Andreiadis Breakthrough Curves

8/11/2019 Andreiadis Breakthrough Curves

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Polytechnic University of BucharestFaculty of Engineering in Foreign Languages

Chemical Engineering Department

Breakthrough CurvesDetermination of Specific Parameters

student: Eugen S. Andreiadis

group: 1254E / 2004 - 2005

coordinator: as. ing. Maria Mihaly


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2.

ntroduction

olid-phase extraction (SPE) is a simple, fast technique for the clean up and isolation ofanalytes from complex matrices. It has many advantages over more traditional extraction

and clean-up procedures such as high recovery rates, the ability to extract multiple

components from one sample and, most importantly, the components of interest are isolated

in a highly pure, concentrated form.

In addition, the SPE method allows for the quick and simple analysis of the properties of

various solid phases, as regards the number of theoretical plates, the linear capacity, the

recovery factor or the type of adsorption, to name but a few. The present paper aims to

illustrate this method of analysis, by presenting the results obtained for the commonly used

C18-bonded silica phase, as well as the results obtained by testing new types of materials,prepared using two different matrixes.

heoretical Aspects

2.1.The Breakthrough Curve

he breakthrough curve (BC, also known as frontal chromatogram) represents the

evolution of the solution concentration in function of adsorption parameters like contact

time between liquid and solid phase, solvent concentration and temperature (see Figure 1).

Figure 1. A typical breakthrough

curve and the fundamental

chromatographic parameters

IS

T

T

VB VR VE V0

Volume of the effluent

Concentrationofthe

analyte

c0

nadsorbed

nlost

1.

2.


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3.

In the case shown in the figure, the total amount of the analyte originally present in the

sample is the product of the analyte concentration and sample volume, c0 V0. The amount

lost (nlost) due to breakthrough is graphically represented by the area under the frontal

chromatogram. Thus, the amount retained in the SPE column (nadsorbed) equals the difference

between the total amount and the amount lost, graphically corresponding to the area above

the frontal chromatogram.

The breakthrough curve can give precious information regarding the cartridge and the solid

phase inside, like the number of theoretical plates, the linear capacity or the recovery factor.

2.2.Methods for BC parameters evaluation

everal fundamental parameters characterize the curve: the breakthrough volume VB, the

equilibrium volume VE, the retention volume VRand the total volume V0.

The precise determination of these parameters is subject to debate. Following, we shall

present and compare two methods found in literature for the evaluation of the parameters

and an original method based on the extreme points of the third and first derivative curve.

Standard deviation method

Using this method the retention time of the analyte (VR) can be determined as the value

corresponding to half the initial concentration [1], as indicated in Figure 2.

VR= 0.5 c0 (1)

Figure 2.Determination of

the parameters using the

standard deviation method

The breakthrough volume(VB) is usually defined as:

VB= VR- 2 V (2)

where V is the standard deviation of the derivative curve which can be determined

graphically from the breakthrough curve as shown in Figure 2. Vis in direct relation to the

S

VB VR VE V0

Volume of the effluent

Concentrationoftheanalyte

c0

0.5 c0

0.841 c0

0.159 c0

V V*


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4.

efficiency of the SPE column, that is, the number of theoretical plates (N) which can be

calculated from the breakthrough curve using the equation:

( )

=R R V

2V

V VN (3)

Analogously, the equilibrium volume(VE) can be defined as:

VE= VR+ 2 V* (4)

where V* can be determined graphically from the breakthrough curve as shown in Figure 2.

This value is usually different from that of V because of the asymmetry of the breakthrough

curves.

The capacity factor of the solute, k, can be calculated from the fundamental equation of

chromatography:

VR= VM (1 + k) (5)where VMrepresents the hold-up volume of the SPE cartridge. Thus,

R

M

Vk 1

V= (6)

A very important parameter, the recoveryr, can also be directly related to the breakthrough

curve. It is defined as the amount of analyte that can be recovered after the SPE procedure,

expressed in percentage of the total amount of the analyte originally present in the sample.

