Deformation Behavior of Polystyrene-Grafted Nanoparticle Assemblies with Low Grafting Density

Finite Element Analysis of the Structure and Working Principle of Solid-State Shear Milling (S3M) Equipment

Solid-state shear milling (S3M) equipment is an evolution from traditional stone mills, enabling the processing of polymer materials and fillers through crushing, mixing, and mechanochemical reactions at ambient temperature. Due to the complex structure of the mill-pan, empirical data alone are insufficient to give a comprehensive understanding of the physicochemical interactions during the milling process. To provide an in-depth insight of the working effect and mechanism of S3M equipment, finite element method (FEM) analysis is employed to simulate the milling dynamics, which substantiates the correlation between numerical outcomes and experimental observations. A model simplification strategy is proposed to optimize calculation time without compromising accuracy. The findings in this work demonstrate the S-S bond breakage mechanism behind stress-induced devulcanization and suggest the structural optimizations for enhancing the devulcanization and pulverization efficiency of S3M equipment, thereby providing a theoretical foundation for its application in material processing.

Regulating Charge Carrier Dynamics in Stable Perovskite Nanorods for Photo-Induced Atom Transfer Radical Polymerization

Semiconducting nanocrystals have attracted world-wide research interest in artificial photosynthesis due to their appealing properties and enticing potentials in converting solar energy into valuable chemicals. Compared to 0D nanoparticles, 1D nanorods afford long-distance charge carriers separation and extended charge carriers lifetime due to the release of quantum confinement in axial direction. Herein, stable CsPbBr3 nanorods of distinctive dimensions are crafted without altering their properties and morphology via grafting hydrophobic polystyrene (PS) chains through a post-synthesis ligand exchange process. The resulting PS-capped CsPbBr3 nanorods exhibit a series of enhanced stabilities against UV irradiation, elevated temperature, and polar solvent, making them promising candidates for photo-induced atom transfer radical polymerization (ATRP). Tailoring the surface chemistry and dimension of the PS-capped CsPbBr3 nanorods endows stable, but variable reaction kinetics in the photo-induced ATRP of methyl methacrylate. The trapping-detrapping process of photogenerated charge carriers lead to extended lifetime of charge carriers in lengthened CsPbBr3 nanorods, contributing to a facilitated reaction kinetics of photo-induced ATRP. Therefore, by leveraging such stable PS-capped CsPbBr3 nanorods, the effects of surface chemistry and charge carriers dynamics on its photocatalytic performance are scrutinized, providing fundamental understandings for designing next-generation efficient nanostructured photocatalyst in artificial photosynthesis and solar energy conversion.

Nanoparticle Brushes: Macromolecular Ligands for Materials Synthesis

ConspectusColloidal nanoparticles have unique attributes that can be used to synthesize materials with exotic properties, but leveraging these properties requires fine control over the particles' interactions with one another and their surrounding environment. Small molecules adsorbed on a nanoparticle's surface have traditionally served as ligands to govern these interactions, providing a means of ensuring colloidal stability and dictating the particles' assembly behavior. Alternatively, nanoscience is increasingly interested in instead using macromolecular ligands that form well-defined polymer brushes, as these brushes provide a much more tailorable surface ligand with significantly greater versatility in both composition and ligand size. While initial research in this area is promising, synthesizing macromolecules that can appropriately form brush architectures remains a barrier to their more widespread use and limits understanding of the fundamental chemical and physical principles that influence brush-grafted particles' ability to form functional materials. Therefore, enhancing the capabilities of polymer-grafted nanoparticles as tools for materials synthesis requires a multidisciplinary effort, with specific focus on both developing new synthetic routes to polymer-brush-coated nanoparticles and investigating the structure-property relationships the brush enables.In this Account, we describe our recent work in developing polymer brush coatings for nanoparticles, which we use to modulate particle behavior on demand, select specific nanoscopic architectures to form, and bolster traditional bulk polymers to form stronger materials by design. Distinguished by the polymer type and capabilities, three classes of nanoparticles are discussed here: nanocomposite tectons (NCTs), which use synthetic polymers end-functionalized with supramolecular recognition groups capable of directing their assembly; programmable atom equivalents (PAEs) containing brushes of synthetic DNA that employ Watson-Crick base pairing to encode particle binding interactions; and cross-linkable nanoparticles (XNPs) that can both stabilize nanoparticles in solution and polymer matrices and subsequently form multivalent cross-links to strengthen polymer composites. We describe the formation of these brushes through "grafting-from" and "grafting-to" strategies and illustrate aspects that are important for future advancement. We also examine the new capabilities brushes provide, looking closely at dynamic polymer processes that provide control over the assembly state of particles. Finally, we provide a brief overview of the technological applications of nanoparticles with polymer brushes, focusing on the integration of nanoparticles into traditional materials and the processing of nanoparticles into bulk solids.

