Letter pubs.acs.org/macroletters
Molecular Exchange Kinetics of Micelles: Corona Chain Length Dependence Thomas Zinn,† Lutz Willner,‡ Vitaliy Pipich,§ Dieter Richter,‡ and Reidar Lund*,† †
Department of Chemistry, University of Oslo, Postboks 1033 Blindern, 0315 Oslo, Norway Jülich Centre for Neutron Science JCNS and Institute for Complex Systems ICS, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany § Jülich Centre for Neutron Science JCNS, Forschungszentrum Jülich GmbH, Outstation at MLZ, Lichtenbergstrasse 1 85747 Garching, Germany ‡
ABSTRACT: The rate of molecular exchange in diblock copolymer micelles is strongly dependent on the chain length of the core-forming insoluble block. Less is known about the influence of the soluble block forming the micellar corona. In this study we present a time-resolved small angle neutron scattering (TR-SANS) study exploring systematically the effect of corona chain length on the dynamics of chain exchange. As a model system we have taken amphiphilic AB diblock copolymers of the type C27H55-poly(ethylene oxide)x (C27−PEOx) with varying x between 4 and 36 kg/mol in aqueous solution in which well-defined spherical micelles with partially crystalline cores are formed. The TR-SANS results show that the chain exchange slows down considerably upon increasing PEO molecular weight, while the characteristic “attempt time” constant, τ0, was found to increase with a power law dependence τ0 ∼ M9/5 PEO. The results are in excellent agreement with the Halperin and Alexander model1 and can be attributed to a reduced diffusion rate through the micellar corona. Our results clearly demonstrate that the rate for molecular exchange is not directly coupled to the solubility of the amphiphile and the critical micellar concentration, as has previously been indicated.
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KZAC experiments were conducted on a variety of different micellar model systems. As a primary result, it was found that the kinetics is governed by single chain exchange, in agreement with theory. The studies further showed a good correspondence with the predicted strong dependency on interfacial tension13 and temperature.6,14 The effect of the insoluble block length on the exchange kinetics has been extensively studied, scaling, a linear dependence but contrary to the Ea ∼ M2/3 B between the activation energy and the molecular weight was found.14,15 The Ea ∼ MB scaling was attributed to the short insoluble block which does not have the conformational freedom to adopt a spherical globular shape during expulsion as assumed in the Halperin and Alexander model.14 The dependence on the corona block length is generally assumed to be much less important. Nevertheless, from previous experiments it is known that in the semidilute regime the kinetics is slowed down significantly and is attributed to an osmotic penalty from overlapping corona chains.2,16 Similarly, it was shown that addition of corona homopolymers to a micellar solution leads to a deceleration of the kinetics when the concentration of free polymers were high enough to penetrate
ontinuous dynamic exchange of amphiphiles is a major prerequisite for micelles to reach and attain their thermal equilibrium state. For polymeric micelles containing extended corona chains, the process is dominated by single chain (unimer) exchange. Intermicellar fusion and fission events are essentially suppressed by entropic repulsion. The rate limiting step of the kinetics is the expulsion of the unimer which is wellunderstood as a thermally activated first-order process. Within this picture the time scales of exchange are related to the potential barrier for expulsion given by the excess surface area created by the expelled hydrophobic part of the chain. The process obeys an Arrhenius law τ = τ0 exp(Ea/kBT),1−3 and following the classical theory of Halperin and Alexander,1 the activation energy scales as Ea ∼ γ · M2/3 B , where γ and MB are the interfacial tension and the molecular weight of the insoluble block, respectively. More than a decade ago, our research team introduced a novel time-resolved small-angle neutron scattering (TRSANS)/contrast variation technique to quantitatively monitor the molecular exchange process of micellar systems in situ,3−6 which we will refer to as the kinetic zero average contrast technique (KZAC). Contrary to previous methods such as fluorescence7−9 and temperature jump experiments,10−12 the KZAC method imposes negligible perturbation from its thermal equilibrium. In recent years, numerous TR-SANS/ © XXXX American Chemical Society
Received: May 20, 2016 Accepted: July 4, 2016
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DOI: 10.1021/acsmacrolett.6b00395 ACS Macro Lett. 2016, 5, 884−888
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ACS Macro Letters Table 1. Structural and Chemical Properties of C27−h-PEOx and C27−d-PEOx Polymers and Micellesa MPEO (kg/mol) n
NPEO
P
Rm (Å)
Rc (Å)
Tm (°C)
ΔHfus (kJ/mol)
τ0 (s)
Ea (kJ/mol)
4.2b 10.4b 21.2b 36.0b 4.4c 10.9c 20.4c 38.5c
95 236 482 818 91 227 425 802
96 39 41 30 122 41 38 23
109 142 208 282 108 147 204 268
26 18 18 16 27 20 18 15
54.4 44.3 43.5 42.6
34.6 34.4 36.4 39.5
0.29 1.08 3.49 20.9
159 157 154 149
a
Molecular weight of PEO, MPEO n , number of EO repeat units, NPEO, aggregation number, P, core radius, Rc, micellar radius, Rm, core block melting point, Tm, enthalpy of fusion, ΔHfus, attempt time, τ0, and activation energy, Ea. bC27−h-PEOx. cC27−d-PEOx.
