Role of Internal Chain Dynamics on the Rupture Kinetic of Adhesive Contacts

We study the forced rupture of adhesive contacts between monomers that are not covalently linked in a Rouse chain. When the applied force ($f$) to the chain end is less than the critical force for rupture ($f_c$), the reversible rupture process is coupled to the internal Rouse modes. If $f/f_c>1$ the rupture is irreversible. In both limits, the nonexponential distribution of contact lifetimes, which depends sensitively on the location of the contact, follows the double-exponential (Gumbel) distribution. When two contacts are well separated along the chain, the rate limiting step in the sequential rupture kinetics is the disruption of the contact that is in the chain interior. If the two contacts are close to each other, they cooperate to sustain the stress, which results in an “all-or-none” transition.

Figure 1

The survival probabilities $P_{rs}(t)$ for a single contact $(r,s)=(1,100)$ (a),(d), (20,80) (b),(e), and (40,60) (c),(f), with $f=1\mathrm{pN}$ (a)–(c) and 40 pN (d)–(f), and with $\gamma =1$ (solid lines) and 0.01 (dashed lines). The lifetime distributions $P_{rs}(t)$ are shown in the insets. Notice the variations in time scales in the panels. The chain structures for the intact single contact (20,80), before and after the rupture are shown.

Figure 2

The $Q\mathrm{\text{−}}Q$ plots (empty circles) of lifetimes $P_{rs}(t)$ for single contact $(r,s)=(1,100)$ (x-axis) versus lifetimes $p\exp (t)$ (y-axis), for $f=40\mathrm{pN}$ and $\gamma =1$ (a) and $\gamma =0.01$ (b). The rate $K$ in $p_{\exp }(t)$ is set to the inverse of the average contact lifetime (the maximum likelihood estimate) [7].

Figure 3

The survival probabilities $P_{\mathrm{tot}}(t)$ for contact pairs (1,100) and (20,80) (a); (1,100) and (40,60) (b); and (20,80) and (40,60) (c); (1,100) and (2,99) (d); (20,80) and (21,79) (e); and (40, 60) and (41, 59) (f), for $f=40\mathrm{pN}$ (solid lines) and 80 pN (dashed lines), all with $\gamma =1$. The lifetime distributions $P_{\mathrm{tot}}(t)$ are shown in the insets. Time scales vary greatly in all panels. Structures are for the intact pair (20,80) (40,60), disrupted contact (20,80) and intact contact (40,60), and both contacts disrupted are shown.