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1 Lecture 5 Non-Ideal Conditions Gradient Elution Equations related to resolution Most of these are directly or indirectly related to k L σ2 tR′ = t R – tM H = = Lecture 5 N L √ Non-ideal conditions tR′ nAnalyte in the stationary phase N k = = Rs = (γ – 1) tM nAnalyte in the mobile phase 4 t′ k B R(B) (B) H = A + + C·u α = = u tR(A)′ k(A) cs 2 (tR(B) – tR(A)) ∆t Kc = Rs = Rs = cm wb(A) + wb(B) wb 2 2 √ tR t′R N α–1 k(B) N = 16 Neff = 16 Rs = wb wb 4 α 1–k(B) AM0925 - Quality parameters and optimization in Chromatography AM0925 - Quality parameters and optimization in Chromatography Equations related to resolution Equations related to resolution If k is not constant: k is not constant under the following conditions: L σ2 tR′ = t R – tM H = = Gradient elution N L Gradually increasing solvent strength and decreasing k ′ n √N tR Analyte in the stationary phase Sample or analyte overload k = = Rs = (γ – 1) t nAnalyte in the mobile phase 4 M The stationary phase changes properties because it is influenced t′ k B by the analyte R(B) (B) H = A + + C·u α = = u tR(A)′ k(A) In adsorption chromatography there may be competition for the stationary phase (saturation) cs 2 (tR(B) – tR(A)) ∆t Kc = Rs = Rs = Multiple retention mechanisms (“active sites”) cm wb(A) + wb(B) wb More than one k per analyte 2 2 t t′ √N α–1 k R R (B) Ad sorption in partition chromatography N = 16 Neff = 16 Rs = wb wb 4 α 1–k(B) AM0925 - Quality parameters and optimization in Chromatography AM0925 - Quality parameters and optimization in Chromatography Equations related to resolution Gradient elution Isothermal (in GC) or isocratic (in LC) conditions are conditions where This section covers the following topics temperature and solvent strength is constant throughout the separation leading to constant k Reasons for non-ideal conditions Elution patterns typically follow an exponential How do we measure and describe efficiency under non- function ideal conditions Too low eluent strength = too long time How do we measure and describe selctivity under non- ideal conditions Reasons for asymmetric peaks Time How do we measure and describe non-ideal peak shapes “The general elution problem in chromatography” (tailing/fronting) Too high eluent strength = too low resolution Time AM0925 - Quality parameters and optimization in Chromatography AM0925 - Quality parameters and optimization in Chromatography 1 Gradient elution Gradient elution The general elution problem is solved by applying a gradient of Eluent strength (elution/solvent strength) temperature in GC or of elution strength in LC For the same compound and the same stationary (solid) phase, a higher eluent strength will lead to higher portion of the analyte in the mobile phase, and lower k. Low solvent strength High solvent strength k = 80/20 = 4 k = 50/50 = 1 Gradient elution: The first compounds eluted with low eluent strength, the Solvent strength Solvent last compounds eluted with high eluent strength Time 20 % 50 % 80 % 50 % Gradient elution is suitable for a large range of analyte properties Amount of analyte in the stationary phase Detector response Retention factor, k = Amount of analyte in the mobile phase AM0925 - Quality parameters and optimization in Chromatography Time AM0925 - Quality parameters and optimization in Chromatography Gradient elution Gradient elution Eluent strength (elution/solvent strength) One of the problems with gradient elutions is that plate number and plate height is no longer meaningful concepts For the same compound and the same stationary (solid) phase, a higher eluent 2 strength will lead to higher portion of the analyte in the mobile phase, and lower k. t N = 16 R Low solvent strength High solvent strength wb k = 80/20 = 4 k = 50/50 = 1 Why is plate number a meaningless concept in programmed chromatography? - An extreme case… 20 % 50 % 80 % 50 % Amount of analyte in the stationary phase Retention factor, k = Amount of analyte in the mobile phase AM0925 - Quality parameters and optimization in Chromatography AM0925 - Quality parameters and optimization in Chromatography Gradient elution Gradient elution One of the problems with gradient elutions is that plate number and plate One of the problems with gradient elutions is that plate number and plate height is no longer meaningful concepts height is no longer meaningful concepts 2 2 t t N = 16 R N = 16 R wb wb Assume we have the k ≈ ∞ following gradient (which has a typical shape). And Solvent Solvent strength two peaks in the Solvent strength Time chromatogram Time If we prolong the trapping phase the k in the beginning of the retention time would increase, but chromatogram is ≈ infinite peak widths and separation would be (solvent trapping) the same (since analytes are not moving) ⇒ N is icreasing but there is no gain in separation Time Time AM0925 - Quality parameters and optimization in Chromatography AM0925 - Quality parameters and optimization in Chromatography 2 Gradient elution Efficiency in gradient elution One of the problems with gradient elutions is that plate number and plate How do we describe chromatographic efficiency under programmed height is no longer meaningful concepts conditions? 