Microphase separation in polyelectrolytic diblock copolymer melt: weak segregation limit

The authors present a generalized theory of microphase separation for charged-neutral diblock copolymer melt. The stability limit of the disordered phase for salt-free melt has been calculated using random phase approximation (RPA) and self-consistent-field theory (SCFT). Explicit analytical free energy expressions for different classical ordered microstructures (lamellar, cylinder, and sphere) are presented. The authors demonstrate that the chemical mismatch required for the onset of microphase separation (chi*N) in charged-neutral diblock melt is higher and the period of ordered microstructures is lower than those for the corresponding neutral-neutral diblock system. Theoretical predictions on the period of ordered structures in terms of Coulomb electrostatic interaction strength, chain length, block length, and chemical mismatch between blocks are presented. SCFT has been used to go beyond the stability limit, where electrostatic potential and charge distribution are calculated self-consistently. Stability limits calculated using RPA are in perfect agreement with the corresponding SCFT calculations. Limiting laws for the stability limit and the period of ordered structures are presented and comparisons are made with an earlier theory. Also, transition boundaries between different morphologies have been investigated.     

Aggregates in solution of binary mixtures of amphiphilic diblock copolymers with different chain length

The polydispersity effect of amphiphilic AB diblock copolymers on the self-assembled morphologies in solution has been investigated by the real-space implementation of self-consistent field theory (SCFT) in two dimensions (2D). The polydispersity is artificially obtained by mixing binary diblock copolymers where the hydrophilic or hydrophobic blocks are composed of two different lengths while the other block length is kept the same. The main advantage is that this simple polydispersity can easily distinguish the difference of aggregates in the density distribution of long and short block length intuitionally and quantitatively. The morphology transition from vesicles to micelles is observed with increasing polydispersity of copolymers due to the length segregation of copolymers. For polydisperse hydrophilic or hydrophobic blocks, the short blocks tend to distribute at the interfaces between hydrophilic and hydrophobic blocks while the long blocks stretch to the outer space. More specifically, by quantitatively taking the sum of all the concentration distribution of long and short chains over the inside and outside surface areas of the vesicle, it is found that long blocks prefer to locate on the outside surface of the vesicle while short ones prefer the inside. Such length segregation leads to large curvature of the aggregate, thus resulting in the decrease of the aggregate size.     

Properties of polymer blends and triblock copolymers obtained by neutron scattering

Static and dynamic scattering properties of polymer blends and block copolymers are examined within the random phase approximation (RPA). A self-consistent theoretical scheme for a simultaneous analysis of elastic and quasielastic scattering data is presented. The case of a triblock copolymer made of an ordinary central block and two deuterated lateral blocks in a matrix of deuterated homopolymers is considered in detail. The theoretical predictions of the RPA are compared with the experimental data obtained by elastic neutron scattering experiments using mixtures of deuterated poly(dimethylsiloxane) homopolymers and copolymers made of three blocks of approximately equal sizes. The lateral blocks are deuterated poly(dimethylsiloxane) and the central one is an ordinary poly(dimethylsiloxane). A good agreement is found in the whole range of wavevectors covered by the experiments. An extension of the RPA to the analysis of the dynamical scattering data for the same systems is put forward. It is shown how the time relaxations of the bare response functions obtained from the single chain dynamics are used to extract the intermediate scattering function characterizing the system of interacting chains. © 1996 John Wiley & Sons, Inc.     

Applications of self-consistent field theory in polymer systems

1Introduction Owing to the specificity of the long chain,polymers present complexity and versatility.These molecules in the system can be various in their topological struc-tures,such as linear,star,comb or circle structures;meanwhile they can be polymeri…     

