Fig. 1 displays the variation in the radius of gyration (Rg) with f, where we also designate the maximum and minimum values of Rg with error bars.
In order to clearly manifest the significant effects contributed from water, we repeat the simulation on the same system, however, the water is treated implicitly as a comparison. To clarify, the solvent is taken into account as a continuum dielectric with a dielectric constant. It clearly shows that with the same charge density f, the value of Rg for the PMAA chain when the water is treated via a F3C model is greater than that when the water is treated implicitly. This indicates that the existence of real water causes a greater degree of stretching in the charged polymer chain. As the charge density f increases, due to the fact that the repulsive degree of the electrostatic interactions between the COO- groups becomes more significant, Rg shows an increasing behavior. Later we will show that the organization of water molecules surrounding the PMAA chain also plays an important role in the PMAA chain conformation behavior.
Figure 1. Plot of the radius of gyration (Rg) of PMAA versus charge density f when the solvent water is treated explicitly via a F3C model and implicitly via a continuum dielectric, respectively.
In aqueous solutions, the hydration behavior of molecules is a complex subject, but worth further exploration. In order to investigate the distribution of water molecules surrounding the PMAA chain, we analyze the radial distribution functions of the oxygen (O) and hydrogen (H) atoms of water with respect to the O atom in the COO- group, the O atom of carbonyl (-C=O) in the COOH group, and the O atom of hydroxyl (-OH) in the COOH group of the PMAA at various values of charge density f, in Figs. 2 and 3, respectively, This radial distribution function gA-B(r) indicates the local probability density of finding B atoms at a distance r from A atoms averaged over the equilibrium density. In Fig. 2, where the distribution of water (H and O atoms) is analyzed from the central O atom in the COO- group, we observe two prominent peaks for the hydrogen RDF profiles and one for the oxygen RDF profiles regardless of the charge density f values. The observed high and sharp first peaks as well as the first minimum values close to 0 for both gO(COO
-)-H and gO(COO
-)-O manifest the fact that these COO- groups are strongly hydrophilic in nature and therefore attract a large amount of water molecules to form shell-like layers surrounding them. In addition, the first peak of the hydrogen RDF profiles occurs at 1.4 Å, which is less than the normal hydrogen bonding length of 1.8 Å [13], indicating that the interaction between the O atom of the COO- group and the H atom of the water molecule is stronger than the strength of hydrogen bonds in bulk water. This is expected as polar water molecules and negatively charged oxygen atoms have a stronger interaction than in bulk water.
Figure 2. The radial distribution functions of oxygen (O) and hydrogen (H) atoms of water with respect to the O atom in the COO- groups at various values of charge density f.
Next, we discuss the distribution of water surrounding the COOH group, as shown in Fig. 3. we find the height of the first peaks in Fig. 3 is less than 1, i.e., the local water density surrounding the COOH groups is even smaller than that of bulk water. To clarify, only a small amount of hydrogen bonds form between the water molecules and the COOH groups.
Indeed, for the noncharged PMAA case (f = 0), we
observe that when the distance from the COOH group is smaller than Rg (≒10Å), all the water distribution profiles are far less than 1.0. This indicates that the COOH groups appear to be less hydrophilic in nature and therefore fewer water molecules could remain inside the coiled PMAA chain.
(a) (b)
Figure 3. The radial distribution functions of hydrogen (H) atoms of water with respect to the O atom of -C=O and -OH in the COOH groups at various values of charge density f.
Fig. 4(a) presents the vibration spectra of the water oxygen types, O0, O1, and O2, which are obtained by applying the Fourier transformation to the VACF profiles. O0, O1, and O2 belong to the water molecules in the bulk state, with a single hydrogen bond formed with the COO- group, and with two hydrogen bonds formed with the COO- groups, respectively. The O0 spectrum shows a major peak centered around 58cm-1 and a broad shoulder peak at around 200-300cm-1, which has been observed in other MD studies [14,15]. When water molecules have stronger interactions with charged COO- groups, through the formation of the hydrogen bonds (O2 > O1
> O0), we observe that both spectrum peaks shift to higher wavenumbers. Worthy of note, is that the second peak of the O2 spectrum (i.e., the bridged water molecules between two neighboring COO -groups) moves significantly toward 400cm-1. Moreover, the second peak becomes more significant while the first peak shows an opposite trend. Similar to the low frequency Raman spectra of liquid water reported by Walrafen et al.[16], these results imply that the second peak is primarily associated with the H-bonded O-O intermolecular stretching vibration, whereas the first peak is attributed to the non-H-bonded molecules. In Fig. 4(b) we present the hydrogen spectrum, which is typically related to the libration (400-1200cm-1), intramolecular bending (1200-2200cm-1) and intramolecular stretching (2200-4000cm-1) motions. It is apparent that the presence of the charged COO- groups has a significant influence on the resulting hydrogen spectrum. The hydrogen atoms are divided into four types of H0, H1y, H1n, and H2. Note, for the water molecules with only one hydrogen bond formed with the COO- group, the two types of hydrogen-bonded and non hydrogen-bonded
H atoms are denoted as H1y and H1n, respectively.
We find that for the H1y and H2 atoms, which are strongly connected to the oxygen atoms of the COO -groups, both the libration and bending peaks shift significantly from a lower frequency for H0 towards a higher frequency, whereas the stretching peak shifts oppositely. For the H1n atoms, which are not directly adsorbed into the oxygen atoms of the COO- groups, the shifting degrees of the main peak positions are not as significant as those obtained from the strongly bonded H1y and H2 atoms.
(a)
(b)
Figure 4. Vibration spectra of (a) oxygen and (b) hydrogen atoms of water in different interaction states with the COO -groups.
CONCLUSION
We employ all-atom molecular dynamics simulations to study a single molecule of PMAA at
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Since bridged water molecules significantly limit torsional and bending degrees of the backbone monomers, it is reasonable to conclude that the rod-like chain conformation, exhibited by the strongly charged polymer chain, is significantly enhanced via the bridged water. Furthermore, this influence slows down water diffusion and enables the two characteristic peaks of the oxygen spectrum to shift to higher frequencies. When water molecules bridge between two neighboring COO- groups, we observe a significant increase to the second peak of the corresponding oxygen spectrum ( 100cm≈ -1). This is not surprising since the second peak is mainly attributed to the H-bonded O-O intermolecular stretching vibration. In addition, the strong H-bonded interaction also causes a respective increase of 386 cm-1 and 111cm-1 to the libration and bending peaks of the hydrogen spectrum and a decrease of 151cm-1 to the stretching peak.
ACKNOWLEDGMENTS
This work was supported by the National Science Council of the Republic of China under Grant Number NSC-94-2212-E-110-005, NSC-095-SAF-I-564-623-TMS, and NSC 95-2221-E-002-155.
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