Self-assembled pattern formation of block copolymers on the surface of the sphere using self-consistent field theory

The spherical surface is spatially discretized with triangular lattices to numerically calculate the Laplace-Beltrami operator contained in the self-consistent field theory (SCFT) equations using a finite volume method. Based on this method we have developed a spherical alternating-direction implicit (ADI) scheme for the first time to help extend real-space implementation of SCFT in 2D flat space to the surface of the sphere. By using this method, we simulate the equilibrium microphase separation morphology of block copolymers including AB diblocks, ABC linear triblocks and ABC star triblock copolymers occurred on the spherical surface. In general, two classes of microphase separation morphologies such as striped patterns for compositionally symmetric block copolymers and spotted patterns for asymmetric compositions have been found. In contrast to microphase separation morphology in 2D flat space, the geometrical characteristics of a sphere has a large influence on the self-assembled morphology. For striped patterns, several of spiral-form and ring-form patterns are found by changing the ratio of the radius of a sphere to the averaging width of the stripes. The specific pattern such as the striped and spotted pattern with intrinsic dislocations or defects stems from formed periodic patterns due to microphase separation of block copolymers arranged on the curved surface.     

Wetting-driven structure ordering of a copolymer/homopolymer/nanoparticle mixture in the presence of a modulated potential

We investigate pattern formation on a solid substrate of a diblock copolymer-homopolymer mixture containing doping wettable nanoparticles with a preferential attraction for one component of the copolymers, using a three-order-parameter model. The presence of doping nanoparticles under the surface-interaction modulation breaks the isotropy in the process of microphase-separation and macrophase-separation. This leads to the formation of orientational microphase and macrophase structures due to the interplay between the phase separation and wetting particle ordering under a modulated potential at the late stage. Simulations suggest that the microphase morphology and macrophase morphology can be changed through adjustment of the wetting strength, the amplitude as well as the period of the modulated potential. It provides some important insights for changing microphase and macrophase structures in polymer blends by wetting-driven spinodal decomposition.     

非对称半结晶两嵌段共聚物的微相分离与结晶行为的模拟退火研究

利用模拟退火方法研究非对称半结晶两嵌段共聚物熔体分别在弱分离和强分离条件下的结晶过程.考察微相分离作用和结晶作用的相对强度对柱状组成的两嵌段共聚物平衡形态的影响.研究结果表明,当嵌段间的相互排斥作用较弱时,结晶便破坏了柱状畴;当此相互作用足够强时,结晶过程可以有效地被限制在熔体微相分离所形成的柱状畴内.另外,介于上述两种情形之间还存在一个模板区域,此时熔体形成的柱状畴大部分被保留下来,但在局部会变形或连通.这些结果和文献报道的实验结果一致.当嵌段间的相互排斥作用非常强时,结晶被抑制,微相分离主导最终形态,观察到了非晶态结构.     

Self-assembly of rod-coil block copolymers from weakly to moderately segregated regimes

We report on the self-assembly behaviour of two homologue series of rod-coil block copolymers in which, the rod, a π -conjugated polymer, is maintained fixed in size and chemical structure, while the coil is allowed to vary both in molecular weight and chemical nature. This allows maintaining constant the liquid crystalline interactions, expressed by Maier-Saupe interactions, ω , while varying the tendency towards microphase separation, expressed by the product between the Flory-Huggins parameter and the total polymerization degree, χN . Therefore, the systems presented here allow testing directly some of the theoretical predictions for the self-assembly of rod-coil block copolymers in a weakly segregated regime. The two rod-coil block copolymer systems investigated were poly(DEH-p-phenylenevinylene-b-styrene), whose self-assembly takes place in the very weakly segregated regime, and poly(DEH-p-phenylenevinylene-b-4vinylpyridine), for which the self-assembly behaviour occurs under increased tendency towards microphase separation, hereby referred to as moderately segregated regime. Experimental results for both systems are compared with predictions based on Landau expansion theories.     

