Mechanisms of retention in HPLC

HPLC 3 (Amsterdam) Mechanisms of retention in HPLC María Celia García-Álvarez-Coque José Ramón Torres-Lapasió Department of Analytical Chemistry University of Valencia Valencia, Spain https://sites.google.com/site/fuschrom/ Part 4

Mechanisms of retention in HPLC HPLC 3 (Amsterdam) Index. Retention in reversed-phase, normal-phase and HILIC. Secondary equilibria in reversed-phase liquid chromatography: Part A 3. Secondary equilibria in reversed-phase liquid chromatography: Part B 4. Retention modelling (quantification or prediction): Part A 5. Retention modelling (quantification or prediction): Part B 6. Gradient elution 7. Pea profile and pea purity 8. Computer simulation

HPLC 3 (Amsterdam) 4.. Introduction 4.. Isocratic elution in RPLC at fixed ph 4... Use of polynomial models with hydro-organic mobile phases 4... Polarity models 4..3. Micelles and ionic liquids in the mobile phase 4..4. Silanol effect 4.3. ph as experimental factor 4.3.. Hydro-organic mobile phases 4.3.. Micellar mobile phases 4.4. Quantitative structure-retention relationships (QSRR) 4.5. Recommended literature 3

HPLC 3 (Amsterdam) 4.. Introduction Interpretive optimisation strategies are based on the accurate description (modelling) of chromatographic behaviour. The first step in these strategies consists of gathering information about the chromatographic behaviour of the compounds in the sample, covering a reasonably wide factor region usually attending only to retention. For this purpose, either isocratic or gradient experiments can be used. Isocratic elution Gradient elution 4 Experimental design : distribution of the experiments within the factor domain

HPLC 3 (Amsterdam) For each solute, a relationship that describes the retention is obtained as a function of the experimental factors. This function will allow the prediction of isocratic or gradient retention times at different conditions. Alternatives convenient algebraic expression (empirical or mechanistic) parameters searched on a least-squares basis blac-box algorithm (as neural networs) Quality (accuracy and precision) of predictions is decisive for the reliability of optimisations or any other applications, and depends on: 5 information richness provided by the training data in the experimental design distribution of the experimental points equation selected to fit the training data fitting procedure ranges of experimental factors elution mode (isocratic or gradient)

HPLC 3 (Amsterdam) 4.. Introduction 4.. Isocratic elution in RPLC at fixed ph 4... Use of polynomial models with hydro-organic mobile phases 4... Polarity models 4..3. Micellar media and ionic liquids in the mobile phase 4..4. Silanol effect 4.3. ph as experimental factor 4.3.. Hydro-organic mobile phases 4.3.. Micellar mobile phases 4.4. Quantitative structure-retention relationships (QSRR) 4.5. Recommended literature 6

HPLC 3 (Amsterdam) 4.. Isocratic elution in RPLC at fixed ph 4... Use of polynomial models with hydro-organic mobile phases The concentration of organic solvent in the mobile phase is the factor most frequently optimised in RPLC. Advantages large impact on both elution strength and selectivity a very convenient property: flexibility and accuracy in the implementation of changes in this factor Hence, the importance of obtaining reliable retention models involving the concentration of organic solvent as factor!!! 7

HPLC 3 (Amsterdam) RPLC retention (solute i) in terms of solubility parameters (Schoenmaers et al.): ln [( δ δ ) ( δ ) ] t t v δ Ri i i M i S i + t RT n ln n S M (4.) i : solute retention factor t Ri : solute retention time t : dead time R : gas constant (.9865 cal K mole ) T : absolute temperature (K) v i : solute molar volume (cm 3 mole ) δ : polarity parameter (cal.5 cm.5 ) n M : moles of mobile phase n S : moles of stationary phase Water (w) / organic solvent (o) binary mixtures: δ M δ j ϕ j j (.) δ ( δ + ϕ δ M ϕ) w o (4.) φ : organic solvent volume fraction 8

