Using molecular dynamics computer simulations we investigate the aging dynamics of a gel. We start from a fractal structure generated by the DLCA-DEF algorithm, onto which we then impose an interaction potential consisting of a short-range attraction as well as a long-range repulsion. After relaxing the system at T=0, we let it evolve at a fixed finite temperature. Depending on the temperature T we find different scenarios for the aging behavior. For T>0.2 the fractal structure is unstable and breaks up into small clusters which relax to equilibrium. For T<0.2 the structure is stable and the dynamics slows down with increasing waiting time. At intermediate and low T the mean squared displacement scales as t^{2/3} and we discuss several mechanisms for this anomalous time dependence. For intermediate T, the self-intermediate scattering function is given by a compressed exponential at small wave-vectors and by a stretched exponential at large wave-vectors. In contrast, for low T it is a stretched exponential for all wave-vectors. This behavior can be traced back to a subtle interplay between elastic rearrangements, fluctuations of chain-like filaments, and heterogeneity.
We show that the aging of the mechanical relaxation of a gelatin gel exhibits the same scaling phenomenology as polymer and colloidal glasses. Besides, gelatin is known to exhibit logarithmic structural aging (stiffening). We find that stress accelerates this process. However, this effect is definitely irreducible to a mere age shift with respect to natural aging. We suggest that it is interpretable in terms of elastically-aided elementary (coil$\to$helix) local events whose dynamics gradually slows down as aging increases geometric frustration.
The aging dynamics after shear rejuvenation in a glassy, charged clay suspension have been investigated through dynamic light scattering (DLS). Two different aging regimes are observed: one is attained if the sample is rejuvenated before its gelation and one after the rejuvenation of the gelled sample. In the first regime, the application of shear fully rejuvenates the sample, as the system dynamics soon after shear cessation follow the same aging evolution characteristic of normal aging. In the second regime, aging proceeds very fast after shear rejuvenation, and classical DLS cannot be used.…
We performed Langevin dynamics simulations of amphiphilic polymers that contain strongly associating stickers connected by long soluble chain segments. We explored the aging of a thermoreversible gel which is crosslinked by aggregates (clusters) of the stickers and observed a dramatic increase of their lifetime with aging. We find that the observed aging is the result of structural reorganization of the network: the number of crosslinks decreases with time as small clusters disintegrate and their stickers are reabsorbed by large clusters that grow and become more stable by forming additional i…
We use large-scale computer simulations to explore the non-equilibrium aging dynamics in a microscopic model for colloidal gels. We find that gelation resulting from a kinetically-arrested phase separation is accompanied by `anomalous' particle dynamics revealed by superdiffusive particle motion and compressed exponential relaxation of time correlation functions. Spatio-temporal analysis of the dynamics reveals intermittent heterogeneities producing spatial correlations over extremely large length scales. Our study is the first microscopically-resolved model reproducing all features of the spo…
Colloidal gel aging is investigated using very long runs of brownian dynamics simulations. The Asakura Oosawa description of the depletion interaction is used to model a simple colloid polymer mixture. Several regimes are identified during gel formation. The Intermediate scattering function displays a double decay characteristic of systems where some kinetic processes are frozen. The $β$ relaxation at short times is explained in terms of the Krall-Weitz model for the decorelation due to the elastic modes present. The $α$ relaxation at long times is well described by a stretched exponential, sh…
We monitor the relaxation of internal stresses in a fractal colloidal gel on cessation of flow and find a weak power law decay, $σ_i \sim t^{-α}$ over 5 decades of time where $α\approx 0.07$. The system exhibits physical aging of the elastic modulus, $G' \sim t^β$, with $β\approx α$. Imposition of zero stress after waiting time $t_w$ results in strain recovery as the system relaxes without constraint. Remarkably, recoveries at different $t_w$ can be shifted to construct a master curve where data are scaled vertically by $1/σ_i(t_w)$ and plotted horizontally as $(t-t_w)/t_w^μ$ where $μ\approx 1…
