Slow Relaxation Mode Research Articles

Rheological signatures of gelation and effect of shear melting on aging colloidal suspension

Colloidal suspensions that are out of thermodynamic equilibrium undergo physical aging wherein their structure evolves to lower the free energy. In aqueous suspension of Laponite, physical aging accompanies increases of elastic and viscous moduli as a function of time. In this work we study temporal evolution of elastic and viscous moduli at different frequencies and observe that freshly prepared aqueous suspension of Laponite demonstrates identical rheological behavior reported for the crosslinking polymeric materials undergoing chemical gelation. Consequently at a certain time tan{\delta} is observed to be independent of frequency. However, for samples preserved under rest condition for longer duration before applying the shear melting, the liquid to solid transition subsequent to shear melting shows greater deviation from classical gelation. We also obtain continuous relaxation time spectra from the frequency dependence of viscous modulus. We observe that, with increase in the rest time, continuous relaxation time spectrum shows gradual variation from negative slope, describing dominance of fast relaxation modes to positive slope representing dominance of slow relaxation modes. We propose that the deviation from gelation behavior for the shear melted suspensions originates from inability of shear melting to completely break the percolated structure thereby creating unbroken aggregates. The volume fraction of such unbroken aggregates increases with the rest time. For small rest times presence of fewer number of unbroken aggregates cause deviation from the classical gelation. On the other hand, at high rest times presence of greater fraction of unbroken aggregates subsequent to shear melting demonstrate dynamic arrest leading to inversion of relaxation time spectra.

Nitrobenzene anti-parallel dimer formation in non-polar solvents

We investigated the dielectric and depolarized Rayleigh scattering behaviors of nitrobenzene (NO2-Bz), which is a benzene mono-substituted with a planar molecular frame bearing the large electric dipole moment 4.0 D, in non-polar solvents solutions, such as tetrachloromethane and benzene, at up to 3 THz for the dielectric measurements and 8 THz for the scattering experiments at 20 °C. The dielectric relaxation strength of the system was substantially smaller than the proportionality to the concentration in a concentrated regime and showed a Kirkwood correlation factor markedly lower than unity; gK ∼ 0.65. This observation revealed that NO2-Bz has a tendency to form dimers, (NO2-Bz)2, in anti-parallel configurations for the dipole moment with increasing concentration of the two solvents. Both the dielectric and scattering data exhibited fast and slow Debye-type relaxation modes with the characteristic time constants ∼7 and ∼50 ps in a concentrated regime (∼15 and ∼30 ps in a dilute regime), respectively. The fast mode was simply attributed to the rotational motion of the (monomeric) NO2-Bz. However, the magnitude of the slow mode was proportional to the square of the concentration in the dilute regime; thus, the mode was assigned to the anti-parallel dimer, (NO2-Bz)2, dissociation process, and the slow relaxation time was attributed to the anti-parallel dimer lifetime. The concentration dependencies of both the dielectric and scattering data show that the NO2-Bz molecular processes are controlled through a chemical equilibrium between monomers and anti-parallel dimers, 2NO2-Bz ↔ (NO2-Bz)2, due to a strong dipole-dipole interaction between nitro groups.

Slow relaxation mode of sodium lignosulfonate in saline solutions

Abstract Sodium lignosulfonate (NaLS) was dissolved in saline solutions, and the dissolving process was examined by a combination of static and dynamic light scattering. When NaLS was dissolved in 1.2 mol l-1 NaCl solution for 24 h and filtered through a 0.45 μm syringe filter, only a fast relaxation mode was observed, which was attributed to the co-diffusion of NaLS molecular ions and counterions. When the concentration of NaCl was below 1.2 mol l-1 or the dissolving time was <24 h, an additional slow relaxation mode (SRM) appeared due to hindered motions of electrostatically interacting chains. Without filtering or filtering followed by rising temperature to 38°C, SRM appeared due to aggregation, which occurred at a position similar to that caused by electrostatic interaction. For poly(sodium styrenesulfonate) (NaPSS) and modified bamboo lignin derivate with open polyelectrolyte structures, 0.1 mol l-1 NaCl was enough to inhibit the electrostatic interaction. For NaLS with a closed polyelectrolyte structure, the SRM could not be removed until the concentration of NaCl reached 1.2 mol l-1. Above observations give insights for the first time into the relationship between the SRM caused by electrostatically interacting chains and the diffusion mode due to NaLS aggregation, and the influence of the closed polyelectrolyte structure on the SRM.

