Chemistry for Everyone
If You Were a Molecule in a Chromatography Column, What Would You See? John Mattice Department of Crop, Soil, and Environmental Sciences, University of Arkansas, Fayetteville, AR 72704;
[email protected] In his book Mr. Tompkins in Paperback (1), George Gamow demonstrates the effect of the Heisenberg uncertainty principle by increasing the size of particles from atoms to billiard balls and also increases the value of Planck’s constant from 6.5 × 10‒27 to near unity. He then describes what we would see if we were watching billiard balls collide on a table. We can use a similar approach to help new students understand chromatography. When teaching chromatography, we often show the students both gas chromatography (GC) and high performance liquid chromatography (HPLC) columns. We describe typical lengths and diameters of columns, particle size of packing, and thickness of stationary phase. We also explain how the separation process occurs and how processes such as resistance to mass transfer, multiple flow paths, and stagnant mobile phase contribute to band broadening, resulting in wider peaks, lower efficiency, and poorer resolution. Some of this is easier for the students to grasp if they can picture what is happening in the column. To do this, we can ask them to imagine themselves as small as the analyte molecule. That is difficult. Alternatively, we can ask them to imagine that the analyte molecules are enlarged to human size and imagine that they are moving down a large column. If the ratio of size of molecule to size of column is the same in each case, what would they see if they were a molecule traveling down the column?
all bond lengths are equal. The length of segments AB and AC is 139.5 pm, the angle of BAC is 120°, and the angle of ABD is 30°. Therefore the length of segment AD is (139.5 pm)(sin 30) = 69.75 pm. The length of AE is 69.75 + 139.5 + 69.75 = 279 pm. Assuming that peropyrene is planar, the length from one end of the molecule to the other is 3(279 pm) + 2(139.5 pm) = 1116 pm or 1.116 nm. A person who is six feet one inch tall has a height of 1.85 m or 1.85 × 109 nm. Therefore this person is 1.66 × 109 times as tall as this molecule is long:
Size Considerations
How Wide Would a GC Capillary Column Be? If you are approximately 1.66 × 109 times as big as the molecule, then to keep the ratio of size of molecule to size of column the same, the column would have to be 1.66 × 109 times as wide.
Assume you are the same size as a peropyrene molecule (Figure 1), which would be similar in size to many compounds that are analyzed by HPLC or GC. If we assume that the carbon–carbon bond length of 139.5 picometers (pm) in benzene (2) is a good approximation for the bond lengths in peropyrene, we can calculate the length of the molecule. Figure 2 shows one resonance structure for part of the peropyrene molecule where
1. 85 t 10 9 nm 1.116 nm
If we expanded molecules to human size, how big would chromatography columns be if we kept the same ratio of size of molecule to size of column? What would you see if you were a molecule moving down the column? What Would You See If You Were Injected onto a Typical GC Column? A typical GC capillary column is 30 m long with an internal diameter (id) of 0.25 mm and a stationary phase thickness of 0.25 μm.
1. 66 t 10 9 0.25 mm 10 6 km /mm 420 km
1 mi = 1.609 km, therefore
420 km 1.609 km / mi
Figure 1. Structure of peropyrene.
B
A
D
E
C
Figure 2. Sub-unit of peropyrene for calculation of length of peropyrene molecule. Point D is midway between carbon atoms B and C.
1. 66 t 10 9
260 mi
The column would have an internal diameter of 420 km or 260 mi. The distance between Indianapolis, IN, and Cleveland, OH, is 423 km, or 263 mi (3), so opposite edges of the column would be on these two cities. If you were driving a car from one side of the column to the other at 110 km/hr (68 mph), it would take almost 4 hours. If you were a molecule in the center of the column, you would have to travel at least 210 km across the column (transverse motion due to turbulence and diffusion) before you came in contact with the stationary phase. Note that if you were near one wall of the column, but were randomly moving across to the far side of the column, at a minimum you would have to go close to 420 km. Keep in mind that the transverse movement is random, so the actual distance you travel would be considerably more than this. All the time you are randomly
© Division of Chemical Education • www.JCE.DivCHED.org • Vol. 85 No. 7 July 2008 • Journal of Chemical Education
925
Chemistry for Everyone
moving across the column you would also be experiencing a net movement down the column in the mobile phase. If a clone of you (a different molecule of the same compound) had started out next to the stationary phase and immediately moved into the stationary phase, it would remain behind while you were moving down the column in the mobile phase. If there were millions of clones that all started out together in a narrow band across the front of the column, over time the band would become broader, leading to wider chromatographic peaks. The wider the column id, the more band broadening can occur, because there is more room for transverse movement in the mobile phase before contacting the stationary phase. Meanwhile, molecules that have penetrated the stationary phase will not be moving down the column until they diffuse back to the surface and re-enter the mobile phase. How Thick Would the Stationary Phase Be?
