This content will become publicly available on February 14, 2023

Surrogate Modeling with Gaussian Processes for an Inverse Problem in Polymer Dynamics
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 more »
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NSF-PAR ID:
10332579
Journal Name:
International Journal of Computational Methods
Page Range or eLocation-ID:
2143003
ISSN:
0219-8762
Extensional flow properties of polymer solutions in volatile solvents govern many industrially-relevant coating processes, but existing instrumentation lacks the environment necessary to control evaporation. To mitigate evaporation during dripping-onto-substrate (DoS) extensional rheology measurements, we developed a chamber to enclose the sample in an environment saturated with solvent vapor. We validated the evaporation-controlled DoS device by measuring a model high molecular weight polyethylene oxide (PEO) in various organic solvents both inside and outside of the chamber. Evaporation substantially increased the extensional relaxation time$$\lambda _{E}$$${\lambda }_{E}$for PEO in volatile solvents like dichloromethane and chloroform. PEO/chloroform solutions displayed an over 20-fold increase in$$\lambda _{E}$$${\lambda }_{E}$due to the formation of an evaporation-induced surface film; evaporation studies confirmed surface features and skin formation reminiscent of buckling instabilities commonly observed in drying polymer solutions. Finally, the relaxation times of semi-dilute PEO/chloroform solutions were measured with environmental control, where$$\lambda _{E}$$${\lambda }_{E}$scaled with concentration by the exponent$$m=0.62$$$m=0.62$. These measurements validate the evaporation-controlled DoS environment, and confirm that chloroform is a good solvent for PEO, with a Flory exponent of$$\nu =0.54$$$\nu =0.54$. Our results are the first to control evaporation during DoS extensional rheology, and provide guidelines establishing when environmental control is necessary to obtain accurate rheological parameters.