Initial copolymer concentration influence on self-assembly of PS₃₈-b-P(AA₁₉₀-co-MA₂₀) in water

Abstract

The self-assembly of polystyrene-b-poly(acrylic acid-co-methyl acrylate) [PS₃₈-b-P(AA₁₉₀-co-MA₂₀)] in water was studied. The initial block copolymer concentration greatly influences the morphologies of the resulting aggregates. The morphology of the resulting micelles changes from core–shell spheres with diameter 60 nm to 60–130 nm near-spherical aggregates, and further to 70 nm hollow aggregates, when the initial polymer concentration ranges from 0.20 to 0.50 mg mL⁻¹ and further to 2.0 mg mL⁻¹. The structure of the core–shell spheres and hollow aggregates is further characterized by light scattering. It is found that the core–shell micelles and the hollow aggregates are kinetically frozen in water; the aggregation number of polymer chains N_agg and molecular weight M_W of the core–shell micelles and hollow aggregates are relatively large and the solubility of the two morphological micelles in water is poor; the structure of the core–shell spheres is incompact and the hollow aggregates is porous.

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1. Introduction

It has been known for many years that when amphiphilic block copolymers are dissolved in a selective solvent for one of the blocks, colloidal size aggregates or micelles can be formed as a result of association of the insoluble blocks.¹ Depending on the composition of the block copolymers, two types of micelles can be distinguished: star and crew-cut micelles, although there is no sharp boundary between these two classes of micelles.^2–5 The star micelles have relatively large coronas consisting of the long soluble block and relatively small cores consisting of the short insoluble block. It has been suggested that there are three major contributions to the free energy of micellization, namely the interactions in the core, in the corona, and at the core–solvent interface.³ Today, most experimental and theoretical work has been devoted to these types of micelles. Aggregates of another kind, namely crew-cuts, in which the dimension of the cores is relatively larger than that of coronas, have recently received experimental attention, and a wide range of morphologies has been observed.^6–12 Zhang and Eisenberg discussed the preparation and observation of various morphologies of aggregates made from block copolymers of polystyrene-b-poly(acrylic acid) (PS-b-PAA) with relatively long PS block.¹³ Aggregates of several different morphologies such as spheres, rods, lamellae, vesicles and large compound micelles (LCMs) etc. were prepared in a low molecular weight solvent system from the block copolymers of the same type differing only in the relative block lengths.¹³ Shen and Eisenberg also found crew-cut micelles with many morphologies such as spheres, rods, lamellae, vesicles, large compound vesicles (LCVs) and hexagonally packed hollow hoops (HHHs) etc., were formed in a ternary system of PS-b-PAA/dioxane/H₂O system.¹⁴ Compared with the various morphologies of the crew-cuts, the star micelles self-assembled by amphiphilic block copolymer generally are spherical. To the best of our knowledge, nonspherical star micelles in solution of block copolymers have been observed only rarely, and mostly indirectly. This suggests that there is still a long way to go to approach the formation of the star micelles with various morphologies.

The self-assembly of PS-b-PAA in water provides a good instance in which the existence of various morphological aggregates were formed from the same block copolymer family in low molecular weight solvents. For polystyrene-b-poly(acrylic acid-co-methyl acrylate) [PS₃₈-b-P(AA₁₉₀-co-MA₂₀)], where the subscripts represent the average number of repeat units based upon the number weight average, the total number of the repeat units is 248 and the PAA block length is much longer than the PS block. Thus, the amphiphilic block copolymer of PS₃₈-b-P(AA₁₉₀-co-MA₂₀) will possibly form star or quasi-star micelles with relatively thick shells consisting of the long soluble blocks of PAA and cores consisting of the insoluble PS block. In the present paper, we report the formation of core–shell spheres and hollow aggregates self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀), only different in copolymer concentration and then further study the structure by transmission electron microscopy (TEM) and a combination of static light scattering (SLS) and dynamic light scattering (DLS).

