Quasi-two-dimensional dispersions of Brownian particles with competitive interactions: phase behavior and structural properties.

Competing short-range attractive (SA) and long range repulsive (LR) particle interactions can be used to describe three-dimensional charge-stabilized colloid or protein dispersions at low added salt concentrations, as well as membrane proteins with interaction contributions mediated by lipid molecules. Using Langevin dynamics (LD) simulations, we determine the generalized phase diagram, cluster shapes and size distributions of a generic quasi-two-dimensional (Q2D) dispersion of spherical SALR particles confined to in-plane motion inside a bulk fluid. The SA and LR interaction parts are modelled by a generalized Lennard-Jones potential and a screened Coulomb potential, respectively. The microstructures of the detected equilibrium and non-equilibrium Q2D phases are distinctly different from those observed in three-dimensional (3D) SALR systems, by exhibiting different levels of hexagonal ordering. We discuss a thermodynamic perturbation theory prediction for the metastable binodal line of a reference system of particles with SA interactions only, which in the explored Q2D-SALR phase diagram region separates cluster from non-clustered phases. The transition from the high-temperature (small SA) dispersed fluid (DF) phase to the lower-temperature equilibrium cluster (EC) fluid phase is characterised by a low-wavenumber peak height of the static structure factor (corresponding to a thermal correlation length of about twice the particle diameter) featuring a distinctly smaller value (≈1.4) than in 3D SALR systems. With decreasing temperature (increasing SA), the cluster morphology changes from disk-like shapes in the equilibrium cluster phase, to double-stranded anisotropic hexagonal cluster segments formed in a cluster-percolated (CP) gel-like phase. This transition can be quantified by a hexagonal order parameter distribution function. The mean cluster size and coordination number of particles in the CP phase are insensitive to changes in the attraction strength.

Self-Assembly of All-DNA Rods with Controlled Patchiness.

Double-stranded DNA (dsDNA) fragments exhibit noncovalent attractive interactions between their tips. It is still unclear how DNA liquid crystal self-assembly is affected by such blunt-end attractions. It is demonstrated that stiff dsDNA fragments with moderate aspect ratio can specifically self-assemble in concentrated aqueous solutions into different types of smectic mesophases on the basis of selectively screening of blunt-end DNA stacking interactions. To this end, this type of attractions are engineered at the molecular level by constructing DNA duplexes where the attractions between one or both ends are screened by short hairpin caps. All-DNA bilayer and monolayer smectic-A type of phases, as well as a columnar phase, can be stabilized by controlling attractions strength. The results imply that the so far elusive smectic-A in DNA rod-like liquid crystals is a thermodynamically stable phase. The existence of the bilayer smectic phase is confirmed by Monte-Carlo simulations of hard cylinders decorated with one attractive terminal site. This work demonstrates that DNA blunt-ends behave as well-defined monovalent attractive patches whose strength and position can be potentially precisely tuned, highlighting unique opportunities concerning the stabilization of nonconventional DNA-based lyotropic liquid crystal phases assembled by all-DNA patchy particles with arbitrary geometry and composition.

Self assembling cluster crystals from DNA based dendritic nanostructures.

Cluster crystals are periodic structures with lattice sites occupied by several, overlapping building blocks, featuring fluctuating site occupancy, whose expectation value depends on thermodynamic conditions. Their assembly from atomic or mesoscopic units is long-sought-after, but its experimental realization still remains elusive. Here, we show the existence of well-controlled soft matter cluster crystals. We fabricate dendritic-linear-dendritic triblock composed of a thermosensitive water-soluble polymer and nanometer-scale all-DNA dendrons of the first and second generation. Conclusive small-angle X-ray scattering (SAXS) evidence reveals that solutions of these triblock at sufficiently high concentrations undergo a reversible phase transition from a cluster fluid to a body-centered cubic (BCC) cluster crystal with density-independent lattice spacing, through alteration of temperature. Moreover, a rich concentration-temperature phase diagram demonstrates the emergence of various ordered nanostructures, including BCC cluster crystals, birefringent cluster crystals, as well as hexagonal phases and cluster glass-like kinetically arrested states at high densities.

