Cox-Merz Rule Research Articles

Rheo-optics of giant micelles: SALS patterns of cetyltrimethylammonium tosylate solutions in presence of sodium bromide

In this work, we present a systematic study based on Small-Angle Light Scattering (SALS) patterns of the simple shear flow response of semi-diluted solutions of cetyltrimethylammonium tosylate (CTAT; 5.5 wt.% - 0.12 M) in the presence of sodium bromide (NaBr) at different [NaBr]={0,0.12,0.19,0.25,0.3} M concentrations. We evidence a relationship between rheological and light scattering data that reveals a transition into a fast-breaking regime in the dynamics of wormlike micelles formed by the CTAT/NaBr system (Macías et al., 2011; Fierro et al., 2021). This transition into a micellar fast-breaking regime with salt addition ([NaBr]≥0) appears marked by the following features: (i) a decrease in the relaxation time of the material λ0, accompanied by (ii) a decrease of the viscosity level at low shear rates η0 (Macías et al., 2011; Fierro et al., 2021; Schubert et al., 2003; Alkschbirs et al., 2015; Bandyopadhyay et al., 2003). With these, (iii) the formation of butterfly-like patterns is recorded originating from concentration fluctuations, evolution that is accompanied by: (iv) shear banding in the form of non-monotonic flow curves and (v) slow oscillatory transient responses in start-up flow tests captured theoretically with the Bautista–Manero–Puig (BMP) model. In addition, the Cox–Merz rule is fulfilled at molar salt-to-surfactant ratios of R≥1.5. This results in shorter structure-recovery time-scales than the characteristic-time of the flow (Macías et al., 2011; Fierro et al., 2021; Manero et al., 2002). In the case of the elastic modulus G0, the variation was small, which suggests a transition from an entangled to a multiconnected network, as suggested by Kadoma & van Egmond (1997), Kadoma et al. (1997) and Fierro et al. (2021). From a theoretical perspective, we provide predictions for the shear–stress and the first normal-stress growth coefficients in transient start-up simple shear flow using the BMP model. Here, banding R=1.5 solutions display overshot responses at relatively high shear rates (γ̇=10−30s−1), in-line with experimental findings on the start-up flow of wormlike micellar solutions (Soltero et al., 1999; Lerouge et al., 2004; Hu & Lips 2005; Pipe et al., 2010; Mohammadigoushki et al., 2019). Our results are consistent with those reported in other investigations (Macías et al., 2011; Fierro et al., 2021; Schubert et al., 2003; Alkschbirs et al., 2015; Bandyopadhyay et al., 2003; Kadoma et al., 1997; Soltero et al., 1999; Lerouge et al., 2004; Hu & Lips 2005; López-Barrón et al., 2014) and reveal the influence of the Br−-ion used on the mechanical and optical response of the CTAT-NaBr system.

Contact stress decomposition in large amplitude oscillatory shear of concentrated noncolloidal suspensions

The concentrated noncolloidal suspensions show complex rheological behavior, which is related to the existence of contact stress. However, determining the contact stress in time-varying flow like oscillatory shear is challenging. Herein, we propose a contact stress decomposition method to decompose the total stress directly into contact stress and hydrodynamic stress in large amplitude oscillatory shear (LAOS). The results of hydrodynamic stress and contact stress are consistent with those determined by the shear reversal experiment. The contact stress decomposition also explains the failure of the Cox–Merz rule in noncolloidal suspensions because the particle contacts exist in steady shear but are absent in small amplitude oscillatory shear. The intracycle and intercycle of contact stress are further analyzed through the general geometric average method. The intracycle behaviors exhibit strain hardening, strain softening, and shear thickening. The intercycle behaviors show bifurcations in stress-strain and stress-strain rate relations, where the transition strains at different concentrations define the state boundaries between the discrete particle contacts, the growing of particle contacts, and the saturated contacts. We also established a phenomenological constitutive model using a structural parameter to describe the shear effect on the buildup and breakdown of particle contacts. The contact stress of noncolloidal suspensions with wide ranges of particle concentrations and strain amplitudes under LAOS can be well described by the model.

