Localization of a random copolymer at an interface: an exact enumeration study

James, E W; Soteros, C E; Whittington, S G

doi:10.1088/0305-4470/36/46/003

Cited by 10 publications

(5 citation statements)

References 14 publications

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“…They have proved particularly useful in the determination of universal behavior and scaling laws for polymer systems ranging from individual chains to melts. The critical behavior of SAWs is also closely related to that of the Ising model and to percolation [8,9,10,11,12,13,14,15,16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

2018

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Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is (a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and (b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

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Section: Introductionmentioning

confidence: 99%

Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

2018

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“…The wider cocontinuous window in the presence of the AC block copolymer than the AB3 block copolymer may be due to that the AC block copolymer had higher asymmetry than the AB3 block copolymer although the compositions were the same. The both blocks of AB3 copolymer and PS block of AC were stretched in their corresponding homopolymer sides of the interface, while the random block of AC copolymer formed loops crossing the interface rather than stretched conformation in one side of the interface. , The asymmetry is actually the volume ratio of the two parts of a block copolymer chain respectively located in the minor phase side and in the major phase side of the interface. In the case of AC block copolymer, the looped random block would equally distribute on both sides of the interface since the molar composition was 0.5.…”

Section: Resultsmentioning

confidence: 99%

Tuning Polymer Blends to Cocontinuous Morphology by Asymmetric Diblock Copolymers as the Surfactants

Luo

Wang

et al. 2011

Macromolecules

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We investigated the influence of the chain asymmetry of the styrene (S)Àmethyl methacrylate (MMA) copolymer (surfactant) on the morphology of the polystyrene (PS)/poly(methyl methacrylate) (PMMA) blends. It was, for the first time, demonstrated that the chain asymmetry of the block copolymer surfactant would have significant influence on the structure of the polymer blend in the melt mixing process. In the PS/PMMA = 30/70 blends, the addition of asymmetric AB diblock copolymers tuned the morphology from the droplet-in-matrix structure to the cocontinuous structure. At 20 wt % asymmetric AB block copolymer (PMMA 110 -block-PS 430 ) dosage, the onset of the cocontinuous interval of the PS/PMMA blends was lowered to PS/PMMA = 20/80 and the cocontinuous interval was broadened to PS/PMMA = 20/80À30/70, compared with the onset at PS/PMMA = 45/55 and the interval at PS/PMMA = 45/55À50/50 of the PS/PMMA blends without the copolymers. The reason was that the packing of the asymmetric block copolymer on the interface provided the bending energy being against the interfacial energy when the longer block of the copolymer was in the minor phase side, suppressing the breakup of the minor phase fibers during melt mixing. With the addition of 20 wt % AC block copolymer (P(S-ran-MMA) 220 -block-PS 320 ), which was more asymmetric than the AB block copolymer (PMMA 110 -block-PS 430 ) of the same molecular weight and monomer composition, the PS/PMMA blends showed an even wider cocontinuous interval at PS/PMMA = 10/90À30/70.

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“…This discrete model has already been investigated in physics (see [14] or [21]) and mathematics (see [13]) in the case K = 0 and under the name copolymer with adsorption. This Date: July 3, 2018. model is very natural, because it interpolates between two classes of models that have received a lot of attention in the literature:…”

Section: 1mentioning

confidence: 99%

“…This type of model, which we call h-model, with a pinning term at the interface in competition with a repulsion effect (given here by h N i=1 Λ i ), has already been investigated in the literature (see [14], or [8]). It has been proven, for instance, that some properties of the h-model can be extended to the wetting model by letting the parameter h tend to ∞ (see [18]).…”

Section: 3mentioning

confidence: 99%

Copolymer at selective interfaces and pinning potentials: Weak coupling limits

Pétrélis¹

2009

Ann. Inst. H. Poincaré Probab. Statist.

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We consider a simple random walk of length N , denoted by (Si) i∈{1,...,N} , and we define (wi) i≥1 a sequence of centered i.i.d. random variables. For K ∈ N we define ((γ −K i , . . . , γ K i )) i≥1 an i.i.d sequence of random vectors. We set β ∈ R, λ ≥ 0 and h ≥ 0, and transform the measure on the set of random walk trajectories with the HamiltonianThis transformed path measure describes an hydrophobic(philic) copolymer interacting with a layer of width 2K around an interface between oil and water.In the present article we prove the convergence in the limit of weak coupling (when λ, h and β tend to 0) of this discrete model towards its continuous counterpart. To that aim we further develop a technique of coarse graining introduced by Bolthausen and den Hollander in [6]. Our result shows, in particular, that the randomness of the pinning around the interface vanishes as the coupling becomes weaker.

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Localization of a random copolymer at an interface: an exact enumeration study

Cited by 10 publications

References 14 publications

Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

Confined Polymers as Self-Avoiding Random Walks on Restricted Lattices

Tuning Polymer Blends to Cocontinuous Morphology by Asymmetric Diblock Copolymers as the Surfactants

Copolymer at selective interfaces and pinning potentials: Weak coupling limits

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