2. Experimental section

2.1 Synthesis of the block polymer

Polystyrene-block-poly(methyl acrylate) (PS₃₈-b-PMA₂₁₀) was synthesized by atom transfer radical polymerization (ATRP).¹⁶ The crude copolymer may contain some homopoly(methyl acrylate) and homopolystyrene. The elimination of the homopolymers was achieved by successive extraction first with methanol and then with cyclohexane at room temperature for 6 days. The polydispersity index (PDI) of PS₃₈-b-PMA₂₁₀ measured by gel permeation chromatography (GPC) was 1.28. The composition of PS₃₈-b-PMA₂₁₀ was determined by nuclear magnetic resonance (¹HNMR), from which the degree of polymerization was calculated. 2 g PS₃₈-b-PMA₂₁₀ was hydrolyzed in 50 mL 20 wt.% NaOH aqueous solution at 90 °C for 72 h. The product was deposited by slowly adding the polymer solution into 40 mL 33 vol% hydrochloric acid. The precipitate was centrifugated and washed with 5 vol% dilute hydrochloric acid and deionized water each for six times. The product was then dried at 50 °C in a vacuum oven for 24 h. The molar ratio of residual methyl acrylate units in the hydrolysate product versus the initial methyl acrylate units before hydrolysis is about 10%, indicating that about 10 mol% methyl acrylate units exist in the PAA chains. The content of the residuary methyl acrylate units was calculated from the ratio of the ¹HNMR intensities of the OCH₃ signal (at δ = 3.7) and the aromatic signal (at δ = 6.6–7.3) of the copolymers before and after hydrolysis. The block-copolymer was abbreviated as PS₃₈-b-P(AA₁₉₀-co-MA₂₀).

2.2 Preparation of the micelle solutions

The block copolymer PS₃₈-b-P(AA₁₉₀-co-MA₂₀) was first dissolved in N,N-dimethylformamide (DMF) to make a copolymer solution series with the initial copolymer concentration ranging from 0.10 to 2.0 mg mL⁻¹, respectively. Subsequently, a given volume of deionized water was added to 2.0 mL of the polymer solution with different concentrations at a rate of 1 drop (1 drop equals about 7 μL) every 10 s with stirring. As the addition of water progressed, the quality of the solvent decreased gradually. The formation of the aggregates of PS₃₈-b-P(AA₁₉₀-co-MA₂₀), as indicated by the appearance of turbidity in the solution, typically occurred when the water content reached 6–15 vol%, depending on the concentration of the block copolymer in DMF. After 2 h, the addition of water was continued until 20 vol% of water had been added. The solution series were kept for another 2 h with stirring and then 1.6 mL water was continuously added drop by drop with stirring. The solution series were kept overnight and 18.0 mL water was further added, and then the solution series were dialyzed against water for 4 days to remove DMF to produce the micelle solution series. The final polymer concentration of the copolymer solution series was in the range from 0.010 to 0.20 mg mL⁻¹, respectively.

2.3 Transmission electron microscopy (TEM) observation

TEM observation was performed on a Philips EM400ST microscopy operating at an acceleration voltage of 80 kV. For the observation of the size and distribution of the copolymer aggregates, a small drop of the micelle solution was deposited onto a copper EM grid, which had been precoated with a thin film of polyvinyl formal and then coated with carbon, and then dried at atmospheric pressure and room temperature.

2.4 Specific refractive index increment (dn/dc) measurement

The specific refractive index increment (dn/dc) was determined using the Wyatt Optilab DSP interferometric refractometer at a wavelength of 514 nm at 25 °C. Four concentrations were measured for each dn/dc determination. The dn/dc values were determined from the slope of a plot of refractive index versus polymer concentration.

