Water ordering or disordering properties

Through perturbation

One of the hypotheses mentioned earlier is the possibility that AF(G)Ps and their mimics function by ordering or disordering surrounding water in order to inhibit

portant issues we aim to clarify during ice crystal growth as well as in solution. If

these oligomers are capable of distorting the bulk or hydrating water significantly,

one would expect to observe some of this activity in solution and at room tem- perature. In order to achieve this we characterised the water around the polymer by calculating the radial distribution functions (RDFs) of water oxygens (O) to the polymeric oxygens (OX), the hydration number and the orientational order of hydrating waters.

Fig. 4.8 shows the RDF results for each oligomer and highlights the probabil- ity of finding a water oxygen close to the polymeric oxygen. We find that these RDFs exhibit characteristic peaks for PVA at 0.28 nm (strong), 0.47 nm, 0.66 nm, 0.87 nm and 1.07 nm (weak), as well as for PEG at 0.28 nm, 0.48 nm (strong), 0.83 nm and 1.13 nm (weak). These positions agree with those reported by other similar studies and the shapes of the RDFs are comparable to theirs.[57,181–184]The probability of finding a water oxygen close to the polymer oxygen is highest at 0.28 nm, which is characteristic of hydrogen bonding between the two species, and declines on ap- proach to the bulk water, which is further away from the polymer. It is apparent that PVA has multiple peaks, all of which are more pronounced and narrower than cor- responding PEG polymers and indicates well defined hydration shells, with strongly confined water molecules. It is also describes the longer-range ordering induced by interactions with PVA, which is unsurprising because PVA has two atoms which are capable of hydrogen bonding with surrounding water molecules, while PEG only has one.

The RDFs for PEG have markedly taller peaks for the second shell than the first one, which hints at another type of interaction being prioritized for short range interaction with the oligomers. As a result there is also a higher probability that water will be found some distance away. One such example could be a preference for polymer-polymer interactions or some form of hydrophobic solvation. For both types of polymers the height of the peaks are reduced somewhat with increasing chain length. We attribute this to the ability of longer polymers to fold and tem- porarily mask or bury its own oxygen groups from waters around it.

(a) (b) Figure 4.8: RDF between water oxygen and polymer oxygen atoms at 298 K. Three repeats are included for each chain length.

(a) (b)

Figure 4.9: RDF between water oxygen and polymer oxygen atoms at 260 K. Three repeats are included for each chain length.

Because it is possible for the polymers to influence the structure of surround-

ing water molecules via hydrogen bonding or through hydrophobic interactions or both, we plot the RDF for water oxygens with polymeric carbons in Fig. 4.10. The relative importance of these interactions can also be evaluated through several other types of analysis; the solvent accessible surface areas, the hydrogen bonding as well as the RDF of both hydrophilic and hydrophobic groups in water. The O-CS RDFs for PEG reveal peaks at 0.38 nm which merges with a weak shoulders at 0.50 nm, and again for the next two weak peaks at 0.65 nm and 0.76 nm. In contrast, PVA

oligomers have well separated peaks at 0.37 nm, 0.51 nm and 0.79 nm, all of which are lower in height than for PEG. A comparison of the two RDFs for PEG oligomers (O-

OSand O-CS) indicates that water oxygens can approach more closely to the oxygen

atoms (0.28 nm) than the carbon atoms (0.38 nm), however the relative heights of the peaks may be indicative of a particular type of hydrophobic interaction. This

is further emphasised by the taller second shoulder in the O-OS RDFs, which con-

firm that the water oxygens are likely to be dispelled some distance away from the polymeric oxygen as a result of the hydrophobic repulsion. A similar comparison of the two RDFs of PVA reveals that waters largely reside at a distance of 0.28 nm and preferentially interact with its polymeric oxygen. Consequently, we can suggest that the PEG polymer largely interacts with solvent via hydrophobic interactions, while PVA does so via hydrophilic interactions provided by its hydroxyl side groups. These attributes remain true at cold temperatures, and the RDF peaks and troughs are simply more pronounced as a result of reduced thermal energy available for molecules to move outside of their respective shells.

(a) (b) Figure 4.10: RDF between water oxygen and polymer carbon atoms at 298 K.

(a) (b)

Figure 4.11: RDF between water oxygen and polymer carbon atoms at 260 K.

Through hydration indices

A histogram of hydration numbers is shown in Fig. 4.12 for both types of oligomers. Carbohydrates have previously been used to demonstrate the importance of hydra-

tion in IRI activity.[6,305] In order to consider this, we investigate the hydration

numbers of oligomers within a 0.35 nm cut-o↵ distance. The longer the polymer, the wider the distribution because more conformations are accessible and so the

hydrating water will also be altered just as much. Wefind a much narrower distri-

bution for PVA. Throughout the trajectory the 5-mers of both polymer encounter approximately the same number of waters with the same frequency. With polymers

larger than five units long, we find that PEG consistently has a larger hydration number than PVA. This too is reflected in the broader RDFs in Fig. 4.8 and is sur- prising as it indicates that more hydrophilic groups does not necessarily translate into larger hydration sphere, but could mean the reverse.

(a) (b)

Figure 4.12: Probability density showing the average hydration number of thewhole

polymer at 298 K.

