Research Papers

Deformation of Pyramidal PDMS Stamps During Microcontact Printing

[+] Author and Article Information
Congrui Jin

Department of Mechanical Engineering,
State University of New York at Binghamton,
Binghamton, NY 13902
e-mail: cjin@binghamton.edu

Qichao Qiao

Department of Mechanical Engineering,
State University of New York at Binghamton,
Binghamton, NY 13902

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 14, 2016; final manuscript received April 8, 2016; published online May 11, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(7), 071011 (May 11, 2016) (9 pages) Paper No: JAM-16-1143; doi: 10.1115/1.4033432 History: Received March 14, 2016; Revised April 08, 2016

Microcontact printing (MicroCP) is a form of soft lithography that uses the relief patterns on a master polydimethylsiloxane (PDMS) stamp to form patterns of self-assembled monolayers (SAMs) of ink on the surface of a substrate through conformal contact. Pyramidal PDMS stamps have received a lot of attention in the research community in recent years, due to the fact that the use of the pyramidal architecture has multiple advantages over traditional rectangular and cylindrical PDMS stamps. To better understand the dynamic MicroCP process involving pyramidal PDMS stamps, in this paper, numerical studies on frictionless adhesive contact between pyramidal PDMS stamps and transversely isotropic materials are presented. We use a numerical simulation method in which the adhesive interactions are represented by an interaction potential and the surface deformations are coupled by using half-space Green's functions discretized on the surface. It shows that for pyramidal PDMS stamps, the contact area increases significantly with increasing applied load, and thus, this technique is expected to provide a simple, efficient, and low-cost method to create variable two-dimensional arrays of dot chemical patterns for nanotechnology and biotechnology applications. The DMT-type and Johnson–Kendall–Roberts (JKR)-type-to-DMT-type transition regimes have been explored by conducting the simulations using smaller values of Tabor parameters.

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Grahic Jump Location
Fig. 1

The parameter ho is the initial air gap, i.e., the separation of the surfaces in the absence of applied and adhesive forces, and then due to surface interaction as well as the external loads, the surfaces will deform and the separation between the two points will change from ho to h. α is the displacement (in the z direction) at infinity of body 1 with respect to body 2.

Grahic Jump Location
Fig. 2

A right square pyramid with a base size of m×m and a height of n has been used in the simulation

Grahic Jump Location
Fig. 5

Normalized pressure distributions P for the printing substrate pressed by the pyramidal PDMS stamp when the normalized indentation depth: (a) D = 1.0 and (b) D = 9.0 during approach. The normalized contact region length obtained directly from the numerical simulation is denoted by Lc=|2Xc|=|2Yc|, where (Xc, Yc) is the coordinate for the tensile peak stress at the corner of the contact area.

Grahic Jump Location
Fig. 6

The contact region length lc versus the force f curves for the pyramidal PDMS stamp with five different values of n. It also shows the comparison between our numerical results and the experimental data provided by Li et al. [21].

Grahic Jump Location
Fig. 7

The contact region length lc versus the displacement α curves for the pyramidal PDMS stamp with five different values of n

Grahic Jump Location
Fig. 8

The normalized force F versus the normalized displacement D curves for the pyramidal PDMS stamps using different values of Tabor parameters

Grahic Jump Location
Fig. 9

The normalized contact region length Lc versus the normalized force F curves for the pyramidal PDMS stamps using different values of Tabor parameters

Grahic Jump Location
Fig. 10

The normalized contact region length Lc versus the normalized displacement D curves for the pyramidal PDMS stamps using different values of Tabor parameters

Grahic Jump Location
Fig. 11

Normalized pressure distributions P for the printing substrate pressed by the pyramidal PDMS stamp when the normalized indentation depth D = 9.0 during approach with four different values of Tabor parameter: (a) μ  = 0.1, (b) μ  = 0.4, (c) μ  = 0.6, and (d) μ  = 0.8

Grahic Jump Location
Fig. 3

(a) The normalized force versus the normalized displacement curves for the monomial indenters with different values of d and (b) the normalized force f¯ versus the normalized contact radius c¯ curves. It shows that our numerical results agree very well with the analytical solutions, and the magnitude of the normalized pull-off force is monotonically increasing with increasing d.

Grahic Jump Location
Fig. 4

The force f versus the displacement α curves for the pyramidal PDMS stamp with five different values of n



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