Spherical Micelles with Nonspherical Cores: Effect of Chain Packing on the Micellar Shape

Abstract

Self-assembly of amphiphilic polymers into micelles is an archetypical example of a “self-confined” system due to the formation of micellar cores with dimensions of a few nanometers. In this work, we investigate the chain packing and resulting shape of C_n-PEOx micelles with semicrystalline cores using small/wide-angle X-ray scattering (SAXS/WAXS), contrast-variation small-angle neutron scattering (SANS), and nuclear magnetic resonance spectroscopy (NMR). Interestingly, the n-alkyl chains adopt a rotator-like conformation and pack into prolate ellipses (axial ratio ϵ ≈ 0.5) in the “crystalline” region and abruptly arrange into a more spheroidal shape (ϵ ≈ 0.7) above the melting point. We attribute the distorted spherical shape above the melting point to thermal fluctuations and intrinsic rigidity of the n-alkyl blocks. We also find evidence for a thin dehydrated PEO layer (≤1 nm) close to the micellar core. The results provide substantial insight into the interplay between crystallinity and molecular packing in confinement and the resulting overall micellar shape.

Introduction

The self-assembly of polymers and the resulting multitude of different nanostructures have found application in a range of fields.¹⁻³ Generally, association is driven by a reduction in the surface energy, in water notably by the hydrophobic effect.⁴ However, other driving forces such as electrostatic interaction (“coacervation”)⁵ or crystallization may also be involved. The latter is being exploited to create novel nanostructures in crystallization-driven self-assembly (CDSA).⁶⁻¹⁰ Crystallization, or at least packing into semiordered structures, is also important in more complex systems such as in the cell membrane.¹¹

To better understand complex phenomena, it is customary to employ simpler, well-defined model systems. An excellent example is n-alkyl-functionalized poly(ethylene oxide) (C_n-PEOx) polymers, where the index n denotes the number of carbon atoms in the n-alkyl block and x the PEO molecular weight in kg/mol (compare Figure 1a). These polymers have been used as model materials to investigate fundamental properties of nonionic amphiphilic block copolymers. When dissolved in water, C_n-PEOx forms well-defined micellar entities. The highly hydrophobic, core-forming n-alkyl blocks represent the simplest hydrocarbons and are uniform (”monodisperse”). The hydrophilic, shell-forming PEO blocks, on the other hand, are chemically stable and are synthesized with very low polydispersities (Đ < 1.05) by sophisticated living polymerization techniques. Therefore, C_n-PEOx has been employed extensively to investigate phenomena like micellar aggregation behavior,¹²⁻¹⁹ molecular exchange kinetics,²⁰⁻²⁴ or macroscopic rheology.^25,26 A peculiar feature of C_n-PEOx with n ≥ 18 is (partial) core crystallization below a certain temperature as observed via differential scanning calorimetry (DSC), nuclear magnetic resonance spectroscopy (NMR), and density measurements,²⁷⁻²⁹ which may affect micellar structures and properties. For instance, Plazzotta et al. found that core freezing lead to segregation in a mixture of C₁₈-PEO1 and C₁₈-PEO5, even though the core blocks were identical.³⁰ The same group later exploited core freezing to trigger the release of a hydrophobic cargo from the micellar core.³¹ However, the exact nature of the crystalline phase and how optimal packing is achieved in a confined state within a nanometer-sized micellar core are still open questions, in particular, how the conformational and spatial order affects the overall morphology of the micelles.

Figure 1.

(a) Chemical structure of C_n-PEOx. (b) Sketch to illustrate the scattering model. (c) Sketch of the local polymer volume fraction assumed in the model.

We recently reported on the effect of core crystallization on the molecular exchange kinetics between C_n-PEOx micelles.^21,23 Surprisingly, the effect is rather straightforward: In crystalline samples, the melting enthalpy is simply added to the thermal (hydrophobic) activation energy of the respective molten sample, and the melting enthalpy can easily be tuned by coassembling C_n-PEOx with different n-alkyl block lengths.¹⁹ However, it is not yet clear what kind of order the n-alkyl chains adopt in the crystalline core. In bulk crystalline phases, n-alkane molecules align in parallel and arrange in an all-trans conformation. In addition, there is a second solid-like phase before the actual melting transition, the so-called rotator phase. Here, the n-alkane molecules retain their parallel orientation but gain a rotational degree of freedom around the longitudinal axis.³² Both phases are suitable candidates for the state of the C_n-PEOxn-alkyl blocks in solidified micellar cores. However, in our previous works where the structure of C_n-PEOx micelles was examined, we assumed that the core was spherical even though it is unclear how crystallized, all-trans n-alkyl chains can arrange in a spherical domain.

In the present paper, we address this issue using scattering techniques in combination with NMR spectroscopy. Wide-angle X-ray scattering (WAXS) yields information about the spatial order of the n-alkyl chains in both molten and crystalline condition within the micellar cores. We use small-angle neutron scattering (SANS) with contrast matching and detailed modeling of micellar form factors to determine the shape of the core. In addition, line width analysis of regular ¹H solution NMR spectra gives an idea about the general chain mobility while ¹³C solid-state NMR (ssNMR) reveals further details: ¹³C chemical shifts indicate the n-alkyl isomerization, all-trans vs trans-gauche. In the liquid phase, overall anisotropy and the rate of CH bond reorientation are quantified by the order parameter S_CH, whereas in the solid phase the dispersion of the relaxation rate in the rotating frame R_1ρ sheds light on the correlation time τ_c.

