Association Properties of Diblock Copolymers of Ethylene Oxide and 1

Copolymers E96B18, E184B18, E315B17, and E398B19 (E = oxyethylene unit, B = oxybutylene unit) were synthesized and characterized by gel permeation ...
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J. Phys. Chem. B 1999, 103, 11269-11274

11269

Association Properties of Diblock Copolymers of Ethylene Oxide and 1,2-Butylene Oxide in Aqueous Solution. Copolymers with Oxyethylene-Block Lengths in the Range 100-400 Chain Units Withawat Mingvanish, Shao-Min Mai, Frank Heatley, and Colin Booth* Department of Chemistry, UniVersity of Manchester, Manchester M13 9PL, U.K.

David Attwood School of Pharmacy, UniVersity of Manchester, Manchester M13 9PL, U.K. ReceiVed: July 23, 1999; In Final Form: October 1, 1999

Copolymers E96B18, E184B18, E315B17, and E398B19 (E ) oxyethylene unit, B ) oxybutylene unit) were synthesized and characterized by gel permeation chromatography (for distribution width) and 13C NMR spectroscopy (for absolute molar mass and composition). Dynamic and static light scattering was used to determine micellar properties in dilute aqueous solution at three temperatures (25, 40, and 50 °C): that is, hydrodynamic radius and hydrodynamic expansion factor, mass-average molar mass, and thermodynamic expansion factor. At a given temperature, the values of the radii and expansion factors increased as E-block length was increased, whereas values of the micelle association number decreased. The tube-inversion method was used to define the mobile-immobile (hard gel) phase boundary. At room temperature (20 °C), hard gels were formed in the concentration range 3.5-8 wt % copolymer depending on E-block length, the lowest value being for the copolymer with the longest E block (E398B19).

1. Introduction Dilute aqueous micellar solutions of block copolyethers are known to form micellar solutions and their more concentrated solutions to form liquid-crystal mesophases (gels). Gels of EmPnEm triblock copolymers [E denotes an oxyethylene unit, OCH2CH2, P an oxypropylene unit, OCH2CH(CH3), and m and n block lengths] have been advocated for a number of biomedical and pharmaceutical applications.1-4 From a physicochemical viewpoint, the formation and structures of the micelles are of interest, as well as the mesophases formed therefrom. A number of reviews summarize recent work.5-7 Since 1994, a limited range of block copolymers of ethylene oxide and 1,2-butylene oxide [B ) oxybutylene, OCH2CH(C2H5)] in both diblock and triblock form have become available from The Dow Chemical Co., Freeport, TX.8,9 Independently, studies of the self-association properties of diblock and triblock E/B copolymers were initiated in Manchester in the early 1990s.10-12 A number of recent studies have confirmed, as might be expected, that spherical micelles of diblock EmBn copolymers act as effective hard spheres. An accessible property in dilute solution is the excluded volume of a micelle (u), which can be expressed as the thermodynamic volume Vt ) u/8 (or as the corresponding thermodynamic radius, rt). The property of interest is the space-filling potential of the micelles acting as hard spheres, in which case the critical concentration for gelation depends (for a given geometry) on the effective hard-sphere volume fraction of the micelles.13,14 It is convenient to define a thermodynamic swelling factor (here called δt) as the ratio of the thermodynamic volume (Vt) to the anhydrous volume (Va) of a micelle, δt ) Vt/Va. For hard spheres, the critical volume * To whom correspondence should be addressed.

