Viscoelastic properties of phosphoric and oxalic acid-based chitosan hydrogels

In a previous work, we have shown that chitosan true physical gelation occurs in some organic and inorganic acids (Hamdine et al. 2004). Two systems presenting similar gelation mechanisms were characterized furthermore in order to investigate the sol–gel transition: the chitosan–phosphoric acid and the chitosan–oxalic acid systems. By performing rheological measurements in the framework of linear viscoelasticity, we have investigated the effect of time, temperature, and polymer concentration on the gelation evolution. For both acid-based systems, gelation occurred above a critical polymer concentration around 5% w/v (g/100 ml) of chitosan. Isothermal time sweep experiments showed that the gelation occurs in three stages: (i) incubation; (ii) rapid increase of G′; and (iii) a last stage where G′ slowly reached its equilibrium value due to slow molecular diffusion. At the gel point, G′ and G′′ scaled with ω ⁿ , with n=0.55 for both acid-based systems and a fractal dimension d _f of 1.9. Cooling–heating cycles revealed that the gels showed thermoreversibility after one sequence, but became permanent during subsequent cycles.This revised version was published online in October 2005 with corrections to the author's name.     

Molecular dynamics of the glass relaxation process of the soft phase in block copolymers: effect of molecular architecture

To determine the impact of molecular architecture on the molecular dynamics of the glass relaxation processes of soft blocks in different types of block copolymers, model block copolymers with a variation in both molecular architecture and chemical composition were studied. Four block copolymer models, namely, two styrene–butadiene–styrene (S-B-S) block copolymers and two styrene–styrene butadiene–styrene (S-SB-S) were chosen. In each pair of block copolymers, one is linear triblock and the other is star asymmetric. For the sake of comparison, two polybutadiene (PB) homopolymer samples, having similar chain lengths of the PB blocks present in the S-B-S block copolymers, have been investigated. Dynamic mechanical measurements have been carried out for the real and imaginary parts of the complex shear modulus (G′, G”) in the temperature and frequency ranges from −110 to 30 °C and from 10⁻² to 15.9 Hz, respectively. Complete master curves have been constructed for all samples investigated. Moreover, broadband dielectric spectroscopy has been carried out to cover wide temperature and frequency windows, −120 to 0 °C and 10⁻¹ to 10⁷ Hz, respectively. The results showed that the molecular dynamics of the glass relaxation process of the PB or statistical PSB soft phases in the block copolymers is dramatically changed when compared to the PB homopolymer. In addition, the molecular architecture is found to be an important factor in determining the molecular mobility of the soft blocks. The results are discussed in terms of the applied confinement of the counter PS hard phase, block lengths, domain thicknesses and the type of end-to-end junctions between the different polymeric blocks. Paper presented 3rd Annual European Rheology Conference (AERC 2006) April 27–29, 2006, Crete, Greece.     

Field-induced gelation, yield stress, and fragility of an electro-rheological suspension

 Electro-rheological suspensions (ERS) are known to undergo liquid-to-solid transition under the application of an electric field. Long-range interaction between neighboring particles results in sample-spanning particulate structures which behave as soft solids. Here, we studied the rheological expression of this field-induced transition which has many similarities with chemical gelation. This similarity shows in mechanical spectroscopy on a suspension of monodisperse silica in PDMS as model ERS. Upon application of the electric field, dynamic moduli G′, G′′ grow by orders of magnitude and evolve in a pattern which is otherwise typical for gelation of network polymers (random chemical or physical gelation). At the gel point, the slow dynamics is governed by power-law relaxation behavior (frequency-independent tan δ). A low field strength is sufficient to reach the gel point and, correspondingly, the percolating particle structure at the gel point is still very fragile. It can be broken by the imposition of low stress. For inducing a finite yield stress, the field strength needs to be increased further until the long-range electrostatic interaction generates string-like particle alignments which become clearly visible under the optical microscope. The onset of fragile connectivity was defined experimentally by the tan δ method. The ERS was probed dynamically at low frequencies where the transition is most pronounced, and also in steady shear where the rate of structure formation equals the rate of internal breaking. Received: 1 May 2001 Accepted: 11 August 2001     

