MSOP1015 Pharmaceutical Analysis Lecture 2: Chromatographic theory 2024-2025 - PDF

MSOP1015 Pharmaceutical Analysis Lecture 2: Chromatographic theory Dr. Andrew J Hall Senior Lecturer in Chemistry Room A120, Anson Building [email protected] Recommended text e-book available Quantitative C...

MSOP1015 Pharmaceutical Analysis Lecture 2: Chromatographic theory Dr. Andrew J Hall Senior Lecturer in Chemistry Room A120, Anson Building [email protected] Recommended text e-book available Quantitative Chemical Analysis Daniel C. Harris Drill Hall Library 8th ed. – 14 copies Learning outcomes At the end of this lecture you should appreciate/understand: the information contained within a chromatogram the “plate” theory of chromatography the “rate” theory of chromatography the consequence of the Van Deemter equation in HPLC and GC the importance of resolution in chromatography A HPLC chromatogram Separation of barbiturates by high performance liquid chromatography column Discovery C18, 15 cm x 4.6 mm I.D., 5 µm particles (504955) column temp. ambient mobile phase [A] methanol; [B] water (45:55, A:B) flow rate 1 mL/min injection 10 µL detector UV, 214 nm https://www.sigmaaldrich.com/technical-documents/articles/analytical- applications/hplc/hplc-analysis-of-barbiturates-g000190.html A GC chromatogram Separation of opiates and related substances by gas chromatography https://blog.restek.com/?p=7090 Chromatograms How are they produced? Injection B A Solvent Solvent flow flow Unretained compound Chromatograms What information do we get? Vr(B) or tr(B) Vr(A) or tr(A) Vo or t0 Injection Volume or time Vo / t0 = void volume Volume or time taken for solvent or unretained compounds to pass through the column Vr / tr= retention volume/time for the respective analytes Chromatograms Capacity factor (k) The capacity factor is a measure of the amount of time an analyte spends in the column Vr - Vo tr - to k= k= Vo to Vo = void volume to = retention time of unretained compound Vr = analyte retention volume tr = analyte retention time Chromatograms Capacity factor (k) – manipulation of equation During a HPLC experiment, compound X was found to have a capacity factor (k) equal to 5 If V0 for the column was 1 mL and the solvent flow rate was 1 mL/min Then Vr (X) = 6 mL and tr (X) = 6 minutes Chromatograms Selectivity () The selectivity is a measure of the spacing between two peaks Vr(B) or tr(B) Vr(A) or tr(A) k(B) = k(A) Injection Volume or time Column efficiency Number of theoretical plates (n) tr t0 tr - t0 (= tr’) n = 5.54 (tr/W1/2)2 h Injection h/2 W1/2 Efficiency is usually expressed in theoretical plates per metre, i.e. efficiency = n x 100/L [L = column length (in cm)] Column efficiency Further considerations More strictly Neff = 5.54 (t’r/W1/2)2 where Neff = number of effective plates and t’r = tr – t0 Another commonly used term is the “Height Equivalent of a Theoretical Plate” (HETP or H) H = L/Neff H is the length of column required for a single partition step to occur Band broadening Chromatographic peaks have width This is because molecules of a single compound travel through the column in different times The longer the time spent by an analyte on the column, the more individual molecules can spread out ➔ band broadening The more rapidly a peak broadens, the less efficient the column Rate theory of chromatography Introduction A more realistic description of the processes at work inside a column Accounts for time taken for solute to equilibrate between phases (mobile and stationary) Plate model assumes infinitely fast equilibration The shape of a chromatographic peak is affected by the rate of elution Also affected by the different paths available to solute molecules on their journey through the column packed with stationary phase Rate theory of chromatography The Van Deemter equation (for LC) This has resulted from a consideration of the various mechanisms that contribute to band broadening A B H = + + Csu + Cmu½ (1 + Cm/u1/2) u u = linear velocity of the mobile phase A = “eddy” diffusion term B = rate of diffusion of molecule in the mobile phase Cs = resistance to mass transfer of a molecule in the stationary phase Cm = resistance to mass transfer due to diameter and shape of stationary phase Rate theory of chromatography The eddy diffusion term (A) Mobile phase moves through column packed with stationary phase Solute molecules take different random paths on their journey Band broadening occurs as the different paths have different lengths Rate theory of chromatography The longitudinal diffusion term (B) This is band broadening due to diffusion of solute along the length of the column in the flowing mobile phase If the mobile phase velocity is high the analyte will spend less time on the column, leading to a decrease in the effect of longitudinal diffusion Rate theory of chromatography Resistance to mass transfer in stationary phase (Cs) Depends on diffusion coefficient of solute molecule in the stationary phase (Ds) and the thickness of the stationary phase (dthickness) Mobile phase flow X Y Solid Cs = d2thickness/Ds support Stationary phase Thinner and