In the previous technology article series, I provided a more or less stream-of-consciousness, rambling introduction to the nanoscale and phenomena. The next few articles will be more technical in nature and centered around relating structure and property with particle-filled materials. These articles are largely abstracted from my dissertation and are centered around the behavior of fluid systems subject to well controlled stresses. However, the more general theme of understanding how the bulk response of a material is derived its structure is a central research topic for Akron Ascent Innovations and seems to be worthy of inclusion here.
The following set of articles will begin with a brief introduction on structure-property relationships in systems containing nanoparticles, then transition into more technical descriptions of how we mathematically approach these problems of predicting changes in bulk response at the individual particle level. This will include the relatively simple case of spherical particles, then introduce the much more complicated case of non-spherical particles. Viscoelasticity (the ability of material to behave as a semi-liquid and a semi-solid) will also be addressed.
Nanoparticles in Context
Nanoparticles are of significant interest to academic and commercial fields, particularly those related to mechanical, electronic, photonic, and biological applications. The unique properties associated with nanoparticles originate from the substantial increase in surface area to volume ratio as particle dimension decreases, and the existence of quantum size effects not present in bulk materials. For example, in semi-conducting metal oxide nano-crystals, also known as quantum dots (QDs), the electronic band gap depends on the fraction of non-coordinated atoms at the particle surface [see Alivisatos, Science 1996; 273:993-37]. Their optoelectronic properties are therefore size-dependent and can be tailored. The distance between neighboring QDs also influences the optical characteristics due to short-range quantum coupling. Significant electronic energy transfer occurs at interparticle distances of up to 10 nm. As the distance decreases, the quantum size effects diminish, and their properties approach those of the bulk material. Nanoparticles also possess large surface area to volume ratios that are crucial for applications as catalysts, gas storage devices, efficient energy conversion, and barrier property enhancement. One example highlighting the challenges in mixing nanoparticles in a polymer medium is shown in the figure below. Preservation of particle dispersion during handling at all length scales is critical, particularly for sensor and multi-functional composite applications. The resulting higher-order microstructure must also be well controlled to realize the desired change in properties in the bulk.
The ability to predict mesoscale structure based on the various attributes of nanoparticles, particularly particle size, size distribution, aspect ratio, and chemical functionality, is necessary to understand and potentially tailor the physical response of multi-functional materials. Recently, molecular-scale modeling approaches have indicated that simple estimates of particle shape and local order in a fluid are sufficient to predict various categories of structural order for many convex polyhedral [Damasceno Science 2012; 337 (6093):453-7]. However, these discontinuous nano-scale modeling approaches implicitly assume local constitutive relationships that may introduce considerable error if interfacial interactions or non-local coupling between mechanical fields are present. Extensive experimental investigations have been attempted, but little detail on the fundamental physics of the nanoparticles is possible because of challenges in achieving reproducible properties of an ensemble of individual nanoparticles.
Fluid Response (Rheology) as a Structural Probe
The current gap in knowledge bridging between continuum and molecular scale behaviors may be partially attributed to the lack of characterization methods available to visualize meso-scale interactions. Rheological measurements are useful as a meso-structural characterization tool because of the intimate relationship between the molecular-scale characteristics of a fluid and its resistance to deformation and flow). The availability of rigorous mathematical tools to analyze the kinematics of deformation enables the measured response to be directly related to the material physics across an exceptionally broad range of length and time scales. This framework has been used with tremendous success to understand the molecular-scale structure/morphology and dynamics of polymers, and significant progress has been made regarding the dynamics of glass-forming liquids.
Most work on the rheology of nanoparticle suspensions has been inherently phenomenological because of the lack of effective methods to disperse nanoparticles into various media with adequate reproducibility. As a consequence, reported properties are often conflicting and inconsistent, which pose significant barriers to applications. The poorly defined microstructure also prevents clear understanding of the role of the nanoparticles on bulk response. Investigations into the melt-state rheology of polymer nanocomposites have similarly been limited to empirical observations that depend on various experimental conditions, particularly processing method, nanoparticle type, material supplier, and pre-treatment. These challenges have resulted in a significant gap between the atomic and molecular-scale properties of individual nanoparticles, and the poorly understood, and often conflicting, macroscopic performance of nanoparticle suspensions and nanocomposites.
Dispersion and Micro-structural Challenges
Most prior research has focused solely on developing methods to achieve random dispersions on local length scales, which should be favorable for optical and some mechanical properties (see Vaia and Maguire, Chemistry of Materials 2007; 19(11): 2736-51). For simultaneous improvement of multiple properties, more complex morphologies of the dispersed phase may be desirable (for interesting examples, see Torquato, Journal of Applied Physics 2003; 94(9): 5748-5]. If the shape and interaction of nanoparticles are well controlled, the mesoscale organization of nanoparticles may be potentially guided to favor formation of higher-order structures (some good examples will be listed under “nanocrystals” at the end). These approaches have potential advantages because properties may be modified across multiple length scales. This provides unique opportunities for simultaneous improvements in properties that are typically in opposition, such as stiffness and ductility. Higher order structures may be able to interact with their environment on multiple length scales, which is desirable for photonic crystals and other optical systems (see Joannopoulous, Nature 1997; 386(6621): 143-9). The parameters governing dispersion and organization, and the resulting macroscale properties of the composite material, remain poorly understood from theoretical and empirical viewpoints.
