Chem. 230 – 9/30 Lecture
Announcements I
• Quiz 1 Results
– Solutions have been
posted
– See class distribution
– Large number of high
scores (best ever #
90%+)
– Also significant
numbers of low scores
Score Range
N
60-62 (100%+)
2
54-60
7
48-53
3
42-47
4
36-41
2
<36
3
Announcements II
• Second Homework Set Are Online (due 10/7)
• Today’s Topics – Mainly Chromatographic
Theory
– Basic definitions (more questions)
– Rate Theory (cause of band broadening – Sect. 3.2)
– Intermolecular Forces and Their Effects on
Chromatography (Sect. 4.1)
– Optimization – if time
Chromatographic Theory
Questions on Definitions
4.
5.
6.
List 3 main components of chromatographs.
A chemist perform trial runs on a 4.6 mm diameter
column with a flow rate of 1.4 mL/min. She then
wants to scale up to a 15 mm diameter column (to
isolate large quantities of compounds) of same length.
What should be the flow rate to keep u (mobile phase
velocity) constant?
A chemist purchases a new open tubular GC column
that is identical to the old GC column except for having
a greater film thickness of stationary phase. Which
parameters will be affected: KC, k, tM, tR(component
X), β, a.
Chromatographic Theory
Questions on Definitions
7. What “easy” change can be made to increase
KC in GC? In HPLC?
8. A GC is operated close to the maximum
column temperature and for a desired analyte,
k = 10. Is this good?
9. If a new column for problem 8 could be
purchased, what would be changed?
10. In reversed-phase HPLC, the mobile phase is
90% H2O, 10% ACN and k = 10, is this good?
11. Column A is 100 mm long with H = 0.024 mm.
Column B is 250 mm long with H = 0.090 mm.
Which column will give more efficient
separations (under conditions for determining
H)?
Chromatographic Theory
Questions on Definitions
5.756
6.659
250
7.872
200
150
2.208
2.842
50
2.599
100
0
1
2
3
4
5
6
7
8
min
17.5
min
ADC1 A, ADC1 CHANNEL A (LILLIAN\102507000009.D)
VWD1 A, Wavelength=210 nm (LILLIAN\102507000009.D)
ADC1 A, ADC1 CHANNEL A (LILLIAN\102507000006.D)
VWD1 A, Wavelength=210 nm (LILLIAN\102507000006.D)
12.754
mV
1000
Unretained pk
1.204
1.201
14.242
800
600
400
0
2.5
5
7.5
12.5
15.436
12.821
8.309
8.444
10
14.103
0
7.173
200
2.696
2.695
– Which column shows a
larger N value?
– Which shows better
resolution (1st 2 peaks top
chromatogram)?
– Which shows better
selectivity (larger a; 1st 2
peaks on top)?
– Should be able to calculate
k, N, RS, and α
mV
0.841
0.845
0.926
0.924
1.042
1.470
1.473
1.613
1.616
• Given the two
chromatograms to the
right:
ADC1 A, ADC1 CHANNEL A (MONIQUE\062608000004.D)
ADC1 B, ADC1 CHANNEL B (MONIQUE\062608000004.D)
VWD1 A, Wavelength=205 nm (MONIQUE\062608000004.D)
15
Chromatographic Theory
Rate Theory
• We have covered parameters measuring column
efficiency, but not covered yet what factors influence
efficiency
• In order to improve column efficiency, we must
understand what causes band broadening (or
dispersion)
• van Deemter Equation (simpler form)
where H = Plate Height
B
u = linear velocity
H  A   Cu
u
and A, B, and C are
“constants”
Chromatographic Theory
Rate Theory
Most efficient
velocity
H
C term
B term
A term
U
Chromatographic Theory
Rate Theory
Inside of column
(one quarter shown)
• How is u determined?
