Association of Diblock and Triblock Copolymers of Ethylene Oxide and

Jul 10, 1996 - Surface Activity, SANS, and Viscosity Studies in Aqueous Solutions of Oxyethylene and Oxybutylene Di- and Triblock Copolymers. Saurabh ...
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Langmuir 1996, 12, 3404-3412

Association of Diblock and Triblock Copolymers of Ethylene Oxide and Butylene Oxide in Aqueous Solution Ga-Er Yu, Yung-Wei Yang, Zhuo Yang, David Attwood, and Colin Booth* Departments of Chemistry and Pharmacy, Manchester Polymer Centre, Manchester M13 9PL, U.K.

V. Mark Nace The Dow Chemical Company, Texas Operations, Research and Development, Freeport, Texas 77541 Received October 19, 1995. In Final Form: April 26, 1996X The association properties of block copolymers of ethylene oxide (E) and 1,2-butylene oxide (B) manufactured by The Dow Chemical Company were studied by static and dynamic light scattering. The critical micelle concentrations and micelle association numbers so obtained were combined with literature values for related copolymers in order to discuss the effect of block architecture on the association properties of linear diblock and triblock copolymers. The measurements significantly increase the available data for EmBnEm triblock copolymers and provide new insight into effects caused by E-block distributions originating from the different rates of reaction of ethylene oxide with primary and secondary oxyanions during copolymerization.

1. Introduction Water soluble block copolymer surfactants are widely used in a variety of domestic and industrial applications. These compounds typically contain a poly(oxyethylene) block as the hydrophilic component and either an alkyl, poly(oxypropylene), or poly(oxybutylene) block as the hydrophobic component. Block copolymers of ethylene oxide and 1,2-butylene oxide, i.e., diblock EmBn and triblock EmBnEm copolymers (E ) oxyethylene, B ) oxybutylene), were introduced as commercial products by The Dow Chemical Company in 1993, with first descriptions of these copolymers appearing in the commercial1 and scientific2 literature in 1994. A study by dynamic and static light scattering of the association properties of four of these industrially-synthesized copolymers in aqueous solution is the subject of this paper. So far as we are aware this is the first such study of these new surfactants. Commonly, academic interest has centered on commercially-available triblock copolymers of ethylene oxide and propylene oxide, usually EmPnEm (P ) oxypropylene) but with some reports on other architectures (e.g., EmPn, PnEmPn). The current state of this work can be judged from recent publications3-9 and the references therein. As discussed by Schmolka10 block copolymers of ethylene oxide and butylene oxide were patented by Lundsted (to X

Abstract published in Advance ACS Abstracts, June 15, 1996.

(1) Dow Chemical Co., Freeport, Texas, Technical Literature, B-Series Polyglycols. Butylene Oxide/Ethylene Oxide Block Copolymers, 1994. (2) Nace, V. M.; Whitmarsh, R. H.; Edens, M. W. J. Am. Oil Chem. Soc. 1994, 71, 777. (3) Almgren, M.; Brown, W.; Hvidt, S. Colloid Polym. Sci. 1995, 273, 2. (4) Wanka, G.; Hoffmann, H.; Ulbricht, W. Macromolecules 1994, 27, 4145. (5) Mortensen, K.; Brown, W.; Jorgensen, E. Macromolecules 1994, 27, 5654. (6) Zhou, Z.-K.; Chu, B. Macromolecules 1994, 27, 2025. (7) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Macromolecules 1994, 27, 2414. (8) Wang, Q.-G.; Yu, G.-E.; Deng, Y.-L.; Price, C.; Booth, C. Eur. Polym. J. 1993, 29, 665. (9) Yu, G.-E.; Deng, Y.-L.; Dalton, S.; Wang, Q.-G.; Attwood, D.; Price, C.; Booth, C. J. Chem. Soc., Faraday Trans. 1992, 88, 2537.