Experimental Section

Synthesis

The C_n-PEOx polymers were prepared via ring-opening living anionic polymerization of ethylene oxide (EO) in toluene. Details of the synthesis were extensively presented in previous articles.^15,33 Besides the ordinary proteated C_n-hPEOx, deuterated and partly deuterated polymers were synthesized following the same protocol. Fully deuterated C₂₂-dPEO5 was prepared from d-EO and partly deuterated C₂₈-dhPEO5 from a 82/18 molar mixture of d- and h-EO, leading to a random distribution of monomers along the PEO chains.

The polymers were characterized by size-exclusion chromatography (SEC) using a multidetector chromatographic setup consisting of an autosampler, an isocratic pump (both Agilent Technologies, Series 1260 infinity), a column oven (Shimadzu CTO-20A), a refractive index (RI) detector (Optilab rEX), and an 18 angle light scattering detector (DAWN HELEOS-II), both detectors from Wyatt Technologies, for absolute molar mass determination. The polydispersities were determined to be Đ ≤ 1.04 for all polymers. As a consistency check, M_n of the proteated polymers was additionally calculated from ¹H NMR spectra measured in deuterochloroform. The polymer characteristics are specified in Table 1.

Table 1. Polymer Characteristics.

polymera	NPEOb	Mnb (g/mol)	Mnc (g/mol)	Mwc (g/mol)	Mw/Mnc
C28-dhPEO5d	102	5240	5130	5260	1.03
C28-hPEO3e	53	2750	2670	2780	1.04
C28-hPEO5e,f	110	5250	5240	5150	1.02
C22-dPEO5g	118		5980	6100	1.02
hPEO5e,g,h			5000i
hPEO3e,h			3000i

^ah: proteated; d: deuterated; dh: partially deuterated.

^bFrom NMR.

^cFrom SEC.

^dUsed in SAS experiments.

^eUsed in WAXS experiments.

^fUsed in ¹³C NMR experiments.

^gUsed in ¹H NMR experiments.

^hCommercial product of Sigma-Aldrich.

ⁱSupplier specification.

Sample Preparation

For all samples in this work, dry polymer powder was dissolved in H₂O or D₂O. Ultrapure H₂O (18.2 MΩ cm) was taken from a Millipore water purification system, and D₂O with 99.90% D was purchased from Eurisotop, France. To ensure well-equilibrated, homogeneous samples, the solutions were shaken for at least 1 h at 70 °C, well above all relevant melting points, and then left to cool overnight at room temperature while still being shaken. For SANS measurements, C₂₈-dhPEO5 with 82% dEO content was dissolved in D₂O, which is very close to the dhPEO match point. Volume fractions of ϕ = 0.5 and 4 vol % were prepared and used also for SAXS to ensure consistent measurements of the two complementary methods. For the WAXS study, the polymers were dissolved in H₂O at volume fractions of ϕ = 5 vol %. ¹H NMR spectra of C₂₂-dPEO5 were recorded in D₂O at ϕ = 0.5 vol %. Traces of 3-(trimethylsilyl)-2,2,3,3-tetradeuteropropionic acid (TMSP-d₄, Sigma-Aldrich) were added to calibrate the chemical shifts. For comparison, a measurement in deuterochloroform was done at a similar concentration. Solid-state ¹³C NMR experiments were performed on a 50 vol % gel sample prepared from C₂₈-hPEO5 in D₂O. The gel was obtained by directly dissolving the polymer powder in D₂O. Homogenization was achieved by several heating (to 70 °C) and centrifugation cycles—in between turning the vial upside down. In a previous work we could successfully demonstrate that this procedure leads to micelles identical with those at low volume fractions.³³ The transparent gel was then transferred into a disposable magic angle spinning (MAS) insert purchased from Bruker.

Small-Angle Neutron Scattering

Small-angle neutron scattering (SANS) experiments on C₂₈-dhPEO5 in D₂O were performed at the time-of-flight instrument Sans2d at the STFC ISIS Neutron and Muon Source in Didcot, United Kingdom,^34,35 using neutron wavelengths λ = 2–14 Å. At a detector distance of 4 m, this allowed to cover a Q range of about 0.004–0.7 Å^–1, where Q = 4π sin(2θ/2)/λ is the scattering vector and 2θ is the scattering angle. The collection time was 50 min per sample and temperature. To follow the structural evolution of the core during melting, measurements were done between 40 and 70 °C, well below and above the melting temperature of T_m = 57 °C. The scattering patterns were reduced and background-corrected according to instrument standard procedures. To avoid structure factor contributions, measurements were done in dilute solution at 0.25 vol %. Complementarily, a 4 vol % sample was measured to improve the scattering statistics at high Q, where the structure factor contribution is negligible. Both data sets were normalized by concentration—which yielded a perfect overlap at intermediate Q—and then combined to obtain the pure form factor with high signal-to-noise ratio over the entire Q range.

Small-Angle X-ray Scattering (SAXS)

SAXS experiments were performed at the in-house Bruker NanoStar instrument at the Norwegian Centre for X-ray Diffraction, Scattering and Imaging (RECX) at the University of Oslo, Norway, using Cu Kα radiation of λ = 1.54 Å. The instrument covers a Q range of 0.009–0.3 Å^–1, and the collection time was 60 min. The exact same samples from the SANS beamtime were measured at both 40 and 70 °C to provide reference scattering patterns with PEO contribution, both below and above the core melting transition. Data reduction and background correction were performed according to instrument standard procedures, and the high- and low-concentration measurements were combined in the same way as for the SANS measurements.

Wide-Angle X-ray Scattering (WAXS)

WAXS experiments were performed at beamline ID02 (ESRF, France) using an X-ray energy of 12.46 keV (wavelength λ = 0.995 Å). The WAXS detector (Rayonix LX-170HS) permits to cover a Q range of approximately 0.5 Å^–1 < Q < 5.0 Å^–1.

