Thomas
Zinn†
a,
Lutz
Willner
a,
Reidar
Lund
*b,
Vitaliy
Pipich
c,
Marie-Sousai
Appavou
c and
Dieter
Richter
a
aJülich Centre for Neutron Science JCNS and Institute for Complex Systems ICS, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany. E-mail: l.willner@fz-juelich.de
bDepartment of Chemistry, University of Oslo, Postboks 1033 Blindern, 0315 Oslo, Norway. E-mail: reidar.lund@kjemi.uio.no
cJülich Centre for Neutron Science JCNS, Forschungszentrum Jülich GmbH, Outstation at MLZ, Lichtenbergstraße 1, 85747 Garching, Germany
First published on 17th April 2014
Here we present an extensive small-angle neutron scattering (SANS) structural characterization of micelles formed by poly(ethylene oxide)-mono-n-alkyl ethers (Cn–PEOx) in dilute aqueous solution. Chemically, Cn–PEOx can be considered as a hybrid between a low-molecular weight surfactant and an amphiphilic block copolymer. The present system, prepared through anionic polymerization techniques, is better defined than other commercially available polymers and allows a very precise and systematic testing of the theoretical predictions from thermodynamical models. The equilibrium micellar properties were elaborated by systematically varying the n-alkyl chain length (n) at constant PEO molecular weight or increasing the soluble block size (x), respectively. The structure was reminiscent of typical spherical star-like micelles i.e. a constant core density profile, ∼r0, and a diffuse corona density profile, ∼r−4/3. Through a careful quantitative analysis of the scattering data, it is found that the aggregation number, Nagg initially rapidly decreases with increasing PEO length until it becomes independent at higher PEO molecular weight as expected for star-like micelles. On the other hand, the dependency on the n-alkyl length is significantly stronger than that expected from the theories for star-like block copolymer micelles, Nagg ∼ n2 similar to what is expected for surfactant micelles. Hence the observed aggregation behavior suggests that the Cn–PEOx micelles exhibit a behavior that can be considered as a hybrid between low-molecular weight surfactant micelles and diblock copolymer micelles.
Diblock copolymers and small surfactant molecules basically show the same spontaneous self-association of single molecules (unimers) into micellar aggregates. Depending on the conditions and molecular parameters, spherical, cylindrical or vesicular micelles are usually formed.22 Nagarajan and Ganesh5 developed a thermodynamic treatment of block copolymers in a selective solvent by deriving the total Gibbs free energy for a micellar solution. Analytical and self-consistent calculations are inherently difficult for such multicomponent systems. However, for block copolymer micelles it has been shown that the pseudo-phase approximation5i.e. that the micelles can be viewed thermodynamically as a distinct “phase”, is a reasonable assumption. This is valid for a very low cmc (critical micelle concentration), i.e. when the fraction of free chains is comparatively small and the aggregation number is large. This assumption is usually fulfilled for amphiphilic block copolymers in water where the interfacial tension assumes large values. Moreover by utilizing the self-similar properties of polymers, scaling theories have been applied with great success.3,4,8,9 These theories provide rather simple predictions of the general dependency of molecular parameters that can be systematically tested by experiments. For low-molecular weight surfactants, however, both the pseudo-phase approximation and scaling theories cannot generally be used and demands much more detailed analysis. It is therefore interesting to study systems which are hybrids between the two, i.e. amphiphilic molecules where one part is polymer-like and the other is of low molecular weight. In this way the limitations of the theories can be elaborated.
