Effect of Cyclization on the Association Behavior of Block Copolymers

Apr 4, 1998 - The critical micelle concentrations (cmc) of the two copolymers were similar for solutions at 40−50 °C, but the temperature dependenc...
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Langmuir 1998, 14, 2278-2285

Effect of Cyclization on the Association Behavior of Block Copolymers in Aqueous Solution. Comparison of Oxyethylene/Oxypropylene Block Copolymers Cyclo-P34E104 and E52P34E52 Ga-Er Yu, Caroline A. Garrett, Shao-Min Mai, Haydar Altinok, David Attwood, Colin Price, and Colin Booth* Manchester Polymer Centre, Department of Chemistry and School of Pharmacy, University of Manchester, Manchester M13 9PL, UK Received September 22, 1997. In Final Form: February 2, 1998 Triblock copolymer E52P34E52 was prepared by sequential anionic polymerization of propylene oxide followed by ethylene oxide. Some of this copolymer was cyclized via acetal closure to yield a cyclic diblock copolymer, cyclo-P34E104, which was characterized by gel permeation chromatography (GPC) and nuclear magnetic resonance (NMR) spectroscopy. Light scattering methods were used to study the micellization and micellar properties of the two copolymers: dynamic light scattering for hydrodynamic properties of the micelles, static light scattering for micellar molar mass and critical micellization conditions. The gelation of concentrated solutions was also studied. The critical micelle concentrations (cmc) of the two copolymers were similar for solutions at 40-50 °C, but the temperature dependence of the cmc was smaller for the linear copolymer. The cyclic copolymer in solution at 50-55 °C formed micelles with larger association numbers and hard-sphere volumes than its linear triblock counterpart.

1. Introduction The self-association (micellization and gelation) of triblock EmPnEm copolymers [E ) oxyethylene, OCH2CH2; P ) oxypropylene, OCH2CH(CH3)] has been well researched, as summarized in recent reviews1-3 and papers.4-7 This activity reflects the commercial availability of these materials, for example, the Pluronic range from BASF, and the similar Synperonic PE range from ICI C&P. There is less information available for other architectures. Investigations of three PnEmPn copolymers available from BASF have been reported (P21E25P21,7 P15E156P15,8,9 and P14E24P1410). Comparative studies include the two different triblocks (E13P30E13 and P14E24P14),10 diblock with triblock (E26P29 and E14P30E14),11 and all three linear architectures for copolymers of (nominally) 38 P units and 100 E units.12 A study of water-soluble copolymers with 8 B units [B ) oxybutylene, OCH2CH(C2H5)] and ∼40 E units (i.e., including cyclo-B8E42) has been reported in related papers.13,14 A second study of effect of cyclization has been carried out with copolymers E72B27E72 and cyclo-B27E144.15 (1) Chu, B.; Zhou, Z.-K. In Nonionic Surfactants, Polyoxyalkylene Block Copolymers, Surfactant Science Series Vol. 60; Nace, V. M. Ed.; Marcel Dekker: New York, 1996. (2) Almgren, M.; Brown, W.; Hvidt, S. Colloid Polym. Sci. 1995, 273, 2. (3) Chu, B Langmuir 1995, 11, 414. (4) Yu, G.-E.; Altinok, H.; Nixon, S. K.; Booth, C.; Alexandridis, P.; Hatton, P. A. Eur. Polym. J. 1997, 33, 673. (5) Noolandi, J.; Shi, A.-C.; Linse, P. Macromolecules 1996, 29, 5907. (6) Wanka, G.; Hoffmann, H.; Ulbricht, W. Macromolecules 1994, 27, 4145. (7) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Macromolecules 1994, 27, 241. (8) Mortensen, K.; Brown, W.; Jorgensen, E. Macromolecules 1994, 27, 5654. (9) Mortensen, K. Macromolecules 1997, 30, 503. (10) Zhou, Z.-K.; Chu, B. Macromolecules 1994, 27, 2025. (11) Yang, L.; Bedells, A. D.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1992, 88, 1447. (12) Altinok, H.; Yu, G.-E.; Nixon, S. K.; Gorry, P. A.; Attwood, D.; Booth, C. Langmuir 1997, 13, 5837.

