Polyferrocenylsilane Crystals in Nanoconfinement ... - ACS Publications

Oct 10, 2012 - Department of Chemistry, University of Toronto, 80 St. George Street, ... School of Chemistry, University of Bristol, Bristol BS8 1TS, ...
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Polyferrocenylsilane Crystals in Nanoconfinement: Fragmentation, Dissolution, and Regrowth of Cylindrical Block Copolymer Micelles with a Crystalline Core Jieshu Qian,† Yijie Lu,† Graeme Cambridge,† Gerald Guerin,*,† Ian Manners,*,‡ and Mitchell A. Winnik*,† †

Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6 School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom

‡

S Supporting Information *

ABSTRACT: Two samples of rod-like micelles in decane were prepared by seeded growth from a sample of a poly(isoprene-b-ferrocenyldimethylsilane) diblock copolymer (PI1000−PFS50, where the subscripts indicate the degree of polymerization). These micelles were uniform in length with a mass/length of 1.9 molecules/nm. The longer micelles (L-1250) had a number-average length Ln = 1243 nm, whereas the shorter micelles (L250) had Ln = 256 nm. We used transmission electron microscopy (TEM) to examine the behavior of these micelles when dilute solutions of L-1250 or L-250 or their mixtures were heated at temperatures ranging from 40 to 75 °C and then cooled to room temperature. At 55 °C, the L-1250 sample underwent kinetically controlled fragmentation to give a broad distribution of micelle lengths. At this temperature, fragmentation was much less prominent in the L-250 sample. At higher temperatures, micelles with narrow distributions of lengths were obtained in each case (Lw/Ln ≈ 1.01). This process operates under thermodynamic control, and Ln values increased strongly with an increase in temperature. These results indicate that the micelles fragment, and polymer molecules dissolve, as the samples were heated. The fraction of surviving fragments decreased significantly at elevated temperatures, presumably reflecting a distribution of crystallinity in the cores of the micelle precursor. When the solutions were cooled, the surviving fragments served as seeds for the epitaxial growth of the micelles as the polymer solubility decreased. The most striking result of these experiments was the finding that fragments formed from the L-1250 micelles had a distribution of dissolution temperatures shifted by about 5 °C to higher temperature than the shorter L-250 micelles.

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INTRODUCTION

received much less attention than polymer crystallization under nanoconfinement. In the bulk state, the confinement of the crystallizable block can be achieved by heating the block copolymer above the melting temperature (Tm) of the crystalline block but below the order−disorder transition temperature (TODT) of the block copolymer. In this range of temperatures (between Tm and TODT), the block copolymer undergoes microphase separation generating various nanoscale morphologies.1 These include spheres, cylinders, bicontinuous structures, or lamellae.2 When the segregation force of the block copolymer is weak, and both blocks are above their glass transition temperatures (Tg), the morphology that was created by phase separation is easily destroyed when the crystalline block crystallizes. This phenomenon is known as “breakout” and has been investigated extensively by Register and Ryan.3 In contrast, when the segregation force of the block copolymer is strong or the

Over the past 10−15 years, interest in polymer crystallization has broadened from the study of homopolymer crystallization to focus increasing attention on block copolymers with a crystalline block. If the second block is an amorphous polymer in the bulk state, these polymers are often referred to as “crystalline-coil” block copolymers. The reason for this interest is related to chemical differences in the polymer blocks, which leads to microphase separation in the bulk state and micelle formation in selective solvents. In both instances, crystallization is confined to domains of nanometer dimensions. Several studies have shown that these confinement effects can perturb the shape of the crystalline domains, the packing or orientation of polymer chains in the crystal, and the crystallization kinetics, an ensemble of consequences of frustrated crystal nucleation and growth. Confinement effects can also affect the properties of the crystalline phase, such as the distribution of melting points, the susceptibility to fracture, and the nature of crystal reorganization upon annealing. These features of nanoconfined polymer crystals, which are the subject of this paper, have © 2012 American Chemical Society

Received: July 16, 2012 Revised: September 17, 2012 Published: October 10, 2012 8363

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were heated and then cooled.22 They found that in solvents in which the polymer was molecularly dissolved at temperatures higher than the crystallization temperature of the PE block, worm-like micelles formed via a nucleation and growth process, with lengths controllable by varying the crystallization temperature. However, in other solvents selective for the non-PE blocks, spherical micelles formed at high temperature with an amorphous (molten) PE core. Upon cooling, crystallization took place in the confinement of the precursor micelles. Thus, spherical micelles with a semicrystalline core were formed. As a part of their study, the authors also investigated the effect of annealing on the crystalline core of worm-like micelles formed by PS340−PE700−PMMA360 (PMMA = poly(methyl methacrylate)) triblock terpolymer in toluene. Microdifferential scanning calorimetry (μDSC) annealing experiments on a 10 g/ L solution of the polymer in toluene showed that the asprepared worm-like micelles exhibited a broad melting peak ranging from 35 to 55 °C with a maximum value of 48.9 °C, while an intense and sharp peak at 50.4 °C was observed for the worm-like micelles after annealing the solution at 45 °C for 3 h. The authors attributed the increase of the main peak of melting temperature to the increase of the crystal thickness. This effect is consistent with the predictions of the Gibbs−Thomson equation.23 Moreover, the melting peak became much narrower after annealing, indicating a more uniform distribution of crystal thicknesses. PFS block copolymers exhibit a number of interesting features due to the nature of the CDSA process. For example, 1D micelles formed by these polymers undergo seeded growth.24 When a solution of a molecularly dissolved PFS block copolymer (unimer) is added to a solution of micelles of that PFS block copolymer in a selective solvent, no new micelles form. The added polymer grows epitaxially off the ends of preformed micelles to make them longer. If the added polymer has a different corona-forming chain than the micelle itself, unique structures called “block comicelles” are formed. If the micelles in the selective solvent are sonicated to form very small seed nuclei, then seeded growth leads to the formation of elongated micelles of uniform and controlled length.25 These PFS block copolymer micelles are a useful platform with which to study nanoconfinement effects on the solution behavior of 1D polymer crystals. Here we examine the behavior of rigid-rod block copolymer micelles of PI1000−PFS50 (see structure in Scheme 1) when

