Steve Granick

Janus Particle Synthesis, Assembly, and Application

Janus particles are colloidal particles with more than a single type of surface chemistry or composition, ranging in size from hundreds of nanometers to a few micrometers. Like traditional colloids, they are large enough to be observed under optical microscopy in real time and small enough to diffuse by Brownian motion, but their interesting and useful new properties of directional interaction bring new research opportunities to the fields of soft matter and fundamental materials research as well as to applications in other disciplines and in technologies such as electronic paper and other multiphase engineering. In this review, a variety of methods that have been used to synthesize Janus particles are introduced. Following this, we summarize the use of Janus particles as basic units that assemble into novel structures and tune important material properties. The concluding sections highlight some of the technological applications, including recent progress in using Janus particles as microprobes, micromotors, electronic paper, and solid surfactants.

Effective temperature concept evaluated in an active colloid mixture

Significance In the long-standing debate on whether the insights of statistical thermodynamics could apply to nonequilibrium systems, a key unsolved problem is whether it is useful to postulate an emergent effective temperature, different from the thermal temperature. Here, we introduce a two-component system of driven Janus colloids such that collisions induced by external energy sources play the role of temperature. We find that this nonequilibrium system quantitatively behaves as if at equilibrium, with collisions caused by differential rhythmic motion between the two components acting as a strict analog to thermal motion. We demonstrate that the effective temperature can serve as a common control parameter for both kinetics and phase behavior. Thermal energy agitates all matter, and its competition with ordering tendencies is a fundamental organizing principle in the physical world; this observation suggests that an effective temperature might emerge when external energy input enhances agitation. However, despite the repeated proposal of this concept based on kinetics for various nonequilibrium systems, the value of an effective temperature as a thermodynamic control parameter has been unclear. Here, we introduce a two-component system of driven Janus colloids, such that collisions induced by external energy sources agitate the system, and we demonstrate quantitative agreement with hallmarks of statistical thermodynamics for binary phase behavior: the archetypal phase diagram with equilibrium critical exponents, Gaussian displacement distributions, and even capillarity. The significance is to demonstrate a class of dynamical conditions under which thermodynamic analysis extends quantitatively to systems that are decidedly nonequilibrium except that the effective temperature differs from the physical temperature.

Giant capsids from lattice self-assembly of cyclodextrin complexes

Proteins can readily assemble into rigid, crystalline and functional structures such as viral capsids and bacterial compartments. Despite ongoing advances, it is still a fundamental challenge to design and synthesize protein-mimetic molecules to form crystalline structures. Here we report the lattice self-assembly of cyclodextrin complexes into a variety of capsid-like structures such as lamellae, helical tubes and hollow rhombic dodecahedra. The dodecahedral morphology has not hitherto been observed in self-assembly systems. The tubes can spontaneously encapsulate colloidal particles and liposomes. The dodecahedra and tubes are respectively comparable to and much larger than the largest known virus. In particular, the resemblance to protein assemblies is not limited to morphology but extends to structural rigidity and crystallinity—a well-defined, 2D rhombic lattice of molecular arrangement is strikingly universal for all the observed structures. We propose a simple design rule for the current lattice self-assembly, potentially opening doors for new protein-mimetic materials.

Dynamic cross-correlations between entangled biofilaments as they diffuse

Significance Highly entangled biofilaments are ubiquitous in the cytoskeleton and present a paradigm in polymer physics and biophysics. Here, rather than conventionally seeking to understand the self-diffusion of a single tagged entangled polymer we inquire into dynamic cross-correlations between nearby filaments as they diffuse anisotropically in aqueous solution. Our combined fluorescence tracking experiments and statistical mechanical modeling show that the continuum limit is reached only at distances beyond the filament length, in this system beyond the large distance of ≈15 µm. This noncontinuum behavior at micron-scale distance may be related to the “crowding” problem in biological function. Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 104 times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales.

Real-Space, in Situ Maps of Hydrogel Pores

We characterize the porosity of hydrogels by imaging the displacement trajectories of embedded tracer particles. This offers the possibility of characterizing the size and projected shape of individual pores as well as direct, real-space maps of heterogeneous porosity and its distribution. The scheme shows that when fluorescent spherical particles treated to avoid specific adsorption are loaded into the gel, their displacement trajectories from Brownian motion report on the size and projected shape in which the pore resides, convoluted by the particle size. Of special interest is how pores and their distribution respond to stimuli. These ideas are validated in agarose gels loaded with latex particles stabilized by adsorbed bovine serum albumin. Gels heated from room temperature produced an increasingly more monodisperse pore size distribution because increasing temperature preferentially enlarges smaller pores, but this was irreversible upon cooling, and shearing agarose gels beyond the yield point destroyed larger pores preferably. The method is considered to be generalizable beyond the agarose system presented here as proof of concept.

