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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12.3K 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

Controlling the Size, Shape and Stability of Supramolecular Polymers in Water

For aqueous based supramolecular polymers, the simultaneous control over shape, size and stability is very difficult1. At the same time, the ability to do so is highly important in view of a number of applications in functional soft matter including electronics, biomedical engineering, and sensors. In the past, successful strategies to control the size and shape of supramolecular polymers typically focused on the use of templates2,3, end cappers4 or selective solvent techniques5. 
Here we disclose a strategy based on self-assembling discotic amphiphiles that leads to the control over stack length and shape of ordered, chiral columnar aggregates. By balancing electrostatic repulsive interactions on the hydrophilic rim and attractive non-covalent forces within the hydrophobic core of the polymerizing building block, we manage to create small and discrete spherical objects6,7. Increasing the salt concentration to screen the charges induces a sphere-to-rod transition. Intriguingly, this transition is expressed in an increase of cooperativity in the temperature-dependent self-assembly mechanism, and more stable aggregates are obtained. 
For our study we select a benzene-1,3,5-tricarboxamide (BTA) core connected to a hydrophilic metal chelate via a hydrophobic, fluorinated L-phenylalanine based spacer (Scheme 1). The metal chelate selected is a Gd(III)-DTPA complex that contains two overall remaining charges per complex and necessarily two counter ions. The one-dimensional growth of the aggregate is directed by &pi;-&pi; stacking and intermolecular hydrogen bonding. However, the electrostatic, repulsive forces that arise from the charges on the Gd(III)-DTPA complex start limiting the one-dimensional growth of the BTA-based discotic once a certain size is reached. At millimolar concentrations the formed aggregate has a spherical shape and a diameter of around 5 nm as inferred from 1H-NMR spectroscopy, small angle X-ray scattering, and cryogenic transmission electron microscopy (cryo-TEM). The strength of the electrostatic repulsive interactions between molecules can be reduced by increasing the salt concentration of the buffered solutions. This screening of the charges induces a transition from spherical aggregates into elongated rods with a length &gt; 25 nm. Cryo-TEM allows to visualise the changes in shape and size. In addition, CD spectroscopy permits to derive the mechanistic details of the self-assembly processes before and after the addition of salt. Importantly, the cooperativity -a key feature that dictates the physical properties of the produced supramolecular polymers- increases dramatically upon screening the electrostatic interactions. This increase in cooperativity results in a significant increase in the molecular weight of the formed supramolecular polymers in water.

The goal of this experiment is to determine and control the size, shape and stability of self-assembled discotic amphiphiles in water. For aqueous based supramolecular polymers such level of control is very difficult. We apply a strategy using both repulsive and attractive interactions. The experimental techniques applied to characterize this system are broadly applicable.

For aqueous based supramolecular polymers, the simultaneous control over shape, size and stability is very difficult1. At the same time, the ability to do ...

Micro 3D Printing Using a Digital Projector and its Application in the Study of Soft Materials Mechanics

Buckling is a classical topic in mechanics. While buckling has long been studied as one of the major structural failure modes1, it has recently drawn new attention as a unique mechanism for pattern transformation. Nature is full of such examples where a wealth of exotic patterns are formed through mechanical instability2-5. Inspired by this elegant mechanism, many studies have demonstrated creation and transformation of patterns using soft materials such as elastomers and hydrogels6-11. Swelling gels are of particular interest because they can spontaneously trigger mechanical instability to create various patterns without the need of external force6-10. Recently, we have reported demonstration of full control over buckling pattern of micro-scaled tubular gels using projection micro-stereolithography (P&mu;SL), a three-dimensional (3D) manufacturing technology capable of rapidly converting computer generated 3D models into physical objects at high resolution12,13. Here we present a simple method to build up a simplified P&mu;SL system using a commercially available digital data projector to study swelling-induced buckling instability for controlled pattern transformation.
A simple desktop 3D printer is built using an off-the-shelf digital data projector and simple optical components such as a convex lens and a mirror14. Cross-sectional images extracted from a 3D solid model is projected on the photosensitive resin surface in sequence, polymerizing liquid resin into a desired 3D solid structure in a layer-by-layer fashion. Even with this simple configuration and easy process, arbitrary 3D objects can be readily fabricated with sub-100 &mu;m resolution.
This desktop 3D printer holds potential in the study of soft material mechanics by offering a great opportunity to explore various 3D geometries. We use this system to fabricate tubular shaped hydrogel structure with different dimensions. Fixed on the bottom to the substrate, the tubular gel develops inhomogeneous stress during swelling, which gives rise to buckling instability. Various wavy patterns appear along the circumference of the tube when the gel structures undergo buckling. Experiment shows that circumferential buckling of desired mode can be created in a controlled manner. Pattern transformation of three-dimensionally structured tubular gels has significant implication not only in mechanics and material science, but also in many other emerging fields such as tunable matamaterials.

