid crystal in water, in which the surfactant layer curvature is convex toward water (positive curvature), whereas lipophilic surfactants produce a reverse-type one with negative curvature. Since the types or shapes of the self-organized structures are highly dependent on the hydrophile-lipophile property of surfactant, there have been many attempts to figure out the correlation between the chemical structure of surfactants and the shape of aggregates. In the case of nonionic surfactants, the surfactant layer curvature changes from negative to positive with increasing the hydrophilic chain length (e.g., polyoxyethylene (EO) chain) because the repulsion between the hydrophilic groups increases with increasing the EO-chain length at constant temperature.1-4 Hence, the shape of the self-organized structure changes from reverse spherical micelle to normal micelle via layerlike or rodlike structures with increasing the EO chain. The effective cross sectional area per surfactant in the aggregates also increases with increasing EO-chain length of surfactant when the hydrophobic-chain length is fixed. According to the packing model,5-7 the shape of selforganized structure is determined by the so-called critical packing parameter, VL/(aSleff), where VL is the volume of * Corresponding author. Phone & Fax: +81-45-339-4190. E-mail:
[email protected]. † Yokohama National University. ‡ Dow Corning Toray Silicone Co. Ltd.
hydrophobic part of surfactant, aS is the effective cross-sectional area per surfactant molecule at the interface, and leff is the effective length of the hydrophobic chain, respectively. In such a theory, however, the effect of the hydrophobic-chain length on aS is usually neglected or, at least, is considered to be constant, since the hydrophobic part can be, in general, regarded to be in a amorphous liquid state such as pure melted hydrocarbon. Hence, leff is considered to be equal to lmax or the leff/lmax is constant (= 0.7) in the packing theory, where lmax is the hydrophobic-chain length in its extended form.6 The hydrophobic-chain length is assumed not to influence the aS. Actually, experimental results on the normal-type self-organized structures show that the aS is not largely dependent on the hydrocarbon chain length of surfactant when the carbon number of surfactant is in the range of C10-C18.1,3,8 Thus, it has been considered that the aS is determined only by the balance between the repulsion of the head polar group and the interfacial tension at the hydrophobic surface of the self-organized structure in the packing theory. In this theory, the large aS means that the surfactant is very hydrophilic and normal-type of self-organized structure tends to form. However, there must be a contribution of hydrocarbon-chain part of surfactant on aS and leff.9 In the classical Winsor’s R theory8 or Griffin’s HLB system,10 the balance between the interaction of hydrophilic part and that of hydrophobic part is considered to determine the surfactant layer curvature, although these theories do not give quantitative information about the shape of aggregates. The two classical theories are essentially
10.1021/jp003314h CCC: $20.00 © 2001 American Chemical Society Published on Web 05/18/2001
5420 J. Phys. Chem. B, Vol. 105, No. 23, 2001 identical,11 and they are in contradiction with the critical packing model mentioned above. There is a statistical thermodynamic approach to the configuration effect of the hydrocarbon chain in the surfactant bilayer, and it shows that leff/lmax decreases with increasing the hydrocarbon-chain length.12 It is also wellknown that the end-to-end distance of a random flight polymer chain is proportional to N,1/2 where N is the degree of polymerization.13 It means that a longer chain tends to have a shrunk-bulky structure and the chain length may affect the surfactant layer curvature. However, the carbon number of commonly used hydrocarbon surfactant is in a range of C10C18, although there have been some attempts to use a longerchain surfactants with branched chain or double bond.14,15 Since Krafft temperatures for long and linear hydrocarbon-chain surfactants are high and the surfactants tend to be in a solid state at room temperature, it is difficult to figure out how the hydrophobic chain length affects the self-organization in hydrocarbon-type surfactant