FORMULATIONS
Optimization of the transfer of agrochemicals to the target requires careful analysis of the various steps involved in the application (22). Most agrochemicals are applied as liquid sprays, particularly for foliar application. Hydraulic nozzles are commonly used for this spraying process to produce droplets in the range 100-400 um. For application parameters such as the droplets size spectrum, and their impaction and adhe-sion, wetting and spreading are of prime importance.
In addition to these "surface chemical factors", i.e.
the interaction with various interfaces, other parame-ters that affect biological efficiency are deposit for-mation, penetration and interaction with the site of action. Enhancement of penetration is sometimes cru-cial to avoid removal of the agrochemical by envi-ronmental conditions such as rain and/or wind. All of these factors are affected by the surfactants and poly-mers added to the formulation and hence the surface chemistry of the various processes involved is cru-cial in designing formulations with optimum biological efficacy.
In a spraying process, a liquid is forced through an orifice (the spray nozzle) to form droplets by the appli-cation of hydrostatic pressure. The effect of surfactants and/or polymers on the droplet size spectrum of a spray can be described in terms of their effects on the surface tension. Since surfactants lower the surface tension of the liquid, one would expect that their presence in the spray solution would result in the formation of smaller droplets. However, when considering the role of sur-factants in droplet formation, one should consider the dynamics of surfactant adsorption at the air/liquid inter-face. In a spraying process, a fresh liquid surface is continuously being formed. The surface tension of this
liquid depends on the relative ratio between the time taken to form the interface and the rate of adsorption of the surfactant from the bulk solution to the air/liquid interface. The rate of adsorption of a surfactant molecule depends on its diffusion coefficient D and its concentra-tion, according to the following:
where T is the surface excess (number of moles of surfactant adsorbed per unit area), t is the time, 8 is the diffusion layer thickness, NA is the Avogadro constant and 6 is the fraction of the surface already covered by adsorbed molecules.
Equation (4.13) shows that the rate of adsorption increases with an increase in both D and c. The diffusion coefficient of a surfactant molecule may be calculated from the Stokes-Einstein equation, as follows:
D=—— (4.14)kT
6TTT]R
where k is the Boltzmann constant, T is the absolute temperature, r\ is the viscosity of the medium and R is the radius of the surfactant molecule. Equation (4.14) predicts that smaller molecules diffuse faster and hence they reduce the dynamic surface tension more effi-ciently. However, the situation is more complex, since micelles play a major role in determining the kinetics of adsorption. The shorter the lifetime of the micelle and the smaller its size, then the more efficient is the sur-factant in reducing the dynamic surface tension. For full detail, the reader should refer to a recent text by Dukhin, et al. (23).
If the rate of formation of the interface is much faster the rate of adsorption of the surfactant, the surface tension of the spray solution will not be far from that of pure water. Alternatively, if the rate of surfactant adsorption is faster than the rate of formation of the fresh interface, the surfactant will lower the dynamic surface tension and hence smaller droplets are produced.
With liquid jets, an important factor may be considered that enhances surfactant adsorption (24). Addition of surfactants reduces the surface velocity (which is in general lower than the mean velocity of flow of the jet) below that obtained with pure water. This results from surface tension gradients which enhances adsorption (the molecules will move to the areas with high surface tension).
Surface chemistry also plays a major role in droplet impaction and its subsequent adhesion. The latter pro-cess is determined by the difference between the surface
energy of the drop in flight, E0, and its value at the target surface, Es. This difference should exceed the kinetic energy of the drop (0.5 mi;2, where m is the mass of the drop and v its velocity) for adhesion to take place.
The parameter E0 simply depends on the dynamic sur-face tension (Eo = 4jrR2y), whereas £s depends on the contact angle 0 of the drop on the substrate (25), as follows:
E°~ Es = i _ o.39[2(l - cos 0) - sin2 0 cos0]
x 1 -cos6> + -(cos3 ( 9 - 1) (4.15) The term (EQ — Es)/Eo is the minimum energy barrier between attached and free drops which is necessary for the kinetic energy to overcome, expressed as a fraction of the free energy of the free drop. A plot of (E0 — Es)/E0 versus 0 is shown in Figure 4.7, which illustrates that this ratio decreases rapidly from its value of unity when 0 = 0° to a near-zero value when 6 > 160°. The master curve shown in Figure 4.7 can be used to calculate the critical contact angle required for the adhesion of water droplets with various sizes and velocities. For droplets with a size of 100 |im, and a velocity of 0.25 ms"1, the critical contact angle for adhesion is 160° and in this case no surfactant is
required for adhesion. However, with larger droplets (200-400 urn) and higher velocities, the critical contact angle required for adhesion becomes smaller than 90°.
