Diffusion of single long polymers in fixed and low density matrix of obstacles confined to two dimensions

Abstract

Diffusion properties of a self-avoiding polymer embedded in regularly distributed obstacles with spacing a = 20 and confined in two dimensions is studied numerically using the extended bond fluctuation method which we have developed recently. We have observed for the first time to our knowledge, that the mean square displacement of a center monomer φ M/2 (t) exhibits four dynamical regimes, i.e., φ M/2 (t) ∼ t νm with νm ∼ 0.6, 3/8, 3/4, and 1 from the shortest to longest time regimes. The exponents in the second and third regimes are well described by segmental diffusion in the "self-avoiding tube". In the fourth (free diffusion) regime, we have numerically confirmed the relation between the reptation time τ d and the number of segments M , τ d ∝ M 3 .

Polymer Surface Diffusion in the Dilute Limit

“…Chains below a critical M may be expected to diffuse between surface obstacles as models predict for a two-dimensional chain [6][7][8][9], but there should come a point where this process is so slow that hopping over these obstacles becomes the faster process instead (still slow but not quite so slow). This would be consistent with the fact that chains with M < 3,000 g-mol -1 fail to adsorb at all, showing that while the time-8 averaged conformation is the predicted pancake [2], transient loops also exist.…”

“…Furthermore, this quartz system provides the pathway to test the model that stronger scaling, D ~ M -3/2 , holds if obstacles force chains to diffuse in curvilinear fashion, which is what computer simulations of two-dimensional polymer diffusion predict [5][6][7][8][9]. To this end, we compared polymer diffusion on ultrasmooth (thermally annealed) quartz with diffusion on quartz that is less smooth, being only mechanically-polished.…”

“…Secondly, it is known that surface disorder can in principle guide chains to diffuse between obstacles [8,9], the resulting reptation-type diffusion scaling as D ~ M -3/2 [10][11][12] but the limits to which this holds for chains that may not be strictly two-dimensional owing to their weak segmental sticking energy are not known. Third, when chains possess extremely high M such that 2D diffusion becomes extremely slow, it is evident that other mechanisms might become rate-limiting; but this possibility has not been considered previously, to the best of our knowledge.…”

Surface Diffusion of Poly(ethylene glycol)

“…On the other hand, for regularly placed obstacles, recent simulations find a clear D ∼ N -3/2 law for the case of a single value of widely separated obstacles. 11 Further simulations regarding this question are desirable.…”

“…10 In other words, the center-of-mass diffusion coefficient, D, scaled as D ∼ N -1 (Rouse behavior). A surface that contains impenetrable obstacles which require the chain to diffuse around them does strengthen the dependence on N, 11,12 but different simulation studies seem not to agree on the consequences of such obstacles on the N scaling of D. We return to this in the Discussion section.…”