Effect of Polymer-Substrate Interactions on the Surface Morphology of Polymer Blend Thin Films

Surface structures and compositions of poly(Styrene-block-Ethylene/Butylene-block-Styrene) (SEBS)/Poly(Methyl Methacrylate) (PMMA) blend films have been studied by Atomic Force Microscopy (AFM) and X-ray Photoelectron Spectroscopy (XPS). Substrates with different hydrophobicity and SEBS with and without Maleic Anhydride (MA) grafting were used to study the effect of polymer-substrate interactions. It is indicated that the surface energy of the substrate (substrate/air) plays a crucial role on the surface composition of the polymer component. For a fixed surface, the adsorption of polymer on the substrate is also important. The hydrophilic sites of SEBS-g-MA can prevent the dewetting of the SEBS-g-MA from the substrate. The dewetting of PMMA from the SEBS-g-MA will make the PMMA protrusions more pronounced, and the SEBS-g-MA phase domains are enlarged after annealing treatment. An adsorption scheme is suggested to explain the phase inversion and height difference observed in the various polymers used. In addition, SEBS triblock copolymers form wormlike and meshlike microphase separation morphologies on the hydrophilic and hydrophobic substrates, respectively.     

Effect of Polymer-Substrate Interactions on the Surface Morphology of Polymer Blend Thin Films: Comparison between Simulation and Experiment

Microphase and macrophase separation phenomena can simultaneously appear in ABA/C copolymer blend systems due to the immiscibility among monomers A, B, and C. In this work, the surface morphologies and compositions of ABA/C blend thin films confined between two walls, which were used to mimic SEBS/PMMA films, have been simulated by a lattice Monte Carlo (MC) method. The effect of the polymer-wall interaction on the surface morphologies and compositions of thin films was investigated as a function of blend composition and film thickness. It is shown that the simulated surface morphologies of thin films resulting from the macrophase separation between copolymer ABA and homopolymer C and the microphase separation between block A and block B in ABA copolymer are similar to the experimental surface morphology of SEBS/PMMA polymer blend films observed by atomic force microscope (AFM). The effect of substrate on the surface morphologies by MC simulation is qualitatively consistent with the experimental results. The composition profiles of thin films are given to characterize the micro- and macrophase separation in thin films. It is indicated that the surface energy of the substrate (substrate/air) plays a crucial role on the surface composition. For a fixed surface, the adsorptions of polymer on the substrate and film thickness are also important.     

Investigation of phase separation in multiblock copolymers consisting of polysulfone and a liquid crystalline polymer

Multiblock copolymers (MBCPs) consisting of polysulfone (PSU) segments and segments of the liquid crystalline poly(ethyleneterephthalate-co-oxybenzoate) (PET/HBA) form rather complex morphologies. Scanning electron microscopy (SEM), small-angle X-ray scattering (SAXS), and atomic force microscopy (AFM) investigations of two block copolymers with significantly different block molecular weights proved the existence of both macro-and microphase separation. These morphologies, existing on different length scales, were found to be superimposed in the samples. A suitable fractionation procedure was used to suppress macrophase separation. Then, it was found that microphase separation is controlled by the segment molecular weights.     

Critical microphase properties of crosslinked polymer blends with quenched random impurities

We extend published works dealing with microphase separation in crosslinked polymer blends to the case where these are surrounded by random impurities. To study their influence on critical microphase properties, from a static and kinetics point of view, we first assume that the (real) disorder caused by impurities is quenched. Second, the replica theory is used to study such critical properties, upon the impurities concentration and their interaction strength. More precisely, we compute the spinodal temperature and structure factor. We find that the spinodal temperature is shifted towards its lower and higher values, for attractive and repulsive impurities, respectively. The obtained expression for the static structure factor suggests that, contrarily to repulsive impurities, the crosslinked mixture scatters better in the presence of attractive ones. Thereafter, the study is extended to kinetics of microphase separation, when the mixture is impregnated by small random impurities. Kinetics is investigated through the growth rate, and in particular, we demonstrate that the latter is increased by the presence of repulsive impurities. This is natural, since these play a stabilizer role. Finally, the discussion is extended to crosslinked polymer blends immersed in a good solvent, which induces drastic changes of the critical microphase properties.     

Monomolecular film and absorption behavior of polymers having carboxyl groups

π-A isotherms of monolayers of various copolymers containing carboxyl groups derived from acrylic acid (AA) were measured. The conformation of polymer adsorbed on the water surface and interaction forces between polymer and water surface (considered to be a model for the surface of inorganic powders) owing to AA groups is discussed based on the π-A isotherms.

