Force-induced desorption of a linear polymer chain adsorbed on an attractive surface

Abstract

We consider a model of self-avoiding walk on a lattice with on-site repulsion and an attraction for every vertex of the walk visited on the surface to study force-induced desorption of a linear polymer chain adsorbed on an attractive surface and use the exact enumeration technique for analyzing how the critical force for desorption f c (T ) depends on the temperature. The curve f c (T )gives the boundary separating the adsorbed phase from the desorbed phase. Our results show that * Electronic address: pramod@justice.com, yashankit@yahoo.com, ysingh@bhu.ac.in When a long flexible polymer chain interacts with an impenetrable surface its conformational properties are strongly modified in comparison with its bulk properties [1, 2]. This is due to a subtle competition between the lowering of internal energy near an attractive surface and the loss of entropy due to constraints imposed by the impenetrable surface. For a strongly attractive surface, the polymer chain sticks to the surface, and for weak attraction it prefers to stay away from the surface. Thus there is a transition from the state when chain is mostly attached to the surface (adsorbed) to the state of detachment (desorbed) when the temperature is increased. The transition between theses two states is marked by a transition temperature T a with the adsorbed phase for T < T a and the desorbed phase for T > T a .A model of self avoiding-walk on a lattice with on-site repulsion and attraction energy for every vertex of the walk visited on the surface provides an adequate model for understanding the adsorption-desorption transition [3, 4, 5]. We extend this model of self-avoiding walk to study the force-induced desorption of a linear polymer chain adsorbed on an attractive surface and calculate the critical force f c (T ) for desorption as a function of temperature.Response of a polymeric chain to externally applied force can be measured experimentally by using techniques like optical or magnetic tweezers [6] and atomic force microscope [7].We consider self-avoiding walks (SAW s) that start from a point on an impenetrable surface and experience a force f in a direction perpendicular to the surface at the other end.The applied force, because of its direction, favours desorption and one expects a critical force, f c (T ), for desorption. At a given T when the applied force f is less than f c (T ) the polymer will be adsorbed while for f > f c (T ) the polymer will be desorbed. The curve f c (T ), therefore, gives the boundary that separates the desorbed phase from the adsorbed phase in the (f, T ) plane.Let z = 0 represents the surface and walks start from a point (origin) on the surface. In case of two dimensions (2-d) the surface is a line whereas in case of three dimensions (3-d) the surface is a plane. Since the surface is impenetrable, walks are restricted to half of the space (z ≥ 0) only. We enumerated all SAW s upto a certain length on a square lattice in 2-d and on a cubic lattice in 3-d. Let C N (N s , h) be the number of SAW s of N vertex (a vertex of...

Temperature effects in the mechanical desorption of an infinitely long lattice chain: Re-entrant phase diagrams

“…As an example we discuss a fivechoice model in which immediate step reversals are forbidden. We compare the results with numerical data of Krawczyk et al 11 and Mishra et al 13 for SAWs on a simple cubic lattice. The former authors used a so-called flat PERM algorithm for chain lengths up to N = 256; they also extrapolated to N → ϱ.…”

“…Following the argument of Mishra et al 13 we write the reduced chemical potential of the ͑fully͒ adsorbed chain as ads ͑͒ =− − S ads and the chemical potential of the ͑com-pletely͒ stretched chain as str ͑u͒ =−u since the entropy of the fully stretched state is zero. This leads to the straight line equation u tr = + S ads with unit slope and intercept S ads , the entropy of the fully adsorbed state.…”

“…͑18͒. The symbols in these diagrams are the numerical data for SAWs with = 1, taken from Krawczyk et al 11 ͑circles͒ for N = 256 and Mishra et al 13 ͑crosses͒ for N → ϱ ͑extrapolated͒. For obtaining T / T c from these numerical data we used the estimates T c = 2.8 ͑Ref.…”

“…For obtaining T / T c from these numerical data we used the estimates T c = 2.8 ͑Ref. 11͒ and T c = 2.5, 13 which are the temperatures where in the simulations the desorption force vanishes.…”

“…Temperature effects in mechanical desorption were studied by direct enumeration methods for self-avoiding walks on simple square and cubic lattices by Mishra et al 13 Data for short chains with N up to 20-30 segments were analyzed, and several extrapolation procedures were employed. The phase diagram is defined by the detachment curve, which represents the dependence of the critical desorption force on the temperature, at fixed adsorption energy .…”