1. 66 t 10 9 0.25 N m 10 6 m / N m 420 m
The stationary phase would be approximately a quarter mile deep (4.5 football fields). You would have the potential to go in almost a quarter mile before you came to the edge of the column. Then you would have to diffuse all the way back and transfer from the stationary phase to the mobile phase before you started down the column again. Since the stationary phase is not moving, there would be no turbulence. Your movement would be due only to diffusion. Since diffusion is random, the total distance you travel from entering to leaving the stationary phase may be considerably more than 840 m or one half mile. While you are diffusing all the way to the glass wall of the column, other clones may diffuse only a couple of meters into the stationary phase and then diffuse back out. Meanwhile, other clones may have yet to enter the stationary phase and are moving down the column in the mobile phase leaving the others behind, again leading to band broadening. The thicker the stationary phase, the more band broadening can occur. In order to have narrow bands leading to narrow peaks, we do not want any molecule to get very far in front or behind the other molecules of the same compound. Therefore, we do not want any analyte molecule to get very far away from the interface of the mobile and stationary phases. The molecule in the stationary phase will not have far to go to get back in the mobile phase and follow the molecules that had moved out front in the mobile phase, and the molecules out front will not have far to go to move into the stationary phase, allowing the molecules that were behind in the stationary phase to come closer to them. Therefore, for maximum efficiency, we would want narrow columns with thin stationary phases.
The distance from the Earth to the Moon is 386,000 km (240,000 mi) and the circumference of a circle is equal to πd, where d is the diameter, therefore 6 circumference Q 386, 000 km 1. 21 t 10 km
50 t 10 6 km 1. 21 t 10 6 km
41
The column would loop 41 times around the Earth and the Moon. Even though you may have started off in the very center of the column and have to traverse at least 210 km to reach the stationary phase, you should be able to do so numerous times as you travel down the 50 million km column. If you were a molecule starting on a chromatographic journey, you would be looking at a 50 million km trip that would take you 41 times in a circular orbit around the Earth and Moon. During the trip you would be randomly moving in a gas that was flowing down a column that was 420 km wide. At times you would come in contact with a liquid stationary phase coating the inside of the column, and you might penetrate that liquid. While in the liquid you would randomly move in any direction. You may randomly move all the way to the glass edge of the column, 420 m away from the surface. Eventually you would randomly come back to the surface again, re-enter the mobile phase, and continue your journey down the column. What Would You See If You Were Injected onto a Typical HPLC Column? Typical columns are 2.0 or 4.6 mm in diameter with a length of 25 cm. They are also typically packed with 5.0 μm diameter particles with 100 Angstrom (Å) pores. The stationary phase is chemically bonded to the surface of the particles. How Wide Would the HPLC Column Be? If the column were 2.0 mm in diameter, then the width on the human molecule scale would be
1. 66 t 10 9 2.0 mm 10 6 km/mm 3300 km m 3300 km m 1.609 km /mi
2000 mi
It is 3335 km or 2072 mi from El Paso, TX, to Boston, MA (3). If you and a friend were taking turns driving non-stop from one side of the column to the other at 110 km/hr, it would take approximately 30 hr to drive across the column.
How Long Would the GC Capillary Column Be? 9 3 6 1. 66 t 10 30 m km /10 m 50 t 10 km
50 t 10 6 km 1.609 km /mi
31 t 10 6 mi 31 million mi
Capillary columns are usually held in a circular frame that holds the column in a coil. If we had a coil large enough that one side went around the Earth and the other side went around the Moon as in Figure 3, how many times around the Moon would our column go? 926
Earth
Moon
column Figure 3. If molecules were the size of humans, a GC capillary column that was scaled up the same degree would go around the Moon and the Earth 41 times.
