Langmuir 2009, 25, 3487-3493
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Internal Structural Characterization of Triblock Copolymer Micelles with Looped Corona Chains Fernando C. Giacomelli,†,‡ Izabel C. Riegel,§,† Cesar L. Petzhold,† Na´dya P. da Silveira,† and Petr Sˇteˇpa´nek*,‡ Institute of Chemistry, UniVersidade Federal do Rio Grande do Sul, AV. Bento Gonc¸alVes 9500, 91501-970 Porto Alegre, Brazil, and Institute of Macromolecular Chemistry, HeyroVsky´ Sq. 2, 162 06 Prague 6, Czech Republic ReceiVed December 24, 2008. ReVised Manuscript ReceiVed January 26, 2009 We report the characterization through SAXS measurements of micelles produced from a new series of block copolymers: one diblock and four triblock copolymers bearing short poly[5-(N,N-diethylamino)isoprene] and long polystyrene blocks. Micellar aggregates produced in DMF (selective solvent for polystyrene) from the same set of samples were previously successfully characterized through light scattering measurements. The X-ray scattering profiles of starlike (from the diblock copolymer sample) and flowerlike micelles (from the triblock copolymers samples) could be fitted using the spherical copolymer micelle model proposed by Pedersen and Gerstenberg (Macromolecules 1996, 29, 1363.) where in the case of flowerlike micelles, the particles were understood as formed by hypothetical diblock copolymers having half of the true polymeric molar mass. Using the spherical copolymer micelle model, it could be possible to attest the unswollen nature of the micellar cores. The total micellar size suggested thus that the chains forming the corona are extended which is mainly related to a small core surface area per corona chain entering the core (Ac/n), which also induced a small number of aggregation (Nagg) of all self-assembled particles. The total micellar size fits well with our previous light scattering measurements.
Introduction The property of amphiphilic block copolymers to undergo self-organization in selective solvents is well understood. This ability imparts them to a number of very interesting properties1 and, due to the growing interest in potential applications,1,2 the study of new designed systems is of noteworthy importance. The diblock copolymers dissolved in a block selective solvent produce core-shell micelles, where the insoluble block forms a compact core and the soluble block forms the swollen shell of the resultant structure,3 sometimes referred as starlike micelles (Figure 1, left). The micelle formation is driven by unfavorable interactions described quantitatively by the solubility parameter or by the Flory-Huggins interaction parameter between the solvent and core-forming block. The latter tends to aggregate to reduce its contact with the poor solvent. On the other hand, triblock copolymers of ABA-type dissolved in selective solvents for the middle (B) block represent a much more complex situation, where the formation of well-defined micelles by a closed association mechanism is only possible if the middle block is looped with the outer blocks taking part of the same micellar core (Figure 1, right). They are refered to as flowerlike micelles. The looping of the middle block is followed by an entropy loss which sometimes suppresses micellization and leads to the formation of branched structures,4 mainly dependent on the middle block length5 and concentration.6
Figure 1. Expected arrangements of well-defined micelles produced from diblock (left) and ABA triblock copolymers dissolved in a B-selective solvent (right).
* Corresponding author. E-mail:
[email protected]. Telephone: +420 2 96809211. Fax: +420 2 96809410. † Institute of Chemistry, Universidade Federal do Rio Grande do Sul. ‡ Institute of Macromolecular Chemistry. § Current address: RS 239, 2755 - Centro Universita´rio Feevale, Novo Hamburgo, RS, Brazil.
Currently, we have been focused on the micellization behavior of a new series of triblock copolymers bearing poly[5-(N,Ndiethylamino)isoprene], referred here as PAI, as outer blocks in triblock copolymers where the major middle block is always formed by polystyrene (PS). In such series of copolymers, it was already demonstrated that the short PAI outer blocks can be quaternized leading the formation of crew-cut aggregates in water.7 Furthermore, the micellization capacity of the triblock copolymers was successfully studied also in DMF, where PAI is completely insoluble. Well-defined separated flowerlike micelles are likely to be produced from copolymers bearing a PS middle block with a reasonable length (degree of polymerization NPS ∼ 130-270), however, only when sufficient amount of PAI is present in the copolymer composition (weight fraction
(1) Alexandris, P.; Lindman, B. Amphiphilic Block Copolymers: Self-Assembly and Applications; Elsevier: Amsterdam, 2000. (2) Hadjichristidis, N.; Pispas, S.; Floudas, G. A. Block Copolymers: Synthetic Strategies, Physical Properties and Applications; Wiley: New York, 2003. (3) Hamley, I. W. The Physics of Block Copolymers; Oxford University Press: New York, 1998. (4) Balsara, N. P.; Tirrell, M.; Lodge, T. P. Macromolecules 1991, 24, 1975.
