Self-assembled, wormlike-cylinder network of polystyrene-block-poly(ethylene oxide) micelles in solution



We report the formation of a highly entangled and interconnected, self-assembled, wormlike-cylinder network of polystyrene-block-poly(ethylene oxide) in N, N-dimethylformamide/water. In this system, N,N-dimethylformamide was a common solvent and water was a selective solvent for the poly(ethylene oxide) blocks. The degrees of polymerization of the polystyrene and poly(ethylene oxide) blocks were 962 and 227, respectively. The network was formed at copolymer concentrations higher than 0.4 wt % and consisted of self-assembled, wormlike cylinders that were interconnected by Y-shaped, T-shaped, and multiple junctions. The network morphology was visualized with transmission electron microscopy. Capillary viscometry measurements revealed an order-of-magnitude increase in the inherent viscosity of the colloidal system upon the formation of the network. A similar effort to obtain a wormlike-cylinder network in an N,N-dimethylformamide/acetonitrile system, in which acetonitrile was a selective solvent for the poly(ethylene oxide) blocks, was unsuccessful even at high copolymer concentrations; instead, the wormlike cylinders showed a tendency to align. The viscosity measurements also did not show a substantial increase in the inherent viscosity. Thus, the solvent played a critical role in determining the formation of the self-assembled, wormlike-cylinder network. This formation of the network resulted from an interplay between the end-capping energy, bending energy (curvature), and configurational entropy of the self-assembled, wormlike-cylinder micelles that minimized the free energy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3605–3611, 2006


Micelles in aqueous media or mixed with organic solvents can be formed via the self-assembly of amphiphilic block copolymers.1–8 A wide range of micelle morphologies of block copolymers in solutions have been recently reported, and these morphologies possess better stability than those formed by small-molecule amphiphiles such as surfactants.9–15 These block copolymer micelles can be potentially used in specific biological and medical applications.16–18

To obtain different micelle morphologies of block copolymers in solutions, two sets of parameters need to be taken into account. The first set consists of molecular parameters associated with the block copolymer itself, such as the chemical nature (hydrophobicity or hydrophilicity) of the blocks, the block and overall molecular weights, the miscibility of the blocks, and the block copolymer architectures (linear, star, graft, etc.). The second set of parameters comes from the solution system, such as the type of solvent and solvent quality, the solvent/nonsolvent ratio, the copolymer concentration, the pH value, the additives, and the temperature. Both sets of parameters can be used to control self-assembled micelle morphologies. The micelle morphologies that have been reported by the variation of one or more of the aforementioned parameters include but are not limited to spheres, cylinders,19 wormlike shapes, helical shapes,20 bilayers, and vesicles.21

Among these self-assembled micelle morphologies, an interesting but rarely observed morphology is a wormlike-cylinder network, which consists of junctions between wormlike-cylinder micelles. To the best of our knowledge, this morphology has been reported for only two block copolymer systems. The first system that can form the network is an aqueous solution of polybutadiene-block-poly(ethylene oxide)12 with a degree of polymerization of polybutadiene of 170 and a weight fraction of poly(ethylene oxide) (PEO) of 0.34. It has also been reported for a polybutadiene-block-poly(acrylic acid) (PBD103-b-PAA75) in which the network is formed with Y-shaped junctions above a minimum additive concentration.14 The overall molecular weights in these two cases do not exceed 15,000 g/mol. Another system that forms an entangled, wormlike-cylinder network is the poly(ethylene oxide)-block-poly(propylene oxide)-block-poly(ethylene oxide) (PEO19-b-PPO43-b-PEO19) small-molecule surfactant in water when the system is heated in a water solution of this ABA triblock copolymer. An increase in the viscosity is understood to arise because of the growth and entanglement of wormlike micelles.22, 23

We have reported micelle morphological changes in a polystyrene-block-poly(ethylene oxide) (PS-b-PEO) in N,N-dimethylformamide (DMF)/water and DMF/acetonitrile, with the degrees of polymerization of the polystyrene (PS) and PEO blocks being 962 and 227, respectively. With an increasing selective solvent concentration (water or acetonitrile), the micelle morphology undergoes changes from spheres to wormlike cylinders and then to vesicles.24 In this report, we focus on the formation of a wormlike-cylinder network in the system of PS962-b-PEO227 with DMF/water. In comparison with other reported copolymers, the molecular weight of this diblock copolymer is close to 10 times higher. The wormlike-cylinder network is obtained in DMF/water in a narrow range of water concentrations and above a 0.4 wt % initial copolymer concentration. The network formation has been monitored with transmission electron microscopy (TEM) and viscosity measurements. It is surprising that such a network is not formed in the diblock copolymer in DMF/acetonitrile even though acetonitrile is also a selective solvent for the PEO blocks. In the DMF/acetonitrile system, the diblock copolymer forms wormlike cylinders that tend to align with one another at high copolymer concentrations up to 8 wt %.


