7 WETTABILITY AND ABSORBENCY OF PAPER
7.1 Basic concepts
Spontaneous spreading of a liquid on a solid occurs only if the free energy of the system decreases during this
process. The wetting tendency of a liquid in contact with a solid is reflected by the initial spreading coefficient, as follows:
S = -AGS/A
= Yso-Y- m (7.21) where AG8 is the free energy change due to spreading;
yso, ysi and y(= y\v) denote the interfacial free ener-gies per unit areas (surface tensions) of the solid-air, solid-liquid and liquid-vapour interfaces, respectively.
A liquid drop will completely wet the solid surface when S > 0, while only partial wetting will be the result if S < 0. A large positive S value favours the spreading of a liquid. Equation (7.21) shows importantly that the equilibrium wetting behaviour is controlled by the sur-face chemistry of the different materials in question.
The equilibrium state of a partially wetting droplet put in contact with a flat solid surface can be derived by using the principle of free-energy minimization. The optimum state is a hemispherical cap (see Figure 7.33), with a contact angle given by Young's equation:
cosfl = ysv~Vsl (7.22) Y
where ysv is the liquid-vapour interfacial tension, taking into account the surface pressure exerted by equilibrium-adsorbed vapour film at the solid surface. The "sv"
surface tension can be written as follows:
/sv = Yso - ^SV (7.23) where 7rsv is the "sv" surface pressure. The surface pressure can at any arbitrary interface be calculated by using the Gibbs integral method, yielding the following:
/
Pm
V(P) din P (7.24)
where F ( P ) is the amount of adsorbed vapour. The central parameter in wetting science is the contact angle,
Solid
Figure 7.33. Side-view of a partially wetting drop on a solid surface showing the macroscopic contact angle and the three interfacial tension vectors acting on the three-phase contact line (tcl)
Vapour
Liquid
which can easily be observed directly by using various optical techniques or indirectly by measuring capillary forces, as described below. Since the surface tension, y, also can be determined quite readily, it is possible to deduce the wetting tension ysv — ysi for systems exhibiting partial wetting.
In many practical applications, the wetting liquid in question is a solution, e.g. an aqueous solution contain-ing surface-active components. Then, the possibility of adsorption at all interfaces surrounding the three-phase contact-line (tcl) must be considered. According to the Gibbs isotherm for adsorption at the ij interface:
d^- = -rl7djLi (7.25) Under the assumption that the solution is ideal, one can therefore write:
TT1J = RT f ri 7( c ) d i n c (7.26) Jo
where the spreading pressure 7T,-7-(= yt° — ytj) is the dif-ference between the surface tension of the pure solvent and the surface tension of the solution at concentration c.
In the case of partial wetting, preferential solute adsorp-tion at the "si" interface will increase the wetting ten-dency of the solution, as is often the case when adding surfactants to a solution in contact with a hydropho-bic surface, while preferential adsorption at the "sv"
interface will cause dewetting, as often is observed when small amounts of cationic surfactants are added to solution in contact with a negatively charged surface.
This effect is commonly referred to as autohydrophobic-ity. If the adsorption isotherms are known, the contact angle of the solution can be calculated by combining equations (7.22) and (7.26).
7.7./ Wetting of rough and chemically heterogeneous surfaces
As has been pointed out several times, the surface of paper is far from being a smooth ideal surface. This has great consequences on the wetting behaviour that is observed. For "random" rough surfaces, the influence of surface roughness can be described by using Wenzel's equation:
cos(9r= — cos6> (7.27)
pr°j
which simply states that the contact angle can be calculated if the ratio between the actual-to-projected surface areas are known. The important conclusion drawn from equation (7.27) is that roughness promotes
Figure 7.34. Illustration of the effect that surface roughness has on the wetting of a solid by a liquid drop. The plot shows schematically the evolution of the cosine of the contact angle on a rough surface ((9R) versus the same quantity on a smooth surface with the same surface composition (0e). The theoretical line refers to equation (7.27)
wetting in the partial wetting regime (0 < 0 < 90°), while the wetting tendency decreases in the non-wetting regime (0 < 0 < 90°). Figure 7.34 show schematically how the roughness effect may manifest itself in practice.
If the roughness defects are sharp and large enough, the contact angle may be pinned also for wetting liquids and Wentzel's equation is no longer valid. This situation may give rise to a large hysteresis in the measurement of advancing and receding contact angles. Due to pinning of the contact line, the advancing contact angle, 0a, is always larger than the receding contact angle, Ox.