systems. Silicone surfactants have unique characteristics.16,17 They are very surface-active due to the weak cohesive energy of the lipophilic chains, poly(dimethylsiloxane) groups, which consist of many methyl groups. Different from conventional hydrocarbon surfactants, even very long poly(dimethylsiloxane) chain surfactants, can be used because they are in liquid state at room temperature. The phase behavior of copolymer-type silicone surfactants in water has been studied as a function of temperature.18-20 Recently, the phase behavior and the selforganized structures of trisiloxane-type nonionic surfactants were also studied as a function of temperature.21,22 We constructed the phase diagram of the trisiloxane surfactant-water system as a function of its EO-chain length at constant temperature.23 With increasing the EO-chain length, the surfactant layer curvature changes from negative to positive. However, the trisiloxane moiety is not big enough to know the effect of the hydrophobic-chain length on aS and leff because its hydrophobic volume is similar to that of C18 group. If an A-B type silicone surfactant with a long and linear lipophilic chain is available, not only the effect of the lipophilic chain length on the phase behavior but also the unique property of the silicone surfactant would be figured out. In this context, we have constructed the phase diagram of water-polyoxyethylene-type silicone surfactant with a linear lipophilic chain. The structures of liquid crystals were analyzed by means of small-angle X-ray scattering. Finally, the effect of both hydrophilic and lipophilic chain lengths on the selforganization is discussed. Experimental Section Materials. Me3SiO-(Me2SiO)m-2-Me2SiCH2CH2CH2-O(CH2CH2O)nH was obtained from Dow Corning-Toray Co Ltd., Japan. Me is a methyl group attached to Si, m is the total number of silicone, and n is the average number of the EO units. They are abbreviated as SimC3EOn in the present paper. Their purities are 92.1% for Si5.8C3EO36.6, 99% for Si5.8C3EO51.6, 99.5% for Si14C3EO3.2, 99.9% for Si14C3EO7.8, 96.4% for Si14C3EO12, 97.7% for Si14C3EO15.8, 97.9% for Si25C3EO3.2, 96.2% for Si25C3EO7.8, 93.7% for Si25C3EO12.2, 93.1% for Si25C3EO15.8, and 94.6% for Si25C3EO51.6. The main impurity is unreacted polyethers, CH2dCHCH2-O-(CH2CH2O)nH. The polydispersity index of poly(dimethylsiloxane) part, M h w/M h n, is 1.02 for Si5.8, 1.19 for Si14, and 1.20 for Si25, where M h w is the weight average molecular weight and M h n is the number average molecular weight. The M h w/M h n values for polyoxyethylene part are 1.21, 1.26, 1.16, 1.20, and 1.13 for EO3.2, EO7.8, EO12.2,
Kunieda et al.
Figure 1. Molar volume of Si14C3EOn as a function of the EO unit, n. The slope of the line corresponds to the molar volume per EO unit.
EO15.8, and EO51.6, respectively. Si14C3EOn with a different EOchain length was obtained by mixing the above surfactants to construct a phase diagram as a function of the EO-chain length. Molar Volumes of Surfactants. The molar volume of surfactant is calculated by the following equation:
VS ) MS/FS
(1)
where MS and VS are the molecular weight and the molar volume of surfactant, respectively. It is known that arithmetic additivity approximately holds concerning the molar volumes of each functional group in the surfactant.1,23,24 Then the molar volume of the surfactant (VS) is the sum of molar volumes of each group in the surfactant, and the following relation holds:
VS ) VL + nVEO + VOH
(2)
where VL, VEO, and VOH are the molar volumes of the lipophilic part, the oxyethylene (EO) group, and the hydroxyl group, respectively, and n is the number of EO units. The experimental data show that VS is proportional to n for various pure polyoxyethylene alkyl ethers, CmEOn, and eq 2 indeed holds. VEO is 38.8, and VOH is 8.8 cm3/mol, according to the previous data of pure C12EOn.2,25 The densities of silicone surfactants (Si14C3EOn, n ) 3.2 and 7.8) were directly measured by a digital density meter (Anton Paar 40) at 20 °C because they are in a liquid state at this temperature. The densities of longer-EO-chain surfactants were estimated by extrapolating the density values of the surfactant ethanol solutions to 100% surfactant as a function of the surfactant concentration. The densities are 0.9755 g cm-3 for Si14C3EO3.2, 0.9973 g cm-3 for