PHAR2202 Drug Design - Analytical Methods - Separations

Separations

Introduction

• Separation is key to both analysis and purification.
• Examples of compounds that can be separated: proteins, RNA/DNA, metabolites, drugs, cells, antibodies.

Liquid-Liquid Extractions

• The analyte/sample is in equilibrium between two phases.
• Typically, the most polar solvent (often water) is designated as "Phase 1".
• A larger distribution constant ($K_D$) indicates that the sample compound is less water-soluble and more efficiently extracted into the upper, organic phase.

Partition Coefficient or Distribution Constant

• Formula: $K<em>D = \frac{[\text{sample}]</em>{\text{Phase 2}}}{[\text{sample}]_{\text{Phase 1}}}$
  • $[\text{sample}]_{\text{Phase 2}}$ = concentration of sample in phase 2
  • $[\text{sample}]_{\text{Phase 1}}$ = concentration of sample in phase 1

Single-Step Extractions

• Example: A sample is more soluble in ethyl acetate than water, with a $K_D$ of 3.
• Scenario: Extract 100 mL of 0.010 M sample in water with 500 mL ethyl acetate. Question: What fraction of A remains in the water?
• Considerations:
  • Is it better to use more or less ethyl acetate (EtOAc)?
  • What if five extractions are performed with 100 mL EtOAc each?

Fraction of Analyte Remaining in Phase 1 after One Extraction

• Formula: $f<em>{\text{Phase 1,1}} = \frac{1}{1 + K</em>D (V<em>2/V</em>1)}$
  • $V_n$ = volume of phase n used in the extraction
  • Phase 1 is the more polar phase, usually water.

Multiple Extractions

• Formula for the fraction of analyte remaining in Phase 1 after $n$ extractions:
  • $f<em>{\text{Phase 1,n}} = \left[ \frac{1}{1 + K</em>D (V<em>2/V</em>1)} \right]^n$
• The extent of solute extraction using 1 to 10 extractions (phase ratio = 1.0) for a mixture of two solutes (A and B) with concentration distribution ratios of 2 and 0.1, respectively.

pH-Dependent Extractions

• HA is a weak monoprotic acid with $K_a = 1.20 \times 10^{-3}$.
• $K_D(HA) = 550$ (ethyl acetate / water)
• $K_D(A^-) ≈ 0$. If extracting the acid in water with ethyl acetate, the overall partition coefficient depends on pH because two species (HA and A-) must be considered.
• Equilibrium: $HA \rightleftharpoons H^+ + A^-$
• $K<em>D = \frac{[\text{tot. analyte}]</em>{\text{Phase 2}}}{[\text{tot. analyte}]<em>{\text{Phase 1}}} = \frac{[HA]</em>{\text{Phase 2}}}{[HA]<em>{\text{Phase 1}} + [A^-]</em>{\text{Phase 1}}}$
• The total concentration of HA depends on pH.

Derivation of pH-Dependent Extraction Equation

• Divide numerator and denominator by $[HA]_{\text{water}}$:
  • $K<em>D = \frac{\frac{[HA]</em>{\text{ethyl acetate}}}{[HA]<em>{\text{water}}}}{1 + \frac{[A^-]</em>{\text{water}}}{[HA]<em>{\text{water}}}} = \frac{K</em>{D,HA}}{1 + \frac{[A^-]<em>{\text{water}}}{[HA]</em>{\text{water}}}} = \frac{K<em>{D,HA}}{1 + \frac{K</em>a}{[H^+]_{\text{water}}}}$
• Where: $K_a = \frac{[A^-][H^+]}{[HA]}$

Concept Check

• How much of a 100 mL of 0.01M sample remains in the water after 1 extraction with 200 mL ethyl acetate at:
  • pH = 5
  • pH = 1
  • After 5 extractions?
• Formula to use: $f<em>{\text{Phase 1,n}} = \left[ \frac{1}{1 + K</em>D (V<em>2/V</em>1)} \right]^n$

Chromatography

• Chromatography is similar to a series of extraction steps.
• If compounds with much smaller $K_D$ values could be separated using continuous extraction, consider water as the mobile phase and ethyl acetate as the stationary phase.