S0743-7463(95)00910-3 CCC: $12.00

Wyandotte Chemical Corp., now BASF Corp.) and Spriggs (to Dow Chemical Co.) in the 1950s. Later Szymanowski and co-workers11 described the preparation and the technological properties of diblock and triblock E/B copolymers, and Lee et al.12 compared the surface activity of EmBnEm and EmPnEm block copolymers. Most recently, information on the association and surface properties of E/B block copolymers has stemmed largely from our laboratories. Studies of linear copolymers have included a range of block architectures (diblock EmBn and triblock EmBnEm and BmEnBm),13-23 and work on cyclic-diblock copolymers is in hand.24 In part, this range of the academic studies was made possible by the simpler preparative chemistry of the E/B system (compared to the E/P system), since the transfer reaction which complicates the anionic (10) Schmolka, I. R. In Nonionic Surfactants; Surfactant Science Series, Vol. 1, Schick, M. J., Ed.; Marcel Dekker: New York, 1967; p 300. (11) Szymanowski, J.; Prochaska, K. Fette Seifen Anstrichmittel 1981, 83, 172. Myszkowski, J.; Szymanowski, J.; Goc, W.; Alejski, K. Tenside Deterg. 1982, 19, 7. Szymanowski, J.; Myszkowski, J.; Prochaska, K.; Szafraniak, K. Tenside Deterg. 1982, 19, 11. (12) Lee, J. H.; Kopecek, J.; Andrade, J. Polym. Mater. Sci. Eng. 1987, 57, 613. (13) Sun, W.-B.; Ding, J.-F.; Mobbs, R. H.; Attwood, D.; Booth, C. Colloid Surf. 1991, 32, 103. (14) Luo, Y.-Z.; Nicholas, C. V.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C. Colloid Polym. Sci. 1992, 270, 1094. (15) Nicholas, C. V.; Luo, Y.-Z.; Deng, N.-J.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C. Polymer 1993, 34, 138. (16) Luo, Y.-Z.; Nicholas, C. V.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C.; Zhou, Z.-K.; Chu, B. J. Chem. Soc., Faraday Trans. 1993, 88, 539. (17) 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. (18) Tanodekaew, S.; Deng, N.-J.; Smith, S.; Yang, Y.-W.; Attwood, D.; Booth, C. J. Phys. Chem. 1993, 97, 11847. (19) Yang, Z.; Pickard, S.; Deng, N.-J.; Barlow, R. J.; Attwood, D.; Booth, C. Macromolecules 1994, 27, 2371. (20) Deng, N.-J.; Luo, Y.-Z.; Tanodekaew, S.; Bingham, N.; Attwood, D.; Booth, C. J. Polym. Sci., Part B, Polym. Phys. 1995, 33, 1085. (21) Yang, Y.-W.; Deng, N.-J.; Yu, G.-E.; Zhou, Z.-K.; Attwood, D.; Booth, C. Langmuir 1995, 11, 4703. (22) Nace, V. M. J. Am. Oil Chem. Soc. 1996, 73, 1. (23) Yang, Y.-W.; Yang, Z.; Zhou, Z.-K.; Attwood, D.; Booth, C. Macromolecules 1996, 29, 670. (24) Yu, G.-E.; Zhou, Z.-K.; Price, C.; Booth, C. Pacifichem ’95, Abstracts, Honolulu, 1995.

© 1996 American Chemical Society

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Langmuir, Vol. 12, No. 14, 1996 3405 Table 1. Molecular Characteristics of the Copolymers GPCa

specified commercial description and batch number BM45-1600 (GJ02016106) B20-5000 (GE01016102) B40-1900 (GF05016105) B20-3800 (GI04016105) d

wt % E

Mn/g mol-1

55

1520

79

formulac

NMR mol % B* d

formulab

Mn/g mol-1

Mw/Mn

Mn/g mol-1

wt % E

E18B9

1600

1.05

1630

54

4790

E43B14E43

4800

1.08

4720

80

0

E43B12E43

60

1820

E13B10E13

1800

1.10

1950

63

13

E14B10E14

79

3660

E33B10E33

3800

1.09

3800

81

5

E35B10E35

E20B10

a Molar masses as if poly(oxyethylene). b Formula calculated from NMR results. c Formula calculated from specified characteristics. Mol % B ends from 13C NMR, i.e., 100[IB*/(IB* + IE*)] where IB* and IE* represent the integrals of end-group carbons.

polymerization of propylene oxide25 is not a problem in the polymerization of 1,2-butylene oxide. Comparison of association properties has been made between EmBnEm and EmPnEm triblock copolymers21,22 and between EnBn and EmCn (C ) methylene) diblock copolymers,21 and it has been established21 that a B unit is about four times as hydrophobic as a P unit and roughly equivalent to a C unit. As described elsewhere,2 an important consideration in the sequential block copolymerization of 1,2-butylene oxide followed by ethylene oxide is the difference in reactivity of the secondary oxyanion of the B end compared with that of the primary oxyanion of an E end. Because of slow initiation of the E blocks, the E-block length distributions in EmBnEm copolymers (and in BnEm copolymers when the B block is prepared first) are wide, and a fraction of B-block ends (proportional to the logarithm of the average E-block length)2 may not be ethoxylated. This wide E-block-length distribution leads to species with low solubilities in water, sufficiently so as to cause clouding at temperatures below the critical micelle concentration (cmc), followed in some instances by clearing as the insoluble species are solubilized in micelles formed at and above the cmc. This behavior has been noted for a related oxyethylene/oxypropylene copolymer E13P30E13 (L64)26 and was also reported recently19 for solutions of an oxyethylene/oxybutylene triblock copolymer E21B8E21. It is an important consideration in the present study. More importantly, compared with expectation for a copolymer with a narrow E-block-length distribution, a copolymer with a wide E-block-length distribution has a low critical micelle concentration and a high micellar association number. These effects have been noted previously23 but are particularly well illustrated by the larger data set made available by the new results from this work. 2. Experimental Section 2.1. Copolymers. Details of the copolymers investigated are listed in Table 1. The general procedures used in their synthesis and characterization have been described.2 In order to allow comparison with recent work22 they were used as received, without purification. Their specified characteristics are listed in Table 1. The molecular characteristics of the actual samples used in the light scattering experiments were individually checked by gel permeation chromatography (GPC) and 13C NMR. GPC was carried out using tetrahydrofuran at 20 °C as eluent, the columns and equipment used being similar to those described recently.27 Calibration was by poly(oxyethylene) samples of known molar mass. The GPC curves of each copolymer contained (25) Yu, G.-E.; Masters, A. J.; Heatley, F.; Booth, C.; Blease, T. G. Macromol. Chem. Phys. 1994, 195, 1517. (26) Zhou, Z.-K.; Chu, B. Macromolecules 1988, 21, 2548. (27) Sun, T.; Yu, G.-E.; Price, C.; Booth, C.; Cooke, J.; Ryan, A. J. Polym. Commun. 1995, 36, 3775.

