Micellar Morphologies of Block Copolymer Solutions near the Sphere

Article pubs.acs.org/Macromolecules

Micellar Morphologies of Block Copolymer Solutions near the Sphere/Cylinder Transition Chya Yan Liaw,†,§ Kevin J. Henderson,† Wesley R. Burghardt,‡ Jin Wang,§ and Kenneth R. Shull*,† †

Department of Materials Science and Engineering and ‡Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, United States § Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, United States ABSTRACT: The thermoreversible self-assembly of poly(methyl methacrylate)-b-poly(tert-butyl methacrylate) (PMMA−PtBMA) diblock copolymers in 2-ethylhexanol has been studied in the transition regime between spherical and cylindrical morphologies. In these materials the PMMA block exhibits a strong temperature dependence of the solvent quality that leads to reversible micelle formation, and the PtBMA block is a versatile polymer that can be hydrolyzed for further use as a polyelectrolyte. Self-consistent field theory was used in combination with a variety of experimental techniques to develop a simple criterion for the location of the sphere/cylinder transition in solutions with concentrations above the micelle overlap threshold. It is shown that the effective volume fraction of PMMA core, accounting for solvent swelling of the micelle core, is equal to ≈0.27 at the sphere/cylinder transition. For the spherical domain morphologies, a transition between disorded micelles and micelles packed on a body-centered-cubic lattice occurs when the micelle hydrodynamic radius of the micelle is comparable to the intermicelle spacing in the ordered micellar structure.

■

INTRODUCTION The self-assembly of block copolymers in selective solvents has been thoroughly studied over the past few decades. When dissolved in a selective solvent, which is good for one block while poor for the others, block copolymers will assemble into micellar aggregates, with characteristic sizes ranging from 10 to 200 nm.1,2 The insoluble blocks form a compact dense core shielded by the soluble blocks that are extended toward the solvent. Various morphologies of micelles can be obtained by tuning the relative volume fractions of the constituent blocks or by altering solvent solubility. Additional chemical treatments, such as ionic cross-linking or attachment of reactive groups to the block copolymers, will give rise to enhanced mechanical,3 optical,4 or electrical properties.5,6 Compared to micelles formed from small-molecule surfactants, polymeric micelles are more thermodynamically and kinetically stable.7 Polymeric micelles also exhibit slow disassembly and unimer exchange rates, enabling them to remain kinetically stable for extended periods of time.8 These factors make polymer micelles an ideal material system for extensive uses such as spherical drug delivery agents9,10 and structure-directing agents to precisely control the morphology of inorganic nanoparticles.11,12 Block copolymer solutions generally form the same sorts of structures formed in block copolymer melts, which for linear block copolymer consisting of two monomer types include spheres, hexagonally packed arrays of cylinders, lamellae, and bicontinuous gyroid strucures.13,14 Gels with an elastic character can be formed from sphere-forming ABA triblock copolymers at relatively low concentrations provided that the © XXXX American Chemical Society

polymer concentration is high enough to form a percolating network of “bridging” B blocks linking spherical A domains into a 3-dimensional network.15,16 Sphere-forming diblock copolymer solutions form elastic materials only at higher concentrations where the micelle coronas overlap substantially to form ordered crystalline arrays of micelles.15,17 These spherical diblock copolymer gels typically have moduli in the range of several kilopascals and have relatively low yield strains, typically on the order of 10%.18,19 Cylindrical micelles form gels through a different mechanism, with an elastic response dominated by the mechanical response of the cylinders themselves.20 The anisotropic nature of cylindrical micelles enables a range of applications inaccessible to sphere-forming micellar block copolymer solutions. For example, cylindrical micelles have been used as precursors for the fabrication of metallic nanowires of different characteristic sizes.21 Cylindrical micelles are also ideal candidates for flow-intensive drug delivery because they orient and stretch under flow, which enhances the efficiency of drug delivery in certain situations.22,23 Incorporating cylindrical micelles of poly(ethylene oxide)-bpoly(ethylene-alt-propylene) into epoxy has been shown to be an effective strategy for enhancing the toughness.24 Another potential application of cylindrical micelles is their use as a biomineralization template, in which the micelles exert control over the nucleation and growth of an inorganic component. An Received: August 26, 2014 Revised: December 4, 2014

A

DOI: 10.1021/ma501763x Macromolecules XXXX, XXX, XXX−XXX

Article

Macromolecules

dependent, enabling us to develop kinetically stable structures at room temperature that were formed by equilibrium processes at elevated temperatures. Our experimental model system for investigating the formation of cylindrical micellar structures are poly(methyl methacrylate)-b-poly(tert-butyl methacrylate) (PMMA-PtBMA) diblock copolymers dissolved in 2-ethylhexanol, a PtBMA-selective solvent. This system of completely amorphous block copolymers is particularly appealing for the following reasons: (1) A strong temperature dependence of PMMA/2-ethylhexanol interactions places the micelle completion temperature in a convenient experimental window. (2) The PMMA cores become glassy at temperatures above room temperature, such that morphological features formed by annealing at intermediate temperatures are locked into place upon cooling. (3) PtBMA is easily processed thermally or by an acid-catalyzed reaction to form poly(methacrylic acid) (PMAA),45 converting the corona into a water-soluble polyelectrolyte. The general behavior of the system is illustrated in Figure 1. Above about 80 °C, both PMMA and PtBMA can be dissolved

important analogue here is human bone tissue, a hierarchical biocomposite mainly composed of collagen fibrils and hydroxyapatite crystals.25,26 A variety of complex organic aggregates have been used as organic templates for investigating mineral formation in a structured organic template, including reconstituted collagen27,28 and agarose gels,29,30 and this principle could be extended toward the fabrication of anisotropic mineral structures using aligned cylindrical copolymer micelles. Various strategies have been employed to produce cylindrical diblock copolymer micelles. For block copolymer melts, asymmetric diblocks form micelles in which the minority block (A) constitutes the spherical or cylindrical core while the majority blocks (B) form the matrix. When adding a solvent that is selective to the minority block (A), the swelling effect causes the effective volume fraction of the minority block to increase and to potentially exceed that of the majority block, resulting in the formation of reverse micelles in which block B constitutes the core and the swollen block A comprises the matrix. Hamley et al. have investigated the phase behavior of poly(styrene)-b-poly(isoprene) diblocks in solvents with varied selectivity and elucidated the interplay between block composition, temperature-dependent solvent selectivity, and solution concentration which leads to multiple phase transitions in micellar systems.31,32 While many studies have focused on spherical and lamellar micelles, research on cylindrical micelles has been more limited. It has been reported that in the case of coil−rod or coil− crystalline copolymer elongated micelles are more accessible33−35 than for the coil−coil systems where both blocks are amorphous. In some instances crystallization drives the formation of cylindrical micelles when the insoluble block is able to crystallize.36 Several groups have studied asymmetric copolymers forming cylindrical micelles with shorter crystalline core-forming blocks such as poly(ferrocenysilane),21,34,36 polyacrylonitrile,35 poly(ethylene oxide),37 and poly(ε-caprolactone)33 when the copolymers were dissolved in selective solvents for the longer noncrystallized block. External fields also facilitate a transition from spherical to cylindrical domain morphologies in completely amorphous systems. Park et al. used a roll-casting process to facilitate the formation of cylindrical domains.38 Lee and co-workers have demonstrated an electric-field-induced sphere-to-cylinder transition in a polar solvent containing a micelles with a poly(styrenesulfonate) (PSS) block.39 In these experiments randomly distributed spherical micelles with loosely packed PSS coronas were initially formed in dilute solutions. When an electric field was applied, the order in these solutions was enhanced, and the micelles gradually developed into cylinders. Morphological transitions from spheres to cylinders have also been induced by altering the swelling properties of the corona block by adding salt or by changing the pH.40−42 Structural transitions can also be triggered by simply adding a homopolymer of the solventinsoluble block component, thereby changing the effective volume ratio of the core and corona fractions.43,44 While a variety of useful design principles have emerged from this previous work, progress toward a design approach based on thermodynamic considerations has been much more limited, a situation resulting from the difficulty in separating equilibrium, thermodynamic effects from nonequilibrium kinetic effects in real experimental systems. A unique feature of the system that we have chosen to work with is that dynamics associated with rearrangements of the micelle cores are strongly temperature

