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Manipulation of thin sheets by folding and cutting offers opportunity to engineer structures with novel mechanical properties, and to prescribe complex force–displacement relationships via material elasticity in combination with the trajectory imposed by the fold pattern. Here we study the mechanics of a cellular Kirigami that rotates and buckles upon compression, presenting an example of a design strategy that we call ”flexigami”. The addition of diagonal cuts to an equivalent closed cell permits the cell to collapse reversibly without incurring significant tensile strains in its panels. Using finite-element modeling and experiments we show how the mechanical behavior of the cell is governed by the coupled rigidity of the panels and hinges and we design cells to achieve reversible force response ranging from smooth mono-stability to sharp bi-stability. We then demonstrate the cell-based construction of laminates with multi-stable behavior and a rotary-linear boom actuator, as well as self-deploying cells with shape memory alloy hinges. Advanced digital fabrication methods can enable the realization of this and other so-called flexigami designs that derive their overall mechanics from fold and panel elasticity, for applications including deployable structures, soft robotics and medical devices., National Science Foundation (Grant EFRI-1240264), U. S. Army Research Office (Contract W911NF-13-D-0001)

Significant improvements to the throughput of additive manufacturing (AM) processes are essential to their cost-effectiveness and competitiveness with traditional processing routes. Moreover, high-throughput AM processes, in combination with the geometric versatility of AM, will enable entirely new workflows for product design and customization. We present the design and validation of a desktop-scale extrusion AM system that achieves a much greater build rate than benchmarked commercial systems. This system, which we call ‘FastFFF’ is motivated by our recent analysis of the rate-limiting mechanisms to conventional fused filament fabrication (FFF) technology. The FastFFF system mutually overcomes these limits, using a nut-feed extruder, laser-heated polymer liquefier, and servo-driven parallel gantry system to achieve high extrusion force, rapid filament heating, and fast gantry motion, respectively. The extrusion and heating mechanisms are contained in a compact printhead that receives a threaded filament and augments conduction heat transfer with a fiber-coupled diode laser. The prototype system achieves a volumetric build rate of 127 cm 3 /hr, which is approximately 7-fold greater than commercial desktop FFF systems, at comparable resolution; the maximum extrusion rate of the printhead is ∼14-fold greater (282 cm 3 /hr) than our benchmarks. The performance limits of the printhead and motion systems are characterized, and the tradeoffs between build rate and resolution are assessed and discussed. High-speed desktop AM raises the possibility of new use cases and business models for AM, where handheld parts are built in minutes rather than hours. Adaptation of this technology to print high-temperature thermoplastics and composite materials, which require high extrusion forces, is also of interest.

Cellulose nanocrystals (CNC) are naturally-derived nanostructures of growing importance for the production of composites having attractive mechanical properties, and improved sustainability. Polymer–CNC composite gels display a number of the distinctive features of colloidal glasses and their response to the flow conditions encountered during processing of composites can be tuned by chemical additives.

Improved capabilities in microfluidics, electrochemistry, and portable assays have resulted in the development of a wide range of point-of-use sensors intended for environmental, medical, and agricultural applications in resource-limited environments of developing countries. However, these devices are frequently developed without direct interaction with their often-remote intended user base, creating the potential for a disconnect between users' actual needs and those perceived by sensor developers. As different analytical techniques have inherent strengths and limitations, effective measurement solution development requires determination of desired sensor attributes early in the development process. In this work, we present our findings on design priorities for point-of-use microbial water sensors based on fieldwork in rural India, as well as a guide to fieldwork methodologies for determining desired sensor attributes. We utilized group design workshops for initial identification of design priorities, and then conducted choice-based conjoint analysis interviews for quantification of user preferences among these priorities. We found the highest user preference for integrated reporting of contaminant concentration and recommended actions, as well as significant preferences for mostly reusable sensor architectures, same-day results, and combined ingredients. These findings serve as a framework for future microbial sensor development and a guide for fieldwork-based understanding of user needs.

