The authors thank Anton Paar for use of the MCR 702 rheometer through their VIP academic research program. We also thank Dr. Abhishek Shetty for the comments in the instrument setup.

1. Rheometer Setup
<ol>
	<li>With the rheometer configured in the SMT mode (see note), attach the upper and lower drive geometries. To maintain as close to a homogeneous shear field as possible, use a 50 mm plate (PP50) as the lower fixture, and a 2-degree cone (CP50-2) for the upper fixture. 
	Note: The rheometer we use (see the Table of Materials) can be configured in either a combined motor-transducer (CMT) or separate motor transducer (SMT) mode. With only a single motor integrated in the rheometer head, it acts as a traditional CMT stress-controlled rheometer and the data obtained require inertia corrections. With two motors incorporated in a SMT mode, the upper motor operates solely as a torque transducer and the bottom motor acts as a drive unit thus converting the rheometer into a typical strain-controlled rheometer.
	<ol>
		<li>Attach the bottom and top geometries.</li>
		<li>Click the zero-gap button in the control panel.</li>
		<li>Navigate to start service function under the Measuring set tab on top. Run the inertia calibrations for the upper and lower measuring systems, found in the dropdown menu.</li>
		<li>Run adjustments for the upper and lower motors.</li>
		<li>Specify the desired temperature in the control panel. 
		Note: The measurements at which experiments on XG and PEO solutions are performed are 25 &#177; 0.1 &#176;C and 35 &#177; 0.1 &#176;C, respectively.</li>
	</ol>
	</li>
	<li>Load the material of interest on top of the bottom geometry with a spatula or pipette, ensuring no air bubbles are entrained in the sample. 
	Note: Approximate volumes of material required to completely fill a geometry are provided in the rheometry software under Setup | Measuring Systems.
	<ol>
		<li>Load 1.14 mL to fill the cone-and-plate geometry. Load higher viscosity samples with a spatula, and less viscous materials with a pipette. 
		Note: A spatula is used to load the polymer solutions.</li>
		<li>Command the measuring system to trim gap and gently trim the excess material at the edge of geometry with a square-ended spatula, ensuring the spatula remains perpendicular to the axis of the rheometer. 
		Note: The quality of material loading will affect the rheological results significantly and any apparent under- or over-filling should be avoided.</li>
		<li>Press the continue button in the rheometry software to move to the measurement gap. 
		Note: A complete loading process is illustrated in Figure 2.</li>
	</ol>
	</li>
</ol>
2. Running Oscillatory Shear Tests
Note: Two ways of running oscillatory shear tests are introduced. The first approach is designed for sinusoidal stresses and strains only and was used to collect the data we report here. The second method allows for arbitrary stress or strain schedules to be set.
<ol>
	<li>Sinusoidal oscillatory shear 
	<ol>
		<li>Navigate to Large amplitude oscillatory shear-LAOS under My apps in the software. Go to the Measurement box and click strain variable.</li>
		<li>Specify the initial (1%) and final values (4,000%) of a strain amplitude sweep. Specify the imposed frequency of 0.316 rad/s. Define the desired total number of strain amplitudes as 16 in the specified amplitude range, which results in the point density of 5 points per decade.</li>
		<li>Check the Get waveform box at the top to collect transient responses.</li>
		<li>Click the start button at the top to start the experiments and the raw data will be displayed in the rheometry software automatically.</li>
	</ol>
	</li>
	<li>Arbitrary Stress or Strain Schedules
	<ol>
		<li>To impose arbitrary-defined deformation, click Waveform sine generator under My apps in the software.</li>
		<li>Define a list of strain values that correspond to the function that is to be applied (not restricted to sinusoidal waveform). Generate the value list in an external program.</li>
		<li>Click edit under the strain value in the measurement box. Copy and paste these numbers into the value list.</li>
		<li>Specify the number of data points, point duration, and interval time to adjust the imposed frequency. For instance, specify the number of data points and the interval time as 512 points and 6.2832 s, respectively, if a cycle of sinusoidal strain is pasted into strain value list with 512 points and the frequency of 1 rad/s is desired. 
		Note: This approach is not recommended for running sinusoidal oscillatory shear due to the limited number of oscillatory cycles, and also due to the fact that automatic corrections which are enabled in an oscillatory test mode on the rheometer are disabled in this mode. Nonetheless, because there are no assumptions of sinusoidal strain built into the SPP framework, one can arbitrarily define imposed strain functions according to the processing conditions or end use the materials may experience, and the SPP framework remains applicable to analyze the rheological response.</li>
		<li>Check the Get waveform box at the top. Then click the start button at the top to start the experiments.</li>
	</ol>
	</li>
</ol>
3. Performing SPP analysis (SPP-LAOS software)
Note: The SPP analysis software is a MATLAB-based freeware package for analyzing rheological data with the SPP framework and is attached as Supplementary Files 1&#8210;621.
<ol>
	<li>Format the data files to be tab-delimited text (.txt) consisting of four columns in the order of {Time (s), Strain (-), Rate (1/s), Stress (Pa)}. 
	Note: Users may need to modify the number of header lines in the function files to be able to process their data. See sample data files (Supplementary Files 7&#8210;9).</li>
	<li>To run SPP-LAOS software, open the m-file named RunSPPplus_v1.m in MATLAB. 
	Note: While RunSPPplus_v1.m is the main script to run the analysis, the package contains other function files that will be called from the main script, including SPPplus_read_v1.m, SPPplus_fourier_v1.m, SPPplus_numerical_v1.m, SPPplus_print_v1.m and SPPplus_figure_v1.m.</li>
	<li>Navigate to the section labeled User-defined variables, and specify the following variables.
	<ol>
		<li>Filename: Specify the name of .txt file that will be used for the SPP analysis. 
		Note: The file must match the above format requirement.</li>
		<li>Run state: Place the vector as [1, 0] to run Fourier analysis mode for regular oscillatory shear response. 
		Note: The software employs two different methods of calculating the instantaneous SPP moduli,&#160;<img alt="Equation 3" src="/files/ftp_upload/58707/58707eq3.jpg" />&#160;and&#160;<img alt="Equation 4" src="/files/ftp_upload/58707/58707eq4.jpg" />, based on Fourier transformation and numerical differentiation. The Fourier transform approach is designed for periodic input, such as oscillatory shear tests. Arbitrary time-dependent tests, which include, but are not limited to sinusoidal protocols, can be analyzed with the numerical differentiation approach.</li>
		<li>Run state: Input the vector as [0, 1] to run numerical-differentiation analysis mode for arbitrary time-dependent tests.</li>
