Retention and phase distribution Lecture 2 Retention and phase distribution

Basic concepts of retention and column dimensions The retention factor Retention time Holdup time Adjusted retention time Distribution constant Phase ratio

The retention factor

Two different analytes in a chromatographic system The retention factor Mobile phase Two different analytes in a chromatographic system

The retention factor Mobile phase

The retention factor k = 0.67 k = 0.05 Mobile phase Amount of analyte in the stationary phase Amount of analyte in the mobile phase Retention factor: k =

Analytes with k = 0 moves with the same speed as the mobile phase The retention factor Analytes with k = 0 moves with the same speed as the mobile phase Mobile phase k = 0 Amount of analyte in the stationary phase Amount of analyte in the mobile phase Retention factor: k =

Analytes with k =  are trapped The retention factor Analytes with k =  are trapped Mobile phase  k = Amount of analyte in the stationary phase Amount of analyte in the mobile phase Retention factor: k =

Analytes with k =  are trapped The retention factor Analytes with k =  are trapped The retention factor is in elder literature referred to as capacity factor and denoted with k′ Mobile phase  k = Amount of analyte in the stationary phase Amount of analyte in the mobile phase Retention factor: k =

A chromatogram with two analytes, A and B Retention time A chromatogram with two analytes, A and B B A Detector signal 1 2 3 4 5 6 7 8 9 10 min

Retention time t0 (injection time) is the time when the analytes enter the column B Injection t0 A Detector signal 1 2 3 4 5 6 7 8 9 10 min

Retention time tR (retention time) is the time when the analytes leave the column B Injection tR(A) A Detector signal 1 2 3 4 5 6 7 8 9 10 min

Retention time tR (retention time) is the time when the analytes leave the column B Injection tR(B) tR(A) A Detector signal 1 2 3 4 5 6 7 8 9 10 min

Retention time tM (holdup time) is the retention time of an unretained analyte k = 0 B A Detector signal tM An unretained compound 1 2 3 4 5 6 7 8 9 10 min

It is the time the mobile phase uses through the column Retention time tM (holdup time) is the retention time of an unretained analyte k = 0 B The holdup time is sometimes referred to as the ‛dead time’ or retention time of an unretained analyte It is the time the mobile phase uses through the column A Detector signal tM An unretained compound 1 2 3 4 5 6 7 8 9 10 min

Retention time t′R (adjusted retention time) is tR – tM B t′R(B) A Detector signal tM t′R(A) 1 2 3 4 5 6 7 8 9 10 min

Retention time t′R (adjusted retention time) is tR – tM B t′R(B) A Detector signal tM All compounds spend the same in the mobile phase, which equals tM. t′R is therefore the time spent in the stationary phase (tR – tM) 1 2 3 4 5 6 7 8 9 10 min

Retention time B t′R(B) A t′R(A) tM Adjusted retention time: Eq (1) Detector signal tM t′R(A) 1 2 3 4 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: Eq (2)

Retention time Adjusted retention time: Eq (1) The relationship between the retention factor, k, and t′R is: Retention factor: Eq (2)  

80 A B

A B 80 tR is the total time spent from A to B tM is the time spent on the road t′R is the time spent off the road The mobile phase velocity, u, is 80

A B 80 tR is the total time spent from A to B tM is the time spent on the road t′R is the time spent off the road The mobile phase velocity, u, is 80

A note on mobile phase velocity Injector Detector High pressure High mobile phase density 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

A note on mobile phase velocity 1 2 Injector Detector High pressure High mobile phase density 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

A note on mobile phase velocity Injector Detector High pressure High mobile phase density 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 / tM) 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. mL/min at STP).

The distribution constant, Kc cm cs The distribution constant, Kc, is the ratio of the concentrations in the stationary phase and the mobile phase

The distribution constant, Kc cm Vm nm = cm • Vm cs Vs ns = cs • Vs 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

The distribution constant, Kc cm Vm nm = cm • Vm cs Vs ns = cs • Vs 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

The distribution constant, Kc cm Vm nm = cm • Vm cs Vs ns = cs • Vs 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 The distribution constant is often called the “partition coefficient”, and denoted by K

The distribution constant, Kc cm Vm nm = cm • Vm cs Vs ns = cs • Vs 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 cs cm Vs Vm k = = Kc / β •

The distribution constant, Kc cm Vm nm = cm • Vm cs Vs ns = cs • Vs 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)

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 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 Retention factor k = 2 nm = 100 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

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 Distribution constant Kc = 2 cs = 100/10 = 10 Since the volumes are equal the concentration ratio is also 2/1 The distribution constant Kc = 2

Which factors affect k and Kc ? Double the volume of the mobile phase V = 20 V = 10

Which factors affect k and Kc ? Double the volume of the mobile phase cm = 100/20 = 5 Distribution constant Kc = 2 cs = 100/10 = 10 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.

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

Which factors affect k and Kc ? Back to the original system with equal volumes and distribution constant of 2 cm = 50/10 = 5 Distribution constant Kc = 2 cs = 100/10 = 10

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 Distribution constant Kc = 0.5 cs = 50/10 = 5 The distribution constant will decrease

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 Retention factor k = 0.5 ns = 50 The distribution constant will decrease And the same with the retention factor

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.

Summary of definitions and relationships

Summary of definitions and relationships Four equations to learn and use in exercise set 2