We study the fluctuations of a Brownian micro particle trapped with optical tweezers in a gelatin solution undergoing a fast local temperature quench below the sol-gel transition. Contrary to what was previously reported, we observe no anomalous fluctuations in the particle's position that could be interpreted in terms of an effective temperature. A careful analysis with ensemble averages shows only equilibrium-like properties for the fluctuations, even though the system is clearly aging. We also provide a detailed discussion on possible artifacts that could have been interpreted as an effecti…
The phenomenon of aging in soft matter systems is an intriguing and interesting. In his study we investigate the microstructure and aging dynamics of fluorescent nanoclay gels formed from the mixture of small (~25) and large (~250) aspect ratio nanodiscs using various experimental techniques. We examine how the presence of one kind of clay in other clay of different nature affect the aging dynamics, microstructure and the final resulting phase. Viscosity of the dispersions grows as a power-law with waiting time of the system and the dispersions initially show Maxwellian behaviour but deviated …
We study the rotational diffusion of aging Laponite suspensions for a wide range of concentrations using depolarized dynamic light scattering. The measured orientational correlation functions undergo an ergodic to non-ergodic transition that is characterized by a concentration-dependent ergodicity-breaking time. We find that the relaxation times associated with rotational degree of freedom as a function of waiting time, when scaled with their ergodicity-breaking time, collapse on two distinct master curves. These master curves are similar to those previously found for the translational dynamic…
This paper has been temporarily withdrawn by the authors. We have recently found that noise in the experiments is at the origin of the supposed "back-and-forth" motion which is discussed in the first version of the paper. As a consequence, figs 4 and 5 as well as their discussion are incorrect. Figure 1 and the general trend of fig. 2 are still valid. At this time, we are uncertain whether or not the short time behavior of cI, shown in fig. 3, is affected by measurement noise. We are working on a new version of the paper, using new techniques that allow us to correct for the experimental noise…
Optical tweezers (OTs) can detect pico-Newton range forces operating on a colloidal particle trapped in a medium and have been successfully utilized to investigate complex systems with internal structures. Laponite clay particles in an aqueous medium self-assemble to form microscopic networks over time as electrostatic interactions between the particles gradually evolve in a physical aging process. We investigate the forced movements of an optically trapped micron-sized colloidal probe particle, suspended in an aging Laponite suspension, as the underlying Laponite microstructures gradually dev…
The aging of a charged colloidal system has been studied by Small Angle X-rays Scattering, in the exchanged momentum range Q=0.03 - 5 nm-1, and by Dynamic Light Scattering, at different clay concentrations (Cw =0.6 % - 2.8 %). The static structure factor, S(Q), has been determined as a function of both aging time and concentration. This is the first direct experimental evidence of the existence and evolution with aging time of two different arrested states in a single system simply obtained only by changing its volume fraction: an inhomogeneous state is reached at low concentrations, while a h…
The behavior of microgels near surfaces and their adsorption is studied by simple scaling theory. Two different types of microgels can be studied, i.e., fractal type microgels and randomly crosslinked polymer chains. In the first case the gel can be described mainly by introducing a spectral dimension. The second type requires more attention and uses the number of crosslinks as parameter. The main result is that soft gels with weakly coupled crosslinks and a low number of crosslinks adsorb much better than hard gels, with many crosslinks. Similar results for fractal gels and branched polymer a…
NANOG assembles into self-limiting aging micelles that drive a sol-gel transition and modulate DNA dynamics
Centre for Regenerative Medicine, Institute for Regeneration and Repair（再生医学中心，再生与修复研究所）；School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学院）；School of Molecular Biosciences, University of Glasgow（格拉斯哥大学生物分子科学学院）；Institute for Stem Cell Research, School of Biological Sciences, University of Edinburgh（爱丁堡大学生物科学学院干细胞研究所）