Knowing this quantity allows for the concentration of the analyte in the sample to be

calculated from the concentration determined in the sample extract.

The amount adsorbed in the cartridge can be denoted by nsand in the special case where the

total volume V0 is safely in excess of the equilibrium volume, ns is equal to the linear

capacity of the column, ns, limwhich can be expressed by the equation [2]:

ns, lim= VMk c0 (7)

The recovery factor can now be calculated as:

s

0 0

nr 100%

c V= (8)

or, when possible, in the simplified expression:

M

0

V kr 100%

V= (9)

Direct Method

This method is very similar to the first, and allows the calculation of the fundamental

parameters using the following relations:

VR

= 0.5 c0

(1)VB= 0.05 c0 (10)


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VE= 0.95 c0 (11)

For the determination of the other quantities, like the number of theoretical plates, the linear

capacity and the recovery factor, the same relations used in the first method are applicable

here (3, 6, 8).

Third Derivative Method

We are going to present now in some detail an original method based upon the extreme

points of the third and first derivative curve. The disadvantage of the first two methods is

their inflexibility in the calculation of the parameters, which directly depend on the value of

c0and dont consider the actual shape of the curve. More than often, the BC curve has an

asymmetric character, which is not taken into account by the two methods. Using

derivatives, however, emphasises the particular characteristics of each curve. In this paper,

we aim at showing that this method yields comparable results, carrying however a greater

physical significance.

A prerequisite for any of the three methods, and especially for this one, is the smoothing of

the experimental data. Due to the presence of noise and the recording of a very large number

of experimental values (around 3000 points), the data obtained presents minor fluctuations.

Although not visible in an analogue analysis, such fluctuations are a nuisance when

computer-aided interpretation is performed, especially when we are interested in the shape

of a high-order derivative, which exacerbates the irregularities.

For plotting and visualisation of data, we have used a demo version of TableCurve 2D

version 5. The program offers several smoothing algorithms, and we preferred the Savitzky-

Golay procedure which works best with high-order derivatives. This time-domain method of

smoothing is based on least squares polynomial fitting across a moving window within the

data. The method was originally designed to preserve the higher moments within time-

domain spectral peak data. The TableCurve 2D implementation of the Savitzky-Golay

algorithm offers sequential internal smoothing passes to improve overall noise reduction.

Figure 3 compares the shape of a Savitzky-Golay interpolated curve with a non-interpolated one.

Figure 3. Savitzky-Golay interpolated and non-interpolated data

Our method for the evaluation of the fundamental parameters of a breakthrough curve isbased on the following observations:

Savitzky-Golay Smoothed DataBC curve (detail), n=200

15.5 16.5 17.5 18.5 19.5

Volume, mL

250

300

350

400

450

500

Potential,microV

250

300

350

400

450

500

Potential,microV

Savitzky-Golay Smoothed DataBC curve (detail), n=2

15.5 16.5 17.5 18.5 19.5

Volume, mL

250

300

350

400

450

500

Potential,microV

250

300

350

400

450

500

Potential,microV


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6.

the first maximum of the third derivative corresponds to the breakthrough volume;

the minimum of the third derivative (or the maximum of the first) corresponds to the

retention volume;

the second maximum of the third derivative corresponds to the equilibrium volume.

The TableCurve 2D program allows us to visualize the shape of the derivativessuperimposed on the breakthrough curve, so it is easy to compare the results obtained and

see if they have physical significance.

Using a small moving window (parameter Win n) we carefully smooth the data so that the

first region of the curve (where V0 is read) doesnt get altered by the algorithm. Usually a

value for n of 100-200 for total volumes around 130 mL is enough to obtain meaningful

results. The first maximum of the third derivative is read at this point (see Figure 4).

Figure 4. BC curve and its third derivative, for n=150, order 4 and 10 passes.

The arrow shows the first maximum of the derivative, corresponding to VB

For the retention volume, a stronger smoothing (n around 300) is required, until the first

derivative has the expected shape (Figure 5). To read the equilibrium volume, an even

stronger smoothing (values up to 800 for n) has to be applied, to get the corresponding shape

of the third derivative for large volumes (Figure 6).