Small-angle X-ray/neutron scattering (SAXS/SANS) techniques have proven to be a powerful method in order to examine the structures of micellar aggregates on a nanometer length scale and many comparisons between experimental data and theories have been reported in the literature.13,27–29 Contrary to many other techniques, SAXS/SANS provide quantitative information of the detailed shape and size of nanostructures in solution. In addition, SANS provides additional advantages in terms of contrast variation through relatively simple hydrogen/deuterium substitution that allows the different parts of the micelles (core, shell) to be selectively highlighted. However, there are only very few systematic studies testing the existing thermodynamical theories for micelles by varying molecular parameters and investigating the resulting structures using SANS/SAXS. Amphiphilic block copolymers of the type poly(diene)–PEO, with polyisoprene or polybutadiene, or the saturated analogues PE or PEP, as insoluble blocks and n-alkyl PEOs have been studied more intensively in the past because of their chemical similarities to low-molecular weight non-ionic surfactants, CnEm. For instance, commercially available “Brij” surfactants, Cn–PEO,30,31 poly(ethylene-co-propylene)-b-poly(ethylene oxide), PEP-b-PEO,32–35 poly(butadiene)-b-poly(ethylene oxide) PB-b-PEO36–38 or poly(styrene)-b-poly(ethylene oxide), PS-b-PEO39,40 have been used to study the structure of block copolymer micelles by scattering techniques applying X-rays or neutrons. Cn–PEO surfactants are interesting because they can be purchased in various PEO lengths and thereby bridge the gap between low-molecular weight surfactants and polymeric surfactants. However, as Brij surfactants are industrial products, impurities might exist which requires care when comparing theory and experiments.
In this paper, we present a structural investigation of poly(ethylene oxide)-mono-n-alkyl ether block copolymer micelles by SANS. These Cn–PEO polymers were synthesized using state-of-the-art anionic polymerization leading to very well defined materials in terms of very low degree of impurities and near monodisperse PEO blocks (Mw/Mn ≤ 1.05). Moreover, the control of the synthesis allowed us to accurately vary both the length of the n-alkyl group and the PEO block beyond that for Brij surfactants which are generally only available with C12 or C18 hydrophobic blocks and rather short PEO segments. By a careful quantitative analysis of the SANS data with a core–shell model, we analysed the micellar structure for a series of Cn–PEO5 polymers with n ranging from 18 to 30 and for C27 with three further PEO molecular weights of 10 kg mol−1, 20 kg mol−1 and 40 kg mol−1. In addition from previous work we know that the system is able to attain equilibrium since molecular exchange is active for all n-alkyl–PEO micelles.41 This allows an accurate and sensible comparison with existing thermodynamic predictions which often is complicated for regular amphiphilic block copolymers due to slow equilibration kinetics and non-ergodic behavior.42
The structure of the microdomains primarily depends on the degree of polymerization N = NA + NB, the composition and the interactions between the constituents that are thermodynamically described by the Flory–Huggins interaction parameter χ. With the assumption of a highly asymmetric linear diblock (NA ≫ NB) and the dilute solution limit micellar aggregates typically reveal a spherical shape. The topology of these micelles is divided into two distinct regions: the micellar core with a radius Rc and the micellar corona with a thickness D = Rm − Rc where Rm is the overall micellar radius. The structure of the micellar entity on a thermodynamic level is given by the free energy per aggregated chain in the assembly mic which can be expressed in terms of mentioned parameters of the polymer. mic can then be summarized by three main essential contributions:
mic = core + corona + int | (1) |
(2) |
The micelle free energy per aggregated chain in units of kBT is given by eqn (3).
(3) |
The equilibrium aggregation number of the micellar entity is given by minimization of the free energy with respect to Nagg. This leads to the following scaling expressions
(4) |
(5) |
The minimization of eqn (3) leads to a term (NB−2Nagg)1/6 which can be approximated in the limit of NA ≫ NB by 1.3 The core radius is obtained by inserting eqn (4) into (2) which leads to the following expression:
(6) |
Eqn (4)–(6) are obtained for the SSL but as the γ increases the transition to the SSSL occurs at a critical value γ★ where the core block chains exhibit an almost fully elongated conformation:
(7) |
The latter eqn (7) is obtained from eqn (6) by assuming Rc ∼ NB. Inserting eqn (7) into eqn (4) yields a characteristic NB2-dependence on the aggregation number:
Nagg ∼ NB2 | (8) |
This type of behavior is typically observed for low-molecular weight surfactant micelles. Contrary to amphiphilic block copolymer micelles the NB2-dependence is satisfied inherently. In this case the micellar size and shape are given by geometrical constrains due to the chain packing inside the core and was introduced by Israelachvili and coworkers more than 30 years ago.46 In order to emphasize the difference to the surfactant approach the interfacial tension controls the morphology of the micelle rather than a balance between the two opposing forces of the chain deformation and minimization of the interfacial area.