Automated handling of microscale objects is essential for manufacturing of next-generation electronic systems. Yet, mechanical pick-and-place technologies cannot manipulate smaller objects whose surface forces dominate over gravity, and emerging microtransfer printing methods require multidirectional motion, heating, and/or chemical bonding to switch adhesion. We introduce soft nanocomposite electroadhesives (SNEs), comprising sparse forests of dielectric-coated carbon nanotubes (CNTs), which have electrostatically switchable dry adhesion. SNEs exhibit 40-fold lower nominal dry adhesion than typical solids, yet their adhesion is increased >100-fold by applying 30 V to the CNTs. We characterize the scaling of adhesion with surface morphology, dielectric thickness, and applied voltage and demonstrate digital transfer printing of films of Ag nanowires, polymer and metal microparticles, and unpackaged light-emitting diodes., National Science Foundation (U.S.) (CMMI-1463181), Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (contract W911NF-13-D-0001)

Understanding wettability and mechanisms of wetting transition are important for design and engineering of superhydrophobic surfaces. There have been numerous studies on the design and fabrication of superhydrophobic and omniphobic surfaces and on the wetting transition mechanisms triggered by liquid evaporation. However, there is a lack of a universal method to examine wetting transition on rough surfaces. Here, we introduce force zones across the droplet base and use a local force balance model to explain wetting transition on engineered nanoporous microstructures, utilizing a critical force per unit length (FPL) value. For the first time, we provide a universal scale using the concept of the critical FPL value which enables comparison of various superhydrophobic surfaces in terms of preventing wetting transition during liquid evaporation. In addition, we establish the concept of contact line-fraction theoretically and experimentally by relating it to area-fraction, which clarifies various arguments about the validity of the Cassie-Baxter equation. We use the contact line-fraction model to explain the droplet contact angles, liquid evaporation modes, and depinning mechanism during liquid evaporation. Finally, we develop a model relating a droplet curvature to conventional beam deflection, providing a framework for engineering pressure stable superhydrophobic surfaces.

Scalable manufacturing of structured materials with engineered nanoporosity is critical for applications in energy storage devices (i.e., batteries and supercapacitors) and in the wettability control of surfaces (i.e., superhydrophobic and superomniphobic surfaces). Patterns formed in arrays of vertically aligned carbon nanotubes (VA-CNTs) have been extensively studied for these applications. However, the as-deposited features are often undesirably altered upon liquid infiltration and evaporation because of capillarity-driven aggregation of low density CNT forests. Here, it is shown that an ultrathin, conformal, and low-surface-energy layer of poly perfluorodecyl acrylate, poly(1H,1H,2H,2H-perfluorodecyl acrylate) (pPFDA), makes the VA-CNTs robust against surface-tension-driven aggregation and densification. This single vapor-deposition step allows the fidelity of the as-deposited VA-CNT patterns to be retained during wet processing, such as inking, and subsequent drying. It is demonstrated how to establish omniphobicity or liquid infiltration by controlling the surface morphology. Retaining a crust of entangled CNTs and pPFDA aggregates on top of the patterned VA-CNTs produces micropillars with re-entrant features that prevent the infiltration of low-surface-tension liquids and thus gives rise to stable omniphobicity. Plasma treatments before and after polymer deposition remove the crust of entangled CNTs and pPFDA aggregates and attach hydroxyl groups to the CNT tips, enabling liquid infiltration yet preventing densification of the highly porous CNTs. The latter observation demonstrates the protective character of the pPFDA coating with the potential application of these surfaces for direct contact printing of microelectronic features., United States. Air Force. Office of Scientific Research (FA9550-11-1-0089), Massachusetts Institute of Technology. Department of Chemical Engineering, University of Toledo, MIT-Chevron university partnership program, Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (Contract DAAD-19-02D-002), National Science Foundation (U.S.) (award CMMI- 463181), United States. Air Force. Office of Scientific Research, Skolkovo Foundation

