Micellization of amphiphilic diblock copolymers: Corona shape and mean-field to scaling crossover

Abstract

The aggregation behaviour of six amphiphilic poly(ethylene-propylene)-blockpolyethylene oxide (PEP-PEO) copolymers in water was investigated with the aim to study systematically the influence of a growing soluble block on the structural properties of the micelle. The polymers were prepared such that they differ in the PEO content over a large range of molecular weights, while the PEP size was kept constant. The micelles were characterized by small-angle neutron scattering (SANS) involving contrast variation experiments. Data analysis was performed by a spherical core/shell model with either constant or radial decreasing density profile in the corona and constant density in the core for both cases. The main new result is that we have observed a coronal shape crossover from a micelle with homogeneous density distribution for polymers of low PEO content to a starlike micelle with a hyperbolic density profile for polymers of high PEO content. With respect to the aggregation number this corresponds to a crossover from the mean-field to the scaling behavior of a starlike micelle.Introduction. -It is well known that above a critical polymer concentration (cmc) diblock copolymers in a selective solvent self-assemble into micellar structures. Usually, these structures have a spherical shape in which the insoluble block forms a closely packed inner core and the soluble block an outer corona swollen by the solvent. Essential characteristics of the micelle are the equilibrium aggregation number, P , the core radius, R C , and the overall radius, R M . For a given block copolymer/solvent system the structural parameters can be influenced in particular by changing block copolymer molecular weight and composition.A number of theoretical models were developed to predict the micellar properties and their dependence on block copolymer characteristics [1][2][3][4][5][6][7]. Generally, two different approaches may be distinguished. The first uses mean-field approximations to estimate the enthalpic and entropic contributions to the free energy of micellization. This concept generally is polymer specific and allows a quantitative calculation of micellar parameters but is strictly speaking limited to micelles having thin and dense coronas with roughly uniform concentration profiles, n(r) const. The second approach is based on scaling considerations, which estimate the different contributions to the free energy. In particular two scaling regimes of micellar structures are discussed: i) starlike micelles, where the degree of polymerization, N B , of the soluble block surpasses greatly that of the unsoluble block, N A , and ii) an intermediate regime,

Small-angle neutron scattering of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers

“…6b) while the density profile falls off smoothly at the polymer/solvent interface for the power law model. In similar studies on micellar systems the density profile in the corona region was crucial to fit SANS data from poly(ethylene -propylene)-block-polyethylene oxide (PEP -PEO) copolymer micelles in water [11]. A continuously decreasing density profile following a hyperbolic function shape for the micelle interface showed a better fit than a homogeneous density profile for the shell (for high PEO content polymers) which is consistent with the results presented here.…”

Dynamics of star-burst dendrimers in solution in relation to their structural properties

“…Within a so-called ''blob'', a spherical volume with radius , the dendrons have to be described as a selfavoiding random walk and excluded-volume interaction has to be considered. 36 Following a similar ansatz of Dozier et al 37 for highfunctionality stars, which has also, in a different modification, been successfully applied to polymeric micelles, 38 we split the dendrimer form factor into the sum of two terms…”

Formation of Block Copolymer Micelles in Solution: A Monte Carlo Study of Chain Length Dependence

“…This study 44 (as well as ref 42) has the merit that data close to the cmc could be taken, and it was shown that the micelle formation near the cmc is spread out over about a full decade in concentration. Finally, we mention the work of Willner et al, 45 who studied the structure of micelles varying the length of the block in the corona over a wide range and showed that the starlike model is applicable only for N B . N A , while the theory of Nagarajan and Ganesh 27 works better for not so large N B .…”

“…9,11,14,18,[23][24][25][26][27] In fact, this point has already been made by several authors, and systemspecific predictions 27 have been made for several blockcopolymer-solvent systems and also carried out a comparison with experiment. 37 Further experimental studies where these theoretical predictions are tested can be found in refs [38][39][40][41][42][43][44][45]. Such studies are also clearly difficult to perform, since the critical micelle concentration (φ cmc ) seems to decrease almost exponentially with N, at least according to the model calculations.…”