		<li>Omega (Fourier analysis): Specify the angular frequency of oscillation, with units of rad/s.</li>
		<li>M (Fourier analysis): Define number of higher harmonics to be included in the SPP analysis. Adjust this number to include all the higher harmonics above the noise floor. 
		Note: This number must be a positive odd number and varies with amplitude and material. We include up to the 3rd harmonic in the MAOS regime, and up to the 55th harmonic at the largest amplitude investigated.</li>
		<li>p (Fourier analysis): Specify the total number of periods of measuring time in the input data, which has to be a positive integer. 
		Note: The more periods of data that are collected, the higher the time resolution of the SPP parameters.</li>
		<li>k (numerical differentiation): Define the step size for the numerical differentiation, which has to be a positive integer.</li>
		<li>num_mode (numerical differentiation): Specify num_mode to be either &#8220;0&#8221; (standard differentiation) or &#8220;1&#8221; (looped differentiation). 
		Note: There are two procedures implemented in the numerical differentiation scheme. The &#8220;standard differentiation&#8221; makes no assumptions about the form of the data. It utilizes a forward difference to calculate the derivative for the first 2,000 points of the data, a backward difference for the final 2,000 points, and a centered difference elsewhere. The &#8220;looped differentiation&#8221; assumes that the data is taken under steady-state periodic conditions, and includes an integer number of periods. These assumptions allow a centered difference to be calculated everywhere by looping over the ends of the data.</li>
		<li>Select the run button at the top once all the variables are specified. 
		Note: The software will compute all SPP metrics associated with the data, and then display figures associated with the current analysis run and output a text file containing all the calculated SPP metrics for further analysis.</li>
		<li>Iteratively adjust the number of harmonics to be included in the analysis from the output Fourier spectrum. Include all higher odd harmonics above the noise floor.</li>
	</ol>
	</li>
</ol>
4. Interpreting a LAOS Response
<ol>
	<li>Navigate to the Cole-Cole plot of the instantaneous SPP moduli <img alt="Equation 3" src="/files/ftp_upload/58707/58707eq3.jpg" /> and <img alt="Equation 4" src="/files/ftp_upload/58707/58707eq4.jpg" /> that is automatically generated by the SPP software. 
	Note: A curve in the Cole-Cole plot is considered as the trajectory of the viscoelastic material state, and interpretations can be formed within an oscillation, in intra-cycle processes, or between successive periods, in inter-cycle processes.</li>
	<li>Interpret stiffness by the instantaneous elastic modulus,<img alt="Equation 13" src="/files/ftp_upload/58707/58707eq13.jpg" />, and an increase/decrease of <img alt="Equation 3" src="/files/ftp_upload/58707/58707eq3.jpg" /> that indicates stiffening/softening. See Figure 3.</li>
	<li>Interpret a material&#39;s viscosity based on the instantaneous viscous modulus, <img alt="Equation 4" src="/files/ftp_upload/58707/58707eq4.jpg" />. An increase/decrease in this parameter represents thickening/thinning.</li>
	<li>Transfer the focus to another Cole-Cole plot of the time derivatives of transient moduli <img alt="Equation 14" src="/files/ftp_upload/58707/58707eq14.jpg" /> and <img alt="Equation 15" src="/files/ftp_upload/58707/58707eq15.jpg" />, which provide quantitative information about how much a response is stiffening (<img alt="Equation 16" src="/files/ftp_upload/58707/58707eq16.jpg" />), softening (<img alt="Equation 17" src="/files/ftp_upload/58707/58707eq17.jpg" />), thickening (<img alt="Equation 18" src="/files/ftp_upload/58707/58707eq18.jpg" />), thinning ((<img alt="Equation 19" src="/files/ftp_upload/58707/58707eq19.jpg" />)). See Figure 3. 
	Note: With the values of the derivatives, the rate at which materials undergo stiffening/softening or thickening/thinning can be quantitatively determined.</li>
	<li>Read the center of a trajectory (in a time-weighted average sense) in the Cole-Cole plot of <img alt="Equation 20" src="/files/ftp_upload/58707/58707eq20.jpg" /> as the dynamic moduli, [<img alt="Equation 1" src="/files/ftp_upload/58707/58707eq1.jpg" /> <img alt="Equation 21" src="/files/ftp_upload/58707/58707eq21.jpg" />]. 
	Note: The dynamic moduli are averaged parameters over a cycle of deformation, and are insufficient to provide local information under LAOS.</li>
	<li>Track the relative motion of the trajectory across amplitudes to understand the inter-cycle physics. 
	Note: Focusing on the relative motion of time-weighted average center is equivalent to a traditional strain amplitude sweep of the dynamic moduli. Nonetheless, one can easily analyze the across-amplitude motion of other specific points, for instance, the strain extrema.</li>
	<li>Determine the transient differential viscosity <img alt="Equation 22" src="/files/ftp_upload/58707/58707eq22.jpg" /> and overlay it on top of a steady-shear flow curve. Compare the transient LAOS response with steady-shear conditions.</li>
	<li>Determine the points of maximum <img alt="Equation 12" src="/files/ftp_upload/58707/58707eq12.jpg" /> at the large amplitudes in the Cole-Cole plot of <img alt="Equation 20" src="/files/ftp_upload/58707/58707eq20.jpg" />. See the star labeled in Figure 4c.
	<ol>
		<li>Record the values of <img alt="Equation 23" src="/files/ftp_upload/58707/58707eq23.jpg" /> at those instants.</li>
		<li>Plot them on top of the amplitude sweep of the dynamic moduli. See Figure 4d. 
		Note: Pay attention to any correspondence between the maximum transient elastic modulus and the linear viscoelastic <img alt="Equation 1" src="/files/ftp_upload/58707/58707eq1.jpg" />.</li>
	</ol>
	</li>
	<li>Locate the instants of maximum <img alt="Equation 12" src="/files/ftp_upload/58707/58707eq12.jpg" /> in the elastic Lissajous figure and record the corresponding strain values. See the star labeled in Figure 4a.</li>
	<li>If <img alt="Equation 24" src="/files/ftp_upload/58707/58707eq24.jpg" />, then determine the equilibrium strain <img alt="Equation 25" src="/files/ftp_upload/58707/58707eq25.jpg" /> and the elastic strain <img alt="Equation 26" src="/files/ftp_upload/58707/58707eq26.jpg" />. 
	Note. With the displacement stress <img alt="Equation 27" src="/files/ftp_upload/58707/58707eq27.jpg" />, when <img alt="Equation 28" src="/files/ftp_upload/58707/58707eq28.jpg" /> the equilibrium strain can be determined as <img alt="Equation 29" src="/files/ftp_upload/58707/58707eq29.jpg" /> and the elastic strain can therefore be determined as the difference between strain and equilibrium strain5,13. The requirement of <img alt="Equation 24" src="/files/ftp_upload/58707/58707eq24.jpg" /> is derived and discussed elsewhere15.</li>
	<li>Plot the elastic strain as a function of the imposed strain amplitude. See Figure 4e. If the elastic strain is independent of the strain amplitude, then indicate this critical strain on the amplitude sweep as in Figure 4d.</li>
</ol>

