Transition pathways connecting crystalline and quasicrystalline phases are studied using an effic... more Transition pathways connecting crystalline and quasicrystalline phases are studied using an efficient numerical approach applied to a Landau free-energy functional. Specifically, minimum energy paths connecting different local minima of the Lifshitz-Petrich model are obtained using the highindex saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state.
The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (... more The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (DBCPs) is studied using the polymeric self-consistent field theory. The theoretical study predicts that the double-diamond and the "plumber's nightmare" phases, which are metastable for neat diblock copolymers, could be stabilized in block copolymers with designed dispersity, namely, binary blends composed of a gyroid-forming DBCP and a homopolymer-like DBCP. The spatial distribution of different monomers reveals that these two types of DBCPs are segregated such that the homopolymer-like component is localized at the nodes to relieve the packing frustration. Simultaneously, the presence of a local segregation of the two DBCPs on the AB interface regulates the interfacial curvature. These two mechanisms could act in tandem for homopolymer-like diblock copolymers with proper compositions, resulting in larger stability regions for the novel bicontinuous phases.
Phase behavior of diblock copolymer/homopolymer blends (AB/C) is investigated theoretically. The ... more Phase behavior of diblock copolymer/homopolymer blends (AB/C) is investigated theoretically. The study focuses on a special case where all three binary pairs, A/B, B/C and C/A, are miscible. Despite the miscibility of the binary pairs, a closed-loop immiscible region exists in the AB/C blends when the A/C and B/C pair interactions are sufficiently different. Inside the closed-loop, the system undergoes microphase separation, exhibiting different ordered structures. This phenomenon is enhanced when the homopolymer (C) interacts more strongly to one of the blocks (A or B).
Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants and block... more Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such surface tension, bending moduli and line tension. Understanding how the molecular property of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.
The phase behavior of polydisperse ABA triblock copolymers is studied using dissipative particle ... more The phase behavior of polydisperse ABA triblock copolymers is studied using dissipative particle dynamics simulations, focusing on the emergence and property of bicontinuous structures. Bicontinuous structures are characterized by two separate, intermeshed nanoscopic domains extending throughout the material. The connectivity of polymeric bicontinuous structures makes them highly desirable for many applications. For conventional monodisperse diblock and triblock copolymers, regular bicontinuous structures (i.e., gyroid and Fddd) can be formed over a narrow composition window of ~3%. We demonstrate that the composition window for the formation of bicontinuous structures can be regulated by designed polydispersity distributions of ABA triblock copolymers. In particular, introducing polydispersity in both A and B blocks can lead to a significant enhancement of the composition window of bicontinuous structures with both continuous A and B domains. The mechanism of the bicontinuous struc...
We propose a general framework of computing interfacial structure. If an ordered phase is involve... more We propose a general framework of computing interfacial structure. If an ordered phase is involved, the interfacial structure can be obtained by simply minimizing the free energy with compatible boundary conditions. The framework is applied to Landau- Brazovskii model and works efficiently.
The relative stability of two-dimensional soft quasicrystals is examined using a recently develop... more The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.
The equilibrium properties of block copolymer micelles confined in polymer thin films are investi... more The equilibrium properties of block copolymer micelles confined in polymer thin films are investigated using self-consistent field theory. The theory is based on a model system consisting of AB diblock copolymers and A homopolymers. Two different methods, based on the radius of gyration tensor and the spherical harmonics expansion, are used to characterize the micellar shape. The results reveal that the morphology of micelles in thin films depends on the thickness of the thin films and the selectivity of the confining surfaces. For spherical (cylindrical) micelles, the spherical (cylindrical) symmetry is broken by the presence of the one-dimensional confinement, whereas the top-down symmetry is broken by the selectivity of the confining surfaces. Morphological transitions from spherical or cylindrical micelles to cylinders or lamella are predicted when the film thickness approaches the micellar size.
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent... more The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. Finally the region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions.
