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The chemical and physical evolution of primitive materials in protoplanetarydisks are determined by the types of environments they are exposed to and theirresidence times within each environment. Here a method for calculatingrepresentative paths of materials in diffusive protoplanetary disks isdeveloped and applied to understanding how the vertical trajectories thatparticles take impact their overall evolution. The methods are general enoughto be applied to disks with uniform diffusivity, the so-called"constant-$\alpha$" cases, and disks with a spatially varying diffusivity, suchas expected in "layered-disks." The average long-term dynamical evolution ofsmall particles and gaseous molecules is independent of the specific form ofthe diffusivity in that they spend comparable fractions of their lifetimes atdifferent heights in the disk. However, the paths that individual particles andmolecules take depend strongly on the form of the diffusivity leading to adifferent range of behavior of particles in terms of deviations from the mean.As temperatures, gas densities, chemical abundances, and photon fluxes willvary with height in protoplanetary disks, the different paths taken byprimitive materials will lead to differences in their chemical and physicalevolution. Examples of differences in gas phase chemistry and photochemistryare explored here. The methods outlined here provide a means of integratingparticle dynamics with chemical models to understand the formation andevolution of primitive materials in protoplanetary disks over timescales of$10^5$-$10^6$ years.

Residence Times of Particles in Diffusive Protoplanetary Disk Environments I. Vertical Motions