amorphous block is in its glassy state, crystallization is normally confined to those regions with predefined morphologies dictated by the microphase separation. The study of such confinement effects on crystalline−glassy block copolymers was pioneered by Lotz for the poly(ethylene oxide-b-styrene) (PEO−PS) system in the late 1960s.4 In the early 2000s, the Register group carried out systematic studies of the crystallization under nanoconfinement in one, two, and three dimensions, including examination of confinement effects on crystal orientation.5 This specific topic has received a lot of attention in the recent literature and has been extensively reviewed by Chen et al.6 Compared to the number of papers about crystallization of block copolymers under confinement in the bulk, there are fewer studies of the effects of nanoconfinement on the crystallization of block copolymers in solution. Early papers on micelle formation by crystalline−coil block copolymers described raft-like lamellar micelles.7 A theoretical paper by Vilgis and Halperin explained this result in terms of the tendency of polymers to form a folded lamellar structure in the crystal.8 In the late 1990s, we reported that polydimethylferrocenylsilane (PFS) diblock copolymers such as PFS50−PDMS300 (PDMS = polydimethylsiloxane, the subscripts refer to the degree of polymerization) formed rod-like micelles in hexane, a good solvent for the PDMS block.9 The surprising feature of this result was that elongated micelles formed for compositions with a long corona-forming block, normally expected to form spherical star-like micelles.10 A related polymer PI−PFS (PI = polyisoprene), in solvents selective for the PI block, formed platelet micelles when the PI chain was similar in length or shorter than the PFS block, but rod-like micelles structures were found when the PI block was longer than the PFS block.11 We argued that the one-dimensional micelles from these various PFS block copolymers with long corona chains were formed as a consequence of the crystallization of the PFS in the micelle core.12 For example, WAXS measurements of these micelles in concentrated solution13 and films formed by these micelles14 show Bragg peaks characteristic of PFS homopolymer crystallized from solution. One infers that the structure of the micelles consists of a semicrystalline PFS core (with widths on the order or 15−20 nm) surrounded by a solvent-swollen corona of the coil block. Over the past several years, other examples have been reported of block copolymers that form fiber-like micelles with a semicrystalline core.15 These examples include diblock copolymers with poly(ε-caprolactone) (PCL),16 polyacrylonitrile,17 stereoregular polylactide,18 or regioregular poly(3hexylthiophene)19 as the core-forming block. The Discher group20 reported examples of filamentous PCL−PEO block copolymer micelles with an amorphous PCL core, which subsequently crystallized in the micellar state. In contrast, Xu et al.21 reported conditions in which self-assembly of PCL−PEO diblock copolymers led directly to micelles with a semicrystalline core. We like to draw a strong distinction between crystallization following self-assembly and crystallization accompanying self-assembly. When microphase separation in solution occurs by direct conversion of soluble polymer into micelles with a semicrystalline core, we refer to the micelle formation process as “crystallization-driven self-assembly” (CDSA). Very recently, the Schmalz group examined crystallization under confinement as solutions of triblock copolymers containing a semicrystalline polyethylene (PE) middle block

Scheme 1. Structure of PI1000−PFS50 (n = 1000, m = 50)

dilute solutions of these micelles were annealed at various temperatures in decane. We compare two micelle samples of different but uniform length. An initial micelle solution was obtained by heating the polymer in decane to ca. 100 °C for 30 min. Over time, upon cooling, it formed long (5−20 μm) thin micelles with a uniform core width (TEM) of ca. 15 nm. After sonication to form fragments, followed by seeded growth, the two micelle samples were obtained. One was characterized by Ln ≈ 250 nm (Lw/Ln = 1.03), which we refer to as L-250; the other, with Ln ≈ 1250 nm (Lw/Ln = 1.01), is denoted L-1250. 8364