At such high levels of smoothing, the first part of the interpolated breakthrough curve

presents visible alteration (although the rest of it remains pretty much unchanged), as can be

seen from Figure 7 which compares the shape of the interpolated curve for different values

of the moving window n. However, since we are no longer interested in the breakthrough

volume (which we read at the lowest possible level of smoothing assuring real significancefor the parameter), this exhibits no impediment to our estimations.

Savitzky-Golay Smoothed Data

BC curve and its 3rd derivative, n=150

0 40 80 120

Volume, mL

-7.5

-5

-2.5

0

2.5

5

7.5

10

Potential,V

0

10000

20000

30000

40000

50000

60000

70000

Potential,V

VB


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Figure 5. BC curve and its first derivative, for n=250, order 4 and 10 passes.

The arrow shows the maximum of the derivative, corresponding to VR

Figure 6. BC curve and its third derivative, for n=500, order 4 and 10 passes.

The arrow shows the minimum of the derivative, corresponding to VR,and the second maximum, corresponding to VE.

Savitzky-Golay Smoothed DataBC curve and its 1st derivative, n=250

0 40 80 120

Volume, mL

0

250

500

750

1000

1250

1500

Potential,V

0

10000

20000

30000

40000

50000

60000

70000

Potential,V

VR

Savitzky-Golay Smoothed DataBC curve and its 3rd derivative, n=500

0 40 80 120

Volume, mL

-4

-3

-2

-1

0

1

2

3

P

otential,V

0

10000

20000

30000

40000

50000

60000

70000

P

otential,V

VR

VE


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We can also obtain the value of the retention volume from the third derivative (see Figure 6),

as the maximum of the first corresponds to the minimum of the third. But for precise results,

we recommend the first derivative, since its more simplified shape allows the positioning of

the maximum even at low levels of smoothing, compared to the third derivative. Low levels

of smoothing imply a less alteration of the primary data, hence a higher precision.

Roughly, an estimate of the relative uncertainty in the calculation of the parameters, based

on the fluctuations observed, would give a value of about 5%. A more detailed analysis

would have to be carried out in order to asses the precision of the method.

Figure 7. Savitzky-Golay interpolated curve for n = 150 and n = 500

One last observation should be made regarding the total volume of the sample V0. Since we

conducted an online experiment, there was no preset volume to be run through the cartridge,

instead we allowed for the upper plateau of the breakthrough curve to be reached (totaladsorption) and we stopped after some period of linearity. In order to asses a meaningful

value for V0 (which cannot be the volume at which the experiment was stopped, but an

earlier volume), we decided to make use of the detectors precision.

Indeed, after a time (volume) the plateau of the BC curve becomes linear, except for

background noise fluctuations. We measured the baseline noise in a separate experiment and

we decided to take as reference a value ten times greater than the background. This quantity

(in units of potential), subtracted from the maximum attained potential, gives the value

corresponding to the total volume V0.

xperimental

3.1.Summary

e have tested the behaviour of C18-bonded silica cartridges using para-chloraniline

(PCA) in different conditions of flow and analyte concentration. The parameters of

each acquired breakthrough curve were computed using all the three methods presented inthe first part of this paper. A comparison between the methods is made, as well as an

E

W

Savitzky-Golay Smoothed DataBC curve (first region, detail), n=150

0 10 20 30

Volume, mL

-500

0

500

1000

1500

2000

Potential,microV

-500

0

500

1000

1500

2000

Potential,microV

Savitzky-Golay Smoothed DataBC curve (first region, detail), n=500

0 10 20 30

Volume, mL

-500

0

500

1000

1500

2000

Potential,microV

-500

0

500

1000

1500

2000

Potential,microV

3.


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interpretation of the results for C18. Following, several new materials were tested using BC

curves, and compared to the traditional C18stationary phase, in order to find possible new

stationary phases to be used in chromatographic and SPE applications.