fraction for packing in a body-centered cubic structure is φc ) 0.68. For a gel with body-centered cubic structure formed at a given temperature from a solution of effective hard-sphere micelles, transformation of this well-known relationship to a critical gel concentration (cgc in g dm-3) gives

cgc/(g dm-3) ) 680Fa/δt

(1)

where Fa is the density of the anhydrous copolymer in g cm-3 (hence the factor of 1000), and δt accounts for an increase in volume due to swelling. As well as investigating the effect of temperature, our experiments have included the effect of changing solvent quality by adding electrolyte to approach theta conditions15 and the effect of changing the length of the hydrophilic E block.16,17 With regard to the latter, results reported16,17 for solutions of diblock EmBn copolymers in water confirm that the critical gel concentration is very sensitive to the E-block length: that is for solutions at 25 °C, the cgc was found to vary from ca. 23 wt % for E18B10 to ca. 7 wt % for E210B16. Moreover, reasonable agreement with eq 1 was found within this range.16,17 The experiments described herein extend this work to longer E-block lengths, so allowing the effect of E-block length on the critical gel concentration to be explored in more detail. 2. Experimental Section 2.1. Copolymers. The diblock copolymers (see Table 1 for details) were prepared by sequential anionic polymerization of ethylene oxide followed by 1,2-butylene oxide. The methods used in preparation and characterization have been described previously.12,18 The monofunctional initiator was 2-(2-methoxyethoxy)ethanol activated by reaction with potassium metal (mole ratio OH/K ≈ 5). Vacuum line and ampule techniques

10.1021/jp992547+ CCC: $18.00 © 1999 American Chemical Society Published on Web 12/07/1999

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TABLE 1: Molecular Characteristics of the Copolymersa

a

copolymer

wt % E (NMR)

Mn/103 g mol-1 (NMR)

Mw/Mn (GPC)

Mw/103 g mol-1

E96B18 E184B18 E315B17 E398B19

76.5 86.2 91.9 92.8

5.5 9.4 15.1 18.9

1.03 1.03 1.04 1.06

5.7 9.7 15.7 20.0

Estimated uncertainties: (2% in wt % E; (3% in Mn, Mw/Mn, and block lengths; (5% in Mw. Mw calculated from Mn and Mw/Mn.

were used. Characterization of the copolymers by gel permeation chromatography [GPC, calibrated with poly(oxyethylene) standards] indicated narrow chain length distributions, that is, Mw/Mn ≈ 1.05, where Mw and Mn are the mass-average and number-average molar masses, respectively. Absolute values of Mn of the precursor poly(oxyethylene)s and the final copolymers by 13C NMR spectroscopy were based on the assignments of Heatley et al.19 Comparisons of integrals of the resonances of carbons associated with chain units, end groups, and junction groups confirmed the diblock structure but showed the presence of homopoly(oxybutylene) impurity in the two longest copolymers. This material was removed by precipitation from solution in dichloromethane by addition of excess hexane. Relevant molecular characteristics obtained for the copolymers (purified as required) are listed in Table 1. 2.2. Light Scattering. Details of the methods used and their applicability to micellar solutions of the type under investigation have been discussed previously.15,20-22 Solutions were clarified by filtering through Millipore Millex filters (Triton free, 0.22 µm, sometimes 0.10 µm) directly into the cleaned scattering cell. No difference was found for results on solutions treated by the two filtration techniques, and it was concluded that all the solute passed through both grades of filter. Static light scattering (SLS) intensities were measured by means of either a Brookhaven BI 200S or a Malvern PCS100 instrument, in each case using vertically polarized incident light of wavelength λ ) 488 nm supplied by an argon-ion laser (Coherent Innova 90) operated at 500 mW or less. The intensity scale was calibrated against benzene. Dynamic light scattering (DLS) measurements were made under similar conditions, using a Brookhaven BI 9000 AT digital correlator to acquire data. Experiment duration was in the range 5-20 min, and each experiment was repeated two or more times. In both methods, scattered light intensity was usually measured at an angle θ ) 90° to the incident beam. The correlation functions from dynamic light scattering (DLS) were analyzed by the constrained regularized CONTIN method23 to obtain distributions of decay rates (Γ), hence distributions of the apparent mutual diffusion coefficient [Dapp ) Γ/q2, q ) (4πn/λ)sin(θ/2), n ) refractive index of the solvent], and ultimately of the apparent hydrodynamic radius (rh,app, radius of the hydrodynamically equivalent hard sphere corresponding to Dapp) via the Stokes-Einstein equation

rh,app ) kT/(6πηDapp)