Predicting macroscale response from an assumed configuration of characteristic inclusions is one of the fundamental problems in statistical mechanics, and is relevant to disciplines spanning structural scales from the atomic and molecular level (such as kinetic theories of gases and liquids, polymer physics, electron transport), to the continuum-level (multi-phase flow, fracture mechanics, and transport in heterogeneous media). Alternatively, the same tools may be used to interrogate the molecular-structure of materials based on the associated change in volume-averaged and time-averaged properties.
The introduction of a small concentration of nanoparticles can substantially improve the thermomechanical, optical, and electrical properties of polymers, but the specific particle-level mechanism responsible for the improvement is generally unclear. In several cases, there has been significant investment in systems based on flawed assumptions regarding the scalability and generality of a specific observation. The resulting performance of the “nano”-composites is generally inconsistent and well below expectations, which pose significant barriers to commercial applications. These early problems reflect inherent problems in the field related to the lack of available techniques to process and characterize materials on the nanoscale. Most processing techniques used today are top-down, mechanical methods developed for micron-scale fiber composites and particulate filled systems. Common characterization techniques are similarly limited by compromises between time, resolution, and sampling size, and may not be sensitive to the relevant processes for a desired property of interest.
For non-spherical nanoparticles, most research to date has focused solely on achieving random dispersions on local length scales. Any resulting properties that do not meet expectation are generally explained based on experiences with micron-scale fillers, in particular, inadequate dispersion and interfacial adhesion. This level of discussion ignores the most exciting features of nanoparticles, which is that they interact with their environment on a much smaller length scale than their micron-scale counterparts. This distinction offers tremendous opportunities to design functional materials with properties tailored to specific applications by controlling material structure from the bottom-up.
Controlling the mesoscale organization of nanoparticles into higher-order structures also offers potential for targeting properties across length scales. An important example relevant to this work is colloidal liquid crystals (see figure below). High aspect ratio plate-like particles are widely used as rheological modifiers and for polymer composite applications, and increasing the degree of order is expected to provide greater improvements in certain properties, particularly modulus, strength, and barrier properties. Achieving long-range organization offers new properties associated with the higher-order structure, such as specific wavelength filtering of light (photonic liquid crystals).
From a practical perspective, the behavior of nanoparticle-filled fluids is of interest for heat transfer fluids, flow modifiers for commercial products, and microfluidic devices and sensors. From a fundamental perspective, well designed experimental studies are needed to provide clear microstructural mechanisms associated with specific macroscale properties, which will be useful to distinguish relevant properties in more complex systems.
In the next section, the origins of rheological and viscoelastic response of suspensions will be briefly reviewed. Relevant equations and descriptions used in later sections are presented. Theoretical and experimental description of model systems with well-defined microstructure and interactions are provided, along with some concluding remarks on the usefulness of rheology to probe nanoscale phenomena.
Quantum Dots and Energy States
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Kagan C, Murray C, Nirmal M, Bawendi M. Electronic Energy Transfer in CdSe Quantum Dot Solids. Physical Review Letters. 1996; 76(9):1517-20.
Artemyev M, Bibik A, Gurinovich L, Gaponenko S, Woggon U. Evolution from Individual to Collective Electron States in a Dense Quantum Dot Ensemble. Phys Rev B. 1999; 60(3):1504-6.
Sun D, Wong M, Sun L, Li Y, Miyatake N, Sue H-J. Purification and Stabilization of Colloidal ZnO Nanoparticles in Methanol. J Sol-Gel Sci Techn. 2007; 43(2):237-43.
Zhang X, Sun D, Sue HJ, Nishimura R. Colloidal Crystallization of Surfactant‐Free ZnO Quantum Dots. ChemPhysChem. 2011; 12(18):3533-8.
Sun D, Miyatake N, Sue H-J. Transparent PMMA/ZnO Nanocomposite Films Based on Colloidal ZnO Quantum Dots. Nanotechnology. 2007; 18(21):215606.
Sun D, Sue H-J. Tunable Ultraviolet Emission of ZnO Quantum Dots in Transparent Poly (Methyl Methacrylate). Applied Physics Letters. 2009; 94(25):253106-3.
Sun D, Sue H-J, Miyatake N. Optical Properties of ZnO Quantum Dots in Epoxy with Controlled Dispersion. The Journal of Physical Chemistry C. 2008; 112(41):16002-10.
Sun D, Everett WN, Wong M, Sue H-J, Miyatake N. Tuning of the Dispersion of Ligand-Free ZnO Quantum Dots in Polymer Matrices with Exfoliated Nanoplatelets. Macromolecules. 2009;42(5):1665-71.
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Fluid Flow (Rheology) as a Structural Probe
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Particle Self-Assembly and Colloidal Liquid Crystals
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