Rheology of automotive adhesives during dispensing: A direct comparison of epoxy and rubber based systems via drag and pressure driven flows

Construction of vehicles requires adhesive dispensing for body-in-white assembly, hemming of closure panels, decking of windshields and the manufacture of battery packs. Knowledge of the rheological properties of adhesives applied using common dispensing systems is important for optimization of dispensing and application conditions. However, flow behavior of adhesives at shear rates used in dispensing is not well understood. Therefore, this study combines parallel plate and capillary rheology techniques to directly compare the rheological properties of an epoxy structural adhesive used in hemming applications and a rubber ‘topical sealer’ used to seal water leak paths across the range of shear rates observed in dispensing. Shear viscosity (η) and complex viscosity (η*) master curves were created from time-temperature-superposition (TTS) of steady shear and dynamic oscillatory data. Both adhesives did not follow the Cox-Merz rule. It was found that the Carreau-Yasuda model fit the steady shear viscosity master curve of the epoxy structural adhesive, while a simpler power law model fit the steady shear viscosity master curve of the rubber topical sealer. An inexpensive capillary rheometer was developed to simulate the adhesive dispensing process. Viscosity data was corrected for entrance pressure losses and a non-Newtonian flow front using Bagley and Weissenberg-Rabinowitsch corrections, respectively. It was observed that complex viscosity master curves better predicted viscosity during dispensing, as compared to steady shear viscosity master curves. Linear stress ramp measurements showed that the adhesives have widely different yield stresses, while the capillary rheometry measurements showed they have similar viscosities during dispensing. Furthermore, the capillary rheometer ‘shot meter’ pressures were related to the apparent and doubly corrected viscosity values through power law functions. A new quality control method based on the capillary rheology data is proposed.

Rheological Analysis and Evaluation of Measurement Techniques for Curing Poly(Methyl Methacrylate) Bone Cement in Vertebroplasty.

Vertebroplasty is a minimally invasive surgical procedure used to treat vertebral fractures, which conventionally involves injecting poly(methyl methacrylate) (PMMA) bone cement into the fractured vertebra. A common risk associated with vertebroplasty is cement leaking out of the vertebra during the injection, which may occur due to a lack of understanding of the complex flow behavior. Therefore, experiments to quantify the cement's flow properties are necessary for understanding and proper handling of the bone cement. In this study, we aimed to characterize the behavior of PMMA bone cement in its curing stages to obtain parameters that govern the flow behavior during injection. We used rotational and oscillatory rheometry for our measurements, as well as a custom-made injector setup that replicated a typical vertebroplasty setting. Our results showed that the complex viscoelastic behavior of bone cement is significantly affected by deformations and temperature. We found that the results from rotational tests, often used for characterizing the bone cement, are susceptible to measurement artifacts caused by wall slip and "ridge"-like formations in the test sample. We also found the Cox-Merz rule to be conditionally valid, which affects the use of oscillatory tests to obtain the shear-thinning characteristics of bone cement. Our findings identify important differences in the measured flow behavior of PMMA bone cement when assessed by different rheological methods, an understanding that is crucial for its risk-free usage in downstream medical applications.

A reexamination of the Cox–Merz rule through the lens of recovery rheology

Empirical rules play a crucial role in industrial and experimental settings for efficiently determining the rheological properties of materials, thereby saving both time and resources. An example is the Cox–Merz rule, which equates the steady-shear viscosity with the magnitude of the complex viscosity obtained in oscillatory tests. This empirical rule provides access to the steady-shear viscosity that is useful for processing conditions without the instabilities associated with experiments at high shear rates. However, the Cox–Merz rule is empirical and has been shown to work in some cases and fail in others. The underlying connection between the different material functions remains phenomenological and the lack of a comprehensive understanding of the rheological physics allows for ambiguity to persist in the interpretation of material responses. In this work, we revisit the Cox–Merz rule using recovery rheology, which decomposes the strain into recoverable and unrecoverable components. When viewed through the lens of recovery rheology, it is clearly seen that the steady-shear viscosity comes from purely unrecoverable acquisition of strain, while the complex viscosity is defined in terms of contributions from both recoverable and unrecoverable components. With recovery tests in mind, we elucidate why the Cox–Merz rule works only in a limited set of conditions and present an approach that could allow for universal comparisons to be made. This work further highlights the significance of recovery rheology by showing how it is possible to extend beyond phenomenological approaches through clear rheophysical metrics obtained by decomposing the material response into recoverable and unrecoverable components.