– u = L/tM
– u = F/A* (A* =
effective crosssectional area)
Shaded area =
cross-sectional area
= area*porosity
• “Constant” Terms
– A term: This is due to
eddy diffusion
– Eddy diffusion results
from multiple paths
X
X
X
dispersion
Chromatographic Theory
Rate Theory
• A Term
– Independent of u
– Smaller A term for: a) small particles, b)
spherical particles, or c) no particles (near
zero)
– Small particles (trend in HPLC) results in
greater pressure drop and lower flow rates
Chromatographic Theory
Rate Theory
• B Term – Molecular Diffusion
– Molecular diffusion is caused by random motions of
molecules
– Larger for smaller molecules
– Much larger for gases
– Dispersion increases with time spent in mobile phase
– Slower flow means more time in mobile phase
at start
X
X
X
Band broadening
Chromatographic Theory
Rate Theory
• C term – Mass transfer to and within the stationary
phase
– Analyte molecules in stationary phase are not moving and get
left behind
– The greater u, the more dispersion occurs
– Less dispersion for smaller particles and thinner films of
stationary phase
– Less dispersion for solute capable of faster diffusion (smaller
molecules)
X
X
dispersion
Column particle
Chromatographic Theory
Rate Theory
• More generalities
– Often run at u values greater
than minimum H (saves on
time; reduces time based σ
which can increase sensitivity
depending on detector)
– For open tubular GC, A term
is minimal, C term minimized
by using smaller column
diameters and stationary
phase films
– For packed columns, A and C
terms are minimized by using
small particle sizes
Low flow conditions
Higher flow
conditions
Chromatographic Theory
Rate Theory
Some Questions:
1. What are advantages and disadvantages of
running chromatographs at high flow rates?
2. Why is GC usually operated closer to the
minimum H value than HPLC?
3. Which term is nearly negligible in open tubular
GC?
4. How can H be decreased in HPLC? In open
tubular GC?
Chromatographic Theory
Effects of Intermolecular Forces
• Phases in which intermolecular forces are
important: solid surfaces, liquids, liquidlike layers, supercritical fluids (weaker)
• In ideal gases, there are no intermolecular
forces (mostly valid in GC)
• Intermolecular forces affect:
– Adsorption (partitioning to surface)
– Phase Partitioning
– Non-Gausian Peak Shapes
Chromatographic Theory
Intermolecular Forces – Types of Interactions
Interactions by decreasing strength
• Ion – Ion Interactions
– Strong attractive force between oppositely charged ions
– Of importance for ion exchange chromatography (ionic solute
and stationary phase)
– Also important in ion-pairing used in reversed-phase HPLC
– Very strong forces (cause extremely large K values in absence of
competitors)
– From a practical standpoint, can not remove solute ions from
stationary phase except by ion replacement (ion-exchange)
• Ion – Dipole Interactions
– Attractive force between ion and partial charge of dipole
dM+
d+
:N=C-CH3
Chromatographic Theory
Intermolecular Forces – Types of Interactions
Interactions by decreasing strength – cont.
• Ion – Dipole Interactions – cont.
– Determines strength of ionic solute – solvent
interactions, ionic solute – polar stationary phase
interactions, and polar solute – ionic stationary phase
interactions
– Important for some specific columns (e.g. ligand
exchange for sugars or Ag+ for alkenes)
• Metal – Ligand Interactions
– ion – ion or ion – dipole interaction, but also involve d orbitals
Chromatographic Theory
Intermolecular Forces – Types of Interactions
Interactions by decreasing strength – continued
(non-ionic interactions = van der Waal
interactions)
• Van der Waals Forces
– dipole – dipole interactions (requires two molecules with dipole
moments)
• important for solute – solvent (especially reversed phase HPLC) and
solute – stationary phase (especially normal phase HPLC)
• Hydrogen bonding is a particularly strong dipole-dipole type of
bonding
– dipole – induced dipole interactions
• induced dipoles occur in molecules with no net dipole moment
• larger, more electron rich molecules can get induced dipoles more
readily
– induced dipole – induced dipole interactions (London Forces)
• occur in the complete absence of dipole moments
• also occur in all molecules, but of less importance for polar
molecules
Chromatographic Theory
Intermolecular Forces – Types of Interactions
• Modeling interactions
– Somewhat of a one-dimensional model can be
made by assigning a single value related to
polarity for analytes, stationary phases, and
mobile phases (See section 4.3)
– These models neglect some interactions
however (e.g. effects of whether an analyte
can hydrogen bond with a solvent)
Chromatographic Theory
Intermolecular Forces – Asymmetric Peaks
- More than one possible
cause (e.g. extra-column
dispersion)
- One common cause is
sample or analyte
overloading of column
- Analyte loading shown →
- More common with solid
stationary phase
- More common with open
tubular GC; less common
with HPLC
5% by mass ea.
20% by mass ea.
