Adhesive energy

Fig. XII-12. Top friction traces for two calcium alkylbenzenesulfonate monolayers on mica where the monolayers are in a liquidlike state. A—in inert air atmosphere B—in saturated decane vapor. Bottom contact radius-load curves showing adhesion energy measured under the same conditions as the friction traces. (From Ref. 53.)...

The most-often cited theoretical underpinning for a relationship between practical adhesion energy and the work of adhesion is the generalized fracture mechanics theory of Gent and coworkers [23-25] and contributed to by Andrews and Kinloch [26-29]. This defines a linear relationship between the mechanical work of separation, kj, , and the thermodynamic work of adhesion ... 

Some of the recent work in contact mechanics is focused on understanding the adhesion of viscoelastic polymers and dynamic contributions to the adhesion energy this work is summarized in Section 5. Sections 6.1 and 6.2 include some of the current applications of contact mechanics in the field of adhesion science. These include possible studies on contact induced interfacial rearrangements and acid-base type of interactions. 

They argue that the Hertzian load (Ph) is not signifieantly affected by the finite size effeets, therefore the JKR expression relating the load to the contact radius and adhesion energy (Eq. 11) should still be valid. Using a combined analytical and computational approach, Hui et al. [36] found that a correction given by Shull et al. for the eompression of such thin lenses was accurate for moderately large eontact radius... 

SFA has been traditionally used to measure the forces between modified mica surfaces. Before the JKR theory was developed, Israelachvili and Tabor [57] measured the force versus distance (F vs. d) profile and pull-off force (Pf) between steric acid monolayers assembled on mica surfaces. The authors calculated the surface energy of these monolayers from the Hamaker constant determined from the F versus d data. In a later paper on the measurement of forces between surfaces immersed in a variety of electrolytic solutions, Israelachvili [93] reported that the interfacial energies in aqueous electrolytes varies over a wide range (0.01-10 mJ/m-). In this work Israelachvili found that the adhesion energies depended on pH, type of cation, and the crystallographic orientation of mica. 

Fig. 17. Adhesion energy G measured as a function of the surface density of the interfacial chains. It may noted that the strength measured in a peel test (a) is about 5 times larger than that measured using the JKR method (b). Further, a maximum exists in the value of G as function of the surface chain density. This is because of swelling effects at larger values of surface chain density. The open symbols represent the data for elastomer molecular weight Mo = 24,000 and the closed symbols represent the data for Mo = 10,000.

The premise of the above analysis is the fact that it has treated the interfacial and bulk viscoelasticity equally (linearly viscoelastic experiencing similar time scales of relaxation). Falsafi et al. make an assumption that the adhesion energy G is constant in the course of loading experiments and its value corresponds to the thermodynamic work of adhesion W. By incorporating the time-dependent part of K t) into the left-hand side (LHS) of Eq. 61 and convoluting it with the evolution of the cube of the contact radius in the entire course of the contact, one can generate a set of [LHS(t), P(0J data. By applying the same procedure described for the elastic case, now the set of [LHS(t), / (Ol points can be fitted to the Eq. 61 for the best values of A"(I) and W. 

Starting with the experimentally found form of the adhesion energy functional given by Gent and Petrich [116], Falsafi et al. [117] have proposed and used the following empirical form to further decouple the bulk and interfacial processes... 

CR 3nd tp are the contributions from chain recoiling and interfacial dynamics (i.e. drag forces and disentanglement), respectively, and / ve is the viscoelastic loss function which has interfacial and bulk parts. / is a characteristic length of the viscoelastic medium, t is the contact time and n is the chain architecture factor. Fig. 21 illustrates the proposed rate dependency of adhesion energy. 

Fig. 21. Patterns of rate dependency of adhesion energy observed in contact mechanical measurements (Eqs. 63 and 64) [117].

Godail and Packham [77,78] have applied these ideas to the adhesion of ethylene-octene copolymers laminated to polypropylene. Variations in adhesion energy found with different laminating temperatures were interpreted in terms of... 

In studying contact between films of polyethylene (PE) and polyethylene terephthalate (PET) bonded to quartz cylinders, they observed an increase in adhesion energy with contact time for a PE/PE pair, but not for PE/PET or PET/PET combinations. They interpreted this as evidence for the development of nanoscale roughness due to the interdiffusion of chains across the PE/PE interface [84],... 

Theoretically, these intermolecular interactions could provide adhesion energy in the order of mJ/m. This should be sufficient to provide adhesion between the adhesive and the substrate. However, the energy of adhesion required in many applications is in the order of kJ/m. Therefore, the intermolecular forces across the interface are not enough to sustain a high stress under severe environmental conditions. It is generally accepted that chemisorption plays a significant role and thus, physisorption and chemisorption mechanisms of adhesion both account for bond strength. 

The energy release rate (G) represents adherence and is attributed to a multiplicative combination of interfacial and bulk effects. The interface contributions to the overall adherence are captured by the adhesion energy (Go), which is assumed to be rate-independent and equal to the thermodynamic work of adhesion (IVa)-Additional dissipation occurring within the elastomer is contained in the bulk viscoelastic loss function 0, which is dependent on the crack growth velocity (v) and on temperature (T). The function 0 is therefore substrate surface independent, but test geometry dependent. 

Among all the low energy interactions, London dispersion forces are considered as the main contributors to the physical adsorption mechanism. They are ubiquitous and their range of interaction is in the order 2 molecular diameters. For this reason, this mechanism is always operative and effective only in the topmost surface layers of a material. It is this low level of adhesion energy combined with the viscoelastic properties of the silicone matrix that has been exploited in silicone release coatings and in silicone molds used to release 3-dimensional objects. However, most adhesive applications require much higher energies of adhesion and other mechanisms need to be involved. 

Deruelle, M., Tirrell, M., Marciano, Y., Hervet, H. and Leger, L, Adhesion energy between polymer networks and solid surfaces modified by polymer attachment. Faraday Discuss., 98, 55-65 (1995). 

It is known that the possible interaction between two materials 1 and 2 is determined by their surface energies, which consist of two components, dispersive, and specific or polar, y . When hydrogen bonding and acid-base interactions are also involved, the adhesion energy between the two materials, Wa will be" ... 

In the case of supported metalhc particles, the construction is modified by introducing the adhesion energy (Wulff-Kaishew construction) [Henry, 1998]. The equilibrium shape is a Wulff polyhedron, which is truncated at the interface by an amount Ahs, according to the relation Ahs/hj = /3/(t where /3 is the adhesion energy of the crystal on the substrate. 

E. Evans and D. Needham Attraction Between Lipid BUayer Membranes in Concentrated Solutions of Nonadsorbing Polymers Comparison of Mean-Field Theory with Measurements of Adhesion Energy. Macromolecules 21, 1822 (1988). 

Nardin, M. and Schultz, J. (1993). Effect of elastic moduli and interfacial adhesion energy on the critical fiber aspect ratio in single fiber composites. J. Mater. Sci. Lett. 12, 1245-1247. 

Fig. 18 a Schematic of probe tack measurements of a thin adhesive film along a temperature gradient, b Compilation of probe tack data during loading and unloading cycles for different temperatures. c Total adhesion energy, calculated from the area under the load-displacement curve shown in b divided by maximum contact area, as a function of temperature. The error bars represent one standard deviation of the data, which is taken as the experimental uncertainty of the measurement. (Reproduced with permission from [86])... 

In comparison, the adhesive energy per unit area Wa between two different solids is given by ... 

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