consortium r&d sur la chimie de la partie humide

MOLECULAR MODELLING REVIEW OF THE ASSOCIATION BETWEEN POLY(ETHYLENE OXIDE) AND COFACTOR Roger Gaudreault1-3*, M.A. Whitehead1 and Theo G.M. van de Ven1,2 1

Department of Chemistry, McGill University, 801 Sherbrooke St. W, Montreal, QC, Canada, H3A 2K6 2 Pulp & Paper Research Centre, McGill University, 3420 University St., Montreal, QC Canada, H3A 2A7 E-mail: [email protected] phone : (514)398-6177; fax : (514) 398-8254 3 Cascades Canada Inc., Recherche et Développement, 471 Marie-Victorin Boul., Kingsey Falls, QC, Canada, J0A 1B0 *Corresponding author: E-mail: [email protected]; phone: (819) 363-5705; fax: (819) 363-5755

ABSTRACT This review provides a better understanding of the underlying molecular mechanism of the association between poly(ethylene oxide) (PEO) and cofactor, a flocculation system used in papermaking. This association is necessary to induce fibre-fines flocculation. The binding of PEO or PEG based molecules with electrolytes is discussed. Salt is essential to induce the association between PEO and cofactor. Molecular Orbital PM3 calculations, supported by experimental evidence, prove the original idea, that the driving force for the association between PEO and the cofactor was hydrogen bonding, is invalid. The theoretical method provides structures and energies not obtainable from experiment, and predicts properties and interactions that can be tested experimentally.

INTRODUCTION In modern papermaking, the use of retention aids, to help to effectively incorporate fines and fillers into a sheet of paper, is widespread. Various single, dual and multi-component retention aid systems are available; consequently, the optimization of wet-end papermaking is a complex problem. Mill operators have to choose the best retention aid system for their particular process. The mechanisms that govern the action of these retention aids are still not fully understood, making this choice very difficult. Without a knowledge of the basic mechanisms of these retention aids, costly trial-and-error runs have to be performed. The paper industry drastically reduced its water consumption in the last two decades. This has lead to an increase in dissolved and colloidal substances in process waters, which interfere with cationic flocculants. One of the flocculating systems, which is more effective than charged polymers in highly contaminated closed systems, is the PEO poly(ethylene oxide)/cofactor retention aid system. The association between PEO and cofactor is essential to

flocculate cellulose fibres, fines and fillers, but is poorly understood. Various cofactors are known to associate with PEO and increase its flocculation efficiency. This association was believed to be hydrogen bonding between the ether oxygen of PEO and the cofactor phenolic hydroxyl groups. Recent experiments have cast doubt on the hypothesis that hydrogen bonding is the major driving force for association; cofactors that do not form conventional hydrogen bonds (R— OHO) with PEO, such as poly (naphtalene sulfonate), polystyrene sulfonate, and cofactors with fully dissociated phenolic groups at high pH, are also effective cofactors. The flocculation of cellulose fibres, fines and fillers, by a PEO/cofactor system has been described by several mechanisms: transient polymer network [1-3], complex bridging [4], association-induced polymer bridging [5-6], asymmetric polymer bridging [7], and temperature induced flocculation [8]. Goto et al. [9] speculated that the surface charge and the density of phenolic hydroxyl groups in the cofactor are important for flocculating colloids. Using PEO and tyrosine-containing water soluble polypeptide (TCP), Lu [10] extended the complex bridging mechanism by considering TCP deactivation and PEO saturation. However, previous mechanisms have fundamental shortcomings. For papermaking conditions, kinetic calculations show PEO/cofactor association complexes to adsorb on fibres before cofactor-induced PEO clustering. Consequently, this prevents the formation of a transient network on papermaking time scales. Association-induced polymer bridging [5-6] is similar to complex bridging [4] with the difference that it also explains why PEO/cofactor complexes adsorb on cellulose fibres. The temperature-induced flocculation is a classical mechanism in colloidal flocculation theory [8], and does not apply under realistic papermaking conditions because the operating conditions are well below the cloud point temperature. More recently, Gaudreault [11-14] showed that salt is essential for the PEO to associate with cofactor and a new mechanism was proposed for the non-clustering cofactors: surface-induced clustering coupled to associationinduced polymer bridging mechanism. Although Lindström and Glad-Normark [15] showed that flocculation of pulp fibres were sensitized by electrolytes, none of the previous mechanisms noted that salt is essential for the PEO to associate with cofactor, a necessary step to induce fibres/fines flocculation [11-14]. Gas phase theoretical Molecular Mechanics (MM) calculations [16,17], which build in the hydrogen bond, showed the OH groups of the phenolic rings of the phenol-formaldehyde resin (PFR) to form hydrogen bonds with alternate PEO oxygen 7 Å apart. Isotactic PVPh (poly(vinyl phenol)) oligomers gave hydrogen bonds on every fourth or fifth PEO oxygen where the R—OHO distances were < 2.37 Å, with an angle of 130 to 180 degrees [17]. Hydrogen bonding in a water insoluble PVPh/PEO complex was assumed by Zhang et al. [18], to explain the 13C solid-state NMR results. The water soluble ionic cofactor PVPh-co-KSS (poly(vinyl phenol-co-potassium styrene sulfonate))/PEO complex, gave 1H NMR results that