(2)

where k is the Boltzmann constant, and η is the viscosity of the solvent at temperature T. In practice, intensities I(Γ) delivered by the CONTIN program at logarithmically spaced values of decay rate were transformed to I(logΓ) ) I(Γ)Γ to obtain intensity distributions of log(Γ), and so of log(rh,app). Normalization of I(log rh,app) gave the intensity fraction distributions presented in Section 3.3. Average values of Γ, delivered by the CONTIN program by integration over the intensity distributions, were similarly converted to intensity-average values of rh,app.

The basis for analysis of static light scattering (SLS) was the Debye equation

K*c/(I - Is) ) 1/Mw + 2A2c + ...

(3)

where I is the intensity of light scattering from solution relative to that from benzene, Is is the corresponding quantity for the solvent, c is the concentration (in g dm-3), Mw is the massaverage molar mass of the solute, A2 is the second virial coefficient (higher coefficients being neglected in eq 3), and K* is the appropriate optical constant. Values of the specific refractive index increment, dn/dc, its temperature increment, and other quantities necessary for the calculations have been given previously.12,15,22 In fact, values of dn/dc are very similar for poly(oxyethylene) and poly(oxybutylene), making dn/dc insensitive to exact composition of the copolymers and making a correction for refractive index difference within the copolymer unnecessary.24 2.3. Sol-Gel Boundary. Samples of solution (0.5 g) were enclosed in small tubes (internal diameter ca. 10 mm) and observed while slowly heating the tube in a water bath within the range 0-100 °C. The heating/cooling rate was 0.5 deg min-1 or less. Additional data points in the range from 0 to -10 °C were obtained by cooling the tubes in an acetone/dry ice bath, care being taken to avoid freezing the solution at the lowest temperatures. The change from a mobile to an immobile system (or vice versa) was determined by inverting the tube. The method served to define a sol-gel transition temperature to (1 °C. The hard gels were found to be immobile in the inverted tubes over time periods of days to several months. In favorable cases, this simple method of detecting gelation, which is sensitive to the yield stress of the gel, has been shown to define the same hard-gel phase boundary as rheometry and differential scanning calorimetry.25 3. Results and Discussion 3.1. Clouding. Solutions of the copolymers did not cloud over the concentration and temperature ranges investigated (c e 30 wt %, T e 100 °C). 3.2. Critical Micelle Concentration (cmc). An attempt was made to determine the cmc of copolymer E96B18 using the ringdetachment method described elsewhere.18,26 Long equilibration times at low concentrations are known to be a problem for copolymers with long B blocks (see, e.g., ref 26), and the experiment gave only an indication of a very low value, that is, cmc e 0.008 g dm-3 at 25 °C. However, recent work,16,20,27 has demonstrated that the cmcs of EmBn diblock copolymers in solution at 30 °C correlate well with B-block length over the range B4 to B16: see Figure 1, in which the scatter arises in part from variation in E-block length. Extrapolation of the leastsquares straight line to B20 and use of the values of Mn in Table 1 to convert to working units of g dm-3 does indeed indicate very low values of the cmc at 30 °C for copolymers with B blocks in the range B17 to B19, that is cmc ) 0.002-0.0004 g dm-3. The lengthy E-blocks of the longer copolymers should lead to an increase in cmc over that predicted from Figure 1,

Ethylene Oxide and 1,2-Butylene Oxide Copolymers

Figure 1. Logarithm of critical micelle concentration (in mol dm-3) versus B-block length for aqueous solutions of EmBn copolymers at 30 °C. Results from refs 16, 20, and 27.

