Polymer science: research advances, practical applications and educational aspects (A. Méndez-Vilas; A. Solano, Eds.)
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Effects of water adsorption in hydrophilic polymers
K. Kulasinski1
1
Chair of Building Physics, Swiss Federal University of Technology Zurich, ETH Zurich, Stefano-Franscini-Platz 5, 8093
Zürich, Switzerland
The origin of the adsorption-induced phenomena in hydrophilic polymers, such as cellulose, lies at the atomistic scale. We
use molecular dynamic simulations to investigate the mechanisms by which the adsorbing polymers change their
properties upon water adsorption. Despite of their limited spacial and temporal capabilities MD simulations are able to
reproduce the hygroscopic swelling and moisture softening effects in several natural polymeric systems, such as crystalline
and amorphous cellulose, hemicellulose, or lignin. The revealed picture of adsorption shows a complex dependency
between system porosity, water concentration, chemical potential and number of hydrogen bonds. Clear correlation
between the number of hydrogen bonds, porosity and mechanical moduli implies that the dynamics of hydrogen bonds is
an underlying mechanism of the adsorption process in hydrophilic polymers. The adsorbed water molecules, attracted by
sorption sites tend to break the hydrogen bonds between the polymer residues that are responsible for the mechanical
stability of the system. As a result, the number of hydrogen bonds decreases with water concentration which causes a
substantial decrease in elastic modulus. This plasticization effect causes the polymer matrix to yield under swelling
pressure exerted by the water molecules clustered in the nanopores under higher-than-bulk density. Thus, as the adsorbed
amount increases, the pore structure of the polymer evolves in such a way that the average pore size increases and the
pores merge. The evolution of the pores topology makes that the diffusion of water changes non-linearly with water
content. Highlighting the central role of hydrogen bonds in adsorption process helps understanding the concept of
hydrophilicity in polymers and enables further research in a more application-oriented direction, e.g. wood industry,
moisture sensors/actuators.
Keywords: adsorption; hydrophilicity; hydrogen bond; softening; swelling; porosity;
1. Introduction
The phenomenon of water adsorption in porous materials is of broad interest from physical and engineering point of
view [1]. In particular, the adsorption in microporous polymeric systems with hydrophilic properties draws the research
attention, as it concerns many common biological tissues and engineering materials, such as wood, grassy plants, or
some bacteria species [2]. The adsorption of water in such systems is known to induce reversible changes in their
structure which can be macroscopically observed as hygroscopic expansion, loss of mechanical stiffness, or even
moisture-induced shape memory effect. [3]
The origin of the adsorption-induced phenomena lies at the atomistic scale [4]. For this reason, the explanations of
these are researched through nanoscale-resolution experiments such as NMR [5], FTIR [4], or SAXS [6], as well as by
modelling approaches, e.g. molecular dynamics (MD) [7], Monte Carlo [8], or FEM [9] simulations. Despite of its
limited size and simulation time MD simulations are able to reproduce the hygroscopic swelling and moisture softening
effects in several natural polymeric systems, such as crystalline and amorphous cellulose, hemicellulose, or lignin.
The aim of this study is to understand the physics of adsorption-induced phenomena by studying different natural
hydrophilic polymers using Molecular Dynamics simulations. To this end, three different molecular systems has been
chosen: amorphous cellulose, galactoglucomannan – one of the major hemicelluloses and cellulose microfibril
consisting of crystalline cellulose core and amorphous hemicellulose. These polymers are naturally occurring in wood
cell wall and thus can be constructed and validated against available measurements [3,7,10,11]. The study addresses
changes of physical and mechanical properties of polymer and water during adsorption by investigating them at wide
range of water concentration – from dry state until saturation. The phenomena described here are not exclusive for
cellulosic materials and should be valid for any hydrophilic polymer system, since the subtleties in chemical
composition play minor role in the adsorption mechanism, as will be demonstrated.
2. Materials and methods
The presented results are obtained via Molecular Dynamics (MD) simulations using Gromacs 5.0.2 [12] with Gromos
53a6 force field [13]. The three studied structures, amorphous cellulose, cellulose microfibril, and hemicellulose
(galactoglucomannan) are initially constructed in the dry state and then subsequently hydrated to different water
concentrations, up to the respective saturation value [14]. The models are in full periodic boundary conditions in order
to minimize the finite-size effects. The simulations are carried out at 300 K regulated by Nosé-Hoover [15] thermostat
and at stress-free conditions by the applied Parinello-Rahman barostat [16]. The long-range electrostatic forces are
accounted for by implementing particle-mesh Ewald summation [17].