7th International Paper and Coating Chemistry Symposium, 2009, Hamilton, Canada, June 10-12, 2009, 263-276.

did not exclude hydrogen bonding [19], but suggested that other interactions were possible. Lu et al. [20] found that water soluble polypeptides with high tyrosine content, phenolic moieties, form complexes with high molecular weight PEO in 1mM CaCl2. Using Fourier transform infrared spectroscopy (FTIR), Modgi et al. [21] claimed that they showed the existence of hydrogen bonding between PEO and PFR. Before this work, a few articles have been published on the molecular modelling of PEO [22-32], but very little about cofactors [16,17]. This work contributes at the theoretical level, through molecular modelling, to the understanding of PEO/cofactor interactions by having a closer look at the expected hydrogen bonding. Gas phase Molecular Mechanics and PM3 semiempirical Molecular Orbital Theory calculations were performed to determine the (PEO)n (n = 3 and 6) and cofactor structures [33,34] (Figure 2). The common characteristics of these model cofactors are that they have aromatic rings and are negatively charged under papermaking conditions.This study used three phenolic model cofactors: gallic acid (GA) (Figure2b), corilagin (1-O-Galloyl-1,3,6hexahydroxydiphenoyl (-β-D-glucopyranose), with molecular formula C27H22O18 and molecular weight of 634.08 g mol-1 (Figure 2c) and TGG (1,3,6-tri-O-Galloyl-β-D-Glucose) (Figure 2d) to provide a framework for interpreting the experimental observations. GA has been theoretically [35] and experimentally [36,37] studied and corilagin has also been theoretically [33,34] and experimentally [12,38-41] studied. TGG chemistry, which consists of a sugar that has been esterified three times with gallic acid, has been previously described [33,34,42-45]. Bond length, bond angle, enthalpy of association (∆Hf), Gibbs free energy (∆G), entropy (∆S), electron density and delocalized molecular orbital (DLMO) of the PEO/cofactors (Gallic acid, corilagin, TGG) complexes, and the related conformational changes are calculated. PROPERTIES OF POLY(ETHYLENE OXIDE) (PEO) Poly(ethylene oxide), -(CH2CH2O)n-, is flexible and is a polyether that can be synthesized with various molecular weights. A proposed working definition divides the PEO’s with molecular weights less than 105, which are liquid at room temperature, from those with molecular weights greater than 105 which are solid [46]. The liquids are called poly (ethylene glycol) PEGs, while the solids are called PEO. Crystalline PEO, shown in Figure 1 (left), has oxygen inside the helical molecular structure. However, the molecular structure shown in Figure 1 (right), with oxygen outside, is the expected conformation in solution, because the ether oxygens are more accessible to form hydrogen bond with water molecules. This conformation is energetically more stable than the crystalline structure [11]. PEO properties have been extensively studied [46-58]. Aray et al. [59] studied a PEO structure which is most likely crystalline.

Figure 1. Molecular structure of poly(ethylene oxide) (PEO): (left) crystalline (Courtesy of Dr. Julie Giasson and Dr. Christian Lauzier; Cascades inc, R&D Consortium) [11]; A periodic box is shown together with repeat units one of which is in the overlapping spheres model representation; and (right) the most stable gas phase structure obtained by performing a complete 360° scan of all the dihedral angles of the PEO using PM3 [34].

Applications PEO has numerous applications [46]: (1) drag reduction (adding only 0.03% of PEO (MW >4 million) to aqueous solutions can increase the flow rate by 100%, at a fixed pump pressure); (2) adhesives (high concentration (> 10 %) solutions of PEO exhibit wet tack properties); (3) lotions (PEO provides a unique lubricious property that has been successfully exploited for personal-care products); (4) jet cutting and drift control (PEO solutions reduce mist formation); (5) batteries (typically, a salt such as potassium iodide KI or lithium perchlorate LiClO4 is complexed with PEO in a methylene chloride solvent, and (6) removal of extractible and non-process elements (Netfloc process : oxidized and partially oxidized fatty and resin acids (FRA) are removed from bleach plant filtrate which increases the water absorption properties of pulp and the FRA can then be recycled for other purposes) [60]. Interactions of PEO with cofactors High molecular weight PEO is being used as a flocculant in the manufacture of newsprint and related papers [15,61-65]. Cofactors generally have phenolic hydroxyl groups which are presumed to form hydrogen-bonded complexes with PEO [3,66-67]. Hydrogen bonding is not the only effect because there are cofactors which cannot form hydrogen bonds with PEO, yet are effective, such as SNS and polystyrene sulfonated sodium salt (PSS-Na) [13,14]. Cofactors can form two types of association complexes with PEO: (i) equilibrium association complexes, consisting of a single PEO molecule on which several cofactor molecules are adsorbed, called nonclustering cofactor (possibly in equilibrium with PEOclusters). For example, at corilagin: PEO ratio 1:1, there are about 16000 corilagin molecules per PEO molecule, which equals 5 PEO monomer units per aromatic ring, similar to other cofactors [13]. This correlates with results from Cong et al. [19], who reported that for every vinyl phenol moiety there were 4.9 polyether repeat units within 5 Ǻ of an aromatic ring. Secondly, (ii) non-equilibrium complexes consisting of PEO clusters, induced by clustering cofactors [63]. Also, cofactors may or may not adsorb on fibres and fines. The most important cofactors are:


Phenol formaldehyde resin (PFR) and modified phenolic resin (MPR) Water soluble phenol formaldehyde resin (PFR), a common cofactor [68], is a clustering cofactor [68,69], while a carboxylated MPR is a non-clustering cofactor [63]. Poly(sulfonated kraft lignin) (SKL) The non-clustering cofactor affects the size of the PEO molecule in solution: in the presence of sulfonated kraft lignin (SKL), PEO takes on an extended configuration [63], while with MPR the size appears to diminish [70]. Poly(sodium naphtalene sulfonate) (SNS) PEO and SNS form an association complex that can flocculate fines by polymer bridging [70]. SNS is a non-clustering cofactor [63]. Tannic Acid (TA) Tannic acid (TA) has a very complex and non-uniform chemistry [71,72]. Attia and Rubio [73] published a method for the determination of very low concentrations of PEO. The method consists of measuring the turbidity produced by mixing the polymer solution with a dilute solution of TA in the presence of 1 M NaCl. Even though, there is no commercial application of TA, it was found to be a clustering cofactor [63] and a good cofactor [13]. Poly(p-vinylphenol) Poly(p-vinylphenol), a PEO cofactor [68,74,75], was most effective at intermediate pH values where the poly-phenol was present as dispersed particles in the colloid size range. They proposed that “the flocculation involved hydrogen bond complexes between the PVPh particles and PEO” [74]. Molecular mechanics calculations of PEO/PVPh complexes indicated that hydrogen bonding with adjacent or alternating polyether oxygens along the PEO chain was less favourable than that for complexes with bonding of every fourth or fifth oxygen [17]. Tyrosine containing polypeptide (TCP) Lu et al. [10,20], which refined the complex bridging mechanism proposed earlier by Xiao et al. [4,76], showed that tyrosine-containing water soluble polypeptide (TCP), which is poly(Glutamic acid, Tyrosine) (1:1) having a phenolic group, is an effective PEO cofactor to flocculate precipitated calcium carbonate (PCC). They [20] emphasized that the minimum molecular weight of (1:1 poly(Glu, Tyr)) required for binding to high molecular weight PEO, in the presence of 1 mM CaCl2, is between 1.1 and 36 kDa.

MOLECULAR MODELLING Molecular Modelling Methods The theoretical methods used to build the PEO and cofactor conformers follow previous procedures [33,34], using Gaussian GW03 Revision B.02 and GaussViewW Version 3.07 [77-79]. All PM3 results were obtained at 0 K; the correction to 298.15 K was made [80] using a scaling factor of 0.976 [81] to give theoretical results closer to experiment. PM3 Semi-Empirical Molecular Orbital Theory is reliable for conformational analysis of hydrogen bonded molecules [8286]. The Complexes The PM3 optimised gas phase PEO structures capable of forming complexes with cofactor had initial intermediate structures Aopt. The various gas phase cofactor conformers gave Bopt, characteristic of the conformer structure. Following Williams [87], equation 1 is a simplified version that describes the formation of PEO/cofactor complexes. Initially, Aopt and Bopt are brought together, changing their conformation to fit into each other, A’opt and B’opt, and subsequently re-optimized as a complex to give (A’B’)opt, the most stable possible complex structure. The short version of the equation is shown below: Aopt + Bopt

(A’B’)opt

(1)

The heats of formation (Hf,0K) as well as the enthalpies of association ΔH0 K of all molecules and complexes were initially calculated at 0 K, giving the enthalpy of association as: ( A' B ' ) opt

H 0 K

 H f ,0 Kopt   ( H f ,opt0 K  H f ,opt0 K ) ( A' B ' )

A

B

(2)

A PEO trimer was chosen to study the interactions with a small cofactor (gallic acid) and a PEO hexamer for the interaction with larger cofactors (TGG and corilagin) [33,34], because TGG is a precursor of tannic acid (TA) [42-45], a known cofactor for PEO and a close analogue of corilagin. Moreover, corilagin was shown to function as a cofactor as well [12-14]. Gallic acid, which has hydrophilic OH’s and a COOH group and a hydrophobic phenyl ring, is a sub-unit of larger cofactors such as TGG and corilagin (Figure 2).

Folic acid (FA) Even though FA (lactam form) has a smaller molecular weight, 441.40 g mol-1, than TA, corilagin, PSS-Na and other typical commercial cofactors, with PEO it flocculates microcrystalline cellulose (MCC) in the presence of salt [11,13].


1,80578 Å

OH O OH

C OH

1,70358Å

OH CH3

O

OH O

4

b) Gallic acid

a) PEO

1,81368 Å OH O OH

C O OH

CH2

OH O OH

O

OH O

OH

C

Figure 3. Molecular structure of (PEO)3/gallic acid complexes: a) one R—OHO, one R—OHH and one R—CHH, and b) two R—OHO and one R—CHH bonds [88].

OH

O

OH

c) Corilagin

OH O

C

OH

No bond in TGG

d) TGG

Figure 2. PM3 Molecular structures of a) PEO hexamer, b) Gallic acid [34-37], c) Corilagin [33,34,38-41] and d) TGG [33,34,42-45]. Oxygen atoms are indicated in red, carbon in blue and hydrogen in white.

