高等食品分析(Advanced Food Analysis) V....

高等食品分析(Advanced Food Analysis)

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V. CHROMATOGRPAHY *Chromatographic methods: 1. Plane chromatography (PC and TLC) 2. Gas chromatography (GC) 3. Liquid chromatography (LC) 4. Other separation methods: Supercritical fluid

chromatography (SFC) and capillary electrophoresis

*Separation based on rate process: Field: Electrophoresis, centrifugation, mass spectrometry Barrier (porosity): Membrane (UF, RO), dialysis, gas diffusion

*Separation based on equilibrium between phases: Gas-liquid: Gas-liquid chromatography (GLC), distillation Gas-solid: Gas-solid chromatography (GSC), sublimation Liquid-liquid: Liquid-liquid chromatography (LLC), extraction Liquid-solid: Liquid-solid chromatography (LSC), crystallization

or precipitation


52

V. CHROMATOGRPAHY

*Phases: Gas, supercritical fluid (gas under pressure at certain temp.), liquid and solid.

*Chromatography: Tswett (1906) Chromatography = Chroma + graphein (Greek) Color write First used to describe the research work on the separation of

colored pigments into bands on a column of chalk. *Definition of chromatography: "Chromatography is a method in which the components of a mixture are separated on an adsorbent column in a flowing system."—Tswett (1906)

"A method used primarily for the separation of the components of a sample, in which the components are distributed between two phases, one of which is stationary while the other moves. The stationary phase may be a solid, or a liquid supported on a solid, or a gel. The stationary phase may be packed in a column, spread as a layer, or distributed as a film, etc.; in these definitions 'chromatographic bed' is used as a general term to denote any of the different forms in which the stationary phase may be used. The mobile phase may be gaseous or liquid."

—International Union of Pure and Applied Chemistry (1974) *Chromatographic methods: Classified based on equilibration

process, which is governed by the type of stationary phase. 1. Adsorption chromatography: Based on adsorption. Stationary type: Plane: TLC (solid supported on an inert plate) Column: Solid on which sample components are adsorbed. Mobile phase: Liquid: LSC or CC; gas: GSC The components distribute between the two phases through a

combination of adsorption and desorption processes.


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V. CHROMATOGRPAHY 2. Partition chromatography: Based on solubility. Stationary type: Plane: PC (a layer of water adsorbed on a sheet of paper) Column: Liquid supported on an inert solid. Mobile phase: Liquid: LLC; gas: GLC 3. Bonded phase chromatography: Based on partition. Stationary phase: Organic species bonded to a solid surface. Mobile phase: Liquid: BPLC; gas: BPGC; supercritical fluid: SFC 4. Ion-exchange chromatography: Based on ion-exchange. Stationary phase: ion-exchange resin. Separation mechanism is based on ion-exchange equilibrium. 5. Molecular exclusion chromatography (gel permeation

chromatography, gel filtration): Based on pore penetration. Stationary phase: molecular sieve. Molecules are separated according to their size by their ability to

penetrate a sieve-like structure.


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V. CHROMATOGRPAHY *Elution development (elution chromatography): Most widely used in the GSC, GLC, LLC and LSC. Small sample is introduced onto the column and eluted with a

mobile phase, which has a lesser affinity for stationary phase than sample components.

Used for analytical separation due to complete separation.

Simple elution: Eluted with the same solvent. Stepwise elution: Changing the eluent after predetermined period

of time to increase eluting power. Gradient elution: Using a gradual change in composition of the

eluting solvent to achieve separation. May be linear, steadily increasing or decreasing, or logarithmic

and may be a concentration, pH, polarity or ionic strength gradient.


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V. CHROMATOGRPAHY *Chromatographic requirements: 1) Reproducible chromatograms: Stable mobile phase flow rate

and pressure, achieved using accurate control system. 2) Stable stationary phase, with no column bleed (GC) or

dissolution (HPLC), achieved using bonded stationary phases or operating the column at temperatures well below the operating limits.

3) Obtaining sharp chromatographic peaks with minimal tailing (sharp narrow peaks produce the greatest concentrations of solute in the mobile phase).

4) Using a mobile phase that can be efficiently removed from the eluent in an interface, has minimal spectral interference with the spectra of the eluted components, is thermal stable and does not react with the components at the elevated temperatures of an interface.

