Dip-Pen Nanolithography Simulator

Write Mode

Ink / Molecule

Relative humidity 40%

Dwell time 10 s

Tip write speed 1.0 µm/s

Live Readout

Feature size

— nm

Meniscus ⌀

— nm

Eff. diffusivity D

— cm²/s

Features written

How it works

Dip-pen nanolithography (DPN, Piner & Mirkin 1999) uses an AFM tip coated with an "ink" of molecules. Under ambient humidity a nanoscale water meniscus condenses in the gap between tip apex and substrate, forming a liquid bridge through which ink molecules diffuse onto the surface.

Dot mode — for a tip held stationary, the deposited spot grows as a classic 2D point-source diffusion problem:

r(t) = √(4·D·t)

D  — effective molecular diffusivity through the meniscus (cm²/s)
t  — dwell time (s)
r  — deposited feature radius

Line mode — dragging the tip at speed v shortens the residence time at each point, so line width shrinks as speed increases (a simplified, qualitative model of the same transport-limited trend reported in DPN literature):

w(v) ≈ d_meniscus · √(v_ref / v),   v_ref = 1 µm/s

Humidity controls two things at once: it enlarges the meniscus neck (more contact area) and raises the effective diffusivity D_eff = D₀·(RH/40%), since a larger liquid bridge moves more ink per second. Smaller, faster-diffusing molecules (alkanethiols) write far larger features per second than bulky, slow proteins — exactly why DPN protein arrays need much longer dwell times than small-molecule arrays.

Ink dropdown — sets the baseline diffusivity D₀ for three molecule classes spanning three orders of magnitude.
Humidity slider — grows/shrinks the meniscus and rescales D.
Dwell time / write speed — the two levers real DPN instruments use to dial in feature size, exactly as modeled here.

Real-world relevance: DPN builds sub-100 nm protein, DNA and nanoparticle arrays for biosensors and is one of the few techniques that can pattern soft biomolecules without damaging them — unlike e-beam or two-photon lithography, which use energetic beams instead of gentle chemical transport.

Gold substrate Water meniscus Deposited ink

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