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ARTICLES Influence of Poly(ethylene glycol) Molecular Mass on Separation and Ordering in Solutions of CiEj Nonionic Surfactants: Depletion Interactions and Steric Effects S. Makulska,† E. Chudy,† K. Urbaniak,† S. A. Wieczorek,‡ A. Zywocinski,‡ and R. Holyst*,‡ WMP-SNS, Cardinal Stefan Wyszynski UniVersity, Dewajtis 5, 01-815 Warsaw, Poland, and PAS Department III, Institute of Physical Chemistry, Kasprzaka 44/52, 01-224 Warsaw, Poland ReceiVed: February 10, 2007; In Final Form: May 10, 2007
We study ternary mixtures of nonionic surfactants CiEj (i ) 12; j ) 5, 6, 8) and poly(ethylene glycol) (PEG) in water. For sufficiently large molecular mass of PEG (M >Msep ∼ 600), we observe a lowering of phase separation temperature with an increase in polymer concentration. The value of Msep is consistent with the analysis based on depletion interactions between micelles induced by polymer chains. We also demonstrate that there is another critical molecular mass of PEG (M ) M* ∼ 2000) necessary to induce ordering in the surfactant-rich phase. This critical molecular mass follows from two requirements: (a) PEG has to reduce the separation temperature below a temperature of hexagonal-isotropic phase transition in a binary surfactantwater mixture and (b) the PEG radius of gyration has to be larger than the size of the water channels in the hexagonal phase.
Introduction Poly(ethylene glycol) (PEG) is a water-soluble polymer that has various applications; many of them are associated with the polymer/surfactant or polymer/protein/surfactant mixtures.1,2 We try to give a brief overview of these applications, paying special attention to the separation and ordering that PEG induces in various systems (protein solutions, colloidal suspensions, and surfactant mixtures) and presenting our work in a broader perspective. When added to protein solutions, PEG induces a separation into a protein-rich phase and a water/polymer-rich phase and helps in protein crystallization.2-6 The crystallization (instead of aggregation of proteins or glass formation of complexes) is promoted near the liquid-liquid separation point,7 and proper choice of polymer molecular mass and concentration brings the mixture into this crystallization slot, promoting ordering (crystallization) in the protein-rich phase.8,9 Many diseases known as condensation diseases are initiated by the loss of solubility of proteins in aqueous solutions.10 One example is a sickle cell anemia caused by the polymerization of mutated hemoglobin (HbS) into linear fibers.11,12 HbS carries the same function as normal hemoglobin until it separates from the solution and forms a dense protein-rich phase, which is the primary step before polymerization. PEG was used to initiate the separation in this protein mixture to demonstrate that the necessary condition for polymerization is indeed the initial phase separation and formation of the protein-rich phase.12 PEG is also known as an effective agent for inducing ordering in surfactant solutions and controlling the stability and volume fractionofmicroemulsionsinwater/oil/surfactant/PEGmixtures.13-16 * Author to whom correspondence should be addressed. E-mail: holyst@ ptys.ichf.edu.pl. † Cardinal Stefan Wyszynski University. ‡ Institute of Physical Chemistry.
