Domain size equilibration in sphere‐forming block copolymers

Abstract

The kinetics of domain size equilibration were studied for asymmetric poly(ethylene‐alt‐propylene)‐b‐poly(dimethyl siloxane) (EPDMS) and polyisoprene‐b‐poly(dimethyl siloxane) (IDMS) block copolymers in the body‐centered cubic ordered phase. Small‐angle X‐ray scattering measurements of the principal peak position (q*) were made as a function of time after temperature jumps within the ordered state. The equilibration times were remarkably long, especially on cooling and for temperatures below 100 °C. For example, after a quench to 40 °C, q* for EPDMS had not fully equilibrated even after several weeks of annealing; IDMS required several days to equilibrate at the same temperature. In contrast, a lamella‐forming EPDMS sample was able to adjust q* within the timescale of the measurements (i.e., minutes) with both heating and cooling over the same temperature range. Measurements of tracer diffusion indicated that chain mobility was not the rate‐limiting step, although differences in mobility did account for the differences between EPDMS and IDMS. Rather, the limiting step was the required reduction in the number density of spheres on cooling; the disappearance of spheres, either by evaporation or by fusion, provided a large kinetic barrier. Lamellae, however, could adjust domain dimensions simply by local displacements of individual chains. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 715–724, 2003

Dodecagonal quasicrystalline order in a diblock copolymer melt

“…Theory (32,33) and experiments (34,35) show that the number density of micelle-like point particles increases with decreasing temperature, reducing the free unimer concentration and sharpening the local composition profile at the core-corona interface. The particle aggregation number (i.e., the number of diblock chains per particle) and particle volume increase slightly with decreasing temperature, as also occurs in the ordered BCC phase (36). At a certain temperature, the number density must saturate as the particles become tightly packed and the unimer concentration approaches zero.…”

“…At this point, further cooling actually drives a reduction in particle number density due to the increasing core-corona interfacial tension, which favors larger spherical micelles (i.e., greater aggregation number). However, due to a high (and steeply temperature-dependent) energy penalty associated with transporting a core block through the corona region (∼exp[αχN]), single-chain diffusion across domains drops precipitously at reduced temperatures (36)(37)(38). This freezes collective particle-level reorganization necessary to accommodate the thermodynamic drive toward fewer, larger particles or the redistribution of particle volumes necessary to form the σ phase.…”

Dynamic polymeric micelles versus frozen nanoparticles formed by block copolymers

“…65 Therefore, the kinetics of phase transitions in dense suspensions can be very slow even if the exchange rate is fast. For instance, Cavicchi et al 66 observed very slow kinetics after temperature jumps within the body centered cubic (bcc) phase of polymer micelles, but rapid changes after jumps within the lamellar phase. Self diffusion of polymers in the system was fast in both cases.…”

Directly Observing Micelle Fusion and Growth in Solution by Liquid-Cell Transmission Electron Microscopy

“…1 There are multiple mechanisms by which particles can undergo phase transitions and growth with the problem of characterizing a given system often approached using powerful, routine, but indirect in situ scattering techniques. [2][3][4][5][6][7][8] These methods provide an adequate bulk-averaged overview of the sample size and morphology based on assumptions of the nature of the nanostructures and theoretical fitting of the raw data. For many systems, including amphiphilic block copolymer (BCP) micelles, a delicate interplay exists between the kinetic and thermodynamic parameters, [9][10][11][12][13][14][15][16][17][18] which govern their size, morphology and dynamic behavior.…”

“…[25][26][27] However, we lack techniques for directly observing nanoparticle-by-nanoparticle dynamics and transformations as they occur. 5,7,8,22,[28][29][30][31][32][33] Typically, amphiphilic BCP assembly is performed via direct dissolution into a selective solvent, 2,24 or via gradual solvent exchange methods from common solvents to a solvent selective for one blocks. 11 After solvent-switch, and dependent on the preparation conditions, the assemblies will either equilibrate over time, forming the lowest free energy structure, or be kinetically trapped, yielding metastable morphologies and often resulting in the "freezing" of complex, and functionally desirable morphologies.…”