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.     

Continuous polydispersity in a self-consistent field theory for diblock copolymers

An efficient algorithm is presented for numerically evaluating a self-consistent field theoretic (SCFT) model of an AB diblock copolymer that incorporates continuous polydispersity in one of the blocks. An interesting segregation effect is found in which chains of intermediate molecular weight are concentrated at domain interfaces. This model of continuous polydispersity is also implemented in the random phase approximation (RPA) to study the order-disorder transition and predicts that the stability of the disordered, homogeneous phase decreases as the polydispersity in one of the blocks increases. The RPA predictions are confirmed by SCFT calculations. Our approach and results are particularly relevant to block copolymers prepared by quasiliving synthesis techniques, where the polymerization of one block is much more controlled than the other block.     

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.     

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.     

Architectural effects on the stability limits of ABC block copolymers

The random phase approximation has been used to extend the Leibler theory for the stability limit of a homogeneous melt of A–B diblock copolymers to examine the onset of microphase and macrophase separation in a variety of ABC block copolymer systems. The stability limit is located by the divergence of the collective structure factor of the melt. We introduce and analyze three models for ABC block copolymers: linear triblocks, random comb copolymers where a fixed number of A and B teeth are placed randomly along a C backbone, and statistical comb copolymers, with A or B teeth spaced regularly, but with sequences constructed using a two parameter Markov process. We compute order-disorder stability boundaries for the segregation strength parameter _χABN at threshold as a function of _χACN, _χBCN, composition, and other model parameters, and compare the results for the three different architectural models. An interesting “reentrant order-disorder transition” is located in several model phase diagrams, and is associated with a peculiar situation in which more incompatibility causes less segregation. In the case of statistical combs, macrophase separation into two liquid phases can be favored over microphase separation. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 849–864, 1997     

Scattering properties,stability analysis,and phase separation of polyelectrolyte mixtures

The conditions of stability for weakly charged polyelectrolyte mixtures are analyzed from a scattering theory developed previously. In the thermodynamic limit of zero wave vector q = 0, it is found that electrostatic interaction induces a compatibility enhancement which is discussed for various cases of charge distributions. The condition of microphase separation transition at the wave vector for which the scattering is a maximum is also discussed. © 1993 John Wiley & Sons, Inc.     

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。     

Microphase separation in oxyethylene/oxybutylene copolymers with diblock and triblock architectures

EBE and BEB triblock copolymers were prepared and characterized. Microphase separation in the melt state was studied, and the results combined with those for EB and BEB copolymers reported previously. The microphase separation temperature (MST) was determined from the temperature dependence of SAXS. There was a large difference in MST between the diblock and triblock copolymers as expected from theory. The Flory‐Huggins parameter (χ) was independent of block architecture for all three series provided that the E block lengths in the EBE copolymers exceeded 65.     

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.     

Controlling electrostatic co-assembly using ion-containing copolymers: from surfactants to nanoparticles

In this review, we address the issue of the electrostatic complexation between charged-neutral diblock copolymers and oppositely charged nanocolloids. We show that nanocolloids such as surfactant micelles and iron oxide magnetic nanoparticles share similar properties when mixed with charged-neutral diblocks. Above a critical charge ratio, core-shell hierarchical structures form spontaneously under direct mixing conditions. The core-shell structures are identified by a combination of small-angle scattering techniques and transmission electron microscopy. The formation of multi-level objects is driven by the electrostatic attraction between opposite charges and by the release of the condensed counterions. Alternative mixing processes inspired from molecular biology are also described. The protocols applied here consist in screening the electrostatic interactions of the mixed dispersions, and then removing the salt progressively as an example by dialysis. With these techniques, the oppositely charged species are intimately mixed before they can interact, and their association is monitored by the desalting kinetics. As a result, sphere- and wire-like aggregates with remarkable superparamagnetic and stability properties are obtained. These findings are discussed in the light of a new paradigm which deals with the possibility to use inorganic nanoparticles as building blocks for the design and fabrication of supracolloidal assemblies with enhanced functionalities.     

