Dynamics of micelles of the triblock copolymers poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) in aqueous solution

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Abstract

A number of results reported on the kinetics of exchange of triblock copolymers poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide), PEO–PPO–PEO, between micelles and the intermicellar aqueous solution are reviewed and analyzed to extract the rate constants k+ for the entry of a copolymer into a micelle and k for the exit of a copolymer from a micelle. Contrary to what is generally observed for conventional surfactants, the rate constant for the entry of a copolymer into a micelle is slower to much slower than for a diffusion-controlled process and decreases as the degree of polymerization of the PO block, nPO, increases. The effect of the degree of polymerization of the EO block, nEO, on the two rate constants is significant only for low values of nEO. The variation of k with nPO strongly suggests that the free copolymer molecule adopts a conformation where the PO block is tightly coiled with little contact with water and not a fully extended and hydrated conformation, in contrast to what is commonly assumed when analyzing the dependence of the cmc on the polymerization degree of the hydrophobic block

Introduction

Amphiphilic block copolymers have been extensively investigated in view of their many applications [1]. In aqueous solutions these copolymers give rise to micelles at concentrations C above the critical micellization concentration, cmc. Similarly to surfactant micelles, amphiphilic block copolymer micelles are not frozen objects, at least when the copolymer molecular weight is relatively low. The two main spontaneous dynamic processes that occur in micellar solutions of surfactants, i.e., the exchange of surfactants between micelles and bulk phase and the micelle formation/breakdown, also occur in micellar solutions of amphiphilic block copolymers. In the case of micellar solutions of conventional surfactants, whether ionic, nonionic or zwitterionic, it has been consistently found that the entry of a surfactant into its micelles is nearly controlled by diffusion, with values of the entry rate constant k+ in the 108–109 M 1 s 1 range for surfactants with an alkyl chain containing up to 14 to 18 carbon atoms, depending on the surfactant [2], [3]. The value of k+ decreases very slowly upon increasing surfactant chain length. On the contrary, the rate constant k for the exit of a surfactant from its micelles decreases exponentially when the carbon number m of the surfactant alkyl chain is increased, by a factor close to 3 per additional methylene group [2], [3]. This factor corresponds to an increment of about 1.1kT per methylene group in the free energy of transfer of a surfactant from a micelle to the aqueous phase. Micelles of conventional surfactants form and breakdown either by a series of reactions of entry/exit of a single surfactant at a time into/from micelles [4] or by reactions of fusion/fission (also referred to as fragmentation/coagulation) involving submicellar aggregates [5], depending on the experimental conditions (nature and concentration of the surfactant; ionic strength; additives; temperature; etc.). These results also hold for dimeric (gemini) surfactants with a short alkyl chain (say 8 carbon atoms) [6]. However, gemini surfactants with a longer alkyl chain (12 carbon atoms) depart from this scheme and the entry rate constant was found to be up to 100-fold slower than for a diffusion-controlled process [7].

The dynamics of amphiphilic block copolymer micelles in aqueous solution has been investigated both experimentally [8], [9] and theoretically [10], [11], [12] with the view to understand the mechanism by which block copolymer micelles form and break down and also for determining the rate constants for the copolymer exchange between micelles and bulk phase. It has been found that these processes are more complex and also much slower than with surfactants [8], [9]. Actually, in most instances, the processes are so slow as to be referred to as ‘frozen’, with the systems taking days, months or even longer times to reach equilibrium, after being submitted to a perturbation that affects micelles [8], [9].