Hydrodynamics of immiscible binary fluids with viscosity contrast: a multiparticle collision dynamics approach.

We present a multiparticle collision dynamics (MPC) implementation of layered immiscible fluids A and B of different shear viscosities separated by planar interfaces. The simulated flow profile for imposed steady shear motion and the time-dependent shear stress functions are in excellent agreement with our continuum hydrodynamics results for the composite fluid. The wave-vector dependent transverse velocity auto-correlation functions (TVAF) in the bulk-fluid regions of the layers decay exponentially, and agree with those of single-phase isotropic MPC fluids. In addition, we determine the hydrodynamic mobilities of an embedded colloidal sphere moving steadily parallel or transverse to a fluid-fluid interface, as functions of the distance from the interface. The obtained mobilities are in good agreement with hydrodynamic force multipoles calculations, for a no-slip sphere moving under creeping flow conditions near a clean, ideally flat interface. The proposed MPC fluid-layer model can be straightforwardly implemented, and it is computationally very efficient. Yet, owing to the spatial discretization inherent to the MPC method, the model can not reproduce all hydrodynamic features of an ideally flat interface between immiscible fluids.

DNA Self-Assembly Mediated by Programmable Soft-Patchy Interactions.

Adding shape and interaction anisotropy to a colloidal particle offers exquisitely tunable routes to engineer a rich assortment of complex-architected structures. Inspired by the hierarchical self-assembly concept with block copolymers and DNA liquid crystals and exploiting the unique assembly properties of DNA, we report here the construction and self-assembly of DNA-based soft-patchy anisotropic particles with a high degree of modularity in the system's design. By programmable positioning of thermoresponsive polymeric patches on the backbone of a stiff DNA duplex with linear and star-shaped architecture, we reversibly drive the DNA from a disordered ensemble to a diverse array of long-range ordered multidimensional nanostructures with tunable lattice spacing, ranging from lamellar to bicontinuous double-gyroid and double-diamond cubic morphologies, through the alteration of temperature. Our results demonstrate that the proposed hierarchical self-assembly strategy can be applied to any kind of DNA nanoarchitecture, highlighting the design principles for integration of self-assembly concepts from the physics of liquid crystals, block copolymers, and patchy colloids into the continuously growing interdisciplinary research field of structural DNA nanotechnology.

Thermophoresis of a Colloidal Rod: Contributions of Charge and Grafted Polymers.

In this study, we investigated the thermodiffusion behavior of a colloidal model system as a function of the Debye length, λDH, which is controlled by the ionic strength. Our system consists of an fd-virus grafted with poly(ethylene glycol) (PEG) with a molecular mass of 5000 g mol-1. The results are compared with recent measurements on a bare fd-virus and with results of PEG. The diffusion coefficients of both viruses are comparable and increase with the increasing Debye length. The thermal diffusion coefficient, DT, of the bare virus increases strongly with the Debye length, whereas DT of the grafted fd-virus shows only a very weak increase. The Debye length dependence of both systems can be described with an expression derived for charged rods using the surface charge density and an offset of DT as adjustable parameters. It turns out that the ratio of the determined surface charges is inverse to the ratio of the surfaces of the two systems, which means that the total charge remains almost constant. The determined offset of the grafted fd-virus describing the chemical contributions is the sum of DT of PEG and the offset of the bare fd-virus. At high λDH, corresponding to the low ionic strength, the ST values of both colloidal model systems approach each other. This implies a contribution from the polymer layer, which is strong at short λDH and fades out for the longer Debye lengths, when the electric double layer reaches further than the polymer chains and therefore dominates interactions with the surrounding water.

Tumbling of Quantum Dots: Rheo-Optics.