Self-assembly in block polyelectrolytes

The self-consistent field theory (SCFT) complemented with the Poisson-Boltzmann equation is employed to explore self-assembly of polyelectrolyte copolymers composed of charged blocks A and neutral blocks B. We have extended SCFT to dissociating triblock copolymers and demonstrated our approach on three characteristic examples: (1) diblock copolymer (AB) melt, (2) symmetric triblock copolymer (ABA) melt, (3) triblock copolymer (ABA) solution with added electrolyte. For copolymer melts, we varied the composition (that is, the total fraction of A-segments in the system) and the charge density on A blocks and calculated the phase diagram that contains ordered mesophases of lamellar, gyroid, hexagonal, and bcc symmetries, as well as the uniform disordered phase. The phase diagram of charged block copolymer melts in the charge density--system composition coordinates is similar to the classical phase diagram of neutral block copolymer melts, where the composition and the Flory mismatch interaction parameter χ(AB) are used as variables. We found that the transitions between the polyelectrolyte mesophases with the increase of charge density occur in the same sequence, from lamellar to gyroid to hexagonal to bcc to disordered morphologies, as the mesophase transitions for neutral diblocks with the decrease of χ(AB). In a certain range of compositions, the phase diagram for charged triblock copolymers exhibits unexpected features, allowing for transitions from hexagonal to gyroid to lamellar mesophases as the charge density increases. Triblock polyelectrolyte solutions were studied by varying the charge density and solvent concentration at a fixed copolymer composition. Transitions from lamellar to gyroid and gyroid to hexagonal morphologies were observed at lower polymer concentrations than the respective transitions in the similar neutral copolymer, indicating a substantial influence of the charge density on phase behavior.     

Depletion-induced surface alignment of asymmetric diblock copolymer in selective solvents

Phase separation of asymmetric diblock copolymer near surfaces in selective solvents is theoretically investigated by using the real-space version of self-consistent field theory (SCFT). Several morphologies are predicted and the phase diagram is constructed by varying the distance between two parallel hard surfaces (or the film thickness) W and the block copolymer concentration f(P). Morphologies of the diblock copolymer in dilute solution are found to change significantly with different film thicknesses. In confined systems, stable morphologies found in the bulk solution become unstable due to the loss of polymer conformation entropy. The vesicle phase region contracts when the repulsive interaction between the blocks is strong (strong segregation regime). The mixture of vesicles, rodlike and spherelike micelles and the mixture of vesicles and sphere-like micelles disappear in contrast to the weakly segregating regime. The walls strongly affect the phase separation of block copolymer in selective solvent, and the depletion layer near the surface contributes much to the micelle formation of the block copolymer. Interestingly, the self-assembled morphologies stay near the walls with the distance on the order of the radius of gyration of the block copolymer. The oscillation of the polymer distribution near the walls allows the surface phase separation to be observed due to the strong repulsion between the blocks A and B.     

An Efficient Algorithm for Self-consistent Field Theory Calculations of Complex Self-assembled Structures of Block Copolymer Melts

Self-consistent field theory (SCFT),as a state-of-the-art technique for studying the self-assembly of block copolymers,is attracting continuous efforts to improve its accuracy and efficiency.Here we present a fourth-order exponential time differencing Runge-Kutta algorithm (ETDRK4) to solve the modified diffusion equation (MDE) which is the most time-consuming part of a SCFT calculation.By making a careful comparison with currently most efficient and popular algorithms,we demonstrate that the ETDRK4 algorithm significantly reduces the number of chain contour steps in solving the MDE,resulting in a boost of the overall computation efficiency,while it shares the same spatial accuracy with other algorithms.In addition,to demonstrate the power of our ETDRK4 algorithm,we apply it to compute the phase boundaries of the bicontinuous gyroid phase in the strong segregation regime and to verify the existence of the triple point of the O70 phase,the lamellar phase and the cylindrical phase.     

Phase behavior of a blend of polymer-tethered nanoparticles with diblock copolymers

Using the self-consistent field theory (SCFT), we investigate the phase behavior of a mixture of diblock copolymers and nanoparticles with monodisperse polymer chains tethered to their surfaces. We assume the size of the nanoparticles to be much smaller than that of the attached polymer chains and therefore model the particles with their grafted polymer "shell" as star polymers. The polymer chains attached to the particles are of the same species as one of the blocks of the symmetric diblock copolymer. Of primary interest is how to tune the shell of the particle by changing both the length and number of tethered polymers in order to achieve higher loading of nanoparticles within an ordered structure without macrophase separation occurring. We find that the phase behavior of the system is very sensitive to the size of the particle including its tethered shell. The region of microphase separation is increased upon decreasing the star polymer size, which may be achieved by shortening and/or removing tethered polymer chains. To explore the possible structures in these systems we employ SCFT simulations that provide insight into the arrangement of the different species in these complex composites.     

