Micellar self-assembly, bridging and gelling behaviour of two reverse triblock poly(butylene oxide)–poly(ethylene oxide)–poly(butylene oxide) copolymers with lengthy hydrophilic blocks

Abstract

Triblock polyethyelene oxide–polybutylene oxide-based block copolymers overcome some of the synthetic drawbacks of commercially available Pluronic block copolymers as well as providing a more hydrophobic environment to solubilise poorly aqueous-soluble compounds. These facts can be exploited to use this class of copolymers as efficient drug delivery nanocarriers (A. Cambón et al., Int. J. Pharm., 2013, 445, 47–57), and their interactions with biologically relevant entities and biological performance should be regulated by the nature, conformation and state of the copolymeric chains. For this reason, in this work we investigated the self-assembly process of two of these reverse triblock poly(butylene oxide)–poly(ethylene oxide)–poly(butylene oxide) block copolymers, BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀, to obtain a clear picture of their self-assembly behaviour in order to correlate it with their biological performance. As a consequence of their particular structure, BO₂₀EO₄₁₁BO₂₀ possesses a rich rheological behavior characterized by the formation of flower-like micelles (ca. 10 to 30 nm in size) and intermicellar bridging at low copolymer concentrations, as shown by atomic force microscopy and rheology data. Conversely, BO₈EO₉₀BO₈ displays a behaviour more similar to that observed for diblock EO_mBO_m and direct triblock EO_mBO_nEO_n copolymers, with single non-associated micelles at low concentrations, and a flow behaviour typical of mesoscopic ordered cubic structures. Strikingly, the relatively wide Poisson distribution of the copolymeric chains makes the present copolymers behave also rather distinctly to conventional associative thickeners.

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Introduction

Hydrophobically end-capped poly(oxyethylene oxide)s have applications in paint coatings, personal care products and in the oil industry because of their ability to dramatically modify rheological properties.^1–4 The industrially important type are the HEUR (hydrophobically ethoxylated urethane) associating polymers, which comprise lengthy poly(oxyethylene) chains end-capped via urethane links by alkyl chains. Corresponding poly(oxyethylene) dialkyl ethers and esters have been also used.^5,6 Their desirable properties originate from molecular association of the hydrophobic ends of the chains in dilute solution and, above a critical micelle concentration (cmc), from the association of molecules into micelles in which the chains can either loop or extent.⁷ The bridging of chains between micelles, a dynamic process, leads to the formation of transient micelle clusters and networks.

Conventional triblock copolymers with hydrophobic end blocks, in particular triblock poly(oxyalkylene)s, offer a different synthetic route with the potential for interesting differences in properties and potential applications, as reported for PO_nEO_mPO_n,^8,9 BO_nEO_mBO_n^10–13 and SO_nEO_mSO_n,^14,15 where EO, PO, BO and SO denote ethylene oxide, propylene oxide, butylene oxide and styrene oxide blocks, respectively. Amongst them, PO_nEO_mPO_n copolymers have been the most extensively studied due to their commercial availability in a range of compositions. However, these copolymers present several drawbacks as, for example, their inherent polydispersity after oxyanionic polymerization as a consequence of the transfer reaction from hydrogen abstraction during the polymerization of the PO blocks,¹⁶ which results in an important diblock component in the synthesized material. This gives rise to variations in their physico-chemical properties from batch to batch which can preclude their use in different applications where an accurate reproducibility of the physico-chemical properties is required such as, for example, in drug delivery since these copolymers are amphiphilic and are able to self-assemble into nanoscopic core–shell micelles. The micellar core may serve as a reservoir for hydrophobic cargos while the corona provides stability and stealthiness into the aqueous biological medium.

An alternative to PO_nEO_mPO_n copolymers is BO_nEO_mBO_n ones provided that transfer is not a problem in the laboratory polymerization of butylene oxide and, hence, the chain distributions are much narrower. In addition, the larger relative hydrophobicity of BO blocks compared to PO (six-fold as estimated from the ratio of the logarithms of the cmcs)¹⁷ allows the formation of polymeric micelles and of transient micelle clusters and/or networks by bridging of extended chains between micelles^13,18 at much lower concentrations than PO_nEO_mPO_n do. This may enable their use as nanocarriers to solubilize much higher concentrations of poorly aqueous soluble drugs in a reproducible manner¹⁹ in the form of injectable solutions, oral suspensions and/or sub-dermal gelling depots^19–21 provided that these copolymers have been proved to be biocompatible.²² However, a detailed and complete characterization of the physico-chemical properties of this class of copolymers is still lacking: a deep knowledge about the correlations between copolymer structure and reflected properties must be key to explain, for example, the biological activity of some of these copolymers, for example, as enhancers of drug toxicity to cancerous cells by inhibiting the P-glycoprotein P efflux pump mechanism,¹⁹ which seems to be regulated by the nature, conformation and state of the copolymeric chains.

Hence, in this work we analyze the physico-chemical behaviour in aqueous solution of two BO_nEO_mBO_n block copolymers: BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀, which largely differ in the hydrophilic block length. This should result in large differences in the micellization process, intermicellar interactions and, thus, solution behaviour. In particular, as a result of its long BO blocks and extremely lengthy EO ones copolymer BO₂₀EO₄₁₁BO₂₀ clearly shows the formation of micellar clusters formed by micellar bridging as observed from dynamic light scattering (DLS), atomic force microscopy (AFM), and rheometry. Due to their shorter EO and BO blocks, copolymer BO₈EO₉₀BO₈ behaves more similarly to a solution of interacting micelles, which pack in a mesoscopic structure (a gel) at large concentrations, although some extent of bridging could be also detected. The differences in the copolymer structures allows us then to observe the effects of both the collapse of longer BO blocks in solution of reverse copolymeric structures and the splitting of BO units number between two blocks, especially in dilute solution since the range of hydrophobicity has been much restricted for these copolymers i.e. from BO₄ to BO₁₂, 8 to 24 BO units per molecule.¹⁷

Materials and methods

Materials

Triblock copolymers were prepared by oxyanionic polymerisation as previously reported.¹⁰ Briefly, dry 1,2-butylene oxide was initiated by polyethylene glycol monomer of different molecular weights activated by mixing with KOH and heating while stirring under vacuum (70 °C, 0.1 mmHg, 100 h) to remove water. Vacuum line and ampoule techniques served to exclude moisture. Gel permeation chromatography (GPC) was used to characterize the distribution widths of the products as the ratio of mass-average to number-average molar mass, i.e. M_w/M_n by using a Waters GPC system equipped with a 1515 pump and a 2410 refractive index detector (Waters, Milford, MA). Chloroform was used as eluent, and monodisperse PEO was employed as standard. ¹³C NMR spectra recorded on a Bruker ARX400 spectrometer (Bruker, Milton, ON, Canada) in deuterated chloroform were used to obtain absolute values of block length and composition, and to verify block architecture. Table 1 summarises the molecular characteristics of the copolymers.