J. Phys. Chem. B, Vol. 103, No. 51, 1999 11271

Figure 3. Reciprocal of apparent hydrodynamic radius versus copolymer concentration for aqueous solutions of copolymer E315B17 at (b) 25, (O) 40, and (9) 50 °C.

TABLE 2: Micellar Characteristics from Dynamic Light Scattering: EmB10 Copolymers in Watera copolymer

T/°C

D/10-11 m2 s-1

rh/nm

δh

E96B18

25 40 50 25 40 50 25 40 50 25 40 50

1.58 2.34 3.07 1.26 1.88 2.29 1.14 1.63 2.05 0.94 1.33 1.77

15.5 15.0 14.1 19.5 18.7 18.9 21.6 21.6 21.1 26.0 26.5 24.5

11.0 9.2 7.6 17.6 13.8 13.9 31.6 24.4 20.3 36.4 31.2 24.5

E184B18 E315B17 E398B19

a D, translational diffusion coefficient, to (5%; r , hydrodynamic h radius, to (5%; δh, hydrodynamic expansion factor relative to anhydrous volume, to (15%.

Figure 2. Dynamic light scattering. Intensity fraction distribution of the logarithm of apparent hydrodynamic radius for aqueous solutions of copolymer E315B17 at 25 °C and the concentrations (g dm-3) indicated.

but the effect should be small. For example, in working units the values of the cmc reported16 for copolymers E106B16 and E210B16 in aqueous solution at 30 °C are identical (within experimental error) at ca. 0.004 g dm-3. Considering that the temperature dependence of the cmc is known to be small (even zero) for copolymers of the type under consideration,27 then, given very low values of the cmc, micellar dissociation would not be expected to have any significant effect in light scattering experiments carried out on copolymer solutions of concentration greater than 1 g dm-3 at any of the temperatures used in the present work, range 25-50 °C. 3.3. Dynamic Light Scattering (DLS). Satisfactory results were obtained from the DLS experiments on copolymer solutions at 25, 40, and 50 °C at concentrations up to 30 g dm-3 (E96B18) or 20 g dm-3 (E184B18, E315B17, and E398B19). The lowering of the upper limit accommodated the increased effect of intermicellar interaction as the E-block length was increased. Intensity fraction distributions of apparent hydrodynamic radius [log(rh,app)] obtained for copolymer E315B17 at 25 °C are shown in Figure 2. This system was chosen as the copolymer with the shortest B block in the best solvent, and so the most likely to show any effect of the molecule-micelle equilibrium

at low concentration. In fact, as seen in Figure 2, the single narrow peaks with maxima in the range rh,app ≈ 20-23 nm indicate only micelles formed by closed association. The slightly broader peaks found for the low concentration probably reflect the response of the CONTIN program to scatter in the measured low intensities. The trend toward lower values of log(rh,app) at higher concentration is consistent with an increase in intermicellar interaction with increase in concentration, as might be expected for micelles formed from copolymers with long E blocks. The intensity fraction distributions found for the other copolymers were qualitatively similar to those shown in Figure 2 and also to those illustrated previously16 for micellar solutions of related copolymers, E106B16 and E210B16. In Figure 3 the reciprocal of the intensity average of rh,app is plotted against copolymer concentration for solutions of copolymers E315B17. Through eq 2, 1/rh,app is related to the intensity average of Dapp but is compensated for change in temperature and viscosity. These and similar plots for the other three copolymers were extrapolated linearly to zero concentration to obtain true values of rh: see Table 2, in which rh is the inverse of the intensity average of 1/rh. The temperature dependences of rh of the micelles of the four copolymers are illustrated in Figure 4. Some years ago it was observed that the hydrodynamic radii of micelles of EmPnEm copolymers in aqueous solution were insensitive to change in temperature.28 The effect was attributed to compensation between an increase in association number of the micelle and a decrease in swelling of the micelle fringe as temperature was increased. Since that time, there have been confirmatory reports,5

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Figure 4. Effect of temperature on hydrodynamic radius (rh evaluated at c ) 0) for the EmBn copolymers indicated.

including many of the studies of micelles of EmBn copolymers referenced in this paper. The present data (summarized in Figure 4) cover a far wider range of E-block lengths than heretofore: for all four copolymers, they indicate a very slight decrease in the value of rh as T is increased. The last column in Table 2 lists the hydrodynamic expansion factor defined as

δh ) Vh/Va

Figure 5. Static light scattering. Debye plots for aqueous solutions of copolymer E398B19 at the temperatures indicated. The curves were calculated using eqs 5 and 6.