The results of this work are referred to in Section 3.6. To the best of our knowledge, no laboratory has reported the synthesis and properties of a cyclic E/P copolymer. Results for copolymer E52P34E52 and its cyclic analogue cyclo-P34E104 are presented in this paper. The two copolymers were prepared in our laboratory and characterized by gel permeation chromatography (GPC) and nuclear magnetic resonance (NMR) spectroscopy, their micellization was studied by static and dynamic light scattering (DLS), and the gelation of their concentrated solutions was investigated by tube inversion. The motivation for this work derived in part from the inviting possibility of eventually designing a drug delivery system that combines the solubilizing power of hydrophilic cyclic polymers for hydrophobic molecules with the selfassociation (micellization, gelation) and adsorption properties of amphiphiles. 2. Experimental Section 2.1. Copolymers. The preparation of copolymer E52P34E52 starting from a highly difunctional sample of poly(propylene glycol) (Emkapyl 2000, P34, ICI C&P) has been described previously.12 Characterization by GPC and 13C NMR spectroscopy (details reported previously)12 gave the molar masses and compositions listed in Table 1. Additionally, the block composition of E52P34E52 was confirmed by the correspondence of integrals of resonances arising from junction and end-group carbons. The cyclization of E52P34E52 followed the general procedure described previously,16,17 that is, reaction of a hydroxy-ended copolymer with dichloromethane (DCM) under Williamson conditions and at high dilution (concentration maintained below (13) Yang, Z.; Pickard, S.; Deng, N.-J.; Barlow, R. J.; Attwood, D.; Booth, C. Macromolecules 1994, 27, 2371. (14) Yu, G.-E.; Yang, Z.; Attwood, D.; Price, C.; Booth, C. Macromolecules 1996, 29, 8479. (15) 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. (16) Yan, Z.-G.; Yang, Z.; Price, C.; Booth, C. Makromol. Chem., Rapid Commun. 1993, 14, 725. (17) Yu, G.-E.; Sinnathamby, P.; Price, C.; Booth, C. Chem. Commun. 1996, 31.

S0743-7463(97)01050-0 CCC: $15.00 © 1998 American Chemical Society Published on Web 04/04/1998

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Langmuir, Vol. 14, No. 9, 1998 2279

Table 1. Molecular Characteristics of the Copolymersa copolymer

Mw/Mn

Mn, g mol-1

Mw, g mol-1

mol % E

wt % E

E52P34E52 cyclo-P34E104

1.07 1.08

6550 6450

7000 6950

75 75

70 70

a M calculated from M and M /M ; estimated uncertainties: w n w n Mw/Mn, (0.01; Mn, (150 g mol-1; mol % and wt % E, (1%.

Figure 1. GPC curves illustrating the preparation and purification of the crude product of cyclization of copolymer E52P34E52. 10-5 mol dm-3). Under these conditions, ring closure is via an acetal linkage; that is:

The following reactions are involved in the cyclization:

-OCH2CH2O-K+ + CH2Cl2 f -OCH2CH2OCH2Cl + KCl (i) -OCH2CH2OCH2Cl + -CH2CH2O-K+ f -OCH2CH2OCH2OCH2CH2O- + KCl

(ii)

In the reaction, a solution of copolymer E52P34E52 (6 g) in a mixture of DCM and hexane (65/35 by volume, 100 cm3) was slowly added by syringe pump (67 h) to a stirred suspension of powdered KOH (85%, 7 g) in the DCM-hexane mixture (100 cm3). The temperature was held at 30 °C. The resulting mixture was stirred for a further 24 h to ensure complete reaction of all hydroxy groups. The use of a DCM-hexane mixture (i.e., a poor solvent) had been found in related work17 to improve conversion to cyclic product. The solution was separated from excess KOH, additional DCM was added (50 cm3), and the whole solution was washed with water (30 cm3 aliquots) until the washings were neutral. Evaporation of the organic phase gave a crystalline solid. The formation of predominantly cyclo-P34E104 was confirmed by analytical GPC and 13C NMR. GPC curves are illustrated in Figure 1. That of the triblock starting material contained a single narrow peak. After cyclization, the major peak in the GPC curve of the crude product was found at higher elution volume (as

