Phase equilibria in random multiblock copolymers

Subbotin, A. V.; Semenov, A. N.

doi:10.1140/epje/i200101101

Cited by 13 publications

(28 citation statements)

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“…54,56,59,64 At the small-limit, the study of random copolymers has explored how random sequences may lead to the emergence of microphase separated structures or affect polymer miscibility. 51,[65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81] This is a traditional way of imbuing a polymer material with the advantageous properties of two monomer chemistries. 37 Theory often relates these local sequence effects to effective interaction parameters or other local physical parameters.…”

Section: Does Sequence Matter?mentioning

confidence: 99%

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

2020

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Polymer science has been driven by ever-increasing molecular complexity, as polymer synthesis expands an alreadyvast palette of chemical and architectural parameter space. Copolymers represent a key example, where simple homopolymers have given rise to random, alternating, gradient, and block copolymers. Polymer physics has provided the insight needed to explore this monomer sequence parameter space. The future of polymer science, however, must contend with further increases in monomer precision, as this class of macromolecules moves ever closer to the sequence-monodisperse polymers that are the workhorses of biology. The advent of sequence-defined polymers gives rise to opportunities for material design, with increasing levels of chemical information being incorporated into long-chain molecules; however, this also raises questions that polymer physics must address. What properties uniquely emerge from sequence-definition? Is this circumstance dependent? How do we define and think about sequence dispersity? How do we think about a hierarchy of sequence effects? Are more sophisticated characterization methods, as well as theoretical and computational tools needed to understand this class of macromolecules? The answers to these questions touch on many difficult scientific challenges, setting the stage for a rich future for sequence-defined polymers in polymer physics.

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Section: Does Sequence Matter?mentioning

confidence: 99%

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

2020

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“…Since we want to compare the structure formation of MD with SCMF, we have to stay in the regime which is accessible to both models. However, this is an indication that the prediction of a lamellar phase, as in [SS02], holds. A snapshot of this configuration is shown in in figure 3.5(b).…”

Section: Lamellar Phasementioning

confidence: 95%

“…Their results show that no microphase separation will occur for random copolymers, [SY05a,SY05b], but they find a microphase separation for random block copolymers with a block length greater than 2 [SY05b]. Subbotin and Semenov used the weak segregation approach in the search for the type of microphases formed by a random block copolymers and found many different phases, hexagonal, bcc, and lamellar, for values of f close but not equal to 1 2 [SS02]. At a value of f = 1 2 , they predict that there is only a lamellar phase, besides the ubiquitous homogeneous phases, present in the phase diagram.…”

Section: Random Block Copolymersmentioning

confidence: 99%

“…The phase behaviour of random block copolymers has been investigated in meanfield calculations [FML92,NdlCC93,SS02] and is still subject of research today in mean-field theory and numerical SCFT [vdHMZ11]. The particle-based simulation of random block copolymers has not received as much attention, due to the large system size and long relaxation times required.…”

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confidence: 99%

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Random Block Copolymer Melts in the Bulk and at Selective Substrates

Steinmüller¹

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Meine Diplomarbeit in Physik handelte von der Simulation von Atomkernen. Der Wechsel aus der Kern-und Hadronenphysik ein paar Größenordnungen in Raum und Zeit hinauf in das Gebiet der weichen Materie war ein großer Schritt, aber leichter zu bewältigen, als ich erst dachte. Der Dank dafür gebührt zuallererst Marcus Müller, der mich in seine Arbeitsgruppe aufnahm. Bei der Einarbeitung in das Gebiet der Polymerphysik und der Bearbeitung der Fragestellung dieser Doktorarbeit stand er mir mit Rat und Tat zur Seite. Das Wissen von Kostas Daoulas über Monte Carlo Simulationen von Polymerschmelzen war entscheidend dafür, dass ich mit der Arbeit zügig beginnen konnte. Als nächstes möchte ich mich bei meinen Zimmergenossen für die angenehme Arbeitsatmosphäre bedanken. Je remercie Fabien de m'aider à parler français et à effectuer les simulations de dynamique moléculaire. Nikita danke ich dafür, einfach Nikita zu sein. Allen anderen Gruppenmitgliedern danke ich für die schöne Zeit hier, die auch über das reine Arbeiten hinausging. Für die Zusammenarbeit im Rahmen der Simulation von Zufallsblockkopolymeren danke ich Grant Smith, Dmitry Bedrov und Keith Hambrecht von der University of Utah. Mein ganz besonderer Dank gebührt Martin Hömberg, für die Hilfe bei Fragen zu Algorithmen, zur Parallelprogrammierung, zur Nutzung der Rechenzentren und zu guter Letzt noch für das Korrekturlesen der Doktorarbeit. Die Simulationen wurden in den Rechenzentren der GWDG, des HLRN und des Jülich Supercomputing Centre durchgeführt. Das Projekt wurde von der DFG im Rahmen des SPP 1369 "Polymer-Solid Contacts: Interfaces and Interphases" finanziell gefördert. Meinen Eltern und meiner Schwester danke ich für ihr unerschütterliches Vertrauen. v Zusammenfassung Zufallsblockkopolymere sind Polymere, die aus zwei verschiedenen, zufällig aneinandergefügten Typen von Blöcken bestehen. Diese Blöcke enthalten jeweils nur eine Art Monomer und eine gegenseitige Abstoßung führt hierbei zur Domänenbildung. Wenn diese Domänen unterschiedliche mechanische Eigenschaften besitzen -eine ist härter, die andere weicher -lassen sich damit beispielsweise gummiartige Werkstoffe herstellen, die ohne ein chemisches Vernetzungsmittel auskommen. Weiterhin ist die von Zufallsblockkopolymeren ausgebildete Struktur interessant für Direktmethanolbrennstoffzellen, wo diese als Protonenaustauschmembranen verwendet werden. Am Kontakt zwischen Elektroden und Membran kann sich ein ausgedehntes Gebiet bilden, das sich in seinen Eigenschaften von denen der unmittelbaren Oberfläche (Kontaktfläche) und des Volumen unterscheidet: die Interphase. Wir verwenden für die Simulation der Polymerschmelzen zwei verschiedene vergröberte Modelle, eines mit weichen Wechselwirkungen und ein Lennard-Jones Kugel-Feder Modell. Im weichen Modell equilibriert die Schmelze schneller, während im Lennard-Jones Modell die Dynamik und die mechanischen Eigenschaften realistischer sind. Unser Ziel ist es, Parameter für diese Modelle zu finden, um die equilibrierten Strukturen des weichen Modells als Ausgangspu...

