Deformation of Nanoscopic Polymer Structures in Response to Well‐Defined Capillary Forces
Source abstract
Abstract
The development of strategies to measure the properties of materials with nanoscopic dimensions is a necessary but challenging topic in nanoscale science and technology. Here, combinatorial arrays of specially designed test structures are used to quantify the deformation of micro‐ and nanoscale polymer beams in response to well‐defined capillary forces. In the Figure, increasing capillary forces from left to right act on beams 95 nm wide.
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Research context
OpenAlex topics: Surface Modification and Superhydrophobicity · Polymer Surface Interaction Studies · Carbon Nanotubes in Composites
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (32)
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1. 10.1557/S088376940004163410.1557/S0883769400041634 ↗
2. 10.1063/1.138021810.1063/1.1380218 ↗
3. 10.1116/1.59070010.1116/1.590700 ↗
4. 10.2494/photopolymer.14.51310.2494/photopolymer.14.513 ↗
5. 10.1126/science.141150510.1126/science.1411505 ↗
6. 10.1088/0957-4484/6/1/00310.1088/0957-4484/6/1/003 ↗
7. 10.1063/1.134917910.1063/1.1349179 ↗
8. 10.1103/PhysRevLett.59.194210.1103/PhysRevLett.59.1942 ↗
9. 10.1063/1.11863910.1063/1.118639 ↗
10. 10.1038/356266a010.1038/356266a0 ↗
11. 10.1103/PhysRevB.57.1258810.1103/PhysRevB.57.12588 ↗
12. 10.1103/PhysRevLett.71.331910.1103/PhysRevLett.71.3319 ↗
13. 10.1016/S1359-6454(97)00270-X10.1016/S1359-6454(97)00270-X ↗
14. 10.1557/JMR.1986.060110.1557/JMR.1986.0601 ↗
15. 10.1063/1.128777110.1063/1.1287771 ↗
16. 10.1016/S0022-5096(02)00062-510.1016/S0022-5096(02)00062-5 ↗
17. 10.1063/1.11311510.1063/1.113115 ↗
18. The functioning of the test structures rests on this important assumption but with the proper exposure and development conditions it is possible to use electron beam lithography to produce nearly vertical sidewalls in PMMA; see M. J. Bowden inIntroduction to Microlithography 2nd ed. (Eds: L. F. Thompson C. G. Willson M. J. Bowden) American Chemical Society Washington DC1994 Ch. 2.
19. A 3D modeling software (Surface Evolver) was used to delimit the geometries under which the 2D cylindrical model of the meniscus shape can be used to estimate the initial capillary pressures generated in the test structures. It was calculated that the 2D model estimates the actual capillary pressure to within 5 % for pools having a length to width ratio greater than 15. Surface Evolver can be downloaded at http://www.susqu.edu/brakke/
20. The radius of the cylinder can be estimated asr = W/(2 cos θ) whereWis the pool width and θ is the contact angle of the rinse liquid with the sidewalls.
21. Applying a 2D model of the rinse liquid meniscus the Young–Laplace capillary pressure difference between the rinse liquid and the atmosphere is ΔP = γ/r where γ is the rinse liquid surface tension andris the meniscus’ radius of curvature. Therefore the pressure in the inner pool isPIP =Patm – 2γ cos θ/IPWand the pressure in the outer pool isPOP =Patm – 2γ cos θ/OPW wherePatmis the atmospheric pressure. SinceIPW< OPWis maintained thenPIP < POPmust always hold causing the beams to collapse towards each other.
22. F. P. Beer E. R. Johnston Jr. inMechanics of Materials McGraw‐Hill New York1981.
23. 10.1143/JJAP.31.295410.1143/JJAP.31.2954 ↗
24. 10.1149/1.222078210.1149/1.2220782 ↗
25. 10.1116/1.132128010.1116/1.1321280 ↗
26. International SEMATECH The International Technology Roadmap for Semiconductors: 2002 Update 2002.
27. 10.1143/JJAP.32.605910.1143/JJAP.32.6059 ↗
28. 10.1063/1.141549710.1063/1.1415497 ↗
29. 10.1021/ma001932q10.1021/ma001932q ↗
30. 10.1021/ma981212810.1021/ma9812128 ↗
31. 10.1103/PhysRevLett.77.200210.1103/PhysRevLett.77.2002 ↗
32. D. R. Lide CRC Handbook of Chemistry and Physics 80th ed. CRC Press Boca Raton FL1999.