Effect of molecular architecture on phase behavior of graft copolymers

Influence of molecular architecture on phase behavior of graft copolymer melts was studied by using a reciprocal-space self-consistent filed theory (SCFT). The phase diagrams were examined as functions of the architectural parameters describing the graft copolymers (i.e., the number of grafts and the position of first junction). In comparison with the well-known phase diagram of diblock copolymers, the phase diagrams of the graft copolymers are asymmetric. When the number of grafts or the position of first junction varies, the boundaries of order-order transitions have shifts due to the variation in the chain stretching energy. The change in molecular architecture also significantly alters the domain spacing of ordered structures but has weak impact on the density distributions of graft copolymers. For comparison of the theoretical predictions with the existing experimental results, the phase diagrams of graft copolymers were also calculated at strong segregation. The SCFT calculations can accurately capture the characteristics of the phase behavior of graft copolymer melts.     

Microdomain morphology of cylinder-forming diblock copolymers under spherical shell confinement

The topic of self-assembly of cylinder-forming diblock copolymers(DBCPs) under spherical shell confinement in different surface fields is explored using real-space self-consistent field theory calculations(SCFT).Using this approach we observed various microstructures of cylinder-forming DBCPs at different confinement dimensions and surface fields.From detailed searching for the microdomain morphologies,an obvious conclusion is that the interactions between the confinement surface and the polymers have a great effect on the self-assembly.Most of the microstructures are unique and not reported in bulk or under planar and cylindrical confinements.     

Microphase separation in melts of double comb copolymers

Within the random-phase approximation, the conditions providing instability of a spatially homogeneous state of melts of double comb copolymers relative to microphase separation have been studied. As compared with the case of diblock copolymer melt connectivity between branch points of linear diblock copolymers and a backbone (densely grafted comb copolymer) is expected to assist the transition from the spatially homogeneous state to the microphase separated state; in other words, this factor decreases the incompatibility parameter at the transition point. Two characteristic types of spinodal behavior as a function of the number of repeating units have been found: one type is observed when the fragment of backbone between neighboring branch points is long; another type of behavior takes place when this distance is small. In one of the cases under study, the period of microstructure abruptly changes with variation of the interaction parameters of the system.     

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…     

Effect of chain stiffness on the morphology of diblock copolymer melts

The authors have studied the microphase separation of symmetric diblock copolymers with variable block stiffness and different block chain lengths using coarse-grained molecular dynamics simulations. The simulation results show that for symmetric diblock copolymers, a combination of chain length and relative stiffness between the blocks may play the major role in determining the equilibrium morphology of the system. When the variation in stiffness between blocks is small, the equilibrium morphology of the diblock system is found to be lamellar; this is also the case for systems with small chain lengths, regardless of the difference in block stiffness. However, in systems with longer chains with modest variation in stiffness between the blocks, an ordered cylindrical phase is formed in which the stiffer blocks form cylinders completely surrounded by the flexible components. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2556–2565, 2009     

Tuning block copolymer phase behavior with a selectively associating homopolymer additive

We use polymer random phase approximation (RPA) theory to calculate the microphase separation transition (MST) spinodal for an AB + C diblock copolymer–homopolymer blend where the C homopolymers are strongly attracted to the A segment of the copolymers. Our calculations indicate that one can shift the MST spinodal value of the A ? B segmental interaction parameter (χ_ABN)_S to significantly lower values [i.e., (χ_ABN)_S < 10.5] upon the addition of a selectively attractive C homopolymer. For a sufficiently attractive C homopolymer, (χ_ABN)_S can be pushed to negative values, indicating microphase separation in what would appear to be a completely miscible diblock copolymer. Furthermore, we show that microphase separation can occur in diblock copolymer–homopolymer blends where the segmental interactions between all polymer constituents are attractive. By tuning the value of (χ_ABN)_S with a homopolymer additive, one is therefore able to tune the effective copolymer segregation strength and thus dramatically affect the blend phase behavior. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2083–2090, 2009     

Geometrical constraints on microstructural development in block copolymer ultrathin films