TABLE 1. HEATS OF FORMATION OF PEO, COFACTORS AND WATER [34] Molecule

Conformer

-1 H f ,0K (kcal mol )

PM3/GW03

Gallic acid (GA)

-198.24

(PEO)3

-136.79

(PEO)6

-256.71

TGG

Tripod

-670.42

Corilagin*

Boat

-650.24

Corilagin*

Chair

-637.57

Water**

-53.44**

*Corilagin has a covalent bond between R3 and R6 phenolic rings. **For non-clustered single H2O molecule. N.A.: Not applicable.

(PEO)3/Gallic acid For the PEO/Gallic acid complex, with a single R—OHO bond (Figure 3a), the ethylene oxide trimer (PEO)3 was used. The (PEO)3/gallic acid, readily complexes at 0 K since the complex (Hf,0 K = -341.41 kcal mol-1) is more stable than the sum of the reactants (-335.03 kcal mol-1) [34] and the enthalpies of association at 0 K and 298 K, are -6.38 kcal mol-1 and -4.72 kcal mol-1 respectively [34,88] (Figure 3a). This is similar to a typical hydrogen bond enthalpy [89]  -5 kcal mol-1 and to the experimental interaction energy in a water dimer [90] -5.4 ± 0.7 kcal mol-1.

The (PEO)3/gallic acid complex, which has two R—OHO bonds (Figure 3b), also readily complexes at 0 K, since the complex (Hf,0 K = -347.19 kcal mol-1) is more stable than the sum of the reactants (-335.03 kcal mol-1) [34,88]. Thus, the enthalpy of association at 0 K is -12.16 kcal mol-1. However, the positive ΔG value (8.43 kcal mol-1) shows that the complex in figure 3a will not form at room temperature (298.15 K), because the gain of association enthalpy does not overcome the loss in entropy. By analogy, the complex in Figure 3b will also not form at room temperature. Although the (PEO)3/GA complex with two ROHO is more stable than the complex with one RCHH hydrogen bond, there is no correlation between the number of hydrogen bonds and the enthalpy of association for these complexes. (PEO)3/Gallic acid complex with one R—OHO bond DLMOs, which describe the bonding between PEO and cofactor, giving the wavefunctions and eigenvalues, were calculated. Brion et al. [91] showed that the molecular orbital theory is an accurate method to assess chemical bonding; electron momentum spectroscopy (EMS) measurements and associated theoretical calculations, together with the evidence from frontier orbital theory and scanning tunneling microscopy (STM) experiments, strongly suggest that the delocalised canonical molecular orbital (CMO), or the KohnSham orbital (KSO), densities provide a theoretically valid operational definition of orbital electron densities, and orbitals. Figure 4 shows DLMO 13 (top right), one of the 60 occupied DLMOs, is the only DLMO, which totally covers one phenolic hydroxyl and one ether oxygen of the PEO. There is a pinch in the DLMO at the postulated hydrogen bond. Moreover, DLMO 18 (Figure 4 bottom right) shows two unusual interactions: ROHH and R CHH. The existence of such interactions has been reported [92,93]. The electron density () between the two specific atoms, using the density matrix was determined. The density matrix was used by Tretiak et al. [94] to study conjugated and aggregated molecules. The density matrix P , with elements P gives the contributions of the atomic orbitals (AO) in the DLMO [95].


Figure 4. Molecular structure of the (PEO)3/gallic acid complex (Figure 3a): (i) the hydrogen bond is shown in the top left diagram as a dotted line “to connect ROH to O“, as ROHO. In the lower diagram on the left, two additional hydrogen bonds ROHH and RCHH are shown. The DLMO 13 (top right) with eigenvalue of –1.039 eV and DLMO 18 (bottom right) with eigenvalue -0.821 eV, describe the ROHO as well as ROHH and RCHH interactions respectively. They both show a distinct pinch in the DLMO (arrows) [88].

Table 2 shows that the RPhenolOHOEther interaction has a total electron density of 0.0323 e/au3, of which 0.0210 is found between the 1s atomic orbital of the hydrogen proton of the phenolic group and the 2pyO atomic orbital of the ether oxygen atom: the 2pxO and 2pzO together contribute only 0.0057 e/au3. The RPhenolOHOEther bond has a HO bond length, d, of 1.833Å and ln  of the total electron density, 0.0323 e/au3, is -3.43. These results fit perfectly well with the linear 1n bcp versus d relationship, given by Alkorta and Elguero [96]. TABLE 2. CHARACTERIZATION OF INTERMOLECULAR BONDS IN (PEO)3/GALLIC ACID HAVING ONE ROHO BOND [34] Inter-atomic interactions

Bond length (Å)

Bond angle [°]