2.5 Light scattering (LS) measurement

Light scattering is a convenient method of characterizing polymer solutions, which gives the hydrodynamic diameter (D_h), weight-average molecular weight (M_W), radius of gyration (R_g), and the second virial coefficient (A₂) of the particles in dilute solution.^16–19

On the basis of LS theory, for a relatively high dilute macromolecule solution or strongly interacting particles (for example, polyelectrolytes) at concentration C (g mL⁻¹) and at the scattering angle θ, the angular dependence of the excess absolute average scattered intensity, known as the excess Rayleigh ratio [R(θ,C)], can be approximated as

[KC/R(θ,C)]^0.5 = [1/M_W]^0.5[1 + (R²_gq²)/6][1 + A₂C] (1)

where K is the optical constant and K = 4π²n²(dn/dc)²/(N_Aλ⁴₀) with N_A, n, λ₀ being Avogadro's number, the solvent refractive index and the wavelength of laser, respectively, dn/dc is the specific refractive index increment, A₂ is the second virial coefficient, M_W is weight-average molecular weight, R_g is the radius of gyration, q is the magnitude of the scattering wave vector and q = (4πn/λ₀)sin(θ/2), respectively. For a given very dilute polymer solution, eqn. (1) can be expressed as

[KC/R(θ,C)]^0.5 ≈ [1/M_W]^0.5[1 + (R²_gq²)/6] (2)

After measuring R(θ,C) at a set of θ, we can determined the apparent value of gyration radius R⁰_g and after measuring R(θ,C) at a set of C and θ, we determined M_W, R_g and A₂ from the Berry plot.

On the basis of DLS theory, the intensity–intensity time correlation function G⁽²⁾(t,θ) in the self-beating mode can result in a line width distribution G(Γ). For a pure diffusive relation, G(Γ) can be converted to a translational diffusion coefficient distribution G(D) by

Γ/q² = D = D⁰(1 + f〈R²_g〉q²) = D⁰₀(1 + k_dC)(1 + f〈R²_g〉q²) (3)

where k_d is the diffusion second virial coefficient, D is the translational diffusion coefficient and f is a dimensionless number. In this study, the superscript “0” and subscript “0” indicate that q = 0 and C = 0, respectively, unless specified otherwise.

For a pure diffusive relation, G(Γ) can also be converted to a hydrodynamic radius distribution f(R_h) by using the Stokes–Einstein equation

R_h = k_bT/(6πηD) (4)

where k_b, T, and η are the Boltzmann constant, the absolute temperature and the solvent viscosity, respectively. In this study, the inversion was fulfilled by the CONTIN program supplied with the BI-9000AT digital time correlator.

In this study, DLS and SLS experiments were performed on light scattering spectrometer (BI-200SM) equipped with a digital correlator (BI-9000AT) at 532 nm. A given weight of water was first filtered with a 0.2 µ Millipore filter into a clean scintillation vial, then a given weight of the final micelle solution was filtered with a 0.8 µ Minipore filter into water in the clean scintillation vial. More than three concentrations were used to determine the weight-average molecular weight, radius of gyration, and second virial coefficient of the resulting micelles with the aid of a Debye plot. All LS measurements were performed at 25 °C.

3. Results and discussion

3.1 TEM study

Generally, star micelles can be prepared directly by dissolving a highly asymmetric block copolymer in a solvent selective for the long block or by the water addition method. However, because both the methyl acrylate units in the PAA chains and PS block in PS₃₈-b-P(AA₁₉₀-co-MA₂₀) cannot dissolve in water, the block copolymer is first dissolved in DMF, which is a common solvent for both blocks of the copolymer, to make a dilute polymer solution series. Subsequently, water is added slowly into the polymer solution with different polymer concentration to associate the polymer chains into micelles. With the addition of water into the polymer/DMF solution, micelles are formed because water is the block-selective solvent for PAA block, but a precipitant for PS block. During micellization, the insoluble PS chains form the core of the resulting micelles, while the soluble PAA chains form the shell of the micelles. At last, a large amount of water (18 mL) is added into the micelle solution, where the micelles are kinetically frozen in the water-rich solvent.^20,21

