Copolymer-homopolymer blends: global energy minimisation and global energy bounds

We study a variational model for a diblock-copolymer/homopolymer blend. The energy functional is a sharp-interface limit of a generalisation of the Ohta-Kawasaki energy. In one dimension, on the real line and on the torus, we prove existence of minimisers of this functional and we describe in complete detail the structure and energy of stationary points. Furthermore we characterise the conditions under which the minimisers may be non-unique. In higher dimensions we construct lower and upper bounds on the energy of minimisers, and explicitly compute the energy of spherically symmetric configurations.Comment: 31 pages, 6 Postscript figures; to be published in Calc. Var. Partial Differential Equations. Version history: Changes in v2 w.r.t v1 only concern metadata. V3 contains some minor revisions and additions w.r.t. v2. V4 corrects a confusing typo in one of the formulas of the appendix. V5 is the definitive version that will appear in prin

Stability of monolayers and bilayers in a copolymer-homopolymer blend model

We study the stability of layered structures in a variational model for diblock copolymer-homopolymer blends. The main step consists of calculating the first and second derivative of a sharp-interface Ohta-Kawasaki energy for straight mono- and bilayers. By developing the interface perturbations in a Fourier series we fully characterise the stability of the structures in terms of the energy parameters. In the course of our computations we also give the Green's function for the Laplacian on a periodic strip and explain the heuristic method by which we found it.Comment: 40 pages, 34 Postscript figures; second version has some minor corrections; to appear in "Interfaces and Free Boundaries

Pathways toward controlled assembly of functional polymer-based nanostructures

This thesis deals with a common drawback that is often encountered in self-assembled nanostructured soft matter. Even though spontaneous self-assembly can be used to create diverse nanostructures, the structures, as such, are typically polydomain, consisting of locally ordered small domains that lack mutual orientation and/or long range correlation. As a result, the material remains macroscopically isotropic and disordered. The aim here is to explore feasible ways, on one hand, to control the assembly and, on the other hand, to obtain macroscopically anisotropic materials and functions. We show the first example of how charge-transfer complexation between C60 fullerenes and electron-donating units of block copolymers can enable control of the morphology and properties of fullerene based materials. We also study the alignment of randomly oriented domains of nanostructured material over macroscopic length scales by using a real-time rheo-optical apparatus in combination with more detailed ex-situ structural characterization. Alignment of randomly oriented domains is not only useful for obtaining macroscopically anisotropic materials and functions but it can also be a prerequisite for detailed characterization of the local structures. This aspect is demonstrated for hierarchical liquid crystalline (LC) diblock copolymer structures which, upon inducing shear alignment, exhibit coexistence of two orthogonal orientations of the LC phase within the copolymer lamellae. Furthermore we demonstrate that ionic complexes forming a columnar LC phase can be efficiently aligned within polymer blends upon shearing, taken that the matrix polymers have sufficiently high molecular weight. This concept allows a simple route for macroscopically aligned nanocomposites with conjugated columnar LC functional additives. Finally, control of the nanoscale morphology in polymer/fullerene nanocomposite thin film devices is shown to allow tuning of the electrical switching that can enable construction of a memory unit. The working principles of such thin film organic memory devices have remained debated and the first systematic approach is here undertaken to tailor the active material composition and to study the morphology vs. functionality relationship

Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere

On the two dimensional sphere, we consider axisymmetric critical points of an isoperimetric problem perturbed by a long-range interaction term. When the parameter controlling the nonlocal term is sufficiently large, we prove the existence of a local minimizer with arbitrary many interfaces in the axisymmetric class of admissible functions. These local minimizers in this restricted class are shown to be critical points in the broader sense (i.e., with respect to all perturbations). We then explore the rigidity, due to curvature effects, in the criticality condition via several quantitative results regarding the axisymmetric critical points.Comment: 26 pages, 6 figures. This version is to appear in ESAIM: Control, Optimisation and Calculus of Variation

Ordered Structures from Nanoparticles/Block Copolymer Hybrids: Ex-situ Approaches toward Binary and Ternary Nanocomposites