Table 1 Molecular characteristics of the copolymers

Polymers	Mn^a (g mol^−1)	Mw/Mn^b	Mw (g mol^−1)	cmc^c (g dm^−3)
a Estimated by NMR.b Estimated by GPC; Mw calculated from Mn and Mw/Mn. Estimated uncertainty: Mn to ±3%; Mw/Mn to ±0.01.c Values from ref. 10.
BO8EO90BO8	5100	1.07	5457	0.33
BO20EO411BO20	21 000	1.08	22 680	0.01

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Dynamic and static light scattering (DLS and SLS)

SLS intensities were measured by means of an ALV-5000F (ALV-GmbH, Germany) instrument with vertically polarized incident light (λ = 488 nm) supplied by a diode-pumped Nd:YAG solid-state laser (Coherent Inc., CA, USA) and operated at 2 W, and combined with an ALV SP-86 digital correlator with a sampling time of 25 ns to 100 ms (for DLS). Measurements were made at an angle θ = 90° to the incident beam, as appropriate for particles smaller than the light wavelength. The intensity scale was calibrated against scattering from toluene. Solutions were filtered through Millipore Millex filters (Triton free, 0.22 μm porosity) directly into cleaned scattering cells and allowed to equilibrate at the requested temperature for 10 min before measurement. Each experiment was repeated at least three times. Sampling time was 5–10 min for each run in order to define an optimal correlation function.

To obtain the micellar molecular weights and aggregation number, Debye plots i.e. plots based on

where I is the light scattering intensity from solution relative to that from toluene, I_s is the corresponding quantity for the solvent, c is the concentration (in g dm⁻³), M^m_w is the mass-average molar mass of the solute, A₂ the second virial coefficient, and K* the appropriate optical constant, were used. K* includes the specific refractive index increment (dn/dc), whose insensitiveness to composition in BO_nEO_mBO_n systems is already known (dn/dc = 0.135 cm³ g⁻¹).²³

For DLS, the correlation functions were analyzed by the CONTIN method to obtain the intensity distributions of decay rates (Γ).²⁴ From the decay rate distributions the apparent diffusion coefficients D_app = Γ/q², q = (4πn_s/λ)sin(θ/2) were derived, being n_s the solvent refractive index. Values of the apparent hydrodynamic radius (r_h,app, radius of the hydrodynamically equivalent hard sphere corresponding to D_app) were calculated from the Stokes–Einstein equation

r_h,app = kT/(6πηD_app) (2)

where k is the Boltzmann constant and η is the viscosity of water.

Transmission electron microscopy (TEM)

Micellar solutions of both copolymers were applied dropped over carbon-coated copper grids, blotted, washed, negatively stained with 2% (w/v) phosphotungstic acid, air-dried, and then examined with a Phillips CM-12 transmission electron microscope operating at an accelerating voltage of 120 kV.

Clouding

Copolymer solutions were prepared by weighting the requested amount of each copolymer followed by the addition of the same volume of cold water (1 mL). Copolymer solutions were homogenized under stirring at low temperature before being stored at least for one day (T ∼ 4 °C) to ensure complete dissolution. Clouding temperatures (T_cl) were determined by slowly heating (0.2 °C min⁻¹) the copolymer solutions from 0 to 90 °C by both visual inspection and detection of the transmitted light through solutions by means of a Cary Eclipse UV-vis spectrophotometer equipped with a temperature control Peltier device and a multi-cell sample holder (Cary 100, Agilent, Germany). As a result, a plot of transmitted intensity versus temperature was obtained. The cloud point was determined as the midpoint of an abrupt decrease in the transmitted light intensity from a plot of transmitted intensity vs. temperature, as previously described.¹⁸

Rheology

Solutions were prepared by weighting powder copolymer and deionized water into small tubes and subsequent mixing in the mobile state before being stored for at least one day at low temperature (ca. 4 °C). Rheological characterisation was carried out using a controlled stress AR2000 rheometer (TA instruments, DE, USA) with Peltier temperature control. Samples were investigated using cone-plate geometry and a solvent trap to maintain a water-saturated atmosphere around the sample cell to avoid evaporation. The temperature dependence of storage (G) and loss (G′′) moduli was measured either by temperature scans (1–90 °C) at frequency f = 1 Hz and heating rates of 1 °C min⁻¹ or via frequency scans at several temperatures. Experiments were carried out in oscillatory shear mode, with the strain amplitude (A) maintained at a low value (A < 0.5%) by means of the autostress facility of the software. This ensured that measurements of G′ and G′′ were in the linear viscoelastic region. A dynamic time sweep test under A = 0.5% and f = 1 Hz was performed before each frequency scan at a fixed temperature to ensure that the sample truly reached the equilibrium state.

Atomic force microscopy (AFM)

AFM images of block copolymer solutions were performed on freshly cleaved mica substrates. The measurements were performed in a JEOL instrument (model JSPM 4210) in noncontact mode using nitride cantileversNSC15 from MicroMasch, U.S.A. (typical working frequency and spring constant of 325 kHz and 40 N m⁻¹, respectively). The AFM samples were dried in air or under a nitrogen flow when required. Control samples (freshly cleaved mica and buffer solution) were also investigated to exclude possible artifacts. Topography and phase-shift data were collected in the trace and retrace direction of the raster, respectively. The offset point was adapted accordingly to the roughness of the sample. The scan size was usually 500 nm (aspect ratio, 1 × 1), with a sample line of 256 points and a step size of 1 μm. The scan rate was tuned proportionally to the area scanned and kept within the 0.35–2 Hz range. Each sample was imaged several times at different locations on the substrate to ensure reproducibility. Diameters and heights of copolymer aggregates were determined by sectional analysis taken from the average of several sections through the aggregates.

