Observation of a reversible thermotropic order-order transition in a diblock copolymer

Hajduk, Damian A.; Grüner, Sol M.; Rangarajan, Pratima; Register, Richard A.; Fetters, Lewis J.; Honeker, Christian C.; Albalak, Ramon J.; Thomas, Edwin L.

doi:10.1021/ma00080a024

Cited by 155 publications

(208 citation statements)

References 7 publications

(8 reference statements)

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“…26 The transition pathway from lamellae to cylinders indicated by their data suggests that they were observing spinodal decomposition rather than nucleation. Sakurai et al examined the reverse transition in poly͑styrene-block-butadiene-block-styrene͒ triblock copolymers, where a nonequilibrium cylinder phase produced by a selective solvent transforms into a stable lamellar phase upon annealing.…”

Section: Introductionmentioning

confidence: 99%

Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

Wickham

Shi

Wang

2003

The Journal of Chemical Physics

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The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the mean-field Landau-Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet interfacial profile, an analytic expression for the interfacial free energy of an interface of arbitrary orientation between cylinders and lamellae is found. The interfacial free energy is anisotropic and is lower when the cylinder axis is perpendicular to the interface than when the cylinders lie along the interface. Consequently, the droplet shape computed via the Wulff construction is lens like, being flattened along the axis of the cylinders. The size of the critical droplet and the nucleation barrier are determined within classical nucleation theory. Near the lamellar-cylinder phase boundary, where classical nucleation theory is applicable, critical droplets of size 30-400 cylinders across with aspect ratios of 4 -10 and nucleation barriers of (30-40)k B T are typically found. The general trend is to larger critical droplets, higher aspect ratios, and smaller nucleation barriers as the mean-field critical point is approached.

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Section: Introductionmentioning

confidence: 99%

Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

Wickham

Shi

Wang

2003

The Journal of Chemical Physics

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“…1 In recent years, several groups have also investigated issues concerning the kinetic pathways in various order-order and order-disorder transitions of these selfassembly fluids. [4][5][6][7][8] Laradji et al, 9 and independently the present authors, 10 developed theories of anisotropic fluctuations in ordered block copolymer phases. The instability associated with these anisotropic fluctuations can be used to understand the initial structural evolution in transitions between different ordered morphologies and from an ordered phase to the disordered phase.…”

Section: Introductionmentioning

confidence: 99%

Transient instability upon temperature quench in weakly ordered block copolymers

Wang

1999

The Journal of Chemical Physics

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We report a novel transient instability upon temperature quench in weakly ordered block copolymer microphases possessing a soft direction or directions, such as the lamellar and hexagonal cylinder ͑HEX͒ phases. We show that reequilibration of the order parameter is accompanied by transient long wavelength undulation of the layers or cylinders-with an initial wavelength that depends on the depth of the temperature quench-that eventually disappears as the structure reaches its equilibrium at the new temperature. Such undulation leads to a transient transverse broadening of the scattering peaks near the Bragg positions. We argue that this instability might be responsible for the experimentally observed unusual ordering dynamics of the HEX phase of a diblock copolymer after quenching from the disordered state.

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“…Specifically we study the kinetic pathways of HEX to disordered and HEX to bcc phases after a sudden temperature jump. This study is motivated by the general intrinsic interest in understanding kinetics of phase transitions involving spatially modulated phases, in particular, by recent experiments on diblock copolymers [3][4][5][6][7]. To be concrete, we shall use diblock copolymers as the context; however, we believe the phenomenology is quite general for the class of systems described by the free energy Eq.…”

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Kinetic Pathways of Order-Disorder and Order-Order Transitions in Weakly Segregated Microstructured Systems

1996

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The kinetics of hexagonal to disordered and hexagonal to body-centered-cubic phase transitions in weakly segregated, microstructured systems (e.g., diblock copolymers) is studied using a time-dependent Ginzburg-Landau (TDGL) approach. Both computer simulation of the TDGL equation and analysis of a simplified two-mode model reveal nontrivial pathways during the transition.PACS numbers: 81.10. Aj, 81.30.Hd, 83.70.Hq A wide variety of chemical and physical systems, such as Langmuir films, ferrofluids, and diblock copolymers, exhibit ordered periodic domain structures [1]. Irrespective of differences in the systems, the domain structures have surprisingly similar appearance: stripes and circular droplets in two dimensions, and lamellae, hexagonal (HEX) cylinders, and body-centered-cubic (bcc) spheres in three dimensions. Although the specific origins may differ from system to system, the formation of spatially periodic patterns can be attributed to the competing shortrange and long-range interactions. Near the order-disorder transition, these systems can be phenomenologically described by an order parameter free energy functional of the formwhere c͑ r͒ is the order parameter, e.g., the local magnetization in magnetic systems, or the local density contrast between the two types of monomers in diblock copolymers. t is related to the distance from the order-disorder transition temperature, and the coefficients b, c, u, and y are phenomenological parameters which can be computed from more microscopic models. The last term in Eq.(1) represents the long-range repulsion, which penalizes longwavelength inhomogeneities. The equilibrium properties of systems described by Eq. (1) have been the subject of extensive experimental and theoretical studies [1,2]. In this Letter, we address the phenomenology of the kinetics of the various order-order and order-disorder transitions in weakly segregated, microstructured systems, using a time-dependent Ginzburg-Landau approach. Specifically we study the kinetic pathways of HEX to disordered and HEX to bcc phases after a sudden temperature jump. This study is motivated by the general intrinsic interest in understanding kinetics of phase transitions involving spatially modulated phases, in particular, by recent experiments on diblock copolymers [3][4][5][6][7]. To be concrete, we shall use diblock copolymers as the context; however, we believe the phenomenology is quite general for the class of systems described by the free energy Eq. (1), and will not limit our choice of parameters specifically to those for diblock copolymers [8].For conserved order parameters, as is appropriate for diblock copolymers, we may write the time-dependentHere M is a mobility coefficient, which we assume to be a constant; h͑ r, t͒ is a random force, which for a system in equilibrium at temperature T , satisfies the fluctuationdissipation relationAs a minimal model, we ignore any hydrodynamic effects and possible nonlocality in the mobility coefficient [10,11]. We will also ignore the noise term in subsequen...

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Observation of a reversible thermotropic order-order transition in a diblock copolymer

Cited by 155 publications

References 7 publications

Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

Nucleation of stable cylinders from a metastable lamellar phase in a diblock copolymer melt

Transient instability upon temperature quench in weakly ordered block copolymers

Kinetic Pathways of Order-Disorder and Order-Order Transitions in Weakly Segregated Microstructured Systems

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