expected for a cyclized polymer of the same molar mass)18 and signals assigned to chain-extended polymer were found at lower elution volumes. A conversion of linear to cyclic copolymer of 80% was estimated from the area under the curve of deconvoluted major peak relative to the total area. The 13C NMR spectra of the unpurified product showed the expected resonances from internal carbons, together with resonances attributed to CH2 adjacent to the acetal link (-CH2OCH2OCH2-, δ ) 66.8 ppm), and CH2 of the acetal link (-CH2OCH2OCH2-, δ ) 95.5 ppm), with the relative integrals confirming that the block lengths were equivalent to those of the starting copolymer. No signals attributable to end groups (i.e., -CH2CH2OH, expected at δ ) 61.4 ppm) were detected, confirming the absence of starting material. Because chain-extended polymer (whether cyclic or linear) is less soluble than the required cyclic product, cyclo-P34E104, purification was effected by precipitation fractionation. The reaction product was dissolved in toluene (120 cm3) at 20 °C. Hexane was slowly added until the stirred solution became cloudy (∼240 cm3). Equilibrium phase separation was ensured by heating the cloudy solution until it cleared (35 °C), and then cooling it slowly with gentle stirring to 20 °C. A clear concentrated phase separated from a clear dilute phase and was removed. GPC of the copolymer from the dilute phase served to show that the chain-extended copolymer had been largely removed. The separation procedure was repeated until all chain-extended polymer was judged to be absent by GPC (see Figure 1). Approximately 3 g of purified cyclic product was recovered by evaporating the solvent; that is an overall yield of 50%. The 13C NMR spectra confirmed the composition of the purified cyclic copolymer. Chain length was obtained from the integrated intensity of resonances from backbone carbons (E and P) relative to that from carbons associated with the acetal link. Within experimental error, these quantities were unchanged from those of the original triblock copolymer (see Table 1), and the equivalent overall formula cyclo-P34E104 was adopted. Given that limited chain extension occurs, and bearing in mind the chain length distribution in the copolymer, the formation of rings from extended chains (i.e., with two P34 blocks), as well as those formed from single precursor molecules, is unavoidable. The fractionation process will remove large rings along with long chains, but rings originating from two short copolymer molecules will be similar in size to those originating from one long copolymer molecule, and will not be separated by precipitation fractionation. GPC carried out in a good solvent for both blocks cannot distinguish between rings of different architecture but the same hydrodynamic size. NMR spectroscopy simply returns an average consistent with the original copolymer, because there is one acetal link per P block in all species. In fact, evidence from dynamic light scattering from micellar solutions of the cyclic copolymer in water, presented in Section 3.2, is consistent with a small mass fraction of chain-extended rings. 2.2. Clouding. Clouding was investigated by visual inspection of 1-10 wt % aqueous solutions of the copolymers contained in small sealed tubes and equilibrated at low temperature before heating in a water bath at 1 °C min-1 or less. 2.3. Static and Dynamic Light Scattering. The methods used for examination of micellar solutions by static (SLS) and dynamic (DLS) light scattering have been described and discussed in several recent publications.12,14,15,19-21 A brief summary follows. Dust was removed from solutions for light scattering by filtering through Millipore filters (Millex-GV 0.22 µm) immediately into the scattering cell. Refractive index increments were measured at temperatures in the range 20-40 °C using an Abbe´ precision refractometer. The SLS intensities were measured with a Malvern PCS100 instrument with vertically polarized incident light of wavelength 488 nm supplied by an argon laser (Coherent Innova 90) operated at 500 mW or less. (18) See, e.g., Wright, P. V.; Beevers, M. S. In Cyclic Polymers; Semlyen, J. A., Ed.; Elsevier: London, 1986; Ch. 3. (19) Yang, Y.-W.; Deng, N.-J.; Yu, G.-E.; Zhou, Z.-K.; Attwood, D.; Booth, C. Langmuir 1995, 11, 4703. (20) Yang, Y.-W.; Yang, Z.; Zhou, Z.-K.; Attwood, D.; Booth, C. Macromolecules 1996, 29, 670. (21) Yang, Z.; Yang, Y.-W.; Zhou, Z.-K.; Attwood, D.; Booth, C. J. Chem. Soc., Faraday Trans. 1996, 92, 257.