Results and discussion

Clouding

Clouding temperatures (T_cl) were firstly determined for solutions of copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ in the concentration range 0.1–10 wt% by visual inspection and UV-vis spectroscopy following the methodology of Zhou et al.¹⁸ For BO₈EO₉₀BO₈ the cloud-point profile exhibited a shallow minimum at 0.75 wt% (at 43 °C), whilst for BO₂₀EO₄₁₁BO₂₀ this minimum was observed at 1.5 wt% (at 41 °C) (Fig. 1). For both copolymers T_cl starts again to increase at larger concentrations from their respective minima. In general, copolymer BO₈EO₉₀BO₈ displayed lower T_cl than BO₂₀EO₄₁₁BO₂₀ as a consequence of their lower EO/BO ratio: regardless copolymer BO₂₀EO₄₁₁BO₂₀ contains much longer BO blocks which should largely decrease T_cl, the extremely long hydrophilic EO block counterbalances this effect and favors an important enhancement of T_cl,²⁵ in agreement with previous observations.^11,26 This behavior is further supported when comparing, for example, copolymer BO₈EO₉₀BO₈ with the structurally related BO₇EO₄₀BO₇: by doubling the EO block length while keeping almost constant the BO one results in a great increase of T_cl from 35 °C to 75 °C at a copolymer concentration of 10 wt%.¹⁸ In addition, an increase in the BO block length while keeping constant the EO one leads to an important decrease in T_cl, for example, from 53 to 41.5 °C at 2 wt% when comparing, for example, copolymers BO₁₀EO₄₁₀BO₂₀ and BO₂₀EO₄₁₁BO₂₀, or from 66 to 57 °C for copolymers BO₁₄EO₃₇₈BO₁₄ and BO₂₁EO₃₈₅BO₂₁, respectively.²⁷ However, it is worth mentioning that for concentrations above 3.5 wt% the more efficient packing of BO₂₀EO₄₁₁BO₂₀ micelles and their subsequent packing and ordering in solution (gel formation) leads to a sharper T_cl increase above those values corresponding to copolymerBO₁₀EO₄₁₀BO₂₀ (Fig. 1a). High T_cl coincident with gel formation have been also observed in related systems, i.e. aqueous solutions of copolymers BO₁₂EO₁₁₄BO₁₂ and BO₁₂EO₂₂₇BO₁₂.^12,13,28

Fig. 1 (a) Clouding temperatures for BO_nEO_mBO_n triblock copolymers as a function of concentration: () BO₈EO₉₀BO₈ and () BO₂₀EO₄₁₁BO₂₀. For comparison, structurally-related copolymers () BO₅EO₉₁BO₅ and () BO₁₀EO₄₁₀BO₁₀¹¹ are also shown. (b) Minimum clouding temperatures copolymers as a function of BO/EO block length ratio for BO_nEO_mBO_n triblock with () BO < 10 and () BO > 10. The present BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ copolymers are shown in green and red, respectively.

Provided that the cmc values of the present copolymers were previously found to be below 0.35 mg mL⁻¹ (see Table 1),¹⁰ the cloud point behavior would represent the phase transition of a copolymer micellar solution which phase separates at a temperature well above the T_cl. On the other hand, plotting T_cl values against EO/BO ratio at fixed copolymer concentration (1 wt%) an empirical correlation for BO_nEO_nBO_n copolymers with short (≤10) and long (≥10) BO blocks could be observed (Fig. 1b). The lowest values of T_cl are directly dependent on copolymer hydrophobicity, that is, T_cl at the minimum decreases as the EO/BO ratio does (Table S1†).

Population size distributions

DLS measurements of micellar solutions of copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ at different concentrations were carried out at 10 and 25 °C. Selected intensity fraction distributions of log r_h,app (r_h,app being the apparent hydrodynamic radius, e.g. the radius of gyration of the hydrodynamically equivalent hard sphere) are illustrated in Fig. 2a for copolymer BO₈EO₉₀BO₈ at 25 °C as an example. At the lowest concentration analysed (0.1 wt%), the population distribution showed a single peak attributed to flower-like micelles (r_h,app ∼ 13 nm). At larger concentrations (0.25 wt%), two peaks were observed in the intensity-fraction population distributions, which can correspond to micelles and micelle clusters formed by micellar bridging (r_h,app = 140 nm), respectively. Further increases in copolymer concentration leads to an enhancement of the light scattered by flower-like micelles and to a certain reduction (in intensity) in the population distribution of the micellar clusters, which shifts to larger sizes and becomes broader (ca. 200 nm). This behaviour can be probably a consequence, on one hand, of a better packing of BO blocks inside micelles as the copolymer concentration increases and, on the other, to an extension of bridging resulting in associated larger micellar clusters.

Fig. 2 (a) Intensity-weighted population distributions obtained by DLS for copolymer BO₈EO₉₀BO₈ in solution at 25 °C (black, green and blue lines correspond to 0.1, 0.5 and 1 wt% solutions, respectively) and copolymer BO₂₀EO₄₁₁BO₂₀ (1 wt%, red line). (b) TEM image of BO₂₀EO₄₁₁BO₂₀ micelles at a concentration of 0.5 wt% (scale bar 200 nm). (c) AFM image of BO₂₀EO₄₁₁BO₂₀ copolymer showing interchain bridges between micelles. (d) Reciprocal apparent hydrodynamic radius, 1/r_h,app, against concentration for copolymers BO₈EO₉₀BO₈ (, ) and BO₂₀EO₄₁₁BO₂₀ (, ) in solution at 10 °C (open symbols) and 25 °C (filled symbols).

Owing to the special chain architecture of BO_nEO_mBO_n-type block copolymers, the formation of flower-like micelles involves the bending of the hydrophilic EO blocks while keeping the two-end BO blocks in the same micellar core, which is an entropically-loss process. Another possibility is that the two BO blocks in one polymer chain can reside in two adjacent micelles while the EO block is used as a bridge. This kind of cross-linking among the micelles can finally promote an open network structure (the so-called micellar clusters), which is reflected in the DLS population distributions.

