Concentration Superposition Research Articles

Time–Concentration Superposition for Linear Viscoelasticity of Polymer Solutions

The concentration dependence of linear viscoelastic properties of polymer solutions is a well-studied topic in polymer physics. Dynamic scaling theories allow qualitative predictions of polymer solution rheology, but quantitative predictions are still limited to model polymers. Meanwhile, the scaling properties of non-model polymer solutions must be determined experimentally. In present paper, the time-concentration superposition (TCS) of experimental data is shown to be a robust procedure for studying the concentration scaling properties of binary and ternary polymer solutions. TCS can not only identify whether power law scaling may exist or not, and over which concentration range, but also unambiguously estimate the concentration scaling exponents of linear viscoelastic properties for a range of non-model polymer solutions.

Modulation of soft glassy dynamics in aqueous suspensions of an anisotropic charged swelling clay through pH adjustment

HypothesisSodium-montmorillonite (Na-Mt) particles are geometrically anisometric that carry a pH dependent anisotropic surface charge. Therefore, it should be possible to manipulate the particle–particle interaction of colloidal range Na-Mt suspensions through pH changes which in turn should alter the soft glassy dynamics of Na-Mt suspensions. ExperimentsRheological experiments were used to probe the impact of pH mediated colloidal particle–particle interaction on the physical aging, linear viscoelastic response, and yield stress behavior of Na-Mt suspension. FindingsThe temporal evolution of the storage modulus (G') was stronger in the acid regime (pH < 9.5) than the base (pH ≥ 9.5) pH regime. Horizontal shifting of the aging curves in the acid and base regimes led to aging time–H+ concentration and aging time–OH– concentration superposition. An aging time–Na-Mt concentration superposition was also observed in both pH regimes. The critical stress associated with the viscosity bifurcation behavior increased linearly with G' but with different slopes for acid and base regime. We propose that positively charged patches on the Na-Mt particle edge merge with the characteristic surface as a function of H+ ions in the system. This leads to a strongly associated microstructure at low pH and a relatively weak but associated microstructure at natural pH, hence confirming the hypothesis.

Temperature, time, pressure, and CO2concentration dependence of rheological properties for poly(methyl methacrylate)/expanded graphite composites

The effects of temperature, pressure, and supercritical carbon dioxide (scCO2) concentration are investigated on the rheological behavior of poly(methyl methacrylate)/expanded graphite (PMMA/EG) composites with 1, 4, and 7 wt. % EG. The validity of the time-temperature superposition and time-pressure-scCO2 concentration superposition principles for the PMMA/EG composites is explored. At atmospheric pressure, the time–temperature superposition principle holds for the composites with 1 and 4 wt. % EG but fails for that with 7 wt. % EG. This is demonstrated by the rheological master curves and the van Gurp–Palmen plots. The scanning electron microscopy micrographs, the Cole–Cole plots, and weighted relaxation spectra reveal that the composite with a higher content (7 wt. %) of EG exhibits a stronger interfacial interaction between the PMMA chains and EG layers and delayed chains’ relaxation. The viscosity evolution with testing time for the PMMA/EG composite samples during time sweep testing demonstrates that the EG layers hinder the dissolution of scCO2 into the PMMA matrix to some extent. Different from the time–temperature superposition principle, the time–pressure–scCO2 concentration superposition principle is valid for all the prepared PMMA/EG composite samples. This is because the dissolved scCO2 at the PMMA matrix-EG layer interfaces reduces the interfacial interaction between the PMMA chains and EG layers and weakens the effect of the EG layers on the chains’ relaxation.

A time–temperature–moisture concentration superposition principle that describes the relaxation behavior of epoxide molding compounds for microelectronics packaging

Time–temperature superposition is a well-established principle used in the constitutive description of viscoelastic polymers. To expand the description to moisture-induced plasticization effects, two epoxide-based molding compounds used in microelectronics packaging were characterized by dynamic mechanical analysis under varying temperature and moisture controlled environments in their glassy regime. Conditions of up to 85 °C and 85% relative humidity, relevant for industry-defined reliability standards, were applied. By relating the transient ambient conditions to the actual moisture concentration of the samples, temperature-, and moisture concentration-dependent relaxation functions were obtained. By applying a time–temperature–moisture concentration superposition, it is shown, that the materials' behavior can be described assuming a linear dependence of the relative free volume on both temperature and concentration. The two parameters can be super-positioned in the description of the shift of the relaxation time constant spectrum with negligible cross-correlation for the conditions of industrial interest.

