Winter-Chambon Criterion Research Articles

Gelation of PU elastomers: rheological characterization for liquid additive manufacturing

AbstractPolyurethane (PU) is a versatile polymer with many applications in a wide range of products. A novel 3D printing technology called liquid additive manufacturing (LAM) extended its possibilities by generating PU elastomers with gradient properties in continuous processing. LAM, being a relatively new technique, has not been extensively researched, particularly in terms of the curing behavior of the liquid resin. In this work, we investigated the effect of composition on gelation time tGP as measured by time-resolved mechanical spectroscopy (TRMS) and analyzed using the Winter–Chambon criterion with the assistance of the IRIS software. This method is more accurate than the previous approach, which involved time sweeps with a constant frequency. It was found that the gel time tGP first decreased and then increased with increasing polyol ratio, ranging from 231 to 378 min. Furthermore, the crosslink densities of the different PU elastomers measured from the rheological and tensile tests were calculated and compared based on the theory of rubber elasticity. The crosslink density decreased with an increasing polyol ratio in both methods. However, the crosslink density values obtained from the rheological measurements were higher than those from the tensile tests. These findings demonstrate that adjusting the polyol ratio is an effective means of achieving gradient properties. The composition effects we measured offer valuable insights for the design of LAM–PU elastomers.

Thermo-rheological and kinetic characterization and modeling of an epoxy vitrimer based on polyimine exchange.

The present study describes the development of cure kinetics and chemo-rheological models for an epoxy vitrimer based on polyimine exchange to elucidate the potential in terms of processing and accurate process selection. Reaction kinetics is investigated using differential scanning calorimetry. A good agreement between the model and data can be demonstrated for different stoichiometries by selecting a parallel reaction approach consisting of an nth-order and an autocatalytic approach. The suggested chemo-rheological model captures the intrinsically high viscosity of the resin over a broad temperature and curing range, even after the gelation point. The Di-Benedetto equation represents the glass transition temperature advancement with cure while combining the rheological Winter-Chambon criterion and the kinetic model determines the degree of cure at the gelation. These results give important advice for improved process modeling of vitrimeric resins, facilitate accurate process selection, and pave the way towards the development of composites based on the matrix system investigated in this work.

Phase separation and rheological behavior of a new biphenyl poly(aryl-ether-ketone)-bismaleimide composite resin

Ex-situ toughening technology is a good solution to improve the toughness of intrinsically brittle thermosetting resin matrix fiber composites. In order to better combine the ex-situ toughening technology with resin transfer molding (RTM) process to prepare high performance bismaleimide (BMI) resin matrix composites, in this paper, based on a new thermoplastic biphenyl polyether ketone (PAEK-B) resin, the phase separation behavior of the PAEK-B in BMI resin and carbon fiber composites, and the rheological properties of PAEK-B/BMI composite resin were studied. The results show that the phase separation behavior of PAEK-B occurs in the injection window temperature of BMI resin for a certain time, and the phase separation structure is maintained in the carbon fiber (CF)/PAEK-B/BMI composites prepared by RTM process. The solution of PAEK-B in the BMI resin is affected by the injection temperature of BMI resin. The initial viscosity of the BMI resin decreases with the increase of injection temperature, but the inflection point time of the PAEK-B/BMI composite resin decreases; The PAEK-B/BMI composite resin accords with the Winter-Chambon criterion. The tanδ of the composite resin has no dependence on the frequency, and the gel activation energy of the composite resin increases with the increase of PAEK-B content.

