A mean-field phase diagram for conformationally symmetric diblock melts using the standard Gaussian polymer model is presented. Our calculation, which traverses the weak- to strong-segregation regimes, is free of traditional approximations. Regions of stability are determined for disordered (DIS) melts and for ordered structures including lamellae (L), hexagonally packed cylinders (H), body-centered cubic spheres (QIm3m), close-packed spheres (CPS), and the bicontinuous cubic network with Ia3d symmetry (QIa3d). The CPS phase exists in narrow regions along the order−disorder transition for χN ≥ 17.67. Results suggest that the QIa3d phase is not stable above χN ∼ 60. Along the L/QIa3d phase boundaries, a hexagonally perforated lamellar (HPL) phase is found to be nearly stable. Our results for the bicontinuous Pn3m cubic (QPn3m) phase, known as the OBDD, indicate that it is an unstable structure in diblock melts. Earlier approximation schemes used to examine mean-field behavior are reviewed, and compa...

Unifying Weak- and Strong-Segregation Block Copolymer Theories

This article describes hybrid materials and systems in which the core integrity of inorganic nanobuilding blocks (NBBs) is preserved and reviews the main synthetic procedures presented in the literature. The relation between the NBB and the resulting hybrid networks is discussed for several striking examples:  silicon and tin oxo clusters, polyoxometalates, and transition metal−oxo-based clusters. This approach is extended to nanoparticule-based hybrids. The chemical strategies offered by the coupling of soft chemistry processes and this approach based on functional NBBs allows, through an intelligent and tuned coding, to develop a new vectorial chemistry that is able to direct the assembly of a large variety of structurally well-defined clusters or nanoparticles into complex architectures.

Designed Hybrid Organic−Inorganic Nanocomposites from Functional Nanobuilding Blocks

Methods to pattern substrates with dense periodic nanostructures that combine top-down lithographic tools and self-assembling block copolymer materials are provided. According to various embodiments, the methods involve chemically patterning a substrate, depositing a block copolymer film on the chemically patterned imaging layer, and allowing the block copolymer to self-assemble in the presence of the chemically patterned substrate, thereby producing a pattern in the block copolymer film that is improved over the substrate pattern in terms feature size, shape, and uniformity, as well as regular spacing between arrays of features and between the features within each array compared to the substrate pattern. In certain embodiments, the density and total number of pattern features in the block copolymer film is also increased. High density and quality nanoimprint templates and other nanopatterned structures are also provided.

https://science.sciencemag.org/content/sci/321/5891/936.full.pdf

Density multiplication and improved lithography by directed block copolymer assembly

Nanostructures have attracted huge interest as a rapidly growing class of materials for many applications. Several techniques have been used to characterize the size, crystal structure, elemental composition and a variety of other physical properties of nanoparticles. In several cases, there are physical properties that can be evaluated by more than one technique. Different strengths and limitations of each technique complicate the choice of the most suitable method, while often a combinatorial characterization approach is needed. In addition, given that the significance of nanoparticles in basic research and applications is constantly increasing, it is necessary that researchers from separate fields overcome the challenges in the reproducible and reliable characterization of nanomaterials, after their synthesis and further process (e.g. annealing) stages. The principal objective of this review is to summarize the present knowledge on the use, advances, advantages and weaknesses of a large number of experimental techniques that are available for the characterization of nanoparticles. Different characterization techniques are classified according to the concept/group of the technique used, the information they can provide, or the materials that they are destined for. We describe the main characteristics of the techniques and their operation principles and we give various examples of their use, presenting them in a comparative mode, when possible, in relation to the property studied in each case.

/pdf/characterization-techniques-for-nanoparticles-comparison-and-2ubze3ehrc.pdf

Characterization techniques for nanoparticles: comparison and complementarity upon studying nanoparticle properties

X-ray scattering is a structural characterization tool that has impacted diverse fields of study. It is unique in its ability to examine materials in real time and under realistic sample environments, enabling researchers to understand morphology at nanometer and angstrom length scales using complementary small and wide angle X-ray scattering (SAXS, WAXS), respectively. Herein, we focus on the use of SAXS to examine nanoscale particulate systems. We provide a theoretical foundation for X-ray scattering, considering both form factor and structure factor, as well as the use of correlation functions, which may be used to determine a particle’s size, size distribution, shape, and organization into hierarchical structures. The theory is expanded upon with contemporary use cases. Both transmission and reflection (grazing incidence) geometries are addressed, as well as the combination of SAXS with other X-ray and non-X-ray characterization tools. We conclude with an examination of several key areas of research w...

Small Angle X-ray Scattering for Nanoparticle Research

High-temperature-resolution small-angle X-ray scattering (SAXS) experiments were performed to elucidate the order-disorder transition at temperature T (T ODT ) and the crossover from the disordered state characterized by the Brazovskii-type non-mean-field theory to the disordered state characterized by the Leibler mean-field theory at T (T MF ) for low molecular weight polystyrene-block-polyisoprene copolymers having about equal block molecular weights. Across T ODT , the inverse peak scattered intensity I m -1 and the peak width σ q clearly show a very sharp discontinuity, but the characteristic length D of the concentration fluctuations shows almost no change. The second-order scattering maximum existing below T ODT definitely disappears above T ODT , indicating that the spatial concentration fluctuation profile changes from a square-wave-type to a sinusoidal-wave-type profile upon increasing T through T ODT . The crossover temperature T MF is clearly identified from the changes in the temperature dependencies of I m -1 , σ q 2 , and D with T : ∂I m -1 /∂(1/T), ∂σ q 2 /∂(1/T), and ∂D/∂(1/T)all show a discontinuity at the same temperature T MF . The temperature dependence D at T > T MF is explained by that of the radius of gyration R g0 of the unperturbed block copolymer chains, while that at T < T MF is much greater than that of R g0 .