HPLC 3 (Amsterdam) ln t t ν [( δ δ ) ( δ ) ] Ri i i M i S δi + t RT n ln n S M δ ( δ + ϕ δ M ϕ) w o ln c + c ϕ + c ϕ (4.3) Quadratic model Parameters c, c and c gather all the constants and solute/mobile phase/stationary phase properties, and have particular values for a given solute and column/solvent system. decimal logarithms log c + c ϕ + c log c + c ϕ ϕ (4.4) (4.5) linear model narrow concentration ranges These equations are also valid in the presence of specific interactions in the presence of additives. 9

HPLC 3 (Amsterdam) Two flavonoids eluted with acetonitrile/water mixtures ln 4 3 log c + c ϕ + c ϕ log c + c ϕ - 3 36 4 44 48 5 Acetonitrile (%, v/v)

HPLC 3 (Amsterdam) Linear model log w c + c ϕ log S ϕ (4.5) c (intercept): extrapolated log value if water were the mobile phase S (slope): sensitivity of retention to changes in the organic solvent content (elution strength) Simplifies the retention model to a straight-line. Valid for narrow concentrations of organic solvent, which is usual in RPLC. In wide concentration ranges, deviations from linearity are observed. The deviations are especially significant at the highest and lowest concentrations of organic solvent.

HPLC 3 (Amsterdam) Ternary systems (two organic solvents and water) log c + c ϕ + c ϕ + c ϕ ϕ + c ϕ + c ϕ (4.6) φ, φ : concentrations of organic solvents The search for an appropriate model has not finished here!!! Review Niitas and Papa-Louisi (J. Chromatogr. 6 (9) 737 755) Most models are logarithmic, but there are other proposals. Model proposed by Jandera for NPLC, applied to RPLC: excellent accuracy in RPLC [ a + bϕ] n (4.7)

HPLC 3 (Amsterdam) More retention models!!! e ln w aϕ + bϕ e ln ( aϕ ( ϕ )) e ln w ϕ a + bϕ e aϕ ln + ϕ e ln w ϕ ln(+ bϕ ) c + bϕ e ln w ϕ ln(+ ϕ ) c + ϕ e ln (+ bϕ) 4 e ln o + aϕ + bϕ e ln (+ bϕ) 3 e ln o aϕ + bϕ ln e + bϕ bϕ ( + ) ln aϕ e e ln alnϕ /ϕ o 3

HPLC 3 (Amsterdam) 4... Polarity models Linear relationships between log and mobile phase polarity parameters that depend on solvent content are interesting models. Dimroth-Reichardt parameter E T (3) Normalised N E T (3) limited range of linearity : 8% acetonitrile and % methanol Normalised polarity parameter proposed by Bosch and Rosés N P M extends the linearity to % acetonitrile and methanol For acetonitrile-water: P N M..68ϕ +.34ϕ (4.8) For methanol-water: P N M..33ϕ +.47ϕ (4.9) 4

HPLC 3 (Amsterdam) A model was developed, which isolates the polarity contributions of the three agents involved in the separation system (solute, stationary phase and mobile phase). log (log ) + ps ( PM P N N S ) (4.) Descriptors N P M N P S : mobile phase polarity : stationary phase polarity (log ) : retention in a hypothetical mobile phase with the same polarity as the stationary phase p S : solute polarity 5 The separation of the polarities of solute, mobile phase and stationary phase in the polarity model is not perfect: p S mainly gathers the solute contributions. However, it is not an absolute value, but a relative measurement that depends on the column environment (stationary and mobile phase nature).

HPLC 3 (Amsterdam) log N (log ) + ps ( PM P N S ) (4.) fitted with the data for a set of compounds Advantages of the polarity model A simple model: only needs nowledge of one parameter per solute: p S N P S two descriptors for the column ((log ) and ) N P M is obtained from the mobile phase composition This facilitates transference of values to new columns and solvent systems by establishing simple correlations between p S -values for small sets of selected reference compounds. 6

HPLC 3 (Amsterdam) N P S When (log ) and are fitted individually for each solute: s N m log q + p P c + c P N m (4.) log (log ) + ps ( PM P N N S ) (4.) Predictions performed by imposing common column parameters are necessarily poorer than those when all parameters in the equation are fitted for each individual solute, which are preferable for optimisation purposes!!! 7

HPLC 3 (Amsterdam) log c + c ϕ log c + c P N M two-parameter models log c + c ϕ + c ϕ three-parameter model The two-parameter polarity model is valid for wider concentration ranges and comparable in accuracy to the quadratic model!!! 8

