Neem does act as a mild systemic, and lasts about 2 weeks per treatment. It's very effective if used properly. It's an antifeedant (upsets the digestive system) and the active ingredient, azadirachtin, mimics/replaces a hormone essential to completion of insect's metamorphic cycle. Since insects cannot reach the stage of being sexually mature, neem ingestion renders them unable to reproduce.
When using neem oil, you might find it doesn't have much in the way of rapid knockdown (quick death of bugly uggers), but that doesn't mean it isn't quietly doing its job. The best neem oil product is pure, cold-pressed oil. The best way to use it is by preparing a suspension of 1 quart or liter of hot, acidified (with 1 tablespoon of white vinegar/ quart or liter) distilled water, to which you would add 4.5 teaspoons of insecticidal soap concentrate + the appropriate amount of neem oil and shake well. Make sure you A) keep shaking the suspension as you spritz, and B) use all of the product that day and discard anything that remains unused. The reason for acidifying distilled water is, neem oil is highly susceptible to something called alkaline hydrolysis. See something I wrote about the effect of hydrolysis on insecticides and other chemical mixtures:
Hydrolysis
pH is based on a logarithmic scale from 1 to 14. Where a pH of 7 is neutral, a pH of 6 is 10 times more acidic than a pH of 7. Many insecticides are sensitive to pH levels because of something called hydrolysis, which is a chemical process whereby larger molecule with insecticidal properties are broken (cleaved) into smaller (ionic) particles that may totally lack any insecticidal properties when they recombine with other smaller particles. How much effect hydrolysis has on insecticides depends on the insecticide's chemistry, water pH, water temp, exposure to sunlight, and how long the mixture has been in the spray container.
Neem oil and insecticidal soaps are susceptible to alkaline hydrolysis, which means that a pH greater than 7.0 causes degradation, so adjusting your spray water to a pH from 5.5 - 6.5 for neem products and no lower than 8.0 for insecticidal soap applications is beneficial; whereas some pesticides are affected by acid hydrolysis at pH levels below 7.0, they should be mixed with water adjusted to pH levels from 7.5 - 8. In either case, the sooner you use the spray mixture, the more effective it will be. White vinegar or citric acid (from a wine-making supply store) are very effective at reducing water's pH.
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