The microemulsion in contact with a water-rich phase containing PEG (or dextran) decreases its volume, and a water-rich phase grows at the expense of microemulsion. The relative volume fractions of these phases depend on the PEG concentration: the higher the concentration, the smaller the volume of the microemulsion. Such behavior does not depend on the chemistry of the polymer used (dextran or PEG), and Kabalnov et al. concluded that it is a purely steric effect.13 They observed that the effect strongly depends on the molecular mass of the polymer used and occurs only when the polymer size is larger than the water channels in microemulsion, that is, when the polymer is not incorporated into the microemulsion. They also observed that the addition of polymer can induce ordering, but have not studied this effect in detail. They only noted that the dextran concentration at which the liquid-crystalline phase appeared (in coexistence with microemulsion, oil-rich, and water-rich phase) depended on dextran molecular mass.13 In a recent paper, we studied the hexagonal ordering induced by PEG in C12E6-water solution.1 We found a simple mathematical formula predicting how much PEG 6000 is necessary to induce ordering in this solution (even at high dilution of surfactant). The formula is valid for a high molecular mass of polymers. Here we report experiments that generalize our previous results and provide answers to the following questions: What is the minimal molecular mass of PEG necessary to induce hexagonal ordering in the system? How is this molecular mass related to the properties of the hexagonal phase? Is the formula valid for other nonionic surfactant from the same homologous group? Is the critical molecular mass similar for all surfactants studied? In this work we demonstrate using PEG 20 000, 8000, 6000, 4000, 2000, 1000, 400, and 300 and three surfactants CiEj (i ) 12 and j ) 5,6,8) that indeed there is a critical mass of PEG,
10.1021/jp071145w CCC: $37.00 © 2007 American Chemical Society Published on Web 06/20/2007
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M*, necessary to induce ordering in these solutions. We demonstrate that the hexagonal ordering is induced when the polymer radius of gyration, RG, is larger than the size of the water channels, Lwater, in the hexagonal phase. For MPEG < M* (i.e., Lwater > RG), the surfactant-rich phase does not order after the phase separation. Moreover, we find the second requirement for the ordering, namely, PEG has to reduce the separation temperature to below the temperature of the hexagonal-isotropic phase transition in a binary surfactant-water mixture. Because our results can be explained by purely steric effects, we expect that they are valid for other surfactant and polymer systems in the absence of strong polymer-surfactant enthalpic association. Materials and Methods We used three nonionic surfactantssn-dodecyl pentaoxyethene monoether (C12E5), n-dodecyl hexaoxyethene monoether (C12E6), and n-dodecyl octaoxyethene monoether (C12E8)s purchased from Fluka, of purity better than 98%. The melting temperatures given by Fluka Chemicals Co. are as follows: 2123 °C for C12E5, 27-28 °C for C12E6, and 30-33 °C for C12E8. The molecular weights are, respectively, 406.61, 450.66, and 538.77. The molecular weights of PEG, purchased from Fluka, were on average 20 000, 8000, 6000, 4000, 2000, 1000, 400, and 300. The measured polydispersity (using mass spectroscopy and size exclusion gel permeation chromatography (GPC)) was typically PDI ) 1.09 and Mn ) 990 for PEG 1000 (average mass between 950 and 1050) up to PDI ) 1.13 and Mn ) 16 300 for PEG 20 000 (average mass between 16 000 and 24 000). For PEG 4000, the molecular weight given by Fluka was between 3500 and 4500, and PEG 8000 had a molecular weight between 7000 and 9000. The melting temperature for PEG 2000 was between 50 °C to 53 °C, and for PEG 4000 it was between 58 °C and 61 °C. In the experiments it was important to have low polydispersity for smaller molecular weights of PEG, but not for high molecular weights, because the studied effects (induced hexagonal order) depended strongly on the molecular weight for low molecular weights only. We prepared mixtures of PEG with surfactant at room temperature in a humid atmosphere to avoid the evaporation of water. We made samples using Superior Marienfeld cover glasses, 15 and 12 mm in diameter, cleaned in an ultrasound bath, and washed in acetone. We placed two short copper wires (10 µm in diameter) as spacers, or strips of aluminum foil (11-13 µm thick) between the glass plates. We sealed the samples with glue along the wires or strips, leaving tiny holes to inject our mixtures. We injected a few microliters of solution between the glasses, and sealed the holes to avoid the evaporation of water. We studied the samples using a Nikon Eclipse E400 microscope with crossed polarizers equipped with a LINKAM THMS 600 heating/cooling stage. The computer program that controlled the stage was LinkSys 2.36. The temperature was controlled up to 0.01 °C. First, we put the sample under the microscope. Then we started heating, and, after achieving a temperature of about 80-90 °C, we started cooling. Those cycles were repeated several times. Phase Separation in CiEj-Water Solutions Induced by PEG As we mentioned in the Introduction, the first step toward ordering induced by PEG is initial separation into two isotropic phases. That is why we first studied the separation process in our ternary mixtures. In Figure 1 we show the phase diagrams
Figure 1. The phase diagrams for C12Ej-water binary mixtures (j ) 5,6,8) (after ref 17). The region denoted as H and marked by bold lines is the region where the hexagonal phase is stable in the systems. A cartoon of the hexagonal phase is shown in Figure 2, and the parameters characterizing this phase are given in Table 3. For all surfactants studied, the minimal concentration of surfactant in the hexagonal phase is cmin s > 38% w/w. The size of the water channels in the hexagonal phase is 1.2 nm for C12E8, 1.5 nm for C12E6, and 1.6 nm for C12E5 (see Table 3). For concentration of surfactant cs ∼ 50% w/w, the hexagonal phase is stable for temperature T < 20 °C for C12E5, T < 38 °C for C12E6, and T < 55 °C for C12E8.
