Structural model of native cotton cellulose
Existing structural models of cellulose explain many physicochemical properties. However, for a more detailed study of sorption properties of cellulose, it is necessary to take into account the formation of a porous system between structural elements and the distribution of adsorption centers on cellulose active surface. Hence, the above structural models need to be clarified.
We propose the model of structural organization of cotton cellulose with the crystallinity of 0.7 (Fig. 1) based on the above review and results of our researches (Grunin et al. 2017, 2018). Cellulose macrofibril is formed by four partially co-crystallized MFs, each of which consists of four EFs, interconnected by relatively weak donor–acceptor hydrogen bonds. MF has an average transverse size of 60–80 Å and a length of up to several micrometers. The internal layered structure of EF is an alternation of aggregates of central and angular chains within the two-chain monoclinic unit cell (cellulose Iβ). The distance between adjacent EF layers in planes with the type (1,1,0), (− 1,− 1,0) and (− 1,1,0), (1,− 1,0) is 6 Å and 5.4 Å, respectively (Nishiyama et al. 2008; Li and Renneckar 2011). According to Dubinin’s classification (Dubinin and Kadlec 1987), pores between structural elements of cellulose are classified as micro- and mesopores. This model allows visualizing the process of water adsorption on active cellulose surface.
Authors (Brown 2004; Verlhac et al. 1990; Nishiyama et al. 2003) proposed close variants of the supramolecular structure of cellulose. However, they did not take into account the specifics of the arrangement of cellulose chains, hydrophilic and hydrophobic regions of EF, and co-crystallization of EFs in MF.
The specificity of water adsorption process on cellulose
It was discussed (Grunin et al. 2013, 2018) that the penetrating and adsorption abilities of water molecules are stimulated by thermal motion and dipole–dipole interaction with surface-active centers (SAC) of cellulose. Surface hydroxyl groups of cellulose usually play the role of SACs. Based on simulations (Nishiyama et al. 2008; Nishiyama 2009) and atomic force microscopy data (Baker et al. 2000), our calculation shows that the distance between nearby SACs of cellulose is 6.5 Å in average.
The value of electric field strength of individual surface hydroxyl group E at the distance r from its center is calculated by the relation (Adamson and Gast 1997):
$$E = \frac{{\mu^{\prime}}}{{4\pi \varepsilon_{0} r^{3} }}\sqrt {3\cos^{2} \alpha + 1} ,$$
(6)
where \(\mu^{\prime}\) is the –OH group electric dipole moment; α is the angle between the chosen direction and the axis of the dipole; r is the distance from the center of the dipole to the point of water molecule location; ε0= 8.85 × 10−12 F/m.
The surface hydroxyl group of cellulose has an electric dipole moment of 4.51 × 10−30 ℃ m, whereas water molecule has an electric dipole moment of 6.15 × 10−30 ℃ m (Gregg and Sing 1982).
Values of the module of electric field strength created by the SAC depending on distance are presented in Table 2 (calculations were performed for the case α = 0°).
Table 2 The parameters of electric fields created by SACs of cellulose, depending on the distance Based on data in Table 2, we assume that a high heterogeneity of electric field is enhanced by a large number of SACs in pores of cellulose.
The energy of the dipole–dipole interaction of water molecule with the individual surface hydroxyl group is given by the expression (Adamson and Gast 1997):
$$W = \mu E\cos \theta ,$$
(7)
where μ is the electric dipole moment of the water molecule; θ is the angle between the vectors μ and E.
According to the data (Table 2), as a water molecule approaches an SAC of cellulose, their dipole–dipole interaction energy increases sharply and at the distance of 2.5–3 Å reaches the value of 19.2 kJ/mol, and it becomes commensurate with the energy of hydrogen bond of type –O–H···O– (Adamson and Gast 1997).
