Analytical Chemistry Expert

Chromatography Fundamentals

Separation principle:
  Analytes distribute between stationary phase and mobile phase.
  Retention factor: k = (tR - tM)/tM  (tR = retention time, tM = dead time)
  Selectivity: α = k₂/k₁  (relative retention)
  Resolution: RS = 2(tR2-tR1)/(w1+w2)  RS ≥ 1.5 for baseline separation

Van Deemter equation (band broadening):
  H = A + B/u + Cu
  H = plate height (smaller = better column)
  A = eddy diffusion (packing irregularity)
  B/u = longitudinal diffusion (faster flow reduces this)
  Cu = mass transfer resistance (slower flow reduces this)
  Optimal flow rate: u_opt = √(B/C)
  N = L/H  (theoretical plates, higher = better)

Peak characteristics:
  Gaussian peak: w = 4σ (base width), w₁/₂ = 2.355σ
  N = 16(tR/w)² = 5.545(tR/w₁/₂)²
  Asymmetry factor: As = b/a  (ideal = 1.0)
  Tailing (As > 1): active sites, overloading
  Fronting (As < 1): column overload

High Performance Liquid Chromatography (HPLC)

Modes:
  Reversed phase (RP-HPLC): nonpolar stationary (C18, C8), polar mobile
    Most common, for organic analytes
    Mobile phase: water + organic modifier (MeOH, ACN)
    Gradient elution: increase organic over time

  Normal phase: polar stationary (silica), nonpolar mobile
    For water-sensitive, nonpolar analytes
    Mobile phase: hexane + polar modifier

  Ion exchange: ionic stationary phase, aqueous mobile
    For ions, amino acids, sugars
    Cation exchange: -SO₃H (strong), -COOH (weak)
    Anion exchange: -NR₃⁺ (strong), -NHR₂⁺ (weak)

  Size exclusion (SEC/GPC): porous particles, no retention
    Separate by size: large molecules elute first
    Used for polymers, proteins (MW determination)

  Hydrophilic interaction (HILIC): polar stationary, organic-rich mobile
    For polar, hydrophilic compounds

Detectors:
  UV-Vis: most common, 190-800 nm, needs chromophore
  Diode array (DAD): full spectrum, peak purity assessment
  Fluorescence: very sensitive, selective, needs fluorophore
  Refractive index (RID): universal, less sensitive, no gradient
  Evaporative light scattering (ELSD): semi-universal, gradient OK
  Mass spectrometry (LC-MS): gold standard for identification + quantitation
  Conductivity: for ions (ion chromatography)

Method development (RP-HPLC):
  1. Choose column: C18 most common, C8 for large molecules
  2. Start: 50/50 water/ACN or MeOH, adjust pH with buffer
  3. Optimize gradient: 5-95% organic over 15 min, then adjust
  4. Adjust pH: affects ionization of ionizable analytes
    Acids: low pH (suppress ionization, better peak shape)
    Bases: high pH or ion-pair reagent
  5. Adjust column temperature: usually 25-40°C

Gas Chromatography (GC)

Requirements: analyte must be volatile and thermally stable
  Derivatization to improve volatility/stability if needed

Carrier gases: He (best), N₂ (cheap), H₂ (fast, flammable)

Columns:
  Packed: older, low efficiency, preparative
  Capillary (WCOT): fused silica, 0.1-0.53 mm ID, 10-100m
    Most common: 0.25 mm × 30m
  Stationary phases: polydimethylsiloxane (DB-1, nonpolar)
    Phenyl groups (DB-5, 5% phenyl, most versatile)
    Polyethylene glycol (Carbowax, polar)
    "Like dissolves like": polar analytes → polar column

Detectors:
  FID (flame ionization): universal for organics, very sensitive
    Destroys sample, insensitive to H₂O, CO₂, inorganic
  TCD (thermal conductivity): universal, less sensitive, nondestructive
  ECD (electron capture): selective for halogenated, very sensitive
  NPD (nitrogen-phosphorus): selective for N, P compounds
  FPD (flame photometric): selective for S, P
  MS (GC-MS): gold standard, library matching for identification

Kovats retention index:
  I = 100[n + (log tRx - log tRn)/(log tRn+1 - log tRn)]
  Compound retention relative to n-alkanes
  Database searchable, instrument-independent (same phase)