The resulting polymers were characterized by a combination of size exclusion chromatography (SEC) and 1H-NMR (proteated polymers). NMR-spectra were recorded in CDCl3. The number average molecular weight of the PEO component was then calculated using the integral intensity of the n-alkyl block as the internal reference. SEC measurements were done with tetrahydrofuran/N,N-dimethylacetamide (85/15) as the eluent at 50 °C using a set of three Agilent PlusPore GPC columns with a continuous distribution of pore sizes and PEO standards for calibration. Determined polydispersity indices were typically small in the order of Mw/Mn ≤ 1.04. The chromatograms, however, revealed small contents (1%) of an impurity at elution volumes corresponding to approximately twice the alkyl–PEO molecular weight. Most likely this is due to the presence of spurious amounts of water which cannot be removed even with rigorous drying procedures for the monomer and solvent. Water can participate in the H+/K+ exchange described above and thus may act as a difunctional initiator for the EO polymerization. Deuterated polymers were only analyzed by SEC. Their number average molecular weights were calculated by relating the SEC data to those of the proteated counterparts and by taking into account the deuteration. The important polymer characteristics are summarized in Table 1.
Polymer | Labela | M Cn | M n (PEO) |
---|---|---|---|
a Type of isotope labelling: (h) hydrogen/(d) deuterium. b Molecular weight of respective n-alkane [g mol−1]. c M n (PEO) in [kg mol−1]. | |||
C18–PEO5 | hh | 254.5 | 4.0 |
dd | 292.2 | 4.0 | |
C21–PEO5 | hh | 296.6 | 4.1 |
hd | 4.4 | ||
C24–PEO5 | hh | 338.7 | 4.2 |
hd | 4.2 | ||
C27–PEO5 | hh | 380.7 | 4.2 |
hd | 4.4 | ||
C27–PEO10 | hh | 10.4 | |
hd | 10.9 | ||
C27–PEO20 | hh | 21.2 | |
hd | 20.4 | ||
C27–PEO40 | hh | 36.0 | |
hd | 38.5 | ||
C28–PEO5 | hh | 394.8 | 4.6 |
hd | 4.8 | ||
C30–PEO5 | hh | 422.8 | 4.3 |
hd | 4.1 |
Label | C18 | C21 | C24 | C27 | C28 | C20 |
---|---|---|---|---|---|---|
h | −0.349 | −0.343 | −0.339 | −0.335 | −0.334 | −0.333 |
d | 6.520 |
The coherent macroscopic scattering cross-section of the micellar solutions dΣ/dΩ (Q) in the dilute limit i.e. S(Q) ≈ 1 was analyzed according to
(9) |
The micellar form factor P(Q) is given by
P(Q) = (ρCn − ρ0)2Nagg2VCn2Ac2(Q) + (ρPEO − ρ0)2Nagg(Nagg − B(0))VPEO2Ash2(Q) + 2(ρCn − ρ0)(ρPEO − ρ0)Nagg2VCnVPEOAc(Q)Ash(Q) + VPEO2Δρsh2B(Q) | (10) |
(11) |
(12) |
The individual Ac(Q) for the core and the shell Ash(Q) are calculated based on assuming a compact homogeneous core density profile, ncore = const. and the star-like shell density profile, nshell ∼ r−4/3, respectively.52 Thus, the scattering amplitudes can be written as:
(13) |
(14) |
where C is a normalization constant . In eqn (13) and (14) the Gaussian factor gives a smooth core–corona interface where σint is a measure of the surface roughness. The Fermi cut-off function in eqn (14) is used to terminate the corona region to finite size. For the analysis σm was set to 10% of Rm. Finally, data analysis incorporates instrumental resolution effects according to a wavelength spread, finite collimation and detector resolution.53,54