Atomic orbitals in the MO 1s – 1s 1sH – 2px0 1sH – 2py0 1sH – 2pz0 H

RPhenol— OHOEther

1.833

165.38

0

electrondensity 3

(e/au ) 0.0056 0.0045 0.0210 0.0012 Σ = 0.0323

hydrogen atoms share the same electron density. Table 2 shows that these HH bonds in ROHH and RCHH have smaller electron densities (0.0125 and 0.0121) than the ROHO (0.0323) interaction, even though the bond lengths are shorter. Klooster et al. [93] reported that HH distances are typically 1.7 to 2.2 Å for MHHN bonds, where M stands for metal compared with the present results 1.728 and 1.720. The ROHH and RCHH interactions were removed from (PEO)3/gallic acid and the enthalpy of formation was calculated to be 0.45%, or -1.54 kcal mol-1 more stable than the complex containing the ROHH and RCHH [34]. The enthalpies of association were -7.92 and -6.03 kcal mol-1 at 0 K and 298.15 K respectively. The electron density () for the ROHO interaction, when the ROHH and RCHH were removed, increased to 0.0337 from 0.0323. Complexes with these bonds are energetically less stable than the complexes without it [34]. PEO)3 /Gallic acid complex with two R—OHO bonds Table 3 shows that a total of 11 DLMOs cover 3 intermolecular H-Bonds (Figure 3b). Out of these 11 DLMOs, 7 are from RCHH type and two of ROHO type and two of ResterOH type. TABLE 3. BOND CHARACTERIZATION IN (PEO)3/GALLIC ACID COMPLEX WITH TWO ROHO BONDS [88] Bond characterization in Gallic acid /(PEO)3 Complex DLMO (#)

Interactions

Inter or intra molecular H-bond

Atom Label (#)

Bond length (Å)

LUMO

Eigen Value (eV)

-0.024

HOMO

-0.339

47

Rphenol – CH … HPEO

inter

27-11

1,70358

-0.492

25


inter

27-11

1,70358

-0.664

19


inter

27-11

1,70358

-0.774

15


inter

27-11

1,70358

-0.889

13


inter

27-11

1,70358

-1.041

11


inter

27-11

1,70358

-1.100

7

Rester – O … HPEO

inter

39-23

1,80578

-1.341

4

Rphenol – OH … OPEO

inter

35-7

1,81368

-1.421

3

Rester – O … HPEO

inter

39-23

1,80578

-1.475

1

Rphenol – OH… OPEO

inter

35-7

1,81368

-1.552

1


inter

27-11

1,70358

-1.552

Solvation of Gallic acid

RPhenol— OHHPEO

1.728

155.02

1sH – 1sH

0.0125

RPhenol— CHHPEO

It was necessary to study the solvation of PEO/cofactor systems, because the association occurs in water. Water molecules were added to give a monolayer around GA, which required about 43 water molecules (Equation 3 and Figure 5) [97]. GA  ( H 2 O) 43 , not considering GA dissociation, readily

1.720

148.67

1sH – 1sH

0.0121

hydrates at 0 K:

The ROHH and RCHH interactions have been suggested as possible hydrogen bonds, because the two 7th International Paper and Coating Chemistry Symposium, 2009, Hamilton, Canada, June 10-12, 2009, 263-276.

GA -198.24

+ +

( H 2 O ) 43 -2551.66

GA  ( H 2 O) 43

(3)

-2767.26

showed that this complex does not form at room temperature because of entropic effect [34].

The complex ( H f , 0 K = -2767.26 kcal mol-1) is more stable than the sum of the reactants (-2749.90 kcal mol-1). From Equation 3, the hydration enthalpy of GA  ( H 2 O) 43 is -17.36 kcal mol-1 at 0 K.

Figure 6. The (PEO)6/corilagin-boat complex with the PEO hexamer inside the cavity of the cofactor corilagin-boat, are shown [12,34]. Figure 5. Top view and side view of the first shell of 43 water molecules around Gallic acid ( GA  ( H 2 O) 43 ) [97].

Figure 5 also shows that the water molecules form a sphere around the hydrophobic part of GA without any direct contact. However, the water molecules around the hydrophilic part are closer to the solute and more regularly oriented. This correlates well with results of Malardier et al. [84,85] obtained for the water distribution around styrene-maleic anhydride, where the hydrophilic interactions were found to be direct and long range, while the hydrophobic interactions were found to be indirect and short range.

In a chain with two adjacent ROHO and RCHO bonds in the (PEO)6/Corilagin-chair complex, the HO atoms are covered by two DLMOs, 4 and 6, one of which is shown in Figure 7 (right). The so-called polarization-enhanced hydrogen bond, which is stronger [98,99], occurs in the (PEO)6/Corilagin-chair complex, as shown by the DLMO.

We have seen that for small (PEO)3/cofactor system, there is no correlation between the number of hydrogen bonds and the enthalpy of association. We now discuss larger systems. (PEO)6/Cofactor (PEO)6/TGG The hexamer ((PEO)6) was used to ensure that PEO is larger than the model cofactor (TGG), and to minimize end group effects (CH3 and OH). (PEO)6/TGG readily complexes at 0 K since the complex (Hf,0 K = -944.49 kcal mol-1) is more stable than the sum of the reactants (-927.13 kcal mol-1). The enthalpy of association (ΔH0 K) in gas phase, is -17.36 kcal mol-1 [34,88]. (PEO)6/Corilagin

Figure 7 PM3 optimized molecular structure of (PEO)6/Corilagin-chair complex shows two adjacent hydrogen bonds. These hydrogen bonds: R  OH    O and R  CH    O are indicated by (dotted lines, left). On the right, one out of two DLMOs with eigenvalue -1.505 eV covering this so-called polarizationenhanced hydrogen bond has a distinct pinch at both hydrogen bonds (indicated by arrows) [34].

