ABSTRACT Investigations on thermal transport in cross-linked elastomers subjected to elongational... more ABSTRACT Investigations on thermal transport in cross-linked elastomers subjected to elongational deformations are reviewed and discussed. The focus is on experimental research, in which the deformation-induced anisotropy of the thermal conductivity tensor in several common elastomeric materials is measured using novel optical techniques developed in our laboratory. These sensitive and noninvasive techniques allow for the reliable measurement of thermal conductivity (diffusivity) tensor components on samples in a deformed state. When combined with measurements of the stress in deformed samples, we are able to examine the validity of the stress–thermal rule, which predicts a linear relationship between the thermal conductivity and stress tensor in deformed polymeric materials. These results are used to shed light on possible underlying mechanisms for anisotropic thermal transport in elastomers. We also present results from a novel experimental technique that show evidence of a deformation dependence of the heat capacity, which implies that, in addition to the usual entropic contribution, there is an energetic contribution to the stress in deformed elastomers.
A simple mean-field microswimmer model is presented. The model is inspired by the nonequilibrium ... more A simple mean-field microswimmer model is presented. The model is inspired by the nonequilibrium thermodynamics of multi-component fluids that undergo chemical reactions. These thermodynamics can be rigorously described in the context of the GENERIC (general equation for the nonequilibrium reversible–irreversible coupling) framework. More specifically, this approach was recently applied to non-ideal polymer solutions [T. Indei and J. D. Schieber, J. Chem. Phys. 146, 184902 (2017)]. One of the species of the solution is an unreactive polymer chain represented by the bead-spring model. Using this detailed description as inspiration, we then make several simplifying assumptions to obtain a mean-field model for a Janus microswimmer. The swimmer model considered here consists of a polymer dumbbell in a sea of reactants. One of the beads of the dumbbell is allowed to act as a catalyst for a chemical reaction between the reactants. We show that the mean-squared displacement (MSD) of the ce...
A complete propagation of error procedure for passive microrheology is illustrated using syntheti... more A complete propagation of error procedure for passive microrheology is illustrated using synthetic data from generalized Brownian dynamics. Moreover, measurement errors typical of bead tracking done with laser interferometry are employed. We use the blocking transformation method of Flyvbjerg and Petersen (J Chem Phys 91(1):461–466 1989 ) applicable to estimating statistical uncertainty in autocorrelations for any time series data, to account properly for the correlation in the bead position data. These contributions to uncertainty in correlations have previously been neglected when calculating the error in the mean-squared displacement of the probe bead (MSD). The uncertainty in the MSD can be underestimated by a factor of about 20 if the correlation in the bead position data is neglected. Using the generalized Stokes-Einstein relation, the uncertainty in the MSD is then propagated to the dynamic modulus. Uncertainties in the bead radius and the trap stiffness are also taken into account. A simple code used to aid in the calculations is provided.
We use straightforward energy and entropy balances to test the thermodynamic consistency of micro... more We use straightforward energy and entropy balances to test the thermodynamic consistency of microstructural rheological models. The method utilizes the same mathematical methods as classical transport phenomena, so it is much simpler to use than the much more rigorous GENERIC formalism. The cost of this simplicity is that fewer restrictions are actually tested than those in either the single-generator or the two-generator formalisms. The proposed test does provide, however, a separation of energy and entropy, leading to an interesting internal energy balance. More importantly, it leads to two requirements for non-negative entropy production: one closely related to a virtual work argument, important during flow, and a second that guarantees adherence to the second law of thermodynamics during microstructural relaxation. These criteria do not appear to be in conflict with the requirements of the more rigorous formulations and are much simpler to implement. Several illustrative example...
ABSTRACT Investigations on thermal transport in cross-linked elastomers subjected to elongational... more ABSTRACT Investigations on thermal transport in cross-linked elastomers subjected to elongational deformations are reviewed and discussed. The focus is on experimental research, in which the deformation-induced anisotropy of the thermal conductivity tensor in several common elastomeric materials is measured using novel optical techniques developed in our laboratory. These sensitive and noninvasive techniques allow for the reliable measurement of thermal conductivity (diffusivity) tensor components on samples in a deformed state. When combined with measurements of the stress in deformed samples, we are able to examine the validity of the stress–thermal rule, which predicts a linear relationship between the thermal conductivity and stress tensor in deformed polymeric materials. These results are used to shed light on possible underlying mechanisms for anisotropic thermal transport in elastomers. We also present results from a novel experimental technique that show evidence of a deformation dependence of the heat capacity, which implies that, in addition to the usual entropic contribution, there is an energetic contribution to the stress in deformed elastomers.
A simple mean-field microswimmer model is presented. The model is inspired by the nonequilibrium ... more A simple mean-field microswimmer model is presented. The model is inspired by the nonequilibrium thermodynamics of multi-component fluids that undergo chemical reactions. These thermodynamics can be rigorously described in the context of the GENERIC (general equation for the nonequilibrium reversible–irreversible coupling) framework. More specifically, this approach was recently applied to non-ideal polymer solutions [T. Indei and J. D. Schieber, J. Chem. Phys. 146, 184902 (2017)]. One of the species of the solution is an unreactive polymer chain represented by the bead-spring model. Using this detailed description as inspiration, we then make several simplifying assumptions to obtain a mean-field model for a Janus microswimmer. The swimmer model considered here consists of a polymer dumbbell in a sea of reactants. One of the beads of the dumbbell is allowed to act as a catalyst for a chemical reaction between the reactants. We show that the mean-squared displacement (MSD) of the ce...
A complete propagation of error procedure for passive microrheology is illustrated using syntheti... more A complete propagation of error procedure for passive microrheology is illustrated using synthetic data from generalized Brownian dynamics. Moreover, measurement errors typical of bead tracking done with laser interferometry are employed. We use the blocking transformation method of Flyvbjerg and Petersen (J Chem Phys 91(1):461–466 1989 ) applicable to estimating statistical uncertainty in autocorrelations for any time series data, to account properly for the correlation in the bead position data. These contributions to uncertainty in correlations have previously been neglected when calculating the error in the mean-squared displacement of the probe bead (MSD). The uncertainty in the MSD can be underestimated by a factor of about 20 if the correlation in the bead position data is neglected. Using the generalized Stokes-Einstein relation, the uncertainty in the MSD is then propagated to the dynamic modulus. Uncertainties in the bead radius and the trap stiffness are also taken into account. A simple code used to aid in the calculations is provided.
We use straightforward energy and entropy balances to test the thermodynamic consistency of micro... more We use straightforward energy and entropy balances to test the thermodynamic consistency of microstructural rheological models. The method utilizes the same mathematical methods as classical transport phenomena, so it is much simpler to use than the much more rigorous GENERIC formalism. The cost of this simplicity is that fewer restrictions are actually tested than those in either the single-generator or the two-generator formalisms. The proposed test does provide, however, a separation of energy and entropy, leading to an interesting internal energy balance. More importantly, it leads to two requirements for non-negative entropy production: one closely related to a virtual work argument, important during flow, and a second that guarantees adherence to the second law of thermodynamics during microstructural relaxation. These criteria do not appear to be in conflict with the requirements of the more rigorous formulations and are much simpler to implement. Several illustrative example...
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