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Applied Rheology

SPE Library content related to rheology
Melt Rupture of Bimodal Molecular Weight Polyethylene in Simple Shear With Slip
M. Sattari, Y. W. Inn, P. M. Wood-Adams, March 2023

The melt rupture of a bimodal molecular weight distribution polyethylene is studied under simple shear with slip and time-to-rupture is analyzed. The time-to- rupture results show that there is a negative power law relation between the nominal shear rate and the time- to-rapture. The relationship between time to rupture and stress changes with the slip regime. Moving from weak to strong slip, there is a shift in the time-to- rupture curve down.

Confinement and Complex Viscosity
Steacy Coombs, March 2023

Whereas much is known about the complex viscosity of polymeric liquids, far less is understood about the behaviour of this material function when macromolecules are confined. By confined, we mean that the gap along the velocity gradient is small enough to reorient the polymers. We examine classical analytical solutions [Park and Fuller, JNNFM, 18, 111 (1985)] for a confined rigid dumbbell suspension in small-amplitude oscillatory shear flow. We test these analytical solutions against the measured effects of confinement on both parts of the complex viscosity of a carbopol suspension and three polystyrene solutions. From these comparisons, we find that both parts of the complex viscosity decrease with confinement, and that macromolecular orientation explains this. We find the persistence length of macromolecular confinement, ?? , to be independent of both ?? ?? and?? ?? 0.

Effect of Shear of and Pressure on Structure for Binary Blends of Bisphenol — A Polycarbonate and Poly(methyl Methacryslate)
Masayuki Yamaguchi, March 2023

The effect of applied shear flow and pressure on the miscibility and structure for the binary blends of bisphenol-A polycarbonate (PC) and low-molecular-weight poly(methyl methacrylate) (PMMA) was studied using a conventional capillary rheometer. The lower critical solution temperatures (LCSTs) of PC/PMMA (70/30) and PC/PMMA (80/20) were found to be 260 and 270°C, respectively, without flow field under atmospheric pressure. During capillary extrusion at/below 250°C, however, shear induced demixing was detected. Moreover, pressure induced demixing was also detected at high pressure. Finally, surface segregation of PMMA fraction was observed without phase separation for PC/PMMA (90/10).

Experimental Characterization and Modelling of the Pressure Dependence of the Viscosity for Injection Molding Simulations
Steffen Verwaayen, March 2023

The pressure dependence of melt viscosity of thermoplastic materials is difficult to measure and is therefore often neglected, although it can have a major influence on the results of an injection molding simulation. Current viscosity models provide the ability to model this dependence. Therefore, the viscosity is measured in a high- pressure capillary rheometer and the pressure dependence of the viscosity is determined in an online rheometer for a polypropylene. The generated experimental data is used as input to fit the Carreau-WLF model. The accuracy of the models varies depending on the input data chosen. In particular, the pressure dependence of the viscosity could not be correctly represented while maintaining good viscosity representation. A correction of the neglected pressure during the high-pressure capillary rheometer measurement improved the modeling of the pressure dependence of the viscosity slightly.

Exploiting Structure-Process Property Relationships of Branched Polycarbonates for Industrial Applications
Manojkumar Chellamuthu, Ph.D., March 2023

Current electrification market needs materials with good balance of Flow, Flame Property and Mechanical Performance. In this talk, we will discuss the rheological features of three commercially available linear, branched and hyper-branched polycarbonates (PCs) using comprehensive investigations. Applications of rheological properties to enhance Z-strength in Large Format Additive Manufacturing (LFAM) will also be discussed. Additionally, high temperature extensional Rheometer (CaBER) was used to understand the evolution of microstructure at high temperatures. The experiments were performed at temperatures ranging from T = 250 to 370 °C to a maximum Hencky strain of ten. At lower end of the temperature range, no significant degradation of the linear and branched Polycarbonate (PC) was observed either in the shear or extensional measurements. Beyond, T > 300 °C branched PC showed a dramatic increase in extensional viscosity which helps in Flame performance (anti-drip) better than its linear counterpart.

Introducing a Differentiable, Shear-Thinning Viscosity Model
Paul Van Huffel, March 2023

A differentiable model for non-Newtonian, shear- thinning viscosity is presented as derived by integrating the log-log domain derivative function of the Carreau-Yasuda viscosity model. This work starts with the discovery of the log-log domain derivative function as this is the foundation for the statement of the new viscosity model. Potential uses for this work include development of explicit or hybrid flow solvers for polymer flows and possibly extending into the incorporation of effects based on the rate of change of the spherical (i.e. expansion/compression) and deviatoric parts of the rate-of-strain tensor, although this model specifically deals with the deviatoric part. A fitting experiment of rheometer data that was initially fit for each temperature curve as part of another work is used to demonstrate the flexibility of having a variable curve shape parameter as opposed to a fixed value, and a simulation of a conical section is used to compare the apparent wall shear rate in a converging channel versus the numerically obtained shear rate by a finite element analysis of the same conical channel.

