Side chain effect on the self-assembly of coil-comb copolymer by self-consistent field theory in two dimensions

The phase behavior of coil-comb copolymers A–(B_m+1C_m) (side chain number m = 1–5) is investigated by real-space self-consistent field theory (SCFT). Depending on the copolymer composition and architecture, eight two-dimensional ordered phases are observed, including two-color lamellae (LAM₂), three-color lamellae (LAM₃), hexagonal cylinders (HEX), core–shell hexagonal phase (CSH), hexagon outside hexagonal phase (HEX₂), two interpenetrating tetragonal phase (TET₂), lamellae with beads inside (LAM + BD), and lamellae with core–shell beads (LAM₃ + CSB). When the volume fractions are comparable, i.e., f_A ≈ f_B ≈ f_C, LAM_3 phase is found to be stable for m = 1 while the hexagonal phases (core–shell hexagonal phase CSH or hexagon outside hexagonal phase HEX₂) are stable if m > 1. The phase region of the hexagonal phases HEX, CSH or HEX₂ enlarges with increasing m. For short coil length, such as f_A = 0.1, the phase diagram is complex, especially when m = 1. For longer coil length, the lamellae become the dominant phase. The phase transition from lamellar phase to hexagonal phase is observed with the increase of the side chain length when the side chain number m is large, which is in agreement with the experimental results. Our results give a good way to tailor the phase behavior of block copolymer and are very useful to further study the hierarchical structure of the coil-comb block copolymer.     

A numerical study of spherical polyelectrolyte brushes by the self-consistent field theory

The self-consistent field theory (SCFT) is employed to numerically study the scaling laws of brush height and the amount of counter-ions trapped inside a spherical polyelectrolyte (PE) brush immersed in a good solvent with no added salt ions. In particular, the curvature effect of the grafting substrate on the brush height and the amount of counter-ions trapped inside the PE brush is carefully examined. It is found that the brush height shows a non-trivial dependence on the radius of the grafting substrate. The numerical result reveals that the brush height scales linearly with respect to the grafting density and the average degree of ionization of PE chains in the planar surface limit, but not in the opposite limit. The numerical results show that, in a salt-free solution, about 96% of the counter-ions are trapped within the range of extension of grafted PE chains in the planar surface limit, irrespective of other system parameters. On the contrary, for the grafting substrate with high curvature, i.e., the radius of the grafting substrate is much smaller than the brush height, the amount of counter-ions trapped inside the PE brush approaches zero in the large system size limit. The underlining mechanisms governing the curvature effect of the grafting substrate on the brush height and the amount of counter-ions trapped inside PE brushes are elucidated.     

Microstructures of lamella-forming diblock copolymer melts under nanorod-array confinements

The microstructures of lamellae-forming diblock copolymer melts confined in nanorod arrays are investigated using the real-space self-consistent field theory. The nanorod array leads to the incomplete confinement at each direction so that the confinement-dimension is fractional between zero and two. This incomplete confinement can yield a rich variety of mixture microstructures by varying its fractional confinement-dimension, such as the mixture of concentric lamellae and parallel lamellae and the mixture of the concentric lamellae and cylinders, as well as a series of continuous network mixtures. By comparing with the available simulations and experiments, these novel microstructures can be understood based on the symmetry competition and structural frustration that originated from the incomplete confinement. Our theoretical predictions may be helpful to the design of nanomaterials.     

Cylindrical phase of diblock copolymers confined in thin films. A real-space self-consistent field theory study

We have used real-space self-consistent field theory to search possible morphology of an asymmetric AB diblock copolymer thin film confined between two homogeneous hard walls. The volume fraction of the A block is fixed to be f=0.3, as expected, a cylindrical phase is stable without confinement (in the bulk). Our simulation reveals that under confinement, in addition to parallel and perpendicular cylinders, other phases, such as flat lamellae, perforated lamellae, undulated cylinders and undulated lamellae, are also stable due to the block-substrate interactions. Three new structures, i.e. undulated lamellae, undulated cylinders and parallel cylinders with non-integer period, are observed to be stable with suitable film thickness and block-substrate interaction. By systematically varying the film thickness and the interaction parameters between the two blocks, phase diagrams are constructed for typical block-substrate interactions. We compare the phase diagrams for weak and strong substrate preference and discuss the effects of confinement and substrate preference on the stability of various structures.     