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mL of L-1250, which contains micelles of 250 and 1250 nm with number ratio of 3:1; a solution of L-Mix1/3 was obtained by mixing 0.2 mL of L-250 with 0.6 mL of L-1250, which contains micelles of 250 and 1250 nm with number ratio of 1:3. All the mixture solutions were diluted by decane to c = 0.0200 mg/mL, followed by heating at different temperatures for 30 min in an oil bath. TEM images were taken using a Hitachi H-7000 TEM instrument. Micelle length distributions were determined using the software program ImageJ from the National Institutes of Health. For sample L250 and L-Mix1/1, 400 micelles were traced, whereas for L-1250 and L-Mix3/1 and L-Mix1/3, 200 micelles in several images were traced in order to obtain the length distribution. The number-average micelle length (Ln) and weight-average micelle length (Lw) were calculated using eq 1 from measurements of the contour lengths (Li) of individual micelles, where N is the number of micelles examined in each sample. The distribution of micelle length is characterized by both Lw/Ln and the ratio σ/Ln, where σ is the standard deviation of the length distribution. To measure the width (d) of the micelles, 50 measurements were performed in different regions of the micelles, and values of dn and dw were calculated with equations similar to eq 1.

One anticipates that when solutions of these uniform micelles in decane are heated at high enough temperatures, the micelles will dissolve completely. New micelles will form upon cooling, with a different length and very different length distribution than the sample before heating. We find that this does indeed occur for solutions of PI1000−PFS50 micelles heated above 90 °C. Upon cooling, these solutions produced micelles that resembled those formed in the initial micelle preparation (see Figure S1A). When dilute solutions of L-250 and L-1250 micelles were heated at somewhat lower temperatures and then cooled, the behavior was more complex and much more interesting. At moderate temperatures (e.g., 55 °C), fragmentation was the dominant process, leading to shorter micelles with a broad length distribution. The length distribution for these samples was reminiscent of solvent-induced fragmentation of similar micelles described in ref 26. At somewhat higher temperatures, for example, 65−75 °C, the micelles that formed upon cooling had a narrow length distribution that not only depended upon the annealing temperature but also differed for the L-250 sample and the L-1250 sample. The change in length of the micelles is a clear indication that fragmentation was accompanied by partial dissolution of the polymer at these intermediate temperatures, followed by epitaxial deposition of the polymer on the surviving fragments as the solution cooled. A careful analysis of these data indicates the most surprising result, that fragments formed from the longer micelles had, on average, a higher dissolution temperature than those of the shorter micelles.

■

N

Ln =

■

∑i = 1 NL i i N

∑i = 1 Ni

N

Lw =

2 ∑i = 1 NL i i N

∑i = 1 NL i i

(1)

RESULTS AND DISCUSSION In the sections below, we describe the effect of thermal annealing on dilute solutions of two samples of rod-like PI1000− PFS50 block copolymer micelles, both with a narrow length distribution. These samples were prepared by seeded growth. A sample of PI1000−PFS50 block copolymer was suspended in decane, heated to ca. 100 °C to dissolve the polymer and then cooled to room temperature. The micelles formed in this way had a uniform core width (dn = 15.4 nm, dw = 15.7 nm) with lengths on the order of 5−10 μm. Two TEM images of these micelles and their width distribution histograms are presented in Figure S1 of the Supporting Information. By sonicating the solution with a 70 W ultrasonic cleaning bath, we obtained shorter micelles characterized by Ln = 58 nm and Lw/Ln = 1.10. A TEM image of the micelle seeds and their length distribution histogram are presented in Figure S2. These seeds were used for the subsequent growth of PI1000−PFS50 block copolymer micelles of controlled length. In order to obtain the L-1250 micelles, additional block copolymer (1.20 mg) dissolved in THF (0.150 mL, 8.00 mg/ mL) was added to a micelle seed solution (3 mL, c = 0.0200 mg/mL) in decane at room temperature and allowed to age for 1 week. The L-250 micelle sample was prepared similarly, by adding a smaller amount of PI1000−PFS50 block copolymer (0.210 mg) in THF (0.150 mL, 1.40 mg/mL) to an identical micelle seed solution (3 mL, c = 0.0200 mg/mL). Both samples were then diluted with decane to give solutions with an identical polymer concentration, c = 0.0200 mg/mL. Our experimental design for the thermal annealing experiments is summarized in Scheme 2. Solutions of L-1250 or L250 micelle samples, or their mixtures, were heated at a given temperature, ranging from 40 to 90 °C for 30 min and then allowed to cool to room temperature and age for 1 day. In some instances the annealing time was varied. The micelles present in the solution following this treatment were analyzed by TEM. It is useful to keep in mind, when considering the results described below, that the solubility of PI1000−PFS50 in decane increases dramatically with increasing temperature but that the concentration of free polymer molecules in solution at room temperature (ca. 23 °C) is undetectably small.26

