Relaxation Exponent Research Articles

Critical dynamics of the sol-gel transition studied using particle-tracking microrheology.

The formation of tetra-PEG gels, a model network with a well-defined structure, was investigated using particle-tracking microrheology. The dynamic scaling and critical relaxation exponents in the sol-gel transition were determined by applying the time-cure superposition method. Some values of the exponents differed from those of the Rouse model theory. This was attributed to the failure of the theoretical assumption that the cluster structure formation follows the percolation model theory on a three-dimensional lattice.

A Rheological Study on the Effect of Tethering Pro- and Anti-Inflammatory Cytokines into Hydrogels on Human Mesenchymal Stem Cell Migration, Degradation, and Morphology.

Polymer-peptide hydrogels are being designed as implantable materials that deliver human mesenchymal stem cells (hMSCs) to treat wounds. Most wounds can progress through the healing process without intervention. During the normal healing process, cytokines are released from the wound to create a concentration gradient, which causes directed cell migration from the native niche to the wound site. Our work takes inspiration from this process and uniformly tethers cytokines into the scaffold to measure changes in cell-mediated degradation and motility. This is the first step in designing cytokine concentration gradients into the material to direct cell migration. We measure changes in rheological properties, encapsulated cell-mediated pericellular degradation and migration in a hydrogel scaffold with covalently tethered cytokines, either tumor necrosis factor-α (TNF-α) or transforming growth factor-β (TGF-β). TNF-α is expressed in early stages of wound healing causing an inflammatory response. TGF-β is released in later stages of wound healing causing an anti-inflammatory response in the surrounding tissue. Both cytokines cause directed cell migration. We measure no statistically significant difference in modulus or the critical relaxation exponent when tethering either cytokine in the polymeric network without encapsulated hMSCs. This indicates that the scaffold structure and rheology is unchanged by the addition of tethered cytokines. Increases in hMSC motility, morphology and cell-mediated degradation are measured using a combination of multiple particle tracking microrheology (MPT) and live-cell imaging in hydrogels with tethered cytokines. We measure that tethering TNF-α into the hydrogel increases cellular remodeling on earlier days postencapsulation and tethering TGF-β into the scaffold increases cellular remodeling on later days. We measure tethering either TGF-β or TNF-α enhances cell stretching and, subsequently, migration. This work provides rheological characterization that can be used to design new materials that present chemical cues in the pericellular region to direct cell migration.

Origin of ργ/T scaling of primary and secondary conductivity relaxation times in mixture of water with protic ionic liquid.

Murali et al. [J. Phys. Chem. Lett., 2024, 15, 3376-3382] made ambient and high pressure dielectric measurements of a supercooled aqueous mixture of an acidic ionic liquid to find the presence of the primary (σ) conductivity relaxation together with the secondary (ν) conductivity relaxation originating from the water clusters confined by the cations and anions with relaxation times τσ and τν respectively. From the isothermal and isobaric conductivity relaxation data found on varying thermodynamic conditions (i.e. T and P) at constant τσ are the invariance of (i) the frequency dispersion or the Kohlrausch function exponent (1 - n) of the primary conductivity relaxation, and (ii) the ratio of the primary and secondary conductivity times, τσ/τν. This co-invariance of τσ, τν, and (1 - n) at constant τσ was observed before in non-aqueous ionic liquids, but it is found for the first time in aqueous ionic liquids. The new data together with PVT measurements enable Murali et al. to show additionally that both τσ and τν are functions of ργ/T with a single exponent γ = 0.58. The Coupling model is the only theory predicting the co-invariance of τσ, τν, and (1 - n) as well as the ργ/T scaling of both τσ and τν. It is applied herein to address and explain the data of the ionic liquid-water mixture.

