Validity of the Stokes-Einstein Relation in Soft Colloids up to the Glass Transition

Glassy phases of the Gaussian core model

We present results from molecular dynamics simulations exploring the supercooled dynamics of the Gaussian Core Model in the low- and intermediate-density regimes. In particular, we analyse the transition from the low-density hard-sphere-like glassy dynamics to the high-density one. The dynamics at low densities is well described by the caging mechanism, giving rise to intermittent dynamics. At high densities, the particles undergo a more continuous motion in which the concept of cage loses its meaning. We elaborate on the idea that these different supercooled dynamics are in fact the precursors of two different glass states.

Concentration and temperature dependent interactions and state diagram of dispersions of copolymer microgels

We investigate by means of small angle neutron scattering experiments and numerical simulations the interactions and inter-particle arrangements of concentrated dispersions of copolymer poly(N-isopropylacrylamide)-poly(ethylene glycol methyl ether methacrylate) (PNIPAM-PEGMA) microgels across the volume phase transition (VPT). The scattering data of moderately concentrated dispersions are accurately modeled at all temperatures by using a star polymer form factor and static structure factors calculated from the effective potential obtained from simulations. Interestingly, for temperatures below the VPT temperature (VPTT), the radius of gyration and blob size of the particles significantly decrease with increasing the effective packing fraction in the non-overlapping regime. This is attributed to the presence of charges in the system associated with the use of an ionic initiator in the synthesis. Simulations using the experimentally corroborated interaction potential are used to explore the state diagram in a wide range of effective packing fractions. Below and slightly above the VPTT, the system undergoes an arrest transition mainly driven by the soft repulsion between the particles. Only well above the VPTT the system is found to phase separate before arresting. Our results highlight the versatility and potential of copolymer PNIPAM-PEGMA microgels to explore different kinds of arrested states balancing attraction and repulsion by changing temperature and packing fraction.

Microfluidic osmotic compression of a charge-stabilized colloidal dispersion: Equation of state and collective diffusion coefficient

We show, using a model coupling mass transport and liquid theory calculations for a charge-stabilized colloidal dispersion, that diffusion significantly limits measurement times of its equation of state (EOS), osmotic pressure vs composition, using the osmotic compression technique. Following this result, we present a microfluidic chip allowing one to measure the entire EOS of a charged dispersion at the nanoliter scale in a few hours. We also show that time-resolved analyses of relaxation to equilibrium in this microfluidic experiment lead to direct estimates of the collective diffusion coefficient of the dispersion in Donnan equilibrium with a salt reservoir.

Conservation of the Stokes-Einstein relation in supercooled water

The Stokes-Einstein (SE) relation is commonly regarded as being breakdown in supercooled water. However, this conclusion is drawn by testing the validity of some variants of the SE relation rather than its original form, and it appears conflicting with the fact that supercooled water is in its local equilibrium. In this work, we show by molecular dynamics simulations that the Stokes-Einstein relation is indeed conserved in supercooled water. The inconsistency between the original SE relation and its variants comes from two facts: (1) the substitutes of the shear viscosity in the SE variants are only approximate relations; and (2) the effective hydrodynamic radius actually decreases with decreasing temperature, instead of being a constant as assumed in the SE variants.

Violation of Stokes-Einstein and Stokes-Einstein-Debye relations in polymers at the gas-supercooled liquid coexistence

Molecular dynamics simulations are performed on a system of model linear polymers to look at the violations of Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations near the mode coupling theory transition temperatureT_cat three (one higher and two lower) densities. At low temperatures, both lower density systems show stable gas-supercooled-liquid coexistence whereas the higher density system is homogeneous. We show that monomer density relaxation exhibits SE violation for all three densities, whereas molecular density relaxation shows a weak violation of the SE relation nearT_cin both lower density systems. This study identifies disparity in monomer mobility and observation of jumplike motion in the typical monomer trajectories resulting in the SE violations. In addition to the SE violation, a weak SED violation is observed in the gas-supercooled-liquid coexisting domains of the lower densities. Both lower density systems also show a decoupling of translational and rotational dynamics in this polymer system.

