Spatial resolution in polymerization of sample features at nanoscale

Abstract

Recent developments in laser nanotechnologies allow overcoming optical limitations at the 100 nm level of spatial resolution. However, at such distances spatial restrictions on nanostructuring can be imposed by nonlocal response of the media. In the present paper, we consider nanostructuring by means of locally initiated radical polymerization of multifunctional monomers. Such local initiation can be provided, for instance, by femtosecond laser techniques. We theoretically analyze the limitations imposed by diffusion on the formation of two separate nanofeatures such as voxels, rods, and plates. Owing to the percolationlike transition occurring during the polymerization process, mathematical criteria for possible separation of such features are formulated. We develop a theoretical approach by consecutively taking into account diffusion of radicals of growing length. This approach allows us to estimate a characteristic spatial scale which determines the spatial resolution for the particular polymerizing system. For several realistic polymerizable resins, this resolution limit was estimated to be on the order of 10-100 nm.

Micro additive manufacturing using ultra short laser pulses

“…Pikulin et al [95] published extensive work theoretically analyzing feature size limitations by diffusion of initiators. Therefore, basic rate equations for initiation, propagation and termination are formalized and developed into a differential equation for the kinetics of radicals and monomers during polymerization.…”

Fluctuation limitations on the voxel minimal size at laser nanopolymerization

“…Based on relationship (9), the size of the above threshold region corresponding to the critical case can be estimated as (10) where b ~ 1 is a phenomenological parameter inde pendent of the shape of distribution f(r), K 2 = B(1/2, ν + 1)/2 ≈ 0.69, and B is the beta function. The for mula for the critical width of distribution f(r) has the form (with regard to (5)) (11) To make sure that this formula and the above numerical experiment deal with the same critical width, we will compare the position of the maximum of D[z cmass ] with the result of calculation by formula (11) at different amplitudes A (see Fig. 6).…”

“…If so, the chain mean length depends on the concentration of radia tion induced active centers. Diffusion, which may conversion the chains during their growth, is neglected [11]. Other nonlocal factors, such as heat conduction and shrinkage, as well as steric factors, which may also add to the formation of a network polymer, are also disregarded.…”

“…An example of such a redistribu tion is the diffusion of growing polymer chains dis cussed elsewhere [11]. In this work, we consider limi tations that are imposed on the resolution due to the fluctuations of the voxel size and position.…”

Die Entwicklung von Substrattopographien im Mikro‐ und Nanobereich zur Steuerung von Zellfunktionen

“…Bei alternativen Ansätzen wurde versucht, Polymersubstrate mit Strukturen in einer Fernordnung herzustellen, darunter mit Diblockcopolymeren [54] für Lamellen mit Nanorillen [55] und mit Nanokü-gelchen-Lithographie [56] für Vertiefungen. [57] Leistungsfähige [58,59] oder das "Molekül-Origami". [60,61] Die Integration nanotopographischer Merkmale in ein dreidimensionales Gerüst bleibt aber eine Herausforderung.…”