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The authors have nothing to disclose.

We have demonstrated how to correctly perform large amplitude oscillatory shear rheometry tests using a commercial rheometer, and to run the SPP analysis freeware to interpret and understand the nonlinear stress responses of two distinct polymer solutions. The SPP framework, which has previously been shown to correlate with structural changes and facilitate understandings of numerous colloidal systems, can be equally applied to polymer systems. The responses of two concentrated polymeric solutions to LAOS have been inves...

Concentrated polymeric solutions are used in a variety of industrial applications primarily to increase viscosity, including in foods1 and other consumer products2, enhanced oil recovery3, and soil remediation4. During their processing and use, they are necessarily subjected to large deformations over a range of timescales. Under such processes, they demonstrate rich and complex nonlinear rheological behaviors that depend on the flow or deformation conditions1. Understanding these complex nonlinear rheological behaviors is essential for successfully controlling processes, designing superior products, and maximizing energy efficiency. Aside from the industrial importance, there is a great deal of academic interest in understanding the rheological behaviors of polymeric materials far from equilibrium.
Oscillatory shear tests are a staple component of every thorough rheological characterization because of the orthogonal application of strain and strain rate5, and the ability to independently control the length and time scales probed by tuning the amplitude and frequency. The stress response to small amplitude oscillatory shear strains, which are small enough not to disturb a material&#39;s internal structure, can be decomposed into components in phase with the strain and in phase with strain rate. The coefficients of the components in phase with the strain and the strain rate are collectively referred to as the dynamic moduli6,7, and individually as the storage modulus, <img alt="Equation 1" src="/files/ftp_upload/58707/58707eq1.jpg" />, and loss modulus, <img alt="Equation 2" src="/files/ftp_upload/58707/58707eq2.jpg" />. The dynamic moduli lead to clear elastic and viscous interpretations. However, interpretations based on these dynamic moduli are valid only for small strain amplitudes, where the stress responses to sinusoidal excitations are also sinusoidal. This regime is generally referred to as the small amplitude oscillatory shear (SAOS), or the linear viscoelastic regime. As the imposed deformation becomes larger, changes are induced in the material microstructure, which are reflected in the complexity of the non-sinusoidal transient stress responses8. In this rheologically nonlinear regime, which more closely mimics industrial processing and consumer usage conditions, the dynamic moduli act as poor descriptions of the response. Another way to understand how concentrated soft materials behave out of equilibrium is therefore required.
A number of recent studies9,10,11,12,13,14,15,16 have shown that materials pass through diverse intra-cycle structural and dynamical changes elicited by larger deformations in the medium amplitude oscillatory shear (MAOS)15,17 and large amplitude oscillatory shear (LAOS) regimes. The intra-cycle structural and dynamical changes have different manifestations, such as breakage of microstructure, structural anisotropy, local rearrangements, reformation, and changes in diffusivity. These intra-cycle physical changes in the nonlinear regime lead to the complex nonlinear stress responses that cannot be simply interpreted with the dynamic moduli. As an alternative, several approaches have been suggested for the interpretation of the nonlinear stress responses. Common examples of this are Fourier transform rheology (FT rheology)18, power series expansions11, the Chebyshev description19, and the sequence of physical processes (SPP)5,8,13,14,20 analysis. Although all of these techniques have been shown to be mathematically robust, it is still an unanswered question as to whether any of these techniques can provide clear and reasonable physical explanations of nonlinear oscillatory stress responses. It remains an outstanding challenge to provide concise interpretations of rheological data that correlate to structural and dynamical measures.
In a recent study, the nonlinear stress response of the Soft Glassy Rheology (SGR) model8 and a soft glass made of colloidal star polymers7under oscillatory shear was analyzed through the SPP scheme. Temporal changes in the elastic and viscous properties inherent in nonlinear stress responses were separately quantified by the SPP moduli, <img alt="Equation 3" src="/files/ftp_upload/58707/58707eq3.jpg" /> and <img alt="Equation 4" src="/files/ftp_upload/58707/58707eq4.jpg" />. Furthermore, the rheological transition represented by the transient moduli was accurately correlated to microstructural changes represented by the distribution of mesoscopic elements. In the study of the SGR model8, it was clearly shown that rheological interpretation via the SPP scheme accurately reflects the physical changes under all oscillatory shear conditions in the linear and nonlinear regimes for soft glasses. This unique capability to provide accurate physical interpretation of nonlinear responses of soft glasses makes the SPP method an attractive approach for researchers studying out-of-equilibrium dynamics of polymer solutions and other soft materials.
The SPP scheme is built around viewing rheological behaviors as occurring in a three-dimensional space (<img alt="Equation 5" src="/files/ftp_upload/58707/58707eq5.jpg" />) that consists of the strain (<img alt="Equation 6" src="/files/ftp_upload/58707/58707eq6.jpg" />), strain rate (<img alt="Equation 7" src="/files/ftp_upload/58707/58707eq7.jpg" />), and stress (<img alt="Equation 8" src="/files/ftp_upload/58707/58707eq8.jpg" />)5. In a mathematical sense, the stress responses are treated as multivariable functions of the strain and strain rate (<img alt="Equation 9" src="/files/ftp_upload/58707/58707eq9.jpg" />). As the rheological behavior is regarded as a trajectory in <img alt="Equation 5" src="/files/ftp_upload/58707/58707eq5.jpg" /> (or a multivariable function), a tool for discussing the properties of a trajectory is required. In the SPP approach, the transient moduli <img alt="Equation 3" src="/files/ftp_upload/58707/58707eq3.jpg" /> and <img alt="Equation 4" src="/files/ftp_upload/58707/58707eq4.jpg" /> play such a role. The transient elastic modulus <img alt="Equation 3" src="/files/ftp_upload/58707/58707eq3.jpg" /> and viscous modulus <img alt="Equation 4" src="/files/ftp_upload/58707/58707eq4.jpg" /> are defined as partial derivatives of the stress with respect to the strain (<img alt="Equation 10" src="/files/ftp_upload/58707/58707eq10.jpg" />) and the strain rate (<img alt="Equation 11" src="/files/ftp_upload/58707/58707eq11.jpg" />). Following the physical definition of differential elastic and viscous moduli, the transient moduli quantify the instantaneous influence of strain and strain rate on the stress response respectively, whereas other analysis methods cannot provide any information on elastic and viscous properties separately.