Determination of critical gel-sol transition point of Highly Concentrated Micellar Casein Concentrate using multiple waveform rheological technique

The purpose of this study was to determine critical gel-sol transition point of Highly Concentrated Micellar Casein Concentrate (HC-MCC) during heating of cold gel. We applied Winter–Chambon criterion (tan δ becomes independent of frequency) on multiwave oscillatory rheological data as a robust alternative to a conventional rheological method which typically treats crossover of storage modulus (G’) and loss modulus (G”) as a gel-sol transition point. We found that the conventional method indicates a pseudo-gel sol transition point which is frequency dependent and does not represent true physical state of the material. Gel-sol transition temperature obtained with multiple waveform rheological method (11.1 °C) was significantly (P < 0.05) different as compared to the conventional method (21–27 °C). While using the convergent point of tan δ (indicating its frequency dependence) from different frequencies obtained from standard temperature sweep and extracted from multiwave test showed about the same gel-sol transition point (11.1 °C). The low frequency dependence of the sample at 5 (n = 0.06) and 11.1 °C (n = 0.07) also confirmed the sample is a strong gel at these temperatures, while the high frequency dependence at 25 °C (n = 0.7) demonstrated a viscoelastic liquid behavior. These findings demonstrated that employing Winter–Chambon criterion can be an effective way for determining of true gel-sol transition point of HC-MCC, and multiwave oscillation was a quick measurement for analyzing the sample. This study would also draw the attention of researchers to avoid the wrong practice of determining temperature-induced phase transition without considering the frequency dependence.

Gelation of Konjac glucomannan crosslinked by organotitanium chelated with different ligands

Konjac Glucomannan (KGM) gels can be formed in the presence of organotitanium as crosslinkers which were chelated by different organic compounds. Organotitanium cross-linking agent is a chelate formed by coordination between tetrabutyl titanate and different organic compounds. The gel network was formed through the crosslinking reaction between titanium ions dissociated from organotitanium crosslinkers and the cis-diol hydroxyl groups on the mannose units of polysaccharide chains. Effect of concentration and species of ligands on rheological properties of the complex gels was studied by dynamic viscoelastic measurements. The gelation kinetics of the gels were investigated and the critical gelation points of the gels were accurately determined according to the Winter-Chambon criterion. The effects of kinds and concentrations of ligands on the shear storage modulus (G’), the loss modulus (G”), and the sol-gel transition points were studied. The sol-gel transition time varies with different ligands in the organotitanium crosslinkers. The sol-gel transition time and temperature were obviously observed and in good agreement with Winter–Chambon criterion.

Dynamical heterogeneity in the gelation process of a polymer solution with a lower critical solution temperature.

The gelation of a hydrophobically modified hyaluronic acid aqueous solution which shows a lower critical solution temperature of about 25 °C was investigated by multi-particle tracking microrheology. The linear viscoelasticity of the gelling system is converted from the microrheological data. The critical gelling temperature Tgel = 36.3 °C was determined from the loss tangent by the Winter-Chambon criterion. The critical exponent n = 0.62 was determined from the shift factors of the time-cure superposition. The length scales of the dynamic heterogeneity of the gelling system were analyzed using a proposed framework where single-particle and multi-particle non-Gaussian parameters were compared. The length scale of the dynamic heterogeneous regions monotonically decreases during the gelation process, consistent with the nucleation-and-growth mechanism of phase separation. Distributions of local viscosity in the gelling system were extracted from the observed distributions of particle displacement as a time-dependent fingerprint of the dynamic heterogeneity of the gelling system. The results and analyzing methods proposed in the present work can be applied to other microrheological studies.

Similarity in Linear Viscoelastic Behaviors of Network Formation and Degradation Processes

The design of the network formation and degradation processes is required to control hydrogel's life cycle. There have been many studies to optimize both processes of the hydrogel for biomaterials. The conventional studies based on the assumption that the network formation and degradation processes are equivalent. The premise of the similarity is not self-evident, which is difficult to investigate experimentally. It is because of the difficulty in the experimental determination of the connectivity of the network. In this study, we utilized the Tetra gel with slow degradation units to observe a continuous process from network formation to degradation of a single hydrogel. We measured the time-development of the linear viscoelastic properties during the network formation and degradation processes using a single system. The linear viscoelasticity at the same connectivity and the critical points for gelation and degradation well agreed. These results strongly suggest that the network formation and degradation go along the identical path toward the opposite directions. Based on our findings, we propose a simplified criterion for the gelation over the Winter-Chambon criterion based on the observation. These findings will help a basis for the sol-gel transition behavior of the polymer gels.

