dk2131_ch07

7Tailoring Adhesion of Adhesive Formulationsby Molecular Mechanics/Dynamics

A. PizziEcole Nationale Superieure des Technologies et Industries du Bois,

Universite de Nancy l, Epinal, France

I. INTRODUCTION

Molecular mechanics in the broader sense of the term is a computational technique whichis, among other things, particularly suited for determining at the molecular level theinteractions at the interface of well-defined polymers. It has already been used, in manyfields, for instance, to calculate the most stable conformation, hence the conformation ofminimum energy, of biological materials such as proteins, for the interactions of oxygen,carbon monoxide, and carbon dioxide on the functioning of the heme of respiratoryproteins, for the design and activity forecasting of pharmacological drugs or other biolo-gically active materials to fit the active sites of enzymes, for the determination of thestructure of a variety of high-tech materials, to determine the structure and propertiesof a variety of synthetic and natural polymers, and even to model homogeneous andheterogeneous catalysis processes. The variety and number of applications of this techni-que in the past few years are indeed great and it has positively influenced many fields ofscience.

What exactly is molecular mechanics? It is the study of the interactions of noncovalently bonded atoms in one or more molecules which determine the spatial conforma-tion of such a structure or its change of conformation induced by a neighboring molecule.In short, it is the modeling of the structures of molecules, their structural interactions andmodifications, and hence of their macroscopic and microscopic properties derived fromthe molecular level according to first principles in physics and physical chemistry. Itsmundane appearance is that of a computational technique, and today extensive computa-tion is always included. However, it is indeed much more than just a computationaltechnique: it is the technique par excellence to explain our physical world from first,molecular, and atomic principles.

While it has now been used for almost thirty years in many other fields the applica-tion of this technique in the field of adhesion and adhesives, namely to theoretical andapplied problems of adhesion and to the optimization of adhesion, is still relatively in itsinfancy. A few notable applications of this technique to adhesion and adhesives do, how-ever, exist and this chapter is aimed at describing them, and their relevant consequences

Copyright © 2003 by Taylor & Francis Group, LLC

without pretending to be either exhaustive or limiting as to what regards any other futureapplications. As molecular mechanics and molecular dynamics are really ‘‘going back tobasics’’ techniques aimed at explaining at molecular level the behavior of materials, thereis no doubt that their use is also bound to grow in the field of adhesion just as rapidly andeffectively as it has occurred in other scientific and technological fields, once the potentialof such a technique is understood.

In the field of adhesion, in its broadest sense, several different pioneering trends arealready on record, namely:

(i) studies of the adhesion of generalized particles to generalized surfaces, or ofgeneralized particle to generalized particle

(ii) studies of the adhesion of polymers well defined at molecular level to surfacesequally well defined at molecular level

(iii) studies of the dynamic, differential, competitive adsorption, hence adhesion, ofmolecularly well-defined oligomers to an equally molecularly well-defined sur-face in the presence of solvents, such as, for instance, in the modeling ofchromatography.

This chapter will address these three sectors of activity.

II. ALGORITHMS USED IN MOLECULAR MECHANICS

Different molecular mechanics systems and programs exist. There are programs that allowsimultaneous variation of bonds and bond angles as well as allowing bond rotation, andthere are programs in which instead all the covalent bond lengths and bond angles betweencovalently bonded atoms are fixed to specific values without allowance for their adjust-ment or modification during computation. It cannot be said that one system is better thanthe other as either of the two systems can be more apt at resolving a particular problem: itmight then be necessary to choose the system according to the problem at hand.

The first type of program, based on an unconstrained force field approach is morecomprehensive but suffers from the limitation of the size of molecules that can be inves-tigated due to the extent of computations needed. It is thus very apt for the study ofsmaller molecules or systems of molecules up to 40–60 atoms, but this limitation is alsofictitious because it really depends on the capacity and calculation rate of the computerused. Such unconstrained force field programs tend to suffer furthermore from the pro-blem that the automatic search for the minimum of energy might lead the program tominimize on a local rather than total minimum, and if particular attention is not exercisedcompletely false results can be obtained (the ‘‘black-box’’ syndrome).

The second type of program, based on a constrained force field approach, is gen-erally taken to render computation more rapid. It is then particularly useful when bigmolecules, such as polymers are involved. All these programs are based on the finding thatconformational studies in the field of biological macromolecules have shown that theconformational energy of a molecule can be represented with accuracy even when bondlengths and angles between covalently bonded atoms are prefixed [1], and is represented bya sum of four types of contributions namely

Etot ¼ EvdW þ EH-bond þ Eele þ Etor ð1ÞEtot represents the total conformational energy of the molecule as a function of all theinternal angles of rotation. EvdW represents the contribution to the total energy due to


van der Waals interactions between all the couples of unlinked atoms whose relativeposition depends on one or more internal bond rotational angles ð�o, oÞ (in degrees).This contribution can be expressed by Buckingham-type functions

EvdW ¼Xij

aij expð�bijrijÞ � cijr�6ij

ð2Þ

where the coefficients a, b, and c depend on the couple i , j of atoms, or by Lennard-Jones-type functions

EvdW ¼Xij

dij

r12ij

!� cij

r6ij

!" #ð3Þ

Both types of functions are commonly used. Several sets of a, b, c, and d, coefficients areavailable [1–3]. Equally good results can be obtained using Lennard-Jones-type functionsalone or Buckingham-type functions alone or mixtures of Lennard-Jones and Buckinghamfunctions [4]. The attraction coefficients cij in these expressions are generally but notalways calculated with the formula of Slater and Kirkwood [5]:

3

2exp

h

m1=2

� ��i�j

� ��iNi

� �1=2

þ �jNj

� �1=2" #

ð4Þ

where �i and �j are the values of the polarizability of the atoms i and j, and Ni and Nj arethe numbers of effective electrons, respectively.

