Electrolyte systems in isotachophoresis and their application to some protein separations

Electrolyte systems in isotachophoresis and their application

to some protein separations

Citation for published version (APA):

Routs, R. J. (1971). Electrolyte systems in isotachophoresis and their application to some protein separations. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR43649

DOI:

10.6100/IR43649

Document status and date: Published: 01/01/1971 Document Version:

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ELECTROLYTE SYSTEMS IN ISOTACHOPHORESIS

AND THEIR

APPLICATION TO SOME PROTEIN SEPARATIONS

ELECTROLYTE SYSTEMS IN ISOTACHOPHORESIS

AND THEIR

APPLICATION TO SOME PROTEIN SEPARATIONS

ELECTROLYTE SYSTEMS IN ISOTACHOPHORESIS

AND THEIR

APPLICATION TO SOME PROTEIN SEPARATIOI\IS

PROEFSCHRIFT

TER VERKRIJGING VAN DE GRAAD VAN DOCTOR IN DE TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL TE EINDHOVEN OP GEZAG VAN DE RECTOR MAGNIFICUS DR. IR. A.A.TH.M. VAN TRIER, HOOGLERAAR IN DE AFDELING DER ELECTROTECHNIEK, VOOR EEN COMMISSIE UIT DE SENAAT TE VERDEDIGEN OP DINSDAG

9 NOVEMBER 1971 DES NAMIDDAGS TE 16 UUR

DOOR

ROBERT JOHN ROUTS GEBOREN TE BRISBANE

1971

DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOREN PROF.DR.IR.A.I.M.KEULEMANS

EN

P·

81

p. 1 01

P· 117

ERRATA

Fig.4.5~:

The leading ion is acetate and

not chloride as indicated. The acetate

con-centration is 0.003 M.

The concentration of acrylamide is 3 grams

per 100 ml.

Fig.6.21: The thermostat temperature was

4°C.

\

I

I

ACKNOWLEDGEMENT

This investigation was made at the laboratories of LKB Produkter AB in Stockholm, to whom I am indebted for various kinds of support.

For numerous discussions and positive criticism I want to express my gratitude to Dr. Frans Everaerts and Dr. Lennart Arlinger. I also wish to thank Dr. Herman Haglund, Dr. Anders Vestermark and Dr. Hilary Davies for their valuable help.

I am very grateful to Mr. Per Just Svendsen for his interest in the investigation and his skillful advice. My thanks are extended to Mr. Berl Larsson for his technical assistance, to Mr. Curt Sivers for his programming work, to Mr. Leo Fitzgerald for linguistic revision of this monograph, to Mrs. Iris Gustafson for the typing of this thesis, to Mr. Gosta Larsson and Mr. Jean Bohman for assistance with the illustrations.

CONTENTS

INTRODUCTION 1. Principle

2. Scope of this monograph

LITERATURE REVIEW 1. The early period

2. The rediscovery of the method 3. The latest developments

II ·ZONE CONCENTRATIONS AND ION MOBILITIES IN

ISO-T ACHOPHORESIS

1.

Introduction

2.

Theoretical model for isotachophoretically moving zones

2.1 The balance of electric current

2.2 The balance of mass

2.3

The electroneutral ity eguations

2.4

Equilibrium equations

3.

Application of the equations to some electrolyte systems

3.1 Divalent leading ion and monovalent terminating ion

3.2

Polyvalent electrolyte systems

11 11

13

14

14

16

21

23

23

24

25

28

30

31

31

32

34

4.

Limitations of the theoretical model

34

4.1

The influence of diffusion on the zone boundaries 34

4.2

The influence of ion-ion interaction

38

4.3

Constant current density

40

4.4

Electroendosmotic flow

40

4.5

Hydrostatic flow

41

4.6

The influence of the radial temperature gradient on the

shape of the zone boundary

41

Ill CALCULATIONS AND MEASUREMENTS OF

ISOTACHO-PHORETIC ELECTROLYTE SYSTEMS

44

1. Introduction 44

2.

pH and temperature in a capillary column

45

2.1

Experimental

46

2.2

The shape of the terminator concentration boundary

47

2.3

Results

49

2.4

Temperature measurements on the capillary tube

51

3.

pH measurements in a sucrose gradient 55

3.1

Apparatus

55

3.2

The validity of the theoretical model in a sucrose density

gradient

56

3.3

Results

58

4.

Measurements of pH and conductivity in a polyethylene tube

61

4.1

Apparatus

61

4.2

Results

₆₃

5.

pH measurements in polyacrylamide gels 66

5.1 Apparatus

66

5.2 Results

67

IV CONSIDERATIONS ON THE USE OF THE THEORETICAL MODEL FOR ISOTACHOPHORETICAL ELECTROLYTE

SYs-TEMS 71

1. Introduction 71

2. Selection of electrolyte systems 71

3. Some disturbing phenomena 76

3.1 Disturbance of the boundaries by highly mobile ions 76 3.2 Interrupted pH gradient

3.3 Precipitation during the separation 3.4 Decreasing voltage gradient

V ISOTACHOPHORESIS, A METHOD FOR PROTEIN SEPARA-TION

78

79 80

84 1. Electrophoretic methods in protein chemistry 84 2 lsotachophoresis, an additional electrophoretic method for