We demonstrate controlled pattern transformation of swelling gel tubes by elastic instability. A simple projection micro stereo-lithography setup is built using an off-the-shelf digital data projector to fabricate three-dimensional polymeric structures in a layer-by-layer fashion. Swelling hydrogel tubes under mechanical constraint display various circumferential buckling modes depending on dimension.

Buckling is a classical topic in mechanics. While buckling has long been studied as one of the major structural failure modes1, it has recently drawn new ...

Studying Dynamic Processes of Nano-sized Objects in Liquid using Scanning Transmission Electron Microscopy

Samples fully embedded in liquid can be studied at a nanoscale spatial resolution with Scanning Transmission Electron Microscopy (STEM) using a microfluidic chamber assembled in the specimen holder for Transmission Electron Microscopy (TEM) and STEM. The microfluidic system consists of two silicon microchips supporting thin Silicon Nitride (SiN) membrane windows. This article describes the basic steps of sample loading and data acquisition. Most important of all is to ensure that the liquid compartment is correctly assembled, thus providing a thin liquid layer and a vacuum seal. This protocol also includes a number of tests necessary to perform during sample loading in order to ensure correct assembly. Once the sample is loaded in the electron microscope, the liquid thickness needs to be measured. Incorrect assembly may result in a too-thick liquid, while a too-thin liquid may indicate the absence of liquid, such as when a bubble is formed. Finally, the protocol explains how images are taken and how dynamic processes can be studied. A sample containing AuNPs is imaged both in pure water and in saline.

This protocol describes the operation of a liquid flow specimen holder for scanning transmission electron microscopy of AuNPs in water, as used for the observation of nanoscale dynamic processes.

Samples fully embedded in liquid can be studied at a nanoscale spatial resolution with Scanning Transmission Electron Microscopy (STEM) using a ...

Preparation of Liquid Crystal Networks for Macroscopic Oscillatory Motion Induced by Light

A strategy based on doped liquid crystalline networks is described to create mechanical self-sustained oscillations of plastic films under continuous light irradiation. The photo-excitation of dopants that can quickly dissipate light into heat, coupled with anisotropic thermal expansion and self-shadowing of the film, gives rise to the self-sustained deformation. The oscillations observed are influenced by the dimensions and the modulus of the film, and by the directionality and intensity of the light. The system developed offers applications in energy conversion and harvesting for soft-robotics and automated systems.
The general method described here consists of creating free-standing liquid crystalline films and characterizing the mechanical and thermal effects observed. The molecular alignment is achieved using alignment layers (rubbed polyimide), commonly used in the display manufacturing industry. To obtain actuators with large deformation, the mesogens are aligned and polymerized in a splay/bend configuration, i.e., with the director of the liquid crystals (LCs) going gradually from planar to homeotropic through the film thickness. Upon irradiation, the mechanical and thermal oscillations obtained are monitored with a high-speed camera. The results are further quantified by image analysis using an image processing program.

The goal of the protocol is to create liquid crystalline polymer films that can mechanically oscillate under continuous light irradiation. We describe in great detail the conception of free-standing films, from the liquid crystal alignment method to the photo-actuation. The experimental protocol applied to prepare this material is broadly applicable.

A strategy based on doped liquid crystalline networks is described to create mechanical self-sustained oscillations of plastic films under continuous ...

