New fast SCFT algorithm applied to binary diblock copolymer/homopolymer blends

We present an efficient strategy for mapping out the classical phase behavior of block copolymer systems using self-consistent field theory (SCFT). With our new algorithm, the complete solution of a classical block copolymer phase can be evaluated typically in a fraction of a second on a single-processor computer, even for highly segregated melts. This is accomplished by implementing the standard unit-cell approximation (UCA) for the cylindrical and spherical phases, and solving the resulting equations using a Bessel function expansion. Here the method is used to investigate blends of AB diblock copolymer and A homopolymer, concentrating on the situation where the two molecules are of similar size.

Multiple hydrogen bonds induce formation of nanoparticles with internal microemulsion structure by an amphiphilic copolymer

A particulate microemulsion is generated in a simple two-component system comprising an amphiphilic copolymer (Pluronic P123) in mixtures with tannic acid. This is correlated to complexation between the poly(ethylene oxide) in the Pluronic copolymer and the multiple hydrogen bonding units in tannic acid which leads to the breakup of the ordered structure formed in gels of Pluronic copolymers, and the formation of dispersed nanospheres containing a bicontinuous internal structure. These novel nanoparticles termed ‘‘emulsomes’’ are self-stabilized by a coating layer of Pluronic copolymer. The microemulsion exhibits a pearlescent appearance due to selective light scattering from the emulsion droplets. This simple formulation based on a commercial copolymer and a biofunctional and biodegradable additive is expected to find applications in the fast moving consumer goods sector.

Structure variation and evolution in microphase-separated grafted diblock copolymer films

The phase behavior of grafted d-polystyrene-block-poly(methyl methacrylate) diblock copolymer films is examined, with particular focus on the effect of solvent and annealing time. It was observed that the films undergo a two-step transformation from an initially disordered state, through an ordered metastable state, to the final equilibrium configuration. It was also found that altering the solvent used to wash the films, or complete removal of the solvent prior to thermal annealing using supercritical CO2, could influence the structure of the films in the metastable state, though the final equilibrium state was unaffected. To aid in the understanding to these experimental results, a series of self-consistent field theory calculations were done on a model diblock copolymer brush containing solvent. Of the different models examined, those which contained a solvent selective for the grafted polymer block most accurately matched the observed experimental behavior. We hypothesize that the structure of the films in the metastable state results from solvent enrichment of the film near the film/substrate interface in the case of films washed with solvent or faster relaxation of the nongrafted block for supercritical CO2 treated (solvent free) films. The persistence of the metastable structures was attributed to the slow reorganization of the polymer chains in the absence of solvent.

Efficiency of pseudo-spectral algorithms with Anderson mixing for the SCFT of periodic block-copolymer phases

This study examines the numerical accuracy, computational cost, and memory requirements of self-consistent field theory (SCFT) calculations when the diffusion equations are solved with various pseudo-spectral methods and the mean field equations are iterated with Anderson mixing. The different methods are tested on the triply-periodic gyroid and spherical phases of a diblock-copolymer melt over a range of intermediate segregations. Anderson mixing is found to be somewhat less effective than when combined with the full-spectral method, but it nevertheless functions admirably well provided that a large number of histories is used. Of the different pseudo-spectral algorithms, the 4th-order one of Ranjan, Qin and Morse performs best, although not quite as efficiently as the full-spectral method.

Dynamics of interacting edge defects in copolymer lamellae

It is known that terraces at the air-polymer interface of lamella forming diblock copolymers do not make discontinuous jumps in height. Despite the underlying discretized structure, the height profiles are smoothly varying. The width of a transition region of a terrace edge in isolation is typically several hundreds of nanometres, resulting from a balance between surface tension, chain stretching penalties, and the enthalpy of mixing. What is less well known in these systems is what happens when two transition regions interact with one another. In this study, we investigate the dynamics of the interactions between copolymer lamellar edges. We find that the data can be well described by a model that assumes a repulsion between adjacent edges. While the model is simplistic, and does not include molecular level details, its agreement with the data suggest that some of the the underlying assumptions provide insight into the complex interplay between defects.