Viscoelastic properties of dibenzylidene sorbitol (DBS) physical gels at high frequencies

The rheological behavior of Dibenzylidene D-Sorbitol (DBS) gels formed in ethylene glycol, glycerol, mineral oil, ethanol, and chlorobenzene was studied using oscillatory squeezing flow viscometry. The storage (G ^′) and loss (G ^″) moduli were measured as a function of gellant concentration (0.5–2 w/w) and type of solvent. As expected greater values of gel strength (G ^′) were observed for gels containing higher concentrations of DBS. In addition, both storage and loss moduli of 2% systems were mostly frequency independent over the studied range, whereas 0.5% gels did exhibit some degree of dependence. We also found that the solvent plays an important role in the properties of the gels. Among the parameters that affect the viscoelastic properties of DBS gels, the solvent polarity and its ability to form hydrogen bonding may have significant effects on the gel rheology.     

Shear-induced long-range alignment of BCC-ordered block copolymers

Effect of large shear on an asymmetric block copolymer with nanospherical domains has been studied using rheology and small angle X-ray scattering. The material investigated was a triblock copolymer poly[styrene-b-(ethylene-co-butylene)-b-styrene] swollen in a midblock-selective solvent. When cooled below the order–disorder transition temperature (T _ODT), the system forms a locally ordered structure of grains with body-centered cubic (BCC) lattice. Isothermal shearing, either at constant rate or with large amplitude oscillatory shear (LAOS) at low frequencies and strain amplitude greater than or equal to 2.0, leads to the destruction of the BCC lattice (isothermal “shear melting”). Upon cessation of the shear, the BCC structure recovers with kinetics similar to the one after thermal quench from above T _ODT. Under certain experimental conditions, LAOS leads to alignment of the BCC lattice. The lattice orientation depends primarily on shearing frequency. At low frequencies, there exists an upper and lower bound on strain amplitude where monodomain textures can be obtained. Upon alignment, the modulus drops by about 30% of that of the polycrystalline structure. Measurement of rheological properties offers an indirect method for distinguishing between polycrystalline structure (grains) and monodomain texture.     

Uniaxial elongational behavior of poly(vinyl chloride) physical gel

A poly(vinyl chloride) (PVC,  M_w = 102×10³)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition behavior with elevating temperature. The critical gel temperature (T_gel) characterized with a power–law relationship between the storage and loss moduli, G^′ and G^″, and frequency ω, G￠=G^￠￠/tan  ( np/2 ) μ wⁿ{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the T_gel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations were expressed by the neo-Hookean model at high temperature (135°C) near the T_gel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature. These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions.     

Long time stress relaxation of a triblock copolymer with asymmetric composition

The long-time stress relaxation was examined for poly(styrene)-poly(ethylene- co-butylene)-polystyrene triblock copolymer with asymmetric composition in the microphase separated state. Stress relaxation data from a parallel plate rheometer were extended to very long times by using a newly built compression instrument. Three properties were measured, the relaxation time spectrum, the equilibrium modulus, and the instantaneous modulus. Relaxation experiments over several months (without zero drift) allowed determination of extremely long relaxation times as found in soft solids and in liquids near the gel point. In this way, we can distinguish solid from liquid behavior within the experimental time frame. The BCC lattice structure of the test polymer behaves as liquid except at low temperature where an equilibrium modulus was observed in an experiment that lasted over a period of 4 months. The corresponding instantaneous modulus was observed to be constant for the same material and for the same time period.     

