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Research Papers

# Multiscale Modeling of Adsorbed Molecules on Freestanding Microfabricated Structures

[+] Author and Article Information
Matthew R. Begley, Marcel Utz

Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA 22901

For charged (i.e., polyelectrolyte) brushes, the surface stress in the adsorbed layer driving deformation increases with increasing molecular length, as will be illustrated later.

For ds-DNA in water, the relationship between volume fraction and molarity is roughly $c≈(0.64l∕mol)NbpM$, where $Nbp$ is the number of base pairs and $M$ is the number of moles of DNA per liter.

The pair correlation function is defined such that $2πρg(r)dr$ yields the number of particles in an annulus of width $dr$ and radius $r$ from a given particle.

Begley et al. (14) illustrated this for cases of deformation involving large displacements, encompassing both plate (i.e., bending-dominated) and membrane (i.e., stretch-dominated) regimes.

This is identical to results published elsewhere, except for the modification due to the effective modulus of the adsorbed groups, $λ′$.

J. Appl. Mech 75(2), 021008 (Feb 25, 2008) (8 pages) doi:10.1115/1.2793130 History: Received May 08, 2006; Revised October 12, 2006; Published February 25, 2008

## Abstract

This paper outlines a multiscale model to quantitatively describe the chemomechanical coupling between adsorbed molecules and thin elastic films. The goal is to provide clear, quantitative connections between molecular interactions, adsorption distribution, and surface stress, which can be integrated with conventional thin film mechanics to quantify device performance in terms of molecular inputs. The decoupling of molecular and continuum frameworks enables a straightforward analysis of arbitrary structures and deformation modes, e.g., buckling and plate/membrane behavior. Moreover, it enables one to simultaneously identify both chemical properties (e.g., binding energy and grafting density) and mechanical properties (e.g., modulus and film geometry) that result in chemically responsive devices. We present the governing equations for scenarios where interactions between adsorbed molecules can be described in terms of pair interactions. These are used to quantify the mechanical driving forces that can be generated from adsorption of double-stranded DNA and $C60$ (fullerenes). The utility of the framework is illustrated by quantifying the performance of adsorption-driven cantilevers and clamped structures that experience buckling. We demonstrate that the use of surface-grafted polyelectrolytes (such as DNA) and ultracompliant elastomer structures is particularly attractive since deformation can be tuned over a very wide range by varying grafting density and chemical environment. The predictions illustrate that it is possible to construct (1) adsorption-based tools to quantify molecular properties such as polymer chain flexibility and (2) chemically activated structures to control flow in microfluidic devices.

###### FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 7

Grafting density and hcp lattice spacing as a function of salt concentration under which adsorption occurs using the full potential for DNA developed by Strey (13).

Figure 8

Surface stress predictions for hcp grafting of DNA developed by assuming nearest-neighbor interactions and the full potential for DNA developed by Strey (13)

Figure 9

Cantilever deflections and stiffness as a function of C60 adsorption spacing, comparing several silicon and PDMS microcantilevers

Figure 10

Predicted cantilever deflections as a function of the persistence of semiflexible polymers for several adsorption spacings (hexagonal nearest-neighbor interactions using the Strey potential)

Figure 11

Predicted clamped PDMS film deflections as a function of DNA adsorption spacing at several salt concentrations. At a fixed concentration, there is a critical adsorption spacing that triggers out-of-plane buckling.

Figure 1

Schematic illustrations of chemically activated structures to control fluid motion [(a) and (b)]. Top view of a cantilever suspended at a junction of two microfluidic channels. [(c) and (d)]. Side view of a conventional microfluidic valve spanning two chambers: The Value is functionalized with polyelectrolyte surface and actuated by controlling electrostatic screening in the top reservoir.

Figure 2

Predictions of grafting density versus binding energy for nearest-neighbor repulsion using parameters appropriate for Debye screening of short DNA (40bp). The molecular pair potential is given by ϕ(r)=ϕoe−r∕ro∕r∕ro.

Figure 3

Elementary beam models with continuum surface stress on the upper surface

Figure 4

Simulation snapshot (top) and pair correlation function (bottom) determined from MC simulations of C60 adsorption. Only the details of the first peak factor into surface stresses.

Figure 5

Surface stresses generated by adsorption of C60 fullerenes as a function of characteristic separation in a hexagonal array

Figure 6

Critical adsorption spacing for a hexagonal array of semiflexible polymers (e.g., DNA), where bare interactions and thermal fluctuations are equivalent.

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