TABLE 3: Micellar Characteristics from Static Light Scattering: EmB10 Copolymers in Watera copolymer

T/°C

10-5 Mw/g mol-1

Nw

δt

E96B18

25 40 50 25 40 50 25 40 50 25 40 50

9.3 9.9 9.9 11.7 13.0 13.2 8.9 11.4 12.7 13.5 16.5 16.5

163 174 174 121 134 136 57 73 81 68 83 83

9.5 8.9 8.5 13.8 13.0 12.5 17.0 16.1 15.2 20.4 18.6 16.0

E184B18

(4) E315B17

where Vh is the average hydrodynamic volume and Va is the average anhydrous volume of the micelles, the latter being calculated from the micellar molar mass determined by SLS (see Section 3.4) and the anhydrous density of the copolymer (Fa ≈ 1.11-1.06 g cm-3 according to temperature and composition).29 Parameter δh illustrates very well the marked effect of temperature on the hydrodynamic expansion of the E-block coils in the micelle fringe. 3.4. Static Light Scattering (SLS). SLS experiments were performed on copolymer solutions at the temperatures and concentrations described for the DLS experiments (Section 3.3) but with a lower limit of approximately 1 g dm-3. The Debye equation (eq 3 of Section 2.2) was used to analyze the data. Used for scattering at 90°, the equation assumes small particles relative to the wavelength of the light. Radii of gyration estimated as 0.775rh (i.e., as if the micelles were uniform spheres) are in the range 11-20 nm or less based on the values of rh listed in Table 2, and a small effect from intraparticle interference is to be expected at the high end of this range. However, from published tables30 the maximum effect for the largest micelles is to increase Mw by 4%. Given the likely error from other sources, this correction was ignored. Equation 3 truncated to the second term could not be used in the present experiments because micellar interaction caused significant curvature of the Debye plot even in the low concentration range. This feature is illustrated in Figure 5, in which K*c/(I - Is) is plotted against concentration for copolymer E398B19 in solution at 25 and 50 °C, the intermediate data for solutions at 40 °C being omitted for clarity of presentation. Rather than accommodate the curvature by use of a virial expansion, so introducing a number of adjustable coefficients, we have used a method based on scattering theory from hard spheres incorporating the Carnahan-Starling equation.31,32 This is equivalent to using the virial expansion for the structure factor for hard spheres taken to its seventh term but requires only two adjustable parameters, Mw and δt, as described below. The new parameter, δt, relates to the volume excluded by one micelle to

E398B19

a

Micelle molar mass (Mw) and thermodynamic expansion factor (δt) to (10%; micelle association number (Nw) to (11%.

another, and it applies as an effective parameter for compact micelles irrespective of their exact structure. In the procedure, the interparticle interference factor (structure factor, S) in the scattering equation

K*c/(I - Is) ) 1/SMw

(5)

1/S ) [(1 + 2φ)2 - φ 2(4φ - φ 2)] (1 - φ)-4

(6)

is approximated by

where φ is the volume fraction of equivalent uniform spheres. Values of φ were calculated from the volume fraction of micelles in the system by applying a thermodynamic expansion factor δt, as defined in Section 1. Concentrations were converted to volume fractions using the densities of anhydrous copolymer (Fa) as described in Section 3.3. Fits of eqs 5 and 6 to the data are shown as solid lines in Figure 5. This procedure, applied to the light scattering data for solutions of all four copolymers at three temperatures, gave the values of the fitting parameters, Mw and δt, listed in Table 3, together with association numbers of the micelles calculated from

Nw ) Mw,mic/Mw,mol

(7)

using the value of Mw,mol listed in Table 1. It is apparent that values of the expansion factors δh and δt increase regularly with increase in E-block length (see Figure 6a) and are not sensitive to small changes in B-block length. However, this is not the case for micelle association numbers.