Rheology of SiO2/(acrylic polymer/epoxy) suspensions. I. Linear viscoelasticity

Linear viscoelastic properties of SiO₂/(AP/EP) suspension with various SiO₂ volume fractions (ϕ) in a blend of acrylic polymer (AP) and epoxy (EP) were investigated at various temperatures (T). The AP/EP contained 70 vol.% of EP. The SiO₂ particles were treated with epoxy silane coupling agent. The effects of the SiO₂ particles are more pronounced in the terminal zone: a transition from viscoelastic liquid (ϕ ≤ 30 vol.%) to viscoelastic solid (ϕ ≥ 40 vol.%) was observed which can be interpreted as a critical gelation occurring at a critical particle content and critical gel temperature. The SiO₂/(AP/EP) systems exhibited a critical gel behavior at ϕ ≅ 35 vol.% and T ≅ 100°C characterized with a power–law relationship between the storage and loss moduli (G ^′ and G ^″) and frequency (ω); G ^′ = G ^″/tan(nπ/2) ∝ ω ⁿ . The critical gel exponent (n) was estimated to be about 0.45. The gelation occurred with increasing T.     

Nonlinear rheological properties and stability of dibenzylidene sorbitol fiber networks in poly(propylene oxide)

Dibenzylidene sorbitol (DBS) is known to gel organic liquids and polymers such as poly(propylene oxide) (PPO) by forming long fibers and fiber networks. Potential applications of these networks depend on their ability to withstand large deformations without significant morphological changes. Therefore, we studied the nonlinear rheological properties of the DBS fiber network in PPO for different DBS concentrations. We found that the concentration dependence of critical deformation (transition from linear to nonlinear viscoelastic region) and gel strength (G′ plateau in the linear region) can be explained on the basis of a model for densely cross-linked fiber gels (MacKintosh et al., Phys Rev Lett 75:4425–4428, 1995). Performing periodic strain sweeps, we found that the decrease in gel strength during the deformation cycles can be ascribed to reversible fiber coarsening. Additionally, start-up experiments showed a strong shear thinning behavior, which is in quantitative agreement with the SGM model (Sollich, Phys Rev E 58:738–759, 1998).     

Rheological properties of poly(vinyl chloride)/plasticizer systems—relation between sol–gel transition and elongational viscosity

Poly(vinyl chloride) (PVC)/di-isononyl phthalate systems with PVC content of 45.5 (PVC8) and 70.4 wt% (PVC6) were prepared by a hot roller at 150 °C and press molded at 180 °C. The dynamic viscoelasticity and elongational viscosity of PVC8 and PVC6 were measured in the temperature range from 150 to 220 °C. We have found that the storage and loss shear moduli, G′ and G″, of PVC8 and PVC6 exhibited the power-law dependence on the angular frequency ω at 190 and 210 °C, respectively. Correspondingly, the tan δ values did not depend on ω. These temperatures indicate the critical gel temperature T _gel of each system. The critical relaxation exponent n obtained from these data was 0.75 irrespective of PVC content, which was in agreement with the n values reported previously for the low PVC concentration samples. These results suggest that the PVC gels of different plasticizer content have a similar fractal structure. Below T _gel, the gradual melting of the PVC crystallites takes place with elevating temperature, and above T _gel, a densely connected network throughout the whole system disappears. Correspondingly, the elongational viscosity behavior of PVC8 and PVC6 exhibited strong strain hardening below T _gel, although it did not show any strain hardening above T _gel. These changes in rheological behavior are attributed to the gradual melting of the PVC crystallites worked as the cross-linking domains in this physical gel, thereby inapplicability of the of time–temperature superposition for PVC/plasticizer systems.     