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The amorphous cellulose consists of randomly oriented three cellulose chains, each of 180 glucose residues [10,11].
The hemicellulose contains 4 amorphous chains consisting of mannose, glucose and galactose in 4:1:0.4 ratio [3,11].
The microfibril is a composite structure with 36 crystalline cellulose chains arranged in a form of rectangle and
surrounded by 10 hemicellulose chains [3]. The crystalline cellulose adsorbs water only on crystal surfaces and its high
stiffness along the chains plays an important role in adsorption process [3]. The models correspond to the regions
naturally occurring in softwood secondary cell wall layer and have been validated against available experimental data
[7].
The presented results are extracted from equilibrated 10 ns runs at constant water concentration. The chemical
potential of water molecules, equivalent to their free energy, is determined by one-step perturbation method [10,18].
The porosity or free volume is sampled by random water molecule insertion in a structure with all water molecules
removed [11]. This also allows estimating the local density of adsorbed water knowing their mass and the average
volume they occupy. Existence of a hydrogen bond, either water-polymer or polymer-polymer, requires a geometrical
criterion where the distance between donor and acceptor is smaller than 0.35 and the angle donor-hydrogen-acceptor is
smaller than 30° [19]. The energy of a hydrogen bond EHB can be estimated from the slope of potential energy, EP,
versus number of hydrogen bonds, NHB:
(1)
The elastic modulus E along direction X at a given concentration c is calculated by determining the system box
length in a given direction X at 0 stress and σ=100 MPa tensile stress,
(2)
with the tensile stress chosen in such a way that the system remains in the linear elastic regime. The diffusivity (selfdiffusion coefficient) D is calculated using Einstein’s equation that uses the linear part of the mean square displacement
of water molecules as a function of time t,
∑
(3)
where N is the number of molecules and r(t) is the ith molecule’s position at time t.
3. Results
3.1
Forces driving adsorption
Most of the biopolymers occurring in plants are hydrophilic to different extent meaning they are very likely to adsorb
the water molecules of their environment [20,21]. The attractive character of polymers like cellulose is a result of their
adsorption sites, the exposed OH bonds with a large dipole moment, that through Coulomb forces attract other polar
molecules such as water [1]. An example of cellulose residue with oxygen and hydrogen tagged red and white,
respectively, is presented in Fig. 1a. The bulk adsorption however would not be possible without a way for water
molecules to reach other sorption sites than those located on the surface. The amorphous regions of polymers are
characterized a porous structure with pore size typically below 1 nm that allows water molecules to diffuse into the bulk
polymer structure [11,22]. A system of connected pores of amorphous cellulose is shown in Fig. 1b.
The amount of adsorbed molecules (c) depend on the external chemical potential μ that is related to the relative
humidity RH through Kelvin equation,
RH
exp
(4)
where kB is Boltzmann constant, T is temperature and μsat is the chemical potential of the saturated vapor. The higher the
chemical potential, the higher the RH and thus the higher the water concentration. The dependence between chemical
potential (or RH) and concentration is the adsorption isotherm that is a characteristic of a material. The adsorption
isotherms of the studied polymeric systems are presented in Fig. 1c. Their typical exponential-like shape is a result of
the interaction with other water molecules. At the initial stage of adsorption, when the material is nearly dry, the water
molecules are dispersed more or less uniformly within the material’s pores such that the water molecules do not form
clusters and do not feel the presence of each other [10]. This phenomenon and the availability of the sorption sites,
whose binding energy is strongly negative, as will be shown later, makes that the chemical potential at the initial stage
of adsorption differs by 20 kJ/mol or more from the saturation state chemical potential. Arrival of next water molecules
into the pores increases the chemical potential as the water molecules start forming clusters and the ratio of sorption
sites to water molecules can easily exceed 1. This means that there are two types of adsorbed water molecules: those
being bound at sorption sites and those that are not. Not bound molecules are in a state close to bulk liquid and their
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relative amount increases with concentration by which the average chemical potential approaches that of saturated
vapor or, equivalently, liquid water. The state of adsorbed water will be further discussed in section 3.4.
