Are effect sizes and sample sizes related? No. An effect size exists independently of your ability to measure it. But sample sizes are related to your effect size estimates.
When researchers study an effect, they usually estimate its size in one of two families of indexes. The quality of your estimate will reflect the statistical power of your study, and one of the biggest factors affecting statistical power is sample size.
For a good introduction to effect sizes – how to measure them, report them, and interpret them – check out my book Effect Size Matters: