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The linear viscoelasticity of polydisperse samples and their discretization into a blend ofn_fmonodisperse fractions is compared. The molecular weight distribution of the polydisperse sample is described using a lognormal distribution, which has two parameters that are related to the weight‐averaged molecular weight,Z_w, and the polydispersity index, ρ. Due to its success on similar systems, a variant of the double reptation model is used to describe the linear rheology. GivenZ_wand ρ, the optimal number of monodisperse fractions is obtained using the Bayesian information criterion. It quantifies and negotiates the tradeoff between accuracy (discrepancy with the response of the polydisperse sample) and complexity (number of fractions). The optimal number of fractions was found to be somewhat insensitive toZ_w; however, it increased with ρ from about 6 for ρ = 1.01 to about 20 for ρ = 2.0. Changing the underlying viscoelastic model had only a weak effect on the conclusions. Furthermore, using a blend of monodisperse fractions was found to be preferable to direct sampling even when an ensemble of chains was requested.

 

Synthetic materials that mimic the ability of natural occurring features to self‐actuate in response to different stimuli have wide applications in soft robotics, microdevices, drug delivery, regenerative medicine, and sensing. Here, unexpected and counter‐intuitive findings are presented in which a strongly polyelectrolytic hydrogel repels from strong polar solvents upon partial exposure (e.g., partial hydration by water). This repulsion drives the actuation and self‐folding of the gel, which results in rapid formation of different three‐dimensional shapes by simply placing the corresponding two‐dimensional films on water. A detailed investigation into the role of hydrogel chemistry, pH, and morphology on hydration‐triggered actuation behavior of the gels and their nanocomposites is described. Finally, a computational model is developed in order to further elucidate mechanisms of actuation. Modeling partial hydration as a repulsive driving force, it tracks the evolution of the shape of the thin film that results from restoring elastic forces. Taken together, the results indicate that an interplay between elastic and Coulombic repulsive forces leads to seemingly unexpected behavior of actuation of strongly polyelectrolytic gels away from polar solvents, leading to a novel and simple fabrication strategy for diverse 3D devices.

 

An open‐source software package “pyReSpect” is presented to extract relaxation spectra from stress relaxation experiments. It employs nonlinear Tikhonov regularization to obtain the continuous relaxation spectrum (CRS), and robust new algorithm to automatically determine a discrete relaxation spectrum (DRS) with a parsimonious number of modes. The new algorithm uses the CRS to guess the location of the modes, a nonlinear least squares optimization to fine‐tine the guess, and an information criterion to determine an optimal number of modes. The program is subjected to three validation tests, where data are generated from synthetic spectra, and three additional tests drawn from a variety of macromolecular architectures and sources. On the validation tests, pyReSpect is able to extract the original spectra. In all cases, the DRS follows the shape of the CRS, and offers additional regularization. Overall, pyReSpect is an excellent choice to obtain the DRS when the number and placement of modes is not known in advance.

 

When rheological models of polymer blends are used for inverse modeling, they can characterize polymer mixtures from rheological observations. This requires repeated evaluation of potentially expensive rheological models. We explored surrogate models based on Gaussian processes (GP-SM) as a cheaper alternative for describing the rheology of polydisperse binary blends. We used the time-dependent diffusion double reptation (TDD-DR) model as the true model; it takes a 5-dimensional input vector specifying the binary blend as input and yields a function called the relaxation spectrum as output. We used the TDD-DR model to generate training data of different sizes [Formula: see text], via Latin hypercube sampling. The optimal values of the GP-SM hyper-parameters, assuming a separable covariance kernel, were obtained by maximum likelihood estimation. The GP-SM interpolates the training data by design and offers reasonable predictions of relaxation spectra with uncertainty estimates. In general, the accuracy of GP-SMs improves as the size of the training data [Formula: see text] increases, as does the cost for training and prediction. The optimal hyper-parameters were found to be relatively insensitive to [Formula: see text]. Finally, we considered the inverse problem of inferring the structure of the polymer blend from a synthetic dataset generated using the true model. Surprisingly, the solution to the inverse problem obtained using GP-SMs and TDD-DR was qualitatively similar. GP-SMs can be several orders of magnitude cheaper than expensive rheological models, which provides a proof-of-concept validation for using GP-SMs for inverse problems in polymer rheology.