¹H Nuclear Magnetic Resonance Spectroscopy

Conventional solution proton nuclear magnetic resonance spectroscopy (¹H NMR) was performed at the University of Oslo NMR Center using a Bruker Avance I 600 MHz NMR spectrometer equipped with a TCI cryo probe. The program Topspin 2.1 (patch level 6) was used for both acquisition and processing. C₂₂-dPEO5 samples dissolved in D₂O and CDCl₃ at ∼0.5 vol % were measured in standard 5 mm NMR tubes in a temperature range T = 10–50 °C (T_m = 29 °C). In D₂O, minute amounts of TMSP-d₄ were used to calibrate the chemical shifts, whereas in deuterochloroform the residual CHCl₃ signal at 7.24 ppm was used. After the set temperature was reached, the spectrometer was shimmed and the sample left to equilibrate for 10 min before a second round of shimming as well as tuning and matching were performed, followed by the actual measurement. To suppress the residual H₂O signal, an excitation sculpting (pulse program: zgesgp) suppression scheme³⁶ was employed.

¹³C Solid-State Nuclear Magnetic Resonance Spectroscopy

Magic angle spinning (MAS) solid-state carbon nuclear magnetic resonance spectroscopy (¹³C ssNMR) was performed at the NMR Center of Lund University using a Bruker Avance Neo 500 MHz NMR spectrometer equipped with a Bruker 4 mm HCP E-free MAS probe. Topspin 4.0 (patchlevel 7) was used for both acquisition and processing. An ∼50 vol % C₂₈-hPEO5 gel in D₂O was filled into disposable MAS inserts (Bruker) in a 4 mm rotor and spun at 4–6 kHz.

First, polarization transfer experiments using cross-polarization (CP)³⁷ and refocused insensitive nuclei enhanced by polarization transfer (refocused-INEPT)^38,39 were performed at T = 41–74 °C. A spin rate of 6 kHz was applied to assess the CH bond reorientation of the n-alkyl and PEO blocks around the melting transition of the core (T_m = 57 °C). Prior to the measurement, the sample was heated to 76 °C for equilibration and then cooled again to 40 °C. Afterward, the temperature was increased stepwise with 5 min equilibration time before the start of each experiment.

Second, the longitudinal relaxation rate R₁ and the relaxation rate in the rotating frame R_1ρ of ¹³C were determined below the melting transition, T = 41–55 °C, revealing details about the CH bond reorientation correlation time τ_c in the solid phase. The experiments used CP polarization transfer and a MAS spin rate of 6 kHz. R₁ was measured with the inversion recovery method of Torchia,⁴⁰ and R_1ρ was measured using an on-resonance spin-lock, applied to ¹³C after CP.

Third, R-type proton detected local field (R-PDLF) experiments⁴¹ were performed just above the melting transition, T = 57–77 °C, using refocused-INEPT polarization transfer and a spin rate of 4 kHz, to determine the liquid order parameter S_CH of CH bonds in the n-alkyl block:

1

where θ is the angle between a ¹³C–¹H internuclear vector and the magnetic field.

More details about the ¹³C NMR experiments can be found in the Supporting Information.

Scattering Model

In previous publications, we used a spherical core–shell model to describe scattering data from C_n-PEOx micelles.^15,19,23,29 This model, however, fails in describing the SANS data with dominant core scattering contribution due to deviation from spherical shape and a dehydrated corona layer as outlined below.

Figure 1b shows a sketch of a newly developed, aspherical scattering model, including the important geometrical parameters. The micellar core is modeled as a homogeneous ellipsoid of revolution with an equatorial radius R_c and polar radius ϵR_c. Thus, ϵ < 1 corresponds to an oblate and ϵ > 1 to a prolate shape. The general scattering amplitude for such an ellipsoid of revolution is given by⁴²

2

where R_eff is an effective radius depending on the equatorial radius R as well as the angle α between the axis of the ellipsoid and the scattering vector Q⃗:

3

Thus, with the effective core radius R_c,eff = R_eff(R_c,α), the core scattering amplitude is

4

It contains a Debye–Waller factor accounting for an interface roughness σ_int1 between core and first shell. The first shell of dehydrated polymer is assumed to be homogeneous and of constant thickness d₁ around the ellipsoidal core, so that the scattering amplitude is

5

with the effective inner and outer radii R_c,eff and R_s1,eff = R_c,eff + d₁, another Debye–Waller factor with interface roughness σ_int2 between the shells as well as the respective volumes of core and first shell:

6

7

The second shell of hydrated polymer has a constant thickness d₂ and is modeled with a density profile ∝ r^–4/3 according to the Halperin theory⁴³ for starlike micelles

8

A Fermi-like cutoff function at the effective micellar radius R_s2,eff = R_s1,eff + d₂ with width σ_out was introduced to account for the finite length of the polymer blocks and C is a normalization constant:

9

The density profiles assumed in this model, including rough interfaces, are sketched in Figure 1c. Finally, the model considers the so-called “blob” scattering,⁴⁴ a scattering contribution arising from the internal polymer structure in the second shell:

10

where ν is an effective surface coverage and P_Beau(Q) is the Beaucage form factor.⁴⁵

The actual fit parameters of the model are the aggregation number N_agg, the thicknesses d₁ and d₂ of the shells, the asphericity ϵ, the interface roughnesses σ_int1 and σ_int2, the radius of gyration R_g in the Beaucage form factor, and the surface coverage ν. The relative width of the outer surface was fixed at σ_out = 0.1, based on previous studies.^15,19 All other model parameters are calculated in the following way: The molecular volume of an n-alkyl chain is calculated from its molecular weight and density, V_M,Cn = M_Cn/d_Cn, which determines the core radius via