The SPP approach enriches the interpretation of the oscillatory shear tests. With the SPP analysis, the complex nonlinear rheological behaviors of concentrated polymeric solutions in LAOS can be directly related to the linear rheological behaviors in SAOS. We show in this work how the maximum transient elastic modulus (<img alt="Equation 12" src="/files/ftp_upload/58707/58707eq12.jpg" />max) near the strain extrema corresponds to the storage modulus in the linear regime (SAOS). Furthermore, we show how the transient viscous modulus (<img alt="Equation 4" src="/files/ftp_upload/58707/58707eq4.jpg" />) during a LAOS cycle traces the steady state flow curve. In addition to providing details of the complex sequence of processes that concentrated polymer solutions go through under LAOS, the SPP scheme also provides information regarding the recoverable strain in the material. This information, which is not obtainable through other approaches, is a useful measure of how much a material will recoil once stress is removed. Such behavior has impact on the printability of concentrated solutions for 3D printing applications, as well as screen printing, fiber formation, and flow cessation. A number of recent studies5,8,13 clearly indicate that the recoverable strain is not necessarily the same as the strain imposed during LAOS experiments. For instance, a study of soft colloidal glasses under LAOS13 found that the recoverable strain is only 5% when significantly larger total strain (420%) is imposed. Other studies16,21,22,23,24 using the cage modulus21 also conclude that linear elasticity can be observed under LAOS at the point close to the strain maxima, implying that the materials experienced relatively small deformation at those instants. The SPP scheme is the only framework for understanding LAOS that accounts for a shift in the strain equilibrium that leads to a difference between the recoverable and the total strains.
This article aims to facilitate understandings and ease of use of the SPP analysis method by providing a detailed protocol for a LAOS analysis freeware, using two concentrated polymer solutions, a 4 wt% xanthan gum (XG) aqueous solution and a 5 wt% PEO in DMSO solution. These systems are chosen because of their broad range of application and rheologically interesting properties. Xanthan gum, a natural high-molecular-weight polysaccharide, is an exceptionally effective stabilizer for aqueous systems and commonly applied as a food additive to provide desired viscosification or in oil drilling to increase viscosity and yield points of drilling muds. PEO has a unique hydrophilic property and is often used in pharmaceutical products and controlled release systems as well as soil remediation activities. These polymeric systems are tested under various oscillatory shear conditions that are intended to approximate processing, transport, and end-use conditions. Although these practical conditions may not necessarily involve flow reversal as in oscillatory shear, the flow field can be easily approximated and tuned with the independent control of applied amplitude and imposed frequency in an oscillatory test. Furthermore, the SPP scheme can be used as described here to understand a broad range of flow types, including those that do not include flow reversals such as the recently-proposed UD-LAOS25, in which large amplitude oscillations are applied in one direction only (leading to the moniker &#34;uni-directional LAOS&#34;). For simplicity, and for illustrative purposes, we restrict the current study to traditional LAOS, which does include periodic flow reversal. The measured rheological responses are analyzed with the SPP approach. We demonstrate how to use the SPP software with simple explanations on salient calculation steps to improve readers&#39; understanding and usage. A legend for interpreting the SPP analysis results is introduced, according to which the type of rheological transition is identified. Representative SPP analysis results of the two polymers under various oscillatory shear conditions are displayed, in which we clearly identify a sequence of physical processes that contains information on the material&#39;s linear viscoelastic response as well as the steady-state flow properties of the material.
This protocol provides salient details of how to accurately perform nonlinear rheological experiments, as well as a step-by-step guide to analyzing and understanding rheological responses with the SPP framework, as shown in Figure 1. We begin by providing an introduction to the instrument setup and calibrations, followed by specific commands for making a commercially-available rheometer collect high-quality transient data. Once the rheological data have been obtained, we introduce the SPP analysis freeware, with a detailed manual. Further, we discuss how to understand the time-dependent response of the two concentrated polymer solutions within the SPP scheme, by comparing the results obtained from LAOS with the linear-regime frequency sweep and the steady-state flow curve. These results clearly identify that the polymer solutions transition between distinct rheological states within an oscillation, allowing for a more detailed picture of their nonlinear transient rheology to emerge. These data can be used to optimize processing conditions for product formation, transport, and use. These time-dependent responses further provide potential pathways to clearly form structure-property-processing relationships by coupling the rheology with microstructural information obtained from small-angle scattering of neutrons, X-rays, or light (SANS, SAXS, and SALS, respectively), microscopy, or detailed simulations.