In Eq. (2), bij is fixed to a constant value [1,6–10] and aij is determined by imposingthe minimum at the distance that is the sum of the van der Waals radii of the atoms orgroups considered [1,6–10]. The van der Waals interactions are always calculated here asthe sum of the single interactions between each couple of unlinked atoms.

Eele describes the electrostatic contribution to the total energy. Dipolar momenta arehere expressed, in the so-called monopolar approximation, by means of partial charges thevalues of which are fixed in such a manner as to reproduce the dipolar momenta of bothbonds as well as the total dipolar momentum. Using partial charges, the dipolar interac-tions can be calculated with a Coulomb-type law of the form Eele¼�ij (qi qj)/(" rij) where qiand qj are the charges of the two atoms i and j, rij is the distance between i and j and " is thedielectric constant.

Etor describes the contribution to the total energy due to hindered rotation aroundskeletal bonds. The formulas generally used for the torsional potentials are those of Brantand Flory [2,6–10] where the torsional barriers used can be of different values [2,6–10]. It isnecessary to point out, however, the limiting condition that must be imposed on therotational degrees of freedom. Rotations around bonds that have very high torsionalbarriers (C¼C, C¼O), and single bonds between them affected by their conjugation, asin the case of polypeptides, must not be considered [11].

EH-bond represents the hydrogen bond (H-bond) contribution between couples ofnoncovalently bonded atoms. Several functions, even very simplified and empiricalones, have been used, and often with good success. The H-bond, however, is at best adifficult interaction to describe through a function which is capable of both giving goodresults while really taking into account the physicochemical reality of the interaction. It isfor this reason that there is a multitude of empirical simplified functions for its calculation.Where the H-bond is of little or no importance often the molecular mechanics calculationsare just done on the basis of only the van der Waals interactions (and not with bad results,as in the earlier days of protein structure refinement). In systems in which the H-bond


contribution is important or determining to the results it is better to use a more compli-cated but more comprehensive function proposed by Stockmayer which has already beenfound to give very representative results in polypeptide sequences [11] and in cellulosesystems [12]:

EH-bond ¼ 4"�

r

� 12� �

r

� 6� �� a�b

r3

� �

� ½2 cos�a cos�b � sin�a sin�b cosð�0a � �0b Þ ð5Þ

which takes into consideration the angular dependence of the H-bond. The first term inEq. (5) describes the interaction between the hydrogen atom and the oxygen atom parti-cipating in the H-bond, and it is nothing else than a Lennard-Jones potential with theexpression in simplified form. The second term describes the H-bond as an electrostaticinteraction between two point-like dipoles of magnitudes �a and �b centered on theoxygen and hydrogen atoms. The directional character of the H-bond is assured by theangular dependence of this function, and �a and �b are the angles that the C–O and O–Hbonds form with the C–O- - -H–O segment linking the hydrogen and oxygen atoms (Fig.1). The value (�a� �b) (in degrees) is the angle between the planes containing the H-bondand the O–H and C–O bonds (Fig. 1). The ", �, and � are obtained by minimizing the firstterm of Eq. (5) at the van der Waals distance between the hydrogen and oxygen atoms,and the whole function at a H-bond distance of 2.85 A with aligned C–O and O–H bonds.

Also in many of the unconstrained force field type programs today similar expres-sions for the H-bond based on a Lennard-Jones first term as above or a Buckingham firstterm [13] followed by a term describing the dipolar and angular dependence of the H-bondare used. However, there are also a number of programs in which the H-bond is describedjust as a Buckingham function without any consideration being taken of the directionalityof the H-bond, or even by simpler expressions. There is nothing very wrong with thesesimplified approaches in cases where the H-bond is not of fundamental importance to thestudy, but they cannot be used reliably in cases where the H-bond is of determiningimportance.

III. GENERALIZED PARTICLE/SURFACE ANDPARTICLE/PARTICLE MODELS

The mechanics of particle adhesion and the deformations resulting from the stressesgenerated by adhesion forces have now been studied both experimentally and theoretically

Figure 1 Dihedral angle (�1� �2) of importance in the calculation of H-bond energy and showing

the importance of directionality in this type of interaction. (From Ref. 8.)


for a long time. Most of the approaches taken on the subject stem from a thermodynamicrather than a molecular viewpoint, such as the use of the so-called Johnson–Kendall–Roberts (JKR) model [14]. The first time that such a type of problem was approachedfrom a molecular viewpoint was the proposal by Derjaguin et al. of a new adhesion model(the Derjaguin–Muller–Toporov (DMT) model) [15]. Soon afterwards, the Muller–Yushchenko–Derjaguin (MYD) model was proposed by Muller et al. [16,17] by assumingthat the adhesion forces, and hence the interaction between a particle and a substratecould be represented by Lennard-Jones potential functions. With this theory it is notpossible as yet to speak of a molecular mechanics approach. Nonetheless, this is thefirst educated assumption and understanding that the interaction of generalized particles,atoms, and molecules can be described even for problems and theories of adhesionthrough Lennard-Jones functions, one of the classical type of potential functions usedto describe interactions in molecular mechanics. This insight perhaps opened the way tothe subsequent use of molecular mechanics in the field of adhesion. The JKR and DMTmodels have since been shown to be particular subsets of the more general MYD theory.They have been extensively studied [18–21] and models have been presented.

