Effects of Block Lengths on the Association Numbers and Micellar Sizes of B n E m B n Type Triblock Copolymer Micelles in Aqueous Solution Tianbo Liu, † Zukang Zhou, †,‡ Chunhung Wu, †,§ Vaughn M. Nace, | and Benjamin Chu ⊥ * ,†, Department of Chemistry, State University of New York at Stony Brook, Stony Brook, New York 11794-3400, The Dow Chemical Company, Texas Operations, Freeport, Texas 77451-3257, and Department of Materials Sciences and Engineering, State University of New York at Stony Brook, Stony Brook, New York 11794-2275 Received May 27, 1997 Revised Manuscript Received July 30, 1997 Introduction. The association behaviors of block copolymers in selective solvents have been extensively reported during the last few years. 1,2 It has been noted that the core-shell micellar structure is fairly common for closed association mechanisms. In an open associa- tion mechanism, more open and extended structures are sometimes formed at low polymer concentrations and the polymer solution becomes a gel-like network at high concentrations. The bridging function is achieved from an extended soluble middle block between the small clusters formed by the poorly solvated end blocks. 3,4 Although the characterization of the micellar systems has become routine, the results from different research groups and through different physical techniques can sometimes be amazingly different. 1 This problem, combined with the limit in the number of available samples and the uncertainties among the samples (e.g., different polydispersities), makes it difficult for the readers to draw conclusive results, e.g., quantitative relations between micellization parameters and the block lengths of block copolymers. The most noticeable study in this area is on alkylpoly(oxyethylene) glycol ethers (C n E m ) in aqueous solution where the quantita- tive effects of chain lengths on cmc and thermodynamic parameters were systematically reported. 5,6 However, even for the polymers C n E m , which show very good chemical homogeneity and can be used as a standard model, there is no report on the relations between chain length and association number or micellar size. Yang et al. 7,8 made some valuable attempts on studying block poly(oxyalkylene)s (B n E m ,B n E m B n , and E n B m E n , where B and E were oxybutylene and oxyethylene, respec- tively) in aqueous solution. However, due to the limited numbers (three B n E m B n samples with one being in the unimer state) of samples studied, they were not able to make quantitative conclusions. In spite of the shortage of experimental data, theoretical approaches on the relation between the block length and the micellar properties for diblock copolymer micelles have been developed and reviewed. 2 Here we present the linear relations between the micellar lengths and two impor- tant micellar parameters: the association number (n w ) and the hydrodynamic radius (R h ) in B n E m B n /water systems. (The data of B 7 E 22 B 7 and B 10 E 271 B 10 are reported for the first time, while the others are cited from the literature. 9-11 ) All of the measurements were performed in the regions where only close-associated micelles were formed. We took advantage of the fact that our samples cover very large ranges on both the B block length (10-24 BO units) and the E block length (46-271 EO units). This makes it possible to yield convincing and accurate enough conclusions on the dominant factors behind the basic micellization param- eters of these block copolymer micelles. Experimental Procedures. Several triblock co- polymers, including B 5 E 91 B 5 , B 6 E 46 B 6 , B 7 E 22 B 7 , B 10 E 271 B 10 , and B 12 E 260 B 12 , were involved in our study. In order to avoid the anomalous micellization behavior before the onset of critical micellization formation, 12 the polymers were purified by hexane 13 or hot octane (only for B 10 E 271 B 10 ) extraction. The light scattering meas- urements and sample preparation have been described elsewhere. 12 The polymer solutions were prepared by first dissolving the B n E m B n copolymer in water at low temperatures (<5 °C) in order to ensure complete solute dissolution. The polymer solution was then filtered by a Millipore sterile filter (pore size 0.1 µm). The CON- TIN 14 method was used to analyze the intensity- intensity time correlation function G (2) (τ). All the light scattering experiments were performed at 25 °C except for B 7 E 22 B 7 , for which the measurements were done at 15 °C because of its low clouding temperature (18 °C for a 1 wt % solution). Results and Discussion. Figure 1 shows a plot of the average association number (n w ) of B n E m B n block copolymer micelles versus the total number of oxy- butylene (BO) units in the polymer chain. For closed- associated micelles, there exists a critical micelle con- centration (cmc), above which the formation of micelles becomes increasingly important. The cmc value can be measured by detecting the sharp increase in the scat- tered intensity with increasing polymer concentration at a certain fixed temperature. 9-11 The n w of micelles can be measured by static light scattering (SLS) and then calculated by using the modified Debye equation: 7 where H ≡ 4π 2 n Bz 2 (dn/dc) 2 /N A λ 4 is an optical parameter with n Bz being the refractive index of a reference standard, benzene; dn/dc, the refractive index increment * To whom correspondence should be addressed. † Department of Chemistry, SUNY. ‡ Present address: 54-109, Chang-Chun-Yuan, Peking Univer- sity, Beijing, 100871, P. R. China. § Present address: Chemistry Department, Tamkang Univer- sity, Tamsui 25137, Taiwan. | Dow Chemical Co. ⊥ Department of Materials Sciences and Engineering, SUNY. Figure 1. Plot of the average association number of BnEmBn triblock copolymer micelles in water at 25 °C versus the number of hydrophobic BO units in a polymer chain. H(c - c cmc )/[R Bz (I - I cmc )/I Bz ] ) 1/M w + 2A 2 (c - c cmc ) (1) 7624 Macromolecules 1997, 30, 7624-7626 S0024-9297(97)00732-8 CCC: $14.00 © 1997 American Chemical Society