protein separation 85

2.1 Classification of isotachophoresis among the

electro-phoretic methods 85

2.2 Comparison of isotachophoresis with other high resolv-ing. electrophoretic methods

3. Application of the theoretical model to electrolyte systems for the analysis of proteins

3.1 Leading and terminating electrolyte systems 3.2 Ampholyte mixtures as spacer ions

VI SOME SEPARATIONS OF HEMOGLOBINS AND HUMAN SE-RUM BY ISOTACHOPHORESIS 1. Introduction

86

89

89

90 93

93

9

2 The use of carrier ampholytes and stabilising media for the

isotachophoretic analysis of proteins 94

2.1 UV-detection in capillary tubes 94

2.2 Carrier ampholytes as spacer ions 97

2.3 Stabilisation of the protein zones 100

3. The separation and identification of human serum proteins in

6 mm polyacrylamide gels 105

3.1 Materials and methods 105

3.2 Tris acetate as leading electrolyte ₁₀₇

4. The choice of the electrolyte systems for human serum

separations 111

4.1 Theoretical calculations on the electrolyte conditions 111 4.2 Cacodylic acid as leading ion for preparative protein

separations 115

5. Conclusion 120

APPENDIX 121

SYMBOLS, INDICES AND ABBREVIATIONS 127

REFERENCES 129

SUMMARY 133

SAMENVATTING 135

INTRODUCTION

Electrophoresis is a separation principle which continues to gain more and more importance in biochemistry and clinical chemistry. Although many principles of the high-resolution electrophoretic methods of the present time were dealt with at the beginning of the twentieth century, it was not until the sixties that these principles were rediscovered and became an answer to the urgent need for separation techniques within the biochemical field.

Electrophoresis is a term which, from the beginning, was used to describe the movement of charged colloidal particles in an electric field. Later, it was also used for ions. Although Martin and Synge (6) suggested the more feasible name ionophoresis for the migration of small ions, the term electrophoresis was retained, mainly for historical reasons.

One of the newest electrophoretic methods is called isotachophoresis. Workers in several laboratories developed the technique independently (see literature review).

1. PRINCIPLE

The principle of the isotachophoresis technique can be described as follows. Consider three zones, containing the negative ions A, 8 and C respectively (see fig. 1 ). P is the common positive counter-ion. The mobilities of A, 8 and C are in the order mA>m 8>mc. If an electric field is applied, the ions will separate and move in consecutive zones in immediate contact with each other. The velocities of all zones are then equal. The concentrations of 8 and C will adapt to the concentration of A in the first zone according to the Kohlrausch regulating function:

P+ P+ P+

+ - -

+---

+

-e

Zone- 3 Zonl!' 2 Zone 1

e

c-

s-

A---+

--+

--+

Fig. 1 The ions A-, B- and C- are migrating in separate zones. The mobility of

the ions decreases from A- to C- (mA>mB>mC)

c m (m +m )

A1 ₌ A1 B2 P2 (1)

c m (m + m ) B2 B2 A1 P1

cAl concentration of A in zone 1 molcm-3 CB2 concentration of B in zone 2 molcm- 3 mAl mobility of A in zone 1 cm2v-1sec-1 mB2 mobility of B in zone 2 cm2v- 1sec-1 mp1 mobility of P in zone 1 am2v- 1 sec - l

The first zone, containing ions with the highest mobility, is called the leading-ion zone or leading electrolyte (fig. 2). The ions with the lowest mobility migrate as the terminating electrolyte, or terminator. All ions with intermediate mobilities will move, in the order of their mobilities, between the leading-ion zone and the terminating electrolyte.

One of the most important properties of the method is the self-restoring power of the zone boundaries. Convection and diffusion effects, which tend to destroy the sharp separation of the zones, are counteracted by the difference in voltage drop between the zones.

8

terminating ion or 111 C-terminating electrolyte buffer ion p+ sample ions leading ion A-or

- - +

leading electrolyte

Fig. 2 The electrolyte containing the ions with the highest mobility is the leading electrolyte. The ions with the lowest mobility are called terminating ions.

-

-

+

The separation of the sernple proceeds between the A and C zone. P is the counter-ion.

2. SCOPE OF THIS MONOGRAPH

Until now isotachophoresis has been applied mainly to the separation of small ions, e.g. metals, inorganic and organic acids. In this work a set of equations is developed to calculate the electrolyte conditions for such separations. Calculations of the electrolyte parameters based on this theoretical model are checked experimentally. The equations are also used to discuss some phenomena which can disturb the isotachophoretic migration.

It is shown that the electrolyte conditions for the separation of proteins can also be computed. A comparison is made between the existing high-resolution electrophoretic methods and isotachophoresis, with respect to protein separation. The use of ampholytes as »Spacers>> for protein mixtures is discussed. Finally separations of proteins in capillary tubes, in 6 mm polyacrylamide gels, and on a preparative scale are dealt with.

Chapter I

LITERATURE REVIEW

1. THE EARLY PERIOD

Experiments by Lodge (1) and Whetham (2, 3) were the basis on which Kohlrausch (4) developed his theory for ionic displacement Kohlrausch stated that when two ion zones, separated by a sharp boundary, move in an electric field, the velocities of these two zones should be identical.

velocity of A in zone 1

velocity of 8 in zone 2

em

sec-

1

cmsec-1

(1.1)

Such a sharp boundary can only exist when the mobility of the ion species in zone 2 is smaller than the mobility of the ion species in zone 1. From equation (1.1) it is easy to derive the Kohlrausch regulating function or, as he called it, the »beharrlige funktion»:

c A1 m A1 -=--~-_{c m +m} 82 A1 P1 m +m 82 P2 (1.2) m 82

It took until 1923 before the principle of the Kohlrausch moving boundaries was applied for the first time, by Kendall (7). He succeeded in the separation of the rare earth metals and some simple acids by, as he called it, the ion migration method (7, 9). He stated that the ions not only separate but also adapt their concentrations to the concentration of the first ion zone,

according to the Kohlrausch regulating function. Kendall also attempted to separate Cl35 and

ct

37 with a mobility difference of 1. 7%, as shown by

Lindemann (8). However, Kendall could not detect any separation of these two ions, even after very long runs. The fact that other isotopes could not be separated, either, was very disappointing for him. He concluded that the Lindemann theory was invalid. (He showed, however, (10, 11) that it was possible to isolate the radiactive radium from a barium residue of carnotite). Kendall (10) considered it necessary to be able to follow the separation in a convenient way. Therefore he suggested the use of a coloured ion which had a mobility intermediate to the ions of interest. A concentrated coloured band would then automatically indicate the end of the experiment. Other detection methods he mentioned were temperature and conductivity meas-urements in the zones. He pointed out that, when analysing metals, spectroscopic detection was very easily achieved. Finally, in those cases where radioactive materials were to be analysed, measurement of radioactivities supplied the necessary information.