Effects of Bloom number on phase transition of gelatin determined by means of rheological characterization

This study shows the impact of the Bloom number on the melting and gelation behavior of porcine gelatin. Different batches of gelatin were prepared in concentrations of 2, 3, and 5 wt% having Bloom numbers of 100, 180, 240, and 260. Using asymmetrical flow field-flow-fractionation, the molecular weight of gelatin was determined. It was observed that higher Bloom numbers correspond to higher molecular weights. Systematic strain and temperature sweep tests were conducted to determine the yielding point and the phase transition temperatures. The latter was established by the crossover point method and the Winter-Chambon criterion, and small differences between these two methods were recorded. By increasing the Bloom number, the dynamic moduli were increased, as well as the gelation and melting temperatures. The same trend is valid for the gelatin concentration. On the other hand, the Bloom number does not considerably affect the yielding phenomenon under large amplitude oscillatory shear deformations. In conclusion, the Bloom number has a similar rheological effect on gelatin as the molecular weight, and considerable alterations of the viscoelastic gel properties can be expected at significantly different Bloom numbers.

Rheological Study on the Thermoreversible Gelation of Stereo-Controlled Poly(N-Isopropylacrylamide) in an Imidazolium Ionic Liquid.

The thermoreversible sol-gel transition for an ionic liquid (IL) solution of isotactic-rich poly (N-isopropylacrylamides) (PNIPAMs) is investigated by rheological technique. The meso-diad content of PNIPAMs ranges between 47% and 79%, and molecular weight (Mn) is ~35,000 and ~70,000 g/mol for two series of samples. PNIPAMs are soluble in 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl) imide ([BMIM][TFSI]) at high temperatures but undergo a gelation with decreasing temperatures. The transition temperature determined from G’-G” crossover increases with isotacticity, consistent with the previous cloud-point result at the same scanning rate, indicating imide groups along the same side of backbones are prone to be aggregated for formation of a gel. The transition point based on Winter-Chambon criterion is on average higher than that of the G’-G” crossover method and is insensitive to tacticity and molecular weight, since it correlates with percolation of globules rather than the further formation of elastic network (G’ > G”). For the first time, the phase diagram composed of both G’-G” crossover points for gelation and cloud points is established in PNIPAM/IL mixtures. For low-Mn PNIPAMs, the crossover-point line intersects the cloud-point line. Hence, from solution to opaque gel, the sample will experience two different transitional phases, either clear gel or opaque sol. A clear gel is formed due to partial phase separation of isotactic segments that could act as junctions of network. However, when the partial phase separation is not faster than the formation of globules, an opaque sol will be formed. For high-Mn PNIPAMs, crossover points are below cloud points at all concentrations, so their gelation only follows the opaque sol route. Such phase diagram is attributed to the poorer solubility of high-Mn polymers for entropic reasons. The phase diagram composed of Winter-Chambon melting points, crossover points for melting, and clear points is similar with the gelation phase diagram, confirming the mechanism above.

Rheokinetics and Characteristics of Resulted Gels during Isothermal Gelation Process for Lower Concentrated PAN/DMSO/H2O Solutions

Isothermal gelation processes for relatively low concentration PAN/DMSO/H2O solutions are studied by rheology. Winter–Chambon criterion is unitedly used to investigate the rheological kinetics and the structural and mechanical characteristics of the resulted gels are evaluated. It is found that during the isothermal gelation procedure, two coincident points appear sequentially, where loss tangent tan δ is independent of frequency. The occurrence of two coincident points suggests that the critical gel forms first, then it evolves into the second self-similar structure, and the average distance between crosslinks of network becomes shorter. The results also show that decreasing temperature, increase of PAN concentration or H2O content will lead to faster gelation kinetics and formation of more elastic and compact critical gel and the second self-similar structure. At the same temperature, the later formed second self-similar structure is always more elastic and compact than the critical gel, and the corresponding gel stiffness is stronger.