11

The partial molecular volume of a single PEO chain in the dehydrated layer is V_M,PEO,s1 = V_s1/N_agg and therefore the mass fraction of PEO in the first shell

12

This leaves the remaining partial PEO molecular volume in the hydrated second shell to be

13

so that the overall micellar volume becomes V_mic = N_agg(V_M,Cn + V_M,PEO,s1 + V_M,PEO,s2). Lastly, the molecular volume of a solvent molecule is V_M,solv = M_solv/d_solv. With these quantities and the respective scattering lengths b_x, the scattering length densities are calculated as

14a

14b

14c

14d

and the contrasts are

15

Finally, the scattering cross section of the micelle isa

16

where the integration over α performs a rotational average to account for the anisotropic shape of the micelle. With the blob scattering added incoherently, the overall macroscopic scattering cross section then is

17

The scattering model was used to simultaneously analyze the SAXS and SANS data of C₂₈-dhPEO5.

Results and Discussion

Core Crystallization in n-Alkyl-PEO Micelles

Previous SAXS experiments in combination with density measurements and differential scanning calorimetry (DSC) have shown the n-alkyl cores in C_n-PEOx micelles crystallize.^19,21,23,29 Increasing the temperature above the melting point T_m, melting of the n-alkyl chains can be observed in the SAXS curves by a significant increase in the core scattering contribution caused by the lowered n-alkyl density and therefore increased core contrast (see Figure 2a for an example data set of C₂₈-PEO5). In addition, DSC melting traces revealed a clear endothermic phase transition at T_m (see Figure 2b). By comparing the melting enthalpy obtained from DSC with the melting enthalpy of the corresponding bulk n-alkanes, we could estimate a degree of crystallinity around 30–50%.^19,28 Furthermore, our observed transition temperatures are quite close to the bulk melting temperatures of corresponding n-alkanes,³² and the difference can be excellently described by a simple Gibbs–Thomson behavior.^23,29 Nonetheless, one cannot describe the state of the n-alkane blocks within the core as crystalline in a classical sense because the maximum domain size is very small as it is constrained by the micellar core radius R_c. To obtain direct evidence of the n-alkyl crystallization and information about their conformation inside the crystalline domains, we performed wide-angle X-ray scattering (WAXS) experiments on selected C_n-PEOx micelles. Because the crystallites inside the micellar cores are very small (≤R_c), any Bragg peaks are heavily affected by Scherrer broadening.⁴⁶ Therefore, to increase the chances of observing Bragg scattering, we used a shorter PEO block, C₂₈-hPEO3, as this molecule forms larger micelles.¹⁵ WAXS data above and below the melting point are shown in Figure 2c together with data from hPEO3 homopolymer in solution. As evidenced by the hPEO3 reference data, the main features of the C₂₈-hPEO3 WAXS curves originate from the hPEO3 corona. Only the large peak around Q ≈ 1–2 Å^–1 seems to stem from the n-alkyl core. Interestingly, there is a pronounced spike on top of it (marked by an arrow) that vanishes above the melting transition. The exact same effect, only less pronounced, was also observed in C₂₈-hPEO5 micelles, shown in Figure S1. We identify this feature at Q = 1.5 Å^–1 as the dominant (110) reflection of the normal n-alkane orthorhombic crystal lattice,⁴⁷ which was also found by Yin and Hillmyer⁴⁸ in crystalline polyethylene micellar cores as well as by Fu et al.⁴⁹ in n-alkanes confined in microcapsules. Both groups, however, also observed the second-most dominant (200) reflection at 1.66 Å^–1, but since it is much weaker than the (110) reflection, it is not discernible in our data. Nonetheless, we conclude that the crystalline n-alkyl chains in C_n-PEOx micellar cores adopt a conformation similar to that in bulk.

Figure 2.

(a) Temperature-dependent SAXS curves of C₂₈-hPEO5 in H₂O, taken from ref (19). Note the increased core scattering contribution at intermediate Q for T ≥ 55 °C. (b) NanoDSC trace of C₂₈-hPEO5 in H₂O, also taken from ref (19). The melting point is at T_m ≈ 57 °C. (c) WAXS curves of C₂₈-hPEO3 at 5 vol % above and below the melting transition. The arrow marks a pronounced spike that vanishes below the melting transition. For comparison, the positions of the dominant (110) and (200) Bragg reflections of the normal n-alkane orthorhombic crystal lattice are indicated. In addition, a scaled WAXS curve of hPEO3 homopolymer is shown.

Effect of Crystallization on the Core Shape

In all our previous works on the C_n-PEOx system, we used a spherical core–shell model for starlike micelles which yielded very good agreement with experimental small-angle scattering data (see for instance Figure 2a).^{15,16,19,20,23,29} However, it is not obvious how (partially) crystalline n-alkyl chains could be arranged in a spherical core. Vilgis and Halperin predicted that diblock copolymers with crystallizing solvophobic blocks would form disklike cores, where the core chains align along their axis and the solvophilic chains stick out from the basal planes.^50,51 These micelles are only stable in the starlike limit, though, when the corona chains are much longer than the core chains. Interestingly, in this case the corona would still be approximately spherical, rendering it hard to discriminate them from regular spherical starlike micelles unless the structure of the core can be isolated experimentally. Therefore, we set out to have a closer look on the actual core shape. Neutron scattering offers an opportunity to investigate the core selectively because of the unique dependence of the scattering signal on the isotopic composition of the sample. For this purpose, we prepared C₂₈-dhPEO5 with 82% deuterated PEO which has almost no contrast to D₂O, enhancing the scattering signal of the n-alkyl core.