Si14C3EO7.8, 1.021 g cm-3 for Si14C3EO12, and 1.035 g cm-3 for Si14C3EO15.8. Their molar volumes are plotted against the EO unit number as is shown in Figure 1. In Figure 1, the line, whose slope is VEO ) 38.8 cm3/mol is fitted to the experimental data. From the intersection at n ) 0, we obtain the molar volume of lipophilic part, 1137 cm3/mol, or 1.89 nm3 per surfactant. The molar volumes of Si25C3EOn and Si5.8C3EOn are calculated by eq 2 using the values obtained for Si14C3EOn. The volumes of lipophilic parts for Si5.8C3-, and Si25C3- are 0.84 and 3.29 nm3/molecule, which are considerably larger than that of oleyl group, 0.513 nm3/ molecule.1 When the surfactant concentrations were calculated for the construction of the phase diagram, the impurity was neglected, and the surfactants were regarded as 100% pure. When the
A-B-type Silicone Surfactants in Water
J. Phys. Chem. B, Vol. 105, No. 23, 2001 5421
Figure 2. Phase diagrams of binary water-Si14C3EOn systems as a function of temperature: (a) water-Si14C3EO3.2 system, (b) water-Si14C3EO7.8 system, (c) water-Si14C3EO12 system, and (d) water-Si14C3EO15.8 system. I2, H2, and LR are reverse discontinuous cubic, reverse hexagonal, and lamellar liquid crystals, respectively. Om indicates a surfactant liquid phase containing small amounts of water, and W indicates excess water phase. S is a solid-present region, and II is a two-phase region.
volume fraction of the lipophilic part of the surfactant, φL, was calculated in order to analyze the SAXS data, the impurity was regarded as a solvent. Since the polyethers are highly watersoluble, they are considered not to participate in the formation of the self-organized structures. Silicone-Chain Length in its Extended Form. The polydimethylsiloxane chain is more flexible than conventional hydrocarbon chains because the bond angle of Si-O-Si is wide and the Si-O bond can freely rotate. Under the condition that the Si-O-Si and O-Si-O bond angles are 143° and 110° and the Si-O bond length is 0.164 nm,26 the hydrophobic chain length, Me3SiO-(Me2SiO)m-2-Me2SiCH2CH2CH2-, in its extended form was calculated. Taking into account the terminal propylene group, we calculate SimC3- length to be 2.1 nm for m ) 5.8, 3.9 nm for m ) 14, and 6.7 nm for m ) 25, respectively. The effective cross sectional area of the extended silicone chain was calculated to ∼0.50 nm2, which is considerably larger than that of the hydrocarbon chain, 0.20-0.22 nm2. Determination of Phase Boundary. Various amounts of water and surfactant were sealed in ampules. These ampules were well shaken and left at constant temperature. Homogeneity was attained using a vortex mixer and repeated centrifugation through a narrow constriction in the sample tubes. The phase equilibria were determined by visual observation. The types of
liquid crystals were identified by means of a polarized optical microscope and small-angle X-ray scattering (SAXS). Small-Angle X-ray Scattering (SAXS). The interlayer spacing of liquid crystals was measured using SAXS, performed on a small-angle scattering goniometer with an 18kW Rigaku Denki rotating anode goniometer (Rint-2500) at about 25 °C. The samples of liquid crystals were lapped by plastic films for the measurement (Mylar seal method). Results and Discussion Phase Diagrams of Binary Water-SimC3EOn Systems. Phase diagrams of water-Si14C3EOn (n ) 3.2, 7.8, 12, and 15.8), Si25C3EOn (n ) 3.2, 7.8, and 12.2) or Si5.8C3EO36.6 systems were constructed as a function of temperature and are shown in Figures 2a-d, 3a-c, and 4. Only one type of liquid crystal is present in each phase diagram except that corresponding to the water-Si5.8C3EO36.6 system, in which a discontinuous normal micellar cubic phase (I1) and a normal hexagonal phase (H1) are formed. In water-Si14C3EOn systems, the type of liquid crystals changes from surfactant liquid (Om) to lamellar liquid crystal (LR) via discontinuous reverse micellar cubic phase (I2) and reverse hexagonal liquid crystal (H2) when the EO-chain length increases from 3.2 to 15.8, as shown in Figure 2a-d. At high
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Figure 4. Phase diagrams of binary water-Si5.8C3EO36.6 system as a function of temperature. Wm, I1, and H1 are aqueous micellar solution, normal discontinuous cubic, and normal hexagonal liquid crystals, respectively.
