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ABSTRACT: Using videomicroscopy imaging, we demonstrate the existence of a short-ranged equilibrium attraction between heavy silica colloids diffusing on soft surfaces of cross-linked polymer gels. The intercolloid potential can be tuned by changing the gel stiffness or by coating the colloids with a polymer layer. On sufficiently soft substrates, the interaction induced by the polymer matrix leads to large-scale colloidal aggregation. We correlate the in-plane interaction with a colloid-surface attraction.
Physical Review Letters 09/2011; 107(13):136101. · 7.37 Impact Factor
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ABSTRACT: We describe a microfluidic device for mapping phase diagrams of aqueous samples as a function of concentration and temperature. This double-layer (poly)dimethylsiloxane (PDMS) device contains a storage layer, in which hundreds of nanolitre sized aqueous droplets can be simultaneously formed and stored. A second layer, separated by a thin, water-permeable PDMS-membrane contains twelve reservoir channels filled with different salt solutions. When there is a difference between the concentrations of salt in the reservoir solutions and the aqueous droplets, water migrates across the membrane and causes the droplets to reversibly shrink or expand and the concentration of all solutes inside the droplets changes. We now incorporate a temperature stage that generates a linear gradient in temperature across the chip oriented perpendicular to the concentration gradient. Robust operation of several variants of the PhaseChip is demonstrated with examples in liquid-liquid phase separation and protein crystallization experiments.
Lab on a Chip 07/2010; 10(13):1696-9. · 5.67 Impact Factor
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ABSTRACT: We employ the PhaseChip, a (poly)dimethylsiloxane (PDMS) microfluidic device, for statistical studies of protein crystal nucleation. The PhaseChip is designed to decouple nucleation and growth of protein crystals and so improve their yield and quality. Two layers of fluidic channels containing salt reservoirs and nanoliter-sized wells for protein drops in oil are separated by a thin PDMS membrane, which is permeable to water, but not to salt or macromolecules such as protein. We reversibly vary the supersaturation of protein inside the stored droplets by controlling the chemical potential of the reservoir. Lysozyme in the presence of sodium chloride is used as a model system. We determine the crystal nucleation rate as a function of protein supersaturation by counting the number of crystal nuclei per droplet, as demonstrated by Galkin and Vekilov.1.
Crystal Growth & Design 04/2009; 9(4):1806-1810. · 4.72 Impact Factor
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ABSTRACT: We describe a single microfluidic device and two methods for the passive storage of aqueous drops in a continuous stream of oil without any external control but hydrodynamic flow. Advantages of this device are that it is simple to manufacture, robust under operation, and drops never come into contact with each other, making it unnecessary to stabilize drops against coalescence. In one method the device can be used to store drops that are created upstream from the storage zone. In the second method the same device can be used to simultaneously create and store drops from a single large continuous fluid stream without resorting to the usual flow focusing or T-junction drop generation processes. Additionally, this device stores all the fluid introduced, including the first amount, with zero waste. Transport of drops in this device depends, however, on whether or not the aqueous drops wet the device walls. Analysis of drop transport in these two cases is presented. Finally, a method for extraction of the drops from the device is also presented, which works best when drops do not wet the walls of the chip.
Lab on a Chip 03/2009; 9(2):331-8. · 5.67 Impact Factor
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ABSTRACT: The phase behavior of the system of parallel rigid triblock copolymers is examined using the second-virial density functional theory. The triblock particle consists of two identical infinitely thin hard rods of finite lengths on the opposite ends of one central hard cylinder with nonzero length and diameter. Stability analyses and free energy calculations show that the system of parallel particles can form not only uniform nematic and smectic A phases, but a smectic-C phase too. The stability and structure of the tilted structure is controlled by only the diameter and the length of the central cylinder segment. Interestingly, the diameter effects only the layer tilting and the periodicity, but not the packing fraction of the nematic to smectic-C transition. For all values of cylinder length the usual smectic-A and smectic-C transitions compete with each other and no nematic-columnar transition is observed. At low and high cylinder length the smectic-A phase is stabilized first, while the smectic C is the most stable for intermediate length values.