Within the field of modern technology, nanomatrials, such as nanoparticles (NP), nanorods (NR), quantum dots (QD) etc. are, probably, the most prominent and promising candidates for current and future technological applications. The interest in nanomaterials arise not only form the continuous tendency towards dimensions minimisation of electronic devices, but also due to the fact, that new and, often, unique properties are acquired by the matter at the length scale between 1 and 100 nm. The ability to organize nanoparticles into ordered arrays extends the range of useful NP-based systems that can be fabricated and the diversity of functionalities they can serve. However, in order to successfully exploit nanoparticle assemblies in technological applications and to ensure efficient scale-up, a high level of direction and control is required. Recently, block copolymers (BCP) have attracted much attention as a powerful and very promising tool for creation of nanoscale ordered structures owing to their self-assembling properties. In addition, these systems offer the possibility to fabricate nanostructured composite materials via incorporation of certain nanoadditives (i.e. NPs). The concept is that by selective inclusion of the nanoparticles into one of the blocks of a self-assembling copolymer, the nanoparticles are forced into a defined spatial arrangement determined by the phase morphology of the block copolymer. In present work self-assembling phenomena of block copolymers was exploited to fabricate binary (NP/BCP) and ternary (NP1/NP2/BCP) composites, filled with pre-synthesized nanoparticles of various nature. Polystyrene-block-polyvinylpyridine block copolymers (PS-b-PVP) of various composition and molecular weight were used for fabrication of nanocomposites. The first part of the thesis focuses on fabrication of functional BCP-based composites containing magnetic nanoparticles (MNP), selectively assembled within one of the blocks of BCP matrix. Magnetic nanoparticles (MNPs) were selected among others since, as for today, there is the least number of successful results reported in literature on their selective incorporation into one of the phases of a BCP matrix. From the application point of view fabrication of periodic arrays of “magnetic domains” with periodicity on nanometer scale is also of interest for potential use in high-density magnetic data storage devices. For this purpose, ferrite-type MNP (Fe3O4, CoFe2O4) having apparent affinity toward polyvinylpyridine (PVP) phase were prepared using simple one-pot synthesis. Highly selective nanoparticles segregation into PVP domains of BCP was achieved owing to the presence of sparse stabilizing organic shell on the nanoparticles surface. Importantly, as-prepared MNPs did not require any additional surface modification step to acquire affinity towards PVP phase. Appropriate selection of annealing conditions allowed to produce patterns of nearly perfect degree of lateral order over relatively large surface large area (more than 4 sq µm). The second task of present work was fabrication of ternary NP1/NP2/BCP hybrid composites with two different types of nanoparticles being selectively localized in different microdomains of phase segregated block copolymer matrix. So far as only few studies have been reported on developing of approaches toward ternary composites, creation of alternative and straight forward routes toward such systems is still a challenge. In the frame of this part of present work, silver nanoparticles (AgNPs) covered with polystyrene shell were prepared, with the purpose to be incorporated into polystarene phase of phase separated PS-b-PVP block copolymer matrix. Two different approaches were tested to achieve desired three-component system. First, supposed simple blending of block copolymer and two kinds of nanoparticles having specific affinity toward different blocks of BCP in common solvent. After preparation of MNP/AgNP/BCP composite thin film and subsequent solvent vapour annealing, different domains of microphase segregated PS-b-PVP BCP were filled with different type of nanoparticles. Alternatively, step-wise approach for nanoparticles incorporation was developed and implemented for successful selective nanoparticles incorporation. For this purpose polystyrene stabilized AgNPs (i.e. NP1) were initially mixed with PS-b-PVP BCP to produce composite thin films having nanoparticles selectively located within PS microdomains, while citrate-stabilized second type nanoparticles (i.e NP2) were deposited from their aqueous solutions into PVP domains of AgNP/PS-b-PVP composites. By partition of nanoparticles incorporation procedure into two distinct steps it was also possible to increase effective loading of each type of NPs into BCP matrix

In-situ Investigation of the shear-induced alignment of Diblock Copolymer Melts using Rheo-SAXS, Rheo-Dielectric and FT-Rheology

In-situ flow alignment of self-assembled block copolymer melts have been investigated in detail under mechanical large amplitude oscillatory shear (LAOS) utilizing new and unique Rheo-SAXS and Rheo-Dielectric techniques. Significant correlations between the non-linear mechanical and dielectric responses were detected which strongly depended on the shear-induced structural changes. Furthermore, a novel de-orientation process was observed which is also observed via FT-Rheology and Rheo-Dielectri

Multi-Crystalline polymer systems: Biodegradable triblock terpolymers and nanostructured blends. Morphology, Crystallization and properties

268 p