Order-Disorder Transition of Low Molecular Weight Polystyrene-block-Polyisoprene. 1. SAXS Analysis of Two Characteristic Temperatures

Low molecular weight polystyrene-block-polyisoprene (SI diblock) copolymers having a wide range of compositions were synthesized via anionic polymerization, and the order-disorder transition temperatures (T ODT ) of the block copolymers were determined using dynamic viscoelastic measurements. We have shown that logarithmic plots of dynamic storage modulus (G') versus dynamic loss modulus (G) are very effective to determine the T ODT S of the block copolymers. The experimentally determined T ODT S are compared with the predictions made from currently held theories. We point out that the reliability of the predicted T ODT of a block copolymer depends, among many factors, on the accuracy of the expression for the Flory-Huggins interaction parameter X. We observed that the SI diblock copolymers having a low volume fraction of polystyrene or polyisoprene block (e.g., less than about 0.2) exhibited liquidlike rheological behavior at temperatures below their T ODT S, for instance at temperatures as low as about 30°C below the T ODT . We attribute this observation to the existence of defects in the long-range spatial order of microdomains (grain-boundary defects) which are continuous in three-dimensional space. Using the Onuki analysis that the extent of composition fluctuations of a block copolymer near the critical temperature, at a given temperature difference AT = T - T c from the critical temperature T c , is determined very much by the temperature dependence of the Flory-Huggins interaction parameter x, we have shown that the extent of composition fluctuations for SI diblock copolymers in the disordered state near the critical temperature is very small. Specifically, we have shown that for the same extent of composition fluctuations e, defined by e = 2 (1 - X/X c ), where X c is the value of X at the critical point, a temperature difference ΔT of 1°C for an SI diblock copolymer corresponds to ca. 20°C for a 1,2-polybutadiene-block-1,4-polybutadiene copolymer. This difference in AT between the two block copolymer systems is attributed to the difference in the temperature coefficient B appearing in the expression, X = A + B/T. Using the Onuki analysis, we have shown further that the extent of composition fluctuations in the disordered state near the critical temperature varies little with block copolymer composition.

Effect of Volume Fraction on the Order-Disorder Transition in Low Molecular Weight Polystyrene-block-Polyisoprene Copolymers. 1. Order-Disorder Transition Temperature Determined by Rheological Measurements

We investigated the order−order transition (OOT) and the order−disorder transition (ODT) in a polystyrene-block-polyisoprene-block-polystyrene copolymer (Vector 4111, Dexco Polymers Co.), which has a weight-average molecular weight of 1.4 × 105 and a 0.183 weight fraction of polystyrene (PS) blocks, using small-angle X-ray scattering (SAXS) and rheological measurements. Specifically, SAXS experiments reveal that Vector 4111 undergoes an OOT at 179−185 °C with (i) hexagonally-packed cylindrical microdomains of PS at T ≤ 179 °C, (ii) the coexistence of cylindrical and spherical microdomains of PS at 180 °C ≤ T ≤ 185 °C, and (iii) spherical microdomains of PS in a cubic lattice at 185 °C < T ≤ 210 °C, and (iv) the cubic lattice of the spheres is distorted with a further increase of temperature so that the lattice disordering transition occurs at temperatures between 210 (onset) and 214 °C (completion) and the spherical microdomain structure of PS with a liquidlike short-range order persists even up to 220 °C...

Order−Order and Order−Disorder Transitions in a Polystyrene-block-Polyisoprene-block-Polystyrene Copolymer

Incorporation of Metal Nanoparticles into Block Copolymer Nanodomains via in-Situ Reduction of Metal Ions in Microdomain Space

We have investigated the ordering dynamics of a triblock copolymer of a polystyrene-block-polyisoprene-block-polystyrene with asymmetric composition from the disordered sphere phase, where spherical microdomains exist but they have only a short-range liquidlike order, to the cylindrical and spherical microdomains with a long-range order. The ordering process was explored in situ by time-resolved small-angle X-ray scattering (SAXS), and the microdomain structures during the ordering process were observed by transmission electron microscopy (TEM) on specimens frozen at particular times in the ordering process. The SAXS observations show that there is an incubation period before the formation of the cylindrical and spherical microdomains with a long-range order. The coexistence of the ordered grains and the disordered spheres was observed in the TEM pictures taken during the ordering of both cylinders and spheres. The coexistence of the ordered grains and disordered spheres together with the existence of the...

Ordering Dynamics of Cylindrical and Spherical Microdomains in Polystyrene-block-Polyisoprene-block-Polystyrene. 1. SAXS and TEM Observations for the Grain Formation

Naoki Sakamoto

Papers

Order-Disorder Transition of Low Molecular Weight Polystyrene-block-Polyisoprene. 1. SAXS Analysis of Two Characteristic Temperatures

Effect of Volume Fraction on the Order-Disorder Transition in Low Molecular Weight Polystyrene-block-Polyisoprene Copolymers. 1. Order-Disorder Transition Temperature Determined by Rheological Measurements

Order−Order and Order−Disorder Transitions in a Polystyrene-block-Polyisoprene-block-Polystyrene Copolymer

Incorporation of Metal Nanoparticles into Block Copolymer Nanodomains via in-Situ Reduction of Metal Ions in Microdomain Space

Ordering Dynamics of Cylindrical and Spherical Microdomains in Polystyrene-block-Polyisoprene-block-Polystyrene. 1. SAXS and TEM Observations for the Grain Formation