(5) Zhou, Z.; Yang, Y.-W.; Booth, C.; Chu, B. Macromolecules 1996, 29, 8357. (6) Liu, T.; Zhou, Z.; Wu, C.; Nace, V. M.; Chu, B. J. Phys. Chem. B 1998, 102, 2875. (7) Riegel, I. C.; Eisenberg, A.; Petzhold, C. L.; Samios, D. Langmuir 2002, 18, 3358.
10.1021/la804254k CCC: $40.75 2009 American Chemical Society Published on Web 02/12/2009
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wPAI > 0.06). Besides, a longer middle block produces bridged micelles even at concentration as low as 1.5% w/w).8 Nevertheless, light scattering measurements could not provide fruitful informations about the micellar internal structure, which can be done using the resources of small-angle X-ray scattering (SAXS). The characterization of block copolymer micelles through SAXS is a current topic and can provide a large amount of structural information, if suitable fitting models for the scattering profiles are available. Recently, two publications related to the scattering profile of block copolymer micelles came up in the literature.9,10 The form factor of such kind of particle is basically analyzed by models which assume centro-symmetry where the micelles are understood as particles with homogeneous distribution of electron density such as the use of homogeneous sphere or the core-shell form factor. The other category of models assumes noncentrosymmetry of the micellar objects for example, the series of models for scattering profiles of block copolymer micelles with different core geometries developed by Pedersen and Gerstenberg.11,12 The structural characterization of triblock copolymer micelles with looped corona through SAXS, on the other hand, is extremely limited to the best of our knowledge, and there is no fitting models developed specifically for block copolymer micelles with such special architecture, which makes such study quite challenging, although possible. For example, flowerlike triblock copolymer micelles were successfully prepared from poly(lactide)-b-poly(ethylene oxide)-b-poly(lactide) in water. They were characterized through small angle neutron scattering (SANS) and then a modified version of the centro-symmetric core-shell model, including the scattering contribution of the monomermonomer interaction within the corona chains was used in the fitting procedure with very good results.13 This monomermonomer interaction from the dissolved chains in the micellar corona, which is generally referred as “blob” scattering14,15 produces an additional scattering intensity, intrinsically described in the noncentrosymmetric block copolymer micelle models developed and mentioned above.12 These models were successfully used to describe the scattering profile of more complex block copolymer micelles systems, such as the one formed from diblock copolymers with strong acid groups15 in the case where only spherical shape micelles were present. Lecommandoux et al.16 used one of the models proposed by Pedersen and Gerstenberg with the core having a spherical geometry (spherical copolymer micelle model) to fit SANS scattering profile of micelles formed from the double hydrophilic block copolymer Jeffamine-b-poly(L-glutamic acid) at low temperatures where Jeffamine core was water swollen. Plestil et al. have studied onion-type block copolymer micelles17 and comicellization of diblock copolymers18 through SAXS and SANS experiments. (8) Giacomelli, F. C.; Riegel, I. C.; Silveira, N. P.; Stepa´nek, P. Langmuir 2009, 25, 731. (9) Castelletto, V.; Hamley, I. W. Curr. Opin. Colloid Interface Sci. 2002, 7, 167. (10) Pedersen, J. S.; Svaneborg, C. Curr. Opin. Colloid Interface Sci. 2002, 7, 158. (11) Pedersen, J. S.; Gerstenberg, M. C. Macromolecules 1996, 29, 1363. (12) Pedersen, J. S. J. Appl. Crystallogr. 2000, 33, 637. (13) Agrawal, S. K.; Sanabria-DeLong, N.; Tew, G. N.; Bhatia, S. R. Macromolecules 2008, 41, 1774. (14) Castelletto, V.; Parras, P.; Hamley, I. W.; Baverback, P.; Pedersen, J. S.; Panine, P. Langmuir 2007, 23, 6896. (15) Kaewsaiha, P.; Matsumoto, K.; Matsuoka, H. Langmuir 2007, 23, 9162. (16) Agut, w.; Brulet, A.; Taton, D.; Lecommandoux, S. Langmuir 2007, 23, 11526. (17) Plestil, J.; Krı´z, J.; Tuzar, Z.; Procha´zka, K.; Melnichenko, Y. B.; Wignall, G. D.; Talingting, M. R.; Munk, P.; Webber, S. E. Macromol. Chem. Phys. 2001, 202, 553. (18) Plestil, J.; Kona´k, C.; Hu, X.; Lal, J. Macromol. Chem. Phys. 2006, 207, 231.
