Byers, J.A. 1988b. Novel diffusion-dilution method for release of semiochemicals: Testing pheromone component ratios on western pine beetle. Journal of Chemical Ecology 14:199-212.

Abstract-- Each of the pheromone components of the Western pine beetle, Dendroctonus brevicomis LeC. (Coleoptera: Scolytidae), exo-brevicomin (E) and frontalin (F), were released in the forest at various ratios 0.01: 1, 0.1:1, or 1:1 to a constant dose of the opposite component (E or F) plus the host monoterpene myrcene (M), which were each released at 1.5 mg/day. The components were released by a new method that combines the principles of chemical diffusion through a tube with mole percentage dilution of the chemical. Both sexes of D. brevicomis were attracted similarly at comparable ratios (and release rates) of E or F and showed similar logarithmic relationships (r2 = 0.92-0.99). The dark beetle predator, Temnochila chlorodia (Mannerheim) (Coleoptera: Trogositidae) was apparently less sensitive to E than D. brevicomis, being relatively less attracted to amounts of E equivalent to that released by 70 females, while none were attracted to that from seven females (while this rate still attracted significant numbers of conspecifics). The apparent insensitivity of bark beetles to extreme ratios between pheromone components in contrast to moths is discussed. The advantages of the diffusion- dilution method of releasing semiochemicals compared to previous methods of absorbents, wicks, capillary tubes, and semipermeable plastic membranes are also discussed.

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Diffusion-Dilution Method of Semiochemical Release.:

Fick's differential equations describing diffusion can serve to determine the instantaneous rate of release of a semiochemical from a capillary test-tube:

release rate = -3.141593 * r * r * D * (C2 - C1) / x

where:
r = radius of the tube opening
D = diffusion coefficient
C2 = liquid concentration
C1 = 0 (assuming convection carries vapor away)
x = distance between micro test-tube opening and meniscus level of liquid
(Villars and Benedek, 1974) (* = BASIC symbol for multiply). More complicated equations (Brooks, 1980) are needed to describe the release over time as the level of the liquid decreases in the tube. In practice, however, it is usually more accurate to measure the release rate over the expected experimental period because one does not know precisely the diffusion coefficient (D) and other contributing factors (e.g., meniscus curvature, surface tension, and temperature effects). Tilden and Bedard (1985) and others (Browne, 1978; Byers and Wood, 1980; byers, 1982; Tilden et al., 1983) have used 52-mm-long x 3.5-mm-ID glass tubes sealed at the bottom to dispense western pine beetle pheromone and aggregation components, exo-brevicomin (E) and myrcene (M), by filling the tubes to a level about 40 mm below the opening. Similarly, they have used 62-mm-long x 2.2-mm-ID tubes to dispense the pheromone component frontalin (F) by filling to a level about 50 mm below the opening. At these distances, diffusion is rather constant over time (pseudo zero order; Brooks, 1980), and so the measured release rate of each has been considered constant at about 1.5 mg/day (Tilden and Bedard, 1985).

The concentration (C2) is actually the vapor pressure of the semiochemical, and this can be varied according to Raoult's law, which states that the vapor pressure (release rate) of a volatile substance (semiochemical) is proportional to its mole fraction in a solvent. The following equation can then be derived for purposes of diluting semiochemicals with solvent in order to obtain a specific semiochemical release rate:

mls = fws * (gsem / fwsem - fsem * gsem / fwsem) / fsem / gs

where:
mls = milliliters of solvent
fws = formula weight (or molecular weight) of solvent
gs = grams solvent per milliliter (density)
gsem = grams of semiochemical fwsem = formula weight of semiochemical
fsem = mole fraction of semiochemical or the proportion of the release rate when neat (0 < fsem <= 1)

For example, a stock solution of E in ethanol that would yield a release rate 10% that of a neat solution of E and that is to be made using 0.5 g of E would require 0.52 ml of E (0.5 g * ml/0.96 g) and 1.6 ml ethanol
([46 g/mole * (0.5 g/156 g/mole - 0.1 * 0.5 g/156 g/mole)/0.1] * ml/0.828 g).
Stock solutions of E in ethanol that should release about 1%, 0.1% and 0.01%, and so forth, that of a neat solution (pure semiochemical) can then be made simply from the 10% solution by serial 1:10 (1 + 9) dilutions.

Chemical Ecology