Rheological Study on Blend Solutions of Non-mulberry Silk Fibroin and Gelatin Biopolymers

In current research work, we have studied the blending effect of non-mulberry silk fibroin (10% weight/volume basis) and gelatin (20% weight/volume basis) in formic acid. Several blends as SF10G0, SF2G8, SF3G7, SF5G5 and SF0G10 have been made and their rheological behaviour was investigated. The blend solutions were subjected to a steady shear rheological study in the variety of range of shear rates, namely 0.01–500 sec-1 and the viscosities of blend solutions were noticed to decrease in comparison to pure silk solution. The frequency sweep was employed in dynamic rheological tests to determine complex viscosity of these solutions from range of angular sweep 0.1–100 rad/sec. The consistent shear-thinning behaviour was noted for all the blends. The difference in numerical values of shear and complex viscosities indicated disobedience of Cox-Merz rule. Such analysis can be utilised for tailoring the properties of solution prior to processing them to create a versatile range of materials.

The effect of sequential extraction on the physicochemical and rheological properties of Naematelia aurantialba polysaccharides

To overcome the difficulty of separation and low rate of extraction caused by highly viscous polysaccharides from Naematelia aurantialba (NA), four N. aurantialba polysaccharides (NAPs) were sequentially extracted using water (enzyme−/ultrasound-assisted extraction), alkali (0.1 mol/L NaOH), and acid (0.1 mol/L HCl), and named E-NAP, U-NAP, Al-NAP, and Ac-NAP. The properties of four NAPs were different. The yields of NAPs were 26.05 % (Ac-NAP) > 20.33 % (Al-NAP) > 17.99 % (U-NAP) > 12.77 % (E-NAP), respectively. The monosaccharide composition of NAPs was composed primarily of mannose, xylose, glucose, glucuronic acid, and galactose. Sequential extraction improved the purity and solubility of NAPs, but decreased the particle size, thermal stability, water retention, and crystallinity. Two polysaccharides, U-NAP and Al-NAP, had a triple helix structure. All the NAPs were pseudoplastic fluids with concentration/frequency-dependent entangled structure. Al-NAP with the highest viscosity exhibited an elastic gel, while Ac-NAP with the lowest viscosity was a viscous gel. The behavior of NAPs differed from that predicted using the Cox-Merz rule, and in particular, E-NAP and U-NAP more significantly deviated from the rule. In this study, four NAPs with different properties were extracted sequentially, which provided a theoretical basis for the down-stream processing with high added-value and utilization of NA and NAP.

The identification of the generalised Maxwell fluid for n-hexadecane liquids via non-equilibrium molecular dynamics simulations

ABSTRACT Linear viscoelasticity is very important for chain-molecular fluids. The generalised Maxwell constitutive equation is classical in which the linear viscoelastic fluids consist of a series of spring and dashpot. It is significant to identify the generalised Maxwell fluid of linear viscoelasticity for n-hexadecane liquids through non-equilibrium molecular dynamics simulations of small-strain amplitude oscillatory shear flows. For describing a characteristic of material viscoelasticity, the predicted relaxation modulus curves at different temperatures exhibit three regions: transition, rubbery, and flow. Additionally, the Cox-Merz rule is verified in which the complex oscillation-shear viscosity almost equals the steady-state shear viscosity with respect to shear rates.

Effects of pre-formulation and post-cooking method on the rheological and gelation properties of 3D printed chicken products

This study investigated the influence of oil type (olive, soybean, and peanut oil) and post-cooking methods (oven bake and microwave) on the quality of 3D printed chicken meat products. The Ostwald-de-Waele model was used to describe the flow behavior of chicken meat paste (R2 > 0.995). Oil-fortified groups present significantly lower consistency index (K) and flow behavior index (n), indicating better fluidity. A modified Cox-Merz rule was applied by multiplying angular frequency with shift factors (αSF). Surprisingly, the values of αSF are well-correlated with accuracy parameters of 3D printed cubes (|r| >0.8). For post-heating methods, baking results in higher fluid loss but contributes to a smoother surface. The microwaved gels showed better fluid retention ability and higher accuracy but lost the detail shape of the 3D printing model. Overall, the PO (peanut oil) meat emulsion group presented better textural properties and flat surfaces than other oil-added counterparts.