Characterization of Dielectric Responses of Human Cancer Cells in the Terahertz Region

Terahertz time-domain attenuated total reflection spectroscopy, in combination with a two-interface model, is used to determine the complex dielectric constants of cultured human cancer cells (DLD-1, HEK293 and HeLa). Picosecond and sub-picosecond water dynamics are dominant in the measured complex dielectric constants of these cells. We demonstrate that dielectric responses below 1.0 THz best characterize the particular water dynamics of cancer cells when compared with extracellular water. Debye-Lorentz fitting revealed that this is due to a significantly attenuated slow relaxation mode and enhanced fast relaxation mode of the water in these cancer cells. These findings could lead to a new procedure to digitally evaluate cellular activities or functions, in terms of intracellular water dynamics, and remove the veil from the mysterious intracellular milieu.

Kinetics of anisotropic ordering in Laponite dispersions induced by a water-air interface

In this work, we report the kinetics of ordering occurring at the water-air interface of Laponite dispersions. Propagation of such ordering into the bulk and its relaxation dynamics were systematically studied through light scattering measurements. Depolarization ratio D(p), which accounted for the optical anisotropy, was measured as a function of depth from the interface and aging of the samples. The extent of spatial ordering was found to be several decades larger than the typical particle size. Spatial ordering originated from the interface and percolated into the bulk with aging time t(w). Growth in D(p) with waiting time was found to follow power-law behavior given as D(p)~t(w)(n), with n increasing from 0.1 to 4 as one moved away from the interface into the bulk. D(p) decreased exponentially with depth h given as D(p)~e(-(h/h(0))), where h(0) is the decay length, increasing from 0.4 to 0.75 mm with aging time. Dynamic structure factor measurements performed on the samples at various aging times, depths, and temperatures yielded two distinct relaxation times: one fast mode followed by a slow mode. The fast mode remained invariant while slow mode relaxation time followed an exponential decay with depth. This study indicated that the arrested phase nucleated from the interface and propagated into the bulk, which was not observed when the surface was insulated with a layer of hydrophobic liquid. Dilution of the concentrated samples destroyed the aforesaid ordering and made the dispersion homogeneous implying the ordered state was a glass.

Inertial effects of adsorbed glycerol monostearate crystals on the shear rheology of water/canola oil interfaces

Glycerol monostearate (GMS) in canola oil dispersions (1.0%, 2.0%, and 3.0% w/w) were cooled down from 70 to 30°C at a rate of 10.0°C/min forming CD1.0, CD2.0, and CD3.0 crystal dispersions. Interfaces were prepared by pouring CDs over water, and were subjected to a constant shear stress. The creep compliance-time response of the interfaces depended on CD concentration, interfacial film aging time, and shear stress application time. Interfacial rheology experimental data were described by a nearly instantaneous response followed by an exponentially decaying function with two relaxation modes, the latter related to Kevin–Voigt elements connected serially involving inertial effects at relatively short times. The faster relaxation mode was related to the formation of a two-dimensional solid-like structure, while the slower relaxation mode was attributed slow crystal adsorption–desorption diffusional effects in the interface vicinity. The inertial effects had important influence on the interfacial rheology response.

Restricted diffusion of small probe particles in a laponite dispersion

Evanescent wave microscopy is used to study the dynamics of probe particles inside a laponite suspension, when the size of the latex probes is of the order of the diameter of the laponite disks. A correlation procedure is introduced that allows us to study quantitatively the diffusion of small probes. For all studied sizes, the motion exhibits two modes: a fast relaxation mode and a slow relaxation mode. In the fast relaxation mode, the probes diffuse in a viscous medium, whose viscosity does not depend on the diameter of the probes and is slightly larger than the viscosity of water. Then, the diffusion of the particles is restricted over distances larger than their diameters, which increase when the particle diameter decreases. In this regime, the probe particles experience the elasticity of the solution and the apparent elastic modulus increases when the diameter of the probe particle increases, whereas for large enough particles, the macroscopic behavior is recovered, in which the diffusing particles experience a homogeneous medium, and the macroscopic elastic modulus is recovered.

