Quantification of van der Waals forces in bimodal and trimodal AFM.

The multifrequency formalism is generalized and exploited to quantify attractive forces, i.e., van der Waals interactions, with small amplitudes or gentle forces in bimodal and trimodal atomic force microscopy (AFM). The multifrequency force spectroscopy formalism with higher modes, including trimodal AFM, can outperform bimodal AFM for material property quantification. Bimodal AFM with the second mode is valid when the drive amplitude of the first mode is approximately an order of magnitude larger than that of the second mode. The error increases in the second mode but decreases in the third mode with a decreasing drive amplitude ratio. Externally driving with higher modes provides a means to extract information from higher force derivatives while enhancing the range of parameter space where the multifrequency formalism holds. Thus, the present approach is compatible with robustly quantifying weak long range forces while extending the number of channels available for high resolution.

Effect of Molecular Architecture on the Self-Assembly of Bottlebrush Copolymers.

The characteristics of a new architecture of bottlebrush copolymers (BBCPs) self-assembly were studied using self-consistent field theory. In this molecule, a series of AB linear diblock side chains were connected at the diblock junction using a C backbone. The control over the linker length and its chemical nature created an additional constraint on the intrinsic AB diblock microphase separation. Increasing side-chain crowding by increasing the grafting density and total degree of polymerization induced improved phase separation. This was reflected in the overall reduction in the effective interaction parameter between the diblocks as well as the abrupt increase in phase density when crossing the order-disorder transition. Side-chain crowding resulted in an increase in the equilibrium domain spacing compared to a linear diblock. On the other hand, the localization of block C at the AB interface generated a diffuse domain boundary and reduction in side-chain stretching. The unique behavior of BBCPs was observed in 1D confined systems where the molecule showed the natural tendency to orient domains parallel to neutral confinement in contrast to the behavior of confined diblocks. Such behavior largely depended on the degree of incompatibility between the AB blocks and BBCP structure. A ternary phase diagram was constructed for different proportions of each block. Rich morphologies of core-shell domains and tiling patterns were observed including octagonal and pentagonal polygons. The unique architecture of this bottlebrush molecule and its improved nanoscale properties make it an attractive candidate for various applications of nanotechnology.

Imparting Superhydrophobicity with a Hierarchical Block Copolymer Coating.

A robust and transparent silica-like coating that imparts superhydrophobicity to a surface through its hierarchical multilevel self-assembled structure is demonstrated. This approach involves iterative steps of spin-coating, annealing, and etching of polystyrene-block-polydimethylsiloxane block copolymer thin films to form a tailored multilayer nanoscale topographic pattern with a water contact angle up to 155°. A model based on the hierarchical topography is developed to calculate the wetting angle and optimize the superhydrophobicity, in agreement with the experimental trends, and explaining superhydrophobicity arising through the combination of roughness at different lengthscales. Additionally, the mechanical robustness and optically passive properties of the resulting hydrophobic surfaces are demonstrated.

Emergent symmetries in block copolymer epitaxy.

The directed self-assembly (DSA) of block copolymers (BCPs) has shown promise in fabricating customized two-dimensional (2D) geometries at the nano- and meso-scale. Here, we discover spontaneous symmetry breaking and superlattice formation in DSA of BCP. We observe the emergence of low symmetry phases in high symmetry templates for BCPs that would otherwise not exhibit these phases in the bulk or thin films. The emergence phenomena are found to be a general behavior of BCP in various template layouts with square local geometry, such as 44 and 32434 Archimedean tilings and octagonal quasicrystals. To elucidate the origin of this phenomenon and confirm the stability of the emergent phases, we implement self-consistent field theory (SCFT) simulations and a strong-stretching theory (SST)-based analytical model. Our work demonstrates an emergent behavior of soft matter and draws an intriguing connection between 2-dimensional soft matter self-assembly at the mesoscale and inorganic epitaxy at the atomic scale.

Directed self-assembly of a two-state block copolymer system.