<table><tbody><tr><td>SPP analysis software</td><td>Simon Rogers Group (UIUC)</td><td>SPPplus_v1p1</td><td>Attached as supplementary files</td></tr><tr><td>MATLAB</td><td>Mathwork</td><td></td><td></td></tr><tr><td>Rheometer</td><td>Anton Paar</td><td>MCR 702 TwinDrive</td><td></td></tr><tr><td>50mm 2-degree cone</td><td>Anton Paar</td><td>CP50-2</td><td>Upper measuring system</td></tr><tr><td>50mm plate</td><td>Anton Paar</td><td>PP50</td><td>Lower measuring system</td></tr><tr><td>Xanthan gum (XG)</td><td>Sigma-Aldrich</td><td>11138-66-2</td><td></td></tr><tr><td>Polyethylene oxide (PEO)</td><td>Sigma-Aldrich</td><td>25322-68-3</td><td>Mv=1,000,000</td></tr><tr><td>Dimethyl sulfoxide (DMSO)</td><td>Sigma-Aldrich</td><td>67-68-5</td><td></td></tr></tbody></table>

studying large amplitude oscillatory shear response of soft materials

We investigate the sequence of physical processes exhibited during large amplitude oscillatory shearing (LAOS) of polyethylene oxide (PEO) in dimethyl sulfoxide (DMSO) and xanthan gum in water &#8212; two concentrated polymer solutions used as viscosifiers in foods, enhanced oil recovery, and soil remediation. Understanding the nonlinear rheological behavior of soft materials is important in the design and controlled manufacturing of many consumer products. It is shown how the response to LAOS of these polymer solutions can be interpreted in terms of a clear transition from linear viscoelasticity to viscoplastic deformation and back again during a period. The LAOS results are analyzed via the fully quantitative Sequence of Physical Processes (SPP) technique, using free MATLAB-based software. A detailed protocol of performing a LAOS measurement with a commercial rheometer, analyzing nonlinear stress responses with the freeware, and interpreting physical processes under LAOS is presented. It is further shown that, within the SPP framework, a LAOS response contains information regarding the linear viscoelasticity, the transient flow curves, and the critical strain responsible for the onset of nonlinearity.

Representative results of the SPP analysis from XG and PEO/DMSO solutions under oscillatory shear tests are presented in Figures 4 and 5. We first present the raw data as elastic (<img alt="Equation 30" src="/files/ftp_upload/58707/58707eq30.jpg" />) and viscous (<img alt="Equation 31" src="/files/ftp_upload/58707/58707eq31.jpg" />) Lissajous-Bowditch curves in Figures 4a, 4b, 5a and 5b. ...

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials

We present a detailed protocol outlining how to perform nonlinear oscillatory shear rheology on soft materials, and how to run the SPP-LAOS analysis to understand the responses as a sequence of physical processes.

We investigate the sequence of physical processes exhibited during large amplitude oscillatory shearing (LAOS) of polyethylene oxide (PEO) in dimethyl ...

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12.4K Views.  University of Illinois at Urbana-Champaign. We present a detailed protocol outlining how to perform nonlinear oscillatory shear rheology on soft materials, and how to run the SPP-LAOS analysis to understand the responses as a sequence of physical processes.