Copolymer BO₂₀EO₄₁₁BO₂₀ possessed a similar behaviour as BO₈EO₉₀BO₈ except that sizes of micelles and micellar clusters become larger due to the lengthy EO blocks of this copolymer. At this respect, it is worth mentioning that micellar cluster sizes for this copolymer reaches ca. 900 nm, and even a third much larger population at ca. 3000–4000 nm can be observed probably being a result of the formation of insoluble aggregated material as a consequence of cluster aggregation (Fig. 2a). For both BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ the micellar shape was nearly spherical as observed by TEM and AFM, with their diameters (ca. 22 ± 4 and 32 ± 5 nm for BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ as calculated from TEM, respectively), in fair agreement with those obtained from DLS in spite of the usual dehydration of the copolymer corona and subsequent shrinking of the copolymer structure upon solvent evaporation during sample preparation (Fig. 2b). From AFM images a deformation of the EO corona can be observed as a result of bridging and subsequent formation of micellar clusters (Fig. 2c).

Intensity-average values of 1/r_h,app were calculated for micelles by integrating over the micelles peak in the intensity distributions of decay rate. Since the dissymmetry ratio was found to be near unity, the values obtained were essentially z-averages. Micellar hydrodynamic radii (r_h) were obtained as the intercept of each curve at c = 0 (Fig. 2d and Table 2) from plots of 1/r_h,app against copolymer concentration. 1/r_h,app is proportional to the apparent diffusion coefficient, D_app, but without the influence of temperature and solution viscosity. It can be observed that the average values of r_h,app increased as concentration did, i.e. the apparent diffusion coefficient (D_app = kT/6πηr_h,app) decreased (Fig. 2d). Also, micellar sizes become smaller as the temperature decreases. This was as expected provided that water becomes a better solvent for micelles as the temperature is lowered and, hence, micellar bridging (and hence clustering) was reduced.

Table 2 Micellar data obtained from DLS experiments at 10 and 25 °C for copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀

Polymer	T (°C)	10^5 MW (g mol^−1)	rh (nm)	Nw	10^−4 A2 (mol cm^3 g^−2)
BO8EO90BO8	10	1.4	9.7	25	−8.3
	25	2.1	13.0	38	−19.7
BO20EO411BO20	10	2.4	10.6	11	−10.7
	25	3.8	18.9	17	−60.2

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The negative slopes of plots in Fig. 2d and, hence, the negative second virial coefficients (A₂) derived as reported previously (Table 2, see ESI† for additional details)²⁹ implies a substantial attractive contribution to their intermicellar interaction, resulting in small excluded volumes for the micelles of BO_nEO_mBO_n copolymers, especially for BO₈EO₉₀BO₈ due to its shorter EO corona which, in turn, results in small values of A₂. This is consistent with the micelles having a fraction of their BO blocks extended into the solvent and available for interaction, either with BO blocks protruding from a second micelle or by entering the core of a second micelle, as confirmed visually (Fig. 2c and d), and considering that Van der Waals attraction and polymer depletion forces would not play significant roles in the present relatively dilute micellar systems.^18,23 In either case, the effect results in transient micellar linking, which implies a second equilibrium in the system:

NA ↔ A_N (molecule/micelle equilibrium)

MA_N ↔ (A_N)_M (micelle/linked-micelles equilibrium)

Both BO and EO block lengths will affect these interactions: longer BO-end blocks imply that the intermicellar interaction can become stronger, while central EO blocks can make the BO blocks to be more or less extended into the solution.³⁰ The smaller (more negative) A₂ values for copolymer BO₂₀EO₄₁₁BO₂₀ compared to those of BO₈EO₉₀BO₈ might be a consequence of the longer BO and EO blocks of the former copolymer which favoured direct contacts between micelles even at very low concentrations. Also, A₂ coefficients increases (become less negative) as temperature raises as a consequence of water becoming a worst solvent for micelles; this would make EO coronas to be less hydrated and shrunk, and it would decrease the extent of bridging in agreement with static light scattering data (see below).

In summary, the present data would support the view that for molecules of this type limited open molecular association accompanies closed association to micelles. This means (in a simplified model) that several components are in equilibrium: molecules, micelles, and micellar associates (bridged micelles).

Micellar properties

Since the hydrodynamic radii of the present micelles (listed in Table 2) are small compared to the light wavelength, intraparticle interference can be neglected. Clustering at higher concentrations changes this picture, but we here focused on the behaviour in the dilute micellar regime. Debye plots for copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ at 10 and 25 °C are shown in Fig. 3. These plots indicate associates of higher molar mass at 25 °C compared with 10 °C for both copolymers, as expected for water to be a poorer solvent at the highest temperature. The overall scattering behavior of BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ copolymer solutions is consistent with a closed association process into micelles, but the slopes and curvatures of the Debye plots at the highest concentrations (specially for copolymer BO₂₀EO₄₁₁BO₂₀) are much changed compared with those for EO_nBO_n or EO_nBO_mEO_n copolymers. Although at low concentrations the present copolymers, and especially BO₈EO₉₀BO₈, tend to loop in isolated micelles there is a finite probability of bridging because the system is in dynamic equilibrium, which implies an attractive intermicellar interaction. Hence, the minima and low positive slopes seen in Fig. 3b for BO₂₀EO₄₁₁BO₂₀ results from the competition between repulsive and attractive interactions between the micelles, which are less important for copolymer BO₈EO₉₀BO₈ at 25 °C, in agreement with our interpretation of the DLS results in the former section. The repulsive interaction, effectively a hard-sphere interaction, clearly dominates at the largest concentrations where higher virial coefficients are required to describe the slope of the Debye plots. The effect of the attractive interaction between micelles, which derives from bridging, is seen at lower concentrations where A₂ dominates, and represented by the upturns in the plots for copolymer BO₂₀EO₄₁₁BO₂₀. In this case, such upturns cannot be ascribed to the micelle-molecule equilibrium, i.e. the dissociation of micelles at concentrations approaching the critical micelle concentration, provided that the concentration range analyzed is well above the copolymers cmcs.

Fig. 3 Debye plots for (a) BO₈EO₉₀BO₈ and (b) BO₂₀EO₄₁₁BO₂₀ copolymers at 10 °C (open symbols) and 25 °C (filled symbols).