Linear flow dichroism is shown to be a powerful tool to characterize the hydrodynamic dimensions of extremely small nonspherical colloids in solution. Dispersions of prolate and oblate quantum dots (QDs) are employed to investigate the validity of flow dichroism as a characterization tool. Shape-anisotropic QDs are important from an application perspective, where it is necessary to have a good knowledge of their hydrodynamic dimensions to predict and control their orientation during solution processing. Flow dichroism quantifies the tumbling motion of QDs in shear flow by optical means, which provides a characteristic signature of the particle shape, hydrodynamic friction, and size distribution. The effects of particle size and shape, size polydispersity, and shear rate on the temporal evolution of the flow-induced alignment are discussed in detail on the basis of numerical solutions of the Smoluchowski equation that describes the motion for the probability of the orientation of colloids in shear flow. It is shown that the combination of flow-dichroism experiments and the theoretical approach on the basis of the Smoluchowski equation provides a means to measure hydrodynamic aspect ratios and polydispersity, which for such small particles is not feasible with standard methods similar to light scattering. Flow dichroism will be useful not only for shape-anisotropic colloidal QDs, but also for other nanoscale systems.

Near wall dynamics of a spherical particle in crowded suspensions of colloidal rods - dynamic information from TIRM revisited.

We performed total internal reflection microscopy (TIRM) experiments to determine the depletion potentials between probe spheres and a flat glass wall which are induced by long and thin, rod-shaped colloids (fd-virus), and probe the spatially resolved dynamics of the probe spheres. The dynamic information from the same raw TIRM intensity time traces is extracted in three different ways: by determining the spatially averaged diffusion constant of the probe sphere normal to the wall, by measuring the position dependence of the diffusion coefficient, and by measuring the particle's local drift velocity. Up to a concentration of about 6 times the overlap concentration of the rod-like colloids, the spatially averaged diffusion coefficient and the amplitude of the depletion potential are in surprisingly good agreement with theoretical predictions in which mutual interactions between the rods are neglected, that is, where the concentration is less than the overlap concentration. On increasing the depletant content even further, however, both the static and the averaged dynamic quantities begin to deviate from such theoretical predictions. In particular we find large deviations from the prediction by Mao, Cates, and Lekkerkerker [J. Chem. Phys., 1997, 106, 3721] based on the third order virial expansion for the rod concentration. It is shown that there are significant inaccuracies in TIRM measurements of diffusion coefficients due to the limited time range in which the mean squared displacements vary linearly in time, whereas mean displacements give much more accurate information concerning the probe sphere dynamics.

Peptide model systems: Correlation between thermophilicity and hydrophilicity.

In recent years, the response of biomolecules to a temperature gradient has been utilized to monitor reactions of biomolecules, but the underlying mechanism is not well understood due to the complexity of the multicomponent system. To identify some underlying principles, we investigate the thermal diffusion of small amide molecules in water systematically. We re-analyze previous measurements of urea and formamide and compare the results with acetamide, N-methylformamide, and N,N-dimethylformamide, amides with a lower hydrophilicity. It turns out that less hydrophilic substances do not show the typical temperature dependence of water soluble macromolecules. Analyzing temperature and concentration dependent measurements using an empirical expression originally derived for nonpolar mixtures, we find that the so-called isotope contribution depends strongly on the hydrophilicity of the solute. This can be qualitatively understood by comparing with molecular dynamic simulations of Lennard-Jones fluids. The hydrophobic/hydrophilic balance also influences the structure in the fluid and with that the thermal expansion coefficient, which correlates with the thermal diffusion coefficient. Furthermore, we observe a clear correlation of the temperature and concentration dependence of the Soret coefficient with the hydrophilicity, which can be quantitatively described by the partition coefficient log P.

Clustering and dynamics of particles in dispersions with competing interactions: theory and simulation.