Ethylene Oxide and 1,2-Butylene Oxide Copolymers

J. Phys. Chem. B, Vol. 103, No. 51, 1999 11273

Figure 8. Sol-gel diagrams transition temperatures plotted against reduced concentration (c/cgc) for aqueous solutions of EmBn block copolymers: (b) E96B18, (O) E184B18, (9) E315B17, and (0) E398B19.

Figure 6. (a) Hydrodynamic (δh) and thermodynamic (δt) expansion factors (as indicated) and (b) association number versus E-block length. The errors are as indicated in Tables 2 and 3. The straight lines lead the eye toward regularities (or irregularities) in the results.

Figure 7. Sol-gel diagrams from tube inversion for aqueous solutions of EmBn block copolymers: (b) E96B18, (O) E184B18, (9) E315B17 and (0) E398B19.

As shown in Figure 6b, the expected regular fall in association number with increase in hydrophilicity of the copolymers as the E-block length is increased at constant B-block length (B18) is disturbed by the relatively low value for copolymer E315B17 (short B block) and the relatively high value for copolymer E398B19 (long E block). As discussed further in Section 3.5, gelation is controlled by micelle size rather than by Nw, and in that context inconsistency in values of Nw is unimportant. 3.5. Sol-gel Behavior. Mobile-immobile boundaries determined by tube inversion under controlled conditions are shown in Figure 7. For the two copolymers with the longest E blocks (E315B17 and E398B19) it proved difficult to define the high-temperature boundary by tube inversion, as the transition was to an extremely viscous solution, possibly a soft gel.

Consequently, the high-temperature boundaries determined by tube inversion for these two copolymers may be too high. The minimum concentrations for gel formation occurred at temperatures in the range 0-20 °C and at concentrations in the range 3.5-7.5 wt %, depending on E-block length: see Figure 7. That of copolymer E398B19 (3.5 wt % at 20 °C) is significantly lower than any previously reported for aqueous micellar solutions of block copolyethers. The similar shapes of the boundaries in Figure 7 suggest a plot against concentration reduced in proportion to the cgc. This is shown in Figure 8. Correspondence of the boundaries found for copolymers E96B18 and E184B18 is essentially complete: that of the two longer copolymers fails at the upper boundary, as might be expected in view of the difficulty with the tubeinversion method in this region (described above). As discussed below, this regularity of behavior reflects the common origin of the gels in the cubic packing of spherical micelles. Small-angle X-ray and neutron scattering (SAXS and SANS) experiments on aqueous gels of related copolymers (E106B16, E210B16) have shown a body-centered-cubic structure characteristic of packed spherical micelles.16,33 Corresponding SAXS experiments on micellar gels of the present have confirmed that they also have cubic structures: either fcc (E96B18 and E184B18) or bcc (E315B17 and E398B19).34 Consequently, the variation of the critical gel concentration is understandable in terms of waterswollen spherical micelles packing as hard spheres. Previous discussion of this point can be found in, for example, refs 1317 and 35-38. In the particular case of a bcc structure, the cgc (in g dm-3) is simply given by eq 1; for an fcc structure, the corresponding equation is

cgc/(g dm-3) ) (740Fa/δt)

(8)