Comparing the morphology and phase diagram of H-shaped ABC block copolymers and linear ABC block copolymers

By using a combinatorial screening method based on the self-consistent field theory (SCFT) for polymers, we have investigated the morphology of H-shaped ABC block copolymers (A2BC2) and compared them with those of the linear ABC block copolymers. By changing the ratios of the volume fractions of two A arms and two C arms, one can obtain block copolymers with different architectures ranging from linear block copolymer to H-shaped block copolymer. By systematically varying the volume fractions of block A, B, and C, the triangle phase diagrams of the H-shaped ABC block copolymer with equal interactions among the three species are constructed. In this study, we find four different morphologies (lamellar phase (LAM), hexagonal lattice phase (HEX), core-shell hexagonal lattice phase (CSH), and two interpenetrating tetragonal lattice (TET2)). Furthermore, the order-order transitions driven by architectural change are discussed.     

Aggregate morphologies of amphiphilic ABC triblock copolymer in dilute solution using self-consistent field theory

The complex microstructures of amphiphilic ABC linear triblock copolymers in which one of the end blocks is relatively short and hydrophilic, and the other two blocks B and C are hydrophobic in a dilute solution, have been investigated by the real-space implementation of self-consistent field theory (SCFT) in two dimensions (2D). In contrast to diblock copolymers in solution, the aggregation of triblock copolymers are more complicated due to the presence of the second hydrophobic blocks and, hence, big ranges of parameter space controlling the morphology. By tailoring the hydrophobic degree and its difference between the blocks B and C, the various shapes of vesicles, circlelike and linelike micelles possibly corresponding to spherelike, and rodlike micelles in 3D, and especially, peanutlike micelles not found in diblock copolymers are observed. The transition from vesicles to circlelike micelles occurs with increasing the hydrophobicity of the blocks B and C, while the transition from circlelike micelles to linelike micelles or from the mixture of micelles and vesicles to the long linelike micelles takes place when the repulsive interaction of the end hydrophobic block C is stronger than that of the middle hydrophobic block B. Furthermore, it is favorable for dispersion of the block copolymer in the solvent into aggregates when the repulsion of the solvent to the end hydrophobic block is larger than that of the solvent to the middle hydrophobic block. Especially when the bulk block copolymers are in a weak segregation regime, the competition between the microphase separation and macrophase separation exists and the large compound micelle-like aggregates are found due to the macrophase separation with increasing the hydrophobic degree of blocks B and C, which is absent in diblock copolymer solution. The simulation results successfully reproduce the existing experimental ones.     

Liquid crystalline side-group block copolymers with triblock structure: Investigations on the influence of the block arrangement on the morphology and the LC-phase behavior

Liquid crystalline triblock copolymers with LC inner block and amorphous outer blocks have been synthesized by “living” anionic polymerization and investigated using DSC, TEM, and small-angle x-ray diffraction. All samples of poly[styrene-block-2-(3-cholesteryloxycarbonyloxy) ethyl methacrylate-block-styrene] (PS-b-PChEMA-b-PS) show liquid crystalline behavior and phase separation between the blocks. Compared to triblock copolymers with PS inner block (PChEMA-b-PS-b-PChEMA) and diblock copolymers (PS-b-PChEMA) the LC block copolymers with PS outer blocks have the same properties. The LC behavior and the morphology do not depend on the block arrangement; they are only influenced by the volume fractions of the blocks. Those samples in which the liquid crystalline subphase is not continuous (spheres) only a nematic phase was found, whereas in all samples with a continuous liquid crystalline subphase, the smectic A phase of the homopolymer was observed. © 1996 John Wiley & Sons, Inc.     