While all these theories have helped our understanding of particle adhesion, all ofthem suffer from the considerable drawback of treating the mechanical response of mate-rials as something totally independent of the molecular level parameters influencing adhe-sion. As the intermolecular potential of a material determines, or at least stronglyinfluences, both its mechanical properties as well as its surface energy the possibilityexists that a more holistic adhesion model could be conceived by going back to thedrawing board and starting from first principles. This, added to the fact that the theoriesbriefly referred to above do not always predict the correct value of the power law depen-dence of the contact radius on particle radius prompted some attempts in this direction.Notable in this respect are two investigations, and only here for the first time in thischapter one can really speak of a molecular mechanics approach to some form of adhe-sion. The first investigation [22] was based on molecular mechanics calculations of theinteraction of acrylic-type monomers with an idealized model surface composed of arectangular parallelepiped of generalized, idealized atoms treated as spheres arranged atregular nodes of a square grid network and constitutes the first example ever of this type ofapproach. The second one followed four years later and went further [23–25]. It was amolecular dynamics study along very similar lines as the previous one, defining theinteraction between the two surfaces of generalized, idealized atoms treated as spheres.It is this latter study which will be briefly presented and discussed, with all its advantagesand limitations, because it is a more clear-cut case of a generalized model of particleadhesion based on molecular mechanics. The former and earlier model will not be dis-cussed further as it really constitutes a hybrid case between the type of approach presentedin the following section of this chapter dealing with examples of even earlier but concep-tually more correct nongeneralized models, and the type of approach based on particleadhesion proper.

Before getting more involved in the finer points of particle adhesion studies bymolecular mechanics it must be pointed out that such an approach suffers from consider-able drawbacks. Molecular mechanics and dynamics by definition involve interactionsbetween clearly defined types of atoms, with clearly defined atomic characteristics,placed in clearly defined molecular structures. Thus, a generalized, fictitious surface ofonly, let’s say nitrogens, or even worse of generalized spheres, is a rather extreme physicalapproximation. It is by definition incorrect in a molecular mechanics and dynamics inves-tigation. Such a drawback needs to be pointed out to put in perspective and understand


the limitations inherent in a model pretending to describe atomic and molecular interac-tions in real systems by a molecular mechanics approach oversimplified at the physicallevel. Nonetheless, valuable information has been gathered by this type of approach. It isfurthermore a very good approach for the description of particle/particle interactionswhen the particles themselves are composed of well-defined atom types interacting witheach other both at the particle/particle interface and within the body of the particle itself.

The more advanced work today on particle adhesion [23–25] builds then on theassumption that particles interact through a Lennard–Jones-type potential function,namely

E ¼ �4"�

r

� 6� �

r

� 12� �ð6Þ

where " is the binding energy between an atom and its nearest neighbor and � is thedistance between the two atoms when the value of the potential energy represented bythe above function is neither attractive nor repulsive: namely at the crossover intersectionpoint of the function with the axis. The authors of the theory recognized that the choice ofthis potential was purely empirical [25].

At first a flat surface of atoms was generated in a stepwise manner allowing theenergetics associated with the creation of the surface to be determined, and then two ofthese surfaces were brought together and allowed to form a bond. The pairs of matedsurfaces were then separated in a constrained tension test to form two fracture surfaces.The potential energy of the system and the axial stresses used to produce the displacementsobserved were monitored. The molecular mechanics computational modeling part con-sisted in assembling a parallelepiped of generalized atoms as spheres, arranged in a pre-determined regular array. The computational model used in tension, compression, andshear modes allows examination of the stresses produced when free surfaces approach oneanother. The parallelepiped of atoms constituting each surface was composed of 768atoms aligned parallel to the X, Y, and Z axes of a reference system. The parallelepipedof atoms was then constituted of 24, 8, and 8 layers of atoms in the X, Y, and Z directions,respectively. By the time the first 100 iterations were terminated the system temperaturehad fallen to half of its original value as a consequence of the equipartitioning of theenergy into kinetic and potential contributions. The lateral dimensions of the surface thatwas about to be created were then fixed by putting back the atoms in their previouspositions after each computation inducing, as a consequence, a gradual increase of thegaps between atoms without actual movement of the atoms. This effectively suppressed theusual atomic motions allowing the variation of the apparent potential energy of the systemas the surfaces were separated be followed computationally. Once the size of the interatomgaps had increased to the size of the cut-off radius there was no further increase inpotential energy with increasing gap size. Once the gap was established the atomic motionsand temperature dependence were reactivated to allow the system to relax into its newstate of equilibrium.

Once the free surfaces in equilibrium were computationally generated they werebrought closer to one another by a very slow approach rate of 10,000 iterations toreduce the gap between the surfaces to one cut-off radius. The slow approach was neces-sary to minimize or eliminate complications arising from spheres’ (atoms’) impact ener-gies. All this allowed changes in potential energy and the following of the resulting surfaceinteractions which developed at constant temperature and constant dimensions. Duringthe approach the mutual attraction increased monotonically until a certain critical stresslevel was reached. At such a critical stress the two surfaces lept into mutual contact as the


strain energy increased because the rate of energy storage due to elastic deformationequated to the rate at which energy was provided by the attraction between the surfaces.Thus the model was able to reproduce, at least qualitatively, the leap-to-contact effectbetween a particle and a planar surface observed experimentally using atomic forcestechniques [26–28]. In the cases where the surfaces were pulled, rather than lept, intocontact the stresses were not uniform and traveling waves were generated. Additionaltraveling waves were also generated when the surfaces struck one another. These waves,which interacted with each other, correspond to atomic level kinetic energy and can beinterpreted as an increase in temperature. As a consequence, the authors came to theinteresting conclusion that in a real system this implied that energy loss occurred even ifonly elastic deformations resulting from the forces of adhesion were considered: hence, notall the energy is recoverable on surface separation as not all the energy of the system isstored elastically.