Topographical Design and Thermal-Induced Organization of Interfacial Water Structure to Regulate the Wetting State of Surfaces

Smart surfaces with superhydrophobic/superhydrophilic characteristics can be controlled by external stimuli, such as temperature. These transitions are attributed to the molecular-level conformation of the grafted polymer chains due to the varied interactions at the interface. Here, tunable surfaces were prepared by grafting two well-known thermo-responsive polymers, poly(N-isopropylacrylamide) (PNIPAM) and poly(oligoethylene glycol)methyl ether acrylate (POEGMA₁₈₈) onto micro-pollen particles of uniform morphology and roughness. Direct Raman spectra and thermodynamic analyses revealed that above the lower critical solution temperature, the bonded and free water at the interface partially transformed to intermediate water that disrupted the "water cage" surrounding the hydrophobic groups. The increased amounts of intermediate water produced hydrogen bonding networks that were less ordered around the polymer grafted microparticles, inducing a weaker binding interaction at the interface and a lower tendency to wet the surface. Combining the roughness factor, the bulk surface assembled by distinct polymer-grafted-pollen microparticles (PNIPAM or POEGMA₁₈₈) could undergo a different wettability transition for liquid under air, water, and oil. This work identifies new perspectives on the interfacial water structure variation at a multiple length scale, which contributed to the temperature-dependent surface wettability transition. It offers inspiration for the application of thermo-responsive surface to liquid-gated multiphase separation, water purification and harvesting, biomedical devices, and printing.

Polymer-Grafted Nanoparticles (PGNs) with Adjustable Graft-Density and Interparticle Hydrogen Bonding Interaction

Polymer-grafted nanoparticles (PGNs) receive great attention because they possess the advantages of both the grafted polymer and inorganic cores, and thus demonstrate superior optical, electronic, and mechanical properties. Thus, PGNs with tailorable interparticle interactions are indispensable for the formation of a superlattice with a defined and ordered structure. In this work, the synthesis of PGNs is reported which can form interparticle hydrogen-bonding to enhance the formation of well-defined 2D nanoparticle arrays. Various polymers, including poly(4-vinyl pyridine) (P4VP), poly(dimethyl aminoethyl acrylate) (PDMAEMA), and poly(4-acetoxy styrene) (PAcS), are attached to silica cores by a "grafting from" in a mini emulsion-like synthesis approach. SiO₂ -PAcS brushes are deprotected by hydrazinolysis and converted into poly(4-vinyl phenol) (PVP), containing hydroxyl groups as potential hydrogen-bonding donor sites. Understanding and controlling interparticle interactions by varying grafting density in the range of 10^-2 -10^-3 chain nm^-2 , and the formation of interparticle hydrogen bonding relevant for self-assembly of PGNs and potential formation of PGN superlattice structures are the motivations for this study.

Tuning Hierarchical Order and Plasmonic Coupling of Large-Area, Polymer-Grafted Gold Nanorod Assemblies via Flow-Coating

Solution-based printing of anisotropic nanostructures is foundational to many emerging technologies, such as energy storage devices, photonic elements, and sensors. Methods to rapidly (>mm/s) manufacture large area assemblies (≫cm²) with simultaneous control of thickness (<10 nm), nanoparticle spacing (<5 nm), surface roughness (<5 nm), and global and local orientational order are still lacking. Herein, we demonstrate such capability using flow-coating to fabricate robust, self-supporting mono- and bilayer films of polystyrene-grafted gold nanorods (PS-AuNRs) onto solid substrates. The relationship among solvent evaporation, deposition speed, substrate surface energy, concentration, and film thickness for solutions of such hairy hybrid nanoparticles spans the Landau-Levich and evaporative film formation regimes. In the Landau-Levich regime, solvent evaporation rapidly concentrates the PS-AuNRs, leading to the formation of thin films with distinct, randomized side-by-side domains. Alternatively, processing at slower velocities in the evaporative regime results in the global alignment of PS-AuNRs. Processing speed and substrate surface energy afford tuning of the film's optical extinction of a given PS-AuNR via fine control of inter-rod distance and subsequent plasmonic coupling between neighboring nanorods. Because the concept of the polymer-grafted nanorod can be expanded to a variety of different polymer canopies, shapes, and core materials, the processing-structure relationships established in this work will have important implications on the future development of anisotropic nanostructure-based applications.