Figure 1. Schematic representation of spherical and cylindrical micelles.

in 2-ethylhexanol. As the temperature decreases, PMMA becomes less soluble, leading to the formation of micelles with PMMA cores and PtBMA coronas. The corona blocks remain soluble to temperatures well below room temperature, so the micelles are sterically stabilized by the PtBMA corona blocks that extend into the solvent. The equilibrium micellar geometry (spheres, cylinders, etc.) can be predicted by using self-consistent field theory to determine the geometry with the lowest overall free energy. The primary controlling parameter determining the preferred micelle geometry is fcore, the effective volume fraction of the core-forming block. Block copolymers with fcore close to 0.5 are expected to form lamellar structures, whereas polymers with very small values of fcore will form spherical PMMA cores. We are interested in the intermediate situation, where cylindrical structures are favored. Because the solvent composition of the core changes as the temperature is decreased and the PMMA becomes more incompatible with the solvent, fcore depends on both the temperature and the copolymer composition and the overall copolymer concentration in solution. In the present paper, reversible transitions between spherical and cylindrical micelles were induced by adjusting fcore via changes in the temperature and solution concentration. Transitions between the different geometries were confirmed experimentally with a combination of shear rheometry, smallangle X-ray scattering, and measurements of the sample birefringence after shear alignment. In addition, characteristic micelle sizes were measured with dynamic light scattering. SelfB


Article

Macromolecules

where T is the temperature in °C. Our rationalization for using this relation is based on the similar observed behavior for PMMA−PtBMA−PMMA triblock copolymer solutions in nbutanol and 2-ethylhexanol.54 In Figure 2 we show calculated volume fraction profiles for solutions with an overall polymer volume fraction of 0.25, with

consistent mean-field theory calculations were also performed and are consistent with experimentally observed values of micelle sizes and the characteristic value of fcore where the sphere/cylinder transition occurs. The outcome of our work is a strategy for designing block copolymers with cylindrical micelle microdomains and a procedure for optimally aligning these structures. We begin with a description of the theoretical calculations for the sphere/cylinder transition in the following section, followed by the description of our experimental procedure and results.

■

SELF-CONSISTENT FIELD THEORY CALCULATIONS Self-consistent field theory (SCFT) accounts for the connectivity of chain segments of amorphous polymers by treating the molecular conformations as random walks that are perturbed by mean field that depends on the local composition.46,47 We have used this approach to calculate equilibrium volume fraction profiles and geometry of micelles for a range of temperatures. The detailed description of our approach can be found elsewhere.48 Any given polymer solution contains two molecular components (solvent and polymer) and three chemical species (PMMA, PtBMA, and solvent). In our notation, the subscripts “M”, “T”, and “S” denote PMMA, PtBMA, and the solvent, respectively. A polymer chain is referred to by its total degree of polymerization, Nc, and f M, the relative volume fraction of the coreforming M block. Interactions between the M, T, and S components are described by three Flory−Huggins interaction parameters: χMS, χTS, and χMT. Because we use the SCFT calculations to understand the preferred micellar geometry and not to determine the packing of individual micelles, we use a one-dimensional unit-cell approximation, together with the assumption of reflective boundary at the midpoint between two adjacent micelles.49−52 For a given concentration and temperature, the equilibrium micelle radius (the length from the micelle core to the reflecting boundary) is determined by minimizing the free energy of the system with respect to the location of the reflecting boundary; the equilibrium geometry is the one with the lowest overall free energy. In this unit cell approximation, the overall polymer volume fraction, Φp, is given by the expression Φp =

k R mk

∫0

Rm

r k − 1ϕp(r ) dr

Figure 2. SCFT calculated, one-dimensional volume fraction profiles of a micelle plotted against the normalized distance from the micelle core (r/Rg) for solutions with Φp = 0.25, Nc = 534, and f M = 0.652. (a) T = 60 °C (cylinder) (b) T = 50 °C (sphere), and (c) T = 25 °C (sphere, same aggregation number as the one formed at 50 °C). The dashed lines represent the location of the reflecting boundary, which designates the micelle radius.

(1)

where ϕp(r) is the local polymer volume fraction at position r and Rm is the location of the reflecting boundary. The micelle geometry is specified by k, with k = 1 for lamellar micelles, k = 2 for cylindrical micelles, and k = 3 for spherical micelles. Micellization in our experimental system is driven by the PMMA/solvent interactions, and the results do not depend significantly on the values chosen for χTS and χMT. We used χTS = 0.45, characteristic of a good solvent, and χMT = 0.05, characteristic of moderately immiscible polymers. The most important variable is χMS, which describes the interactions between the core-forming PMMA block and the 2-ethylhexanol, which is used as the solvent in our experiments. In order to estimate the χMS that corresponds to a given value of temperature, we used the following expression that has been found to approximate the thermodynamic interactions between PMMA and n-butanol system:53 χMS = 1.45 − 0.0115T

Nc = 534, f M = 0.652, and T = 60 °C (part a), 50 °C (part b), and 25 °C (part c). In each case r = 0 corresponds to the center of the micelle core. The calculations indicate the thermodynamically equilibrium micelle geometry is cylindrical at 60 °C, and this is the symmetry that is assumed for the corresponding figure (Figure 2a). The micelles are predicted to be spherical at 50 °C, which is the approximate temperature below which the micelles are no longer able to equilibrate. We assume spherical micellar symmetry for the micelle calculation for 50 °C (Figure 2b). For the 25 °C calculation in Figure 2c we assume that the micelles are kinetically frozen, with the same overall aggregation number and symmetry as the micelles formed at 50 °C. The