Chemical heterogeneity is also highly important when discussing the wetting of paper. For surfaces composed of different surface groups that are ideally mixed, the contact angle can be estimated simply from the relative fractions of the two components " 1 " and
"2", as follows:
cos Gi+2 = / i cos Ox + f2 cos O2 (7.28) However, this situation is seldom realized in papermak-ing systems for which the chemical heterogeneity is often observed on the micron-size scale. This can give rise to contact line pinning on defects due to line ten-sion effects, which also causes contact-angle hysteresis.
This is illustrated below in Figure 7.35, which shows a large difference between the advancing and reced-ing contact angles measured on paper. In the advancreced-ing mode, the measured contact angle increases rapidly with
Super wetting
Theory Super
repellent
(C7-C7ref)/atom%
Figure 7.35. Quasi-static advancing and receding contact angles versus the fibre surface coverage of AKD sizing agents (given as the relative C/-to total carbon ratio minus that measured for the non-sized reference, as described below). The Cl value represents aliphatic carbons (see Section 8)
increased surface coverage of hydrophobic domains, whereas small contact angles are measured in the reced-ing mode. This is in agreement with previous findreced-ings for heterogenous materials (45). In the study of paper wettability, it is always important to consider if reced-ing or advancreced-ing wettreced-ing modes apply to the practical problem at hand.
7,1.2 Wetting dynamics
Wetting dynamics is highly important in converting operations, coating, and printing on paper, since equi-librium conditions are seldom realized in these fast pro-cesses. The spreading of a liquid on a solid can be driven by hydraulic pressure, inertia, gravity and wetting ten-sion. The energy of the moving liquid can be dissipated through viscous drag in the bulk liquid or by molecu-lar friction at the wetting front. Together, this generates a seemingly overwhelming challenge in formulating an understanding of wetting dynamics, in particular when considering the various possible wetting geometries and the large range of wetting speeds encountered in prac-tice. Comprehensive reviews of this difficult topic have been published by de Gennes (46), Blake (47) and Kistler (48). Here, we will only touch upon some rather trivial issues related mostly to the spontaneous spreading of liquids and solutions on solid surfaces.
When discussing wetting dynamics, the dynamic contact angle 0d is the central parameter. In the so-called capillary regime, spreading is promoted by the in-plane and out-of-balance interfacial tension force, which often is expressed as follows:
Fs = Y cos(6>d - 0) (7.29) from which one can conclude that the spreading force is largest far from equilibrium for completely wetting systems. A net dissipation associated with the motion of a spreading liquid compensates the unbalanced capillary force. The main theories available for describing wetting dynamics differ in the way in which one accounts for this dissipation. In the hydrodynamic approach, dissipation occurs by viscous drag in the bulk liquid, whereas according to the molecular kinetic theory, the dissipation takes place at the moving three-phase contact line. In the hydrodynamic theories, the dependence of spreading rate on the contact angle is, in the case of the complete wetting regime, accounted for by the 0% ~ Ca power law. This is referred to as the Hoffman-Voinov-Tanner law. For partial wetting, the approximate spreading law Ol — O3 — Ca is suggested; Ca = TJU/Y is the capillary number, where r\ is the liquid viscosity, U the spreading rate, and y the surface tension. Hence, the rate of spreading in the complete wetting regime is given by the following:
U ~ -Ol (7.30)
showing (as in the case of capillary flow discussed below) that the rate is proportional to the surface tension and inversely proportional to the viscosity. In the capillary spreading regime, the radius of a spreading drop is predicted to exhibit an approximate r ~ r1/10
dependence. It should be noticed that deviations from the spreading laws referred to above are common, in particular for high Ca numbers. The dynamic contact angle 0d is often observed to rise rapidly for Ca > 0.2.
In high-speed coating processes, this often results in the entrainment of air and ultimately to a situation in which the substrate is not coated at all.
For spontaneous wetting processes involving com-plex solutions under conditions of fast hydrostatic equi-libration, the wetting dynamics are often controlled by the kinetics of interfacial adsorption and its effect on the dynamic wetting tension. Due to the fact that several interfaces are involved and that mass transfer can occur over the three-phase contact line, it is frequently difficult to predict wetting rates for such systems. However, in the case of drop spreading on hydrophobic surfaces, the time-limiting step is often the adsorption at the expand-ing liquid-vapour interface. Inserted into the surface
Contact angle/degrees
tension balance in equation (7.22), the dynamic contact angle then becomes:
cos0d(f) = (7.31)
Y(O
This simple law can be used to predict the spontaneous spreading of ink drops on hydrophobic paper from surface tension relaxation data.