Column Chromatography

• Components: mobile phase, column, stationary phase, fraction collector and/or detector, chromatogram.

Describing a Chromatogram

• Time/volume are interchangeable if the flow rate is known.

• $t<em>R' = t</em>R - t_M$

• $t_R$ = Retention time:

  • The time it takes for the analyte to pass from the injection point to the detector.

• $t_M$ = Void time:

  • The time it takes for an unimpeded molecule (e.g., the solvent) to pass from the injection point to the detector.

• $t_R'$ = Adjusted retention time

Retention Factor

• $k = \frac{t<em>R'}{t</em>M}$
• This measure is unitless and unaffected by flow rate or column dimensions.
• A high $k$ value indicates that the compound spends significant time in contact with the stationary phase.
• Ideally, $k$ = 1 to 5 for good resolution.

Factors Defining Good Resolution

• High degree of separation between compounds (difference in $t_R$).
• The distribution of an analyte between stationary and mobile phases in chromatography can be described as an equilibrium.
  • $A<em>M \rightleftharpoons A</em>S$
    • $A_M$ = mol analyte in the mobile phase
    • $A_S$ = mol analyte adsorbed on the stationary phase
• $k = \frac{A<em>M}{A</em>S} = \frac{[A]<em>M V</em>M}{[A]<em>S V</em>S}$
  • $V_S$ = volume of stationary phase
  • $V_M$ = volume of mobile phase
• $k = K<em>D (\frac{V</em>S}{V_M})$

Peak Breadth and Resolution

• The breadth of the peak is important for resolution.
• Traces with the same difference in $t_R$ can have different peak shapes and resolutions.
• Resolution depends on both retention time ($t_R$) and peak width ($w$).

Gaussian Peak Shape

• Peaks should ideally appear Gaussian in shape.
• $\sigma$ = standard deviation
• $w_b$ = width at base = $4\sigma$
• $w_h$ = width at half height = $2.355 \sigma$

Theoretical Plates

• 'Plate height' ($H$) and 'number of theoretical plates' ($N$) are measures of column efficiency.
• These terms originate from early chromatographic and distillation theory, where a chromatographic column was treated as a number of separate layers in contact, called 'theoretical plates'.
• Each plate can be thought of as a separating funnel containing two immiscible layers in contact.

Calculation of Theoretical Plates

• Theoretical plates depend on retention time and peak width.
• Half peak height and tangent line methods are used to calculate $N$.
• $N = (\frac{t_R}{\sigma})^2$

Concept Check: Calculating Theoretical Plates

• Given chromatograms with retention times and peak widths, calculate the number of theoretical plates.

Height Equivalent to a Theoretical Plate (HETP)

• The number of theoretical plates ($N$) increases with column length, so normalization for column length is needed.
• Columns are graded by their HETP.
• $H = \frac{L}{N}$
  • Where: $L$= column length

Factors Causing Peaks to Broaden

• Eddy diffusion
• Longitudinal/molecular diffusion
• Resistance to mass transfer

Types of Diffusion Problems

Eddy Diffusion

• Different molecules take different paths through the column.
• Affected by column length, flow rate, and the size/shape of particles.

Molecular (Longitudinal) Diffusion

• Molecules in the center move faster.
• Affected by column length and flow rate.

Resistance to Mass Transfer

• The analyte takes time to equilibrate between the stationary and mobile phases.
• At high mobile phase velocity and strong analyte affinity for the stationary phase, the analyte in the mobile phase moves ahead of the analyte in the stationary phase.

Van Deemter Plot

• HETP varies with flow rate.
• $HETP = A + \frac{B}{u} + Cu$
  • $A$ = eddy diffusion
  • $B$ = molecular diffusion
  • $C$ = resistance to mass transfer
  • $u$ = linear flow velocity

Improving Resolution

• Basic resolution equation:
• $k = \frac{t<em>R - t</em>M}{t_M}$
• $\alpha = \frac{t'<em>{R1}}{t'</em>{R2}}$
• $N = (\frac{t_R}{\sigma})^2$

