= TLC retardation factor
{c}
{title2=$R_f$}
For <thin-layer chromatography>, define the <TLC retardation factor> using distances along the development direction:
$$
R_f=\frac{d_{\rm spot}}{d_{\rm front}}
=\frac{y_{\rm spot}-y_0}{y_{\rm front}-y_0}.
$$
The origin coordinate is $y_0$; use the centre of a resolved spot and a front marked at the end of development. Both distances begin at the origin, never at the plate bottom. The ratio is dimensionless. An immobile spot has $R_f=0$; a spot at the front has $R_f=1$, where separation from other fast components may be poor. This distance ratio is distinct from the <chromatographic partition coefficient> and from a column retention time.
For an original stylized plate, choose absolute vertical coordinates $y_0=1\,\mathrm{cm}$, $y_{\rm front}=11\,\mathrm{cm}$, $y_A=4\,\mathrm{cm}$ and $y_B=8\,\mathrm{cm}$ above the plate bottom. The <solvent> distance is therefore $10\,\mathrm{cm}$, while the spot distances are $3\,\mathrm{cm}$ and $7\,\mathrm{cm}$:
$$
R_{f,A}=\frac{4-1}{11-1}=0.3,\qquad
R_{f,B}=\frac{8-1}{11-1}=0.7.
$$
Using $4/11$ or $8/11$ would wrongly include the unused centimetre below the origin. These chosen positions do not represent measured <pigments> or the protocol's plate dimensions.
\Image[/thin-layer-chromatography-origin-readout.png]
{title=Read <TLC retardation factors> from the origin, not the plate bottom}
{id=image-thin-layer-chromatography-origin-readout}
{description=Original stylized <thin-layer chromatography> plate with deliberately chosen coordinates, not experimental data. The pencil origin at $1\,\mathrm{cm}$ lies below both spots and the front at $11\,\mathrm{cm}$. All three measurement arrows start at the origin. The two colours label anonymous components and do not identify particular <pigments>.}
The <TLC retardation factor> depends on the sample, <chromatographic stationary phase>, <eluent> composition, and <temperature>; plate handling and development conditions must also match when comparing runs. The moving wet front and possible surface <adsorption> require their own transport assumptions. The equilibrium mobile fraction $f_m$ in the <chromatographic partition coefficient> model is not unconditionally equal to $R_f$; even that model depends on the phase <volume (thermodynamics)> ratio. Coincident <TLC retardation factors> alone never prove chemical identity.
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