Rheological percolation, gel‐like behavior and electrical conductivity of multi‐walled carbon nanotubes filled ethylene‐vinyl acetate copolymer/acrylonitrile‐butadiene rubber nanocomposites

AbstractReasonable studies on the composite systems containing conductive nanoparticles are very important to manufacture the materials with physico‐mechanical tailor‐made properties. In this work, rheological percolation, gel‐like behavior and electrical properties of multi‐walled carbon nanotubes (MWCNTs) filled ethylene‐co‐vinyl acetate/acrylonitrile‐butadiene copolymer blends containing 0–7 wt% MWCNTs were studied. The Winter‐Chambon criterion validity was evaluated for physical gelation of the system. The rheological and electrical percolation threshold, gel point (Pg), relaxation exponent (n), gel strength (Sg), and the fractal dimension (df) at the gel point were calculated. The formation of physical gel and rheological percolation threshold were both found to occur at 1 wt% MWCNTs concentration. Based on the df value determined, it was revealed that the system behaved similar to the one in which the excluded volume interactions were nearly screened. It was also found that the storage modulus (G′) near the Pg followed a power‐law scaling relationship in the form where is the distance from Pg. The electrical conductivity of the nanocomposites increased with the increase in MWCNTs loading after the nanofillers content surpassed a certain value. A schematic model was proposed to demonstrate the variation of electrical conduction with the increase in MWCNTs concentration. The excluded volume and hard‐core models were also employed to estimate the average aspect ratio of the nanofillers embedded in the system.Highlights Morphology and gel‐like behavior of EVA/NBR/MWCNTs system were studied Winter‐Chambon criterion was found to be valid for the gelation of the system Rheological percolation and gel point were occurred at the same MWCNTs loading It was found excluded volume interactions were nearly screened at gel point A schematic model for microstructure development was suggested for the system

Physico-chemical, microbiological, and sensory characteristics of yogurt as affected by various ingredients

l-Glutamine, quercetin, slippery elm bark, marshmallow root, N-acetyl-d-glucosamine, licorice root, maitake mushrooms, and zinc orotate have been reported to help treat leaky gut. The purpose of this research was to explore the impact of these functional ingredients on the physico-chemical, microbiological, and sensory properties of yogurt. The milk from same source was equally divided into 9 pails and the 8 ingredients were randomly assigned to the 8 pails. The control had no ingredient. Milk was fermented to yogurt. The pH, titratable acidity, syneresis, viscosity, color (L*, a*, b*, C*, and h*), Streptococcus thermophilus counts, and Lactobacillus delbrueckii spp. bulgaricus counts of yogurts were determined on d 1, 7, 14, 21, 28, 35, and 42, whereas coliform counts, yeast and mold counts, and rheological characteristics were determined on d 1 and 42. The sensory study was performed on d 3 and particle size of the functional ingredients (powder form) was also determined. When compared with control, the incorporation of slippery elm bark into yogurts led to less syneresis. l-Glutamine increased pH and n' values (relaxation exponent derived from G') and lowered titratable acidity values. N-Acetyl-d-glucosamine incorporation resulted in higher n' and lower titratable acidity values, whereas maitake mushroom led to lower n' values. Incorporating quercetin increased the growth of L. bulgaricus. Adding maitake mushrooms increased the growth of S. thermophilus but lowered apparent viscosity values, whereas quercetin decreased its S. thermophilus counts. Quercetin decreased L* and a* values but increased b* values, and maitake mushroom increased a* values. Thixotropic behavior increased with the addition of licorice root and quercetin. Adding slippery elm bark, N-acetyl-d-glucosamine, licorice root, maitake mushrooms, and zinc orotate into yogurt did not affect the sensory properties, whereas yogurts with quercetin had the lowest sensory scores. Overall, most of these ingredients did not cause major changes to yogurt properties.

Novel Liquor-Based Hot Sauce: Physicochemical Attributes, Volatile Compounds, Sensory Evaluation, Consumer Perception, Emotions, and Purchase Intent.