To realize engineered materials and structures via origami methods and other folding construction techniques, fundamental understanding of paper folding mechanics and their dependency on paper micro/nanostructure is needed. Using selected papers commonly used in origami designs, we establish the relationship between the mechanical properties of fibrous paper and their corresponding ability to form and retain simple creases and mountain/valley folds. Using natural fiber paper (abaca), synthetic fiber paper (Tyvek), and a metalfiber laminate paper, we studied how the fold radius depends on the load applied using a controlled rolling apparatus. After folding, we examined the resultant micro- and nanoscale deformation using electron microscopy. In general we found that the fold radius follows a power law, decreasing with the applied rolling force. At a critical strain, each paper exhibits a transition between elastic and plastic behavior, after which the trend asymptotically approaches the minimum fold radius with increased applied force. Finally, we present examples of centimeter-scale two-dimensionally "mountain fold" patterns and relate the folding characteristics observed in these designs to the mechanical properties of the papers in folding. Keywords: Deformation; Fibers; Synthetic fibers; Laminates; Electron microscopy; Metal fibers; Construction; Stress; Mechanical properties; Nanoscale phenomena, National Science Foundation (U.S.) (Grant EFRI-1240264)

Whereas 3D printing of thermoplastics is highly advanced and can readily create complex geometries, 3D printing of metals is still challenging and limited. The origin of this asymmetry in technological maturity is the continuous softening of thermoplastics with temperature into a readily formable state, which is absent in conventional metals. Unlike conventional metals, bulk metallic glasses (BMGs) demonstrate a supercooled liquid region and continuous softening upon heating, analogous to thermoplastics. Here we demonstrate that, in extension of this analogy, BMGs are also amenable to extrusion-based 3D printing through fused filament fabrication (FFF). When utilizing the BMGs’ supercooled liquid behavior, 3D printing can be realized under similar conditions to those in thermoplastics. Fully dense and amorphous BMG parts are 3D printed in ambient environmental conditions resulting in high-strength metal parts. Due to the similarity between FFF of thermoplastics and BMGs, this method may leverage the technology infrastructure built by the thermoplastic FFF community to rapidly realize and proliferate accessible and practical printing of metals.

The importance of additive manufacturing (AM) to the future of product design and manufacturing infrastructure demands educational programs tailored to embrace its fundamental principles and its innovative potential. Moreover, the breadth and depth of AM spans several traditional disciplines, presenting a challenge to instructors, along with the opportunity to integrate knowledge via creative and demanding projects. This paper presents our approach to teaching AM at the graduate and advanced undergraduate level, in the form of a 14-week course developed and taught at the Massachusetts Institute of Technology. The lectures begin with in-depth technical analysis of the major AM processes and machine technologies, then focus on special topics including design methods, machine controls, applications of AM to major industry needs, and emerging processes and materials. In lab sessions, students operate and characterize desktop AM machines, and work in teams to design and fabricate a bridge having maximum strength per unit weight while conforming to geometric constraints. The class culminates in a semester-long team design-build project. In a single semester of the course, teams created prototype machines for 3D printing of molten glass, 3D printing of soft-serve ice cream, robotic deposition of biodegradable material, direct-write deposition of continuous carbon fiber composites, large-area parallel extrusion of polymers, and in situ optical scanning during 3D printing. Several of these projects led to patent applications, follow-on research, and peer-reviewed publications. We conclude that AM education, while arguably rooted in mechanical engineering, is truly multidisciplinary, and that education programs must embrace this context. We also comment on student feedback, our experience as instructional staff, and our adaptation of this course to a manufacturing-focused master’s degree program and a one-week professional short program. Keywords: Education; Teaching; Design

Small-holding farmers in the developing world suffer from sub-optimal crop yields because they lack a soil diagnostic system that is affordable, usable, and actionable. This paper details the fabrication and characterization of an integrated point-of-use soil-testing system, comprised of disposable ion-selective electrode strips and a handheld electrochemical reader. Together, the strips and reader transduce soil ion concentrations into to an alphanumeric output that can be communicated via text message to a central service provider offering immediate, customized fertilizer advisory. The solid-state ion-selective electrode (SSISE) strips employ a two-electrode design with screen-printable carbon nanotube ink serving as the electrical contacts for the working and reference electrodes. The working electrode comprises a plasticizer-free butyl acrylate ion-selective membrane (ISM), doped with an ion-selective ionophore and lipophilic salt. Meanwhile, the reference electrode includes a screen-printed silver-silver chloride ink and a polyvinyl-butyral membrane, which is doped with sodium chloride for stable reference potentials. As a proof of concept, potassium-selective electrodes are studied, given potassium's essential role in plant growth and reproduction. The ISE-based system is reproducibly manufactured to yield a Nernstian response with a sub-micromolar detection limit (pK+ of 5.18 ± 0.08) and near-Nernstian sensitivity (61 mV/decade) in the presence of a 0.02 M strontium chloride extraction solution. Analysis of soil samples using the printed electrodes and reader yielded a correlation coefficient of R2 = 0.89 with respect to values measured via inductively coupled plasma atomic emission spectroscopy (ICP-AES). The reliable performance of this system is encouraging toward its deployment for soil nutrient management in resource-limited environments., Massachusetts Institute of Technology. Tata Center for Technology and Design, National Science Foundation (U.S.) (award number DMR-1419807)

