Lecture 2 Retention and phase distribution AM 0925

Lecture 2 Retention and phase distribution AM 0925 - Quality parameters and optimization in chromatography

Basic concepts of retention and column dimensions • The retention factor • Retention time • Holdup time • Adjusted retention time • Distribution constant • Phase ratio AM 0925 - Quality parameters and optimization in chromatography

The retention factor AM 0925 - Quality parameters and optimization in chromatography

The retention factor Mobile phase Two different analytes in a chromatographic system AM 0925 - Quality parameters and optimization in chromatography

The retention factor Mobile phase AM 0925 - Quality parameters and optimization in chromatography

The retention factor Mobile phase k = 0. 67 Retention factor: k= k = 0. 05 Amount of analyte in the stationary phase Amount of analyte in the mobile phase AM 0925 - Quality parameters and optimization in chromatography

The retention factor Analytes with k = 0 moves with the same speed as the mobile phase Mobile phase k=0 Retention factor: k= Amount of analyte in the stationary phase Amount of analyte in the mobile phase AM 0925 - Quality parameters and optimization in chromatography

The retention factor Analytes with k = are trapped Mobile phase k= Retention factor: k= Amount of analyte in the stationary phase Amount of analyte in the mobile phase AM 0925 - Quality parameters and optimization in chromatography

The retention factor Analytes with k = are trapped The retention factor is Mobile phase in elder literature referred to as capacity factor and denoted with k′ k= Retention factor: k= Amount of analyte in the stationary phase Amount of analyte in the mobile phase AM 0925 - Quality parameters and optimization in chromatography

Retention time A chromatogram with two analytes, A and B Detector signal B A 0 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 8 9 10 min

Retention time t 0 (injection time) is the time when the analytes enter the column B Detector signal Injection t 0 A 0 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 8 9 10 min

Retention time t. R (retention time) is the time when the analytes leave the column B Detector signal Injection t. R(A) A 0 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 8 9 10 min

Retention time t. R (retention time) is the time when the analytes leave the column B t. R(B) Detector signal Injection t. R(A) A 0 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 8 9 10 min

Retention time t. M (holdup time) is the retention time of an unretained analyte k=0 Detector signal B A t. M 0 An unretained compound 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 8 9 10 min

Retention time t. M (holdup time) is the retention time of an unretained analyte k=0 Detector signal B A t. M 0 The holdup time is sometimes referred to as the ‛dead time’ or retention time of an unretained analyte An unretained compound 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 8 It is the time the mobile 9 10 min phase uses through the column

Retention time t′R (adjusted retention time) is t. R – t. M Detector signal B t′R(B) 0 A t′R(A) t. M 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 8 9 10 min

Retention time t′R (adjusted retention time) is t. R – t. M Detector signal B t′R(B) 0 A t′R(A) t. M 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 All compounds spend the same in the mobile phase, which equals t. M. t′R is therefore the time 8 spent 9 in the 10 stationary min phase (t. R – t. M)

Retention time Eq (1) Adjusted retention time: Detector signal B t′R(B) 0 A t′R(A) t. M 1 2 3 4 AM 0925 - Quality parameters and optimization in chromatography 5 6 7 8 9 10 min

Retention time Adjusted retention time: Eq (1) The relationship between the retention factor, k, and t′R is: Retention factor: AM 0925 - Quality parameters and optimization in chromatography Eq (2)

80 A AM 0925 - Quality parameters and optimization in chromatography B

80 A B t. R is the total time spent from A to B t. M is the time spent on the road t′R is the time spent off the road The mobile phase velocity, u, is 80 AM 0925 - Quality parameters and optimization in chromatography

A note on mobile phase velocity Injector High pressure High mobile phase density Detector Low pressure Low mobile phase density In chromatography, high pressure is usually applied to force the mobile phase through the column Because of the compressibility of gases, the density of the mobile phase in GC is much higher at the inlet than at the outlet of the column AM 0925 - Quality parameters and optimization in chromatography

A note on mobile phase velocity Injector 1 High pressure High mobile phase density 2 Detector Low pressure Low mobile phase density In chromatography, high pressure is usually applied to force the mobile phase through the column Because of the compressibility of gases, the density of the mobile phase in GC is much higher at the inlet than at the outlet of the column Because the number of mobile phase molecules that pass any cross section of the column must be the same (same mass flow), this means that the actual mobile phase velocity is much higher at the outlet than at the inlet of the column (molecules must move faster) moles/s in 1 = moles/s in 2 AM 0925 - Quality parameters and optimization in chromatography

A note on mobile phase velocity Injector High pressure High mobile phase density Detector Low pressure Low mobile phase density In chromatography, high pressure is usually applied to force the mobile phase through the column Because of the compressibility of gases, the density of the mobile phase in GC is much higher at the inlet than at the outlet of the column Because the number of mobile phase molecules that pass any cross section of the column must be the same (same mass flow), this means that the actual mobile phase velocity is much higher at the outlet than at the inlet of the column (molecules must move faster) When we use the term mobile phase velocity we usually refer to linear mobile phase velocity which is column length divided by holdup time (L / t. M) The term flow rate usually refers to the volume the mobile phase will fill at standard temperture and pressure divided my the time unit (e. g. m. L/min at STP). AM 0925 - Quality parameters and optimization in chromatography