The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (... more The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (DBCPs) is studied using the polymeric self-consistent field theory. The theoretical study predicts that the double-diamond and the “plumber’s nightmare” phases, which are metastable for neat diblock copolymers, could be stabilized in block copolymers with designed dispersity, namely, binary blends composed of a gyroid-forming DBCP and a homopolymerlike DBCP. The spatial distribution of different monomers reveals that these two types of DBCPs are segregated such that the homopolymer-like component is localized at the nodes to relieve the packing frustration. Simultaneously, the presence of a local segregation of the two DBCPs on the AB interface regulates the interfacial curvature. These two mechanisms could act in tandem for homopolymer-like diblock copolymers with proper compositions, resulting in larger stability regions for the novel bicontinuous phases.
aSchool of Mathematical Sciences, Laboratory of Mathematics and Applied Mathematics, Peking Unive... more aSchool of Mathematical Sciences, Laboratory of Mathematics and Applied Mathematics, Peking University, Beijing 100871, China; bSchool of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China; cDepartment of Physics and Astronomy, McMaster University, Hamilton, Canada L8S 4M1; dBeijing International Center for Mathematical Research, Center for Quantitative Biology, Peking University, Beijing 100871, China
The phase behaviour of binary blends composed of A 1 B 1 and A 2 B 2 diblock copolymers is system... more The phase behaviour of binary blends composed of A 1 B 1 and A 2 B 2 diblock copolymers is systematically studied using the polymeric selfconsistent field theory, focusing on the formation and relative stability of various spherical packing phases. The results are summarized in a set of phase diagrams covering a large phase space of the system. Besides the commonly observed body-centered-cubic (BCC) phase, complex spherical packing phases including the Frank-Kasper A15 and σ and the Laves C14 and C15 phases could be stabilized by the addition of longer A 2 B 2-copolymers to asymmetric A 1 B 1-copolymers. Stabilizing the complex spherical packing phases requires that the added A 2 B 2-copolymers have a longer A-block and an overall chain length at least comparable to the host copolymer chains. A detailed analysis of the block distributions reveals the existence of inter-and intradomain segregation of different copolymers, which depends sensitively on the copolymer length ratio and composition. The predicted phase behaviours of the A 1 B 1 /A 2 B 2 diblock copolymer blends are in good agreement with available experimental and theoretical results. The study demonstrated that binary blends of diblock copolymers provide an efficient route to regulate the emergence and stability of complex spherical packing phases.
The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavi... more The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavior and structural properties of many-body systems. In particular, polymeric SCFT has been successfully applied to inhomogeneous polymeric systems such as polymer blends and block copolymer melts. The polymeric SCFT is commonly derived using field-theoretical techniques. Here we provide an alternative derivation of the SCFT equations and SCFT free energy functional using a variational principle. Numerical methods of solving the SCFT equations and applications of the SCFT are also briefly introduced.
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A phase field model with two phase fields, representing the concentration and the head–tail separ... more A phase field model with two phase fields, representing the concentration and the head–tail separation of amphiphilic molecules, respectively, has been constructed using an extension of the Ohta–Kawasaki model (Macromolecules, 1986, 19, 2621–2632).
The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as ... more The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as coarse-grained model of lipids and the bolalipids, are studied using the self-consistent field theory (SCFT). Specifically, solutions of the SCFT equations, corresponding to membranes in different geometries (planar, cylindrical, spherical, and pore) have been obtained for a model system composed of amphiphilic AB diblock copolymers and ABA triblock copolymers dissolved in A homopolymers. The free energy of the membranes with different geometries is then used to extract the bending modulus, Gaussian modulus, and line tension of the membranes. The results reveal that the bending modulus of the triblock membrane is greater than that of the diblock membrane. Furthermore, the Gaussian modulus and line tension of the triblock membrane indicate that the triblock membranes have higher pore formation energy than that of the diblock membranes. The equilibrium bridging and looping fractions of the triblock copolymers are also obtained. Implications of the theoretical results on the elastic properties of biologically equivalent lipid bilayers and the bolalipid membranes are discussed.
Among the various ordered morphologies selfassembled from block copolymers, the spherical packing... more Among the various ordered morphologies selfassembled from block copolymers, the spherical packing phases are particularly interesting because they resemble the familiar atomic crystals. The commonly observed spherical morphology of block copolymers is the body-centered-cubic phase. Recently, a number of novel spherical packing phases, i.e., the complex Frank−Kasper phases originally obtained in metallic alloys, have been observed in block copolymer melts. Theoretical studies have revealed that conformational asymmetry of the different blocks provides a key mechanism to stabilize the Frank−Kasper phases. Furthermore, local segregation of different copolymers in blends of diblock copolymers and copolymer architectures provides additional mechanisms to enhance the stability of the complex ordered phases. In this Viewpoint we summarize recent advances in our understanding of the formation of the nonclassical spherical packing phases in AB-type block copolymers, emphasizing the formation mechanisms of these fascinating complex ordered structures.
Proceedings of the National Academy of Sciences of the United States of America, Jan 30, 2018
Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly... more Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order-disorder transition temperature (). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank-Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)--poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEX) upon heating and cooling. The process-path-dependent formation of crystalline ord...