Video: Studying Large Amplitude Oscillatory Shear Response of Soft Materials

Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

A new small-angle neutron scattering (SANS) sample environment optimized for studying the microstructure of complex fluids under simple shear flow is presented. The SANS shear cell consists of a concentric cylinder Couette geometry that is sealed and rotating about a horizontal axis so that the vorticity direction of the flow field is aligned with the neutron beam enabling scattering from the 1-2 plane of shear (velocity-velocity gradient, respectively). This approach is an advance over previous shear cell sample environments as there is a strong coupling between the bulk rheology and microstructural features in the 1-2 plane of shear. Flow-instabilities, such as shear banding, can also be studied by spatially resolved measurements. This is accomplished in this sample environment by using a narrow aperture for the neutron beam and scanning along the velocity gradient direction. Time resolved experiments, such as flow start-ups and large amplitude oscillatory shear flow are also possible by synchronization of the shear motion and time-resolved detection of scattered neutrons. Representative results using the methods outlined here demonstrate the useful nature of spatial resolution for measuring the microstructure of a wormlike micelle solution that exhibits shear banding, a phenomenon that can only be investigated by resolving the structure along the velocity gradient direction. Finally, potential improvements to the current design are discussed along with suggestions for supplementary experiments as motivation for future experiments on a broad range of complex fluids in a variety of shear motions.

A shear cell is developed for small-angle neutron scattering measurements in the velocity-velocity gradient plane of shear and is used to characterize complex fluids. Spatially resolved measurements in the velocity gradient direction are possible for studying shear-banding materials. Applications include investigations of colloidal dispersions, polymer solutions, and self-assembled structures.

A new small-angle neutron scattering (SANS) sample environment optimized for studying the microstructure of complex fluids under simple shear flow is ...

Dielectric RheoSANS &#8212; Simultaneous Interrogation of Impedance, Rheology and Small Angle Neutron Scattering of Complex Fluids

A procedure for the operation of a new dielectric RheoSANS instrument capable of simultaneous interrogation of the electrical, mechanical and microstructural properties of complex fluids is presented. The instrument consists of a Couette geometry contained within a modified forced convection oven mounted on a commercial rheometer. This instrument is available for use on the small angle neutron scattering (SANS) beamlines at the National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR). The Couette geometry is machined to be transparent to neutrons and provides for measurement of the electrical properties and microstructural properties of a sample confined between titanium cylinders while the sample undergoes arbitrary deformation. Synchronization of these measurements is enabled through the use of a customizable program that monitors and controls the execution of predetermined experimental protocols. Described here is a protocol to perform a flow sweep experiment where the shear rate is logarithmically stepped from a maximum value to a minimum value holding at each step for a specified period of time while frequency dependent dielectric measurements are made. Representative results are shown from a sample consisting of a gel composed of carbon black aggregates dispersed in propylene carbonate. As the gel undergoes steady shear, the carbon black network is mechanically deformed, which causes an initial decrease in conductivity associated with the breaking of bonds comprising the carbon black network. However, at higher shear rates, the conductivity recovers associated with the onset of shear thickening. Overall, these results demonstrate the utility of the simultaneous measurement of the rheo-electro-microstructural properties of these suspensions using the dielectric RheoSANS geometry.

Here, we present a procedure for the measurement of simultaneous impedance, rheology and neutron scattering from soft matter materials under shear flow.

A procedure for the operation of a new dielectric RheoSANS instrument capable of simultaneous interrogation of the electrical, mechanical and ...

Challenges in Rheological Characterization of Highly Concentrated Suspensions &#8212; A Case Study for Screen-printing Silver Pastes

A comprehensive rheological characterization of highly concentrated suspensions or pastes is mandatory for a targeted product development meeting the manifold requirements during processing and application of such complex fluids. In this investigation, measuring protocols for a conclusive assessment of different process relevant rheological parameters have been evaluated. This includes the determination of yield stress, viscosity, wall slip velocity, structural recovery after large deformation and elongation at break as well as tensile force during filament stretching.
The importance of concomitant video recordings during parallel-plate rotational rheometry for a significant determination of rheological quantities is demonstrated. The deformation profile and flow field at the sample edge can be determined using appropriate markers. Thus, measurement parameter settings and plate roughness values can be identified for which yield stress and viscosity measurements are possible. Slip velocity can be measured directly and measuring conditions at which plug flow, shear banding or sample spillover occur can be identified clearly. 
Video recordings further confirm that the change in shear moduli observed during three stage oscillatory shear tests with small deformation amplitude in stage I and III but large oscillation amplitude in stage II can be directly attributed to structural break down and recovery. For the pastes investigated here, the degree of irreversible, shear-induced structural change increases with increasing deformation amplitude in stage II until a saturation is reached at deformations corresponding to the crossover of G' and G'', but the irreversible damage is independent of the duration of large amplitude shear. 
A capillary breakup elongational rheometer and a tensile tester have been used to characterize deformation and breakup behavior of highly filled pastes in uniaxial elongation. Significant differences were observed in all experiments described above for two commercial screen-printing silver pastes used for front side metallization of Si-solar cells.

A protocol for a robust and application relevant rheological characterization of highly concentrated suspensions is presented. Silver pastes used for screen-printing application in solar cell production are employed as model systems.

A comprehensive rheological characterization of highly concentrated suspensions or pastes is mandatory for a targeted product development meeting the ...

A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials

This study offers a combined experimental and finite element (FE) simulation approach for examining the mechanical behavior of soft biomaterials (e.g. brain, liver, tendon, fat, etc.) when exposed to high strain rates. This study utilized a Split-Hopkinson Pressure Bar (SHPB) to generate strain rates of 100-1,500 sec-1. The SHPB employed a striker bar consisting of a viscoelastic material (polycarbonate). A sample of the biomaterial was obtained shortly postmortem and prepared for SHPB testing. The specimen was interposed between the incident and transmitted bars, and the pneumatic components of the SHPB were activated to drive the striker bar toward the incident bar. The resulting impact generated a compressive stress wave (i.e. incident wave) that traveled through the incident bar. When the compressive stress wave reached the end of the incident bar, a portion continued forward through the sample and transmitted bar (i.e. transmitted wave) while another portion reversed through the incident bar as a tensile wave (i.e. reflected wave). These waves were measured using strain gages mounted on the incident and transmitted bars. The true stress-strain behavior of the sample was determined from equations based on wave propagation and dynamic force equilibrium. The experimental stress-strain response was three dimensional in nature because the specimen bulged. As such, the hydrostatic stress (first invariant) was used to generate the stress-strain response. In order to extract the uniaxial (one-dimensional) mechanical response of the tissue, an iterative coupled optimization was performed using experimental results and Finite Element Analysis (FEA), which contained an Internal State Variable (ISV) material model used for the tissue. The ISV material model used in the FE simulations of the experimental setup was iteratively calibrated (i.e. optimized) to the experimental data such that the experiment and FEA strain gage values and first invariant of stresses were in good agreement.