11/2007;
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ABSTRACT: The phase behavior of the system of parallel rigid triblock copolymers is examined using the second virial density functional theory. The triblock particle consists of two identical infinitely thin hard rods of finite lengths on the opposite ends of one central hard cylinder with nonzero length and diameter. Stability analyses and free energy calculations show that the system of parallel particles can form not only uniform nematic and smectic A phases but also a smectic C phase. The stability and structure of the tilted structure are controlled by only the diameter and the length of the central cylinder segment. Interestingly, the diameter affects only the layer tilting and the periodicity, but not the packing fraction of the nematic to smectic-C transition. For all values of cylinder length the usual smectic A and smectic C transitions compete with each other and no nematic-columnar transition is observed. At low and high cylinder lengths the smectic A phase is stabilized first, while the smectic C is the most stable for intermediate length values.
The Journal of Chemical Physics 11/2007; 127(15):154902. · 3.33 Impact Factor
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ABSTRACT: A microfluidic device denoted the Phase Chip has been designed to measure and manipulate the phase diagram of multicomponent fluid mixtures. The Phase Chip exploits the permeation of water through poly(dimethylsiloxane) (PDMS) in order to controllably vary the concentration of solutes in aqueous nanoliter volume microdrops stored in wells. The permeation of water in the Phase Chip is modeled using the diffusion equation, and good agreement between experiment and theory is obtained. The Phase Chip operates by first creating drops of the water/solute mixture whose composition varies sequentially. Next, drops are transported down channels and guided into storage wells using surface tension forces. Finally, the solute concentration of each stored drop is simultaneously varied and measured. Two applications of the Phase Chip are presented. First, the phase diagram of a polymer/salt mixture is measured on-chip and validated off-chip, and second, protein crystallization rates are enhanced through the manipulation of the kinetics of nucleation and growth.
Journal of the American Chemical Society 08/2007; 129(28):8825-35. · 9.91 Impact Factor
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ABSTRACT: We present experimental measurements of the cholesteric-smectic phase transition of suspensions of charged semiflexible rods as a function of rod flexibility and surface charge. The rod particles consist of the bacteriophage M13 and closely related mutants, which are structurally identical to M13, but vary either in contour length and therefore ratio of persistence length to contour length, or surface charge. Surface charge is altered in two ways; by changing solution pH and by comparing M13 with fd virus, a virus which differs from M13 only by the substitution of a single charged amino acid for a neutral one per viral coat protein. Phase diagrams are measured as a function of particle length, particle charge, and ionic strength. The experimental results are compared with existing theoretical predictions for the phase behavior of flexible rods and charged rods.
Physical Review E 08/2007; 76(1 Pt 1):011705. · 2.26 Impact Factor
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ABSTRACT: A high throughput, low volume microfluidic device has been designed to decouple the physical processes of protein crystal nucleation and growth. This device, called the Phase Chip, is constructed out of poly(dimethylsiloxane) (PDMS) elastomer. One of the Phase Chip's innovations is to exploit surface tension forces to guide each drop to a storage chamber. We demonstrate that nanoliter water-in-oil drops of protein solutions can be rapidly stored in individual wells thereby allowing the screening of 1000 conditions while consuming a total of only 10 mug protein on a 20 cm(2) chip. Another significant advance over current microfluidic devices is that each well is in contact with a reservoir via a dialysis membrane through which only water and other low molecular weight organic solvents can pass, but not salt, polymer, or protein. This enables the concentration of all solutes in a solution to be reversibly, rapidly, and precisely varied in contrast to current methods, such as the free interface diffusion or sitting drop methods, which are irreversible. The Phase Chip operates by first optimizing conditions for nucleation by using dialysis to supersaturate the protein solution, which leads to nucleation of many small crystals. Next, conditions are optimized for crystal growth by using dialysis to reduce the protein and precipitant concentrations, which leads small crystals to dissolve while simultaneously causing only the largest ones to grow, ultimately resulting in the transformation of many small, unusable crystals into a few large ones.
