4


August/September 2010


collapse of the column and some columns can be used over a reasonably long time without total degradation [12, 13]


. It can be


summarized that although the domain of high-temperature liquid chromatography potentially extends up to 374 °C, the useful temperature range for routine analysis is currently limited to approximately 200 °C. This is quite reasonable because specially designed heating systems as well as suitable stationary phases both generating and withstanding these temperatures are now commercially available.


It is useful to have defined what can be understood of high-temperature HPLC, but now the question has to be addressed why is it beneficial to increase temperature?


First of all I would like to discuss the influence of temperature on efficiency and speed. This is based on the van-Deemter equation, which should be known to every chromatographer and can be written as:


Equation 1


Here, the height equivalent to a theoretical plate Hu


(HETP) depends on three terms,


which are the band broadening due to Eddy diffusion (A-term), longitudinal diffusion (B- term) and the resistance to mass transfer between and within the mobile and stationary phases (C-term) and the mobile phase flow rate u. While the A-term can be regarded not to depend on temperature, the remaining B and C-term are both temperature-dependent. This is because the B-term is directly proportional to the diffusion coefficient DM


,


which is also a function of temperature. Equation 2


Equation 3


From a purely theoretical standpoint, the goal is always to minimize band broadening and thus minimizing H by adjusting the flow rate of the mobile phase to the optimum linear velocity. At velocities higher and lower than the optimum linear velocity there is an increase of H. However, when the temperature is increased, the profile of this curve changes. At elevated temperatures, the minimum of the Hu


-curve is shifted to higher linear velocities. In


addition, there is a much flatter increase of H at flow rates higher than the optimum. This means that if a separation is carried out at a mobile phase flow rate which is much higher than the optimum flow rate, the loss of


where T is the absolute temperature, M2 molecular weight of the solvent, V1


molar volume of the solute and η is the viscosity of the mobile phase. Ψ2


is the association factor for the solvent, which is is the is the


Figure 1. Viscosities of the binary mixture methanol (1) – water (2) at different temperatures. Additional data can be found in reference [15]


.


efficiency at higher temperatures is less pronounced than at lower temperatures. The net benefit of operating HPLC columns at higher temperatures therefore is that the operator has not to worry so much about the flow rate as long as it is higher than the optimum linear velocity. However, it needs to be stressed that there is no absolute increase in the efficiency, because it is not possible to lower the minimum of the van-Deemter curve [14]


.


Another advantage of increasing the temperature is that the viscosity maximum of the mobile phase can be significantly reduced [15]


.


When a solvent gradient is applied, often a huge pressure maximum is observed. Every practitioner will have noticed that mixtures consisting of water and methanol are much more troublesome than the corresponding mixtures of water and acetonitrile at ambient temperature. However, by steadily increasing the temperature, this pressure maximum can be totally avoided as is shown in Figure 1.


The decrease of the mobile phase’s viscosity at higher temperatures is also linked with the possibility to significantly speed up a chromatographic separation. In order to evaluate the effect of temperature on the theoretical gain in speed, we have to take a closer look at the diffusion coefficient DM


of


the solute in the mobile phase. According to Wilke and Chang, the diffusion coefficient can be written as:


Equation 4 Equation 5


Here, ΔH is the enthalpy of transfer of the solute from the mobile into the stationary phase, ΔS is the entropy of transfer of the solute from the mobile into the stationary phase, R is the ideal gas constant and β is the volume phase ratio of the stationary and mobile phase. At least theoretically, for most analytes a plot of the natural logarithm against the inverse absolute temperature (ln k


generally assumed to be 1 for non-polar solvents, 1.9 for methanol and 2.6 for water [16]


.


If it is assumed that the molar volume of the solute is not influenced by temperature, the diffusion coefficient is directly proportional to the temperature and inversely proportional to the viscosity of the mobile phase, which is also a function of temperature. Remember that for liquids, the viscosity will always decrease as the temperature is increased. It can now be derived that at least theoretically, a tremendous gain in speed might be achieved when the temperature is increased up to 250 °C. The highest “speed” factors result if a solvent system consisting of water and isopropanol is considered. Then – at least theoretically – it would be possible to decrease the time for a separation which is carried out at 25 °C by the factor of 50 when the separation is carried out at 250 °C [15]


. So


while there is no absolute increase in the efficiency when the temperature is increased, temperature can be used to dramatically increase the speed of a separation.


The question remains how temperature can be incorporated into method development?


In principal, the effect of temperature on retention can be described by the van’t Hoff equation, which can be written as:


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