Лако-красочные материалы — производство

The thermodynamic model of adhesion, generally attributed to Sharpe and Schonhorn [35], is certainly the most widely used approach in adhesion science at present. This theory is based on the belief that the adhesive will adhere to the substrate because of interatomic and intermolecular forces established at the interface, provided that an intimate contact is achieved. The most common interfacial forces result from van der Waals and Lewis acid- base interactions, as described below. The magnitude of these forces can generally be related to fundamental thermodynamic quantities, such as surface free energies of both adhesive and adherend. Generally, the formation of an assembly goes through a liquid — solid contact step, and therefore criteria of good adhesion become essentially criteria of good wetting, although this is a necessary but not sufficient condition.

In the first part of this section, wetting criteria as well as surface and interface free energies are defined quantitatively. The estimation of a reversible work of adhesion W from the surface properties of materials in contact is therefore considered. Next, various models relating the measured adhesion strength G to the free energy of adhesion W are examined.

1. Wetting Criteria, Surface and Interface Free Energies, and Work of Adhesion In a solid-liquid system, wetting equilibrium may be defined from the profile of a sessile drop on a planar solid surface. Young’s equation [36], relating the surface tension у of materials at the three-phase contact point to the equilibrium contact angle в, is written as

ySV = ySL + yLV cos в (2)

The subscripts S, L, and V refer, respectively, to solid, liquid and vapor phases, and a combination of two of these subscripts corresponds to the given interface (e. g., SV corre­sponds to a solid-vapor interface). The term уSV represents the surface free energy of the substrate after equilibrium adsorption of vapor from the liquid and is sometimes lower than the surface free energy уS of the solid in vacuum. This decrease is defined as the spreading pressure л (л = yS — ySV) of the vapor onto the solid surface. In most cases, in particular when dealing with polymer materials, л could be neglected and, to a first approximation, yS is used in place of ySV in wetting analyses. When the contact angle has a finite value (в > 0°), the liquid does not spread onto the solid surface. On the contrary, when в = 0°, the liquid totally wets the solid and spreads over the surface spon­taneously. Hence a condition for spontaneous wetting to occur is

yS > ySL + yLV (3)

or

S = y S — y SL — yLV > 0 (4)

the quantity S being called the spreading coefficient. Consequently, Eq. (4) constitutes a wetting criterion. It is worth noting that geometrical aspects or processing conditions, such as surface roughness of the solid and applied external pressure, are able to restrict the applicability of this criterion.

However, a more fundamental approach leading to the definition of other wetting criteria is based on analysis of the nature of forces involved at the interface and allows calculation of the free energy of interactions between two materials to be made. For low — surface-energy solids such as polymers, many authors have estimated the thermodynamic surface free energy from contact-angle measurements. The first approach was an empirical one developed by Zisman and co-workers [37-39]. They established that a linear relation­ship often exists between the cosine of the contact angle, cos в, of several liquids and their surface tension, yLV. Zisman introduced the concept of critical surface tension, yc, which corresponds to the value of the surface energy of an actual or hypothetical liquid that will just spread on the solid surface, giving a zero contact angle. However, there is no general agreement about the meaning of yc and Zisman himself has always emphasized that yc is not the surface free energy of the solid but only a closely related empirical parameter.

For solid-liquid systems, taking into account Dupre’s relationship [40], the adhesion energy WSL is defined as

wsl = ys + Уlv — ysL = yLV(1 + cos e) (5)

in agreement with Eq. (2) and neglecting the spreading pressure. Fowkes [41] has proposed that the surface free energy y of a given entity can be represented by the sum of the contributions of different types of interactions. Schultz et al. [42] have suggested that y may be expressed by only two terms: a dispersive component (London’s interactions) and a polar component (superscripts D and P, respectively), as follows:

y = yD + yP (6)

The last term on the right-hand side of this equation corresponds to all the nondispersion forces, including Debye and Keesom interactions, as well as hydrogen bonding. Fowkes [43] has also considered that the dispersive part of these interactions between solids 1 and 2 can be well quantified as twice the geometric mean of the dispersive component of the surface energy of both entities. Therefore, in the case of interactions involving only dis­persion forces, the adhesion energy W12 is given by

