Sharp and Fast: Sensors and Switches Based on Polymer Brushes with Adsorption-Active Minority Chains

We propose a design for polymer-based sensors and switches with sharp switching transition and fast response time. The switching mechanism involves a radical change in the conformations of adsorption-active minority chains in a brush. Such transitions can be induced by a temperature change of only about ten degrees, and the characteristic time of the conformational change is less than a second. We present an analytical theory for these switches and support it by self-consistent field calculations and Brownian dynamics simulations.

Figure 1

(a) Cartoon of the two states of the switching minority chain. (b) Average chain end height $⟨z_e⟩$ vs adsorption energy $ϵ$ for different values of the minority chain length $N$ (as indicated) in a brush with chain length $N_b=100$ and grafting density $\sigma =0.2$.

Figure 2

(a) Landau free energy [logarithm of the end distribution $P_e(z)$] for switch chains of different length $N$ integrated into a brush with chain length $N_b=100$ and grafting density $\sigma =0.2$, at the midpoint ${ϵ}_m$ of the transition. Solid red line: $N=105$, ${ϵ}_m=0.190$; dashed green line: $N=110$, ${ϵ}_m=0.246$; dotted blue line: $N=115$, ${ϵ}_m=0.293$. (b) Width of the transition between the adsorbed and desorbed chain, defined as $\delta ϵ=H\hspace{0.17em}(d⟨z_e⟩/dϵ{)}^{-1}$ evaluated at ${ϵ}_m$ ($H$ is the brush height) as a function of chain increment $\mathrm{\Delta }=N-N_b$.

Figure 3

Scaling plots for the width of the transition (a) and the barrier height for the adsorbing minority chain (b) in brushes with different grafting densities, plotted according to the theoretical predictions of Eqs. (8) (a) and (9). Here ,$N$ is the minority chain length and $\mathrm{\Delta }=N-N_b$ the chain length difference between switch chains and brush chains ($N_b$ is the brush chain length). Open symbols represent SCF data for $N_b=100$ and $\sigma =0.1$,0.2, 0.3; filled diamonds in panel (b) show data from single-chain Langevin dynamics simulations; see text below.

Figure 4

(a) Mean switching times for the switch chain in a brush with brush chain length $N_b=100$ and grafting density $\sigma =0.2$ at the adsorption transition (see text) as a function of the length increment $\mathrm{\Delta }=N-N_b$. Symbols: data from Brownian dynamics simulations; dashed green line: Arrhenius estimate [Eq. (10)]; solid red line: refined estimate based on Kramers’ theory [Eq. (11)] with $N_{\text{eff}}=N-N_b/3$. (b) Time evolution of the end monomer position $z$ and corresponding end monomer distribution $P_e(z)$ for $\mathrm{\Delta }=6$.