Role of Grain Boundary Defects During Grain Coarsening of Lamellar Block Copolymers

Abstract

The evolution of grain size and shape as well as type and frequency of grain boundary structures during thermal annealing of lamellar diblock copolymer microstructures is established using large area image reconstruction and analysis. Grain coarsening is found to proceed via an initial transient stage that is characterized by the rapid relaxation of unstable "frozen-in" defects such as kink boundaries and the subsequent quasi-stationary coarsening that is dominated by the continuous relaxation of low-angle symmetric tilt boundaries. The particular relevance of low-angle symmetric tilt boundaries to grain coarsening is interpreted as the consequence of both the associated decrease of boundary energy as well as the availability of favorable kinetic pathwayssuch as grain boundary splittingto facilitate the coarsening process. The inverse relation between grain boundary energy and frequency suggests that the reduction of boundary energy is a relevant governing parameter for the evolution of grain boundary structuresas it is in inorganic materials. The existence of "inert" boundary types (such as asymmetric tilt and twist) thatwithin the experimental windowdo not participate in the coarsening process is expected to have dominant influence on the final morphology that can be attained by thermal annealing of the microstructure. The reduction of the density of inert boundaries during the film preparation process should therefore provide a strategy for increasing the coarsening kinetics in block copolymer films during thermal annealing and thus a path toward a higher degree of order in block copolymer microstructures.

Retardation of Grain Growth and Grain Boundary Pinning in Athermal Block Copolymer Blend Systems

“…The grain structure analysis process was performed analogous to the procedures described in "Grain Coarsening-I", and we refer to this previous article regarding the technical details of the grain mapping process. 15 Figure 2 depicts an exemplary grain map representing the as-cast PS−PI/hPS (ϕ hPS = 3 wt %). A complete account of grain maps for all PS−PI/hPS blend systems after 0, 3, and 7 days of thermal annealing is presented in Figures S1−S11 (see Supporting Information).…”

“…All grain size distributions in as-cast systems follow a log-normal distribution while PS−PI/hPS blend systems increasingly deviate from the log-normal type with increasing time of thermal annealing. The gray shaded area delineates the range of grain sizes that was considered for grain structure analysis (see ref 15). …”

“…Analysis of the grain characteristics as well as type and frequency of grain boundary defects was performed by image analysis following a procedure that has been described in detail in "Grain Coarsening-I". 15 Analysis of the relative energies of boundary defects in block copolymers and their blends was performed by analysis of dihedral angles as described previously. 31 Small-Angle X-ray Scattering (SAXS).…”

“…16 The grain growth exponent n (relating the average radius of grain ⟨R(t)⟩ to the time of thermal annealing via ⟨R(t)⟩ ∼ t 1/n ) was found to be n ≅ 1.8, consistent with normal grain growth kinetics that is commonly observed in periodically ordered materials such as metals or ceramics, thus suggesting that the reduction of GB energy plays a major role as driving force for grain coarsening. 15,17−20 However, it is important to note that the grain coarsening characteristics of pristine materials do rarely translate to blend systems. This is because filler species (such as additives or impurities) can interact with GB defects and alter both the energetics and kinetics of structure evolution.…”

Differential Geometry and Continuum Mechanics

“…Concrete physical situations where the kinematic construct we have just outlined occur are commonplace. In connection to fundamental, (un)loaded, microstructure of materials, such terminating boundaries (or domain walls) occur as grain boundaries and triple junction lines in polycrystalline metals [DW72, BZB+12, LXBC10,HLL+12] or layered polymeric materials [LB06,RFL+12]. As agents of failure, some examples are weak interfaces between matrix and fiber in fiber-reinforced polymer composites, or two such phase boundaries spaced closely apart enclosing a matrix weak zone in such materials, e.g.…”