Headspace GC:
  Volatile compounds from solid/liquid matrix
  Static: equilibrium headspace
  Dynamic: purge and trap
  Applications: residual solvents, flavor, blood alcohol

Mass Spectrometry

Ionization methods:
  EI (electron ionization): hard, 70 eV electrons, for GC-MS
    Produces M⁺• and fragments, reproducible, library searchable
  CI (chemical ionization): soft, [M+H]⁺ or [M-H]⁻, less fragmentation
  ESI (electrospray): very soft, for LC-MS, large biomolecules
    Produces multiply charged ions: [M+nH]ⁿ⁺
    m/z = (M + n×1.008)/n
  APCI (atmospheric pressure CI): LC-MS for smaller molecules
  MALDI (matrix-assisted laser desorption): large biomolecules, polymers
    Mostly singly charged, requires matrix
  FAB (fast atom bombardment): for polar, nonvolatile compounds

Mass analyzers:
  Quadrupole (Q): unit mass resolution, fast scanning, low cost
    Selected ion monitoring (SIM): very sensitive quantitation
  Ion trap: MSⁿ capability, small, traps ions
  Time-of-flight (TOF): high resolution, exact mass, fast
    m/z = (2eV/m)×t²  (flight time → mass)
  Magnetic sector: high resolution, exact mass, expensive
  Orbitrap: ultra-high resolution (>100,000), exact mass
  FT-ICR: highest resolution, research use

Tandem MS (MS/MS):
  Q1: select precursor ion
  Q2: collision induced dissociation (CID)
  Q3: scan or select product ions
  MRM (multiple reaction monitoring): most sensitive for quantitation
  Data-dependent acquisition (DDA): survey scan + MS/MS of top ions
  Data-independent acquisition (DIA): all ions fragmented

High resolution MS:
  Exact mass measurement: identify elemental formula
  Mass accuracy: <5 ppm for formula confirmation
  Isotope pattern: confirms formula (M, M+1, M+2 ratios)

Atomic Spectroscopy

def atomic_spectroscopy_methods():
    return {
        'AAS (Atomic Absorption Spectroscopy)': {
            'principle':    'Atoms absorb light at characteristic wavelengths',
            'flame AAS':    'Air-acetylene (2300°C) or N₂O-acetylene (2700°C)',
            'GFAAS':        'Graphite furnace: lower LOD, smaller sample, slow',
            'LOD':          'ppb (μg/L) for flame, ppt (ng/L) for GFAAS',
            'limitation':   'One element at a time',
            'best_for':     'Trace metals: Pb, Cd, Cu, Fe, Zn, Ca, Mg'
        },
        'ICP-OES (Optical Emission Spectroscopy)': {
            'principle':    'Plasma (6000-10000°C) excites atoms → emit light',
            'advantage':    'Multi-element (30-40 simultaneously)',
            'LOD':          'ppb range',
            'plasma':       'Argon ICP at 27 MHz RF',
            'best_for':     'Major and minor elements, quality control'
        },
        'ICP-MS': {
            'principle':    'ICP ionizes atoms → mass spectrometry',
            'advantage':    'Multi-element, isotope ratios, very low LOD',
            'LOD':          'ppt range (ng/L)',
            'isotope':      'Isotope dilution: most accurate quantitation',
            'limitation':   'Isobaric interferences (⁵⁶Fe⁺/⁴⁰Ar¹⁶O⁺)',
            'best_for':     'Ultra-trace metals, environmental, geological'
        },
        'XRF (X-ray fluorescence)': {
            'principle':    'X-rays eject core electrons → characteristic X-rays emitted',
            'advantage':    'Non-destructive, solid samples, multi-element',
            'limitation':   'Surface analysis, matrix effects',
            'best_for':     'Alloys, geological samples, environmental screening'
        }
    }

Electroanalytical Methods

Potentiometry:
  Measure equilibrium potential (no current)
  E = E°cell + (RT/nF)ln(aOx/aRed)
  Ion-selective electrodes (ISE): glass (pH), fluoride, calcium, nitrate
  Reference electrodes: SCE (Ag/AgCl/KCl), Ag/AgCl

  pH glass electrode:
    E = const - 0.05916·pH  at 25°C
    Junction potential: source of error, use ionic strength adjustment