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Figure 2. Molecular structure of the PAI (left) and PS (right) units forming blocks. Table 1. Molecular Characteristics of the Block Copolymers copolymera
Mw (g mol-1)b
wPAIc
Mw/Mn
PAI4PS135PAI4 PAI6PS155PAI6 PAI9PS126PAI9 PAI11PS271PAI11 PAI8PAI132
15100 17800 15600 31200 14800
0.07 0.09 0.16 0.10 0.07
1.16 1.20 1.26 1.20 1.06
a The numbers subscripted are the weight average degree of polymerization of each block determined using Mw and the weight fraction of PAI (wPAI). b Determined using Mn and Mw/Mn from GPC measurements. c Weight fraction of PAI determined from 1H NMR relative to PS.
The structural characterization of the produced particles was successfully done using the available copolymer micelle models. Je´roˆme et al.19 studied the self-assembly of poly(ethylene oxide)b-poly(-caprolactone) in aqueous solutions. The micellar substructure was elucidated through the fitting of SANS data with two analytical models, being one of them the spherical copolymer micelle model (according to the nomenclature used in ref 16). Herein, we wish to perform the internal structural characterization of micelles self-assembled mainly from triblock copolymer samples having short outer core-forming blocks at both ends. The resulting scattering profiles could be fitted using the spherical copolymer micelle model available in the literature. The characteristics of the micellar core as well as the conformation of the chains forming the micellar corona are discussed throughout the manuscript.
Experimental Section Samples and Solutions. Figure 2 depicts the molecular structure of PAI (left) and PS (right) units. The molecular characteristics of the studied samples are given in Table 1. The detailed synthesis procedure is provided elsewhere.20 The solutions were prepared by direct dissolving the dry polymers in pure dimethylformamide (DMF), since the PAI blocks represented always a small fraction in the copolymers composition. The resulting solutions were gently stirred at room temperature overnight. Afterward, samples were left at 50 °C for about 12 h to achieve equilibrium structures. Having in mind that the homopolymer PAI has a glass transition temperature Tg ∼ -30 °C and that micellar size is concentration independent as shown hereafter, the micelles should not be kinetically frozen. Instead, an equilibrium unimeraggregate exchange should take place. The solvent DMF was purchased from Aldrich in the highest purity commercially available and used as received. SAXS Measurements. Small-angle X-ray scattering (SAXS) data were collected using a pinhole camera (Molecular Metrology SAXS system) attached to microfocused X-ray beam generator (Osmic MicroMax 002) operating at 45 kV and 0.66 mA (30 W) and yielding a beamline with wavelength λ ) 1.54 Å. The collimated beam crossed the samples through a vacuum chamber and was diffracted to a 2D gas-filled multiwire Gabriel design detector with an active diameter area of 20 cm. The solutions were filled into 2 mm diameter glass capillaries and sealed. The (19) Vangeyte, P.; Leyh, B.; Heinrich, M.; Grandjean, J.; Bourgaux, C.; Je´roˆme,R. Langmuir 2004, 20, 8442. (20) Petzhold, C. L.; Stadler, R. Macromol. Chem. Phys. 1995, 196, 2625.
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20 to 65 °C and the solutions were not affected by either temperature or temperature cycles, showing a high stability of the aggregates, being probably related to the very poor solubility of PAI in DMF. SAXS measurements are used in order to shed some light on the internal structural characterization and conformation of chains within the micelles. The SAXS scattering intensity I(q) of an isotropic solution of monodisperse particles embedded in a matrix with a constant electronic density, after normalization with the background scattering by the capillary filled with the solvent is given by:
I(q) ) NP(q)S(q) Figure 3. Small-angle X-ray scattering pattern for polymer PAI4PS135PAI4 dissolved in pure DMF and c ) 3.0% w/w. The solid line shows the fit performed using the Debye function.
