Phenol release from pNIPAM hydrogels: Scaling Molecular Dynamics simulations with Dynamical Density Functional Theory

Abstract

We employed molecular dynamics simulations (MD) and Bennett's acceptance ratio method to compute the free energy of transfer (Delta G_trans) of phenol, methane, and 5-fluorouracil (5-FU) between bulk water and water-pNIPAM mixtures with different polymer volume fractions (phi_p). To this end, we first calculate the solvation free energies in both media to obtain Delta G_trans. Phenol and 5-FU (a drug used in cancer treatment) adsorb onto the pNIPAM surface and exhibit negative values of Delta G_trans irrespective of temperature, both above and below the lower critical solution temperature (T_c) of pNIPAM. In contrast, methane changes the sign of Delta G_trans, being positive below and negative above T_c. In all cases, and in contrast with some theoretical predictions, Delta G_trans shows a linear dependence on pNIPAM concentration up to high polymer densities. We also compute the diffusion coefficient (D) of phenol in water-pNIPAM mixtures as a function of phi_p in the dilute limit. Both Delta G_trans and D as functions of phi_p are key inputs to estimate the release halftime of hollow pNIPAM microgels using dynamic density functional theory (DDFT). Our scaling approach reproduces the experimental value of 2200 s for microgels of 50 micrometer radius without a cavity, at phi_p approximately 0.83 and 315 K.

Figures (7)

• Figure 1: Snapshots corresponding to the cells taken as the starting points for transfer free energy and diffusion coefficient calculations. The polymer density increases from left to right, as labeled. Temperature is 295 K for the top row and 315 K for the one at the bottom.
• Figure 2: Transfer free energy from bulk water to a water polymer mixture for phenol, a), 5-FU, b), and methane, c), as a function of the polymer volume fraction, $\phi_p$. Black and red curves and symbols correspond to 295 K and 315 K, respectively.
• Figure 3: Mean square displacement (MSD) as a function of time, $t$, for diluted phenol in pNIPAM-water mixtures at 295 K. The red and blue curves correspond to $\phi_p=$ 0.07 and 0.44, as labeled. Note that the MSD scales differ a couple of orders of magnitude (red left, blue right).
• Figure 4: Normalized diffusion coefficients as a function of $\phi_p$ for $295$ K (black) and $315$ K (red). The black and red dashed lines are fits to the corresponding data, $D/D_0=10^{-6.5\phi_p}$ and $D/D_0=10^{-5.5\phi_p}$, respectively.
• Figure 5: Normalized density profiles as a function of time for the diffusion of phenol through a pNIPAM membrane at 315 K by means of MD, a), and DDFT, b). We use dark green and thick lines for the pNIPAM profile at time zero, which is set as similar as possible for MD and DDFT. The thin lines with different colors correspond to phenol profiles at different times, as labeled. c) The normalized extent of membrane crossing. Black, red, and blue lines and symbols correspond to the right, membrane, and left cargo normalized densities. The normalization is made by taking the initial density at the right as a reference. Lines correspond to theory and symbols to simulations. The inset of panel c) shows the same data in a log-log representation.