Proceso de Transporte y Almacenamiento

Following the guidelines from Figure 1.4 for commensurate BCP morphology and NP shape, this thesis begins a systematic exploration of a model polymer functionalized nanoplate integrated into a lamellar-forming BCP. The alignment and morphological effects of nanoplates in lamellar diblock copolymer thin films is investigated by experimentally and/or theoretically studying the influence of NP loading, NP separation, and microdomain orientation with variations in BCP molecular weight. The presented work not only expands our knowledge of PNC phase behavior, but also introduces a framework to further study the parameters that affect nanoplate alignment in BCP nanocomposites. The discussions in the ensuing chapters adapt the thermodynamic insights gained from directing the location of isotropic NPs in BCP domains to understand the factors that impact nanoplate orientation. Ultimately, the goal is to establish a platform to intentionally manipulate the assembly of nanoplates to exploit their shape and orientation-dependent properties. Our ability to control anisotropic NP alignment in PNCs through self-assembling techniques lends itself to creating multifunctional materials with unique properties for various applications.

Chapter 2 establishes a well-defined system to investigate the alignment of nanoplates in a lamellar-forming poly(styrene-b-methyl methacrylate) (PS-b-PMMA) BCP with domains oriented parallel to the substrate. Monodisperse gadolinium trifluoride rhombic nanoplates doped with ytterbium and erbium [GdF3:Yb/Er (20/2 mol%)] are synthesized and grafted with phosphoric acid functionalized polyethylene glycol (PEG-PO3H2). Designed with chemical specificity to one block, the nanoplates align in the PMMA domain at low volume fractions (ϕ = 0.0083 and ϕ = 0.017). At these low NP loadings, the BCP lamellae are ordered and induce preferential alignment of the GdF3:Yb/Er nanoplates. However, at high volume fractions (ϕ = 0.050 and ϕ = 0.064), the BCP lamellae are disordered with isotropically dispersed nanoplates. The transition from an ordered BCP system with aligned nanoplates to a disordered BCP with unaligned nanoplates coincides with

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the calculated overlap volume fraction, ϕ* = 0.051, where the pervaded space of the NPs begin to overlap. Two phenomena are observed in the results: the effect of lamellar formation on nanoplate orientation and the overall phase behavior of the PNCs.

Chapter 3. Within the ordered PS-b-PMMA BCP lamellae in Chapter 2, the oriented GdF3:Yb/Er nanoplates grafted with PEG-PO3H2 further assemble into aligned strings at small interparticle separations. Herein, we investigate the origin of these aligned assemblies using X-ray scattering, electron microscopy, and hybrid particle/self-consistent field theory (hSCFT) simulations. From previous reports, the insertion of a nanoplate in a BCP microdomain is expected to perturb the polymer chains and produce a local domain bulge as the PS/PMMA interface distorts to optimize conformational entropy. While experimental techniques are unable to directly resolve this small distortion, the 2D simulations of the equilibrium BCP nanocomposite structure clearly show bulge formation around the nanoplates. As a function of particle separation, the potential of mean force (PMF) calculation reveals a global minimum corresponding to an equilibrium interparticle spacing of 7.0 nm, which agrees well with a mean experimental value of 6.42 nm. Furthermore, the PMF calculation exhibits a small activation barrier due to the high curvature penalty between two nanoplates at a separation distance of 21.7 nm. Ultimately, nanoplate strings form to fulfill the criteria where the energy benefit of decreasing interfacial area and minimizing chain stretching outweighs the energy penalty associated with reducing the translational entropy affiliated with evenly distributing the nanoplates. The simulations also illustrate a narrow tolerance for orientation angles, supporting the high degree of nanoplate alignment observed experimentally. We anticipate that the ability to align and couple anisotropic nanoparticles in BCPs presents opportunities to create functional PNC with orientation-dependent properties.

Chapter 4. The ability to precisely tune the orientation of anisotropic NPs in thin film PNCs is relevant to designing new materials with properties tailored for a specific application. Although in-plane or parallel orientation of these non-spherical NPs has been readily shown, out-of-plane or

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vertical alignment of nanorods and nanoplates in PNCs is less trivial. Methods to create composites with vertical particle structures often rely on multistep processes. However, self-assembling BCPs offer a versatile platform to create hierarchical hybrid materials with minimal operations. To direct out-of-plane alignment of anisotropic NPs, and more specifically the GdF3:Yb/Er nanoplates synthesized in Chapter 2, the research herein exploits symmetric PS-b-PMMA (Mn = 73k-b-73k g/mol and Mn = 95k-b-95k g/mol) with lamellar microdomains oriented perpendicular to the substrate. We show that functionalizing the nanoplate surfaces with PEG-PO3H2 brushes is critical to dispersing the NPs in the PMMA domain without disrupting the equilibrium BCP morphology. Subsequently and most notably, vertically oriented lamellar domains successfully guides out-of- plane alignment of the nanoplates through self-assembly. We expect that the approach disclosed in this Chapter will benefit applications that are based on out-of-plane NP alignment by proposing an easy-to-implement technique to attain these vertically oriented hierarchical PNC films.

There are limited theoretically predicted phase diagrams for PNCs because conventional modeling techniques are largely unable to predict the macroscale phase behavior of PNCs. In Chapter 5, we show that recent field-based methods, including PNC field theory (PNC-FT) and theoretically informed Langevin dynamics (TILD), can be used to calculate phase diagrams for polymer-grafted nanoparticles (gNPs) incorporated into a polymer matrix. We calculate binodal curves for the transition from the miscible, dispersed phase to the macrophase separated state as functions of important experimental parameters, including the ratio of the matrix chain degree of polymerization (P) to the grafted chain degree of polymerization (N), the enthalpic repulsion between the matrix and grafted chains, the grafting density (σ), the size of the NPs, and the NP volume fraction. We demonstrate that thermal and polymer conformational fluctuations enhance the degree of phase separation in gNP-PNCs, a result of depletion interaction effects. We support this conclusion by experimentally investigating the phase separation of PMMA-grafted silica NPs in a PS matrix as a function of P/N. The simulations only agree with experiments when fluctuations

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are included because fluctuations are needed to properly capture the depletion interactions between the gNPs. We clarify the role of conformational entropy in driving depletion interactions in PNCs and suggest that inconsistencies in the literature may be due to polymer chain length effects since conformational entropy increases with increasing chain length.

Chapter 6 summarizes the main conclusions from each chapter of this dissertation and also discusses additional projects, proposed for future work. Appendix A, Appendix B, Appendix C, and Appendix D contains the supporting information for Chapter 2, Chapter 3, Chapter 4, and Chapter 5, respectively.

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