EXPERIMENTAL SECTION

The PI1000−PFS50 (Mn = 81 600 g/mol, Mw/Mn = 1.02) block copolymer was synthesized by sequential anionic polymerization in THF and is the same sample described previously.27 A micelle solution of PI1000−PFS50 was prepared by heating a polymer sample (0.162 mg) in decane (8.10 mL, c = 0.0200 mg/mL) in a 20 mL vial at 100 °C for 30 min in oil bath on top of a hot plate. The temperature of the oil bath was controlled by an IKATRON ETS-D5 (Germany) thermometer. After heating the solutions for 30 min, the heater was turned off and the solutions were allowed to cool slowly to room temperature (the cooling rate was ∼1.5 °C/min). One day later, the solution was placed in 70 W ultrasonic cleaning bath and sonicated for 10 min at 23 °C followed by an additional 10 min at 23 °C. In this way, we obtained shorter micelles characterized by Ln = 58 nm and Lw/Ln = 1.10. We refer to the solution obtained after sonication as the “seeds” solution. In the seeded growth experiments, micelles of number-averaged length of about 1250 nm were prepared by injecting a THF solution (0.15 mL) containing PI1000−PFS50 polymer (1.20 mg) into a PI1000− PFS50 seeds solution (3 mL, c = 0.0200 mg/mL). Similarly, micelles of number-averaged length of about 250 nm were obtained by adding another THF solution (0.15 mL) containing PI1000−PFS50 polymer (0.210 mg) into a PI1000−PFS50 seeds solution (3 mL, c = 0.0200 mg/ mL). These two samples are referred to as L-1250 and L-250. These solutions were allowed to age in the dark for a week. Aliquots of the two solutions were transferred to new vials and diluted with decane to c = 0.0200 mg/mL. Aliquots (0.5 mL) of these micelle solutions were then heated at different temperatures for 30 min in an oil bath followed by slow cooling to room temperature. For a kinetics study, aliquots of the L-1250 solutions were heated at 55 and 70 °C (±0.3 °C) for different lengths of time. For preparation of micelle mixtures, 0.50 mL of each L-250 and L1250 solution was taken out and mixed together to obtain a mixture solution, denoted as L-Mix1/1, which contains both micelles of 250 and 1250 nm with the same number concentration. Similarly, a solution of L-Mix3/1 was obtained by mixing 0.6 mL of L-250 with 0.2 8365

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at ca. 1300 nm corresponds to the initial sample. We also note that there a small number of micelles with lengths greater than 1500 nm. Upon prolonged heating (24 h, Figure 1E), there were very few surviving long micelles. The main population of micelle lengths was centered at ca. 600 nm, while the micelle distribution broadened significantly (Lw/Ln = 1.16). In none of the images, however, did we observe micelles with lengths shorter than 200 nm. These kinetics measurements are summarized in Figure 1F, where we plot the decrease in Ln values over time as well as the changes in the standard deviation σ (shown as error bars in the plot) of the length distribution. The values of Ln, Lw, Lw/Ln, and σ/Ln for all four samples are presented in Table S1. The behavior of the sample at 70 °C is different. Not only have the micelles grown in length, but the length distribution has narrowed. This can be seen for the sample annealed for 30 min in the TEM image presented in Figure 2A and the corresponding histogram of the length distribution in Figure 2B. In addition, the mean length and the width of the length distribution are almost independent of annealing time. After 10 min annealing, Ln ≈ 1500 nm (cf. Figure S4), and this value increased only slightly to ca. 1670 nm at longer times. A histogram of the length distribution for 24 h annealing is presented in Figure 2C, and the time evolution of Ln and σ are presented in Figure 2D. For all of these samples, we find Lw/Ln = 1.01. Full details are collected in Table S2. Effect of Heating on the L-250 nm Micelle Sample and Comparison with L-1250. A TEM image and the length distribution histogram of the L-250 sample are shown in Figures 3A and 3D. The sample is characterized by Ln = 256 nm and Lw/Ln = 1.03. Representative TEM images of the L-250 sample after being annealed at 55 and 70 °C for 30 min are shown in Figures 3B and 3C, while the corresponding histograms of length distribution are shown in Figures 3E and 3F. For the sample annealed 30 min at 55 °C, one sees some fragmentation, but it is much less significant than for the longer L-1250 micelle sample. In the histogram of the length

Scheme 2. Drawing of Experimental Design

Effect of Heating on the L-1250 nm Micelle Sample. In order to investigate the effect of mild heating on the L-1250 nm micelle samples, we took four aliquots of a solution at c = 0.0200 mg/mL, annealed each at 55 °C for a different time (10 min, 30 min, 2 h, and 24 h) and then allowed the solutions to cool to room temperature. A representative TEM image of the L-1250 micelle sample prior to heating is shown in Figure 1A, and a length distribution histogram obtained from multiple TEM images is presented in Figure 1B. These micelles are characterized by Ln = 1243 nm and Lw/Ln = 1.01. TEM images of these four L-1250 samples annealed at 55 °C are shown in Figure S3. In these figures, one sees that the number of short micelles present on the TEM grids increased as heating time increased. In order to obtain quantitative information about the length distributions of these samples, we measured the lengths of all of the micelles in the field of view from multiple TEM images for each sample. Histograms obtained in this way are presented in Figure 1. After 10 min annealing (Figure 1C), the changes in the length distribution were small, with the appearance of a small shoulder located at shorter micelle lengths. After 30 min of annealing (Figure 1D), the main population of micelles broadened considerably. There are two peaks in the length distribution, at ca. 1300 nm and at 800 nm as well as a significant number of micelles with lengths ranging from 300 to 600 nm. It is likely that the part of the distribution with a peak