Study of the model during subsequent separation of the two surfaces, this corre-sponding to a tension, showed clearly the existence of hysteresis effects. This hysteresismight account for the effect of Young’s modulus on particle adhesion, which is not pre-dicted in the JKR model. In the simulation of the process of separation of the two surfacesand of the fracture mechanics of the model, fracture finally occurred only when theinteratomic spacing of some regions exceeded the critical value to an extent that furtherseparation reduced suddenly the energy. This occurred suddenly and over a very smallnumber of iterations. Even in the case of surface separation, waves were generated whichdecayed as a function of time thus generating thermal energy which was then lost by themodeled system. Thus, even during elastic deformation, surface separation energy lossmechanisms exist. The maximum stress experienced in the leap-to-contact decreased withincreasing temperature while the average stress, shortly after leap-to-contact, was muchless sensitive to the temperature. Finally there was a distinct offset between the initial andfinal potential energies due to microstructural changes in the interfacial regions as the twolayers of atoms near each of the two surfaces contained numerous site defects, namelyatom sites which were empty.

IV. ADHESION MODELS FOR WELL-DEFINED POLYMERS TOWELL-DEFINED SURFACES

Contrary to the generalized approach already presented, models describing the adhesionbetween a polymer well defined at a molecular level and another, equally molecularlywell-defined substrate also exist. These are models in which molecular mechanics anddynamics are applied in their more accepted role described in the Introduction. It mustbe realized that such models derive from a need different from what has prompted thedevelopment of the generalized models already described. They stem from the need tosolve some applied problem of adhesion or to upgrade the performance of some adhe-sive systems in situations where the use of an experimental method would take too long,or is not able to give any clear results. It is for this reason that such models need to usethe most precise and well-defined information possible or available on the moleculesinvolved as well as using the sets of potential functions which describe in the mostaccurately conceptual manner the molecular behavior of the chemical species involved:all the research work that uses this approach is then applied to ‘‘real’’ case, not toidealized models, and is of considerable sophistication. Furthermore, all this type ofresearch work is most commonly supported by direct or indirect experimental results


which prove that molecular mechanics predicted well the improvements that needed tobe implemented to upgrade adhesion or to upgrade an adhesive system. Notwithstand-ing their applied use, the sophistication of such a type of an approach has yielded veryinteresting results on the fundamental side of the science of adhesion and of the inter-face and it offers considerable promise and opportunities for more progress in thefuture.

The first of such studies [8] appeared in 1987 and thus preceded by a couple of yearsthe first of the generalized approach studies [22]. It concerned the adhesion of phenol–formaldehyde (PF) polycondensates and resins to cellulose, hence to wood. It was fol-lowed later by other studies on the adhesion to crystalline and amorphous cellulose ofurea–formaldehyde (UF) resins [7], of more complex PF oligomers [10], of water [29,30],of chromates [31], and finally of the more complex case of ternary systems in which twointerfaces exist, namely in the situation of adhesion to cellulose and wood of an acrylicundercoat composed of a photopolymerizable primer onto which was superimposed analkyd/polyester varnish [32,33]. The molecular mechanics algorithms used for all thesestudies were those already presented at the beginning of this chapter. The only differencewas that for just the last of the studies mentioned the negligible importance of H-bondingto that particular system led to disregarding it in the calculations. Before the first of thesestudies, the understanding of the phenomenon of adhesion between a well-defined pair ofadhesive and adherend had never been attempted by means of calculation of all the valuesof secondary interactions between the non covalently bonded atoms of the two moleculesinvolved. This approach was rendered possible by the codification, again by molecularmechanics (or conformational analysis, as this technique was known in earlier days) fromthe data of earlier x-ray diffraction studies, of the spatial conformation of native crystal-line cellulose (or cellulose I) [12], of the several mixed conformations possible for amor-phous cellulose [12], and also of PF oligomers [34].

This initial molecular mechanics calculation was limited to the interaction withcrystalline cellulose I of all the three possible PF dimers in which a methylene bridgelinks two phenol nuclei ortho–ortho, para–para and ortho–para. As not much wasknown as to how the system would react the investigation was very extensive. As celluloseconstitutes as much as 50% of wood, where its percentage crystallinity is as high as 70%,this study also inferred applicability to a wood substrate. As even dried wood alwayscontains a certain amount of water the influence of the water was taken into accountby introducing into the calculations the effect of a parameter related to the dielectricconstant of water.

The results obtained clearly indicated that adhesion of PF resins to cellulose waseasily explained as a surface adsorption mechanism, a fact which, while very acceptedtoday, was not evident in the wood gluing field and in the literature up to that time. Thisresults also indicated that the interaction of the PF dimers with cellulose on all possiblesites was more attractive than the average attraction by the cellulose molecule for thesorption of water molecules. In a few cases only, the interaction of water molecules withthe few strongest sorption sites of cellulose was more attractive than that of PF dimers.This implied that in general even for the more difficult to wet crystalline cellulose the PFdimers, and by inference also higher PF oligomers, were likely to displace water to adhereto the cellulose surface. This was an important findings as it did show for the first time bynumerical values that in wood bonding the adhesion of the polymer resin to the woodmust be considerably better than the adhesion of water molecules to the wood. It is ofimportance first for ‘‘grip’’ by the adhesive of the substrate surface and secondly, in thecured adhesive state, in partly determining the level of resistance to water attack of the


interfacial bond between adhesive and adherend. This result added a new dimension to thewell-known water and weather resistance of PF-bonded lignocellulosic materials: it is notonly due to the imperviousness to water of the cured PF resin itself, as believed up to then,but also to the imperviousness to water of the adhesive/adherend interfacial bond, a bondexclusively formed through secondary forces. A further deduction, with some appliedinference, from the results was that a PF resin used to impregnate wood was likely todepress the water sorption isotherm of both wood and cellulose according to the numberof substrate sorption sites which, on curing, have been denied to water, a deduction laterconfirmed experimentally.