HPLC 3 (Amsterdam) 5 compounds eluted with methanol / water 3 3 log pred log pred Quadratic model - - 3 log exp Linear model - - 3 3 log exp log pred 9 Polarity model - - 3 log exp

HPLC 3 (Amsterdam) 4..3. Micelles and ionic liquids in the mobile phase Among the chromatographic modes using mobile phases with additives, micellar liquid chromatography deserves a special mention. Modelling Polynomial equations Mechanistic models based on equilibrium considerations gave a meaning to the coefficients in the polynomial equations improved understanding of the retention mechanism Pure MLC (mobile phases containing only surfactant): K AS AM + [ M] c + c [ M] + K [ M] KAS KAS AM K (4.) (4.3) [M] : concentration of surfactant molecules involved in micelle formation K AS : partition of the solute between bul water and stationary phase K AM : partition of the solute between bul water and micelle

HPLC 3 (Amsterdam) Pure MLC K AM K AS

HPLC 3 (Amsterdam) Hybrid MLC Hybrid micellar medium (mobile phases containing both surfactant and organic solvent): + K K AS AM + K + K + K + K SD AD MD AD ϕ ϕ ϕ ϕ [ M] (4.4) K SD, K AD and K MD : account for the displacement of the partition equilibria by the organic solvent K SD only for highly hydrophobic solutes. In other cases: K + K AS AM + K + K + K AD MD AD ϕ ϕ ϕ [ M] log c + c φ + c [M] + c φ [M] (4.5) Eq. (4.5) is also valid for mobile phases containing ionic liquids, where the molar concentration of ionic liquid [IL] is used instead of [M].

HPLC 3 (Amsterdam) RPLC with ionic liquids CH3 C N CH 3 C N R + A R + A CH 3 C N CH 3 C N A A R + R + R + R + 3 4. Retention modelling (quantification or prediction): Part A MLC CH 3 C N CH 3 C N CH3 C N CH 3 C N CH 3 C N K MD K AD CH 3 C N CH3 C N CH3 C N K SD A CH3 C N

HPLC 3 (Amsterdam) 4..4. The silanol effect Basic compounds experience a combined retention mechanism when separated with bonded-silica stationary phases and organic solvent-water mixtures that includes hydrophobic (partition into the bonded phase), and silanophilic interactions (attraction of the cationic solutes to the anionic silanols). In the absence of any additional interaction, masing of silanols will decrease the retention. + (4.6) : retention factor with silanols totally exposed for interaction : hydrophobic contribution : silanophilic contributions BH + BH + silanols BH + 4

HPLC 3 (Amsterdam) Horváth model Evaluation of the silanol suppressing potency by addition of amines without additive + (4.6) Secondary equilibrium SiO + A + SiO A + (4.7) with additive + + K A [ A] (4.8) K A : silanol / protonated amine binding constant Et 3 NH + [A] : amine molar concentration Et3 NH+ Et3 NH+ Et3 NH+ Silanophilic contribution to retention K + K + K A [ A ] A A [ A] [ A] [ A] [ A] (4.9) + (4.) K A 5

HPLC 3 (Amsterdam) BH + BH + [ A] K A + [ A] (4.) Et3 NH+ The binding constant K A : evaluates the ability of the amine to bloc silanol sites can be obtained by regressing the left term versus the concentration of amine 6

HPLC 3 (Amsterdam) Horváth model applied to ionic liquids [ A] K A + [ A] (4.) R + K A was also applied to measure the ability of the cation BH + BH + A of an ionic liquid to bloc silanol sites. A The retention is affected by the attraction of the cationic solute to the adsorbed anion on the stationary phase. A third contribution should be considered corresponding to the extra interaction: R + R + + + 3 The Horváth equation can only be applied to ionic liquids, where the absorption of the anion is negligible. 7

HPLC 3 (Amsterdam) 4.. Introduction 4.. Isocratic elution in RPLC at fixed ph 4... Use of polynomial models with hydro-organic mobile phases 4... Polarity models 4..3. Micellar and ionic liquids in the mobile phase 4..4. Silanol effect 4.3. ph as experimental factor 4.3.. Hydro-organic mobile phases 4.3.. Micellar mobile phases 4.4. Quantitative structure-retention relationships (QSRR) 4.5. Recommended literature 8