Figure 1. (A) TEM image and (B) length distribution histogram of PI1000−PFS50 micelle sample L-1250 as prepared. Scale bar is 500 nm. (B) Ln = 1243 nm, Lw/Ln = 1.01, σ/Ln = 0.109. (C−E) Length distribution histograms of sample L-1250 after being annealed at 55.0 °C for (C) 10 min (Ln = 1153 nm, Lw/Ln = 1.02, σ/Ln = 0.158), (D) 30 min (Ln = 1014 nm, Lw/Ln = 1.09, σ/Ln = 0.307), and (E) 24 h (Ln = 752 nm, Lw/Ln = 1.16, σ/Ln = 0.400). (F) Time dependence of micelle length Ln of sample L-1250 micelle after being annealed at 55 °C. (The error bars are the standard deviations σ in length for each sample as determined from the histograms of the length distribution. The solid line is a guide for the eye.) 8366

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Figure 2. (A) TEM image of PI1000−PFS50 micelle sample L-1250 after being annealed at 70 °C for 30 min; scale bar is 500 nm. (B, C) Length distribution histograms of L-1250 after being annealed at 70 °C for (B) 30 min (Ln = 1686 nm, Lw/Ln = 1.01, σ/Ln = 0.098) and (C) 24 h (Ln = 1661 nm, Lw/Ln = 1.01, σ/Ln = 0.087). (D) Time dependence of micelle length Ln of sample L-1250 micelle after being annealed at 70 °C. (The error bars are the standard deviations σ in length for each sample as determined from the histograms of the length distribution. The solid line is a guide for the eye.)

Figure 3. (A−C) TEM images of PI1000−PFS50 micelle sample L-250 as prepared and L-250 after being annealed at (B) 55.0 °C and (C) 70.0 °C for 30 min. (Scale bars are 500 nm.) (D−F) Histograms of the length distribution of the corresponding micelles are shown in (A−C). (D) Ln = 256 nm, Lw/Ln = 1.03, σ/Ln = 0.160, (E) Ln = 245 nm, Lw/Ln = 1.06, σ/Ln = 0.249, and (F) Ln = 542 nm, Lw/Ln = 1.02, σ/Ln = 0.149.

distribution, one also sees evidence for the formation of some micelles longer than those in the initial sample, suggesting that some of the polymer dissolved at this temperature and deposited on the ends of remaining micelles as the solution was cooled. As we saw for the L-1250 micelle sample, annealing the L-250 sample at 70 °C for 30 min led to an increase in micelle length as well as a narrowing of the length distribution. To compare the results for the L-1250 and L-250 nm micelle samples, we plot Ln (and σ) versus annealing temperatures (30 min at 40−75 °C) in Figure 4 and compare these values to those of the initial samples at room temperature. For this experiment, the annealed samples were aged for 1 day at room

temperature before samples were taken for TEM analysis. One can see that when the micelle solutions were heated at 40 °C, changes in length and length distribution were negligible. At 55 °C, shorter micelles with a broader length distribution were obtained, and this effect was much more prominent for the longer micelles. When the solutions were heated at higher temperatures (65−75 °C), longer micelles were obtained with a very narrow length distribution. When experiments were carried out at higher annealing temperatures, (≥80 °C), longer micelles formed, but they were too long to obtain accurate length information from their TEM images. 8367

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conditions, two processes operate in parallel. The micelles undergo kinetically driven heat-induced fragmentation along with thermodynamically driven dissolution of polymer molecules. The signature of polymer dissolution is that, upon cooling the solution, some of the micelles become longer than in the initial sample. There is a suggestion in Figure 1D that some polymer dissolved at 55 °C. We imagine that at 70 °C fragmentation is more rapid than at 55 °C, but it is accompanied by polymer dissolution. The increase in micelle length and narrowing of the length distribution indicates that a large fraction of the micelle fragments dissolved completely, leaving a smaller number of seeds for micelle growth upon cooling of the solution. In their 1968 classic study of self-seeding,29 Blundell and Keller showed an example of a polyethylene single crystal in xylene that fragmented as the solution was reheated. Thus, they were the first to report the temperature-induced fragmentation of crystals during a self-seeding experiment. Our results on the fragmentation of PI1000−PFS50 block copolymer micelles, with a semicrystalline PFS core should be viewed in this context. We find, for example, that fragmentation of PI1000−PFS50 micelles is very sensitive to their length: The seed micelles obtained by sonication showed no signs of fragmentation upon heating. For the L-250 sample, fragmentation was detected but was not particularly prominent. But for the L-1250 sample, fragmentation was significant when the micelle solutions were annealed at 55 °C. These results are consistent with a sonication study of the fragmentation rate (kf) for PFS48−PI264 block copolymer micelles, which showed that kf ∼ L2.6,32 i.e., a strong decrease in fragmentation rate with a decrease in micelle length. Deeper insights are possible into the fragmentation− dissolution process on heating and subsequent micelle regrowth on cooling. To obtain this information, we plot in Figure 5A the ratio of the initial Ln values for the L-250 and L-1250 samples to the values obtained (final Ln) after annealing at different temperatures. The values of 1.0 at 25 and 40 °C are consistent with no change in the sample under these mild conditions. Values greater than 1.0 at 55 °C for L-250 and at 55, 60, and 65 °C for L-1250 indicate that there were more micelles of overall shorter length. (The comparison of the length distribution histograms for the L-250 and L-1250 samples after annealing at 60 °C for 30 min is shown in Figure S5.) That is to say that fragmentation dominated over polymer dissolution under these conditions. At higher temperatures, longer micelles (with a narrow length distribution) were formed and this ratio decreased substantially. We have previously argued that in this type of self-seeding experiment all of the polymer that dissolved upon heating became incorporated into the micelles on cooling.28 This argument was based on findings that the critical micelle concentration for these PI1000−PFS50 block copolymer micelles at room temperature was undetectably small.26 From this perspective and the known value of the mass per unit length of the micelles (1.9 polymer molecules/nm),27 we can calculate from Ln the number concentration of micelles present in each solution. These values are plotted in Figure 5B. The data in Figures 5A,B make it clear that the presence of longer micelles formed on cooling is a direct consequence of fewer micelles in the sample. During the heating stage, micelles fragment, polymer dissolves, and the number of fragments that can serve to nucleate micelle growth decreases. This effect is particularly prominent for samples annealed at T > 60 °C. We imagine that there is a distribution of degrees of crystallinity

