Seth Fraden

Structure of electrorheological fluids

Specially synthesized silica colloidal spheres with fluorescent cores were used as model electrorheological fluids to experimentally explore structure formation and evolution under conditions of no shear. Using confocal scanning laser microscopy we measured the location of each colloid in three dimensions. We observed an equilibrium body-centered tetragonal phase and several nonequilibrium structures such as sheet-like labyrinths and isolated chains of colloids. The formation of nonequilibrium structures was studied as a function of the volume fraction, electric field strength, and starting configuration of the colloid. We compare our observations to previous experiments, simulations, and calculations.

What Is the Origin of Chirality in the Cholesteric Phase of Virus Suspensions

We report a study of the cholesteric phase in monodisperse suspensions of the rodlike virus fd sterically stabilized with the polymer polyethylene glycol (PEG). After coating the virus with neutral polymers, the phase diagram and nematic order parameter of the fd-PEG system then become independent of ionic strength. Surprisingly, the fd-PEG suspensions not only continue to exhibit a cholesteric phase, which means that the grafted polymer does not screen all chiral interactions between rods, but paradoxically the cholesteric pitch of this sterically stabilized fd-PEG system varies with ionic strength. Furthermore, we observe that the cholesteric pitch decreases with increasing viral contour length, in contrast to theories which predict the opposite trend. Different models of the origin of chirality in colloidal liquid crystals are discussed.

Testing Turing’s theory of morphogenesis in chemical cells

Significance Turing proposed that intercellular reaction-diffusion of molecules is responsible for morphogenesis. The impact of this paradigm has been profound. We exploit an abiological experimental system of emulsion drops containing the Belousov–Zhabotinsky reactants ideally suited to test Turing’s theory. Our experiments verify Turing’s thesis of the chemical basis of morphogenesis and reveal a pattern, not previously predicted by theory, which we explain by extending Turing’s model to include heterogeneity. Quantitative experimental results obtained using this artificial cellular system establish the strengths and weaknesses of the Turing model, applicable to biology and materials science alike, and pinpoint which directions are required for improvement. Alan Turing, in “The Chemical Basis of Morphogenesis” [Turing AM (1952) Philos Trans R Soc Lond 237(641):37–72], described how, in circular arrays of identical biological cells, diffusion can interact with chemical reactions to generate up to six periodic spatiotemporal chemical structures. Turing proposed that one of these structures, a stationary pattern with a chemically determined wavelength, is responsible for differentiation. We quantitatively test Turing’s ideas in a cellular chemical system consisting of an emulsion of aqueous droplets containing the Belousov–Zhabotinsky oscillatory chemical reactants, dispersed in oil, and demonstrate that reaction-diffusion processes lead to chemical differentiation, which drives physical morphogenesis in chemical cells. We observe five of the six structures predicted by Turing. In 2D hexagonal arrays, a seventh structure emerges, incompatible with Turing’s original model, which we explain by modifying the theory to include heterogeneity.

Development of model colloidal liquid crystals and the kinetics of the isotropic–smectic transition

We have prepared a homologous series of filamentous viruses with varying contour length using molecular cloning techniques. These viruses are monodisperse enough to form a stable smectic phase. Two systems are studied. The first system consists of viruses to the surfaces of which the polymers are covalently bound. Through studies of the isotropic–cholesteric phase transition we demonstrate that covalently attached polymers alter the effective diameter of the virus. Additionally, we have produced mixtures of viruses whose ratio of effective diameters varies by a factor of five. The second system is composed of mixtures of rod–like viruses and non–absorbing Gaussian polymers. With this system we study the kinetics of the isotropic–smectic phase transition and describe observations of a number of novel metastable structures of unexpected complexity.

Enhanced stability of layered phases in parallel hard spherocylinders due to addition of hard spheres

There is increasing evidence that entropy can induce microphase separation in binary fluid mixtures interacting through hard particle potentials. One such phase consists of alternating two-dimensional liquidlike layers of rods and spheres. We study the transition from a uniform miscible state to this ordered state using computer simulations, and compare results to experiments and theory. We conclude the following: (1) There is stable entropy driven microphase separation in mixtures of parallel rods and spheres. (2) Adding spheres smaller than the rod length decreases the total volume fraction needed for the formation of a layered phase, and therefore small spheres effectively stabilize the layered phase; the opposite is true for large spheres. (3) The degree of this stabilization increases with increasing rod length.