Fig. 1 shows the TEM images of the micelles self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀) with different initial copolymer concentrations. The results show that when the initial copolymer concentration is 0.10 mg mL⁻¹, the resulting micelles are spheres with diameter about 60 nm as shown in Fig. 1A. When the initial copolymer concentration increases to 0.20 mg mL⁻¹, the morphology and the diameter of the resulting micelles are similar to those in Fig. 1A, which is shown in Fig. 1B. To clearly study the spheres self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀) with initial copolymer concentration at 0.20 mg mL⁻¹, a magnified image of the spheres is inserted on the top left corner of Fig. 1B. Clearly, the spheres have a typical core–shell structure with core radius about 23 nm and shell about 8 nm. However, when the initial polymer concentration further increases to 0.50 mg mL⁻¹, near-spherical aggregates with size ranging from 60 to 130 nm are formed as shown in Fig. 1C. When the initial concentration further increases to 2.0 mg mL⁻¹, near-spherical hollow aggregates with one or more cavities are formed as shown in Fig. 1D. The hollow nature of the aggregates is evidenced from a much higher transmission in the center than the periphery of the aggregates. The size of the mono-cavity aggregates is about 70 nm and the wall thickness is about 25 nm. The size of the multi-cavity aggregates is larger than the mono-cavity aggregation, which possibly suggests the formation of a multi-cavity aggregate is due to the fusion of several mono-cavity aggregates. The hollow aggregates are similar to typical crew-cut vesicles, whereas, they are quasi-spherical and the relative wall thickness is much larger than that of typical vesicles.

Fig. 1 TEM images of the micelles self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀) with initial copolymer concentration at 0.10 mg mL⁻¹ (A), 0.20 mg mL⁻¹ (B), 0.50 mg mL⁻¹ (C) and 2.0 mg mL⁻¹ (D), respectively.

The core–shell spheres self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀) with initial copolymer concentration 0.20 mg mL⁻¹ or 0.10 mg mL⁻¹ are distinguished from crew-cut micelles by two peculiarities. The first is that the core–shell spheres have a shell as thick as 8 nm, whereas the thickness of typical crew-cut micelles or aggregates is about 1 nm or even less,¹³ which suggests that the core–shell micelles are somewhat similar to classical star micelles. The second is that the size of the core–shell spheres is larger than that of crew-cuts. We think one of the possible reasons is that more chains of the block copolymer are associated to form the large-sized aggregates when water is added into the polymer solution. The second reason is possibly due to the low initial polymer concentration. Polymer micelles are usually prepared with a higher initial copolymer concentration, i.e., about 1–3% by weight.^6–8 However, Jiang et al. found hollow spheres as large as 476 nm could be formed by the polymer mixture of polyimide and poly(4-vinyl pyridine) with concentration at 1.2 mg mL⁻¹ and the size of the hollow spheres further increased to 768 nm when the polymer concentration decreased to 0.3 mg mL⁻¹.²² It shows that low polymer concentration possibly favors formation of large-sized and incompact aggregates. The other reason is possibly due to the residual methyl acrylate units in the long chains of PAA block, which possibly affect the stretching dimension of the PAA chains, although it needs further study. On all accounts, the diameter of the core–shell spheres and the hollow aggregates is larger than typical crew-cuts, while smaller than large compound micelles (LCMs).³

3.2 LS study

Of all the micelles self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀) with different initial polymer concentration discussed above, the core–shell spheres in Fig. 1B and the near-spherical hollow aggregates with one or more cavities in Fig. 1D are the most interesting. Thus, both of the core–shell spheres and the hollow aggregates were further characterized by LS.

3.2.1 DLS study. DLS measurement can give the hydrodynamic radius R_h and the hydrodynamic radius distribution f(R_h) of the resulted micelles through measuring a series of micelle solutions with different polymer concentrations at a series of scattering angles basing on eqn. (4).