The moving boundary method which Macinnes and Longsworth (12) used to determine transference numbers in 1932, was based on the Kohlrausch moving boundary theory. In specially designed electrophoresis apparatus, they ran the ion species of interest as a leading ion. The velocity of the zone boundary between this ion and an arbitrarily chosen terminating ion was measured. The voltage was supplied by a constant current source. The following equation enabled them to calculate the transference number of the leading ion: t T A1 v c F A1 A1 it

transference number of A in zone 1 volume the zone boundary passed

Faradays constant current density time

(1.3)

Furthermore, they considered the influence of convection and diffusion on the boundary sharpness and found it to be very small. They measured transference numbers of K+, Na +, Ag +, H+ and u+ at several concentra-tions and found their results in excellent agreement with the Debye-Huckei-Onsager theory.

Surprisingly enough, Kendalls work was forgotten for a few decades. During this period other types of electrophoretic methods were developed. Tiselius (14, 15) published his work on the separation with the free boundary method in 1925. Today, the free-boundary method is used mainly for the determination of mobilities and isoelectric points of purified proteins.

2. THE REDISCOVERY OF THE METHOD

Already in their paper on ionophoresis in 1946, Consden, Gordon and Martin ( 16) pointed out that the separation based on mobilities, such as Kendall had performed, was a field with many possibilities that had not, up to that time, been explored. In the same year, Martin (17) separated chloride, acetate, aspartate and glutamate by this method.

Longsworth (13) realized the importance of Kendall's work and continued it in 1953. He avoided using agar gel, because no optical detection method could be applied. In a Tiselius boundary apparatus, he introduced a mixture of metal ions, Ca, Ba, Mg between two ion zones, called the leading solution (CsCI) and the trailing solution (LiCI). The mobilities of the metal ions decreased when going from the leading to the trailing solution. Schlieren scanning patterns showed very clearly the sharpness of the boundaries between the zones. Because the migration distance in the Tiselius apparatus is quite short, Longsworth introduced a counterflow of leading solution. The counterflow was adjusted in such a way that the zones stayed in the detection region until the separation was complete. Longsworth also showed that when all components are separated a steady state is reached on passage of a constant current. When separating acids, and especially amino acids, he

stressed the importance of the pH in the trailing solution. Hydroxyl ions can destroy the steady state situation because of their high mobility.

Poulik (1957) (18) was not aware that he was working with systems which were regulated by Kohlrausch's function. He used, as he called it, a »a discontinuous buffer system» of borate and citrate and found improved resolution of his protein separations.

Kaimakov and Fiks (19) reported in 1961 the use of a separation chamber filled with quartz sand to eliminate convection problems. They filled the cell with »indicator electrolyte» with a higher mobility than their test solutions, which they introduced on top of the electrolyte. By using counterflow they obtained the steady state concentrations according to Kohlrausch's law. In this way the transport number and the mobility of H+ were determined as a function of its concentration. Transport numbers of lithium·chloride and copper(ll)chloride were measured by Kaimakov (20), and Konstantinov and Kaimakov (21), respectively, in 1962. In their paper on »The use of the Kohlrausch relation for the determination of transport numbers in highly concentrated electrolyte solutions», Konstantinov, Kaimakov and Vashav·

skaya (22) extended the measurements of transport numbers made by

Hartley {23) and Gordon and Kay (24) in dilute solutions {<0.1 N), to very concentrated solutions. They determined the transport numbers, using the Kohlrausch equation:

cA1 _ TA1

-CB2 TB2 (1.4)

The transport number T 82 was easy to calculate when using a leading electrolyte of known concentration and transport number and determining the c82 by conductivity measurements after the steady state was reached. In principally the same apparatus as that used by Kaimakov and Fiks (19), they measured transport numbers of Cu2+ and Cd2+. The same authors (25) published measurements of transport numbers in solutions of copper (II)

chloride, cobalt chloride, zinc and cadmiumchloride.

Konstantinov and Oshurkova (26) published in 1963 an analytical application of the moving boundary method. Their separation chamber was a capillary tube with an inner diameter of 0.1 mm and a wall thickness of 0.05 mm. The basis for the choice of these dimensions was calculations of the diffusion coefficient and the temperature distribution over the cross section of the tube. They separated 1

o-

7 to 10-8 g of material. Measurements of the refractive indices of the ion zones by photographic methods gave a registration of the zone boundaries.

In 1964 Kaimakov and Sharkov (27) reported the use of microthermistors to detect zone boundaries.

In the same year Konstantinov and Fiks (28, 29, 30) published a work on the separation of isotopes by »Countercurrent electromigration», in fact the same method they had published in 1961 (19). They derived some differential equations describing the separation process and proved that even if a system had not yet reached Kohlrausch's steady state, it could yield enrichment of certain isotopes. They performed their experiments in a column filled with silica sand. The first isotope of interest was that of lithium (30). Later, Troshin (31), Fiks (32), Konstantinov and Bakulin (32), Konstantinov, Kaimakov and Bosargin (34), measured, respectively, the mobility differences between isotopes of potassium, rubidium, chloride, and uranyl ions.

In 1966 Konstantinov and Oshurkova (35) repeated their 1963 paper on capillary tube separation. This time they gave a more extended derivation of the equations for the influence of diffusion, of convection caused by temperature differences between the zones and of counterflow on the zone boundary sharpness. One year later they published a paper (36) on the separation of amino acids in a capillary tube, according to the moving boundary principle. They claimed the separation of the amino acids as positive ions, using H+ as leading ion, and the separation of the amino acids as negative ions, using OH- as leading ion. They worked with very high ion-concentrations (5N leading ion). It is therefore highly questionable whether their electrolyte systems were still obeying the Kohlrausch regulating function.

