Structure and Hydrogen Bonding of Water in Polyacrylate Gels: Effects of Polymer Hydrophilicity and Water Concentration Sriramvignesh Mani, Fardin Khabaz, Rutvik V. Godbole, Ronald C. Hedden and Rajesh Khare * Department of Chemical Engineering, Texas Tech University, Box 43121 Lubbock, TX 79409-3121
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Structure and Hydrogen Bonding of Water
in Polyacrylate Gels: Effects of Polymer
Hydrophilicity and Water Concentration
Sriramvignesh Mani, Fardin Khabaz, Rutvik V. Godbole,
Ronald C. Hedden and Rajesh Khare*
Department of Chemical Engineering, Texas Tech University,
where the symbols O x and O x , y in the relations denote the oxygen atom belonging to the ‘x’
functional group and the oxygen atom belonging to the ‘x’ functional group in the ‘y’ monomer,
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respectively. We attribute the observed differences in water affinity to three factors: (1) The
hydroxyl group offers two possibilities for hydrogen bonding since both oxygen and hydrogen
atoms of the group can form a hydrogen bond with a water molecule (while carbonyl and alkoxy
groups offer only one possibility), (2) higher electron density around the carbonyl oxygen than
the alkoxy oxygen, and (3) steric environment of these groups, specifically, that the alkoxy group
is in a relatively crowded environment compared to the carbonyl and the hydroxyl groups.
III. C1. At low concentrations, water is well-dispersed in the polyacrylate systems and
predominantly forms hydrogen bonds with the polymer, while at high concentrations,
water forms clusters with predominance of water-water hydrogen bonding
Water-water RDF:
For studying the distribution of water molecules in the system, we first focus on the water-water
RDF (Figure S7 in Supporting Information) for polyacrylate gel systems containing identical
amounts of water (water mole fraction = 0.017 in all systems, which is the same as that measured
experimentally for the PBA gel swollen to equilibrium). The water-water RDF shows only one
peak for all systems with the peak height being the highest for PBA and the lowest for PHEA.
This observation can be explained as follows: Due to the presence of the hydroxyl group (in
addition to the carbonyl and alkoxy that are also present on BA), HEA monomer offers more
sites for hydrogen bonding than the BA monomer. Thus, water is more likely to be hydrogen
bonded to a polymer oxygen than to itself in PHEA gel. The effect also occurs to a smaller
extent in the P(BA50-HEA50) copolymer gel.
Water clustering at low water concentration:
Information about the distribution of water molecules in the system can be obtained by
quantifying the probability of water molecule cluster formation. In this analysis, two water
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molecules were considered to be in the same cluster if the distance between their oxygen atoms
was less than the cluster cut-off distance value of 3.5 Å. This value of the cluster cut-off
distance corresponds to the location of the first minimum in the water-water RDF. Following the
approach used in the literature,22,26 the algorithm employed for this purpose consisted of picking
a water molecule at random and searching for another water molecule lying within the specified
cluster cut-off distance from it. If a molecule(s) was found, it was added to the cluster. The
process was continued until all water molecules that reside within the cluster cut-off distance of
any of the molecules in the cluster were found. Figure 6 displays the cluster size probability
distribution (ordinate is the probability that a randomly chosen water molecule will belong to the
cluster of a given size) for the three polymer gel systems containing the same amount of water
(i.e. same mole fraction of water as that in the PBA gel swollen to equilibrium). As seen for this
case, the cluster size probability distribution is the same for all three polymers with most of the
water molecules
existing as single molecules in the system, and only about 15% existing in the form of pairs. We
also note that ethanol is present at low concentration in all of the systems (as seen from Tables
1.1 and 1.2) and the clustering behavior of ethanol is very similar to that of water (Figure S8 in
Supporting Information) in systems with low water content.
Figures 4 (see earlier text), 7a and 7b show the probabilities of water-water and water-
polymer hydrogen bond formation for a water molecule in the PBA, P(BA50-HEA50) and
PHEA gel systems (all with water mole fraction = 0.017) respectively. As seen from these
figures, when the water concentration in the system is low, the water molecules predominantly
form hydrogen \bonds with polymer with the probability of forming a hydrogen bond with
another water molecule being very small.