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Chemistry for Everyone
For a 4.6 mm id column the corresponding diameter would be 7600 km (4700 mi). For comparison, the distance from Honolulu, HI, to Tampa, FL, is 7546 km or 4690 mi (4). The Earth is curved, so imagine this distance drawn out as a straight line.
distance from the end of the chain to the solid support (the Mt. Everest diameter particle). As an estimate, we can say the depth of the C18 stationary phase is 2300 pm or 2.3 nm. The depth in the human size molecule system would be
How Long Would the HPLC Column Be?
1. 66 t 10 9 25 cm 10 5 km/cm 420, 000 km 420,000 km 1.609 km / mi
260, 000 mi
Our column would stretch a little farther than from the Earth to the Moon. How Big Would the Particles of Packing Be?
1. 66 t 10 9 5.0 Nm 10 6 m/N m 8300 m 8300 m 1609 m/mi
5. 2 mi
Note that this is a much thinner stationary phase than in GC. These C18 chains would be bonded all over the surface of the solid support. It might look similar to a kelp bed in the ocean, and we would diffuse into and out of it just as a diver or a sea otter could go into and out of the kelp. How Much Space Would Be Between the Particles? Figure 5 shows the Mt. Everest size spherical particles. Points A, B, and C are the center of the particles. Point D is equidistant from the edge of each particle, and point E is where the edges touch. The segment lengths |AB|, |BC|, and |CA| = 2r where r is the radius of the circle (sphere). Angle EBC = 60° and angle EBD = 30°. Therefore the lengths |EC| and |ED| are
Mt. Everest is 5.5 mi above sea level, so imagine a sphere with a diameter equal to the height of Mt. Everest. The particles have a generally spherical shape, but have an irregular surface, similar to mountain valleys. Superimposed on this generally spherical shape are pores, which provide more surface area. When you and your clones start down the column, you will each be moving independently. You will each randomly take different paths around the mountains. After a given period of time you may each have moved the same distance, but some will have moved further down the column than others, simply because of the paths they took.
How Big Are the Pores? A typical pore size is 100 (Å) or 10–8 m.
1. 66 t 10
9
100 Å 10
10
m /Å 16 . 6 m or about 55 f t
These pores would be approximately as wide and deep as a 4- or 5-story house. They would be similar to caves in the silica that, in this case, are about ten times as big as the analyte molecules. Mobile phase that is in these caves will not be moving downstream as the rest of the mobile phase. It would be similar to a cave in the side of a river. There will be exchange of water (mobile phase), but it will be slow. Any particles or molecules that enter these caves may spend considerable time in them randomly moving about before they exit back into the main stream. How Deep Would the Stationary Phase Be? The most common stationary phase is C18, which is a carbon chain 18 carbons long bonded to the solid support particles. Figure 4 shows part of the carbon chain; bonds are shown, but carbon atoms are not shown. The angle of ABC is 109° and angle of ABD is 54.5°. Using 154 pm as the carbon–carbon bond length for alkanes (2), the length of segment AD, |AD|, is calculated as (154 pm)(sin 54.5) = (154 pm)(0.814) = 125 pm. In an 18 carbon chain there would be 17 segments of |AD|, so the length of the chain is 17(125 pm) = 2120 pm plus the bonding
1. 66 t 10 9 2. 3 nm m /10 9 nm 3. 8 m or 12 to 13 ft
EC BC sin 60p 0. 866 2r 1. 732 r ED EB taan 30p 0. 577 r DC EC ED 1. 732 r 0. 577 r 1. 155 r
Point D is therefore 1.155r − r = 0.155r away from the edge of the particles. The particles in the human size molecule system were 8300 m in diameter, therefore r = 4150 m. If you were at point D in the column flowing around the particles, you would be approximately 643 m (7 football fields placed end to end) from any of the particles: 0.155 4150 m 643 m
Note that this is a much shorter distance to any surface with a stationary phase than in a GC capillary column, which should help keep bands narrow, but keep in mind that the capillary B
A
D
C
Figure 4. Part of a C18 chain. Only the bonds between carbon atoms are shown; the carbon and hydrogen atoms are not shown.
A
E
B
D
C
Figure 5. Three spherical particles touching each other. Point D is equidistant from each edge and point E is where both edges touch.