Polyacrylic esters having a small amount of AA groups formed the expanded type of monolayer. AA groups cause an increase in the interaction force between the polymer and water surface. Polymethyl methacrylate having a small amount of AA groups formed condensed-type monolayers, while with a large amount of AA groups it showed two types of monolayer collapse. Though polystyrene could not spread as a mono-layer, poly (styrene-acrylic acid) [p(St-AA)] copolymer formed a monolayer when the AA content was over 4 mol %. The adsorbance of P(St-AA) on water, calculated from π-A isotherm, is the same as that obtained on α-Fe₂O₃ independently. This means the conformation of the polymer on the solid surface and the interaction force can be discussed by using the π-A isotherm.     

Freezing and microphase separation in random copolymers

Summary A two-letter random copolymer with attraction between similar monomers and repulsion between different ones is investigated using the replica method. This type of interactions favors microphase separation (MPS) in a compact state of a polymer or in a melt. Frustrations between interactions and polymeric bonds may lead to freezing transition in a phase where only a few conformations dominate and replica symmetry is broken. Our analysis reveals that stiff polymers have a frozen phase and do not undergo transition to a phase with microdomain structure. In flexible polymers the microphase transition may occur before freezing. A complete phase diagram showing the interplay between the two phase transitions is constructed for the two-letter random copolymer. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Theory of microphase separation in charged crosslinked polymer blends with arbitrary charge distribution

In this paper, we are interested in the phase behavior and scattering properties of charged crosslinked polymer blends in solution. The system undergoes a microphase separation, below some critical temperature. To study such a transition, use is made of the standard de Gennes theory based on an analogy with a dielectric medium. This analogy is extended to include the effects of the initial composition fluctuations in order to improve its agreement with experimental data in the small wave vector range. The excluded-volume interactions are explicitly introduced through the blob model. The charge effects on the phase behavior are examined, for any charge distribution of polyions and for any salt concentration. This completes a previous study which was concerned with the situation where only one species is charged. The early kinetics of microphase separation is discussed, and the charges contribution to the growth rate is also evaluated.     

Adsorption of hydrophobic polyelectrolytes onto oppositely charged surfaces

We present a scaling theory for the adsorption of a weakly charged polyelectrolyte chain in a poor solvent onto an oppositely charged surface. Depending on the fraction of charged monomers and on the solvent quality for uncharged monomers, the globule in the bulk of the solution has either a spherical conformation or a necklace structure. At sufficiently high surface charge density, a chain in the globular conformation adsorbs in a flat pancake conformation due to the Coulombic attraction to the oppositely charged surface. Different adsorption regimes are predicted depending on two screening lengths (the Debye screening length monitored by the salt concentration and the Gouy-Chapman length monitored by the surface charge density), on the degree of ionization of the polymer and on the solvent strength. At low bulk ionic strength, an increase in the surface charge density may induce a transition from an adsorbed necklace structure to a uniform pancake due to the enhanced screening of the intra-chain Coulombic repulsion by the counterions localized near the surface. Received 12 April 2001     

Diagrammatic analysis of correlations in polymer fluids: Cluster diagrams via Edwards’ field theory

Edwards’ functional integral approach to the statistical mechanics of polymer liquids is amenable to a diagrammatic analysis in which free energies and correlation functions are expanded as infinite sums of Feynman diagrams. This analysis is shown to lead naturally to a perturbative cluster expansion that is closely related to the Mayer cluster expansion developed for molecular liquids by Chandler and co-workers. Expansion of the functional integral representation of the grand-canonical partition function yields a perturbation theory in which all quantities of interest are expressed as functionals of a monomer-monomer pair potential, as functionals of intramolecular correlation functions of non-interacting molecules, and as functions of molecular activities. In different variants of the theory, the pair potential may be either a bare or a screened potential. A series of topological reductions yields a renormalized diagrammatic expansion in which collective correlation functions are instead expressed diagrammatically as functionals of the true single-molecule correlation functions in the interacting fluid, and as functions of molecular number density. Similar renormalized expansions are also obtained for a collective Ornstein-Zernicke direct correlation function, and for intramolecular correlation functions. A concise discussion is given of the corresponding Mayer cluster expansion, and of the relationship between the Mayer and perturbative cluster expansions for liquids of flexible molecules. The application of the perturbative cluster expansion to coarse-grained models of dense multi-component polymer liquids is discussed, and a justification is given for the use of a loop expansion. As an example, the formalism is used to derive a new expression for the wave-number dependent direct correlation function and recover known expressions for the intramolecular two-point correlation function to first-order in a renormalized loop expansion for coarse-grained models of binary homopolymer blends and diblock copolymer melts.     

