Thermodynamics and Kinetics of Defect Motion and Annihilation in the Self-Assembly of Lamellar Diblock Copolymers

Abstract

The thermodynamics of dislocations in thin films of lamella-forming diblock copolymers and their climb and glide motions are investigated using single-chain-in-mean-field (SCMF) simulations and self-consistent field theory (SCFT) in conjunction with the string method. The glide motion of a defect perpendicular to the stripe pattern is characterized by large free energy barriers. The barriers not only stem from altering the domain topology; an additional barrier arises from a small-amplitude but long-range domain displacement. In contrast, the climb motion along the stripes does not involve a free energy barrier in accord with the continuous translational invariance along the stripe. Thus, the perpendicular distance (“impact parameter”) between a pair of defects is approximately conserved. Dislocation pairs with opposite Burgers vectors attract each other and move toward each other (“collide”) via climb motion. We find that the forces between apposing defects significantly depend on system size, and the Peach–Koehler force in smectic structures only becomes accurate for extremely large system sizes. Moreover, we observe in SCMF simulations that the defect annihilation time qualitatively and nonmonotonously depends on the defects’ perpendicular distance and rationalize this finding by the collective kinetics along the minimum free energy path (MFEP) and the single-chain dynamics in an inhomogeneous environment.

Non-native three-dimensional block copolymer morphologies

“…The topological defects in BCP phases (disclinations, dislocations, grain boundaries) are high energy5758; at equilibrium the expected areal defect density would be very low. The much larger defect densities observed experimentally are thus metastable, arising from the ordering history, rather than equilibrium fluctuations59. While the local ordering (morphology) is determined thermodynamically, the defectivity is kinetic.…”

Minimum free-energy paths for the self-organization of polymer brushes

“…Our theory is a combination of a molecular theory for soft materials at interfaces 1,32,33 and the improved string method for minimal energy paths. 34 The improved string method has been used before in combination with simulations and SCF theories to explore lipid bilayers, [35][36][37] block copolymers [38][39][40][41] and the collapse of a single hydrophobic chain in solution. 27 The present work reports its first application to study the self-organization of polymer brushes.…”

Defect Removal by Solvent Vapor Annealing in Thin Films of Lamellar Diblock Copolymers

“…The mechanism of defect removal by added solvent (reducing χ) is very similar to thermal annealing (TA), where χ ∼ 1/T 2,9,10,12,13 . The presence of a threshold value of incompatibility in N χ eff (given by a threshold of φ or R) in SVA has also been seen in TA 2,[9][10][11][12][13][14] , where N χ is a function of T . For small N χ eff (large swelling ratio), defects are unstable and can be removed spontaneously as there are no energy barriers to overcome.…”

“…In order to facilitate the fabrication of defect-free films, further treatments are needed. As examples to techniques that have been developed to tailor the self-assembly behavior of BCP thin films we mentioned electric field alignment 4,5 , shear alignment 6,7 , microwave annealing 8 , and thermal annealing 1,2,[9][10][11][12][13][14][15][16] . Besides these approaches, solvent vapor annealing (SVA) 1,3,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] has been used to enhance the mobility of polymer chains, and to facilitate the annihilation of defects.…”