Design of bicontinuous polymeric microemulsions

Fredrickson, Glenn H.; Bates, Frank S.

doi:10.1002/(sici)1099-0488(199712)35:17<2775::aid-polb2>3.0.co;2-q

Cited by 85 publications

(130 citation statements)

References 5 publications

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“…For concentrations, ⌽, smaller than the Lifshitz critical value according to ⌽ LL ϭ2␣ 2 /(1ϩ2␣ 2 ) ϭ0.0596 the critical point occurs for Qϭ0, corresponding to macrophase separation. 11,23 For larger ⌽ the maximum occurs at a steadily growing Q* value, corresponding to microphase separation. These critical values of (⌫ S ,Q*) are depicted by the open circles in Fig.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Thermal composition fluctuations near the isotropic Lifshitz critical point in a ternary mixture of a homopolymer blend and diblock copolymer

Schwahn

Mortensen

Frielinghaus

et al. 2000

The Journal of Chemical Physics

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We have studied thermal composition fluctuations of a ternary symmetric homopolymer/diblock copolymer system of PEE/PDMS/PEE-PDMS ͓PEE and PDMS being poly͑ethyl ethylene͒ and poly͑dimethyl siloxane͒, respectively͔ in its disordered state with small angle neutron scattering for concentration ⌽ of diblocks up to 15%. The phase diagram shows three characteristic regimes; ͑1͒ below the Lifshitz concentration ⌽ LL Х9%; ͑2͒ in the very near vicinity of the Lifshitz concentration; and ͑3͒ above ⌽ LL . In the regime ͑1͒ of low diblock content the maximum neutron intensity is obtained at Qϭ0 and phase separation into macroscopic large domains is observed at low temperatures. With increasing diblock content the thermal fluctuations indicate a crossover from 3d-Ising to isotropic Lifshitz critical behavior with critical exponents of the susceptibility ␥ ϭ(1.62Ϯ0.01) and correlation length ϭ(0.99Ϯ0.04) appreciably larger than in the 3d-Ising case. In the structure factor this crossover is accompanied by a strong reduction of the Q 2 term leading to the dominance of the Q 4 term; the restoring force of the thermal fluctuations is strongly reduced as the Q 2 term is proportional to the surface energy. Near the Lifshitz critical temperature a further crossover was observed leading to the appreciably larger critical exponents ␥ϭ(2.44Ϯ0.08) and ϭ(1.22Ϯ0.08) and a stabilization of the disordered regime visible through a decrease of the phase boundary by nearly 10 K. This crossover is interpreted by the formation of fluctuation induced inhomogeneous diblock distribution at the interface of the thermal fluctuations. ͑2͒ In the intermediate regime between 9% and 12% diblock content the Lifshitz line was crossed twice upon increasing the temperature from low to high temperatures; at low and high temperatures the structure factor S(Q) shows diblock character ͑maximum of S(Q) at Q 0͒ while at intermediate temperature blendlike character ͑maximum of S(Q) at Qϭ0͒. At low temperatures a transition to a bicontinuous microemulsion phase is proposed. ͑3͒ At diblock content of 15% a weak order-disorder transition was observed. The data in the Lifshitz critical range and larger than the Lifshitz line could be interpreted by a recently developed theory of Kielhorn and Muthukumar who considered the effect of thermal fluctuations in ternary homopolymer/diblock copolymer samples and from which the Flory-Huggins parameter could be evaluated.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Thermal composition fluctuations near the isotropic Lifshitz critical point in a ternary mixture of a homopolymer blend and diblock copolymer

Schwahn

Mortensen

Frielinghaus

et al. 2000

The Journal of Chemical Physics

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“…However, in the case of blends of components with unequal molecular weights, the Scott line composition is determined by the relationship α A ϕ A 2 = α B ϕ B 2 (where α i is the ratio of the degree of polymerization of the polymer i over the degree of polymerization of the BCP). 5 Such a relationship suggests that the ratio of the donor and acceptor volume fractions corresponding to the Scott line is likely to be very small for polymer/solvent mixtures. On the other hand, high efficiency organic solar cells are typically based on symmetric or near-symmetric donor/acceptor blend ratios.…”

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Achieving Bicontinuous Microemulsion Like Morphologies in Organic Photovoltaics

et al. 2015

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It is believed that the optimal morphology of an organic solar cell may be characterized by cocontinuous, interpenetrating donor and acceptor domains with nanoscale dimensions and high interfacial areas. One well-known equilibrium morphology that fits these characteristics is the bicontinuous microemulsion achieved by the addition of block copolymer compatibilizers to flexible polymer–polymer blends. However, there does not exist design rules for using block copolymer compatibilizers to produce bicontinuous microemulsion morphologies from the conjugated polymer/fullerene mixtures typically used to form the active layer of organic solar cells. Motivated by these considerations, we use single chain in mean field simulations to study the equilibrium phase behavior of semiflexible polymer + flexible–semiflexible block copolymer + solvent mixtures. Based on our results, we identify design rules for producing large channels of morphologies with characteristics like that of the bicontinuous microemulsion.