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The intensity was calibrated against benzene. Measurements at angles of 90° to the incident beam were made for solutions at a given temperature covering a range of concentrations. Additional measurements at 45° and 135° confirmed negligible angular dependence of scattering. The DLS measurements were made with the Malvern instrument already described combined with a Brookhaven BI9000AT digital correlator. Measurements of scattered light were made at an angle of 90° to the incident beam. Experiment duration was in the range 5-20 min, and each experiment was repeated two or more times. In addition to the determination of molar mass and critical micelle concentration (cmc), SLS was used to determine the critical micelle temperatures (cmt) of aqueous solutions of the copolymers. In this method, the intensity of light scattered at 90° from a solution of given concentration was measured at intervals of 0.5 or 1 °C as the temperature was raised at a rate of e0.5 °C min-1. Allowance was made for thermal lag by calibrating the cell temperature against the bath temperature in a preliminary experiment. The cmt of a solution was defined as the temperature at which the scattering curve left the baseline established for the molecular solution at low temperatures. 2.4. Gelation. Samples (0.5 g) were enclosed in small tubes (i.d., ∼10 mm), and observed while slowly heating (or cooling) the tube in a water bath within the range 0-85 °C. The heating/ cooling rate was 0.5 °C min-1. The change from a mobile to an immobile system (or vice versa) was determined by inverting the tube. The method served to define the sol-gel transition temperatures to (1 °C. When checked, the gels were found to be immobile in the inverted tubes over time periods of days to weeks. This simple method of detecting gelation, which is sensitive to the yield stress of the gel, has been shown to define the same stiff-gel phase boundaries as other methods, for examples, rheometry and differential scanning calorimetry.22 Of course, detection of subtle effects requires use of more searching techniques, for example, rheology,2,22 X-ray, and neutron diffraction.23-25

3. Results and Discussion All experiments using the cyclic copolymer were carried out on only 3 g of purified material (see Section 2.1). For this reason, our preference was to explore thoroughly the properties of the linear triblock copolymer and use these results as a pointer to significant experiments for the cyclic copolymer. 3.1. Clouding. Aqueous solutions of the copolymers covering the concentration range 1-10 wt % did not cloud in the temperature range 20-90 °C. 3.2. Dynamic Light Scattering. The correlation functions from DLS were analyzed by the constrained regularized CONTIN method26 to obtain distributions of decay rates (Γ). These distributions were tested against changes in the regularizer and were found to be stable. The decay rates gave distributions of apparent diffusion coefficient [Dapp ) Γ/q2, where q ) (4πn/λ) sin(θ/2)] and hence of apparent hydrodynamic radius (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. Plots of intensity fraction against logarithm of apparent hydrodynamic radius for 40 g dm-3 solutions of copolymer E52P34E52 at various temperatures are shown in Figure 2. (22) Li, H.; Yu. G.-E.; Price, C.; Booth, C.; Hecht, E.; Hoffmann, H. Macromolecules 1997, 30, 1347. (23) Pople, J. A.; Hamley, I. W.; Fairclough, J. P. A.; Ryan, A. J.; Komanschek, B. U.; Gleeson, A. J.; Yu, G.-E.; Booth, C. Macromolecules 1997, 30, 5721. (24) Mortensen, K. Prog. Colloid Polym. Sci. 1993, 91, 69. (25) Mortensen, K.; Pedersen, J. S. Macromolecules 1993, 26, 805. (26) Provencher, S. W. Makromol. Chem. 1979, 180, 201.

Figure 2. Effect of temperature on DLS from aqueous solutions of copolymer E52P34E52. Intensity fraction, I[log(rh,app)], versus logarithm of apparent hydrodynamic radius for a 40 g dm3 solution at 25, 40, and 50 °C (as indicated).

The intensity distribution at 25 °C indicates a molecular solution (rh,app at the peak ≈ 2 nm), at 50 °C indicates a micellar solution (rh,app at the peak ≈ 7 nm), and at 40 °C is consistent with a solution just above its cmt. Accordingly, investigation of micellar properties for the cyclic copolymer was confined to temperatures (45-55 °C) well above the cmt values of solutions in the range 10-70 g dm-3. The conditions for micellization of the cyclic copolymer were judged to be adequately investigated by determination of cmt and cmc values using SLS (see Section 3.3). Figure 3a shows intensity distributions of log(rh,app) for copolymer E52P34E52 in solutions of different concentration at 50 °C. At the lowest concentration shown (4 g dm-3), the intensity distribution is consistent with a molecular solution with a small mass fraction of micelles, a broadened peak being typical of the output of CONTIN analysis under these circumstances. At higher concentrations (20 to 40 g dm-3, see Figure 3a), the distributions indicate micellar solutions. Figure 3b shows corresponding plots for solutions of the cyclic copolymer at 50 °C. It is clear that cyclo-P34E104 associates in water to form micelles by a closed process, the trend with concentration being similar to that found for copolymer E52P34E52. This conclusion is supported by the results from SLS (see Sections 3.3 and 3.4). A difference in results for the two copolymers is the broad peak at rh,app ≈ 100 nm, found for cyclo-P34E104 solutions, which becomes obvious at high concentrations (see Figure 3b). The intensity distributions of log(rh,app) obtained for aqueous solutions of other cyclic block copolymers cyclo-B8E42 and cyclo-B27E144 have been found to contain similar peaks at high values of rh,app.14,15 This effect is attributed to a fraction of the cyclic copolymer containing two hydrophobic blocks, and so being capable of linking micelles to form micellar clusters, much as established for PnEmPn and BnEmBn copolymers in water.8,10,12,20,21,27 Approximate calculations (examples given previously)14,15 indicate that the mass fraction of micelles in such clusters is very small, consistent with