(a) (b)

Figure 4.13: Probability density showing the average hydration number of thewhole

polymer at 260 K.

Through tetrahedral ordering

In Fig. 4.14 and Fig. 4.15 we plot the tetrahedral orientation of water and polymeric oxygens. We find a characteristic peak at 0.80 and a subtle shoulder at ⇠0.5 for

ordered and disordered regions respectively. In pure water, the transition from 298 K to 260 K caused an increase in tetrahedrality from 0.80 to 0.84, and in population from 2.55 to 3.32 (by approx. 30%). At both temperatures, we do not observe any remarkable tetrahedral ordering or disordering of the water oxygens within 0.35 nm of the polymeric oxygens, by either of the polymers nor as a function of chain length. A comparison of PVA and PEG polymers did reveal a weak 0.04 shift for the PEG simulations to disordered regions. No such shifts were observed for any of the PVA systems. Rather PVA exhibits a minuscule decline in heights of the ordered peaks.

This is reflected in the fact that the same transition from 0.80 (at 298 K) to 0.84 (at

260 K) in the presence of PVA5−56increased the population of the ordered region by just 25–28% and by 24–30% in the presence of PEG5−56. Generally, these disordering changes for both types of polymers are accompanied by a growing shoulder at⇠0.5, but it is important to stress that these changes are very faint.

(a) (b) Figure 4.14: Probability density distribution of the tetrahedral order parameter of interfacial water at 298 K. Interfacial water molecules lie within a 0.35 nm radius

from the polymer oxygen atoms. For each oxygen, the Q4 is calculated using its

four nearest neighbours. Error bars are stdevs between repeats.

(a) (b)

Figure 4.15: Probability density distribution of the tetrahedral order parameter of interfacial water at 260 K. Interfacial water molecules lie within a 0.35 nm radius

from the polymer oxygen atoms. For each oxygen, the Q4 is calculated using its

four nearest neighbours. Error bars are stdevs between repeats.

In order to account for the steric interferences from whole polymer the Q2

and Q3 values were also calculated for simulations at 298 K. The distributions from

these calculations are shown in Fig. 4.16 and Fig. 4.17 respectively. The Q2 and Q3

analyses are useful because steric obstruction from the polymers could prevent the approach of four neighbouring water molecules, while they may still be able to ac-

commodate clusters of two or three neighbours. As a result these distributions could prove to be better representations of the orientational order of surrounding water

molecules than the Q4distributions. The results reveal that the use of fewer water

molecules increases the likelihood that the oxygen atoms will simultaneously occupy the angles required to form tetrahedral arrangements. As a result the shoulders at

0.5 is reduced and any bimodal features are lost for Q2 and Q3 distributions of all

(a) (b) Figure 4.16: Probability density distribution of the tetrahedral order parameter of interfacial water at 298 K. Interfacial water molecules lie within a 0.35 nm radius

from the polymer oxygen atoms. For each oxygen, the Q2is calculated using its two

nearest neighbours. Error bars are stdevs between repeats.

(a) (b)

Figure 4.17: Probability density distribution of the tetrahedral order parameter of interfacial water at 298 K. Interfacial water molecules lie within a 0.35 nm radius

from the polymer oxygen atoms. For each oxygen, the Q3 is calculated using its

three nearest neighbours. Error bars are stdevs between repeats.

Compared to pure water, the results obtained for the Q2and Q3distributions

are not remarkably di↵erent to the polymeric systems, yet again. The Q4 results

for PVA suggest a slight decrease in tetrahedrality, while in Q3there appears to be

some small amounts of ordering, and no marked di↵erence in the Q2 analysis. For

di↵erence for both the Q2and Q3distributions.

In order to determine which of these distributions provides the most accurate description of the system, the average number of oxygen molecules which surround the polymeric oxygen atoms were also recorded. The results are shown in Fig. 4.18 and it reveals that each PVA oxygen atom is normally surrounded by 3 oxygen atoms, which can belong to either a water molecule or another polymeric oxygen.

The results from the Q3parameters therefore provide the most suitable description

of PVA at 298 K and 260 K. The same is also true for PEG oligomers, however there are occasions where the oligomers are equally as likely to have 2 oxygen atoms close to the polymeric oxygen. Regardless of the temperature, this never occurs for PVA

so only the Q3distributions were calculated for the polymeric systems at 260 K, and

the results are shown for PVA in Fig. 4.20. At the lower temperature, there is still

no significant ordering or disordering by the PVA or PEG oligomers compared to

pure water. This suggests that the tetrahedral ordering of surrounding liquid water may not be as important as first expected.

(a) (b) Figure 4.18: Probability density distribution of the number of oxygens which ap- proach the polymeric oxygen at 298 K. Error bars are stdevs between repeats.

(a) (b)

Figure 4.19: Probability density distribution of the number of oxygens which ap- proach the polymeric oxygen at 260 K. Error bars are stdevs between repeats.

Figure 4.20: Probability density distribution of the tetrahedral order parameter of interfacial water at 260 K for PVA oligomers. Interfacial water molecules lie

within a 0.35 nm radius from the polymer oxygen atoms. For each oxygen, the Q3is

calculated using its three nearest neighbours. Error bars are stdevs between repeats.