How to better focus waves by considering symmetry and information loss

Significance With applications from electromagnetic communications, to biological and astronomical imaging, to lithography and warfare, waves transmit information, and optimal wave focusing is essential. Here we demonstrate the need to amend the belief that spherical or cylindrical wavefronts necessarily focus at their center of curvature. Instead the effective focus shifts toward the source with decreasing apertures, producing astigmatism when, as increasingly shown for modern applications, the wavefronts are not axially symmetric. This leads to significant degradation of axial resolution in nonaxisymmetric light-focusing applications. These conclusions, derived from diffraction theory and validated by application to optical bioimaging, offer a general strategy to likewise improve the resolution of virtually any other wave-based application whose efficacy depends on focusing energy to points or lines. We amend the general belief that waves with extended spherical wavefront focus at their center of curvature. Instead, when the spherical symmetry of waves is broken by propagating them through a finite aperture along an average direction, the forward/backward symmetry is broken and the focal volume shifts its center backward along that direction. The extent of this focal shift increases as smaller apertures are used, up to the point that the nominal focal plane is out of focus. Furthermore, the loss of axial symmetry with noncircular apertures causes distinct focal shifts in distinct axial planes, and the resulting astigmatism possibly degrades the axial focusing resolution. Using experiments and simulations, focal shift with noncircular apertures is described for classical and temporal focusing. The usefulness of these conclusions to improve imaging resolution is demonstrated in a high-resolution optical microscopy application, namely line-temporal focusing microscopy. These conclusions follow from fundamental symmetries of the wave geometry and matter for an increasing number of emerging optical techniques. This work offers a general framework and strategy to understand and improve virtually any wave-based application whose efficacy depends on optimal focusing and may be helpful when information is transmitted by waves in applications from electromagnetic communications, to biological and astronomical imaging, to lithography and even warfare.

Enzyme leaps fuel antichemotaxis

Significance Challenging the traditional view that enzyme kinetics are only a matter of catalyzing chemical reactions, there is mounting evidence that the enzyme catalysis enhances enzyme mobility. This is significant to programming spatio-temporal patterns of molecular response to chemical stimulus, which is common to living matter as well as to significant chemical technology. This paper shows that the enhanced diffusivity of enzymes is a “run-and-tumble” process analogous to that performed by swimming microorganisms, executed in this situation by molecules that lack the decision-making machinery of microorganisms. The result is that enzymes display “antichemotaxis” when they turn over substrate; they migrate in the direction of lesser reactant concentration. There is mounting evidence that enzyme diffusivity is enhanced when the enzyme is catalytically active. Here, using superresolution microscopy [stimulated emission-depletion fluorescence correlation spectroscopy (STED-FCS)], we show that active enzymes migrate spontaneously in the direction of lower substrate concentration (“antichemotaxis”) by a process analogous to the run-and-tumble foraging strategy of swimming microorganisms and our theory quantifies the mechanism. The two enzymes studied, urease and acetylcholinesterase, display two families of transit times through subdiffraction-sized focus spots, a diffusive mode and a ballistic mode, and the latter transit time is close to the inverse rate of catalytic turnover. This biochemical information-processing algorithm may be useful to design synthetic self-propelled swimmers and nanoparticles relevant to active materials. Executed by molecules lacking the decision-making circuitry of microorganisms, antichemotaxis by this run-and-tumble process offers the biological function to homogenize product concentration, which could be significant in situations when the reactant concentration varies from spot to spot.

DNA molecules deviate from shortest trajectory when driven through hydrogel

Dynamic fluorescence-based single-molecule imaging of λ-DNA molecules driven through agarose hydrogels by DC electric fields reveals that passage through the hydrogel (98.5% water content) induces mobility orthogonal to the external field. Tortuous paths followed by the DNA molecules, which are heavily entangled in the hydrogel mesh as their contour length is nearly 100 times the hydrogel mesh size of 200 nm, cause them to appear to diffuse orthogonal to the driving force. The higher the driving field, from 2 to 16 V/cm, the higher the off-axis dispersion is, over the same time interval. We measure the off-axis displacement distribution over 3 orders of magnitude of probability density and find a master curve after normalizing for time (t) elapsed, but the power of time for normalizing increases with the external field, from t0.25 to t0.6 with increasing field. Comparing trajectories over the same distance traveled in the electric field direction, we observe whereas for the highest field strengths DNA molecules come closest to taking the shortest trajectory between two points in space, deviations from the shortest trajectory grow larger and larger (up to 40% larger) as one approaches the case of small yet finite external field strength.

Longer-Lasting Electron-Based Microscopy of Single Molecules in Aqueous Medium

Use of electron-based microscopy in aqueous media has been held back because aqueous samples tend to suffer from water radiolysis and other chemical degradation caused by the high energy of incident electrons. Here we show that aqueous liquid pockets in graphene liquid cells at room temperature display significantly improved stability when using deuterated water, D2O. Reporting transmission electron microscopy (TEM) experiments based on common imaging conditions, we conclude that use of D2O outperforms adding radical scavengers to H2O regardless of imaging details; it increases the lifetime of dissolved organic macromolecules by a factor of 2-5, and it delays by even longer the appearance of radiolysis-induced bubbles, by a factor of time up to 10. We quantify statistically the consequences of minimizing the electron voltage and dose and conclude that the D2O environment increases sample longevity without noticeable sacrifice of contrast that is critical for direct imaging of weakly scattering organic macromolecules and biomolecules.

Liquid-Cell Electron Microscopy of Adsorbed Polymers

Individual macromolecules of polystyrene sulfonate and poly(ethylene oxide) are visualized with nanometer resolution using transmission electron microscopy (TEM) imaging of aqueous solutions with and without added salt, trapped in liquid pockets between creased graphene sheets. Successful imaging with 0.3 s per frame is enabled by the sluggish mobility of the adsorbed molecules. This study finds, validating others, that an advantage of this graphene liquid-cell approach is apparently to retard sample degradation from incident electrons, in addition to minimizing background scattering because graphene windows are atomically thin. Its new application here to polymers devoid of metal-ion labeling allows the projected sizes and conformational fluctuations of adsorbed molecules and adsorption-desorption events to be analyzed. Confirming the identification of the observed objects, this study reports statistical analysis of datasets of hundreds of images for times up to 100 s, with variation of the chemical makeup of the polymer, the molecular weight of the polymer, and the salt concentration. This observation of discrete polymer molecules in solution environment may be useful generally, as the findings are obtained using an ordinary TEM microscope, whose kind is available to many researchers routinely.