Characterisation of rheology and microstructures of κ-carrageenan in ethanol-water mixtures

The effects of ethanol (up to 20 wt%) on the rheological properties and structural characteristics of κ-carrageenan gel were investigated by Field Emission Scanning Electron Microscopy (FESEM) and Small Angle X-ray Scattering (SAXS). Both the sol-gel and gel-sol transition temperatures shifted to higher degree (from 36.8 ± 0.5 to 52.5 ± 1.4 °C and from 51.2 ± 0.6 to 67.0 ± 0.5 °C, respectively) upon 20 wt% ethanol addition (P < 0.05). The critical relaxation exponent n and the critical gel strength Sg obtained from Winter-Chambon criterion decreased and increased, respectively as the ethanol concentration increased. The κ-carrageenan gel was formed due to the formation of fibrillar networks, and the fibrillar density increased upon ethanol addition via FESEM. Moreover, upon 20 wt% ethanol addition, the average radius of gyration of κ-carrageenan strand increased from 1.18 ± 0.03 of control to 1.55 ± 0.02 nm by SAXS. A mechanism underlying the effect of ethanol on the κ-carrageenan gelation was proposed based on coil to double helix transition followed by the helix aggregation.

Improved viscoelastic, thermal, and mechanical properties of in situ microfibrillar polypropylene/polyamide 6,6 composites via direct extrusion using a triple-screw extruder

Improved viscoelastic, thermal, and mechanical properties ofin situmicrofibrillar polypropylene/polyamide 6,6 compositesviadirect extrusion using a triple-screw extruder.

Rheology of the ultrasound-induced gelation in poloxamer aqueous solutions

The rheological behavior of the ultrasound-induced gelation of poloxamer aqueous solutions (Pluronic F-127, Sigma-Aldrich) is analyzed in this work. A new rheometric technique is proposed in which ultrasonic pulses are applied to the sample under shear flow. An ultrasonic transducer was adapted to the lower plate of a controlled-stress rheometer with a parallel-plate fixture (AR-1000 TA Instruments). Solutions were tested under linear oscillatory-shear flow at constant angular frequency in time sweeps with and without ultrasound. The mechanical response of the ultrasound-formed gels was evaluated under linear oscillatory and instantaneous stress relaxation tests. Results suggest that these solutions produce “weak gels” according to the Winter-Chambon criterion.

Thermoreversible gelation and scaling behavior of Ca2+-induced κ-carrageenan hydrogels

The effect of calcium cations (Ca2+) on thermoreversible gelation properties, microstructure, and scaling behavior of κ-carrageenan in aqueous solution was studied by micro-differential scanning calorimetry (micro-DSC), field emission scanning electron microscopy (FESEM) and rheology. It was found that κ-carrageenan molecules self-associated into fibrils, and the diameter and number of fibrils increased with increasing Ca2+ ion concentration. The formation and melting of κ-carrageenan hydrogel was thermally reversible and extremely sensitive to Ca2+ ions. The viscoelastic property at the gel point was examined using the Winter-Chambon criterion to obtain the critical relaxation exponent n and the critical gel strength Sg. n and Sg were found to decrease and increase with increasing Ca2+ ion concentration respectively. The normalized gel strength, Sg/Ca2+, was not independent of Ca2+ ion concentration, suggesting a strong effect of Ca2+ ions on both size and density of junctions formed during gelation. A schematic diagram has been proposed to explain how Ca2+ ions could facilitate the coil-helix transition, leading to the formation of more aggregates acting as junctions.