a single narrow peak, which compares favorably with the GPC curves reported for commerical EmPnEm copolymers (see, e.g., ref 9) which generally show two peaks or a peak with a pronounced shoulder. The GPC results are summarized in Table 1. The values of Mn are as if the samples were poly(oxyethylene), and the values of Mw/Mn give a measure of the width of the molecular size distribution. Proton-decoupled 13C NMR spectra were obtained by means of a Varian Unity 500 spectrometer operated at 125.5 MHz, with the samples dissolved in CDCl3 (0.1 g cm-3). Delay times were in the range 15-20 s, which allowed total relaxation between pulses. Spectral assignments were taken from previous work.28 For each of the triblock copolymers a slight excess of E end groups over EB junctions indicated the presence of 2-3 mol % of homopoly(oxyethylene). All the copolymers contained approximately 2 mol % head-to-head (followed immediately by tail-to-tail) placements in their B blocks. The spectra of two of the triblock copolymers gave evidence of unethoxylated B ends. Values of Mn, wt % E, and the mole percent of unethoxylated ends found for the copolymers, all corrected for homo-poly(oxyethylene) impurity, are listed in Table 1. They largely agree with the specified values. The specified formulas listed in column four of Table 1 are used below to denote the copolymers. 2.2. Static and Dynamic Light Scattering. Solutions for light scattering were clarified by filtering through Millipore (Millex) filters (0.22 µm porosity) directly into the cleaned scattering cell. Distilled water used in making up the solutions was filtered through either 0.10 or 0.22 µm porosity filters. Static light scattering (SLS) intensities were measured by means of a Malvern PCS100 instrument with vertically polarized incident light of wavelength 488 nm supplied by an argon-ion laser (Coherent Innova 90) operated at 500 mW or less. The intensity scale was calibrated against benzene. Measurements were made at an angle of 90° to the incident beam, and for selected solutions at 45° and 135°, in order to check the dissymmetry of the scattered light. Intensities were measured either for solutions at a given temperature over a range of concentration (to measure average molar mass) or for solutions at a given concentration over a range of temperature (to measure critical micelle temperature, cmt). Dynamic light scattering (DLS) measurements were made by means of the Malvern instrument described above combined with a Brookhaven BI 9000 AT digital correlator. These measurements were usually made with the detector at an angle of 90° to the incident beam. The results of dynamic light scattering (DLS) were analyzed by the constrained regularization CONTIN method,29 thus gaining information on the distribution of decay rates (Γ). The decay rate distributions were transformed to distributions of apparent diffusion coefficients (Dapp ) Γ/q2) and hence distributions of apparent hydrodynamic radii (rh,app, radius of the hydrodynamically-equivalent hard sphere corresponding to Dapp) via the Stokes-Einstein equation

rh,app ) kT/(6πηDapp)

(1)

where k is the Boltzmann constant and η is the viscosity of water at temperature T. Values of η were taken from ref 30. (28) Heatley, F.; Yu, G.-E.; Sun, W.-B.; Pywell, E. J.; Mobbs, R. H.; Booth, C. Eur. Polym. J. 1990, 26, 583. (29) Provencher, S. W. Makromol. Chem. 1979, 180, 201. (30) Handbook of Chemistry and Physics, 57th ed.; Weast, R. C., Ed.; CRC Press: Cleveland, OH, 1976; p F-51.

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The basis for analysis of static light scattering (SLS) was the Rayleigh-Gans-Debye equation, which we write

I - Is ) K*cMw

(2)

where I is intensity of light scattered from solution relative to that from benzene, Is the corresponding quantity for pure solvent, c is the concentration (in g dm-3), Mw the mass-average molar mass of the solute, and

K* ) (4π2/NAλ4)(nB2/RB)(dn/dc)2

(3)

where NA ) Avogadro’s constant, nB and RB ) refractive index and Rayleigh ratio of benzene respectively, and dn/dc ) refractive index increment. Refractive index increments were determined for copolymers E13B10E13 and E18B9 by the method described previously.17 The values found for solutions at 20 °C, i.e., 0.136 cm3 g-1 (E13B10E13) and 0.131 cm3 g-1 (E18B9), were close to that obtained previously17,18,21 for comparable copolymers over a range of compositions (i.e., 0.135 cm3 g-1) which, considering the probable experimental error of the measurements ((0.003 cm3 g-1), allowed use of the same value in this study. The temperature derivative of dn/dc obtained previously17 (i.e., -2 × 10-4 cm3 g-1 K-1) was used to derive values of dn/dc ) 0.134 and 0.131 cm3 g-1 at 25 and 40 °C, respectively. The refractive index and Rayleigh ratio of benzene were taken from the literature.31-33