θ-Solvent-Mediated Double-Shell Polyethylene Glycol Brushes on Nanoparticles for Improved Stealth Properties and Delivery Efficiency

Antifouling polymer brushes are widely used to inhibit the formation of protein corona on nanoparticles (NPs) and subsequent accumulation in the liver and spleen. Herein, we demonstrate a θ-solvent-mediated method for the preparation of gold nanoparticles with a high polyethylene glycol (PEG) grafting density. Reaching the θ-solvent by adding salt (e.g., Na₂SO₄) can significantly increase the grafting density of the PEG brush to 2.08 chains/nm². The PEG polymer brush prepared in the θ-solvent possesses a double-shell structure consisting of a concentrated polymer brush (CPB) and a semidilute polymer brush (SDPB), denoted as NP@CPB@SDPB, while those prepared in a good solvent have only a SDPB shell, i.e., NP@SDPB. Compared to the NP@SDPB structure, the NP@CPB@SDPB structure decreases the liver accumulation from 34.0%ID/g to 23.1%ID/g, leading to an increase in tumor accumulation from 8.5%ID/g to 12.8%ID/g. This work provides new insights from the perspective of polymer physical chemistry into the improved stealth properties and delivery efficiency of NPs, which will accelerate the clinical translation of nanomedicine.

Effect of Dispersity on the Conformation of Spherical Polymer Brushes

We show that dispersity (D̵) markedly alters the conformation of spherical polymer brushes. The average lengths (l_b) of poly(tert-butyl acrylate) (PtBA) brushes of varying D̵ grafted to nanoparticles were measured using dynamic light scattering. In the semidilute polymer brush (SDPB) regime, the l_b of PtBA and polymers from earlier studies of various D̵ could be cleanly collapsed onto a master curve as a function of the scaling variable N_wσ^1/3, where N_w is the weight-average degree of polymerization and σ is the grafting density. In the concentrated polymer brush (CPB) regime, however, l_b collapsed onto a bifurcated curve as a function of the scaling variable N_wσ^1/2, indicating D̵ more strongly affects the average length of brushes with low N_wσ^1/2. We propose that the stretching of the stem near the particle surface due to interchain interactions in the CPB regime leads to greater l_b in broad dispersity brushes of low but not high N_wσ^1/2.

Structure and thermodynamics of grafted silica/polystyrene dilute nanocomposites investigated through self-consistent field theory

Polymer/matrix nanocomposites (PNCs) are materials with exceptional properties. They offer a plethora of promising applications in key industrial sectors. In most cases, it is preferable to disperse the nanoparticles (NPs) homogeneously across the matrix phase. However, under certain conditions NPs might lump together and lead to a composite material with undesirable properties. A common strategy to stabilize the NPs is to graft on their surface polymer chains of the same chemical constitution as the matrix chains. There are several unresolved issues concerning the optimal molar mass and areal density of grafted chains that would ensure best dispersion, given the nanoparticles and the polymer matrix. We propose a model for the prediction of key structural and thermodynamic properties of PNC and apply it to a single spherical silica (SiO2) nanoparticle or planar surface grafted with polystyrene chains embedded at low concentration in a matrix phase of the same chemical constitution. Our model is based on self-consistent field theory, formulated in terms of the Edwards diffusion equation. The properties of the PNC are explored across a broad parameter space, spanning the mushroom regime (low grafting densities, small NPs and chain lengths), the dense brush regime, and the crowding regime (large grafting densities, NP diameters, and chain lengths). We extract several key quantities regarding the distributions and the configurations of the polymer chains, such as the radial density profiles and their decomposition into contributions of adsorbed and free chains, the chains/area profiles, and the tendency of end segments to segregate at the interfaces. Based on our predictions concerning the brush thickness, we revisit the scaling behaviors proposed in the literature and we compare our findings with experiment, relevant simulations, and analytic models, such as Alexander's model for incompressible brushes.

