Abstract
A methodology to calculate minimum free-energy paths based on the combination of a molecular theory and the improved string method is introduced and applied to study the self-organization of polymer brushes under poor solvent conditions. Polymer brushes in a poor solvent cannot undergo macroscopic phase separation due to the physical constraint imposed by the grafting points; therefore, they microphase separate forming aggregates. Under some conditions, the theory predicts that the homogeneous brush and the aggregates can exist as two different minima of the free energy. The theoretical methodology introduced in this work allows us to predict the minimum free-energy path connecting these two minima as well as the morphology of the system along the path. It is shown that the transition between the homogeneous brush and the aggregates may involve a free-energy barrier or be barrierless depending on the relative stability of the two morphologies and the chain length and grafting density of the polymer. In the case where a free-energy barrier exists, one of the morphologies is a metastable structure and, therefore, the properties of the brush as the quality of the solvent is cycled are expected to display hysteresis. The theory is also applied to study the adhesion/deadhesion transition between two opposing surfaces modified by identical polymer brushes and it is shown that this process may also require surpassing a free-energy barrier.
Highlights
Soft materials exhibit a subtle competition between physical interactions, chemical equilibria and entropic forces that enables their self-assembly into organized structures.[1,2,3,4] Block-copolymers,[5,6,7] amphiphilic molecules[3, 8] and colloids[9, 10] are typical examples of soft materials that exhibit rich selfassembly behaviours
Understanding the parameters that control the free-energy barriers between different structures in soft material is of prime importance because these barriers can be used to stabilize a desired metastable structure, and because they may trap the system into an undesired metastable state preventing to obtain the desired equilibrium morphology
Self-assembly in polymer brushes results from the fact that physical grafting of the polymers to the substrate prevents macroscopic phase separation in a poor solvent, the polymers aggregate into microscopic structures, in a process known as microphase separation.[1, 12, 14]
Summary
Soft materials exhibit a subtle competition between physical interactions, chemical equilibria and entropic forces that enables their self-assembly into organized structures.[1,2,3,4] Block-copolymers,[5,6,7] amphiphilic molecules[3, 8] and colloids[9, 10] are typical examples of soft materials that exhibit rich selfassembly behaviours. Due to the complexity of their freeenergy landscapes, self-assembled soft materials are, in many cases, in metastable states (i.e. local minima of the free energy) rather than in thermodynamic equilibrium (global minimum of the free energy). The relaxation from a metastable state towards equilibrium must proceed through a free-energy barrier and, it can be very slow if the height of the barrier is large enough compared with the available thermal energy (kBT). Understanding the parameters that control the free-energy barriers between different structures in soft material is of prime importance because these barriers can be used to stabilize a desired metastable structure, and because they may trap the system into an undesired metastable state preventing to obtain the desired equilibrium morphology. Thin layers of end-grafted polymers, known as polymer brushes,[11] in a poor solvent self-organize into aggregates of different shape, such as micelles, stripes and continuous layers with solvent-filled holes.[1, 12,13,14,15,16,17,18,19,20,21,22,23,24,25] Self-assembly in polymer brushes results from the fact that physical grafting of the polymers to the substrate prevents macroscopic phase separation in a poor solvent, the polymers aggregate into microscopic structures, in a process known as microphase separation.[1, 12, 14] Microphase separation of single-component or mixed polymer brushes is appealing for applications in smart surfaces[23] and nanoparticles,[26,27,28] bottom-up patterning[24] and nanoparticle motion.[29]
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