Fig. 2A shows the plot of the translational diffusion coefficient (D) of the core–shell spheres as used in Fig. 1Bversusq² at 25 °C with polymer concentration at 0.020 mg mL⁻¹. From the fit line, a translational diffusion coefficient at a given polymer concentration (D⁰) is calculated by extrapolating q² to 0. With a similar method, values of D⁰ of the core–shell spheres with polymer concentration at 0.010 mg mL⁻¹, 0.0060 mg mL⁻¹, 0.0040 mg mL⁻¹ and 0.0020 mg mL⁻¹ are calculated, which are listed in Table 1. Then further plotting D⁰ to polymer concentration C, the translational diffusion coefficient D⁰₀ is calculated by extrapolating C to 0 as shown in Fig. 2B. Based on eqn. (4), the hydrodynamic radius R⁰_h and R_h are calculated, which are shown as an insert in Fig. 2B. From the fit lines in Fig. 2B, the translational diffusion coefficient (D⁰₀) of the core–shell micelles is 3.738 × 10⁻⁸ cm² s⁻¹ and the hydrodynamic diameter (D_h) is 131.2 nm. The results are also summarized in Table 1.

Fig. 2 Plot of D of the core–shell spheres versusq² at 25 °C with polymer concentration at 0.020 mg mL⁻¹ (A) and plot of D⁰ and D_hversus polymer concentration C (B).

Table 1 Summary of D, R_h, R_g, M_W, N_agg and ρ of the core–shell spheres self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀) in water with initial polymer concentration at 0.20 mg mL⁻¹

C/mg mL^−1	D ^0/cm^2 s^−1	R ^0h/nm	D ^00/cm^2 s^−1	R h/nm	R ^0g/nm	R g/nm	R ^0g/R^0h	M W/g mol^−1	A 2/mol mL g^−2	N agg	ρ/g cm^−3
0.020	3.737 × 10^−8	65.6	3.738 × 10^−8	65.6	55.3	60.1	0.843	1.19 × 10^8	6.12 × 10^−5	6100	0.167
0.010	3.833 × 10^−8	64.0			56.4		0.881
0.0060	3.728 × 10^−8	65.8			56.2		0.854
0.0040	3.775 × 10^−8	64.9			54.1		0.834
0.0020	3.685 × 10^−8	66.5			56.2		0.845

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Fig. 3A shows the plot of the diffusion coefficient (D) of the hollow aggregates used in Fig. 1D with polymer concentration at 0.20 mg mL⁻¹versusq². Similar to the calculation methods as discussed above, the plot of D⁰ of the hollow aggregates versus polymer concentration C is calculated and shown in Fig. 3B, from which, the values of D⁰₀ and R⁰_h and R_h of the hollow aggregates in water with different copolymer concentrations are calculated. The translational diffusion coefficient (D⁰₀) of the hollow aggregates is 1.629 × 10⁻⁸ cm² s⁻¹ and the hydrodynamic diameter (D_h) is 300.8 nm, which are all summarized in Table 2.

Fig. 3 Plot of D of the hollow aggregates versusq² at 25 °C with polymer concentration at 0.20 mg mL⁻¹ (A) and plot of D⁰versus polymer concentration C.

Table 2 Summary of D, R_h, R_g, M_W, N_agg and ρ of the hollow aggregates self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀) in water with initial polymer concentration at 2.0 mg mL⁻¹

C/mg mL^−1	D ^0/cm^2 s^−1	R ^0h/nm	D ^00/cm^2 s^−1	R h/nm	R ^0g/nm	R g/nm	R ^0g/R^0h	M W/g mol^−1	A 2/mol mL g^−2	N agg	ρ/g cm^−3
0.20	1.723 × 10^−8	142.3	1.629 × 10^−8	150.4	165.9	161.9	1.17	9.74 × 10^7	−7.33 × 10^−5	5000	0.0114
0.101	1.700 × 10^−8	144.2			166.9		1.16
0.0596	1.653 × 10^−8	148.3			167.8		1.13
0.0452	1.644 × 10^−8	149.1			164.4		1.10