*Partition: Competition between two phases for solute molecules. At equilibrium: nM nS (1) => KD = nS/nM (2)

Where KD: Distribution (partition) coefficient. nM: No. of molecule (solute) in the mobile phase. nS: No. of molecule (solute) in the stationary phase. *Chromatogram:

Res

pons

e

Start

Retention Time

t

t

M

R


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V. CHROMATOGRPAHY

*Retention time: tR = tR' + tM (3)

Where tR: Solute retention time. tR': Adjusted retention time. tM: Column dead time (for an unretained component, e.g.

air (or methane) for GC). *Retention volume: VR = VM + KD VS (4) Where VR: Retention volume. VM: Mobile phase volume. VS: Stationary phase volume. KD: Distribution coefficient. *Retention time vs. retention volume: VR = tR Fc and VR' = tR' Fc (5)

Where Fc: Column flow rate.


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V. CHROMATOGRPAHY *Resolution: R = (Efficiency) (Capacity factor) (Selectivity) R = (1/4) [L/H]1/2 [k/(k+1)][ (-1)/ (6) R = (1/4) [N]1/2 [k/(k+1)][ (-1)/ (7) Where k: Capacity factor. = k2/k1: Relative retention, selectivity. L/H = N: Efficiency, theoretical plates. L: Length of column. H: HETP (height equivalent to a theoretical plate). *Capacity factor, k: Rate of solute migration. Ideally, k = 1-10 for both resolution and retention time. k = (Time in phase S)/(Time in phase M) k = tR'/tM = (tR - tM)/tM = tR/tM - 1 (8) k = VR'/VM = (VR - VM)/VM = KD (VS/VM) (9) => tR = (1 + k) tM (10) => tR = (1 + k) (L/) (Since tM = L/) (11) Where : Average mobile phase velocity. *To reduce tR, shorten column length or increase flow rate.

Changes in mobile phase flow rate affect the retention times, but k remains unchanged, see (11).

k = 0 => No resolution. k = 1 => k/(k+1) = 0.5 => 50% increase in R. k = 9 => k/(k+1) = 0.9 => 90% increase in R. k moves from 0 to 9 => Increase in R moves from 0 to 90%. Increases in k enhance R, but elongate elution times. Optimizing k to improve resolution:

1. GC, increasing column temp. or temp. programming. 2. SFC, reducing density. 3. HPLC, changing solvent composition (gradient elution or

solvent programming).


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V. CHROMATOGRPAHY Example:

a b c

tM tRb tRc

1 2 3 min ka = (tRa - tM)/tM = 0; kb = 1; kc = 2 => b,c = 2/1 = 2

k = 0

k = 105

k = 5

Time-consuming, wasting solvent or gas, losing sensitivity.

*Relative retention, selectivity, : For k2 > k1, > 1 = tR2'/tR1' = (tR2 - tM)/(tR1 - tM) = k2/k1 (12) = VR2'/VR1' = (VR2 - VM)/(VR1 - VM) = k2/k1 (13) *Elution problem:

1a

1b

2a

2b

2c

1. a and b: Same k, same , but different N. 2. a —> b: Change in N (efficiency) by changing the column. a —> c: Change in (selectivity).


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V. CHROMATOGRPAHY

To increase while maintaining k in the range of 1 to 10: 1. Changing mobile phase composition including change in pH. 2. Changing column temperature. 3. Changing stationary phase composition. 4. Using special chemical effects, e.g., adsorbent impregnated

with silver salt improves separation of olefins. *Parameters for the peak curve:

Wb

h

h/2Wh

Where Wh: Peak width at 1/2 height. Wb: Peak width at the base. h: Height of a triangle formed by drawing tangent to the curve (peak).

The width of each peak (Wb) is a measure of the statistical

distribution of the retention time. , standard deviation of the curve = One-half the width at the

half-height (HWHM, half width at half maximum). Wb = 4 or = Wb/4 (14) Wh = [5.54]1/2 (15)


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V. CHROMATOGRPAHY *Peak shape terms:

1 2 3

1. Gaussian—ideal shape. 2. Tailing—surface adsorption effects or dead volume. 3. Fronting—overloaded or sample capacity exceeded.

*Peak width vs. retention time: Wb1/Wb2 = [t1/t2]1/2 At the same peak height (16)

Peak broadening is due to longitudinal diffusion molecular diffusion through the column.