Figure 4. Small-angle X-ray scattering patterns for PAI11PS271PAI11 triblock copolymer sample dissolved in pure DMF in different concentrations: 1.5% (filled circles) and 3.0% w/w (open squares). The curves were normalized by the copolymer concentration taken as the weight fraction of polymer present.
scattering patterns were collected after an exposure time at about 2 h in average. Two different configurations were used in order to cover a wide range of wave vector (q) (from q ) 0.04 to 3.0 nm-1) where q ) (4π/λ) sin θ (2θ is the scattering angle). The images in all cases were found to be isotropic and the treatment has been made taking into account the 360° azimuthal scan. The resulting I Vs q scattering curves were corrected by subtraction of the scattering of pure DMF and further placed on absolute scale using glassy carbon as standard. All measurements (unless otherwise noted) were performed at room temperature. Data Analysis. We have attempted to use two different models to fit the scattering profiles of the produced micelles that are described in the Results and Discussion section. The fitting procedures have been made using the SASfit program which uses the least-squares fitting approach, consisting in minimize the squared chi (χ2). The SASfit software package was developed by J. Kohlbrecher and it is available at http://kur.web.psi.ch/sans1/ SANSSoft/sasfit.html.
Results and Discussion The micelle formation from samples depicted in Table 1 was previously reported and studied by light scattering measurements.8 Flowerlike micelles are likely to be produced when the triblock copolymers are directly dissolved in DMF. In this case, the micelles generated have a looped corona-forming block as depicted in Figure 1 (right). On the other hand, only one block copolymer of the studied series (PAI8PS132) generates starlike micelles such as in Figure 1 (left). It was found that for all the samples, the micellar hydrodynamic sizes are copolymer concentration independent up to a concentration of 3.0% w/w. The temperature dependence was studied over the range from
(1)
wherein N is in the number of particles per unit volume, P(q) is the form factor of an individual particle, and S(q) is related to the interference particle factor, which arises from long-range correlations between scattering centers. For widely separated systems, which means in relatively low polymer concentration, S(q) ∼ 1 and then I(q) is proportional to the form factor P(q) of the scattering objects, linked to their size and shape. We wish to access the internal structure characterization of single particles and thus, solutions having relatively low amounts of polymer were prepared (up to c ) 3.0% w/w). Figure 3 shows the X-ray scattering profile of sample PAI4PS135PAI4 taken at c ) 3.0% w/w. The curve shows basically a plateau in the low q region followed by a q-2 scattering dependence at high-q range. This behavior is characteristic of flexible polymer chains in a good solvent. We thus fitted the scattering profile according to the relation:
I(q) ) I(0)Fchain(q, RG)
(2)
where I(0) is the scattering intensity at zero angle and Fchain(q, RG) is the self-correlation term of Gaussian chains given by the Debye function:
Fchain(q, RG) )
2[exp(-q2RG2) - 1 + q2RG2] (q2RG2)2
(3)
From the fit procedure it was extracted the radius of gyration of the dissolved polymer chains (RG), which was equal to 5.1 nm. Considering the hydrodynamic radius (RH) for the same polymer dissolved in DMF previously determined by light scattering measurements (RH ) 3.2 nm),8 the structure sensitive parameter F ) (RG/RH) ) 1.7 is obtained, which is typical for monodisperse polymers dissolved in a good solvent and in a random coil conformation.21 It should be mentioned that this is one of the two samples (see Table 1) that have the smallest amount of PAI in the present series and this result evidences that the amount of PAI is not enough to induce any kind of aggregation in the triblock copolymer sample where the corona chains should be looped, delaying the process of micellization. We show henceforth that the diblock copolymer with nearly the same composition (PAI8PS132) is able to self-aggregate in DMF. Figure 4 depicts the SAXS patterns measured for sample PAI11PS271PAI11 dissolved in DMF in two different concentrations (c ) 1.5 and 3.0% w/w). The curves were normalized by the copolymer concentration, taken as the weight fraction of polymer present. First, one can notice that the scattering profiles are obviously different if compared with the one shown in Figure 3. Therefore, the curves could not be fitted using the Debye function. The presence of aggregates is suggested by the pronounced X-ray scattering in the region of smaller angles. Since the curves (21) Burchard, W. Cellulose 2003, 10, 213.