Dispersions of particles with short-range attractive and long-range repulsive interactions exhibit rich equilibrium microstructures and a complex phase behavior. We present theoretical and simulation results for structural and, in particular, short-time diffusion properties of a colloidal model system with such interactions, both in the dispersed-fluid and equilibrium-cluster phase regions. The particle interactions are described by a generalized Lennard-Jones-Yukawa pair potential. For the theoretical-analytical description, we apply the hybrid Beenakker-Mazur pairwise additivity (BM-PA) scheme. The static structure factor input to this scheme is calculated self-consistently using the Zerah-Hansen integral equation theory approach. In the simulations, a hybrid simulation method is adopted, combing molecular dynamics simulations of colloids with the multiparticle collision dynamics approach for the fluid, which fully captures hydrodynamic interactions. The comparison of our theoretical and simulation results confirms the high accuracy of the BM-PA scheme for dispersed-fluid phase systems. For particle attraction strengths exceeding a critical value, our simulations yield an equilibrium cluster phase. Calculations of the mean lifetime of the appearing clusters and the comparison with the analytical prediction of the dissociation time of an isolated particle pair reveal quantitative differences pointing to the importance of many-particle hydrodynamic interactions for the cluster dynamics. The cluster lifetime in the equilibrium-cluster phase increases far stronger with increasing attraction strength than that in the dispersed-fluid phase. Moreover, significant changes in the cluster shapes are observed in the course of time. Hence, an equilibrium-cluster dispersion cannot be treated dynamically as a system of permanent rigid bodies.

Role of Hydrogen Bonding of Cyclodextrin-Drug Complexes Probed by Thermodiffusion.

Temperature gradient-induced migration of biomolecules, known as thermophoresis or thermodiffusion, changes upon ligand binding. In recent years, this effect has been used to determine protein-ligand binding constants. The mechanism through which thermodiffusive properties change when complexes are formed, however, is not understood. An important contribution to thermodiffusive properties originates from the thermal response of hydrogen bonds. Because there is a considerable difference between the degree of solvation of the protein-ligand complex and its isolated components, ligand-binding is accompanied by a significant change in hydration. The aim of the present work is therefore to investigate the role played by hydrogen bonding on the change in thermodiffusive behavior upon ligand-binding. As a model system, we use cyclodextrins (CDs) and acetylsalicylic acid (ASA), where quite a significant change in hydration is expected and where no conformational changes occur when a CD/ASA complex is formed in aqueous solution. Thermophoresis was investigated in the temperature range of 10-50 °C by infrared thermal diffusion forced Rayleigh scattering. Nuclear magnetic resonance measurements were performed at 25 °C to obtain information about the structure of the complexes. All CD/ASA complexes show a stronger affinity toward regions of lower temperature compared to the free CDs. We found that the temperature sensitivity of thermophoresis correlates with the 1-octanol/water partition coefficient. This observation not only establishes the relation between thermodiffusion and degree of hydrogen bonding but also opens the possibility to relate thermodiffusive properties of complexes to their partition coefficient, which cannot be determined otherwise. This concept is especially interesting for protein-ligand complexes where the protein undergoes a conformational change, different from the CD/ASA complexes, giving rise to additional changes in their hydrophilicity.

Smectic phase in suspensions of gapped DNA duplexes.

Smectic ordering in aqueous solutions of monodisperse stiff double-stranded DNA fragments is known not to occur, despite the fact that these systems exhibit both chiral nematic and columnar mesophases. Here, we show, unambiguously, that a smectic-A type of phase is formed by increasing the DNA's flexibility through the introduction of an unpaired single-stranded DNA spacer in the middle of each duplex. This is unusual for a lyotropic system, where flexibility typically destabilizes the smectic phase. We also report on simulations suggesting that the gapped duplexes (resembling chain-sticks) attain a folded conformation in the smectic layers, and argue that this layer structure, which we designate as smectic-fA phase, is thermodynamically stabilized by both entropic and energetic contributions to the system's free energy. Our results demonstrate that DNA as a building block offers an exquisitely tunable means to engineer a potentially rich assortment of lyotropic liquid crystals.

Accumulation of formamide in hydrothermal pores to form prebiotic nucleobases.

