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Nuclear magnetic resonance detects the response of atomic nuclei with a magnetic moment to a radio frequency magnetic field in a steady magnetic field. Its striking possibility is to measure a nuclear property through an ordinary electrical signal from a bulk sample: an enormous number of tiny magnetic moments can produce a measurable change in a receiving circuit.

For a nucleus with spin angular momentum $\mathbf{J}$, define its gyromagnetic ratio by $\mathbf{\mu }=\gamma \mathbf{J}$. Throughout this article $\gamma$ is angular, measured in radians per second per tesla; $\gamma /(2\pi )$ is the corresponding value in cycles per second per tesla. With ${\mathbf{B}}_0=B_0\hat{\mathbf{z}}$, the Hamiltonian is $H=-\gamma B_0{J}_z$. Adjacent energy levels differ byThus a measured resonance frequency and a calibrated magnetic field determine $|\gamma |$. Converting that into a nuclear magnetic moment also requires the spin quantum number: the maximum projection has magnitude $|\gamma |\hslash I$. This simple experiment does not by itself determine the sign of $\gamma$.

The Rabi molecular beam magnetic resonance experiment detects transitions through changes in a selected molecular beam. The bulk experiments below instead detect electrical consequences of nuclear magnetization in matter at ordinary density. A small Boltzmann distribution population imbalance is multiplied by a very large number of nuclei. For noninteracting spin one-half nuclei of number density $n$ and positive $\gamma$, their equilibrium magnetization isThis follows by weighting the two projections $\pm \gamma \hslash /2$ with their Boltzmann distribution probabilities. It explains both the smallness of the bulk polarization at ordinary temperature and the value of many nuclei contributing to one receiving circuit.

NMR spectroscopy measures resonant responses of atomic nuclei to applied electromagnetic radiation in a magnetic field. In residual-group monitoring of polyurethane formation, distinguishable signal integrals supply a relative residual-group readout; overlap or very weak signals can limit that inference.

Size-exclusion chromatography separates dissolved molecules by their hydrodynamic size in the chosen solvent. A larger species that cannot enter the packing's pores travels with the liquid between particles and elutes earlier. Smaller species explore more internal liquid and elute later. The column is not a sieve that permanently traps the large species: exclusion makes them leave first. “Gel filtration” is common for aqueous separations; “gel permeation chromatography” is common for organic-solvent analysis of polymers. SEC molar mass calibration translates size-dependent elution into a standard-relative estimate of molar mass, rather than a universal absolute measurement.

This makes SEC useful for separating proteins from small dissolved species, comparing protein aggregation, and characterizing dissolved polymer chains. The residual-group monitoring of polyurethane formation experiment already illustrates polymer calibration: its reported molar masses are relative to polystyrene standards. Size-exclusion characterization of chain polymers explains why an elution trace alone cannot count chains or establish their growth mechanism.