Relaxation Dynamics and Underlying Mechanism of a Thermally Reversible Gel from Symmetric Triblock Copolymer

We report a novel thermally responsive system from poly(butyl methacrylate)-b-poly(methacrylic acid)-b-poly(butyl methacrylate) (PBMA-b-PMAA-b-PBMA) triblock copolymer in dimethylformamide (DMF) solvent. This system shows a sol–gel transition by cooling below a critical temperature Tc. The network relaxation times of these gels rightly fall in the typical rheological experiment window, permitting us to investigate the relaxation dynamics and underlying mechanism, with a combination of linear rheology, time-resolved small-angle X-ray scattering (SAXS), and temperature-elevated nuclear magnetic resonance (NMR) measurements. Both time–temperature superposition (TTS) and time–concentration superposition (TCS) are well held in this system. The relaxation dynamics at temperatures below and above Tc are quite different, giving two different activation energies E1a and E2a, respectively. The E1a, being polymer concentration independent, is related to micelle formation of end-blocks, while the concentration depend...

Expression, crosslinking, and developing modulus master curves of recombinant resilin

Resilin is a disordered elastomeric protein found in specialized regions of insect cuticles, where low stiffness and high resilience are required. Having a wide range of functions that vary among insect species, resilin operates across a wide frequency range, from 5Hz for locomotion to 13kHz for sound production. We synthesize and crosslink a recombinant resilin from clone-1 (exon-1+exon-2) of the gene, and determine the water content (approximately 80wt%) and dynamic mechanical properties, along with estimating surface energies relevant for adhesion. Dynamic moduli master curves have been developed, by applying the time-temperature superposition principle (TTSP) and time-temperature concentration superposition principle (TTCSP), and compared with reported master curves for natural resilin from locusts, dragonflies, and cockroaches. To our knowledge, this is the first time dynamic moduli master curves have been developed to explore the dynamic mechanical properties of recombinant resilin and compare with resilin behavior. The resulting master curves show that the synthetic resilin undergoes a pronounced transition with increasing ethanol concentrations, with the storage modulus increasing by approximately three orders of magnitude. Although possibly a glass transition, alternate explanations include the formation of intramolecular hydrogen bonds or that the chitin binding domain (ChBD) in exon-2 might change the secondary structure of the normally disordered exon-1 into more ordered conformations that limit deformation.

Dielectric study on temperature–concentration superposition of liquid to glass in fructose–water mixtures

Broadband dielectric measurements of fructose–water mixtures with various fructose concentrations, Cf (wt.%), in the range of 5–94.6wt.% were carried out in the frequency range of 2mHz–50GHz at 25 and 0°C, to clarify the dynamics of water and fructose molecules in the mixtures from liquid to glass states as a function of Cf. For the mixtures with Cf below 45wt.%, a single relaxation process originating from the reorientational motion of water, i.e., ν relaxation, was observed. In contrast, in the mixtures with Cf above 45wt.%, in addition to the ν relaxation, α relaxation resulting from the cooperative motion of two components appears at a lower frequency than that of the ν relaxation. The temperature dependences of the relaxation time and strength of the α and ν relaxations are governed by the deviation from the glass transition temperature. Similarly, the concentration dependences of the relaxation time and strength are governed by the deviation from the glass transition concentration, which was defined as the concentration at which the relaxation time is 100s. This means that the temperature–concentration superposition appears to be valid for the ν and α relaxations.

Synthesis and rheological characterization of water-soluble glycidyltrimethylammonium-chitosan.

In this study, chitosan (CS) grafted by glycidyltrimethylammonium chloride (GTMAC) to form GTMAC-CS was synthesized, chemically identified, and rheologically characterized. The Maxwell Model can be applied to closely simulate the dynamic rheological performance of the chitosan and the GTMAC-CS solutions, revealing a single relaxation time pertains to both systems. The crossover point of G′ and Gʺ shifted toward lower frequencies as the CS concentration increased but remained almost constant frequencies as the GTMAC-CS concentration increased, indicating the solubility of GTMAC-CS in water is good enough to diminish influence from the interaction among polymer chains so as to ensure the relaxation time is independent of the concentration. A frequency–concentration superposition master curve of the CS and GTMAC-CS solutions was subsequently proposed and well fitted with the experimental results. Finally, the sol-gel transition of CS is 8.5 weight % (wt %), while that of GTMAC-CS is 20 wt %, reconfirming the excellent water solubility of the latter.

Solve Chloride Ions Diffusion Problem by Separation Variable Method for Reinforced Concrete Slab in Marine Environment

Concrete slab as a part of marine engineering structure should surly be suffered from chloride ions corrosion. The relevant chloride ions diffusion problem in a concrete slab immersed in seawater was solved by means of separation variable method in this paper. In comparison with the solutions obtained by error function and numerical calculation methods, we proved this general- ized solution was the correct answer for the bilateral chloride ion diffusion in a concrete slab. Ac- cording to calculation and analysis, we found that the bilateral diffusion would cause greater harm than one side diffusion, but concentration superposition would not occur; chloride ion diffusion rate would speed up when concentration gradient increase caused by the increasing chloride ion concen- tration at one side surface. A mutation of chloride ion concentration gradient might occur where dif- fusion coefficient changed, but the chloride ion concentration distribution kept continuous.

Synthesis and viscoelastic characterization of sulfonated chitosan solutions

In this study, sulfonated chitosan (SCS) with a water-soluble property was synthesized and rheologically characterized. The Maxwell Model can accurately describe a regular chitosan (CS) solution. The G′, G″ crossover shifted toward lower frequencies as the CS concentration increased, revealing an increase of relaxation time. A frequency–concentration superposition master curve of CS solution was therefore plotted and well fitted by the experiment result. However, a modified Maxwell Model, which captures the occurrence of the quasi-plateau region of G′ in the low-frequency range, representing the initially falsely connected structure between the sulfonic acid groups and the protonated ammonium groups, was proposed for the SCS solution. The crossover of G′ and G″ was found to be independent of the SCS concentration, indicating its lower molecular weight yields a high overlap concentration, Ce. The rheological properties of SCS solutions can be affected as the following factors are increased in the order of declining effect; pH level > temperature > salt concentration.

Small strain deformation measurements of konjac glucomannan solutions and the influence of borate cross-linking

The dynamic rheology of aqueous solutions of konjac glucomannan has been evaluated over a range of concentrations up to 2.35%, and the effect of borate cross-linking of such solutions evaluated in the range 0.02–40mM borate. In preliminary work, conventional parallel plate geometries were employed and in situ cross-linking was investigated. For borate cross-linked samples a superior method, however, was found to be measurement of pre-formed cores of cross-linked polymer into which a four-bladed vane geometry was introduced. In order to compare with other associating polymer systems, rheological data were analysed by defining plateau moduli, corresponding relaxation times and zero shear viscosities and the scaling behaviour of these parameters with polymer and cross-linker concentrations was established. Maxwell fits and time–concentration superposition procedures were investigated. The rheological properties of the cross-linked polymer were shown to be the result of both increased network connectivity and retarded network dynamics.

Toxic Gas Continuity Diffusion Algorithm of Multi-Tanks Based on Meshing Technique

According to the techniques of the mashing and the Gaussian plume modeling, combining all kinds of the factors variation, such as the tanks leak velocity, the leak height, the wind direction and speed, and the environmental stabilization grade, the concentration distributing rules of the toxic gas continuous diffusion in the tank farm are simulated. Firstly, focusing on the central of the tank farm in chemical industrial park, mashes the tank farm as the research units for quantitative analysis and superposition calculation. Secondly, constructs the diffusion concentration distributing model of the toxic gas leak based on the Gaussian plume theory. Finally, by the condition of the single-leak hazard installation and the multiple-leak major hazard installations, the toxic gas continuous diffusion algorithms are studied, viz. in accordance with any of the influence factors variation, carve up the time sections, and then basing on Matlab technique, integrating the concentration superposition effects, simulate the concentrated distribution process of the noxious substance during the influence fields. Taking ammonia gas tank farm leakage as example, the simulation results show that the method may provide technological support for major hazard prevention and control in chemical industry park.