HPLC 3 (Amsterdam) 4.3. ph as experimental factor 4.3.. Hydro-organic mobile phases For ionisable solutes, ph is an additional experimental factor with a large influence on retention and selectivity. When the analysed mixture contains one or more compounds with acid-base behaviour, ph tuning can offer unique opportunities to reach resolution. However, changes in retention with ph are particularly hard to model. Not surprisingly, a widely extended practice consists of fixing the ph at a convenient value. With this practice, the benefits of this experimental factor on selectivity are lost. A + H + HA A + H + HA B + H + HB + 4 7 ph B + H + HB + 9

HPLC 3 (Amsterdam) RPLC retention of ionisable compounds Weighted mean of the retention of the basic and acidic species A δ A + HA δ HA A K h A + HA K h + HA + K h + K h + K h (4.) : the measured retention factor A : retention factor for basic species δ A : molar fraction for basic species HA : retention factor for acidic species δ HA : molar fraction for acidic species K ( K a ) : apparent protonation constant (taes into account all interactions of both acid-base species with the stationary phase and mobile phase components) 3

HPLC 3 (Amsterdam) log K pk a Remember that HA Since the intrinsic retention for each acid-base species is different, a sudden change in retention will happen at ph values close to the logarithm of the apparent protonation constant (or pk a ). Retention factor A - Depending on the charge of the acidic and basic species, the retention may decrease, increase, or remain constant with ph. Retention factor BH + B 3 ph

HPLC 3 (Amsterdam) Incomplete equilibria of ionisable compounds The protonation process covers several ph units. Therefore, when the woring ph range of the stationary phase is narrow (e.g. 3 7 for conventional RPLC columns), the change in retention will be only fully sampled for some compounds. For this reason, the retention plots of compounds with acid-base behaviour often show partial equilibria, giving rise to different patterns. As a result of the incomplete information, fitting of the experimental data can be hard, since the retention of the acidic and basic species should be extrapolated. 3

HPLC 3 (Amsterdam) 6 8 4 amiloride 3 4 5 6 7 ph 3 triamterene 3 4 5 6 ph 7 6 4 bumetanide 3 4 5 6 7 ph Diuretics.5 M sodium dodecyl sulphate 4% propanol 6 8 trichloromethiazide 4 3 4 5 6 7 ph 33

HPLC 3 (Amsterdam) Fixed organic solvent content A δ A + HA δ HA A K h A + HA K h + HA + K h + K h + K h (4.) Dividing by HA (f A / HA ) yields a more convenient fitting behaviour: A + K h HA + K h HA f + K h + f K h + K h f K h HA f + K h ( + K h f ) HA (4.) log log HA + log f + K h + K h ( f ) log HA + log f + logk + h logk h ( f ) (4.3) 34

HPLC 3 (Amsterdam) Simultaneous effect of organic solvent and ph To account for the simultaneous effect of organic solvent and ph, the equations that describe the retention with regard to both factors are combined. A + HA K h + K h log log + Sϕ + T ϕ w (4.5) The change in the protonation constant with changes in the concentration of organic solvent should also be considered. log K log K + Q ϕ + Q ϕ w (4.6) log K log Kw + Qϕ for simplicity w : retention in pure water K w : protonation constant in pure water As a consequence of this relationship, the retention surfaces are twisted and shifted. Both factors (organic modifier and ph) interact with each other. 35 This complicates the treatment notably.

HPLC 3 (Amsterdam) log log HA + log f + + (log Kw + mϕ ) h (log Kw + mϕ ) h ( f ) (4.4) (log w,ha Sϕ) + log f + + (log Kw + mϕ ) h (log Kw + mϕ ) h ( f ) w,a + K w ( S A h ϕ + T ϕ ) ( Q ϕ + Q A ϕ ) + w,ha K w h + K w [( S HA h + Q ) ϕ + ( T ( Q ϕ + Q HA ϕ ) + Q ) ϕ ] (4.7) quadratic relationships ( RA + SA ϕ + TA ϕ ) + + ( RHA + SHA ϕ + THA ϕ ) ( Q + Qϕ + Q ϕ ) h h (4.8) easier fitting S, T, Q, Q : coefficients that describe the influence of the organic modifier on the retention factor and protonation constant 36

