Theory of Chromatography Lecture 2 PDF

02/10/2023 Theory of Chromatography vevox.app 126-545-180 Nikola P. Chmel L2 CH3F2 1 Outline Lecture 1 What is Analytical Science Errors and units What is chromatography? Terminology Classification History Theoretical plate model Rate theory Kinetic theory Normal phase chromatography (column, TLC) R...

02/10/2023 Theory of Chromatography vevox.app 126-545-180 Nikola P. Chmel L2 CH3F2 1 Outline Lecture 1 What is Analytical Science Errors and units What is chromatography? Terminology Classification History Theoretical plate model Rate theory Kinetic theory Normal phase chromatography (column, TLC) Reverse phase chromatography (HPLC) Gas chromatography Other chromatographic techniques Lecture 2 Lecture 3 Lecture 4 2 1 02/10/2023 Theory of Chromatography The Theoretical Plate Model of Chromatography Proposed by Martin and Synge in 1941 based on the theory of distillation The Rate Theory of Chromatography Proposed by van Deemter in 1956 accounts for the dynamics of the separation 3 Theoretical Plate Model The plate model supposes that the chromatographic column contains a large number of separate layers, called theoretical plates. 4 2 02/10/2023 Theoretical Plate Model The plate model supposes that the chromatographic column contains a large number of separate layers, called theoretical plates. column Separate equilibrations of the sample between the stationary and mobile phase occur in these "plates". The analyte moves down the column by Theoretical plate transfer of equilibrated mobile phase from one plate to the next. 5 Chromatographic principle Mobile phase Sample mixture Equilibrium established at each point (ideally) Stationary phase The molecules of the mixture interact with the molecules of the Mobile and Stationary Phase Each molecule interacts differently with MP and SP Retardation of rate of movement of molecules Different distribution coefficients and different net rates of migration 6 3 02/10/2023 Theoretical Plate Model Hypothetical zone in which two phases establish an equilibrium with each other column Theoretical plate Assumptions: The chromatographic column is treated as a static system in equilibrium Each species is in equilibrium between stationary and mobile phase Column is of fixed length Flow is held constant Describes the mechanism of retention and gives an equation that allows the calculation of the retention volume of a solute and the column efficiency. 7 Theoretical Plate Model Hypothetical zone in which two phases establish an equilibrium with each other column Theoretical plate It is important to remember that the plates do not really exist They are a fabrication of the imagination that helps us to understand the processes at work in the column. 8 4 02/10/2023 Theoretical Plate Model They serve as a way of measuring column efficiency, either by stating the number of theoretical plates in a column, N (the more plates the better), or by stating the plate height, H; the Height Equivalent to a Theoretical Plate (the smaller the better). HETP = L / N N= 5.54 tR2 w1/22 = 16 tR2 wb2 where w1/2 is the peak width at half-height. Columns behave as if they have different numbers of plates for different solutes in a mixture. 10 Theoretical Plate Model They serve as a way of measuring column efficiency, either by stating the number of theoretical plates in a column, N (the more plates the better), or by stating the plate height, H; the Height Equivalent to a Theoretical Plate (the smaller the better). High N, low H Low N, high H 11 5 02/10/2023 Theoretical Plate Model H (or HETP) = plate height = length of column required for each MP/SP equilibrium to be established N = L/H = length of column/H = number of theoretical plates column Theoretical plate 12 Theoretical Plate Model VR: Retention volume: volume of mobile phase required to elute a solute tR: Retention time: time required to elute a solute t0: time for solvent or non-retained solute to elute k: Capacity factor (partition ratio or retention factor) t'R(A) tR(A) t0 13 6 02/10/2023 Theoretical Plate Model VR: Retention volume: volume of mobile phase required to elute a solute tR: Retention time: time required to elute a solute t0: time for solvent or non-retained solute to elute k: Capacity factor (partition ratio or retention factor) t'R(A) tR(A) t0 L u=t 0 Mobile phase velocity: u[cm/sec] = L[cm]/t0[sec] 14 Theoretical Plate Model