Introduction to Chromatographic Separations Analysis of complex samples usually involves previous separation prior to compound determination. Two main separation methods instrumentation are available: based on Chromatography Electrophoresis Chromatography is based on the interaction of chemical species with a mobile phase (MP) and a stationary phase (SP). The MP and the SP are immiscible. The sample is transported by the MP. The interaction of species with the MP and the SP separates chemical species in zones or bands. The relative chemical affinity of chemical species with the MP and the SP dictates the time the species remain in the SP. MP + sample SP Detector Two general types of chromatographic techniques exist: Planar: flat SP, MP moves through capillary action or gravity Column: tube of SP, MP moves through gravity or pressure. 151
Classification of Chromatographic Methods Chromatographic methods can be classified on the type of MP and SP and the kinds of equilibrium involved in the transfer of solutes between phases: Column 1: Type of MP Column 2: Type of MP and SP Column 3: SP Column 4: Type of equilibrium Concentration profiles of solute bands A and B at two different times in their migration down the column. 152
Migration Rates of Solutes Two-component chromatogram illustrating two methods for improving separation: (a) Original chromatogram with overlapping peaks; (b) improvement brought about an increase in band separation; (c) improvement brought about by a decrease in the widths. Distribution constant or partition ratio or partition coefficient: It describes the partition equilibrium of an analyte between the SP and the MP. If K = K c and SP = S and MP = M K c = c S / C M = n S / V S n M / V M Where V S and V M are the volumes of the two phases and n S and n M are the moles of A in SP and MP, respectively. 153
Retention Time Retention time is a measured quantity. From the figure: t M = time it takes a non-retained species (MP) to travel through the column = dead or void time. t R = retention time of analyte. The analyte has been retained because it spends a time t S in the SP. The retention time is then given by: t R = t S + t M The average migration rate (cm/s) of the solute through the column is: Where L is the length of the column. The average linear velocity of the MP molecules is: 154
Relationship Between Retention Time and Distribution Constant The Rate of Solute Migration: The Retention Factor Retention factor = capacity factor = k A = k A. However: k A K C or k A K A Where V S and V M are the volumes of SP and MP in the column. Knowing that: => An equation can be derived to obtain K C of A (K A ) as a function of experimental parameters. => 155
Band Broadening and Column Efficiency The shape of an analyte zone eluting from a chromatographic column follows a Gaussian profile. Some molecules travel faster than the average. The time it takes them to reach the detector is: t R τ. Some molecules travel slower than the average molecule. The time it takes them to reach the detector is: t R + t The selectivity factor can be measured from the chromatogram. Selectivity factors are always greater than unity, so B should be always the compound with higher affinity by the SP. Selectivity factors are useful parameters to calculate the resolving power of a column. So, the Gaussian provides an average retention time (most frequent time) and a time interval for the total elution of an analyte from the column. The magnitude of Dt depends on the width of the peak. 156
Considering that: v_ = L / t R => L = v_ x or L ± L = v_ x [t R ± t] The equation above correlates chromatographic peaks with Gaussian profiles to the length of the column. Both t and L correspond to the standard deviation of a Gaussian peak: t L σ If σ = t, σ units are in minutes. If σ = L, σ units are in cm. The width of a peak is a measure of the efficiency of a column. The narrower the peak, the more efficient is the column. => The efficiencies of chromatographic columns can be compared in terms of number of theoretical plates. 157
The Plate Theory The plate theory supposes that the chromatographic column contains a large number of separate layers, called theoretical plates. Separate equilibrations of the sample between the stationary and mobile phase occur in these "plates". The analyte moves down the column by transfer of equilibrated mobile phase from one plate to the next. It is important to remember that theoretical plates do not really exist. They are a figment of the imagination that helps us to understand the processes at work in the column. As previously mentioned, theoretical plates also serve as a figure of merit to measuring column efficiency, either by stating the number of theoretical plates in a column (N) or by stating the plate height (H); i.e. the Height Equivalent to a Theoretical Plate. The number of theoretical plates is given by: N = L / H If the length of the column is L, then the HETP is: H = σ 2 / L Note: For columns with the same length (same L): The smaller the H, the narrower the peak. The smaller the H, the larger the number of plates. => column efficiency is favored by small H and large N. It is always possible to using a longer column to improve separation efficiency. 158