Viscoelastic behavior of polymerizing systems

Experimental data of the dynamic viscoelastic properties, storage modulus (G′), loss modulus (G′′), and phase shift (δ) as well as of the viscosity, η, are reported for the polymerization of a free radical polymerization system (methyl methacrylate) which exhibits the Trommsdorff effect. A rheometer-reactor assembly developed in our laboratory is used for this purpose. It is observed that in the early stages of reaction, data lie in the terminal zone. As the polymerization progresses, the Trommsdorff effect leads to a sharp increase in both the polymer concentration and the weight average molecular weight, and the viscoelastic properties then lie in the entanglement zone. A modulus crossover point (when G′ = G′′) is identified that could be used as an identification of the point where the Trommsdorff effect starts assuming significance. Received: 17 September 1998 Accepted: 9 December 1998     

Gelation behavior of polysaccharide-based interpenetrating polymer network (IPN) hydrogels

We report the preparation and rheological characterization of interpenetrating polymer network (IPN) hydrogels made from alginate and hydrophobically modified ethyl hydroxyl ethyl cellulose (HMEHEC). To our knowledge, there have been no studies of the gelation behavior of IPNs. We found that the rheology of these systems can be easily tuned, with the elastic modulus of the IPN strongly dependent on the relative ratio of HMEHEC to alginate. The sol–gel transition of these systems was found to satisfy the Winter–Chambon criterion for gelation at various crosslinker densities. From the power law relationship of the dynamic moduli (G ^′ ~G ^″ ~ω ⁿ), the exponent n appears to be dependent on both the crosslinker density and relative amount of two polymers. The value of n was found to be ~0.5 for all samples for stoichiometric amounts of crosslinker. The effect of molecular weight of HMEHEC on the gel point and viscoelastic exponent has also been reported. Alginate seems to dominate the kinetics of the process but the effect of high molecular weight HMEHEC on the gel point, especially at lower proportion was also evident.     

Beschreibung des visko-elastischen Verhaltens des polymeren Mischsystems Phenolnovolakharz-Nitrilkautschuk (PF/NBR) mit Hilfe der Van-der-Poel-Gleichung

Zusammenfassung Morphologische Untersuchungen an dem polymeren Mischsystem Phenolnovolakharz-Nitrilkautschuk haben gezeigt, daß diese Mischungen eine Struktur aufweisen, in der harte kugelige PF-Teilchen in einer Kautschukmatrix bzw. weiche Kautschukteilchen in einer Harzmatrix eingebettet sind. Mit Hilfe der morphologischen und mechanisch-dynamischen Untersuchungen wird versucht, das viskoelastische Verhalten von Polyblends mit der Van-der-Poel-Gleichung zu beschreiben. Es konnte gezeigt werden, daß bis zu ModulwertenGhart/Gweich ~ 100 eine gute Übereinstimmung mit der Van-der-Poel-Gleichung gefunden wird. Hohe Modulverhältnisse der harten Einlagerungskomponente zur weichen KomponentenGhart/Gweich ~ 1000, wie sie im kautschukelastischen Bereich auftreten, zeigen eine Übereinstimmung mit der Van-der-Poel-Gleichung nur bei einer Volumenkonzentration der harten EinlagerungskomponenteV _f < 0,3. Diese Ergebnisse werden mit anderen bekannten theoretischen Überlegungen über den Zusammenhang zwischen Elastizitätsmodul und Zusammensetzung von Verbundwerkstoffen verglichen.Schlüsselwörter Phenolnovolakharz-Nitrilkautschuk-System, viskoelastisches Verhalten, Torsionspendel, Van-der-Poel-Gleichung

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Summary Morphological investigations of the polymer compound-system novolak resin-nitril rubber (PF/NBR) have shown, that these mixtures exhibit structures, in which hard spherical particles are embedded in a rubber matrix, respectively soft rubber particles in a resin matrix.An attempt was made to describe the viscoelastic behaviour of these polyblends by means of morphological and dynamic-mechanical investigations with the relation given by Van der Poel.Up to ratios of the moduliGhard/Gsoft ~ 100 a good agreement with the Van-der-Poel equation was found. In the rubber elastic region at ratiosG hard/G soft ~ 1000 this agreement was found for volume concentrations of the phenolic componentV _f ~ 0.3 only.The results are compared with other existing theories on the correlation between elastic modulus and composition of compound materials.