Resolution Equation

• $R = \frac{\sqrt{N}}{4} \times \frac{(\alpha - 1)}{\alpha} \times \frac{k}{(k + 1)}$
  • $N$ = number of theoretical plates
  • $\alpha$ = separation factor (i.e., $t'<em>{R1} / t'</em>{R2}$)
  • $k$ = retention factor for the second peak

Concept Check

• Normal phase silica column (ethyl acetate / hexane).
• Calculate the retention factor $k$ of the peak from compound #2 at 6.7 min.
• Calculate the selectivity factor for compound #1 (at 3.3 min) relative to the void volume and for compound #2 (at 6.7min) relative to compound #1.
• Calculate the number of theoretical plates for this column. If the column length is 15 cm, calculate the HETP (in µm). Does it matter which peak you use to calculate this value?

Liquid Chromatography

Types of Liquid Chromatography

• Thin-layer chromatography (TLC)
• Preparative layer chromatography (PLC)
• Centrifugal chromatography
  • Analytical
  • Semi-prep
  • Preparative
• Automated versions (Combi-flash)
• High-pressure liquid chromatography (HPLC)
  • Analytical
  • Semi-prep
  • Preparative

General Principles of Liquid Chromatography

• Column (analytical or preparative scale)
• Mobile phase (= eluent) with time polarity gradient or isocratic
• Stationary phase (separates based on polarity, size, affinity, ionic strength, etc.)
• Fractions & detectors

Stationary Phases – Particle Beds

• Microporous particles: Pores were too small for mobile phase flow. Analyte diffused in and out of the pores, which was slow and led to band broadening.
• Perfusion particles: Larger particles crossed by large channels, allowing solvent flow thus increasing access to the smaller pores and reducing diffusion, which means less band broadening.
• Pellicular particles: Solid ‘glass’ core with a very thin coat/shell of stationary phase, reducing the path length that analyte can diffuse through pores, and band broadening. Stationary phases.

How an HPLC Works

• Inline solvent filter, pre-column, injection valve, pump, detector, backpressure regulator, and waste reservoir (or fraction collector).

Stationary Phases - Monoliths

• Particles in monolithic columns are similar to perfusion particles in pore geometry but are long rods instead of spheres.
• Pores in a monolithic column have approximately 6 entry/exit points (instead of a single entry/exit way), reducing analyte residence times in pores and band-broadening.

Separations Based on Polarity

Normal Phase

• Polar stationary phase, non-polar eluent
• Good for less polar organics
• Adsorption: analyte sticks to the solid support

Reverse Phase

• Non-polar stationary phase, polar eluent
• Good for polar organics
• Partition: analyte partitions into the liquid layer that sticks to the solid support
• Most common normal phase is silica/alumina gel (= Adsorption chromatography)
• Most common reverse phase is C-18 silica gel (= Partition chromatography)
• Eluents matching the stationary phase = faster elution

Normal Phase vs Reverse Phase

• Normal Phase
  • Polar Stationary Phase
  • Non-polar Eluent
  • Good for less polar organics
  • Example: Ethyl acetate (polar) and Hexane (non-polar)
• Reverse Phase
  • Non-polar Stationary Phase
  • Polar Eluent
  • Good for polar organics
  • Example: Water (polar) and Methanol (non-polar)
• Eluents matching the stationary phase result in faster elution.

Normal Phase Silica Gel Chromatography

• Historically, the most common stationary phase for adsorption chromatography is silica-gel ($SiO_2$).
• It is not glass but an open, hydrated form of $SiO_2$, hence 'gel'.
• It is a very polar stationary phase.
• Types of silica:
  • Pore size (Å): 25, 60, 60, 70
  • Particle size (µm): 40, 40-63, 150, 75-200
  • Mesh size: 400, 200-400, 100, 70-200.
  • HETP decreases (better separation) when flow decreases at a given column pressure

Silica vs Alumina as a Stationary Phase

• Alumina (which comes in several pH-adjusted forms) is a similar stationary phase, generally less polar than silica-gel.
• Eluotropic strength (e°) for various solvents on Silica and Alumina:
  • Solvent: n-pentane, n-hexane, i-propyl ether, chloroform, DCM, THF, EtOAc, acetonitrile, dioxane, i-PrOH, MeOH, water
  • e° SiO2: 0, 0, 0.32, 0.26, 0.30, 0.53, 0.48, 0.52, 0.51, 0.60, 0.70, >0.73
  • e° Alumina: 0, 0.01, 0.28, 0.36, 0.40, 0.51, 0.60, 0.55, 0.61, 0.82, 0.95, >0.95