Values of M^m_w were obtained by simply applying the Debye equation for copolymer BO₈EO₉₀BO₈ and by linear extrapolation of experimental data at c < 5 mg mL⁻¹ and by for BO₂₀EO₄₁₁BO₂₀, respectively, and calculated from N_w = M^m_w/M_w (Table 2). The almost ideal behavior of the BO₈EO₉₀BO₈ system at low concentration is attributed to counter-balanced attractive and repulsive interactions of micelles in the dilute solution range and the polymer ability to pack in single micelles at low concentrations due to its much shorter blocks, as commented previously (see Fig. 2a).

Association numbers for copolymer BO₈EO₉₀BO₈ were larger than those of BO₂₀EO₄₁₁BO₂₀ as corresponds to a copolymer with a lower EO/BO ratio and much shorter EO block length: the increment of N_w due to the presence of longer BO blocks for copolymer BO₂₀EO₄₁₁BO₂₀ was counter-balanced by the N_w decrease expected by their longer EO blocks, as observed for other poly(oxyalkylene)s copolymers.¹⁶ Also, N_w values for these copolymers slightly increased as temperature rose provided that water becomes a poorer solvent for the poly(oxyethylene) blocks, as previously mentioned.¹⁷ Association numbers of copolymer BO₂₀EO₄₁₁BO₂₀ are similar to those obtained for the structurally related copolymer BO₁₀EO₄₁₀BO₁₀ despite its larger BO block length, and are lower than those of other BO_mEO_nBO_m with lengthy EO blocks such as BO₁₄EO₃₇₈BO₁₄ (N_w = 18),²⁹ BO₁₂EO₂₇₀BO₁₂ (N_w = 28)³⁰ and BO₁₂EO₂₆₀BO₁₂ (N_w = 29).¹⁸ In this regard, it is worth mentioning that BO_mEO_nBO_m copolymers possessing EO < 300 units exhibit an increase in N_w as their hydrophobic block length increases as observed for BO₅EO₉₁BO₅, BO₆EO₄₆BO₆,³⁰ BO₇EO₄₀BO₇,¹⁸ BO₁₀EO₂₇₁BO₁₀ and BO₁₂EO₂₇₀BO₁₂,³⁰ for example. Conversely, BO_mEO_nBO_m copolymers with EO > 300 units decrease their N_w values as the BO block length increases as, for example, from 18 to 9 for BO₁₄EO₃₇₈BO₁₄ and BO₂₁EO₃₈₅BO₂₁, or from 8 to 7 for BO₁₀EO₄₁₀BO₁₀ and BO₂₀EO₄₁₁BO₂₀, respectively. This trend is a consequence of steric restrictions of the lengthy EO corona to efficiently pack more hydrophobic chains inside the micellar core nuclei.¹⁷

On the other hand, Fig. 4a shows the dependence of N_w on BO-block length for different BO_mEO_nBO_m reported so far.¹⁷ Values of N_w were adjusted for differences in n (the EO block length) using the scaling exponent N_w ∼ (n′)^1.07, where n′ (n′ = n − n_crit, n_crit = 4 is the effective hydrophobic block length, that is, the minimum hydrophobic block length in reverse BO_mEO_nBO_m for micellization) is the effective hydrophobic block length. The line through the data points of log(N_w/n′^1.07) against log(m) has a slope of −0.84. Attwood et al. previously obtained an exponent of −0.63,¹⁷ whilst Föster et al. derived an exponent of −0.71 for short C_nEO_m copolymers with n = 8–16 and m = 4–23.³¹ The difference may arise from introducing BO_mEO_nBO_m copolymers with extremely lengthy EO blocks (EO > 375 units) and long BO blocks (BO > 14) in Fig. 4a, which possess relatively low aggregation numbers due to their very long chains. On the other hand, Fig. 4b effectively verified that data points plotted as log(N_w/m^0.84) against log(n′) do indeed fit satisfactorily to a straight line of slope 1.0 with evident correspondence with scaling exponents of N_w as a function of the EO block length (ca. 1.07) derived from diblock and non-bridging triblock copolymers.

Fig. 4 (a) Dependence of the association number on (a) EO-block length, m, and (b) effective hydrophobic block length, n′. Association numbers are corrected for variation in hydrophobic and hydrophilic block lengths, respectively. () denote the copolymers studied.

Rheological behaviour

Tube inversion. Tube inversion was used to obtain a preliminary definition of the mobile–immobile regions of the phase diagram of each copolymer. For both polymers the mobile region (sol) transforms progressively into a viscous fluid and, then, to a gel as the concentration increases. For BO₈EO₉₀BO₈ a mobile viscous fluid was present up to a concentration of 6 wt% whilst an immobile gel was formed above (Fig. 5). The gel phase progressively converts into a very viscous fluid, resembling a high temperature boundary, in the temperature range 40 to 70 °C depending on concentration: the higher the concentration the larger the boundary temperature was. In the case of copolymer BO₂₀EO₄₁₁BO₂₀, a mobile more or less viscous fluid is present up to 8 wt%, whilst an immobile transparent gel is formed above such value within a determined temperature range, which is broader as the copolymer concentration increases. At 12 wt%, the gel phase of the present copolymer is present along the whole temperature range analyzed. Comparison of phase transitions of BO_nEO_mBO_n copolymers with lengthy EO blocks (EO > 350 units) showed that the transition point from sole to soft gel largely depends on the EO block length at temperatures below room temperature, whilst the change from soft-gel to hard gel is dominated by the BO/EO ratio, that is, the most hydrophobic the copolymer is, the gel phase appears at lower concentrations and temperatures.²⁹

Fig. 5 Phase diagrams depicted by using tube inversion and rheometry data from temperature scan for (a) BO₈EO₉₀BO₈, and (b) BO₂₀EO₄₁₁BO₂₀. () denote clouding boundaries obtained UV-vis, whereas () are experimental points measured by rheometry. Lines were only drawn to guide the eye.

To perfectly define the boundaries of the phase diagrams and to further characterize the flow behaviour of semi-dilute and concentrated copolymer solution, rheometry measurements were also performed.