Experimental Evaluation of H and N Calling σ in time units (minutes or seconds) as τ: => σ / τ = cm / s Considering that: v_ = L / t R = cm /s We can write: L / t R = σ / τ or τ = σ = σ L / t R v_ If the chromatographic peak is Gaussian, approximately 96% of its area is included within ± 2σ. This area corresponds to the area between the two tangents on the two sides of the chromatographic peak. The width of the peak at its base (W) is then equal to: W = 4τ in time units or W = 4σ in length units. Substituting τ = W / 4 in the equation above we obtain: σ = LW / 4t R Substituting σ = W / 4 in the same equation we obtain: τ = Wt R / 4L Substituting σ = LW / 4t R in the HEPT equation: H = LW 2 / 16t R 2 Substitution of this equation in N gives: N = 16 (t R / W) 2 These two equations allow one to estimate H and N from experimental parameters. If one considers the peak of the width at the half maximum (W 1/2 ): N = 5.54 (t R / W 1/2 ) 2 In comparing columns, N and H should be obtained with the same compound! 159
Kinetic Variables Affecting Column Efficiency The plate theory provides two figures of merit (N and H) for comparing column efficiency but it does not explain band broadening. Table 26-2 provides the variables that affect band broadening in a chromatographic column and, therefore, affect column efficiency. The effect of these variables in column efficiency is best explained by the theory of band broadening. This theory is best represented by the van Deemter equation: H = A + B / u+ C S. u + C M. U where H is in cm and u is the velocity of the mobile phase in cm.s -1. The other terms are explained in Table 26-3. Table 26-3: f(k) and f (k) are functions of k λ and γ are constants that depend on the quality of the packing. B is the coefficient of longitudinal diffusion. C S and C M are coefficients of mass transfer in stationary and mobile phase, respectively. Before we try to understand the meaning of the van Deemter equation, a better understanding of chromatographic columns is needed. 160
Some Characteristics of Gas Chromatography (GC) Columns Two general types => Open Tubular Columns (OTC) or Capillary Columns => Packed Columns OTC: => Wall Coated Open Tubular (WCOT) Columns => Support Coated Open Tubular (SCOT) Columns => The most common inner diameters for capillary tubes are 0.32 and 0.25mm. Packed Columns: => Glass tubes with 2 to 4mm inner diameter. => Packed with a uniform, finely divided packing material of solid support, coated with a thin layer (005 to 1µm) of liquid stationary phase. Solid Support Material in OTC and Packed Columns Diatomaceous Earth: skeletons of species of single-celled plants that once inhabited ancient lakes and seas. 161
Some Characteristics of HPLC Columns Only packed columns are used in HPLC. Current packing consists of porous micro-particles with diameters ranging from 3 to 10µm. The particles are composed of silica, alumina, or an ion-exchange resin. Silica particles are the most common. Thin organic films are chemically or physically bonded to the silica particles. The chemical nature of the thin organic film determines the type of chromatography. SP for normal-phase chromatography Typical microparticle SP for partition chromatography 162
Another Look at the van Deemter Equation H = A + B/u + C S u + C M u The multi-path term A or Eddy-Diffusion: => This term accounts for the multitude of pathways by which a molecule (or ion) can find its way through a packed column. A = 2λd p where: λ is a geometrical factor that depends on the shape of the particle: 1 λ 2. d p is the diameter of the particle. Using packing with spherical particles of small diameters should reduce eddy -diffusion. Injection Detector 163
The Longitudinal Diffusion Term B/u: Longitudinal diffusion is the migration of solute from the concentrated center of the band to the more diluted regions on either side of the analyte zone. B/u = 2γD M /u where: γ is a constant that depends on the nature of the packing and it varies from 0.6 γ 0.8. D M is the diffusion coefficient in the mobile phase. D M α T / µ, where T is the temperature and µ is the viscosity of the mobile phase. As u infinite, B/u zero. So, the contribution of longitudinal diffusion in the total plate height is only significant at low MP flow rates. Its contribution is potentially more significant in GC than HPLC because of the relatively high column temperatures and low MP viscosity (gas). Initial band Diffusion of the band with time The initial part of the curve is predominantly due to the B/u term. Because the term B/u in GC is larger than HPLC, the overall H in GC is about 10x the overall H in HPLC. 164
The Stationary-Phase Mass Transfer Term C S u: C S = mass transfer coefficient in the SP. C S α d f 2 / D S where d f is the thickness of the SP film and D S is the diffusion coefficient in the SP. => Thin-film SP and low viscosity SP (large D S ) provide low mass transfer coefficients in the SP and improve column efficiency. The Mobile-Phase Mass Transfer Term C M u: C M = mass transfer coefficient in the MP. C M α d p 2 / D M where d p is the diameter of packing particles and D M is the diffusion coefficient in the MP. The contribution of mass transfer in the SP and MP on the overall late height depends on the flow velocity of the mobile phase. Both phenomena play a predominant role at high MP flow rates. Liquid SP coated on solid support Cartoon with example of SP mass-transfer in a liquid SP: different degrees of penetration of analyte molecules in the liquid layer of SP lead to band-broadening Porous in silica particle Cartoon with example of MP masstransfer: stagnant pools of MP retained in the porous of silica particles lead to bandbroadening. 165
Summary of Methods for Reducing Band Broadening Packed Columns: Most important parameter that affects band broadening is the particle diameter. If the SP is liquid, the thickness of the SP is the most important parameter. Capillary Columns: No packing, so there is no Eddy-diffusion term. Most important parameter that affects band broadening is the diameter of the capillary. Gaseous MP (GC): The rate of longitudinal diffusion can be reduced by lowering the temperature and thus the diffusion coefficient. The effect of temperature is mainly noted at low flow rate velocities where the term B/u is significant. Temperature has little effect on HPLC. Effect of particle diameter in GC Effect of particle diameter in HPLC Note: m = µm 166