3.2.Experimental Setup

ractically, one can obtain a breakthrough curve if the solution of an analyte of c0

concentration is pumped through a conditioned SPE cartridge and the effluent is

monitored online. For this, the cartridge is directly connected to the HPLC pump, and the

solute passes initially through the cartridge and then in the detector, while the signal from

the detector is acquired using a computer (Figure 8).

Figure 8. Experimental setup

An offline system has also been developed, in which the cartridge is put on a vacuum pump

ensuring the passage of the solute through the cartridge; the solute, recovered at the exit of

the cartridge, is analyzed by liquid chromatography. Using this system, it is necessary to

pass through the cartridge and to collect, in time, ratios containing a definite volume of

solute (5 mL for example). However, this method is very time-consuming and governed by alarge uncertainty concerning the sample volume.

3.3.Calibration Curves

he breakthrough curves are recorded as potential variation (in V) against time (in min).

The quantity on the abscissa can easily be changed into volume (mL) by multiplying

with the flow. From this the volume of the fittings, measured separately for our experimental

device, has to be subtracted.

In order to transform the electrical potential into units of concentration (mg/L) the following

procedure was applied. First, several samples of known concentration were injected into the

column. It was obtained thus a linear dependence between the concentration and the area of

the peak obtained by injection of the sample. Then, several breakthrough curves were

recorded at different concentrations, followed by injection of the sample. Using the previous

linear relationship, the area of the peaks obtained by injection was correlated with the

concentration. Moreover, the area can be correlated with the height of the breakthrough

curves plateau (the potential). Combining the two relationships, we obtain an equation for

the transformation of electrical potential into the corresponding concentration.

P

T

Solution

Pump UV D PC

Cartridge


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esults and Interpretation

or all the tabulated results, the first line correspond to the second method explained in

the theoretical part, the second line correspond to the first method and the third line

correspond to the third method (with derivative curve). We expect to have similar values,

and to test in this way the validity of the new method.

4.1.Study of C18-bonded silica stationary phase

Influence of analyte concentration

e have studied for different concentrations the parameters of the breakthrough curvein order to have a reference and an order of magnitude. The results (N, k and r) for

different concentrations are supposed be the same because these parameters characterise the

couple solid phase (C18) - analyte (PCA). However, we expect an influence of the

concentration on retention volume, breakthrough and equilibrium volume.

The experimental data and the parameters of the curves are given in Table 1. Indeed, as

predicted, the values of N, k and r are stable when concentration changes. Moreover, n s(the

quantity adsorbed during the experiment) increases with the increase of concentration,

which is logical, since the same volume of sample contains a larger quantity of analyte to be

adsorbed.

We can observe that the values of the breakthrough volume obtained by the second method

(first line) are notably different and greater than the ones obtained by the other two methods.

The results given by the third derivative method are however similar to those given by the

first method.

Table 1. Influence of analyte concentration upon adsorption on C18

Conc (mg/L) VB(mL) VE(mL) VR(mL) N k n (mmol/g) r %

30.470 89.199 55.186 15.477 191.956 4.560E-04 47.72422.519 95.395 55.186 8.044 191.956 4.560E-04 47.7241

23.650 92.250 54.667 8.955 190.142 4.504E-04 47.277

30.320 83.495 54.362 15.948 189.077 8.562E-04 48.296

22.029 88.329 54.362 7.967 189.077 8.562E-04 48.2962

23.140 87.360 53.700 8.852 186.762 8.409E-04 47.720

27.586 89.661 55.485 11.867 193.003 1.253E-03 50.327

16.827 96.561 55.485 5.416 193.003 1.253E-03 50.3273

19.880 92.460 53.980 7.011 187.741 1.229E-03 48.908

25.726 84.356 51.965 11.730 180.696 1.644E-03 48.304

16.330 89.934 51.965 5.595 180.696 1.644E-03 48.3044

17.625 85.075 51.625 6.186 179.507 1.623E-03 47.980

RF

W

4.