Concentration and temperature dependence of storage and loss moduli. Oscillatory tests were performed in order to determine the linear viscoelastic region in which oscillatory shear measurements need to be performed ensuring, at the same time, that the system is frequency-dependent (see Fig. S1†). G′′ values were consistently smaller than the G′ ones for both copolymers (not shown). A linear region in which the G′ value was almost independent of strain was observed. In addition, for both copolymers G′ and G′′ increases as copolymer concentration does being G′ larger for BO₈EO₉₀BO₈ than for BO₂₀EO₄₁₁BO₂₀; however, it is observed that while for BO₈EO₉₀BO₈ the linear viscoelastic region becomes wider as the concentration increases, for copolymer BO₂₀EO₄₁₁BO₂₀ the opposite behaviour is found. This different behaviour results from differences in packing and flow behaviour between both copolymers. In particular, as observed from DLS data, copolymer BO₈EO₉₀BO₈ would form smaller free micelles and relatively strong bridging micelles; these would involve the formation of a more compact, stronger and flexible nanostructure (for example, reflected in a sol–hard gel transition around a copolymer concentration of 5–6 wt%, see below for further details) which would help to explain the increase of the linear viscoelastic region with concentration. By contrast, copolymer BO₂₀EO₄₁₁BO₂₀ would form larger sized micelles which would lead to less compact structures as the copolymer concentration increases (reflected, for example, in the formation of gel structures at larger concentration compared to copolymer BO₈EO₉₀BO₈, see below) generating weaker nanostructures; as an additional consequence, a decrease of the lineal viscoelastic region with the copolymer concentration occurs.

Once determined the linear viscoelastic region, temperature scans in the range 1–90 °C of log(G′) at f = 1 Hz for copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ were performed. The dependence of G′ on concentration and temperature is provided by the examples shown in Fig. 6. At 1 wt%, copolymer samples are unstructured fluids (sols, with G′ < 10 Pa and G′′ > G′). At 2 wt% copolymer BO₈EO₉₀BO₈ was a viscous complex fluid characterized by 10 < G′ < 1000 Pa and G′ > G′′ (i.e. a soft gel adopting Hvidt's et al. notation),³² in the temperature range 16 to 63 °C, and it became a sol below and above such temperature interval (Fig. 6a). In particular, the observed decrease in G′ at high temperatures and, thus, the transition from a viscous fluid to a sol can be associated with a worsening solvent environment compressing the EO-block corona. In the concentration range from 3 to 5 wt%, this copolymer was a viscous fluid in the whole temperature range analyzed above 5 °C. At 6 wt% copolymer BO₈EO₉₀BO₈ became a gel (arbitrarily defined by G′ > G′′ and G′ > 1000 Pa at f = 1 Hz, a hard gel adopting Hvidt's et al. notation) within the temperature range 5–20 °C and above it becomes a viscous fluid. The gel region subsequently expands within a broader temperature range as the copolymer concentration increases (from 0 to 27 °C, at 8 wt% and until 70 °C at 10 wt%); above the upper limit temperature the copolymers becomes a soft gel. Hence, despite their reverse structure, copolymer BO₈EO₉₀BO₈ displayed a behaviour similar to diblock EO_nBO_m and triblock EO_nBO_mEO_n copolymers, in which micellar packing determines the moduli behaviour as the polymer concentration increases.

Fig. 6 Temperature scans in the range 1–90 °C of G′ at f = 1 Hz for copolymers (a) BO₈EO₉₀BO₈ and (b) BO₂₀EO₄₁₁BO₂₀ at different concentrations. (c) Plots of G^′_max against concentration for copolymers () BO₈EO₉₀BO₈ and () BO₂₀EO₄₁₁BO₂₀.

Despite possessing longer hydrophobic and hydrophilic blocks, the larger EO/BO ratio and the existence of bridging which may difficult effective cubic packing makes copolymer BO₂₀EO₄₁₁BO₂₀ to remain in a sol state up to a concentration of 3 wt% (Fig. 6b). At 4 wt% it already became a viscous fluid between ca. 30 and 50 °C and 5 and 6 wt% in the whole temperature range. At 7 and 8 wt% this copolymer is a gel between 24–45 °C and 14–57 °C, respectively and a viscous fluid in the remaining temperature interval. At 10 wt%, the copolymer is a gel above 20 °C and in the whole temperature range at 12 wt%. All the above data allowed a more exact definition of the phase diagram, as shown in Fig. 5. On the other hand, maximum values of G′(T), G^′_max of copolymer BO₂₀EO₄₁₁BO₂₀ are similar to those of structurally related copolymers with EO blocks ∼400 units such as BO₂₁EO₃₈₅BO₂₁ and BO₁₄EO₃₇₈BO₁₄; in addition, copolymer BO₈EO₉₀BO₈ possesses G^′_max values larger than the latter copolymers despite having much lower BO and EO units as a consequence of a better cubic packing of micelles with shorter solvated EO coronas. Despite de observed differences, both BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ copolymers G′ values increased markedly with concentration, with a predominant elastic behavior (G′ > G′′) in most of the temperature and concentration ranges analyzed, as occurred for other reverse BO_nEO_mBO_n copolymers with lengthy EO blocks (Fig. S2†).

As discussed elsewhere³³ for aqueous micellar gels of copoly(oxyalkylene)s of different block architectures, the onset of gelation and the associated increase in G′ with T at low temperatures for copolymer BO₂₀EO₄₁₁BO₂₀ is associated with an increase in the extent of micellization and, in the present case, with the extent of bridging. This is in contrast with the behavior observed for BO₈EO₉₀BO₈ whose G′ values in the gel region (at 10 wt%) are fairly constant until relatively high temperatures (>70 °C) at which then decrease. This observed decrease in G′ at high temperatures can be associated with a worsening solvent environment compressing the EO-block corona and, thereby, with a decrease in the effective micellar volume fraction. This viscous fluid after the immobile gel phase has been shown to be composed by small micellar domains with the same structure as the gel phase as observed by SAXS and SANS;³⁴ hence, it can be characterized as a defective cubic structure, as previously observed for related EO_mBO_n and EO_mBO_nEO_m copolymers.³³

Frequency scans. Effects of changes in the extent of micellar bridging and packing are apparent in the different mechanical responses of the system to the applied frequency. Hence, the frequency dependence of the modulus was determined for solutions of copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ in the concentration range 1–10 wt%. For example, Fig. 7a shows an 1 wt% solution for copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ at 10 °C, with values of G′′ exceeding those of G′ over most accessible frequency range, except at high frequencies, where a moduli crossover occurs from which a relaxation time t = 0.90 and 0.35 s, respectively, could be determined. The behavior can be approximated to that of a Maxwell element:where G_∞ is the plateau value of G′ at high frequency, τ is the relaxation time, and ω = 2πf (f = frequency in Hz). At all temperatures investigated, the slopes of the best straight lines through the data points were near to values of 2(log G′) and 1(log G′′) which are expected when ωτ ≪ 1, i.e. typical of a Newtonian fluid.