uniform stationary phase reduce the effect of these processes As the u decreases this term contributes less to band broadening Rate theory of chromatography Resistance to mass transfer due to stationary phase (Cm) Depends on shape and diameter (dpacking) of the stationary phase particles and on the diffusion of a molecule in the mobile phase (Dm) solvent flow X Cm = d2packing/Dm Y solvent flow Thinner and uniform stationary phase reduce the effect of these processes As the u decreases this term contributes less to band broadening Rate theory of chromatography Practical considerations Low diffusion constant for analyte in mobile phase increases efficiency via the A term but decreases it via the Cm term….. On balance a higher diffusion coefficient is more favourable Contributions of A, Csu and Cmu½ terms to band broadening are similar except at very high flow rates (Csu term dominate) The B term makes a higher contribution at low flow rates (low u) Compromise made between analysis time and flow rate… Rate theory of chromatography Van Deemter plots https://www.restek.com/Technical-Resources/Technical- Library/Pharmaceutical/pharm_A016 Rate theory of chromatography Factors that increase column efficiency Stationary phase that are made of small, uniformly-sized and regularly shaped particles Stationary phase coating that are thin and even High temperature High diffusion coefficient in the mobile phase High diffusion coefficient in the stationary phase Advantages of smaller particles http://www.chromacademy.com Advantages of smaller particles Real-world example http://www.phenomenex.com/Kinetex/TechnicalResources Van Deemter equation for GC Different emphasis on relative importance of each term Interactions between analytes and stationary phases are much simpler H = A + B/u + Cu H = a measure of column efficiency u = carrier gas velocity A = “eddy” diffusion term B = 2 x diffusion coefficient of analyte in the gas (mobile) phase Cs = composed of terms relating to diffusion of analyte in gas phase and liquid stationary phase Types of GC Packed column and capillary (open-tubular) Open tubular capillary GC Eddy diffusion does not play a role C term largely composed of transverse diffusion coefficient Liquid phase Transverse Longitudinal Gas flow Liquid phase Transverse diffusion effect can be reduced by using capillaries with smaller internal diameters GC mobile phases and efficiency B/u term most favourable for nitrogen but nitrogen is only more efficient at low flow rates More common to use helium – good efficiency without reducing flow rate Use of hydrogen is becoming common – high efficiency at high flow rates GC mobile phases Benefits of hydrogen https://www.restek.com/Technical-Resources/Technical- Library/Petroleum-Petrochemical/petro_PCTJ1729-UNV Resolution Expression 1 Selectivity factor () describes separation of band centres Ignores peak width ➔ Another measure of how good the separation is: resolution (Rs) 2(trA – trB) trA & trB: retention times of analytes A and B Rs = WA & WB: widths of each peak at the baseline WA + WB Baseline resolution is when Rs ≥ 1.5 Resolution Expression 2 Resolution may also be calculated as follows trA – trB Rs = 1.18 WA0.5 + WB0.5 trA & trB: retention times of analytes A and B WA0.5 & WB0.5: widths of each peak at the baseline Baseline resolution is when Rs ≥ 1.5 Resolution How a chromatogram might look https://chem.libretexts.org/Courses/Northeastern_Univer sity/12%3A_Chromatographic_and_Electrophoretic_Method s/12.2%3A_General_Theory_of_Column_Chromatography Resolution A fundamental equation Useful to relate the resolution of a separation to the following: Number of plates in the column (N) Selectivity factor () Retention factors of the solutes (k) N0.5  – 1 kB Rs = 4  1+k efficiency selectivity retention  = (kB / kA) k = (kA + kB)/2 Resolution Consequences of the fundamental equation Increase efficiency by a factor of 2 ➔ only a 1.41x increase in resolution Increasing capacity factor has a more marked effect on resolution To increase k in LC: change the mobile phase composition To increase k in GC: change the temperature Resolution Making improvement in experimental workflow Increase efficiency by a factor of 2 ➔ only a 1.41x increase in resolution Increasing capacity factor has a more marked effect on resolution To increase k in LC: change the mobile phase composition To increase k in GC: change the temperature uation 5. Resolution Fig. 10.8 Example of changing mobile phaseEffect in LCof changing solvent A 8.9 min composition on the B 9.65 min t 0 = 1.2 capacity fact or of tw o analytes on a reverse- phase column. 1. Water/aceton itrile A 10.9 min 50:50. B 13.2 min 2. Water/aceton itrile 52:48. 1 2 Peak asymmetry (As) As= B/A http://www.chromacademy.com/HPLC_Column_Ch aracterization_and_Selection_Essential_Guide.html Learning outcomes Take-home points You should now appreciate/understand: the information contained within a chromatogram the “plate” theory of chromatography the “rate” theory of chromatography the consequence of the Van Deemter equation in HPLC and GC the importance of resolution in chromatography