Continuum models for directed self-assembly

Müller, Marcus; Rey, Juan Carlos Orozco

doi:10.1039/c7me00109f

Cited by 25 publications

(37 citation statements)

References 77 publications

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“…The obtained Equation ( 4 ) is known [ 30 , 31 ] to properly describe the transition from the random state of the DBC system to the ordered lammelae morphology. Mathematically, this transition occurs when control parameter

reaches the critical value of 0.25.…”

Section: Theory and Simulationsmentioning

confidence: 99%

Conductivity of Insulating Diblock Copolymer System Filled with Conductive Particles Having Different Affinities for Dissimilar Copolymer Blocks

Chervanyov

2020

Polymers

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We investigate the electrical response of the insulating diblock copolymer system (DBC) filled with conductive spherical fillers depending on the affinities of these fillers for copolymer blocks and the interaction between fillers. We demonstrate that the contrast (difference) between the affinities of the fillers for dissimilar copolymer blocks is a decisive factor that determines the distribution of these fillers in the DBC system. The distribution of filler particles, in turn, is found to be directly related to the electrical response of the DBC-particle composite. In particular, increasing the affinity contrast above a certain threshold value results in the insulator-conductor transition. This transition is found to be caused by the preferential localization of the fillers in the microphases of the DBC system having larger affinity for these fillers. The effect of the interaction between fillers is found to be secondary to the described effect of the affinity contrast that dominates in determining the distribution of fillers in the composite. This effect of the inter-particle interactions is shown to be significant only when the affinity contrast and filler volume fraction are sufficiently large.

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reaches the critical value of 0.25.…”

Section: Theory and Simulationsmentioning

confidence: 99%

Conductivity of Insulating Diblock Copolymer System Filled with Conductive Particles Having Different Affinities for Dissimilar Copolymer Blocks

Chervanyov

2020

Polymers

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“…The scaled bulk free energy W is specified below and can alternately be written as a function of (φ A , φ B ) by virtue of (1). The coefficients G i j and α may be derived from molecular considerations using the random phase approximation [23,28,39]. For simplicity, we take G 11 = G = G 22 and G 12 = 0.…”

Section: Density Functional Modelmentioning

confidence: 99%

“…Like SCFT, it was originally formulated for investigating equilibria, but also readily extends to dynamic circumstances [27]. Both paradigms have successfully reproduced various aspects of polymer systems [28], including phase diagrams for diblock mixtures [26,29], nanoparticle formation in copolymersolvent mixtures [30,31], and amphiphilic structure formation [32,33]. These models are derivatives of phase field models such as the Cahn-Hilliard theory of phase separation [34], which have proven to yield considerable mathematical understanding, including good quantitative approximations.…”

Section: Introductionmentioning

confidence: 99%

Theoretical prediction of morphological selection in amphiphilic systems

Glasner

2019

Phys. Rev. E

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Biological and synthetic amphiphilic systems exhibit a wide range of morphologies. A density functional model for amphiphilic polymer phase mixtures is utilized to quantify localized equilibria and their stability, and ultimately predict and explain morphological preference. This is done by utilizing matched asymptotic expansions, which produces explicit connections between model parameters and macroscopic properties of equilibrium structures. Bilayers, cylindrical, and spherical micelle and vesicle configurations are found, and formulas which connect their geometry to ambient chemical potential are derived. Dynamics are studied in the context of a free boundary problem which describes the evolution of the hydrophobic-solvent domain interface. Linearization of this problem is used to explicitly determine growth rates and parameter regions of stability. All equilibria are found to have two branches of solutions terminating at a fold in the bifurcation diagram which signals the crossover from competitive stability to instability leading to ripening behavior. Ideally flat bilayers are determined to always possess a long wavelength buckling instability, suggesting that curved structures should be generically preferred. Spherical micelles exhibit morphological instabilities which are suppressed by large enough surface tension. Cylindrical micelles may have short-wavelength pearling and long-wavelength Rayleigh-Plateau-type instabilities. In addition, ideally infinite cylinders have an undulatory instability, suggesting that only finite length structures should be observed. A morphological phase diagram can be assembled which takes into account both existence and stability of different geometries. Consistent with experimental evidence, a bifurcation sequence from spheres to cylinders to vesicles is found as either surface tension or polymer composition increases. Coexistence of different stable morphologies is also observed.

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“…the absolute squared of the Fourier transform, of a linear combination n s = s 1 n 1 + s 2 n 2 + s + c + + s − c − of the fluid and ion concentrations. We choose the prefactors s σ and s ± representing relative scattering length densities as s 1 = 1.4, s 2 = 6.4, s − = 2.1 and s + = 0 from the experimental values for a D 2 O/3MP mixture with the antagonistic salt NaBPH 4 1 . Note that we do not aim to quantitatively match the experimental data, as we are operating at different volume fractions and neglecting potentially important system parameters such as permittivity and viscosity differences between the fluids.…”

Section: Length Scalesmentioning

confidence: 99%

How antagonistic salts cause nematic ordering and behave like diblock copolymers

Jung

Rivas

Harting

2019

The Journal of Chemical Physics

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We present simulation results and an explanatory theory on how antagonistic salts affect the spinodal decomposition of binary fluid mixtures. We find that spinodal decomposition is arrested and complex structures form only when electrostatic ion-ion interactions are small. In this case fluid and ion concentrations couple and the charge field can be approximated as a polynomial function of the relative fluid concentrations alone. When the solvation energy associated with transfering an ion from one fluid phase to the other is of the order of a few k B T , the coupled fluid and charge fields evolve according to the Ohta-Kawasaki free energy functional. This allows us to accurately predict structure sizes and reduce the parameter space to two dimensionless numbers. The lamellar structures induced by the presence of antagonistic salt in our simulations exhibit a high degree of nematic ordering and the growth of ordered domains over time follows a power law. This power law carries a time exponent proportional to the salt concentration. We qualitatively reproduce and interpret neutron scattering data from previous experiments of similar systems. The dissolution of structures at high salt concentrations observed in these experiments agrees with our simulations and we explain it as the result of a vanishing surface tension due to electrostatic contributions. We conclude by presenting 3D results showing the same morphologies as predicted by the Ohta-Kawasaki model as a function of volume fraction and suggesting that our findings from 2D systems remain valid in 3D.

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Continuum models for directed self-assembly

Cited by 25 publications

References 77 publications

Conductivity of Insulating Diblock Copolymer System Filled with Conductive Particles Having Different Affinities for Dissimilar Copolymer Blocks

Conductivity of Insulating Diblock Copolymer System Filled with Conductive Particles Having Different Affinities for Dissimilar Copolymer Blocks

Theoretical prediction of morphological selection in amphiphilic systems

How antagonistic salts cause nematic ordering and behave like diblock copolymers

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