Simulations and density functional calculations of surface forces in the presence of semiflexible polymers

We simulate interactions between adsorbing and nonadsorbing surfaces immersed in solutions containing monodisperse semiflexible chains. Apart from the nature of the surfaces, we investigate responses to changes of the intrinsic chain stiffness, the degree of polymerization, and the bulk concentration. Our simulations display a sufficient accuracy and precision to reveal free-energy barriers that are small on a typical scale of surface force simulations, but still of the same order as the expected van der Waals interactions. Two different approaches have been tested: grand canonical simulations, improved by configurational-biased techniques, and a perturbation method utilizing the isotension ensemble. We find the former to be preferable when the surfaces are nonadsorbing, whereas the isotension approach is superior for calculations of interactions between adsorbing surfaces, especially if the polymers are stiff. We also compare our simulation results with predictions from several versions of polymer density functional theory. We find that a crucial aspect of these theories, in quantitative terms, is that they recognize that end monomers exclude more volume to the surrounding than inner ones do. Those theories provide satisfactorily accurate predictions, particularly when the surfaces are nonadsorbing.

Figure 1

The polymers are modeled as hard spheres of diameter $\sigma$ connected by rigid bonds of length $\sigma$ (see dashed box). The quadratic surfaces with side length $L$ are located in $z=0$ and $z=h$.

Figure 2

(Color online) (a) Net osmotic pressure curves as a function of separation in solutions containing flexible polymers $(ϵ=0)$ of various chain lengths. The surfaces are repulsive, and $n_b{\sigma }^3=0.1$. (b) Free energy of interaction per unit surface area for the system in (a), obtained as described in the text above. The dashed line corresponds to a van der Waals interaction with a Hamaker constant of ${10}^{-20}\mathrm{J}$.

Figure 3

(a) Net osmotic pressure curves as a function of separation in the presence of semiflexible polymers $(ϵ=6)$ of various chain lengths. The surfaces are repulsive, and $n_b{\sigma }^3=0.1$. (b) Free energy of interaction per unit surface area for the system in graph (a).

Figure 4

Interactions between surfaces immersed in a solution of ideal semiflexible decamers, with $ϵ=14$. Results using the GCE and IE approaches, respectively, are displayed. (a) Net osmotic pressures. (b) Net interaction free energies.

Figure 5

Size effects in the IE method for a system of hard-sphere polymers. The surfaces are adsorbing. Results from simulations with 16 and 36 chains are compared.

Figure 6

(a) Net osmotic pressures obtained from Eq. (21) for three various bulk monomer densities of a 20-mer with $ϵ=11$. $n_b{\sigma }^3=0.028$ (long-dashed line), $n_b{\sigma }^3=0.031$ (dashed line), and $n_b{\sigma }^3=0.040$ (solid line). The squares in the inset show the pressure calculated using the virial equation [Eq. (26)] for $n_b{\sigma }^3=0.040$. The surfaces are attractive. (b) Net free energy of interaction per surface area for the system in graph (a).

Figure 7

Free energy per surface area as a function of intrinsic chain stiffness. The graphs are grouped into three different bulk density regimes. The surfaces are attractive and $r=20$.

Figure 8

Two of the curves in Fig. 7b ($ϵ$ = 11 and 14), together with a typical vdW interaction. The inset is a magnification around $6\sigma$ and reveals the relevant free-energy barriers.

Figure 9

Free energy of interaction per surface area as a function of the slit width. The system contains 30-mers. $n_b{\sigma }^3=0.022$.

Figure 10

(Color online) Comparisons between density functional predictions and simulated data of the interaction between repulsive surfaces in the presence of semiflexible $(ϵ=6)$ hard-sphere polymers at a bulk monomer density of $n_b{\sigma }^3=0.1$. (a) 10-mers. (b) 20-mers. In this case, predictions by the locally incompressible fluid approach (LIF), are also included. (c) 30-mers.

Figure 11

(Color online) Comparisons between simulation results and density functional predictions of forces between attractive surfaces in the presence of semiflexible hard-sphere polymers. (a) 20-mers, $ϵ=8$, $n_b{\sigma }^3=0.029$. (b) 30-mers, $ϵ=6$, $n_b{\sigma }^3=0.022$.

Figure 12

(Color online) Comparing DFT approaches employing Eqs. (33) and Eq. (39) for the excess part of the free-energy functional. The former does not discriminate between monomers, whereas the second takes into account that end monomers exclude more volume than the others. TPT1, GFD-AME, and TPTD1-AME belong to the first category, while TPTD1 and GFD belong to the second. The surfaces are attractive, the stiffness parameter is $ϵ=8$, and the bulk monomer density is $n_b{\sigma }^3=0.04$. (a) 30-mers. (b) 200-mers.

Figure 13

A summary of the qualitative response of the interaction between adsorbing surfaces to changes of the bulk monomer concentration. The solution contains semiflexible 30-mers, with $ϵ=8$.

Figure 14

A summary of the response of the interaction between adsorbing surfaces to changes of the intrinsic chain stiffness using explicit and implicit solvent models. The solution contains semiflexible 30-mers, with $n_b{\sigma }^3$. (a) Implicit solvent. (b) Explicit solvent.