Complex microstructures of ABC triblock copolymer thin films directed by polymer brushes based on self-consistent field theory

The morphology and the phase diagram of ABC triblock copolymer thin film directed by polymer brushes are investigated by the self-consistent field theory in three dimensions. The polymer brushes coated on the substrate can be used as a good soft template to tailor the morphology of the block copolymer thin films compared with those on the hard substrates. The polymer brush is identical with the middle block B. By continuously changing the composition of the block copolymer, the phase diagrams are constructed for three cases with the fixed film thickness and the brush density: identical interaction parameters, frustrated and non-frustrated cases. Some ordered complex morphologies are observed: parallel lamellar phase with hexagonally packed pores at surfaces (LAM₃ ^ll -HFs), perpendicular lamellar phase with cylinders at the interface (LAM^⊥-CI), and perpendicular hexagonally packed cylinders phase with rings at the interface (C₂^⊥-RI). A desired direction (perpendicular or parallel to the coated surfaces) of lamellar phases or cylindrical phases can be obtained by varying the composition and the interactions between different blocks. The phase diagram of ABC triblock copolymer thin film wetted between the polymer brush-coated surfaces is very useful in designing the directed pattern of ABC triblock copolymer thin film.     

Phase behavior and microstructural length scales of a diblock copolymer in the presence of a selective solvent

We employ self-consistent mean-field (SCMF) theory in studying the phase behavior as well as the microstructural domain sizes for a diblock copolymer in the presence of a selective solvent. First we examine the effects of solvent addition on the formation of fcc and bcc packed spheres. As has been found in experiments, the so-called “normal” spheres, i.e., formed by the minority blocks, tend to pack into the bcc array, while the “inverted” spheres formed by the majority blocks favor the fcc packing. Upon increasing the solvent selectivity and/or solvent amount, the formed inverted spheres tend to pack from bcc to fcc. This thermotropic transition of bcc → fcc upon increasing the solvent selectivity is induced by the fact that the intermicellar interactions vary from long-range to short-range via a combination of the solvent exclusion from the cores and an increase in the aggregation number. In analyzing the effects of solvent addition on the microstructural sizes, the SCMF results have successfully captured the crossover behavior of characteristic domain spacing from decreasing with added solvent to increasing by increasing the solvent selectivity. Further, the variation of the characteristic domain spacing when the systems transform to a more curved structure changes from a discontinuous decreasing behavior to even a discontinuous increasing behavior upon increasing the solvent selectivity and/or the formation of inverted structures.     

Order to disorder transition of comb copolymer Am+1Bm: a self-consistent field study

The order to disorder transition of comb copolymers A_m+1B_m is investigated by the self-consistent field theory. Although there are only two components in a molecule, the side chain number m affects the phase diagram largely due to the fact that the architecture of a comb copolymer is not invariant under the interchange of A- with B-monomers. With the increase of the side chain number, the interaction (Flory-Huggins) parameter of the order-to-disorder transition (ODT) increases at the same composition and the lowest ODT occurs at the smaller volume fraction of the main chain f_A. The influences of the side chain density and the side chain length on the phase behavior were discussed in detail. The relation exists with the fixed main chain length. The comb copolymer with the large side chain number m and the long main chain sections (or short side chain) is more stable. The results are helpful to design nano- or bio-materials with complex architecture or tailor the phase behavior of comb copolymers.     