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Fig. 4 shows the hydrodynamic diameter distribution f(D_h) of the core–shell spheres and the hollow aggregates with the initial copolymer concentration at 0.20 mg mL⁻¹ and 2.0 mg mL⁻¹, respectively. The result shows both the hydrodynamic radii of the core–shell spheres and the hollow aggregates are narrowly distributed with the diameter ranging from 82.8 to 178.1 nm and 138.4 to 501.8 nm, respectively. The D_h of the core–shell spheres and hollow aggregates can be calculated from f(D_h) by ∫^∞₀f(D_h)D_hdD_h. Clearly, the hydrodynamic diameter of the hollow aggregates is much larger that of the core–shell spheres. The reason is partly due to the cavity nature of the hollow aggregates, which we will subsequently discuss further.

Fig. 4 The hydrodynamic diameter distribution f(D_h) of the core–shell spheres (A) and the hollow aggregates (B) with the initial copolymer concentration at 0.20 mg mL⁻¹ and 2.0 mg mL⁻¹, respectively.

It must be noted that the values of the hydrodynamic diameter of the core–shell spheres and hollow aggregates are much larger than those observed by TEM. This is because the core–shell spheres and hollow aggregates are water swollen due to the soluble PAA block, while TEM observation shows the diameter of the dried core–shell spheres and hollow aggregates.

3.2.2 SLS study. SLS measurements give the weight-average molecular weight (M_W), the gyration radius (R_g) and the second virial coefficient (A₂) through measuring a series of micelles with different concentrations at a series of scattering angles on eqn. (2). For cut–cut micelles, it is well known that crew-cut micelles of PS-b-PAA are usually kinetically frozen in water because of the glass nature of the PS block at room temperature and much shorter length of soluble PAA block in the block-selective solvent.^6,7 Thus, they usually can be studied by SLS in a very dilute solution. However, it is not easy to study the micelles self-assembled by block copolymer in an extremely dilute solution by SLS, especially for star micelles, because star micelles may not be kinetically frozen and the rate of unimer macromolecules exchange between micelles and unimer macromolecules may be relatively fast.^20,21 This means star micelles self-assembled by block copolymer may disassemble or partly disassemble to unimers in an extremely dilute solution, which will cause big error when the weight-average molecular weight M_W of star micelles is measured by SLS. For typical star micelles, to our understanding, the accurate weight-average molecular weight (M_W) can be calculated by SLS only if the aggregates are kinetically frozen. As discussed above, the hydrodynamic radius of the core–shell spheres fluctuates from 54.1 to 56.4 nm with the block copolymer concentration ranging from 0.020 to 0.0020 mg mL⁻¹. This suggests that the core–shell spheres are kinetically frozen with the polymer concentration above 0.0020 mg mL⁻¹.

Similar to the core–shell spheres, the rate of the disassembly of the hollow aggregates is also negligible with polymer concentration above 0.0452 mg mL⁻¹ at room temperature. To further confirm these, the gyration radii (R_g) of the core–shell spheres and hollow aggregates with different block concentrations are measured as in the following discussion.

Fig. 5 shows the Berry plot of [I⁻¹]^0.5 of the core–shell spheres versusq² with block copolymer concentration at 0.020 mg mL⁻¹, where I is the scattering intensity of the samples at a scattering angle θ. Thus, the gyration radius at a given block copolymer concentration (R⁰_g) can be calculated as

R⁰_g = (6S/T)^0.5 (5)

where S is the slope and T is the intercept of the fit line. The R⁰_g values of the core–shell spheres with different polymer concentrations are also calculated with a similar method as discussed above and the results are shown in Fig. 5B. Besides, the plot of the R⁰_g/R⁰_h value versus polymer concentration is also inserted in Fig. 5B.

Fig. 5 Berry plot of [I⁻¹]^0.5 of the core–shell spheres versusq² with polymer concentration at 0.020 mg mL⁻¹ (A) and plot of R⁰_g and R⁰_g/R⁰_hversus polymer concentration C (B).