2 t Separation number, SN (or “Trennzahl”, TZ): N = 16 R wb The number of peaks that can be resolved in the space between two members of a homologous series with Rs ≈ 1 It is mathematically possible to calculate N with gradient C13 chromatography, but it is a completely meaningless concept from a C12 C14 chemical point of view SN = 10 ⇒⇒⇒ We need an alternative way of measuring chromatographic Alkanes efficiency separated by GC However, even though N is a meaningless concept with gradient elution it Detector response is still a useful concept in describing the quaity of chromatographic columns Time A column that has a high N will still be a good column in gradient tR(z+1) – tR(z) chromatography. SN = + 1 (Eq. 20) wh(z) + wh(z+1) AM0925 - Quality parameters and optimization in Chromatography AM0925 - Quality parameters and optimization in Chromatography Efficiency in gradient elution Efficiency in gradient elution How do we describe chromatographic efficiency under programmed How do we describe chromatographic efficiency under programmed conditions? conditions? Separation number, SN (or “Trennzahl”, TZ): Separation number, SN (or “Trennzahl”, TZ): The number of peaks that can be resolved in the space between two The number of peaks that can be resolved in the space between two members of a homologous series with Rs ≈ 1 members of a homologous series with Rs ≈ 1 The separation number is a measure of efficiency that is valid both in C12 C13 C14 programmed chromatography and in isocratic/isothermal chromatography so it is useful for comparing programmed chromatography with non-programmed SN = 10 chromatography. Alkanes You need a homologous series w separated wh(z) h(z+1) The SN may be different in different regions of the chromatograms, so it is by GC important to give the references (z and z+1) together with the number Detector response You may have to log-transform the retention scale if applied with isocratic or isothermal chromatography Time tR(z) tR(z+1) tR(z+1) – tR(z) tR(z+1) – tR(z) SN = + 1 (Eq. 20) SN = + 1 (Eq. 20) wh(z) + wh(z+1) wh(z) + wh(z+1) AM0925 - Quality parameters and optimization in Chromatography AM0925 - Quality parameters and optimization in Chromatography Efficiency in gradient elution Efficiency in gradient elution How do we describe chromatographic efficiency under programmed How do we describe chromatographic efficiency under programmed conditions? conditions? Separation number, SN (or “Trennzahl”, TZ): Separation number, SN (or “Trennzahl”, TZ): The number of peaks that can be resolved in the space between two The number of peaks that can be resolved in the space between two members of a homologous series with Rs ≈ 1 members of a homologous series with Rs ≈ 1 n-alkanes is frequently applied But any homologous series can be used n-alkanes is frequently applied But any homologous series can be used n-Hexane CH 3 - Saturated fatty acids n-Hexane CH 3 - Saturated fatty acids CH CH 3 - Polysiloxanes 3 - Polysiloxanes n-Heptane CH 3 CH 3 n-Heptane It CHis3 quite commonCH 3 to find homologous seres in - Alcolhols samples for GC-analyses,- Alcolhols often you will also n-Octane CH 3 n-Octane CH 3 CH 3 - Alkyl phenols have homologousCH 3 series- in Alkyl reversed phenols phase LC. CH CH n-Nonane CH 3 3 n-Nonane CH 3 3 - Alkyl benzenes If there is no homologous- Alkyl series benzenes that is suitable n-Decane CH 3 See G. Castello / J. Chromatogr . A 842 n-Decane CH 3 See G. Castello / J. Chromatogr . A 842 CH → ”peak capacity”CH 3 (1999) 51–64 for alternatives 3 (1999) 51–64 for alternatives n-Undecane CH 3 CH 3 n-Undecane CH 3 CH 3 etc… etc… tR(z+1) – tR(z) tR(z+1) – tR(z) SN = + 1 (Eq. 20) SN = + 1 (Eq. 20) wh(z) + wh(z+1) wh(z) + wh(z+1) AM0925 - Quality parameters and optimization in Chromatography AM0925 - Quality parameters and optimization in Chromatography 3 Efficiency in gradient elution Gradient elution The “peak capacity”, P, is loosely defined as the total number of Relative retention, α, is applied also in chromatography. However, peaks that can be baseline resolved within a chromatographic the equation involving k is not strictly valid, and the transferability separation between systems is poor It is often difficult to define the start and end of a chromatogram, so it is t′ α = R(B) often useful to give the peak capacity relative to some reference points , tR(A)′ e.g.
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