Atmospheric Pressure Fabrication of Large-Sized Single-Layer Rectangular SnSe Flakes

Tin selenide (SnSe) belongs to the family of layered metal chalcogenide materials with a buckled structure like phosphorene, and has shown potential for applications in two-dimensional nanoelectronics devices. Although many methods to synthesize SnSe nanocrystals have been developed, a simple way to fabricate large-sized single-layer SnSe flakes remains a great challenge. Herein, we show the experimental method to directly grow large-sized single-layer rectangular SnSe flakes on commonly used SiO2/Si insulating substrates using a straightforward two-step fabrication method in an atmospheric pressure quartz tube furnace system. The single-layer rectangular SnSe flakes with an average thickness of ~6.8 &#197; and lateral dimensions of about 30 &#181;m &#215; 50 &#181;m were fabricated by a combination of vapor transport deposition technique and nitrogen etching route. We characterized the morphology, microstructure, and electrical properties of the rectangular SnSe flakes and obtained excellent crystallinity and good electronic properties. This article about the two-step fabrication method can help researchers grow other similar two-dimensional, large-sized, single-layer materials using an atmospheric pressure system.

A protocol is presented demonstrating a two-step fabrication technique to grow large-sized single-layer rectangular shaped SnSe flakes on low-cost SiO2/Si dielectrics wafers in an atmospheric pressure quartz tube furnace system.

Tin selenide (SnSe) belongs to the family of layered metal chalcogenide materials with a buckled structure like phosphorene, and has shown potential for ...

The Diffusion of Passive Tracers in Laminar Shear Flow

A simple method to experimentally observe and measure the dispersion of a passive tracer in a laminar fluid flow is described. The method consists of first injecting fluorescent dye directly into a pipe filled with distilled water and allowing it to diffuse across the cross-section of the pipe to obtain a uniformly distributed initial condition. Following this period, the laminar flow is activated with a programmable syringe pump to observe the competition of advection and diffusion of the tracer through the pipe. Asymmetries in the tracer distribution are studied and correlations between the pipe cross-section and the shape of the distribution is shown: thin channels (aspect ratio &#60;&#60; 1) produce tracers arriving with sharp fronts and tapering tails (front-loaded distributions), while thick channels (aspect ratio ~1) present the opposite behavior (back-loaded distributions). The experimental procedure is applied to capillary tubes of various geometries and is particularly relevant to microfluidic applications by dynamical similarity.

A protocol for the study of the diffusion of passive tracers in laminar pressure-driven flow is presented. The procedure is applicable to various capillary pipe geometries.

A simple method to experimentally observe and measure the dispersion of a passive tracer in a laminar fluid flow is described. The method consists of ...

Fabrication of Soft Pneumatic Network Actuators with Oblique Chambers

Soft pneumatic network actuators have become one of the most promising actuation devices in soft robotics which benefits from their large bending deformation and low input. However, their monotonous bending motion form in two-dimensional (2-D) space keeps them away from wide applications. This paper presents a detailed fabrication method of soft pneumatic network actuators with oblique chambers, to explore their motions in three-dimensional (3-D) space. The design of oblique chambers enables actuators with tunable coupled bending and twisting capabilities, which gives them the possibility to move dexterously in flexible manipulators, to become biologically inspired robots and medical devices. The fabrication process is based on the molding method, including the silicone elastomer preparation, chamber and base parts fabrication, actuator assembly, tubing connections, checks for leaks, and actuator repair. The fabrication method guarantees the rapid manufacturing of a series of actuators with only a few modifications in the molds. The test results show the high quality of the actuators and their prominent bending and twisting capabilities. Experiments of the gripper demonstrate the advantages of the development in adapting to objects with different diameters and providing sufficient friction.

Here we present a fabrication method of soft pneumatic network actuators with oblique chambers. The actuators are capable of generating coupled bending and twisting motions, which broadens their application in soft robotics.

Soft pneumatic network actuators have become one of the most promising actuation devices in soft robotics which benefits from their large bending ...