Figure 3. Phase diagrams of binary water-Si25C3EOn systems as a function of temperature: (a) water-Si25C3EO3.2 system, (b) waterSi25C3EO7.8 system, and (c) water-Si25C3EO12.2 system. Phase notation is the same as that in Figure 2.
temperature, the liquid crystal is melted and a two-phase region consisting of a liquid surfactant phase (Om), and excess water phase (W) appears. The maximum temperature of each liquid crystal should be adjacent to the phase boundary of the Om + W region according to the phase rule, but there is a gap probably due to the presence of a small amount of impurity (unreacted poly(ethylene glycol)). Nevertheless, since the transition from Om + W to liquid crystal + W occurs almost at constant temperature, the influence of the impurity on the phase behavior
is not very large. In ordinary hydrocarbon-type nonionic surfactant systems such as CmEOn, C18:1EOn (polyoxyethylene oleyl ether), etc., LR phase, normal hexagonal liquid crystal (H1) phase, or normal discontinuous cubic phase (I1) is formed if the EO chain length is 7.8-15.8.1,25 Note that the volume of Si14C3- group is 3.5 times larger than that of the C18- group. In longer-hydrophobic-chain Si25C3EOn systems, only the surfactant liquid phase (Om) and the optically isotropic I2 phase appear in the range of EO-chain from 3.2 to 15.8. The maximum temperature for the I2 phase or the maximum solubilization of water into the I2 phase increases with increasing the EO-chain length as is shown in Figure 3b-c. In the case of normal-type self-organized structures, the thermal stability is related to the hydrophobic-chain length. When the EO-chain length is 51.6, the LR phase appears, although the phase diagram was not constructed. On the other hand, an aqueous micellar solution phase (Wm) is formed, and both I1 and H1 phases are successively produced at a high concentration of surfactant in the water-Si5.8C3EO51.6 system. The present phase diagrams clearly show that the surfactant layer curvature tends to be negative as the hydrophobic chain length of surfactant increases and reversetype self-organized structures are formed. On the other hand, the surfactant layer curvature tends to be positive when the EOchain length increases and normal-type self-organized structures are formed in a long-EO-chain surfactant system. Note that a discontinuous reverse micellar cubic phase (I2) is rarely formed in ordinary hydrocarbon surfactant systems, although it is formed in some phospholipid,27 polyoxypropylene-polyoxyethylene copolymer,28 and sugar-related surfactant systems.29 In the case of conventional polyoxyethylenetype nonionic surfactant systems, there is no report on the formation of I2 phase. Phase Diagram of the Water-Si14C3EOn System as a Function of EO-Chain Length. The phase diagram of waterSi14C3EOn system was constructed as a function of the EOchain length, n, at 20 °C and is shown in Figure 5. The volume ratio of the hydrophilic moiety to surfactant, nVEO/VS, is plotted vertically. The corresponding EO number is also plotted on the right-hand axis. The same kind of phase diagrams were constructed for trisiloxane-type nonionic surfactant, polyoxyethylene dodecyl, or oleyl ethers.1,23,25 Three types of liquid crystals, discontinuous reverse cubic phase I2, reverse hexagonal
A-B-type Silicone Surfactants in Water
J. Phys. Chem. B, Vol. 105, No. 23, 2001 5423 TABLE 1: Range of nVEO/VS for Each Liquid Crystal in Water-Surfactant Systems surfactant C12EOna C18:1EOnb trisiloxanec Si14C3EOn Si25C3EOn phase Om I2 H2 LR Wm a
0-0.24 d d 0.3-0.43 0.46
0-0.2 d 0.2-0.26 0.3-0.48 0.48
0-0.42 d d 0.45-0.6 0.6
0-0.13 0.13-0.21 0.21-0.28 0.28 e
0-0.09 0.09-0.24 e -0.05 e
Ref 2. b Ref 1. c Ref 23. d Not found. e Not examined.
