### ### MechE-CSE PhD Thesis Defense Announcement

Wednesday, October 26, 2016 | 2:00 PM | 3-442

### MechE-CSE PhD Thesis Defense Announcement

Wednesday, October 26, 2016 | 2:00 PM | 3-442

**Development of Macroscopic Nanoporous Graphene Membranes for Gas Separation **

*Michael S. H. Boutilier *

Separating components of a gas from a mixture is a critical step in several important industrial processes including natural gas purification, hydrogen production, carbon dioxide sequestration, and oxy-combustion. For such applications, gas separation membranes are attractive because they offer relatively low energy costs but can be limited by low flow rates and low selectivities.

Nanoporous graphene membranes have the potential to exceed permeance and selectivity limits of existing gas separation membranes. This is made possible by the atomic thickness of the material, which can support sub-nanometer pores that enable molecular sieving while presenting low resistance to permeate flow. The feasibility of gas separation by graphene nanopores has been demonstrated experimentally on micron-scale areas of graphene. However, scaling up to macroscopic membrane areas presents significant challenges, including graphene imperfections and control of the selective nanopore size distribution across large areas.

The overall objective of this thesis research is to develop macroscopic graphene membranes for gas separation. This is accomplished by first investigating the inherent permeance of graphene. Micron-scale tears and nanometer-scale intrinsic defects are identified as leakage pathways in graphene. Stacking multiple graphene layers is shown to reduce leakage exponentially.

A model for the permeance of multilayer graphene is developed to guide the design process. A combination of measurements, imaging, and simulations are used in model construction and parameter estimation. The model, accounting for tears and intrinsic defects in graphene, accurately explains the measured flow rates. This analysis further demonstrates that the inherent permeance of multilayer graphene can be accounted for without contribution from interlayer transport. This model is applied to membranes with created selective nanopores. The results suggest that high membrane selectivity should be possible even with defective graphene by careful membrane design.

Fabrication methods are developed to realize the selective membrane design established with the aid of the model. Approaches to seal or mitigate the effects of micron and nanometer scale defects in graphene are investigated. Interfacial polymerization and atomic layer deposition are shown to effectively seal micron-scale tears and nanometer-scale defects in graphene to gas flow. The support membrane beneath graphene is optimized to reduce the contribution of tears and intrinsic defects to overall gas transport.

Methods of creating a high density of selectively permeable nanopores are explored. Knudsen selectivity is achieved using macroscopic three layer graphene membranes on polymer supports by high density ion bombardment. Separation ratios exceeding the Knudsen effusion limit are achieved with single layer graphene on optimized support structures by low density ion bombardment followed by oxygen plasma etching, providing evidence of molecular sieving based gas separation in macroscopic graphene membranes.

Thesis Committee:

Rohit Karnik (chair), Associate Professor of Mechanical Engineering

Nicolas G. Hadjiconstantinou, Professor of Mechanical Engineering

John Hart, Associate Professor of Mechanical Engineering

### ### Thursday, November 3rd, 2016 | 12:00 PM* | 37-212

### Thursday, November 3rd, 2016 | 12:00 PM* | 37-212

*Pierre Lermusiaux *

* Lunch Available at 11:45

### ### Thursday, December 8th, 2016 | 12:00 PM* | 37-212

### Thursday, December 8th, 2016 | 12:00 PM* | 37-212

*Antonio Huerta *

* Lunch provided at 11:45

### ### Thursday, March 23rd 2017 | 12:00 PM* | 37-212

### Thursday, March 23rd 2017 | 12:00 PM* | 37-212

*Serkan Gugercin *

* Lunch available at 11:45

### ### Thursday, April 27th 2017 | 12:00 PM* | 37-212

### Thursday, April 27th 2017 | 12:00 PM* | 37-212

*Misha Kilmer *

* Lunch provided at 11:45

### ### To Be Rescheduled - New Date TBA

### To Be Rescheduled - New Date TBA

**A NONPARAMETRIC PROBABILISTIC APPROACH FOR QUANTIFYING UNCERTAINTIES IN LOW- AND HIGH-DIMENSIONAL NONLINEAR MODELS **

*Charbel Farhat *

A. Bos^1 and C. Farhat^{1,2,3}

^1 Department of Aeronautics and Astronautics

^2 Department of Mechanical Engineering

^3 Institute for Computational and Mathematical Engineering

Stanford University, Stanford, CA 94305, USA

C. Soize

Laboratoire Mod\'elisation et Simulation Multi Echelle

MSME UMR 8208 CNRS, Universit\'e Paris-Est, 5 bd Descartes

77454 Marne-la-Vallee, France

A nonparametric probabilistic approach for modeling uncertainties in projection-based, nonlinear, reduced-order models is presented. When experimental data is available, this approach can also quantify uncertainties in the associated high-dimensional models.

The main underlying idea is two-fold. First, to substitute the deterministic Reduced-Order Basis (ROB) with a stochastic counterpart. Second, to construct the probability measure of the Stochastic Reduced-Order Basis (SROB) on a subset of a compact Stiefel manifold in order to preserve some important properties of a ROB. The stochastic modeling is performed so that the probability distribution of the constructed SROB depends on a small number of hyperparameters. These are determined by solving a reduced-order statistical inverse problem.

The proposed nonparametric probabilistic approach for taking into account model form uncertainties can be interpreted as a stochastic-based method for extracting fundamental information or knowledge from test or High-Dimensional Model (HDM) data that is not captured by a deterministic HDM or ROM, respectively. In this approach, one essentially parameterizes the approximation basis in order to capture the variabilities instead of parameterizing the governing equations. Its mathematical properties are analyzed through theoretical developments and numerical simulations. Its potential is demonstrated through several example problems from nonlinear computational structural dynamics.

* Lunch available at 11:45