Potential of Mean Force between Bare or Grafted Silica/Polystyrene Surfaces from Self-Consistent Field Theory

We investigate single and opposing silica plates, either bare of grafted, in contact with vacuum or melt phases, using self-consistent field theory. Solid-polymer and solid-solid nonbonded interactions are described by means of a Hamaker potential, in conjunction with a ramp potential. The cohesive nonbonded interactions are described by the Sanchez-Lacombe or the Helfand free energy densities. We first build our thermodynamic reference by examining single surfaces, either bare or grafted, under various wetting conditions in terms of the corresponding contact angles, the macroscopic wetting functions (i.e., the work of cohesion, adhesion, spreading and immersion), the interfacial free energies and brush thickness. Subsequently, we derive the potential of mean force (PMF) of two approaching bare plates with melt between them, each time varying the wetting conditions. We then determine the PMF between two grafted silica plates separated by a molten polystyrene film. Allowing the grafting density and the molecular weight of grafted chains to vary between the two plates, we test how asymmetries existing in a real system could affect steric stabilization induced by the grafted chains. Additionally, we derive the PMF between two grafted surfaces in vacuum and determine how the equilibrium distance between the two grafted plates is influenced by their grafting density and the molecular weight of grafted chains. Finally, we provide design rules for the steric stabilization of opposing grafted surfaces (or fine nanoparticles) by taking account of the grafting density, the chain length of the grafted and matrix chains, and the asymmetry among the opposing surfaces.

Projectile Impact Shock-Induced Deformation of One-Component Polymer Nanocomposite Thin Films

Matrix-free assemblies of polymer-grafted nanoparticles (PGNs) enable mechanically robust materials for a variety of structural, electronic, and optical applications. Recent quasi-static mechanical studies have identified the key parameters that enhance canopy entanglement and promote plasticity of the PGNs below T_g. Here we experimentally explore the high-strain-rate shock impact behavior of polystyrene grafted NPs and compare their energy absorption capabilities to that of homopolystyrene for film thicknesses ranging from 75 to 550 nm and for impact velocities from 350 to 800 m/s. Modeling reveals that the initial shock compression results in a rapid temperature increase at the impact site. The uniformity of this heating is consistent with observations of greater kinetic energy absorption per mass (E_p^*) of thinner films due to extensive visco-plastic deformation of molten film around the penetration site. Adiabatic heating is insufficient to raise the temperature at the exit surface of the thickest films resulting in increased strain localization at the impact periphery with less melt elongation. The extent and distribution of entanglements also influence E_p^*. Structurally, each NP acts as a giant cross-link node, coupling surrounding nodes via the number of canopy chains per NP and the nature and number of entanglements between canopies anchored to different NPs. Load sharing via this dual network, along with geometrical factors such as film thickness, lead to extreme E_p^* arising from the sequence of instantaneous adiabatic shock heating followed by visco-plastic drawing of the film by the projectile. These observations elucidate the critical factors necessary to create robust polymer-nanocomposite multifunctional films.

Ion-Conducting Thermoresponsive Films Based on Polymer-Grafted Cellulose Nanocrystals

Mechanically robust, thermoresponsive, ion-conducting nanocomposite films are prepared from poly(2-phenylethyl methacrylate)-grafted cellulose nanocrystals (MxG-CNC-g-PPMA). One-component nanocomposite films of the polymer-grafted nanoparticle (PGN) MxG-CNC-g-PPMA are imbibed with 30 wt % imidazolium-based ionic liquid to produce flexible ion-conducting films. These films with 1-hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (MxG-CNC-g-PPMA/[H]) not only display remarkable improvements in toughness (>25 times) and tensile strength (>70 times) relative to the corresponding films consisting of the ionic liquid imbibed in the two-component CNC/PPMA nanocomposite but also show higher ionic conductivity than the corresponding neat PPMA with the same weight percent of ionic liquid. Notably, the one-component film containing 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (MxG-CNC-g-PPMA/[E]) exhibits temperature-responsive ionic conduction. The ionic conductivity decreases at around 60 °C as a consequence of the lower critical solution temperature phase transition of the grafted polymer in the ionic liquid, which leads to phase separation. Moreover, holding the MxG-CNC-g-PPMA/[E] film at room temperature for 24 h returns the film to its original homogenous state. These materials exhibit properties relevant to thermal cutoff safety devices (e.g., thermal fuse) where a reduction in conductivity above a critical temperature is needed.