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“…On the other hand, the critical correlation λ c (larger values of λ increase the preference for homopolymers), above which macroscopic phase separation occurs at all, increases with Q: Upon increasing in a random block copolymer melt the number Q of blocks per polymer and thereby the number of different A-B-sequences, the relative variance in A content (composition) decreases as 1/ √ Q. Accordingly, the energy reduction of two A-rich and B-rich, homogeneous phases relative to the disordered state diminishes, such that the limit Q → ∞ eventually thwarts macroscopic phase separation, except for a homopolymer blend [104,118,62].…”

Section: Routes From Macroscopic To Microscopic Phase Separation: Pha...mentioning

confidence: 99%

Multiphase coexistence with sequence fractionation in random block copolymers

Heydt¹

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Random binary block copolymers emerge from linking permanently and at random prepolymer blocks of two different chemical species A and B. The competitive interplay of conformational entropy, connectivity within one polymer, temperature-dependent incompatibility between A and B, and incompressibility gives rise to a complex phase behavior with a variety of possible morphologies of A-and B-rich domains. Technical applications of the self-organized structures in block copolymers include nanoscale templates and medical drug delivery via copolymer micelles.For random Q-block copolymers, this work addresses theoretically the conjectured coexistence of macroscopic phase separation and a structured phase of microscopic A-and B-rich domains. Sequence fractionation according to the copolymers' internal structure promotes the coexistence of phases with different morphologies in equilibrium, as is revealed by a theory with explicit account for the exchange of individual sequences. In our semi-microscopic model, one block comprises M identical segments. The Markovian block-type sequence distribution is characterized by the type correlation λ of adjacent blocks and the global A content. Our focus is on block copolymer distributions with A B exchange symmetry, for which phase transitions from the disordered state are continuous within mean-field theory. Upon increasing the incompatibility χ (by decreasing temperature) in the disordered state, we observe the formation of the known global, ordered phases: for λ > λ c , two coexisting macroscopic A-and B-rich phases, and for λ < λ c , a microstructured (lamellar) phase with nonzero wave number, k(λ). In addition, we encounter a fourth region in the λ-χ plane where these three phases coexist with different, for Q ≥ 3 non-Markovian, sequence distributions. The three-phase region is reached, either from the macroscopic phases via a third lamellar phase that is rich in alternating sequences, or starting from the lamellar state, via two additional homogeneous, homopolymer-enriched phases; in both cases, the incipient phases have zero volume fraction. The four regions of the phase diagram meet at a multicritical point (λ c , χ c ), at which A-B segregation vanishes. Since our analytical method assumes weak segregation for the lamellar phase, it proves reliable particularly in the vicinity of (λ c , χ c ). For random triblock copolymers, Q = 3, we find that both the character of this point and the critical exponent of the segregation amplitude change substantially with the number M of segments per block: The lamellar wave number vanishes continuously on approach to (λ c , χ c ) only for M < 7. The results for Q = 3 in the continuous-chain limit M → ∞ are compared to numerical self-consistent field theory (SCFT), which is accurate at larger segregation.

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Phase equilibria in random multiblock copolymers

Cited by 13 publications

References 1 publication

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

Random Block Copolymer Melts in the Bulk and at Selective Substrates

Multiphase coexistence with sequence fractionation in random block copolymers

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