Slow dynamics in transient polyelectrolyte hydrogels formed by self-assembly of block copolymers

Transient polyelectrolyte hydrogels were formed by self-assembly of triblock copolyelectrolytes with a central hydrophilic block, poly(acrylic acid) (PAA), and two hydrophobic end blocks, poly(n-butyl acrylate(50%)-stat-acrylic acid(50%)) [P(nBA(50%)-stat-AA(50%))]. The relaxation of the concentration fluctuations was investigated by dynamic light scattering as a function of the concentration, the pH, the temperature, and the ionic strength. A relatively fast mode was observed at all polymer concentrations caused by cooperative diffusion of the polymers. Above the critical percolation concentration a second slow relaxation mode was observed caused by a linear displacement of small heterogeneities in the network with constant velocity. The relative amplitude of the slow mode was determined by the strength of the electrostatic repulsion. The velocity of the displacement in the transient network is shown to be directly correlated to the terminal relaxation time of the shear modulus and has the same Arrhenius temperature dependence. Both the velocity of the displacement and the mechanical relaxation strongly slow down with decreasing degree of ionization below 0.7 and increasing ionic strength above 0.5 M. A ballistic relaxation process has been reported earlier for colloidal gels, and the present study shows that it can also occur in polymeric networks.

Principal Component Relaxation Mode Analysis of an All-Atom Molecular Dynamics Simulation of Human Lysozyme

A new relaxation mode analysis method, which is referred to as the principal component relaxation mode analysis method, has been proposed to handle a large number of degrees of freedom of protein systems. In this method, principal component analysis is carried out first and then relaxation mode analysis is applied to a small number of principal components with large fluctuations. To reduce the contribution of fast relaxation modes in these principal components efficiently, we have also proposed a relaxation mode analysis method using multiple evolution times. The principal component relaxation mode analysis method using two evolution times has been applied to an all-atom molecular dynamics simulation of human lysozyme in aqueous solution. Slow relaxation modes and corresponding relaxation times have been appropriately estimated, demonstrating that the method is applicable to protein systems.

Determination of the complex dielectric constant of an epithelial cell monolayer in the terahertz region

We present a method to determine the complex dielectric constant of a cell monolayer using terahertz time-domain attenuated total reflection spectroscopy combined with a two-interface model. The imaginary part of the dielectric constant of the cell monolayer shows a lower absorption of slow relaxation mode than that of the liquid medium. This result allows us to estimate the intracellular water dynamics on a picosecond time scale, and the existence of weakly hydrated water molecules inside the cell monolayer was indicated. This method will provide a perspective to investigate the intracellular water dynamics in detail.

Evaluation of relaxation spectra of linear, short, and long-chain branched polyethylenes

The frequency dependent rheological data of several different linear, short- and long-chain branched metallocene catalyzed polyethylenes are assessed with respect to the relaxation spectra. For linear mLLDPEs with M w /M n ≈ 2, a “master spectrum” is established by normalizing on the molar mass. For samples with a distinctly different molar mass distribution, deviations from the “master spectrum” can be observed. It is also demonstrated how the long-chain branches in polyethylenes of different structure influence the spectrum. Depending on the length of branches in long chain branched materials, it is shown that an increasing in the degree of long-chain branching can be clearly observed in the slow relaxation modes, while the fast ones are only affected by high degrees of long-chain branching.

Dynamics and Large Strain Behavior of Self-Healing Hydrogels with and without Surfactants

Polyacrylamide hydrogels formed via hydrophobic interactions between stearyl groups in aqueous micellar solution of sodium dodecyl sulfate (SDS) present two faces depending on which state they are. The gels containing SDS micelles exhibit, in addition to the fast mode, a slow relaxation mode in dynamic light scattering (DLS) and time-dependent elastic moduli, indicating the temporary nature of the hydrophobic associations having lifetimes of the order of seconds to milliseconds. The gels where SDS had been removed after their preparation behave similar to chemically cross-linked ones with time-independent elastic moduli, a high degree of spatial inhomogeneity, and a single relaxation mode in DLS. Because of this drastic structural change, the physical gels are insoluble in water with a gel fraction close to unity. In surfactant containing gels, a large proportion of physical cross-links dissociate under force, but they do so reversibly, if the force is removed they reform again. The reversible disengageme...