3. Results and Discussion Results are presented covering two interlinked aspects of the association properties of the copolymers. Micellization. The nature of the association, the critical conditions for micellization, and the conditions for essentially complete micellization of the copolymers. Micellar Properties. Determination of hydrodynamic radius, mass-average molar mass, and related properties by extrapolation of results obtained for micellar solutions to infinite dilution. 3.1. Micellization. Intensity fraction distributions of log rh,app were obtained by dynamic light scattering for aqueous solutions of all the copolymers across a wide concentration range at 25 and 40 °C. Additionally for the three triblock copolymers, temperature dependences of static light scattering were determined for solutions of concentration down to or below their reported22 critical micelle concentrations. In view of the low scattering intensities at the low cmc’s of solutions of E18B9, this copolymer was not investigated in this way. 3.1.1. Copolymer E18B9. Intensity fraction distributions of log rh,app were obtained for solutions of copolymer E18B9 at 25 and 40 °C. A concentration range of 1.9-100 g dm-3 was covered in seven steps: three examples for solutions at 25 °C are shown in Figure 1. The distributions obtained for moderately-dilute solutions (c ) 10-20 g dm-3) were narrow, but they broadened slightly as concentration was increased to 100 g dm-3. The values of rh,app ) 5-6 nm at the peaks were characteristic of micelles. The displacement of the peaks toward lower values of rh,app as concentration was increased is the usual behavior for micelles acting as hard spheres, and is discussed in section 3.2.1. For the most dilute solution investigated (i.e., c ) 1.9 g dm-3) the distribution was significantly broader; see Figure 1. This was attributed to the presence of a small intensity fraction of large particles (rh,app > 25 nm) which was unresolved by the CONTIN analysis. The constraints of CONTIN, particularly the principle of parsimony, act against resolution of (31) Johnson, B. L.; Smith, J. In Light Scattering From Polymer Solutions, Huglin, M. B., Ed.; Academic Press: London, 1972; p 29. (32) Dixon, A. L.; West, C. J. International Critical Tables; McGrawHill: New York, 1930; Vol. 7, p 38. (33) Gulari, E.; Chu, B. Biopolymers 1979, 18, 2943.

Figure 1. Dynamic light scattering from aqueous solutions of oxyethylene/oxybutylene block copolymer E18B9 at 25 °C. Intensity-fraction distributions of logarithmic apparent hydrodynamic radius, log10 rh,app, for solutions of concentration 100, 5.8, and 1.9 g dm-3 as indicated.

weak signals, but the method provides qualitative evidence of their presence through the broadening of the intensity distribution. It was concluded that a very small fraction of particulate insoluble material was present in the sample, which contributed little to the scattering intensity (relative to scattering from micelles) except at very low sample concentrations. In this respect, it is noted that the intensity of scattering depends on the product of mass concentration and particle molar mass (through the Rayleigh equation, I ) KcM), so a small intensity fraction of large particles represents a negligible mass fraction. For example, assuming a molar mass of 105 g mol-1 for the micelles (see section 3.2.2 for justification) and one of 107 g mol-1 for the particles (consistent with, say, poly(oxybutylene) particles with a hydrodynamic radius of 20 nm), and further assuming ideal scattering, then an intensity fraction of 0.1 (10%) would originate from a mass fraction of only 0.001 (0.1% wt %) of particles, which would not be detected by conventional methods of analysis (e.g., NMR). For solutions of copolymer E18B9 at 25 °C and c > 5 g dm-3, the results indicated essentially complete micellization and complete solubilization of all species. The intensity fraction distributions obtained for solutions at 40 °C were narrow over the whole concentration range studied, including a 1.0 g dm-3 solution. 3.1.2. Copolymer E43B14E43. Intensity fraction distributions of log rh,app were obtained for six solutions of copolymer E43B14E43 at 25 °C in the concentration range 4.0-100 g dm-3. Examples are shown in Figure 2. The distributions were broader than those found for the diblock copolymer and, at comparable concentrations, peaked at lower values of rh,app. Otherwise they showed the same general features, with the narrowest distributions found at concentrations in the range 10-30 g dm-3 and with distinct broadening of the distributions at the lowest concentration investigated (i.e., 4 g dm-3, ca. 10 × cmc). This too was attributed to the presence of a small intensity fraction of insoluble particles. The intensity fraction distributions obtained for solutions at 40 °C over the same concentration range were all narrow, but a solution of concentration 1.1 g dm-3 gave a broadened distribution. Plots of scattering intensity against temperature were obtained for solutions in the range c ) 0.22-5.1. Examples are shown in Figure 3. Critical micellization temperatures, defined by the points at which the scattering curves depart from their baselines, are listed in Table 2. The conventional plot for representation of critical micelle concentrations and temperatures is one of log c against

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Figure 2. Dynamic light scattering from aqueous solutions of oxyethylene/oxybutylene block copolymer E43B14E43 at 25 °C. Intensity-fraction distributions of logarithmic apparent hydrodynamic radius, log10 rh,app, for solutions of concentration 4.0, 14.5, and 100 g dm-3 as indicated.

Figure 3. Static light scattering intensity versus temperature for aqueous solutions of copolymer E43B14E43 of concentration 0.22, 0.87, and 5.1 g dm-3 as indicated. The intensity scales and baselines have been adjusted for clarity of presentation. Table 2. Critical Micelle Temperatures from Light Scatteringa copolymer

c/g dm-3

cmt/°C

E43B14E43

5.1 4.2 2.7 1.6 0.87 0.43 0.28 0.22 6.2 4.1 2.1 1.1 0.95 0.49 0.31 15.9 9.1 8.9 5.0 4.3

12 14 13 17 19 25 26 29 14 16 18 22 25 28 32 18 21 22 25 29

E13B10E13

E33B10E33

a

Estimated uncertainty in cmt, (2 deg.

1/T; see Figure 4. The results fit satisfactorily to a straight line, as discussed further in Section 3.2.6. 3.1.3. Copolymer E13B10E13. Intensity fraction distributions of log rh,app obtained for solutions of copolymer E13B10E13 at 25 °C across the concentration range 4.8100 g dm-3 were similar to those found for copolymer E43B14E43; see the examples shown in Figure 5. A minor

Figure 4. Critical concentrations and temperatures for micellization of oxyethylene/oxybutylene block copolymers in aqueous solution. Logarithm of concentration versus reciprocal critical micelle temperature (from SLS) for copolymer: (9) E43B14E43; (2) E13B10E13; (b) E33B10E33.