Slip of styrene–butadiene rubbers: The effects of pressure and viscous heating

During the processing of elastomeric compounds under high flow rates, significant pressure drops (106–108 Pa) are encountered. Under such conditions, the viscosity of these compounds is significantly affected by pressure and viscous heating. Moreover, strong flow rates may cause these systems to slip at the wall, violating the classical no-slip boundary condition of fluid mechanics. To determine the slip velocity by the well-known Mooney method, the effects of pressure and viscous heating should be considered. In this work, an experimental methodology is developed to determine the slip velocity of styrene–butadiene compounds in capillary flow corrected for the effects of pressure and viscous heating. First, the temperature increase due to viscous heating is measured during the extrusion process and accounted for in correcting the experimental data to infer the slip velocity. Consequently, the corrected experimental data for the effects of pressure and viscous heating are used to calculate the slip velocity from the deviation of the linear viscoelastic behavior (deviation from the Cox–Merz rule). The Mooney method is also used to confirm the calculated slip velocity of the elastomeric compounds.

Aroma compounds retention and release from protein-polysaccharide-based bilayer emulsion gels: A thermodynamic and kinetic study

Thermodynamic and kinetic behavior of five aroma compounds (ACs) with different molecular structures in bilayer-stabilized emulsion gels (BEGs) depending on starch type (ST) and starch concentration (SC) during refrigerated storage time (RST) was investigated. The internal phase of BEGs was stabilized by myofibrillar proteins (MPs) and gum arabic, while the external phase was thickened and texturized with MPs and starches (waxy maize starch, potato starch) differing in amylose/amylopectin ratio. Oscillatory and rotational shear modes were used to evaluate rheological properties of BEGs, and the results are presented in terms of: Herschel-Bulkley parameters, quality factor and divergence from the Cox-Merz rule, which were modeled using a first order kinetic equation. Thermodynamic models composed of myosin and ACs were applied to determine the Stern-Volmer quenching constants, binding and thermodynamic parameters: enthalpy (ΔH), entropy (ΔS) and Gibb’s free energy (ΔG). Retention (R), release rate constant (kr) and mechanism of release (nr) values were significantly (p ≤ 0.05) dependent on: ST, SC and ACs type. After 12 days of refrigerated storage, the R values were ranged from 0.34 to 0.77, whereas those of kr and nr determined during RST were in ranges 6.21–102 × 10−3 (day−1) and 0.55–0.86, respectively. The gas-BEGs partition coefficient (kg/e) of ACs was measured at thermodynamic equilibrium and the enthalpy of vaporization was calculated from the variations of kg/e with temperature changes (30–60 °C). From a practical point of view, these results may have important implications for the development of commercial emulsion-type food with controlled ACs retention during RST.

Wall Slip-Free Viscosity Determination of Filled Rubber Compounds Using Steady-State Shear Measurements.

The high-pressure capillary rheometer (HPCR) represents a state-of-the-art instrument for the determination of rheological properties for plastics and rubber compounds. Rubber compounds have an increased tendency to exhibit flow anomalies depending on the compound ingredients and the processing parameters. Combined with non-isothermal effects due to dissipative material heating, this causes rheological material measurements and the resulting material parameters derived from them to be affected by errors, since the fundamental analytical and numerical calculation approaches assume isothermal flow and wall adhesion. In this paper, the applicability of the empirical rheological transfer function of the Cox-Merz rule, which establishes a relationship between shear viscosity measured with a HPCR and complex viscosity measured with a closed cavity rheometer (CCR), is investigated. The Cox-Merz relation could not be verified for an unfilled EPDM raw polymer or for filled, practical rubber compounds. Using a closed cavity rheometer, a methodology based on ramp tests is then introduced to collect wall slip-free steady-state shear viscosity data under isothermal conditions. The generated data show high agreement with corrected viscosity data generated using the HPCR, while requiring less measurement effort.

Applicability of the Cox–Merz Relationship for Mayonnaise Enriched with Natural Extracts

The Cox and Merz rules are empirical correlations between the apparent viscosity of polymers with the effect of shear rate and the complex dynamic viscosity with the effect of frequency. In this study, the rheological properties of mayonnaise-type emulsions enriched with Averrhoa carambola extracts were investigated using small-amplitude oscillatory shear (SAOS) and steady shear flow. The results showed that the shear-thinning behavior of the samples was non-Newtonian with yield stress and had time-dependent characteristics, as evidenced by curves from non-oscillatory measurements. It was observed that the experimental data on the complex and apparent viscosity of the samples obeyed the Cox–Merz rule.