One series of amphiphilic copolymers, the triblock poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide), PEO–PPO–PEO (EO = ethylene oxide; PO = propylene oxide), show a relatively fast relaxation behavior that permits its study by means of chemical relaxation methods. These copolymers are not the simplest ones from the structural viewpoint. Nevertheless they have been much investigated essentially because they are commercially available with a wide range of composition and molecular weight [1], [13], [14]. In aqueous solution they give rise to micelles with a core mainly made up of PO chains and a corona made up of EO chains and water at temperatures above the so-called critical micellization temperature, cmT [13], [14] (the value of the cmc of a copolymer solution of concentration C is close to C at a temperature equal to the cmT). The cmc of PEO–PPO–PEO aqueous solutions decreases very rapidly as the temperature is increased [13], [14]. The relaxation processes observed with micellar solutions of PEO–PPO–PEO copolymers have been assigned with reasonable certainty to micellar equilibria [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25]. The relaxation behavior of these systems is similar to that of surfactant solutions, with two well separated relaxation processes that have been mainly investigated by the temperature-jump (T-jump) technique, with Joule effect or laser heating. The time dependence of the intensity of light scattered by the copolymer solution after rapidly raising the solution temperature has been used to monitor the relaxation [16], [17], [18], [20], [22], [23], [24]. The slower of the two relaxation processes has been assigned to the micelle formation/breakdown. The concentration dependence of the associated relaxation time suggested that this process mainly occurred via fusion/fission of submicellar aggregates [16], [20], [21], [22]. This process can be quite slow and it is not always observed. It is not further considered in this paper. The faster relaxation has been attributed to the copolymer exchange between micelles and bulk phase [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25]. It occurs in a convenient time-scale and data have been reported for PEO–PPO–PEO copolymers of varied composition and molecular weight. Hecht and Hoffmann reported the first investigation of the relaxation behavior of PEO–PPO–PEO copolymers [15]. They observed a single relaxation process which they attributed to the copolymer exchange and reported values of the entry rate constant in a micelle about 100 times slower than for a diffusion-controlled process. Since this pioneering study kinetic data have become available for more PEO–PPO–PEO copolymers [16], [18], [20], [25].

The primary purpose of starting this work was to analyze the available kinetic data for PEO–PPO–PEO solutions in order to extract values of the rate constants k+ and k and see their trends when the degree of polymerization of the EO and PO blocks varied. As a second step, we wanted to analyze these data in order to obtain information on the conformation of the free (non-micellar) block copolymer in water. Indeed two widely differing models are present in the literature: one where the hydrophobic block is coiled but contacts between water and hydrophobic units are permitted [26] and another where the hydrophobic block forms a globule that permits water/hydrophobic unit contacts only at the surface of the globule [10], [12]. A first attempt to achieve these goals unfortunately used incorrect values for some of extracted rate constants [9].

As is shown below the determination of reliable values of the rate constants is difficult owing to the lack of data, mainly of values of the micelle aggregation number. Another difficulty arises because the k+ and k values are not all obtained at the same temperature and must, therefore, be corrected for temperature on the basis of available theories for polymer solutions. Nevertheless, the set of k+ and k values reported below permitted us to reach some valuable conclusions. Most notably, both k and k+ are found to decrease as the degree of polymerization nPO of the PO block increases. The entry of a copolymer in a micelle is close to being diffusion-controlled for copolymers with a short hydrophobic block but becomes much slower as nPO is increased. The effect of the degree of polymerization nEO of the EO block on the two rate constants is much weaker. The variations of the rate constants with nPO support a model of the free (non-micellar) copolymer where the hydrophobic block is strongly coiled, forming a globule, with little contact with water.

Section snippets

Evaluation of the rate constants for the exchange of PEO–PPO–PEO copolymers between micelles and bulk phase

Table 1 lists the copolymers for which kinetic data have been reported for the exchange process and their characteristics: molecular weight, Mw, PO weight percent and cmc value at the temperature at which the kinetic data are reported. The values of the rate constants k+ and k for the entry/exit of a copolymer in/from its micelles have been extracted from the reported data as follows on the basis of Eqs. (1), (2):1/τ1=(k/N)(N/σ2+Cred)andkk+/cmcIn Eq. (1), τ1 is the relaxation time measured

Theory for the analysis of the dependence of the exit rate constant on the polymerization degree of the hydrophobic block

The treatment that follows is based on the available data from a scaling analysis of micelle formation by amphiphilic block copolymers. At this level of approximation the equilibrium structure of triblock copolymer micelles is identical to the structure of diblock copolymer micelles that would be obtained by cutting the hydrophobic blocks at their middle. Our analysis follows standard models [10], [35], [36] for diblock copolymer micelles comprising N copolymer chains, each with polymerization

Discussion and concluding remarks

The above discussion is restricted to the variation of the copolymer exit rate constant with the length of the hydrophobic block characterized by the degree of polymerization nPO. However, the rate constant k+ for the entry of a copolymer in micelles is expected to show a similar dependence because once a free copolymer collides with a micelle it can be considered as incorporated only after the hydrophobic globule uncoils and penetrates into the core. This unfolding and penetration will also

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