The values obtained at 25 °C (converted to g dm-3) are plotted against Fa/δt in Figure 9. Data for related copolymers with lengthy E blocks, E90B10 and E106B16,16,17 are included. The use of either of eqs 1 or 8 to predict the cgc from dilute solution measurements of micellar excluded volume, whether determined by light scattering or SANS,17 is seen to be satisfactory, although the accuracy of determination of δt (indicated by the error bars in Figure 9) does not allow distinction of the two structures. Rough extrapolation of the data in Figure 6a to higher values of E-block length followed by reference to Figure 9 indicates gelation at concentrations below 2 wt % for an aqueous micellar

11274 J. Phys. Chem. B, Vol. 103, No. 51, 1999

Figure 9. Critical gel concentration for aqueous solutions of EmBn block copolymers versus the ratio of anhydrous density to thermodynamic expansion factor (Fa/δt): (b) present work, (2) E106B16 from ref 16, and (9) E90B10 from ref 17. The error bars for Fa/δt are (10% (as indicated in Table 3).

solution of a copolymer with an E700 block. Work is in hand to test this prediction by preparation of appropriate copolymers. 4. Conclusions Micelle properties and sol-gel curves were obtained for four oxyethylene/oxybutylene diblock copolymers: E96B18, E184B18, E315B17, and E398B19. At a given temperature, the values of the hydrodynamic radius and hydrodynamic expansion factor, and the thermodynamic expansion factor all increase as the E-block length is increased from 96 to 398 oxyethylene units, whereas the micelle association number decreases. A small perturbation in the E-block length dependence of the association number results from the minor inconsistency (18 ( 1) in B-block length, but the two expansion factors increase linearly with E-block length. At 20 °C, hard gels (i.e., gels immobile to tube inversion) form at critical gel concentrations (cgc) of 3.5-8 wt % copolymer, depending on E-block length. Related work confirms the cubic structure of the gels. Gel-sol (T versus c) boundaries approximately superimpose when plotted against the reduced concentration variable c/cgc. Given cubic structures, the values of the cgc correlate well with the values of the thermodynamic expansion factor δt. Acknowledgment. We thank Mr. S. K. Nixon for help with the GPC experiments. The Thai Government provided a Research Studentship for W.M. The Engineering and Physical Research Council (UK) provided financial assistance for synthesis of block copolymers through Grant GR/L22645. References and Notes (1) Schmolka, I. R.; Bacon, L. R. J. Am. Oil Chem. Soc. 1967, 44, 559.

