{"id":1962,"date":"2026-02-05T14:44:17","date_gmt":"2026-02-05T13:44:17","guid":{"rendered":"https:\/\/bioeducator.eu\/?page_id=1962"},"modified":"2026-02-05T16:58:00","modified_gmt":"2026-02-05T15:58:00","slug":"what-are-the-theoretical-plates","status":"publish","type":"page","link":"https:\/\/bioeducator.eu\/?page_id=1962&lang=en","title":{"rendered":"What are the theoretical plates?"},"content":{"rendered":"\n

Every analyst performing column chromatography comes across the concept of theoretical plates. This parameter says a lot about the chromatographic column and its condition. If you have read \u2018Introduction to HPLC<\/a>\u2019, you know that a chromatography column does not contain any plates. So what are theoretical plates and how do they affect separation? You will find out in this article.<\/p>\n\n\n\n

The Game of Resolution<\/h2>\n\n\n\n
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Resolution (Rs) is the holy grail of chromatography<\/a>. This parameter tells us whether two components of a mixture have left the column separately or merged into a single unreadable signal.<\/p>\n\n\n\n

Three factors influence resolution: retention (how long substances remain on the column), selectivity (how much they \u2018like\u2019 the stationary phase relative to each other) and efficiency. It is efficiency \u2013 the ability of the column to maintain a narrow band of substances \u2013 that forms the basis of the shelf theory.<\/p>\n<\/div>\n\n\n\n

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\"Low<\/figure>\n<\/div><\/div>\n<\/div>\n\n\n\n

What are theoretical plates?<\/h2>\n\n\n\n

When we hear about \u2018plates\u2019 inside a column, our intuition tells us to think of physical steps or partitions. Nothing could be further from the truth. Theoretical plates are mathematical abstractions.<\/p>\n\n\n\n

Let us imagine that the chromatographic process is a series of successive discrete extraction stages. A molecule of a substance comes into contact with the stationary phase. Equilibrium is established, and then the mobile phase moves it one step further to the next \u2018micro-stage\u2019. The more such steps (plates) we can fit into the column, the better the separation will be.<\/p>\n\n\n\n

The Legacy of Martin and Synge: The Distillation Model<\/h2>\n\n\n\n

In 1941, Archer Martin and Richard Synge (later Nobel laureates) proposed a model based on the fractional distillation process. At that time, distillation was the best-described separation process, and distillation columns actually had physical shelves (plates).<\/p>\n\n\n\n

Martin and Synge attempted to describe the behaviour of a chromatography column as if it were a distillation column. In this model, the substance moves down the column in a series of discrete steps.<\/p>\n\n\n\n

On each „plate” the moving and stationary phases are in perfect balance.<\/h3>\n\n\n\n

Although this model was brilliant in its simplicity, it had one major drawback: it was static. It assumed that equilibrium is reached immediately, which is impossible in the actual flow of liquids or gases.<\/p>\n\n\n\n

Column efficiency: N and H parameters<\/h2>\n\n\n\n

To describe the performance of a column, we use two key parameters:<\/p>\n\n\n\n

Number of theoretical plates (N)<\/strong><\/p>\n\n\n\n

The higher the N value, the more efficient the column and the narrower the peaks. We calculate it from the chromatogram based on retention time (tR) and peak width (w):<\/p>\n\n\n\n

N<\/mi>=<\/mo>16<\/mn>(<\/mo>t<\/mi>R<\/mi><\/msub>w<\/mi><\/mfrac>)<\/mo><\/mrow>2<\/mn><\/msup><\/mrow>N = 16 \\left( \\frac{t_R}{w} \\right)^2<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

As can be easily seen, the number of theoretical plates will be characteristic for a specific substance and separation conditions, and even for a specific apparatus. Therefore, it is important to always determine it under the same conditions.<\/p>\n\n\n\n

\"P\u00f3\u0142ki<\/figure>\n\n\n\n

Height equivalent to theoretical plate (H or HETP)<\/strong><\/p>\n\n\n\n

This parameter tells us how „thick” a single plate is. Since the column has a specific length (L), the relationship is simple:<\/p>\n\n\n\n

H<\/mi>=<\/mo>L<\/mi>N<\/mi><\/mfrac><\/mrow>H = \\frac{L}{N}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

Analytical objective:<\/strong> We want H to be as small as possible. A low H value means that more plates can fit into each centimetre of the column. It translates into higher efficiency.<\/p>\n\n\n\n

The Van Deemter equation, or how to control productivity<\/h2>\n\n\n\n

In 1956, Dutch engineer Jan van Deemter and his colleagues noticed that a static model was not enough. In reality, analyte molecules do not wait patiently for equilibrium to be established \u2013 they are in constant motion, diffusing and colliding with the filling elements.<\/p>\n\n\n\n

Their Kinetic Theory of Dispersion is described by the equation:<\/p>\n\n\n\n

H<\/mi>=<\/mo>A<\/mi>+<\/mo>B<\/mi>u<\/mi><\/mfrac>+<\/mo>C<\/mi>\u22c5<\/mo>u<\/mi><\/mrow>H = A + \\frac{B}{u} + C \\cdot u<\/annotation><\/semantics><\/math><\/div>\n\n\n\n

Where u is the linear velocity of the mobile phase. The equation describes the relationship between flow velocity and column efficiency. However, in addition to flow, three components can be observed that are closely related to the column design. These three components are three different types of diffusion that occur during separation.<\/p>\n\n\n\n

Equation Components:<\/strong><\/p>\n\n\n\n