Polymer | Label | N agg | R m [Å] | R c [Å] | D [Å] |
---|---|---|---|---|---|
C18–PEO5 | hh | 28 | 78 | 15 | 63 |
dd | 30 | 79 | 16 | 63 | |
C21–PEO5 | hh | 45 | 87 | 19 | 68 |
hd | 53 | 89 | 20 | 69 | |
C24–PEO5 | hh | 75 | 103 | 23 | 80 |
hd | 80 | 100 | 24 | 76 | |
C27–PEO5 | hh | 96 | 109 | 26 | 83 |
hd | 122 | 108 | 27 | 81 | |
C27–PEO10 | hh | 39 | 142 | 18 | 124 |
hd | 41 | 147 | 18 | 129 | |
C27–PEO20 | hh | 41 | 208 | 18 | 190 |
hd | 38 | 204 | 18 | 186 | |
C27–PEO40 | hh | 30 | 282 | 16 | 266 |
hd | 23 | 268 | 15 | 253 | |
C28–PEO5 | hh | 95 | 110 | 26 | 84 |
hd | 107 | 112 | 27 | 85 | |
C30–PEO5 | hh | 125 | 111 | 30 | 81 |
hd | 120 | 101 | 29 | 72 |
The found aggregation numbers Nagg are then plotted as a function of the number of EO repeat units, NPEO, in Fig. 2(a). As already qualitatively discussed above there is a steep decay in Nagg from C27–PEO5 to C27–PEO10 while for the higher PEO molecular weights Nagg depends only weakly on the PEO chain length. In the scaling theory for starlike micelles of Halperin3 the dependence of Nagg on the corona chain length is not explicitly considered. There, the aggregation number essentially depends only on the size of the core block. Zhulina and coworkers9 on the other hand have shown that in the limit of long chains Nagg shows a weak logarithmic dependence, Nagg ∼ (lnN)−6/5. This dependence is depicted by the solid line in Fig. 2(a). Apparently, the data points are well represented for large NPEO but do not agree for the initial strong drop between C27–PEO5 and C27–PEO10. On the basis of a pseudo mean-field phase approximation Nagarajan and Ganesh5 proposed that the corona block size has a stronger influence on the aggregation behavior, especially when the solvent is a very good solvent. For PEO–PPO micelles in water they numerically calculated the following empirical scaling relationship: Nagg ∼ N−0.51. This dependence is shown as a dashed line in Fig. 2(a). It can be seen that the experimental trend is well reproduced by this relationship including the data point for C27–PEO5 micelles in intermediate contrast and under full contrast measured in D2O (see triangle Fig. 2(a)). The observed decrease of Nagg can be qualitatively explained by a change of the balance between entropic and enthalpic contributions with the growing PEO block.56 This should lead to a larger steric hindrance of the head-groups on the hydrophobic core surface such that the system is shifted to a new equilibrium structure with smaller aggregation numbers. Furthermore, Fig. 2(b) depicts the micellar shell thickness D as a function of NPEO. We see that the experimental data are in excellent agreement with the theoretical prediction D ∼ N3/5 for star-like micelles3 which is shown by the straight line. Thus, the aggregation behavior at constant n-alkyl chain length is determined by the polymer character of the hydrophilic PEO block.