The current study prescribes a coupled experiment-finite element simulation methodology to obtain the uniaxial dynamic mechanical response of soft biomaterials (brain, liver, tendon, fat, etc.). The multiaxial experimental results that arose because of specimen bulging obtained from Split-Hopkinson Pressure Bar testing were rendered to a uniaxial true stress-strain behavior when simulated through iterative optimization of the finite element analysis of the biomaterial.

This study offers a combined experimental and finite element (FE) simulation approach for examining the mechanical behavior of soft biomaterials (e.g. ...

Bioengineering

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An analog, macroscopic method for studying molecular-scale hydrodynamic processes in dense gases and liquids is described. The technique applies a standard fluid dynamic diagnostic, particle image velocimetry (PIV), to measure: i) velocities of individual particles (grains), extant on short, grain-collision time-scales, ii) velocities of systems of particles, on both short collision-time- and long, continuum-flow-time-scales, iii) collective hydrodynamic modes known to exist in dense molecular fluids, and iv) short- and long-time-scale velocity autocorrelation functions, central to understanding particle-scale dynamics in strongly interacting, dense fluid systems. The basic system is composed of an imaging system, light source, vibrational sensors, vibrational system with a known media, and PIV and analysis software. Required experimental measurements and an outline of the theoretical tools needed when using the analog technique to study molecular-scale hydrodynamic processes are highlighted. The proposed technique provides a relatively straightforward alternative to photonic and neutron beam scattering methods traditionally used in molecular hydrodynamic studies.

An experimentally accessible analog method for studying molecular hydrodynamic processes in dense fluids is presented. The technique uses particle image velocimetry of vibrated, high-restitution grain piles and allows direct, macroscopic observation of dynamical processes known and predicted to exist in strongly interacting, high density gases and liquids.

An analog, macroscopic method for studying molecular-scale hydrodynamic processes in dense gases and liquids is described. The technique applies a ...

Sample Preparation in Quartz Crystal Microbalance Measurements of Protein Adsorption and Polymer Mechanics

In this study, we present various examples of how thin film preparation for quartz crystal microbalance experiments informs the appropriate modeling of the data and determines which properties of the film can be quantified. The quartz crystal microbalance offers a uniquely sensitive platform for measuring fine changes in mass and/or mechanical properties of an applied film by observing the changes in mechanical resonance of a quartz crystal oscillating at high frequency. The advantages of this approach include its experimental versatility, ability to study changes in properties over a wide range of experimental time lengths, and the use of small sample sizes. We demonstrate that, based on the thickness and shear modulus of the layer deposited on the sensor, we can acquire different information from the material. Here, this concept is specifically exploited to display experimental parameters resulting in mass and viscoelastic calculations of adsorbed collagen on gold and polyelectrolyte complexes during swelling as a function of salt concentration.

The quartz crystal microbalance can provide accurate mass and viscoelastic properties for films in the micron or submicron range, which is relevant for investigations in biomedical and environmental sensing, coatings, and polymer science. The sample thickness influences which information can be obtained from the material in contact with the sensor.

In this study, we present various examples of how thin film preparation for quartz crystal microbalance experiments informs the appropriate modeling of ...

Chemistry

Enhancing Targeted Cancer Diagnosis by Quantifying Single-Cell Mechanics

Shear Assay Protocol for the Determination of Single-Cell Material Properties

Irregular biomechanics are a hallmark of cancer biology subject to extensive study. The mechanical properties of a cell are similar to those of a material. A cell's resistance to stress and strain, its relaxation time, and its elasticity are all properties that can be derived and compared to other types of cells. Quantifying the mechanical properties of cancerous (malignant) versus normal (non-malignant) cells allows researchers to further uncover the biophysical fundamentals of this disease. While the mechanical properties of cancer cells are known to consistently differ from the mechanical properties of normal cells, a standard experimental procedure to deduce these properties from cells in culture is lacking. 
This paper outlines a procedure to quantify the mechanical properties of single cells in vitro using a fluid shear assay. The principle behind this assay involves applying fluid shear stress onto a single cell and optically monitoring the resulting cellular deformation over time. Cell mechanical properties are subsequently characterized using digital image correlation (DIC) analysis and fitting an appropriate viscoelastic model to the experimental data generated from the DIC analysis. Overall, the protocol outlined here aims to provide a more effective and targeted method for the diagnosis of difficult-to-treat cancers.

Author Spotlight: Shear Assay Protocol for the Determination of Single-Cell Material Properties  

This protocol outlines the quantification of the mechanical properties of cancerous and non-cancerous cell lines in vitro. Conserved differences in the mechanics of cancerous and normal cells can act as a biomarker that may have implications in prognosis and diagnosis.

Irregular biomechanics are a hallmark of cancer biology subject to extensive study. The mechanical properties of a cell are similar to those of a ...