the micellar corona.17 To our knowledge, systematic experimental data showing directly the effect of the soluble chain length on the molecular exchange rate has not been reported yet. The relaxation spectrum of block copolymer micelles is generally extremely broad due to finite polydispersity of the core forming polymer block that leads to a broad distribution of rate constants and an almost logarithmic decay.5,15,18 This sometime obscures the interpretation of data which involves numerical calculations and exact knowledge of the chain length distribution. To this end, we recently introduced a well-defined model system consisting of monodisperse n-alkyl groups of variable length (C18−C30) covalently attached to poly(ethylene oxide) (PEO) prepared through anionic polymerization. These polymers form spherical micelles in aqueous solution consisting of partially crystallized n-alkane cores and extended PEO coronas with starlike density distribution.19,20 Contrary to block copolymers, the molecular kinetics of these micelles comply to a single exponential decay reflecting a unique rate constant and hence an activation barrier for expulsion.21 Recently, we investigated the role of chain packing (“crystallization”), chain stretching, and conformational loss on the molecular exchange kinetics of micelles with semicrystalline cores.14,19 The results showed pronounced entropic contributions that favor molecular exchange through the relief of conformational constraints when a chain is released from a micelle. It is therefore of great interest to investigate how the chain exchange is affected upon increasing the corona chain length, which should inevitably augment the entropic penalty associated with micellization. In this Letter, we systematically investigate the role of the soluble PEO block on the rate of molecular exchange using C27−PEOx polymers, where x is varied from 4 to 36 kg/mol using the TR-SANS/KZAC method. The data clearly show that, with increasing PEO molecular weight kinetics slows down significantly. Performing a detailed analysis of the temperature dependence, we observe that the activation energy is independent or only weakly dependent on the length of the PEO, whereas the characteristic diffusion time is significantly dependent on the PEO block size. For the KZAC experiments, copolymers consisting of either proteated C27−h-PEOx or deuterated C27−d-PEOx poly(ethylene oxide) have been prepared with almost identical molecular characteristics. The C27-block was proteated in all cases. Synthetic protocols as well as a detailed analysis of structural and thermodynamical properties of micelles in dilute solution have been presented elsewhere.19,20 The structural parameters of the micelles, the aggregation number P, the core radius Rc, and the micellar radius Rm, are summarized in Table 1. The table also includes the core block melting point and the
corresponding enthalpy of fusion obtained from nano-DSC measurements.19 To probe the chain exchange kinetics, two solutions of deuterated and proteated micelles are individually prepared in a H2O/D2O solvent mixture having a composition that matches the average contrast of the two differently labeled polymers. The two solutions are mixed in a 1:1 ratio, and the scattered intensity, I(t), is monitored over time. The extent of exchange can be expressed by a dimensionless relaxation function R(t) given by3,6,13 ⎡ I(t ) − I ⎤1/2 ∞ R (t ) = ⎢ ⎥ ⎣ I0 − I∞ ⎦
(1)
with I0 and I∞ the scattered intensity of the initial state just after mixing at t = 0 and of the final state at (t → ∞), where all chains are equally redistributed among the micelles at a given temperature.3 The TR-SANS experiments were performed at T = 22.5, 26.8, 30.5, and 34.5 °C and additionally for C27−PEO5 at 18.5 °C. All experiments were performed in 1 vol % aqueous solution, except C27−PEO36, which was investigated at 0.25 vol % in order to avoid visible excluded volume effects at higher concentrations. All temperatures are well below the confined nalkyl melting point Tm. The relaxation curves at 30.5 °C for the various C27−PEOx samples are depicted in a semilogarithmic representation in Figure 1. All data display a linear dependence in a semilogarithmic plot indicating a single exponential decay on the form R(t) = exp(−t/τ). We should note at this point that a single exponential relaxation is only obtained for block copolymers consisting of a monodisperse core forming block
Figure 1. Relaxation curves R(t) as a function of PEO molecular weight at 30.5 °C. Solid lines show the corresponding linear fit curves. 885
DOI: 10.1021/acsmacrolett.6b00395 ACS Macro Lett. 2016, 5, 884−888
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ACS Macro Letters which for the present case is the C27-alkyl group. The polydispersity of the PEO of ≤1.03 is considered to be insignificant because of the comparable weak dependence on the PEO block length. As the data clearly show, the relaxation times significantly increase with increasing PEO molecular weight. This observation can be directly related to an effect of the soluble corona chain length, as all other parameters, including the core block, remain exactly the same. A similar behavior can be found for all other temperatures investigated. The temperature dependence was evaluated more quantitatively using an Arrhenius analysis depicted in Figure 2 where
Figure 3. Dependence of PEO molecular weight on the Arrhenius parameters. The activation energy, Ea (black squares), is almost independent or only weakly decreasing, while the “attempt time”, τ0, significantly increases with MPEO. The molecular weight dependence of the diffusion time is compatible with the scaling τ0 ∼ M9/5 PEO behavior predicted by Halperin and Alexander.1 The black line serves as a guide to the eye only.
the chain undergoing a release process will experience a larger friction with other chains, leading to an effective reduction in the attempt time and, thus, slower exchange kinetics. As indicated in Figure 4, this leads to a significant change in the Figure 2. Arrhenius plots showing the variation of the time constant τ for the different C27−PEOx chain exchange kinetics as a function of inverse temperature.
log τ is plotted versus 1/T. As seen, the data display almost parallel straight lines following the Arrhenius equation: τ(T) = τ0 · exp (Ea/RT), where R is the universal gas constant and T is the absolute temperature. The parallel lines indicate similar activation energies Ea. This contrasts the temperature dependence of Cn−PEO5 micelles with varying hydrophobic block length, where the data display different slopes reflecting changes in the activation barrier.14 Since the activation energy within experimental precision is constant the Arrhenius behavior reveal different prefactors, τ0. The extracted prefactors τ0 and Ea are plotted in Figure 3 as a function of the PEO molecular weight. As seen in Figure 3, τ0 increases substantially with the length of the PEO chain indicating a significant influence from the corona chains on the exchange rate. Comparing with the theory of Halperin and Alexander,1 the relaxation time τ(T) is indeed expected to depend on the length of the coronal chains, but only for asymmetric micelles with starlike morphology, that is, when the number of monomers of the corona block, NA, is significantly larger than for the core block, NB, that is, NA ≫ NB: (2)
Figure 4. Schematical illustration of the expulsion process. With increasing PEO block length, the attempt time increases due to the slower diffusion caused by a thicker corona layer. In terms of the Halperin and Alexander theory,1 this leads to a significant change in the free energy profile, F(y) over the chain displacement coordinate y. In addition, the slower the diffusion, the longer the residence time and, hence, the higher probability for reinsertion, thus, leading to slower exchange kinetics.
with Ea the activation energy predicted to scale as Ea(NB) ∼ 2 γN2/3 B lB, where lB is the segment length of the core block and γ is the interfacial tension. For the present case, we expect τ0 to scale as τ0 ∼ M9/5 PEO. Comparing with the fitted line in Figure 3, we find a good agreement with our data. Within the Halperin and Alexander theory, the origin of this strong dependence was attributed to the increased diffusion time through the corona constituted by longer chains. As the length of the corona chains are increased,
free energy profile, F(y) over the “reaction coordinate”, y, that is defined as the distance of the block copolymer junction from the core−corona interface. We might also note that increased residence time within the corona also increases the probability of reinsertion, thus, leading to an “unsuccessful” exchange event and thus slower overall rates. For the activation energy, we find almost constant values in the range of Ea = 149−159 kJ/mol with a slight decreasing
τ(T ) ∼ exp(Ea(NB)/kBT )NB2/25NA9/5
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ACS Macro Letters
by Lodge and co-workers.16,17 However, in these cases, the slowing down has a different origin that, according to Halperin,2 is an effect of coronal screening and a resulting increase of osmotic pressure due to an increase in the effective corona polymer concentration. This yields an additional term to the activation barrier. The slower kinetics with increasing PEO molecular weight observed in the present work relates to a slower diffusion because of the longer corona chains rather than the polymer concentration within the corona. It should be pointed out that our work also shows that the molecular exchange kinetics do not follow the same trend as the critical micelle concentration (cmc), which is sometimes claimed.23,26 Instead, the chain exchange becomes slower, whereas the cmc is known to increase with increasing PEO molecular weight at fixed hydrophobic block length. Summarizing, this work provides substantial insight into the molecular mechanism for micellar exchange kinetics of micelles. Given the importance to the stability of micelles and the physical understanding of micellization, the current findings demonstrate a strategy to tune the exchange rates independently of the cmc by simply varying the hydrophilic block length.