TLC plate Chromatogram

The longer the retention time, the broader the peak. *Resolution: Resolution is complete at R = 1.5. A measure of the degree of separation of adjacent peaks. R = tR/4 = (tR1-tR2)/[0.5(Wb1+Wb2)] = 2 (tR1 - tR2)/(Wb1 + Wb2) (17) *Efficiency of separation (theoretical plates, n or N): n = [tR/]2 = 16 [tR/Wb]2 = 5.54 [tR/Wh]2 (18)


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V. CHROMATOGRPAHY *Bandspreading:

Long

Open tube (capillary)

Short

Packed column

Stationary phase coated on the wall

Bandspreading

*Effective theoretical plates, Neff:

Neff = 16 [tR'/Wb]2 (19) => Neff = 16[tR'/Wb]2[tR/tR]2 = 16 [tR/Wb]2 [tR'/tR]2 Neff = N [k/(1+k)]2 (20) At large k, k+1 ~ k => Neff = N

0 k 200

106N

Neff

Practical useful efficiency


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V. CHROMATOGRPAHY *HETP (height equivalent to a theoretical plate): H = 2/L (21) H = L/n or H = L/N (22) => n = L/H = L/(2/L) = L2/2 = L2/[Wb/4]2 = 16 [L/Wb]2 (23)

Substitute L, Wb in length with tR, Wb in time => N = 16 [L/Wb]2 = 16 [tR/Wb]2 (17) (23) Where H is constant for a given system.

The lower the HETP, the more efficient the column will be. For

high efficiency, high N is required. To avoid long column, HETP is as short as possible. Increase in N is effective by reducing H rather than lengthening the column.

Decrease in particle size of packing improves H, but for liquid mobile phase, where B/ is negligible, reduction in solvent viscosity increases diffusion coefficient in mobile phase, thus improves H.

*Factors affecting bandspreading: 1. Resistance to mass transfer in stationary and mobile phases. 2. Diffusion through the column (longitudinal diffusion). 3. Uneven flow velocity across the column. (packed column).


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V. CHROMATOGRPAHY *Resolution vs. efficiency: R = (Efficiency) (Capacity factor) (Selectivity) Diffusion Interaction R = (1/4) [L/H]1/2 (k/k+1) (-1/) (6) => R = (1/4) [N]1/2 (k/k+1) (-1/) (7) => N = 16 R2 [k+1/k]2 [/]2 (24) => R=(1/4)[0.5(N1+N2)]1/2[(tR1'-tR2')/0.5(tR1'+tR2')] (25) From (10)(21) => tR = (NH/) (k+1) (26) => tR = 16 R2(H/) [(k+1)3/k2] [/]2 (27) => N1 : N2 = R12 : R22 or tR1 : tR2 = R12 : R22 or

H1 : H2 = R22 : R12 (28) *Example: R = 1, k = 3, = 1.3 n = 16 [1]2 [(1+3)/3]2 [1.3/(1.3-1)]2 = 534 For typical = 1.01, n = 16 [1]2 [(1+3)/3]2 [1.01/(1.01-1)]2 = 290161 *Linear velocity,

= Fc/Ac = Fc/r2Ee (29) Where Ac: Cross section area of column. Ee: Interparticle porosity (usually ca. 0.5). The larger the column, the lower the linear velocity will be. *Van Deemter equation:

H = A + B/ + C = A + B/µ + (Cs + Cm) µ (30) H = HE + HL + HS + HM (31) Where A, B and C are approx. constant for a given system. : The linear velocity of the carrier fluid in cm/sec. HE: Radial diffusion (Eddy diffusion). HL: Longitudinal diffusion. HS: Stationary phase mass transfer. HM: Mobile phase mass transfer.


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V. CHROMATOGRPAHY *Eddy diffusion (radial diffusion)—A term: Uneven flow path.

HE = A = 2 dp (32) Where : Packing factor, 1-8. 20-40 mesh: = 1, 200-400 mesh: = 8. dp: Average packing particle diameter. Independent of linear velocity (), diffusion coefficient (D). A term is 0 for open tubular GC columns due to single path flow. *Longitudinal diffusion—B/ term: Bandspreading process.

HL = B/ = 2 DM/ (33) Where : Linear velocity of mobile phase. Obstruction factor, packed: 0.6-0.8, open: 1. DM: Diffusion coefficient in mobile phase. Important at low mobile-phase velocity. Important in GC than LC, since diffusion coefficient (diffusivity)

of solutes in gases are at least 104 greater than in liquids. Diffusion Coefficient (cm2/s) Gas 10-1 Supercritical 10-3 Liquid 10-5 Solid ?