The most important result, however, was that there were significant differences in thevalues of minimum total energy in the interaction of the three PF dimers with cellulose. Itwas possibly the more important conclusion, because it also had the more immediateindustrial application. The ortho–ortho and ortho–para dimers had much greater averagerelative Etot of interaction with the cellulose surface than the para–para dimer. In generalthe distribution of the methylene linkage in standard commercial PF resins at that timeindicated a higher proportion of the ortho–para and para–para linkage over the ortho–ortho linkages. Experimental results confirmed this finding [35]. Maximization of theproportions of ortho–ortho and ortho–para linkages and decrease of the relative propor-tion of the para–para coupling is easily obtained in PF resin manufacturing by the additionof ortho–orientating additives [37–40]. As a consequence, the adhesion and performanceimprovement caused by a shift in the relative proportions of methylene bridge couplingrenders possible the reduction by about 10% of the quantity of PF adhesive resins used ina product such as wood particleboard, at parity of performance. Alternatively, it doesimprove the performance at parity of quantity: not bad results if one considers thatapproximately 2 million tons of PF resins are used for wood bonding each year. It isnot claimed here that the molecular mechanics result converted the PF resins industry tomaximize ortho–coupling, but the theoretical justification it offered contributed to greatlyaccelerating the already existing empirical trend in such a direction. Maximization ofortho–coupling in commercial PF resins is now a much more common practice. Furtherconfirmation of this was later obtained by studies of dynamic, differential, and competitiveadsorption [9] which will be discussed in the next section of this chapter.

The findings also contributed to the visualization of the conformation of minimumenergy of a resin on a substrate: the equivalent of a static, schematic photograph of theconformation of the two molecules at the interface. An example of this is shown in Fig. 2.It also contributed to the understanding, although this came from later work [7], that notonly the energy at the interface but also the conformation of minimum energy of amolecule on a substrate was quite different from the conformation of minimum energyof the same molecule when alone, or when on a different substrate. This was confirmedlater by x-ray studies determining the degree and/or lack of crystallinity of hardened UFresins in the presence or absence of cellulose [41]. It is also for this reason that idealizedmodels are limited to never being able to complete with ‘‘real’’ models to solve adhesionproblems.

Further molecular mechanics investigations in the same direction but for UF resinsalso followed, with equally interesting results. In these the efficiency of resin adhesion toboth amorphous and crystalline celluloses was computed by following the synthesis of theresin. This was achieved by calculating by molecular mechanics the adhesive/adherendinteractions with the two types of cellulose for each isomeride produced throughthe reaction of urea with formaldehyde. This was done up to the level of trimer.The adhesive/adherend interactions were calculated for urea, monomethylene diureas,


and dimethylene triureas, and their mono-methylolated, dimethylolated and trimethylo-lated species [6,7]. All the results found correspondence in already existing experimentalresults [42–44]. It was found, for example, that the lack of water- and weather-resistance oflignocellulosic materials bonded with UF resins did not appear to be due, to any largeextent, to failure of their adhesion to cellulose. However, contrary to the case of PF resinsexposed above, failure in the presence of water of UF resins to adhere to cellulose was alsofound to be only a minor contributory factor to their lack of water resistance. Thisconfirmed that the lability to water attack of UF resins resided mainly in the hydrolysisof their amidomethylenic bond, a fact since confirmed experimentally. More important isthe finding, later confirmed by x-ray diffraction [41], that when UF resins are interactingwith cellulose some of the conformations that would be forbidden when the UF resin iscured alone become possible and are allowed. This same experimental study also con-firmed that the secondary forces binding together linear chains, not cross-linked, of UFoligomers with cellulose were stronger than the intermolecular forces between the UFoligomers themselves. The molecular mechanics method used allowed the start of thepolymerization of UF resins on the surfaces of cellulose be followed. This was achieved

Figure 2 Example of planar projection of one of the configurations of an ortho–para PF dimmer

on the surface of a schematic cellulose crystallite showing a phenolic dimmer (a dihydroxy

diphenyl methane) conformation of minimal energy and main dimer–cellulose hydrogen bonding.

(From Ref. 8.)


by comparing the different energy levels of the different oligomers as the reaction proceedsfrom one oligomer to the next one (Fig. 3). The experimental consequence of this studywas the development of a method to evaluate comparatively the applied performanceof UF resin prepared according to different procedures just starting from the relativeabundance of the various UF oligomers in each resin and their molecular mechanics

Figure 3 Averages, minima, and averages per atom of the interaction energy of UF oligomers with

crystalline cellulose I (in kcal/mol) (negative signs indicate attractive interactions hence adhesion).

(From Refs. 6, 7.)


calculated energy of interfacial interaction [6,7,45]. Similar results were also obtained witha more comprehensive investigation of the oligomers of PF resins [10].

It is however, with the more complex and comprehensive investigation of ternarysystems that this molecular mechanics approach started to yield results of greater intereston the fundamental principles of adhesion [32]. Ternary systems present two interfacesbecause they are composed of three molecular species, namely the cellulose substrate, aphotopolymerizable primer resin, and a top coat alkyd/polyester varnish [32]. This workwas started mainly to address the concept of flexibility of a surface finish system onlignocellulosic materials but led to some unexpected and rewarding results on adhesiontoo. Examples of the visualization of the conformations of minimum energy of ternarysystems are shown in Figs. 4–6.

