Conformational properties of a polymer tethered to an interacting flat surface

Abstract

The conformational properties of a lattice self-avoiding polymer chain tethered to an interacting and impenetrable flat surface were simulated using a dynamic Monte Carlo method. The results show that the conformational size reaches a minimum at the critical adsorption point (CAP) and that the scaling behavior of the polymer at the CAP is the same as that in the bulk solution. The results provide a new method to determine the CAP of polymer chains. Polymer Journal (2010) 42, 383-385; doi:10.1038/pj.2010.9; published online 17 March 2010Keywords: critical adsorption point; Monte Carlo simulation; self-avoiding chain INTRODUCTIONThe adsorption of polymer chains on surfaces by means of physical or chemical interactions is an important subject in polymer and biological sciences. A polymer chain may adsorb or desorb, depending on interactions with the surface. This phenomenon is relevant to many technological applications such as in polymer compatibilizers, colloid stabilizers and polymeric surfactants. [1][2][3] In many biological systems, ligands are attached to a surface through flexible tether chains. 4,5 The conformation of the attached tether chains will affect the binding of the ligand to a receptor and will thus influence the whole biological process. 6 The adsorption phenomenon is also a part of many physical systems; for example, polymer chains grafted to colloid particles and block copolymers at liquid-air interfaces. 7 The adsorption of polymers has attracted a large number of theoretical and experimental studies. [7][8][9][10][11][12] The growing interest in polymers interacting with substrates warrants a thorough understanding of the static and dynamic properties of the tethered chain.A mathematical model often used for studying the adsorption of tethered polymers on surfaces is the self-avoiding walk (SAW) chain in a three-dimensional (3D) simple cubic lattice that interacts with a flat surface and is restricted to lie on one side of the surface. 13-17 Every walk step that contacts the surface is assigned an interaction energy e (in units of k B T, where k B is the Boltzmann constant and T is the temperature). It is well accepted that a single chain adsorbed on an attractive surface exhibits a phase transition from a desorbed state to an adsorbed state when the adsorption strength increases beyond a critical value. The CAP e c was estimated to be about À0.29 for polymers on the simple cubic lattice. [9][10][11][12]16,18,19 In this work, we studied how the conformational properties of the chain change from a desorbed state for e4e c to an adsorbed state for eoe c . We found that both the mean square end-to-end distance /R 2 S

Critical adsorption of an end-grafted diblock copolymer on a flat surface

“…The oR A 2 4 displays a minimum value near the CAP T c = 1.625, which is in agreement with the behavior of the homogeneous polymer. 17,19 Therefore, the place where oR A 2 4 is minimum is defined as the critical adsorption temperature for a finitely long polymer. 19 At high temperatures, T4T c , the oR A 2 4 changes little with the temperature but increases with an increase in the length of block B.…”

“…17,19 Therefore, the place where oR A 2 4 is minimum is defined as the critical adsorption temperature for a finitely long polymer. 19 At high temperatures, T4T c , the oR A 2 4 changes little with the temperature but increases with an increase in the length of block B. At low temperatures, ToT c , the oR A 2 4 is mainly determined by the temperature.…”

“…[17][18][19] The dependence of T c (A n B m ) on the length of the A block is checked for copolymer A n B m . To this end, we choose A n B n as an example, and T c (A n B n ) is estimated from the minimum of oR A 2 4.…”

“…[10][11][12][13] A single homogeneous polymer interacting with a flat surface has been well investigated to identify the phase transition from a desorbed state to an adsorbed state with a temperature decrease beyond a critical adsorption point (CAP) T c . [11][12][13][14][15][16][17][18][19] Crossover scaling laws for a variety of quantities below, above and at the CAP have been formulated and verified by Monte Carlo (MC) simulation of self-avoiding walks. 11 Every monomer contacting the surface is assigned a monomer-surface attraction energy − E (or scaled energy ε = E/k B T with k B being the Boltzmann constant and T the temperature).…”

“…The crossover exponent, ϕ, is somewhat disputable and lies in a range between ϕ = 0.59 11,14,15 and ϕ = 0.5. 14,[20][21][22] Recently, the scaling relationship for the adsorption of a single chain has been tested by MC simulation on a cubic lattice, [15][16][17][18][19] and the adsorption transition of a polymer is well known. [17][18][19][20][21][22] Although extensive investigations of the CAP of homogeneous polymers have been carried out, there are few studies on the adsorption transition of copolymers.…”