Cox–Merz rules from general rigid bead-rod theory

The value of this work is in its macromolecular explanations of both Cox–Merz rules, thus of when to expect them to work. For polymeric liquids and their solutions, the measured values of the steady shear viscosity and the magnitude of the complex viscosity often equate, within experimental error, when compared at common shear rate (in units of t−1) and angular frequency (in units of rad t−1). Called the first Cox–Merz rule, this remarkable empiricism, with one exception, has defied most macromolecular explanations. This one exception is the suspension of multi-bead rods and its special case of rigid dumbbells. The second Cox–Merz rule equates approximately the slope of the first derivative of steady shear viscosity with respect to shear rate with the real part of the complex viscosity when compared at common shear rate (in units of t−1) and angular frequency (in units of rad t−1). In this paper, we explain both Cox–Merz rules for all axisymmetric macromolecules, be they prolate or oblate, of almost any lopsidedness. Furthermore, through the lens of general rigid bead-rod theory, we define under what conditions these rules do not apply. Specifically, the first Cox–Merz rule fails when the macromolecules are too oblate.

Experimental Validation of a Micro-Extrusion Set-Up with In-Line Rheometry for the Production and Monitoring of Filaments for 3D-Printing.

The main objective of this work is to validate an in-line micro-slit rheometer and a micro-extrusion line, both designed for the in-line monitoring and production of filaments for 3D printing using small amounts of material. The micro-filament extrusion line is first presented and its operational window is assessed. The throughputs ranged between 0.045 kg/h and 0.15 kg/h with a maximum 3% error and with a melt temperature control within 1 °C under the processing conditions tested for an average residence time of about 3 min. The rheological micro slit is then presented and assessed using low-density polyethylene (LDPE) and cyclic olefin copolymer (COC). The excellent matching between the in-line micro-rheological data and the data measured with off-line rotational and capillary rheometers validate the in-line micro-slit rheometer. However, it is shown that the COC does not follow the Cox-Merz rule. The COC filaments produced with the micro-extrusion line were successfully used in the 3D printing of specimens for tensile testing. The quality of both filaments (less than 6% variation in diameter along the filament's length) and printed specimens validated the whole micro-set-up, which was eventually used to deliver a rheological mapping of COC printability.

Shedding light on the viscoelastic behavior of artificial and human tears: A microrheological approach

This study conducts research on the viscoelastic properties of biological fluids, including both hyaluronic acid-containing lubricating eye drops and human tears, by means of passive microrheology. By tracking the Brownian motion of tracer particles of various sizes in the fluids, we were able to probe their viscoelastic properties. The results showed that the viscoelastic properties of artificial tears, such as Newtonian viscosity and relaxation time, scale to the concentration and macromolecular size of hyaluronic acid, resembling unentangled semidiluted solutions. Moreover, human tears were found to have a viscosity that is 50% greater than that of pure water, comparable to artificial tears containing 0.1% hyaluronic acid, but with a relaxation time one order of magnitude longer than ophthalmic solutions. This behavior was attributed to their intricate composition. The distinctive aspect of this study lies in demonstrating the feasibility of measuring the rheological properties of human tears, a biofluid of great interest, using extremely small sample volumes and microrheology, providing comprehensive information across a wide range of frequencies approaching those corresponding to blinking upon the application of the Cox–Merz rule. These findings are of significant value as they pave the way for future research on small volumes of tears from ophthalmic patients.

Structural and shear and extensional rheological properties of hairy basil seed mucilage for potential application as oropharyngeal dysphagia diets

In this study, mucilage was extracted from the swollen hairy basil (Ocimum × africanum Lour.) seeds using ultrasonic-assisted extraction. Clear mucilage (BSM) was subsequently obtained by centrifugation for studies on its structural and shear and extensional rheological properties. The results revealed that the extracted BSM was rich in galactose and xylose, but low in mannose and galacturonic acid contents which indicated the presence of arabinogalactan and xylan. Small amounts of proteins (∼5%) were also detected. The average molecular weight of BSM was estimated as ∼480 kDa. Shear rheology results showed that aqueous dispersions of BSM at 1.0–2.5%w/v exhibited solid-like viscoelastic behavior with small frequency dependency, resembling a cross-linked gel. All BSM samples also exhibited shear thinning behavior that could be described by the power law model. However, the Cox-Merz rule was not obeyed for all studied BSM gels. The gel's elasticity was enhanced with increasing BSM concentration. For extensional rheology, the apparent extensional viscosity showed an extensional strain-softening behavior and demonstrated higher filament breakup time and extensional viscosity with increasing BSM concentration. A comparison between BSM and commercial thickening agents widely used in dysphagia management showed comparable rheological characteristics, thus suggesting the promising potential of BSM as a thickening agent for this application.