Figure 4. Mean micelle length Ln versus heating temperatures for (A) L-250 and (B) L-1250 annealed for 30 min. The error bars are the standard deviations σ for each sample calculated from the histograms of the length distributions.

In Table S3, we have compiled values of Ln, Lw, Lw/Ln, and σ/Ln for the L-1250 samples, as prepared and after annealing at each of the six temperatures shown in Figure 4. Corresponding values for the L-250 samples are presented in Table S4. In a previous report,28 we described the behavior of solutions of the micelle seeds themselves when solutions in decane were annealed at various temperatures ranging from 40 to 90 °C followed by cooling to room temperature. In those experiments, we found that long micelles were formed, with Ln values that increased sensitively with even small increases in annealing temperature and with a narrow length distribution for each sample. To explain this increase in length, we drew an analogy to the phenomenon of “self-seeding” of crystalline polymers29−31 and hypothesized that the small micelles of the original sample were characterized by a distribution of dissolution temperatures. As the temperature was increased, more polymer dissolved, accompanied by the disappearance of a larger fraction of the original short micelles. Upon cooling the sample, the polymer in solution grew epitaxially onto the ends of the remaining micelle seeds. Fewer seeds led to longer micelles. In keeping with recent findings about the self-seeding behavior of semicrystalline polymers,31 we found that there was an exponential decrease in the fraction of remaining seeds with an increase in annealing temperature. We also found that the mean length of the micelles and its length distribution were independent of the annealing time. Thus, this one-dimensional self-seeding growth process, like the more conventional crystalline polymer systems studied by Reiter and co-workers,31 operated under thermodynamic, rather than kinetic, control. Fragmentation and Dissolution upon Heating and Regrowth upon Cooling. The results in Figures 1 and 2 show that when longer micelles are subjected to self-seeding 8368

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Mix3/1 (L-250/L-1250 = 3:1), L-Mix1/1, and L-Mix1/3, respectively. All solutions were then diluted with decane to c = 0.0200 mg/mL. Representative TEM images of these samples before and after heating are presented in Figure S6, with corresponding histograms in Figure S7. The images obtained from the newly prepared mixtures show the coexistence of L250 and L-1250 micelles. We constructed histograms of the length distributions from these images and calculated mean values and length distributions of the mixtures, obtaining Ln = 518 nm and Lw/Ln = 1.72 for the L-Mix3/1 sample, Ln = 735 nm and Lw/Ln = 1.47 for the L-Mix1/1 sample, and Ln = 1041 nm and Lw/Ln = 1.17 for L-Mix1/3. The Ln values of these mixtures are very close to the theoretical number-average length due to the mixing of the L-250 and L-1250 samples. These micelle solutions were very stable. We did not observe any noticeable change in the length or the length distribution of these samples stored at room temperature over a time scale of months. Samples of these mixtures were then heated at different temperatures for 30 min and then allowed to cool to room temperature and age for 1 day. Representative TEM images of the three micelle mixture solutions after being annealed at 55 and 70 °C are shown in Figure S6 with the corresponding histograms of length distribution shown in Figure S7. We summarize these results on the effect of the heating for each of the micelle mixtures in Figures 6A−C, where we plot Ln versus heating temperature. The values of Ln, Lw, Lw/Ln, and σ/Ln for these samples after being annealed at each temperatures are presented in Table S5 (L-Mix3/1), Table S6 (L-Mix1/1), and Table S7 (L-Mix1/3) in the Supporting Information. A number of key observations can be made from the data in Figure 6. The first is that at 25 and 40 °C the bimodal populations remain intact. This observation indicates that neither fragmentation nor polymer dissolution takes place to any significant extent at these temperatures. The second important observation comes from the results at 55 °C. Here one observes a merging of the micelle length distributions. From the histograms of the length distribution presented in Figures S7B,E,H, one can see that this broadening is primarily a consequence of the fragmentation of the L1250 sample. At 60 °C, the distributions are still broad but they start to narrow. The contour length distributions sharpened considerably at 65 °C for all three mixtures and remained sharp at higher temperatures. Values of Ln increased strongly for higher annealing temperatures. To obtain deeper insights into the behavior of the mixed samples upon annealing, in Figure 7 we plot values of Ln against the number fraction f(L-1250) of L-1250 micelles in the sample. Separate curves are plotted for data obtained annealing temperatures of 65, 70, and 75 °C. In Figure 7A, the x-axis describes the number fraction of L-1250 micelles in the mixture as prepared at room temperature before annealing. The values at x = 0 refer to the L-250 sample itself, and the values at x = 1 refer to the L-1250 sample. One of our goals in carrying out this analysis was to test the idea that micelles and fragments from the L-1250 sample and from the L-250 sample had different distributions of dissolution temperatures. If the number fraction of L-1250 in the L-1250/L-250 mixtures was not temperature dependent, one would expect Ln to be a linear function of f(L-1250). For example, values of Ln calculated from the bimodal mixtures of L-1250 and L-250 depicted at 25 and 40 °C in Figure 6 vary linearly with initial sample composition (see Figure S8).