of binary CiEj-water solutions.17 All these surfactants separate from water at high enough temperatures: C12E5 separates from water at temperatures higher than 31 °C, C12E6 separates at temperatures higher than 50 °C and C12E8 separates at temperatures higher than 78 °C for dilute solutions. The separation
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TABLE 1: The Radius of Gyration for Different PEG Molecular Masses Calculated According to the Equation22,23 RG ) 0.02M0.58 nm M [Da]
Rg [Å]
20000 8000 6000 4000 2000 1000 400
63 37 31 25 16 11 6
d a Lwater
C12E5
C12E6
C12E8
58 Å 21 Å 16 Å
59 Å 22 Å 15 Å
60 Å 24 Å 12 Å
a d is the size of the unit cell, a is the average size of the molecule in the hexagonal column, and Lwater is the width of the water channels between cylinders (see Figure 2).
TABLE 2: Values of r ) RG/a, Where RG ) 0.02M0.58 nm Is the Polymer Radius of Gyration as a Function of the Molecular Mass,22,23 M, and a Is the Radius of Micellesa C12E5 C12E6 C12E8
TABLE 3: Parameters of the Hexagonal Phase for Surfactants C12E5,28,29 C12E6,30 and C12E831,a
PEG 20000
PEG 6000
PEG 1000
PEG 400
r ) 2.33 r ) 2.25 r ) 2.17
r ) 1.15 r ) 1.10 r ) 1.07
r ) 0.41 r ) 0.39 r ) 0.38
r ) 0.22 r ) 0.21 r ) 0.21
a The radius of a micelle is 2.7 nm for C12E5, 2.8 for C12E6, and 2.9 nm for C12E8 assuming a spherical micelle at small surfactant concentration.24-26 This size is larger than the size of cylinders in the hexagonal phase (see Table 3). Here, r is calculated for four different PEG chain lengths and three different surfactants. The ratio r determines the influence of a polymer on phase separation in the mixture. When r falls below 0.3, the polymer does not appreciably influence the separation in surfactant/water mixtures. It follows that the critical mass of PEG for which we find r ) 0.3 is Ms ) 600. Thus we expect that PEG 400 or PEG 300 does not influence a separation temperature in the system. We have verified experimentally that, indeed, PEG 1000 reduces the separation temperature, while PEG 400 does not.
temperature grows with surfactant concentration. Phase transition in binary surfactant/water mixtures is due to the dehydration of the surfactant heads and the progressive increase in the influence of the van der Waals attraction between surfactant micelles. Adding PEG to the binary mixture induces additional attractiveinteractionsbetweenmicelles(depletioninteractions).2,4,15,18-21 These interactions dominate and strongly reduce the separation temperature in the PEG/surfactant/water mixtures in comparison to the surfactant/water mixtures. The origin of depletion interactions can be traced back to the conformational entropy of polymer chains.18,19 The center of mass of a polymer molecule cannot get closer to the micelle than a certain characteristic distance. This distance is proportional to the sum of the radius of gyration of a polymer, RG, and the radius of a micelle, a. The center of mass of a polymer cannot get closer to the micelle because it would result in a decrease in its conformational entropy. If two micelles are close to each other, separated by a distance smaller than 2(a + RG), a polymer cannot enter between them. This depletion zone (zone depleted from polymers) causes an imbalance of osmotic pressures (induced by polymers outside the zone between the micelles). The osmotic pressures push the micelles together and lead to the phase separation into two phases. One of them is the surfactant-rich phase, the other is the polymer-rich phase. According to the Asakura and Oosawa theory,18,19 the transition strongly depends on the ratio r ) RG/ a. It was shown theoretically that the ratio r specifies the range of attractive interactions, and, for short range attraction21 (i.e., for r < 0.3), we do not expect any influence of PEG on phase separation (see also Tables 1and 2). Table 2 shows this ratio for different molecular masses of PEG and different surfactants. The radius of gyration of PEG in water depends on its molecular mass M in the following way:22,23 RG ) 0.02M0.58 nm (see Table 1). The hydrodynamic radius of a micelle is 2.7 nm for C12E5, 2.8 nm for C12E6, and 2.9 nm for C12E8, as presented in refs 24-26. The true radius of a micelle can be smaller than the