Mit 7 Abbildungen und 6 Tabellen     

Effect of nanofillers on the phase separation and rheological properties of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) blends

The viscoelastic characteristics of the blends of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) (PMMA/SAN) were investigated at various temperatures below, near, and above the phase separation temperature. The investigated polymer system is characterized by a lower critical solution temperature. Rheological behavior of the blends in the region of a phase separation was compared with change of the light scattering intensity. The presence of nanofillers in the blend results in that the phase separation occurs at a higher temperature. At the isothermal conditions, the phase separation begins earlier and proceeds with a higher rate as compared with the same blend without filler. The results of the study show the considerable change of the viscoelastic characteristics of PMMA/SAN when the polymer system passes from the homogeneous state to the heterogeneous one. Such characteristics as the dependence of the storage modulus (G ^′) on the loss modulus (G ^″), the dependence of the loss viscosity (η ^″) on the dynamic viscosity (η ^′), the dependences of the complex viscosity (η*), and the free volume fraction (f) on the blend composition are the most sensitive to the phase separation. The phase separation affects the characteristics G ^′(ω), where ω is the frequency only in a low-frequency range. Temperatures of phase separation were estimated using dependence G ^′(T) at ω, which is the constant in the range of low frequencies.     

Time- and temperature-dependent crosslinking behaviour of a silicone resin

The crosslinking behaviour of a silicone resin which is interesting from a technical point of view was investigated by means of rheology. In order to accelerate the crosslinking process, zinc acetylacetonate and aluminium acetylacetonate were applied as latent catalysts. The effect of the type of catalyst, its concentration, and the temperature on crosslinking was determined by isothermal dynamic-mechanical measurements. A radial gradient in crosslinking causes the gel point to be reached earlier at the outer edge of the sample in the rheometer. This radial gradient is averaged when measuring G′ and G″. Therefore, since the physically well-defined state of critical gelation (gel point) could not be obtained from the data, the time at which a distinct crosslinking state is reached was determined by the crossover of the moduli G′ and G″. For this distinguished point, the denotation gelation index GI is introduced. The gelation indices measured at different temperatures follow an Arrhenius-type relationship. Activation energies between 89 and 126 kJ/mol were determined. They were found to be dependent on the type of catalyst used but independent of its concentration. The activation energies of the crosslinking processes enable the calculation of the gelation index at temperatures not measured directly.     

Grafting of polyamide 6 on a styrene–acrylonitrile maleic anhydride terpolymer: melt rheology at the critical gel state

In this work, we studied the melt rheology of multigraft copolymers with a styrene–acrylonitrile maleic anhydride (SANMA) terpolymer backbone and randomly grafted polyamide 6 (PA 6) chains. The multi-grafted chains were formed by interfacial reactions between the maleic anhydride groups of SANMA and the amino end groups of PA 6 during melt blending. Because of the phase separation of SANMA and PA 6, the grafted SANMA backbones formed nearly circular domains which were embedded in the PA 6 melt with a diameter in the order of 20 to 40 nm. The linear viscoelastic behaviour of PA 6/SANMA blends at a sufficiently large SANMA concentration displayed the characteristics of the critical gel state, i.e. the power relations G′ ∝ G′′ ∝ ω ^0.5. In elongation, the PA 6/SANMA blend at the critical gel state showed a non-linear strain hardening behaviour already at a very small Hencky strain. In contrast to neat PA 6, the elasticity of the PA 6/SANMA blends was strongly pronounced, which was demonstrated by recovery experiments. Rheotens tests agreed with the linear viscoelastic shear oscillations and the measurements using the elongational rheometer RME. Increasing the SANMA concentration led to a larger melt strength and a reduced drawability. The occurrence of the critical gel state can be interpreted by the cooperative motion of molecules which develops between the grafted PA 6 chains of neighbouring micelle-like SANMA domains.     

