Heterogeneity of the Segmental Dynamics in Cylindrical and Spherical Phases of Diblock Copolymers

Abstract

We have performed simulations of a simple bead-spring model for cylindrical and spherical phases of diblock copolymers. We have analyzed in detail the dynamic heterogeneity of the structural α-relaxation of the component confined in the minority domains. In analogy with previous investigations on the lamellar phase of the same bead-spring model, the analysis reveals moderate gradients of mobility in the investigated temperature range, which qualitatively probes time scales up to 100 ns. Thus α-relaxation times measured at different distances from the domain center spread over less than one decade. The spatial extension of the gradients of mobility is apparently consistent with that previously observed in the lamellar phase of the same model. Gradients of mobility do not seem to be related to gradients of density within the domains, which are indeed absent. We have performed an analysis of selfand effective concentrations, a concept usually invoked to explain the α-relaxation in polymer mixtures and that has been recently adapted to the analysis of experimental data of diblock copolymers in ordered phases. The simulation results reveal a strong disagreement with the proposed empirical relation between self-and effective concentration, as well as with the Flory-Fox mixing rule for the dynamics. This suggests that the use of these relations may bias the analysis of experimental data.

End-to-End Vector Dynamics of Nonentangled Polymers in Lamellar Block Copolymer Melts: The Role of Junction Point Motion

“…This is consistent with recent computational investigations on the α-relaxation in bead−spring copolymers with lamellar, 18 cylindrical, and spherical morphologies. 19 A thorough experimental characterization of the segmental dynamics in the different morphologies of the PI−PDMS copolymers is beyond the scope of this work and will be shown elsewhere. 34 The most striking result from the present BDS experiments is the bimodal character of the NM relaxation of the PI blocks in the PI−PDMS lamellae, unlike the single NM peak observed in the cylindrical and spherical morphologies.…”

“…15,17 Recent simulations confirmed this picture. 18,19 A recent study by Sanz et al 16 addressed the effect on the α-relaxation when the confining matrix crosses its glass transition temperature, T g , i.e., when going from a "hard" to a "soft" confinement. It was found that the low-T g (fast) component did not exhibit any discontinuity upon crossing the T g of the confining (slow) phase.…”

Correspondence between the rigid amorphous fraction and nanoconfinement effects on glass formation

“…Spatially resolved measurements have suggested that this enhancement emerges from a layer of enhanced T g and suppressed dynamics adjacent to the substrate—a phenomenon that resembles the RAF. More broadly, examples of these effects also include alterations of glass formation behavior in nanolayered polymers, “bound rubber” layers in filled rubber, alterations in the T g of polymer nanocomposites, the emergence of “suppressed mobility domains” around ionic aggregates in ionomeric polymers, and shifts in the T g of block copolymers relative to homopolymers . Like the RAF in semicrystalline polymers, all of these systems exhibit evidence of a domain near internal or external interfaces in which dynamics and glass formation behavior are profoundly altered.…”

An Emerging Unified View of Dynamic Interphases in Polymers

“…[ 9 ] While this fi eld has most heavily focused on polymers [ 4,6 ] and small molecules liquids [ 7,10,11 ] confi ned in thin fi lm or pore geometries, polymers with internal nanostructure, such as those shown [ 12 ] in Figure 1 , have been reported to exhibit similar alterations in dynamics for half a century or more. These observations include the following: deviations of T g from pure-state values in block copolymer nanodomains, noted as early as the 1960s; [13][14][15][16][17][18][19][20][21] shifts in segmental dynamics around particles in nanocomposites [22][23][24][25][26][27][28][29] and fi lled rubbers, [30][31][32][33][34] which are believed to contribute to mechanical reinforcement effects in these systems; observation of a rigid amorphous fraction with suppressed segmental dynamics and enhanced T g around crystalline domains in semicrystalline polymers; [ 35 ] and evidence of suppressedmobility domains surrounding ionic aggregates in ionomers. [36][37][38] Despite strong parallels in the phenomenology of near-interface dynamics in these materials, they have commonly been treated as fundamentally distinct systems, each with unique underlying physics.…”