In middle- and high-school chemistry, molecules are often treated as tiny points, but polymers are chains made of thousands to millions of atoms. Flory statistically analyzed the "random-coil" shapes formed when these chains bend freely and derived formulas for their average size and form. He also proposed the Flory–Huggins theory, expressing how easily a polymer mixes with a solvent through a free-energy equation. This allowed engineers to design processing conditions for synthetic fibers such as nylon and polyester in a scientific way. Moreover, he developed a mathematical model of network formation (gelation) during crosslinking reactions, explaining the elasticity of rubber and the hardening of adhesives. His work laid the groundwork for medical polymers and separators in lithium-ion batteries.

Using statistical mechanics, Flory derived expressions for the end-to-end distance, radius of gyration and other conformational properties of ideal chains, predicting how they scale with chain length. By including excluded-volume effects he demonstrated scaling laws that link the ideal θ condition to good-solvent behavior, influencing modern polymer physics. In the Flory–Huggins theory he employed a lattice model to obtain the mixing free energy ΔG=RT(φ1 ln φ1+φ2 ln φ2+χφ1φ2), where the χ parameter relates to solvent–polymer interaction energy. Moreover, the Flory–Stockmayer theory quantified the gel point and molecular-weight distribution in branched-chain polymerizations, rigorously defining critical conditions for infinite networks when monomers with functionality ≥3 are present. Through viscosity studies he established the empirical Mark–Houwink relation [η]=K M^a, creating a practical route to estimate molecular weight. These results directly inform elastomer design, composite materials and biopolymer research, and they serve as benchmarks for molecular simulations today.

Flory incorporated self-avoidance into the random-flight model and, through a simple scaling argument, anticipated the critical exponent ν≈0.588 long before renormalization-group results. His lattice-based Flory–Huggins expression provided a conduit to SCFT and fractional free-energy theories, stimulating experimental validations of the χ–T correlation. For gelation he expressed the critical conversion as p_c=1/(f−1) using the degree of branching p and average functionality f, and derived the elastic free energy F=½NkT(α^2−1−ln α^2) by a variational approach, laying the foundation of rubber elasticity theory. He further delivered precise composition-drift descriptions in step-growth and radical copolymerizations through instantaneous monomer reactivity ratios r1 and r2. From living radical polymerization to self-assembled soft matter, Flory’s formulations continue to undergird numerous contemporary theoretical models.