Dahlquist criterion

After some early uncertainty in the literature about the nature of the pressure sensitive bond, Dahlquist [5,6] related modulus data to tack-temperature studies and observed that the compression modulus of the adhesive had to be less than about 3 X 10 dyne/cm (3 x lO Pa) before any adhesive tack was observed. This was explained as the highest modulus that still allowed the adhesive to be sufficiently compliant to wet out or come into molecular contact with the substrate and form dispersive bonds. As other investigators [7-9] accepted this requirement it was termed the Dahlquist Criterion . 

The pure diblock-triblock blends previously described cannot develop sufficient tack onto surfaces, in particular because the modulus level in the terminal zone is too high (Dahlquist criterion [3]). In order to improve tack properties, tackify-ing resins are added to the copolymer blend. They have in fact two important effects [4, 5] ... 

In Fignre 5, the storage modulus of a typical cross-linked rubber is compared to that of a PSA made from a mixture of the rubber and tackifier. The rubber has a low which is why it is soft and mbbery at room (or use) temperature, but its modulus is too high for it to be a PSA. Addition of tackifier decreases the modulus below the Dahlquist criterion and allows for the mixture to be a PSA. The effect of dilution of the rubber network with a tackifier can be predicted by rnbber elasticity theory nsing the equation below (31,32). The effect of fillers can also be predicted. 

The dynamic shear modulus of pressure-sensitive adhesives at one second must be less than 3 x 10 dyn/cm, known as the Dahlquist criterion (92,96,97). The Dahlquist criterion is best met by employing a tackifier on an adhesive at 40 to 70°C above Tg. 

To achieve a good compromise between wetting the surface (adhesion) and bearing a load (cohesion) the modulus should be in the range of 0.1 to 1 MPa in the time fi-ame of the bonding process , that is 1-100 s (Dahlquist criterion [211], p. 101). 

Dahlquist [6] noted that there seems to be a minimum value of the compliance of a PSA in order for it to exhibit tack or equivalently, a maximum value of the modulus. He analyzed data on rheological properties as a function of time (or frequency) and temperature as well as tack as a function of dwell time, separation rate and temperature. He observed that only those materials with sufficiently high compliance in the 1-s time scale at the temperature of use were tacky. This so-called Dahlquist criterion is expressed as follows for various common rheological measurements... 

Fig. 3. Linear viscoelastic master curves of PSA in relation to Dahlquist criterion for tack.

In contrast to common rubbers, the entanglement molecular weight. Me, of most acrylics is sufficiently high that without dilution they meet the Dahlquist criterion discussed earlier (G <3x 10 dynes/cm, 10 Pa) and exhibit tacL With little or no cross-finking the neat polymers form a pressure-sensitive adhesive with some cohesion. To obtain adequate cohesion it is common to use polar monomers which can form hydrogen bonds, and usually also some level of cross-linking. (Acrylics are also discussed in O Chap. 14.)... 

Acrylic pressure-sensitive polymers consist mainly of a soft monomer with a low Tg and high Me. The three most common soft monomers are butyl acrylate, iso-octyl acrylate, and 2-ethylhexyl acrylate. All three have a Tg below —40°C and an Me above 15,000 Da see O Table 15.2. When polymerized on their own they meet the Dahlquist criterion at room temperature and well below. To increase peel, often a hard monomer is incorporated. These are high Tg monomers, and most are low Me. By moving up the Tg of the overall polymer, these hard monomers increase the viscous loss and thus the peel force, in much the same way as increasing the rate of peel. In addition, the lower Me hard monomers, such as MMA also increase the stiffness of the adhesive which further increases the peel force. Polar monomers are invariably incorporated to increase cohesive strength through intermolecular hydrogen... 

Without dilution both natural rubber and styrenic block copolymers are stififer than the Dahlquist criterion and therefore have no tack. Tackifiers gained their name because of their... 

Figure 4 Comparison of the storage modulus and tack of a PSA as a function of temperature. The frequency of measurement is 1 Hz. When the modulus of the adhesive goes below 3x10 dyn cm , the tack starts to reach a maximum. This is the definition of the Dahlquist criterion for tack.

Flgire 5 Comparison of the storage modulus of a tackified (dark line) and an untaddfied (lighter line) elastomer as a fundion of temperature. Also shown is the Dahlquist criterion which indicates the point at which the tackified material displays tack. 

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