Fig. 2 (a) Aggregation number Naggvs. number of EO repeat units, NPEO: () hh labeled polymer, () hd labeled polymer and () obtained under full contrast in D2O. Solid line represents the scaling law of the micellar star-model,9 dashed line a semi-empirical dependence deduced by Nagarajan and Ganesh for PPO–PEO micelles.5 (b) Shell thickness D vs. NPEO in log–log representation. Solid line represents a slope of 3/5. |
The scattering data presented in Fig. 1(b) for the different hh Cn–PEO5 micellar solutions in D2O show that the intensity increases with n, directly demonstrating a growth of the micelles in terms of an increasing Nagg accompanied by an increasing core size. Although the PEO molecular weight stays constant the shell thickness D increases slightly (see Table 3). This might be due to a slightly higher PEO density near the core surface leading to a stronger chain stretching of the PEO block. It should be stressed again that the interfacial tension, γ, of the water–n-alkane interface is almost constant (≈50 m Nm−1) within the higher members of the homologous series of n-alkanes.55 Thus, any effect on the micellar properties is mainly due to the increase of the hydrocarbon chain length. The aggregation number Nagg as a function of the n-alkyl chain length is depicted in Fig. 3. We included recent experimental data found for poly(ethylene oxide)-mono-n-alkyl ethers Cn–PEO.30,31,57,58 In order to exclude any effects of the hydrophilic block on the aggregation number Nagg was scaled by NPEO0.51 which was found above to be a reasonable description of the PEO length on Nagg. We observe that Nagg systematically increases with increasing n. The system almost reveals the characteristic n2 dependence for the aggregation number that is denoted by the solid line in Fig. 3. The deviation from this behavior is larger for the C18–PEO5 and C21–PEO5 but still in good agreement with the n2 power law. The n2 scaling can then be associated by either assuming a simple geometrical model as for low-molecular weight surfactants that inherently give the n2 scaling law26 or the super strong segregation regime as outlined in the theoretical section. Given the hybrid nature of our system, it is tempting to speculate that this behavior reflects the surfactant properties of the hydrocarbon core. This is furthermore supported by the fact that the area a per molecule on the core surface does not vary substantially with n. Here we find a mean value of about (93 ± 6) Å2 which suggest that Nagga = 4πRc2 is similar to what is found for surfactant micelles.46 Thus, the n-alkyl chain linearly increases with n and if we allow a homogeneous compact core,59 it follows that Nagg scales with n2. A comparison of Rc with the maximal possible length, lmax, of an alkane chain 1.53 + 1.265 (n − 1) [Å]59 shows that the experimental values found for the micelles in the core are systematically smaller. For example for C24 we find Rc = 23 Å whereas lmax = 31 Å. Apparently, the alkyl chains do not assume a fully extended all-trans configuration. This was also observed by Sommer et al.31 on Brij700 where Rc is reduced by a factor of about 0.75 for C18. This corresponds to a more flexible conformation in the bulk state i.e. the all-trans configuration is perturbed due to kinks along the backbone. According to Tanford the average chain length of a more flexible n-alkyl chain is given by lflex = 1.53 + 0.925(n − 1) [Å].59 The latter analytical expression nicely agrees with the experimental data e.g. lflex[C24] = 23 Å. Thus, the conformation of the alkyl chains can be considered as more flexible which coincides with the assumption that the spherical core has a homogeneous density profile. It should be mentioned that long alkyl chains might crystallize60,61 partly resulting in a non-spherical core domain. Crystalline micellar cores together with the high interfacial tension and a temperature insensitive aggregation number would support micelles in the super-strong segregation limit (SSSL) where the micellar coronas are still spherical. Since the scattering data are an average over an ensemble of micelles, any deviation of the micellar core from spherical geometry is not easy to deduce directly. The rather broad core–corona interface (σint ≈ 5 Å) might be an indication for a more elliptical shape of the core. Since, our scattering data cannot capture this possibility, it has not been considered here. But there is evidence of a phase transition, differential scanning calorimetry, density measurements and SAXS data suggest that n-alkyl micellar cores are partly crystalline at low enough temperatures. The discussion of these results goes beyond the scope of the present work and will be shown in an upcoming publication.