Antiviral Potential of Nanoparticles-Can Nanoparticles Fight Against Coronaviruses?

Infectious diseases account for more than 20% of global mortality and viruses are responsible for about one-third of these deaths. Highly infectious viral diseases such as severe acute respiratory (SARS), Middle East respiratory syndrome (MERS) and coronavirus disease (COVID-19) are emerging more frequently and their worldwide spread poses a serious threat to human health and the global economy. The current COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). As of 27 July 2020, SARS-CoV-2 has infected over 16 million people and led to the death of more than 652,434 individuals as on 27 July 2020 while also causing significant economic losses. To date, there are no vaccines or specific antiviral drugs to prevent or treat COVID-19. Hence, it is necessary to accelerate the development of antiviral drugs and vaccines to help mitigate this pandemic. Non-Conventional antiviral agents must also be considered and exploited. In this regard, nanoparticles can be used as antiviral agents for the treatment of various viral infections. The use of nanoparticles provides an interesting opportunity for the development of novel antiviral therapies with a low probability of developing drug resistance compared to conventional chemical-based antiviral therapies. In this review, we first discuss viral mechanisms of entry into host cells and then we detail the major and important types of nanomaterials that could be used as antiviral agents. These nanomaterials include silver, gold, quantum dots, organic nanoparticles, liposomes, dendrimers and polymers. Further, we consider antiviral mechanisms, the effects of nanoparticles on coronaviruses and therapeutic approaches of nanoparticles. Finally, we provide our perspective on the future of nanoparticles in the fight against viral infections.

Polymer-guided assembly of inorganic nanoparticles

The self-assembly of inorganic nanoparticles is of great importance in realizing their enormous potentials for broad applications due to the advanced collective properties of nanoparticle ensembles. Various molecular ligands (e.g., small molecules, DNAs, proteins, and polymers) have been used to assist the organization of inorganic nanoparticles into functional structures at different hierarchical levels. Among others, polymers are particularly attractive for use in nanoparticle assembly, because of the complex architectures and rich functionalities of assembled structures enabled by polymers. Polymer-guided assembly of nanoparticles has emerged as a powerful route to fabricate functional materials with desired mechanical, optical, electronic or magnetic properties for a broad range of applications such as sensing, nanomedicine, catalysis, energy storage/conversion, data storage, electronics and photonics. In this review article, we summarize recent advances in the polymer-guided self-assembly of inorganic nanoparticles in both bulk thin films and solution, with an emphasis on the role of polymers in the assembly process and functions of resulting nanostructures. Precise control over the location/arrangement, interparticle interaction, and packing of inorganic nanoparticles at various scales are highlighted.

Uniaxial Deformation and Crazing in Glassy Polymer-Grafted Nanoparticle Ultrathin Films

The deformation behavior of neat, glassy polymer-grafted nanoparticle (PGN) monolayer films is studied using coarse-grained molecular dynamics simulations and experiments on polystyrene-grafted silica. In both the simulations and experiments, apparent crazing behavior is observed during deformation. The PGN systems show a relatively more uniform, perforated sheet craze structure and significantly higher strain at break than reference homopolymers of the same length. Short chain, unentangled PGN monolayers are also simulated for comparison; these are brittle and break apart without crazing. The entangled PGN simulations are analyzed in detail for systems at both high and moderate graft density. Stress-strain curves show three distinct regions: yielding and strain localization, craze widening, and strain hardening preceding catastrophic failure. The PGN stress-strain behavior appears more similar to that of longer chain, highly entangled homopolymer films than to the reference homopolymer films of the same length as the graft chains, suggesting that the particles effectively add additional entanglement points. The moderate graft density particles have higher strain-to-failure and maximum stress than the high graft density particles. We suggest this increased robustness for lower graft density systems is due to their increased interpenetration of graft chains between neighboring particles, which leads to increased interparticle entanglements per chain.