ionic surfactant is related to nVEO/VS by the following equation:1
HLB number ) 20(F(EO(n)/FS)(nVEO/VS)
Figure 5. Phase diagram of the water-Si14C3EOn system as a function of the EO-chain length at 20 °C. nVEO/VS is the molar volume ratio of the EO chain to the surfactant.
phase H2, and lamellar liquid crystal LR are observed with increasing EO-chain length of surfactant, as shown in Figure 5. The, I2 phase was identified by its appearance (extremely viscous, transparent and optically isotropic), and from its position on the phase diagram, its structure could not be determined because only one SAXS peak was observed. It is considered that the I2 phase consists of a discontinuous-type reverse micellar cubic phase because it exists between the surfactant liquid (Om) and the H2 phases.30 The H2 and LR phases were identified by their SAXS peak ratios. It was very difficult to determine the phase boundary between a single LR phase and LR + W region in Figure 5 because the intensity of the SAXS peak is considerably low at high water content. Since the boundary was determined by visual inspection, the accuracy is low compared with other boundaries. However, the interlayer spacing measured by SAXS is continuously increased with increasing water content in the single LRphase region when the EO-chain length is fixed. It is sure that there is a single-phase region up to the phase boundary. The boundaries between two-phase regions were determined by direct observation and optical microscope. In the Om + W region, an excess water phase is separated from a fluid surfactant-liquid phase containing a small amount of water (Om), whereas the mass of an isotropic viscous reverse cubic phase (I2) and the excess water phase are present in the I2 + W region. The accuracy of the boundary between Om + W and I2 + W regions is n ) 4.5 ( 0.5 in the EO-unit scale. In the H2 + W region, a dispersion of an optically anisotropic liquid crystal was observed by optical microscope, whereas vesicles were found in the LR + W region. The accuracy of the boundary between I2 + W and H2 + W regions is n ) 8 ( 1, and that between H2 + W and LR + W regions is n ) 12 ( 0.5. In the case of C18:1EOn system, the H2 phase is formed between n ) 2.2-3.0, and the LR phase is produced between n ) 3.4-7.6.1 Hence, as the hydrophobic-chain length of surfactant increases, a same type of self-organized structure tends to form at longer EO-chain length. HLB of Surfactant and Macroscopic Phase Behavior. It is well-known that the hydrophile-lipophile balance (HLB) of surfactant and the macroscopic phase behavior are highly related with each other. In fact, both hydrophilic and hydrophobic chain lengths affect the surfactant layer curvature in the present systems. Griffin’s HLB number for polyoxyethylene-type non-
(3)
where VS and VEO are the molar volumes of surfactant and EO unit, respectively. F(EO(n) and FS are the densities of the EO chain and the surfactant. Since both densities are not very different, the vertical axis, nVEO/VS, in Figure 5 is considered to be the Griffin’s HLB number on the volume base. nVEO/VS ) 1 means that the surfactant having infinitely long EO chain. The EO-chain ranges for various self-organized structures in a dilute region of some water-nonionic surfactant systems are summarized in Table 1. It is very interesting that the nVEO/VS ranges for each liquid crystal are almost the same, except for the trisiloxane surfactant systems. For the same type of self-organized structure to be formed, the ratio between the EO-chain length and the hydrophobic chain length should be equal even for the present silicone surfactants as far as a linear straight chain surfactant is concerned. The Griffin’s HLB number is