The SANS data are shown in Figure 3a and were merged together from a low- and high-concentration sample as described in the Experimental Section (individual data sets shown in the Supporting Information). The temperature was increased stepwise from 40 to 70 °C to reveal changes during the melting transition. Indeed, there is a very distinct change in the scattering pattern between 55 and 57 °C. In addition, the same samples were measured with SAXS at 40 and 70 °C which serves as comparison with dominant corona scattering (see Figure 3b,c). These SAXS curves can be fitted very well with our established spherical core–shell model for starlike micelles, but we were not able to reproduce the core-selective SANS data with reasonable parameters. Therefore, we created a micellar scattering model with an anisotropic core shape but approximately spherical corona which was introduced in detail above. Although Halperin and Vilgis suggested a cylindrical or disklike shape for crystalline micellar cores,^50,51 we chose an ellipsoidal model. Considering that the hydrocarbon core is only partially crystalline and that the hydrophilic blocks have a disordering effect, we deemed a proper disklike shape unlikely. Furthermore, a globular shape reduces the unfavorable core–corona interface area. It also allows a flexible description of possible shapes, from more compressed, almost disklike, oblates to more elongated, prolate shapes. In any case, the scattering signals of cylindrical and ellipsoidal shapes are barely discernible, so that a distinction is without practical importance (compare Figure S2).

Figure 3.

(a) SANS curves of C₂₈-dhPEO5 in D₂O at increasing temperatures around the melting transition. The data have been shifted by factors of 20 for the sake of clarity. Black lines represent model fits which are discussed in more detail in the main text. (b) Simultaneous fit of SAXS and SANS data at 40 °C. (c) Simultaneous fit of SAXS and SANS data at 70 °C. The black dashed line is a simultaneous fit using our conventional, spherical core–corona model.

The ellipsoidal core–shell model did, though, still deviate systematically from the experimental data in the intermediate Q range, indicating that there was an additional scattering contribution from a structure on a length scale between core and shell. We finally were able to reproduce all scattering curves satisfactorily (black lines in Figure 3) by assuming a thin layer of dehydrated PEO just around the core, where the polymer volume fraction is highest. Such a layer can occur when the polymer grafting density on the core surface is very high.^52,53 As PEO is known to phase-separate at high concentrations,⁵⁴ it is particularly prone to form such a dehydrated layer, which has been reported for densely PEO-grafted nanoparticles.⁵⁵⁻⁵⁷ These two new features, aspherical core and dehydrated PEO layer, have not been detected before because the starlike PEO corona dominates the scattering signal under usual full-contrast conditions. Also, since d₁ + d₂ ≫ R_c, the overall micelle appears approximately spherical despite an ellipsoidal core (compare Figure 1b). The model fits still deviate from the SANS data at lowest Q. These data points, though, have a high experimental uncertainty because of their sensitivity to exact subtraction of primary beam contributions and are thus considered less relevant. It should also be noted that a spherical core with dehydrated PEO layer does not agree with the SANS data; both ellipsoidal deformation and a dehydrated layer are necessary to obtain good agreement. On the other hand, we cannot exclude inhomogeneity in the thickness of the inner PEO layer, d₁. For instance, in areas of high core surface curvature, the polymer crowding is expected to be less severe, and thus the dehydration layer could be thinner. However, the resolution of SANS experiments is not good enough to resolve such minor details, and we therefore chose the simplest option, a constant layer thickness around the core.

The consistency of the new anisotropic model with our previous results using a spherical core–shell model was ensured by fitting SAXS and SANS data simultaneously at 40 and 70 °C. The main fitting parameters are shown in Table 2, whereas an extensive listing of all parameters is given in Table S1. Fit parameters were the aggregation number N_agg, the thicknesses d₁ and d₂ of the shells, the asphericity ϵ, the interface roughnesses σ_int1 and σ_int2, the radius of gyration R_g in the Beaucage form factor, and the surface coverage ν. The scattering lengths b_x were calculated based on the polymer characterization (Table 1) and tabulated atomic scattering lengths.⁵⁸ To simplify calculations and facilitate comparison with literature data, PEO parameters other than b_PEO were calculated as if the polymer was fully proteated. The densities of the C₂₈ core and hydrated PEO shell are based on previous results,¹⁹ and the density of the dehydrated PEO shell was assumed to equal the bulk PEO density.⁵⁹ Densities needed to be slightly adjusted to fit the SAXS data (see Table S1). The temperature-dependent density of D₂O was taken from ref (60). Because the contrast of the hydrated PEO is very low in the SANS experiments (compare Table S1), the latter are insensitive to R_g and ν and also d₂ and σ_int2 are rather ill-defined. The overall micellar radius R_m = R_c + d₁ + d₂ ≈ 105–120 Å as well as the R_g ≈ 50 Å, determined mostly from the SAXS data, though, are in perfect agreement with previous findings.¹⁹ Also, the temperature-independent N_agg has been reported in the same article. Furthermore, the interface roughness between the n-alkyl core and the dehydrated PEO shell decreases slightly above the melting transition. Supposedly, the partially crystalline C₂₈ chains are incommensurate with a smooth interface while the molten state allows a more effective packing. In the crystalline phase, the core diameter along the short axis is about 2ϵR_c ≈ 36 Å. Tanford⁴ calculated the length of a fully stretched n-alkyl tail as l ≈ (1.5 + 1.265(n – 1)) Å, which for C₂₈ gives about 36 Å. Therefore, at least in the middle of the ellipsoidal core, the C₂₈ chains can adopt an all-trans conformation, while the spatial constraints toward the rim may lead to some molecular disorder.

Table 2. Main Model Parameters Used for the Fits Shown in Figure 3^a.