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Figure 7a. Hydrogen bond probability distribution in P(BA50-HEA50) gel with water mole
fraction = 0.017.
Figure 6. Cluster size distribution of water molecules in polyacrylate gels with water mole
fraction = 0.017. Results are shown using the following symbols: PBA (solid black circle),
P(BA50-HEA50) (solid red triangle) and PHEA (solid blue diamond).
Effect of water concentration on the clustering behavior:
The effect of water concentration on the cluster formation behavior can be determined by
studying the cluster size distribution in the three gels (PBA, P(BA50-HEA50) copolymer, and
PHEA) that are swollen to equilibrium. As was seen in Table 2, there is a large difference in the
water content in the three systems, which could affect the clustering behavior of water in these
systems. Figure 8 presents a comparison of the water cluster size distribution in the three gels
that are swollen to equilibrium. The main observation from this figure is that water forms very
large clusters in the P(BA50-HEA50) copolymer and PHEA gel systems. In fact, even though
PHEA is highly hydrophilic, still almost all of the water molecules in the PHEA gel reside within
a single cluster rather than being distributed throughout the polymer matrix.
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Figure 7b. Hydrogen bond probability distribution in PHEA gel with water mole fraction =
0.017.
The effect of water concentration on the probability of water-water and water-polymer
hydrogen bond formation can be seen by comparing the results presented in Figures 9 and
Figure S9 in Supporting Information with those presented earlier in Figures 7a and 7b.
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Figure 9. Hydrogen bond probability distribution in PHEA gel swollen to equilibrium.
Figure 8. Cluster size distribution of water molecules in gels swollen to equilibrium. Results
are shown using the following symbols: PBA (in inset) (solid black circle), P(BA50-HEA50)
(solid red triangle) and PHEA (solid blue diamond).
A key observation from these figures is that unlike the behavior at low water
concentration (seen earlier in Figure 7a and 7b), when water concentration is high, water
predominantly forms hydrogen bonds with other water molecules rather than forming hydrogen
bonds with the polymer.
In summary, the following conclusions can be drawn for the effects of water
concentration on the distribution of water molecules in the swollen gel systems. If there is
scarcity of water, in all polymers studied, a majority of water molecules are in an unassociated
state with only a small fraction (~ 15%) forming pairs. Also, water predominantly forms
hydrogen bonds with the polymer functional groups rather than with other water molecules at
this low concentration. As water concentration increases, water begins to form clusters
accompanied by the formation of a larger number of water-water hydrogen bonds than water-
polymer hydrogen bonds. For the system with the highest water concentration (PHEA gel
swollen to equilibrium), water predominantly forms hydrogen bonds with other water molecules,
and most of the water molecules associate into a single, very large cluster.
III.D. Increase in water concentration accelerates hydrogen bond dynamics of water
molecules, whereas an increase in polymer hydrophilicity slows down hydrogen bond
dynamics of the water molecules near the polymer sites
In addition to the static properties like the probability of hydrogen bond formation and
water clustering, the hydrogen bond dynamics of water molecules are also of interest from the
point of view of pervaporation based separation using polymer membranes. As water molecules
move, the hydrogen bond network gets continuously broken and reformed over time. The
dynamics of the hydrogen bonds were quantified by calculating the time autocorrelation function
(ACF) defined as follows:30, 70, 72-74
27
C ( t )=⟨h (0 )h (t )⟩⟨h2( t )⟩ (6)
In this expression, <…> represents the ensemble average over all hydrogen bonding pairs in the
system. The function h (t ) takes a value of either one or zero as follows. If a particular tagged
(i.e. hydrogen bonded at timet=0 ) pair of molecules is hydrogen bonded at time t, h (t )=1 ;
otherwise h (t )=0 . Based on this expression, the ACF can be calculated in two ways70: (1) For a
continuous time ACF, h (t ) takes a value of 1 only if the same tagged molecules remain hydrogen
bonded continuously from time t=0 to time t , and (2) For an intermediate time autocorrelation
function, h (t ) takes a value of 1 if the same tagged molecules that were hydrogen bonded at time
t=0 are also hydrogen bonded at time t (irrespective of the hydrogen bonding state at
intermediate times). In what follows, we only report results for the continuous time
autocorrelation function; the results for the intermediate time autocorrelation function are
qualitatively similar, although the decay of the ACF is slow for that case. We note that any
motion of the water molecule – by translation, rotation or vibration – that can break an existing
hydrogen bond, will lead to a decay of the continuous time ACF.