hydrodynamic radius. Moreover, the measurements24-26 were done in a dilute regime where spherical micelles are formed. For higher concentrations, spherical micelles grow and form cylindrical micelles. Cylindrical micelles have a much smaller radius; that is, for C12E5, the radius of a cylindrical micelle is 2.1 nm (see Table 3). Our experimental results are in accordance with the depletion theory. From the depletion theory (see also Table 2) it follows that, for M < Msep ) 600 (r ) RG/a < 0.3), the polymer should not influence the separation temperature. Indeed we find that PEG 1000 reduces the phase separation temperature in surfactant-polymer mixtures, but PEG 400 does not influence the transition temperature. The addition of 9% w/w of PEG 400 or PEG 300 to the 10% w/w C12E6 solution does not change the separation temperature in comparison to the binary 10% C12E6water mixture (equal to 52 °C). Adding 8% of PEG 6000 to 10% C12E6-water solution reduces the separation temperature from 52 °C to 19 °C. In fact, 19 °C is only the spinodal (cloud point) temperature. The temperature of phase coexistence is even lower, since these mixtures are notoriously metastable, that is, homogeneous PEG/nonionic surfactant/water mixtures can be stable even 20-30° above the coexistence temperature.27 In a quick experiment where we heat the sample, we are able to easily observe only the cloud point temperature. But careful experiments (with many heating-cooling cycles) reveal the temperature of the phase coexistence and large metastability regions in the mixture.27 The separation temperature strongly depends on the molecular weight: for PEG 20 000 (8% w/w) in 10% C12E6, the cloud point temperature is 7 °C, but the separation temperature is 0 °C in this case. For C12E8 (10% w/w), we found that the cloud point temperature was reduced from 80 °C to 18 °C when 20% of PEG 6000 was added. In C12E5 (10% w/w), 4% of PEG 6000 reduced the cloud point temperature from 36 °C to 21 °C. The existence of a critical molecular weight of PEG (Msep ) 600) needed to reduce the separation temperature follows from the depletion theory and is supported quantitatively by our results. The depletion interactions21 induced by PEG 1000 are sufficiently long-ranged to reduce the separation temperature (r > 0.3), but too short-ranged (r < 0.3) for PEG 400 to affect the phase separation (see Table 2). Ordering in CiEj-Water Solutions Induced by PEG When the concentration of PEG is large enough, we observe hexagonal ordering in the surfactant-rich phase.1 From Figure 1, it follows that, when the surfactant concentration is cs > cmin s ∼ 38% w/w, the binary surfactant/water mixture forms a hexagonal phase for temperatures above 0 °C. The parameters of the hexagonal phase are given28-31 in Table 3, and the hexagonal phase is shown schematically in Figure 2. The hexagonal phase is stable up to 20 °C for C12E5, up to 38 °C for C12E6, and up to 55 °C for C12E8. This hexagonal ordering can be induced even when the surfactant concentration is very small by adding PEG of sufficiently large molecular mass and
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Figure 2. A schematic picture of a hexagonal phase. Its parameters are given in Table 3. From these parameters we can estimate the width of water channels between cylinders Lwater ) d - 2a in this phase and compare it to the radius of gyration of PEG given in Table 2. Here, d is the distance between cylindrical micelles, a is the radius of the micelle, and Lwater is the width of the water channels between cylinders.
sufficiently large concentration. The ternary mixture separates into surfactant-rich and polymer-rich phases, and, when the concentration of surfactant in the surfactant-rich phase exceeds cmin s , the hexagonal ordering appears. The mechanism of the induced order is simple: added polymer decreases the chemical potential of water in a polymer-rich phase in comparison to the surfactant-rich phase. Consequently, it decreases the content of water in the surfactant-rich phase and increases, in this way, the surfactant concentration in the surfactant-rich phase. Under the assumption that the interface is permeable to water molecules, only chemical equilibrium is attained when the chemical potentials of water are equal in both phases. This simple idea was used to derive the equation for the concentration of polymer needed to induce hexagonal ordering in surfactant solution:1
(
CPEG z MPEG ) ‚ ‚ 1 - CPEG y MCiEj (1
cmin s - cmin s )
-
)
cs 1 - cs
(1)
where CPEG is the concentration of PEG with respect to water in the ternary mixture, MPEG is the molecular mass of PEG, MCiEj is the molecular mass of surfactant CiEj, cmin is the s minimal concentration of surfactant in the surfactant-rich phase to get an ordered (hexagonal) phase, cs is the concentration of surfactant in the ternary mixture (with respect to water), z is the experimentally obtained factor of value 2 for C12E6 (and we verified here that z ) 1 for C12E5 and z ) 4,5 for C12E8), and y is the number of oxygen atoms in the PEG chain (e.g., y ) 137 for PEG 6000). The concentration of PEG needed to induce order in surfactant solutions does not practically depend on the molecular mass of PEG because, for high molecular mass, MPEG/y in eq 1 is a constant. However, this equation was derived under the assumption that PEG has a sufficiently high molecular mass, such that the PEG molecule cannot penetrate the water channels of size Lwater in the ordered phase and that the polymer network in the polymer-rich phase cannot be penetrated by the micelles. In other words, the assumption is that the interface between the hexagonally ordered phase and the polymer-rich phase acts as a semipermeable membrane: the interface is permeable to water but impermeable to micelles or PEG. This is a key assumption behind eq 1. In Figure 3 we show the optical textures of the ordered hexagonal phase obtained for C12E5,
Figure 3. The texture of the hexagonal phase observed under crosspolarizers for different surfactant and PEG mixtures: (a) 10% of C12E5 and 1.5% of PEG 6000; (b) 10% of C12E6 and 10% of PEG 20000; (c) 10% of C12E8 and 16% of PEG 8000.
TABLE 4: The Minimal Concentration of PEG (See Eq 1) Needed to Induce the Hexagonal Phase in C12E5a,b PEG molecular mass [Da]
cPEG [wt %]
temperature [°C] hexagonal phase
20000 8000 6000 4000 2000
>1.5% >1.5% >1.5% >1.5% >5%
T < 20 T < 20 T < 20 T < 20 hexagonal phase hardly visible lack of hexagonal order
1000
a 10% w/w with respect to water (see also Figure 1). b The temperature range of the stability of the induced hexagonal phase is given in the last column. It corresponds to the range of temperatures where the hexagonal phase is stable in the binary surfactant/water systems.
C12E6, and C12E8 surfactant mixtures under cross-polarizers. In order to check that eq 1 does not depend on the molecular mass, we have performed a series of experiments for 10% solutions of CiEj mixtures and PEG of different mass (see Tables 4-6.) Equation 1 was checked experimentally for a PEG 6000/C12E6/ H2O system in our previous paper,1 and here it was applied to PEG/C12Ej/water mixtures (j ) 5,6,8) for various masses of PEG (20 000, 8000, 6000, 4000, 2000, and 1000). First, we found
7952 J. Phys. Chem. B, Vol. 111, No. 28, 2007 TABLE 5: The Minimal Concentration of PEG (See Eq 1) Needed to Induce the Hexagonal Phase in C12E6a,b PEG molecular mass [Da]
cPEG [wt %]
temperature [°C] hexagonal phase
20000 8000 6000 4000 2000 1000
>8% >8% >8% >8% >8%
T < 38 T < 38 T < 38 T < 38 T < 38 lack of hexagonal order
a 10% w/w with respect to water (see also Figure 1). b The temperature range of the stability of the induced hexagonal phase is given in the last column. It corresponds to the range of temperatures where the hexagonal phase is stable in the binary surfactant/water systems.
TABLE 6: The Minimal Concentration of PEG (See Eq 1) Needed to Induce the Hexagonal Phase in C12E8a,b PEG molecular mass [Da]
cPEG [wt %]
temperature [°C] hexagonal phase
20000 8000 6000 4000 2000 1000
>16% >16% >16% >16% >30.0%
T < 55 T < 55 T < 55 T < 55 T < 55 lack of hexagonal order
a 10% w/w with respect to water (see also Figure 1). b The temperature range of the stability of the induced hexagonal phase is given in the last column. It corresponds to the range of temperatures where the hexagonal phase is stable in the binary surfactant/water systems. PEG 2000 reduces the separation temperature below 55 °C (hexagonalisotropic transition temperature in the binary mixture of C12E8/water) only at a high concentration of 30% w/w.
