Simulation of a flexible polymer tethered to a flat adsorbing surface

Abstract

A lattice self-avoiding polymer chain with one end attached to an adsorbing flat surface is simulated using Monte Carlo method. The chain model has z ¼ 26 bond vectors with bond length being 1, ffiffi ffi 2 p , and ffiffi ffi 3 p on the simple cubic lattice. The dependence of the number of surface contacts M on temperature T in the unit E/k B with E the interacting energy and k B the Boltzmann constant and chain length N is investigated by a finite-size scaling lawnear the critical adsorption point T c . It was estimated that T c ¼ 1.625 and the exponents / ¼ 0.52 and d ¼ 1.63. It was observed that both mean square end-to-end distance hR 2 i and mean square radius of gyration hR 2 g i reach minimum at T c . And we discover that the asphericity parameter hAi is independent of chain length at T c . A simple relationship is discovered between T c and bond vector number n b for lattice chain models, and which can be extended to nonlattice chain models by introducing an attraction range fraction f.

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

“…It is interesting that the T c of the long A n B n is the same as that of a homogeneous polymer with the same model. 17 At T c = 1.625, we obtain the exponent ϕ = 0.51, which is also close to that of the homogeneous polymer ϕ = 0.52. 17 The results clearly show that the tail block B does not change the CAP and critical exponents of the infinitely long copolymer A n B n if the surface attraction of monomer A is stronger.…”

“…17 At T c = 1.625, we obtain the exponent ϕ = 0.51, which is also close to that of the homogeneous polymer ϕ = 0.52. 17 The results clearly show that the tail block B does not change the CAP and critical exponents of the infinitely long copolymer A n B n if the surface attraction of monomer A is stronger. However, the tail block B can change the contact number as well as conformational properties of the finitely long copolymer A n B n .…”

“…Therefore, the critical adsorption temperature, T c , of the A block is located among the region (1.60, 1.65) according to the finite-size scaling theory. 17,18,30 The location of T c is estimated by analyzing oM A 4 using the finite-size scaling theory. The values of oM A 4 at other temperatures in the interval (1.60, 1.65) can be obtained by quadratic interpolation from the simulation data.…”

“…[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.…”