Monte Carlo phase diagram for diblock copolymer melts

Beardsley, Tom; Matsen, Mark W.

doi:10.1140/epje/i2010-10651-x

Cited by 56 publications

(104 citation statements)

References 39 publications

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“…Pairwise interaction energies are given by ε AA = ε BB = 0 and ε AB = ε = χ kT/(z − 2), where χ is the FloryHuggins parameter and z (=12) is the coordination number. Each simulation is equilibrated at T * (=kT/ε), and parallel tempering 40 overcomes local free energy minima at low T and long relaxation times.…”

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Communication: Molecular-level insights into asymmetric triblock copolymers: Network and phase development

Tallury

Mineart

Woloszczuk

et al. 2014

The Journal of Chemical Physics

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Molecularly asymmetric triblock copolymers progressively grown from a parent diblock copolymer can be used to elucidate the phase and property transformation from diblock to network-forming triblock copolymer. In this study, we use several theoretical formalisms and simulation methods to examine the molecular-level characteristics accompanying this transformation, and show that reported macroscopic-level transitions correspond to the onset of an equilibrium network. Midblock conformational fractions and copolymer morphologies are provided as functions of copolymer composition and temperature.

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confidence: 99%

Communication: Molecular-level insights into asymmetric triblock copolymers: Network and phase development

Tallury

Mineart

Woloszczuk

et al. 2014

The Journal of Chemical Physics

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“…Model F is an FCC lattice model. Models H [21][22][23], S1 [22,23], and F [24][25][26][27] have been studied previously. The term "model" refers to set of choices for the functional form of the pair and bond potentials, and for values of all parameters except N and one parameter that is varied to control χ e .…”

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confidence: 99%

Universality of Block Copolymer Melts

et al. 2014

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Simulations of five different coarse-grained models of symmetric diblock copolymer melts are compared to demonstrate a universal (i. e., model-independent) dependence of the free energy on the invariant degree of polymerization N , and to study universal properties of the order-disorder transition (ODT). The ODT appears to exhibit two regimes: Systems of very long chains (N > ∼ 10 4 ) are well described by the Fredrickson-Helfand theory, which assumes weak segregation near the ODT. Systems of smaller but experimentally relevant values, N < ∼ 10 4 , undergo a transition between strongly segregated disordered and lamellar phases that, though universal, is not adequately described by any existing theory.PACS numbers: 82.35. Jk,64.70.km,64.60.De Universality is a powerful feature of polymer statistical mechanics that allows the behavior of real systems to be predicted on the basis of simple generic models and scaling arguments. The paradigmatic example is the scaling theory of dilute and semidilute polymer solutions in good solvents [1][2][3], which predicts a universal dependence of all properties on two thermodynamic state parameters (an excluded volume parameter and an overlap parameter). Historically, this scaling hypothesis was verified by comparing experiments on diverse chemical systems with varied chain lengths and concentrations [3][4][5]. Here, we compare simulations of diverse models to verify an analogous scaling hypothesis about the equation of state and order-disorder transition (ODT) of symmetric diblock copolymers, and to characterize this transition.We consider a dense liquid of AB diblock copolymers, with N monomers per chain, and a fraction f A of A monomers. We focus on the symmetric case, f A = 1/2. Self-consistent field theory (SCFT) is the dominant theoretical approach for block copolymers [6][7][8]. SCFT describes polymers as random walks with a monomer statistical segment length b, which we take to be equal for A and B monomers. The free energy cost of contact between A and B monomers is characterized by an effective Flory-Huggins interaction parameter χ e . Let g denote a dimensionless excess free energy per chain, normalized by the thermal energy k B T . SCFT predicts a free energy g for each phase that depends only upon f A and the product χ e N , or upon χ e N alone for f A = 1/2. This yields a predicted phase diagram [6, 7] that likewise depends only on f A and χ e N . For f A = 1/2, SCFT predicts a transition between the disordered phase and lamellar phase at (χ e N ) ODT = 10.495.SCFT is believed to be exact in the limit of infinitely long, strongly interpenetrating polymers [9, 10]. The degree of interpenetration in a polymer liquid is characterized by a dimensionless concentration C ≡ cR 3 /N , in which c is monomer concentration, c/N is molecule concentration, and R = √ N b is coil size. Alternatively, interpenetration may be characterized by the invariant degree of polymerization. A series of post-SCF theories [10][11][12][13][14][15][16][17][18], starting with the Fredrickson...

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“…To account for polydispersity, we locate the ODT by simulation. This is done by evaluating the average number of A-B contacts, n AB , as a function of χN using parallel tempering [13]. To gauge the level of metastability, Fig.…”

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confidence: 99%