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scattering profile of the micelles formed from our current set of block copolymers as it will be shown soon. Briefly, the model accounts for micelles containing a homogeneous spherical core and anchored Gaussian chains to the core, as depicted in the scheme of Figure 5. The micellar form factor Pmic(q) comprises four terms: selfcorrelation of the core, self-correlation of the chains, cross term between core and chains and the cross term between different chains, according to the equation:
Pmic(q) ) Nagg2βcore2Fcore(q, Rc)Naggβchain2Fchain(q, RG(chain)) + Nagg(Nagg - 1)βchain2Schain-chain(q) + Figure 5. Scheme for the micellar form factor analysis according to the spherical copolymer micelle model. It considers a dense spherical core of radius Rc and Gaussian chains with radius of gyration RG(chain) attached to the core. Table 2. Parameters Used for the Determination of βcore and βcorona for the Set of Different Block Copolymers Studied parameter
value
VPAI VPS σPAI σPS σDMF
2.57 × 10-22 cm3 1.65 × 10-22 cm3 8.6 × 1010 cm-2 9.6 × 1010 cm-2 8.8 × 1010 cm-2
superimpose, it means that the micellar size and shape are essentially concentration independent. The micellar structure does not undergo pronounceable changes as noticed by the very small differences in the high-q region and even in the very low-q range where interparticle interactionsS(q)scan be frequently seen. One can also notice that in the high-q region, the scattering curves follow also a q-2 dependence. For concentrations lower than 1.5% w/w, the scattering pattern also remained very similar to those shown in Figure 4, however, with the experimental points much sparser due to lower scattering intensity. The forward curves were thus obtained in a single concentration (3.0% w/w) which gives a reasonable signal-tonoise statistics without affecting the micellar structure and still with no interference of S(q), as suggested by results shown in Figure 4. For the whole set of samples, except for PAI4PS135PAI4, we have attempted to fit P(q) using two different models. The simplest one was the core-shell model9,10 with the central core composed by PAI and the outer shell formed by PS chains. It was concluded that this model describes the scattering profile in a reasonable way, but only in the low-q range and fails to describe the high-q region. While the scattering profile follows q-2 dependence (Figure 4), the model predicts a q-4 scattering decay. The deviation in the high-q region is related to the “blob” scattering coming from the internal structure of the polymer chains dissolved in the corona, which is even more pronounced in our current set of samples due to the fact that the micelles are formed by a thick corona and a small core, and thus the scattering contribution coming from the corona chains dominates the X-ray scattering profile. Therefore, instead of a single model, a more sophisticated one which assumes noncentro-symmetry of the objects was needed in order to analyze the full range of q studied. The most exciting results were obtained using the model proposed by Pedersen and Gerstenberg for the form factors P(q)sof block copolymer micelles with a spherical core.11 We found that the nomenclature used in ref 16 was convenient, and here we used the same description for this model (spherical copolymer micelle model). It well reproduced the experimental
2Nagg2βchainβcoreScore-chain(q) (4) Nagg is aggregation number of the micelles and βcore and βchain accounts for the excess scattering length of the core-forming block (PAI) and the corona-forming block (PS). Also in eq 4, Fcore(q, Rc) is the self-correlation of the spherical core of radius Rc and it is expressed in terms of the form factor amplitude of a sphere with a smoothly decaying scattering density at the surface:
[
Fcore(q, Rc) ) [Φ(q, Rc)]2 ) 3
sin(qRc) - qRc cos(qRc) (qRc)3
]
2
(5)
The chains self-term is described by the Debye function as in eq 3, however, RG (in eq 3) accounts in the spherical copolymer micelle model for the radius of gyration of the polymer chains attached to the micellar core and we refer to it as RG(chain). The core-chain term is given by
Score-chain(q) ) ψ(q, RG(chain))Φ(q, Rc)
sin[q(Rc + dRG(chain))] q(Rc + dRG(chain)) (6)
where the function Ψ(q,RG(chain)) is
ψ(q, RG(chain)) +
1 - exp(-q2RG(chain)2)
(7)
q2RG(chain)2
and d ∼ 1 should be used in order to mimic the nonpenetration of the corona chains into the core, which is physically impossible. When d ∼1, the starting point of the Gaussian chains is displaced to a value R′ ∼ Rc + RG(chain) away from the center of the particle. Finally, the chain-chain term is given by eq 8.