In their articles on »ion focusing», Schumacher and Friedli (37) emphasized the need of a pH gradient for their experiments. In 1964 Schumacher and Studer (39) considered therefore the natural pH gradient according to Svensson (38). They rejected his method because it did not supply them with the optimal pH distribution. Instead, they proposed to use the Kohlrausch regulating function for the creation of a pH gradient. Naturally, the pH will adapt, in the same way as the other concentrations, to the electrolyte conditions in the leading ion zone. When running a mixture of weak acids, they obtained a pH gradient from 1.6 to 3.2. They also showed that the separation method was useful for quantitative work on weak acids.

Ornstein and Davis (40, 41) introduced their l>disc electrophoresis» in 1964. In fact they were the first ones to apply the Kohlrausch regulating function to the separation of proteins. They placed a protein mixture between a terminating ion (glycine) and a leading ion (chloride). Although the proteins were separated according to their mobilities, it was impossible to detect them, because their zones were extremely narrow. Therefore, in the second stage of the procedure zone electrophoresis was used, which allowed every protein to move at a different velocity. Polyacrylamide gel was used as stabilizing medium, acting at the same time as a molecular sieve. In this way the mobilities of proteins could be controlled by varying the pore size in the gel. Ornstein (40) derived several equations with which it was possible to calculate the mobilitie!: and pH values of the electrolyte systems he needed in his experiments. Today, the disc electrophoresis method is among the most important electrophoretic methods, because of its simplicity, high resolution and short separation time.

In 1966 Vestermark (42) introduced an electrophoretic method called »eons electrophoresiS», still another name for Kendall's l>ion migration method». Vestermark described »electrophoretic experiments resulting in the arrange-ment of compounds in consecutive zones». The separation experiarrange-ments were made on thin-layer strips. He showed that the adaptation of all concentra-tions to that of the leading ion, could be extremely useful for the concentration of dilute samples. His most important contribution to this type 19

of electrophoresis was his »Spacer» technique. Kendall (10) had already stated that it would be most convenient to have a coloured material with a mobility such that it would migrate between two ions of interest. Vestermark used such materials, mainly amino acids, to »Space» proteins in human sera and the components of red-beet juice.

Later, Westermark (43) described the separation of red-beet juice which had been incubated with 35

s

sulfate, using auto-radiography as the detection method. Vestermark and Wiedemann (44) used methylamine as a spacer for the separation of sodium and potassium isotopes. -y-counting and densito-meter tracings of autoradiographs gave the necessary information about the quality of the separation. Eriksson (45) separated insect hemolymph components on cellulose strips. In 1969 Westermark et al. (46) showed the application of the technique to the analysis of Hg2

+

_{and CH 3Hg}

+.

In his papers on »Counterflow ionophoresis» (Gegenstromionophorese), in 1966, Preetz (47) gave a theoretical treatment of counterflow in isotacho-phoresis. In a second article, Preetz and Pfeifer (48) described an apparatus specially designed for measurements of potential gradient and ion concentra-tion. Preetz also performed experiments in capillary tubes. A further development (49) of counterflow ionophoresis is continuous counterflow electrophoresis. Between two glass plates a flow of electrolyte is applied, perpendicular to the ion migration direction.

In 1966 Everaerts (50), not aware of Preetz and Konstantinov's work, discussed »displacement electrophoresis» in capillary tubes. Mixtures of strong acids were separated. A thermocouple was used as a detector. Together with Martin (51) he showed the separation of chloride, nitrate, oxalate, acetate and hydrocarbonate. The thermocouple detection gave two types of information:

1) qualitative: each zone having its own specific resistance and therefore its own temperature;

2) quantitative: the length of the »temperature steps» were an indication of the quantity of an ion species in a sample.

the influences of diffusion, electroendosmosis and pH on the separation. They showed analyses of mixtures of weak acids, metals and some fruit juices. They also considered the use of non-aqueous solvents for isotacho-phoresis.

Hello (54) described the moving boundary analysis in 1968 and used it for the separation of H+ and Li+.

Frederikson (55) showed that conductometric measurement, by using platinum electrodes inserted in the electrophoresis tube, gave very high resolution of the zone boundaries.

3. THE LATEST DEVELOPMENTS

In 1970 Everaerts et al. (56) applied counterflow in capillary tubes by creating a difference in the electrolyte level in the electrode compartments. The level difference was regulated by a plunger in a reservoir connected to the leading electrolyte compartment. This plunger was operated by the signal of a thermocouple mounted on the wall of the tube. The advantage of using such a regulated counterflow was that ions with small mobility differences could also be separated, because the effective separation length was increased.

In his review article in April 1970, Haglund (57) listed all the names used for the described technique. Most of the names were either too general or were wrong in principal. Therefore the name isotachophoresis was introduced. The Kohlrausch principle of equal (iso) velocities (tacho) of the zones is the central theory of the method.

Svendsen and Rose (58) introduced preparative isotachophoresis in polyacryl-amide gels. They separated human blood proteins in a pH gradient formed by

carrier ampholytes (»ampholine»), which are used in isoelectric focusing. These ampholytes acted as spacers for different protein mixtures. They found that much higher sample amounts could be applied compared to other electrophoretic techniques.

Arlinger and Routs (60) reported the use of a UV photometer as a detector in 21

capillary isotachophoresis. They proved in this way that the boundary width, which Konstantinov (35) ~nd Everaerts (52) estimated to be very small, was less than 1 mm. They also demonstrated the separation of proteins (hemo-globin and ceruloplasmin) using ampholine as spacers.

Vestermark (61) measured pH differences between leading and terminating ions for univalent electrolyte systems. He performed his experiments in a sucrose gradient.

Everaerts and Verheggen (62, 63) presented new constructions of their capillary apparatus. They replaced the original straight capillary tube with a helical tube. The terminator compartment was constructed in such a way that samples could be applied by a microsyringe. In the other compartment (the leading electrolyte compartment) the electrode was separated from the capillary by a cellulose-acetate membrane, to avoid hydrostatic flow. Analysis of weak acid mixtures showed a reproducibility of 0.5% in this new apparatus.

