Evaluation of molecular weight distribution from dynamic moduli

A method to evaluate molecular weight distribution (MWD) from dynamic moduli is presented here. It relies on the least-square fitting of the dynamic data to a model whose parameters depend on the MWD. In particular, the analytical solution for the relaxation modulus previously obtained from the double reptation model, with the Tuminello step relaxation function and the Generalized Exponential Function (GEX) describing the MWD (Nobile and Cocchini 2000), has been used. A Finite Element Approximation (FEA) has been applied to calculate dynamic moduli from the relaxation modulus as a function of MWD. The sensitiveness of the GEX-double reptation dynamic moduli on the model parameters has also been investigated and the results show that large changes of the M_w/M_n ratio weakly affect the dynamic moduli, while small changes of the M_z/M_w ratio significantly deform the dynamic moduli curves. The use of rheological data to obtain MWD, by the model used in this paper, will, therefore, be able to give rather well defined M_z/M_w ratios, while more uncertainty will be presented in the M_w/M_n results. The so-called GEX-rheological model for the dynamic moduli was applied to fit the experimental data of different polymers in order to obtain the best-fit parameters of the MWD of these polymers, without the need for the inversion of the double reptation integral equation. The stability of the results has been confirmed through the evaluation of the 90% confidence intervals for the first molecular weight averages. Finally, concerning the M_w and M_z values, the predictions obtained from the dynamic moduli measurements differ by less than 10% from those obtained from GPC measurements while, as expected, more uncertainty is present in the M_n predictions. Received: 6 February 2000 Accepted: 22 August 2000     

Rheological properties of suspensions of polyethylene-coated aluminum nanoparticles

Ultrafine aluminum powder was identified as very promising fuels for novel energetic materials formulations. However, the large specific surface area of this powder facilitates its oxidation and greatly reduces its shelf life. Therefore, different coating processes were proposed to solve this problem. The rheology of viscous suspensions of nanoparticles still remains poorly understood and the effect of the coating of such particles on the flow behavior is even more difficult to assess. We have studied the rheology of ultrafine aluminum suspensions in three low molecular weight polymers of different viscosities: a hydroxy-terminated polybutadiene, a polypropylene glycol, and a polysiloxane. The nanosize aluminum powder was previously coated by a thin layer of high-density polyethylene using an in situ polymerization process. The rheological characterization of the suspensions was conducted by the means of steady and oscillatory shear flow measurements for noncoated and coated particles. The effect of the coating process on the rheology of the suspensions is discussed in terms of the interactions between the particles and the suspending fluids.     

Effect of mixing structure on the hygroscopic behavior of ultrafine ammonium sulfate particles mixed with succinic acid and levoglucosan

Understanding the interactions between water and atmospheric aerosols is critical for estimating their impact on the radiation budget and cloud formation. The hygroscopic behavior of ultrafine(100 nm)ammonium sulfate particles internally mixed with either succinic acid〔slightly soluble) or levoglucosan(soluble) in different mixing structures(core-shell vs. well-mixed) were measured using a hygroscopicity tandem differential mobility analyzer(HTDMA). During the hydration process(6-92% relative humidity(RH)), the size of core-shell particles(ammonium sulfate and succinic acid) remained unchanged until a s|ow increase in particle size occurred at 79% RH; however, an abrupt increase in size(i.e., a clear deliquescence) was observed at ~72% RH for well-mixed particles with a similar volume fraction to the core-shell particles(80:20 by volume). This increase might occur because the shell hindered the complete dissolution of the core-shell particles below 92% RH. The onset RH value was lower for the ammonium sulfate/levoglucosan core-shell particles than the ammonium sulfate/succinic acid core-shell particles due to levoglucosan's higher solubility relative to succinic acid. The growth factor(GF) of the core-shell particles was lower than that of the well-mixed particles, while the GF of the ammonium sulfate/levoglucosan particles was higher than that of ammonium sulfate/succinic acid particles with the same volume fractions. As the volume fraction of the organic species increased, the GF decreased. The data suggest that the mixing structure is also important when determining hygroscopic behavior of the mixed particles.     

