what is a theoretical plate?

Answer 1

In chromatography, a model can be constructed in which materials travel plate to plate. It is just a model, but it can be used to create parameters to evaluate real plates.

Answer 2

Theoretical Plates

Answer 3

I believe you're talking about theoretical plates in chromatography?
Here is the definition of plate theory from wikipedia:
"Plate theory
The plate theory of chromatography was developed by Archer John Porter Martin and Richard Laurence Millington Synge. The plate theory describes the chromotography system, the mobile and stationary phases, as being in equilibrium. The partition coefficient K is based on this equilibrium, and is defined by the following equation:
K= concentration of solute in stationary phase/concentration of solute in mobile phase

K is assumed to be independent of concentration, and can change if experimental conditions are changed, for example temperature is increased or decreased. As K increases, it takes longer for solutes to separate. For a column of fixed length and flow, the retention time (tR) and retention volume (Vr) can be measured and used to calculate K."

The basic idea is that a method with better separation would have more theoretical plates, whereas one with less separation would have fewer theoretical plates. THis is sort of a way to compare different columns and conditions.

Answer 4

The theoretical plates in chromatography is just a theoretical equation indicates the efficiency of the separation in a chromatographic column, where more theoretical plates numbers means more separation efficiency

Answer 5

Terms and Definitions

Retention Time (tR)
Retention time (tR) is the time it takes a solute to travel through the column. The retention time is assigned to the corresponding solute peak. The retention time is a measure of the amount of time a solute spends in a column. It is the sum of the time spent in the stationary phase and the mobile phase.

Retention Time of an Unretained Compound (tM) or Hold-Up Time
The hold-up time or unretained peak time (tM or to ) is the time for an unretained compound to travel through the column. An unretained solute�s molecules do not enter the stationary phase, and they travel down the column at the same rate as the carrier gas. This is equivalent to the time a compound spends in the mobile phase. It is the same for all compounds in a single chromatographic run. The unretained peak time is obtained by injecting an unretained compound and determining its retention time. A list of some unretained compounds can be found in "Selecting Columns" section.

Retention Factor (k)
The retention factor (k) is another measure of retention. It is the ratio of the amount of time a solute spends in the stationary and mobile phases (carrier gas). It is calculated using Equation 1. The retention factor was previously called the partition factor or capacity factor. Since all solutes spend the same amount of time in the mobile phase, the retention factor is a measure of retention by the stationary phase. It is a relative measurement and is linear. For example, a solute with a k = 6 is twice as retained by the stationary phase (but not the column) as a solute with a k = 3. The retention factor does not provide absolute retention information; it provides relative retention information. An unretained compound has k = 0.

Equation 1. Retention factor (k)

Retention Index (I)
Retention index (I) is a measure of the retention of a solute relative to the retention of normal alkanes (straight chain hydrocarbons) at a given temperature and column. Equation 2a is used to calculate retention indices for isothermal temperature conditions. For temperature program conditions, Equation 2b can be used.

Equation 2. Retention Indices

The retention index for a normal alkane is its number of carbons multiplied by 100. For example, n-dodecane (n-C12H26) has I = 1200. If a solute has I = 1478, it elutes after n-C14 and before n-C15, and it is closer to n-C15. Retention indices normalize instrument variables so that retention data can be compared for different GC systems. Retention indices are also good for comparing retention characteristics for different columns.

Separation Factor (a)
The separation factor is a measure of the time or distance between the maxima of two peaks. It is calculated using Equation 3. If a = 1, then the peaks have the same retention and co-elute.

Equation 3. Separation Factor (a)

Number of Theoretical Plates (N) or Column Efficiency
Column efficiency is expressed by the number of theoretical plates (N). The number of theoretical plates can be calculated using either form of Equation 4. Theoretical plates is a concept and a column does not contain anything resembling physical distillation plates or any other similar feature. Theoretical plates numbers are an indirect measure of peak width for a peak at a specific retention time. Columns with high plate numbers are considered to be more efficient (i.e., higher column efficiency) than columns with lower plate numbers. A column with a high number of plates will have a narrower peak at a given retention time than a column with a lower number of plates.

Equation 4. Theoretical Plates or Efficiency (N)

High column efficiency is beneficial since less peak separation (i.e. lower a�s) is required to completely resolve narrow peaks. On stationary phases where the as of those solutes are larger, less efficient columns can be used.Where as are small, more efficient columns are needed. Column efficiency is a function of the column dimensions (diameter, length and film thickness), the type of carrier gas and its flow rate or average linear velocity, and the compound and its retention. For column comparison purposes, the number of theoretical plates per meter (N/m) is often used.

Theoretical plate numbers are only valid for a specific set of conditions. Isothermal temperature conditions are required and temperature programs result in highly inflated plate numbers. Also, the retention factor (k) of the test solute used to calculate plate numbers should be greater than 5. Less retained peaks result in inflated plate numbers. When comparing theoretical plate numbers between columns, the same temperature conditions and peak retention (k) are required for the comparison to be valid.