Formamide is one of the important compounds from which prebiotic molecules can be synthesized, provided that its concentration is sufficiently high. For nucleotides and short DNA strands, it has been shown that a high degree of accumulation in hydrothermal pores occurs, so that temperature gradients might play a role in the origin of life [Baaske P, et al. (2007)Proc Natl Acad Sci USA104(22):9346-9351]. We show that the same combination of thermophoresis and convection in hydrothermal pores leads to accumulation of formamide up to concentrations where nucleobases are formed. The thermophoretic properties of aqueous formamide solutions are studied by means of Infrared Thermal Diffusion Forced Rayleigh Scattering. These data are used in numerical finite element calculations in hydrothermal pores for various initial concentrations, ambient temperatures, and pore sizes. The high degree of formamide accumulation is due to an unusual temperature and concentration dependence of the thermophoretic behavior of formamide. The accumulation fold in part of the pores increases strongly with increasing aspect ratio of the pores, and saturates to highly concentrated aqueous formamide solutions of ∼85 wt% at large aspect ratios. Time-dependent studies show that these high concentrations are reached after 45-90 d, starting with an initial formamide weight fraction of[Formula: see text]wt % that is typical for concentrations in shallow lakes on early Earth.

Ultrafiltration of charge-stabilized dispersions at low salinity.

We present a comprehensive study of cross-flow ultrafiltration (UF) of charge-stabilized suspensions, under low-salinity conditions of electrostatically strongly repelling colloidal particles. The axially varying permeate flux, near-membrane concentration-polarization (CP) layer and osmotic pressure profiles are calculated using a macroscopic diffusion-advection boundary layer method, and are compared with filtration experiments on aqueous suspensions of charge-stabilized silica particles. The theoretical description based on the one-component macroion fluid model (OCM) accounts for the strong influence of surface-released counterions on the renormalized colloid charge and suspension osmotic compressibility, and for the influence of the colloidal hydrodynamic interactions and electric double layer repulsion on the concentration-dependent suspension viscosity η, and collective diffusion coefficient Dc. A strong electro-hydrodynamic enhancement of Dc and η, and likewise of the osmotic pressure, is predicted theoretically, as compared with their values for a hard-sphere suspension. We also point to the failure of generalized Stokes-Einstein relations describing reciprocal relations between Dc and η. According to our filtration model, Dc is of dominant influence, giving rise to an only weakly developed CP layer having practically no effect on the permeate flux. This prediction is quantitatively confirmed by our UF measurements of the permeate flux using an aqueous suspension of charged silica spheres as the feed system. The experimentally detected fouling for the largest considered transmembrane pressure values is shown not to be due to filter cake formation by crystallization or vitrification.

Near-wall dynamics of concentrated hard-sphere suspensions: comparison of evanescent wave DLS experiments, virial approximation and simulations.

In this article we report on a study of the near-wall dynamics of suspended colloidal hard spheres over a broad range of volume fractions. We present a thorough comparison of experimental data with predictions based on a virial approximation and simulation results. We find that the virial approach describes the experimental data reasonably well up to a volume fraction of ϕ≈ 0.25 which provides us with a fast and non-costly tool for the analysis and prediction of evanescent wave DLS data. Based on this we propose a new method to assess the near-wall self-diffusion at elevated density. Here, we qualitatively confirm earlier results [Michailidou, et al., Phys. Rev. Lett., 2009, 102, 068302], which indicate that many-particle hydrodynamic interactions are diminished by the presence of the wall at increasing volume fractions as compared to bulk dynamics. Beyond this finding we show that this diminishment is different for the particle motion normal and parallel to the wall.

Flow instability due to coupling of shear-gradients with concentration: non-uniform flow of (hard-sphere) glasses.