Three photopolymerizable primer monomers, namely the linear hexanediol diacry-late (HDDA), the branched trimethylol propane triacrylate (TMPTA), and the lineartripropyleneglycol diacrylate (TPGDA), and a model of a linear unsaturated polyester/alkyd varnish repeating unit were used for the study. A model of the two top chains of anelementary cellulose I crystallite was used as a substrate, the refined conformation ofwhich had already been reported [12].

The number of degrees of freedom for such calculations is considerable and parti-cular techniques, already used in previous work [7–10], were used to facilitate the compu-tation. At the end the total varnish/primer/cellulose assembly was allowed to adjust andminimize the energy of its configuration.

Figure 4 Example of planar projection of the minimal energy configuration of a ternary system

composed of a cellulose I schematic elementary crystallite surface, the photopolymerizable acrylic

primer tripropyleneglycol diacrylate (TPGDA), and a polyester finish. (From Refs. 72, 73.)


The applied part of this study relied on a standard peel test in which closelyset vertical and horizontal cut lines had been incised on the specimen surface, andon a dynamic thermomechanical analysis of finish flexibility at constant temperature[32,33,46].

Figure 5 Example of perspective view of the ternary system in Fig. 4. (From Refs. 72, 72.)

Figure 6 Example of view along the cellulose crystallite axis of a ternary system similar to that in

Fig. 4 but using a different photopolymerizable acrylic primer, namely trimethylolpropane triacry-

late (TMPTA). (From Ref. 73.)


An equation correlating TMA deflection and interaction energy at the interface wasfound by its study:

E ¼ �km

�fand conversely f ¼ �km

�Eð7Þ

where � is the coefficient of branching by reactive sites, equal to both Flory’s coefficient ofbranching for polycondensates [47] and a similar coefficient based on reactive carbons ineach monomer for radical polymerization compounds. E is the interaction energy of themolecule of monomer with the substrate, hence the thermodymanic work of adhesion,calculated by molecular mechanics. f is the relative deflection obtained for the system bythermomechanical analysis (TMA), m is the maximum ideal number of internal degrees offreedom of the monomer once it is bound in the network. When m is measured experi-mentally by TMA it is the number-average number of internal degrees of freedom of thesegments between cross-linking nodes. k is a constant. This equation can be used todetermine the energy of interfacial interaction starting from a measure of TMA deflection,or vice versa. It is then a useful experimental tool.

The results and effectiveness of Eqs. (7) were checked also for other, quite differentpolymers, namely the polycondensates of resorcinol–formaldehyde, of melamine–urea–formaldehyde (MUF), of PF, and of quebracho and pine polyflavonoid tannins hardenedwith formaldehyde. The comparison of the energies of interaction obtained by measures ofTMA deflection and the use of this formula compared well with the results alreadyobtained for their energy of adhesion with crystalline cellulose in previous work [16–10].It appears, then, that the formula works also for entanglement rather than just cross-linked networks.

It was also interesting to relate what was discussed above to existing models relatingadhesion strength and adhesion energy. In the rheological model [48–53] the peel adhesionstrength G is simply equal to the product of the adhesion energy E and a loss function �which corresponds to the energy irreversibly dissipated in viscoelastic or plastic deforma-tions in the bulk materials and at the crack tip and which depends on both peel rate v andtemperature T. Thus

G ¼ E�ðv,T Þ ð8ÞThe value of � is usually far higher than that of E and the energy dissipated can then beconsidered as the major contribution to the adhesion strength G. It is more convenient inthe above equation to use the intrinsic fracture energy G0 of the interface in place of E tohave G¼G0�(v, T ). When viscoelastic losses are negligible, � tends to one and G musttend towards E. However, the resulting threshold value G0 is generally a few orders ofmagnitude higher than E. Carre and Schultz [54] have concluded that the value of G0 canbe related to E for cross-linked elastomer/substrate assemblies through the expression

G0 ¼ EgðMcÞ ð9Þwhere g is a function of molecular weight Mc between cross-linked nodes and correspondsto molecular dissipation.

This lead to a few interesting considerations as regards the results obtained bymolecular mechanics on the primer/cellulose interfaces. From the equation obtained torelate the flexibility at the interface to the interaction energy it is evident that E�m/(�f )(the negative sign of E obtained by molecular mechanics is a convention to indicateattraction rather than repulsion). The concept of Mc is intrinsic in the (m/n)/� ratiorelating the number of degrees of freedom m per number of atoms n of the segments


between cross-linking nodes as determined by �. This means that g(Mc) can be representedby m(�f) and hence

G0 � Em=ð�f Þ thus G0 � E2 ð10Þ

This is an important aspect and would at least partly explain in a manner somewhatdifferent from the more accepted explanations why G0 is generally 100 to 1000 timeshigher than the thermodynamic work of adhesion [48]. It indicates that G�E�(v, T )m(�f ), or differently expressed G�E2�(v, T ). Apart from this the interesting considera-tion still holds that the flexibility at the interface is inversely proportional to both theintrinsic fracture energy and to the peel adhesion strength at least where the effect of � isminimized.