7,1.3 Adhesion
The thermodynamic work of adhesion between two materials A and B is given by the following:
Wa = (yA + ye) - KAB (7.32) For a solid and a liquid, this can be expressed as follows:
Wa = (Ksv + 7rsv + K)-Ksi (7.33) where (ysw -\- 7TSV) is the surface energy of the solid in air.
If the spreading pressure term is omitted, then the work of adhesion refers to the separation of the liquid from a solid, which still is covered with an adsorbed vapour layer. Substituting (KSV — Ksi) with y cos 6 by using the Young equation gives the following:
Wa = y ( l + c o s 0 ) + 7rsv (7.34) This equation describes quite accurately the situation of an adhesive drop on a solid surface. The surface energies do not alter profoundly as the liquid solidifies, although stresses may build up due to shrinkage. Hence, the equation is also valid for the situation of a solid adhesive on a substrate. It follows that the adhesion maximum is obtained when cos 0 = 0, that is when the liquid spreads completely. This implies the existence of larger forces between the liquid molecules and the solid, compared to that between the liquid molecules themselves, which further implies a high 7TSV value. The adhesive force will tend to zero for contact angles above 90°, in which case 7rsv is small.
The work of cohesion of a liquid Wc is defined as that which is required to create two new interfaces with a total interfacial tension of 2K • Under conditions of complete wetting, Wa = 2y + 7rsv, which shows that the work of adhesion for completely wetting liquids is always larger than the work of cohesion. Adhesion problems generally require the consideration of aspects other than wetting alone. An important issue is to determine the surface energies of solids. The surface tensions of liquid-vapour and liquid-air interfaces can easily be determined from the pressure difference across
an interface having principal curvature radii of rx and r2, as follows:
AP = y ( - + - ) (7.35) Vi r2j
which reduces for a spherical drop to the well-known relationship, A P = 2y/r. No such simple and direct method of measuring the surface energy exists for solid surfaces, due to their rigidity. However, it is the surface energy of the solid that to a large degree determines wetting, adhesion, cohesion and friction properties.
In a study that has proven highly useful in the design of products with prescribed wettability, Zisman found that a liquid drop will wet a surface completely when its surface tension, y, is smaller than a criti-cal value, Kc, which is characteristic of the solid (49).
This critical surface tension of wetting is often mea-sured by using a homologous series of liquids with different surface tension values. By using the following function:
cosO = 1 - const.(K - Kc) (7.36) and plotting cos 9 versus y, Kc is obtained at the inter-cept, cos 6 = 1. The importance of Zisman' s method is that the desired wetting properties for a specified liquid can be obtained by modifying surfaces using coatings or other chemicals with suitable values of yc. Liquids will furthermore completely wet a surface only when y > yc- Hence, when laminating paper with, e.g.
polyethylene, with a surface tension of about 30 mN/m, the paper substrate should preferably have a higher Kc in order to achieve good wetting and adhesion. The adhe-sion will decrease strongly with decreasing Kc below this value. The measured Kc values may vary rather strongly between different commercial grades of, for instance, paper board (50). Increasing the surface ener-gies of surfaces for improved wetting and adhesion in converting operations is often achieved by using corona discharge.
Fowkes and Mostafa (51) demonstrated another fruit-ful approach to the problem of estimating surface ener-gies of solids by separating the surface free energy into different components, of which dispersive and polar acid-base interactions dominate, thus giving the following:
K = yd + yab (7.37) This work was followed by others, notably that of van Oss et al. (52), and was developed into a theory of surface free energies and adhesion (see ref. (53)).
The complete combining rule can for a "polar" system be expressed in terms of the adhesion energy and the contact angle, as follows:
W
a= K ( l + c o s 0 ) = 2 [(y,
LWy
sLW)'
/2+ (XfXs
+)
1^(K
1Vr] (7.38)
By using several liquids with known surface tension components and determining their contact angles in con-tact with a given solid, the surface energy of the solid may be calculated using the above equation. It is worth noting that this theory has been questioned from several standpoints, including the use of the combining geomet-ric mean rule. Furthermore, the surface tension values of the reference liquids used to determine the surface energy components of the solids have been debated. The theory is nevertheless extensively used in practice in an effort to understand the interrelationships between wet-ting, adhesion and molecular surface properties.