Hot sauces are popular peppery condiments used to add flavor and sensory excitement to gastronomical preparations. While hot sauce occupies a retail category well over a century old, a novel production method using liquor as the base preservative rather than traditional vinegar is now commercially available, and its uniqueness begs study. Hot sauces produced with tequila, rum, vodka, and bourbon were compared to traditional vinegar-based hot sauces concerning physicochemical properties, volatile compounds, microbiological quality, sensory scores, emotions, and purchase intent (PI). Under accelerated conditions, pH, titratable acidity (TA), water activity (Aw), viscosity, and color were analyzed weekly for 20 weeks, whereas rheological properties, coliforms and yeasts and molds were examined on weeks 1 and 20. Hexyl n-valerate, butanoic acid, 3-methyl-, hexyl ester, and 4-methylpentyl 3-methylbutanoate were found in high concentrations in the pepper mix as well as the hot sauce produced with vinegar. When compared to vinegar-based hot sauces, liquor-based hot sauces had similar Aw (p > 0.05), higher pH, viscosity, and L* values and lower TA, a*, and b* values (p < 0.05). Samples formulated with liquors increased the relaxation exponent derived from G’ values having a greater paste formation when compared to vinegar-based hot sauces. The sensory evaluation was carried out in Honduras. The liquor-based hot sauces had a significant (p < 0.05) impact on emotion and wellness terms. Bourbon and tequila samples had higher ratings than control samples in several wellness and emotion responses (active, energetic, enthusiastic, good, curious, pleased, stimulated, and wild). Adventurous, joyful, free, worried, refreshed, and healthy scores were not significantly (p > 0.05) different among treatments.

Characterizing rheological properties and microstructure of thioester networks during degradation.

Covalent adaptable networks are designed for applications including cell and drug delivery and tissue regeneration. These applications require network degradation at physiological conditions and on a physiological timescale with microstructures that can: (1) support, protect and deliver encapsulated cells or molecules and (2) provide structure to surrounding tissue. Due to this, the evolving microstructure and rheological properties during scaffold degradation must be characterized. In this work, we characterize degradation of covalent adaptable poly(ethylene glycol) (PEG)-thioester networks with different amounts of excess thiol. Networks are formed between PEG-thiol and PEG-thioester norbornene using photopolymerization. These networks are adaptable because of a thioester exchange reaction that takes place in the presence of excess thiol. We measure degradation of PEG-thioester networks with L-cysteine using multiple particle tracking microrheology (MPT). MPT measures the Brownian motion of fluorescent probe particles embedded in a material and relates this motion to rheological properties. Using time-cure superposition (TCS), we characterize the microstructure of these networks at the gel-sol phase transition by calculating the critical relaxation exponent, n, for each network with different amounts of excess thiol. Based on the measured n values, networks formed with 0% and 50% excess thiol are tightly cross-linked and elastic in nature. While networks formed with 100% excess are similar to ideal, percolated networks, which have equal viscous and elastic components. MPT measurements during degradation of these networks also measure a non-monotonic increase in probe motility. We hypothesize that this is network rearrangement near the phase transition. We then measure macroscopic material properties including the equilibrium modulus and stress relaxation. We measure a trend in bulk network properties that agrees with the values of n. Elastic modulus and stress relaxation measurements show that networks with 50% excess thiol are more elastic compared to the other two networks. As the amount of excess thiol is increased from 0% to 50%, the networks become more elastic. Further increasing excess thiol to 100% reduces the elastically effective cross-links. We hypothesize that these properties are due to network non-idealities, resulting in networks with 50% excess thiol that are more elastic. This work characterizes dynamic rheological properties during degradation, which mimics processes that could occur during implantation. This work provides information that can be used in the future design of implantable materials enabling both the rheological properties and timescale of degradation to be specified.

Relaxation Exponents of OTOCs and Overlap with Local Hamiltonians.

OTOC has been used to characterize the information scrambling in quantum systems. Recent studies have shown that local conserved quantities play a crucial role in governing the relaxation dynamics of OTOC in non-integrable systems. In particular, the slow scrambling of OTOC is seen for observables that have an overlap with local conserved quantities. However, an observable may not overlap with the Hamiltonian but instead with the Hamiltonian elevated to an exponent larger than one. Here, we show that higher exponents correspond to faster relaxation, although still algebraic, and such exponents can increase indefinitely. Our analytical results are supported by numerical experiments.