This work also defined that the relation of G0 to the thermodynamic work of adhe-sion WA in tests varied according to the case considered. Thus, the molecular mechanicsstudy showed in general G0 � W2

A in tests in which viscoelastic dissipation of energy waseliminated or at least strongly minimized. This partly explains why G0 is generally 100 to1000 times higher than the thermodynamic work of adhesion [48]. This is not all, because itwas shown that G0 still included a component based on the viscoelastic properties of thematerial which it might not be possible to separate from G0, then indeed G0 � W2

A.However, if the viscoelastic component is all transferred as it should be into the viscoe-lastic energy dispersion function �(v, T ), then G0 ¼ W2

A. It must be noted that it might notbe possible to really separate completely the viscoelastic dispersion of energy componentfrom G0 as it is intrinsic to it. Conversely, it was also shown that the theoretical case inwhich the viscoelastic component characteristic of the material (not the effect of crack tippropagation within the material) had been minimized or eliminated the expressionG0 � W2

A really meant that WA � G0 W2A rendering acceptable also the alternative

findings by other authors that under certain circumstances G0�WA.All the above, and the fact that by definition the molecular mechanics interaction

energy is proportional to the thermodynamic work of adhesion, hence kEtot¼WA, alsobrings the interesting consideration that

kEtot � G0 � kE2tot where Etot ¼ k½EvdW þ EH�bond þ Eele þ Etor 2 ð11Þ

where the molecular mass Mc of Eq. (9) is represented by the combination of a number ofparameters involved in Eq. (11). Mc is represented by the molecular degrees of freedom;the type of atoms involved; the coefficient of molecular branching/cross-linking; the atomspolarizability; the angle and direction of the interactions; the electrostatic charges; thenumber of effective electrons participating; and the dipolar momenta. The mass is then aparameter used, incorrectly, only as a simplified blanket parameter covering all this.Furthermore, to be conceptually correct even symmetrical and asymmetrical bond/angles stretching movements, and molecular translational movements, even if their con-tribution is quite small, should be considered.

All the calculations which have reported up to now were carried out by maintainingunaltered the structure of the elementary cellulose I crystallite in its conformation ofminimum energy derived from x-ray diffraction data [55–60] refined and minimized inits atomic coordinates and charges [12,61–65]. The blocking of the cellulose crystallitesurface in a fixed, predetermined conformation of minimum energy is a very acceptableassumption given the energetic stability of the crystallite itself. However, it is also ofinterest to investigate what influence the application of a primer or of a finish can have


on the surface conformation of a cellulose crystallite as predicted by a molecularmechanics method. As the calculations involved are considerable, a simpler algorithmwas used [66] for the calculations. Thus, the conformation variation of a system composedof the primer and of the finish superimposed on two parallel chains of the elementarycrystallite of cellulose I was followed. All the component molecules were allowed to move.At the start the two cellulose chains were in their configurations of minimum energyalready calculated. The results obtained were of two types:

(i) the stabilization obtained in terms of total energy of the system indicated thatthe longer was the segment which relied on secondary forces of adhesion to thecellulose surface the better was the stablization of the system by secondaryforces: logically this result should have been expected

(ii) the conformation of the two chains of the cellulose changed, but what wasunexpected was that it changed to the conformation of the crystallite of cellu-lose II [61], i.e. a different, more stable crystalline morphology!

This latter is an interesting result which infers that treatment of a lignocellulosicsurface with a surface finish or other polymers might well alter irreversibly the conforma-tion of the structure of some of the wood constituents. It implies that to discuss adhesionin terms of modification of the conformation of only the applied polymer without takinginto account the variations induced in the substrate itself by the applied polymer mightgive only a very partial view of the process of adhesion at the molecular level. Previous,generalized but still very acceptable models [22] in which the substrate is taken as ahomogeneous surface of hard or soft spheres can describe very well the cases in whichthe substrate is constrained in such a way that it cannot modify its configuration.However, these models cannot explain well the cases in which the substrate moleculechanges its configuration as a consequence of the interactions exercised on it by anotherpolymer species, at the interface: a far reaching conclusion. Notwithstanding this, thesituation for crystalline cellulose I was found to be only partially one of these cases,due to the special limits and constraints to which such a rigid structure is subjected inits natural state.

It is also evident from the above that in the case of the primer substrate systems inwhich the primer is highly cross-linked and the cellulose crystallite is a highly crystallinesolid no diffusion mechanisms at the molecular interface are likely. The situation mightwell be different when one deals with a molecular interface were reorganization of thesubstrate as a consequence of the interfacial interaction forces induced by the finish isindeed possible (see above). This is the case of a primer monomer, or even a primer of alow degree of polymerization or cross-linking, on amorphous cellulose or even on a subelementary cellulose crystallites area. In this case the reported inverse dependence of thepeel energy G of the system on, among others, the inverse of the molecular mass (1/M)2/3

applies [48,l67]. It appears again to be confirmed by the dependence on m and �, twoparameters clearly linked to the molecular mass of the finish monomer, of the surfacefinish and of the segments between cross-linking nodes of the network when this exists.That m, n, and � are the key parameters representing the molecular mass is confirmed bythe known dependence of peel strength on a 2/3 exponent of the molecular mass [48,67].This clearly points out the constraints of rotational degrees of freedom (and rotationalenergy barriers) found for monomers the end atoms of which are constrained [32].Furthermore, the apparent proportionality of the diffusion coefficient of the movementof reptation toM�2 [48,68–70] appears to be confirmed by the direct proportionality of theinterfacial flexibility to the number of degrees of freedom m of the system. The more


flexible is the system, hence the greater is the number of its degrees of freedom per unitmass (or per atom) the easier is interdiffusion. This shows again that it is not the molecularmass of the chemical species as such which will determine either the coefficient of diffusionor the relaxation time of reptation, but these two latter undoubted relation to the flexibilityof the system which depends on the parameters m, n, �, and E, and especially the per atomvalues m/n and E/n.