Steady, dynamic, and creep-recovery rheological properties of myofibrillar protein from grass carp muscle

This study investigated the solution behaviors and sol–gel transition of myofibrillar protein (MP) from grass carp muscle by rheological methods. In steady shear measurements, shear-thinning behavior was observed in the MP solutions and became more apparent with increasing concentration (c), though Newtonian plateaus appeared at c ≤ 0.025 mg/mL. Based on the Cross model, zero shear viscosity (η0) and structural relaxation time (K) increased with increasing c, indicating the reinforcement of chain interaction and entanglement. From the dependence of η0 on c, the MP showed the rod-like polymer features due to its α-helical tail, and the coil overlap concentration (c*) was estimated to be 4.5 mg/mL, at which the MP coils begin to overlap and interpenetrate undergoing the transition from a dilute to concentrated solution. In frequency sweep, the MP system was classified to two regions: an entanglement network or concentrated solution (5 and 10 mg/mL), and a weak gel (15 and 20 mg/mL). Furthermore, the sol–gel transition concentration (cgel) was further identified as 13 mg/mL by the Winter–Chambon criterion. According to the creep-recovery data fitted by the Burger model, the elastic coefficients (G1 and G2) and viscous coefficients (η1 and η2) increased with increasing temperature (5–40 °C), while the maximum deformation (JMAX) and residual deformation (J∞) decreased, leading to an increase in the final percentage recovery (R%). This result indicated that the chain rigidity of MP increased with elevated temperature, the MP gel network formed and became stronger, confirming the denaturation, aggregation and pre-gelation of MP at ∼40 °C.

Thermoreversible gelation and scaling laws for graphene oxide-filled κ-carrageenan hydrogels

The effects of graphene oxide (GO) and ammonia functionalized graphene oxide (AGO) on microstructure, thermoreversible and critical gelation properties of κ-carrageenan in aqueous solution were studied by micro-differential scanning calorimetry (micro-DSC), field emission scanning electron microscopy (FESEM) and rheology. The presence of GO or AGO was able to decrease the gel formation and melting temperatures and reduce gel strength. The effect of AGO was more evident than that of GO. It was observed by FESEM that κ-carrageenan gel was induced by the formation of a fibrillar network, and fibrillar size and density decreased with increasing GO or AGO content. The viscoelastic properties at the gel point were examined using the Winter-Chambon criterion to obtain the critical relaxation exponent n and the critical gel strength Sg. n increased but Sg decreased with increasing GO or AGO content. The more obvious increase in n and decrease in Sg were observed in the AGO/κ-carrageenan solution, which further demonstrated the stronger weakening effect of AGO. A schematic diagram has been proposed to explain the effect of AGO on the gelation of κ-carrageenan, where AGO sheets attracted a number of κ-carrageenan chains through hydrogen bonding and electrostatic interaction between sulfate groups of κ-carrageenan and amine groups of AGO. As a result, the number of free κ-carrageenan chains in solution decreased and the coil-helix transition and aggregation of helices of κ-carrageenan were affected negatively.

Thermoreversible gelation and viscoelasticity of κ-carrageenan hydrogels

The gelation behavior of κ-carrageenan in aqueous solution was studied by microdifferential scanning calorimetry and rheology. It was found that the formation and melting of κ-carrageenan hydrogels were thermally reversible and extremely sensitive to κ-carrageenan concentration. In comparison with the crossover of G′ and G″, the extrapolation method based on multiwave oscillation and Winter–Chambon criterion were able to give more accurate critical gel temperature Tc. At the gel point, the critical relaxation exponent n was almost constant whereas the critical gel strength Sg increased with κ-carrageenan concentration. In the stable gel state, the plateau modulus Ge depended on temperature according to a power-law scaling, Ge ∝ ε2.2, where ε is the relative distance (=|T − Tc|/Tc) and independent of κ-carrageenan concentration. The presence of potassium ions shifted the formation and melting temperatures of κ-carrageenan hydrogel to higher temperatures, and the temperatures for gel formation and melting increased with increasing potassium ions' content.

What is Transition Temperature for Bitumen and How to Measure It?