Beckers and Everaerts (64) reported the separation of metal and acid ions in methanol. They showed that metal ions, especially, were easier to separate in this solvent. Furthermore, they proved that in methanol, hydroxyl ions migrated in a separate zone between nitrate and formate. Preetz and Pfeifer (67) also, did experiments with non-aqueous solvents. They separated osmium chloride and osmium bromide in liquid ammonia. Furthermore, Blasius and Wentzel (66) demonstrated isotachophoresis in non aqueous solvents. They used a gel of 2.5% cellulose-acetate and 97.5% formamide.

Everaerts and van der Put (65) showed that it was possible to separate some amino acids in water-formaldehyde mixtures by isotachophoresis in capillary tubes. They investigated a number of counter-ions, which would be useful for this kind of separation. They found collidine to be the best one.

Postema and Brouwer (68) described the separation process in isotachophore-sis before the steady state is reached. They attempted to calculate the time required to reach this state.

Chapter II

ZONE CONCENTRATIONS AND ION MOBILITIES IN

ISO-TACHOPHORESIS

1. INTRODUCTION

In the introduction of this thesis it has already been pointed out that the mobilities of the sample ions have to be intermediate to those of the leading and terminating ions in order to obtain an isotachophoretic separation. Only then will all ion species move in separate zones, with the same speed.

For the separation of metals and strong acids and bases, the literature contains values of the mobilities, which will give direct information for the choice of the leading and terminating electrolyte systems.

When dealing with partially ionized material, the problem becomes more complex. It is the net mobility, rather than the mobility of the totally ionized molecules, which determines the isotachophoretic behaviour of weak ions. Consden, Gordon and Martin (16) defined the net mobility as the product of the mobility and the degree of ionisation.

Since the net mobility of an ion is pH-dependent, it is clear that it is determined by the ratio of its concentration and the concentration of the counter-ion. Both concentrations are adjusted to the leading electrolyte concentration. We can therefore conclude that the net mobility of an ion species and its place in the isotachophoretic separation are dependent on the electrolyte conditions in the leading ion zone.

Several authors (4, 40, 52, 53) derived equations to describe isotachophoreti· cally moving zones. In this chapter a more extended model will be developed to calculate the concentrations and mobilities of ions in isotachophoretic

systems. It contains an parameters involved in the establishment of the final pH and the net mobilities in the zones. This model should enable us to compute suitable electrolyte conditions for the separation of any kind of material.

2. THEORETICAL MODEL FOR ISOTACHOPHORETICALLY

MOV-ING ZONES

Because every ion zone adapts its concentration to the concentration in the leading ion zone, it is sufficient to consider only two zones. These two zones migrate in a steady state. The first zone fig.2.1) contains the negative ions A-, ... ,Aa- and the second one B-, ...

,stJ-.

The common positive counter-ions are p+, •.... ,P1r+. Furthermore the influence of the protons and hydroxyl ions is taken into account.

3 2 1 zone boundary

• 11'+ + + 1t+ +

P, •.•. P ,H P, .... P ,H

zone 2 zone 1

Fig. 2.1 lsotachophoretically migrating zones of the ions A •.•• ,AOI:- and B-,

p;..

.... ,B •

P

+ ....

,Pn+ is the buffering counter-ion.

The theoretical model, which correlates the concentrations in the second zone and those in the leading electrolyte, contains a number of equations based on the following conditions:

the balance uf electric current

the balance of mass

The concentration of the counter-ion within one zone is constant in the steady state. This means that the amount of P transported into a zone is equal to the amount that leaves the zone.

the electro-neutrality equation

The amounts of positive and negative charge are the same within one zone.

chemical equilibrium equations

The acid and base equilibrium constants determine the concentrations of dissociated and undissociated molecules.

From the derivation of the equations below it will become clear that the balances of current and mass are also applicable to systems with positively charged ions A and 8 and negatively charged ions P. The electro-neutrality and equilibrium equations are different for the cationic and anionic systems.

In the derivation of the following equations it is assumed that: 1) the diffusion effects are negligible,

2) the solutions are very dilute, i.e. the activity coefficients are equal to umty,

3) the area through which the current passes is constant, 4) tile effect of electroendosmosis is negligible,

5) no hydrostatic flow exists,

6) the zone boundaries are straight (there are no radial temperature differences).

A discussion on the feasibility of these assumptions is given in paragraph 4 of this chapter.

2. 1 The balance of electric current

The specific electric conductivity in zone 1 (fig. 3) is:

(2.1)

x,

specific conductivity in zone 1

n-

1cm- 1 c0H1 concentration of OH- in zone 1 grion cm-3 CAli concentration of ion A in zone 1

with charge i grion cm-3

mH1 mobility of H+in zone 1 cm2

v-

1

sec-

1 mAli mobility of ion A in zone 1 with charge i cm2

v-

1

sec-

1

z charge

F charge of one mol Cmol-1

a,{3,1t highest ionisation degree for ions A, B and P

For zone 2 we find

A2

=

F(cOH2mOH2+ cH2mH2+

i::

ic .m .+

~

ic .m ) (2.2)

i=O 821 821 i=O P21 P21

As the current is the same in zones 1 and 2, and the voltage gradient is higher in zone 2, the development of Joule heat will also be higher, which means an increase in temperature. This implies that the mobility values in every zone have to be corrected for the temperature in that zone. This is discussed in the next chapter.

