Peter J. Lu

Gelation of particles with short-range attraction

Nanoscale or colloidal particles are important in many realms of science and technology. They can dramatically change the properties of materials, imparting solid-like behaviour to a wide variety of complex fluids. This behaviour arises when particles aggregate to form mesoscopic clusters and networks. The essential component leading to aggregation is an interparticle attraction, which can be generated by many physical and chemical mechanisms. In the limit of irreversible aggregation, infinitely strong interparticle bonds lead to diffusion-limited cluster aggregation (DLCA). This is understood as a purely kinetic phenomenon that can form solid-like gels at arbitrarily low particle volume fraction. Far more important technologically are systems with weaker attractions, where gel formation requires higher volume fractions. Numerous scenarios for gelation have been proposed, including DLCA, kinetic or dynamic arrest, phase separation, percolation and jamming. No consensus has emerged and, despite its ubiquity and significance, gelation is far from understood—even the location of the gelation phase boundary is not agreed on. Here we report experiments showing that gelation of spherical particles with isotropic, short-range attractions is initiated by spinodal decomposition; this thermodynamic instability triggers the formation of density fluctuations, leading to spanning clusters that dynamically arrest to create a gel. This simple picture of gelation does not depend on microscopic system-specific details, and should thus apply broadly to any particle system with short-range attractions. Our results suggest that gelation—often considered a purely kinetic phenomenon—is in fact a direct consequence of equilibrium liquid–gas phase separation. Without exception, we observe gelation in all of our samples predicted by theory and simulation to phase-separate; this suggests that it is phase separation, not percolation, that corresponds to gelation in models for attractive spheres.

Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture

The conventional view holds that girih (geometric star-and-polygon, or strapwork) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (“girih tiles”) decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West.

Gelation as arrested phase separation in short-ranged attractive colloid–polymer mixtures

We present further evidence that gelation is an arrested phase separation in attractive colloid–polymer mixtures, based on a method combining confocal microscopy experiments with numerical simulations recently established in Lu et al (2008 Nature 453 499). Our results are independent of the form of the interparticle attractive potential and therefore should apply broadly to any attractive particle system with short-ranged, isotropic attractions. We also give additional characterization of the gel states in terms of their structure, inhomogeneous character and local density. (Some figures in this article are in colour only in the electronic version)

Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal

Abstract Icosahedrite, ideally Al63Cu24Fe13, is a new mineral from the Khatyrka River, southeastern Chukhotka, Russia. It occurs as dark gray-black anhedral to subhedral grains up to 100 μm across, closely associated with spinel, diopside, forsterite, nepheline, sodalite, corundum, stishovite, khatyrkite, cupalite, and an unnamed phase of composition AlCuFe. Icosahedrite is opaque with a metallic luster, possesses a gray streak, and is brittle with an uneven fracture. The density could not be determined. For quasicrystals, by definition, the structure is not reducible to a single three-dimensional unit cell, so neither cell parameters nor Z can be given. In plane-polarized incident light, icosahedrite exhibits neither bireflectance nor pleochroism. Between crossed polars, it is isotropic. Reflectance percentages (Rmin = Rmax) for the four standard COM wavelengths are 62.3 (471.1 nm), 60.6 (548.3 nm), 58.1 (586.6 nm), and 56.0 (652.3 nm), respectively. The X-ray powder pattern was indexed on the basis of six integer indices, as conventionally used with quasicrystals, where the lattice parameter (in six-dimensional notation) is measured to be a6D = 12.64 Å, with probable space group Fm3 5̄̄. The four strongest X-ray powder-diffraction lines [d in Å (I/I0) (n1,n2,n3,n4,n5,n6)] are: 2.006 (100) (420 042), 2.108 (90) (422̄ 2̄22), 1.238 (30) (604̄ 064), and 3.41 (25) (311̄ 1̄11). Average results of 34 electron-microprobe analyses gave, on the basis of total atoms = 100, the formula Al63.11Cu24.02Fe12.78Si0.03Co0.01Ca0.01Zn0.01Cr0.02Cl0.01. The simplified formula is Al63Cu24Fe13, which requires the mass fractions Al 43.02, Cu 38.60, Fe 18.38, total 100.00 wt%. The new mineral is named for the icosahedral symmetry of its internal atomic structure, as observed in its diffraction pattern. Both the new mineral and mineral name have been approved by the Commission on New Minerals, Nomenclature and Classification, IMA (2010-042).

