(656b) Characterization of Chemoresponsive Liquid Crystals Using Topological Descriptors and Machine Learning

Chemoresponsive liquid crystals (LCs) provide a versatile materials platform for designing affordable and lightweight gas (analyte) sensors [1]. Specifically, LCs can be designed to change their orientation ordering and optical birefringence when exposed to a certain target chemical environment [2]. The optical response of an LC system contains a rich set of features (e.g., space-time color and brightness patterns) that result from multiple physical processes taking place in the LC film, on the supporting surface, and at different scales (e.g., diffusion of the analyte through the film and binding/reaction events occurring at the surface) [3].

Machine learning techniques have been recently used for characterizing the optical response of LC crystals and to infer analyte species and concentrations from such responses. For example, Smith et. al. analyzed the spatial response of LCs when exposed to dimethyl methylphosphonate (DMMP) or water. The authors extracted response features using filters obtained from a pre-trained convolutional neural network (CNN) and showed that such features can yield a near-perfect classification accuracy of the chemical environment [4]. However, while NN-based feature extraction is powerful, this approach also has some important drawbacks. For example, due to the “black box” nature of CNNs, there is limited explainability for the response features that they are searching for. In addition, since CNNs contain large numbers of parameters, they are prone to overfitting and can be difficult to train.

Recent work has also used topological descriptors to characterize LC responses. Topological descriptors, in particular the so-called Euler Characteristic (EC) and the fractal dimension (FD), have been traditionally used to characterize topological defects in LCs [5]–[9]. For example, Muniandy et al. studied the birefringence textures of isotropic lamellar LC systems using fractal dimension [10] and established a correlation between the FD of the birefringence texture and the morphological structure of the LC system. Smith et. al. applied EC to characterize simulated micrographs for nematic LC systems [11] and demonstrated that EC outperformed traditional tools such as the Fourier transform and Moran's I in distinguishing between LC systems. Solis et. al. used persistent homology to track the structural changes in a LC nanocomposite and revealed the effect of confined geometry on the nematic-isotropic and isotropic-nematic phase transition [12].

In this study, we provide a unifying view of various topological descriptors through the lens of Minkowski functionals (MFs), which describe diverse geometric and topological properties such as shape, convexity, and connectivity [13]. MFs have been traditionally applied to binary fields (e.g., two-phase materials) and thus provide single scalar descriptors. Unfortunately, this approach requires manually selecting a threshold value to binarize the field. Here, propose to use filtration techniques to select multiple threshold values across the domain and compute a series of MF values [14]. Filtration enables capturing of richer topological information from the fields. In addition, we discuss connections between topological descriptors and Gaussian random fields, which enables interpretability of spatial features from a mechanistic perspective. We demonstrate the developments using a couple of case studies; here, we analyze the spatial responses of LC to sulfur dioxide and water, as well as the space-time responses to ozone and chlorine. We compare topological descriptors to state-of-the-art CNNs and show that such descriptors can achieve comparable prediction accuracy but at a much lower computational cost and with higher degree of interpretability.

References:

[1] R. R. Shah and N. L. Abbott, “Principles for Measurement of Chemical Exposure Based on Recognition-Driven Anchoring Transitions in Liquid Crystals,” Science, vol. 293, no. 5533, pp. 1296–1299, 2001, doi: 10.1126/science.1062293.

[2] R. J. Carlton et al., “Chemical and biological sensing using liquid crystals,” Liquid Crystals Reviews, vol. 1, pp. 29–51, 2013, doi: 10.1080/21680396.2013.769310.

[3] J. T. Hunter and N. L. Abbott, “Dynamics of the chemo-optical response of supported films of nematic liquid crystals,” Sensors and Actuators, B: Chemical, vol. 183, pp. 71–80, 2013, doi: 10.1016/j.snb.2013.03.094.

[4] A. D. Smith, N. Abbott, and V. M. Zavala, “Convolutional Network Analysis of Optical Micrographs for Liquid Crystal Sensors,” Journal of Physical Chemistry C, vol. 124, no. 28, 2020, doi: 10.1021/acs.jpcc.0c01942.

[5] A. D. Kiselev, R. G. Vovk, R. I. Egorov, and V. G. Chigrinov, “Polarization-resolved angular patterns of nematic liquid crystal cells: Topological events driven by incident light polarization,” Physical Review A - Atomic, Molecular, and Optical Physics, vol. 78, no. 3, 2008, doi: 10.1103/PhysRevA.78.033815.

[6] E. Pairam et al., “Stable nematic droplets with handles,” Proceedings of the National Academy of Sciences of the United States of America, vol. 110, no. 23, 2013, doi: 10.1073/pnas.1221380110.

[7] J. W. Tsung, Y. Z. Wang, S. K. Yao, and S. Y. Chao, “Crystal-like topological defect arrays in nematic liquid crystal,” Applied Physics Letters, vol. 119, no. 12, 2021, doi: 10.1063/5.0064303.

[8] A. Fernández-Nieves et al., “Novel defect structures in nematic liquid crystal shells,” Physical Review Letters, vol. 99, no. 15, 2007, doi: 10.1103/PhysRevLett.99.157801.

[9] I. Muševič, “Nematic liquid-crystal colloids,” Materials, vol. 11, no. 1. 2017. doi: 10.3390/ma11010024.

[10] S. v. Muniandy, C. S. Kan, S. C. Lim, and S. Radiman, “Fractal analysis of lyotropic lamellar liquid crystal textures,” Physica A: Statistical Mechanics and its Applications, vol. 323, 2003, doi: 10.1016/S0378-4371(03)00026-8.

[11] A. Smith and V. M. Zavala, “The Euler characteristic: A general topological descriptor for complex data,” Computers and Chemical Engineering, vol. 154, 2021, doi: 10.1016/j.compchemeng.2021.107463.

[12] I. Membrillo Solis et al., “Tracking the time evolution of soft matter systems via topological structural heterogeneity,” Communications Materials 2022 3:1, vol. 3, no. 1, pp. 1–11, Jan. 2022, doi: 10.1038/s43246-021-00223-1.

[13] P. Pranav et al., “Topology and geometry of Gaussian random fields I: On Betti numbers, Euler characteristic, and Minkowski functionals,” Monthly Notices of the Royal Astronomical Society, vol. 485, no. 3, 2019, doi: 10.1093/mnras/stz541.

[14] P. Bubenik, “Statistical topological data analysis using persistence landscapes,” Journal of Machine Learning Research, vol. 16, 2015.