Power law rheology is of widespread occurrence in complex materials that are characterized by the presence of a very broad range of microstructural length and time scales. Although phenomenological models able to reproduce the observed rheological features exist, in general a well-established connection with the microscopic origin of this mechanical behavior is still missing. As a model system, this work focuses on a fractal colloidal gel. We thoroughly characterize the linear power law rheology of the sample and its age dependence. We show that at all sample ages and for a variety of rheologi…
We use linear rheology and multispeckle dynamic light scattering (MDLS) to investigate the aging of a gel composed of multilamellar vesicles. Light scattering data indicate rearrangement of the gel through an unusual ultraslow ballistic motion. A dramatic slowdown of the dynamics with sample age $t_{w}$ is observed for both rheology and MDLS, the characteristic relaxation time scaling as $t_{w}^μ$. We find the same aging exponent $μ=0.78$ for both techniques, suggesting that they probe similar physical processes, that is the relaxation of applied or internal stresses for rheology or MDLS, resp…
Colloidal gels are out of equilibrium soft solids composed of attractive Brownian particles that form a space-spanning network at low volume fractions. The elastic properties of these systems result from the network microstructure, which is very sensitive to shear history. Here, we take advantage of such sensitivity to tune the viscoelastic properties of a colloidal gel made of carbon black nanoparticles. Starting from a fluidized state under an applied shear rate $\dot γ_0$, we use an abrupt flow cessation to trigger a liquid-to-solid transition. We observe that the resulting gel is all the m…
Typically, in quiescent conditions, attractive colloids at low volume fractions form fractal gels structured into two length scales: the colloidal and the fractal cluster scales. However when flow interfere with gelation colloidal fractal gels may display three distinct length scales [Dagès, et al., Soft Matter 18, 6645 (2022)]. Following those recent experimental investigations, we derive two models that account for the structure and the rheological properties of such atypical colloidal gels. The gel elasticity is inferred from scaling arguments and the structure is translated into scattering…
We use X-Ray Photon Correlation Spectroscopy to investigate the structural relaxation process in a metallic glass on the atomic length scale. We report evidence for a dynamical crossover between the supercooled liquid phase and the metastable glassy state, suggesting different origins of the relaxation process across the transition. Furthermore, using different cooling rates we observe a complex hierarchy of dynamic processes characterized by distinct aging regimes. Strong analogies with the aging dynamics of soft glassy materials, such as gels and concentrated colloidal suspensions, point at …
When calcium salts are added to an aqueous solution of polysaccharide pectin, ionic cross-links form between pectin chains, giving rise to a gel network in dilute solution. In this work, dynamic light scattering (DLS) is employed to study the microscopic dynamics of the fractal aggregates (flocs) that constitute the gels, while rheological measurements are performed to study the process of gel rupture. As calcium salt concentration is increased, DLS experiments reveal that the polydispersities of the flocs increase simultaneously with the characteristic relaxation times of the gel network. Abo…
We use time-resolved dynamic light scattering to investigate the slow dynamics of a colloidal gel. The final decay of the average intensity autocorrelation function is well described by $g\_2(q,τ)-1 \sim \exp[-(τ/τ\_\mathrm{f})^p]$, with $τ\_\mathrm{f} \sim q^{-1}$ and $p$ decreasing from 1.5 to 1 with increasing $q$. We show that the dynamics is not due to a continuous ballistic process, as proposed in previous works, but rather to rare, intermittent rearrangements. We quantify the dynamical fluctuations resulting from intermittency by means of the variance $χ(τ,q)$ of the instantaneous autoc…
We study a chemical gelation model in two dimensions which includes both monomer aggregations and bond fluctuations. Our numerical simulation shows that a sol-gel transition occurs when an initial monomer concentration is above a critical concentration. Fractal aggregates grow until the sol-gel transition occurs. After the gelation, however, bond fluctuations break the fractal structure and a novel inhomogeneous gel fibre network appears instead. A pore size distribution of the inhomogeneous structure shows the existence of hierarchical structures in the gel phase. It is also found that slow d…
