Over the past several decades, carbon nanotubes (CNT) have risen to the forefront of scientific research due to their unique electrical, mechanical and optical properties. However, transferring these properties from nanoscale materials to industrial-scale products often requires alignment (orientation in the same direction) of CNT. One of the important consequences of alignment is improved conductivity, a highly desirable property in electro-chemical water treatment and closely associated with research endeavors to improve quality of drinking water. Therefore, identification of scalable and cost-effective experimental conditions that maximize alignment of CNT is an important research problem. This is addressed in the project.The proposed research aims to establish statistical methodologies for designing and analyzing efficient experiments that determine conditions for maximizing alignment of CNT, when one or more input factors are prone to internal noise. The proposed research consists of three tasks, with particular focus on addressing the challenges arising from presence of factors with internal noise and complexity of the response surface. (i) Developing a Bayesian approach to response-surface optimization with noisy inputs. Such an approach allows the experimenter to combine data on output, controllable input, and uncontrollable input from different sources; is a natural way of incorporating expert knowledge into the analysis; and provides a natural framework for optimal design of experiments with noisy inputs. (ii) Efficient design of optimization experiments with noisy inputs. The research will focus on developing a comprehensive design strategy, which is a combination of model-free and Bayesian model-based optimal designs. The model-free design will address the challenges arising from internal noise and complex response surface. (iii) Demonstration and validation of the developed methodologies in the co-PI's lab. A series of experiments will be planned to apply the developed statistical methodology in an attempt to identify factors that trigger alignment of CNT and also to identify their optimum levels to maximize alignment. The proposed framework will allow an experimenter to effectively capture the transmission of uncertainty from input variables to output variables by combining data from different sources, and by utilizing a combination of model-free and model-based experimental designs for efficient exploration of complex response surfaces. From a material scientist's perspective, the proposed method will provide a much more accurate quantification of uncertainty, resulting in more reliable predictions about optimal process conditions as determined from laboratory experiments.
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