From our point of view, a water molecule can form the strong hydrogen bond during adsorption on cellulose Iβ in two ways. It will be carried out either by an oxygen atom of a water molecule on –OH group at C-6 of one glucopyranose ring or by two hydrogen atoms of a water molecule on O-2 and O-3 of an adjacent glucopyranose ring of same surface chain. It was discussed (Grunin et al. 2018) that this process is characteristic of each cellobiose residue of a surface chain of EF. From the previous, it follows that the adsorption monolayer is characterized by the relatively ordered arrangement of water molecules on the cellulose surface. Further equilibrium moistening of cellulose leads to the formation of subsequent adsorption layers (Taylor et al. 2008).
The adsorption process is characterized by an adsorption isotherm (Fig. 2), which up to 70% of relative pressure of water vapor is described by the BET equation satisfactorily:
$$w = w_{m} \frac{{C \cdot {p \mathord{\left/ {\vphantom {p {p_{s} }}} \right. \kern-0pt} {p_{s} }}}}{{(1 - {p \mathord{\left/ {\vphantom {p {p_{s} ) \cdot \left[ {1 + (C - 1){p \mathord{\left/ {\vphantom {p {p_{s} }}} \right. \kern-0pt} {p_{s} }}} \right]}}} \right. \kern-0pt} {p_{s} ) \cdot \left[ {1 + (C - 1){p \mathord{\left/ {\vphantom {p {p_{s} }}} \right. \kern-0pt} {p_{s} }}} \right]}}}} ,$$
(8)
where w is the sample moisture content; C is the adsorption equilibrium constant; p/ps is the relative pressure of water vapor.
Equation (8) allows examining the supramolecular structure and hydrophilic properties of cellulose and the state of water adsorbed on its fibers.
Being in adsorbed state, a water molecule experiences motions such as thermal rotational–vibrational and translational with jump-like character (Rowland 1980; Freeman 2003; Grunin et al. 2007). In the framework of the Bloembergen–Purcell–Pound theory (BPP), correlation times describe thermal motions of molecules that have Arrhenius character. This allows associating the activation energies of molecular motions with their correlation times in the first two layers of aqueous adsorbate (Grunin et al. 2016). For the first water adsorption layer:
$$\tau_{1} = \tau_{0} e^{{\frac{{\Delta H^{0} }}{RT}}} ,$$
(9)
and for the second one:
$$\tau_{2} = \tau_{0} e^{{\frac{L}{RT}}} ,$$
(10)
where ΔH0 is the standard enthalpy of adsorption interaction; L is the heat of condensation of adsorbate; R is the universal gas constant; T is the absolute temperature; τ1 and τ2 are the correlation times of first and second adsorbate layers, respectively.
Dividing Eq. (10) by (9) and then taking the logarithm of the result, we get the expression for estimation the net heat of adsorption:
$$\Delta H^{0} - L = RT\ln \frac{{\tau_{1} }}{{\tau_{2} }} .$$
(11)
In the framework of the BPP theory, correlation times in adsorbed water layers are related to their spin–spin relaxation times (under the condition (ωτ)2≫ 1, where ω is the circular NMR frequency, τ is the correlation time) by the formula (Grunin et al. 2016):
$$\frac{{\tau_{1} }}{{\tau_{2} }}\; = \;\frac{{T_{2}^{(2)} }}{{T_{2}^{(1)} }} ,$$
(12)
where \(T_{2}^{(1)}\) and \(T_{2}^{(2)}\) are the true spin–spin relaxation times of first and second adsorbate layers, respectively. The measured spin–spin relaxation time of the first layer is equivalent to its true value due to the very slow proton exchange of cellulose with adsorbed water.
Finally, Eq. (11) takes the following form:
$$\Delta H^{0} \; - \;L\; = \;RT\ln \frac{{T_{2}^{(2)} }}{{T_{2}^{(1)} }} .$$
(13)
We found the relation between the true spin–spin relaxation time of the second adsorption layer and the measured spin–spin relaxation time of adsorbed water bilayer (Grunin et al. 2020):
$$T_{2}^{(2)} \; = \;\frac{{T_{2}^{(1)} \cdot T_{{2{\text{meas}}}} }}{{2T_{2}^{(1)} \; - \;T_{{2{\text{meas}}}} }},$$
(14)
where \(T_{{ 2 {\text{meas}}}}\) is the measured spin–spin relaxation time of adsorbed water bilayer.