This work discusses the sedimentation stability and aging of aqueous suspension of Laponite in the presence of cetyltrimethylammonium bromide (CTAB). The concentration of Laponite was fixed at the constant level $C_l=2$ %wt, which corresponds to the threshold between equilibrium gel IG$_1$ and repulsive gel IG$_2$ phases. The concentration of CTAB $C_s$ was within 0-0.3 %wt. In the presence of CTAB the Laponite aqueous suspensions were unstable against sedimentation and they separated out into upper and bottom layers (U- and B-layers, respectively). The dynamic light scattering technique revea…
Using Z-scan and dynamic light scattering measurements we investigate the nonlinear optics response of a colloidal solution undergoing dynamics slowing down with age. We study the high optical nonlinearity of an organic dye (Rhodamine B) dispersed in a water-clay (Laponite) solution, at different clay concentrations (2.0 wt% - 2.6 wt%), experiencing the gelation process. We determine the clay platelets self diffusion coefficient and, by its comparison with the structural relaxation time, we conclude that the gelation process proceeds through the structuring of interconnecting clay platelets ne…
We introduce a microscopically realistic model of a physical gel and use computer simulations to study its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line determined by geometric percolation, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is supported by a fractal network. The gel dynamics is highly heterogeneous and we propose a theoretical model to quantitatively describe dynamic heterogeneity in gels. We e…
We report a study of the structure of droplets of colloidal gels containing dissolved sodium chloride. The components segregate and form intricate patterns. The salt crystalizes in fractal and multi-fractal dendritic forms which are determined by the material which forms the colloidal gel. Here potato starch, gelatine and carboxymethyl cellulose have been used. The substrate also plays a role in some cases. Photographs and micrographs at different level of magnification are shown.
The physical gelation of colloids produces elastic structures that are commonly used to stabilize complex fluids in multiple industries. However, the ability to control the level of elastic modulus of these materials is limited by the universality of the arrested spinodal decomposition mechanism that governs their formation. We demonstrate that manipulating particle shape can yield very large shifts in gel elasticity relative to this universal behavior, and that these changes are generated by a set of independent mechanisms that act multiplicatively. Modeling demonstrates that this efficient g…
Tracking microscopic irreversibility during yielding of a colloidal fractal gel with Rheo-Echo-XPCS
ESRF, The European Synchrotron（欧洲同步辐射光源）；ENSL, CNRS, Laboratoire de Physique（里昂师范学院，法国国家科学研究中心，物理实验室）；C3M, ESPCI Paris, Université PSL, CNRS（C3M，巴黎高等物理化工学院，巴黎文理研究大学，法国国家科学研究中心）；Univ. Grenoble Alpes, CNRS, Grenoble INP, LRP（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，格勒诺布尔理工学院，L RP）；Department of Polymer Engineering, IPC, University of Minho（米尼奥大学，聚合物工程系，IPC）
Dynamic Light Scattering (DLS) measurements were performed on colloidal suspensions of Laponite\textsuperscript{\textregistered} at different concentrations in the range $C_\text{w}= (1.5÷3.0)$%. The slowing down of the dynamics induced by aging was monitored by following the temporal evolution of autocorrelation functions at different concentrations towards the gel and glass transition. Exploiting analogies with supercooled liquids approaching their glass transitions, an Angell plot for the structural relaxation times was drawn. Finally, the fragility of Laponite\textsuperscript{\textregister…
We study colloidal gels formed by competing electrostatic repulsion and short-range attraction by means of extensive numerical simulations under external shear. We show that, upon varying the repulsion strength, the gel structure and its viscoelastic properties can be largely tuned. In particular, the gel fractal dimension can be either increased or decreased with respect to mechanical equilibrium conditions. Unexpectedly, gels with stronger repulsion, despite being mechanically stiffer, are found to be less viscous with respect to purely attractive ones. We provide a microscopic explanation o…