Effect of mixing structure on the hygroscopic behavior of ultrafine ammonium sulfate particles mixed with succinic acid and levoglucosan

Understanding the interactions between water and atmospheric aerosols is critical for estimating their impact on the radiation budget and cloud formation. The hygroscopic behavior of ultrafine (<100 nm) ammonium sulfate particles internally mixed with either succinic acid (slightly soluble) or levoglucosan (soluble) in different mixing structures (core-shell vs. well-mixed) were measured using a hygroscopicity tandem differential mobility analyzer (HTDMA). During the hydration process (6–92% relative humidity (RH)), the size of core-shell particles (ammonium sulfate and succinic acid) remained unchanged until a slow increase in particle size occurred at 79% RH; however, an abrupt increase in size (i.e., a clear deliquescence) was observed at ∼72% RH for well-mixed particles with a similar volume fraction to the core-shell particles (80:20 by volume). This increase might occur because the shell hindered the complete dissolution of the core-shell particles below 92% RH. The onset RH value was lower for the ammonium sulfate/levoglucosan core-shell particles than the ammonium sulfate/succinic acid core-shell particles due to levoglucosan's higher solubility relative to succinic acid. The growth factor (GF) of the core-shell particles was lower than that of the well-mixed particles, while the GF of the ammonium sulfate/levoglucosan particles was higher than that of ammonium sulfate/succinic acid particles with the same volume fractions. As the volume fraction of the organic species increased, the GF decreased. The data suggest that the mixing structure is also important when determining hygroscopic behavior of the mixed particles.     

A comparison of three different methods for measuring both normal stress differences of viscoelastic liquids in torsional rheometers

A novel pressure sensor plate (normal stress sensor (NSS) from RheoSense, Inc.) was adapted to an Advanced Rheometrics Expansion System rheometer in order to measure the radial pressure profile for a standard viscoelastic fluid, a poly(isobutylene) solution, during cone–plate and parallel-plate shearing flows at room temperature. We observed in our previous experimental work that use of the NSS in cone-and-plate shearing flow is suitable for determining the first and second normal stress differences N ₁ and N ₂ of various complex fluids. This is true, in part, because the uniformity of the shear rate at small cone angles ensures the existence of a simple linear relationship between the pressure [i.e., the vertical diagonal component of the total stress tensor (Π₂₂)] and the logarithm of the radial position r (Christiansen and coworkers, Magda et al.). However, both normal stress differences can also be calculated from the radial pressure distribution measured in parallel-plate torsional flows. This approach has rarely been attempted, perhaps because of the additional complication that the shear rate value increases linearly with radial position. In this work, three different methods are used to investigate N ₁ and N ₂ as a function of shear rate in steady shear flow. These methods are: (1) pressure distribution cone–plate (PDCP) method, (2) pressure distribution parallel-plate (PDPP) method, and (3) total force cone–plate parallel-plate (TFCPPP) method. Good agreement was obtained between N ₁ and N ₂ values obtained from the PDCP and PDPP methods. However, the measured N ₁ values were 10–15% below the certified values for the standard poly(isobutylene) solution at higher shear rates. The TFCPPP method yielded N ₁ values that were in better agreement with the certified values but gave positive N ₂ values at most shear rates, in striking disagreement with published results for the standard poly(isobutylene) solution.

Rheological aspects of dense lignite-water suspensions; time dependence, preshear and solids loading effects

An investigation of the rheological properties of dense lignite-water suspensions is reported here in order to evaluate the parameters that affect the rheology of these suspensions. Different types of particle size distributions were achieved via wet grinding with particle sizes down to 1 μm. Polyelectrolytes and surfactants were used to improve the stability and rheology of suspensions. The achieved solid volume fraction, φ, with acceptable rheological behavior was 0.45, while the ratio of φ/φ _m was close to 0.85; φ _m is the maximum solid volume fraction. Various types of flow tests were performed on lignite-water suspensions with various preshear times and stress levels. Typical shear rates varied in the range between 10^–2 to 10² s^–1. The low shear behavior was found to be quite different from the high shear behavior for the most concentrated suspensions, with a plateau value at low shear rates indicating the appearance of a yield stress. These plateau values, however, depend on shear history, which is responsible for the development of different structures in the sample. The viscosity curves corresponding to the ascending and descending parts of the flow curve were found to be different; these flow curve parts can be described either by well established models or by modified ones. The non-Newtonian time dependent behavior of the lignite-water suspensions is attributed to the high value of the ratio φ/φ _m , the polydispersity of the particle size distribution, and the non-spherical shape of the lignite particles.     