Assessing the shear viscous behavior of continuous carbon fiber reinforced PEKK composites with squeeze flow measurements

Out-of-autoclave processes of carbon fiber thermoplastic composites are gaining interest as they can drastically reduce the economic cost. To optimize consolidation, the flow behavior of these highly filled composites has to be characterized. Here, we propose to measure viscosity of carbon fiber/polyetherketoneketone through squeeze flow experiments in a rheometer. A modified Stefan's law assuming a power law fluid behavior with full anisotropy is developed for square and circular geometries to model the data. Values of the power law parameters K and n are obtained, on the order of 15,000 Pa.sn and 0.02 at 1 bar. Though as expected independent of the samples' geometry and tapes' stacking, K and n depend on the applied pressure and plate size. This is due to localized shear which results in a shear-banding-like phenomenon. Finally, squeeze flow is compared to dynamic measurements and invalidate the Cox-Merz rule for such materials.

Steady State and Dynamic Oscillatory Shear Properties of Carbon Black Filled Elastomers

A correlation between the steady shear viscosity and complex dynamic viscosity of carbon black (CB) filled rubbers was found by evaluating the Cox-Merz rule and an alternative approach originally proposed by Philippoff for dilute polymer solutions, but since applied to amorphous polymers and concentrated suspensions. This was done by measuring the rheological properties of 16 industrially important rubber mixes containing CB N660 at concentrations of 20 and 35% by volume. A capillary rheometer at various shear rates and a dynamic oscillatory shear rheometer at small and large amplitude oscillatory shear (SAOS and LAOS) were used. The apparent viscosity, storage and loss moduli, complex dynamic viscosity and Fourier transform harmonics were measured. Generally, the shear stress, storage and loss moduli increased with increasing CB loading. Also, the ratio of third and fifth stress harmonics to first harmonics increased with increasing strain amplitude and filler loading. Viscous Lissajous figures (shear stress versus shear rate) at a strain amplitude of 14% showed a nearly linear response for compounds containing CB at 20% by volume. All other shear stress responses demonstrated a strong nonlinearity. The stress waveforms at a strain amplitude of 140% for compounds containing 35% CB by volume displayed a backwards tilted shape expected for highly filled compounds. The stress waveforms at a strain amplitude of 1,000% tended toward a rectangular shape expected for pure polymer. Generally, the nonlinear response of the compounds appeared to be dominated by the filler at strain amplitudes of 14% and 140% and by the rubber matrix at a strain amplitude of 1,000%. The Cox-Merz rule was not applicable for any of the compounds with their complex dynamic viscosity being greater than the apparent viscosity. However, a modification of the approach proposed by Philippoff provided reasonable agreement between the apparent viscosity and complex dynamic viscosity.

Characterizing ZSV of SBS modified asphalt using shear rate sweep test and frequency sweep oscillation test

The Zero-shear viscosity (ZSV) of asphalt is frequently measured using shear rate sweep test (η) or frequency sweep test (η*), whose correlation is often established via the cox-merz rule. However, the applicability of cox-merz rule upon SBS modified asphalt (SBSMA) is still debatable. This study aims to characterize ZSV of SBSMA using both shear rate sweep test and frequency sweep test and examine the cox-merz rule for SBSMAs with different SBS contents. The testing temperature is fixed at 60 °C and to enlarge the η* testing frequency range, master curve is created based on a novel double sigmoidal model. Results indicate that cox-merz rule is valid for plain asphalt but not for SBSMA, and the deviation is more evident for highly modified SBSMA (the deviation increases from 0.8 % to 13.2 %). Based on Kramers-Kronig relations, SBSMA must be pure viscous (phase angle δ = 90°) to obtain a strict η* plateau for ZSV measurement, which is quite difficult because SBSMA can only be pure viscous above the SBS polymer glass transition temperature (100 °C). Therefore, it is theoretically impossible to obtain an SBSMA η* plateau at 60 °C that resembles the η plateau, hence the cox-merz rule fails. A η* Newtonian plateau was observed in the master curve, but it was obtained at temperatures higher than 100 °C and cannot be used for 60 °C ZSV measurement either. With reduced frequency, the η* master curve of SBSMA shows 4 stages including a “pseudo-plateau”. The pseudo-plateau should be treated with care and cannot be used for ZSV measurement.