Sample Synthesis and Preparation

The diblock copolymer PS962-b-PEO227 was synthesized with living anionic polymerization based on a standard route published elsewhere.25 In a brief description, the PS precursor was characterized by size exclusion chromatography (SEC) with PS standards. The number-average molecular weight of the PS blocks was 100,000 g/mol (the degree of polymerization was ca. 962), and the polydispersity was 1.03. The number-average molecular weight of the PEO blocks was determined by proton nuclear magnetic resonance to be 10,000 g/mol (the degree of polymerization was ca. 227). The polydispersity of the overall diblock copolymer was 1.04, as determined by SEC with universal calibration. The volume fraction of the PS blocks was thus 0.914. PS962-b-PEO227 was first dissolved in anhydrous DMF via stirring at room temperature for a few days to obtain stock solutions of the required copolymer concentrations. Anhydrous DMF was prefiltered with filters of a 0.02-μm pore size before the stock solutions were made. These stock solutions were then sealed with Teflon tape and stored at room temperature for future preparations of the micelles.

To prepare the micelle morphologies, both water and acetonitrile were chosen as selective solvents of the PEO blocks. The sample preparation procedures were identical to those reported in ref.24. In brief, for the DMF/water system, ∼10 mL of a stock solution was placed in a vial each time. Deionized water was added dropwise to reach a predetermined DMF and water ratio. The contents of the vial were stirred continuously to allow rapid mixing of DMF and water. Each drop added was ∼0.1 wt % water with respect to the total solution weight, and at least a 30-min gap was kept between the addition of consecutive drops. After the predetermined DMF/water ratio was reached, the solutions were sealed and left to equilibrate from 6 h to several days with mild stirring. After the solutions were equilibrated, they were left standing without stirring for at least 30 min before samples were taken for micelle morphological observations. In the DMF/acetonitrile system, a drop with ∼1 wt % acetonitrile with respect to the total solution weight was added every 10 min to the system with continuous stirring. The samples were then sealed and equilibrated at least overnight before samples were prepared for the morphological observations.

Equipment and Experiments

Observations of the micelle morphologies were performed on a Philips Tecnai transmission electron microscope with an accelerating voltage of 120 kV. To ensure that the micelle morphologies observed with TEM retained the original sizes and geometries of the solution, a small amount of the micelle solution was quenched in excess water (at least 100 times) to quickly vitrify the PS blocks to their glassy state. A drop from the quenched solution was then placed on carbon-coated TEM grids. After a few minutes, the excess solution was blotted away with filter paper. The grids were dried at room temperature and atmospheric pressure for several hours before being examined with TEM. Another method for preparing TEM samples was as follows. The quenched samples were placed in dialysis tubes and dialyzed against distilled water for 4 days to remove DMF. The distilled water was changed twice every day. The aqueous solutions were then used to prepare the samples. Both methods generated identical results in TEM experiments. Since morphological changes occurred on a much longer timescale than the quenching time,26 we believe that the morphology of the network does not change because of quenching.

Viscometric experiments were performed on a Schott–Gerate viscometry system with an Ubbelohde capillary viscometer. The time needed for the solutions to flow through the capillary was recorded and used to calculate the inherent viscosity (ηih) of the solutions by comparison with the time needed for the pure solvent to flow through the capillary. The viscometer was placed in a temperature-controlled bath at 25 °C. Meaningful comparisons could be achieved only among the viscosity values of the polymer solutions that were obtained for the systems with the same initial copolymer concentration (4 wt %) but different water and acetonitrile concentrations in the DMF/water and DMF/acetonitrile systems, respectively.


In our recent work, we reported the self-assembled micelle morphologies of PS962-b-PEO227 in DMF/water and DMF/acetonitrile mixtures. With an increasing concentration of the selective solvent (water in the DMF/water system or acetonitrile in the DMF/acetonitrile system), the micelle morphology observed with TEM changed from spheres to wormlike cylinders and then to vesicles.24

In this work, we focus on the concentrations at which the wormlike cylinders are formed in PS962-b-PEO227 in a DMF/water system. Figure 1 shows the worm network formed for a 4 wt % initial copolymer concentration and a 3.9 wt % water concentration in a DMF/water system. The network consists of self-assembled, wormlike cylinders interconnected by Y- and T-shaped junctions [Fig. 1(a)]. The wormlike cylinders are highly entangled, as shown in Figure 1(b). The network can form in a micrometer size [Fig. 1(c)], and we can also observe multiple junctions [Fig. 1(d)]. Such a network structure can be considered a counterpart of the bicontinuous structures formed in the bulk.27 This network is stable and does not change for several months if no additional water is added to the system.