Self-assembly behavior of pH- and thermosensitive amphiphilic triblock copolymers in solution: experimental studies and self-consistent field theory simulations

We investigated, both experimentally and theoretically, the self-assembly behaviors of pH- and thermosensitive poly(L-glutamic acid)- b-poly(propylene oxide)-b-poly(L-glutamic acid) (PLGA-b-PPO-b-PLGA) triblock copolymers in aqueous solution by means of transmission electron microscopy (TEM), scanning electron microscopy (SEM), dynamic light scattering (DLS), circular dichroism (CD), and self-consistent field theory (SCFT) simulations. Vesicles were observed when the hydrophilic PLGA block length is shorter or the pH value of solution is lower. The vesicles were found to transform to spherical micelles when the PLGA block length increases or its conformation changes from helix to coil with increasing the pH value. In addition, increasing temperature gives rise to a decrease in the size of aggregates, which is related to the dehydration of the PPO segments at higher temperatures. The SCFT simulation results show that the vesicles transform to the spherical micelles with increasing the fraction or statistical length of A block in model ABA triblock copolymer, which corresponds to the increase in the PLGA length or its conformation change from helix to coil in experiments, respectively. The SCFT calculations also provide chain distribution information in the aggregates. On the basis of both experimental and SCFT results, the mechanism of the structure change of the PLGA- b-PPO- b-PLGA aggregates was proposed.     

高分子体系相分离动力学及图样生成和选择

高分子共混物的混合熵很小导致其多为热力学不相容体系而发生相分离,形成特定的时空图样。本文根据多年来我们自己的研究工作并结合实例,基于时间分辨的Ginzberg-Landau 方法研究高分子复杂体系相分离动力学及图样选择,重点介绍剪切外场下高分子共混物及嵌段高分子的相分离,耦合化学反应的相分离,在弯曲曲面特别是球面上的相分离,以及TDGL与密度泛函理论的有机结合即动态自洽场理论在具有不同链拓朴结构的嵌段高分子体系中研究相分离动力学。     

Synthesis and properties of self organising semiconducting and luminescent polymers and model compounds

Oligothiophene‐PEO‐block‐co‐polymers and related model compounds have been synthesised and characterised. In the polymers well‐defined oligothiophene blocks (with from two to six α,α‐linked thiophene sequences) were alternated with poly(ethylene oxide) blocks of narrow polydispersity. Model α,α‐linked sexithiophenes were prepared carrying chiral, achiral, mono and narrow polydispersity monomethyl PEO substituents at their terminal alpha positions. All the products were soluble in common organic solvents and organic/aqueous solvent mixtures. UV/vis and fluorescence studies in solution indicated that the oligothiophene segments were molecularly dissolved in good solvents like chloroform. Aggregation of the oligothiophenes occurred in dioxane/water mixtures, consistent with observed shifts of the UV absorption maxima towards the blue and quenching of the fluorescence. An oligothiophene length of three thiophenes (terthiophene) was necessary for aggregation to be observed. The materials formed well‐organised transferable monolayers at the air water interface.     

Unexpected consequences of block polydispersity on the self-assembly of ABA triblock copolymers

Controlled/"living" polymerizations and tandem polymerization methodologies offer enticing opportunities to enchain a wide variety of monomers into new, functional block copolymer materials with unusual physical properties. However, the use of these synthetic methods often introduces nontrivial molecular weight polydispersities, a type of chain length heterogeneity, into one or more of the copolymer blocks. While the self-assembly behavior of monodisperse AB diblock and ABA triblock copolymers is both experimentally and theoretically well understood, the effects of broadening the copolymer molecular weight distribution on block copolymer phase behavior are less well-explored. We report the melt-phase self-assembly behavior of SBS triblock copolymers (S = poly(styrene) and B = poly(1,4-butadiene)) comprised of a broad polydispersity B block (M(w)/M(n) = 1.73-2.00) flanked by relatively narrow dispersity S blocks (M(w)/M(n) = 1.09-1.36), in order to identify the effects of chain length heterogeneity on block copolymer self-assembly. Based on synchrotron small-angle X-ray scattering and transmission electron microscopy analyses of seventeen SBS triblock copolymers with poly(1,4-butadiene) volume fractions 0.27 ≤ f(B) ≤ 0.82, we demonstrate that polydisperse SBS triblock copolymers self-assemble into periodic structures with unexpectedly enhanced stabilities that greatly exceed those of equivalent monodisperse copolymers. The unprecedented stabilities of these polydisperse microphase separated melts are discussed in the context of a complete morphology diagram for this system, which demonstrates that narrow dispersity copolymers are not required for periodic nanoscale assembly.     