Figure 5. Dynamic light scattering from aqueous solutions of oxyethylene/oxybutylene block copolymer E13B10E13 at 25 °C. Intensity-fraction distributions of logarithmic apparent hydrodynamic radius, log10 rh,app, for solutions of concentration 4.8, 17.9, and 100 g dm-3 as indicated.

Figure 6. Static light scattering intensity versus temperature for aqueous solutions of copolymer E13B10E13 of concentration 0.31, 0.49, 1.1, and 4.1 g dm-3 as indicated. The intensity scales and baselines have been adjusted for clarity of presentation.

difference for solutions of c < 10 g dm-3 was the detection of species with rh,app ≈ 1 nm, assumed to be unassociated molecules. Selected plots of scattering intensity against temperature are illustrated in Figure 6. The concentration range covered by these experiments was from 0.31 to 6.2 g dm-3. Except for the solution of lowest concentration, each of the SLS-T curves showed a maximum in intensity as temperature was increased from a low value. Following previous treatment of curves of this type in a related

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Figure 8. Dynamic light scattering from aqueous solutions of oxyethylene/oxybutylene block copolymer E33B10E33 at 40 °C. Intensity-fraction distributions of logarithmic apparent hydrodynamic radius, log10 rh,app, for solutions of concentration 4.3, 10.0, and 20.0 g dm-3 as indicated.

Figure 7. Dynamic light scattering from aqueous solutions of oxyethylene/oxybutylene block copolymer E33B10E33 at 25 °C. Intensity-fraction distributions of logarithmic apparent hydrodynamic radius, log10 rh,app, for solutions of concentration: (a) 20 and 88 g dm-3 as indicated; (b) 4.3 and 10 g dm-3 as indicated.

system,19 the initial rise in scattering intensity was ascribed to phase separation of species with low (or zero) E content and the subsequent fall to solubilization of the insoluble copolymer in micelles. This argument places the cmt at or near the maximum. Accordingly, for solutions of this copolymer of c g 0.49 g dm-3, critical temperatures were defined by the maxima in the scattering curves, as listed in Table 2 and plotted in Figure 4. 3.1.4. Copolymer E33B10E33. Intensity fraction distributions of log rh,app were obtained for five solutions of copolymer E33B10E33 at 25 °C covering the concentration range 4.3-88 g dm-3. Examples are shown in Figure 7. Except at the highest and lowest concentrations there were three peaks in the intensity fraction distributions. These were assigned to molecules (rh,app ≈ 2 nm), micelles (rh,app ≈ 7 nm), and copolymer particles (rh,app ≈ 70 nm). For the solution of highest concentration (c ) 88 g dm-3) it was concluded that the proportion of micelles relative to particles was large enough to allow complete solubilization of otherwise insoluble copolymer particles. However, even at this high concentration the molecules peak remained prominent in the intensity distribution. An approximate calculation, based on the areas under the peaks in the intensity fraction distribution and the Rayleigh equation (as described above), and assuming an association number of 10 for the micelles of copolymer E33B10E33 (see section 3.2.2) gives 75 wt % unassociated molecules in an 88 g dm-3 solution at 25 °C. For the solution of lowest concentration (c ) 4.3 g dm-3) the distribution indicated a predominantly molecular solution. The limited broadening to high values of log10 rh was consistent with only a small intensity fraction of larger species (micelles or particles), and it was concluded

Figure 9. Static light scattering intensity versus temperature for aqueous solutions of copolymer E33B10E33 of concentration 4.3, 5.0, 8.9, and 15.9 g dm-3 as indicated. The intensity scales and baselines have been adjusted for clarity of presentation.

that the copolymer was predominantly in its molecular state, at this concentration. Examples of intensity fraction distributions of log rh,app obtained for solutions of copolymer E33B10E33 at 40 °C are shown in Figure 8. The examples chosen are for the low end of the concentration range. The distributions obtained indicate predominantly micellar solutions at all concentrations higher than 10 g dm-3. Plots of static light scattering intensity against temperature were obtained for solutions in the concentration range 4.3-15.9 g dm-3. Examples are shown in Figure 9. Except for the lowest concentration, each SLS-T curve showed a maximum in intensity as temperature was increased from a low value. Accordingly, for solutions of copolymer E33B10E33 of concentration 5.0 g dm-3 or greater, the critical temperatures listed in Table 2 and plotted in Figure 4 were defined by the maxima in the scattering curves. 3.1.5. Comparison with Previous Results. Critical micelle concentrations determined by measurement of surface tension have been reported for a number of E/B block copolymers in solution at 25 °C.22 Values reported for samples of the present copolymers (or obtained in same way) are listed in Table 3, where they can be compared with values obtained for solutions at 25 °C by interpolation of the smoothed light scattering results via Figure 4. The difference is within the overlap of estimated error in the two experiments and, as described in section 4, is not significant compared with the effect of B-block length on the cmc. Reinterpretation of the surface tension data taking the cmc to be the concentration at which the surface

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Table 3. Critical Micelle Concentrations of Aqueous Solutions at 25 °C Measured by Surface Tension22 and Light Scattering copolymer

method

cmc/g dm-3

E18B9 E43B14E43

surface tension surface tension light scattering surface tension light scattering surface tension light scattering