Steady State and Dynamic Oscillatory Shear Properties of Carbon Black Filled Elastomers
Avraam Isayev, Ph.D., March 2023

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 3rd and 5th stress harmonics to 1st harmonics increased with increasing strain amplitude and filler loading. Viscous Lissajou 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.

Using Thermal and Rheological Techniques to Help Guide Recycled PET Extrusion Processing
Tianhong Chen, Ph.D., March 2023

Polyethylene terephthalate (PET) is one of the most commonly used plastics in our daily life. It is completely recyclable and is the most recycled plastic in the U.S and worldwide. However, recycled PET from different sources may have large variabilities, such as reduced molecular weight, broader molecular weight distribution, different crystallinity, and containing different impurity contents, all of which can affect their processing and application. This presentation will discuss of using thermal and rheological techniques to fingerprint the feedstock resins and help guide extrusion processing. Specifically, we will discuss using differential scanning calorimetry (DSC) to identify the type of impurities, monitor the effect of thermal history on the crystallinity and crystal melting. We will also discuss using rheological techniques to estimate the molecular architecture, measure melt stability, melt viscosity, and help optimize extrusion conditions.

Time, Temperature & Applied Rheology in Wire & Cable
Scott Wasserman, March 2023

Many years ago, Union Carbide Corporation (UCC) had established a well-equipped melt rheology lab designed to accomplish large-scale melt testing to simulate high shear conditions and small-scale dynamic and steady shear capabilities to both predict low deformation phenomena and delineate key features of molecular structure. UCC later initiated an aggressive metallocene catalyst development program to develop polyethylenes (PEs) with unique molecular structures. In an effort to fully characterize the key features of molecular structure that was manifested in the observed viscoelastic properties, we calculated the melt relaxation spectra for the new PEs and in comparing them to incumbent PEs, we found the new PEs to be differentiated. This led to a family of patent applications [1] to protect the technology, and a new parameter, called the “relaxation spectrum index” or “RSI” to quantify the breath of the relaxation time distribution reflecting the novel molecular structures. The RSI proved to be a useful parameter to use to not only delineate interesting features of molecular structure, but also to predict large-scale processing behavior, such as motor load and amperage in extrusion of layers and components for wire and cable applications [2]. This presentation will illustrate the power found in calculating and characterizing the relaxation spectrum with dynamic oscillatory shear experiments. As an illustration, a case study will be presented in which a new compound was to be developed for high-speed thin-walled chemical-foamed telecommunications wire insulation. Many key rheological phenomena needed to be simultaneously considered to design the next-generation product, and the RSI proved to be instrumental in allowing the necessary differentiation between inventive and comparative materials. This led to the development of a powerful set of patent claims [3] to protect the strategic space for UCC (now Dow). The power of this rheology-based approach to intellectual property is that the invention is not limited to a particular composition – instead, the patent claims would be a potential challenge to any composition that meets the critical rheological profile. References 1. G. N. Foster, T. Chen, S. H. Wasserman, D.C. Lee, S. J. Kurtz, L. H. Gross, R. H. Vogel, U.S. Patent 5,798,427 (1998). 2. Wasserman, SH & Adams, JL. “Rheology and Crystallization in Fiber Optic Cable Jacket and Conduit Extrusion,” ANTEC 1997, Toronto, CA April 27-May 2, 1997. 3. S. Maki, G. D. Brown, S. H. Wasserman, D. J. Frankowski, V. Y. He, U.S. Patent 6,455,602 (2002).

Simulation Of Polymer Imprinting And Embossing Using Smoothed Dissipative Particle Dynamics
James St Julien, Donggang Yao, June 2022

A simulation of an imprinting process using Smoothed Dissipative Particle Dynamics is shown. Cavity filling modes and their dependence on die parameters is demonstrated for single and multicavity die, showing results consistent with FEM simulations and experimental data. Particle-based simulation methods can allow for modeling of more complex fluid behaviors.