Mingvanish et al. (2) Schmolka, I. R. J. Biomed. Mater. Res. 1972, 6, 571. (3) Miyazaki, S.; Ohkawa, Y.; Takada, M.; Attwood, D. Chem. Pharm. Bull. 1990, 40, 2224. (4) Edens, M. W. In Nonionic Surfactants: Polyoxyalkylene Block Copolymers; Nace, V. M., Ed.; Marcel Dekker: New York, 1996, Chapter 5. (5) Chu, B.; Zhou, Z.-K. In Nonionic Surfactants: Polyoxyalkylene Block Copolymers; Nace, V. M., Ed.; Marcel Dekker: New York, 1996, Chapter 3. (6) Mortensen, K. J. Phys. Condens. Matter 1996, 8, A103. (7) Alexandridis, P. Curr. Opin. Colloid Interface Sci. 1997, 2, 478. (8) Technical Literature, B-Series Polyglycols. Butylene Oxide/Ethylene Oxide Block Copolymers; The Dow Chemical Co.: Freeport, TX, 1994. (9) Nace, V. M. J. Am. Oil Chem. Soc. 1996, 73, 1. (10) Sun, W.-B.; Ding, J.-F.; Mobbs, R. H.; Attwood, D.; Booth, C. Colloids Surf. 1991, 54, 103. (11) Luo, Y.-Z.; Nicholas, C. V.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C. Colloid Polym. Sci. 1992, 270, 1094. (12) Bedells, A. D.; Arafeh, R. M.; Yang, Z.; Attwood, D.; Heatley, F.; Padget, J. C.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1993, 89, 1235. (13) Mortensen, K.; Brown, W. Macromolecules 1993, 26, 4128. (14) Bedells, A. D.; Arafeh, R. M.; Yang, Z.; Attwood, D.; Padget, J. C.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1993, 89, 1243. (15) Deng, N.-J.; Luo, Y.-Z.; Tanodekaew, S.; Bingham, N.; Attwood, D.; Booth, C. J. Polym. Sci., Part B: Polym. Phys. 1995, 33, 1085. (16) Kelarakis, A.; Havredaki, V.; Derici, L.; Yu, G.-E.; Booth, C.; Hamley, I. W. J. Chem. Soc., Faraday Trans. 1998, 94, 3639. (17) Derici, L.; Ledger, S.; Mai, S.-M.; Booth, C.; Hamley, I. W.; Pedersen, J. S. Phys. Chem. Chem. Phys. 1999, 1, 2773. (18) Yu, G.-E.; Yang, Z.; Ameri, M.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C. J. Phys. Chem., Part B 1997, 101, 4394. (19) Heatley, F.; Yu, G.-E.; Sun., W.-B.; Pywell, E. J.; Mobbs, R. H.; Booth, C. Eur. Polym. J. 1990, 26, 583. (20) Yang, Y.-W.; Deng, N.-J.; Yu, G.-E.; Zhou, Z.-K.; Attwood, D.; Booth, C. Langmuir 1995, 11, 4703. (21) Yang, Y.-W.; Yang, Z.; Zhou, Z.-K.; Attwood, D.; Booth, C. Macromolecules 1996, 29, 670. (22) Yang, Z.; Yang, Y.-W.; Zhou, Z.-K.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1996, 92, 257. (23) Provencher, S. W. Makromol. Chem. 1979, 180, 201. (24) Kratochvil, P. Classical Light Scattering from Polymer Solutions; Elsevier: Amsterdam, 1987; Chapter 5. (25) Li, H.; Yu., G.-E.; Price, C.; Booth, C.; Hecht, E.; Hoffmann, H. Macromolecules 1997, 30, 1347. (26) Yu, G.-E.; Zhou, Z.-K.; Attwood, D.; Price, C.; Booth, C.; Griffiths, P. C.; Stilbs, P. J. Chem. Soc., Faraday Trans. 1996, 92, 5021. (27) Kelarakis, A.; Havredaki, V.; Yu, G.-E.; Derici, L.; Booth, C. Macromolecules 1998, 31, 944. (28) Attwood, D.; Collett, J. H.; Tait, C. J. Int. J. Pharm. 1985, 26, 25. (29) Mai, S.-M.; Booth, C.; Nace, V. M. Eur. Polym. J. 1997, 33, 991. (30) Casassa, E. F. In Polymer Handbook, 3rd ed.; Brandrup, J., Immergut, E. H. Eds.; Wiley: New York, 1989; p 485. Beattie, W. H.; Booth, C. J. Phys. Chem. 1960, 64, 696. (31) Vrij, A. J. Chem. Phys. 1978, 69, 1742. (32) Carnahan, N. F.; Starling, K. E. J. Chem. Phys. 1969, 51, 635. (33) Hamley, I. W.; Mortensen, K.; Yu, G.-E.; Booth, C. Macromolecules 1998, 31, 6958. (34) Hamley, I.; Daniel, C.; Mingvanish, W.; Mai, S.-M.; Booth, C.; Messe, L.; Ryan, A., accepted for publication in Langmuir. (35) Mortensen, K.; Pedersen, J. S. Macromolecules 1993, 26, 805. (36) Malmsten, M.; Lindman, B. Macromolecules 1992, 25, 5440. (37) Hvidt, S.; Jørgensen, E. B.; Brown, W.; Schillen, K. J. Phys. Chem. 1994, 98, 12320. (38) Wanka, G.; Hoffmann, H.; Ulbricht, W. Macromolecules 1994, 27, 4145.