Flow-induced instabilities that lead to non-uniform stationary flow profiles have been observed in many different soft-matter systems. Two types of instabilities that lead to banded stationary states have been identified, which are commonly referred to as gradient- and vorticity-banding. The molecular origin of these instabilities is reasonably well understood. A third type of instability that has been proposed phenomenologically [Europhys. Lett., 1986, 2, 129 and Phys. Rev. E, 1995, 52, 4009] is largely unexplored. Essential to this "Shear-gradient Concentration Coupling" (SCC-) instability is a mass flux that is induced by spatial gradients of the shear rate. A possible reason that this instability has essentially been ignored is that the molecular origin of the postulated mass flux is not clear, and no explicit expressions for the shear-rate and concentration dependence of the corresponding transport coefficient exist. It is therefore not yet known what types of flow velocity- and concentration-profiles this instability gives rise to. In this paper, an expression for the transport coefficient corresponding to the shear-gradient induced mass flux is derived in terms of the shear-rate dependent pair-correlation function, and Brownian dynamics simulations for hard-spheres are presented that specify the shear-rate and concentration dependence of the pair-correlation function. This allows to explicitly formulate the coupled advection-diffusion equation and an equation of motion for the suspension flow velocity. The inclusion of a non-local contribution to the stress turns out to be essential to describe the SCC-banding transition. The coupled equations of motion are solved numerically, and flow- and concentration-profiles are discussed. It is shown that the SCC-instability occurs within the glass state at sufficiently small shear rates, leading to a banded flow-profile where one of the bands is non-flowing.

Structure and rheology of mixed suspensions of montmorillonite and silica nanoparticles.

We present a study of the structure and rheology of mixed suspensions of montmorillonite clay platelets and Ludox TMA silica spheres at pH 5, 7, and 9. Using cryogenic transmission electron microscopy (cryo-TEM), we probe the changes in the structure of the montmorillonite suspensions induced by changing the pH and by adding silica particles. Using oscillatory and transient rheological measurements, we examine the changes in storage modulus and yield stress of the montmorillonite suspensions upon changing the pH and adding silica particles. Cryo-TEM images reveal that changes in pH have a significant effect on the structure of the suspensions, which can be related to the change in charge of the edges from positive at pH 5 to negative at higher pH. Furthermore, at pH 7, the cryo-TEM images show indications of a microphase separation between clay and silica particles. The addition of silica leads to lowering of the storage modulus and yield stress, which we connect to the structural changes of the suspension.

Translational and rotational near-wall diffusion of spherical colloids studied by evanescent wave scattering.

In this article we extend recent experimental developments [Rogers et al., Phys. Rev. Lett., 2012, 109, 098305] by providing a suitable theoretical framework for the derivation of exact expressions for the first cumulant (initial decay rate) of the correlation function measured in Evanescent Wave Dynamic Light Scattering (EWDLS) experiments. We focus on a dilute suspension of optically anisotropic spherical Brownian particles diffusing near a planar hard wall. In such a system, translational and rotational diffusion are hindered by hydrodynamic interactions with the boundary which reflects the flow incident upon it, affecting the motion of colloids. The validity of the approximation by the first cumulant for moderate times is assessed by juxtaposition to Brownian dynamics simulations, and compared with experimental results. The presented method for the analysis of experimental data allows the determination of penetration-depth-averaged rotational diffusion coefficients of spherical colloids at low density.

An electric-field induced dynamical state in dispersions of charged colloidal rods.

The response of concentrated dispersions of charged colloids to low-frequency electric fields is governed by field-induced inter-colloidal interactions resulting from the polarization of electric double layers and the layer of condensed ions, association and dissociation of condensed ions, as well as hydrodynamic interactions through field-induced electro-osmotic flow. The phases and states that can be formed by such field-induced interactions are an essentially unexplored field of research. Experiments on concentrated suspensions of rod-like colloids (fd-virus particles), within the isotropic-nematic phase coexistence region, showed that a number of phases/states are induced, depending on the field amplitude and frequency [Soft Matter, 2010, 6, 273]. In particular, a dynamical state is found where nematic domains form and melt on a time scale of the order of seconds. We discuss the microscopic origin of this dynamical state, which is attributed to the cyclic, electric-field induced dissociation and association of condensed ions. A semi-quantitative theory is presented for the dynamics of melting and formation of nematic domains, including a model for the field-induced dissociation/association of condensed ions. The resulting equation of motion for the orientational order parameter is solved numerically for parameters complying with the fd-virus system. A limit-cycle is found, with a cycling-time that diverges at the transition line in the field-amplitude versus frequency plane where the dynamical state first appears, in accord with experimental findings.