Ohms law gives

current density in zone 1 voltage gradient in zone 1

(2.3)

The balance of current is

Combination of (2.3), (2.4} and (2.5} gives

Insertion of (2.1) and (2.2) in (2.6) results in

G2 cOH1mOH1+cH1mH1+

~

ic .m .+

~

ic .mPI't

i=O Ah All i=O Ph

-

---c m +c m +

~

ic m +

~

ic m

OH2 OH2 H2 H2 i=O B2i B2i i=O P2i P2i

(2.5)

(2.6)

(2.7)

According to the principle of isotachophoresis the velocities of zone 1 and 2 are equal;

uA1 = u82

u velocity of the zones em

sec-

1

Furthermore uA

1 = G1mA1

mA ₁ is the net mobility of the compound A. It is defined as:

or (2.8)

(2.9)

(2.10) (2.11) 'Z1

total concentration of A Insertion of (2.11) in (2.9) results in c* AI (I{ :E c m

i=O Ali Ali

Combination of (2.8) and (2. 12) gives

G 1

£

m c G 2

~

m .c .

i=O A1i Ali= i=O 821 821

c* c*

A1 82

Substitution of (2.13) in (2. 7) results in:

(2.12) (2.13) c* A1 0: .I: mAI.cA1" I=O I I c m

+

c m

+

4

ic .m . +

£

ic m OH2 OH2 H2 H2 i=O B21 B2• i=O P2i P2i

0: 1T

c*

82 cOH1mOH1

+

cH1mH1

+

i~Jc

A1imA1i+

i~O

icP1imP1i

(2.14) This is an extended form of the Kohlrausch regulating function.

2.2 The balance of mass

The boundary between zone 1 and 2 moved with the speed u A _1. The amount of counter-ion which is transported into zone 2 due to this movement is uA ₁cp_1· In the opposite direction there is a migration of P ions which is equal to up1cp1.

The total mass transport of P through boundary 2 is therefore:

Q u c*

+

u c* P1 Al Pl P1 P1 In the same way as uAl and u

82, up1 is defined as:

G1 11'

-~

cP1'mP1' c* 1=0 1 1

P1

Insertion of (2.16) in (2.15) results in:

Q

P1

*

11'

= u c +G ~ m c

Al

P1

1 i=O P1i P1i

It!! the same way

we

find for the transport of P through boundary 3:

11'

Q u c* +G ~ m c P2

=

82 P2 2 i=O P2i P2i

(2.15)

(2.16)

(2.17)

(2.18)

In the steady state (uA1

=

u82) equal amounts of Pare transported through boundaries 2 and 3:

11'

u c*

+

G ~ m c A1 P1 1 i=O P1i Pli

11'

= u c*

+

G ~ m c

82 P2 2 i=O P2i P2i (2.19)

Substitution of (2.8) and transformation of (2.19) results in:

*

*

G 11' G 11'

c -c =- 1 ~ m c

+

2 ~ m c P1 P2

₀

i=O P1i Pli

u

i=O P2i P2i

A1 A1

(2.20)

Insertion of (2.12) and (2.13) in (2.20) gives: 1( ~ m c c* -c* =-c* i=O P1iP1i+ P1 P2 A1

ex

~ m c

i=O A1i Ali

23 The electro-neutrality equations

The balance of charge for zone 1 is: c*

82

1r

~ m c

i=O P2i P2i

~

m c

i=O B2i B2i

ex

n

c z F+~ c z F=c z F+~ c

z

F OH1 OH1 i=O A1i Ali H1 Hl i=O P1i P1i or

a n

c + ~ ic = c + ~ ic OH1 i=O Ali H1 i=O P1i The balance of charge for zone 2 is:

c + £ ic = c +

~

ic OH2 i=O B2i H2 i=O P2i

(2.21)

(2.22)

(2.23)

(2.24)

The equations (2.23) and (2.24) will be different if we turn to a system of positive ions A and B and negative ion P:

tr

a

c +~ic =c +~ic

OH1 i=O P1i H1 i=O A1i

(2.25)

c

+~ic

=c + £ i c

24 Equilibrium equations

The following equations for A, Band Pare valid:

c i c _ A10 . IT k A1i- (c )i i=1 A 1i H1 c _i c = 820 .II k B2i _(c H2 )i j=1 B2j c (c )i c = P10 H1 P1i i II k j=1 P2j c (c )i c = P20 H2 P2i i II k j=1 P2j (2.27) (2.28) (2.29) (2.30)

For the reverse system with A and B as positive ions, the equilibrium equations for A and B are of the type (2.29) and (2.30).

3. APPLICATION OF THE EQUATIONS TO SOME ELECTROLYTE

SYSTEMS

An application of the equations to a system with a divalent leading ion and a monovalent terminator is given. Such an electrolyte system is very useful when a buffering leading ion with high mobility is required.

Secondly, some remarks are made concerning the application of the model for polyvalent ion systems in general.

3. 1 Divalent leading ion and monovalent terminating ion

Consider a system with a divalent, negatively charged leading ion and a monovalent terminator. The buffering counter- ion is also monovalent. As a first approximation the influence of protons and hydroxyl ions is neglected. Equation (2.14) will result in:

c* m c + m c m c

+

m c

A1 A11 A11 A12 A12 821 821 P21 P21

c*

82 m 821 821 c m A11 A11 c + 2m A12 A12 c + m P11 P11 c (2.31) Application of the electroneutrality principle gives:

c +2c =c (2.32)

A11 A12 P11

c = c

821 P21 (2.33)

Combination of (2.31), (2.32) and (2.33) gives

c* m

+

m m c

+

m c

A1 821 P21 A11 A11 A12 A12

c*

82 m 821 (m A11 + m P11 ) c A11 + 2 (m A12 + m P11 ) c A12 (2.34)

Insertion of the equations (2.32) and (2.33) in the equation for the mass balance (2.21) results in:

m (c + 2c )

c* -c* =-c* P11 A11 A12

P1 P2 A 1 m c + m c

A11 A11 A12 A12

m

+ c* P21

82 m 821

The equilibrium equations are (c* -c -c

I

A1 A11 A12 k c H1 ' A1 (c* -c -c ) A1 A11 A12 2 (c

I

H1

(c* 82- c821) c -

k

821- c . 81

H2

(c* - c

I

c

P1

P11

. c

P11

= k

H1

P1

{c* -c

P21l

c P2 . c

P21

= k

H2

P2

k A1 k A2 (2.36) (2.371 (2.381 (2.39) (2.40)

If two of the nine parameters in the seven equations (2.34)-(2.40) are known, the other seven can be calculated. Thus if the pH and the concentration of the leading ion are chosen, all other ion concentrations including the pH in the terminating electrolyte are fixed. Consequently we are able to calculate the net mobility of the terminating ion from the equation (2.11):

c

m

-~.m

(2.41)

82-

c*

821 82

3.2 Polyvalent electrolyte systems

The application of the theoretical model to systems of polyvalent ions yields nonlinear sets of equations, especially when proton and hydroxyl ion influences are included. The use of a computer is necessary to obtain all roots. With increasing nonlinearity the equations will have a rising number of roots which are physically incorrect solutions for the system considered. The correct solution is obtained by rejecting all roots containing negative, imaginary and obviously unrealistic concentrations. In more complicated electrolyte systems it is possible that two realistic roots will be obtained. In this case the right solution can be found experimentally.