(2) C


Article

Macromolecules micelle sizes are normalized by the unperturbed radius of gyration, Rg, for the block copolymer, given as follows:

R g = a Nc/6

(3)

Here a is the statistical segment length of a monomeric repeat unit, assumed to be the same for the M and T repeat units. When the temperature decreases, the PMMA/solvent contact is less favored. Therefore, the solvent content in the core decreases (solvent expulsion from the core). For the kinetically frozen micelle with a fixed aggregation number shown in Figure 2c, the polymer volume fraction in the core increases by ≈30% and the core radius shrinks by ≈10% as the temperature is reduced from 50 to 25 °C. For a simple M/T diblock copolymer melt in the absence of solvent, the predicted phase behavior in the mean-field limit is determined by the value of χ MT and the copolymer composition, represented by a single parameter, f M, the volume fraction of the core-forming M block. In the strong segregation regime (f MχMTNc ≫ 5) the transition from spheres to cylinders occurs for f M ≈ 0.12 and the transition from cylinders to lamellae occurs for f M ≈ 0.32.55 For polymer solutions we can use a similar treatment and use the volume fraction corresponding to the micelle cores, fcore, as the controlling parameter. Calculation of fcore is complicated in the solution case by the fact that the micelle cores contain both polymer and solvent. After accounting for the solvent content in the micelle cores, we obtained the following expression for fcore: fcore = fM Φp

1 1 − ϕMS

Figure 3. General phase map for a diblock copolymer with Nc = 534 and f M = 0.652. Each curve corresponds to a single value of the overall polymer volume percent, ranging from 15 to 50 as indicated. Open squares, filled circles, and the crosses correspond to equilibrium micelle structures of spheres, cylinders, and lamellae, respectively. The dashed line corresponds to fcore = 0.27, which is a good estimate of the transition point between cylindrical and spherical morphologies.

lamella transition occurs for fcore ≈ 0.40 for a wide range of values for Φp, the overall polymer volume fraction in the solution. (2) As the temperature decreases, solvent is expelled from the micelle cores, decreasing fcore and leading to either a lamella-to-cylinder or cylinder-to-sphere transition. The temperature at which this transition occurs increases as Φp increases. Figure 4 shows how ϕMP, the volume fraction of PMMA in the core, changes with temperature for a polymer with Nc = 534

(4)

Here the M block is assumed to be the core-forming block, and the volume fraction of solvent in the micelle core is ϕMS. A similar expression relates fcorona to ϕTS, the solvent fraction in the T corona block: fcorona = (1 − fM )Φp

1 1 − ϕTS

(5)

Values of ϕTS and ϕMS are obtained from the requirement that μMS, solvent chemical within the micelle core, be equal to μTS, the solvent chemical potential in the micelle corona. We approximate the core and corona as homogeneous solutions and use the Flory−Huggins expressions for the solvent chemical potential: μMS = ln ϕMS + 1 − ϕMS + χMS (1 − ϕMS)2 kBT (6) μTS kBT

= ln ϕTS + 1 − ϕTS + χTS (1 − ϕTS)2

Figure 4. Volume fractions of PMMA in the core (ϕMP) plotted against temperature. The black crosses connected by the dotted line corresponds to ϕMP calculated by assuming equilibrium with pure solvent. The triangles (15%), squares (20%), circles (25%), and asterisks (30%) are obtained by equating μMS to μTS.

and f M = 0.652. Values of ϕMP were calculated in two ways: by equating the solvent chemical potential in PMMA and PtBMA phases and by equating the solvent chemical potential in PMMA to pure solvent. In all but the highest temperatures, the simpler approach of assuming equilibrium with pure solvent provides an excellent approximation to ϕMP. While self-consistent field theory provides useful insight from a thermodynamic perspective, it is important to keep in mind that the theory is most suitable for concentrated solutions, so some errors are expected for the lower solution concentrations. In addition, the theory does not account for any kinetic effects. In our experimental system the micelle cores become glassy at low temperature. As a result, the micelles remain in kinetically trapped states as the time scales of the experiments falls below the values necessary for the system to reach thermodynamic equilibrium.16,44 If we account for this fact as described in more

(7)

By equating fcore to 1 − fcorona, and μMS to μTS, two equations are obtained that can be solved numerically to give ϕTS and ϕMS for specified values of f M, Φp, χMS (given by eq 2), and χTS (0.45 in our simulations). These values for ϕMS can then be used in eq 4 to solve for f M. We constructed a general phase map (Figure 3) for the polymer with Nc = 534 and f M = 0.652, with χMS (or T) and fcore as the independent variables. In this plot, each curve represents a single value of Φp and the points on each curve show the values of fcore at various temperature between 0 and 70 °C. The equilibrium structures as a function of temperature and polymer concentration were also determined. The following general conclusions emerge from Figure 3: (1) The sphere/ cylinder transition occurs for fcore ≈ 0.27, and the cylinder/ D


Article

Macromolecules

the SAXS 1D profile was done by using NIST Center for Neutron Research (NCNR) Small-angle scattering (SAS) analysis package in Igor.58 Lorentzian peak fits were used to determine the maximum intensity, position, and full width at half-maximum (fwhm) for the primary scattering peak in each case. Rheometry. Rheological experiments were performed with an Anton Paar Physica modular compact rheometer 300 in a double gap concentric cylindrical fixture. The polymer solution with a volume of ≈4 mL was poured into the gap and heated for 10 min at 90 °C to erase any temperature history, followed by cooling to 0 °C at a rate of 1 °C/min. Data were collected at a constant angular frequency of 10 s−1 and strain amplitude of 1%, which were chosen to ensure the measurements were conducted in the linear regime. Birefringence. Birefringence was investigated with a Linkam CSS450 shear device, illuminating the sample with a HeNe laser with wavelength of 633 nm. The sample of thickness 1.5 mm was sandwiched between two quartz windows placed between two mutually perpendicular polarizers. After loading the sample in the shear cell, the sample was held at 90 °C for 10 min and then cooled at 1.5 °C/min to 20 °C with or without applying mechanical shear. For the unsheared sample, data were collected for the whole cooling and heating process. In the shearing process, samples were cooled to 55 °C while shearing at a linear shear rate of 0.3 s−1. The shear was stopped at 55 °C in order to avoid fracturing the gelled sample. The samples were further cooled with the same cooling rate so the sheared structure could be kinetically trapped, and the data were collected during cooling from 55 to 20 °C and upon subsequent heating to 90 °C without shearing.

detail below, the guideline that the sphere/cylinder boundary occurs at fcore ≈ 0.27 is remarkably helpful.