Enthalpies of formation of lanthanide oxyapatite phases

A family of lanthanide silicates adopts an oxyapatite-like structure with structural formula Ln9.33∎0.67(SiO4)6O2 (Ln 4 La, Sm, Nd, Gd, ∎ = vacancy). The enthalpies of solution, DHS, for these materials and their corresponding binary oxides were determined by high-temperature oxide melt solution calorimetry using molten 2PbO·B2O3 at 1078 K. These data were used to complete thermodynamic cycles to calculate enthalpies of formation from the oxides, ΔHs f-oxides (kJ/mol): La9.33∎0.67(SiO4)6O2 = −776.3 ± 17.9, Nd9.33∎0.67(SiO4)6O2 = −760.4 ± 31.9, Sm9.33∎0.67(SiO4)6O2 = −590.3 ± 18.6, and Gd9.33∎0.67(SiO4)6O2 = −446.9 ± 21.9. Reference data were used to calculate the standard enthalpies of formation from the elements, ΔH0 f (kJ/mol): La9.33∎0.67(SiO4)6O2 = −14611.0 ± 19.4, Nd9.33∎0.67(SiO4)6O2 = −14661.5 ± 32.2, Sm9.33∎0.67(SiO4)6O2 = −14561.7 ± 20.8, and Gd9.33∎0.67(SiO4)6O2 = −14402.7 ± 28.2. The formation enthalpies become more endothermic as the ionic radius of the lanthanide ion decreases.

Identifying and indexing icosahedral quasicrystals from powder diffraction patterns.

We present a scheme to identify quasicrystals based on powder diffraction data and to provide a standardized indexing. We apply our scheme to a large catalog of powder diffraction patterns, including natural minerals, to look for new quasicrystals. Based on our tests, we have found promising candidates worthy of further exploration.

High dynamic range optical projection tomography (HDR-OPT)

Traditional optical projection tomography (OPT) acquires a single image at each rotation angle, thereby suffering from limitations in CCD dynamic range; this conventional usage cannot resolve features in samples with highly heterogeneous absorption, such as in small animals with organs of varying size. We present a novel technique, applying multiple-exposure high dynamic range (HDR) imaging to OPT, and demonstrate its ability to resolve fine details in zebrafish embryos, without complicated chemical clearing. We implement the tomographic reconstruction algorithm on the GPU, yielding a performance increase of two orders of magnitude. These features give our method potential application in high-throughput, high-resolution in vivo 3D imaging.

Orders-of-magnitude performance increases in GPU-accelerated correlation of images from the International Space Station

We implement image correlation, a fundamental component of many real-time imaging and tracking systems, on a graphics processing unit (GPU) using NVIDIA’s CUDA platform. We use our code to analyze images of liquid-gas phase separation in a model colloid-polymer system, photographed in the absence of gravity aboard the International Space Station (ISS). Our GPU code is 4,000 times faster than simple MATLAB code performing the same calculation on a central processing unit (CPU), 130 times faster than simple C code, and 30 times faster than optimized C++ code using single-instruction, multiple-data (SIMD) extensions. The speed increases from these parallel algorithms enable us to analyze images downlinked from the ISS in a rapid fashion and send feedback to astronauts on orbit while the experiments are still being run.

Drying of Complex Suspensions

We investigate the 3D structure and drying dynamics of complex mixtures of emulsion droplets and colloidal particles, using confocal microscopy. Air invades and rapidly collapses large emulsion droplets, forcing their contents into the surrounding porous particle pack at a rate proportional to the square of the droplet radius. By contrast, small droplets do not collapse, but remain intact and are merely deformed. A simple model coupling the Laplace pressure to Darcys law correctly estimates both the threshold radius separating these two behaviors, and the rate of large-droplet evacuation. Finally, we use these systems to make novel hierarchical structures.

Locating Particles Accurately in Microscope Images Requires Image-Processing Kernels to be Rotationally Symmetric

Computerized image-analysis routines deployed widely to locate and track the positions of particles in microscope images include several steps where images are convolved with kernels to remove noise. In many common implementations, some kernels are rotationally asymmetric. Here we show that the use of these asymmetric kernels creates significant artifacts, distorting apparent particle positions in a way that gives the artificial appearance of orientational crystalline order, even in such fully-disordered isotropic systems as simple fluids of hard-sphere-like colloids. We rectify this problem by replacing all asymmetric kernels with rotationally-symmetric kernels, which does not impact code performance. We show that these corrected codes locate particle positions properly, restoring measured isotropy to colloidal fluids. We also investigate rapidly-formed colloidal sediments, and with the corrected codes show that these sediments, often thought to be amorphous, may exhibit strong orientational correlations among bonds between neighboring colloidal particles.