Self-assembly of an A-B diblock copolymer blended with a C homopolymer and a C-D diblock copolymer through hydrogen bonding interaction

In this study, we investigated the miscibility, phase behavior, and self-assembled nanostructures formed from the immiscible crystalline-amorphous diblock copolymer poly(?-caprolactone-b-4-vinyl pyridine) (PCL-b-P4VP, A-B) when blended with the homopolymer poly(vinyl phenol) (PVPh, C) and the diblock copolymer poly(vinyl phenol-b-styrene) (PVPh-b-PS, C-D). Long-range-ordered microphase separation was difficult to achieve in the PCL-b-P4VP/PVPh (A-B/C) blend system because PVPh interacted with both the P4VP and PCL blocks simultaneously through hydrogen bonding interactions. In contrast, we observed sharp, multiple orders of diffraction in the SAXS profiles of the PCL-b-P4VP/PVPh-b-PS (A-B/C-D) blend system, indicating that perfect microphase separation occurred because the incorporation of the PS block induced the PVPh block to hydrogen bond preferentially with the P4VP block. This simple A-B/C-D (PCL-b-P4VP/PVPh-b-PS) diblock copolymer mixture exhibited self-assembly behavior (a three-lamella phase) similar to that of a corresponding ABC triblock copolymer.     

Self-Assembly structures through competitive interactions of miscible crystalline-amorphous diblock copolymer/homopolymer blends

A series of miscible crystalline-amorphous diblock copolymers, (poly(?-caprolactone)-b-(vinyl phenol), PCL-b-PVPh) were prepared through sequential ring-opening and controlled living free radical (nitroxide-mediated) polymerizations and then blended with poly(vinyl pyrrolidone) (PVP) homopolymer. Specific interactions, miscibility, and self-assembly morphologies mediated by hydrogen bonding interactions of this new A-B/C type blend, were investigated in detail. Micro-phase separation of these miscible PCL-b-PVPh diblock copolymers occurs by blending with PVP through competitive hydrogen bonding interaction in this A-B/C blend. FTIR, XRD, and DSC analyses provide positive evidences that the carbonyl group of PVP is a significantly stronger hydrogen bond acceptor than PCL, thus the PCL block is excluded from the PVPh/PVP miscible phase to form self-assembly structure. ¹³C CP/MAS solid-state NMR spectra provide additional evidence confirming that micro-phase separation occurs in the blend system because of the presence of more than two T_1ρ(H) values for this A-B/C blend system. According to the result of the FTIR and SAXS results, the smaller molecular weight system contains a greater fraction of the hydrogen-bonded carbonyl group, cause indirectly the high degree of phase separation among these blends. In addition, the SAXS profiles possess a sharp primary peak and highly long range ordered reflections q/q^∗ ratios of 1:2:3 at lower PVP content, an indication of the lamellar structure in the blend which is consistent with TEM image. The phase behavior and morphology shifts from lamellar to cylinder structure with further increase in the PVP content.     

Study of morphology and phase diagram of the H-shaped (AC)B(CA) ternary block copolymers using self-consistent field theory

By using a combinatorial screening method based on the self-consistent field theory (SCFT) for polymer systems, the micro-phase morphologies of the H-shaped (AC)B(CA) ternary block copolymer system are studied in three-dimensional (3D) space. By systematically varying the volume fractions of the components A, B, and C, six triangle phase diagrams of this H-shaped (AC)B(CA) ternary block copolymer system with equal interaction energies among the three components are constructed from the weaker segregation regime to the strong segregation regime. In this study, thirteen 3D micro-phase morphologies for this H-shaped ternary block copolymer system are identified to be stable and seven 3D micro-phase morphologies are found to be metastable. It is found that in the weaker segregation regime (χ_ABN = χ_ACN = χ_BCN = 45), the minority component can be mixed with other two majority components to form the mixed phase regions, while in the intermediate segregation regime (χ_ABN = χ_ACN = χ_BCN = 60 and 75), the mixed phase regions phase-separate into three distinct phase regions. In the strong segregation regime (χ_ABN = χ_ACN = χ_BCN = 90, 100, and 125), the distinct blocks tend to separate with each other and the phase behavior of this H-shaped (AC)B(CA) ternary block copolymer is similar to that of the three-arm star-like ABC ternary block copolymer. Moreover, the order-disorder transitions and the order-order transitions by varying the interaction parameters are discussed. These results may help in the design of the microstructures of complex block copolymers.     