The capacity of water monolayer was evaluated by solving the BET equation for the adsorption isotherm of water vapor on cotton cellulose (Fig. 2) and amounted to 0.032 g/g. The spin–spin relaxation time of water monolayer was estimated on cotton cellulose sample with moisture content close to the capacity of adsorption monolayer and amounted to 160 μs. The measured spin–spin relaxation time of adsorbed water bilayer was 280 μs. Hence, the ratio of true spin–spin relaxation times of second and first adsorption layers was 7. Substituting the above numerical values into the formula (13), we find that the net heat of adsorption is 4.87 kJ/mol. The value of net heat of adsorption is positive that indicates the dominance of the energy of water monolayer–adsorbent interaction over the condensation energy of adsorbate. The water monolayer–adsorbent interaction is carried out through the formation of hydrogen bonds. This entirely correlates with the above description of the scheme of water monomolecular adsorption on active cellulose surface.
Additional information on the state of adsorbed water can be obtained by analyzing the changing in entropy during adsorption.
The condition of thermodynamic equilibrium of water monolayer–water vapor can be written in the form of equality of total Gibbs free energy differentials (Gregg and Sing 1982):
$$V_{v} dp - S_{v} dT = V_{m} dp - S_{m} dT ,$$
(15)
where Vv and Vm are the volumes of water vapor and water monolayer, respectively; Sv and Sm are the entropies of water vapor and water monolayer, respectively.
Transforming the formula (15), we get
$$(V_{v} - V_{m} )dp = (S_{v} - S_{m} )dT .$$
(16)
Since the volume of water vapor is much larger than the volume of water monolayer, at the initial stage of adsorption the water vapor can be considered as an ideal gas, then the left side of Eq. (16) is given as follows:
$$RT\frac{dp}{p} = (S_{v} - S_{m} )dT .$$
(17)
We transform the relation (17) into the following form:
$$R\frac{dp}{p} = \Delta H_{1} \frac{dT}{{T^{2} }} .$$
(18)
where ΔH1 is the enthalpy equivalent to the heat of mono-adsorption.
Carrying out the integration of Eq. (18), we get
$$RT(\ln p_{1} - \ln p_{0} ) = \Delta H_{1} ,$$
(19)
where p1 is the partial pressure of water vapor when filling water monolayer; p0 is the additive integration constant.
Similarly, we obtain the expression for the integral heat of adsorption:
$$RT(\ln p_{2} - \ln p_{0} ) = \Delta H_{2} ,$$
(20)
where p2 is the partial pressure of water vapor when filling water bilayer; ΔH2 is the enthalpy equivalent to the integral heat of adsorption.
We subtract Eq. (19) from (20):
$$RT\ln \frac{{p_{2} }}{{p_{1} }} = \Delta H_{2} - \Delta H_{1} .$$
(21)
After transforming, the formula (21) is given as follows:
$$R\ln \frac{{p_{2} }}{{p_{1} }} = S_{a} - S_{m} ,$$
(22)
where Sa is the entropy of water adsorbate.
Presenting the relation (22) with relative pressures of water vapor, we find
$$R\ln \frac{{p_{2} }}{{p_{s} }} \cdot \frac{{p_{s} }}{{p_{1} }} = S_{a} - S_{m} .$$
(23)
Thus, the excess of value p2 over p1 indicates the increase in the entropy change during adsorption. In particular, it is also valid for water bilayer adsorption under standard conditions. Analysis of the adsorption isotherm of water vapor on cotton cellulose (Fig. 2) shows that the filling of water monolayer is completed at p1/ps= 11%; meanwhile, the filling of water bilayer is completed at p2/ps= 42%. Applying the numerical values to Eq. (23) results that the difference between entropies of second and first adsorbed layers is 11.13 J/(K mol). This positive value indicates that water molecules in the first layer are more ordered than in the second one, which is in agreement with the above assumptions.
