Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Basics of ChromatographyA. Chromatography vs. Countercurrent distributionB. Type of ChromatographyC. Chromatography Parameters:tR, tM, VR, VM, tR‘, VR’, Wb, Wh. D. Solute Retention: E. Efficiency of Chromatography and Plate Theory: N and H F. Measures of Solute Separation: α, Rs Rs = [N1/2/2][(k2-k1)/(2+k1+k2)Rs = [N1/2/4][(α -1)/(α)]*[k2/(1+ k2)], α = k2/k1G. Fundamental factors affecting resolution: k, k = tR’/tMtR’ = k tMtR = (k+1) tMN = (tR/ σt)2Rs = tR2 – tR1(Wb2+Wb1)/21Asolid Aphase 1Asolid Aphase 2 Hildebrand solubility parameter (δ). δ = (Δ Ev/V)1/2 Where: Δ Ev/V = energy per unit volume, required to completely vaporize a solution of pure compound - ln (KD) = (δ1 – δ2)(δ 1 + δ2 - 2δA)RTVi- ΔHm = Vi (δi- δj)2-Δμi = ΔHi – TΔSi-Δμi = 0RTln(K)00 0--ΔHi = ΔHi β, - ΔHi, α000Hildebrand solubility parameters and kDisadvantages: not accurate because the simple model 2A scientific research activity:ObservationQuestions HypothesisExperimentsSummaryBasic method for problem solving:1. Understanding the question.2. Lay out the parameters regarding this question.3. Try to use concepts and formulas to find the connections.4. Solving the question.2. Cavity formation: a cavity or hole of sufficient size to accommodate the solute molecule is constructed in the solvent. This is an endoergic process, and the amount of the energy involved increases with the size of the solute molecule. 3. In the second stage of the solution process, the solute is allowed to interact with solvent. (1) Dipole-dipole interactions; (2) dipole-induced dipole (Induction interactions), (3) Dispersion interaction (London forces), and (4) acid-base interactions: H-bonding (a. solvent as donor(acid) and solute as accepter(base), b. solvent as acceptor(base) and solute as donor (acid)). XYZ = XYZ0 + cavity formation energy + ∑Solute-solvent interactions XYZ: Free EnergyThe Essence of Chromatography: p14A General model for solvent-solute interactions -- cavity model1. The process of dissolving a solute molecule is broken down to two steps: (a) cavity formation process, and (b) solute/solvent interactionssoluteCavity of solvent molecules3XYZ = XYZ0 + m’Vx + r’R2 + s’π2 +a’ ∑ α2 + b’ ∑ β2HHHlog k = c + mVx + rR2 + sπ2 + a ∑α2 + b ∑β2HHHXYZ = XYZ0 + cavity formation energy + ∑Solute-solvent interactions Capacity factor k and intermolecular interactions(Liquid chromatography)log k = c + rR2 + sπ2 + a ∑α2 + b∑β2 + llogLHHH16(Gas chromatography)System constants (c, m, r, s, a, b, and l): depended on chromatographic system conditions: mobile phase, stationary phase, and temperature. Solute descriptors (R2, π2, ∑α2, ∑β2, logL, and Vx): depended on solute properties16The Essence of Chromatography: p15(Kamlet-Taft parameters)Linear Free Energy Relationship Assumption: Free energy of solute transfer from the mobile to the stationary phase is an additive property. Separation of solute and chromatographic system contributionsF(x,y) = A(x) B(y)4The Meaning of System Constants and Solute Descriptors log k = c + mVx + rR2 + sπ2 + a ∑α2 + b∑β2HHH(Liquid chromatography)log k = c + rR2 + sπ2 + a ∑α2 + b ∑β2 + llogLHHH16(Gas chromatography)Solute descriptors (Vx, R2, π2, ∑α2, ∑β2, and logL ): depended on solute properties16Vx: molar volume calculated via Mcgowan’s method (sum of atomic volumes, then subtract 6.56 for each bond of any type, number of bond= N-1+R, unit: cm3.mol-1). Where, N is the total number of atoms and R is number of rings. This method is suitable for estimating molar volume for all the kinds of compounds. The unit for Vx is cm3.mol-1/100. The Essence of Chromatography: p17Example, atomic volume: C = 16.35, H = 8.71, O = 12.42, calculate the value of Vx for phenol. Phenol = 6*C + 6*H + O – 6.56*(13-1+1) = 77.5 cm3.mol-1 Vx = 0.775 cm3.mol-1/100 (Page 16)R2: The interactions between phases and solute though n and π electron pairs.R2 = 10* Vx[(n2-1)/(n2+2)] – 2.832 Vx + 0.526(n: refractive index of solute, 20oC for sodium d-line) HHH5π2: dipole-dipole, induction interactions H∑α2:hydrogen bond acidity (H donor)H∑β2 : hydrogen bond basicity (H acceptor)HlogL : the solute gas-liquid distribution in hexadecane. Cavity effect and dispersion interactions (London force) in gas chromatography. 16log k = c + mVx + rR2 + sπ2 + a ∑α2 + b ∑β2HHH(Liquid chromatography)log k = c + rR2 + sπ2 + a ∑α2 + b ∑β2 + llogL(Gas chromatography)The meaning of system constants (c, m, r, s, a, b, and l) is corresponding to that of solute descriptors. We can evaluate the properties of chromatographicsystems!It is very important in material characterization, retention prediction, and method development in chromatography6Example: page 19 in The Essence of ChromatographyEvaluation of the properties of chromatographic systemsc = -1.82, m = 2.99, r = 0.46, s = -0.44, a = 0.30, b = -1.88log k = c + mVx + rR2 + sπ2 + a∑α2 + b∑β2HHHCalculate the value of log k for phenol, benzyl alcohol, aniline, toluene, chlorobenzene, and predict the order retention of these molecules in a reversed-phased chromatographic system.System constantslog k (phenol) = -1.82 + 2.99*0.775 + 0.46*0.805 – 0.44*0.89 + 0.3*0.60 –1.88*0.31 = -.2737Order retention of these molecules in this reversed-phased chromatographic systemTR = Tm*(1+k)System parameter Solute parameter8Basics of ChromatographyA. Chromatography vs. Countercurrent distributionB. Type of ChromatographyC. Chromatography Parameters:tR, tM, VR, VM, tR‘, VR’, Wb, Wh. D. Solute Retention: E. Efficiency of Chromatography and Plate Theory: N and H F. Measures of Solute Separation: α, Rs G. Fundamental factors affecting resolution: k, k = tR’/tMtR’ = k tMtR = (k+1) tMN = (tR/ σt)2Rs = tR2 – tR1(Wb2+Wb1)/2K. Evaluation of capacity factor k and chromatographic systems log k = c + mVx + rR2 + sπ2 + a∑α2 + b∑β2HHHSolute descriptorsSystem constants9Diffusion and Fluid Flow1. Diffusion: Diffusion refers to the transport of substance against a concentration gradient. Mass transfer: movement of mass from one place to another Diffusion: movement of mass from region of high concentration to low concentration. J = -D (Flux of mass, D: diffusion coefficient)2. Diffusion is an important process in