Cancer Research

Macro-Rheology Characterization of Gill Raker Mucus in the Silver Carp, Hypophthalmichthys molitrix

The silver carp, Hypophthalmichthys molitrix, is an invasive planktivorous filter feeder fish that infested the natural waterways of the upper Mississippi River basin due to its highly efficient filter feeding mechanism. The characteristic organs called gill rakers (GRs), found in many such filter feeders, facilitate the efficient filtration of food particles such as phytoplankton that are of a few microns in size.
The motivation to investigate the rheology of the GR mucus stems from our desire to understand its role in aiding the filter feeding process in the silver carp. The mucus-rich fluid, in a &#8216;thick and sticky&#8217; state may facilitate the adhesion of food particulates. The permeation and transport through the GR membrane are&#160;facilitated by the action of external shear forces that induce varying shear strain rates. Therefore, mucus rheology can provide a vital clue to the tremendous outcompeting nature of the silver carp within the pool of filter feeding fish. Based on this it was posited that GR mucus may provide an adhesive function to food particles and act as a transport vehicle to assist in the filter feeding process.
The main objective of the protocol is to determine the yield stress of the mucus, attributed to the minimum shear stress required to initiate flow at which irreversible plastic deformation is first observed across a structured viscoelastic material. Accordingly, rheological properties of the GR mucus, i.e., viscosity, storage, and loss moduli, were investigated for its non-Newtonian, shear-thinning nature using a rotational rheometer. &#160;
A protocol presented here is employed to analyze the rheological properties of mucus extracted from the gill rakers of a silver carp, fished at Hart Creek location of the Missouri River. The protocol aims to develop an effective strategy for rheological testing and material characterization of mucus assumed to be a structured viscoelastic material.

Macro-Rheology Characterization of Gill Raker Mucus in the Silver Carp, Hypophthalmichthys molitrix

This protocol presents a method to perform rheology characterization of mucus that resides on gill rakers (GRs) of the silver carp. Viscoelastic characteristics of GR-mucus, obtained by measuring viscosity, storage and loss moduli, are evaluated for the apparent yield stress to understand the filter feeding mechanism in GRs.

The silver carp, Hypophthalmichthys molitrix, is an invasive planktivorous filter feeder fish that infested the natural waterways of the upper Mississippi ...

Calibration Procedures for Orthogonal Superposition Rheology

Orthogonal superposition (OSP) rheology is an advanced rheological technique that involves superimposing a small-amplitude oscillatory shear deformation orthogonal to a primary shear flow. This technique allows the measurement of structural dynamics of complex fluids under non-linear flow conditions, which is important for the understanding and prediction of the performance of a wide range of complex fluids. The OSP rheological technique has a long history of development since the 1960s, mainly through the custom-built devices that highlighted the power of this technique. The OSP technique is now commercially available to the rheology community. Given the complicated design of the OSP geometry and the non-ideal flow field, users should understand the magnitude and sources of measurement error. This study presents calibration procedures using Newtonian fluids that includes recommendations for best practices to reduce measurement errors. Specifically, detailed information on the end-effect factor determination method, sample filling procedure, and identification of the appropriate measurement range (e.g., shear rate, frequency, etc.) are provided.

We present a detailed calibration protocol for a commercial orthogonal superposition rheology technique using Newtonian fluids including end-effect correction factor determination methods and recommendations for best practices to reduce experimental error.

Orthogonal superposition (OSP) rheology is an advanced rheological technique that involves superimposing a small-amplitude oscillatory shear deformation ...

Characterizing Multiscale Mechanical Properties of Brain Tissue Using Atomic Force Microscopy, Impact Indentation, and Rheometry

To design and engineer materials inspired by the properties of the brain, whether for mechanical simulants or for tissue regeneration studies, the brain tissue itself must be well characterized at various length and time scales. Like many biological tissues, brain tissue exhibits a complex, hierarchical structure. However, in contrast to most other tissues, brain is of very low mechanical stiffness, with Young&#39;s elastic moduli E on the order of 100s of Pa. This low stiffness can present challenges to experimental characterization of key mechanical properties. Here, we demonstrate several mechanical characterization techniques that have been adapted to measure the elastic and viscoelastic properties of hydrated, compliant biological materials such as brain tissue, at different length scales and loading rates. At the microscale, we conduct creep-compliance and force relaxation experiments using atomic force microscope-enabled indentation. At the mesoscale, we perform impact indentation experiments using a pendulum-based instrumented indenter. At the macroscale, we conduct parallel plate rheometry to quantify the frequency dependent shear elastic moduli. We also discuss the challenges and limitations associated with each method. Together these techniques enable an in-depth mechanical characterization of brain tissue that can be used to better understand the structure of brain and to engineer bio-inspired materials.

We present a set of techniques to characterize the viscoelastic mechanical properties of brain at the micro-, meso-, and macro-scales.

To design and engineer materials inspired by the properties of the brain, whether for mechanical simulants or for tissue regeneration studies, the brain ...

Studying Large Amplitude Oscillatory Shear Response of Soft Materials

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Chapters in this video

Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

Dielectric RheoSANS — Simultaneous Interrogation of Impedance, Rheology and Small Angle Neutron Scattering of Complex Fluids

Challenges in Rheological Characterization of Highly Concentrated Suspensions — A Case Study for Screen-printing Silver Pastes

A Coupled Experiment-finite Element Modeling Methodology for Assessing High Strain Rate Mechanical Response of Soft Biomaterials

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Sample Preparation in Quartz Crystal Microbalance Measurements of Protein Adsorption and Polymer Mechanics

Shear Assay Protocol for the Determination of Single-Cell Material Properties

Macro-Rheology Characterization of Gill Raker Mucus in the Silver Carp, Hypophthalmichthys molitrix

Calibration Procedures for Orthogonal Superposition Rheology

Characterizing Multiscale Mechanical Properties of Brain Tissue Using Atomic Force Microscopy, Impact Indentation, and Rheometry