(
Schain-chain(q) ) ψ2(q, RG(chain))
sin[q(Rc + dRG(chain))] q(Rc + dRG(chain))
)
2
(8) This model has a large number of fitting parameters, namely: RG(chain), d, Rc, Nagg and the excess scattering length of the core and corona forming blocks (βcore and βcorona). Due to this, usually it is not possible to get a single set of fitting parameters if the excess scattering lengths cannot be fixed,18,22 and sometimes the fitting procedure can lead to ambiguous results. Thus, during the fitting procedures, we held fixed the parameters βcore and βcorona. The values of βcore for different block copolymers were calculated in the following way: (22) Plestil, J.; Pospı´sil, H.; Kadlec, P.; Tuzar, Z.; Krı´z, J.; Gordeliy, V. I. Polymer 2001, 42, 2941.
Copolymer Micelles with Looped Corona Chains
βcore ) NPAIVPAI(σPAI - σDMF)
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(9)
NPAI is the degree of polymerization of PAI core-forming block, VPAI is the volume of one PAI unit, σPAI is the scattering length density of PAI, and σDMF is the scattering length density of DMF. The same was valid for the determination of βcorona, where we used NPS, VPS and σPS. The values of VPAI and VPS were determined taking into account the homopolymer densities (0.89 g/cm3 for PAI determined experimentally and 1.05 g/cm3 for PS) and the molar mass of the units (PAI ) 139 g/mol and PS ) 104 g/mol). It should be mentioned that due to the looping formation, βcore is the determined value for one block at one end of the copolymer chains and for the determination of βcorona, NPS was taken as half of the values given in Table 1, for micelles formed from triblock copolymer samples, which were understood as hypothetical diblock copolymers. The values of scattering length densities for DMF and for PAI and PS unities were determined using the average chemical composition of each component and its density (dx) as:
σx )
bedxNA Σn z Mx i i i
(10)
wherein Mx is the molar mass of each component x (x ) DMF, and PAI or PS unities) and NA is Avogadro’s number. Furthermore, ni accounts for the number of atoms in each component with atomic number zi and be is the Thomson scattering length (the scattering length of an electron be ) 2.817 × 10-13 cm). All the above-mentioned parameters were determined and are given in Table 2. Therefore, the fitting parameters were Nagg, d, Rc and RG(chain). We have concluded that the polydispersity of all particles was low enough as already demonstrated previously through light scattering measurements.8 Thus, it was decided not to include it in the fitting procedures and the quality of fittings was not affected, as can be seen in Figure 6, which portrays the X-ray scattering profiles (I Vs q) and the fitting results (solid lines) achieved using the spherical copolymer micelle model. One can notice the high quality of the fittings suggesting that the model is able to reproduce the experimental curve in the whole q range accessed, including the high-q region. The values of χ2 were always lower than 1.20. It is not surprising that the spherical copolymer micelle model is able to describe the scattering of flowerlike micelles once it was already demonstrated that SANS profiles of micelles having this special architecture can be fitted, but only when the blob scattering is included in a given model.13 It was also shown that the spherical copolymer micelle model is able to fit scattering profiles of micelles having extended chains within their corona19 which we claim hereafter that it is also the case for the current set of samples. The resulting parameters from the fitting procedures are depicted in Table 3. All the Rc values are comparable with the ones calculated theoretically (Rc(theoretic)) using eq 11 and given in Table 4.
Rc(theoretic) )
(
3NaggMwwtPAI 4πNAdPAI
)
Figure 6. SAXS profiles for samples PAI6PS155PAI6, PAI9PS126PAI9; PAI11PS271PAI11 and PAI8PS132 (from top to bottom) dissolved in pure DMF at c ) 3.0% w/w. The solid lines show the best fittings achieved using the spherical copolymer micelle model.
1⁄3
(11)
using Nagg from SAXS measurements, dPAI and wPAI for each copolymer and assuming that the volume fraction of PAI in the micellar core is equal to 1 (dry core). The similar values of Rc and Rc(theoretic) attest the property of DMF as a strong precipitant for PAI and suggest that the small micellar core is compact and not swollen. Comparing the values among the samples, the differences in Rc came basically from a balance of distinct Nagg and wPAI for different samples.