Resolving the mixed-alkali effect on the viscoelastic behavior of supercooled liquids

Relaxation processes in mixed-alkali metaphosphate glasses and supercooled liquids are studied using a combination of calorimetric, electrical impedance spectroscopic and rheological measurements to investigate the atomistic nature of the mixed-alkali effect (MAE) on the glass transition temperature Tg and viscous flow. While Tg and fragility index of single-alkali liquids are controlled by the segmental motion of phosphate chains, the mixed-alkali liquids exhibit the presence of a second relaxation process, which is slower than chain motion and is characterized by a lower activation energy. This process is assigned to the scission and renewal of P-O bonds that relieve the accumulated stress in the network resulting from its matrix-mediated coupling with pairwise hopping of dissimilar alkalis. The viscous flow and glass transition in mixed-alkali phosphate liquids appear to be controlled by this P-O bond scission-renewal process, which is shown to be consistent with a lowering of their fragility index and a concomitant decrease in the stretching exponent of structural relaxation, compared to their single-alkali counterparts.

Rheological and Viscoelastic Properties of Chitosan Solutions Prepared with Different Chitosan or Acetic Acid Concentrations.

Chitosan (Ch) is a partially crystalline biopolymer, insoluble in pure water but soluble in acid solutions. It has attracted interest from researchers to prepare solutions using different acid types and concentrations. This research aims to study both the effect of chitosan (Ch) or acetic acid (Ac) concentrations, at different temperatures, on rheological and viscoelastic properties of Ch solutions. To study the effect of Ch, solutions were prepared with 0.5–2.5 g Ch/100 g of solution and Ac = 1%, whereas to study the effect of Ac, the solutions were prepared with 2.0 g of Ch/100 g of solution and Ac = 0.2–1.0%. Overall, all analyzed solutions behaved as pseudoplastic fluid. The Ch strongly affected rheological properties, the consistency index (K) increased and the index flow behavior (n) decreased as a function of Ch. The activation energy, defined as the energy required for the molecule of a fluid to move freely, was low for Ch = 0.5%. The effect of Ac was less evident. Both K and n varied according to a positive and negative, respectively, parabolic model as a function of Ac. Moreover, all solutions, irrespective of Ch and Ac, behaved as diluted solutions, with G” > G’. The relaxation exponent (n”) was always higher than 0.5, confirming that these systems behaved as a viscoelastic liquid. This n” increased with Ch, but it was insensitive to Ac, being slightly higher at 45 °C.

Attenuation of the Acoustic Activity in Cement Beams under Constant Bending Load Closely Approaching the Fracture Load

The acoustic activity in beam-shaped specimens made of cement is studied, assuming that the beams are loaded in three-point bending under a step-wise loading scheme. Attention is focused to the attenuation of the acoustic activity during the constant-load stage of each specific loading step. The experimental data are analyzed in terms of the interevent time intervals between any two successive acoustic hits (using the F-function concept) and, further, in terms of the power of the acoustic hits (in terms of the recently introduced P-function). It is indicated that while the mechanical load is kept constant, the acoustic activity attenuates steadily, and during the early steps of this attenuation phase, the temporal evolution of both the F- and P-functions is excellently described by an exponential law. Moreover, it is proven that for both the F- and P-functions, the relaxation exponents decrease monotonically with increasing load. This decrease becomes quite abrupt for loads exceeding about 80% of the fracture load, providing an interesting and promising pre-failure indicator, i.e., a warning signal that the specimen is entering into the stage of impending macroscopic fracture. The specific conclusions are in very satisfactory agreement, both qualitatively and quantitatively, with similar ones drawn by considering the temporal evolution of the respective b-value.

Markovian dynamics in de Sitter

The equilibrium state of fields in the causal wedge of a dS observer is thermal, though realistic observers have only partial access to the state. To them, out-of-equilibrium states of a light scalar field appear to thermalize in a Markovian fashion. We show this by formulating a systematic expansion for tracing out the environment. As an example, we calculate the O(λ) correction to the result of Starobinsky and Yokoyama for the relaxation exponents of λϕ4 theory.