Height Equivalent to a Theoretical Plate (H)
Another measure of column efficiency is the height equivalent to a theoretical plate (H). It is calculated using Equation 5 and usually reported in mm. The shorter each theoretical plate, the more plates "contained" in a given length of column. This translates into more theoretical plates per meter and higher efficiency. Small plate heights indicate higher efficiency.

Equation 5. Hight Equivalent to a Theoretical Plate (H)

Utilization of Theoritical Efficiency (UTE%)
Coating efficiency (CE%) is an historical term that compares the measured column efficiency and its theoretical maximum efficiency. It is calculated using Equation 6.

Equation 6. Utilization of Theoretical Efficiency

Historically, Hactual was usually so heavily impacted by hetrogeneities in the stationary phase film that extra-column contributions to Hactual--e.g., injection anomolies, insufficient or misdirected make up gas, mechanical (and electronic) lag times-- could be ignored. Because of improvements in coating technology, this is no longer the case, and Hactual is usually more heavily impacted by extra-column contributions than by the column per se. Column contributions to Hactual become more meaningful with increasing film thickness, or polarity, both of which affect stationary phase diffusion. Many authorities prefer the term "utilization of theoritical efficiency," UTE, which takes the above into account. Typical UTE�s are 85-100% for nonpolar stationary phases and 60-80% for polar ones.

Resolution (Rs)
Equation 7. Resolution (Rs)

The higher the resolution the less the overlap between two peaks. Separation is only the distance or time between two peak maxima (a). Resolution takes both a and the width of the peaks into account. It is calculated using either form of Equation 7. Baseline resolution usually occurs at resolution number of 1.50, however, there is no baseline between the peaks. Numbers greater than 1.50 indicate there is baseline between the peaks. Numbers less than 1.50 indicate there is some peak co-elution. Examples can be found in Figure 2 (Resolution Examples).

Sometimes percent resolution values are used. They are calculated by dividing the height of the valley between the peaks by the total peak height. It is an easier value to visualize than resolution numbers; however, it is not possible to distinguish between different amounts of full baseline resolution (Figure 2, Resolution Examples).

Figure 2. Resolution Examples

Phase Ratio (b)
Table 1. Phase Ratios
FilmThickness Column Diameter (mm)
df (�m) 0.10 0.18 0.20 0.25 0.32 0.45 0.53
0.10 250 450 500 625 800 1125 1325
0.18 139 250 278 347 444 625 736
0.25 100 180 200 313 400 450 663
0.40 63 113 125 156 200 281 331
0.42 - 107 119 149 190 265 315
0.50 - 90 100 125 160 225 265
0.83 - - 60 75 96 136 160
0.85 - - 59 74 94 133 156
1.00 - - 50 63 80 113 133
1.27 - - - 49 63 88 104
1.50 - - - 42 53 75 88
2.55 - - - 25 31 44 52
3.00 - - - 21 27 38 44
5.00 - - - 13 16 23 27

A column�s phase ratio (b) is calculated using Equation 8. If the same stationary phase and column temperature (program or isothermal) are maintained, the change in the phase ratio can be used to calculate the change in a solute�s retention. This relationship is expressed by Equation 9. The distribution constant (KC) is the ratio of the solute concentration in the stationary and mobile phases (cS/cM). The distribution constant is fixed for the same stationary phase, column temperature and solute.

Thus, for a given stationary phase and column temperature, the amount and direction of any change in retention upon a change in column diameter or film thickness can be determined. Equation 9 shows that an increase in the phase ratio results in a corresponding decrease in retention (k) since KC is constant. Conversely, a decrease in the phase ratio results in a corresponding increase in retention (k).

Equation 8. Phase Ratio (b)

Equation 9. Distribution Constant (Kc)

Equation 8 shows that the phase ratio decreases with a decrease in diameter or an increase in film thickness. Either of these column changes results in an increase in solute retention. The phase ratio increases with an increase in diameter or a decrease in film thickness. Either of these column changes results in a decrease in solute retention. Sometimes it is desirable to change column diameter or film thickness to obtain a specific effect (increased efficiency), without changing retention. This can be accomplished by proportionate changes in both the column diameter and the film thickness. For example, if the column diameter is reduced from 0.25 to 0.18 mm I.D., a corresponding change in the film thickness (e.g., 0.25 �m to a 0.18 �m) maintains the same phase ratio. The overall affect is to maintain the same retention while achieving higher efficiency due to the decrease in column diameter. Table 1 lists the phase ratios for the most common column dimensions.

http://www.chem.agilent.com/cag/cabu/terms&def.htm

Answer 6

um....a plate....that exists in theory.....duh