Bounds for interpolating complex effective moduli of viscoelastic materials from measured data

The complex effective moduli of viscoelastic materials can be experimentally measured by a number of techniques giving relaxation data for materials at discrete frequencies. In this paper we present a method which allows one to find bounds on the moduli of the material at the unmeasured frequencies. Our bounds can be very tight, and are, therefore, good approximations to the data. Using our bounds, experimentalists can concentrate their efforts on gathering highly accurate data at only a few frequencies and numerically generate data at other frequencies that may be of interest. Received: 10 August 1999 Accepted: 21 December 2000     

Rheological behavior of concentrated suspensions as affected by the dynamics of the mixing process

The rheological characterizations of concentrated suspensions are generally carried out assuming “well-mixed” suspensions. However, the variation of the concentration distributions of the ingredients of the formulation, i.e., the “goodness of mixing”, the size and shape distributions of the particle clusters and the rheological behavior of the suspension all depend on the thermo-mechanical history that the suspension is exposed to during the mixing process. Here, various experimental tools are used for the characterization of the degree of mixedness (concentration distributions) of various ingredients along with the characterization of rheological material functions, wall slip behavior and the maximum packing fraction of a graphite/elastomer suspension. The degree of mixedness values of the ingredients of the suspensions processed using batch and continuous processes and under differing operating conditions were characterized quantitatively using wide-angle X-ray diffraction and thermo gravimetric analysis and were elucidated under the light of the electrical properties of the suspension as affected by the mixing process. Upon achieving better homogeneity of the graphite particles and the binder and decreases in the size and breadth of the size distributions of particle clusters (as inferred from electrical measurements and maximum packing fraction values), the elasticity (storage modulus) and the shear viscosity (magnitude of the complex viscosity from small-amplitude oscillatory shear and shear viscosity from steady torsional and capillary rheometry) of the suspension decreased significantly and the wall slip velocity values increased. These findings demonstrate the intimate relationships that exist between the rheological behavior of concentrated suspensions and the thermo-mechanical history that they are exposed to during the processing stage and suggest that the preparation conditions for suspensions should be carefully selected and well documented to achieve reproducible characterization of rheological material functions.     

The viscoelastic behavior of melts of virgin and recycled polycarbonate reinforced with short glass fibers

Three series of shear oscillatory tests are performed on polycarbonate melts reinforced with short glass fibers at the temperatures T₁=250 and T₂=290 °C. The content of glass fibers ranges from 0 to 20 wt.%. In the first series, virgin polycarbonate is used, in the other series, dynamic tests are performed on recycled polymer, whereas in the third series, a mixture of virgin with recycled polycarbonates is employed. Constitutive equations are derived for the viscoelastic behavior of a polymer melt at isothermal deformations with small strains. A polymer is treated as an equivalent transient network of strands that rearrange at random times as they are agitated by thermal fluctuations. The time-dependent response of a network is determined by four adjustable parameters that are found by fitting the experimental data. Excellent agreement is demonstrated between the observations and the results of numerical simulation. The study focuses on the effects of temperature and filler content on the material constants in the stress–strain relations.     

Rheological properties of polyacrylates used as synthetic road binders

Most adhesives and binders, including bitumen for asphalt mixture production, are presently produced from petrochemicals after the refining of crude oil. The fact that crude oil reserves are a finite resource means that in the future, it may become necessary to produce these materials from alternative and probably renewable sources. Suitable resources of this kind may include polysaccharides, plant oils and proteins. This paper deals with the synthesis of polymer binders from monomers that could, in future, be derived from renewable resources. These binders consist of polyethyl acrylate (PEA) of different molecular weight, polymethyl acrylate (PMA) and polybutyl acrylate (PBA), which were synthesised from ethyl acrylate, methyl acrylate and butyl acrylate, respectively, by atom transfer radical polymerisation. The rheological properties of these binders were determined by means of oscillatory testing using a dynamic shear rheometer and combinations of stress/strain, temperature and frequency sweeps. The results indicate that PEA can be produced to have rheological properties similar to that of ‘soft’ 100/150 penetration grade bitumen, PMA with similar rheological properties to that of ‘hard’ 10/20 penetration grade bitumen, while PBA, due to its highly viscous nature and low dynamic moduli, cannot be used on its own as a binder. The synthetic polymers were found to be thermo-rheologically simple, and the shift factors, used to produce the dynamic moduli master curves, were found to fit an Arrhenius function.     

Rheological characterization of bimodal colloidal dispersions

In order to investigate the effect of the particle size distribution on the rheological properties of concentrated colloidal dispersions both steady-state shear and oscillatory measurements have been performed on well-characterized bimodal dispersions of sterically stabilized PMMA particles. Replacing a minor amount of large particles by small ones in a concentrated dispersion, keeping the total effective volume fraction constant, decreases the viscosity quite drastically. On the other hand, replacing a small amount of small particles by big ones hardly effects the viscosity at all. This behavior can be attributed to the deformability of the stabilizing polymer layer. A procedure is proposed to calculate the limiting viscosities in a bimodal colloidal dispersion starting from the characteristics of the monodisperse systems. A good agreement has been obtained between the calculated values and the experimental results. The linear viscoelastic properties of the concentrated dispersions have been investigated by means of oscillatory measurements. The plateau values of the storage modulus for the bimodal dispersions decrease with an increasing fraction of the coarse particles. By substituting the bimodal dispersion by an equivalent monodisperse system the storage modulus can be superimposed on the values for the monodisperse suspensions when plotted as a function of the mean interparticle distance.     