essentially the same as the concept of R in Winsor’s R theory, in which the surfactant layer curvature is determined by the ratio of the hydrophobic interaction to hydrophilic interaction.11 The lipophilic part of the trisiloxane surfactant is short and bulky, and its volume is almost the same as that of the oleyl group. However, the maximum length is 1 nm in its extended form, and it is much shorter than the oleyl group, 2.3 nm.22 Since the effective hydrophobic chain length is limited, the surfactant layer curvature is less positive or more negative for the trisiloxane surfactant compared with a linear-chain surfactant at a fixed EO-chain length. Consequently, as far as polyoxyethylene-type nonionic surfactants are concerned, the HLB number can accurately predict the types of self-organized structures, including silicone surfactants, if the lipophilic moiety is a straight chain. The HLB number concept is somewhat in contradiction with the so-called packing model, in which the hydrophobic chain-length is essentially neglected. In the packing theory, if the same type of self-organized structure is considered, the hydrophobic chain length does not affect the packing parameter because it is usually assumed that VL and leff vary proportionally for a linear-chain surfactant. The aS should be also constant if the head is the same. However, the experimental results show the opposite tendency as is shown in Table 1. SAXS Results. To analyze the detailed structures of each liquid crystal, we measured the interlayer spacings of I1, I2, H1, H2, and LR phases as a function of surfactant concentration in each binary water-surfactant system by means of small-angle X-ray scattering. The typical SAXS peaks are shown in Figure 6. The reciprocal spacings of these peaks are found to be in the ratio 1:x3:2 for theH2 phase, 1:2 for the LR phase, 1:x3:2 for the H1 phase, and x3:x4:x8:x11 for the I1 phase. We consider that the four peaks in the I1 phase represent diffractions from the (111), (200), (220), and (311) planes, respectively. The
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Figure 6. Typical SAXS peaks for liquid crystals: (a) I2 phase at 98 wt % Si25C3EO15.8, (b) H2 phase at 80 wt % Si14C3EO12, (c) LR phase at 85 wt % Si25C3EO51.6, (d) H1 phase at 65 wt % Si5.8C3EO36.6, and (e) I1 phase at 38 wt % Si5.8C3EO36.6.
indices of the planes indicate that this particular cubic phase is probably a face-centered cubic (fcc) belonging to the F23 space group.31 The schematic structures of I2, H2, and LR phases are shown in Figure 7. We assumed that spherical micelles (or reverse spherical micelles) are packed in a cubic array in the I1 (or I2) phase, infinitely long rod micelles (or reverse rod micelles) are packed in a hexagonal array in the H1 (or H2) phase, and bimolecular layers are stacked in the LR phase. According to geometrical relations, the following equations hold for the interlayer spacing, d, and the volume fraction of lipophilic part of surfactant, φL, for each liquid crystal
for the I2 phase d ) (36π)1/3
nm1/3
xh2 + k2 + l
VL (1 - φL)2/3 (4) φL 2 aS
for the H2 phase
VL (1 - φL)1/2 d ) (2x3π)1/2 aS φL
for the LR phase
d)
for the H1 phase
VL 1 d ) (2x3π)1/2 aS φL
for the I1 phase
(5)
2VL 1 aS φL
(6)
()
d ) (36π)1/3
1/2
nm1/3
xh2 + k2 + l
(7)
()
VL 1 2 aS φ L
1/3
(8)
where aS and VL are the effective cross sectional area and the volume of lipophilic part per surfactant, respectively. nm is the number of (reverse) micelles in a unit cell. h, k, and l are the Miller indices, and h2+ k2+ l2 is 3 for a face-centered, 2 for a body-centered, 1 for a simple cubic array.
Figure 7. Schematic structures of I2 (a), H2 (b), and LR (c) phases. d is the interlayer spacing measured by SAXS.