	Nagg	d1 (Å)	d2 (Å)	ϵ	σint1 (Å)	σint2 (Å)	Rcc (Å)
SAXS 40 °C	140 ± 10	6 ± 2	76 ± 5	0.48 ± 0.05	4.3 ± 1.2	10.8 ± 4.0	37
SANS 40 °C	b	b	b	b	b	b	b
SANS 53 °C	131 ± 15	10 ± 4	75 ± 25	0.50 ± 0.05	4.0 ± 2.0	7.0 ± 7.0	36
SANS 55 °C	125 ± 10	12 ± 5	85 ± 25	0.51 ± 0.05	3.5 ± 1.0	9.2 ± 5.0	36
SANS 57 °C	135 ± 10	7 ± 3	90 ± 25	0.73 ± 0.05	2.5 ± 1.0	5.0 ± 5.0	33
SANS 59 °C	130 ± 10	9 ± 5	80 ± 25	0.72 ± 0.04	2.0 ± 1.0	5.0 ± 5.0	33
SANS 61 °C	135 ± 10	6 ± 3	75 ± 25	0.72 ± 0.04	2.0 ± 1.0	5.0 ± 4.0	33
SAXS 70 °C	130 ± 10	7 ± 2	67 ± 5	0.72 ± 0.05	2.0 ± 1.0	9.0 ± 4.0	33
SANS 70 °C	b	b	b	b	b	b	b

^aThe complete set is given in Table S1.

^bSANS and SAXS fitted simultaneously.

^cCalculated via eq 11.

The most striking finding, however, is that the asphericity ϵ changes abruptly from ∼0.5 to ∼0.7 at the melting transition (T_m = 57 °C), which causes the very distinct change in the shape of the scattering curves in Figure 3a. The evolution of ϵ is also plotted in Figure 4b. This means the micellar core is a rather flat oblate ellipsoid below the melting transition,b almost disklike as proposed by Halperin and Vilgis, since n-alkyl chains crystallize parallel to each other. Somehow surprisingly, though, the core does not become completely spherical above the melting transition, either, but instead maintains a somewhat oblate shape, as can be seen from ϵ < 1. The effect might be explained by the fact that the uniform n-alkyl chains still preferably align in parallel, but the driving force for alignment is weaker above the melting temperature. The Kuhn length of poly(ethylene), in principle a very long linear alkane, is ∼14 Å,⁶¹ corresponding to about 11 CH₂ repeat units. Thus, the C₂₈ alkyl block has on average only 1–2 kinks in the liquid state, which means that it is still rather rigid, explaining the persisting core anisotropy. This explanation is supported by computer simulations of Lin et al., who found a gradual transition from disk to sphere with decreasing core block rigidity.⁶² Furthermore, Vuorte et al. simulated C₁₈-PEO micelles with noncrystalline cores. They also found a slight anisotropy which might become more pronounced with longer n-alkyl chains.¹⁸ In addition, the persistent core anisotropy in the liquidlike phase can be explained by dynamic fluctuations of the core. As these fluctuations occur on time scales much shorter than the temporal resolution of the scattering experiment, only an averaged ellipsoidal shape is observable. Applying polydispersity in the asphericity ϵ would unnecessarily complicate the scattering model, though, and is therefore omitted here.

Figure 4.

(a) Melting curves of C₂₈- and C₂₂-hPEO5 determined by Nano DSC, taken from ref (19). (b) Asphericity ϵ of the C₂₈-dhPEO5 micellar core, determined from the fits in Figure 3a. The black line is a guide to the eye. (c) FWHM of the characteristic C₂₂-dPEO5 ¹H NMR signals as assigned in Figure 5.

Even though to our knowledge the data set presented here is the most extensive experimental study of core shape change around the melting transition, similar disk–sphere transitions have been reported in the literature.^48,63−67 For example, Yin and Hillmyer compared poly(N,N-dimethylacrylamide)–polyethylene (PDMA–PE) and poly(N,N-dimethylacrylamide)–poly(ethylene-alt-propylene) (PDMA–PEP) in water with TEM and SANS.^48,65 At 120 °C, both polymers formed spherical micelles with a PDMA corona surrounding the hydrophobic core. When cooled to room temperature, however, the PE block crystallized and forced the core into an oblate ellipsoidal shape while the PEP core remained amorphous and spherical. We would like to highlight that the PDMA–PE system is kinetically frozen so there is no molecular exchange between micelles and the system cannot attain the thermodynamically most favorable state.⁴⁸ In contrast, C₂₈-dhPEO5 exhibits active chain exchange, and even at the lowest experimental temperature, 40 °C, molecular exchange takes place within minutes.²³ Interestingly, the aggregation number still remains unchanged above the melting temperature, and only the core shape is altered.

However, crystallization does not always imply an anisotropic core shape. For instance, the simulations of oligo(ethylene sulfide)–poly(ethylene glycol) (OES–PEG) by Sevgen et al. revealed a spherical core shape, even though the OES chains partially crystallized.⁶⁸ In other cases, crystallization leads to aggregation into micellar worms^65,69−71, which is often exploited in CDSA, or it even leads to precipitation.⁷² Thus, the effect of core crystallization on the micellar shape cannot be universally predicted but instead depends strongly on the individual polymer architecture.