Rheological behavior of suspensions of modified and unmodified cellulose nanocrystals in dimethyl sulfoxide

The rheological behavior of cellulose nanocrystal (CNC) and modified CNC (mCNC) suspensions in dimethyl sulfoxide (DMSO) was investigated. The efficiency of the surface modification of CNCs by grafting an organic acid chloride to produce hydrophobic CNCs has been verified by X-ray photoelectron spectroscopy (XPS). The thermal degradation temperature of the mCNCs was found to be 165 versus 275 °C for CNCs. The CNC suspensions in DMSO at 70 °C underwent gelation at very low concentration (1 wt%) after 1 day. The network formation was temperature sensitive and did not occur at room temperature. For gels containing 3 wt% CNCs, the complex viscosity at 70 °C increased by almost four decades after 1 day. For the mCNCs in DMSO, a weak gel was formed from the first day and temperature did not affect the gelation. Finally, the effect of adding 10 wt% of polylactide (PLA) to the solvent on the rheological properties of CNC and mCNC suspensions was investigated. The properties of suspensions containing 1.9 wt% CNCs and mCNCs increased during the first and second days, and PLA did not prevent gel formation. However, the reduced viscosity and storage modulus of the CNC and mCNC gels with PLA were lower than those of samples without PLA.     

Viscoelastic properties of magnetorheological fluids

We have studied the rheological properties of some magnetorheological fluids (MRF). MRF are known to exhibit original rheological properties when an external magnetic field is applied, useful in many applications such as clutches, damping devices, pumps, antiseismic protections, etc. While exploiting parameters such as magnetic field intensity, particle concentration and the viscosity of the suspending fluid, we highlighted the importance of each one of these parameters on rheology in the presence of a magnetic field. We made this study by conducting rheological experiments in dynamic mode at very low strain which facilitates the comprehension of the influence of the structure on MRF rheology. Our results confirmed the link between the magnetic forces which ensure the cohesion of the particles in aggregates, and the elastic modulus. Moreover, we found that the loss modulus varies with the frequency in a similar manner than the elastic modulus. The system, even with the smallest deformations, was thus not purely elastic but dissipates also much energy. Moreover, we demonstrated that this dissipation of energy was not due to the matrix viscosity. Actually, we attributed viscous losses to particle movements within aggregates.     

Rheological behavior of PAN-based electrolytic gel containing tetrahexylammonium and magnesium iodide for photoelectrochemical applications

Polymeric gel electrolyte systems have gained great interest in the last few years due to their suitability for the manufacturing of ionic devices, for example, for dye-sensitized solar cells (DSSCs). In this work, the rheological behavior at fixed temperatures and at fixed frequency of complex systems based on polyacrylonitrile (PAN) and plasticizers such as ethylene carbonate (EC) and propylene carbonate (PC) containing tetrahexylammonium (Hex₄NI) and magnesium iodide (MgI₂) was studied. These results for these PAN-EC-PC gels suggest a structural change of the “strong-to-weak” type at about 60 °C and the beginning of the gel–sol transition at about 75 °C. These transitions occur at higher temperatures for polymer electrolyte gels containing Hex₄NI and even higher with MgI₂, suggesting the possibility of post-factum treatments of the gels and of the DSSCs to improve their performance. The rheological results suggest that the progressive substitution of Hex₄NI with MgI₂leads to a significant improvement in the rheological behavior of the PAN-based electrolytic gel due to the decrease of the mobility of the macromolecules and probably to an increase of the interaction between the inorganic ions and the macromolecules. Moreover, when these gels were used in DSSCs, the sample containing 80(Hex₄NI)/40(MgI₂) showed the best performance considering its rheological and calorimetric behavior as well as energy conversation efficiency and short-circuit current density.     