Figure 1.

Worm network formed with a 4 wt % copolymer concentration and a 3.9 wt % water concentration in a DMF/water mixture: (a) Y- and T-shaped junctions, (b) the entangled network, (c) microscopic magnification, and (d) multiple junctions.

In the DMF/water system, the formation of the network of PS962-b-PEO227, as shown in Figure 1, requires a critical initial copolymer concentration, and this concentration has been determined to be 0.4 wt %. Below this critical concentration, no network appears, although some branching is visible in the wormlike cylinders. This concentration dependence is in accordance with some theoretical predictions28, 29 and experimental observations30 for network formation in small-molecule surfactants.

The network formation is accompanied by an abrupt increase in the macroscopic viscosity of the system. To quantify the magnitude of this increase, capillary viscometry measurements have been conducted. ηih has been calculated as follows:

equation image(1)

where t is the time taken by the copolymer solution to flow through the capillary, t0 is the time taken by pure DMF to flow through the capillary, and C represents the copolymer solution concentration (g/dL).31

Figure 2 shows the change in the ηih values with the addition of water to a 4 wt % initial copolymer concentration in DMF. As we have shown in our recent work,24 adding water induces micellization and morphological changes from spheres to wormlike cylinders and then to vesicles. The viscosity in this figure does not show a substantial increase within the phase morphology of mixed spheres and wormlike cylinders at relatively low water concentrations. However, when the water (which is the selective solvent of the PEO block) concentration reaches 3.9 wt %, it undergoes the micelle morphological change to the wormlike-cylinder network; the ηih value exhibits a sudden increase of over 4 times. Further increasing the water concentration leads to the vesicle morphology, in which no network is formed. The ηih value sharply decreases and returns to almost the original value because of this morphological change.

Figure 2.

Changes in ηih upon the addition of water to a 4 wt % initial copolymer concentration solution in DMF.

However, despite an extensive experimental effort, such a wormlike-cylinder network is not found in the DMF/acetonitrile system even at high copolymer concentrations (up to 8 wt %). When the copolymer concentration is increased, the wormlike cylinders tend to align parallel to one another instead of being interconnected, as shown in Figure 3. Only a mild and gradual increase in ηih can be observed at the onset of the micelle morphological changes from the mixed spheres and rodlike cylinders to the wormlike cylinders. Quantitative measurements of the viscosity values in different micelle morphologies are shown in Figure 4.

Figure 3.

Aligned cylinders with a 2 wt % initial copolymer concentration and a 34 wt % acetonitrile concentration in a DMF/acetonitrile system.

Figure 4.

Changes in ηih upon the addition of acetonitrile to a 4 wt % initial copolymer concentration solution in DMF.

If the wormlike-cylinder micelles are sufficiently long and flexible, they can behave as polymers. They can become entangled and show viscoelasticity.23 A network of wormlike cylinders that are both entangled and interconnected can increase the viscosity by two mechanisms. The mechanism of increasing the viscosity through entanglements can be compared to the increase in the polymer viscosity due to entanglements, with some limitations.23 The interconnections (the Y- and T-junctions) increase the viscosity by introducing crosslinks into the wormlike cylinders, and this can be compared to the increase in the polymer viscosity due to chemical crosslinks. However, because the crosslinks in the worm network are not chemical, it would be interesting to study its viscoelastic behavior. Also, the viscosity of a wormlike-cylinder micelle solution increases with increasing worm length.32 A worm network can be considered a wormlike cylinder with an infinite length, in contrast to individual wormlike-cylinder micelles, which would have a finite length. Thus, for an entangled and interconnected worm network (Fig. 1), in the case of DMF/water, we observe a much greater increase in the viscosity than in the case of wormlike cylinders in DMF/acetonitrile (Fig. 3).

Such a network has been observed for small-molecule surfactants and has been found to be dependent on the concentrations and temperatures.30 The network formation has also been treated theoretically by Safran et al.33 In small-molecule surfactants and microemulsions, an important concept is the spontaneous curvature, which is the “preferred curvature of the amphiphilic monolayer towards water or oil”.33 The spontaneous curvature decreases with increasing temperature and causes the morphological changes from spheres to cylinders that interconnect via junctions.30 An average curvature (H) can be defined as follows:34

equation image(2)

where R1 and R2 are the radii of curvatures in two perpendicular directions in a symmetric geometric object. If we assign positive and negative signs to R1 and R2, H can be called the net curvature. In the case of a sphere, R1 = R2 = R, and H = 1/R. A cylinder possesses R1 = R and R2 = ∞, and H = 1/(2R). When H = 0 because of R1 = −R2, it illustrates a planer bilayer or a saddle-shaped surface.