Effect of Polymer Chemistry on Chain Conformations in Hairy Nanoparticle Assemblies

Matrix-free, polymer-grafted nanoparticles, called hairy nanoparticle assemblies (aHNPs), have proven advantageous over traditional nanocomposites, as good dispersion and structural order can be achieved. Recent studies have shown that conformational changes in the polymer structure can lead to significant enhancements in the mechanical properties of aHNPs. To quantify how polymer chemistry affects the chain conformations in aHNPs, here we present a comparative analysis based on coarse-grained molecular dynamics simulations. Specifically, we compare the chain conformations in an anisotropic cellulose nanoparticle grafted to four common polymers with distinct chemical groups, fragility, and segmental structures, that is, poly(methyl methacrylate) (PMMA), polystyrene (PS), polycarbonate (PC), and polybutadiene (PB). We observe that semiflexible glassy polymers such as PMMA and PS have a higher critical chain length (N_cr), the transition point where the polymer conformation changes from concentrated to semidilute brush regime. Flexible rubbery polymers (PB) can overcome the N_cr barrier at relatively lower molecular weights. We have used theoretical scaling laws based on Daoud-Cotton theory to uncover a direct correlation between empirical constants and physical parameters, such as persistence length and monomer excluded volume. Furthermore, we carried out a systematic study to understand the role of backbone rigidity and side-group size of polymer, and it revealed that the backbone rigidity significantly affects N_cr but the side-group size doesn't seem to have an appreciable effect on N_cr. We find that normalization of the monomer radial distribution curves using N_cr and other key molecular parameters collapses the curves for 110 distinct model aHNP systems studied. Our work paves the way for systematic quantification of these molecular design parameters to accelerate the design of polymer-grafted nanoparticle assemblies in combination with universal scaling relationships.

Control of Dispersity and Grafting Density of Particle Brushes by Variation of ATRP Catalyst Concentration

Silica particles with grafted poly(methyl methacrylate) brushes, SiO₂-g-PMMA, were prepared via activator regeneration by electron transfer (ARGET) atom transfer radical polymerization (ATRP). The grafting density and dispersity of the polymer brushes was tuned by the initial ATRP catalyst concentration ([Cu^II/L]₀). Sparsely grafted particle brushes, which also displayed an anisotropic string-like structure in TEM images, were obtained at very low catalyst concentrations, [Cu^II/L]₀ < 1 ppm. The effect of the initial catalyst concentration on dispersity and initiation efficiency in the particle brush system was similar to that observed in the synthesis of linear PMMA homopolymers. The kinetic study revealed a transition from controlled radical polymerization to a less controlled process at low monomer conversion, when the [Cu^II/L]₀ decreased below about 10 ppm.

Disentangling the Role of Chain Conformation on the Mechanics of Polymer Tethered Particle Materials

The linear elastic properties of isotropic materials of polymer tethered nanoparticles (NPs) are evaluated using noncontact Brillouin light spectroscopy. While the mechanical properties of dense brush materials follow predicted trends with NP composition, a surprising increase in elastic moduli is observed in the case of sparsely grafted particle systems at approximately equal NP filling ratio. Complementary molecular dynamics simulations reveal that the stiffening is caused by the coil-like conformations of the grafted chains, which lead to stronger polymer-polymer interactions compared to densely grafted NPs with short chains. Our results point to novel opportunities to enhance the physical properties of composite materials by the strategic design of the "molecular architecture" of constituents to benefit from synergistic effects relating to the organization of the polymer component.

Polymers on nanoparticles: structure & dynamics

Grafting polymers to nanoparticle surfaces influences properties from the conformation of the polymer chains to the dispersion and assembly of nanoparticles within a polymeric material. Recently, a small body of work has begun to address the question of how grafting polymers to a nanoparticle surface impacts chain dynamics, and the resulting physical properties of a material. This Review discusses recent work that characterizes the structure and dynamics of polymers that are grafted to nanoparticles and opportunities for future research. Starting from the case of a single polymer chain attached to a nanoparticle core, this Review follows the structure of the chains as grafting density increases, and how this structure slows relaxation of polymer chains and affects macroscopic material properties.