Crystal Growth & Design 02/2007; 7(11):2192-2194. · 4.72 Impact Factor
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ABSTRACT: The fundamental nature of the nematic-nematic phase separation in binary mixtures of rigid hard rods is analyzed within the Onsager second-virial theory and the extension of Parsons and Lee which includes a treatment of the higher-body contributions. The particles of each component are modeled as hard spherocylinders of different diameter , but equal length . In the case of a system which is restricted to be fully aligned (parallel rods), we provide an analytical solution for the spinodal boundary for the limit of stability of demixing; only a single region of coexistence bounded at lower pressures (densities) by a critical point is possible for such a system. The full numerical solution with the Parsons-Lee extension also indicates that, depending on the length of the particles, there is a range of values of the diameter ratio where the phase coexistence is closed off by a critical point at lower pressure. A second region of coexistence can be found at even lower pressures for certain values of the parameters; this region is bounded by an "upper" critical point. The two coexistence regions can also merge to give a single region of coexistence extending to very high pressure without a critical point. By including the higher-order contributions to the excluded volume (end effects) in the Onsager theory, we prove analytically that the existence of the lower critical point is a direct consequence of the finite size of the particles. A new analytical equation of state is derived for the nematic phase using the Gaussian approximation. In the case of Onsager limit (infinite aspect ratio), we show that the phase behavior obtained using the Parsons-Lee approach substantially deviates from that with the Onsager theory for the transition due to the nonvanishing third and higher order virial coefficients. We also provide a detailed discussion of the phase behavior of recent experimental results for mixtures of thin and thick rods of the same length, for which the Onsager and Parsons-Lee theories can provide a qualitative description.
Physical Review E 12/2005; 72(5 Pt 1):051704. · 2.26 Impact Factor
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ABSTRACT: We report experimental measurements of the phase behavior of mixtures of thin (charged semiflexible fd virus) and thick (fd-PEG, fd virus covalently coated with polyethylene glycol) rods with diameter ratio varying from 3.7 to 1.1. The phase diagrams of the rod mixtures reveal isotropic-nematic, isotropic-nematic-nematic, and nematic-nematic coexisting phases with increasing concentration. In stark contrast to predictions from earlier theoretical work, we observe a nematic-nematic coexistence region bound by a lower critical point. Moreover, we show that a rescaled Onsager-type theory for binary hard-rod mixtures qualitatively describes the observed phase behavior.
Physical Review Letters 03/2005; 94(5):057801. · 7.37 Impact Factor
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ABSTRACT: 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.
Physical Review E 01/2005; 70(6 Pt 1):061703. · 2.26 Impact Factor
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ABSTRACT: We present experimental measurements of the cholesteric-smectic phase transition of suspensions of charged semiflexible rods as a function of rod flexibility and surface charge. The rod particles consist of the bacteriophage M13 and closely related mutants, which are structurally identical to this virus, but vary either in contour length and therefore ratio of persistence length to contour length, or vary in surface charge. Surface charge is altered in two ways; by changing solution pH and by comparing M13 with {\it fd} virus, a mutant which differs from M13 only by the substitution of a single charged amino acid for a neutral one per viral coat protein. Phase diagrams are measured as a function of particle length, particle charge and ionic strength. The experimental results are compared with existing theoretical predictions for the phase behavior of flexible rods and charged rods. In contrast to the isotropic-cholesteric transition, where theory and experiment agree at high ionic strength, the nematic-smectic transition exhibits complex charge and ionic strength dependence significantly different from predicted phase behavior. Possible explanations for these unexpected results are discussed.