■

EXPERIMENTAL DETAILS

Materials. The PMMA−PtBMA diblock copolymers were synthesized by anionic polymerization in tetrahydrofuran at −78 °C. A detailed description can be found elsewhere.56 Briefly, purified tBMA monomer was polymerized by the addition of an initiator formed by the reaction of sec-butyllithium with 1,1-diphenylethylene. After 20 h, a small amount of the solution was extracted for characterization of the PtBMA molecular weight, and purified methyl methacrylate was introduced into the reactor. After an hour, the polymerization was terminated with anhydrous methanol, and the polymer was precipitated in a methanol/water mixture. The molecular weight and polydispersity of the copolymer were characterized by gel permeation chromatography (GPC), with polystyrene in HPLC-grade tetrahydrofuran as reference standards. The compositions of the polymers were confirmed by proton nuclear magnetic resonance (1H NMR), referenced to the chemical shifts of tetramethylsilane (TMS) at 0 ppm and deuterated chloroform at 7.6 ppm. The number-average molecular weight (Mn), volume fraction of PMMA ( f M), and polydispersity index (PDI) for the polymers discussed in the paper are shown in Table 1. The polymers are denoted M400T134 and

Table 1. Details of the Investigated Block Copolymers polymer

Mn: PMMA (kg/mol)

Mn: PtBMA (kg/mol)

f Ma

PDI

M400T134 M340T134

39 33

18 19

0.652 0.600

1.06 1.10

■

RESULTS AND DISCUSSION Several aspects of polymer micelle have been investigated by complementary techniques. Dynamic light scattering was used to measure the micelle size as a function of concentration and to determine the concentration at which the sample behaved as a gel. Small-angle X-ray scattering (SAXS) and shear rheometry were used to investigate the micelle packing and to investigate the transition between spherical and cylindrical micelles, in addition to the transition temperature between crystalline and disordered arrays of micelles (TODT) and the spinodal temperature (TS), which we use to characterize the temperature below which micelles exist. Birefringence was used to confirm the transition between spherical and cylindrical morphologies. Micelle Formation: Dynamic Light Scattering. Figure 5 shows a semilogarithmic plot of the intensity correlogram, g2 − 1, measured at 25 °C for solutions prepared in two ways. Part a shows the correlation curves for solution concentrations ranging from 5 to 30 wt % after cooling from 90 to 25 °C at a rate of 1.5 °C/min. Solutions with concentrations below 20 wt % exhibit a unimodal distribution. Solutions with higher concentrations exhibit a broadening of the delay time distribution and a suppression of the initial amplitude. These observations for the 25 and 30 wt % solutions are consistent with the behavior of solutions that have reached the gelation threshold.59,60 Solutions at concentrations of 25 wt % and above became solid-like and are no longer completely ergotic. Note that for solution concentrations from 5 to 20 wt % we observed that the derived count rate starts to increase at temperature of about 72 °C, corresponding to the spinodal temperature TS determined by small-angle X-ray scattering as discussed in the following section. Part b shows the correlation data for solutions that were diluted in 2-ethylhexanol to a concentration of 5 wt %. Dilution was made at room temperature, where the glassy nature of the PMMA core ensures the micellar structure formed during the cooling process at higher concentrations is preserved. The correspond-

a

The value of f M was calculated using 1.18 and 1.02 g/cm3 for the bulk densities of PMMA and PtBMA, respectively.

M340T134, where the subscripts refer to respective degrees of polymerization. 2-Ethylhexanol, a selective solvent for PtBMA blocks, was used as the solvent for all of the experiments. Characterization Techniques. Dynamic Light Scattering (DLS). Dynamic light scattering was used to characterize size of micelles in the solution using a Zetasizer Nano ZS (Malvern Instruments), equipped with a HeNe gas laser with output power of 4 mW and wavelength of 633 nm and a backscattering detector positioned at a scattering angle of 173°. Measurements were performed on solutions with concentrations ranging from 5 to 35 wt % in 2-ethylhexanol. The large aggregates in each sample were removed by passing the solution through a 0.45 μm PTFE filter. Solutions were equilibrated at 90 °C for 10 min prior to cooling down to 25 °C at a rate of 1.5 °C/min. A non-negative least-squares algorithm was utilized to extract size information from the measured correlogram. For determination of the micelle size, samples at room temperature were subsequently diluted to a polymer concentration of 5 wt %. Hydrodynamic radii of the micelles were calculated assuming the solution having refractive index of 1.431 and a viscosity for 2-ethylhexanol of 9 × 10−3 Pa·s at the measurement temperature (25 °C).57 The volume of each solution was ≈50 μL and was loaded in a disposable solvent resistant microcuvette (ZEN0040 from Malvern Instruments) that is compatible with the 173° scattering angle of the instrument. Small-Angle X-ray Scattering (SAXS). SAXS experiments were conducted at the 5-ID-D station at Argonne National Laboratory. The polymer solutions were loaded in 1.5 mm diameter quartz capillaries and illuminated with a 17 keV X-ray beam with a flux of approximately 1012 photons/s. After mounting, the samples were allowed to equilibrate at 90 °C for 10 min and gradually cooled down to 0 °C at a cooling rate of 1.5 °C/min. The scattering vector q = 4π sin θ/λ ranges from 0.01 to 0.18 Å−1, where θ is the scattering angle and λ is the wavelength of the incident beam. Scattered X-rays were recorded with a 2-dimensional CCD detector, and the data were integrated over all azimuths to produce a 1D spectrum of intensity vs q. These 1D scattering curves were corrected by the subtraction of the scattering of 2-ethylhexanol in the quartz capillary measured at 25 °C. The fitting of E


Article

Macromolecules

Table 2. Summary of Measured Structural Parameters for Micelles at 25 °Ca Rm (nm)

R h (nm)

Rcore (nm)

fcore

15%

19.4

12.2

0.131

20%

20.7

12.7

0.175

22.9

25% 30%

28.2

13.6

0.2180 0.261

22.5

f micelle 0.53 0.76 >1

order disordered spheres disordered spheres BCC spheres cylinders

From q* at 55 °C. f micelle represents total volume fraction of micelle in the solution. a

micelle parameters obtained from the SAXS experiments. The 30 wt % solution could not be diluted in 2-ethylhexanol at room temperature, a behavior that is consistent with the existence of a cylindrical morphology for this particular solution. Micelle Packing and Geometry. Concentration Effects. The transition between spherical and cylindrical morphologies depends on the value of fcore, which increases with increasing polymer concentration and with increasing temperature. In order to gain a general understanding of the behavior of the system, we begin here with a discussion of the concentration effects. Figure 7a shows the SAXS data for the M400T134 solutions over the concentration range from 5 to 30 wt % for samples that had been cooled to 25 °C. The following general results are obtained. (1) A primary scattering peak gradually is

Figure 5. Correlation functions obtained at 25 °C for solutions that were (a) cooled from 90 °C at a rate of 1.5 °C/min and (b) cooled as described in part (a) and subsequently diluted at room temperature in 2-ethylhexanol to a polymer concentration of 5 wt %.