The measured interlayer spacings as a function of surfactant concentration for each representative liquid crystal are shown in Figure 8a,b. We considered the purity of surfactant to calculate the volume fraction of the lipophilic part of the silicone surfactant. The impurity, water-soluble polyether dissolved in water, does not participate in the formation of aggregates in liquid crystals. Namely, water + polyether is considered to be the solvent. If the shape of aggregates is unchanged and aS is constant with the change in surfactant concentration in each system, the straight lines should pass through the origin of each graph according to eqs 4-8. As is shown in Figure 8a,b, the straight lines fulfill this requirement and aS is considered to be almost constant. In other systems (water + Si25C3EO7.8, water + Si25C3EO12.2, water + Si25C3EO15.8, and water + Si25C3EO51.6), similar results were obtained. Hence, aS is dependent on both EO-chain and hydrophobic-chain lengths of the surfactant. aS was also calculated using eqs 4-8 for each liquid crystal, and the results are shown in Figure 9. The value of aS for the LR phase of trisiloxane surfactant23 is also plotted in Figure 9. The aS increases with increasing the EO numbers in all the surfactant systems. It is clear from Figure 9 that the aS also increases with increasing the hydrophobic-chain length at a fixed EO-chain length of silicone surfactant and the surfactant layer curvature changes from positive to negative. For example, at EO units )
A-B-type Silicone Surfactants in Water
J. Phys. Chem. B, Vol. 105, No. 23, 2001 5425 is not proportional to its volume. The leff/lmax decreases with increasing the hydrophobic-chain length, where lmax indicates the hydrophobic chain length in its extended form. This is the main reason the surfactant layer curvature becomes negative while increasing the aS. Effective Cross Sectional Area. aS increases with increasing EO-chain or hydrophobic-chain length, as shown in Figure 9. aS increases, and the surfactant layer curvature tends to be positive with increasing EO chain length, whereas aS increases, and the surfactant layer curvature becomes negative with increasing lipophilic chain at constant EO-chain length. It is clearly shown that aS is not directly related to the hydrophilelipophile balance of surfactant or the surfactant layer curvature. When the molecular size of surfactant (hydrophilic and/or hydrophobic parts) increases, aS is always increases. Hence, aS is related to the amphiphilicity of surfactant. Namely, both hydrophilic and hydrophobic parts of surfactant are responsible for expanding aS, while the interfacial tension of waterhydrophobic interface tends to shrink it. Since the interfacial tensions of water-silicone oil and water-hydrocarbon are different, 35 and 50 mN/m, respectively,32,33 it may affect the aS, but we need further investigation. Effect of Hydrophobic-Chain Length on the Surfactant Layer Curvature. Most thermodynamic treatments on surfactant aggregation into self-organized structures such as micelles, liquid crystals, etc., consider the standard chemical potential, µN(G), in terms of the molecular interactions and the shape of aggregates. If the aggregation number is sufficiently large and the intermicellar interaction is neglected, the free-energy difference per surfactant molecule from monomeric state (µI) to aggregate (µN(G)) may be represented by
µN(G) - µI ) ∆fH(G) + ∆fI + ∆fL(G) Figure 8. Interlayer spacing, d, of the different types of liquid crystals in (a) water-Si14C3EOn systems: line A, p ) 2/3, I2 phase in waterSi14C3EO7.8 system; line B, p ) 1/2, H2 phase in water-Si14C3EO12 system; line C, p ) 0, LR phase in water-Si14C3EO15.8 system. Interlayer spacing, d, of the different types of liquid crystals in (b) water-Si5.8C3EOn systems: line D, p ) 1/2, H1 phase in water-Si5.8C3EO36.6 system; line E, p ) 1/3, I1 phase in water-Si5.8C3EO51.6 system.
where ∆fH(G) is a hydrophilic term related to the packing of hydrophilic EO-chain in a particular geometry, ∆fI is a surface term related to water-lipophilic-chain interfacial tension and aS, and ∆fL(G) a lipophilic-chain term. ∆fH(G) contains the sum of all interactions of the EO chain, hydration, steric hindrance, hydrogen bonding, etc., and is repulsive. Since the reduction in surfactant free energy from a monomeric state in aqueous solution to the aggregate is mainly attributed to the fact that the contact of the whole hydrophobic chain with water is confined to the interface (aS) of aggregate, ∆fI can be roughly rewritten in the form
∆fI ) -mω/kT + ∆fI′(G)
Figure 9. aS as a function of the nVEO/VS in SimC3EOn and trisiloxane systems. The solid lines Si25, Si14, Si5.8, and trisiloxane represent the water + Si25C3EOn, water + Si14C3EOn, water + Si5.8C3EOn, and water + trisiloxane systems, respectively.