Fig. 3 Aggregation number Nagg as a function of n: () Cn–PEO5, () CnE40,57 () Brij700,31 () Cn–PEO5,58 and () Cn–PEO5.30 The solid line has a slope of 2 and the dashed line of 4/5 expected form the star-model. |
We note that for amphiphilic micelles the same scaling law is theoretically predicted by the SSSL8 and experimentally found by Förster et al.13 A comparison of Nagg to the theoretically predicted scaling laws for star-like block copolymer micelles3 reveals no agreement with our data. The expected power laws for star-like micelles Nagg ∼ N4/5 are too weak and clearly not represented by our data (see dashed line in Fig. 3). In addition, the effect of temperature on the micelles in thermal equilibrium was studied for C24–PEO5 and C30–PEO5 micelles in a temperature range between 20 °C and 60 °C. This is depicted in Fig. 4 which shows the effect of temperature on the aggregation number Nagg and the corona thickness D for C24–PEO5 micelles in water. We find that the aggregation number is within the experimental uncertainty independent of temperature which might be explained by the fact that the interfacial tension is almost temperature insensitive.33 This result coincides with recent findings by Sommer et al.62 for Brij700 in water. Moreover, there is the trend of decreasing micellar size. Since Nagg does not change with temperature this shrinkage is associated with variations in the PEO interactions in water. It is a well-established fact that PEO exhibits a large number of conformations strongly depending on temperature.63,64 As the temperature increases the hydration becomes less effective which leads to a conformational change i.e. a more coiled conformation of PEO. The discussion of the temperature effect follows a model that explains the existence of a lower critical solution temperature (LCST) in PEO–water systems. Thus, the conformation change is not the only reason for the PEO shrinkage but rather the induced decrease of solvent quality. The experimental results however are in qualitive agreement with recent computer simulations.20
Fig. 4 Aggregation number Nagg and corona thickness D as a function of temperature T for C24–PEO5 micelles: () Nagg and () D. |
In particular, we experimentally verified the predicted effects of the hydrophobic and hydrophilic chain length on the aggregation behavior. As demonstrated the aggregation number of the formed micelles increases quadratically with the length of the n-alkyl chain. By changing the molecular weight of the PEO block the aggregation number consistently changes as predicted by the empiric power-law numerically obtained by Nagarajan and Ganesh for PPO–PEO. Moreover, the core size Rc is in accordance with an expression for the chain length of a flexible n-alkyl chain which coincides with the Tanfords model for a liquid-like hydrocarbon chain i.e. hydrocarbon chain having kinks along the chain. This interpretation is also related to simple geometrical constraints on the chain packing as known from low-molecular weight surfactant micelles. However, both the SSSL theory for amphiphilic block copolymers and the surfactant theory predict that the aggregation number follows a quadratic dependence on the hydrophobic block. Considering the hydrophobic n-alkyl block the system is still a surfactant but with the rather long PEO block a polymer character is imposed on the system. The conclusion however is that the chemical hybrid character of Cn–PEOx between a surfactant molecule and a block copolymer is also reflected in the equilibrium micellar properties. Thus, we consider Cn–PEOx polymers as a hybrid material which might close the missing gap to micelles prepared from low-molecular weight non-ionic CnEm surfactants carrying only short n-alkyl chains and EO head-groups, respectively.
Finally, we point out that the detailed characterization of the size and shape of Cn–PEOx micelles serves as an important prerequisite to study the equilibrium chain exchange kinetics of these micellar entities. Details of this study will be presented in a forthcoming paper.
Footnote |
† Present address: Department of Chemistry, University of Oslo, Postboks 1033 Blindern, 0315 Oslo, Norway. |
This journal is © The Royal Society of Chemistry 2014 |