The aging of aggregated structures of monoglycerides in hydrophobic medium is described by a set of different techniques. Polarized microscopy was used to study the mesomorphic behavior as a function of time. Differential scanning calorimetry was utilized to quantitatively monitor changes in the latent heat in different phase transformations that take place in the aging system. Infrared spectroscopy was applied to detect the formation of hydrogen bonding between surfactants. The X-ray diffraction patterns fingerprinted the molecular arrangement in different emerging phases. Infra-red spectrosc…
We study a microscopically realistic model of a physical gel and use computer simulations to investigate its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is supported by a fractal network. Gelation results in a dramatic slowing down of the dynamics, which can be used to locate the transition, which otherwise shows no structural signatures. Moreover, the equil…
To gain insight into the kinetics of colloidal gel evolution at low particle volume fractions $ϕ$, we utilize differential dynamic microscopy to investigate particle aggregation, geometric percolation, and the subsequent transition to nonergodic dynamics. We report the emergence of unexpectedly rich multiscale dynamics upon the onset of nonergodicity, which separates the wave vectors $q$ into three different regimes. In the high-$q$ domain, the gel exhibits $ϕ$-independent internal vibrations of fractal clusters. The intermediate-$q$ domain is dominated by density fluctuations at the length sc…
We investigate the spatio-temporal distribution of microscopic relaxation events, defined through particle hops, in a model polymer glass using molecular dynamics simulations. We introduce an efficient algorithm to directly identify hops during the simulation, which allows the creation of a map of relaxation events for the whole system. Based on this map, we present density-density correlations between hops and directly extract correlation scales. These scales define collaboratively rearranging groups of particles and their size distributions are presented as a function of temperature and age.…
A family of marginally-rigid (isostatic) spring networks with fractal structure up to a controllable length was devised and the viscoelastic spectra $G^{*}(ω)$ calculated. Two non-trivial scaling regimes were observed, (i)~$G^{\prime}\approx G^{\prime\prime}\proptoω^Δ$ at low frequencies, consistent with $Δ=1/2$; (ii)~$G^{\prime}\propto G^{\prime\prime}\proptoω^{Δ^{\prime}}$ for intermediate frequencies corresponding to fractal structure, consistent with a theoretical prediction $Δ^{\prime}=(\ln3-\ln2)/(\ln3+\ln2)$. The cross-over between these two regimes occurred at lower frequencies for lar…
We present dynamic light scattering (DLS) measurements of soft polymethyl-methacrylate (PMMA) and polyacrylamide(PA) polymer gels prepared with trapped bodies (latex spheres or maghemite nanoparticles). We show that the anomalous diffusivity of the trapped particles can be analyzed in terms of a fractal Gaussian network gel model for the entire time range probed by DLS technique. This model is a generalization of the Rouse model for linear chains extended for structures with power law network connectivity scaling, which includes both percolating and uniform bulk gel limits. For a dilute disper…
We report on the fluidization dynamics of an attractive gel composed of non-Brownian particles made of fused silica colloids. Extensive rheology coupled to ultrasonic velocimetry allows us to characterize the global stress response together with the local dynamics of the gel during shear startup experiments. In practice, after being rejuvenated by a preshear, the gel is left to age during a time $t_w$ before being submitted to a constant shear rate $\dot γ$. We investigate in detail the effects of both $t_w$ and $\dot γ$ on the fluidization dynamics and build a detailed state diagram of the ge…
By means of Langevin dynamics simulations, we investigate the gel formation of randomly functionalized polymers in solution, with the ability to form both intra- and intermolecular reversible bonds. Under highly dilute conditions, these polymers form soft nano-objects (so-called single-chain nanoparticles, SCNPs), resulting from the purely intramolecular cross-linking of the reactive functional groups. Here we show that the competition between intra- and intermolecular bonds at finite concentration is governed by a delicate balance of various entropic contributions and leads to a density depen…
Characterizing emergent multiscale dynamics in colloidal nanoparticle gels
University of Michigan（密歇根大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Washington（华盛顿大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）