Chromatographic Theory
Intermolecular Forces – Asymmetric Peaks
• Most common for solid
stationary phase and GC
because
Active sites
Low Concentrations
analyte
X
– Less stationary phase (vs.
liquid)
– GC behavior somewhat like
distillations
• At low concentrations, column
“sites” mostly not occupied by
analyte
• As conc. increase, % sites
occupied by analyte increases,
causing change in analyte –
stationary phase interaction
High Concentrations
X
X
New analyte
X
X
X
Chromatographic Theory
Intermolecular Forces – Asymmetric Peaks
• As concentration increase, interactions
go from analyte – active site to
analyte – analyte
• If interaction is Langmuir type (weak
analyte – analyte vs. strong analyte –
active site), tailing occurs (blocking of
active sites causes additional analyte
to elute early)
• If interaction is anti-Langmuir type
(stronger analyte – analyte
interactions), fronting occurs
(additional analyte sticks longer)
Tailing peak (up
fast, down slow)
Fronting peak (up
slow, down fast)
Chromatographic Theory
Intermolecular Forces – Asymmetric Peaks
• If tailing is caused by saturation of stationary
phase, changing amount of analyte injected will
change amount of tailing and retention times
Response
Tailing Peaks
10000
9000
8000
7000
6000
5000
4000
3000
2000
1000
0
Low Conc. Std
High Conc. Std
0
2
4
Time (min.)
6
8
Chromatographic Theory
Intermolecular Forces – Odd Peak Shapes
Other Reasons for Odd Peak Shapes
• Large volume injections
– Example: 1.0 mL/min. + 0.1 mL injection
Injection plug time = 0.1 min = 6 s (so no peaks
narrower than 6 s unless on-column trapping is used)
• Injections at high temp./in strong solvents
In strong solvent
XX X
Will not partition to
stationary phase until
mobile phase mixes in
In weak solvent
X X X
Analytes stick on
column until stronger
mobile phase arives
Chromatographic Theory
Intermolecular Forces – Odd Peak Shapes
• Analyte exists in multiple
forms
• Extra-column
broadening/turbulent flow
• Multiple types of
stationary phase
Non-polar groups
Low T
High T
6.771
mV
55
6.829
7.533
50
45
7.619
– Example: maltotetraose
(glu[1→4]glu[1→4]glu)
– Has 3 forms (α, β, or
aldehyde on right glu)
– α and β forms migrate at
different rates
– At low T, interconversion is
slow relative to tR. At high
T, interconversion is faster
ADC1 A, ADC1 CHANNEL A (DIXON\HYPER0718000008.D)
VWD1 A, Wavelength=205 nm (DIXON\HYPER0718000008.D)
ADC1 A, ADC1 CHANNEL A (DIXON\HYPER0718000006.D)
VWD1 A, Wavelength=205 nm (DIXON\HYPER0718000006.D)
ADC1 A, ADC1 CHANNEL A (DIXON\HYPER0718000009.D)
VWD1 A, Wavelength=205 nm (DIXON\HYPER0718000009.D)
ADC1 A, ADC1 CHANNEL A (DIXON\HYPER0718000010.D)
VWD1 A, Wavelength=205 nm (DIXON\HYPER0718000010.D)
40
35
30
25
20
6.5
7
7.5
8
8.5
min
X X
Polar groups
OH
OH
Chromatographic Theory
Intermolecular Forces – Some Questions
1.
2.
Describe the dominant
forces involving the
molecules to the right in
interacting with non-polar
molecules? in interacting
with polar molecules
How does going from DB-1
(100% methyl stationary
phase) to DB-17 (50%
methyl – 50% phenyl) in
GC affect elution of fatty
acid methyl esters? (e.g.
C16 vs. C18 vs. C18:1)
H3C
CH3
H2C
CH3
O
H 2C
Chromatographic Theory
Intermolecular Forces – Some Questions
1.
2.
Describe the dominant
forces involving the
molecules to the right in
interacting with non-polar
molecules? in interacting
with polar molecules
How does going from DB-1
(100% methyl stationary
phase) to DB-17 (50%
methyl – 50% phenyl) in
GC affect elution of fatty
acid methyl esters? (e.g.
C16 vs. C18 vs. C18:1)
H3C
CH3
H2C
CH3
O
H 2C
Chromatographic Theory
Intermolecular Forces – Some Questions
3. Silica has many SiOH groups on the surface
(pKa ~2). What interactions will occur with the
analyte phenol, C6H5OH, if the eluent is a
mixture of hexane and 2-propanol?
4. Sugars are often separated on amino columns.
A sugar that has a carboxylic acid group in
place of an OH group will have extremely large
retention times (at least at neutral pH values).
What does this say about the state of the
amino groups?
Chromatographic Theory
Intermolecular Forces – Some Questions
5. In reversed phase HPLC with a C18 column,
benzene and methoxybenzene (anisole) have
very similar retention times. What are the
differences in the interactions between the two
solutes and mobile phases and stationary
phases?