Diffusion as (MW): MW D (× 10-5) Mol. diameter (Å) 10 2.2 2.9 100 0.7 6.2 1,000 0.25 13.2 10,000 0.11 28.5 100,000 0.05 62.0 1,000,000 0.025 132 Drops by ca. 1/2 for one log of MW.


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V. CHROMATOGRPAHY *Stationary phase mass transfer (open tube)—Cs µ term: HS = Cs µ = [2k/3(1+k)2][df2 /DS] µ (34) Where df: Film thickness. DS: Diffusion coefficient in stationary phase. Unimportant in SEC due to no stationary phase. *Mobile phase mass transfer (open tube)—Cm µ term: HM = Cm µ= [(1+6k+11k2)/96(1+k)2][dc2/DM] µ (35) Where dc: Column diameter. *HETP for open tube capillary column: HETP = 2 DM/µ + [2k/3(1+k)2][df2/DS] µ +

[(1+6k+11k2)/96(1+k)2][dc2/DM] µ (36) No A term, and = 1. *HETP for packed GC column: HETP = 2 dp + 2 DM/µ + [2k/3(1+k)2][df2 /DS] µ + [dp2/DM] µ (37) *HETP for packed LSC column: HETP = 2 dp + 2 DM/µ + [(a+bk+ck2)/24(1+k)2][dp2/DM] µ (38) No CS (DS) due to adsorption rather than partition in stationary

phase.


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V. CHROMATOGRPAHY


67

V. CHROMATOGRPAHY *Example: Substances A and B were found to have retention times of 16.40

and 17.63 min, respectively, on a 30.0-cm column. An unretained species passed through the column in 1.30 min. The peak widths (at base) for A and B were 1.11 and 1.21 min, respectively.

Calculate: a. The column resolution; b. The average number of plates in the column; c. The plate height; d. The length of column required achieving a resolution of 1.5; e. The time required to elute substance B on the longer column; f. The plate height required for a resolution of 1.5 on the original

30-cm column and in the original time.

Solution: a. (17) R = 2(17.63-16.40)/(1.11+1.21) = 1.06 b. (18) NA = 16[16.40/1.11]2 = 3493 (18) NB = 16[17.63/1.21]2 = 3397 NAV = (3493 + 3397)/2 = 3445 = 3.45 × 103 c. (21) H = L/N = 30/3.44 x 103 = 8.71 × 10-3 cm d. (28) N1 : N2 = R12 : R22 => 3445 : N2 = (1.06)2 : (1.5)2 => N2 = 6.9 x 103 => L2 = (6.9 x 103) (8.71 × 10-3 cm) = 60.1 cm

e. (28) tR1 : tR2 = R12 : R22 => 17.63 : tR2 = (1.06)2 : (1.5)2 => tR2 = 35.3 min

f. (28) H1 : H2 = R22 : R12 => H2 = (8.71 × 10-3)(1.06)2/(1.5)2 => H2 = 4.3 × 10-3 cm


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V. CHROMATOGRPAHY *Statistical moments: Bandspreading in elution chromatography (separation processes)

can be described by a Gaussian distribution for random processes (e.g., diffusion).

Con

cent

ratio

n (C

)

Time (t)

Gaussian peak

⌠Zero moment M0: │c(t) dt Area (39) ⌡

⌠First moment M1: (1/A) │c(t) dt Retention time (tR) (40) ⌡

⌠Second moment M2: (1/A) │c(t - tR)2 dt Variance (2) (41) ⌡

⌠Third moment M3: [1/A(t2)] │c(t - tR)3 dt Skew (42) ⌡Skew = 0, if it is Gaussian distribution.


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V. CHROMATOGRPAHY *Molecular basis for separation:

Molecule i interacting with phase j Eij = Ed + Eo + Ei + Eab (43) Where Eij: Total interaction energy. Ed: London dispersion force; small number.

Ed = - (3/2) [Ii Ij/(Ii+Ij)] (ij/r6) ~ 1 kcal/mol (44) Eo: Orientation dipole interaction; moderately large no.

Eo = - (2/3) (i2j 2/kTr6) = 1-10 kcal/mol (45) Ei: Induced dipole interaction; moderately large no.