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Chemistry for Everyone Table 1. Comparison of Dimensions on Molecular Scale and Human Molecule Scale GC
HPLC
Parameter
Molecular Scale
Human Scale
Molecular Scale
Column id
0.25 mm
420 km
2.0 mm
3320 km
Column length Stationary phase thickness Particle diameter Maximum distance between particles Pore size
30 m 0.25 μm na na na
50 x 106 km 420 m na na na
25 cm 2.3 nm 5 μm 0.39 μm 10–8 m
420,000 km 3.8 m 8,300 m 643 m 16.6 m
Human Scale
Note: na is not applicable.
column does not have multiple flow paths and stagnant mobile phase. Also note that if you used smaller diameter particles, point D would be closer to the stationary phase on the surface of the particles, analogous to a molecule in the center of a capillary column being closer to the stationary phase in a narrower diameter column. If you were a molecule starting on a journey through a 2.0 mm HPLC column, you would find yourself in a tube that had a diameter of a little over 3300 km or two thousand mi. If you were starting on Earth, opposite sides of the column would be touching El Paso and Boston. The other end of the column would be a little past the Moon. Ahead of you packed in the column you would see roughly spherical boulders with diameters equal to the height of Mt. Everest above sea level. The surface would have caves 16 to 17 m in diameter all over it. The boulders would be touching each other, and you would be traveling in the liquid mobile phase that would be flowing down the column around the boulders. At times you might be the equivalent of the length of 7 football fields away from any particle. There would be numerous paths you could take through all these particles, resulting in band broadening owing to multiple flow paths. If you started next to your clone, you would reach the end of the column at different times simply because you both took different paths around the boulders, which would result in different total distances traveled to reach the end of the column. At times you might randomly move deep into one of the caves where there would not be any net flow down the column. You might drift in this stagnant mobile phase until you eventually drifted back out into the main stream and continued down the column. Even if you had not been in the stationary phase, you still would be left behind the other clones because you were trapped in the stagnant mobile phase. This would lead to band broadening owing to stagnant mobile phase. Each Mt. Everest size boulder, including the caves, would be covered to a depth of a little under 4 m with a stationary phase that looked similar to a kelp bed with one end of the kelp fastened to the boulders. At times you would dissolve in the stationary phase and not move down the column, similar to GC. At other times you would come out of the stationary phase into the mobile phase and continue down the column around the mountains. Summary Table 1 lists the dimensions for all the measurements in both the natural and human molecule systems. Notice that in both cases, as a molecule you are either being swept along by the mobile phase and are going as fast as the mobile phase (no 928
movement with completely stagnant mobile phase) or you are in the stationary phase and not moving at all (except for random diffusion within the stationary phase). Whether you beat your clones to the end of a capillary column will be determined primarily by the percent of the time you spend in the stationary phase. This will be determined by how each of you randomly diffuse in the stationary and mobile phases. Are you moving with the mobile phase a slightly higher percent of the time than your clone? In addition, for the packed column, do you take a longer path through all the boulders than your clone? How much time do each of you spend trapped in stagnant mobile phase? If there are millions of clones, a few will by chance spend a little less time in the stationary phase, take shorter paths through the boulders, and spend less time in stagnant mobile phase. They will come out a little early and be the leading edge of the band of clones (leading edge of the peak on the chromatogram). A few will spend longer in the stationary phase, take longer paths, and spend more time in stagnant mobile phase. They will form the trailing edge of the band (trailing edge of the peak). Most will be in between for all of these phenomena, resulting in a symmetrical peak in the chromatogram. If we have a thinner column with a thinner stationary phase, there will be less opportunity for the clones in front to get very far away from the clones in the rear, since both will never be very far away from the interface of the two phases, resulting in narrower bands and sharper peaks. If we have a capillary column that does not have any packing, then there will be no multiple flow paths and no stagnant mobile phase due to the pores (caves). Since those two phenomena cannot contribute to band broadening, we would expect narrower bands, leading to narrower chromatographic peaks, and better efficiency with the capillary columns compared to packed columns. Literature Cited 1. Gamow, G. Mr. Tompkins in Paperback, 1st ed.; Cambridge University Press: Cambridge, 1971. 2. CRC Handbook of Chemistry and Physics, 60th ed.; Weast, R. C., Ed.; CRC Press, Inc.: Boca Raton, FL, 1979; p F-216. 3. Infoplease. http://www.infoplease.com/ipa/A0004594.html (accessed Feb 2008). 4. Geobytes. http://www.geobytes.com/CityDistanceTool.htm (accessed Feb 2008).
Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Jul/abs925.html Abstract and keywords Full text (PDF) with links to cited URLs
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