Modeling the dynamics of phospholipids in the fluid phase of liposomes

We present the derivation of a new model to describe neutron spin echo spectroscopy and quasi-elastic neutron scattering data on liposomes. We compare the new model with existing approaches and benchmark it with experimental data. The analysis indicates the importance of including all major contributions in the modeling of the intermediate scattering function. Simultaneous analysis of the experimental data on lipids with full contrast and tail contrast matched samples reveals highly confined lipid tail motion. A comparison of their dynamics demonstrates the statistical independence of tail-motion and height-height correlation of the membrane. A more detailed analysis indicates that the lipid tail relaxation is confined to a potential with cylindrical symmetry, in addition to the undulation and diffusive motion of the liposome. Despite substantial differences in the chemistry of the fatty acid tails, the observation indicates a universal behavior. The analysis of partially deuterated systems confirms the strong contribution of the lipid tail to the intermediate scattering function. Within the time range from 5 to 100 ns, the intermediate scattering function can be described by the height-height correlation function. The existence of the fast-localized tail motion and the contribution of slow translational diffusion of liposomes determine the intermediate scattering function for t < 5 ns and t > 100 ns, respectively. Taking into account the limited time window lowers the bending moduli by a factor of 1.3 (DOPC) to 2 (DMPC) compared to the full range.

Effective one-component model of binary mixture: molecular arrest induced by the spatially correlated stochastic dynamics

Spatially correlated noise (SCN), i.e. the thermal noise that affects neighbouring particles in a similar manner, is ubiquitous in soft matter systems. In this work, we apply the over-damped SCN-driven Langevin equations as an effective, one-component model of the dynamics in dense binary mixtures. We derive the thermodynamically consistent fluctuation-dissipation relation for SCN to show that it predicts the molecular arrest resembling the glass transition, i.e. the critical slow-down of dynamics in the disordered phases. We show that the mechanism of singular dissipation is embedded in the dissipation matrix, accompanying SCN. We are also able to identify the characteristic length of collective dissipation, which diverges at critical packing. This novel physical quantity conveniently describes the difference between the ergodic and non-ergodic dynamics. The model is fully analytically solvable, one-dimensional and admits arbitrary interactions between the particles. It qualitatively reproduces several different modes of arrested disorder encountered in binary mixtures, including e.g. the re-entrant arrest. The model can be effectively compared to the mode coupling theory.

Dynamic Equivalence between Soft Star Polymers and Hard Spheres

Understanding the dynamics of soft colloids, such as star polymers, dendrimers, and microgels, is of scientific and practical importance. It is known that the excluded volume effect plays a key role in colloidal dynamics. Here, we propose a condition of compressibility equivalence that provides a simple method to experimentally evaluate the excluded volume of soft colloids from a thermodynamic view. We apply this condition to survey the dynamics of a series of star polymer dispersions. It is found that, as the concentration increases, the slowing of the long-time self-diffusivity of the star polymer, normalized by the short-time self-diffusivity, can be mapped onto the hard-sphere behavior. This phenomenon reveals the dynamic equivalence between soft colloids and hard spheres, despite the apparent complexity of the interparticle interaction of the soft colloids. The methods for measuring the osmotic compressibility and the self-diffusivities of soft colloidal dispersions are also presented.

Coincidence of the freezing and the onset of caging in hard sphere and Lennard-Jones fluids

In this article, we examine the collective particle dynamics, as expressed by the time correlation function of the longitudinal particle current density, of several different fluids in the vicinity of their freezing points/lines. We consider and compare results obtained by dynamic light scattering for a suspension of hard spheres and by molecular dynamics for fluids with hard sphere and Lennard-Jones interactions. The latter are performed along both an isotherm and an isochore. In all cases, we find a qualitative change in the collective dynamics, within the resolution of the data, when their respective freezing lines are crossed. We associate this change with the onset of caging. The new results for the Lennard-Jones fluid reported here confirm that the occurrence of caging, found previously for systems of hard spheres, is a more general feature that distinguishes a metastable fluid from one in thermodynamic equilibrium.

