Structural and thermodynamic aspects of the cylinder-to-sphere transition in amphiphilic diblock copolymer micelles

Abstract

The structure of diblock copolymers micelles depends on a delicate balance of thermodynamic forces driving the system towards equilibrium and kinetic factors which limit the systems' exploration of the phase space. The factors governing the morphological transition between cylindrical and spherical micelles are related to a fine balance between entropic forces from chains within the micellar core and corona. In order to understand and control these structures, it is important to gain insight into the fundamental thermodynamic driving forces governing the structure and answer fundamental questions concerning its equilibrium nature. In this work we aim to understand the relationship between thermodynamics and morphological transitions by investigating the detailed structure of a system undergoing a cylinder-to-sphere transition. We focus on the structural properties of micelles constituted of poly(ethylene-alt-propylene)-poly(ethylene oxide) (PEP1-PEO1, the numbers indicate the molar mass in kg/mole) diblock copolymers in dimethylformamide (DMF)/water solvent mixtures. This system is ideal for fundamental studies as it represents a classical well-segregated block copolymer micelle system where the interfacial tension can be controlled in detail without significantly changing other thermodynamic properties. Using small-angle neutron scattering (SANS) it is shown that the system undergoes a cylinder-to-sphere transition upon addition of DMF which lowers the interfacial tension. By applying a detailed thermodynamic model we show that both the dependence of the structural parameters with the interfacial tension as well as the morphological transition can be quantitatively understood. The transition itself is governed by the interfacial tension which dictates the stretching of chains within both corona and core. At high interfacial tensions (in water-rich solutions) discrepancies between structural data and predictions from the thermodynamic model are observed. A qualitative comparison with some preliminary results on the chain exchange kinetics in the system show that these deviations coincide with the region where this equilibration mechanism is not active, i.e. when the kinetics are frozen at high interfacial tensions.

Equilibrium Chain Exchange Kinetics of Diblock Copolymer Micelles: Effect of Morphology

“…This is consistent with a systematic structural study where we found that the PEP1ÀPEO1 system shows a transition between cylinders and spheres at around 50% DMF mol fraction in the solvent mixture. 24 As it was extensively discussed there, this is a consequence of the balance of the elastic energy associated with the chain stretching inside the micellar cores and the steric/ elastic energy of the corona chains. While the former would favor cylindrical micelles since these exhibit the smallest radius for the same interfacial energy per chain,the corona free energy is higher in cylinders compared to spheres.…”

“…As shown in a previous paper, 24 the system undergoes a thermally induced irreversible cylinder-to-sphere transition in a 51% DMF composition. We thus performed a TR-SANS experiment at D11, ILL on exactly the same micellar solution before and after heating the sample at 70°C for several hours.…”

“…24 Nevertheless, since we are also dealing with the deuterated analogue, d-PEP1À d-PEO1, we will compare and discuss the overall structure of the micelles formed by the two block copolymers. The data are compared and analyzed for two selected DMF/water compositions, (X DMF = 41% and 75%), where the block copolymers either form cylinders or spherical micelles.…”

“…Here s 0 is the area per chain at the interface given by s 0 = 2πR c 3 L/P and s 0 = 4πR c 2 /P, for cylindrical and spherical geometry, respectively. Inserting the numbers given in ref 24, we see that for the PEP1ÀPEO1 micelles the number ξ min increases from about 10À11 Å for the cylinders to about 13 Å for the spherical micelles upon increasing the DMF content. For spherical and cylindrical micelles in 51% DMF the values obtained earlier is about 12 and 13 Å respectively.…”

Fluorophore exchange kinetics in block copolymer micelles with varying solvent–fluorophore and solvent–polymer interactions

“…The micelle diffusion coefficients were measured to be in the range of 2.3 – 3.2 × 10 −11 m 2 /s and the calculated hydrodynamic radii were in the range of 6.1 – 6.8 nm (Table 2) using the Stokes-Einstein relation (equation 1). We estimate the aggregation number of these micelles to be between 110 – 226, using the volume of a PEO-PCL diblock copolymer (and PEO and PCL densities of 1.125 and 1.14 g/mL, respectively), 39–41 and assuming the micelle forms a sphere with hydrodynamic radius reported in Table 2 (this simplified calculation ignores many effects such as swelling of the micelle core with the co-solvent THF, swelling of the corona with water, the diffuse nature of the core-corona interface, and diffuse boundary between the corona and bulk solvent). Using this estimate of the aggregation number, we calculate the micelle concentration to be in the range of 5 – 9 × 10 18 micelles per L solvent, accounting for a critical micelle concentration of 0.002 wt%, reported previously for a PEO-PCL block copolymer in water.…”