Specific features of the temperature behavior of lysozyme diffusivity in solutions with different protein concentrations

The paper presents dynamic light scattering investigations of the temperature behavior of lysozyme diffusivity in solutions with different protein concentrations. The objects are lysozyme solutions with concentrations ranging from 10mg/ml up to 250mg/ml; each sample has been studied at temperatures increasing from 15° to 55°C. The analysis of the autocorrelation functions obtained by DLS for all the solutions has revealed two types of motion with different relaxation times: a fast mode that corresponds to the diffusion of lysozyme molecules and a slow mode associated with the motion of clusters, i.e., complexes consisting of several protein molecules. It is shown that the temperature dependences of the diffusion coefficient of lysozyme in all the solutions are well described by the Arrhenius law. The temperature behavior of the relaxation time of the slow mode has been found to be different for the low- and high-concentration lysozyme solutions. The low-concentration protein solution is characterized by a monotonous decrease in the slow mode relaxation time with increasing temperature. As the lysozyme concentration is increased to 100mg/ml, a considerable change is observed: a minimum in the temperature dependence of the relaxation time of the slow mode appears. Possible reasons for such a behavior of the lysozyme diffusivity are discussed.

Ergodicity breaking and aging dynamics in Laponite–Montmorillonite mixed clay dispersions

Ergodicity breaking and aging dynamics in a mixture of colloidal clays, Laponite (L) and Montmorillonite (MMT), were investigated. The intensity of the light scattered off L-MMT dispersions scaled with solid volume fraction (ϕ) as, I ∼ ϕα, with α = 1.49, for Laponite α = 0.95, for 2 × 10−4 τEB), the slow mode relaxation was no more diffusive and revealed τ2 ∼ q−1, indicating dynamic arrest of the platelets in the glass phase. The temporal evolution of the slow mode relaxation time τ2 in full aging regime i.e. above τEB, followed a power law growth. The τEB was found to decrease with concentration as τEB ∼ exp(−ϕ/ϕ0). A sharp rise in anisotropy, Dp in the L-MMT glass system occurring precisely at the ergodicity breaking time was observed with the overall aging dependence given by Dp ∼ t0.46w. Heterogeneity in these samples was probed from the Cole–Cole plot of rheology data. It is concluded that the aging dynamics was governed by the Laponite platelets with the MMT providing a suitable matrix for appropriate interparticle interactions.

Structure and Dynamics of Supramolecular Polymers Formed by Tris-3,7-dimethyloctyl-cis-1,3,5-cyclohexanetricarboxamide in n-decane via Hydrogen Bonding

Dynamic viscoelastic, dielectric and dynamic flow birefringence measurements were carried out in a highly viscoelastic system (DO3CH/C10), solutions of tris-3,7-dimethyloctyl-cis-1,3,5-cyclohexanetricarboxamide (DO3CH) in n-decane (C10), for a wide concentration (c) range to investigate structure and dynamics of supramolecular polymers formed in the system due to intermolecular hydrogen bonding. The DO3CH/C10 system showed pronounced viscoelastic behavior possessing two relaxation modes: a fast mode with a relaxation time (τ1) independent of c and strength G1 ∝ c2, and a slow mode with the other relaxation time (τ2) highly dependent of c and strength G2 ∝ c1∼1.3. In dielectric and dynamic flow birefringence behavior, singe relaxation modes were clearly observed, which corresponded to the slow relaxation mode with τ2 in viscoelastic behavior. These reveal that two kinds of supramolecular polymers are formed in the system, i.e. a rigid rodlike supramolecular polymer of ca. 45 nm length, which is formed by ∼100 DO3CH molecules via 3-fold hydrogen bonding of amide groups and bear a macro-electric dipole moment of ca. 1100 D, and a flexible supramolecuar polymer with little optical anisotropy and electric dipole moment, which is formed by almost randomly connected DO3CH molecules via hydrogen bonding bearing many defects responsible for a “phantom-crossing” mechanism at entanglement points.