Voltammetry:
  Apply voltage, measure current
  Cyclic voltammetry (CV): scan E, measure I, reverse
    Reversible couple: |Epa - Epc| = 0.059/n V, Ipa = Ipc
    E°′ = (Epa + Epc)/2
    Ip = 2.69×10⁵ n^(3/2) A D^(1/2) v^(1/2) C  (Randles-Sevcik)
  Differential pulse (DPV): very sensitive, LOD ppb
  Square wave (SWV): fast, sensitive, diagnostic
  Stripping analysis (ASV): preconcentrate onto electrode, strip
    Most sensitive for trace metals (ppt achievable)

Amperometry/Coulometry:
  Amperometry: constant E, measure I vs time
    Biosensors (glucose, etc.)
  Coulometry: measure total charge Q = nFmoles
    Faraday's law: n_analyte = Q/nF
    100% current efficiency: absolute method

Conductometry:
  Measure conductance G = κ(A/l)  (κ = specific conductance)
  Conductometric titration: endpoint by conductance change
  Karl Fischer titration: water determination

Sample Preparation

def sample_prep_methods():
    return {
        'Liquid-liquid extraction (LLE)': {
            'principle':    'Distribute analyte between two immiscible solvents',
            'distribution': 'D = [A]org/[A]aq',
            'efficiency':   'E% = 100D/(D+Vaq/Vorg)',
            'optimize':     'pH, salt (salting out), solvent choice',
            'drawback':     'Emulsions, large solvent volumes, manual'
        },
        'Solid phase extraction (SPE)': {
            'principle':    'Load sample, wash matrix, elute analyte',
            'sorbents':     'C18, C8, SAX, SCX, mixed mode, ion exchange',
            'advantages':   'Less solvent, selective, automatable',
            'applications': 'Environmental, pharmaceutical, biological'
        },
        'QuEChERS': {
            'application':  'Pesticides in food (quick, easy, cheap, rugged)',
            'steps':        'Extraction (MeCN) + partitioning (MgSO₄) + dispersive SPE'
        },
        'Microwave digestion': {
            'application':  'Dissolve solid samples for elemental analysis',
            'reagents':     'HNO₃, HCl, HF, H₂O₂ (closed vessel)',
            'advantages':   'Fast, complete digestion, less contamination'
        },
        'Solid phase microextraction (SPME)': {
            'principle':    'Coated fiber equilibrates with headspace or solution',
            'advantage':    'Solvent-free, concentrates analyte, direct GC inject',
            'applications': 'Volatiles, flavor, environmental'
        },
        'Protein precipitation': {
            'agents':       'ACN, MeOH, TCA, ammonium sulfate',
            'use':          'Plasma, serum sample cleanup for drug analysis'
        }
    }

Quantitative Analysis & Statistics

import numpy as np

def calibration_statistics(concentrations, signals):
    """
    Linear calibration curve with statistics.
    """
    x = np.array(concentrations)
    y = np.array(signals)
    n = len(x)

    # Linear regression: y = mx + b
    x_mean, y_mean = x.mean(), y.mean()
    Sxx = np.sum((x - x_mean)**2)
    Sxy = np.sum((x - x_mean)*(y - y_mean))
    Syy = np.sum((y - y_mean)**2)

    m = Sxy / Sxx  # slope
    b = y_mean - m * x_mean  # intercept
    r2 = Sxy**2 / (Sxx * Syy)  # R²

    # Residuals
    y_pred = m * x + b
    residuals = y - y_pred
    se = np.sqrt(np.sum(residuals**2) / (n-2))

    # Uncertainties
    sm = se / np.sqrt(Sxx)
    sb = se * np.sqrt(np.sum(x**2) / (n * Sxx))

    # LOD and LOQ from blank
    s_blank = se  # approximation
    lod = 3 * s_blank / m
    loq = 10 * s_blank / m

    return {
        'slope':        round(m, 6),
        'intercept':    round(b, 6),
        'R_squared':    round(r2, 6),
        'SE_slope':     round(sm, 6),
        'SE_intercept': round(sb, 6),
        'LOD':          round(lod, 6),
        'LOQ':          round(loq, 6)
    }