W12 = 2(yDy D )1/2 (7)

By analogy with the work of Fowkes, Owens and Wendt [44] and then Kaelble and Uy [45] have suggested that the nondispersive part of interactions between materials can be expressed as the geometric mean of the nondispersive components of their surface energy, although there is no theoretical reason to represent all the nondispersive interac­tions by this type of expression. Hence the work of adhesion W12 becomes

W12 = 2(yDy D )1/2 + 2(y p yP )1/2 (8)

For solid-liquid equilibrium, a direct relationship between the contact angle в of the drop of a liquid on a solid surface and the surface properties of both products is obtained from Eqs. (5) and (8). By contact-angle measurements of droplets of different liquids of known surface properties, the components yD and yp of the surface energy of the substrate can then be determined.

More recently, it has been shown, in particular by Fowkes and co-workers [46-49], that electron acceptor and donor interactions, according to the generalized Lewis acid — base concept, could be a major type of interfacial force between the adhesive and the substrate. This approach is able to take into account hydrogen bonds, which are often involved in adhesive joints. Moreover, Fowkes and Mostafa [47] have suggested that the contribution of the polar (dipole-dipole) interactions to the thermodynamic work of adhesion could generally be neglected compared to both dispersive and acid-base con­tributions. They have also consindered that the acid-base component Wab of the adhesion energy can be related to the variation of enthalpy, — AHab, corresponding to the establish­ment of acid-base interactions at the interface, as follows:

W ab = f {—AH ab) nab (9)

where f is a factor that converts enthalpy into free energy and is taken equal to unity, and nab is the number of acid-base bonds per unit interfacial area, close to about 6 pmol/m2. Therefore, from Eqs. (7) and (9), the total work of adhesion W12 becomes

W12 = 2 (kDVD)1/2 + f (—AHab) nab (10)

The experimental values of the variation of enthalpy (—AHab) can be estimated from the work of Drago and co-workers [50,51], who proposed the following relationship:

—AHab = CACB + EAEB (11)

where CA and EA are two quantities that characterize the acidic material at the interface, and similarly, CB and EB characterize the basic material. The validity of Eq. (11) was clearly evidenced for polymer adsorption on various substrates [49]. Another estimation of (—AHab) can be carried out from the semiempirical approach defined by Gutmann [52], who has proposed that each material may be characterized by two constants: an electron acceptor number AN and an electron donor number DN. For solid surfaces, similar numbers, KA and KD, respectively, have been defined and measured by inverse gas chro­matography [53-55]. In this approach, the enthalpy (—AHab) of formation of acid-base interactions at the interface between two solids 1 and 2 is now given by [52,53]

—AHab = KA1KD2 + KA2KD1 (12)

This expression was applied successfully by Schultz et al. [55] to describe fiber-matrix adhesion in the field of composite materials.

Finally, it must be mentioned that acid-base interactions can also be analyzed in terms of Pearson’s hard-soft acid-base (HSAB) principle [56,57]. At present, the application of this concept to solid-solid interactions and thus to adhesion is under investigation.

2. Models Relating the Adhesion Strength G to the Adhesion Energy W Although described also in Section II. F, these models also apply to other types of inter­facial interactions. One of the most important models in adhesion science, usually called the rheological model or model of multiplying factors, was proposed primarily by Gent and Schultz [3,4] and then reexamined using a fracture mechanics approach by Andrews and Kinloch [58] and Maugis [59]. In this model, the peel adhesion strength is simply equal to the product of W by a loss function Ф, which corresponds to the energy irreversibly dissipated in viscoelastic or plastic deformations in the bulk materials and at the crack tip and depends on both peel rate v and temperature T:

G = WФ(v, T) (13)

As already mentioned, the value of Ф is usually far higher than that of W, and the energy dissipated can then be considered as the major contribution to the adhesion strength G. In the case of assemblies involving elastomers, it has been clearly shown in various studies [3,4,58,60-62] that the viscoelastic losses during peel experiments, and consequently, the function Ф, follow a time-temperature equivalent law such as that of Williams et al. [63].