HPLC 3 (Amsterdam) Polarity model A + HA K h + K h log c + c P N M (log Kw + mϕ ) N h log c + cpm + log f + (log Kw + mϕ ) + h ( f ) (4.9) c and c correspond to the acidic species 37

HPLC 3 (Amsterdam) 4.3.. Micellar mobile phases A + HA K h + K h + K K AS AM + K + K + K AD MD AD ϕ ϕ ϕ [ M] + K KAS + K + KMD ϕ + K ϕ AM AD AD + K ϕ K h + KHAD ϕ + K ϕ + K ϕ HMD [ M] + + K [ M] K h HAS HAM HAD (4.3) Polynomial models: acceptable accuracy in narrow ph ranges [ M] + a ϕ + a ph+ a [ M] ϕ + a [ M] ph+ a ϕ ph+ a [ M] ph+ a a a ϕ + 3 3 3 3 33 ph (4.3) 38

HPLC 3 (Amsterdam) 4.. Introduction 4.. Isocratic elution in RPLC at fixed ph 4... Use of polynomial models with hydro-organic mobile phases 4... Polarity models 4..3. Micellar and ionic liquids in the mobile phase 4..4. Silanol effect 4.3. ph as experimental factor 4.3.. Hydro-organic mobile phases 4.3.. Micellar mobile phases 4.4. Quantitative structure-retention relationships (QSRR) 4.5. Recommended literature 39

HPLC 3 (Amsterdam) 4.4. Quantitative structure-retention relationships (QSRR) The ideal optimisation is that one requiring no experiment. Accordingly, considerable effort has been made to estimate retention without any other extra nowledge that several experimental solute descriptors or solute chemical structures. General solvation model (Abraham model) A property for a series of solutes at fixed solvent conditions can be predicted from several solute molecular descriptors: SP e E + s S + a A + b B + vv + c (4.3) SP : solute property (log or polarity parameter p S ) E, S, A, B, V : solute descriptors e, s, a, b, v : characterise differences between the mobile phase and stationary phase in HPLC 4 E : excess molar refraction S : dipolarity/polarizability A : hydrogen-bond acidity B : hydrogen-bond basicity V : McGowan volume e : capability of the environment to interact with solute π- and n-electron pairs s : dipolarity/polarizability a: hydrogen-bond basicity b: hydrogen-bond acidity v : hydrophobic contribution polar contributions

HPLC 3 (Amsterdam) Correlations between retention properties and octanol-water partition coefficients SP c + c log Po/w SP log or p s However, conventional RPLC columns still have silanol groups accessible to solutes and solvent, even when heavily coated and end-capped. Silanols are wealy acidic and may affect the retention: ionised silanols can retain protonated bases by cation-exchange, and neutral silanols can hydrogen bond protonacceptor solutes. Therefore, the conversion of log P o/w into log or p s values needs a hydrogen-bond acidity term or any other term accounting the hydrogen-bond donor interactions: SP c + c log Po/w + c3 A (4.33) Comprehensive databases listing P o/w values are available. Also, P o/w values and hydrogenbond acidity can be predicted from molecular structures. 4

HPLC 3 (Amsterdam) Use of molecular descriptors predicted from molecular structures Software such as CODESSA or Dragon are able to calculate multiple molecular descriptors. Correlations between retention data and the molecular descriptors can be obtained. A step is required where the number of descriptors is reduced so that only a small number of uncorrelated descriptors is ept. Example: in a study including a set of 33 compounds showing a wide variation of chemical characteristics, the solute polarity parameter p s was best described by a model containing, besides log P o/w, three more descriptors: p c + p log P + p (pol/d ) + hl (HOMO- LUMO) + s o/w o/w o /d hd (HDCA) (4.34) pol/d : related to the electrostatic nature HOMO-LUMO : energy-related descriptor HDCA : accounted for hydrogen-bond interactions 4

HPLC 3 (Amsterdam) Unfortunately, current QSRR predictions are not yet sufficiently accurate for optimisation purposes. Reaching the high accuracy level needed in optimisation still requires the assistance of experimental data. However, this approach is interesting for prospective purposes, such as the selection of the separation system. 43