0.035 0.19 0.43 0.38 0.81 1.9 5.9

E13B10E13 E33B10E33

Figure 10. Inverse apparent hydrodynamic radius of micelles versus concentration for solutions at 25 °C (filled symbols) and 40 °C (unfilled symbols): (1 3) E18B9; (9 0) E43B14E43; (2 4) E13B10E13; (O) E33B10E33.

tension just reaches a constant value (rather than the intersection of two best straight lines through low and high concentration data points22) gives values in agreement with those from light scattering. 3.2. Micellar Properties. Micellar radii and molar masses were obtained by extrapolation to zero concentration from those concentration ranges in which the solutions were known to be predominantly micellar (from the DLS intensity-fraction distributions of log rh). Solutions of copolymer E33B10E33 at 25 °C were unsuited to this treatment, but light scattering results obtained for solutions of that copolymer at 40 °C, and of the other three copolymers at 25 and 40 °C, could be so analyzed. 3.2.1. Hydrodynamic Radius and Swelling Factor. Intensity-average apparent hydrodynamic radii were obtained by integrating over the intensity distributions of the micelles using the CONTIN procedure. Plots of 1/rh,app against concentration (c) are shown in Figure 10. The quantity 1/rh,app is proportional to the diffusion coefficient D through the Stokes-Einstein equation (eq 1) but is compensated for changes in solvent viscosity and temperature, so allowing direct comparison of results obtained for solutions at more than one temperature. The temperature dependences of the hydrodynamic radii were very small (i.e., within the uncertainty of measurement), and the two sets of data for a given copolymer could be treated as one; see Figure 10. This is a well established result for block copolyether micelles in aqueous solution, and was explained many years ago34 as a consequence of compensation between an increase in association number and a decrease in swelling of the micellar fringe as temperature is increased. As can be seen in figure 10, the data points fall into two groups, the subdivision largely reflecting the E content of the copolymers. The increase in 1/rh,app with concentration (i.e., a decrease of rh,app itself) is characteristic of micelles acting as hard spheres. (34) Attwood, D.; Collett, J. H.; Tait, C. J. Int. J. Pharm. 1985, 26, 25.

Table 4. Micellar Properties from Light Scatteringa copolymer E18B9 E43B14E43 E13B10E13 E33B10E33 a

T/°C

rh/nm

10-5Mw/g mol-1

Nw

δt

δh

25 40 25 40 25 40 40

6.3 6.5 6.2 6.6 5.1 5.2 5.1

1.2 1.9 0.45 0.80 0.28 0.50 0.34

70 110 9 16 13 23 8

1.9 2.2 3.0 3.5 1.3 1.5 2.7

5.6 3.9 14 9.7 13 7.6 11

Estimated uncertainties: rh, (5%; Mw, Nw, and δt, (10%.

Values of the hydrodynamic radius at zero concentration (rh) were obtained by linear extrapolation (via leastsquares fits) of the individual data sets. These values are listed in Table 4, together with values of the hydrodynamic swelling factor, δh, which is defined as the hydrodynamic volume (νh ) 4πrh3/3) divided by the anhydrous volume νa. Here νa ) Mw/NAF, where Mw is the mass-average molar mass of the micelles determined by static light scattering (see section 3.2.2), NA is Avogadro’s constant, the F is the density of anhydrous copolymer, approximated by 1.07 g cm-3 for the compositions and temperatures under consideration. 3.2.2. Micelle Molar Mass and Thermodynamic Radius. For a nonideal, dilute solution of micelles, the Debye equation35 can be written

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

(4)

where c is the concentration of micelles (in g dm-3), Mw is the mass-average molar mass of the micelles, and A2 is the second virial coefficient (higher terms being omitted) reflecting the interaction of the micelles in solution. As written, the equation assumes small particles relative to the wavelength of the light. Within the concentration ranges where the solutions were largely micellar, our measurements showed that the value of the dissymmetry ratio (I45/I135) was consistently near to unity. In principle, fitting eq 4 to the scattering function K*c/(I - Is) yields values of Mw and A2. Plots of scattering function K*c/(I - Is) against concentration for solutions at 25 °C are shown in Figure 11a. The data are for solutions of copolymers E18B9, E43B14E43, and E13B10E13. Whenever it occurs, and in the absence of other effects (e.g., phase separation of the molecular solution) micellar dissociation at low concentrations is made evident by an upturn in the Debye plot at low c. This effect was not detected for solutions of diblock copolymer E18B9 but was apparent in the Debye plots obtained for the solutions of the two triblock copolymers; see Figure 11a. A simple compensation for dissociation is possible if (i) the concentration of molecules above the critical micelle concentration (cmc) is constant and equal to the cmc and (ii) the contribution of molecules to the scattering intensity can be neglected. These assumptions should hold reasonably well if the association process is closed and the association number of the micelles is high, say 50 or so. In such a case, the Debye equation is often used in the form

K*c′/(I - Is) ) 1/Mw + 2A2c′ ...

(5)

where c′ ) (c - cmc). However, the pronounced curvature of the Debye plots over any reasonable concentration range (see Figure 11a) meant that eq 5, truncated to the second term, could not be used. (35) Debye, P.; Bueche, A. M. J. Chem. Phys. 1950, 26, 1423.