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Influence of sample flow

We aimed to study the shape of the BC curves for different values of the flow, at 3, 4 and 5

mL/min. However, the results obtained at 3 mL/min were rather bad, due to some

experimental errors, and have to be repeated. Here are given the values obtained at flows of

4 and 5 mL/min (Table 2). As expected, we see no remarkable influence of the flow on theintrinsic parameters of the stationary phase - analyte system (N, k and r). However, the

greater the flow, the faster the breakthrough volume is attained.

Table 2. Influence of sample flow upon adsorption on C18

Flow (mL/min) Vb (mL) Ve (mL) Vr (mL) N k ns(mmol/g) r %

35.270 92.604 58.570 20.254 203.791 4.607E-04 53.990

26.090 98.548 58.570 9.417 203.791 4.607E-04 51.3704

28.867 94.747 53.767 14.470 186.995 4.239E-04 47.134

31.396 93.469 57.264 15.309 199.222 4.547E-04 49.51621.228 101.046 57.264 7.004 199.222 4.547E-04 48.9855

23.950 96.100 51.175 10.645 177.934 4.075E-04 43.790

4.2.Study of colloidal silica based materials

ew materials containing a silica-based stationary phase bonded with different

inorganic compounds have been tested for comparison with C18and to see which one,

if any, could be a better choice for chromatographic or solid-phase extraction applications.

The results obtained are given in Table 3. The letter S in the name of the materials denotes

the addition of ferrous sulphate FeSO4 to the colloidal silica matrix, and the number

following represents the temperature at which the phase has been activated. The letter A

denotes the addition of ferrous nitrite Fe(NO3)2, while the letter M, the addition of magnetite

FeO-Fe2O3.

When we compare these results we see that the compound S is very good for an application

in SPE because k and r are rather large; however in comparison with the C18 the efficiency is

smaller. Moreover, it would be interesting to optimise this stationary phase for an

application in chromatography because the results for N are bigger than the results for othercompounds. It is also interesting to note the positive influence of temperature on the number

of plates for both materials A and M.

However, in general the compounds tested with this matrix dont behave very well because,

for example, all the capacity factors are less than 10 which is very little when compared with

a value about 200 found for the C18.

N


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Table 3. Results obtained for colloidal silica based materials

Material Vb (mL) Ve (mL) Vr (mL) N k ns(mmol/g) r %

1.796 5.841 3.183 17.158 5.279 2.010E-05 34.905

S_70 1.327 6.098 3.183 8.629 10.131 2.010E-05 34.905

1.500 4.733 2.733 17.493 8.557 1.709E-05 29.4131.620 4.801 2.644 19.953 4.869 1.593E-05 35.938

S_550 1.188 5.033 2.644 9.562 8.243 1.593E-05 35.938

1.200 3.700 2.250 14.556 6.867 1.338E-05 29.912

1.695 6.584 3.159 14.306 5.084 2.163E-05 29.182

S_1000 1.170 6.626 3.159 6.918 10.045 2.163E-05 29.182

1.333 4.467 2.633 12.626 8.207 1.781E-05 23.865

1.112 8.457 3.429 5.883 2.162 2.938E-05 17.501

A_70 0.295 8.729 3.429 2.632 10.988 2.938E-05 17.501

0.567 5.567 2.900 3.705 9.140 2.598E-05 14.555

0.962 5.681 1.956 11.573 2.888 1.312E-05 21.669

A_550 0.484 5.451 1.956 4.423 5.840 1.312E-05 21.669

0.683 2.867 1.400 11.791 3.895 8.690E-06 14.452

0.879 4.734 1.737 12.358 2.269 1.126E-05 21.715

A_1000 0.499 4.492 1.737 5.074 5.073 1.126E-05 21.715

0.667 2.400 1.300 12.990 3.545 7.809E-06 15.189

0.698 4.816 1.693 8.175 4.579 1.034E-05 19.128

M_70 0.242 4.793 1.693 3.112 4.918 1.034E-05 19.128

0.400 2.533 1.197 6.085 3.184 6.709E-06 12.419

0.932 6.945 2.012 10.262 1.929 1.187E-05 18.186

M_550 0.403 5.978 2.012 3.764 6.035 1.187E-05 18.186

0.650 2.900 1.350 11.041 3.720 7.536E-06 11.2100.923 4.667 1.806 12.686 1.439 1.064E-05 22.664

M_1000 0.523 4.556 1.806 5.118 5.316 1.064E-05 22.664

0.667 2.533 1.333 13.718 3.662 7.294E-06 15.615

4.3.Study of alcoxidic based materials

he second matrix used was an alcoxidic one improved by the addition of different

structural units at different sites. For the Mteos material was added the methyl group,for Teos, the ethyl group and for Pteos one ethyl and one phenyl group.