We examine the behavior of lamellar phases of charged/neutral diblock copolymer thin films contai... more We examine the behavior of lamellar phases of charged/neutral diblock copolymer thin films containing mobile ions in the presence of an external electric field. We employ self-consistent field theory and focus on the aligning effect of the electric field on the lamellae. Of particular interest are the effects of the mobile ions on the critical field, the value required to reorient the lamellae from the parallel configuration favored by the surface interaction to the perpendicular orientation favored by the field. We find that the critical field depends strongly on whether the neutral or charged species is favored by the substrates. In the case in which the neutral species is favored, the addition of charges decreases the critical electric field significantly. The effect is greater when the mobile ions are confined to the charged lamellae. In contrast, when the charged species is favored by the substrate, the addition of mobile ions stabilizes the parallel configuration and thus results in an increase in the critical electric field. The presence of ions in the system introduces a new mixed phase in addition to those reported previously.
nowledge of the anatomy of the facial vasculature and its most relevant clinical applications is ... more nowledge of the anatomy of the facial vasculature and its most relevant clinical applications is crucial for a plethora of surgical and minimally invasive procedures in the face. Access pathways, 1 pedicled and free flap transfer, 2 and explantation and transplantation of total faces are based on the proper assessment and use of the facial veins and arteries. Although the general anatomy, including variations of the facial artery and its branches, has been well described previously, 3-6 reports in the literature are few when referring to the detailed course and variations of the facial vein. 7,8 With the increasing popularity of volumizing facial procedures for rejuvenating purposes, the understanding of the facial fat compartments is essential for long-lasting and safe applications. The facial vein has been previously shown to form the lateral boundary of the deep medial cheek fat, 9-12 the lateral boundary of the premaxillary space (containing the deep nasolabial fat compartment), 7,13 and the medial boundary of the sub-orbicularis oculi fat. 9,14 This pivotal role of the facial vein as a hallmark structure in the face is of great importance when trying to understand the detailed anatomy of the facial fat compartments and to avoid complications. Of those, irreversible blindness resulting from filler or autologous fat transfer procedures is considered the most dangerous one. 15 However, to
Transition pathways connecting crystalline and quasicrystalline phases are studied using an effic... more Transition pathways connecting crystalline and quasicrystalline phases are studied using an efficient numerical approach applied to a Landau free-energy functional. Specifically, minimum energy paths connecting different local minima of the Lifshitz-Petrich model are obtained using the highindex saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state.
The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (... more The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (DBCPs) is studied using the polymeric self-consistent field theory. The theoretical study predicts that the double-diamond and the "plumber's nightmare" phases, which are metastable for neat diblock copolymers, could be stabilized in block copolymers with designed dispersity, namely, binary blends composed of a gyroid-forming DBCP and a homopolymer-like DBCP. The spatial distribution of different monomers reveals that these two types of DBCPs are segregated such that the homopolymer-like component is localized at the nodes to relieve the packing frustration. Simultaneously, the presence of a local segregation of the two DBCPs on the AB interface regulates the interfacial curvature. These two mechanisms could act in tandem for homopolymer-like diblock copolymers with proper compositions, resulting in larger stability regions for the novel bicontinuous phases.
Phase behavior of diblock copolymer/homopolymer blends (AB/C) is investigated theoretically. The ... more Phase behavior of diblock copolymer/homopolymer blends (AB/C) is investigated theoretically. The study focuses on a special case where all three binary pairs, A/B, B/C and C/A, are miscible. Despite the miscibility of the binary pairs, a closed-loop immiscible region exists in the AB/C blends when the A/C and B/C pair interactions are sufficiently different. Inside the closed-loop, the system undergoes microphase separation, exhibiting different ordered structures. This phenomenon is enhanced when the homopolymer (C) interacts more strongly to one of the blocks (A or B).
Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants and block... more Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such surface tension, bending moduli and line tension. Understanding how the molecular property of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.
The phase behavior of polydisperse ABA triblock copolymers is studied using dissipative particle ... more The phase behavior of polydisperse ABA triblock copolymers is studied using dissipative particle dynamics simulations, focusing on the emergence and property of bicontinuous structures. Bicontinuous structures are characterized by two separate, intermeshed nanoscopic domains extending throughout the material. The connectivity of polymeric bicontinuous structures makes them highly desirable for many applications. For conventional monodisperse diblock and triblock copolymers, regular bicontinuous structures (i.e., gyroid and Fddd) can be formed over a narrow composition window of ~3%. We demonstrate that the composition window for the formation of bicontinuous structures can be regulated by designed polydispersity distributions of ABA triblock copolymers. In particular, introducing polydispersity in both A and B blocks can lead to a significant enhancement of the composition window of bicontinuous structures with both continuous A and B domains. The mechanism of the bicontinuous struc...