PAI9PS126PAI9 and PAI11PS271PAI11, which form micelles with a higher Nagg (due to higher PAI content in the copolymer composition), should lead to micelles of larger cores compared to the other two samples. Since to the best of our knowledge there is no other research groups dealing with solution properties of such particular PAI polymer, the comparison of our current set of results with the related literature is somehow complex. However, we believe that these results can be compared at least with the solution properties of copolymers formed by unmodified polyisoprene
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Table 3. Micellar Parameters Acquired Using the Spherical Copolymer Micelle Model for Different Samplesc polymer
Rc
RG(chain)
Nagg
Rmica
d
Naggb
PAI6PS155PAI6 PAI9PS126PAI9 PAI11PS271PAI11 PAI8PS132
1.49 2.48 2.47 1.89
3.41 4.19 7.29 4.03
7 14 15 11
9.7 11.6 19.1 11.2
1.40 1.17 1.28 1.31
21 38 39 20
The micellar radius (Rmic) was estimated as: Rc + (1 + d)RG(chain). b These are the values monitored by light scattering and given in ref 8. c The dimensions Rc, RG(chain) and Rmic are given in nm.
of the corona chains. On the other hand, the small micellar core determined for the samples can lead to a small core surface area per corona chain (Ac/n where n ) 2 for triblock copolymer samples), which requires the PS chains to be extended. The values of Ac/n can be quantitatively determined as follows:
Ac 4πRc2 ) n Nagg
a
Table 4. Micellar Characteristics Calculated Based on SAXS Measurementsa polymer
Rc(theoretic)
L
(Ac/n)
σΝPS6/5
〈r2〉PS1/2
%E
PAI6PS155PAI6 PAI9PS126PAI9 PAI11PS271PAI11 PAI8PS132
1.66 2.89 2.72 1.71
8.2 9.1 16.6 9.3
1.99 2.76 2.55 4.08
5.8 3.3 8.9 5.4
2.2 2.0 2.9 2.9
48.2 56.5 48.8 26.9
a
Dimensions Rc(theoretic), L, 〈r2〉PS1/2 are given in nm. Ac/n is given in nm2.
(PI) and polystyrene. In this way, Pispas et al.23 and Hadjichristidis et al.24 have studied the solution properties of block copolymers comprising PS and PI and having different architectures. They studied the micellization behavior of such block copolymers in selective solvents for PS (DMF, dimethylacetamide (DMAc), and ethyl acetate (EA)) and suggested that the PI micellar core of the self-formed micelles was not swollen in all the solvents, which was compatible with the experimental results observed and with the related literature as well. Moreover, we already know that in mixtures of DMF and THF, the latter a good solvent for PAI, the precipitation of the pure homopolymer starts to occur when a very small amount of DMF is present (∼0.20 v/v). This previous result also suggests the unswollen behavior of the micellar core of the created micelles. Once Rc is known, the coronal thickness (L) can be estimated using the micellar dimension (Rmic) as L ) Rmic - Rc. Values for individual samples are summarized in Table 4. The dimension L increases with increasing length of the middle block, however, it seems to be independent of the block copolymer micelle architecture as it can be seen comparing samples PAI8PS132 and PAI9PS126PAI9. A quantitative estimation of conformation of the PS chains in the corona can be done if the values of L are compared with the values of the end-to-end distance 〈r2〉1/2PS for PS having the same molar mass and immersed in a theta solvent (〈r2〉1/2PS ) lNPS1/2) where l is the length of one PS repeating unit (l ∼ 0.25 nm) and NPS is the number of repeating units of the PS chains.25 Note that NPS should be divided by 2 in case of triblock copolymer micelles. The values are given in Table 4. It can be seen that the values of L are always higher than the values of 〈r2〉1/2PS, suggesting that the PS chains are extended. Due to the fact that all micellar aggregates possesses a small compact core, it is expected that the corona chains are extended. Usually, the conformation of chains in a micellar corona is known to be affected by a variety of parameters namely: curvature of the micellar core, concentration of chains in the corona, chemical nature of the corona chains among others.26 The corona chains are expected to be stretched if either the micellar core is small or if the shell density is pronounced (reflecting a high Nagg). Since Nagg of all micelles is small, it should not be the reason for an extended conformation (23) Mountrichas, M.; Mpiri, M.; Pispas, S. Macromolecules 2005, 38, 940. (24) Fernyhough, C. M.; Chalari, I.; Pispas, S.; Hadjichristidis, N. Eur. Polym. J. 2004, 40, 73. (25) Teraoka, I. Polymer Solutions: An Introduction to Physical Properties; Wiley-Interscience: New York, 2002. (26) Zhang, L.; Barlow, R. J.; Eisenberg, A. Macromolecules 2005, 28, 6055.