Rheological properties of phase transitions in polydisperse and monodisperse colloidal rod systems

AbstractRheological modifiers are added to formulations to tune rheology, enable function and drive phase changes requiring an understanding of material structure and properties. We characterize two colloidal rod systems during phase transitions using multiple particle tracking microrheology, which measures the Brownian motion of probes embedded in a sample. These systems include a colloid (monodisperse polyamide or polydisperse hydrogenated castor oil), surfactant (linear alkylbenzene sulfonate [LAS]), and nonabsorbing polymer (polyethylene oxide [PEO]) which drives gelation by depletion interactions. Phase transitions are characterized at all concentrations using time‐cure superposition. We determine that rheological evolution depends onLAS:colloid. The critical PEO concentration required to form a gel,cc/c*, is independent ofLAS:colloid, critical relaxation exponent,n, is dependent onLAS:colloid, and both are independent of colloid polydispersity.nindicates the material structure at the phase transition. AtLAS:colloid &gt; 16, the scaffold is a tightly associated network and atLAS:colloid = 16 a loosely associated network.

Multiple power-law viscoelastic relaxation in time and frequency domains with atomic force microscopy

Complex viscoelastic materials exhibit power law (PL) relaxations, as opposed to simple materials described by exponential decays. Other interesting materials, like living cells, hold a universal double PL behavior whose exponents depend on the health and type of the cells. Usually, only dynamic assays are considered capable to study such viscoelastic relaxation mechanisms. In this work, we propose analytical responses with single or multiple power-law relaxation behavior by generalizing classical viscoelastic models in terms of fractional derivatives of arbitrary order α (0 1). In addition, we demonstrate that simple atomic force microscopy force curves are powerful methods to directly observe the viscoelastic relaxation of such complex materials. In order to validate our findings, we compare the viscoelastic relaxation exponents measured directly from simple force curves (SFCs) with those measured with dynamic techniques in both living cells and polyacrylamide gels. We believe the fractional models unveiled here describe a variety of complex materials and may be used (with SFCs) to explore sophisticated viscoelastic phenomena.

Origin of the anomalously low Raman exponents in single molecule magnets

The Raman exponent of single-molecular magnetic relaxation may take various unexpected values because of rich phonon spectrum and spin-phonon coupling of molecular crystals. We systematically examine the origins of different abnormalities, and clarify misunderstandings in the past, particularly the appropriateness of the fitting procedures for the exponents. We find that exponential laws raised by optical phonons can yield spurious power laws with low exponents. This observation indicates long-standing misunderstandings for origins of low Raman exponents in a large bulk of single-molecule magnets. Resulting from spin-lattice coupling with optical modes, presence of these exponents suggests the importance of the local dynamical environment for the magnetic relaxation in this regime.

Vibronic barrier effect of magnetic relaxation in single-molecule magnets

Two fundamental puzzles (under-barrier spin relaxation and low Raman exponents) inside magnetic relaxation have long been studied. New theory brings revolutionary treatments, which provide new design rules for high-performant single-molecule magnet.

Variable range hopping and modulus relaxation in NiFe2O4 ceramics

Nickel ferrite ceramics prepared from combustion derived powders have been investigated using dielectric, impedance, and modulus spectroscopy over a wide frequency (0.1 Hz–1 MHz) and temperature range (173–473 K). Step-like dielectric response ε'T,f is related to the surface barrier layer capacitor (SBLC) effect. Dielectric relaxation peaks in ε″(f) masked by the huge dielectric loss are revealed by εder″(f) derived from the ε′(f) data following Kramers – Kronig transformations. Multiple relaxations are evidenced from the asymmetric nature of εder″(f) peaks. Impedance Cole-Cole analysis reveals two relaxation processes corresponding to grain and grain-boundary effects. A maximum in the grain capacitance (Cg) at 293 K is attributed to the collective influence of electron and hole charge carriers on dielectric polarization. The modulus analysis reveals distinctly three relaxations occurring at temperatures T ≥ 323 K, and only two relaxations for T < 323 K. The variation of modulus relaxation frequencies ln(fmax) with (1/T) suggests different conduction mechanisms for temperature above and below 323 K. The two relaxations observed in the entire temperature range originate due to hopping of holes and electrons at equivalent B-sites of NiFe2O4, while the third relaxation seen only at temperatures T > 323 K is attributed to defect hopping. The present analysis based on modulus relaxation, dc conductivity, and power law exponent sT indicates two different conduction mechanisms for Nickel ferrite NiFe2O4 with variable range hopping dominating at lower temperatures, and thermally activated hopping at higher temperatures.

