On the Behavior of the Ethylene Glycol Components of Polydisperse Polyethylene Glycol PEG200

Abstract

Molecular dynamics (MD) simulations are reported for [polyethylene glycol (PEG)200], a polydisperse mixture of ethylene glycol oligomers with an average molar weight of 200 g·mol^-1. As a first step, available force fields for describing ethylene glycol oligomers were tested on how accurately they reproduced experimental properties. They were found to all fall short on either reproducing density, a static property, or the self-diffusion coefficient, a dynamic property. Discrepancies with the experimental data increased with the increasing size of the tested ethylene glycol oligomer. From the available force fields, the optimized potential for liquid simulation (OPLS) force field was used to further investigate which adjustments to the force field would improve the agreement of simulated physical properties with experimental ones. Two parameters were identified and adjusted, the (HO)-C-C-O proper dihedral potential and the polarity of the hydroxy group. The parameter adjustments depended on the size of the ethylene glycol oligomer. Next, PEG200 was simulated with the OPLS force field with and without modifications to inspect their effects on the simulation results. The modifications to the OPLS force field significantly decreased hydrogen bonding overall and increased the propensity of intramolecular hydrogen bond formation at the cost of intermolecular hydrogen bond formation. Moreover, some of the tri- and more so tetraethylene glycol formed intramolecular hydrogen bonds between the hydroxy end groups while still maintaining strong intramolecular interactions with the ether oxygen atoms. These observations allowed the interpretation of the obtained RDFs as well as structural properties such as the average end-to-end distances and the average radii of gyration. The MD simulations with and without the modifications showed no evidence of preferential association of like-oligomers to form clusters nor any evidence of long-range ordering such as a side-by-side stacking of ethylene glycol oligomers. Instead, the simulation results support the picture of PEG200 being a random mixture of its ethylene glycol oligomer components. Finally, additional MD simulations of a binary mixture of tri-and hexaethylene glycol with the same average molar weight as PEG200 revealed very similar structural and physical properties as for PEG200.

Figure 1

(a) Diethylene glycol as an example of ethylene glycol oligomers that make up PEG200 and H-[O-CH₂-CH₂]_n-OH shown with the distance between the oxygen atoms of the terminal hydroxy end groups used in this report as a measure for the end-to-end distance and changes to the hydroxy partial charges explored in this report; (b) illustration of the proper dihedral angle referred to as (HO)–C–C–O in this report for which its potential energy was changed; (c) illustration of possible hydrogen bonding interactions: (A) intramolecular hydrogen bonding between hydroxy end groups (OH–OH), (B) intramolecular hydrogen bonding between hydroxy end group and an ether oxygen atom (OH–OE), and (C,D) is the same as (A,B) but between two different molecules, i.e., intermolecular hydrogen bonding.

Figure 2

Snapshots from MD simulations of PEG200 using the OPLS force field with clustered starting position (a–c) and random starting position (d–f) obtained after energy minimization (a,d), NPT equilibration (b,e), and NVT production run (c,f).

Figure 3

Effects on (a) OH–OH and (b) OH–OE hydrogen bonding from modifying the OPLS force field (unmodified: open circles, modified, and open squares) for MD simulations of 250 H-[O-CH₂-CH₂]_n-OH oligomers by using 1/2 the value of the (HO)–C–C–O dihedral potential energy and (c) of all OPLS force field modifications tested (see Table 4) on the hydrogen bonding of heptaethylene glycol (n = 7): changing proper (HO)–C–C–O dihedral potential to 1/2 (“1/2 Dih.”) or 1/4 (“1/4 Dih.”) of the original value and lowering the polarity of the OH functional group by reducing the magnitude of charges on the hydrogen and oxygen atoms (“1/2 Dih. OH l.p.” and “1/4 Dih. OH l.p.”).

Figure 4

Adjusted ratio of intra- over intermolecular hydrogen bonds between hydroxy hydrogen and (a) hydroxy oxygen and (b) ether oxygen for each oligomer with itself in PEG200 obtained from MD simulations at 328 K using the OPLS force field (circles) and modified (see Table 4) OPLS force field (squares). The ratio numbers were adjusted by the number of possible intra- and intermolecular hydrogen bonds, the respective oligomer mole fraction, and a scaling factor depending on the number of oligomer components as discussed in the text.

Figure 5

Probability distribution of dihedral (HO)–C–C–O angles (see scheme 1) in tetraethylene glycol obtained from MD simulation of PEG200 at 328 K using the OPLS force field (black thin line) and the modified OPLS force field according to Table 4 (red thick line).

Figure 6

Snapshot showing a selected triethylene glycol (a) and tetraethylene glycol (b) oligomer obtained from an MD simulation of PEG200 at 328 K simulation with the unmodified OPLS force field. These typical structural configurations were more dominant in simulations with the modified OPLS force field.

Figure 7

Normalized intramolecular RDFs obtained from simulating PEG200 at 328 K with the OPLS force field (left panel) and the modified (see Table 4) OPLS force field (right panel).

Figure 8

Intermolecular RDFs obtained from simulating PEG200 at 328 K with the OPLS force field (left panels) and the modified (see Table 4) OPLS force field (right panel).

Figure 9

(a) Average end-to-end distance of ethylene glycol oligomers of hydroxy oxygen atoms in and (b) average radii of gyration of ethylene glycol oligomers, HO(CH₂CH₂O)_nH in PEG200 simulated by OPLS force field (circles) and modified OPLS force field (squares). Data points for a binary mixture of tri- and hexaethylene glycol simulated with an OPLS force field (plus) and a modified OPLS force field (cross) are included. Solid lines are linear fits where the tetraethylene glycol data point was excluded. Standard deviations are included in (a) and a dashed line for comparison in the case where oligomers are in a completely stretched linear configuration. Error bars in (a) are similar in magnitude to square symbols but are omitted to reduce clutter. Error bars are omitted in (b) as they would be smaller than the size of the symbols. Also shown as dotted line in (a) is a fit to the data with the worm-like-chain model with a persistence length of 0.3791 nm.