The macroscopic phenomena such as swelling or weakening, studied further in section 3.3, require a thorough
understanding of the molecular processes occurring upon water adsorption. The key mechanism linking the chemical
potential to porosity, stiffness or water diffusion is the dynamics of formation and breaking of hydrogen bonds that will
be examined next.
a)
b)
c)
Fig. 1 (a) Schematic of hydrogen bonding (dashed lines) in cellulose. (b) Exemplary pore network of cellulose near saturation. (c)
Chemical potential of adsorbed water as related to the saturation potential.
3.2 Hydrogen bonds dynamics
The cellulose-like polymeric structures are characterized by a high density of hydrogen bonds (HBs) that stabilize, from
mechanical point of view, the whole structure, e.g. in amorphous cellulose it is up to 424 HBs per nm3 [20]. The density
of HBs depends on the crystallinity of the polymer as well as its composition. The HBs form between the sorption sites
either within the same chain or between different chains, in the latter case importantly reducing chain flexibility. It is
important to mention that HBs, unlike covalent bonds, are dynamic in a sense that they can easily break and (re)form
which depends only on the relative position and arrangement of donor and acceptor. The energy, and therefore the
strength, of a HB lies between that of covalent and Van der Waals bonds which can be easily deducted by comparing
the strength of crystalline cellulose in three different directions where a given interaction is predominant [23].
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a)
b)
Fig. 2 Evolution of hydrogen bonds network: (a) relative amount of hydrogen bonds as compared to the dry state, (b) average
energy of a water-polymer hydrogen bond in amorphous cellulose.
However, the topology of HBs can be changed by water molecules adsorbed in the pores of a hydrophilic system.
While diffusing into the pore structure the water molecules tend to occupy the most energetically favorable spots that
are usually the sorption sites which lead to a water-polymer HB formation. With some probability the presence of a
water molecule can lead to the breakage of a polymer-polymer HB. This competition can be easily observed by
determining the number of polymer-polymer HBs as a function of concentration. In Fig. 2a the relative amount of the
HBs as compared to the dry state is decreasing with the concentration of water. Depending on the type of polymer, the
total loss of HBs can be even 50%. The smaller loss in the case of cellulose microfibril is due to the unavailability of the
crystalline cellulose HBs to water. Interestingly, the loss of HBs is less pronounced at higher concentrations since then
most of the exposed HBs are already being broken and the relative amount of unbound water molecules is increasing.
The breaking of HBs is also happening due to steric repulsion of the polymer chains by the water clustered in pores
where the molecules are in denser state than the bulk liquid, as will be discussed in section 3.4.
The energy of a single HB (always negative) is found to be dependent on water concentration, as depicted in Fig. 2b.
Near the dry state the binding energy is of -5 kJ/mol on average and tends to increase by some 3-4 kJ/mol as the
concentration increases. The increase of the energy and thus decrease of binding force is caused mainly by the
‘disturbing’ presence of other water molecules. The relatively weaker water-polymer HBs make their average lifetime
shorter which in turn affects the water transport [24].
3.3
Macroscopic effects of adsorption on polymer
Breaking of polymer-polymer HBs leads to many effects, among which the overall loss of stiffness can be easily
observed macroscopically [21]. The average Young’s modulus as a function of water concentration is presented in Fig.
3a. Whereas for cellulose and hemicellulose the modulus is averaged over three orthogonal directions, the reported
values for microfibril are those for two directions perpendicular to the crystalline cellulose direction which due to
dominating covalent bonds shows little weakening [3,23]. The effect of weakening, particularly strong at low water
activities, diminishes near saturation as then most of the HBs are already broken. There is however other phenomena
that contribute to the weakening. The water molecules being present in large quantities in the pores, shield the longrange interactions, mainly electrostatic, between the polymers. Additionally, by a simple rule of mixtures it can be
demonstrated that the presence of water clusters is substantially decreasing Young’s and shear modulus (elastic
modulus of water is 0) whereas the bulk modulus is affected to less extent (limited by water bulk modulus of ca. 2 GPa)
[11].
As the water is being adsorbed the capacity of the initial dry pores becomes insufficient for taking up more water
molecules. The water molecules in effect make space for themselves by pushing away the polymer chains. This internal
stress leads to the overall increase in porosity as shown in Fig. 3b. The porosity is initially affected only by little by the
increasing concentration as the molecules are filling up the available pore space. At the later stage of adsorption,
however, the increase in porosity is linear with concentration which can be understood as each adsorbed molecule
contributes equally to the pore volume increase. It is worth noting that not only the size of pores but also their amount
changes [11].