Extensional and shear rheometry of oriented triblock copolymers

 The effects of extensional flow orientation on the rheological properties of two poly(styrene)-poly(ethylene-co-butylene)-poly (styrene) (PS-PEB-PS) triblock copolymers containing either spherical or cylindrical PS microdomains were studied by oscillatory shear and oscillatory extensional experiments. Extensional measurements revealed that below the PS block glass transition temperature pre-oriented triblocks display highly anisotropic mechanical properties. For both polymers, the storage modulus E ′ is higher along the flow direction. Above the PS glass transition temperature the materials are no longer anisotropic and the same storage moduli are obtained along the flow direction and perpendicular to it. Above the PS glass transition temperature the rheological behaviour parallel and perpendicular to the flow direction was also probed in pre-oriented and non-oriented samples by oscillatory shear rheometry. At high frequencies, the mechanical response of the triblocks was found to be independent of the orientation for both copolymers while at low frequencies a strong effect of the flow orientation could be observed. For both polymers the value of the storage modulus was found to be lower along the flow direction that perpendicular to it. This was explained by the ability of PS blocks to relax more easily along the flow direction. Received: 10 September 1999/Accepted: 1 October 1999     

Using oscillatory squeezing flow to measure the viscoelastic properties of dental composite resin cements during curing

We have investigated the rheological changes in two particulate-filled dental composite resin cements during the curing process using a Micro-Fourier Rheometer (MFR). In the MFR, the sample was sandwiched between two parallel plates, and pseudorandom small amplitude squeezing was applied by oscillating the upper plate over a range of frequencies. Fourier transforms of the displacement signal and the resulting time dependent force signal enabled the rapid determination of the dynamic properties G′ and G′′ over the frequency range 2π–200π rad/s . This technique permitted us to follow changes in the rheological properties of the resin cements through the setting period. A typical result was that G′ increased from 2×10³ Pa to 2×10⁵ Pa after about 120 s, and that G′′ changed from 4×10³ Pa to 4×10⁴ Pa over the same period at frequency 40π rad/s. We also found that the dental composite resin cements show linear viscoelastic behaviour over a range of strain amplitudes before curing, but the response becomes distinctly non-linear at the later stages of curing for strain amplitudes γ>0.067%.     

Elasticity and dynamics of particle gels in non-Newtonian melts

We investigate the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based on a mixture of titanium dioxide (TiO₂) nanoparticles and polypropylene. Above a critical volume fraction, Φ _c, the elasticity of the hybrids dramatically increases, and the frequency dependence of the elastic and viscous moduli reflects the superposition of the independent responses of the suspending polymer melt and of an elastic particle network. In addition, the elasticity of the hybrids shows critical behavior around Φ _c. We interpret these observations by hypothesizing the formation of a transient network, which forms due to crowding of particle clusters. Consistent with this interpretation, we find a long-time, Φ-dependent, structural relaxation, which emphasizes the transient character of the structure formed by the particle clusters. For times below this characteristic relaxation time, the elasticity of the network is Φ-independent and reminiscent of glassy behavior, with the elastic modulus, G^′, scaling with frequency, ω, as G^′∼ω ^0.3. We expect that our analysis will be useful for understanding the behavior of other complex fluids where the elasticity of the components could be superimposed.     

The second-law analysis of mixed convection in rectangular ducts

 The rate of entropy generation, S˙ ^′ _G[W/mK], is examined both theoretically and numerically for forced and mixed convection in a rectangular duct heated at the bottom. Under fully-developed flow conditions S˙ ^′ _G is expressed in terms of relevant non-dimensional hydrodynamic and thermal parameters. Numerically, it is demonstrated that S˙ ^′ _G is a single, effective parameter to examine both thermal and hydrodynamic fields and their variations. Received on 22 November 1999