Phase diagram for two-dimensional layer of soft particles

The phase diagram of a monolayer of soft particles described by the Daoud-Cotton model for star polymers is presented. Ground state calculations and grand canonical Monte Carlo simulations are used to determine the phase behavior as a function of the number of arms on the star and the areal coverage of the soft particles. The phase diagram exhibits rich behavior including reentrant melting and freezing and solid-solid transitions with triangular, stripe, honeycomb and kagome phases. These structures in 2D are analogous to the structures observed in 3D. The evolution of the structure factor with density is qualitatively similar to that measured in experiments for polymer grafted nanocrystals [Chen et al., Macromolecules, 2017, 50, 9636].

Glass transition of soft colloids

We explore the glassy dynamics of soft colloids using microgels and charged particles interacting by steric and screened Coulomb interactions, respectively. In the supercooled regime, the structural relaxation time τ_{α} of both systems grows steeply with volume fraction, reminiscent of the behavior of colloidal hard spheres. Computer simulations confirm that the growth of τ_{α} on approaching the glass transition is independent of particle softness. By contrast, softness becomes relevant at very large packing fractions when the system falls out of equilibrium. In this nonequilibrium regime, τ_{α} depends surprisingly weakly on packing fraction, and time correlation functions exhibit a compressed exponential decay consistent with stress-driven relaxation. The transition to this novel regime coincides with the onset of an anomalous decrease in local order with increasing density typical of ultrasoft systems. We propose that these peculiar dynamics results from the combination of the nonequilibrium aging dynamics expected in the glassy state and the tendency of colloids interacting through soft potentials to refluidize at high packing fractions.

Concentration-dependent swelling and structure of ionic microgels: simulation and theory of a coarse-grained model

We study swelling and structural properties of ionic microgel suspensions within a comprehensive coarse-grained model that combines the polymeric and colloidal natures of microgels as permeable, compressible, charged spheres governed by effective interparticle interactions. The model synthesizes the Flory-Rehner theory of cross-linked polymer gels, the Hertz continuum theory of effective elastic interactions, and a theory of density-dependent effective electrostatic interactions. Implementing the model using Monte Carlo simulation and thermodynamic perturbation theory, we compute equilibrium particle size distributions, swelling ratios, volume fractions, net valences, radial distribution functions, and static structure factors as functions of concentration. Trial Monte Carlo moves comprising particle displacements and size variations are accepted or rejected based on the total change in elastic and electrostatic energies. The theory combines first-order thermodynamic perturbation and variational free energy approximations. For illustrative system parameters, theory and simulation agree closely at concentrations ranging from dilute to beyond particle overlap. With increasing concentration, as microgels deswell, we predict a decrease in the net valence and an unusual saturation of pair correlations. Comparison with experimental data for deionized, aqueous suspensions of PNIPAM particles demonstrates the capacity of the coarse-grained model to predict and interpret measured swelling behavior.

Solution Self-Assemblies of Sequence-Defined Ionic Peptoid Block Copolymers

A series of amphiphilic ionic peptoid block copolymers where the total number (1 or 3) and position of ionic monomers along the polymer chain are precisely controlled have been synthesized by the submonomer method. Upon dissolution in water at pH = 9, the amphiphilic peptoids self-assemble into small spherical micelles having hydrodynamic radius in ∼5-10 nm range and critical micellar concentration (CMC) in the 0.034-0.094 mg/mL range. Small-angle neutron scattering (SANS) analysis of the micellar solutions revealed unprecedented dependence of the micellar structure on the number and position of ionic monomers along the chain. It was found that the micellar aggregation number ( N_agg) and the micellar radius ( R_m) both increase as the ionic monomer is positioned progressively away from the junction of the hydrophilic and hydrophobic segments along the polymer chain. By defining an ionic monomer position number ( n) as the number of monomers between the junction and the ionic monomer, N_agg exhibited a power law dependence on n with an exponent of ∼1/3 and ∼3/10 for the respective singly and triply charged series. By contrast, R_m exhibited a weaker dependence on the ionic monomer position by a power law relationship with an exponent of ∼1/10 and ∼1/20 for the respective singly and triply charged series. Furthermore, R_m was found to scale with N_agg in a power-law relationship with an exponent of 0.32 for the singly charged series, consistent with a weakly charged ionic star-like polymer model in the unscreened regime. This study demonstrated a unique method to precisely tailor the structure of small spherical micelles based on ionic block copolymers by controlling the sequence and position of the ionic monomer.