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Yu et al. Table 5. Static Light Scattering: Critical Micelle Concentrations (cmc) and Debye plot corrections (ccorr) cmc/g dm-3 copolymer

25 °C

E18B9 E43B14E43 E13B10E13 E33B10E33

0.035a

a

0.43 0.81 5.9

40 °C 0.037 0.080 1.1

ccorr/g dm-3 25 °C 0.15 1.7 2.2

40 °C 0.25 0.6 1.9

From surface tension.22

Application of the above procedure to the scattering intensities obtained for the three copolymers in solution at 25 °C is illustrated in Figure 11a. Values of cmc used to calculate c′ for solutions of the copolymers were read off the lines in Figure 4, extrapolating where necessary (see Table 5). The correction for copolymer E18B9 was insignificant and, for the other copolymers, was small. For copolymer E18B9 the hard-sphere extrapolation fitted the data across the whole concentration range irrespective of the parameter used (c or c′). Upturns in the Debye function at low concentration were still found in the corrected plots for the two triblock copolymers. For these copolymers, the hard-sphere equations (6) and (7) were fitted to the data points using the true concentration in the moderate concentration range (i.e., the filled points, c > 10-20 g dm-3, see Figure 11a) to obtain the values of Mw and δt, listed in Table 4. Values of the association numbers of the micelles were calculated from Figure 11. Debye plots for aqueous solutions of oxyethylene/ oxybutylene copolymers in aqueous solution at 25 °C: (1 3) E18B9; (9 0) E43B14E43; (2 4) E13B10E13. The full curves were calculated using hard-sphere theory to account for interparticle interference (see eqs 6 and 7 and Table 4). See text for definition of K* and (I - Is). (a) Uncorrected (unfilled symbols) and corrected (filled symbols) Debye plots. The corrected plots are against c′ ) (c - cmc) with the values of the cmc listed in Table 5. The uncorrected plots are against c′ ) c. (b) Corrected Debye plots based on c′ ) (c - ccorr) with values of ccorr (see Table 5) adjusted to obtain a satisfactory fit over the full concentration range.

In recent work16-21 we have adopted a suggestion of Vrij36 and extrapolated to c ) 0 from moderate concentration guided by the Carnahan-Starling equation,37 which is equivalent to a power series expansion for the structure factor for hard spheres taken to its seventh term. In this procedure, the interparticle interference factor (structure factor, S) in the scattering equation

K*c′/(I - Is) ) 1/SMw

(6)

is approximated by

1/S ) [(1 + 2φ)2 - φ2(4φ - φ2)](1 - φ)-4

(7)

where φ is the volume fraction of equivalent spheres. In practice, values of φ were calculated from the actual volume fraction of micelles in the system (corresponding to copolymer concentration c′) by applying a thermodynamic exclusion factor δt, i.e., the thermodynamic volume (νt) relative to anhydrous volume (νa), where the thermodynamic volume is one-eighth of the excluded volume. In our approximate treatment, concentrations were converted to volume fractions assuming a density of dry polymer of F ≈ 1.07 g dm-3 irrespective of temperature. Fitting eqs 6 and 7 to the data gave values of Mw and δt. (36) Vrij, A. J. Chem. Phys. 1978, 69, 1742. (37) Carnahan, N. F.; Starling, K. E. J. Chem. Phys. 1969, 51, 635.

Nw ) Mw(micelle)/Mw(molecule)

(8)

using values of Mw(molecule) calculated from Mn(molecule) and Mw/Mn (see Table 1). The results were further analyzed to determine values of a quantity ccorr which, when used to calculate c′ ) (c ccorr), give satisfactory fits of the data points to the hardsphere extrapolations. Debye plots so adjusted are shown in Figure 11b, and the values of the ccorr so defined are listed in Table 5. The full curves in Figure 11b are identical to those in Figure 11a. Similar treatment of the data obtained for solutions at 40 °C gave the micellar characteristics listed for that temperature in Table 4, together with the values of the ccorr listed in Table 5. No correction was made in extrapolating the data for copolymer E18B9 in solution at 40 °C, since the value of its critical micelle concentration under these conditions was very small. The very different values of the cmc obtained by the cmt method on the one hand and of ccorr obtained by correcting the Debye plot on the other require explanation. Discrepancies of a factor of 2 or so have been noted previously19,20 for EmBnEm block copolymers. The cmt method is designed to detect the early stages of micellization and, to a good approximation, the true cmc is obtained. By contrast, correction of the Debye plot is sensitive to the early stages of micellar dissociation. Only if the copolymer composition distribution is narrow and the micelle association number is high will these two regions relate to the same critical quantity. As discussed in section 1 and revealed by the values of Nw in Table 4, neither of these conditions apply to the present EmBnEm copolymers. Two assumptions were made in applying eqs 6 and 7 directly to solutions of moderate concentration: (i) that the concentration of molecules was insignificant and (ii) that the micellar size was constant over the moderate concentration range. The first condition was met in our experiments by fitting data points at concentrations well above the critical values. The second approximation is