For example, for a drop of 200 urn and a velocity of 1.5 ms"1 (twice the terminal velocity), a contact angle of 54° is required for adhesion. This shows the importance of surfactants in the spray solution.
Many agrochemical applications involve high-ume sprays, whereby with continuous spraying the vol-ume of the drops continues to grow in size by impaction of more spray drops on them and by coalescing with neighbouring drops on the surface. During this process, the amount of spray retained steadily increases provided that the liquid drops that are impacted are also retained.
However, on further spraying the drops continue to grow until they reach a critical size above which they begin to slide down the surface and "drop off (the so-called run-off condition). At the point of run-off, the volume of spray retained is at a maximum. The retention at this point is governed by the movement of liquid drops on the solid surface. Bikerman (26) stated that the percent-age of drops sticking to a plant after having touched it should depend on the tilt of the leaf, the size of the droplets and the contact angle at the plant leaf/droplet/air interface.
Furmidge (27) analysed the process of retention of drops on a tilted substrate by considering the advancing and receding contact angles, 6A and #R, respectively.
This is illustrated in Figure 4.8, which shows the profile and plan view of a drop during sliding.
By using a simple analysis whereby the gravity force (given by mgs'ma, where m is the drop mass, g is the acceleration due to gravity and a is the angle of tilt) is balanced by the difference in the work of dewetting and wetting (determined by the receding and advancing contact angles, respectively) Furmidge derived the following expression for the
Figure 4.8. Profile and plan view of a drop during sliding e
Figure 4.7. Variation of (Eo — Es)/Eo with 9 for a drop on a solid surface
mg
wtil (E0-E5)ZE0
retention factor F:
F = ^ A ( C O S S K - C O ^ Y ( 4 1 6 )
where 0M is the mean value of the contact angles and p is the density of the spray solution. Equation (4.16) shows that F depends on the value of >iA, the difference between 6R and 0A (referred to as the contact-angle hysteresis), and 0M- This is illustrated in Figure 4.9. It can be seen from Figure 4.9 that at any given value of (#A — #R) and J/LA, F increases rapidly with an increase in the contact-angle hysteresis, reaching a maximum and then decreases.
Another surface chemical factor that can affect the efficacy of the foliar spray application of agrochemicals is the extent to which the liquid wets, spreads and covers the foliage surface. A very convenient parameter describing spreading is the spread factor SF, which is simply the ratio of the diameter of the area wetted, D, and the diameter of the drop applied, d, as follows:
SF-°
d (4.17)
The spread factor depends on the contact angle, and provided that O is not too small (>5°), is given by the following expression:
^ - [ ( 1 - C O S
4W
+COS.)]
(4-
18)A plot of SF versus 6 is shown in Figure 4.10 which clearly illustrates the rapid increase in S F when O becomes lower than 35°.
A useful index for measuring the spreading of a liquid on a solid surface is the Harkin spreading coefficient S, (28), which is the change in tension when solid/liquid and liquid/air interfaces are replaced by a solid/air interface:
S = YSA - (KSL + KLA) (4.19)
By using Young's equation (equation (4.10)), S is then given by the following:
S = yu(cos 0 - 1 ) (4.20)
F F
(eA-eR)
Figure 4.9. Variation of the retention value with the contact angle hysteresis
(0A-*R)
0 (degree)
Figure 4.10. Variation of the spread factor with the contact angle
If 6 > 0, S is negative and this implies only partial wetting. In the limit 0 = 0, 5 = 0, and this represents the onset of complete wetting. A positive S value implies rapid spreading of the liquid on the solid surface. This shows the importance of the presence of surfactant and the structure of the interfacial region which determines the values of the surface tension and contact angle.
Several other factors where surface chemistry plays a major role in biological efficacy may be listed. For example, the evaporation of drops and the formation of deposits that may contain various liquid crystalline phases may play a major role in retention of the active ingredient on the leaf surface. This is particularly important for systemic fungicides. These deposits also reduce the loss of the active ingredient by falling rain.
Another important factor is the presence of micelles, which solubilize the active ingredient and may enhance penetration of the chemical through the leaf surface and the cuticle. All of these factors rely on specific interactions between the active ingredient, the surfactant, the leaf surface and the active sites involved. However, a detailed analysis of these effects is beyond the scope of this present chapter.