A new ultrasonic transducer sample cell for in situ small-angle scattering experiments

Ultrasound irradiation is a commonly used technique for nondestructive diagnostics or targeted destruction. We report on a new versatile sonication device that fits in a variety of standard sample environments for neutron and X-ray scattering instruments. A piezoelectric transducer permits measuring of the time-dependent response of the sample in situ during or after sonication. We use small-angle neutron scattering (SANS) to demonstrate the effect of a time-dependent perturbation on the structure factor of micelles formed from sodium dodecyl sulfate surfactant molecules. We observe a substantial change in the micellar structure during and after exposure to ultrasonic irradiation. We also observe a time-dependent relaxation to the equilibrium values of the unperturbed system. The strength of the perturbation of the structure factor depends systematically on the duration of sonication. The relaxation behavior can be well reproduced after multiple times of sonication. Accumulation of the recorded intensities of the different sonication cycles improves the signal-to-noise ratio and permits reaching very short relaxation times. In addition, we present SANS data for the micellar form factor on alkyl-poly (ethylene oxide) surfactant molecules irradiated by ultrasound. Due to the flexibility of our new in situ sonication device, different experiments can be performed, e.g., to explore molecular potentials in more detail by introducing a systematic time-dependent perturbation.

Classical many-particle systems with unique disordered ground states

Classical ground states (global energy-minimizing configurations) of many-particle systems are typically unique crystalline structures, implying zero enumeration entropy of distinct patterns (aside from trivial symmetry operations). By contrast, the few previously known disordered classical ground states of many-particle systems are all high-entropy (highly degenerate) states. Here we show computationally that our recently proposed "perfect-glass" many-particle model [Sci. Rep. 6, 36963 (2016)10.1038/srep36963] possesses disordered classical ground states with a zero entropy: a highly counterintuitive situation . For all of the system sizes, parameters, and space dimensions that we have numerically investigated, the disordered ground states are unique such that they can always be superposed onto each other or their mirror image. At low energies, the density of states obtained from simulations matches those calculated from the harmonic approximation near a single ground state, further confirming ground-state uniqueness. Our discovery provides singular examples in which entropy and disorder are at odds with one another. The zero-entropy ground states provide a unique perspective on the celebrated Kauzmann-entropy crisis in which the extrapolated entropy of a supercooled liquid drops below that of the crystal. We expect that our disordered unique patterns to be of value in fields beyond glass physics, including applications in cryptography as pseudorandom functions with tunable computational complexity.

Fragility and Strength in Nanoparticle Glasses

Glasses formed from nano- and microparticles form a fascinating testing ground to explore and understand the origins of vitrification. For atomic and molecular glasses, a wide range of fragilities have been observed; in colloidal systems, these effects can be emulated by adjusting the particle softness. The colloidal glass transition can range from a superexponential, fragile increase in viscosity with increasing density for hard spheres to a strong, Arrhenius-like transition for compressible particles. However, the microscopic origin of fragility and strength remains elusive, both in the colloidal and in the atomic domains. Here, we propose a simple model that explains fragility changes in colloidal glasses by describing the volume regulation of compressible colloids in order to maintain osmotic equilibrium. Our simple model provides a microscopic explanation for fragility, and we show that it can describe experimental data for a variety of soft colloidal systems, ranging from microgels to star polymers and proteins. Our results highlight that the elastic energy per particle acts as an effective fragility order parameter, leading to a universal description of the colloidal glass transition.