4. LIMITATIONS OF THE THEORETICAL MODEL

In paragraph 2 of this chapter a number of assumptions were made for the derivations of the equation system. We will now discuss the influence of all these points on the model.

4. 1 The influence of diffusion on the zone boundaries

The sharpness of the zone boundaries in isotachophoresis is counteracted by diffusion in the direction opposite to the migration of the zones. Therefore the boundaries will have a certain width, within which the ion concentrations vary from their zone concentrations to zero. The equations in paragraph 2 will be valid when the width of the zone boundary is very small compared to the zone length.

We will now derive an equation which will enable us to calculate the boundary width.

The mass flux of a fully ionized compound A (fig.2.2) with a mobility mA and a charge zA through a certain cross section within the boundary region is given by the Nernst·Pianck flux equation:

mA dp.A

J _ - , c (z FG

+

- l

A - -

z

F A A dx (2.42)

A

mass flux of compound A chemical potential of A

zone I

zone 2

..

X

Fig.2.2 Diffusion pattern at the boundary between the isotachophoretically migrating zones of the ions A and B.

The two terms in equation (2.42) represent the mass transport by migration and diffusion respectively.

Neglecting the activity coefficient we can write for p.A

(2.43)

*All indices refer to the parameter values in the boundary region.

Insertion of (2.43) in (2.42) results in:

J

= -

m A . c (z FG

+

RTdlncA)

A z F A A dx

(2.44) A

The distribution of A in the boundary region moves with a constant speed uA at the steady state. Therefore we can state that

J

=

u c A AA Insertion of (2.45) in (2.44) gives u A m dine

+

...A

RT ____.8.

+

m G z F dx A A 0

For compound B in this zone boundary we can write

u B m dine

+

__!! RT - -8

+

m G

=

0 z F dx B B (2.45) (2.46) (2.47)

Transformation and subtraction of the equations (2.46) and (2.47) gives z-1

CA

-din A z-1 c

B

B uF 1 1

= - -

( - - - ) d x RT m m (2.48)

A

B

If the temperature change between the zones is small, we can integrate equation (2.48):

-1

z

CA

_A_ z-1 c 8 8 uF RT ( = k.e m -m A 8 m m )x A 8 z-1 z-1 If the origin of the coordinate system is chosen at c A c A the integration constant k will be equal to unity. A 8

(2.49)

The equation (2.49) is comparable to those which Longsworth (12), Konstantinov (35) and Everaerts (51) derived for the boundary width. As a numerical example (2.49) gives x==1.15 mm for a potential gradient of 100 Volts per centimeter, and mobility values of A and 8 equal to 40.4.10-5 cm2

v-

1sec-1 and 40.10-5 cm2

v-

1sec-1 respectively. This value is even

decreased when the mobility difference is bigger and when multivalent ions are considered.

It is clear from {2.49) that disturbance of the boundary by diffusion is directly counteracted by the potential gradient. An increase in the potential gradient by a factor of 2 means a decrease of the boundary width by the same factor. On the other hand very high tensions will cause big temperature differences between the zones, which increase convection.

For weak electrolytes, it is more difficult to integrate the equation (2.49), because the mobility values are then depending on x. This can be explained

by the fact that between weak electrolyte zones there usually exists a pH difference as a result of the difference in pK values {this will be shown in the next chapter). In negative ion systems the pH is usually rising from the leading electrolyte to the terminator. Consequently the ions A will obtain a higher net mobility after diffusion into the second zone. Therefore the zone boundaries between weak electrolytes may be sharper than their difference in mobility indicates.

4.2 The influence of ion·ion interaction

In equation (2.1) the conductivity of zone 1 is given as a function of concentration, charge and mobility of the ionic constituents of that zone. The specific conductivity is, however, not a linear function of the concentrations when non·ideal solutions are considered.

The ionic cloud around a migrating ion is egg shaped. Due to this fact the center of charge of the ionic cloud is not the same as the center of charge of the migrating ion (central ion). This causes an electric force on the central ion, in the opposite direction to the force of the external electric field. The electric force due to the shape of the ionic cloud consists of two components:

1. relaxation force: the dislocation of the two charge centers causes an electric field opposite to the external field.

2. electrophoretic force: the center of charge of the ionic cloud tends to

migrate in the direction opposite to the central ion.

The Onsager equation (72) describes the influence of these effects on the ion mobility. For the leading ion we can write:

m = m0 - (A+ Bm0 )c 1/2

A1i A1i Ali Ali

For water at 25°C, A and 8 are given by the following equations:

Where z +z Ali P1i z z q 8

=

0•783 A1i P1i 1/2 1+q z z A1i P1i q =

z

+

z

Ali P1i 2

z

+

z

A1i P1i 2 z m0

+

z m0

P1i Ali Ali P1i

(2.50)

(2.51)

(2.52)

Very accurate correction of the mobility values is not required, because the literature data on the mobilities are quite unreliable. Different references give values varying by up to 3%.