Continuous flow synthesis of plasmonic gold patches and nearly-complete nanoshells on polystyrene core particles

We describe the development of a T-mixer based continuous flow process for the coating of 86–500 nm diameter spherical polystyrene particles with thin gold patches by heterogeneous nucleation and growth. After establishing a suitable flow rate for good mixing and sufficiently uniform product morphology we systematically investigate the main reaction parameters. This reveals a considerable tunability of the patch morphology and, by virtue of the localized surface plasmon resonance of gold, the optical properties of the product dispersions. In order to further widen the range of nanostructures accessible by our process, a second T-mixer was added. This introduced new gold precursor, leading to further growth of the patches that were formed after the first mixer. By this approach, nearly-complete gold nanoshells could be produced in high yield on both small and large core particles, without the unwanted production of free-standing gold nanoparticles. Due to the pronounced optical properties of nearly-complete gold nanoshells on small core particles, we could estimate from electrodynamic simulations the equivalent shell thickness to be as low as 8.6 nm. This is significantly thinner than can be routinely achieved using the standard seeded growth approach to synthesise gold nanoshells. Our results are therefore highly promising for the gram-scale synthesis of plasmon resonant nanostructures with designed optical properties.     

Rheological properties and dispersion stability of magnetorheological (MR) suspensions

In the present article, the rheological responses and dispersion stability of magnetorheological (MR) fluids were investigated experimentally. Suspensions of magnetite and carbonyl iron particles were prepared as model MR fluids. Under an external magnetic field (H ₀) and a steady shear flow, the yield stress depends upon H ₀ ^3/2. The Yield stress depended on the volume fraction of the particle (φ) linearly only at low concentration and increased faster at high fraction. Rheological behavior of MR fluids subjected to a small-strain oscillatory shear flow was investigated as a function of the strain amplitude, frequency, and the external magnetic field. In order to improve the stability of MR fluid, ferromagnetic Co-γ-Fe₂O₃ and CrO₂ particles were added as the stabilizing and thickening agent in the carbonyl iron suspension. Such needle-like particles seem to play a role in the steric repulsion between the relatively large carbonyl iron particles, resulting in improved stability against rapid sedimentation of dense iron particles. Furthermore, the additive-containing MR suspensions exhibited larger yield stress, especially at higher magnetic field strength. Received: 4 April 2000 Accepted: 6 November 2000     

A regularization-free method for the calculation of molecular weight distributions from dynamic moduli data

There are several models for the determination of molecular weight distributions (MWDs) of linear, entangled, polymer melts via rheometry. Typically, however, models require a priori knowledge of the critical molecular weight, the plateau modulus, and parameters relating relaxation time and molecular weight (e.g., k and in =kM). Also, in an effort to obtain the most general MWD or to describe certain polymer relaxation mechanisms, models often rely on the inversion of integral equations via regularization. Here, the inversion of integral equations is avoided by using a simple double-reptation model and assuming that the MWD can be described by an analytic function. Moreover, by taking advantage of dimensionless variables and explicit analytic relations, we have developed an unambiguous and virtually parameter-free methodology for the determination of MWDs via rheometry. Unimodal MWDs have been determined using only a priori knowledge of the exponent and dynamic moduli data. In addition, the uncertainty in rheological MWD determinations has been quantified, and it is shown that the reliability of the predictions is greater for the high-molecular-weight portion of the distribution.     

Rheological characterization of carbon nanotubes/poly(ethylene oxide) composites

Rheological properties of poly(ethylene oxide) nanocomposites embedded with carbon nanotubes (CNTs) were investigated in the present study. It was found that the CNT nanocomposites had a higher effective filler volume fraction than the real filler volume fraction, which yielded a drastic enhancement of shear viscosity. As the CNT loading in the nancomposites increases, non-Newtonian behavior was observed at the low-shear-rate region in the steady shear experiments. Oscillatory dynamic shear experiments showed that more addition of the CNTs led to stronger solidlike and nonterminal behaviors. To identify a dispersion state of the CNTs, field emission scanning electron spectroscopy and transmission electron microscopy were adopted and thermal analysis was also performed by using differential scanning calorimetry. The existence of percolated network structures of the CNTs even at a low CNT loading was verified by rheological properties and electrical conductivities.     

Viscoelastic properties of pig kidney in shear, experimental results and modelling

 In this paper, the results from a series of rheological tests of fresh pig kidney have been reported. Using a standard strain-controlled rheometer, the oscillation strain sweep experiment showed a linear viscoelastic strain limit of the order of 0.2% strain. To determine the components of dynamic moduli in terms of frequency, shear oscillation tests were done at strain 0.2% using a stress-controlled rheometer. Shear stress relaxation tests were carried out with a fixed strain of 0.2% and 0.02 s rise time. The model we have developed uses a multi-mode upper convected Maxwell (UCM) model with variable viscosities and time constants, to which we have added a Mooney hyper-elastic response, both multiplied by a damping function. Different forms of damping functions that control the non-linearity of strain-stress profile have been tested. The model was fitted to our experimental data, and matched the entire test data reasonably well with a single set of parameters. Received: 5 May 2000 Accepted: 16 March 2001