tendency for the higher PEO molecular weights. This could indicate a minute variation of the degree of crystallinity of the micellar core since the enthalpy of fusion would add to the activation energy.19 However, we note that ΔHfus obtained from DSC does not seem to vary significantly with the PEO length (see Table 1). As discussed in a previous work,14 τ0 contains an entropic term associated with a gain of entropy upon releasing the chain into the solution during the exchange process, that is, τ0 = τ†0 exp(−ΔS‡/kB), where ΔS‡ is the entropy of “activation”. It is thus important to verify whether a change in τ0 may reflect a significant difference in the entropy per chain within the micelle. For the present system, the gain in entropy may vary as the degree of core stretching within the corona and the nalkane packing may presumably depend on the PEO chain length. For the latter we have seen that the entropy of fusion estimated from DSC is almost constant for all PEO lengths, and thus, this does not contribute to a significant degree. The entropic costs of elastic stretching of PEO chains within the corona can be estimated using ΔS ≈ kB·
(R m − R c)2 R ee2
where kB is
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the Boltzmann constant and Ree is the end-to-end distance of the PEO chain. Following Gaussian chain statistics, Ree can be 22 estimated by √6 · Rg, taking Rg = 0.215 · M0.588 PEO . Inserting the values for Rm and Rc from Table 1, we obtain values for ΔS between 1.3kB and 1.1kB for the shortest and longest PEO chains, respectively. Hence, we do not expect significant differences in the entropy of activation arising from corona chain deformation for the C27−PEOx series. Rather, the experimental results seem to be in quantitative agreement with the Halperin and Alexander theory. While the present results agree with the theoretical predictions by Halperin and Alexander, they are at odds with a recent computer simulation study using a dissipative particle dynamics by Li and Dormidontova.23 The simulation results indicate a general acceleration of the exchange kinetics upon increasing corona block molecular weight which was attributed to a higher solubility and larger cmc when the hydrophobic block is kept constant.24,25 Experimentally, for a comparable system, the cmc is known to increase with the number of EO repeat units.26−28 Hence, while the cmc reflects the free energy cost for micellization, that is, larger cmc implies weaker driving force for micellization, this is not necessarily directly reflected in the dynamic properties. In summary, we have reported experimental results of the chain exchange kinetics measured on a series of well-defined C27−PEOx polymers with various PEO lengths (x = 4−36 kg/ mol). A significant slowing down of the exchange rate with increasing length of the PEO corona chains was detected. We further found that the activation energy associated with the exchange process is almost constant or slightly reduced, whereas the pre-exponential factor, τ0, clearly increases with the PEO molecular weight. The latter was found to scale as τ0 ∼ M9/5 PEO in accordance with what is predicted in the 1989 paper by Halperin and Alexander.1 The mechanism behind the slowing down is a slower diffusion through the corona layer, 20 which increases roughly according to d = Rm − Rc ∼ N3/5 PEO. Additionally, leading to an increased attempt time, τ0, a longer residence time within the corona increases the probability for reinsertion into the same micelle and thus effectively slower kinetics in a TR-SANS experiment. A slowing down of chain exchange was also observed above the overlap concentration of micelles and upon adding linear corona homopolymer chains
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS T.Z. and R.L. is grateful for financial support through the SYNKNOYT program of the Norwegian Research Council (Grant No. 228573). Heinz Maier-Leibnitz (FRM II) center, MLZ in Garching, Germany, is greatly acknowledged for provision of beam time.
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REFERENCES
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