The (PEO)6/Corilagin-boat complex shows no dependence of the heat of formation (H0K) on the number of inter-molecular H-bonds (Figure 6). For example, for a decrease from 4 to 1 hydrogen bond, the enthalpy of association H0K changes from -15.23 to -14.90 kcal mol-1 [34]. At 298.15 K, H298 K values are even closer: -12.45 and -12.25 kcal mol-1 respectively. Moreover, the thermochemistry analysis also 7th International Paper and Coating Chemistry Symposium, 2009, Hamilton, Canada, June 10-12, 2009, 263-276.

Effect of solvation: TGG/(PEO)6/(H2O)n When water molecules are either surrounding the (PEO)6 /TGG or the complex is put in a water continuum in a periodic box, then as Equation 4 shows (PEO)6/TGG/(H2O)122 complex will not form (Figure 8): (PEO) 6 + TGG + ( H 2 O )122

-256.71+-670.42+-7328.64

( PEO) 6 / TGG /( H 2 O)122 (4) -8174.92

because the total enthalpy of the system at 0 K ( H f ,0 K = -8174.92 kcal mol-1), is less stable than the sum of the reactants (-8255.77 kcal mol-1), and consequently H 0K is +80.85 kcal mol-1. These results show that this system is thermodynamically unstable [97].

Figure 8. Gas phase (PEO)6/TGG) complex (left) and solvated (PEO)6/TGG/(H2O)122 system (right) showing the effect of solvent on (PEO)6/TGG) conformation [97].

TGG/(PEO)6/(H2O)n : Molecular Dynamics (MD) To compliment the MO calculations, this complex was studied using MD followed by MM geometry optimization (Figure 9 and Table 4) [97].

Figure 9. Solvated (PEO)6/TGG/(H2O)906 system showing the effect of solvent on (PEO)/TGG conformation after molecular dynamics (MD) simulations of 7.5ps (top) and 75ps (bottom) followed by molecular mechanics (MM). Structures on the right show the (PEO)6 and TGG conformations after the MDMM calculations [97].

Figures 8 and 9 show that (PEO)6/TGG complex separates as the MD calculation time increases: it does not form in aqueous solution, which agrees with the MO calculations and the experimental results obtained with PEO and corilagin, a very similar cofactor [12,97].

TABLE 4 ENTHALPY BALANCE FOR GAS PHASE AND SOLVATED PEO/TGG SYSTEMS AT 0 K [97]

Computing method

(PEO)6

TGG

(PEO)6/TGG

H f ,0 K

H f ,0 K

H f ,0 K

(kcal/mol) (kcal/mol) PM3 (gas phase)

*

H 0K (kcal/mol)

(kcal/mol)

-256.71

-670.42

-944.49

-17.36

PM3 (solvated)*

-258.95

-657.98

-923.74

-6.91

MD7.5psMM **

-238.70

-573.06

-818.13

-6.37

MD75psMM**

-236.85

-579.50

-817.23

-0.88

( H 2 O )122 ; ** ( H 2 O) 906


Effect of the number of water molecules on the enthalpy per mole of H2O molecules Figure 10, which was constructed using the results of the PM3 Semi-Empirical method, shows that the enthalpy per mole of H2O molecules changes as a function of the number of water molecules, and therefore differs from one system to another ( GA  ( H 2 O) n ) [97]. Our results are consistent with the results

Since there is a possibility that the cofactor would complexed from top and bottom or left to right, a sandwich complex is studied in the following section as well. (PEO)6/Cofactor/(PEO)6 Thermochemistry analysis of the complexes when a cofactor is sandwiched between two PEO hexamer was performed to see whether a cofactor could induce PEO aggregation and overcome the entropic effect.

-64

-4000

-62

-3500 -3000

-60

-2500 -58 -2000 -56 -1500 -54

-1000 Enthalpy per H2O at 0oK

-52

Relative total energy (cm-1) Upadhyay et al.

-500

-50

0 0

20

40

60

80

100

120

140

n (H2O cluster size)

Figure 10. Enthalpy (Gaudreault et al. [97]) and relative total energy (Upadhyay et al. [100]) at 0 K per mole of water molecules as a function of the number of water molecules.

The enthalpy per mole of water becomes more negative as the number of water molecules increases, showing that hydrogen bonding between the H2O makes the total H2O system more stable. This observation is critical when analysing systems with different numbers of H2O molecules. To perform an energy balance, for H2O molecules which are clustered, the enthalpy of H2O in the cluster must be recalculated for each H2O system, otherwise a significant error will occur. For example, when comparing two systems having 40 and 70 H 2O molecules, where the enthalpy per mole of H2O molecules is -59.07 and -60.07 kcal mol-1 respectively (Figure 10), ignoring the change in energy of each H2O in each cluster, would give an error of -30 kcal mol-1. Figure 10 shows a distinct change in the rate of change of the relative energy per H 2O at 10 H2O molecules; after this a slower varying plateau is observed to and beyond 120 H2O molecules [97]. Bondebey et al. [101] using (FT-ICR) mass spectrometry and B3LYP describe a variety of reactions and processes in clusters of up to one hundred water molecules and found they behaved like bulk H2O solutions. However, Bondebey et al. [101] concluded that the bulk behaviour of H2O is regularly exhibited by clusters containing on the order of 10 water molecules, in agreement with the present PM3 results, and those of Stace [102] from gas phase thermochemistry.