We propose a general framework of computing interfacial structure. If an ordered phase is involve... more We propose a general framework of computing interfacial structure. If an ordered phase is involved, the interfacial structure can be obtained by simply minimizing the free energy with compatible boundary conditions. The framework is applied to Landau- Brazovskii model and works efficiently.
The relative stability of two-dimensional soft quasicrystals is examined using a recently develop... more The relative stability of two-dimensional soft quasicrystals is examined using a recently developed projection method which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal and octagonal quasicrystals, are obtained for a simple model, i.e. the Lifshitz-Petrich free energy functional, of soft quasicrystals with two length-scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.
The equilibrium properties of block copolymer micelles confined in polymer thin films are investi... more The equilibrium properties of block copolymer micelles confined in polymer thin films are investigated using self-consistent field theory. The theory is based on a model system consisting of AB diblock copolymers and A homopolymers. Two different methods, based on the radius of gyration tensor and the spherical harmonics expansion, are used to characterize the micellar shape. The results reveal that the morphology of micelles in thin films depends on the thickness of the thin films and the selectivity of the confining surfaces. For spherical (cylindrical) micelles, the spherical (cylindrical) symmetry is broken by the presence of the one-dimensional confinement, whereas the top-down symmetry is broken by the selectivity of the confining surfaces. Morphological transitions from spherical or cylindrical micelles to cylinders or lamella are predicted when the film thickness approaches the micellar size.
The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent... more The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. Finally the region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions.
The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (... more The formation of various bicontinuous phases from binary blends of linear AB diblock copolymers (DBCPs) is studied using the polymeric self-consistent field theory. The theoretical study predicts that the double-diamond and the “plumber’s nightmare” phases, which are metastable for neat diblock copolymers, could be stabilized in block copolymers with designed dispersity, namely, binary blends composed of a gyroid-forming DBCP and a homopolymerlike DBCP. The spatial distribution of different monomers reveals that these two types of DBCPs are segregated such that the homopolymer-like component is localized at the nodes to relieve the packing frustration. Simultaneously, the presence of a local segregation of the two DBCPs on the AB interface regulates the interfacial curvature. These two mechanisms could act in tandem for homopolymer-like diblock copolymers with proper compositions, resulting in larger stability regions for the novel bicontinuous phases.
aSchool of Mathematical Sciences, Laboratory of Mathematics and Applied Mathematics, Peking Unive... more aSchool of Mathematical Sciences, Laboratory of Mathematics and Applied Mathematics, Peking University, Beijing 100871, China; bSchool of Mathematics and Computational Science, Xiangtan University, Hunan 411105, China; cDepartment of Physics and Astronomy, McMaster University, Hamilton, Canada L8S 4M1; dBeijing International Center for Mathematical Research, Center for Quantitative Biology, Peking University, Beijing 100871, China
The phase behaviour of binary blends composed of A 1 B 1 and A 2 B 2 diblock copolymers is system... more The phase behaviour of binary blends composed of A 1 B 1 and A 2 B 2 diblock copolymers is systematically studied using the polymeric selfconsistent field theory, focusing on the formation and relative stability of various spherical packing phases. The results are summarized in a set of phase diagrams covering a large phase space of the system. Besides the commonly observed body-centered-cubic (BCC) phase, complex spherical packing phases including the Frank-Kasper A15 and σ and the Laves C14 and C15 phases could be stabilized by the addition of longer A 2 B 2-copolymers to asymmetric A 1 B 1-copolymers. Stabilizing the complex spherical packing phases requires that the added A 2 B 2-copolymers have a longer A-block and an overall chain length at least comparable to the host copolymer chains. A detailed analysis of the block distributions reveals the existence of inter-and intradomain segregation of different copolymers, which depends sensitively on the copolymer length ratio and composition. The predicted phase behaviours of the A 1 B 1 /A 2 B 2 diblock copolymer blends are in good agreement with available experimental and theoretical results. The study demonstrated that binary blends of diblock copolymers provide an efficient route to regulate the emergence and stability of complex spherical packing phases.
The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavi... more The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavior and structural properties of many-body systems. In particular, polymeric SCFT has been successfully applied to inhomogeneous polymeric systems such as polymer blends and block copolymer melts. The polymeric SCFT is commonly derived using field-theoretical techniques. Here we provide an alternative derivation of the SCFT equations and SCFT free energy functional using a variational principle. Numerical methods of solving the SCFT equations and applications of the SCFT are also briefly introduced.