Figure 10 shows the continuous time ACF of water-water hydrogen bonds in
polyacrylate gels that are swollen to equilibrium. The correlation function decays rapidly for
PHEA and the P(BA50-HEA50) copolymer systems, while it decays slowly for the PBA system.
Noting that there is a significant difference in the water content of these systems (Table 1.1), we
conclude that the higher water content in PHEA and the P(BA50-HEA50) copolymer systems
28
provides greater opportunities for hydrogen bond formation with other water molecules, thus
leading to frequent break-up and formation of water-water hydrogen bonds.
This effect is more clearly seen in inset of Figure 10, which presents a comparison of
water-water hydrogen bond ACF in PHEA gel systems with different water contents: the PHEA
gel swollen to equilibrium (high water content) and the PHEA gel containing the same mole
fraction of water as the PBA gel that was swollen to equilibrium (low water content). Inset of
Figure 10 clearly shows that the ACF decays very rapidly for the PHEA gel with high water
content, whereas the decay is much slower for the PHEA gel with lower water content. The
presence of a large number of water molecules in the high water content systems allows the
29
Figure 10. Dynamics of water-water hydrogen bonds as captured by the continuous ACF,
results are shown for the gels that are swollen to equilibrium. Symbols are: PBA gel – solid
black circle, P(BA50-HEA50) copolymer gel – solid red triangle and PHEA gel – solid blue
diamond. Inset: Comparison of continuous ACF of water-water hydrogen bonds in PHEA gels
containing different amounts of water. Results are shown for the PHEA gel with water mole
fraction = 0.017 (low water content, dashed line) and PHEA gel swollen to equilibrium (high
water content, solid line).
water molecules to break existing water-water hydrogen bonds and readily form new ones with
other water molecules, thus accelerating hydrogen bond dynamics in this system.
30
The effect of polymer hydrophilicity on the dynamics of hydrogen bonds is also of
interest. For this purpose, we focus on hydrogen bond dynamics in three polyacrylate gels that
have the same water mole fraction as that in the PBA gel swollen to equilibrium. We focus only
on the dynamics of the water-polymer hydrogen bonds, since as seen from Figures 4, 7a and 7b,
almost all of the hydrogen bonds in these systems are those between water and polymer. The
rate of decay of the ACFs for the PHEA and the P(BA50-HEA50) copolymer gels (see Figure
11) is about the same and is smaller than that for the PBA gel. This observation suggests that the
local mobility of water molecules is much lower near the highly hydrophilic hydroxyl group,
which is present only in the PHEA and the P(BA50-HEA50) copolymer gel systems. We note
that this observation is consistent with a previous literature report that water molecules have
smaller density fluctuations near hydrophilic surfaces than near hydrophobic surfaces.75
31
Figure 11. Continuous ACF for water-polymer hydrogen bonds in the gels with water mole
fraction = 0.017. Following symbols are used: PBA gel – solid black circle, P(BA50-HEA50)
copolymer gel – solid red triangle and PHEA gel – solid blue diamond.
Finally, an inspection of the ACF for the water-polymer hydrogen bonds in the gel
systems swollen to equilibrium (Figure S10 in Supporting Information), indicates that there are
relatively small differences in the dynamics of water-polymer hydrogen bonds in these systems.
It appears that this behavior is a result of the interplay of two opposing factors. Comparing PBA,
P(BA50-HEA50) copolymer and PHEA gels, water content in the swollen systems increases as
HEA content in the polymer increases, thus accelerating hydrogen bond dynamics. At the same
time, polymer hydrophilicity also increases, which slows down hydrogen bond dynamics.
