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Register a new userOn the universality of the critical scaling exponents during sol-gel transition
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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 thermo-responsive 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 relative distance from the critical point. Interestingly, the longest relaxation time has been observed to diverge symmetrically on both the sides of the critical point and also shows a power-law dependence on relative distance from the critical 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 hyper scaling 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 universality for different kinds of systems undergoing the sol-gel transition.
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Magnetic field driven domain wall dynamics in a ferrimagnetic GdFeCo thin film with perpendicular magnetic anisotropy is studied using low temperature magneto-optical Kerr microscopy. Measurements performed in a practically athermal condition allow for the direct experimental determination of the velocity ($ beta = 0.30 pm 0.03 $) and correlation length ($ u = 1.3 pm 0.3 $) exponents of the depinning transition. The whole family of exponents characterizing the transition is deduced, providing evidence that the depinning of magnetic domain walls is better described by the quenched Edwards-Wilkinson universality class.
Sol-gel transition of carboxylated cellulose nanocrystals is investigated using rheology, SAXS, NMR and optical spectroscopies to unveil the distinctive roles of ultrasounds treatment and ions addition. Besides cellulose fibers fragmentation, sonication treatment induces fast gelling of the solution. Gelation is induced independently on the addition of cations, while the final rheological properties are highly influenced by the type, the concentration as well as on the sequence of the operations since salts must be added before sonication to produce stiff gels. Cations with various charge and dimension have been associated to ultrasounds to induce gelation and the gel elastic modulus increase proportionally with the charge over the ion size ratio. SAXS analysis of the Na+ hydrogel and Ca2+ hydrogel to which the ion was added after sonication shows the presence of structurally ordered domains where water is confined as indicated by 1H-NMR investigation of the dynamic of water exchange in the hydrogels. Conversely, separated phases containing essentially free water, characterize the hydrogels obtained by sonication after Ca2+ addition, confirming that this ion induces irreversible fiber aggregation. The rheological properties of the hydrogels depend on the duration of the ultrasound treatment and it enables the design of materials programmed with tailored energy dissipation response.
Polycrystalline Yb substituted NiZn nanoferrites with the compositions of Ni0.5Zn0.5YbxFe2-xO4 (x= 0.00, 0.04, 0.08, 0.12, 0.16 and 0.20) have been synthesized using sol gel auto combustion technique. Single phase cubic spinel structure has been confirmed by the X ray diffraction (XRD) patterns. Larger lattice constants of the compositions are found with increasing Yb3+ concentration while the average grain size (52 to 18 nm) has noticeable decrease as Yb3+ content is increased. The presence of all existing elements as well as the purity of the samples has also been confirmed from energy dispersive X ray spectroscopic (EDS) analysis. Frequency dependent dielectric constant, dielectric loss, dielectric relaxation time, AC and DC resistivity of the compositions have also been examined at room temperature. The DC resistivity value is found in the order of 10 to power 10 (omega-cm) which is at least four orders greater than the ferrites prepared by conventional method. This larger value of resistivity attributes due to very small grain size and successfully explained using the Verwey and deBoer hopping conduction model. The contribution of grain and grain boundary resistance has been elucidated using Cole Cole plot. The study of temperature dependent DC resistivity confirms the semiconducting nature of all titled compositions wherein bandgap (optical) increases from 2.73 eV to 3.25 eV with the increase of Yb content. The high value of resistivity is of notable achievement for the compositions that make them a potential candidate for implication in the high frequency applications where reduction of eddy current loss is highly required.
Renormalization group theory does not restrict the from of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows a weak universality scenario where some of the exponents (e.g., $beta, gamma, u$) vary keeping others (e.g., $delta , eta$) fixed. Here we report a ferromagnetic phase transition in (Sm$_{1-y}$Nd$_{y}$)$_{0.52}$Sr$_{0.48}$MnO$_3$ $(0.5le yle1)$ single crystal where all critical exponents vary with $y.$ Such variation clearly violates both universality and weak universality hypothesis. We propose a new scaling theory that explains the present experimental results, reduces to the weak universality as a special case, and provides a generic route leading to continuous variation of critical exponents and multicriticality.
All previous experiments in open turbulent flows (e.g. downstream of grids, jet and atmospheric boundary layer) have produced quantitatively consistent values for the scaling exponents of velocity structure functions. The only measurement in closed turbulent flow (von Karman swirling flow) using Taylor-hypothesis, however, produced scaling exponents that are significantly smaller, suggesting that the universality of these exponents are broken with respect to change of large scale geometry of the flow. Here, we report measurements of longitudinal structure functions of velocity in a von Karman setup without the use of Taylor-hypothesis. The measurements are made using Stereo Particle Image Velocimetry at 4 different ranges of spatial scales, in order to observe a combined inertial subrange spanning roughly one and a half order of magnitude. We found scaling exponents (up to 9th order) that are consistent with values from open turbulent flows, suggesting that they might be in fact universal.
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