Relative total energy per H2O (cm-1)

Enthalpy per H2O at 0K (Kcal/mol)

of Upadhyay et al. [100], obtained with ab initio calculations, who observed the onset of a plateau at about 10 water molecules (Figure 10).

(PEO)6/TGG/(PEO)6 (PEO)6/TGG/(PEO)6 readily complexes at 0 K since the complex (Hf,0 K = -1215.26 kcal mol-1) is more stable than the sum of the reactants (-1183.84 kcal mol-1) and where the enthalpy of association (ΔH0 K) in gas phase is -31.42 kcal mol-1 [34,88]. However, the thermochemistry analysis showed that for (PEO)6/TGG/(PEO)6 complex there is no correlation between the enthalpy of association and the number of H-bonds [34,88], and that these complexes have large TΔS values that prevent association.

(PEO)6/Corilagin/(PEO)6 Again, no association occurs at 298.15 K between corilagin conformers with two PEO hexamers because of high entropy [34]. Moreover, there is no correlation between the number of inter-molecular “H- bonds”, and the enthalpy of association for the corilagin complexes. Another possibility is that the PEO hexamer is sandwiched between two cofactors, a complex studied in the following section [34,88]. Cofactor/(PEO)6/Cofactor TGG/(PEO)6/TGG The association between a (PEO)6/TGG complex and another TGG to generate a larger complex (Figure 11), with more possibilities for bonding, shows that TGG/(PEO)6/TGG readily complexes at 0 K since the complex (Hf,0 K = -1617.99 kcal mol-1) is more stable than the sum of the reactants (1597.55 kcal mol-1). The enthalpy (ΔH0 K), in gas phase, is -20.44 kcal mol-1 [88]. Interestingly, the bond characterization of the TGG/(PEO)6/TGG complex showed that there are 6 inter- and one intra-molecular H-bonds [88]. All DLMOs covering hydrogen bonds differ in terms of bond lengths, type, and eigenvalues (Figure 12).

Figure 11. Left) Molecular structure of TGG/(PEO)6/TGG complex, and right) Some of the “H-bonds are indicated by dotted lines” [88].


DLMO-32

DLMO-28

DLMO-31

DLMO-27

DLMO-29

DLMO-19

Enthalpy change (kcal/mol)

-30 Region of association

-25

y  0.4965x -20

R 2  0.841

-15

(PEO)6/cofactor/(PEO)6

-10 (PEO)6/cofactor

-5 Region of no association

(PEO)3/gallic acid

0 0

-10

-20 S

DLMO-16

DLMO-13

-30

-40

-50

(kcal/mol)

DLMO-5 Figure 13. Change in calculated enthalpy as a function of the change in calculated entropy at 298.15 K, for gas phase interactions of PEO/cofactor complexes. The correlation factor R2 was calculated assuming the line goes through the origin. The dotted line is the boundary between regions in which association occurs or is absent [34].

DLMO-4

DLMO-3

DLMO-1

Figure 12. Characterization of intra- and inter-molecular hydrogen bonds in TGG/(PEO)6/TGG complex. They show a distinct pinch in the DLMO (arrows) [88].

A detailed analysis shows that the enthalpy and entropy changes mainly arise from PEO, but the effect of PEO and cofactor combined is usually below 25% of the total entropy changes (TΔS) (Figure 14) [34].

The relationship between the change in enthalpy (Hf) and the change in entropy (S) is discussed extensively in the literature. Searle et al. [103,104] showed that for the gas phase the change in enthalpy of association increases approximately linearly with the change in entropy, with H = 0 at TS = 0. A relatively good correlation, R2 = 0.841, is found, but more importantly all PEO/cofactor complexes are found in the region of no association (Figure 13), because the loss of entropy exceeds the enthalpy gain [14,34].


-60

80 Cofactor PEO

Change in enthalpy (%)

60

40

20

0

-20

-40 0

1

2

3

4

5

6

7

8

9

10

Change in entropy (%)

10

The presence of inorganic salts in aqueous solutions of PEO reduces the cloud point temperature (CPT), defined as the point where a phase separation between the water and PEO occurs [46,120,121]. For example, for PEO with a molecular weight of 4 million, the cloud point is 96.24 oC in pure water, and 92.92oC at 0.1 M KCl for a PEO:water ratio of 0.01 [46]. Englezos et al. [122,123] showed the effect of salt (KCl) on fibre fines and clay retention. Our experimental conditions for MCC flocculation were far from the CPT, which excludes the possibility that salt caused PEO to phase separate [11-14]. However, salt (KCl) is essential in the flocculation mechanism [11-14]. Sartori et al. [113] showed significant binding between PEO (concentrations from 5 to 200 mM expressed in monomer units), and KCl (concentrations of 2.4 and 7.5 mM). Dehydration of ethylene oxide units due to salt effect has been reported [124]. Bordi et al. [125] showed a decrease in conductivity of PEO in a 0.1 M KCl solution for various PEO molecular weights. Beaudoin et al. [126] reported that their results on hydrophobically modified PEO (HMPEO) in the presence of monovalent cations (Na+ and K+) are in agreement with the description of a salting out effect on PEO chains.