def method_validation_parameters():
    return {
        'Accuracy':     'Recovery % = (found/true) × 100; spike recovery',
        'Precision': {
            'Repeatability':     'Same lab, same analyst, same day (RSD%)',
            'Reproducibility':   'Different labs, analysts, days',
            'Intermediate':      'Same lab, different days/analysts'
        },
        'LOD':          '3σ_blank/m (signal 3× noise above blank)',
        'LOQ':          '10σ_blank/m (quantifiable with ≤10% RSD)',
        'Linearity':    'R² ≥ 0.999, range usually 80-120% of target',
        'Selectivity':  'No interference from matrix components',
        'Ruggedness':   'Robustness to small deliberate variations',
        'Range':        'Concentration interval where method is valid',
        'Uncertainty':  'Combined standard uncertainty: u_c = √Σuᵢ²'
    }

def grubbs_outlier_test(data, alpha=0.05):
    """Grubbs test for outliers in small datasets."""
    data = np.array(data)
    n = len(data)
    mean, std = data.mean(), data.std(ddof=1)
    G = abs(data - mean).max() / std
    # Critical values (approximate for common n and alpha=0.05)
    return {
        'G_calculated': round(G, 4),
        'mean':         round(mean, 4),
        'std':          round(std, 4),
        'suspected_outlier': data[abs(data-mean).argmax()],
        'note': 'Compare G to critical value table for n and alpha'
    }

Method Validation

ICH Q2(R1) guidelines (pharmaceutical):
  Specificity: no interference
  Linearity: R² ≥ 0.999, test 5+ concentrations
  Range: LOQ to 120% of specification
  Accuracy: spike recovery 98-102% (or 90-110% for complex matrices)
  Precision:
    Repeatability: ≤1% RSD (6 replicates)
    Intermediate: ≤2% RSD
  LOD: 3σ/m, signal-to-noise ≥ 3
  LOQ: 10σ/m, signal-to-noise ≥ 10, ≤10% RSD

FDA Bioanalytical Method Validation:
  Selectivity: no matrix interference
  Calibration: ≥6 non-zero standards, 4/6 back-calculate within 15%
  QC samples: ≥3 concentrations, ≥2/3 at each level within 15%
  Matrix effect: suppress or enhance signal
  Stability: freeze-thaw, bench-top, long-term

Environmental methods (EPA):
  Method detection limit (MDL): 3.14 × s (n=7 replicates at ~1-5× MDL)
  Practical quantitation limit (PQL): ~5-10× MDL
  Matrix spike/matrix spike duplicate: recovery and precision
  Lab control sample (LCS): spike in reagent water

Common Analytical Techniques Summary

def technique_selection_guide():
    return {
        'Volatile organics': 'GC-MS (headspace or purge&trap)',
        'Semi-volatile organics': 'GC-MS or HPLC-MS/MS',
        'Pesticides in food': 'GC-MS/MS or LC-MS/MS (QuEChERS)',
        'Trace metals': 'ICP-MS or GFAAS',
        'Major metals': 'ICP-OES or flame AAS',
        'Anions (Cl⁻, NO₃⁻, SO₄²⁻)': 'Ion chromatography',
        'Pharmaceutical impurities': 'HPLC-UV or HPLC-MS',
        'Proteins/peptides': 'LC-MS/MS (bottom-up proteomics)',
        'Drug in plasma': 'LC-MS/MS (protein precipitation)',
        'Polymer MW': 'GPC/SEC with RI detector',
        'Surface composition': 'XPS, SIMS, AES',
        'Crystal structure': 'X-ray diffraction (XRD)',
        'Elemental analysis (bulk)': 'CHNS analyzer, XRF',
        'Water content': 'Karl Fischer titration',
        'pH/ions in solution': 'ISE potentiometry',
        'Redox behavior': 'Cyclic voltammetry',
        'Color/turbidity': 'UV-Vis spectrophotometry'
    }

Common Pitfalls

Related Skills

• organic-chemistry-expert: Structure identification by spectroscopy
• inorganic-chemistry-expert: Elemental speciation
• physical-chemistry-expert: Spectroscopic theory
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• environmental-science-expert: Environmental monitoring methods
• pharmaceutical-chemistry: Drug analysis and validation