Annealing-induced rheological and electric resistance variations in carbon black-filled polymer melts

Annealing-induced viscoelastic and electric conduction variations were traced by simultaneous measurement of resistance and dynamic modulus to carbon black (CB)-filled high-density polyethylene, polystyrene, and polypropylene at elevated temperatures. The resistance decay during annealing the melts is closely related to terminal relaxation of polymer chains and the temperature-mediated interfacial tension between CB and the matrix. On the other hand, a time–temperature–concentration superposition principle was disclosed to evolution of dynamic modulus for the filled melts at different temperatures and CB volume fractions. Annealing the filled melts causes a liquid-to-solid-like transition and the differences in kinetic constant for evolution of dynamic modulus among the three systems at the same condition are involved in interfacial tension.

Viscoelastic properties of solutions of polystyrene melts and carbon dioxide: Analysis of a transient shear rheology approach

In this work, the viscoelastic, thermal, and diffusion properties of solutions of polystyrene melts and carbon dioxide (CO2) were analyzed using plate–plate rheometry in the transient mode. The objective of this study was to evaluate a transient shear rheology approach for high viscosity polymer melts, to verify superposition principles for polystyrene/CO2 solutions, and to measure the glass transition temperature as a function of pressure and CO2 concentration. Two different procedures of saturating polystyrene with carbon dioxide were applied, i.e., loading with the blowing agent below the glass transition temperature of polystyrene and at the measurement temperature. Stress-growth experiments in shear were performed in order to measure the transient viscosity of polystyrene/CO2 solutions in the linear regime. A shift of the transient viscosity data to a mastercurve was applied in order to determine the shift factor of the viscosity and the average relaxation time. Our data indicate that the steady-state viscosity and the average relaxation time are proportional to the temperature–pressure–concentration shift factor aT,p,c within experimental scatter, and consequently a time–temperature–pressure–concentration superposition principle holds for polystyrene/CO2 solutions. Whereas the viscosity of polystyrene strongly depends on the applied temperature and pressure, the elastic equilibrium compliance depicts only a weak dependence on temperature and pressure.

Effect of adsorbed poly(ethylene glycol) on the gelation evolution of Laponite suspensions: Aging time-polymer concentration superposition

The effects of the concentration of polyethylene glycol (PEG) and NaCl on the gelation kinetics of aqueous Laponite suspensions were investigated. The PEG concentration cp was increased from 0.063wt.% to 1.0wt.%, and the NaCl concentration cs was increased from 3.0mM to 5.0mM. The gelation process was monitored with the small amplitude oscillatory shear (SAOS) rheology. At each NaCl concentration, the time curves of storage and loss moduli G′ and G″ at different PEG concentrations were shifted horizontally to construct a master curve. Master curves for different NaCl concentrations were shifted further into a main master curve. The results were understood in terms of an increase in steric repulsion with increasing cp. A model based on the theory of interaction-limited coagulation was proposed to describe the dependence of the shift factor on the PEG concentration, taking into account of the interactions between particles. The quantitative description of the observed results has been achieved with this model.

On the relation between hierarchical morphology and mechanical properties of a colloidal 2D gel system

We study a bidimensional gel system formed by a Langmuir film of gold nanoparticles. Its morphology is thoroughly characterized by AFM, SEM, and ellipsometric imaging techniques and shows a complex structure with features on a hierarchy of different sizes following a Levy distribution. The mechanical response arising after the gel point is investigated by Interfacial Shear Rheometry. The film is found to be mainly elastic, with the mechanical moduli scaling as a power law of the reduced concentration, in the same way as the fluctuation time which was measured in a recent X-ray Photon Correlation Spectroscopy experiment. The frequency dependence of the moduli is well described in the framework of the Soft Glass Rheology model (SGR) [Sollich et al. Phys Rev Lett 78, 2020 (1997)]. In this theory a power law distribution of relaxation times is postulated, whose exponent is experimentally determined for the present case. Such a distribution may reflect – in the dynamics – the hierarchical nature of the morphology of the film evidenced by microscopy. A mastercurve can be built, extending time–temperature to a time–concentration superposition principle as in [Cicuta et al. Phys Rev Lett 90, 116103(2003)]. This allows to describe the mechanical response over a frequency range slightly larger than that experimentally accessible. Besides the SGR component, a viscous term is always present, whose origin is investigated also taking into account samples with different preparation histories.