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Langmuir, Vol. 14, No. 9, 1998 2281

Figure 4. Reciprocal apparent hydrodynamic radius versus concentration for aqueous micellar solutions of cyclo-P34E104 at (b) 55 °C and (9) 50 °C, and E52P34E52 at (0) 50 °C. Table 2. Micellar Properties from Dynamic Light Scatteringa copolymer

T, °C

D, 10-11 m2 s-1

rh, nm

δh

E52P34E52 cyclo-P34E104

50 50 55

ca. 5.8 5.6 6.4

ca. 7.5 7.8 7.5

ca. 14 13 7

a D ) diffusion coefficient, r ) hydrodynamic radius, δ ) h h hydrodynamic expansion factor; estimated uncertainties: D and rh, (5%: δh, (10%.

Figure 3. Effect of concentration on DLS from aqueous solutions of E/P copolymers at 50 °C. Intensity fraction, I[log(rh,app)], versus logarithm of apparent hydrodynamic radius for the concentrations (in g dm-3) indicated. (a) E52P34E52; (b) cycloP34E104.

concentration range (measurements were not made at 55 °C), are similar to those for solutions of the cyclic copolymer. Extrapolation of the results to zero micelle concentration gave the values of rh listed in Table 2, and (via eq 1) the corresponding values of D. Strictly speaking, the extrapolation should be to the cmc, but the error is insignificant (see Section 3.3 for values of the cmc). Also listed in Table 2 are values of the hydrodynamic expansion factor, δh, that is, the ratio of micelle hydrodynamic volume (νh) to micelle anhydrous volume (νa), the latter being calculated from the molar mass of the micelles (from SLS, see Section 3.4) and the liquid-state density of the copolymers (1.08 g cm-3). The concentration dependence of apparent mutual diffusion coefficient (in dilute solution) is often expressed as

Dapp ) D(1 + kdc)

(2)

where the expansion is truncated at the second term. Parameter kd is related to the thermodynamic second virial coefficient, A2, through the equation:

the mass fraction of cyclics with two P blocks being significantly 5, where I is intensity of light scattered from solution relative to that from benzene, and Is is the corresponding quantity for the solvent). Similar results for the linear copolymer (details reported previously12) are included. (29) Yu, G.-E.; Yang, Y.-W.; Yang, Z.; Attwood, D.; Booth, C.; Nace, V. M. Langmuir 1996, 12, 3404. (30) Zhou, Z.-K.; Chu, B. J. Colloid Interface Sci. 1988, 126, 171. (31) Brown, W.; Schillen, K.; Hvidt, S. J. Phys. Chem. 1992, 96, 6038.

Figure 6. Excess light scattering intensity (I - Is) versus concentration for aqueous solutions of cyclo-P34E104 at the temperatures (°C) indicated. Calculated excess scattering intensity from molecules is shown as a dashed line. See text for definition of I and Is. Table 4. Critical Micelle Concentrations (g dm-3) from Static Light Scatteringa

a

T, °C

E52P34E52

cyclo-P34E104

55 50 45 40

1.2 2.6 9 34

1.1 2.1 4.5

Estimated uncertainty, (30%.

Comparison of critical micelle conditions for the two copolymers is made in Figure 7with a plot of log(c) against 1/T [i.e., both log(cmc) versus 1/T and log(c) versus 1/cmt]. Results reported previously, obtained by eluent gel permeation chromatography, are also plotted for the linear copolymer (see ref 12 and Table 3 for details). Given the scatter of the data, the results for the two copolymers are very similar. The least-squares lines through the data points for the two copolymers (see Figure 7) indicate a difference in slope, which is discussed in Section 3.5. 3.4. Static Light Scattering. For a nonideal, dilute solution, the Debye equation can be written

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

(4)

where A2 is the second virial coefficient introduced in Section 3.2, and K* is the relevant optical constant. Values of the specific refractive index increment dn/dc, included