In the case of block copolymers, the formation of Y-junctions results in saddle points with a negative curvature, and thus the net curvature of the copolymer network is reduced.14 Therefore, as the Y-junctions populate, the net curvature decreases and finally leads to the formation of a network. The network is also considered to have a favorable configurational entropy because of the existence of several possible configurations of the network.35 These different configurations can be in terms of different branch lengths and branch length distributions that can exist in a network. However, there is also a loss in entropy as the free ends of the wormlike cylinders are constrained to meet at a junction.

In the wormlike-cylinder network, free ends of the wormlike cylinders (also called spherical end caps12, 30) are largely eliminated because of the formation of interconnections. Both the interfacial area per chain and degree of stretching of the core blocks are higher for the spherical geometry than for the cylindrical geometry.36 Therefore, the existence of the spherical end caps is thermodynamically unfavorable. The end-capping energy has been found to be dependent on the curvature, and it decreases as the spontaneous curvature decreases when junctions exist.30 To reduce the end caps, the wormlike cylinders may also form toroids or rings, which have been observed recently in an amphiphilic triblock copolymer system.37 Yet the ring formation requires that the wormlike cylinders should be flexible enough to bend (with a small bending energy).38

In our DMF/water system, the wormlike cylinders with a PS core may not be sufficiently flexible at room temperature because of the high vitrification temperature of the PS blocks. One of the driving forces that form the network can be hypothesized to reduce the free energy by decreasing the number of end caps to form the interconnections if the length of the wormlike cylinders is not very long. Therefore, the formation of the network is a result of interplay between the bending energy (curvature), the end-capping energy, and the network configurational entropy. One factor that influences the bending energy and the network entropy is the number density of the junctions. All these factors contribute to the free energy of the network, which can be expected to attain a configuration that will minimize the free energy. This will decide the relative appearance of end caps and junctions. In the case of block copolymers, the core chain stretching and steric interactions at the junctions and saddle-shaped surfaces also need to be considered.

However, why is this not the case in the DMF/acetonitrile system of PS962-b-PEO227? Does this imply that the end-capping energy is not too unfavorable in this system? We think that this must be associated with the PS–solvent interaction parameters. The PS–water interaction parameter is close to 9 times higher than the PS–acetonitrile interaction parameter,24 indicating that water is a much poorer solvent for PS than acetonitrile. In the DMF/water system, the cylinders should tend to reduce the net curvature by forming a network, whereas in DMF/acetonitrile, they should not. In other words, the diameter of the wormlike cylinders in the DMF/water system should be smaller than that in the DMF/acetonitrile system. However, this is not the case, as indicated by our TEM observations: the average diameter of the wormlike cylinders in the DMF/water system is 35 nm, whereas that in DMF/acetonitrile is 38 nm. Another possibility is that the wormlike cylinders that form in the DMF/acetonitrile system of PS962-b-PEO227 are long enough to downplay the density of the end caps. A further investigation is currently underway.

The branched, wormlike cylinders and network structures are also sometimes considered intermediaries between wormlike and lamellar morphologies.14 It has been observed that the morphological changes from wormlike cylinders to vesicles in PBD103-b-PAA75 occur via branched cylinders and a wormlike-cylinder network,14 whereas in the case of the crew-cut morphology of PS310-b-PAA52 in DMF/water, the change from cylinders to vesicles occurs without the formation of a network.39 In our case (block copolymer PS962-b-PEO227), when the solvent mixture is DMF/water, the change from cylinders to vesicles occurs via branched cylinders and the network, whereas in the DMF/acetonitrile solvent mixture, the change occurs without the formation of the network. Again, the solvent plays a crucial role in determining the morphological pathway of the change from cylinders to vesicles.


We have observed the formation of a self-assembled, wormlike-cylinder network for PS962-b-PEO227 in DMF/water. The network consists of entangled, self-assembled worms that are interconnected by mostly Y- and T-shaped junctions. The formation of this network is accompanied by a more than fourfold increase in ηih of the colloidal system. A similar network is not formed in the DMF/acetonitrile system, in which the wormlike cylinders tend to align, leading to only a marginal increase in ηih of the system. The concentration dependence of the network is similar to that found in small-molecule surfactants. The formation of the network is governed by interplay between the end-capping energy, the bending energy (curvature), and the network configurational entropy. The final configuration of the network should be one that minimizes the free energy. Several reasons have been suggested for the differences in the morphological behavior in these two solvent systems, and detailed work is in progress to get better insight in this respect. It is certain that the solvent plays an important role in determining the phase morphology of wormlike-cylinder micelles and the morphological pathway for the micelle changes.


This work was supported by the National Science Foundation (DMR-0516602).