Rheology and Phase Behavior of Lyotropic Cellulose Nanocrystal Suspensions

The dispersion microstructure and rheological properties of aqueous sulfonated cellulose nanocrystal (CNC) suspensions have been investigated. Between 3.07 and 10.4 vol % the suspensions phase separated into liquid crystalline and isotropic domains. At 12.1 vol %, no isotropic phase was visible, and the samples had the fingerprint texture characteristic of a cholesteric liquid crystal. Below 35 °C, temperature had little influence on rheology and phase behavior. However, between 35 and 40 °C there was a significant change in both the fraction of isotropic phase and the rheological properties. In contrast to many lyotropic suspensions, the steady shear viscosity did not go through a maximum with increasing concentration. Maxima were observed for complex viscosity, storage modulus, and loss modulus at concentrations that appeared fully liquid crystalline. Time–concentration superposition was successful for the loss modulus but not the storage modulus. This suggests that the interface in biphasic samples aff...

Dielectric spectroscopy and confirmation of ion conduction mechanism in direct melt compounded hot-press polymer nanocomposite electrolytes

Solid-type polymer nanocomposite electrolyte (PNCE) comprising poly(ethylene oxide) (PEO), lithium perchlorate (LiClO4) and montmorillonite (MMT) nano-platelets were synthesized by direct melt compounded hot-press technique at 70 °C under 3 tons of pressure. The spectra of complex dielectric function, electric modulus and alternating current (ac) electrical conductivity, and complex impedance plane plots of these materials were investigated in the frequency range 20 Hz to 1 MHz at ambient temperature. The variation of electrode polarization and ionic conduction relaxation times with MMT concentration up to 20 wt.% confirms their strong correlation with direct current ionic conductivity. The predominance of exfoliated MMT structures in PEO matrix and their effect on cation conduction mechanism and ion pairing were discussed by considering a supramolecular transient cross-linked structure. The normalized ac conductivity as a function of scaled frequency of these PNCE materials obey the universal time–concentration superposition behaviour alike the disordered solid ionic conductors.

Viscoelastic properties of highly concentrated maize starch solutions in DMSO

AbstractRheological measurements of highly concentrated dimethylsulfoxide (DMSO) starch solutions were performed. For all experiments commercial maize starch with different AM content was used. The research covered a wide range of polymer concentrations depending on linear fraction contribution and allowed to obtain a starch content up to 40% w/w. The analysis covered the time – concentration superposition method and fitting the continuous Maxwell model to the experimental data using Tikhonov regularization method. The results allowed statements about the viscoelastic behavior of non‐aqueous starch solutions, depending on their molecular structure. If the linear AM is the predominant component of the starch, the system behaves more elastic compared to those composed of branched AP. The effect of variation in molecular constitution is stronger than the effect of concentration of the dispersion. Additionally, the molecular masses of both fractions seems not to be the crucial factor for rheological properties as well as biopolymer solubility in DMSO. Relaxation spectra obtained from Maxwell model show the drift of the main peak to shorter relaxation times when the concentration of biopolymer is rising. The phenomenon testifies about the influence of starch concentration on elastic response of the system.

Self-similarity in electrorheological behavior

In this work we study creep flow behavior of suspension of Polyaniline (PANI) particles in silicone oil under application of electric field. Suspension of PANI in silicone oil, a model electrorheological fluid, shows enhancement in elastic modulus and yield stress with increase in the magnitude of electric field. Under creep flow field, application of greater magnitude of electric field reduces strain induced in the material while application of greater magnitude of shear stress at any electric field enhances strain induced in the material. Remarkably, time evolution of strain in PANI suspension at different stresses, electric field strengths and concentrations show superposition after appropriate shifting of the creep curves on time and strain axes. Observed electric field - shear stress - creep time - concentration superposition demonstrates self-similarity in electrorheological behavior. We analyze the experimental data using Bingham and Klingenberg - Zukoski model and observe that the latter predicts the experimental behavior very well. We conclude by discussing remarkable similarities between observed rheological behavior of ER fluids and rheological behavior of aging soft glassy materials.