We present an extensible-link kinematic model for characterizing the motion trajectory of an arbitrary planar compliant mechanism. This is accomplished by creating an analogous kinematic model consisting of links that change length over the course of actuation to represent elastic deformation of the compliant mechanism. Within the model, the motion trajectory is represented as an analytical function. By Taylor series expansion, the trajectory is expressed in a parametric formulation composed of load-independent and load-dependent terms. Here, the load-independent terms are entirely defined by the shape of the undeformed compliant mechanism topology, and all load-geometry interdependencies are captured by the load-dependent terms. This formulation adds insight to the process for designing compliant mechanisms for high accuracy motion applications because: (1) inspection of the load-independent terms enables determination of specific topology modifications for improving the accuracy of the motion trajectory; and (2) the load-dependent terms reveal the polynomial orders of principally uncorrectable error components of the motion trajectory. The error components in the trajectory simply represent the deviation of the actual motion trajectory provided by the compliant mechanism compared to the ideally desired one. We develop the generalized model framework, and then demonstrate its utility by designing a compliant micro-gripper with straight-line parallel jaw motion. We use the model to analytically determine all topology modifications for optimizing the jaw trajectory, and to predict the polynomial order of the uncorrectable trajectory components. The jaw trajectory is then optimized by iterative finite elements (FE) simulation until the polynomial order of the uncorrectable trajectory component becomes apparent., National Science Foundation (U.S.). Graduate Research Fellowship, United States. Office of Naval Research (N000141010556)

The potential use of additive manufacturing (AM) techniques for processing of food can span from satisfaction of basic necessities to high-end cuisine and fine dining. The purpose of this study was to explore how AM, specifically extrusion-based layer-wise deposition, can be combined with the reverse spherification technique that is widely used in molecular gastronomy. First, by manual extrusion, we identify suitable recipes and ingredient concentrations to form freestanding features in a liquid bath. Subsequently, a desktop extrusion is adapted for the deposition of a calcium solution into an alginate bath first as a two-dimensional (2D) pathway and then as three-dimensional (3D) geometry by layer-wise deposition. The 2D geometries are measured and compared to a nominal geometry, to elucidate how tool speed and extrusion rate influence form and dimensional accuracy. We demonstrate that motorized extrusion-based AM can be combined with reverse spherification to form stable objects by gelation of fruit-based solutions. In addition, a wider set of manual experiments shows the possibility of combining different flavors and the creation of complex multilayer and multiflavor objects. Additional studies on the deposition precision are required to optimize the process of creating a full 3D geometry. This study shows that 3D printing via reverse spherification can bridge the gap between culinary art and AM technology, and enable new capabilities for creation of dining experiences. This is a step toward the digital design and manufacturing of unique edible objects with complex flavors, textures, and geometries.

Additive manufacturing by layerwise photopolymerization, commonly called stereolithography (SLA), is attractive due to its high resolution and diversity of materials chemistry. However, traditional SLA methods are restricted to planar substrates and planar layers that are perpendicular to a single-axis build direction. Here, we present a robotic system that is capable of maskless layerwise photopolymerization on curved surfaces, enabling production of large-area conformal patterns and the construction of conformal freeform objects. The system comprises an industrial six-axis robot and a custom-built maskless projector end effector. Use of the system involves creating a mesh representation of the freeform substrate, generation of a triangulated toolpath with curved layers that represents the target object to be printed, precision mounting of the substrate in the robot workspace, and robotic photopatterning of the target object by coordinated motion of the robot and substrate. We demonstrate printing of conformal photopatterns on spheres of various sizes, and construction of miniature three-dimensional objects on spheres without requiring support features. Improvement of the motion accuracy and development of freeform toolpaths would enable construction of polymer objects that surpass the size and support structure constraints imparted by traditional SLA systems., American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowship, National Institute of Mental Health (U.S.) (University of Michigan Microfluidics in Biomedical Sciences Training Program. 5T32-EB005582), Singapore-MIT Alliance for Research and Technology (SMART)