V. DYNAMIC ADHESION MODELING OF MOLECULARLYWELL-DEFINED SYSTEMS

The molecular mechanics approach just described functions well, but the manner in whichit has been used in the previous section is rather limited to static situations: dynamicsituations can also be described well, although by a series of finite steps of ‘‘before andafter’’ static calculations to ascertain the changes which have occurred or while they areoccurring. Even the most modern molecular mechanics and dynamics programs still workin this manner. It might appear otherwise to a user, but every automatic molecularmechanics or dynamics computational program still works by a sum of small static situa-tion steps, even if infinitesimally small. There is nothing wrong in such an approach ofcourse, as it has been proven to work rather well even in the most complex situations.However, it is interesting to examine how such an approach works for systems in whichmovement at the molecular rather than atomic level is inherent in the definition of thesystem itself.

As regards adhesives proper only two series of studies fall in this category [9,71]. Thefirst one of these models the process of chromatography [9]. There is no doubtthat chromatography is a clear case of differential, competitive sorption, and hence acase of differential, competitive adhesion. Movement is inherent in the definition ofthe system, and predominance of secondary force interfacial interactions is inherent tothe system too.

The study [9] concerns the achiral paper chromatography separation of three dihy-droxydiphenylmethanes (the three PF resin adhesive dimers discussed earlier in this chap-ter) on crystalline cellulose, and checks whether the results, the relative Rf values obtainedby experimental chromatography, correspond to the interaction energies calculated at theinterface. The algorithms used were the same as used for the previous approach. Theresults obtained were excellent, showing not just a trend correspondence between experi-mental Rf values and calculated energy values but even very close numerical correspon-dence with the actual relative values of Rf for the three compounds. One of the mostinteresting findings was that in the case of the interaction with a substrate of a homologousseries of chemical compounds, the solvent or mixture of solvents could be easily modeledby just varying the dielectric constant used in the model. Such a result is of importancebecause it spares in many ternary systems the need to model the third component of thesystem, namely the solvent or the water present either in the polymer or in the substrate(such as in wood and cellulose).

The work was continued on the paper chromatography modeling of UF oligomers[72]. In this series of experiments the limits of the molecular mechanics approach finallystarted to become apparent. While a good trend correspondence with experimental Rf

values was again obtained within each of the two series of UF oligomers tested, corre-spondence was lost when one tried to compare the compounds within a series with thecompounds of the other series. Thus, excellent correspondence existed within the homo-


logous series urea, methylene-bis-urea and dimethylene-triurea, and within the secondhomologous series monomethylol urea, N,N0-dimethylol urea, trimethylol urea, mono-methylol methylene-bis-urea, and N,N0-dimethylol methylene-bis-urea, but not betweenthe two series. It became evident that to compare within two nonhomologous series ofcompounds it would be necessary to model the water in the system as a third group.Thus, the conclusion was that the wise use of the dielectric constant to spare modelinga ternary system was very valid, but only when the molecules to be compared belonged toa homologous series of compounds; If they were not, one needed to model the solvent tooas a separate species [72]. There is no doubt that this can be achieved, either by a classicalmolecular mechanics method, or even better by modeling the solvent through a moleculardynamics approach in which a solvent layer is modeled as in Section III for the generalizedsystem while the substrate and the polymer are still modeled by more classical molecularmechanics approaches. The study of the chromatography of UF adhesives on cellulose didnot have such an industrial importance to warrant such an extensive, further investigation.Thus, the next investigation centered instead on the more difficult ternary systems but for atotally different set of molecules: this is the work on varnish/primer/cellulose systemsreported earlier in this chapter.

The second study [71] is even more interesting and concerns the simulation ofdifferent polymers adsorbed onto an alumina surface. The alumina surface was modelledand a number of different polymers were modeled at the polymer–alumina interface.Among the adhesives modeled on the surface of alumina were polyolefins, several poly-acrylates, polyoxides, polyols, and the polyphenyl bridges in epoxy resins, in diaminodi-phenylsulfones and in diaminodiphenylmethanes (the same PF dimers modeled above onthe surface of cellulose). The authors found that the method not only facilitated visua-lization of the preferred orientation of the adhesive chains with respect to the substratesurface (Figs. 7 and 8), but also indicated which groups were critical in determining suchorientations. Their results again confirmed what was found in all previous studies thateven in such a different series of adhesive/substrate systems the polymer structure whichdeformed easily was favorable to a more optimal orientation for adsorption on thesubstrate surface. The authors could identify which –CH2– groups and phenylenes inthe backbone of the polymer were conductive to such deformations, and that the alkylside groups found it more difficult to yield optimal deformation during the adsorptionprocess, but were still able to produce strong adhesion once they had been adsorbed.Besides, the polyphenyl linkages revealed a wide low energy region in the rotations oftorsional angles, this being favorable to deformation of the polymer chains with pheny-lene linkages in the backbone leading to large adsorption energies. Polar side groupsinstead were found to increase adsorption, confirming previous results, and in line withexpectation. While the range of energy results reported was quite limited, as one couldunderstand by the number of different cases approached, the study can be consideredmore as a purely comparative scan of the behavior of certain adhesives on an aluminasurface rather than an in-depth investigation of the behavior of each adhesive/substratesystem. Notwithstanding this, the calculated results once again could be qualitativelycorrelated with experimental observation, and the order of the energy interactions wasshown to be the same. These results showed again how simulations by molecularmechanics/dynamics could potentially by used to facilitate the design of improvedadhesives.


VI. CONCLUSION

The material discussed in this chapter should give the reader a brief overview of what hasalready been achieved in the field of molecular mechanics to improve adhesion or toexplain adhesion phenomena. More will surely be achieved in times to come by theapplication of such tools to adhesion problems. Molecular mechanics and dynamicsthen present a powerful tool which should not be ignored in the field of adhesion andadhesives.

Figure 7 Simulation of the adsorption of poly(tetrahydrofuran) (PTHF) on an alumina surface for

20 ps. (From Ref. 71.)


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