Force spectrum of a few chains grafted on an AFM tip: Comparison of the experiment to a self-consistent mean field theory simulation

A simulation model based on self-consistent mean field theory (SCMFT) has been developed to inspect the approaching process of the polymer chain grafted AFM tip to a substrate. The effects of various controlling parameters, such as grafting position, chain number, chain length, as well as solvent- and substrate-chain interactions, on the force curve were investigated. Real force spectroscopy of AFM tips modified by poly(ethylene glycol) (PEG) chains interacting with the fresh mica has been recorded, and several typical types of the force curves that correspond to the different states of the grafting chain were assorted. The simulations fit the experimental results well, providing a strong support to the model.     

Synthesis and characterization of perfluorocyclobutyl aryl ether-based amphiphilic diblock copolymer

Perfluorocyclobutyl aryl ether-based amphiphilic diblock copolymer containing hydrophilic poly(ethylene glycol) segment was synthesized by atom transfer radical polymerization (ATRP). Perfluorocyclobutyl-containing methacrylate-based monomer, 4-(4′-p-tolyloxyperfluorocyclobutoxy)benzyl methacrylate, was prepared firstly, which can be polymerized by ATRP in a controlled way to obtain well-defined homopolymers with narrow molecular weight distributions (M_w/M_n ≤ 1.30). The molecular weights increased linearly with the conversions of monomer and the apparent polymerization rate exhibited first-order relation with respect to the concentration of monomer. ATRP of 4-(4′-p-tolyloxyperfluorocyclobutoxy)benzyl methacrylate was initiated by PEG-based macroinitiators with different molecular weights to obtain amphiphilic diblock copolymers with narrow molecular weight distributions (M_w/M_n < 1.35) and the number of perfluorocyclobutyl linkage can be tuned by the feed ratio and the conversion of the fluorine-containing methacrylate monomer. The critical micelle concentrations of these amphiphilic diblock copolymers in water and brine were determined by fluorescence probe technique. The morphologies of the micelles were found to be spheres by TEM.     

Ion-dipole interactions in the dispersion of organoclay nanocomposites based on polystyrene-block-poly(2-vinylpyridine) copolymer

The dispersion characteristics of organoclay nanocomposites based on polystyrene-block-poly(2-vinylpyridine) (S2VP diblock) copolymer were investigated using transmission electron microscopy (TEM), X-ray diffraction (XRD), and solid-state nuclear magnetic resonance (NMR) spectroscopy. For the investigation, S2VP diblock copolymers having three different compositions were synthesized via sequential anionic polymerization. Each S2VP diblock copolymer was used to prepare nanocomposites by solution blending with natural clay (montmorillonite, MMT) or commercial organoclays (Cloisite 30B, Cloisite 10A, Cloisite 15A, and Cloisite 25A from Southern Clay Products). All four organoclays employed were treated with a surfactant having quaternary ammonium salt with N⁺ ion. It was found, via TEM and XRD, that the nanocomposites with MMT show very poor dispersion characteristics regardless of block copolymer composition. However, the block copolymer composition was found to have a profound influence on the dispersion characteristics of the nanocomposites with an organoclay. Specifically, the nanocomposites based on S2VP-5 having 5 wt% poly(2-vinylpyridine) (P2VP) block gave rise to a very high degree of dispersion, irrespective of the chemical structure of the surfactant residing at the surface of the organoclay employed, whereas the dispersion characteristics of the nanocomposites became progressively poorer as the amount of P2VP block in an S2VP diblock copolymer increased from 5 to 25 wt% and to 56 wt%. The observed dispersion characteristics were explained by hypothesizing the presence of ion-dipole interactions between the positively charged N⁺ ions in the surfactant residing at the surface of the organoclay nanoparticles and the dipoles in the P2VP block of S2VP diblock copolymers. The validity of this hypothesis was confirmed using solid-state NMR spectroscopy, by determining the dependence of the composition of S2VP diblock copolymer on the extent of ion-dipole interactions and thus on the dispersion characteristics of the nanocomposites prepared.     