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“…In diblock copolymers the deviation from mean field behavior is even larger and the critical point is replaced by a first order phase transition [5]. Fluctuations in the more complex mixture of a critical binary homopolymer blend and the corresponding symmetrical diblock copolymer lead to the universality class of the isotropic Lifshitz critical behavior as the order parameter is a scalar ͑n 1͒ and the dimension in which the wave vector instability occurs ͑m͒ is equal to the spatial dimension ͑d͒, m d 3 [6][7][8][9][10][11]. In such systems one might expect significant renormalization due to thermal fluctuations as the upper critical dimension is 2 times larger ͑d U 8͒ than that of binary blends ͑d U 4͒ [9].…”

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confidence: 99%

“…(1) describes the system near the consolute line [8]. The degree of polymerization was N PEE 30.5, N PDMS 29.2, and N PEE-PDMS 168 leading to the ratio a p N PEE N PDMS ͞N PEE-PDMS 0.18 [7]. The homopolymers were always mixed with a PEE volume fraction of 0.516.…”

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confidence: 99%

Crossover from 3D Ising to Isotropic Lifshitz Critical Behavior in a Mixture of a Homopolymer Blend and Diblock Copolymer

et al. 1999

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Thermal composition fluctuations and the associated crossover from the 3D Ising to the isotropic Lifshitz universality class have been studied in a three component mixture made of a critical polymer blend and the corresponding diblock copolymer. The critical exponents were found to be appreciably larger than those of the 3D Ising, in agreement with expectations from the larger upper critical dimension. Very near the critical temperature a crossover to a renormalized Lifshitz critical behavior was observed possibly caused by fluctuation induced rearrangements of the diblock copolymers.[ S0031-9007(99) PACS numbers: 61.25. Hq, 64.60.Cn, 64.60.Fr Studies of thermal composition fluctuations in binary mixtures of homopolymers and diblock copolymers have produced a good understanding of the critical behavior [1][2][3]. The critical exponents are of the mean field universality class far from the critical point, whereas fluctuations affect the exponents in the near vicinity of the critical point. The crossover temperature from mean field to nonmean field is estimated by the Ginzburg criterion [1,2], which predicts a 1͞N and 1͞ p N (N degree of polymerization) scaling behavior for blends and diblock copolymers, respectively. In binary polymer blends the 3D Ising critical range has been observed to be appreciably larger than that estimated from the 1͞N scaling law [3], an observation which is mainly attributed to the effect of compressibility [4]. In diblock copolymers the deviation from mean field behavior is even larger and the critical point is replaced by a first order phase transition [5]. Fluctuations in the more complex mixture of a critical binary homopolymer blend and the corresponding symmetrical diblock copolymer lead to the universality class of the isotropic Lifshitz critical behavior as the order parameter is a scalar ͑n 1͒ and the dimension in which the wave vector instability occurs ͑m͒ is equal to the spatial dimension ͑d͒, m d 3 [6-11]. In such systems one might expect significant renormalization due to thermal fluctuations as the upper critical dimension is 2 times larger ͑d U 8͒ than that of binary blends ͑d U 4͒ [9]. This also makes it difficult to calculate the critical exponents [8]. In a recent study on such a polymer mixture mean field critical behavior was surprisingly observed even rather near the isotropic Lifshitz critical point [11]. In the present Letter we report equivalent experiments, however, with a mixture of significantly reduced polymer masses. This study demonstrates a transition from mean field to 3D Ising behavior at small copolymer contents, and a transition from mean field to isotropic Lifshitz critical behavior at higher copolymer contents. The observed critical exponents near the Lifshitz point are significantly larger than those of the 3D Ising universality class.The principal effect of diblock copolymers solved in a homopolymer blend is the reduction of the surface energy which according to the corresponding Hamiltonian of the H 1 2

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Design of bicontinuous polymeric microemulsions

Cited by 85 publications

References 5 publications

Thermal composition fluctuations near the isotropic Lifshitz critical point in a ternary mixture of a homopolymer blend and diblock copolymer

Thermal composition fluctuations near the isotropic Lifshitz critical point in a ternary mixture of a homopolymer blend and diblock copolymer

Achieving Bicontinuous Microemulsion Like Morphologies in Organic Photovoltaics

Crossover from 3D Ising to Isotropic Lifshitz Critical Behavior in a Mixture of a Homopolymer Blend and Diblock Copolymer

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