From the fit lines in Fig. 5 the R⁰_g values of the core–shell spheres with different copolymer concentrations are calculated and listed in Table 1. Clearly, the R⁰_g and R⁰_g/R⁰_h values of the spheres are almost a constant while diluting the core–shell micelle solution from 0.020 to 0.0020 mg mL⁻¹, which suggests that the core–shell spheres are truly kinetically frozen. The values of R⁰_g/R⁰_h of the micelles at different polymer concentrations range from 0.834 to 0.881, which are a little bigger than that of crew-cut micelles (about 0.775),¹⁶ this means the structure of the present spheres is not as compact as typical crew-cuts, which is possibly due to the relatively long soluble PAA block swollen in water.

Similar to the core–shell spheres, Fig. 6A shows the Berry plot of [I⁻¹]^0.5 of the hollow aggregates versusq² with block copolymer concentration at 0.20 mg mL⁻¹. Similarly, the values of R⁰_g of the hollow aggregates with different polymer concentrations are also calculated and shown in Fig. 6B. The R⁰_g/R⁰_h values of the hollow aggregates with different copolymer concentrations are also calculated and the plot of the R⁰_g/R⁰_h value versus polymer concentration is inserted in Fig. 6B. All of the results are also listed in Table 2.

Fig. 6 Berry plot of [I⁻¹]^0.5 of the hollow-aggregates versusq² with polymer concentration at 0.20 mg mL⁻¹ (A) and plot of R⁰_gversus polymer concentration C (B).

Clearly, the R⁰_g and R⁰_g/R⁰_h of the hollow aggregates is also almost a constant while diluting the solution from 0.20 to 0.0452 mg mL⁻¹, which suggests that the hollow aggregates are also truly kinetically frozen as the core–shell spheres discussed above. The R⁰_g/R⁰_h values of the hollow aggregates at different polymer concentrations range from 1.10 to 1.17, which are very close to typical hollow aggregates.^19,22 This further confirms the aggregates self-assembled by PS₃₈-b-P(AA₁₉₀-co-MA₂₀) with initial polymer concentration at 2.0 mg mL⁻¹ are hollow. From these results, we suppose that the hollow aggregates in water are spherical. However, during first evaporation of water and then keeping in vacuo to observe the morphology by TEM, parts of the walls of the hollow aggregates collapse because of the large size of the hollow aggregates and thus near-spherical hollow aggregates are observed by TEM as shown in Fig. 1D.

The nature of the kinetically frozen micelles means that the M_W of the core–shell spheres and hollow aggregates can be measured accurately by SLS. Before performing the SLS measurement, the dn/dc values of the spheres and the hollow aggregates in water are measured at 514 nm at 25 °C, which are 0.320 mL g⁻¹ and 0.187 mL g⁻¹, respectively. It must be noted that there exists a little deviation when the value of dn/dc measured at 514 nm is used for the SLS calculation at 532 nm.

Fig. 7 shows the typical Berry plots of the core–shell spheres and hollow aggregates at 25 °C, where the polymer concentration ranges from 0.020 to 0.0020 mg mL⁻¹ and 0.20 to 0.0452 mg mL⁻¹, respectively. Based on eqn. (2), we have the values of M_W, R_g, A₂, from [KC/R(θ,C)]^0.5_{θ → 0, C → 0}, [KC/R(θ,C)]^0.5_C → 0versusq² and [KC/R(θ,C)]^0.5_θ → 0versusC, respectively. The static results of the core–shell spheres and the hollow aggregates are summarized in Table 1 and Table 2, respectively. The A₂ values of the core–shell spheres and the hollow aggregates are very close to 0, which suggest the solubility of the core–shell spheres and the hollow aggregates is poor. In fact, the core–shell spheres and the hollow aggregates can remain stable in water for about 3–4 months and then start to deposit onto the bottom of the flask. The values of M_W and N_agg of the core–shell spheres and the hollow aggregates are much larger than that of common micelles, which suggests the core–shell spheres and the hollow aggregates are compound micelles. The density of polymer chains of the core–shell spheres (ρ) is much lower than that of the corresponding bulk copolymer, but much higher than the copolymer chains swollen in a good solvent. This possibly reflects the packing of the insoluble PS block in the core and the stretching of the swollen PAA block in the shell. Clearly, the ρ value of the hollow aggregates is much lower than with that of the core–shell spheres, which further confirms the structure of the hollow aggregates.