The fact that microstructures form in microphase-separated block copolymers, endowing the materials with unique thermo-mechanical properties, is well-established. However, no thermodynamic theories directly address the problem of microstructural development in ultrathin films, which might be useful as adhesives or resists. To predict the microstructural dimensions in such films, a model based on unit-cell geometries and material/volume balances is developed. Predictions of the ratio of the characteristic length of the domain core to domain repeat distance are obtained for poly (styrene-butadiene) diblock (SB) copolymers at 298 K. The finite interphase region is included in the volume balances with the parameterf, the volume fraction of interphase material, obtained from a modified version of the Leary-Henderson-Williams thermodynamic theory and shown here not to be a strong function of composition. An approach, implementingf, for accurately estimating the critical molecular weight of microphase separation in the strong-segregation limit (M _c ), as a function of bulk composition for monodisperse SB copolymers at 298 K, is also presented.     

New polymer systems exhibiting microphase separation transition with the formation of nano-microstructures

The concept of microphase separation was up to now widely applied mainly to the conformational transitions in block-copolymer solutions and melts. However, recently it became obvious that this concept has a much more general meaning. It was shown that microphase separation transition can be observed in random copolymers, interpenetrating polymer networks, polyelectrolyte mixtures, poor solvent polyelectrolyte solutions, ionomer solutions and melts, polymer blends and solutions with nonlocal entropy of mixing. In all these examples the emerging microdomain structures correspond to the nanometer scale, therefore the study of these effects can lead to the new ways of obtaining polymer materials with controlled nano-microstructure. In this presentation the review of our recent findings on microphase separation in some of the above-mentioned systems will be presented. 1. The problem of microphase separation in the systems containing weakly charged polyelectrolytes (polyelectrolyte mixtures and poor solvent polyelectrolyte solutions) will be considered. From the methodic point of view, it will be shown that this problem can be solved by direct minimization of the free energy, without the use of “weak segregation” or “strong segregation” assumptions which are common in the theory of block-copolymers. The final phase diagrams exhibit wide macroscopic phase separation regions, which is their main difference from the corresponding phase diagrams for block-copolymer systems. The formation of microdomains is thus coupled with macroscopic phase separation: in most of the cases microdomain structure is formed in one of the coexisting phases after macroscopic phase separation takes place [1] - [2]. 2. The formation of the multiplet structure in ionomer melts and solutions can be also considered as the microphase separation in the random copolymer system with the formation of the “micelles” (or clusters) of ionic links. The parallels with micelle formation in block-copolymer systems can be established if one considers a new “superstrong segregation regime” for block-copolymer microstructures. This regime can be indeed observed for diblock copolymers with one ionomeric and one neutral block [3]. 3. The microphase separation transition in ordinary polymer blends and solutions is also possible. The conditions for this effect are: (i) significant entropic contribution to polymer/polymer or polymer/solvent miscibility, (ii) the nonlocal character of this contribution with a high value of the nonlocality radius. It is argued that one can expect that the entropy nonlocality radius increases in the vicinity of the glass transition for the blend or polymer solutions (in the latter case solvent molecules act like “poor solvent plasticisers”). Computer simulation data supporting the theoretical prediction of microphase separation transition in these systems will be presented [4] - [5].     

聚四氢呋喃-聚甲基丙烯酸甲酯两嵌段共聚物的结晶行为

报导了系列聚四氢呋喃-聚甲基丙烯酸甲酯结晶-非晶(硬段型)两嵌段共聚物的结晶行为，结果表明，其微相分离和结晶规律与文献上唯一进行过系统研究的同类嵌段共聚物(PEO－b－PS)都有较大的差别；结晶段结晶能力的大小是制约这类体系微相分离和结晶规律的一个重要因素．     

Dynamic heterogeneity in diblock copolymer systems

Dynamic light scattering from diblock copolymers in melt and solution in a non-selective solvent reveals different mechanisms for relaxing the composition and orientation fluctuations near the order to disorder transition (ODT). For the former, internal relaxation and copolymer chain diffusion are the main relaxation processes whereas the latter relate to collective orientation of the copolymer chains near the ODT and induced form anisotropy of coherently ordered microstructures below ODT.