Figure 6. Intensity size distribution of micelle solutions diluted in 2ethylhexanol to 5 wt % at 25 °C. Each curve was labeled by the original concentration of the solution. The curves fitted by the Schulz distribution (eq 8) are shown as solid lines. The polydispersity obtained from the fitting results are 0.26, 0.22, 0.27, 0.25, and 0.28 for respective polymer concentrations of 5, 10, 15, 20, and 25 wt %.

ing intensity size distributions are shown in Figure 6. The measured sized distributions were fit to the normalized Schulz distribution:61 ⎛ z+1 ⎞ ⎛ z + 1 ⎞z + 1 z f (R h ) = ⎜ R h⎟ /Γ(z + 1) ⎟ R h exp⎜ − Rh ⎠ ⎝ ⎝ Rh ⎠ (8)

Here Rh is hydrodynamic radius of the micelle, R h is the average micelle radius, and z = 1/p2 − 1, where p is polydispersity, given by the variance of the distribution divided by R h . The values of R h were 18.3, 18.6, 19.4, 20.7, and 28.2 nm for solution concentrations of 5, 10, 15, 20, and 25 wt %. These values of R h are listed in Table 2 along with other

Figure 7. (a) Concentration dependence of SAXS profiles for M400T134 solutions at 25 °C. Arrows indicate the peak locations relative to the main scattering peak. (b) SAXS profiles for the 15 and 25 wt % M400T134 solutions with fitting in the high-q range (solid curves) by eq 12. Curves have been shifted vertically for clarity. F


Article

Macromolecules

Figure 8. Temperature dependence of the SAXS profiles (a) and the storage and loss moduli (b) for 25 wt % solution of M400T134.

observed at q* ≈ 0.017 Å−1 for all polymer concentrations up to 25 wt %. For the 30 wt % sample the scattering peak is shifted to a slightly lower value of q (q* ≈ 0.0165 Å−1). (2) The micelle core size increases as the concentration increased. This is indicated by the shift in position of the first minimum of the form factor. (3) Higher-order peaks are observed for a solution concentration of 25 wt %, suggesting long-range crystalline packing of the micelles. The peaks occur at q = q*·(1, √2, √3, √4, √5, √6, √7), the peaks expected for a body-centered cubic packing of micelles.62,63 (4) For the solution concentration of 30 wt % peaks are observed at q = q*·(1, √3, √7,), which is consistent with hexagonal packing of cylindrical micelles.38 In a more quantitative sense, we can extract two pieces of information from the data. The first of these is a micelle radius, Rm, extracted from the crystalline packing of the micelles in the sample with a polymer concentration of 25 wt %. Assuming that the peak at q = q* corresponds to the (110) peak for hard spheres of radius Rm that pack on a BCC lattice, we obtain

Rm =

π 6 2q*

⎛ [3 sin(qR ) − qR cos(qR )] ⎞2 c c c ⎟ Pc(q , R c) = (Δρ) V0 ⎜ (qR c)3 ⎠ ⎝ 2

(12)

We assume that the scattering in the high q regime is determined by the behavior of Pc , so that Rcore can be obtained by fitting the data to eq 11: Fits for the 15 and 25 wt % samples are shown in Figure 7 and give Rcore = 11.03 nm for the 15 wt % solution and Rc = 14.72 nm for the 25 wt % solution. In both cases a value of 0.12 was used for p, the polydispersity used to determine z in eq 8. Values of Rcore obtained in this way for each of the concentrations are shown in Table 2. Temperature Effects. The concentration dependence of the system behavior is qualitatively consistent with our expectation that as fcore increases the system transitions from disordered spheres to ordered spheres to cylinders. In order to understand these transitions more quantitatively, we need to understand the temperature dependence as well. Representative temperature data, in this case for the 25 wt % sample, are shown in Figure 8. The full temperature dependencies of the parameters obtained from fitting the primary scattering peak are shown in Figure 9. Data from polymer concentrations of 15, 20, 25, and 30 wt % are all included in this SAXS summary figure. Two different temperatures are evident from the temperature dependence of the maximum intensity, Imax, and of q*, the value of q where this maximum intensity is observed. The spinodal temperature, TS, is between 72 and 73 °C for the three higher concentrations and is slightly lower (≈70 °C) for the 15 wt % sample. The spinodal temperature corresponds to the onset of increased scattering intensity as the sample is cooled. It is most accurately determined by plotting 1/Imax as a function of the inverse of of the absolute temperature, with TS corresponding to the temperature where 1/Imax = 0 after a linear extrapolation from the high temperature regime. The procedure is illustrated in Figure 10 for each of the four polymer concentrations of interest to us. Park et al. showed that for the block copolymer solutions investigated in their work TS corresponds to the critical micelle temperature, and we expect that a similar correspondence exists in our system as well.64 In the remainder of this section, we summarize the temperature dependence of the solutions for overall polymer concentrations ranging from 30 down to 15 wt %. 30 wt % M400T134. Our interpretation of the temperaturedependent results for the 30 wt % sample is that cylindrical

(9)

The measured value of 0.0171−1 for q* for the solution with Φp = 0.25 gives Rm = 22.5 nm. The second piece of information that we can obtain from the SAXS data is an estimate of Rc, the radius of the spherical micelle core for the solutions with polymer concentrations of 25 wt % or less. Our assumption here is that the scattering contrast in the system is dominated by the difference in scattering length density between the solvent-swollen PMMA cores of the micelles and the remainder of the solution. The overall scattering intensity is obtained as the product of the structure factor, S(q) and the average form factor, Pc : I(q) ∝ Pc(q)S(q)

(10)

We assume a Schulz distribution of particle sizes, f(Rc) as given by eq 8 so that Pc is given by Pc(q) =

∫0

∞

Pc(q , R c)f (R c) dR c

2

(11)

Here Pc(q,Rc) is the simplest form of the form factor assuming a spherical core with a uniform excess electron density Δρ: G


Article

Macromolecules

Figure 10. Spinodal plots for the calculation of TS for copolymer solutions with concentrations of 15, 20, 25, and 30 wt %.

geometry that exists down to ≈50 °C. As the temperature is decreased further, solvent is driven out of the micelle cores, reducing fcore. At a temperature of ≈50 °C fcore is reduced to the critical value of ≈0.27, for which spherical micelles become favored. At temperatures slightly higher than 50 °C, the PMMA blocks in the micelle cores still have sufficient mobility for the structure to equilibrate to form spherical micelles that pack on a BCC lattice. This spherical morphology persists at all lower temperatures, but the ordered packing disappears at temperatures below ≈10 °C. At this point the micelles have contracted sufficiently so that interactions between micelles are much weaker, and an ordered BCC lattice is no longer favored. The evidence of disordering can also be found in the temperature dependence of moduli in the rheometry data as shown in Figure 8b, where we see that this disordering is accompanied by a dramatic decrease in the storage modulus of the solution. 20 wt % M400T134. For any given temperature, fcore for the 20 wt % solution is less than fcore for the 25 wt % solution. As a result, the 20 wt % system transforms to a spherical morphology at a higher temperature than the 25 wt % solution. Once the spheres form, they pack on a BCC lattice. This ordered packing is lost at a relatively high temperature, however, because of the decreased concentration. Disordered spheres are obtained as the temperature is reduced below about 50 °C, resulting in a decrease in Imax and in the peak width. 15 wt % M400T134. When the polymer concentration reduced to 15 wt %, disordered spherical micelles are formed at or above 63 °C, and this morphology persists as the temperature is decreased. Micelle Ordering Criterion. Our criterion that fcore = 0.27 marks the boundary between spheres and cylinders works well for our samples but does not provide any direct information regarding the packing of the micelles into ordered arrays. This packing is driven by micelle−micelle interactions that come into play when the micellar spacing in the ordered array is comparable to the hydrodynamic diameter of the micelles.