Normal Phase Eluents

• Common systems:
  • Hexane / EtOAc
  • DCM / MeOH
• Increasing eluent polarity = more competition for the stationary phase = faster movement of analyte.
• Take care: equal “eluotropic” strength does not mean equal selectivity for a given analyte
• If the eluent is too polar, it will start to dissolve the stationary phase!

Reverse Phase C-18 Silica

• Stationary phase = modified silica gel.
• Smaller particle sizes are needed to achieve resolution, so HPLC (high pressure) is more common than combi-flash.
• Eluent requirements: filtered (free of particulates), degassed (to avoid bubbles), and not too viscous.

Reverse Phase HPLC Applications

• Can separate a wide range of polar molecules of various molecular weights including;
• Biochemistry: amino acids, proteins, carbohydrates, lipids
• Clinical: drugs, drug metabolites, bile acids, amino acids
• Environmental: pesticides, herbicides, phenol, PCBs
• Food: sweeteners, antioxidants, aflatoxins, additives/preservatives
• Forensic: drugs, poisons, alcohol, narcotics
• Industrial: PAHs, dyes, propellants, surfactants, plasticisers
• Pharmaceutical: antibiotics, sedatives, steroids, analgesics

Concept Check: Reverse Phase HPLC Separation

• Three dipeptides run on a C-18 column in 30% (v/v) methanol / water. $t_M = 2.5$ min.
• Which run has better selectivity? Which run has better efficiency?
• Rank the compounds from most to least polar.
• Which peak corresponds to dipeptide i (FK)?

Reverse Phase HPLC Separation continued

• What does peak A (at $t_R = 2.6$ min in both runs) correspond to?
• Calculate the retention factor ($k'$) for peak B in run 1.
• Calculate the number of theoretical plates ($N$) for this column.
• How could you increase the separation between peaks B and C in run 1 without changing the column?

Predicting Eluent Strength

• Typically, either MeOH / Water or Acetonitrile / Water systems are used, run as a gradient.

• The eluent polarity can be estimated by the polarity index $P'$.

• You can use this to work out the new retention factor: $log<em>{10}(k</em>2/ k<em>1 ) = 0.5(P'</em>2 - P'_1)$.

• Polarity Index ($P'$) values:

  • Cyclohexane: 0.04
  • THF: 4.0
  • MeOH: 5.1
  • MeCN: 5.8
  • H2O: 10.2

• Note: this index is specifically for RP applications

  • $P'<em>{XY} = f</em>X P'<em>X + f</em>Y P'_Y$ ($f$ = vol. fraction)

Concept Check: Eluent Strength

1. Which would be better separated by normal phase, and which by reverse phase?
2. What will be the effect of increasing the polarity of the eluent in normal phase chromatography (eg more EtOAc relative to hexane)? Will compounds run a) more quickly through the column or b) more slowly through the column?
3. Which is the more polar eluent in each case?
   • water / methanol
   • hexane / ethyl acetate
   • dichloromethane / methanol

Reverse phase HPLC separation of anti-anxiety drugs

• A, 4.48 min Oxazepam (1)
• B, 4.92 min Lorazepam (2)
• C, 6.45 min Nitrazepam (3)
• D, 9.94 min Diazepam (4)
• Column length (L) = 150 mm, column internal diameter = 4.2 mm, void retention time ($t<em>0$ or $t</em>m$) = 1.21 min, flowrate = 1.0 mL/min

Liquid Chromatography Types

• Normal Phase
  • Polar stationary phase, non-polar eluent
  • Good for less polar organics
  • Faster elution with polar ethyl acetate and non-polar hexane
• Reverse Phase
  • Non-polar stationary phase, polar eluent
  • Good for polar organics
  • Faster elution with polar water and non-polar methanol. Eluents matching the stationary phase = faster elution