IV. Summary and Conclusions
We carried out MD simulations to study the effect of water concentration and polymer
hydrophilicity on the structure and hydrogen bonding of water in a set of polyacrylate gel
structures. The model structures of linear polyacrylates were first prepared and validated by
comparing their thermal and volumetric properties – glass transition temperature and density –
with experimental values; good quantitative agreement was found for these properties.
Subsequently, model structures of polyacrylate gels swollen by a dilute ethanol mixture were
prepared; these were used to study the water structure and hydrogen bonding in the polymers.
Large differences were observed between the affinities of water molecules for the
hydrophilic functional groups in the polyacrylates: water had the highest affinity for the hydroxyl
groups due to their ability for the formation of two hydrogen bonds, while its affinity was the
lowest for the alkoxy group, presumably due to a combination of lower electron density around
this group and the steric effects. Water concentration was found to have a significant influence
on the structure of water in the polyacrylate gels. In particular, at low concentrations, water
molecules were well-dispersed in these gels and predominantly formed hydrogen bonds with the
polymer. On the other hand, at high concentrations, water was found to form clusters with a
32
predominance of water-water hydrogen bonding accompanied by acceleration of hydrogen bond
dynamics of water molecules. This dependence of system properties on water concentration is
coupled with the dependence on polymer hydrophilicity, since the gels formed by hydrophilic
polymers have a larger water content when swollen to equilibrium. For the gels with the same
water concentration, an increase in polymer hydrophilicity was found to retard hydrogen bond
dynamics of the water molecules near the polymer functional groups. The local mobility of
water molecules was inferred from hydrogen bond dynamics. The local mobility influences the
long length scale translational mobility that is quantified by diffusivity, which is a topic of
current interest. Finally, the distribution of alcohol molecules in the swollen gels is also of
interest from the point of view of separation processes. Alcohol is typically present at very low
concentrations in the product formed by the enzymatic hydrolysis of cellulosic biomass. At
these low concentrations, ethanol did not form clusters in the polyacrylate gel systems.
The interplay between water concentration and polymer hydrophilicity in determining the
structure and local dynamics of water molecules that is elucidated here is useful for interpreting
the results from the laboratory experiments. For example, experimentally, diffusion coefficient
values are measured either by monitoring initial water uptake in a dry gel or the initial mass loss
from a swollen gel. There is a large difference in the water content of these – dry gel and
swollen gel - experimental systems. Our simulation results suggest that the clustering of water
molecules in the high water content systems will lead to a higher diffusion coefficient (since
water will predominantly diffuse through the water cluster rather than through the polymer
matrix) than that measured from the low water content systems. Further quantitative
investigation of this phenomenon is currently underway. This work shows that, in general,
molecular simulations can be used to decipher the mechanisms underlying the concentration
33
dependence of penetrant diffusion coefficient that is commonly observed in systems containing
strongly interacting components.
Acknowledgments
This material is based on the work supported by the National Science Foundation under
the Grant number: NSF CMMI-1335082. The authors also acknowledge the computational
resources provided by the Texas Advanced Computing Center (TACC) at The University of
Texas at Austin for performing the molecular simulations.
Supporting Information
1H NMR spectrum of HEA homopolymer in DMSO-d6, 1H NMR spectrum of BA
homopolymer in CDCl3, 1H NMR spectrum of 50/50 mol% BA/HEA copolymer in CDCl3 and
DMSO-d6 are shown in Figures S1a, S1b, S1c and S1d, respectively. Cluster size distribution
of ethanol molecules in gels swollen to equilibrium is presented in Figure S2. Continuous ACF
for water-polymer hydrogen bonds in the gels swollen to equilibrium is shown in Figure S3.
34
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For Table of Contents (TOC) Use Only
Structure and Hydrogen Bonding of Water in Polyacrylate Gels: Effects of Polymer
Hydrophilicity and Water Concentration
Sriramvignesh Mani, Fardin Khabaz, Rutvik V. Godbole,