It is more convenient to use the intrinsic fracture energy G0 of the interface in place of W in Eq. (13), as follows:

G = G<^(v, T) (14)

Effectively, when viscoelastic losses are negligible (i. e., when performing experiments at very low peel rate or high temperature), Ф! І and G must tend toward W. However, the resulting threshold value G0 is generally 100 to 1000 times higher than the thermodynamic work of adhesion, W.

From a famous fracture analysis of weakly cross-linked rubbers called the trumpet model, de Gennes has derived [64] an expression similar to equation (14) when the crack propagation rate v is sufficiently high. He distinguished three different regions along the trumpet starting from the crack tip: a hard, a viscous, and finally, a soft zone. The length of the hard region is equal to vr, where r is the relaxation time, and then the viscous region extends to a distance Xvr. Factor X is the ratio of the high-frequency elastic modulus to the zero-frequency elastic modulus of the material, and obviously represents the viscoelastic behavior of the rubber. Hence according to this approach, it is shown that the total adhesive work is given by the following expression, similar to Eq. (14):

G — G0X (15)

where G0 is the intrinsic fracture energy for low velocities (i. e., when the polymer near the crack behaves as a soft material).

Carre; and Schultz [65] have reexamined the significance of G0 on cross-linked elastomer-aluminum assemblies and proposed that it can be expressed as

G0 = Wg(Mc) (16)

where g is a function of molecular weight Mc between cross-link nodes and corresponds to a molecular dissipation. Such an approach is based on Lake and Thomas’s argument [66], which states that to break a chemical bond somewhere in a chain, all bonds in the chain must be stressed close to their ultimate strength. More recently, de Gennes [67] has proposed further analysis of this problem. He postulates that the main energy dissipation near the interface could be due to the extraction of short segments of chains in the junction zone during crack opening, this phenomenon being called the suction process. From a volume balance and a stress analysis, the following expression of the intrinsic fracture energy G0 is obtained for low fracture velocity:

G0 = aca2vb (17)

where ac is a threshold stress that can be considered as a material constant to a first approximation, and a2, v, and L are, respectively, the cross-sectional area, the number per unit interfacial area, and the extended length of chain segments sucked out during the crack propagation. At present, no experimental verification of this approach has yet been published. Obviously, this analysis holds only for values of L less than Le (i. e., the critical length at which physical entanglements between macromolecular chains just occur). The case where L > Le implies at least a disentanglement process, but above all, a process of chain scission, which is analyzed below.

Concerning the adhesion phenomena occurring at the fiber-matrix interface in com­posite materials, Nardin and Schultz [68] have recently proposed that the shear strength r, of the interface, measured by means of a fragmentation test on single fiber composites, is related directly to the free energy of adhesion W, calculated from Eq. (10), according to

(E 1/2

G — *r = (-Et) W (18)

In this expression, к is a constant equal to about 0.5 nm, corresponding to a mean intermolecular distance when only physical interactions (dispersive and acid-base inter­actions) are involved; Em and Ef are the elastic moduli of the matrix and the fiber, respectively. This model is equivalent to that of Gent and Schultz [3,4] for a cylindrical geometry and in the case of pure elastic stress transfer between both materials. It is very well verified experimentally for various fiber-matrix systems. The influence of the forma­tion of interfacial layers exhibiting mechanical behavior completely different from that of the bulk matrix has also been examined [31].

Finally, it is worth examining the analyses concerning tack, in other words, the instantaneous adhesion when a substrate and an adhesive are put in contact for a short time t (of the order of 1 s) under a given pressure. This tack phenomenon is of great importance for processing involving hot-melt or pressure-sensitive adhesives. First, it has clearly been shown [69] that the viscoelastic characteristics of the adhesive, in parti­cular its viscous modulus, play a major role on the separation energy. Recently, de Gennes [70] has suggested that the measured tack could be related to both the free adhesion energy W and the rheological properties of the bulk adhesive, as follows:

where and ц0 are the high-frequency and zero-frequency moduli of the adhesive, respectively, and r is the reptation time of the macromolecular chains (see the next sec­tion). The latter equation holds for time t much larger than this reptation time. The experimental verification of this approach is under investigation.