Phenomenological model of viscoelasticity for systems undergoing sol–gel transition

Suman, Khushboo; Shanbhag, Sachin; Joshi, Yogesh M.

doi:10.1063/5.0038830

Cited by 18 publications

(10 citation statements)

References 56 publications

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“…There are multiple particularly interesting features of this data set. One feature of importance, which has been noted in previous time-cure superposition studies [55], is that the shift factors tend to increase with distance from the gel point, t c . This results in the creation of two master curves from the data set -one for the pregel states t < t c and one for the postgel states t > t c .…”

Section: B Time-cure Superposition During Gelationmentioning

confidence: 77%

A Data-Driven Method for Automated Data Superposition with Applications in Soft Matter Science

Lennon¹,

McKinley²,

Swan³

2022

Preprint

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The superposition of data sets with internal parametric self-similarity is a longstanding and widespread technique for the analysis of many types of experimental data across the physical sciences. Typically, this superposition is performed manually, or recently by one of a few automated algorithms. However, these methods are often heuristic in nature, are prone to user bias via manual data shifting or parameterization, and lack a native framework for handling uncertainty in both the data and the resulting model of the superposed data. In this work, we develop a data-driven, nonparametric method for superposing experimental data with arbitrary coordinate transformations, which employs Gaussian process regression to learn statistical models that describe the data, and then uses maximum a posteriori estimation to optimally superpose the data sets. This statistical framework is robust to experimental noise, and automatically produces uncertainty estimates for the learned coordinate transformations. Moreover, it is distinguished from black-box machine learning in its interpretability -specifically, it produces a model that may itself be interrogated to gain insight into the system under study. We demonstrate these salient features of our method through its application to four representative data sets characterizing the mechanics of soft materials. In every case, our method replicates results obtained using other approaches, but with reduced bias and the addition of uncertainty estimates. This method enables a standardized, statistical treatment of self-similar data across many fields, producing interpretable data-driven models that may inform applications such as materials classification, design, and discovery.

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Section: B Time-cure Superposition During Gelationmentioning

confidence: 77%

A Data-Driven Method for Automated Data Superposition with Applications in Soft Matter Science

Lennon¹,

McKinley²,

Swan³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…There are multiple particularly interesting features of this data set. One feature of importance, which has been noted in previous time-cure superposition studies (Suman et al, 2021), is that the shift factors tend to increase with distance from the gel point, . This results in the creation of two master curves from the data set—one for the pregel states and one for the postgel states .…”

Section: Detailed Examples Drawn From Rheologymentioning

confidence: 83%

A data-driven method for automated data superposition with applications in soft matter science

Lennon

McKinley

Swan

2023

DCE

View full text Add to dashboard Cite

The superposition of data sets with internal parametric self-similarity is a longstanding and widespread technique for the analysis of many types of experimental data across the physical sciences. Typically, this superposition is performed manually, or recently through the application of one of a few automated algorithms. However, these methods are often heuristic in nature, are prone to user bias via manual data shifting or parameterization, and lack a native framework for handling uncertainty in both the data and the resulting model of the superposed data. In this work, we develop a data-driven, nonparametric method for superposing experimental data with arbitrary coordinate transformations, which employs Gaussian process regression to learn statistical models that describe the data, and then uses maximum a posteriori estimation to optimally superpose the data sets. This statistical framework is robust to experimental noise and automatically produces uncertainty estimates for the learned coordinate transformations. Moreover, it is distinguished from black-box machine learning in its interpretability—specifically, it produces a model that may itself be interrogated to gain insight into the system under study. We demonstrate these salient features of our method through its application to four representative data sets characterizing the mechanics of soft materials. In every case, our method replicates results obtained using other approaches, but with reduced bias and the addition of uncertainty estimates. This method enables a standardized, statistical treatment of self-similar data across many fields, producing interpretable data-driven models that may inform applications such as materials classification, design, and discovery.

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“…Multiscale complex fluids such as polydisperse and/or branched polymer melts and solutions [69], structured food materials [70,71], the critical gel state in polymeric or colloidal gels [25,[72][73][74], etc., show power-law dependence of relaxation modulus, G(t) = St −n , over a certain range of timescales t. Here, n ∈ (0, 1) is the power-law exponent, and the quasi-property S has units of Pa•s n and characterizes material stiffness. The corresponding storage and loss moduli are [25],…”

Section: Resultsmentioning

confidence: 99%

Kramers-Kronig Relations for Nonlinear Rheology: 2. Validation of Medium Amplitude Oscillatory Shear (MAOS) Measurements

Shanbhag,

Joshi

2022

Preprint

Self Cite

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The frequency dependence of third-harmonic medium amplitude oscillatory shear (MAOS) modulus G * 33 (ω) provides insight into material behavior and microstructure in the asymptotically nonlinear regime.Motivated by the difficulty in the measurement of MAOS moduli, we propose a test for data validation based on nonlinear Kramers-Kronig relations. We extend the approach used to assess the consistency of linear viscoelastic data by expressing the real and imaginary parts of G * 33 (ω) as a linear combination of Maxwell elements: the functional form for the MAOS kernels is inspired by time-strain separability (TSS).We propose a statistical fitting technique called the SMEL test, which works well on a broad range of materials and models including those that do not obey TSS. It successfully copes with experimental data that are noisy, or confined to a limited frequency range. When Maxwell modes obtained from the SMEL test are used to predict the first-harmonic MAOS modulus G * 31 , it is possible to identify the range of timescales over which a material exhibits TSS.

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Phenomenological model of viscoelasticity for systems undergoing sol–gel transition

Cited by 18 publications

References 56 publications

A Data-Driven Method for Automated Data Superposition with Applications in Soft Matter Science

A Data-Driven Method for Automated Data Superposition with Applications in Soft Matter Science

A data-driven method for automated data superposition with applications in soft matter science

Kramers-Kronig Relations for Nonlinear Rheology: 2. Validation of Medium Amplitude Oscillatory Shear (MAOS) Measurements

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