Fig. 7 Frequency scans for the present copolymers at different concentrations and temperatures: (a) BO₈EO₉₀BO₈ (, ) and BO₂₀EO₄₁₁BO₂₀ (, ) at 2 wt% and 10 °C; (b) BO₂₀EO₄₁₁BO₂₀ copolymer at 3 wt% and (, ) 10 °C, (, ) 20 °C, and (, ) 60 °C; (c) BO₈EO₉₀BO₈ copolymer at 5 wt% and (, ) 10 °C and (, ) 40 °C; (d) BO₈EO₉₀BO₈ copolymer at 8 wt% and (, ) 30 °C and (, ) 50 °C; BO₂₀EO₄₁₁BO₂₀ copolymer at 12 wt% at (, ) 10 °C and (, ) 40 °C. Closed symbols denote G′ whilst open ones correspond to G′′.

For copolymer BO₂₀EO₄₁₁BO₂₀ G′′ is consistently larger than G′ in the whole frequency range analysed in the concentration range 2–4 wt% at temperatures below 50 °C except at very frequencies (f > 10 Hz) where a moduli crossover takes place. At larger temperatures, the moduli crossover can be observed at much lower frequencies corresponding to a Maxwell fluid showing, at most, localized cubic order (Fig. 7b).³³ This effect must be a consequence of the attraction of micelles at temperatures at which water is a poor solvent for micelles, and favored by micellar bridging too. A similar behavior can be observed at larger copolymer BO₂₀EO₄₁₁BO₂₀ concentrations (5–7 wt%) and for copolymer for copolymer BO₈EO₉₀BO₈ in the concentration range 2–5 wt% but only at temperatures below room temperature (Fig. 7c). Then, as the concentration is further increase for both copolymers (>8 wt% and 6 wt% for BO₂₀EO₄₁₁BO₂₀ and BO₈EO₉₀BO₈, respectively) an immobile gel with relatively high G′ values (>1 kPa) existed typically below 70 °C depending on copolymer type and concentration, as commented previously. Above such temperature threshold, a viscous fluid was observed (Fig. 7d). This type of viscous fluid at temperatures and concentrations relatively near the gel boundary can be assigned as defective versions of cubic packed gels as mentioned previously; they are characterized by a constant value of G′, the shallow minimum in G′′, and both moduli do not show a crossover point in the measured frequency range as observed in Fig. 7d. Nevertheless, the G′ values for the viscous fluid are much lower compared to those of a pure gel phase, which well exceeded 1 kPa and possessed the characteristic features of immobile gels constituted by cubic packing of spherical micelles completely independent on temperature and frequency.³⁵ The plateau behavior of G′ and the minimum in G′′ have been also observed for colloidal hard spheres near the glass-fluid transition,³⁶ and is also characteristic of the cubic phase in block copolymer melts.³⁷ The frequency-independent regime took place at lower concentrations for copolymer BO₈EO₉₀BO₈ than for BO₂₀EO₄₁₁BO₂₀ due to its larger BO/EO ratio, which favored micellization.

Plots of G′ and G′′ vs. frequency presented in Fig. 7 show a wide variety of characteristics from purely viscous to highly elastic fluids. The observed behaviours seems to confirm the formation of a dynamic network for both copolymers, but specially for BO₂₀EO₄₁₁BO₂₀, which becomes more and more robust as the concentration is increased, as observed for other BO_mEO_nBO_m copolymers with very lengthy EO blocks as BO₁₂EO₁₁₄BO₁₂,¹³ BO₁₀EO₂₂₇BO₁₀,²⁶ BO₁₂EO₂₂₇BO₁₂,²⁸ BO₁₀EO₄₁₀BO₁₀,¹¹ BO₂₁EO₃₈₅BO₂₁ and BO₁₄EO₃₇₈BO₁₄.²⁷ The existence of slow relaxation processes as the copolymer concentration increases also seems to corroborate this point. For BO₈EO₉₀BO₈ micelle packing as effective hard spheres in the gel phase becomes the predominant response at much lower concentrations than for copolymer BO₂₀EO₄₁₁BO₂₀, which agrees with that previously mentioned.

On the other hand, copolymer BO₂₀EO₄₁₁BO₂₀ showed rather different behavior to that observed for other structurally related copolymer, BO₁₀EO₄₁₀BO₁₀. For this copolymer typical values of G′′ exceed those of G′ over a similar accessible frequency range, as also observed for other classical associative thickeners.³⁸ Despite the similar EO length and larger BO blocks compared with BO₁₀EO₄₁₀BO₁₀, the larger polydispersity of BO₂₀EO₄₁₁BO₂₀ (as also occurred for copolymers BO₁₄EO₃₇₈BO₁₄ and BO₂₁EO₃₈₅BO₂₁) can broad the Poisson distribution of BO block-lengths (assuming ideal polymerization),³⁹ which involves a wider temperature range for micellization. Hence, this copolymer effectively behaves as having lower effective BO block lengths with a behavior more related to that observed to BO₁₂EO₁₁₄BO₁₂, BO₁₀EO₂₂₇BO₁₀ or BO₁₀EO₂₂₇BO₁₀ copolymers. Also, both BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ do not behave as classical colloidal suspensions interacting through weak short-range attractive forces, that is, G′ being frequency-independent and increasing with concentration, and G′′ being concentration-independent and increasing linearly with frequency. All these facts allow to scale the moduli against frequency to give smooth master curves,⁴⁰ which allows to gain access to sample's behaviour under frequencies that are not accessible using common instrumentation (see below).