0

2) Cofactor-salt interactions -10

-20

-30 0

1

2

3

4

5

6

7

8

9

10

Number index of cofactor/(PEO)6 complexes Figure 14. Change in enthalpy and entropy at 298.15 K arising from the individual components (cofactor and (PEO)6) for gas phase complexes. Number index refers to different PEO/cofactor (TGG, corilagin, R1R3, R1R6) complexes [34].

INTERACTIONS OF PEO AND COFACTOR WITH ELECTROLYTE (SALT) It has been found that PEO and corilagin (cofactor) were unable to flocculate microcrystalline cellulose (MCC), a model for papermaking fines, and that a small amount of salt was necessary to induce MCC flocculation [11-13]. Besides the fact that salt affects the stability of MCC (which was shown to be negligible for the salt concentrations used), two other possibilities can be explored: salt interacts with 1) PEO or 2) cofactor.

Salt may bind to cofactors via cation π-binding. This may be the reason why all known cofactors contain aromatic rings. Because these ions can also bind to PEO, the ions can form a bridge between PEO and a cofactor. However too much salt can be detrimental for the PEO-cofactor interactions. Laivins et al. [127] concluded that the occasional loss of efficiency of the PEO-based retention aid system in newsprint furnishes containing residual chemicals and containing high salt concentrations, could be ascribed to a “salting out” of the cofactor. Abdallah [128] also observed that when the contact time between salt (0.4 mM CaCl2) and cofactor is increased, the flocculation rate of fines is reduced, and explained this behaviour by a salt-induced aggregation of the cofactor [129]. Therefore, cation association can cause PEO to behave more or less like a positive polyelectrolyte. For negatively charged cofactors this will result in a stronger affinity of the cofactor to PEO. For non-charged cofactor, such as corilagin, it may cause a stronger affinity, because the ions can also bind to the aromatic ring by cation π-binding (Figure 15). The effect of salt has recently been shown to be also important in the reflocculation of fines and fines re-deposition on fibres [130132].

1) PEO-salt interactions The association of ions with non-cyclic PEO has been experimentally studied by many authors [105-114], as well as the complexation with cyclic polyethers of the crown type [115-119]. It was reported that the salt-polyether complexes are induced by ion-dipole interactions between the cation and the negatively charged oxygen atoms of the polyether ring.


the original hypothesis that the main mechanism of complexation between PEO and cofactor is hydrogen bonding is invalid.

Figure 15. PM3 molecular structures of: a) PEO/corilagin and b) corilagin-Na+ complexes.

From Figure 15, it can be seen that the optimized PEO/corilagin complex (Fig. 15a) shows PEO to be in the same place as the Na+ in the corilagin-Na+ complex (Fig. 15b). We can conclude that the cations from the salts, such as Na+, bind to the cofactor and form cofactor-Na+ complexes (as confirmed by UV experiments [11). The driving force for Na+ association with the cofactor seems to be a combination of polar interactions and cation π-binding with the aromatic rings of the cofactor. It is possible that these cofactor-Na+ complexes associate more readily to PEO than the cofactor by itself, possibly because of cation binding to oxygen atoms in PEO. It is also possible that the salt associates with PEO, causing it to stiffen, which consequently lowers the entropy barrier, thus facilitating complexation. Another possibility is that the salt associates with the PEO, to make it behave like a polyelectrolyte, which then associates with the negatively charged cofactor. This mechanism would lower the entropy barrier, which is needed to allow association between these two molecules. Further research is needed to elucidate how the PEO, corilagin (cofactor) and cation (salt) are simultaneously interacting to form a complex, as observed experimentally.

Therefore, it is hypothesized that cation association can cause PEO to behave more or less like a positive polyelectrolyte. For negatively charged cofactors this will result in a stronger affinity of the cofactor to PEO. The ions can also bind to the aromatic rings of the cofactors by cation π-binding, an effect most pronounced for non-charged cofactors. These ions can act as bridges between PEO and cofactor molecules. Perhaps this is the dominant interaction for most cofactors, as it explains why all known cofactors have aromatic rings. For non-charged cofactor, such as corilagin, it may cause a stronger affinity, because the ions can also bind to the aromatic ring by cation π-binding. ACKNOWLEDGEMENTS Financial support from FPInnovations, Paprican Division, and NSERC for an Industrial Research Chair, is gratefully acknowledged.

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CONCLUDING REMARKS Small and larger PEO/cofactor systems were discussed. The PM3 Semi-Empirical Molecular Orbital Theory shows that even though bond lengths, bond angles, DLMOs and electron densities for the PEO/cofactor complexes are consistent with the definition of a hydrogen bond, the number of hydrogen bond does not correlate with the enthalpy of association at 0 K. The fact there is no correlation can be explained by: a) the change in structure of PEO and/or cofactor resulting in different molecular heats of formation, and b) additional nonhydrogen bonding attractive interactions. Moreover, PM3 calculations show that PEO/cofactor complexes do not form at room temperature, neither in the gas phase nor in water, in agreement with experiments. This indicates that other chemical interactions predominate in the bonding mechanism for this type of system at room temperature. Experimental results have shown that salt is needed for the PEO to associate with cofactors. Consequently,

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