A structural signature of the breakdown of the Stokes–Einstein relation in metallic liquids

The study provides a possible structural origin for the breakdown of the Stokes–Einstein relation in metallic liquids.

Tunable slow dynamics in a new class of soft colloids

By means of extensive simulations, we investigate concentrated solutions of globular single-chain nanoparticles (SCNPs), an emergent class of synthetic soft nano-objects. By increasing the concentration, the SCNPs show flattening, and even reentrant behaviour, in the density dependence of their structural and dynamic correlations, as well as a soft caging regime and weak dynamic heterogeneity. The latter is confirmed by validation of the Stokes-Einstein relation up to concentrations far beyond the overlap density. Therefore SCNPs arise as a new class of soft colloids, exhibiting slow dynamics and actualizing in a real system the structural and dynamic anomalies proposed by models of ultrasoft particles. Quantitative differences in the dynamic behaviour depend on the SCNP deformability, which can be tuned through the degree of internal cross-linking.

Swelling, structure, and phase stability of compressible microgels

Microgels are soft colloidal particles that, when dispersed in a solvent, swell and deswell in response to changes in environmental conditions, such as temperature, concentration, and pH. Using Monte Carlo simulation, we model bulk suspensions of microgels that interact via Hertzian elastic interparticle forces and can expand or contract via trial moves that allow particles to change size in accordance with the Flory-Rehner free energy of cross-linked polymer gels. We monitor the influence of particle compressibility, size fluctuations, and concentration on bulk structural and thermal properties by computing particle swelling ratios, radial distribution functions, static structure factors, osmotic pressures, and freezing densities. For microgels in the nanoscale size range, particle compressibility and associated size fluctuations suppress crystallization, shifting the freezing transition to a higher density than for the hard-sphere fluid. As densities increase beyond close packing, microgels progressively deswell, while their intrinsic size distribution grows increasingly polydisperse.

Effect of adding nanometre-sized heterogeneities on the structural dynamics and the excess wing of a molecular glass former

We present the relaxation dynamics of glass-forming glycerol mixed with 1.1 nm sized polyhedral oligomeric silsesquioxane (POSS) molecules using dielectric spectroscopy (DS) and two different neutron scattering (NS) techniques. Both, the reorientational dynamics as measured by DS and the density fluctuations detected by NS reveal a broadening of the α relaxation when POSS molecules are added. Moreover, we find a significant slowing down of the α-relaxation time. These effects are in accord with the heterogeneity scenario considered for the dynamics of glasses and supercooled liquids. The addition of POSS also affects the excess wing in glycerol arising from a secondary relaxation process, which seems to exhibit a dramatic increase in relative strength compared to the α relaxation.

Coupling and Decoupling of Rotational and Translational Diffusion of Proteins under Crowding Conditions

Molecular motion of biopolymers in vivo is known to be strongly influenced by the high concentration of organic matter inside cells, usually referred to as crowding conditions. To elucidate the effect of intermolecular interactions on Brownian motion of proteins, we performed (1)H pulsed-field gradient NMR and fluorescence correlation spectroscopy (FCS) experiments combined with small-angle X-ray scattering (SAXS) and viscosity measurements for three proteins, αB-crystalline (αBc), bovine serum albumin, and hen egg-white lysozyme (HEWL) in aqueous solution. Our results demonstrate that long-time translational diffusion quantitatively follows the expected increase of macro-viscosity upon increasing the protein concentration in all cases, while rotational diffusion as assessed by polarized FCS and previous multi-frequency (1)H NMR relaxometry experiments reveals protein-specific behavior spanning the full range between the limiting cases of full decoupling from (αBc) and full coupling to (HEWL) the macro-viscosity. SAXS was used to study the interactions between the proteins in solution, whereby it is shown that the three cases cover the range between a weakly interacting hard-sphere system (αBc) and screened Coulomb repulsion combined with short-range attraction (HEWL). Our results, as well as insights from the recent literature, suggest that the unusual rotational-translational coupling may be due to anisotropic interactions originating from hydrodynamic shape effects combined with high charge and possibly a patchy charge distribution.