When we observe the results, the Teos seems to be the best compound. For Teos at 70C the

number of theoretical plates is bigger than for other compounds, and also the recovery has a

good value, making it interesting to deepen the study of Teos as a stationary phase in

chromatography. Moreover, the values for k and r at a temperature of 550C are good

compared with the rest of materials, although not similar to the C 18. This would recommend

the use of Teos 550 in SPE applications.

T


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Table 3. Results obtained for alcoxidic based materials

Material Vb (mL) Ve (mL) Vr (mL) N k ns(mmol/g) r %

2.204 6.262 3.479 25.308 11.164 2.169E-05 29.700

Teos_70 3.479 6.278 3.479 13.307 11.164 2.169E-05 29.700

1.875 4.875 3.025 22.723 9.577 1.872E-05 31.0913.931 17.259 8.876 9.316 30.036 8.988E-05 44.269

Teos_550 2.636 18.381 8.876 5.247 30.036 8.988E-05 44.269

1.867 13.867 6.667 4.950 22.310 6.583E-05 32.887

2.015 10.118 4.386 9.949 14.334 3.403E-05 26.912

Teos_1000 0.889 10.627 4.386 3.776 14.334 3.403E-05 26.912

1.333 6.767 3.033 9.769 9.606 2.298E-05 18.009

0.490 5.248 1.548 5.643 4.413 8.599E-06 11.739

Pteos_70 1.548 4.975 1.548 1.678 4.413 8.599E-06 11.739

0.333 2.000 0.767 8.953 1.681 3.283E-06 5.690

2.173 15.923 5.084 8.716 16.776 4.411E-05 25.253

PTeos_550 0.663 18.129 5.084 2.995 16.776 4.411E-05 25.253

1.200 6.250 3.100 7.482 9.839 2.998E-05 14.784

0.933 7.856 2.287 8.104 6.996 1.904E-05 13.596

PTeos_1000 0.212 7.912 2.287 2.705 6.996 1.904E-05 13.596

0.600 2.650 1.325 9.869 3.633 1.009E-05 7.139

1.156 8.610 2.630 9.166 8.196 1.413E-05 21.803

Mteos_70 2.630 7.856 2.630 3.417 8.196 1.413E-05 21.803

0.900 4.000 2.200 8.071 6.692 1.136E-05 17.428

0.759 5.097 1.734 9.661 5.064 1.550E-05 17.637

MTeos_550 0.440 4.624 1.734 4.522 5.064 1.550E-05 17.637

0.533 2.400 1.267 8.574 3.429 1.042E-05 11.9610.837 5.179 1.745 10.922 5.101 1.361E-05 16.311

MTeos_1000 0.421 4.638 1.745 4.338 5.101 1.361E-05 16.311

0.500 2.450 1.250 7.820 3.371 8.988E-06 10.778

onclusionsThe purpose of this study was to test and evaluate a new method for the calculation of BC

parameters. We have seen that the proposed method gives similar values to the methods

described in literature, but also takes into account the particular shape of each curve. Using

this method, we have compared the results obtained for C 18and several other new materials,

at different conditions of concentration and flow. Thus, we have seen that the method is

generally valid and suitable for a wide application. Moreover, various conclusions can be

draw concerning the properties of the analysed materials.

C 5.


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References

1. A. Gelencser, G. Kiss, Z. Krivacsy, Z. Varga-Puchony,J. Chromatogr. A, 1995, 693, 217.

2. I. Liska, J. Krupcik and P.A. Leclercq,J. High Res. Chromatogr., 1989, 12, 577.

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