that the critical concentration of PEG necessary to induce ordering in C12Ej does not depend on the polymer molecular mass, in accordance with eq 1. Moreover, from Tables 4-6 it follows that, for PEG masses smaller than the critical mass M* ∼ 2000, the addition of PEG into the mixture does not induce hexagonal ordering in the surfactant-rich phase after the phase separation. We found that PEG 1000 does not induce ordering in any of the surfactant mixtures (Table 4-6). Comparing Tables 1 and 3, we see that PEG 1000 is much smaller than the size of the water channels in any of the hexagonal phases in C12Ej (j ) 5,6,8) and thus can penetrate them. We observed a hexagonal phase in C12E5 for PEG molecular masses from 20 000 to 4000, with the content of PEG being equal to 1.5%. For PEG 1000, the ordering does not occur, even for 30% of PEG. PEG 2000 is comparable to the size of the water channels in C12E5, and, indeed, for this molecular mass, we had to increase the concentration to more than 5% to observe ordering in C12E5 (see Table 4.); the hexagonal phase was very weakly visible. In the C12E8/water mixture, the hexagonal phase appeared below 55 °C, thus, in order to induce this phase by the addition of PEG, we had to reduce the separation temperature below 55 °C. Adding 17% of PEG 2000 in a C12E8/water mixture does not induce a strong enough attraction between the micelles to achieve this goal: the mixture of 10% of C12E8/water/17% PEG 2000 was homogeneous at 55 °C. However, when we added 30% of PEG 2000, the hexagonal phase appeared even at room temperature (Table 6). Conclusions We have shown experimentally that, for high molecular masses of PEG, eq 1 correctly predicts the concentration of PEG (20 000, 8000, 6000, 4000) necessary to induce hexagonal
Makulska et al. ordering in C12Ej (j ) 5,6,8) aqueous solutions. This concentration of PEG needed to order the surfactant-rich phase (eq 1) does not depend on its molecular mass for these high molecular masses. We have determined that, below a critical mass of PEG, the hexagonal ordering disappears even for very high concentrations of PEG. For surfactant C12E6, the critical mass of PEG is below 2000 (Table 5). For C12E5, the hexagonal phase was hardly visible at high concentrations (>5%) of PEG 2000 (Table 4). We correlated this phase behavior with the size of the water channels in the hexagonal phase and with the radius of gyration of PEG (Tables 1 and 3) and found that PEG induces ordering only when it is not incorporated into the ordered phase, that is, when its radius of gyration is larger than the size of the water channels in the ordered phase (see also discussion on the stability of microemulsion in ref 12). For C12E8, PEG 2000 was not efficient in reducing the separation temperature below 55 °C, and that is why hexagonal ordering was not observed for 17% of PEG. When the concentration of PEG was large enough (30%) to reduce the separation temperature below 55 °C, we also observed a hexagonal phase in C12E8 (Table 6). Thus the critical molecular mass needed to induce hexagonal ordering follows from two requirements: (a) PEG has to reduce the separation temperature below the temperature of the hexagonalisotropic phase transition in binary surfactant-water mixtures, and (b) the PEG radius of gyration has to be larger than the water channels in the hexagonal phase. Additionally, we have also observed, in accordance with the depletion theory of interactions21 between micelles induced by a polymer, that there is a critical mass of polymer needed to induce separation (here, Msep ∼ 600) by the depletion interactions. We verified experimentally that, in our systems of nonionic surfactants, PEG influences separation when its radius of gyration is RG > 0.3a, where a is the radius of a micelle. Our results concerning ordering can be generalized to other systems (polymers plus surfactants), providing that the polymer does not form strong associations with the surfactant. We can, in principle, imagine a situation of cooperative enthalpic interactions between the coronas of the micelles and polymers, causing a new type of ordering