6. A heavily used non-polar GC column is used to
separate non-polar to polar columns. Polar
compounds are observed to tail. A new
column replaces the old column, tailing stops,
and the polar compounds elute sooner.
Explain the observations.
Chromatographic Theory
Intermolecular Forces – Some Questions
7. A megabore GC column (d = 0.53 mm) is
replaced with an 0.25 mm diameter column in
order to improve resolution of constituents
from a sample. However, when the same
sample is injected into the 0.25 mm diameter,
little improvement in resolution and poor peak
shape is seen. What is a possible reason?
How can this be tested?
8. Normal phase HPLC is used to separate esters.
Is better peak shape expected if hexane or
methanol is the solvent? Why?
Chromatographic Theory
Optimization - Overview
• How does “method development” work?
– Goal of method development is to select and improve a
chromatographic method to meet the purposes of the
application
– Specific samples and analytes will dictate many of the
requirements (e.g. how many analytes are being analyzed for
and in what concentration?, what other compounds will be
present?)
– Coarse method selection (e.g. GC vs HPLC and selection of
column type and detectors) is often based on past work or can
be based on initial assessment showing problems (e.g. 20
compounds all with k between 0.2 and 2.0 with no easy way to
increase k)
– Optimization then involves making equipment work as well as
possible (or limiting equipment changes)
Chromatographic Theory
Optimization – What are we optimizing?
• Ideally, we want sufficient resolution (Rs of 1.5 or
greater for analyte/solute of interest peaks)
• We also want the separation performed in a minimum
amount of time
• Other parameters may also be of importance:
– sufficient quantity if performing “prep” scale separation
– sufficient sensitivity for detection (covered more with
instrumentation and quantitation)
– ability to identify unknowns (e.g. with MS detection)
Chromatographic Theory
Optimization – Some trade offs
• Flow rate at minimum H vs. higher flow rates (covered
with van Deemter Equation) – low flow rate not always
desired because of time required and sometimes smaller
S/N
• Maximum flow rate often based on column/instrument
damage – this can set flow rate
• Trade-offs in reducing H
– In packed columns, going to small particle sizes results in
greater back-pressure (harder to keep high flow)
– In GC, small column and film diameters means less capacity and
can require longer analysis times
• Trade-offs in lengthening column (N = L/H)
– Longer times due to more column (often not proportional since
backpressure at same flow rate will be higher)
Chromatographic Theory
Optimization – Improved Resolution Through Increased Column Length
Example:
Compounds X and Y are separated on a 100 mm column. tM = 2 min, tX = 8
min, tY = 9 min, wX = 1 min, wY = 1.13 min, so RS = 0.94. Also, N = 1024
and H = 100 mm/1024 = 0.097 mm
Let’s increase L to 200 mm. Now, all times are doubled:
tM = 4 min, tX = 16 min, tY = 18 min. So DtR (or d) now = 2 min. Before
considering widths, we must realize that N = L/H (where H is a constant for
given packing material).
N200 mm = 2*N100 mm. Now, N = 16(tR/w)2 so w = (16tR2/N)0.5
w200 mm/w100 mm = (tR200 mm/tR100 mm)*(N100 mm/N200 mm)0.5
w200 mm/w100 mm = (2)*(0.5)0.5 = 21-0.5 = (2)0.5
w200 mm = 1.41w100 mm
RS = 2/1.5 = 1.33
Or RS 200/RS 100 = d/wave = (d200/d100)*(w100/w200)= (L200/L100)*(L100/L200)0.5
So RS is proportional to (L)0.5
Chromatographic Theory
Optimization – Resolution Equation
• Increasing column length is not usually the most desired
way to improve resolution (because required time
increases and signal to noise ratio decreases)
• Alternatively, k values can be increased (use lower T in
GC or weaker solvents in HPLC); or α values can be
increased (use different solvents in HPLC or column with
better selectivity) but effect on RS is more complicated
1
 a  1  k B
RS 
N

4
 a  1  k B



Note: above equation is best used when deciding how to improve RS,
not for calculating RS from chromatograms
Chromatographic Theory
Optimization – Resolution Equation
1
 a  1  k B
RS 
N

4
 a  1  k B



• Don’t use above equation for calculating Rs
• How to improve resolution
– Increase N (increase column length, use more efficient column)
– Increase a (use more selective column or mobile phase)
– Increase k values (increase retention)
• Which way works best?
– Increase in k is easiest (but best if k is initially small)
– Increase in a is best, but often hardest
– Often, changes in k lead to small, but unpredictable, changes
in α also