The distribution constant, Kc cm cs The distribution constant, Kc, is the ratio of the concentrations in the stationary phase and the mobile phase AM 0925 - Quality parameters and optimization in chromatography

The distribution constant, Kc cm Vm nm = c m • V m cs Vs ns = c s • V s Note that the amounts (number of analyte molecules) in the phases is a function both of the volume of the phases and the analyte concentration in the phases. The distribution constant, Kc, is the ratio of the concentrations in the stationary phase and the mobile phase AM 0925 - Quality parameters and optimization in chromatography

The distribution constant, Kc cm Vm nm = c m • V m cs Vs ns = c s • V s Note that the amounts (number of analyte molecules) in the phases is a function both of the volume of the phases and the analyte concentration in the phases. Retention factor, k = ns / nm Distribution constant, Kc = cs / cm The phase ratio, β = Vm / Vs AM 0925 - Quality parameters and optimization in chromatography

The distribution constant, Kc cm Vm nm = c m • V m cs Vs ns = c s • V s Note that the amounts (number of analyte molecules) in the phases is a function both of the volume of the phases and the analyte concentration in the phases. Retention factor, k = ns / nm Distribution constant, Kc = cs / cm The phase ratio, β = Vm / Vs AM 0925 - Quality parameters and optimization in chromatography The distribution constant is often called the “partition coefficient”, and denoted by K

The distribution constant, Kc cm Vm nm = c m • V m cs Vs ns = c s • V s Note that the amounts (number of analyte molecules) in the phases is a function both of the volume of the phases and the analyte concentration in the phases. Retention factor, k = ns / nm Distribution constant, Kc = cs / cm The phase ratio, β = Vm / Vs AM 0925 - Quality parameters and optimization in chromatography cs Vs • = Kc / β k= cm Vm

The distribution constant, Kc cm Vm nm = c m • V m cs Vs ns = c s • V s Note that the amounts (number of analyte molecules) in the phases is a function both of the volume of the phases and the analyte concentration in the phases. Distribution constant, Kc = cs / cm Eq (3) The phase ratio, β = Vm / Vs Eq (4) AM 0925 - Quality parameters and optimization in chromatography

Which factors affect k and Kc ? Assume a system with equal mobile phase and stationary phase volumes: Phase ratio β = 1 Mobile phase Vm = 10 Phase ratio, β = 1 Stationary phase AM 0925 - Quality parameters and optimization in chromatography Vs = 10

Which factors affect k and Kc ? Assume a system with equal mobile phase and stationary phase volumes: Phase ratio β = 1 nm = 50 nm = 100 Retention factor k=2 A compound is distributed with 2/3 of the molecules in the stationary phase and 1/3 of the molecules in the mobile phase The retention factor k = 2 AM 0925 - Quality parameters and optimization in chromatography

Which factors affect k and Kc ? Assume a system with equal mobile phase and stationary phase volumes: Phase ratio β = 1 cm = 50/10 = 5 cs = 100/10 = 10 Distribution constant Kc = 2 Since the volumes are equal the concentration ratio is also 2/1 The distribution constant Kc = 2 AM 0925 - Quality parameters and optimization in chromatography

Which factors affect k and Kc ? Double the volume of the mobile phase V = 20 V = 10 AM 0925 - Quality parameters and optimization in chromatography

Which factors affect k and Kc ? Double the volume of the mobile phase cm = 100/20 = 5 cs = 100/10 = 10 Distribution constant Kc = 2 The distribution constant is independent of column dimensions and is therefore not affected by the increased volume. The number of molecules in the mobile phase will therefore double to keep the concentration constant. AM 0925 - Quality parameters and optimization in chromatography

Which factors affect k and Kc ? Double the volume of the mobile phase nm = 100 Retention factor k=1 ns = 100 Becaused of the increased number of molecules in the mobile phase the retention factor, k, will decrease to 1. The retention factor is affected by column dimensions AM 0925 - Quality parameters and optimization in chromatography

Which factors affect k and Kc ? Back to the original system with equal volumes and distribution constant of 2 cm = 50/10 = 5 cs = 100/10 = 10 AM 0925 - Quality parameters and optimization in chromatography Distribution constant Kc = 2

Which factors affect k and Kc ? An increased solvent strength in LC or increased temperature in GC will move more molecules over to the mobile phase cm = 100/10 = 10 cs = 50/10 = 5 The distribution constant will decrease AM 0925 - Quality parameters and optimization in chromatography Distribution constant Kc = 0. 5

Which factors affect k and Kc ? An increased solvent strength in LC or increased temperature in GC will move more molecules over to the mobile phase nm = 100 ns = 50 Retention factor k = 0. 5 The distribution constant will decrease And the same with the retention factor AM 0925 - Quality parameters and optimization in chromatography

Which factors affect k and Kc ? • The distribution constant, Kc, depends on the chemistry of the system and the temperature. • The retention factor, k, depends on chemistry, temperature and column dimensions. • By changing the column dimensions (phase ratio) you can control k independently of the distribution constant. AM 0925 - Quality parameters and optimization in chromatography

Summary of definitions and relationships AM 0925 - Quality parameters and optimization in chromatography

Summary of definitions and relationships Four equations to learn and use in exercise set 2 AM 0925 - Quality parameters and optimization in chromatography

AM 0925 - Quality parameters and optimization in chromatography