Figure 9. Temperature dependence of the maximum intensity, value of q at the intensity maximum (q*) and full width at half maximum for the primary scattering peak for the M400T134 polymer at overall concentrations from 15 to 30 wt %.

micelles are formed at the system is cooled through the spinodal temperature and that these micelles remain cylindrical as the sample is cooled. When the temperature reaches a value of about 50 °C, the polymer mobility in the micelle cores becomes sufficiently slow so that the micelle morphology is no longer able to change. As a result, the cylindrical morphology persists to the lowest temperatures, even when fcore is decreased to the point where the equilibrium micelle geometry is spherical. 25 wt % M400T134. The differences between the behavior observed in this sample and in the 30 wt % sample are most clearly demonstrated in the SAXS data, which show a region of enhanced scattering for temperatures between 10 and 50 °C (see Figure 9a). Higher order peaks appearing in this temperature window are consistent with the existence of the body-centered-cubic packing of spherical micelles discussed in the previous section. We postulate that elongated micelles form during cooling from elevated temperature and that this is the H


Article

Macromolecules

atures, however, as indicated by the development of scattering intensity at temperatures well above 63 °C. In addition, birefringence persists in the sample to temperatures close to 71 °C. An interesting effect for which we do not yet have a clear explanation is the increase in birefringence observed during heating of a shear aligned sample that occurs at a temperature of close to the spinodal temperature of 72 °C.

Alternatively, we can calculate an effective micelle volume fraction, f micelle, from Rcore, R h , and fcore: ⎛ R ⎞3 fmicelle = fcore ⎜ h ⎟ ⎝ R core ⎠

(13)

This equation is valid for values of f micelle less than the hardsphere packing fraction, equal to 0.68 for body-centered-cubic packing. When the value of f micelle is comparable to this hard sphere packing fraction, the micelles will pack on an ordered lattice. This result is consistent with the results for the 20 wt % sample, for which we estimate a value of ≈0.76 for f micelle at 25 °C. Shear Alignment: Birefringence. Because the difference in scattering behavior of spherical and cylindrical morphologies can be quite subtle, we also performed birefringence experiments to definitively demonstrate the existence of anisotropy in samples that we assume to have a cylindrical morphology. Birefringence measurements were performed on M340T134 at 30 and 35 wt % in 2-ethylhexanol as a function of temperature. For the 30 wt % sample, no birefringence was observed with or without shear, consistent with the existence of a spherical domain morphology for this sample. (Note that because f M is lower for this polymer than for the polymer used in the rest of the paper, the sphere/cylinder transition occurs at a slightly higher polymer volume fraction.) For a 35 wt % M340T134 sample, no birefringence was observed when the sample was cooled down without applying any shear, but significant birefringence was observed when shear was applied. The results are shown in Figure 11 for a

■

CONCLUSION This study investigated micellar phase behavior in the vicinity of sphere-to-cylinder transition as a function of temperature and concentration of PMMA−PtBMA diblock copolymer in a selective solvent 2-ethylhexanol. Our primary conclusions are as follows: • Theoretical calculations show sphere-to-cylinder phase transition boundary was found at an effective volume fraction of PMMA core fcore of 0.27. • The value of fcore can be changed in our system either by changing the overall polymer volume fraction or by changing the temperature. The temperature dependence of fcore is attributed to the strong temperature dependence of the thermodynamic interactions between the solvent and core block. Decreasing the temperature drives solvent out of the micelle core, decreasing fcore. The development of a scattering maximum during cooling enables us to identify a spinodal temperature, which we use as structural signature of micelle formation. It is only weakly concentration dependent, occurring at temperatures between 70 and 73 °C for overall polymer concentrations between 15 and 30 wt %. • Experimentally determined transitions between spherical and cylindrical structures were consistent with the theoretical prediction, accounting for the fact that the micelle geometry is not able to equilibrate at temperatures below ≈50 °C. • For the spherical domain morphologies, a transition between disordered micelles and BCC packing of micelles occurs when the micellar spacing in the ordered structure is comparable to the hydrodynamic diameter of the micelles.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (K.R.S.). Notes

Figure 11. Birefringence (Δn) versus time (t) for a 35 wt % M340T134 solution after applying a constant shear rate of 0.3 s−1, taken during cooling from 55 to 20 °C and heating from 20 °C back to 90 °C. The time dependence of the temperature is shown in the upper part of the figure.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the U.S. Department of Energy Office of Science under Contract DE-AC02-06CH11357 and by the National Science Foundation under Award DMR1410968. We also have benefited from facilities provided by the Northwestern University Materials Research Science and Engineering Center, supported by the National Science Foundation under NSF Award DMR-1121262. The X-ray experiments were carried out at the Dupont−Northwestern− Dow Collaborative Access Team Synchrotron Research Center located at Sector 5 of the Advanced Photon Source at Argonne National Laboratory.

sample that was cooled at a rate of 1.5 °C/min from 90 to 20 °C and then heated at this same rate. A shear rate of 0.3 s−1 was applied to the sample for temperatures above 55 °C during the cooling portion of the experiment. Shear alignment of the sample results in substantial birefringence, which decreases significantly when the temperature is increased above ≈63 °C. The data confirm the existence of an anisotropic micellar geometry in this sample, which is preferentially aligned by the application of a shear stress. As a final comment, we note that our focus has been on the regime where a well-developed micellar structure has been formed, in our case at or below Tq (63 °C). The mean field techniques used to model the system are most applicable in this regime. Some structure is clearly formed at higher temper-

■

REFERENCES

(1) Jones, M.-C.; Leroux, J.-C. Polymeric micelles − a new generation of colloidal drug carriers. Eur. J. Pharm. Biopharm. 1999, 48, 101−111. I