Caenorhabditis elegans (C. elegans) is a model organism for understanding aging and studying animal behavior. Microfluidic assay techniques have brought widespread advances in C. elegans research; however, traditional microfluidic assays such as those based on soft lithography require time-consuming design and fabrication cycles and offer limited flexibility in changing the geometric environment during experimentation. We present a technique for maskless photopatterning of a biocompatible hydrogel on an NGM (Agar) substrate, enabling dynamic manipulation of the C. elegans culture environment in vitro. Maskless photopatterning is performed using a projector-based microscope system largely built from off-the-shelf components. We demonstrate the capabilities of this technique by building micropillar arrays during C. elegans observation, by fabricating free-floating mechanisms that can be actuated by C. elegans motion, by using freehand drawing to isolate individual C. elegans in real time, and by patterning arrays of mazes for isolation and fitness testing of C. elegans populations. In vitro photopatterning enables rapid and flexible design of experiment geometry as well as real-time interaction between the researcher and the assay such as by sequential isolation of individual organisms. Future adoption of image analysis and machine learning techniques could be used to acquire large datasets and automatically adapt the assay geometry., National Institutes of Health (U.S.). Microfluidics in Biomedical Sciences Training Program (5T32-EB005582), United States. Air Force Office of Scientific Research. Young Investigator Program (FA9550-11-1-0089)

The skins of many plants and animals have intricate microscale surface features that give rise to properties such as directed water repellency and adhesion, camouflage, and resistance to fouling. However, engineered mimicry of these designs has been restrained by the limited capabilities of top–down fabrication processes. Here we demonstrate a new technique for scalable manufacturing of freeform microstructures via strain-engineered growth of aligned ​carbon nanotubes (CNTs). Offset patterning of the CNT growth catalyst is used to locally modulate the CNT growth rate. This causes the CNTs to collectively bend during growth, with exceptional uniformity over large areas. The final shape of the curved CNT microstructures can be designed via finite element modeling, and compound catalyst shapes produce microstructures with multidirectional curvature and unusual self-organized patterns. Conformal coating of the CNTs enables tuning of the mechanical properties independently from the microstructure geometry, representing a versatile principle for design and manufacturing of complex microstructured surfaces., United States. Defense Advanced Research Projects Agency (HR0011-10-C-0192), United States. Air Force Office of Scientific Research (Young Investigator Program FA9550-11-1-0089)

We present the design of a concentric tube (CT) reactor for roll-to-roll chemical vapor deposition (CVD) on flexible substrates, and its application to continuous production of graphene on copper foil. In the CTCVD reactor, the thin foil substrate is helically wrapped around the inner tube, and translates through the gap between the concentric tubes. We use a bench-scale prototype machine to synthesize graphene on copper substrates at translation speeds varying from 25 mm/min to 500 mm/min, and investigate the influence of process parameters on the uniformity and coverage of graphene on a continuously moving foil. At lower speeds, high-quality monolayer graphene is formed; at higher speeds, rapid nucleation of small graphene domains is observed, yet coalescence is prevented by the limited residence time in the CTCVD system. We show that a smooth isothermal transition between the reducing and carbon-containing atmospheres, enabled by injection of the carbon feedstock via radial holes in the inner tube, is essential to high-quality roll-to-roll graphene CVD. We discuss how the foil quality and microstructure limit the uniformity of graphene over macroscopic dimensions. We conclude by discussing means of scaling and reconfiguring the CTCVD design based on general requirements for 2-D materials manufacturing., National Science Foundation (U.S.). Science, Engineering, and Education for Sustainability (Postdoctoral Fellowship Award 1415129)

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2002., Includes bibliographical references (p. 278)., by Anastasios John Hart., S.M.

