The Laplace approach in microrheology

Li, Qi; Peng, Xiaoguang; Chen, Dongjie; McKenna, Gregory B.

doi:10.1039/c9sm02242b

Cited by 10 publications

(11 citation statements)

References 25 publications

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“…This connection can be made using the generalized Stokes–Einstein equation (GSE), which relates the Laplace transform of the macroscopic modulus, G̃ ( s ), to the unilateral Laplace transform of the mean square displacements of Brownian tracers of radius R embedded in a viscoelastic matrix, ⟨Δ r̃ 2 ( s )⟩: . , Here, we consider that the tracers are the reactive units ( R = 0.5σ LJ ). A direct numerical transform of the time-domain data to the frequency domain is generally unreliable and different methods to convert real-time data to frequency data have been proposed. , Here, we implement the so-called Fourier microrheology method developed by Mason . This method is subject to approximations that are detailed in Supporting Information SI1).…”

Section: Discussionmentioning

confidence: 99%

“…A direct numerical transform of the time-domain data to the frequency domain is generally unreliable and different methods to convert real-time data to frequency data have been proposed. 52,54 Here, we implement the so-called Fourier microrheology method developed by Mason. 55 This method is subject to approximations that are detailed in Supporting Information SI1).…”

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confidence: 99%

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Microscopic Dynamics and Viscoelasticity of Vitrimers

et al. 2022

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We implement a hybrid molecular dynamics/Monte Carlo simulation to study the microscopic dynamics and the macroscopic rheology of vitrimers with a fast bond exchange rate. We show that the linear viscoelastic properties and mean squared displacement of the vitrimers collapse onto master curves by applying the same shift factors that follow the Williams−Landel−Ferry equation at low temperatures and Arrhenius-like behavior at high temperatures. The linkage between the microscopic dynamics and the linear rheology of vitrimers is established using the generalized Stokes−Einstein relationship, which efficiently extends the timescale of simulations and predicts the viscoelasticity. The values of the shift factors are related to the characteristic decay time of the intermediate scattering function, which is accessible in scattering experiments. The same results hold in the case of an all-atom model of an ionic liquid. Our methodology provides a microscopic basis for the time-superposition principle and predicts the macroscopic rheology of thermo-rheologically simple vitrimers.

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Microscopic Dynamics and Viscoelasticity of Vitrimers

et al. 2022

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“…The GSER above can be extended by making an analytic continuation ( s = iω ) and taking a Fourier transformation to obtain the complex modulus G *(ω): where is the Fourier transformed MSD as a function of time t . The time-domain response of the material can also be calculated using a Laplace transformation by invoking the continuum viscoelastic identity in Laplace space sJ̃ ( s ) G̃ ( s ) to extract the compliance J ( t ): which is directly proportional to the mean-square displacement. The compliance J ( t ), as well as storage ( G ′) and loss ( G ″ ) moduli calculated from G *(ω), can be directly compared with macrorheology (section ).…”

Section: Network Mechanics and Dynamicsmentioning

confidence: 99%

Molecular Characterization of Polymer Networks

et al. 2021

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Polymer networks are complex systems consisting of molecular components. Whereas the properties of the individual components are typically well understood by most chemists, translating that chemical insight into polymer networks themselves is limited by the statistical and poorly defined nature of network structures. As a result, it is challenging, if not currently impossible, to extrapolate from the molecular behavior of components to the full range of performance and properties of the entire polymer network. Polymer networks therefore present an unrealized, important, and interdisciplinary opportunity to exert molecular-level, chemical control on material macroscopic properties. A barrier to sophisticated molecular approaches to polymer networks is that the techniques for characterizing the molecular structure of networks are often unfamiliar to many scientists. Here, we present a critical overview of the current characterization techniques available to understand the relation between the molecular properties and the resulting performance and behavior of polymer networks, in the absence of added fillers. We highlight the methods available to characterize the chemistry and molecular-level properties of individual polymer strands and junctions, the gelation process by which strands form networks, the structure of the resulting network, and the dynamics and mechanics of the final material. The purpose is not to serve as a detailed manual for conducting these measurements but rather to unify the underlying principles, point out remaining challenges, and provide a concise overview by which chemists can plan characterization strategies that suit their research objectives. Because polymer networks cannot often be sufficiently characterized with a single method, strategic combinations of multiple techniques are typically required for their molecular characterization.

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“…Shear moduli can also be solved in the Laplace domain ( Mason et al, 1997a ; Mason et al, 1997b ; Xu et al, 1998 ; Winter and Mours, 2006 ). Li et al compared the accuracy of results determined by different approaches ( Li et al, 2020 ).…”

Section: Microrheological Methodologymentioning

confidence: 99%

Passive and Active Microrheology for Biomedical Systems

Mao

Nielsen

Ali

2022

Front. Bioeng. Biotechnol.

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Microrheology encompasses a range of methods to measure the mechanical properties of soft materials. By characterizing the motion of embedded microscopic particles, microrheology extends the probing length scale and frequency range of conventional bulk rheology. Microrheology can be characterized into either passive or active methods based on the driving force exerted on probe particles. Tracer particles are driven by thermal energy in passive methods, applying minimal deformation to the assessed medium. In active techniques, particles are manipulated by an external force, most commonly produced through optical and magnetic fields. Small-scale rheology holds significant advantages over conventional bulk rheology, such as eliminating the need for large sample sizes, the ability to probe fragile materials non-destructively, and a wider probing frequency range. More importantly, some microrheological techniques can obtain spatiotemporal information of local microenvironments and accurately describe the heterogeneity of structurally complex fluids. Recently, there has been significant growth in using these minimally invasive techniques to investigate a wide range of biomedical systems both in vitro and in vivo. Here, we review the latest applications and advancements of microrheology in mammalian cells, tissues, and biofluids and discuss the current challenges and potential future advances on the horizon.

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The Laplace approach in microrheology

Abstract: Use of the Fourier transform in the generalized Stokes–Einstein relation for micro-rheological analysis can give different results from the direct inverse Laplace approach. The latter gives better agreement with bulk rheology and should be preferred.

Cited by 10 publications

References 25 publications

Microscopic Dynamics and Viscoelasticity of Vitrimers

Microscopic Dynamics and Viscoelasticity of Vitrimers

Molecular Characterization of Polymer Networks

Passive and Active Microrheology for Biomedical Systems

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