Competition between Structural Relaxation and Crystallization in the Glass Transition Range of Random Copolymers.

Structural relaxation in polymers occurs at temperatures in the glass transition range and below. At these temperatures, crystallization is controlled by diffusion and nucleation. A sequential occurrence of structural relaxation, nucleation, and crystallization was observed for several homopolymers during annealing in the range of the glass transition. It is known from the literature that all of these processes are strongly influenced by geometrical confinements. The focus of our work is copolymers, in which the confinements are caused by the random sequence of monomer units in the polymer chain. We characterize the influence of these confinements on structure formation and relaxation in the vicinity of the glass transition. The measurements were performed with a hydrogenated nitrile-butadiene copolymer (HNBR). The kinetics of the structural relaxation and the crystallization was measured using fast differential scanning calorimetry (FDSC). This technique was selected because of the high sensitivity, the fast cooling rates, and the high time resolution. Crystallization in HNBR causes a segregation of non-crystallizable segments in the macromolecule. This yields a reduction in mobility in the vicinity of the formed crystals and as a consequence an increased amount of so-called “rigid amorphous fraction” (RAF). The RAF can be interpreted as self-assembled confinements, which limit and control the crystallization. An analysis of the crystallization and the relaxation shows that the kinetic of both is identical. This means that the Kohlrausch exponent of relaxation and the Avrami exponent of crystallization are identical. Therefore, the crystallization is not controlled by nucleation but by diffusion and is terminated by the formation of RAF.

A comprehensive study on the gelation process of silica gels from sodium silicate

The sol-gel route via sodium silicate precursor is known as a practical synthesis method to prepare silica gels in a cost effective way. In the current research, rheological properties of the synthesized silica gels were investigated at different pH values. The gelation time (tgel) was determined from the rheological measurements at different frequencies of 0.1, 0.3 and 0.5 Hz. The results were analyzed using rheological equations of state and the concept of the gelation point was discussed. The results revealed that tgel increases by increasing the pH value. Moreover, it was proved that the fractal value (df) is dependent on the pH value. The relaxation exponent (Δ) value was measured as 0 < Δ < 1/2, which shows that the gel system follows the non-stoichiometrically balanced reactions. Finally, it was shown that the gelation process is divided into three stages, namely, induction, gelation and over curing. The results revealed that by increasing the pH value, stage I is extended while stage II is diminished.

On the universality of the scaling relations during sol-gel transition

The evolution of viscoelastic properties near the sol-gel transition is studied by performing oscillatory rheological measurements on two different types of systems: a colloidal dispersion and a thermoresponsive polymer solution under isothermal and non-isothermal conditions. While undergoing sol-gel transition, both the systems pass through a critical point. An approach to the critical point is characterized in terms of divergence of zero-shear viscosity and the subsequent appearance of the low-frequency modulus. In the vicinity of the critical gel state, both the viscosity and the modulus show a power-law dependence on the relative distance from the critical point. Interestingly, the longest relaxation time has been observed to diverge symmetrically on both sides of the critical point and also shows a power-law dependence on relative distance from the critical gel point. The critical (power-law) exponents of the zero-shear viscosity and modulus are observed to be related to the exponents of the longest relaxation time by the hyperscaling laws. The dynamic critical exponent has also been calculated from the growth of the dynamic moduli. Remarkably, the critical relaxation exponent and dynamic critical exponent predicted from the scaling laws precisely agree with the experimental values from the isothermal as well as non-isothermal experiments. The associated critical exponents show remarkable internal consistency and advocate the universality of scaling relations for different kinds of systems undergoing the sol-gel transition.