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A phase field model with two phase fields, representing the concentration and the head–tail separ... more A phase field model with two phase fields, representing the concentration and the head–tail separation of amphiphilic molecules, respectively, has been constructed using an extension of the Ohta–Kawasaki model (Macromolecules, 1986, 19, 2621–2632).
The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as ... more The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as coarse-grained model of lipids and the bolalipids, are studied using the self-consistent field theory (SCFT). Specifically, solutions of the SCFT equations, corresponding to membranes in different geometries (planar, cylindrical, spherical, and pore) have been obtained for a model system composed of amphiphilic AB diblock copolymers and ABA triblock copolymers dissolved in A homopolymers. The free energy of the membranes with different geometries is then used to extract the bending modulus, Gaussian modulus, and line tension of the membranes. The results reveal that the bending modulus of the triblock membrane is greater than that of the diblock membrane. Furthermore, the Gaussian modulus and line tension of the triblock membrane indicate that the triblock membranes have higher pore formation energy than that of the diblock membranes. The equilibrium bridging and looping fractions of the triblock copolymers are also obtained. Implications of the theoretical results on the elastic properties of biologically equivalent lipid bilayers and the bolalipid membranes are discussed.
Among the various ordered morphologies selfassembled from block copolymers, the spherical packing... more Among the various ordered morphologies selfassembled from block copolymers, the spherical packing phases are particularly interesting because they resemble the familiar atomic crystals. The commonly observed spherical morphology of block copolymers is the body-centered-cubic phase. Recently, a number of novel spherical packing phases, i.e., the complex Frank−Kasper phases originally obtained in metallic alloys, have been observed in block copolymer melts. Theoretical studies have revealed that conformational asymmetry of the different blocks provides a key mechanism to stabilize the Frank−Kasper phases. Furthermore, local segregation of different copolymers in blends of diblock copolymers and copolymer architectures provides additional mechanisms to enhance the stability of the complex ordered phases. In this Viewpoint we summarize recent advances in our understanding of the formation of the nonclassical spherical packing phases in AB-type block copolymers, emphasizing the formation mechanisms of these fascinating complex ordered structures.
Proceedings of the National Academy of Sciences of the United States of America, Jan 30, 2018
Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly... more Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order-disorder transition temperature (). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank-Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)--poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEX) upon heating and cooling. The process-path-dependent formation of crystalline ord...
We examine the behavior of lamellar phases of charged/neutral diblock copolymer thin films contai... more We examine the behavior of lamellar phases of charged/neutral diblock copolymer thin films containing mobile ions in the presence of an external electric field. We employ self-consistent field theory and focus on the aligning effect of the electric field on the lamellae. Of particular interest are the effects of the mobile ions on the critical field, the value required to reorient the lamellae from the parallel configuration favored by the surface interaction to the perpendicular orientation favored by the field. We find that the critical field depends strongly on whether the neutral or charged species is favored by the substrates. In the case in which the neutral species is favored, the addition of charges decreases the critical electric field significantly. The effect is greater when the mobile ions are confined to the charged lamellae. In contrast, when the charged species is favored by the substrate, the addition of mobile ions stabilizes the parallel configuration and thus results in an increase in the critical electric field. The presence of ions in the system introduces a new mixed phase in addition to those reported previously.
nowledge of the anatomy of the facial vasculature and its most relevant clinical applications is ... more nowledge of the anatomy of the facial vasculature and its most relevant clinical applications is crucial for a plethora of surgical and minimally invasive procedures in the face. Access pathways, 1 pedicled and free flap transfer, 2 and explantation and transplantation of total faces are based on the proper assessment and use of the facial veins and arteries. Although the general anatomy, including variations of the facial artery and its branches, has been well described previously, 3-6 reports in the literature are few when referring to the detailed course and variations of the facial vein. 7,8 With the increasing popularity of volumizing facial procedures for rejuvenating purposes, the understanding of the facial fat compartments is essential for long-lasting and safe applications. The facial vein has been previously shown to form the lateral boundary of the deep medial cheek fat, 9-12 the lateral boundary of the premaxillary space (containing the deep nasolabial fat compartment), 7,13 and the medial boundary of the sub-orbicularis oculi fat. 9,14 This pivotal role of the facial vein as a hallmark structure in the face is of great importance when trying to understand the detailed anatomy of the facial fat compartments and to avoid complications. Of those, irreversible blindness resulting from filler or autologous fat transfer procedures is considered the most dangerous one. 15 However, to
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