We demonstrate direct production of graphene on SiO[subscript 2] by CVD growth of graphene at the interface between a Ni film and the SiO[subscript 2] substrate, followed by dry mechanical delamination of the Ni using adhesive tape. This result is enabled by understanding of the competition between stress evolution and microstructure development upon annealing of the Ni prior to the graphene growth step. When the Ni film remains adherent after graphene growth, the balance between residual stress and adhesion governs the ability to mechanically remove the Ni after the CVD process. In this study the graphene on SiO[subscript 2] comprises micron-scale domains, ranging from monolayer to multilayer. The graphene has >90% coverage across centimeter-scale dimensions, limited by the size of our CVD chamber. Further engineering of the Ni film microstructure and stress state could enable manufacturing of highly uniform interfacial graphene followed by clean mechanical delamination over practically indefinite dimensions. Moreover, our findings suggest that preferential adhesion can enable production of 2-D materials directly on application-relevant substrates. This is attractive compared to transfer methods, which can cause mechanical damage and leave residues behind., Guardian Industries, National Science Foundation (U.S.). Graduate Research Fellowship Program

Vertically aligned carbon nanotubes (VACNTs), sometimes called forests or carpets, are a promising material due to their unique physical and scale-dependent physical properties [1-3]. Continuous production of VACNTs is required for large-scale applications in electronic devices, fuel cells and structural composite materials [4] among others. Chemical vapour deposition (CVD) is the only available technique to produce large areas of VACNTs, and most of the studies done for this technique are done for stationary growth in batch CVD processing [5-7]. Recently, it has been demonstrated that there is no significant differences between the VACNTs grown at different velocities up to 1.1 mm/s in terms of quality, morphology and length using a CVD process in a custom cold wall continuous-feed reactor [8]. Here, a controlled process to synthesize aligned CNTs in a continuous manner is discussed. Uniform growth is achieved using different substrates including alumina fibers in bundle form and silicon wafers., Airbus Industrie, Boeing Company, Empresa Brasileira de Aeronáutica, Lockheed Martin, Saab (Firm), Spirit AeroSystems (Firm), Textron, Inc., Composite Systems Technology (Firm), Hexcel (Firm), NECST Consortium

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2006., Includes bibliographical references (p. 323-357)., Carbon nanotubes (CNTs) are long molecules having exceptional properties, including several times the strength of steel piano wire at one fourth the density, at least five times the thermal conductivity of pure copper, and high electrical conductivity and current-carrying capacity. This thesis presents methods of CNT synthesis by atmospheric-pressure thermal chemical vapor deposition (CVD), where effective choice of the catalyst composition and processing conditions enables growth of tangled single-wall CNTs or structures of aligned multi-wall CNTs, on bare silicon, microstructured silicon, and ceramic fibers. Applying mechanical pressure during growth controls the structure of a CNT film while causing significant defects in the CNTs. This mechanochemisty approach is used to "grow-mold" CNTs into 3D-shaped microforms. A new reactor apparatus featuring a resistively-heated suspended platform enables rapid ( 100 °C/s) temperature control and versatile in situ characterization, including laser measurement of CNT film growth kinetics, and imaging of stress-induced film cracking. By thermally pre-treating the reactant mixture before it reaches the substrate platform, aligned CNTs are grown to 3 mm length in just 15 minutes., (cont.) A microchannel array is created for combinatorial flow studies of nanomaterials growth, having velocity range and resolution far exceeding those of conventional furnaces. A detailed design methodology considers compressible slip flows within the microchannels and flow leaks across the array, and the devices are fabricated by KOH etching of silicon. Initial experiments with this system demonstrate chemically-driven transitions in CNT yield and morphology along the microchannels, and flow-directed alignment of isolated CNTs and CNT strands. Applications of aligned CNTs in reinforced composites and electromechanical probes are enabled by the CNT synthesis technologies presented here, and show significant initial promise through collaborative research projects. Overall, controlling the packing density and matrix reinforcement of aligned CNTs gives material attributes spanning from those of energy-absorbing foams to stiff solids; however, significant increases in CNT length, growth rate, and packing density must be achieved to realize macroscopic fibers and films having the properties of individual CNTs. New machines can be created for studying the limiting aspects of growth reactions, for exploring new reaction regimes, and for producing exceptionally long nanostructures, looking ahead to fabrication of CNT-based materials in a continuous and industrially-scalable fashion., by Anastasios John Hart., Ph.D.