Copolymer Association

Langmuir, Vol. 12, No. 14, 1996 3411

known to hold for block copolymer micelles of the present type. For example, it has been shown that the excluded volumes of EmBn and EmBnEm block copolymer micelles determined using solutions in the moderate concentration range serve to predict the close packing condition for formation of cubic phase gels.18,20,38 Also neutron scattering experiments on aqueous solutions of copolymer E25P40E25 (Pluronic P85) carried out over a similarly wide range of concentration have shown micellar size to be independent of concentration.39,40 3.3. Thermodynamic and Hydrodynamic Swelling Factors. As described in section 3.1, the hydrodynamic radii were found to be essentially independent of temperature. The compensating effects of a marked increase in association number (Nw) and a marked decrease in hydrodynamic swelling factor (δh) with increase in temperature which lead to the temperature independence of rh are well documented in the present results (see Table 4). For the same species the thermodynamic exclusion factor (δt) was found to increase slightly with increase in temperature. This parameter, which relates the excluded volume to the anhydrous volume, has been found to be relatively insensitive to temperature for micelles of other E/B copolymers.16,17 The relationship of δh and δt to solvent power differs. The contribution of the poly(oxyethylene) fringe to the excluded volume approaches zero in a theta solvent, where δt approaches a value determined mainly by the B-core volume, whereas the contribution of the fringe to the hydrodynamic volume remains large and finite.20 3.4. Thermodynamics of Micellization. Under certain conditions, the results plotted in Figure 4 can be used to estimate the thermodynamic quantities of micellization. If the association number (N) is single-valued (or the average of a narrow distribution of values), the law of mass action applies and the association equilibrium can be simply written

A a (1/N)AN

K ) [AN]1/N/[A]

(9)

Figure 12. Results for aqueous solutions of EnBmEn copolymers at 25-30 °C: present copolymers by (b) light scattering and (9) surface tension (see Tables 3-5); (2) other EmBnEm copolymers from previous work summarized in refs 21 and 23. (a) Logarithm of cmc versus B content. (b) Mass-average association number versus B content. The full lines represent results for EmBn copolymers taken from ref 21. The dashed lines represent results for Bn/2EmBn/2 copolymers taken from ref 23.

If the association number is large (1/N f 0), then the equilibrium constant K f 1/[A] and, taking [A] to be the cmc, the standard Gibbs energy and enthalpy of micellization can be calculated from:

other oxyethylene/oxybutylene block copolymers by the cmt method, i.e., 80 kJ mol-1 for copolymers E28B5 and E27B7 and 95 kJ mol-1 for copolymer E21B8E21.

∆micG° ≈ RT ln(cmc)

(10)

4. Effect of Block Architecture and Block-Length Distribution

∆micH° ≈ R {d ln(cmc)/d(1/T)}

(11)

The process refers to standard states of copolymer chains in ideally dilute solution at unit concentration (1 mol dm-3) and copolymer chains in the micellar state. In the present case, data over a temperature range are available for the three triblock copolymers (see Figure 4). For these copolymers, the distributions of micellar size (reflecting the distributions of N) are narrow, but the average values (N ) 8-23, see Table 3) are not as large as required (i.e. N ≈ 50)41 for accurate calculation of ∆micG° via eq 10. However, numerical calculations show that the error in using eq 11 under present circumstances is tolerable; ca. +15% in ∆micH°. The slope of the lines in Figure 4 leads directly to a value of ∆micH° ≈ 100 ( 25 kJ mol-1, in agreement with values of ∆micH obtained18,19 for (38) 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. (39) Mortensen, K.; Pedersen, J. S. Macromolecules 1993, 26, 805. (40) Mortensen, K. Prog. Colloid Polym. Sci. 1993, 91, 69. (41) Hall, D. G. In Nonionic Surfactants, Physical Chemistry; Surfactant Science Series 23; Schick, M. J., Ed.; Marcel Dekker: New York, 1987; p 233.

Values of the cmc and Nw found for copolymer E18B9 fit well to the pattern established for EmBn copolymers in previous work.21 Present and previous results for EmBnEm copolymers are plotted in Figure 12, in which the lines indicate the pattern of results established for EmBn diblock copolymers (full line) and Bn/2EmBn/2 triblock copolymers (dashed line) taken from refs 21 and 23. All the results are for copolymers with high E content (mol % E in the range 60-90). In both compilations, the effect of the small temperature range (25-30 °C) is insignificant compared with other effects. The cmc’s of the EmBnEm triblock copolymers show a more complicated dependence on B content than is the case for the other two architectures; see Figure 12a. This results from the wide distribution of E-block lengths in the EmBnEm copolymers with short E blocks. This in turn results from the slow rate of reaction of ethylene oxide with a B oxyanion (B-end) compared with an E oxyanion (see section 1), which means that the copolymers with short E-block lengths contain a proportion of diblock copolymer. In keeping with this, the points to the left of the dashed line in Figure 12a are for m ) 13-33 while

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those to the right are for m ) 40-58. Considering Nw (see Figure 12b) the points to the left of the dashed line are for m ) 21 and 33; i.e., Nw is relatively high for copolymers with short E-block lengths. This effect of E-block-length distribution, which is clearly shown in the present data, makes establishment of ranking orders for cmc and Nw for the triblock copolymers of different architecture (but otherwise similar chain length and composition) difficult to define with the data presently available. The best that can be done is:

cmc

EmBn < BnEmBn e EmBnEm

Nw

EmBn > BnEmBn g EmBnEm

Yu et al.

EmBnEm copolymers with narrow E-block length distributions (i.e., distributions comparable in width with those of the other two architectures) will be needed before a more definite order can be written down. Acknowledgment. We wish to thank Mr. K. Nixon and Dr. F. Heatley for help in characterizing the copolymers by GPC and NMR and Professor S. W. Provencher who kindly supplied a copy of the CONTIN program. Financial support came from the Engineering and Physical Science Research Council and the Government of the Republic of China. LA9509108