Alignment and orientational proliferation of HEX cylinders in a polystyrene-block-polyisoprene-block-polystyrene copolymer in the presence of clay

We investigated the effect of an anisotropic silicate layer on the alignment and orientational proliferation of hexagonally packed cylinder microdomains of a block copolymer in the presence of a clay by using synchrotron small angle X-ray scattering (SAXS), rheology, and transmission electron microscopy (TEM). The block copolymer employed in this study was polystyrene-block-polyisoprene-block-polystyrene copolymer (SIS). The degree of intercalation of the clay in the presence of SIS was examined by wide angle X-ray diffraction (WAXD).Almost all of the HEX cylinders in neat SIS are aligned toward the flow direction after large amplitude oscillatory shearing is applied to the specimens. However, some tactoids in nanocomposites are not aligned, although most tactoids are also aligned to the flow direction. Due to HEX cylinders near tactoids, which are not aligned to the flow direction, the orientational factor of HEX cylinders in SIS/clay nanocomposites is smaller than that of neat SIS. However, once HEX cylinders in SIS/clay nanocomposites are degenerated after experiencing body-centered cubic microdomains, the decrease in the orientational factor from original aligned HEX is smaller compared with neat SIS.     

Effect of nanoparticle surface functionality on microdomain orientation in block copolymer thin films under electric field

The electric field induced microdomain orientations has been an interesting research topic. In this article, the effect of nanoparticle surface functionality on microdomain alignments in block copolymer/nanoparticle hybrid thin films was investigated with transmission electron microscopy experiments. The presence of gold nanoparticles influenced the microdomain orientation behaviors of block copolymer/nanoparticle thin films. The possibility for complete alignment normal to the substrate was illustrated by controlling electric field strength, concentration, and surface ligands of nanoparticles. This work provides basic and essential data to understand the properties and behaviors of emerging block copolymer/nanoparticle hybrid thin films.     

The nature of phase transitions of symmetric diblock copolymer melts under confinement

The effects of confinement, both the structure frustration and the surface field, on phase transitions of symmetric diblock copolymer melts are investigated within several theoretical methods on the mean-field level. Confinements are applied by restricting polymer chains in the finite spaces of slabs. The surface can be neutral or preferential depending on the strength of the surface field. Within the one-dimensional self-consistent mean-field theory, for the neutral surface case, an oscillative behavior is observed for the size dependence of the order-disorder transition (ODT) point (χN)_t due to the structure frustration. The spinodal (χN)_s for this corresponding confined system is also calculated using the Gaussian fluctuation theory and the Landau-Brazovskii theory, and (χN)_s coincides exactly with (χN)_t. On the other hand, the surface effect plays the role to decrease (χN)_t due to the surface-induced spatial oscillation for the preferential surface case. In all confined systems considered, the ODT for symmetric diblock copolymer melts is a continuous second-order phase transition in the present mean-field calculation.     

Exfoliation of organoclay nanocomposites based on polystyrene-block-polyisoprene-block-poly(2-vinylpyridine) copolymer: Solution blending versus melt blending

Exfoliated nanocomposites based on polystyrene-block-polyisoprene-block-poly(2-vinylpyridine) (SI2VP triblock) copolymer were prepared by solution blending and melt blending. Their dispersion characteristics were investigated using transmission electron microscopy, X-ray diffraction, and small-angle X-ray scattering (SAXS). For the study, SI2VP triblock copolymers with varying amounts of poly(2-vinylpyridine) (P2VP) block (3, 5, and 13 wt%) and different molecular weights were synthesized by sequential anionic polymerization. In the preparation of nanocomposites, four different commercial organoclays, treated with a surfactant having quaternary ammonium salt, were employed. It was found from SAXS that the microdomain structure of an SI2VP triblock copolymer having 13 wt% P2VP block (SI2VP-13) transformed from core-shell cylinders into lamellae when it was mixed with an organoclay. It was found further that the solution-blended nanocomposites based on a homogeneous SI2VP triblock copolymer having 5 wt% P2VP block (SI2VP-5) gave rise to an exfoliated morphology, irrespective of the differences in chemical structure of the surfactant residing at the surface of the organoclays, which is attributable to the presence of ion-dipole interactions between the positively charged N⁺ ion in the surfactant residing at the surface of the organoclay and the pyridine rings in the P2VP block of SI2VP-5 and SI2VP-13, respectively. Both solution- and melt-blended nanocomposites based on microphase-separated SI2VP-13 having an order-disorder transition temperature (T_ODT) of approximately 210 °C also gave rise to exfoliated morphology. However, melt-blended nanocomposite based on a high-molecular-weight SI2VP triblock copolymer having a very high T_ODT (estimated to be about 360 °C), which was much higher than the melt blending temperature employed (200 °C), gave rise to very poor dispersion of the aggregates of organoclay. It is concluded that the T_ODT of a block copolymer plays a significant role in determining the dispersion characteristics of organoclay nanocomposites prepared by melt blending.     