where polymer chains serve to order surfactant micelles into an ordered phase not encountered in the binary surfactant/water system. Finally, we should comment on the possible influence of the polydispersity of PEG on the results. At very high molecular mass, we find from eq 1 that the ordering is independent from the molecular mass. Indeed, we have found using PEG 20 000, 8000, 6000, and 4000 that the ordering appears at the same concentration of PEG, irrespective of its molecular mass. Here, polydispersity does not seem to influence the results, especially since we used a highly polydisperse PEG, although this problem needs further study. We especially expect that the polydispersities of PEG 2000 and PEG 1000 can strongly influence the results since a fraction of PEG of mass much smaller than the average can enter into the channels of the hexagonal phase and change the chemical equilibrium between the PEG-rich phase and surfactant-rich phase. This problem requires additional study with PEG of very low polydispersity (such as one used as a standard for GPC). Acknowledgment. This work was supported as a scientific project 2006-2008 and a SONS (SCALES) scientific project 2006-2009 from the budget of the Ministry of Science and Higher Education. We would like to thank Prof. Z. Florjanczyk for discussions concerning polymer characterization and help
Influence of PEG on Nonionic CiEj Solutions in the GPC of PEG, and Artur Brzezicki and Marcin Izydorzak for the mass spectroscopy characterization of PEG. References and Notes (1) Holyst, R.; Staniszewski, K.; Demyanchuk, I. J. Phys. Chem. B 2005, 109, 4881. (2) Tanaka, S.; Ataka, M.; Onuma, K.; Kubota, T. Biophys. J. 2003, 84, 3299. (3) McPhersons, A. Crystallization of Biological Macromolecules; Cold Spring Harbor Laboratory Press: New York, 1999. (4) Kulkarni, A. M.; Chatterjee, A. P.; Schweizer, K. S.; Zukoski, C. F. J. Chem. Phys. 2000, 113, 9863. (5) Tanaka, S. M.; Ataka, M. J. Chem. Phys. 2002, 117, 3504. (6) Garavito, R. M.; Fergusson-Miller, S. J. Biol. Chem. 2001, 276, 32403. (7) Ten Wolde, P. R.; Frenkel, D. Science 1997, 277, 1975. (8) George, A.; Wilson, W. W. Acta Crystallogr., Sect. D: Biol. Crystallogr. 1994, 50, 361. (9) George, A.; Chiang, Y.; Guo, B.; Arabshahi, A; Cai, Z.; Wilson, W. W. Methods Enzymol. 1997, 276, 100. (10) Annuziata, O.; Ogun, O.; Benedek, G. B. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 970. (11) Galkin, O.; Nagel, R. L.; Vekilov, P. G, J. Mol. Biol. 2007, 425. (12) Galkin, O.; Chen, K.; Nagel, R. L.; Hirsch, R. E.; Vekilov, P. G. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 8479. (13) Kabalnov, A.; Olsson, U.; Wennerstrom, H. Langmuir 1994, 10, 2159.
J. Phys. Chem. B, Vol. 111, No. 28, 2007 7953 (14) Bellocq, A. M. Langmuir 1998, 14, 3730. (15) Zacrisson, M.; Andersson, R.; Bergenholtz, J. Langmuir 2004, 20, 3080. (16) Javierre, I.; Bellocq, A. M.; Nallet, F. Langmuir 2001, 17, 5417. (17) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. J. Chem. Soc., Faraday Trans. 1983, 79, 975. (18) Asakura, S.; Oosawa, J. J. Chem. Phys. 1954, 22, 1255. (19) Vrij, A. Pure Appl. Chem. 1976, 48, 471. (20) Lekkerkerker, H. N. W.; Poon, W. C. K.; Pusey, P. N.; Stroobants, A.; Warren, P. B. Europhys. Lett. 1992, 20, 559. (21) Lekkerkerker, H. N. W. Physica A 1997, 244, 227. (22) Devanand, K.; Sesler, J. C. Macromolecules 1991, 24, 5943. (23) Kawaguchi, S.; Imai, G.; Suzuki, J.; Miyahara, A.; Kitano, T. Polymer 1997, 38, 2885. (24) Nilsson, P.; Wennerstronm, H.; Lindman, B. J. Phys. Chem. B 1983, 87, 1377. (25) Johansson, L.; Hedberg, P.; Lofroth, J. J. Phys. Chem. B 1993, 97, 747. (26) Kwon, S. Y.; Kim, M. W. Phys. ReV. Lett. 2002, 89, 258302. (27) Hoyst, R.; Staniszewski, K.; Gapinski, J.; Patkowski, P. J. Phys. Chem. B 2005, 109, 8533. (28) Lang, P.; Braun, Chr.; Steitz, R.; Findenegg, G. H.; Rhan, H. J. Phys. Chem. B 1998, 102, 7590. (29) Lang, P. J. Phys. Chem. B 1999, 103, 5100. (30) Constantin, D.; Oswald, P.; Imperor-Clerc, M.; Davidson, P.; Sotta, P. J. Phys. Chem. B 2001, 105, 668. Constantin, D. Ph.D. Thesis, ENSLyon, 2002. (31) Clerc, M. J. Phys. II (France) 1996, 6, 961.