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Langmuir, Vol. 14, No. 9, 1998 2283

Figure 7. Logarithm of concentration versus reciprocal temperature for aqueous solutions of copolymers E52P34E52 (unfilled symbols) and cyclo-P34E104 (filled symbols). The results are from (O, b) determination of cmt by SLS, (4) determination of cmt by eluent GPC, and (3, 1) determination of cmc by light scattering. Least-squares lines through the data for the two copolymers are shown. Estimated uncertainties in the cmt and cmc data are indicated.

in K*, were consistent with those reported previously.12 As written, eq 4 assumes small particles relative to the wavelength of the light. In the present study, direct use of eq 4 truncated to the second term to measure the molar mass of the micelles was not satisfactory for two reasons. (i) For certain solutions of the cyclic copolymer, scattering from micellar clusters increased the scattering intensity over that expected for individual micelles (see Figure 3b). Correction was made by subtracting the intensity of scattering from clusters (proportional to area under the peak at high values of rh,app) from the total intensity to obtain a corrected excess intensity (I - Is)corr, and incorporating this value into the Debye function, assuming that the mass fraction of material in the clusters could be ignored. (ii) Micellar dissociation at low concentration caused an upturn in the Debye plot at low concentration, as illustrated in Figure 8. This effect was more marked at lower temperatures where water is a better solvent. For solutions of micelles and molecules in equilibrium, the Debye equation can be written as

K*c′/(I - Icmc) ) 1/Mw + 2A2c′...

(5)

where c′ is the concentration of micelles, equal to the total copolymer concentration minus the cmc (i.e., c′ ) c - cmc), and Icmc is the intensity of scattering from unassociated copolymer solution, with c ) cmc. The use of (I - Is) in place of (I - Icmc) is convenient and produces little error. Indeed, so far as correcting the upturn in the Debye function is concerned, use of (I - Is) has the larger effect.14 Application of eq 5 to SLS from solutions of copolymer E52P34E52 has been described previously, when it was shown that the upturn was only partly eradicated.12 Debye plots for solutions of cyclo-P34E104 are illustrated in Figure 9, the plots shown being K*c′/(I - Is)corr versus c′, with values of the cmc taken from Table 3. As expected, the upturn is not entirely eradicated. In our recent work we have found it convenient to follow a suggestion made by Vrij32 and extrapolate Debye plots

Figure 8. Static light scattering (Debye function versus concentration) for aqueous solutions of linear and cyclic copolymers at 45 (squares) and 55 °C (circles): (O, 0) E52P34E52, and (b) cyclo-P34E104. The data for the cyclic copolymer are corrected for the effect of micellar clusters, as explained in the text. See text for definition of I, Is, and K*.

Figure 9. Static light scattering (Debye function versus concentration) for aqueous solutions of cyclo-P34E104 at: (b) 55 °C, ([) 50 °C, and (9) 45 °C. The data are corrected for the effect of micellar clusters and micellar dissociation, as explained in the text. The curves were calculated using eqs 8-10. See text for definition of I, Is, and K*.

to zero concentration from the moderate concentration range guided by the Carnahan-Starling equation,33 which is equivalent to the virial expansion for the structure factor for hard spheres taken to its seventh term. This method allows data at low concentrations, which are most affected by micellar dissociation, to be given little weight in the extrapolation. In the procedure, the interparticle interference factor (structure factor, S) in the scattering equation

K*c′/(I - Is)corr ) 1/(SMw)

(6)

was approximated by (32) Vrij, A. J. Chem. Phys. 1978, 69, 1742. (33) Carnahan, N. F.; Starling, K. E. J. Chem. Phys. 1969, 51, 635.

2284 Langmuir, Vol. 14, No. 9, 1998

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

Yu et al.

(7)

where φ is the volume fraction of equivalent uniform spheres. In practice, values of φ were calculated from the volume fraction of micelles in the system by applying a thermodynamic expansion factor δt, that is, the ratio of the thermodynamic volume (νt) to anhydrous volume (νa), where the thermodynamic volume is one-eighth of the excluded volume:

δt ) (νt/νa)

(8)

In the present analysis, concentrations were converted to volume fractions assuming a density of dry polymer of F ≈ 1.08 g cm-3 irrespective of temperature. Fitting eqs 6-8 to the data (see Figure 9) gave the values of Mw and δt listed in Table 5. Also listed in Table 5 are association numbers of the micelles calculated from

Nw ) Mw(micelle)/Mw(molecule)