Article

Macromolecules (2) Gaucher, G.; Dufresne, M.-H.; Sant, V. P.; Kang, N.; Maysinger, D.; Leroux, J.-C. Block copolymer micelles: preparation, characterization and application in drug delivery. J. Controlled Release 2005, 209, 169−188. (3) Henderson, K. J.; Zhou, T. C.; Otim, K. J.; Shull, K. R. Ionically cross-linked triblock copolymer hydrogels with high strength. Macromolecules 2010, 43, 6193−6201. (4) Anthony, S. P.; Cho, W. J.; Lee, J. I.; Kim, J. K. Synthesis of lead chalcogenide nanopar-ticles in block copolymer micelles: Investigation of optical properties and fabrication of 2-D arrays of nanoparticles. J. Mater. Chem. 2009, 19, 280. (5) Iovu, M. C.; Zhang, R.; Cooper, J. R.; Smilgies, D. M.; Javier, A. E.; Sheina, E. E.; Kowalewski, T.; McCullough, R. D. Conducting block copolymers of regioregular poly(3-hexylthiophene) and poly(methacrylates): Electronic materials with variable conductivities and degrees of interfibrillar order. Macromol. Rapid Commun. 2007, 28, 1816−1824. (6) Scherf, U.; Gutacker, A.; Koenen, N. All-conjugated block copolymers. Acc. Chem. Res. 2008, 41, 1086−1097. (7) Owen, S. C.; Chan, D. P.; Shoichet, M. S. Polymeric micelle stability. Nano Today 2012, 7, 53−65. (8) Lin, W.-J.; Juang, L.-W.; Lin, C.-C. Stability and release performance of a series of pegylated copolymeric micelles. Pharm. Res. 2003, 20, 668−673. (9) Rösler, A.; Vandermeulen, G. W.; Klok, H.-A. Advanced drug delivery devices via self-assembly of amphiphilic block copolymers. Adv. Drug Delivery Rev. 2001, 53, 95−108. (10) Li, Y. Y.; Zhang, X. Z.; Zhu, J. L.; Cheng, H.; Cheng, S. X.; Zhuo, R. X. Self-assembled, thermoresponsive micelles based on triblock PMMA-b-PNIPAAm-b-PMMA copolymer for drug delivery. Nanotechnology 2007, 18, 215605. (11) Smarsly, B.; Antonietti, M. Block copolymer assemblies as templates for the generation of mesoporous inorganic materials and crystalline films. Eur. J. Inorg. Chem. 2006, 2006, 1111−1119. (12) Orilall, M. C.; Wiesner, U. Block copolymer based composition and morphology control in nanostructured hybrid materials for energy conversion and storage: solar cells, batteries, and fuel cells. Chem. Soc. Rev. 2011, 40, 520. (13) Lodge, T. P. Block copolymers: Past successes and future challenges. Macromol. Chem. Phys. 2003, 204, 265−273. (14) Matsen, M. W. Effect of architecture on the phase behavior of AB-type block copolymer melts. Macromolecules 2012, 45, 2161−2165. (15) Madsen, J.; Armes, S. P. (Meth)acrylic stimulus-responsive block copolymer hydro-gels. Soft Matter 2012, 8, 592. (16) Seitz, M. E.; Burghardt, W. R.; Faber, K. T.; Shull, K. R. Selfassembly and stress relaxation in acrylic triblock copolymer gels. Macromolecules 2007, 40, 1218−1226. (17) Fairclough, J. P. A.; Norman, A. I. Structure and rheology of aqueous gels. Annu. Rep., Sect. C 2003, 99, 243−276. (18) Weidisch, R.; Michler, G. H.; Arnold, M.; Hofmann, S.; Stamm, M.; Jérôme, R. Synergism for the improvement of tensile strength in block copolymers of polystyrene and poly(n-butyl methacrylate). Macromolecules 1997, 30, 8078−8080. (19) Kelarakis, A.; Mingvanish, W.; Daniel, C.; Li, H.; Havredaki, V.; Booth, C.; Hamley, I. W.; Ryan, A. J. Rheology and structures of aqueous gels of di-block(oxyethylene−oxybutylene) copolymers with lengthy oxyethylene blocks. Phys. Chem. Chem. Phys. 2000, 2, 2755− 2763. (20) Fielding, L. A.; Lane, J. A.; Derry, M. J.; Mykhaylyk, O. O.; Armes, S. P. Thermo-responsive diblock copolymer worm gels in nonpolar solvents. J. Am. Chem. Soc. 2014, 136, 5790−5798. (21) Gohy, J.-F.; Lohmeijer, B. G. G.; Alexeev, A.; Wang, X.-S.; Manners, I.; Winnik, M. A.; Schubert, U. S. Cylindrical micelles from the aqueous self-assembly of an amphiphilic poly(ethylene oxide)-bpoly(ferrocenylsilane) (PEO-b-PFS) block copolymer with a metallosupramolecular linker at the block junction. Chemistry (Weinheim, Germany) 2004, 10, 4315−4323.

(22) Kim, Y.; Dalhaimer, P.; Christian, D. A.; Discher, D. E. Polymeric worm micelles as nano-carriers for drug delivery. Nanotechnology 2005, 16, S484−491. (23) Cai, S.; Vijayan, K.; Cheng, D.; Lima, E. M.; Discher, D. E. Micelles of different morphologies−advantages of worm-like filomicelles of PEO-PCL in paclitaxel delivery. Pharm. Res. 2007, 24, 2099− 2109. (24) Liu, J. D.; Thompson, Z. J.; Sue, H.-J.; Bates, F. S.; Hillmyer, M. A.; Dettloff, M.; Jacob, G.; Verghese, N.; Pham, H. Toughening of Epoxies with Block Copolymer Micelles of Wormlike Morphology. Macromolecules 2010, 43, 7238−7243. (25) Lakes, R. Materials with structural hierarchy. Nature 1993, 361, 511−515. (26) Hartgerink, J. D.; Beniash, E.; Stupp, S. I. Self-assembly and mineralization of peptide-amphiphile nanofibers. Science 2001, 294, 1684−8. (27) Takashi, S.; Toshimasa, U.; Shuichi, I.; Takeo, F.; M, C.; Koichi, M. Mineral induction by phosphoprotein-reconstituted collagen fibrils complex. Effect of collagen fibril structure on mineral induction. Jpn. J. Conservative Dent. 2000, 43, 826−831. (28) Kikuchi, M.; Ikoma, T.; Itoh, S.; Matsumoto, H. N.; Koyama, Y.; Takakuda, K.; Shi-nomiya, K.; Tanaka, J. Biomimetic synthesis of bone-like nanocomposites using the self-organization mechanism of hydroxyapatite and collagen. Compos. Sci. Technol. 2004, 64, 819−825. (29) Ning, T.-Y.; Xu, X.-H.; Zhu, L.-F.; Zhu, X.-P.; Chu, C. H.; Liu, L.-K.; Li, Q.-L. Biomimetic mineralization of dentin induced by agarose gel loaded with calcium phosphate. J. Biomed. Mater. Res., Part B 2012, 100, 138−144. (30) Li, H.; Estroff, L. A. Calcite growth in hydrogels: Assessing the mechanism of polymer-network incorporation into single crystals. Adv. Mater. 2009, 21, 470−473. (31) Hanley, K. J.; Lodge, T. P.; Huang, C.-I. Phase behavior of a block copolymer in solvents of varying selectivity. Macromolecules 2000, 33, 5918−5931. (32) Lodge, T. P.; Pudil, B.; Hanley, K. J. The full phase behavior for block copolymers in solvents of varying selectivity. Macromolecules 2002, 35, 4707−4717. (33) Du, Z.-X.; Xu, J.-T.; Fan, Z.-Q. Micellar morphologies of poly(εcaprolactone)-b-poly(ethylene oxide) block copolymers in water with a crystalline core. Macromolecules 2007, 40, 7633−7637. (34) Guér in, G.; Wang, H.; Manners, I.; Winnik, M. A. Fragmentation of fiberlike structures: sonication studies of cylindrical block copolymer micelles and behavioral comparisons to biological fibrils. J. Am. Chem. Soc. 2008, 130, 14763−14771. (35) Lazzari, M.; Scalarone, D.; Vazquez-Vazquez, C.; LópezQuintela, M. A. Cylindrical micelles from the self-assembly of polyacrylonitrile-based diblock copolymers in nonpolar selective solvents. Macromol. Rapid Commun. 2008, 29, 352−357. (36) Shen, L.; Wang, H.; Guerin, G.; Wu, C.; Manners, I.; Winnik, M. A . A m i c e l la r s ph e r e - t o - c y li nd e r tr a ns i ti o n o f po l y (ferrocenyldimethylsilane-b-2-vinylpyridine) in a selective solvent driven by crystallization. Macromolecules 2008, 41, 4380−4389. (37) Mihut, A. M.; Drechsler, M.; Möller, M.; Ballauff, M. Sphere-torod transition of micelles formed by the Semicrystalline polybutadieneblock-poly(ethylene oxide) block copolymer in a selective solvent. Macromol. Rapid Commun. 2010, 31, 449−453. (38) Park, C.; Simmons, S.; Fetters, L.; Hsiao, B.; Yeh, F.; Thomas, E. Spherical to cylindrical microdomain transformation by application of a flow field. Polymer 2000, 41, 2971−2977. (39) Lee, S. J.; Park, M. J. Morphological manipulation of ionic block copolymer micelles using an electric field. Langmuir 2010, 26, 17827− 17830. (40) Zhang, L.; Eisenberg, A. Thermodynamic vs kinetic aspects in the formation and morphological transitions of crew-cut aggregates produced by self-assembly of polystyrene-b-poly(acrylic acid) block copolymers in dilute solution. Macromolecules 1999, 32, 2239−2249. (41) Borisov, O. V.; Zhulina, E. B. Morphology of micelles formed by diblock copolymer with a polyelectrolyte block. Macromolecules 2003, 36, 10029−10036. J