(12)
They were determined using the values of Rc and Nagg from SAXS measurements and are given in Table 4. The values are extremely low (in between 1.99 and 4.08 nm2), which should be one of the reasons for the fact that all the samples led to the formation of micelles with a small Nagg and it is also probably responsible to the high degree of extension of the PS corona chains. Je´roˆme et al.19 also reported similar values of Ac/n for micelles having extended poly(ethylene oxide) chains forming the corona. The extension of the corona chains can be qualitatively estimated by the value of σNPS6/5, where NPS is the degree of polymerization of the corona PS chains (NPS/2 for triblock copolymer samples), σ ) l2/(Ac/n).27 The values were always higher than 1 (Table 4), suggesting qualitatively the extended conformation of the corona chains.26 Furthermore, their degree of extension (%E) related to the fully elongated conformation can be determined through the equation
%E )
100L RNPS
(13)
where the corona chains possess a high degree of extension, as suggested by the results. Comparing the samples PAI8PS132 and PAI9PS126PAI9 in Table 4, it can be noticed that the degree of extension of the corona chains in the triblock copolymer sample (56.5%) is considerably higher than in the diblock copolymer (26.9%). This difference is probably related to the higher value of Ac/n for PAI8PS132 and also to the necessity of loop formation in order to have well-defined micelles in PAI9PS126PAI9. Furthermore, even though the sample PAI11PS271PAI11 has the thickest corona, %E for all the triblock copolymers remained roughly similar (∼50%). The related literature concerning the self-assembly of copolymer samples having such special architecture (very short outer core-forming blocks) can be compared with our current results. One may want to have a look for example in the parameters of assemblies formed in aqueous solutions of hydrophobically modified end-capped water-soluble polymers.28-30 Values of Nagg and size found for those systems are comparable with the ones reported herein. The values of Nagg determined via SAXS are smaller than those determined from light scattering measurements. It should be said however that the concentration range used in the SAXS experiments and in the light scattering was different. Even though the values are smaller, they follow the expected tendency were higher amount of PAI led to higher Nagg. The values of Nagg were also determined using the forward scattering from the experimental curves as:
I(q)qf0 )
cNANagg (βcore + βcorona)2 Mw
(14)
and the numbers found match very well with the ones listed in Table 3, determined from the fitting procedures. (27) Zhang, L.; Eisenberg, A. J. Am. Chem. Soc. 1996, 118, 3168. (28) Xu, B.; Li, L.; Yekta, A.; Masoumi, Z.; Kanagalingam, S.; Winnik, M. A.; Zhang, K.; Macdonald, P. M. Langmuir 1997, 13, 2447. (29) Inomata, K.; Kasuya, M.; Sugimoto, H.; Nakanishi, E. Polymer 2005, 46, 10035. (30) Alami, E.; Almgren, M.; Brown, W. Macromolecules 1996, 29, 2229.
Copolymer Micelles with Looped Corona Chains
One unexpected result also comes from the fitting procedure. Usually, the value of d should be ∼ 1 which means a displacement of the Gaussian chains at about ∼ RG(chain) away from the core surface. The best fitting procedures resulted in values slightly higher than 1 (Table 3), and the highest value was found for sample PAI6PS135PAI6. It is suspected that this behavior is related to the fact that the formed micelles have the smallest value of Ac/n. One can even notice a systematic increase in the values of d as the value of Ac/n decreases.
Conclusion We reported the characterization of the internal structure of block copolymer micelles formed by PAI and PS blocks dissolved in DMF. The small-angle X-ray scattering technique was used to help in the description of the micelles. We conclude that the PAI micellar core in all cases was small, however, not swollen, and the PS corona chains have a high degree of extension attributed
Langmuir, Vol. 25, No. 6, 2009 3493
mainly to the small core surface area per corona chain (Ac/n). The values of micellar size fits well with our previous light scattering measurements and the values of Nagg are in accordance with the theoretical values expected, however, they were smaller than those monitored by light scattering, which should be related to the fact that the light scattering measurements of the same set of samples shown in ref 8 were performed in solutions having copolymer concentration c ) 5 mg/mL and the values shown herein were determined from measurements in solutions having copolymer concentration c ) 3.0% w/w, i.e., c ∼ 30 mg/mL. Acknowledgment. We acknowledge support by the Grant Agency of the Czech Republic (Grant No. 202/09/2078). F.C.G. thanks CNPq-Brazil for the fellowship granted. The authors thank J. Plestil for help during SAXS measurements. LA804254K