Ei = - (i2j/r6) = 1-10 kcal/mol (46) Ed + Eo + Ei: Van der Waals forces. Eab: All acid-base interaction including H-bonding and

electrostatic forces. Hard to quantitate. Large no. when present.

Eab ~ EAEB + CACB = 1-50 kcal/mol (47)

Where i or j: Respective dipoles of molecule i or j. r: Distance between centers.

T: Temperature (K). Ii or Ij: Ionization potentials. i or j: Polarizability. EA or EB: Hard effects, electrostatic charge-transfer. CA or CB: Soft covalent effects, electron sharing Lewis

acid-base. Useful for predicting relative behavior but hard to calculate or

estimate on absolute terms due to nonideal behavior and difficulty of selecting an accurate mode.


70

V. CHROMATOGRPAHY *Kovats retention index (RI): For a normal alkane standard, retention index is equal to 100 times

the number of carbons in the compound regardless of column packing, temperature or other gas chromatographic conditions.

RI = 100z + 100 [(log tx' - log tz')/(log tz+1' - log tz')] (48) Where RI: Retention index. tx': Adjusted retention time for substance x.

tz' and tz+1': Corresponding adjusted retention times for normal hydrocarbons with z and z+1 carbon atoms, respectively.

Example: RI for heptane: 700. Reference compounds: n-Alkane, such as pentane and hexane. Index differences (I) between columns can yield supporting data

related to molecular structure. tM can be checked out using butane from a lighter. Within a homologous series, a plot of log tR' vs. C# is linear.

Number of n-alkane carbon atoms

Log

t '

(sec

)R

4 5 6 7 8 9

ButanePentane

HexaneHeptane

OctaneNonane

Kovats retention indices and McReynolds numbers are commonly

used to define overall polarity of stationary phase.


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V. CHROMATOGRPAHY *Quantitation in chromatography: Precision (精確): The degree of agreement between replicate

measurement of the same quantity and does not necessarily imply accuracy.

Accuracy (準確): The degree of agreement between the measured value and the true value (accepted).

Peak areas are independent of broadening and are more satisfactory parameter than peak heights.

Peak area, from integration of detector signal during elution of a component, is proportional to component concentration.

*Quantitation of a sample peak: Sample content (g/g) = (ASPL/AIS)(WIS/WSPL)(RF/RC) (49) Where ASPL: Integrated area of a sample (V•sec). AIS: Integrated area of internal standard (V•sec). WIS: Total amount of internal standard added (g). WSPL: Total sample weight (g). RC: Relative recovery (dimensionless). RF: Response factor (dimensionless). Response factor (RF) = (AIS per g/(ASPL per g) (50) For more accuracy: Response factor (RF) = (SIS/SSPL) (51) Where SIS: Slope of IS regression line of ≥ 6 points. SSPL: Slope of SPL regression line of ≥ 6 points. *Recovery test: ≥ 6 different concentrations. 1. Absolute recovery: 10 or less to 70%. 2. Relative recovery: 90 to 110%, for volatiles, 70 to 90%. Sample A: IS + component C Sample B: IS only. C in A (g/g) = (AC/AIS)(WIS/WA)(RF) C in B (g/g) = (AC/AIS)(WIS/WB)(RF) => RC = (C in A - C in B)/ g C fortified per g sample (52)


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V. CHROMATOGRPAHY *External standard method: Calibration curve method. Using the same component, a curve was established by plotting

concentration vs. peak areas or heights. The curve should consist of ≥ 6 pts, and pass through the origin. Frequent restandardization is necessary for highest accuracy,

especially for the slope correction. *Internal standard method: Highest precision for quantification of chromatography due to

difficulty of accurate injection. Resolution of IS from other components should be > 1.5. IS is added prior to sample preparation. If there is a loss of sample

during extraction or other sample preparation procedure, the losses of sample compound and IS are assumed to be the same.

*Double internal standard method: First IS is added prior to sample preparation mainly for relative

recovery of sample, especially in the low recovery of volatile compounds.

Second IS is added after sample prepared and prior to chromatographic analysis mainly for quantitation.

*Combination of internal and external standard method: Internal standard is added prior to sample preparation for the

determination of relative recovery of analytes. Component quantification of sample in the chromatograms was

mainly based on each external standard due to the differences in response factors for multiple components.


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V. CHROMATOGRPAHY

高等食品分析(Advanced Food Analysis) V....

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