Thermodynamic properties of inhomogeneous fluids

A general method, the method of variation under extension, is presented for expressing the thermodynamic properties of an inhomogeneous fluid as functionals of the local number density, when given a density functional for the total thermodynamic grand potential of the fluid. The method is demonstrated in detail for the van der Waals square-gradient density functional and for the nonlocal density functional which arises in the theory of fluids with long-ranged pair potentials or in the mean-field theory of penetrable-sphere models. As specific examples, we consider the planar and spherical interface between two fluid phases, the line of contact of three fluid phases, the contact line between two surface phases and the planar interface between a solid and fluid.     

End-tethered charged chains at surfaces

We present here a short review covering most of the experimental results on tethering charged chains by an end to a surface. A first class of experiments deals with solid surfaces where charged chains are either chemically grafted or adsorbed through a purposely chosen moiety. Structural studies have been carried out by scattering methods, spectroscopic techniques or microscopy. Forces between the polyelectrolyte layers covering the surfaces have also been obtained by using for instance, the surface force apparatus (SFA). A second class of experiments concerns polyelectrolytes, which are end-tethered to flexible surfaces like air–liquid or liquid–liquid interfaces. These experiments are fewer in number and mainly rely on the adsorption or spreading of charged diblock copolymers at the fluid interfaces.     

Density functional theory of vapor to liquid heterogeneous nucleation: Lennard–Jones fluid on solid substrate

Density functional theory has been applied to investigate the vapor to liquid heterogeneous nucleation on a flat solid surface, by invoking a model free energy density functional along with an exponential density model. The effects of supersaturation of the vapor and the strength of the solid-fluid interaction on the nucleation barrier have been investigated for Lennard–Jones fluid with 12–6 fluid–fluid and 9–3 solid–fluid interaction model. The spinodal decomposition of vapor has been observed at higher supersaturation or at higher strength of the solid–fluid interaction. The shape, density profile and the free energy of formation of droplets of any arbitrary size have been obtained in this work.     

Fabrication of Nanostructured Composite Microspheres Based on the Self‐Assembly of Polymers and Functional Nanomaterials

This Review examines recent developments in the morphological control of polymer microspheres fabricated via the phase separation of polymers as well as the alignment of functional nanoparticles inside microspheres prepared by so‐called bottom‐up synthesis techniques. Several methods for adjusting the internal and surface morphologies of polymer microspheres based on the phase separation of polymer blends and block copolymers are discussed, and the effects of microsphere size on phase separated structures and theoretical simulations of morphologies are also reviewed. The alignment of functional nanoparticles in phase separated polymer microspheres and applications of nanostructured and hybrid polymer microspheres are summarized.     

Demixing of amphiphile–polymer mixtures investigated using density functional theory

We construct a functional for amphiphile–polymer mixtures and investigate the demixing transition by using a proposed version of density functional theory. It is found that increase of the amphiphilic size ratio and polymer length can effectively promote phase separation of the systems. Phase diagrams are plotted to clarify these influences. The results provide an effective way of controlling the stability of the fluid–fluid phase equilibrium of the mixtures.     

Microphase separation in a cross-linked epoxy phenol polymer

The microphase separation on the surface of samples of a cross-liked epoxy phenol (EP) polymer produced by the curing of a composition containing an epoxy diane oligomer (EO) and a phenol formaldehyde oligomer (PO) has been investigated using electron microscopy with decoration by silver chloride. It has been shown that, in the cross-liked EP polymer, there is a quasi-lattice of mixed-type AgCl nanoparticles, which consists of two sublattices. The formation of simple lattices of particles is caused by the microphase separation according to the type of nucleation and growth of fractal clusters of the cross-liked EO; the spinodal decomposition in the binary system; and the formation of interpenetrating polymer networks represented by the superposition of two lattices of particles or two infinite phase clusters (cross-liked EO and PO, respectively).