The ability to directly observe chemical reactions at the single-molecule and single-particle level has enabled the discovery of behaviors otherwise obscured by ensemble averaging in bulk measurements. However powerful, a common restriction of these studies to date has been the absolute requirement to surface tether or otherwise immobilize the chemical reagent/reaction of interest. This constraint arose from a fundamental limitation of conventional microscopy techniques, which could not track molecules or particles rapidly diffusing in three dimensions, as occurs in solution. However, many chemical processes occur entirely in the solution phase, leaving single-particle/-molecule analysis of this critical area of science beyond the scope of available technology. Here, we report the first kinetics studies of freely diffusing and actively growing single polymer−particles at the singleparticle level freely diffusing in solution. Active-feedback single-particle tracking was used to capture three-dimensional (3D) trajectories and real-time volumetric images of freely diffusing polymer particles (D ≈ 10 −12 m 2 /s) and extract the growth rates of individual particles in the solution phase. The observed growth rates show that the average growth rate is a poor representation of the true underlying variability in polymer−particle growth behavior. These data revealed statistically significant populations of fasterand slower-growing particles at different depths in the sample, showing emergent heterogeneity while particles are still freely diffusing in solution. These results go against the prevailing premise that chemical processes in freely diffusing solution will exhibit uniform kinetics. We anticipate that these studies will launch new directions of solution-phase, nonensemble-averaged measurements of chemical processes.

The ability to directly observe chemical reactions at the single-molecule and single-particle level has enabled the discovery of behaviors otherwise obscured by the ensemble averaging in bulk measurements. However powerful, a common restriction of these studies to date has been the absolute requirement to surface tether or otherwise immobilize the chemical reagent/reaction of interest. This constraint arose from a fundamental limitation of conventional microscopy techniques, which could not track molecules or particles rapidly diffusing in three dimensions, as occurs in solution. However, much chemistry occurs in the solution phase, leaving single-particle/-molecule analysis of this critical area of science beyond the scope of available technology. Here we report the first solution-phase studies and measurements of any chemical reaction at single-particle/-molecule level in freely diffusing solution. During chemical reaction, freely diffusing polymer particles (D ~ 10-12 m2/s) yielded single-particle 3D trajectories and real-time volumetric images that were analyzed to extract the growth rates of individual particles. These volumetric images show that the average growth rate is a poor representation of the true underlying variability in polymer-particle growth behavior. These data revealed statistically significant populations of faster- and slower-growing particles at different depths in the sample, showing emergent heterogeneity while particles are still in the solution phase. These results go against the prevailing premise that chemical processes freely diffusing in solution will exhibit uniform kinetics. These new understandings of mechanisms behind polymer growth variations bring about an exciting opportunity to control particle-size and plausibly molecular weight polydispersity by the rational design of conditions to dictate spatial growth gradients. We anticipate that these studies will launch a new field of solution-phase, nonensemble-averaged measurements of chemical reactions.