Figure 5. (A) Ratio of the initial Ln value for the micelle sample to that obtained (final Ln) after annealing for 30 min at the temperature indicated, followed by cooling to 23 °C. (B) The number concentration of micelles present in samples L-1250 and L-250 after they were heated for 30 min and cooled to 23 °C. For all samples, the total polymer concentration c = 0.0200 mg/mL. Sample L-1250 refers to micelles with initial length of ca. 1250 nm before heating, while sample L-250 refers to micelles with initial length of ca. 250 nm before heating.

among the fragments and that this translates into a distribution of dissolution temperatures. Annealing at elevated temperatures leads to an increase in the fraction of the fragments that dissolve and a decrease in the number of fragments that survive. One can read the y-axis in Figure 5B as a measure of the number concentration of micelle fragments in the sample that survive annealing at each temperature and serve as nuclei or seeds for micelle growth when the solution is cooled. From this perspective, one gets a very interesting insight into the difference in behavior of the L-1250 and L-250 micelle samples. The curve for L-1250 in Figure 5A is shifted to about 5 °C higher temperature than that for L-250. There is a similar effect in Figure 5B. The implication of this shift is that the distribution of dissolution temperatures for L-1250 micelles and their fragments is shifted by about 5 °C to higher temperatures compared to that for L-250 micelles and their fragments. This result suggests that the longer micelles have a somewhat higher degree of crystallinity than their shorter counterparts. Preparation and Effects of Heating on 1250 and 250 nm Micelle Mixtures. In order to test some of the ideas presented above and to obtain further insights into the behavior of PI1000−PFS50 block copolymer micelles when subjected to self-seeding conditions, we examined mixtures of the L-250 and L-1250 micelle samples in decane. At room temperature we prepared three mixtures of the two types of micelles. These solutions contain different number ratios (3:1, 1:1, and 1:3) of L-250 and L-1250 micelles. We refer to these solutions as L8369

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Macromolecules

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Figure 7. Plots of the measured value of Ln vs the number fraction of L-1250 micelles ( f(L-1250)) in the L-1250/L-250 micelle mixture in decane following annealing at 65, 70, and 75 °C. In (A), the value of f(L-1250) was calculated for the sample as prepared. In (B), the value of f(L-1250) was calculated from the data in Figure 5B as described in the text. The lines are intended as guides for the eye. In (B), the dashed lines indicate the change in the value of f(L-1250) as a consequence of annealing the sample at each particular temperature. Sample L-1250 refers to micelles with initial length of ca. 1250 nm before heating, while sample L-250 refers to micelles with initial length of ca. 250 nm before heating.

Figure 6. (A−C) Mean micelle length Ln versus heating temperatures for (A) L-Mix3/1, (B) L-Mix1/1, and (C) L-Mix1/3 (L-250/L-1250) solutions annealed for 30 min. The error bars are the standard deviations σ for each sample calculated from the histogram of the length distributions. In (A−C), at low temperatures (25 and 40 °C), the samples contain two sharp populations with narrow length distribution. The open circles with no error bar represent the mean length calculated for these bimodal samples.

We do not have a definitive answer to the question of why fragments of the longer micelles have a higher dissolution temperature than those of the shorter micelles. As a hypothesis for future consideration, we propose that the dissolution temperature is related to the length of the micelle fragments and that the fragments formed by the L-1250 micelle sample are longer at each temperature than those of the L-250 sample. As a qualitative test of this idea, we compared our findings reported here with the dissolution temperatures found for the initial seed micelle sample with Ln = 58 nm and Lw/Ln = 1.10. Here the distribution of dissolution temperatures appeared to be a few degrees lower than that of the L-250 sample, consistent with our hypothesis. More definitive insights may become available from quantitative modeling of the fragmentation−regrowth process. Attempts to develop this kind of model are currently underway.

When one examines the lines drawn through the data points in Figure 7A, the fits are not very good. We obtain correlation coefficients of r2 = 0.973 at 65 °C, 0.954 at 70 °C, and 0.875 at 75 °C. It appears that curved lines would give a better fit to these data. An alternative approach to plotting these data involves calculating values of f(L-1250) at each temperature from the data in Figure 5B. This calculation assumes, as we have shown above, that the number concentration after cooling is equal to the number of surviving seeds at the annealing temperature before cooling. Using these new values of f(L1250), we replot Ln vs f(L-1250) in Figure 7B. The plots in Figure 7B provide better linear fits (r2 = 0.989 at 65 °C, 0.988 at 70 °C and 0.969 at 75 °C) than those in Figure 7A. The enrichment of each mixture in fragments from the sample L-1250 is also emphasized by the dashed lines that connect the data points in Figure 7B. These lines slope to the right and indicate the extent to which the magnitude of f(L1250) increased as the annealing temperature was varied from 65 to 75 °C.

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SUMMARY AND CONCLUSIONS The block copolymer PI1000−PFS50 forms fiber-like micelles in decane with a semicrystalline PFS core of uniform width (d ∼ 15 nm) surrounded by a corona of PI chains. We examined the properties of two micelle samples of uniform length, L-250 8370

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Figure 8. Fragmentation and dissolution of a 1:1 mixture of L-250 and L-1250 PI1000−PFS50 micelles when their solution in decane is heated to 70 °C and then cooled to room temperature. The longer micelles fragment extensively at 55 °C, and we imagine that both micelles fragment at 70 °C, accompanied by dissolution of the least crystalline fragments. Upon cooling, all of the polymer in the sample grows epitaxially off the ends of the surviving seeds.

characterized by Ln = 256 nm and Lw/Ln = 1.03 and L-1250 characterized by Ln = 1243 nm and Lw/Ln = 1.01, when dilute solutions of the micelles in decane were annealed at various temperatures between 40 and 75 °C and then allowed to cool to room temperature. The micelles were stable at room temperature and at 40 °C. At 55 °C, the micelles in the longer sample underwent kinetically controlled fragmentation to form shorter micelles with a broader length distribution. At this temperature, fragmentation of the L-250 sample could be detected but was less prominent. Heating to higher temperatures, from 65 to 75 °C, led to the formation of longer micelles with a narrow length distribution. Here the micelle length depended sensitively on annealing temperature but not on the annealing time. This thermodynamic control of micelle length in the range of 65−75 °C is consistent with the process of self-seeding, in which micelle fragments have a distribution of dissolution temperatures, and a larger fraction of the polymer sample dissolved as the annealing temperature was increased. When the samples were cooled, the polymer that dissolved when the samples were heated condensed on the ends of the remaining fragments, which acted as seed micelles for epitaxial growth. Because the CMC of the polymer is undetectably small at room temperature, we infer that all of the polymer in the sample became incorporated into the elongated micelles. The formation of longer micelles implied the survival of few fragments to act as seeds. Assuming that the mass per unit length of these micelles (ca. 2 block polymer molecules per nm) is independent of their length, we could calculate from the micelle length the number of micelles present in each sample after annealing. By inference, the number corresponds to the number of micelle fragments present at the annealing temperature prior to cooling. This analysis led to the surprising result that the dissolution temperature for the fragments formed from the shorter (L250) micelles was about 5 °C lower that that of the fragments formed by the longer (L-1250) micelle sample. Each sample is characterized by a distribution of dissolution temperatures, and the proper conclusion is that the distribution of dissolution temperatures is shifted by about 5 °C to lower temperatures for the shorter micelles. To confirm this idea, we subjected three mixtures of the L-250 and L-1250 micelles to the self-seeding conditions. Again these results indicated a lower dissolution temperature for the micelles or micelle fragments of the shorter micelle sample. We summarize our view of the fragmentation−dissolution process in Figure 8, depicted for a 1:1 mixture of the L-250 and L-1250 micelles. While the longer micelles fragment at 55 °C, it

is likely that both types of micelles undergo more extensive fragmentation at higher temperature. Regrowth takes place when the samples are cooled. The final length of the micelles is determined by the number of fragments that persist at the annealing temperature and the total concentration of polymer in the sample (constant for all samples).

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ASSOCIATED CONTENT

S Supporting Information *

TEM image of long micelles formed by the self-assembly of PI1000−PFS50 in decane and their width distribution histogram (Figure S1); TEM image of seed micelles for seeded growth and its length distribution histogram (Figure S2); TEM images of L-1250 sample being heated at 55 °C for different lengths of time (Figure S3); histogram of L-1250 after being annealed at 70 °C for 10 min (Figure S4); histograms of L-250 and L-1250 after annealing at 60.0 °C for 30 min (Figure S5); TEM images (Figure S6) and corresponding histograms (Figure S7) of mixtures of L-250 and L-1250 and samples after annealing; plots of Ln vs the f(L-1250) of mixture samples after being annealed at 25 and 40 °C (Figure S8); and tables (Table S1− S7) that collect length information on all samples that have been described in this paper. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (G.G.), Ian.Manners@ bristol.ac.uk (I.M.), [email protected] (M.A.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the Natural Sciences Engineering Research Council of Canada for their support of this research. I. M. thanks the EU for a European Research Council (ERC) Advanced Investigator Grant.

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