VR: Retention volume: volume of mobile phase required to elute a solute tR: Retention time: time required to elute a solute t0: time for solvent or non-retained solute to elute k: Capacity factor (partition ratio or retention factor) (tR)A – t0 k(A) = Ideally, k is between 1 and 5 t0 k : Independent of column dimension and mobile-phase velocity Number of column volumes of MP required to elute a band after the initial volume of the column has been displaced 15 7 02/10/2023 Theoretical Plate Model KC: Distribution constant: the ratio of solute concentrations in stationary and mobile phase KC(A) = CS(A) CM(A) = mS(A) x VM(A) mM(A) x VS(A) = k(A) VM(A) VS(A) Aim: 1 < k(A) < 10 by varying solvent strength (o) then change solvent to enhance selectivity o solvent strength 16 Theoretical Plate Model α: Separation factor describes the selectivity of the chromatographic system for a particular pair of bands It is the ability of a certain set of experimental conditions to discriminate between two components α= kB kA 17 8 02/10/2023 Resolution Resolution Rs defines the degree of separation of two adjacent bands. RS = 2 tR2 − tR1 wb1 + wb2 = 1.18 tR2 − tR1 w0.51 + w0.52 19 Resolution Resolution Rs defines the degree of separation of two adjacent bands. RS = 2 tR2 − tR1 wb1 + wb2 = 1.18 tR2 − tR1 w0.51 + w0.52 20 9 02/10/2023 Resolution Resolution Rs defines the degree of separation of two adjacent bands. % of peak overlap as a function of resolution and ratio of peak areas 21 Resolution Each pair of peaks in the chromatogram has a different Rs value During method development attention focuses on the least resolved pair which contains a component of interest! High values of Rs compensate for: Increased band broadening Column ageing Small variations in conditions 22 10 02/10/2023 Resolution n N N: is the average column plate number for the two bands of interest k: is the average capacity factor α: separation factor of the two peaks k and α are in practice controlled by changing the column packing and by varying the composition of the mobile phase solvent (solvent parameters) N is controlled by changing the mobile phase flow rate, packing particle size and column dimensions 23 Resolution n N N: is the average column plate number for the two bands of interest k: is the average capacity factor α: separation factor of the two peaks k and α are in practice controlled by changing the column packing and by varying the composition of the mobile phase solvent (solvent parameters) N is controlled by changing the mobile phase flow rate, packing particle size and column dimensions 24 11 02/10/2023 Outline Lecture 1 What is Analytical Science Errors and units What is chromatography? Terminology Classification History Theoretical plate model Rate theory Kinetic theory Normal phase chromatography (column, TLC) Reverse phase chromatography (HPLC) Gas chromatography Other chromatographic techniques Lecture 2 Lecture 3 Lecture 4 26 Theory of Chromatography The Theoretical Plate Model of Chromatography Proposed by Martin and Synge in 1941 based on the theory of distillation The Rate Theory of Chromatography Proposed by van Deemter in 1956 accounts for the dynamics of the separation 27 12 02/10/2023 The Rate Theory of Chromatography In the development of the plate theory, a number of different peak dispersion processes are proposed and expressions are developed that describe the contribution of each process to the total variance of the eluted peak. The final equation gives an expression for the variance per unit length of the column. The processes proposed are eddy diffusion longitudinal diffusion resistance to mass transfer in the mobile phase and resistance to mass transfer in the stationary phase 29 The Rate Theory of Chromatography The rate theory has resulted in a number of different equations The Van Deemter Equation H = A + B/u + u [CM +CS] All the equations give a type of hyperbolic function that predicts a minimum plate height at an optimum velocity and, thus, a maximum efficiency. At normal operating velocities it has been demonstrated that the Van Deemter equation gives the best fit to experimental data. 30 13 02/10/2023 Van Deemter model H = A + B/u + u [CM +CS] A: random movement through stationary phase B: diffusion in mobile phase C: interaction with stationary phase H: plate height u: average linear velocity u = L/ t0 31 The Rate Theory of Chromatography Proposed by JJ van Deemter in 1956 The rate theory describes the process of peak dispersion (band spreading) and provides an equation that allows the calculation of the variance per unit length of a column (the height of the theoretical plate, HETP) in terms of the mobile phase velocity and other physical chemical properties of the solute and distribution system. 