Transient binding accounts for apparent violation of the generalized Stokes-Einstein relation in crowded protein solutions

The effect of high concentration, also referred to as crowding conditions, on Brownian motion is of central relevance for the understanding of the physical, chemical and biological properties of proteins in their native environment. Specifically, the simple inverse relationship between the translational diffusion coefficient and the macroscopic solution viscosity as predicted by the generalized Stokes-Einstein (GSE) relation has been the subject of many studies, yet a consensus on its applicability has not been reached. Here, we use isotope-filtered pulsed-field gradient NMR to separately assess the μm-scale diffusivity of two proteins, BSA and an SH3 domain, in mixtures as well as single-protein solutions, and demonstrate that transient binding can account for an apparent violation of the GSE relation. Whereas GSE behavior applies for the single-protein solutions, it does not hold for the protein mixtures. Transient binding behavior in the concentrated mixtures is evidenced by calorimetric experiments and by a significantly increased apparent activation energy of diffusion. In contrast, the temperature dependence of the viscosity, as well as of the diffusivity in single-component solutions, is always dominated by the flow activation energy of pure water. As a practically relevant second result, we further show that, for high protein concentrations, the diffusion of small molecules such as dioxane or water is not generally a suitable probe for the viscosity experienced by the diffusing proteins.

Characteristic length scales of the secondary relaxations in glass-forming glycerol

We investigate the secondary relaxations and their link to the main structural relaxation in glass-forming liquids using glycerol as a model system. We analyze the incoherent neutron scattering signal dependence on the scattering momentum transfer, Q , in order to obtain the characteristic length scale for different secondary relaxations. Such a capability of neutron scattering makes it somewhat unique and highly complementary to the traditional techniques of glass physics, such as light scattering and broadband dielectric spectroscopy, which provide information on the time scale, but not the length scales, of relaxation processes. The choice of suitable neutron scattering techniques depends on the time scale of the relaxation of interest. We use neutron backscattering to identify the characteristic length scale of 0.7 Å for the faster secondary relaxation described in the framework of the mode-coupling theory (MCT). Neutron spin-echo is employed to probe the slower secondary relaxation of the excess wing type at a low temperature ( ∼ 1.13T g . The characteristic length scale for this excess wing dynamics is approximately 4.7 Å. Besides the Q -dependence, the direct coupling of neutron scattering signal to density fluctuation makes this technique indispensable for measuring the length scale of the microscopic relaxation dynamics.

Transport of nanoparticulate material in self-assembled block copolymer micelle solutions and crystals

Water soluble poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) [PEO–PPO–PEO] triblock copolymers self-assemble into thermoreversible micellar crystals comprised of periodically spaced micelles. The micelles have PPO cores surrounded by hydrated PEO coronas and the dimensions of the unit cell of the organized micelles is on the order of several to tens of nanometers. Fluorescence recovery after photobleaching (FRAP) is used to quantify nanoparticle transport in these nanostructured polymer micelle systems. Diffusivity of bovine serum albumin (BSA, D_h ∼ 7 nm) is quantified across a wide range of polymer, or micelle, concentrations covering both the disordered fluid as well as the structured micellar crystal to understand the effects of nanoscale structure on particle transport. Measured particle diffusivity in these micellar systems is reduced by as much as four orders of magnitude when compared to diffusivity in free solution. Diffusivity in the disordered micellar fluid is best understood in terms of diffusion through a polymeric solution, while transport in the structured micellar phase is possibly due to hopping between interstitial sites. These results not only show that the nanoscale structures of the micelles have a measureable impact on particle diffusivity, but also demonstrate the ability to tune nanoscale transport in self-assembled materials.