Isotropic-nematic phase transition in suspensions of filamentous virus and the neutral polymer Dextran

We present an experimental study of the isotropic-nematic phase transition in an aqueous mixture of charged semiflexible rods ( fd virus) and neutral polymer (Dextran). A complete phase diagram is measured as a function of ionic strength and polymer molecular weight. At high ionic strength we find that adding polymer widens the isotropic-nematic coexistence region with polymers preferentially partitioning into the isotropic phase, while at low ionic strength the added polymer has no effect on the phase transition. The nematic order parameter is determined from birefringence measurements and is found to be independent of polymer concentration (or equivalently the strength of attraction). The experimental results are compared with the existing theoretical predictions for the isotropic-nematic transition in rods with attractive interactions.

Isotropic-cholesteric phase transition in colloidal suspensions of filamentous bacteriophage fd

Abstract The co-existence concentrations of the isotropic and cholesteric liquid crystalline phases of the semi-flexible rod-like virus fd in aqueous suspension were measured as a function of ionic strength at room temperature. At several ionic strengths the magnetic-field-induced birefringence, which is proportional to the number of particles in a correlation volume N corr, was measured for fd concentrations spanning the entire isotropic region. From this data the limiting concentration of stability (spinodal) of the isotropic phase, ρ*, was obtained. The co-existence concentrations and ρ* versus ionic strength compare well with predictions based on the theory of Khokhlov and Semenov, modified to include the effects of charge. A theoretical expression for the magnetic birefringence of persistent polymers was derived and agreed well with the data with the exception that N corr at the isotropic to liquid crystal transition was smaller than predicted.

Light Scattering and Phase Behavior of Lysozyme-Poly(Ethylene Glycol) Mixtures

Measurements of liquid-liquid phase transition temperatures (cloud points) of mixtures of a protein (lysozyme) and a polymer, poly(ethylene glycol) (PEG) show that the addition of low molecular weight PEG stabilizes the mixture whereas high molecular weight PEG was destabilizing. We demonstrate that this behavior is inconsistent with an entropic lysozyme-PEG depletion interaction and suggest that an energetic lysozyme-PEG attraction is responsible. In order to independently characterize the lysozyme-PEG interactions, light scattering experiments on the same mixtures were performed to measure second and third virial coefficients. These measurements indicate that PEG induces repulsion between lysozyme molecules, contrary to the depletion prediction. Furthermore, it is shown that third virial terms must be included in the mixtures free energy in order to qualitatively capture our data.

Measuring the nematic order of suspensions of colloidal fd virus by x-ray diffraction and optical birefringence

The orientational distribution function of the nematic phase of the semi-flexible rod-like virus fd is measured by x-ray diffraction as a function of concentration and ionic strength. The angular distribution of the scattered intensity from a single-domain nematic phase of fd arises from only the single particle orientational distribution function at high angle but it also includes spatial and orientational correlations at low angle. Experimental measurements of the orientational distribution function from both the interparticle and intraparticle scattering were made to test whether the correlations present in interparticle scatter influence the measurement of the single particle orientational distribution function. It was found that the two types of scatter yield consistent values for the nematic order parameter. It was also found that x-ray diffraction is insensitive to the orientational distribution functions precise form, and the measured angular intensity distribution is described equally well by both Onsagers trial function and a Gaussian. At high ionic strength the order parameter S of the nematic phase coexisting with the isotropic phase approaches theoretical predictions for long semi-flexible rods S=0.55, but deviations from theory increase with decreasing ionic strength. The concentration dependence of the nematic order parameter was also found to better agree with theoretical predictions at high ionic strength, indicating that electrostatic interactions have a measurable effect on the nematic order parameter. The measured x-ray order parameters are also shown to be proportional to the measured birefringence and the saturation birefringence of fd is measured, enabling a simple, inexpensive way to measure the order parameter.

Isotropic-cholesteric phase transition of filamentous virus suspensions as a function of rod length and charge

The viruses studied are genetically engineered, charged, semiflexible filamentous bacteriophages that are structurally identical to M13 virus, but differ either in contour length or surface charge. While varying contour length (L) we assume the persistence length (P) remains constant, and thus we alter the rod flexibility (L/P) . Surface charge is altered both by changing solution pH and by comparing two viruses, fd and M13, which differ only by the substitution of one charged for one neutral amino acid per virus coat protein. We measure both the isotropic and cholesteric coexistence concentrations as well as the nematic order parameter after unwinding the cholesteric phase in a magnetic field as a function of rod surface charge, rod length, solution ionic strength, and solution pH . The isotropic-cholesteric transition experimental results agree semiquantitatively with theoretical predictions for semiflexible, charged rods at high ionic strength, but disagree at low ionic strength.