07/2004;
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ABSTRACT: We present the first experimental measurements of the isotropic and nematic phases of mixtures of thin, charged semiflexible fd virus, and thick, fd-PEG created by covalently grafting poly-(ethylene glycol) to the the surface of fd, rods. The fd-PEG is sterically stabilized and its phase behavior is independent of ionic strength. The fd is charged. Therefore, by varying the ionic strength of a mixture of fd and fd-PEG, only the effective diameter of the bare fd rods changes, subsequently varying the effective diameter ratio (d=D_fd-PEG/D_fd) from 3.7 to 1. In solution, binary mixtures of fd and fd-PEG are shown to exhibit isotropic-nematic, isotropic-nematic-nematic and nematic-nematic coexisting phases with increasing concentration. We measure the binary phase diagrams as a function of composition, total concentration, and ionic strength. We find a lower critical point in the nematic-nematic coexistence region which has not been observed previously. These experimental results resolve a controversy in the literature concerning the evolution of the nematic-nematic phase separation with concentration. The experimental results are qualitatively described by a rescaled Onsager-type theory for the phase behavior of binary rod mixtures. Comment: shorter version. submitted to PRL
06/2004;
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ABSTRACT: 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. The isotropic-cholesteric transition experimental results agree semi-quantitatively with theoretical predictions for semiflexible, charged rods. Comment: For more information see http://www.elsie.brandeis.edu
06/2004;
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ABSTRACT: 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.
Physical Review E 06/2004; 69(5 Pt 1):051702. · 2.26 Impact Factor
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ABSTRACT: We present an experimental study of the isotropic-nematic phase transition in an aqueous mixture of charged semi-flexible 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. Comment: 8 Figures. To be published in Phys. Rev. E. For more information see http://www.elsie.brandeis.edu
02/2004;
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ABSTRACT: 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.
Physical Review Letters 06/2003; 90(19):198302. · 7.37 Impact Factor
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ABSTRACT: The orientational distribution function of the nematic phase of suspensions of the semiflexible rodlike virus fd is measured by x-ray diffraction as a function of concentration and ionic strength. X-ray diffraction from a single-domain nematic phase of fd is influenced by interparticle correlations at low angle, while only intraparticle scatter contributes at high angle. Consequently, the angular distribution of the scattered intensity 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 (structure factor) and intraparticle (form factor) 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 function's precise form, and the measured angular intensity distribution is described equally well by both Onsager's 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 semiflexible rods S=0.55, but deviations from theory increase with decreasing ionic strength. The concentration dependence of the nematic order parameter also better agrees with theoretical predictions at high ionic strength indicating that electrostatic interactions have a measurable effect on the nematic order parameter. The x-ray order parameters are shown to be proportional to the measured birefringence, and the saturation birefringence of fd is determined enabling a simple, inexpensive way to measure the order parameter. Additionally, the spatial ordering of nematic fd was probed. Measurements of the nematic structure factor revealed a single large peak in contrast to nematics of rigid rods.
Physical Review E 04/2003; 67(3 Pt 1):031708. · 2.26 Impact Factor
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ABSTRACT: is kind of microphase separation might also be relevant to systems of amphiphiles #13# and block copolymers #14#, to bioseparation methods and DNA partitioning in prokaryotes #15#, and to protein crystallization #16, 17#, and the manufacture of composite materials. The phase behavior of a colloidal suspension is found by minimizing the free energy F = U,TS. Hard particles are forbidden to interpenetrate and the interaction energy U is zero as long as the particles are not in contact. Thus phase behavior is determined by maximizing the entropy S. For hard spheres imagine a suspension of billiard balls, and for hard rods substitute billiard cues. Examples of entropically driven ordering exhibited by hard rods are the nematic and smectic liquid crystalline phases, whereas for hard spheres a #uid - crystal transition occurs. These phase transitions have been extensively studied theoretically #2, 3#, by
01/2001;