In this work, ladder-shaped block copolymer structures consisting of parallel bars, bends, and T-junctions are formed inside square confinement. We define binary states by the two degenerate alignment orientations, and study properties of the two-state system. We control the binary states by creating openings around the confinement, changing the confinement geometry, or placing lithographic guiding patterns inside the confinement. Self-consistent field theory simulations show templating effect from the wall openings and reproduce the experimental results. We demonstrate scaling of a single binary state into a larger binary state array with individual binary state control.

Double-Layer Morphologies from a Silicon-Containing ABA Triblock Copolymer.

A combined experimental and self-consistent-field theoretical (SCFT) investigation of the phase behavior of poly(stryrene- b-dimethylsiloxane- b-styrene) (PS- b-PDMS- b-PS, or SDS32) thin films during solvent vapor annealing is presented. The morphology of the triblock copolymer is described as a function of the as-cast film thickness and the ratio of two different solvent vapors, toluene and heptane. SDS32 formed terraced bilayer morphologies even when the film thickness was much lower than the commensurate thickness. The morphology transitioned between bilayer cylinders, bilayer perforated lamellae, and bilayer lamellae, including mixed structures such as a perforated lamella on top of a layer of in-plane cylinders, as the heptane fraction during solvent annealing increased. SCFT modeling showed the same morphological trends as a function of the block volume fraction. In comparison with diblock PS- b-PDMS with the same molecular weight, the SDS32 offers a simple route to produce a diversity of well-ordered bilayer structures with smaller feature sizes, including the formation of bilayer perforated lamellae over a large process window.

Templated Self-Assembly of a PS- Branch-PDMS Bottlebrush Copolymer.

The self-assembly of block copolymers (BCPs) with novel architectures offers tremendous opportunities in nanoscale patterning and fabrication. Here, the thin film morphology, annealing kinetics, and topographical templating of an unconventional Janus-type "PS- branch-PDMS" bottlebrush copolymer (BBCP) are described. In the Janus-type BBCP, each segment of the bottlebrush backbone connects two immiscible side chain blocks. Thin films of a Janus-type BBCP with Mn = 609 kg/mol exhibited 22 nm period cylindrical microdomains with long-range order under solvent vapor annealing, and the effects of as-cast film thickness, solvent vapor pressure, and composition of the binary mixture of solvent vapors are described. The dynamic self-assembly process was characterized using in situ grazing-incidence X-ray scattering. Templated self-assembly of the BBCP within lithographically patterned substrates was demonstrated, showing distinct pattern orientation and dimensions that differ from conventional BCPs. Self-consistent field theory is used to elucidate details of the templated self-assembly behavior within confinement.

Limits of Directed Self-Assembly in Block Copolymers.

Understanding the conditions under which defects appear in self-assembling soft-matter systems is of great importance, for example, in the development of block-copolymer (BCP) nanolithography. Here, we explore the limits of the directed self-assembly of BCPs by deliberately adding random imperfections to the template. Our results show that defects emerge due to local "shear-like" distortions of the polymer-template system, a new mechanism that is fundamentally different from the canonical mechanisms of 2D melting. Furthermore, our results provide a general criterion for melting, obtaining the highest tolerance to random deviations from the perfect template at about 0.1 L0, where L0 is the natural BCP periodicity. These findings establish the limits of directed self-assembly of BCPs and can be extended to other classes of materials with soft interactions.

The Mendeleev-Meyer force project.

Here we present the Mendeleev-Meyer Force Project which aims at tabulating all materials and substances in a fashion similar to the periodic table. The goal is to group and tabulate substances using nanoscale force footprints rather than atomic number or electronic configuration as in the periodic table. The process is divided into: (1) acquiring nanoscale force data from materials, (2) parameterizing the raw data into standardized input features to generate a library, (3) feeding the standardized library into an algorithm to generate, enhance or exploit a model to identify a material or property. We propose producing databases mimicking the Materials Genome Initiative, the Medical Literature Analysis and Retrieval System Online (MEDLARS) or the PRoteomics IDEntifications database (PRIDE) and making these searchable online via search engines mimicking Pubmed or the PRIDE web interface. A prototype exploiting deep learning algorithms, i.e. multilayer neural networks, is presented.