Table 5. Micellar Properties from Static Light Scatteringa copolymer E52P34E52 cyclo-P34E104

T, °C

Mw, 105 g mol-1

Nw

δt

rt, nm

45 50 55 45 50 55

0.5 0.8 1.0 (0.7)b 1.0 1.55

7 11 15 (10) 14 22

2.6 3.0 3.2

3.6 4.4 4.9

2.7 3.3

4.6 5.7

a M ) mass-average molar mass, N ) mass-average association w w number, δt ) thermodynamic expansion factor, rt ) thermodynamic radius; estimated uncertainties: Mw and rt, (5%; Nw and δt, (10%. b Rough estimate from Figure 10 assuming a similar concentration dependence to that found for solutions at higher temperatures.

(9)

and thermodynamic radii calculated from thermodynamic volumes. As mentioned in Section 3.2, results for solutions of the cyclic copolymer at 45 °C were erratic, and the few data points available could not be analyzed with any precision (see Figure 9). As found for many other amphiphilic block copolymers in water,1 the association numbers of the micelles increased with temperature. 3.5. Gelation. Some interest in the present work lay in the definition of gelling systems for possible pharmaceutical use as vehicles for controlled drug release. The general requirement is a mobile sol at room temperature and a hard (cubic) gel at body temperature. As can be seen from Figure 10, a solution of either copolymer with concentration in the range 30-40 wt % could be useful. The formation of a hard gel is usually ascribed to cubic packing of spherical micelles acting as hard spheres.34-36 The results shown in Figure 7 indicate a cmc at 37 °C of ∼50 g dm-3 (∼5 wt %) for copolymer E52P34E52, and somewhat lower for cyclo-P34E104, that is, well below their critical gelation concentrations at that temperature. It has been shown that the hard-sphere volumes of micelles in the gel can be related to micelle excluded volumes (8 × νt) measured by light scattering in dilute solution,35,37,38 or measured by neutron scattering across a wide concentration range.24,25 As seen in Figure 10, at a given temperature the critical gel concentration of the triblock copolymer is lower than that of the cyclic copolymer by ∼3 wt %, which implies a slightly larger micellar hard-sphere volume for the triblock copolymer in aqueous solution at 30-40 °C. The values of rt in Table 5, extrapolated to lower temperature (see Figure 11), prompt the same conclusion. 3.6. Effect of Cyclization. The present results can be considered together with those obtained in previous work for related pairs of linear and cyclic oxyethylene/ oxybutylene block copolymers. For convenience in discussion, representative results are brought together in Table 6, and reported results14,39 for two comparable linear diblock copolymers are included. (34) Malmsten, M.; Lindman, B. Macromolecules 1992, 25, 5440. (35) 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. (36) Jorgensen, E. B.; Hvidt, S.; Brown, W.; Schillen, K. Macromolecules 1997, 30, 2355. (37) Deng, N.-J.; Luo, Y.-Z.; Tanodekaew, S.; Bingham, N.; Attwood, D.; Booth, C. J. Polym. Sci., Part B, Polym. Phys. 1995, 33, 1085. (38) Yang, Y.-W.; Ali-Adib, Z.; McKeown, N. B.; Ryan, A. J.; Attwood, D.; Booth, C. Langmuir 1997, 13, 1860. (39) Yu, G.-E.; Yang, Z.; Ameri, M.; Attwood, D.; Collett, J. H.; Price, C.; Booth, C. J. Phys. Chem., Part B 1997, 101, 4394.

Figure 10. Part phase diagram showing boundaries between mobile and immobile (gel) regions for aqueous solutions of copolymers (b) cyclo-P34E104 and (O) E52P34E52.

Figure 11. Thermodynamic radius versus temperature for copolymers (b) cyclo-P34E104 and (O) E52P34E52.

Critical micelle concentrations are not included in the table because the effect of cyclization on this property has proved difficult to define. The available evidence (present work, and refs 14 and 15) shows the cmc values of cyclic diblock copolymers to be similar to, or at most slightly lower than, those of their corresponding linear triblocks. The temperature dependence of the cmc, which is usually represented by the nominal standard enthalpy of micellization,1,12,40 is found to be low for cyclic copolymers compared with their linear counterparts (see Table 6).