Article

Macromolecules (42) Hales, K.; Pochan, D. J. Using polyelectrolyte block copolymers to tune nanostruc-ture assembly. Curr. Opin. Colloid Interface Sci. 2006, 11, 330−336. (43) Kinning, D. J.; Winey, K. I.; Thomas, E. L. Structural transitions from spherical to nonspherical micelles in blends of poly(styrenebutadiene) diblock copolymer and polystyrene homopolymers. Macromolecules 1988, 21, 3502−3506. (44) Seitz, M. E.; Burghardt, W. R.; Shull, K. R. Micelle morphology and mechanical response of triblock gels. Macromolecules 2009, 42, 9133−9140. (45) Qin, S.-H.; Qiu, K.-Y. Block copolymerization of tert-butyl methacrylate with α,ω-difunctionalized polystyrene macroiniferter and hydrolysis to amphiphilic block copolymer. J. Polym. Sci., Part A: Polym. Chem. 2001, 39, 1450−1455. (46) Bates, F. S.; Fredrickson, G. H. Block copolymer thermodynamics: theory and experiment. Annu. Rev. Phys. Chem. 1990, 41, 525− 557. (47) Fredrickson, G. The Equilibrium Theory of Inhomogeneous Polymers; Oxford University Press: Oxford, 2013. (48) Bras, R. E.; Shull, K. R. Self-consistent field theory of gelation in triblock copolymer solutions. Macromolecules 2009, 42, 8513−8520. (49) Helfand, E.; Wasserman, Z. Block copolymer theory. 4. Narrow interphase approximation. Macromolecules 1976, 9, 879. (50) Vavasour, J.; Whitmore, M. Self-consistent mean field theory of the microphases of diblock copolymers. Macromolecules 1992, 25, 5477. (51) Shi, A.; Noolandi, J. Effects of short diblocks at interfaces of strongly segregated long diblocks. Macromolecules 1994, 27, 2936− 2944. (52) Gompper, G.; Schick, M. Soft Matter; Wiley-VCH: Weinheim, 2006. (53) Llopis, J.; Albert, A.; Usobiaga, P. Studies on poly(ethyl acrylate) in [theta] solvents. Eur. Polym. J. 1967, 3, 259−265. (54) Drzal, P. L.; Shull, K. R. Origins of mechanical strength and elasticity in thermally reversible, acrylic triblock copolymer gels. Macromolecules 2003, 36, 2000−2008. (55) Matsen, M. W.; Bates, F. S. Unifying weak- and strongsegregation block copolymer theories. Macromolecules 1996, 29, 1091−1098. (56) Guvendiren, M.; Shull, K. R. Self-assembly of acrylic triblock hydrogels by vapor-phase solvent exchange. Soft Matter 2007, 3, 619− 626. (57) Bahrmann, H.; Harm, H.-D.; Mayer, D. Ullmann’s Encyclopedia of Industrial Chemistry; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, 2000. (58) Kline, S. R. Reduction and analysis of SANS and USANS data using IGOR Pro. J. Appl. Crystallogr. 2006, 39, 895−900. (59) Boyko, V.; Richter, S. Monitoring of the gelation process on a radical chain cross-linking reaction based on N-vinylcaprolactam by using dynamic light scattering. Macromol. Chem. Phys. 2004, 205, 724− 730. (60) Shibayama, M.; Norisuye, T. Gel formation analyses by dynamic light scattering. Bull. Chem. Soc. Jpn. 2002, 75, 641−659. (61) Kotlarchyk, M.; Chen, S.-H. Analysis of small angle neutron scattering spectra from polydisperse interacting colloids. J. Chem. Phys. 1983, 79, 2461−2469. (62) Torija, M. A.; Choi, S.-H.; Lodge, T. P.; Bates, F. S. Large amplitude oscillatory shear of block copolymer spheres on a bodycentered cubic lattice: are micelles like metals? J. Phys. Chem. B 2011, 115, 5840−5848. (63) Castelletto, V.; Hamley, I. W.; Yuan, X.-F.; Kelarakis, A.; Booth, C. Structure and rheology of aqueous micellar solutions and gels formed from an associative poly(oxybutylene)−poly(oxyethylene)− poly(oxybutylene) triblock copolymer. Soft Matter 2005, 1, 138. (64) Park, M. J.; Char, K.; Bang, J.; Lodge, T. P. Order-disorder transition and critical micelle temperature in concentrated block copolymer solutions. Macromolecules 2005, 38, 2449−2459.

K


Micellar Morphologies of Block Copolymer Solutions near the Sphere

Recommend Documents