The other new feature of C_n-PEOx micelles, which has been found in this study, is the existence of a thin layer of dehydrated PEO around the C₂₈ core (compare d₁ in Table 2). In previous works,^19,29 we investigated the melting point depression in the nanometer-sized micellar n-alkyl cores compared to bulk n-alkanes by means of a generalized Gibbs–Thomson equation.⁷³ The analyses revealed an unusually low interfacial tension between core and corona, around 8–9 mN/m,^19,29 while the n-alkane/water interfacial tension is typically around 50–60 mN/m.^12,74,75 Apparently, the dehydrated PEO layer shields the n-alkyl chains from the solvent. The interfacial tension between PEO and alkanes is around 9–12 mN/m,^76,77 which coincides much better with the interfacial tension between core and corona we found in the Gibbs–Thomson analysis. The dehydrated PEO layer has not been discovered before because the densities of melt and solution PEO are not very different (compare Table S1), and the hydrated PEO corona has a much greater volume compared to the dehydrated shell. Only when the outer corona is nearly matched out, as in this study, the contrast conditions are shifted so that the inner layer becomes visible. Apparently, PEO dehydrates in the immediate vicinity of the core simply because of spatial constraints, imposed by the rather high grafting density of ∼1.1 nm^–2. The phenomenon has been experimentally found on densely polymer-grafted nanoparticles^55,56 by using SAS. Maccarini et al. observed an ∼17 Å dehydrated PEO layer on gold nanoparticles with a grafting density of almost 6 nm^–2, and Grünewald et al. reported an ∼25 Å dehydrated PEO layer on iron oxide nanoparticles with a grafting density of 3.5 nm^–2. Recently, Dahal et al. employed computer simulations to investigate the phenomenon more systematically.⁵⁷ They simulated gold nanoparticles of various sizes and PEO grafting densities and found a distinct dehydration layer of up to 15 Å when the grafting density was higher than 1.5 nm^–2. However, also for lower grafting densities, they observed a thin dehydration layer of ∼5 Å, which coincides with our findings. In our case, the dehydration of PEO might furthermore be promoted by the presence of alkyl blocks in the interfacial area.

n-Alkyl Block Conformation

To further shed light on the conformation of the n-alkyl blocks inside the micellar core, we employed nuclear magnetic resonance (NMR) spectroscopy. First, we performed conventional ¹H solution NMR of C₂₂-dPEO micelles in D₂O to observe the change of the characteristic n-alkyl peaks with temperature and compared it to reference spectra in CDCl₃, a common solvent for both blocks where no micelles form. Example data including peak assignment are shown in Figure 5. In aqueous solution above the melting point (T_m = 29 °C), i.e., in the micellized state with liquidlike core, the n-alkyl peaks (2–5 as assigned in Figure 5) are slightly broadened compared to the unimeric state in deuterochloroform, indicating a minor reduction in mobility due to micellization. This agrees with the findings of Ortony et al., who investigated the internal dynamics of an n-alkyl-functionalized, self-assembling peptide using electron paramagnetic resonance spectroscopy⁷⁸ and found the alkyl blocks buried in the fiber core to have a reduced rotational diffusion rate compared to fully liquid n-alkanes in the melt. When the temperature of the C₂₂-dPEO sample is reduced below the melting point, though, the NMR peaks become undetectably broad (compare the blue spectrum in Figure 5), which means that the n-alkyl chain mobility is strongly restricted. To investigate the peak broadening more quantitatively, we fitted the individual signals with Lorentzian curves, and the determined peak widths (full width at half-maximum, FWHM) are shown in Figure 4c while the fits are shown in Figure S3, together with a more detailed description of the fit procedure.

Figure 5.

¹H NMR spectra of C₂₂-dPEO in CDCl₃ and D₂O. The D₂O spectra were shifted and scaled so that the residual hPEO signals (1′) overlap with the CDCl₃ spectrum. ∗ originates from residual H₂O.

The width of the two residual hPEO peaks (1′ as assigned in Figure 5) is unaltered over the entire temperature range while the n-alkyl peaks (2–5) are broadened very quickly below the melting point (compare Figures 4c and Figure S3). Interestingly, the inner carbons (3 and 4) are broadened immediately below the melting transition: Already at 25 °C they cannot be distinguished from the background anymore, whereas the PEO grafting site (2) and the terminal methyl group (5) can be distinguished at least down to 21 °C (compare Figure S3). This can be rationalized by the fact that the CH₂ group next to the PEO block is most effected by the free polymer and methyl groups generally are rather mobile, while the inner methylenes are more prone to order, which has also been revealed in the computer simulations of Sevgen et al.⁶⁸

To investigate the internal dynamics of the n-alkyl blocks further, we employed magic-angle-spinning ¹³C solid-state NMR spectroscopy (ssNMR). To this end, we produced a high-concentration C₂₈-hPEO gel in D₂O. First, we conducted INEPT and CP experiments at various temperatures around the melting transition, where CP signals arise from restricted, solidlike phases and INEPT signals originate from liquidlike CH bonds with a fast, isotropic reorientation.⁷⁹ The spectra are shown in Figure 6, and there is a clear phase transition around T_m = 57 °C. The peaks were assigned based on the results of Ferreira et al.,⁸⁰ who investigated a similar C₁₂-oligo(ethylene oxide) system. The most dominant peak, at 70 ppm, is the main PEO signal (3), and the resonance at 61 ppm stems from the terminal PEO carbon next to the OH group (1). The PEO block is clearly liquidlike, but there is also a CP signal at 70 ppm (1) which probably originates from the dehydrated PEO in the immediate vicinity of the core which undergoes anisotropic reorientation on account of being anchored to the core surface. The peaks at 24 and 14 ppm are the ultimate CH₂ (5) and terminal CH₃ group (6), respectively. They show a clear liquidlike behavior above the melting transition, but below the melting point the absence of INEPT peaks shows that the reorientational correlation time τ_c is longer than 10 ns.⁸¹ Yet, no significant CP signal arises, which is in agreement with our conclusion from the ¹H NMR spectra that the terminal methyl group and the PEO grafting site remain relatively mobile below the melting transition (τ_c ≈ 1–10 μs⁸¹). Furthermore, there is a strong signal at 31 ppm from the liquid n-alkyl chain above the melting point (5) which interestingly also exhibits a weak CP signal (2*). This points toward a certain degree of anisotropy in the system which agrees with the aspherical core shape found in the SANS experiments. Finally, there is also an INEPT signal at 33 ppm from the penultimate CH₂ group (6) in the C₂₈ chain. Below the melting point, there is a strong CP signal at the same chemical shift (2) which is characteristic for n-alkyl chains in the all-trans conformation.⁸² The increased width of that signal indicates irregular packing, which is reasonable given the spatial constraints within the micellar core.