Effects Of Sample Shape And Adhesive Type On Rheology Of Unidirectional Carbon Fiber Prepregs
Arit Das, Kathleen J. Chan, Michael J. Bortner, David A. Dillard, Davide S.A. De Focatiis, June 2022

The viscoelastic properties of carbon fiber reinforced thermoset composites are of utmost importance during processing such materials using composite forming. The quality of the manufactured parts is largely dependent on intelligent process parameter selection based on the viscoelastic and flow properties of the polymer resin. Viscoelastic properties such as the complex viscosity (η*), storage modulus (G’), loss modulus (G’’), and loss tangent (tanδ) are used to determine the critical transition events (such as gelation) during curing. An understanding of the changes in viscoelastic properties as a function of processing temperature and degree of cure provides insight to establish a suitable processing range for compression forming of prepreg systems. However, tracking viscoelastic properties as a function of cure during the forming process is a challenging task. In this current work, we have investigated the effect of sample size and adhesive type on the rheological properties of a commercially available carbon fiber prepreg material. Specifically, determining the linear viscoelastic region (LVE) as a function of sample configuration and different adhesive chemistries were explored. The results suggest that the square-shaped sample geometries coupled with cyanoacrylate based adhesive are optimum for conducting rheological characterization on the carbon fiber prepreg system.

A Semi-Genetic Process For Fitting Polymer Viscosities And Selecting Best Models
Paul Van Huffel, June 2022

This paper presents a process for fitting corrected viscosity data to constituent and temperature dependent data to a range of two-equation models. The process tests different models to determine the best fit model for each. Rheometer data for polymer melts, after corrections for shear rate and entrance pressure losses, may fit one model better than another, and as such the following constituent models are reviewed in the form as they are commonly applied in commercial software today: 1) Cross Model, 2) Modified Cross Model, and 3) Carreau-Yasuda. Once the constituent model is fit, the following temperature dependent models are compared: 1) WLF, Exponential, Arrhenius, and Masuko-Magill. The differences between the models are presented in order to highlight the need to compare different models to obtain a best fit. Lastly, a solution is presented to the problem of convergent viscosities with respect to shear rate as compared across a range of temperatures as no existing model in common use today can capture this specific behavior.

An Explicit Non-Newtonian Fluid Model For Polymeric Flow With Finite Stretch
Donggang Yao, June 2022

After nearly 80 years of research in constitutive modeling of polymeric fluids, simple yet capable models are still sought after today. In this work, we provide an explicit constitutive equation where the extra stress tensor is an explicit function of the objective velocity gradient while finite stretch of polymer chains are considered. With this model, the basic rheological functions in uniaxial extensional, planar extension and simple shear can all be obtained as closed-form analytical solutions with only elementary mathematical functions involved. The new model demonstrates excellent fitting to some sear and extensional data in the literature, and is able to simultaneously predict the major rheological functions in steady-state shear and extension.

Chemorheological Analysis Of Slow Reacting Polyurethanes
John Reynolds, Michael Bortner, June 2022

Tracking the cure progress of slow reacting, uncatalyzed polyurethane systems is a tedious, time consuming process that has been largely neglected due to the availability of catalysts. The use of catalysts has enabled quick, nonisothermal studies to dominate the field of research, but when catalysis is not an option, these methods become impractical. In this context, we can use chemorheology to correlate viscoelastic data to several previously developed cure models. The models presented here examine viscosity buildup, reaction rate progress, and thermodynamic behavior, while emphasizing the importance of interpretation during data analysis. These chemorheological techniques focus on the development of thermally curing networks during subjection to flow fields, and apply to a vast array of thermosetting polymeric materials.

Complex Viscosity Of Star-Branched Macromolecules From Analytical General Rigid Bead-Rod Theory
S.J. Coombs, M.A. Kanso, K.E. Haddad, A.J. Giacomin, June 2022

The complex viscosity of planar star-branched polymers has been derived from general rigid bead-rod theory, but only for singly-beaded arms. Here, we explore the respective roles of branch functionality, arm length of non-planar arrangements, analytically from general rigid bead-rod theory. For non-planar, we include polyhedral, both regular and irregular. We fit the theory to complex viscosity measurements on polybutadiene solutions, one quadrafunctional star-branched, the other unbranched, of the same molecular weight. We learn that when general rigid bead-rod theory is applied to quadrafunctional polybutadiene, a slightly irregular center-beaded tetrahedron of interior angle 134º is required (with 1,360,000 g/gmol per bead) to describe its complex viscosity behaviour.