Scaling of rheological response. The construction of a master curve through the time–temperature superposition of the measured moduli was performed in order to facilitate comparison of the frequency response at different temperatures of copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀. The moduli and the frequencies for each data set were independently scaled by factors a_T and b_T, respectively, to obtain a superposition of G′ and G′′. The temperature dependence of the moduli was explored for the copolymers in the gel region. Fig. 8a and S3† show the superposition achieved at 8 wt% and 12 wt% for copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀, respectively. The data suggest that there are no changes in the nature of the dynamic mechanical response in the gel phase as a function of temperature in the range 10–50 °C. As already discussed, higher temperatures worsen the solvent environment and progressively compress the micellar corona. The shrinkage of the micellar corona will lead to defects in micellar packing and the bridged network, which may well change the scaling of the viscoelastic behaviour with frequency within the hard gel phase.

Fig. 8 (a) Master curve plots obtained for copolymer BO₈EO₉₀BO₈ at 8 wt% (reference temperature T_r = 10 °C). (b) Arrhenius plot for copolymer () BO₂₀EO₄₁₁BO₂₀, () BO₁₀EO₄₁₀BO₁₀, () BO₂₁EO₃₈₅BO₂₁, and () BO₁₄EO₃₇₈BO₁₄. Concentration for BO₂₀EO₄₁₁BO₂₀, BO₂₁EO₃₈₅BO₂₁, and BO₁₄EO₃₇₈BO₁₄ is 12 wt% whilst for BO₁₀EO₄₁₀BO₁₀ is 15 wt%. (c) Temperature dependence of 1/b_T for copolymers () BO₈EO₉₀BO₈ and () BO₂₀EO₄₁₁BO₂₀ (see also inset) at 8 and 12 wt%, respectively.

The Arrhenius plot of −log(a_T) against 1/T (Fig. 8b and S4†), which has a slope equivalent to a plot of log(relaxation rate) against 1/T, gave activation energy values (the energy related to the relaxation mechanism in crosslinking or bonding processes) through the application of the Williams–Landel–Ferry equation⁴¹

log a_T = −C₁(T − T_r)/(C₂ + (T − T_r)) (4)

where T is the temperature, T_r is the reference temperature to construct the compliance master curve, and C₁ and C₂ are empirical constants to fit the values of the superposition. Therefore, the activation energy, E_a, can be derived as

E_a = 2.303RC₁C₂T²/(C₂ + T − T_r)² (5)

Activation energies of E_a = −11 and −41 kJ mol⁻¹ were obtained for copolymers BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀, respectively, as an average value over all components of the copolymer solutions. The negative values imply that the relaxation time increases as temperature rises, which is in agreement with the progressive hardening of the gel in the temperature range analyzed.¹¹ As can be seen in Fig. 8b, the obtained slope for copolymer BO₂₀EO₄₁₁BO₂₀ (and hence, activation energies) is rather to other BO_nEO_mBO_n copolymers having EO bock lengths >350 units, as for example, BO₁₀EO₄₁₀BO₁₀ (E_a = −40 kJ mol⁻¹) or BO₂₁EO₃₈₅BO₂₁ (E_a = −50 kJ mol⁻¹).^11,27 In fact, there is a slight increase in the slope net value obtained for the BEB block copolymers as the BO/EO ratio increases.

Also, the negative activation energy values indicate that both the disengagement of chain ends from micelles (a positive contribution) and micellization (a negative one) can contribute in contrast to alkyl-ended copolymer solutions, where only disengagement is important provided that their extent of micellization is low over the temperature range of interest and, hence, positive activation energies are obtained.^42,43 This behaviour is confirmed when analyzing the dependence of storage modulus with temperature by plotting 1/b_T against T (see Fig. 8c). Copolymer BO₈EO₉₀BO₈ at 8 wt% exhibits an important decrease of 1/b_T (or storage modulus) with temperature. This decrease is much greater in the low temperature range in agreement with the progressive shrinkage of the cubic mesoscopic structure of packed micelles and the increased tendency as temperature is increased for the copolymers to loop in a single micelle rather than to bridge between micelles.⁴³ Conversely, for copolymer BO₂₀EO₄₁₁BO₂₀ a slight increase of 1/b_T against T can be observed, which points to an increase in the high-frequency storage modulus in the temperature interval analyzed compatible with an increase in the extent of micellization and, then, of bridging. This temperature dependence is greater than that predicted by the kinetic theory of elasticity for a fully formed network.

Conclusions

In summary, the present BO₈EO₉₀BO₈ and BO₂₀EO₄₁₁BO₂₀ copolymers form swollen flower-like micelles with sizes ranging from ca. 13 to 30 nm. Copolymer BO₈EO₉₀BO₈ can form individual micelles in very dilute solutions whilst BO₂₀EO₄₁₁BO₂₀ already display a secondary population at sizes ca. 200–300, which represents interconnected micelles by bridging as confirmed by AFM images. At slightly larger concentrations, these micellar clusters are already observed for both copolymers and even for BO₂₀EO₄₁₁BO₂₀ a third population with sizes ca. 3000–4000 nm is detected which would correspond to the aggregation of several micellar bridged clusters. As a result of their long BO blocks and extremely lengthy EO ones, these two copolymers exhibited very rich phase behaviours. This could be modulated from an unstructured fluid to a viscoelastic one to a fully developed gel by changing the solution temperature and concentration. In particular, bridging could be observe by the appearance of slow relaxation modes at relatively low polymer concentrations as denoted form the frequency scans, specially for copolymer BO₂₀EO₄₁₁BO₂₀ thanks to their lengthy EO blocks and longer BO ones, which favoured a much larger exclusion volume and intermicellar attraction while reaching a less efficient packing of micelles. As the concentration increases the dynamic network becomes more robust as the concentration, which impeded to fit their behaviour to that of Maxwell fluid. At this respect and confirming this view, copolymer BO₈EO₉₀BO₈ displays a more classical behaviour of packed mesoscopic cubic structures in the gel phase at much lower concentrations than BO₂₀EO₄₁₁BO₂₀. The negative values of the activation energy for the relaxation processes derived from master curves might involve both the disengagement of chain ends from micelles (a positive contribution) and micellization (a negative one), with evident predominance of the latter.

Acknowledgements

Authors thank Ministerio de Economía y Competitividad (MINECO) and Xunta de Galicia for research projects MAT2013-40971-R and EM2013-046, respectively. S.B. also thanks MINECO for her Ramón y Cajal fellowship.

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra10176f

‡ These authors contribute equally to this work.

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