Recrystallization processes in cold-crystallized poly(ethylene terephthalate): Interplay between structure evolution and conformational relaxation

The changes induced in the amorphous regions of poly(ethylene terephthalate) as a consequence of recrystallization processes, taking place after cold-crystallization at Tc=100°C, are analyzed by means of isothermal dynamical mechanical spectroscopy and microindentation hardness. Overall, a recrystallization process at either 115 or 125°C causes an increase of the rigidity within the amorphous domains confined by the crystals. Microhardness measurements carried out at room temperature reveal that recrystallization leads to an enhanced mechanical performance of the amorphous regions. The analysis of isothermal segmental relaxation patterns recorded in a frequency interval of 10−3–60Hz indicates the appearance of two distinct contributions, which find correspondence with observations by broad band dielectric spectroscopy on the same systems. The faster one is ascribed to segmental relaxation within the amorphous domains where the confinement by crystals is relatively weak. The slow relaxation mode is associated with regions where the conformational dynamics is strongly restricted by the crystals. A relative increase of the slow process is detected upon recrystallization. A recently developed relaxation function model is employed to estimate the size of the static cooperatively rearranging regions for both, the slow and the fast modes. It is found that this size increases either upon decreasing the temperature or as an effect of recrystallization. In addition, the number of monomers involved in a conformational rearrangement turns out to be significantly larger in the regions associated to the slow mode process.

An unsymmetrical coordination environment leading to two slow relaxation modes in a Dy2 single-molecule magnet

A Dy(2) single-molecule magnet was isolated using a mixed ligand strategy in which the Dy(III) ions adopt distinct coordination environments. This leads to two unique relaxation modes due to a single-ion type relaxation mechanism. Energy barriers were obtained from individually fitting the overlapping peaks.

Hyperdiffusive dynamics in conjugated polymer blends and fullerene absorbing solutions

We have observed the hyperdiffusive dynamics of light scatterers accompanied by their ballistic motion by a dynamic light scattering (DLS) technique in blends of semiconducting polymer (poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene], MEH-PPV) with a low-molecular-weight organic acceptor 2,4,7-trinitrofluorenone, TNF) and in fullerene C60 solution. The DLS autocorrelation function has been found to follow the Kohlrausch-Williams-Watt function with the exponent β in the range of 0.5–2, depending on the laser power, scattering vector, optical absorption and type of sample. We show that the hyperdiffusive dynamics (β > 1) results from laser-induced convection caused by optical absorption at the DLS probing wavelength. The convection appears in the DLS data as a ballistic motion with velocities in the range of 5–60 μm s−1 depending on the laser power, type of sample and their absorption. The convection is driven by the local temperature difference, ΔT ∼ 0.1–0.2 K, as evaluated from thermal lens effect measurements. We demonstrate that by decreasing the absorbed laser power, laser-induced hyperdiffusion can be avoided in both the polymer and fullerene samples so that the inherent thermal molecular motion can be probed. Specifically, in the polymer solutions, we have found a slow relaxation mode with the characteristic spatial spectrum of the inverse relaxation time Γs α q4. This mode has been assigned to the coupled motion of entangled conjugated polymer chains.

Stochastic entangled chain dynamics of dense polymer solutions

We propose an adjustable-parameter-free, entangled chain dynamics model of dense polymer solutions. The model includes the self-consistent dynamics of molecular chains and solvent by describing the former via coarse-grained polymer dynamics that incorporate hydrodynamic interaction effects, and the latter via the forced Stokes equation. Real chain elasticity is modeled via the inclusion of a Pincus regime in the polymer's force-extension curve. Excluded volume effects are taken into account via the combined action of coarse-grained intermolecular potentials and explicit geometric tracking of chain entanglements. We demonstrate that entanglements are responsible for a new (compared to phantom chain dynamics), slow relaxation mode whose characteristic time scale agrees very well with experiment. Similarly good agreement between theory and experiment is also obtained for the equilibrium chain size. We develop methods for the solution of the model in periodic flow domains and apply them to the computation of entangled polymer solutions in equilibrium. We show that the number of entanglements Π agrees well with the number of entanglements expected on the basis of tube theory, satisfactorily reproducing the latter's scaling of Π with the polymer volume fraction φ. Our model predicts diminishing chain size with concentration, thus vindicating Flory's suggestion of excluded volume effects screening in dense solutions. The predicted scaling of chain size with φ is consistent with the heuristic, Flory theory based value.

Confinement effects in bulk supercooled liquids

Supercooled liquids are known to display heterogeneous dynamics, with slow and fast relaxation modes being independent and even spatially separated in dynamically distinct domains. In such a situation, it is imaginable that the very fast modes are surrounded by material that is practically frozen on the relaxation time scale of that fast mode. Here, we show experimental evidence of such a confinement effect. For the fastest few percent of all modes, equilibration appears to be linked to a common process (e.g. macroscopic softening), while the remaining majority equilibrate on the time scale of their individual time constant, as expected for heterogeneous dynamics.