Fig. 7 The typical Berry plots of the core–shell spheres and hollow aggregates at 25 °C, where the polymer concentration ranges from 0.020 to 0.0020 mg mL⁻¹ and 0.20 to 0.0452 mg mL⁻¹, respectively.

In a short summary, core–shell spheres, near-spherical aggregates and hollow aggregates are self-assembled in water when the initial polymer concentration of PS₃₈-b-P(AA₁₉₀-co-MA₂₀) ranges from 0.20 to 0.50 mg mL⁻¹ and further to 2.0 mg mL⁻¹. The structure of the core–shell spheres and hollow aggregates are characterized by TEM and LS. In comparison with crew-cut micelles, the core–shell spheres have a relative incompact structure similar to typical star micelles. The structure of the hollow aggregates is confirmed by the results that the hydrodynamic diameter of the hollow aggregates is much larger than that of the core–shell spheres, while the aggregation number of polymer chains N_agg and density of polymer chains ρ of the hollow aggregates is smaller that that of the core–shell spheres. Besides, the result that R⁰_g/R⁰_h value of the hollow aggregates is about 1.1, which is typical for hollow particles or micelles, further confirms the hollow structure.

4. Conclusions

The self-assembly of PS₃₈-b-P(AA₁₉₀-co-MA₂₀) in water was first studied by TEM. The initial block copolymer concentration greatly influences the morphologies of the resulting aggregates. The core–shell spheres with diameter about 60 nm are formed when the initial polymer concentration ranges from 0.10 to 0.20 mg mL⁻¹. The core–shell spheres have a core about 23 nm and a relatively thicker shell about 8 nm. When the initial polymer concentration continuously increases to 0.50 mg mL⁻¹, near-spherical aggregates with size about 60–130 nm are formed. When the initial polymer concentration further increasing to 2.0 mg mL⁻¹, hollow aggregates with one or more cavities are formed. The size of the hollow aggregates is about 70 nm and the wall thickness is about 25 nm. The core–shell spheres are distinguished from the typical crew-cut micelles by two peculiarities. The first is that the core–shell spheres have a relatively thick shell. The second is that the size of the core–shell spheres is larger than that of typical crew-cuts. The size of the hollow aggregates is about 70 nm. Compared with typical vesicles, the hollow aggregates have a near-spherical morphology and a relatively thick wall as large as 25 nm. The relatively large size of the resulting micelles is ascribed to more associated polymer chains in very dilute polymer concentration and the residual methyl acrylate units in the PAA block chains.

The structure of the core–shell micelles and the hollow aggregates was further characterized by DLS and SLS. The second virial coefficient (A₂) values of the core–shell micelles and hollow aggregates in water are very close to 0, which confirms the poor solubility of the two morphological micelles. Both the calculated aggregation number of polymer chains N_agg and molecular weight M_W of the core–shell micelles and hollow aggregates are relatively large, which suggest the two morphological micelles are compound micelles. The R_g/R_h value of the core–shell spheres is a little larger than that of typical crew-cut micelles, which suggests the structure of the core–shell spheres is incompact. For the hollow aggregates, the value of R_g/R_h is about 1.1 and the density of the polymer chains is much lower than that of the core–shell micelles, which confirms the hollow structure of the hollow aggregates.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 50273015) and Chinese Education Ministry Foundation for Nankai University and Tianjin University Joint Academy.

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