Graft-through Synthesis and Assembly of Janus Bottlebrush Polymers from A-Branch-B Diblock Macromonomers.

We report the synthesis of Janus bottlebrush block copolymers by graft-through polymerization of branched diblock macromonomers. Self-assembly of the bottlebrushes was characterized by small-angle X-ray scattering, atomic force microscopy, and scanning electron microscopy. Phase separation and packing models of the bottlebrushes were computed, and their self-assembly behavior was corroborated experimentally in bulk and in thin films. Lamellar, hexagonal cylinder, and gyroid phases were observed and modeled. The A-branch-B Janus bottlebrush structure provides several unique advantages in the context of bottlebrush polymer assembly, including access to the first examples of gyroid phases.

Multilayer block copolymer meshes by orthogonal self-assembly.

Continued scaling-down of lithographic-pattern feature sizes has brought templated self-assembly of block copolymers (BCPs) into the forefront of nanofabrication research. Technologies now exist that facilitate significant control over otherwise unorganized assembly of BCP microdomains to form both long-range and locally complex monolayer patterns. In contrast, the extension of this control into multilayers or 3D structures of BCP microdomains remains limited, despite the possible technological applications in next-generation devices. Here, we develop and analyse an orthogonal self-assembly method in which multiple layers of distinct-molecular-weight BCPs naturally produce nanomesh structures of cylindrical microdomains without requiring layer-by-layer alignment or high-resolution lithographic templating. The mechanisms for orthogonal self-assembly are investigated with both experiment and simulation, and we determine that the control over height and chemical preference of templates are critical process parameters. The method is employed to produce nanomeshes with the shapes of circles and Y-intersections, and is extended to produce three layers of orthogonally oriented cylinders.

Perpendicular Block Copolymer Microdomains in High Aspect Ratio Templates.

Perpendicular orientation of lamellar microdomains in a high interaction parameter block copolymer was obtained within high aspect ratio gratings functionalized with a preferential sidewall brush. The experiments used polystyrene-block-polydimethylsiloxane (PS-b-PDMS) with molecular weight 43 kg/mol within trenches made using interference lithography. The perpendicular alignment was obtained for both thermal and solvent annealing, using three different solvent vapors, for a range of film thicknesses and trench widths. A platinum (Pt) layer at the base of the trenches avoided the formation of a wetting layer, giving perpendicular orientation at the substrate surface. The results are interpreted using self-consistent field theory simulation and a Ginzburg-Landau analytic model to map the energies of lamellae of different orientations as a function of the grating aspect ratio and the surface energies of the sidewalls and top and bottom surfaces. The model results agree with the experiment and provide a set of guidelines for obtaining perpendicular microdomains within topographic features.

Single cycle and transient force measurements in dynamic atomic force microscopy.

The monitoring of the deflection of a micro-cantilever, as the end of a sharp probe mounted at its end, i.e. the tip, interacts with a surface, forms the foundation of atomic force microscopy AFM. In a nutshell, developments in the field are driven by the requirement of obtaining ever increasing throughput and sensitivity, and enhancing the versatility of the instrument to simultaneously map the topography and quantify nanoscale processes and properties. In the most common dynamic mode of operation, the motion of the driven cantilever is monitored at a single point on its longitudinal axis. Here, we show that from this single point a waveform is obtained that contains all the details about conservative and dissipative interactions. Then a formalism that accounts for multiple arbitrary flexural modes is developed for an indirectly driven cantilever. The formalism is shown to allow recovery of the details of the interaction even in the presence of complex and relevant hysteretic forces when the cantilever oscillates in the steady state. In a different approach, we develop a formalism that monitors the wave profile of the cantilever, i.e. the waveform at five different points on its longitudinal axis. With this formalism the interaction can be reconstructed during a single oscillation cycle even in the transient state of oscillation. Finally, we discuss the potential and advantages of the proposed methods and future technical challenges. Other standard and state of the art techniques and methods are also discussed and compared with the ones presented here. This work should also provide insight into the current high throughput-high sensitivity developments dealing with multifrequency dynamic AFM where information is recovered from multiple eigenmodes.