Development Of A Micro-Capillary Rheometer For High Solids Content Rheology
Michael C. Coco, Michael J. Bortner Ph.D., June 2022

Rheological testing of new material formulations can require significant quantities, specifically when considering development of new chemistries at the laboratory scale. In order to minimize the quantity of material required for evaluation, we are developing approaches suitable for characterization of high solids content formulations using micro-capillary rheometry. The goal of this investigation is to design and produce a micro-capillary rheometer capable of characterizing basic rheological properties, such as viscosity and shear-thinning behavior, while requiring the least amount of sample possible. In our current design, we implement a micro-dispensing approach combined with calibrated force transducers. With this approach we can further elucidate an understanding of the differences between typical capillary rheometry and behavior at reduced dimension flow fields. Issues such as pressure relaxation and free volume compaction can therefore be studied through readily modified geometries and testing rates. This design will lead to a better understanding of micro-capillary rheometer design and enable a unique approach for rheology measurements for new chemistries and formulations, including high solids content formulations (up to 60+ vol%). Additionally, this framework will facilitate the study of a variety of flow geometries applicable to a wide range of applications including precision dispensing of adhesives and sealants, and direct ink write additive manufacturing.

Fabrication Of Expandable Filaments Towards In-Situ Foam 3D Printing Of Microcellular Poly(Lactic Acid)
Karun Kalia, Benjamin Francoeur, Alireza Amirkhizi, Amir Ameli, June 2022

The purpose of this study was to investigate the feasibility of in-situ foaming in fused filament fabrication (FFF) process. Development of unexpanded filaments loaded with thermally expandable microspheres, TEM is reported as a feedstock for in-situ foam printing. Four different material compositions, i.e., two grades of polylactic acid, PLA, and two plasticizers (polyethylene glycol, PEG, and triethyl citrate, TEC) were examined. PLA, TEM and plasticizer were dry blended and fed into the extruder. The filaments were then extruded at the lowest possible barrel temperatures, collected by a filament winder, and used for FFF printing process. The results showed that PLA Ingeo 4043D (MFR=6 g/10min) provides a more favorable temperature window for the suppression of TEM expansion during extrusion process, compared to PLA Ingeo 3052D (MFR=14 g/10min). TEC plasticizer was also found to effectively lower the process temperatures without adversely interacting with the TEM particles. Consequently, unexpanded filaments of PLA4043D/TEM5%/TEC2% was successfully fabricated with a density value of 1.16 g/cm3, which is only ~4.5% lower than the theoretical density value. The in-situ foaming in FFF process was then successfully demonstrated. The printed foams revealed a uniform cellular structure, reproducible dimensions, as well as less print marks on the surface, compared to the solid counterparts.

Fitting Of Tait Coefficients For Molding Simulation
Paul Van Huffel, June 2022

For several decades, the Tait model has been used in simulation software to describe the volumetric mechanical behavior of thermoplastic polymers as they cool. It is used to compute the residual strains and stresses of the polymer as it solidifies, but there is a problem. Many data sets have coefficients where there exists a discontinuity at the transition between the molten and solid domains. This paper outlines some basic checks that can be done to detect this problem and a procedure to fit the coefficients to data so that this problem does not arise.

High Shear Rate Rheology Of Cellulose Nanofibrils
Aliya J. Kaplan, Bradley P. Sutliff, Michael J. Bortner, June 2022

Nanofibrillated cellulose (NFC) has properties ideal for applications in the packaging and medical industries. To understand if cellulose-based polymers could become a replacement for synthetic polymers in these fields, NFC suspensions were repeatedly exposed to elevated shear stresses to simulate industrial processing procedures and allow for observation of changes in material properties. A capillary rheometer was used to run aqueous NFC suspensions of 10 wt% at room temperature at shear rates beyond 30,000 s-1. Due to repeated shear rate exposure, a decrease in volume resulting from unavoidable water loss informed the observable increase in apparent viscosity and suggested that this increasing trend was not caused by a change in material morphology. Noisy data as a result of flocs was detrimental to the analysis of material behavior during rheological testing. Once preprocessing procedures are successfully designed to reduce noise in the data, material behavior at high shear rates will be further defined.

High Shear Viscosity Measurement Of A Natural Rubber And Synthetic Rubber Materials Using The Rubber Screw Rheometer
Myung-Ho Kim, JaeSik Hyun, InSu Seol , Sunwoong Choi, June 2022

The shear rate-dependent viscosity of natural rubber and three types of synthetic rubber was measured using the Rubber Screw Rheometer. Viscosity values with Mooney viscometer, which has traditionally measured rubber viscosity, have a high correlation with the values of RSR shear rate 10 [1/s]. Thus the Mooney Viscosity value can be estimated using the RSR shear viscosity measurement. Also, in the case of virgin rubber, the accuracy of the measured value increases when it has a pre-shear history. It was confirmed that the viscosity measurement value was a measurement value having a deviation within +3% when comparing the three times repeated measurements. The measured value was correlated to Mooney Viscosity successfully with a first- order equation.

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