Modeling Temperature & Ionic Strength Structural Dependence

Figure 6.1.4.1: Calculated deuterium order parameter (SCD) as a function of temperature and

ionic strength for the 6 force fields tested. Transition temperature (Tr) from a more ordered

bicelle structure (SCD > 0.35) to a more disordered micelle structure (SCD ≈ 0) is indicated for

Lastly, we analyze the effects of temperature and ionic strength on the structure of SDS micelles, and examine the effect of counterion condensation on phase transition behavior. Using a preassembled bilayer of 100 SDS molecules, we varied the temperature between 248K and 298K, and ionic strength from 0M to 3.2M. From experimental studies on anionic surfactants, it is known that increased ionic strength leads to an increase in the phase transition temperature (Ttr) from an ordered to disordered phase252. We calculated the deuterium order parameter (SCD)

of the hydrocarbon tails of the SDS molecules, where it is expected that a more ordered bicelle structure will have a higher SCD value than a micelle structure, and the Ttr in our simulations can

be approximated as the inflexion point for this change in SCD value. As illustrated in Figure

6.1.4.1, the trend of ionic strength and Ttr is reflected across all force fields tested, although the

absolute Ttr values and the shift in Ttr values between zero and high ionic strength environments

do vary.

To determine the details of counterion condensation on phase transition we further analyzed the distribution of ions around the SDS head group by computing the weighted number of ions present in the first two solvation shells. Based on the RDFs calculated (data not shown), the 1st and 2nd solvation shell peak at ~0.35nm and ~0.55nm respectively, and this solvation pattern is consistent across all force fields tested. We calculated the weighted count of ions present in each shell, where ion count in the 2nd shell was scaled by a factor of 0.4 to reflect the 1/r2 falloff of the electrostatic contributions of the ions in the 2nd shell relative to the 1st shell, where r is the distance of the solvation shell as observed in the RDFs. Therefore, when counting the number of ions in the second shell, we scaled it by a factor of (1 0.55⁄ )

2

(1 0.35⁄ )2 = 0.4, in order to

as it served as the reference point for the weighting procedure. The sum of these two counts would then give the weighted count of ions used in our analysis.

Figure 6.1.4.2: (a) The high correlation between the total ion count (Nt) and predicted transition

temperature (Ttr), suggest that ion condensation is a primary determinant for predicting Ttr value.

(b) Moderate correlation was observed between the difference in total ion count (ΔNt) and the

difference in phase transition temperature (ΔTtr) when moving from a zero to high ionic strength

environment.

Figure 6.1.4.3: Breakdown of the weighted number of ions present in the 1st and 2nd solvation shell for all 6 force fields tested. While there are no distinct trends across 1st gen ion parameters, all 2nd _{gen ion parameters predict that the contribution of ions in the 2}nd _{solvation shell outweigh}

those from the 1st solvation shell by a factor of 2 to 2.5.

As shown in Figure 6.1.4.2a, the total ion count across both shells was well correlated to the predicted Ttr with R2 = 0.77, indicating that counterion condensation around the SDS head

group is the main determinant of the shift in Ttr. By breaking down the contribution of

counterions as a function of their solvation shells (Figure 6.1.4.3), there is apparently no consistency across all 1st gen ion models. Specifically, contributions from both the 1st and 2nd shell are equivalent across all ionic strength environments tested for the CHARMM36 force field, whereas the GROMOS45A3 force field predicts that 1st shell ion effects are dominant. For GROMOS53A6, there are effectively zero ions in the 1st shell, which suggests that the force field predicts that Na+ _{interacts with the anionic head group of SDS exclusively via water-mediated}

interactions. On the other hand, all 2nd-gen ion models are qualitatively identical and predict that contributions of the 2nd shell outweigh those of the 1st shell across all ionic environments by a factor of ~2 to ~2.5. Interestingly, up to this point, both GROMOS53A6 and GROMOS53A6KBFF force fields are effectively indistinguishable based on macroscopic results, such as SDS micelle structure (formation of crystalline patches), phase transition temperature and its dependence on ionic strength. However, the two force fields are distinctly different in the ionic “microstructure” near the SDS head group. This suggests that experimental data that measures the number of ions in the 1st and 2nd solvation shell can be used as a further means of tuning and validating the finer considerations of the force field. An alternative interpretation of these results is that obtaining the correct details of the microstructure around ionic groups may not be necessary for reproducing the desired properties on the macroscopic scale.

It is also interesting to note that the width of the change in phase transition temperature (ΔTtr) upon changing the ionic strength is also dependent on the force field. Specifically,

CHARMM-based force fields have a ΔTtr of ~20K, whereas GROMOS-based force fields have a

between the difference in ion count (ΔNt) and the difference in phase transition temperature

(ΔTtr). While our results suggests that the differential ion condensation is contributing to the

predicted ΔTtr, the effects of van der Waals interactions, which should not be expected to the

same across different force field families may also play a role in determining the width of the ΔTtr values as a function of ionic strength.