Surface-induced phase transition of asymmetric diblock copolymer in selective solvents

Surface-induced phase transition of asymmetric diblock copolymer in selective solvents is first theoretically investigated by using the real-space version of self-consistent field theory (SCFT). By varying the distance between two parallel hard surfaces (or the film thickness) W and the block copolymer concentration f(p), several morphologies are predicted and the phase diagram is constructed. Self-assembly morphologies of the diblock copolymer in dilute solution are found to change significantly with different film thickness. In confined systems, stable morphologies found in the bulk solution become unstable due to the loss of polymer conformation entropy. We find that in a very dilute block copolymer solution, phase separation can be induced through polymer depletion as the solution becomes more confined. Our findings provide an interesting starting point for a renewed effort in both experimental and theoretical investigations of confined block copolymer solutions.     

On the interaction of the morphological structure and the LC behaviour of LC side group block copolymers

The interaction between morphological structure and phase behaviour of a LC side group block copolymer has been investigated using DSC, TEM and small angle X-ray diffraction. All samples of Polystyrene-block-2-(3-cholesteryloxycarbonyloxy)ethyl methacrylate (PS-b-PChEMA) show a phase separation between the two blocks. It was found that in the case of those samples where the liquid crystalline sub-phase is not continuous (spheres), only a nematic phase is seen, whereas in all samples in which there is a continuous liquid crystalline sub-phase, the smectic A phase of the homopolymer is formed. On the other hand, the block copolymer seems to stabilize the LC phase; no dependency of the clearing temperatures on the molecular weight of the LC blocks has been observed.     

Features of the phase behavior of block copolymers related to their polydispersity

To calculate cloud points of a melt of block copolymers, at which its microphase separation occurs, for the first time in the theory of polymers, a spectral method is used in a model that takes into account the compressibility of the melt and the polydispersity of its macromolecules. A particular case of this calculation for a copolymer whose macromolecules consist of two blocks is described, and the polydispersity of each of them is defined through the exponential Flory distribution.     

Nonconventional morphologies in two-length scale block copolymer systems beyond the weak segregation theory

The order-disorder and order-order transitions (ODT and OOT) in the linear multiblock copolymers with two-length scale architecture A(fmN)(B(N2)A(N2))(n)B((1-f)mN) are studied under intermediate cooling below the ODT critical point where a nonconventional sequence of the OOTs was predicted previously [Smirnova et al., J. Chem. Phys. 124, 054907 (2006)] within the weak segregation theory (WST). To describe the ordered morphologies appearing in block copolymers (BCs) under cooling, we use the pseudospectral version of the self-consistent field theory (SCFT) with some modifications providing a good convergence speed and a high precision of the solution due to using the Ng iterations [J. Chem. Phys. 61, 2680 (1974)] and a reasonable choice of the predefined symmetries of the computation cell as well as initial guess for the iterations. The WST predicted sequence of the phase transitions is found to hold if the tails of the BCs under consideration are symmetric enough (mid R:0.5-fmid R:0.05, a large region of the face-centered cubic phase stability is found (up to our knowledge, first within the SCFT framework) inside of the body-centered cubic phase stability region. Occurrence of the two-dimensional and three-dimensional phases with the micelles formed, unlike the conventional diblock copolymers, by the longer (rather than shorter) tails, and its relationship to the BC architecture is first described in detail. The calculated spectra of the ordered phases show that nonmonotonous temperature dependence of the secondary peak scattering intensities accompanied by their vanishing and reappearance is rather a rule than exception.