Figure 6.

CP and INEPT ¹³C ssNMR spectra of a C₂₈-hPEO gel in D₂O. A clear phase transition is visible around T_m = 57 °C.

However, we wanted to further characterize the state of the hydrocarbon chains in the solid phase and therefore conducted CP R_1ρ and R₁ experiments below the melting point. To determine the n-alkyl ¹³C relaxation rate in the rotating frame R_1ρ, the integrated intensity of the CP peak 2 was measured as a function of the delay time t at different spin lock pulse nutation frequencies ν₁. These data were fitted with a relaxation function , shown in Figures S4–S6. In the same way, the relaxation rate in the laboratory frame, R₁, was obtained. This is shown in Figures S7–S9, and all resulting relaxation rates are plotted together in Figure 7. The huge difference between R_1ρ and R₁ indicates CH bond reorientation on the time scale of microseconds.⁸³ It should be noted, though, that the R₁ relaxation rates agree fairly well with values reported for C₂₁-PEO10-C₂₁ hydrogels.²⁸ In summary, these results point toward a rotator-like phase with mostly all-trans conformation of the C₂₈ blocks. Nonetheless, the molecular packing is perturbed due to the strong spatial confinement in the micellar core, and the bond reorientation is unusually slow, on the milli- to microseconds scale.

Figure 7.

¹³C relaxation rate of all-trans n-alkyl blocks (2 in Figure 6) in the rotating frame R_1ρ and in the laboratory frame R₁ as a function of temperature and spin lock pulse nutation frequency ν₁.

Finally, we performed INEPT-RPDLF experiments to analyze the anisotropy in the micellar core still present above the melting transition by calculating the orientational order parameter S_CH. To this end, we measured the integrated intensity of the INEPT signals (3, 5–8 in Figure 6) as a function of the delay time t₁, shown in Figure S10. For the strongest signal at 31 ppm (5), there is a clear minimum at t_1,min ≈ 16 ± 1 ms, which corresponds to a frequency splitting of 125 ± 8 Hz. With an effective scaling factor 0.315⁸⁴ this gives a dipolar coupling d_CH = Δν_CH/0.315 ≈ 400 ± 25 Hz. Estimating the maximum splitting for a static CH bond to be ∼21 kHz,⁸⁵ we obtain an order parameter of S_CH ≈ 0.02, which agrees with the small but detectable CP signal 2*. At 57 °C, directly at the melting point, the minimum is slightly shifted to shorter delay times which indicates an increased S_CH. This seems reasonable given the system is on the brink of the solid phase. Even though the other alkyl signals 6–8 exhibit a much lower signal-to-noise ratio, they all follow the same trend. Albeit small, the orientational order parameter in the C₂₈ block is finite and thus suggests some molecular order and/or asymmetry in the micellar core above the melting point, in agreement with the residual asphericity found in the SANS experiments. The absolute value of S_CH also agrees fairly with the work of Ferreira et al. on penta(ethylene glycol) mono-n-dodecyl ether (i.e., C₁₂-PEO0.25) lamellae in D₂O.⁸⁰

Conclusion and Outlook

In summary, we performed an extensive study of the nature of the n-alkyl core in partially crystalline C_n-PEOx micelles, both below and above the melting transition. Employing SANS and SAXS, we found the core to be elliptical below the melting transition, in agreement with theoretical predictions and other experimental findings. In addition, we observed a less pronounced but still significantly aspherical core above the melting point and relate this to the relative rigidity of the n-alkyl block, even in the liquidlike state, as well as thermal shape fluctuations. In fact, reports on related C_n-EO_m surfactant micelles with aspherical shape are numerous.⁸⁶⁻⁸⁸ In the future, we aim to investigate the core shape of shorter n-alkyl blocks to see whether the asphericity persists. We furthermore reported a thin layer of dehydrated PEO in the immediate vicinity of the hydrocarbon core. To our knowledge, such a phenomenon has so far only been reported for metallic nanoparticles with extremely high grafting densities, but here we also observe it in polymeric micelles with moderate grafting density. In addition, we characterized the n-alkyl core using NMR. Above the melting transition, the core blocks are liquidlike, with low but finite orientational order in agreement with the persistent asphericity of the core. But below the melting transition, the system exhibits unusually high relaxation rates which point toward a rotator-like phase with mostly all-trans chain conformation and milli- to microseconds reorientation. This is further supported by the WAXS results where we observe a Bragg signal equivalent to normal n-alkane crystalline phases with orthorhombic chain packing. As C_n-PEOx is an excellent model for core-crystalline micelles which have attracted significant attention recently, our findings have implications for a wider field of ongoing research. We hope that this work inspires similar studies on other relevant systems with partially ordered cores.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.macromol.0c01936.

• Detailed parameters of the ¹³C ssNMR experiments; additional WAXS data; a complete listing of the SAS fit parameters; unmerged SANS data of low- and high-concentration C₂₈-dhPEO sample; comparison between the scattering patterns of ellipsoidal and cylindric shapes; details of the ¹H NMR line width analysis; additional plots for the determination of R_1ρ and R₁; additional data for the determination of S_CH (PDF)

The authors declare no competing financial interest.