51.6, the I1 phase changes to the LR phase when the hydrophobicchain length increases from Si5.8C3- to Si25C3-, or the LR phase changes to the I2 phase with the change of Si14C3- to Si25C3at constant n ) 15.8. This means that the effective chain length of the hydrophobic part of linear-chain silicone surfactant, leff,
(9)
(10)
where m is the hydrophobic chain length, ω is a hydrophobic energy change of one methylene group or one silicone unit in water to aggregation state,34 and ∆fI′(G) is a term related to interfacial tension at the hydrophobic part of aggregate. In the packing theory, ∆fI′(G) ) γaS, where γ is the interfacial tension.5,6 The term, -mω/kT, is almost the same for particular surfactant even if the geometry is different. ∆fL(G) is the hydrophobic chain term related to its packing in a particular geometry. The surfactant layer curvature would be mainly determined by the balance between ∆fH(G) and ∆fL(G), which are both repulsive. If the silicone chain is regarded as a random-flight chain in a monomeric state, the unperturbed chain length is proportional to m,1/2 where m is the number of silicone units.13 Since the silicone-chain length in its extended form (lmax) is proportional to m, leff/lmax ∝ 1/m1/2 holds. Hence, in the case of a free chain, the longer the chain is, the smaller the leff/lmax will be. When a longer chain is packed
5426 J. Phys. Chem. B, Vol. 105, No. 23, 2001
Kunieda et al. be considered to be a random-flight chain, leff/lmax decreases with increasing chain length. As a result, the long chain has a shrunk-bulky structure compared with a short chain. This causes the increase in aS and the change in curvature. References and Notes
Figure 10. leff/lmax as a function of silicone unit (m) for each selforganized structure in water-silicone surfactant system.
in a particular geometry and is elongated, the entropy loss would be large in comparison with a shorter chain.35 It causes a large lateral pressure, which makes a surfactant layer curvature negative and expands aS. Judging from the present results in silicone surfactant systems, the surfactant layer curvature becomes less positive or negative with increasing hydrophobic chain length even at constant EOchain length, i.e., constant ∆fH(G). Since aS also increases with increasing the hydrophobic chain length, ∆fL(G) would increase. Figure 10 shows the dependence of leff/lmax on the hydrophobic chain length, where leff is the hydrophobic chain length in aggregate (corresponding to the radius of aggregates for normal cubic or hexagonal phases, to the half thickness of the bilayer for the lamellar phase, and to the half longest distance between aggregates for reverse cubic or hexagonal phases). leff/ lmax indeed decreases when the surfactant layer curvature is changed from positive to negative. In the I1 system, leff/lmax exceeds unity. Perhaps the shape of micelles is not completely spherical.36 In the case of the EO-chain, the similar mechanism can be also considered, although the EO-chain is hydrated. Namely, when the EO chain is long, it tends to have a shrunkbulky structure and expands aS, but the long chain tends to make the surfactant layer curvature positive. Concluding Remarks The phase behavior and self-organized structures of A-Btype silicone surfactant in water were investigated. When polyoxyethylene chain (EO chain) of the surfactant increases, the surfactant layer curvature tends to change from negative to positive. On the other hand, when the hydrophobic dimethyl siloxane chain increases, the surfactant layer curvature changes in the opposite way. However, in both cases, the effective cross sectional area of surfactant at the interface of aggregate increases with increasing either EO-chain or dimethyl siloxane chain. Therefore, the surfactant layer curvature mainly depends on the balance between the hydrophilic and hydrophobic chain lengths as predicted by Griffin and Winsor’s theories. If each chain can
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