The adsorption equilibrium constant C is related to the change in Gibbs free energy by the Van’t Hoff equation (Gregg and Sing 1982):
$$\Delta G^{0} = - RT\ln C .$$
(24)
Since a part of the heat is released during adsorption, the change in entropy is related to the change in Gibbs free energy and the net heat of adsorption in accordance with the following expression (Grunin et al. 2016):
$$\Delta G^{0} = \Delta H^{0} - L + T\Delta S^{0} ,$$
(25)
where ΔS0 is the standard entropy of adsorbate.
Accordingly to the formula (25) and known numerical values, the change in Gibbs free energy is 8.21 kJ/mol.
After substituting relations (13, 23, 24) in (25), we get
$$RT\ln C = RT\ln \frac{{T_{2}^{(2)} }}{{T_{2}^{(1)} }} + RT\ln \frac{{p_{2} }}{{p_{s} }} \cdot \frac{{p_{s} }}{{p_{1} }} .$$
(26)
Consequently, the adsorption equilibrium constant can be estimated by the equation:
$$C = \frac{{T_{2}^{(2)} }}{{T_{2}^{(1)} }} \cdot \frac{{p_{2} }}{{p_{s} }} \cdot \frac{{p_{s} }}{{p_{1} }} .$$
(27)
Using the above numerical values, we establish that the adsorption equilibrium constant is 26.7. This value is in agreement with one that found by solving the BET equation (C = 25).
Sorption process development often leads to supramolecular rearrangements of cellulose. In particular, we studied the effect of equilibrium moistening of cellulose on its crystallinity and the specific surface area. Cotton cellulose samples’ crystallinities at different stages of moistening were estimated by the formula (2). Figure 3 shows the FID signal spectrum from the protons of air-dry cotton cellulose. According to Fig. 3, A1 and A2 are amplitudes values of (3) and (5) components, respectively.
Figure 4 shows the graph of the crystallinity of cotton cellulose versus its moisture content. The cellulose crystallinity decrease in the range from 0.78 to 0.70 is the most intensive with the corresponding moisture content from 0.5 to 8%. It is due to the thermal diffusion of water adsorptive molecules into spaces between MFs with subsequent adsorption on their active surfaces. This process is enhanced by the electric dipole–dipole interaction of adsorptive molecules with SACs of cellulose chains. As indicated above, the formation of –O–H···O– type hydrogen bond occurs. This phenomenon develops especially effectively in places of narrowing of pores between MFs and contributes to the formation of water adsorption layers and the occurrence of proppant pressure. Moreover, the distance increase between cellulose MFs results in the process of their separation and leads to the subsequent disintegration of macrofibril into MFs.
With the decrease in crystallinity from 0.7 to 0.67 with the corresponding moisture content in the range from 8 to 16%, adsorbed water molecules penetrate the structure of cellulose MFs. Water molecules break hydrogen bonds between co-crystallized EFs in the structure of MF adsorbing on active centers of their surfaces.
The work of adsorbed water penetration into spaces between crystalline cellulose formations is defined to a greater extent by the change in Gibbs free energy of the adsorption system. Hence, the proppant pressure from adsorbed water molecules Δp can be defined using the total differential of the Gibbs free energy under isothermal conditions (Adamson and Gast 1997):
$$\Delta p = \frac{{\Delta G^{0} }}{V} ,$$
(28)
where V is the volume of 1 mol of liquid water.
Substituting the numerical values of ΔG0 and V (18 × 10−6 m3) into Eq. (28) results that the proppant pressure value is 4.56 × 108 Pa.
Due to the proppant pressure emerged from the side of adsorbed water molecules, the formation of additional active specific surface of moistened cellulose occurs. It varies from 77.5 to 128 m2/g (using Eq. 5) in the moisture content range from 0.5 to 16% according to the adsorption isotherm (Fig. 2).