The quantitative assessment of single molecule diffusion trajectories by orthogonal regression analysis is reported. This analysis is broadly applicable to any single particle tracking experiments in which diffusion along one dimension (1D) is expected. It affords quantitative data on the (in plane) orientation of 1D trajectories, allowing for their absolute orientations to be determined. Histograms depicting the distribution of trajectory angles provide new physical insights into the degree of trajectory alignment, and by inference, materials order. Estimates of the errors in the trajectory angle and particle positioning along each trajectory are also obtained. The angle results are compared to those from single-step angle determinations. The advantages of the regression method include its simplicity and computational efficiency, and the ability to objectively differentiate between 1D and 2D/immobile trajectories. Its utility is demonstrated through analysis of single molecule diffusion trajectories in surfactant-templated mesoporous silica films as probed by wide-field fluorescence microscopy. The trajectory angle histograms obtained provide quantitative data on mean trajectory orientation and the degree of trajectory alignment in distinct populations and sample regions. Mesopore order was quantitatively assessed by implementation of an order parameter,

= 2-1, calculated from the individual trajectory angles in each of four representative sample regions. The results depict the presence of well-ordered domains (from microns to tens of microns in size), all having

≈ 0.9. The latter corresponds to an ≈14° average deviation of the individual trajectories from the mean trajectory (and mesopore) orientation in each domain.

Single-molecule tracking (SMT) was used to probe the alignment of cylindrical microdomains in polystyrene–poly(ethylene oxide) diblock copolymer (PS-b-PEO) films induced by directional solvent penetration. PS-b-PEO films were supported between two glass plates. Aligned PEO domains were obtained upon horizontal penetration of 1,4-dioxane vapor through the films, while no observable alignment occurred when benzene or toluene was used. Domain alignment was assessed by SMT, using a dye that partitions into PEO. More than 70% of the dye molecules exhibited one-dimensional (1D) diffusion along the dioxane penetration direction. Quantitative assessment of 1D trajectory alignment yielded an order parameter of ca. 0.9. A high degree of domain order was observed across millimeter distances throughout the 4 μm thick films. PEO domain size (ca. 11 nm radius) was determined from the probe positioning error. These results demonstrate the utility of SMT methods for characterization of nanoscale domains in cylinder-forming block copolymer films.

Nanostructured materials such as mesoporous metal oxides and phase-separated block copolymers form the basis for new monolith, membrane, and thin film technologies having applications in energy storage, chemical catalysis, and separations. Mass transport plays an integral role in governing the application-specific performance characteristics of many such materials. The majority of methods employed in their characterization provide only ensemble data, often masking the nanoscale, molecular-level details of materials morphology and mass transport. Single-molecule fluorescence methods offer direct routes to probing these characteristics on a single-molecule/single-nanostructure basis. This article provides a review of single-molecule studies focused on measurements of anisotropic diffusion, adsorption, partitioning, and confinement in nanostructured materials. Experimental methods covered include confocal and wide-field fluorescence microscopy. The results obtained promise to deepen our understanding of mass transport mechanisms in nanostructures, thus aiding in the realization of advanced materials systems.

Single-molecule tracking (SMT) methods are now being employed to probe the morphologies and mass-transport characteristics of self-assembled one-dimensional (1D) nanostructures. Such nanostructures are found in surfactant-templated mesoporous metal oxides, phaseseparated block copolymers, and lyotropic liquid-crystal mesophases. This Perspective begins with a review of investigations in which SMT methods have been employed for in situ visualization of 1D nanostructures and their ability to guide and support 1D diffusion of fluorescent probe molecules. New orthogonal regression methods for the quantitative characterization of 1D nanostructure alignment and order are subsequently discussed. Recent investigations in which the confined orientational motions of single molecules are probed by single-molecule emission polarization measurements are highlighted. These data are used to access high-precision estimates of the effective lateral nanostructure dimensions. The results reveal the important role played by nanoconfined solvents and soft material nanostructures in restricting probe molecule motions. M aterials incorporating ordered, oriented 1D nanostructures have myriad potential applications as membranes and monoliths for use in chemical sensing, catalysis, separations, batteries, and fuel cells. 1,2 Interest in these materials arises in part because both nanostructure size and local chemical composition can be controlled to achieve chemical selectivity. For the purposes of this Perspective, relevant materials include both organic and inorganic assemblies such as lyotropic liquid-crystal mesophases, 3,4 surfactant-templated mesoporous metal oxides, 1,5−14 and phase-separated block copolymers. 2,15,16 Before any of these can be employed in commercial devices, much remains to be learned about the local alignment, organization, continuity, and accessible internal dimensions of their 1D nanostructures. This Perspective highlights recent investigations of these attributes by in situ single-molecule tracking (SMT) methods.One-dimensional nanostructures are commonly investigated by small-angle X-ray and neutron scattering (SAXS and SANS), scanning and transmission electron microscopy (SEM and TEM), and atomic force microscopy (AFM). 1,2,17−20 SAXS and SANS have provided valuable data on the materials' periodicity and, hence, nanostructure size and organization. In porous materials, pore size and surface area are frequently determined by gas adsorption measurements. 21 Scattering anisotropy data have revealed the 1D nature of many such materials and have yielded quantitative measurements of average nanostructure order. 12 SEM, TEM, and AFM afford a microscopic view of these same characteristics. Unfortunately, such methods provide little or no direct information on the partitioning and mass-transport characteristics of greatest relevance to many of their applications.The dynamics and directionality of molecular mass transport within 1D nanostructures have previously been investigated by nuclear magnetic resonance (NMR) sp...

Flow-based approaches are promising routes to preparation of aligned block copolymer microdomains within confined spaces. An in-depth characterization of such nanoscale morphologies within macroscopically nonuniform materials under ambient conditions is, however, often challenging. In this study, single-molecule tracking (SMT) methods were employed to probe the flow-induced alignment of cylindrical microdomains (ca. 22 nm in diameter) in polystyrene-poly(ethylene oxide) diblock copolymer (PS-b-PEO) films. Films of micrometer-scale thicknesses were prepared by overlaying a benzene solution droplet on a glass coverslip with a rectangular glass plate, followed by solvent evaporation under a nitrogen atmosphere. The microdomain alignment was quantitatively assessed from SMT data exhibiting the diffusional motions of individual sulforhodamine B fluorescent probes that preferentially partitioned into cylindrical PEO microdomains. Better overall microdomain orientation along the flow direction was observed near the substrate interface in films prepared at a higher flow rate, suggesting that the microdomain alignment was primarily induced by shear flow. The SMT data also revealed the presence of micrometer-scale grains consisting of highly ordered microdomains with coherent orientation. The results of this study provide insights into shear-based preparation of aligned cylindrical microdomains in block copolymer films from solutions within confined spaces.