Heterogeneous dissipation and size dependencies of dissipative processes in nanoscale interactions.

Here, processes through which the energy stored in an atomic force microscope cantilever dissipates in the tip-sample interaction are first decoupled qualitatively. A formalism is then presented and shown to allow quantification of fundamental aspects of nanoscale dissipation such as deformation, viscosity, and surface energy hysteresis. Accurate quantification of energy dissipation requires precise calibration of the conversion of the oscillation amplitude from volts to nanometers. In this respect, an experimental methodology is presented that allows such calibration with errors of 3% or less. It is shown how simultaneous decoupling and quantification of dissipative processes and in situ tip radius quantification provide the required information to analyze dependencies of dissipative mechanisms on the relative size of the interacting bodies, that is, tip and surface. When there is chemical affinity, atom-atom dissipative interactions approach the energies of chemical bonds. Such atom-atom interactions are found to be independent of cantilever properties and tip geometry thus implying that they are intensive properties of the system; these interactions prevail in the form of surface energy hysteresis. Viscoelastic dissipation on the other hand is shown to depend on the size of the probe and operational parameters.

A method to provide rapid in situ determination of tip radius in dynamic atomic force microscopy.

We provide a method to characterize the tip radius of an atomic force microscopy in situ by monitoring the dynamics of the cantilever in ambient conditions. The key concept is that the value of free amplitude for which transitions from the attractive to repulsive force regimes are observed, strongly depends on the curvature of the tip. In practice, the smaller the value of free amplitude required to observe a transition, the sharper the tip. This general behavior is remarkably independent of the properties of the sample and cantilever characteristics and shows the strong dependence of the transitions on the tip radius. The main advantage of this method is rapid in situ characterization. Rapid in situ characterization enables one to continuously monitor the tip size during experiments. Further, we show how to reproducibly shape the tip from a given initial size to any chosen larger size. This approach combined with the in situ tip size monitoring enables quantitative comparison of materials measurements between samples. These methods are set to allow quantitative data acquisition and make direct data comparison readily available in the community.

Energy dissipation distributions and dissipative atomic processes in amplitude modulation atomic force microscopy.

Instantaneous and average energy dissipation distributions in the nanoscale due to short and long range interactions are described. We employ both a purely continuous and a semi-discrete approach to analyze the consequences of this distribution in terms of rate of heat generation, thermal flux, adhesion hysteresis, viscoelasticity and atomic dissipative processes. The effects of peak values are also discussed in terms of the validity of the use of average values of power and energy dissipation. Analytic expressions for the instantaneous power are also derived. We further provide a general expression to calculate the effective area of interaction for fundamental dissipative processes and relate it to the energy distribution profile in the interaction area. Finally, a semi-discrete approach to model and interpret atomic dissipative processes is proposed and shown to lead to realistic values for the atomic bond dissipation and viscoelastic atomic processes.

Investigation of Nanoscale Interactions by Means of Subharmonic Excitation.

Multifrequency atomic force microscopy holds promise as a method to provide qualitative and quantitative information about samples with high spatial resolution. Here, we provide experimental evidence of the excitation of subharmonics in ambient conditions in the regions where capillary interactions are predicted to be the mechanism of excitation. We also experimentally decouple a second mechanism for subharmonic excitation that is highly independent of environmental conditions such as relative humidity. This implies that material properties could be mapped. Subharmonic excitation could lead to experimental determination of surface water affinity in the nanoscale whenever water interactions are the mechanism of excitation.

Quantifying dissipative contributions in nanoscale interactions.

Imaging with nanoscale resolution has become routine practice with the use of scanning probe techniques. Nevertheless, quantification of material properties and processes has been hampered by the complexity of the tip-surface interaction and the dependency of the dynamics on operational parameters. Here, we propose a framework for the quantification of the coefficients of viscoelasticity, surface energy, surface energy hysteresis and elastic modulus. Quantification of these parameters at the nanoscale will provide a firm ground to the understanding and modelling of tribology and nanoscale sciences with true nanoscale resolution.