Optimization of Column Performance Optimization experiments are aimed at either reducing zone broadening or altering relative migration rates of components. The time it takes for chromatographic analysis is also an important parameter that should be optimized without compromising chromatographic resolution. Column Resolution: It is a quantitative measure of the ability of the column to separate two analytes. It can be obtained from the chromatogram with the equation: In terms of retention factors k A and k B for the two solutes, the selectivity factor and the number of theoretical plates of the column: From the last equation we can obtain the number of theoretical plates needed to achieve a given resolution: 167
For compounds with similar capacity factors, i.e. k A k B : The time it takes to achieve a separation can be predicted with the formula: Where k = k A + k B / 2 168
The General Elution Problem The general elution problem occurs in the separation of mixtures containing compounds with widely different distribution constants. The best solution to the general elution problem is to optimize eluting conditions for each compound during the chromatographic run. In HPLC, this is best accomplished by changing the composition of the mobile phase (Gradient Elution Chromatography). In GC, this is best accomplished by changing the temperature of the column during the chromatographic run. 169
Qualitative and Quantitative Analysis in GC and HPLC Both are done with the help of standards. Qualitative analysis, i.e. compound identification is done via retention time. The retention time from the pure standard is compared to the retention time of the analyte in the sample. Note: retention times are experimental parameters and as such are prone to standard deviation. Quantitative analysis is done via the calibration curve method (or external standard method) or the internal standard method. Calibration curve or external standard method: the procedure is the same as usual. The calibration curve can be built plotting the peak height or the peak area versus standard concentration. The same volume of sample was injected in each case, but Sample B has a much smaller peak. Since the t R at the apex of both peaks is 2.85 minutes, this indicates that they are both the same compound, (in this example, acrylamide (ID)). The Area under the peak ( Peak Area Count ) indicates the concentration of the compound. This area value is calculated by the Computer Data Station. Notice the area under the Sample A peak is much larger. In this example, Sample A has 10 times the area of Sample B. Therefore, Sample A has 10 times the concentration, (10 picograms) as much acrylamide as Sample B, (1 picogram). Note, there is another peak, (not identified), that comes out at 1.8 min. in both samples. Since the area counts for both samples are about the same, it has the same concentration in both samples. 170
Internal Standards An internal standard is a known amount of a compound that is added to the unknown. The signal from analyte is compared to the signal from the standard to find out how much analyte is present. This method compensates for instrumental response that varies slightly from run to run and deteriorates reproducibility considerably. This is the case of mobile phase flow rate variations in chromatographic analysis. Internal standards are also desirable in cases where the possibility of loosing sample during analysis exists. This is the case of sample separation in the chromatographic column. The internal standard should be chosen according to the analyte. Their chemical behavior with regards to the SP and MP should be similar. How to use an internal standard?: a mixture with the same known amount of standard and analyte is prepared to measure the relative response of the detector for the two species. The factor (F) is obtained from the relative response of the detector. Once the relative response of the detector has been found, the analyte concentration is calculated according to the formula: Area of analyte signal Concentration of analyte = F x Area of standard signal Concentration of standard A known amount of standard is added to the unknown X. The relative response is measured to obtain the detector s response factor F. 171
Example of Internal Standards In a preliminary experiment, a solution containing 0.0837M X and 0.066M S gave peak areas of A X = 423 and A S = 347. Note that areas are measured in arbitrary units by the instrument s computer. To analyze the unknown, 10.0mL of 0.146M S were added to 10.0mL of unknown, and the mixture was diluted to 25.0mL in a volumetric flask. This mixture gave a chromatogram with peak areas A X = 553 and A S = 582. Find the concentration of X in the unknown. First use the standard mixture to find the response factor: A X / [x] = F x {A S / [S]} Standard mixture: 423 / 0.0837 = F {347 / 0.0666} => F = 0.9700 In the mixture of unknown plus standard, the concentration of S is: [S] = (0.146M)(10.0mL / 25.0mL) = 0.0584M where: 10.0mL / 25.0mL is the dilution factor Using the known response factor and S concentration of the diluted sample in the equation above: 553 / [X] = 0.9700 (582 / 0.0584) =>[X] = 0.05721M 172
Liquid Chromatography Size exclusion or gel: polystyrene-divinylbenzene Silica with various porous sizes 173
Instrumentation 174
Pumping Systems Pumping systems that allow to change the MP composition during the chromatographic run provide better separation of compounds with wide range of k factors. 175
Detectors UV-VIS absorption cell for HPLC 176