Cyclization Effects on Block Copolymers

Langmuir, Vol. 14, No. 9, 1998 2285

Table 6. Linear and Cyclic Block Copolymers copolymer cyclo-P34E104 E52P34E52 E102P37 cyclo-B8E42 E21B8E21 E41B8 cyclo-B27E144 E72B27E72

∆micH°, kJ mol-1

T, Mw, 105 °C g mol-1 Nw

rt, nm

55 55 45 50 50 50 40 40

5.7 7.5 126 ( 40 4.9 190 ( 20 10.2 13.7 210 ( 20 2.9 4.4 55 ( 10 2.2 4.0 95 ( 20 4.9 7.1 80 ( 10 10.4 12.8 10.0 11.3

1.6 1.0 4.6 0.4 0.15 1.1 5.6 4.5

22 15 67 16 6 44 62 49

rh, nm

ref present present 12 14 14 39 15 15

This effect has been attributed to reduced exposure of the hydrophobic block to water when the copolymer is in its unassociated molecular state.14 The behavior of the cmc itself reflects the fact that it is determined by the Gibbs energy, and so by entropic as well as enthalpic effects. However, the evidence in this area is not strong (see, for example, Figure 7) and studies are few. More work is required. The effect of cyclization on micellar properties is better established because the new results reinforce those obtained previously (see Table 6). At high temperatures (i.e., for well micellized systems), the association numbers and radii (both hydrodynamic and thermodynamic) of cyclic copolymers are larger than those of linear triblock counterparts. For all three pairs it is found that

Nw(cyclic)/Nw(linear) ≈ [rt(cyclic)/rt(linear)]3

(10)

and this correspondence between the two equilibrium (thermodynamic) properties provides useful validation of the results. As for the physical interpretation of the larger size of the well-developed (high temperature) micelles of the cyclic copolymers, we know of no theoretical study of micelle properties of cyclic block copolymers. Marko’s paper41 on microphase separation of cyclic and linear diblock copolymers in the bulk liquid state is not directly relevant because it relates to the lamellar structure, though we have found those results qualitatively valuable. The effect of block architecture in linear block copolymers has been addressed theoretically, notably by Balsara et al.42 and Linse,43 but those treatments have not been extended to the cyclic diblock architecture. However, it is clear that the overriding consideration in determining micelle size is geometrical. The results given in Table 6 illustrate the strong correlation between the maximum possible length of the hydrophobic core-forming stem, that is, Pn for the linear diblock, Pn/2 for the cyclic diblock and linear triblock, and core radii (rc). This effect is illustrated in Figure 12. The explanation of the small difference between rc (and (40) Kellarakis, A.; Havredaki, V.; Yu, G.-E.; Booth, C. Macromolecules 1998, 31, 944. (41) Marko, J. F. Macromolecules 1993, 26, 1442. (42) Balsara, N. P.; Tirrell, M.; Lodge, T. P. Macromolecules 1991, 24, 1975. (43) Linse, P. Macromolecules 1992, 26, 4437.

Figure 12. Schematic representation of chain conformations in micelles formed from linear diblock copolymer, cyclic diblock copolymer, and linear triblock copolymer (as indicated), all having the same overall chain length and block composition.

therefore N) for the cyclic and the triblock is more subtle. We suppose that the statistical weighting of accessible conformations maintains the cyclic copolymer in a more extended conformation in the micelle than is the case for the triblock copolymer; that is, it maintains the P-block in a more hairpin-like conformation. This result is also illustrated in Figure 12. For a given P-block length, the effect is to reduce the micelle core radius of the triblock compared with that of the cyclic copolymer. There is theoretical support for this effect in Linse’s results,43 which show a higher association number for a PEP copolymer (loop in the micelle fringe) than for an EPE copolymer (loop in the micelle core). 4. Conclusions Through present and previous14,15 studies of block copolymers in two related systems (oxyethylene/oxypropylene and oxyethylene/oxybutylene), it is now established that the micellization and gelation of cyclic diblock copolymers is closely related to that of their corresponding linear triblocks, e.g. cyclo-PnEm to linear Em/2PnEm/2. For the systems investigated to date (listed in Table 6), cmc values at room temperature are similar, the temperature dependences of cmc for the cyclic copolymers are smaller, and the association numbers and radii of well-developed micelles are larger. Presently there are no theoretical studies of the micellization of cyclic block copolymers, but the effects observed experimentally have simple physical explanations. Acknowledgment. We thank Mr. K. Nixon for help with GPC. Financial support came from EPSRC. S.M.M. is grateful for an ORS Award and a Manchester University Scholarship. We thank our referee for careful reading of our manuscript, and for comments that have led to improvements in presentation and discussion. LA971050T