In a typical year and for any typical location in India, the lowest temperature of the pavement can go up to 0 °C or below and the highest temperature can reach up to 70 °C or above. During such temperature changes, the binder exhibits behaviour ranging from a glassy material (at lower temperature) to a viscoelastic/non-Newtonian fluid (at higher temperature). The range of temperature change which is of interest to a pavement engineer is the transition between viscoelastic solid to viscoelastic fluid. Two measurements are normally used for quantifying the transition temperature and they are the G′–G″ cross over point and the point when tan δ is independent of frequency (Winter-Chambon criterion). These measures are applicable when the material has a single relaxation time (typically a single constituent material). Since bitumen is a mixture of several complex hydrocarbons each with different relaxation time, it is natural that such measures are also frequency dependent. This investigation will focus attention on determining the frequency dependence of G′–G″ cross over point as well as the relationship of tan δ with frequency. An unmodified binder of VG30 grade as per IS73-2013 and a crumb rubber modified binder of meeting CRMB 60 grade as per IS:15462-2004 were used in this investigation. To estimate the viscoelastic solid–fluid transition temperature, frequency domain tests were performed in the temperature range of 25–75 °C for frequencies in the range of 50–1 Hz. All the tests discussed in this study were performed at two aging conditions, unaged and short-term aged. Due to the frequency dependent nature of bitumen, the transition temperature is not a sharp point as in the case of polymers but occurred gradually over a temperature range. Contrary to what one expected, modification process did not drastically change the transition temperature and one could see a change of only 3 °C for CRMB 60 when compared to VG30. Aging of the modified bitumen proportionally shifted the transition temperature in a similar manner to that of the unmodified bitumen. It was also clearly seen that the Winter-Chambon criterion was not met for all the binders investigated in this study.

Analyzing a fractal gel of charged oblate nanoparticles in a suspension using time-resolved rheometry and DLVO theory.

The disk-like nanoparticles of LAPONITE® are known to self-assemble to form a fractal gel within hours after a sufficiently large concentration of LAPONITE® is dispersed in water containing salt. The concentration of sodium counterions associated with LAPONITE® particles, however, continues to increase over a period of days, suggesting that delamination of LAPONITE® disks from stacks is sluggish and/or dissociation of counterions is slow. In either case, spontaneous self-assembly of LAPONITE® particles occurs even though delamination and/or counterion dissociation has not reached its equilibrium state. In order to determine the nature of the fractal gel as the extent of delamination and/or dissociation progresses towards equilibrium, we subject the LAPONITE® suspension to a freezing-defrosting cycle, which interestingly reinitiates the gelation process in suspension afresh. Application of time-resolved rheometry to a defrosted suspension shows that iso-frequency loss tangent curves intersect at an identical point, validating the Winter-Chambon criterion for a critical fractal gel state. Interestingly, while the time required to form a critical gel is observed to decrease with increased time elapsed since preparation, at which freezing-defrosting is carried out, the fractal dimension of the critical gel is observed to remain unaffected. We also solve DLVO theory for free energy interactions between the negatively charged LAPONITE® particle faces and analyze the observed phenomena.

Linear and nonlinear viscoelasticity of polymer/silica nanocomposites: an understanding from modulus decomposition

We investigate the linear and nonlinear viscoelasticity of a model polymer nanocomposite of fumed silica nanoparticles in poly-(ethylene-co-α-butene) (PEB). Above a critical filler fraction, a space-filling network builds up as a result of cluster agglomeration and causes the material to change from liquid-like to solid-like states. Using the Winter-Chambon criterion, the percolation threshold from the measured dynamic moduli is found to depend strongly on the matrix viscoelasticity even when the particle dispersion is identical. Such phenomenon comes from the implicit assumption in the method that the contribution from particles (or particle agglomerates) should dominate the dynamic moduli, which is usually inapplicable when polymer has a high viscosity (or elasticity). A new method is suggested to decompose the moduli of composites into the hydrodynamic part and the part from particle agglomerates by taking into consideration the different effects of particles on the strain rate and stress. The two portions are shown to depend on oscillatory frequency, which are adopted to extrapolate the dynamic moduli to lower frequency. The percolation threshold from these extrapolated data becomes independent of the matrix viscoelasticity. Furthermore, it is found that the appearance of nonlinear behavior in oscillatory shear is related to the portion of particle agglomerates in storage modulus and the strain rate is the key factor to destroy the structures.