Effect of water-soluble polymers, polyethylene glycol and poly(vinylpyrrolidone),on the gelation of aqueous micellar solutions of Pluronic copolymer F127

The micellization of F127 (E98P67E98) in dilute aqueous solutions of polyethylene glycol (PEG6000 and PEG35000) and poly(vinylpyrrolidone) (PVP K30 and PVP K90) is studied. The average hydrodynamic radius (rh,app) obtained from the dynamic light scattering technique increased with increase in PEG concentration but decreased on addition of PVP, results which are consistent with interaction of the micelles with PEG and the formation of micelles clusters, but no such interaction occurs with PVP. Tube inversion was used to determine the onset of gelation. The critical concentration of F127 for gelation increased on addition of PEG and of PVP K30 but decreased on addition of PVP K90. Small-angle X-ray scattering (SAXS) was used to show that the 30 wt% F127 gel structure (fcc) was independent of polymer type and concentration, as was the d-spacing and so the micelle hard-sphere radius. The maximum elastic modulus (G0 max) of 30 wt% F127 decreased from its value for water alone as PEG was added, but was little changed by adding PVP. These results are consistent with the packed-micelles in the 30 wt% F127 gel being effectively isolated from the polymer solution on the microscale while, especially for the PEG, being mixed on the macroscale.

Effect of architecture on the phase behavior of AB-type block copolymer melts

Equilibrium phase diagrams are calculated for a selection of two-component block copolymer architectures using self-consistent field theory (SCFT). The topology of the phase diagrams is relatively unaffected by differences in architecture, but the phase boundaries shift significantly in composition. The shifts are consistent with the decomposition of architectures into constituent units as proposed by Gido and coworkers, but there are significant quantitative deviations from this principle in the intermediate-segregation regime. Although the complex phase windows continue to be dominated by the gyroid (G) phase, the regions of the newly discovered Fddd (O^70) phase become appreciable for certain architectures and the perforated-lamellar (PL) phase becomes stable when the complex phase windows shift towards high compositional asymmetry.

Influence of a non-ionic amphiphilic copolymer on the self-assembly of a peptide amphiphile that forms nanotapes

The influence of a non-ionic polymeric surfactant on the self-assembly of a peptide amphiphile (PA) that forms nanotapes is investigated using a combination of microscopic, scattering and spectroscopic techniques. Mixtures of Pluronic copolymer P123 with the PA C16-KTTKS in aqueous solution were studied at a fixed concentration of the PA at which it is known to self-assemble into extended nanotapes, but varying P123 concentration. We find that P123 can disrupt the formation of C16- KTTKS nanotapes, leading instead to cylindrical nanofibril structures. The spherical micelles formed by P123 at room temperature are disrupted in the presence of the PA. There is a loss of cloudiness in the solutions as the large nanotape aggregates formed by C16-KTTKS are broken up, by P123 solubilization. At least locally, b-sheet structure is retained, as confirmed by XRD and FTIR spectroscopy, even for solutions containing 20 wt% P123. This indicates, unexpectedly, that peptide secondary structure can be retained in solutions with high concentration of non-ionic surfactant. Selfassembly in this system exhibits slow kinetics towards equilibrium, the initial self-assembly being dependent on the order of mixing. Heating above the lipid chain melting temperature assists in disrupting trapped non-equilibrium states.

HPMA copolymer-aminoglutethimide conjugates inhibit aromatase in MCF-7 cell lines

N-(2-Hydroxypropyl)methacrylamide (HPMA) copolymer–doxorubicin (Dox) has already shown clinical activity in breast cancer patients. Moreover, we have recently found that an HPMA conjugate containing a combination of both Dox and the aromatase inhibitor aminoglutethimide (AGM) shows significantly increased anti-tumour activity in vitro. To better understand the mechanism of action of HPMA copolymer–AGM conjugates several models were used here to investigate their effect on cell growth and aromatase inhibition. Cytotoxicity of HPMA copolymer conjugates containing AGM, Dox and also the combination AGM–Dox was determined by MTT assay in MCF-7 and MCF-7ca cells. Androstenedione (5 × 10− 8 M) stimulates the growth of MCF-7ca cells. Both free AGM and polymer-bound AGM (0.2–0.4 mg/ml) were shown to block this mitogenic activity. When MCF-7ca cells were incubated [3H]androstenedione both AGM and HPMA copolymer–GFLG–AGM (0.2 mg/ml AGM-equiv.) showed the ability to inhibit aromatase. Although, free AGM was able to inhibit isolated human placental microsomal aromatase in a concentration dependent manner, polymer-bound AGM was not, suggesting that drug release is essential for activity of the conjugate. HPMA copolymer conjugates containing aromatase inhibitors have potential for the treatment of hormone-dependant cancers, and it would be particularly interesting to explore further as potential therapies in post-menopausal women as components of combination therapy.

Step edges in thin films of lamellar-forming diblock copolymer

Self-consistent field theory (SCFT) is used to study the step edges that occur in thin films of lamellar-forming diblock copolymer, when the surfaces each have an affinity for one of the polymer components. We examine film morphologies consisting of a stack of ν continuous monolayers and one semi-infinite bilayer, the edge of which creates the step. The line tension of each step morphology is evaluated and phase diagrams are constructed showing the conditions under which the various morphologies are stable. The predicted behavior is then compared to experiment. Interestingly, our atomic force microscopy (AFM) images of terraced films reveal a distinct change in the character of the steps with increasing ν, which is qualitatively consistent with our SCFT phase diagrams. Direct quantitative comparisons are not possible because the SCFT is not yet able to probe the large polymer/air surface tensions characteristic of experiment.