Cooperative surface-induced self-assembly of symmetric diblock copolymers confined films with embedded nanorods

The self-assembly of symmetric diblock copolymers confined films with embedded nanorods is investigated by the self-consistent field (SCF) theory. We obtain some phase diagrams as a function of film thickness H and nanorod diameter D. The increase in preferential nanorod diameter D can promote the formation of incomplete cylindrical and spherical structures near the film surfaces, and can also induce complete lamellar, cylindrical and spherical structures in the interior. The formation of these induced self-assembled structures is due to the competition between inner surface confinement (two parallel surfaces) and outer surface confinement (nanorods). This investigation can provide some insights into the self-assembly of diblock copolymers with complex confinements.     

Perpendicular lamellae induced at the interface of neutral self-assembled monolayers in thin diblock copolymer films

We obtained perpendicular lamellar orientations in thin films of symmetric polystyrene-block-poly(methyl methacrylate), PS-b-PMMA, on self-assembled monolayers (SAMs) of 3-(p-methoxyphenyl)propyltrichlorosilane (MPTS) prepared on silicon wafers. In contrast to completely parallel lamellae on silicon wafers having a native oxide layer, perpendicular lamellae at the MPTS interface with parallel lamellae at the air interface were directly observed by transmission electron microscopy (TEM) in cross-sectional view. The perpendicular lamellae at the MPTS interface were attributed to the non-preferential (neutral) MPTS-covered substrate to both PS and PMMA blocks. The neutrality of the SAMs of MPTS was confirmed by the similar interfacial tension values of the SAMs of MPTS with PS and PMMA, estimated by contact angle measurements.     

Effects of neutral solvent addition on the body-centered cubic spheres of block copolymers

We employ self-consistent mean-field (SCMF) theory in studying the body-centered cubic (bcc) spheres of block copolymers in the presence of a neutral solvent. First we examine the accuracy of the dilution approximation then analyze the dependence of the bcc structural sizes with copolymer volume fraction ?, the interaction parameter χ_AB, and degree of copolymerization N. Our results reveal that both distribution of each component and the micro-structural length scales are greatly influenced by each parameter ?, χ_AB, and N. As expected, with decreasing ?, more solvent distributes non-uniformally in the segregated domains, therefore deviation from the dilution approximation increases. This also suggests that when the effective segregation parameter ?χ_ABN is fixed, a larger deviation is expected as χ_ABN increases (i.e. ? decreases). Although when both χ_ABN and ? are fixed, decreasing N (i.e. increasing χ_AB) enlarges the deviation from the dilution approximation. Furthermore, this solvent non-uniformity behavior is so significant that it even affects the dependence of the domain spacing L^* and the matrix length Λ^* with respect to (χ_AB)_effN=?χ_ABN near the ODT. When the systems are in molten state and/or in the concentrated regime, both L^* and Λ^* exhibit a sharp increase behavior as ODT is approached, due to many of the minority blocks being pulled from the spherical domains and swelling the matrix. With increasing solvent amount and/or χ_ABN, we observe that the increase of the degree for the minority blocks pulled from the spheres into the matrix near the ODT is not as significant as that in the melt. As such, the sharp increase behavior in L^* as well as Λ^* near the ODT smoothens and even disappears.