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As per my textbook:

Partition Chromatography: Partition chromatography is based on continuous differential partiotioning of components of a mixture between stationary and mobile phases. Paper chromatography is a type of partition chromatography. In paper chromatography, a special quality paper known as chromatography paper is used. Chromatography paper contains water trapped in it, which acts as the stationary phase. (highlight mine)

According to the book, paper chromatography is a kind of partition chromatography where the stationary phase is water, as I think it should be, because in partition chromatography a solid is not the stationary phase. For instance, the Wikipedia entry on partition chromatography states:

Chromatographic separation was considered to occur by an adsorption process whereby compounds adhered to a solid media and were washed off the column with a solvent, mixture of solvents, or solvent gradient. In contrast, Martin and Synge developed and described a chromatographic separation process whereby compounds were partitioned between two liquid phases similar to the separatory funnel liquid-liquid separation dynamic. This was an important departure, both in theory and in practice, from adsorption chromatography

But according to the Wikipedia and this site, the stationary phase in paper chromatography is paper (a solid).

So which one is correct? Is paper chromatography really a kind of partition chromatography or adsorption chromatography?

The picture is from my textbook: NCERT class 11, pg-353.

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It's a bit of both, actually, and also ion-exchange chromatography. The cellulose and other components of paper do exhibit adsorption and ion exchange properties with some analytes, but as paper chromatography is usually performed, partitioning between the flowing solvent and trapped water is the major mode of separation. Paper chromatography typically uses water-saturated solvents and enclosed chambers where water vapour can keep water trapped in the paper (the paper is equilibrated with this vapour before development). Since cellulose is very hydrophilic, immiscible or poorly miscible solvents are usually used, which keeps the water stuck to the cellulose as it has much higher affinity for water than the solvent.

This is an early paper showing the apparatus used for paper chromatography of amino acids and this book details the theory involved starting on page 4.

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