32 14 02/10/2023 The Rate Theory of Chromatography Van Deemter plots A plot of plate height vs average linear velocity of mobile phase. Such plots are of considerable use in determining the optimum mobile phase flow rate. 33 Van Deemter model H = A + B/u + u [CM +CS] Term A - molecules may travel unequal distances - independent of u - depends on size of stationary particles or coating (TLC) time Eddy diffusion MP moves through the column which is packed with stationary phase. Solute molecules will take different paths through the stationary phase at random. This will cause broadening of the solute band, because different paths are of different lengths. 34 15 02/10/2023 Van Deemter model H = A + B/u + u [CM +CS] Term B Longitudinal diffusion B = 2γ DM γ: DM: Impedance factor due to packing molecular diffusion coefficient B term dominates at low u and is more important in GC than LC since DM(gas) > 104 DM(liquid) One of the main causes of band spreading is DIFFUSION The diffusion coefficient measures the ratio at which a substance moves randomly from a region of high concentration to a region of lower concentration 36 Van Deemter model H = A + B/u + u [CM +CS] Term C Mobile phase Cs: stationary phase mass transfer Cs = [(df)2]/Ds df: stationary phase film thickness Ds: diffusion coefficient of analyte in SP Stationary phase Elution Bandwidth Slow equilibration Broadened bandwidth CM: mobile phase – mass transfer CM = [(dP)2]/DM for packed columns dP: particle diameter DM: diffusion in MP 38 16 02/10/2023 Van Deemter model H = A + B/u + u [CM +CS] Term C Cs: stationary phase mass transfer CM: mobile phase – mass transfer Mobile phase Stationary phase Elution Bandwidth Slow equilibration Broadened bandwidth C - Resistance to mass transfer The analyte takes a certain amount of time to equilibrate between the stationary and mobile phase. If the velocity of the mobile phase is high, and the analyte has a strong affinity for the stationary phase, then the analyte in the mobile phase will move ahead of the analyte in the stationary phase. The band of analyte is broadened. The higher the velocity of mobile phase, the worse the broadening becomes. 39 Van Deemter model H = A + B/u + u [CM +CS] 40 17 02/10/2023 The Rate Theory of Chromatography More realistic description of the processes at work inside a column. Takes account of the time taken for the solute to equilibrate between the stationary and mobile phase (unlike the plate model, which assumes that equilibration is infinitely fast). The resulting band shape of a chromatographic peak is therefore affected by the rate of elution. It is also affected by the different paths available to solute molecules as they travel between particles of the stationary phase. If we consider the various mechanisms which contribute to band broadening, we arrive at the Van Deemter equation for plate height HETP = A + B / u + C u where u is the average velocity of the mobile phase. A, B, and C are factors which contribute to band broadening. 41 Theory of Chromatography The Rate Theory of Chromatography Proposed by van Deemter in 1956 accounts for the dynamics of the separation The Kinetic of Chromatography First used by Giddings in 1965 Widely used only in the last 10 years 42 18 02/10/2023 Kinetic theory Limitations of van Deemter No allowance for comparison between different chromatographic techniques No allowance for comparison between different types of columns with different flow resistance and permeabilities No consideration of viscosity changes with pressure/temperature system changes Cannot compare systems operating under different pressures 43 Kinetic theory 44 19 02/10/2023 Kinetic theory 45 Recap How do we define and measure: – resolution, – retention (capacity) factor, – selectivity (separation factor), – distribution coefficient? Basic concepts of the theoretical plate model. What is rate theory/van Deemter theory? What are the contributions to band broadening in the column? How does the efficiency change with the mobile phase velocity? 46 20