Morphology induced spinodal decomposition at the surface of symmetric diblock copolymer films

Atomic force microscopy is used to study the ordering dynamics of symmetric diblock copolymer films. The films order to form a lamellar structure which results in a frustration when the film thickness is incommensurate with the lamellae. By probing the morphology of incommensurate films in the early ordering stages, we discover an intermediate phase of lamellae arranged perpendicular to the film surface. This morphology is accompanied by a continuous growth in amplitude of the film surface topography with a characteristic wavelength, indicative of a spinodal process. Using selfconsistent field theory, we show that the observation of perpendicular lamellae suggests an intermediate state with parallel lamellae at the substrate and perpendicular lamellae at the free surface. The calculations confirm that the intermediate state is unstable to thickness fluctuations, thereby driving the spinodal growth of surface structures.

Monte Carlo field-theoretic simulations for melts of symmetric diblock copolymer

Monte Carlo field-theoretic simulations (MCFTS) are performed on melts of symmetric diblock copolymer for invariant polymerization indexes extending down to experimentally relevant values of N̅ ∼ 10^4. The simulations are performed with a fluctuating composition field, W_−(r), and a pressure field, W_+(r), that follows the saddle-point approximation. Our study focuses on the disordered-state structure function, S(k), and the order−disorder transition (ODT). Although shortwavelength fluctuations cause an ultraviolet (UV) divergence in three dimensions, this is readily compensated for with the use of an effective Flory−Huggins interaction parameter, χ_e. The resulting S(k) matches the predictions of renormalized one-loop (ROL) calculations over the full range of χ_eN and N̅ examined in our study, and agrees well with Fredrickson−Helfand (F−H) theory near the ODT. Consistent with the F−H theory, the ODT is discontinuous for finite N̅ and the shift in (χ_eN)_ODT follows the predicted N̅^−1/3 scaling over our range of N̅.

Equilibrium behavior of symmetric ABA triblock copolymer melts

Melts of ABA triblock copolymer molecules with identical end blocks are examined using self-consistent field theory (SCFT). Phase diagrams are calculated and compared with those of homologous AB diblock copolymers formed by snipping the triblocks in half. This creates additional end segments which decreases the degree of segregation. Consequently, triblock melts remain ordered to higher temperatures than their diblock counterparts. We also find that middle-block domains are easier to stretch than end-block domains. As a result, domain spacings are slightly larger, the complex phase regions are shifted towards smaller A-segment compositions, and the perforated-lamellar phase becomes more metastable in triblock melts as compared to diblock melts. Although triblock and diblock melts exhibit very similar phase behavior, their mechanical properties can differ substantially due to triblock copolymers that bridge between otherwise disconnected A domains. We evaluate the bridging fraction for lamellar, cylindrical, and spherical morphologies to be about 40%–45%, 60%–65%, and 75%–80%, respectively. These fractions only depend weakly on the degree of segregation and the copolymer composition.

Effective interaction between monolayers of block copolymer compatiblizer in a polymer blend

The stability of ternary blends of two immiscible homopolymers and a block copolymer compatiblizer depends crucially on the effective interaction between the copolymermonolayers that form between the unlike homopolymer domains. Here, the interaction is calculated for blends involving A and B homopolymers of equal size with ABABdiblock copolymers of symmetric composition using both self-consistent field theory (SCFT) and strong-segregation theory (SST). If the homopolymers are larger than the copolymer molecules, an attractive interaction is predicted which would destroy the blend. This conclusion coupled with considerations regarding the elastic properties of the monolayer suggests that the optimum size of the homopolymer molecules is about 80% that of the copolymer molecule. A detailed examination of the theory demonstrates that the attraction results from the configurational entropy loss of the homopolymer molecules trapped between the copolymermonolayers. We conclude by suggesting how the monolayers can be altered in order to suppress this attraction and thus improve compatiblization.

Improving polymeric microemulsions with block copolymer polydispersity

Recent experiments have demonstrated that block copolymers are capable of stabilizing immiscible homopolymer blends producing bicontinuous microemulsion. The stability of these polymeric alloys requires the copolymer to form flexible, nonattractive monolayers along the homopolymer interfaces. We predict that copolymer polydispersity can substantially and simultaneously improve the monolayers in both of these respects. Furthermore, polydispersity should provide similar improvements in systems, such as colloidal suspensions and polymer/clay composites, that utilize polymer brushes to suppress attractive interactions.