The increase in porosity leads directly to the macroscopic observation of total volume change. The hygroscopic
swelling, presented in Fig. 3c, is found to be linear for most of the concentration range. It should be stressed out that the
linear swelling is possible only because the system as a whole losses its stiffness and therefore it requires less and less
energy for same amount of expansion. The whole process of adsorption has to be however regarded as a complex
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process where the chemical potential, HB energy and density, pore volume and stiffness are all linked together in a
mostly nonlinear way.
a)
b)
c)
Fig. 3 Macroscopic effects of water adsorption: (a) elastic modulus decreasing with water concentration, nearly linear (b) increase
of porosity and (c) the resulting hydroscopic (volumetric) swelling.
3.4
State of adsorbed water
The adsorption of water in polymer affects not only the state of polymer but also that of water. It was already mentioned
that water molecules form HBs changing their energy as the water concentration increases. Initially, near dry state,
water molecules are dispersed throughout the pore system forming clusters containing 1-2 water molecules (Fig. 4a).
The number of small clusters increases with concentration until c<5-10 nm-3. Around that value the clusters start to
merge and continue merging until the maximum water content is achieved (Fig. 4b). The merging obviously increases
the number of water molecules per cluster/pore [10]. Since growth of a pore is only possible by pushing away the
polymer chains, these exert a compressive pressure on water clusters increasing the local density of water.
The average local density of water clusters is shown in Fig. 4c. The density is found out to increase with
concentration, reaching 1.2-1.3 g cm-3 at the saturation, due to mechanic resistance of polymer. The relatively higher
density in the case of microfibril is due to the restraining function of the crystalline cellulose. The high density at
saturation finds confirmation in radial distribution function (RDF) of adsorbed water as compared to bulk liquid (Fig.
4d). Comparison of the two RDFs shows that not only the adsorbed water molecules are closer to each other but their
ordering is higher (more efficient arrangement). I has also been demonstrated that the net volume gain inserting single
water molecule to the system near saturation is smaller than per molecule volume of build liquid [25].
Interestingly, the diffusivity of water molecules is also varying with water concentration. At the initial stage of
adsorption, when most of the water molecules are bound to polymer sorption sites, the diffusion is barely observable.
However, upon increase of concentration and thus increase of non-bound water molecules, the diffusion coefficient
increases. The diffusion coefficient was found to depend on two factors: the relative time water molecules spend at the
sorption sites and the tortuosity, related to pore size (Knudsen diffusion), of the pore system [24]. Due to high local
density of water and complex pore system, the effective diffusion coefficient even at saturation is approximately one
order of magnitude smaller than that of bulk liquid [24].
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a)
b)
d)
c)
e)
Fig. 4 Water clusters (a) near dry state and (b) at saturation. (c) Radial distribution function of water oxygen in bulk liquid and
adsorbed phase. State of the adsorbed water changing with its concentration: (d) density in water clusters, (e) diffusion coefficient.
a)
b)
Fig. 5 Correlations between the determined properties with concentration as parameter: (a) elastic modulus vs. number of HB and (b)
diffusion coefficient vs. porosity.
4. Conclusion
The adsorption of water in hydrophilic polymers such as cellulose is a complex process that is mainly driven by the
formation and breaking of the hydrogen bonds. Due to porous character and flexibility of biopolymers, the water
molecules can easily adsorb being attracted by negative energy hydrogen bonds. It is worth noting that breaking of HBs
is a reversible process enabling the polymers to regain their original shape and stiffness upon desorption and is one of
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the main mechanisms in moisture-induced shape memory effects of wood tissue. Although the presented characteristic
are nonlinear and perhaps not straightforward to model, the strong correlation between the studied properties can be
readily seen when plotting directly one property against another using concentration as parameter. Figure 5 shows the
elastic modulus as a function of relative number of HBs (Fig. 5a) and diffusion coefficient versus porosity. These
relations, to some extent linear, demonstrate the coherence of the discussed phenomena.
The presented research partially fills up the missing knowledge in sorption-induced phenomena occurring in natural
systems containing hydrophilic polymers, such as wood. The applied methodology can be particularly useful in
understanding the process of functionalization of natural polymers, e.g. hydrophobization of sorption sites [26] and
facilitates upscaling to continuum approaches [25].
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