Rapid Manufacturing of Thin Soft Pneumatic Actuators and Robots

This protocol describes a method for rapid manufacturing of soft pneumatic actuators and robots with an ultrathin form factor using a heat press and a laser cutter machine. The method starts with the lamination of thermoplastic polyurethane (TPU) sheets using a heat press for 10 min at the temperature of ~93 &#176;C. Next, the parameters of the laser cutter machine are optimized to produce a rectangular balloon with maximum burst pressure. Using the optimized parameters, the soft actuators are laser cut/welded three times sequentially. Next, a dispensing needle is attached to the actuator, allowing it to be inflated. The effect of geometrical parameters on the deflection of the actuator are studied systematically by varying the channel width and length. Finally, the performance of the actuator is characterized using an optical camera and a fluid dispenser. Conventional fabrication methods of soft pneumatic actuators based on silicone molding are time consuming (several hours). They also result in strong but bulky actuators, which limits the actuator&#8217;s applications. Moreover, microfabrication of thin pneumatic actuators is both time-consuming and expensive. The proposed manufacturing method in the current work resolves these issues by introducing a fast, simple, and cost-effective fabrication method of ultrathin pneumatic actuators.

This protocol describes a method for rapid manufacturing of soft pneumatic actuators and robots with a thin form factor. The fabrication method starts with lamination of thermoplastic polyurethane (TPU) sheets followed by laser cutting/welding of a two-dimensional pattern to form actuators and robots.

This protocol describes a method for rapid manufacturing of soft pneumatic actuators and robots with an ultrathin form factor using a heat press and a ...

Fabrication of Carbon-Based Ionic Electromechanically Active Soft Actuators

Ionic electromechanically active capacitive laminates are a type of smart material that move in response to electrical stimulation. Due to the soft, compliant and biomimetic nature of this deformation, actuators made of the laminate have received increasing interest in soft robotics and (bio)medical applications. However, methods to easily fabricate the active material in large (even industrial) quantities and with a high batch-to-batch and within-batch repeatability are needed to transfer the knowledge from laboratory to industry. This protocol describes a simple, industrially scalable and reproducible method for the fabrication of ionic carbon-based electromechanically active capacitive laminates and the preparation of actuators made thereof. The inclusion of a passive and chemically inert (insoluble) middle layer (e.g., a textile-reinforced polymer network or microporous Teflon) distinguishes the method from others. The protocol is divided into five steps: membrane preparation, electrode preparation, current collector attachment, cutting and shaping, and actuation. Following the protocol results in an active material that can, for example, compliantly grasp and hold a randomly shaped object as demonstrated in the article.

This article describes a fast and simple manufacturing process of ionic electromechanically active composite materials for actuators in biomedical, biomimetic and soft robotics applications. The key fabrication steps, their importance for the actuators&#39; final properties, and some of the main characterization techniques are described in detail.

Ionic electromechanically active capacitive laminates are a type of smart material that move in response to electrical stimulation. Due to the soft, ...

Bacterial Cellulose Spheres that Encapsulate Solid Materials

Bacterial cellulose (BC) spheres have been increasingly researched since the popularization of BC as a novel material. This protocol presents an affordable and simple method for BC sphere production. In addition to producing these spheres, an encapsulation method for solid particles has also been identified. To produce BC spheres, water, black tea, sugar, vinegar, and bacterial culture are combined in a baffled flask and the contents are agitated. After determining the proper culture conditions for BC sphere formation, their ability to encapsulate solid particles was tested using biochar, polymer beads, and mine waste. Spheres were characterized using ImageJ software and thermal gravimetric analysis (TGA). Results indicate that spheres with 7.5 mm diameters can be made in 7 days. Adding various particles increases the average size range of the BC capsules. The spheres encapsulated 10 - 20% of their dry mass. This method shows low-cost sphere production and encapsulation that is possible with easily obtainable materials. BC spheres may be used in the future as a contaminant removal aid, controlled release fertilizer coating, or soil amendment.

This protocol presents an easy, inexpensive method of forming bacterial cellulose (BC) spheres. This biomaterial can function as an encapsulation medium for solid materials, including biochar, polymer spheres, and mine waste.