The influence of the concentration dependency of the mobility on the final outcome of the equations is partly eliminated, because the nominator, as well

as

the denominator, in the equations (2.14) and (2.21) should be corrected. In the equilibrium equations (2.27-2.30) the activity coefficients are not taken into account. The Debye-Huckel limiting law may be useful for the calculation of the influence of these coefficients on the theoretical model:

. 2 1/2

log f = Az I (2.54)

Ali A1i

f activity coefficient for the ion A in zone 1 with charge i

Ali

A

constant

ionic strength of the solution

For an equilibrium of a univalent acid A- +

H+~

AH the equilibrium

constant is given by (721: f f

c}

K= A11 H1 1-a

*

. c A1 (2.55) ionisation degree

T,he ionisation degree depends on the electrolyte concentration, according to the following equation, which is a combination of Arrhenius and Onsager's law:

A

(2.56)

a -

---rno:--A

-(A+

BA )

(c* )

l/2

o

o

A1 39

equivalent conductance of the electrolyte

n-1

cm2 equivalent conductance of the electrolyte

at infinite dilution

The Onsager correction of the Arrhenius law on the dissociation constant. and the Debye-Huckel activity coefficients, balance each other to a certain extent. For acetic acid, a deviation of 2% from the pK value at infinite dilution was measured for an acid concentration of 0.0035 M. The variation in the pK data in literature can be far more than 2%.

4.3 Constant current density

A constant current density is easily maintained by running experiments in tubes or layers with a constant cross section area.

4.4 Electroendosmotic flow

The influence of electroendosmosis on an electrophoretic separation is already described by many authors. The velocity of the electroendosmotic flow u

0 (neglecting the flow profile in the electric double layer) is given by the Helmholtz equation (69).

u = GO

0 _41T11t (2.57)

D dielectric constant of the bulk liquid A sec

v-

1cm-1

~ zeta potential

v

'11 viscosity of the bulk liquid gcm- 1sec-1

influence of electroendosmotic flow. Everaerts (52) increased the viscosity of the bulk liquid by adding a polymer. Hjerten (70) introduced a counterflow of electrolyte to compensate this flow. He also treated the walls of his quartz tubes with methylcellulose to decrease the zeta potential, which can also be decreased by using various forms of electrostatically inactive plastics, instead of glass and quartz.

4.5 Hydrostatic flow

A hydrostatic flow can be used to increase the effective length of the separation tube (see lit. review) or to compensate the electroendosmotic flow as indicated above. One must, however, be aware of the fact that the parabolic profile of a hydrostatic flow can destroy the theoretically straight zone boundaries.

4.6 The influence of the radial temperature gradient on the shape of the

zone boundary

During any electrophoretic experiment there exists a radial temperature gradient in the tube. Since the mobility is dependent on the temperature, the velocity of the ions in the tube

center

will be different from their velocity closer to the wall. Hjerten (70) derived an equation for the velocity in the tube:

velocity of the ions at a distance r from the center of the tube

velocity of the ions at the tube wall constant, equal to 2400 °K

em sec- 1 (2.58)

temperature in a zone at a distance r from the center of the tube

temperature of a zone at the tube wall temperature of the cooling liquid

Hjerten also proved that this difference in mobility causes a parabolic shape of the zone boundary. He derived the following expression:

R 'A K r

2 2 2

Bi (R -r ) 2 4 2 4'A1T

R

KT₀

radius of the tube electric conductivity

thermal conductivity of a zone current (2.59) em

s:r

1cm- 1 J _sec -1 _em -1 oK-1 A

radial distance from the center of the tube em

If the current, the wall temperature and the thermal conductivity (variation 0.2% per centigrade) are equal in every zone, it is clear that the curvature of the zone boundaries is merely dependent on the electrical conductivity. This conductivity decreases from the leading electrolyte to the terminator. The

Fig. 2.3

leading electro(!)

e-

A-migration direction

The influence of the radial temperature gradient on the shape of the zone boundary. The ions D-, E- and F- have low mobilities compared to A-,

boundaries of the zones near the terminator will therefore be more curved than the boundaries of the high conductive zones (fig. 2.3).

Since the parapolic shape can only to a low degree be surpressed by low temperature cooling, the only way to straighten the fronts is to reduce the field strength. The use of a counterflow to restore the boundaries of the terminating zones includes the danger of destroying the straight fronts of the · leading ion zones.

Chapter Ill

CALCULATIONS AND MEASUREMENTS OF ISOTACHO-PHORETIC ELECTROLYTE SYSTEMS

1. INTRODUCTION

In order to check the validity of the theoretical model derived in the preceding chapter, the results of calculations based on this model will be compared to values of the pH and/or conductivity, experimentally found in four different kinds of apparatus.

For the theoretical calculations the computer program »lsogenl was used, which contained the equations derived in paragraph 2 of chapter 2. In this program no corrections were made for the temperature and concentration influence on the mobility. In case theoretically exact results are required, e.g. for mobility measurements, all corrections should be taken into account. An estimation of the magnitude of the influence of concentration and tempera-ture on the mobility values (and thus on the theoretical model) is given in paragraph 6 of this chapter.

The experimental measurements were made in different types of equipment in order to exclude any incidental influence on the separation by the shape of the column, and to study the validity of the equations in several types of stabilizing media:

1. a PTFE capillary tube with an inner diameter of 0.45 mm.

2. a glass column with a cross section at area of 5 cm2. As a stabilizing medium, a sucrose gradient was used.

3. a polyethylene tube with an inner diameter of 1 mm. *»lsogen» program is listed in the appendix.

4. glass tubes with inner diameter of 6 mm. Cross-linked polyacrylamide gel was used as supporting medium.

The diffusion at the boundary between the leading and terminating ion was decreased, either by applying high voltage gradients (apparatus 1 and 3) or by decreasing the diffusion coefficient using stabilising media (apparatus 2 and 4).

Electroendosmotic flow was counteracted by reducing the zeta potential at the wall by using electrostatically inactive plastic tubes (apparatus 1 and 3), or by increasing the viscosity of the electrolytes (apparatus 2 and 4).

Hydrostatic flow was avoided by blocking the separation chamber at one side (apparatus 1, 3, 4), or by levelling the liquids in the electrolyte chambers. The procedure for the experiments in all apparatus was the same. The separation chamber was filled with a leading electrolyte of known concentra-tion and pH. A terminator of a certain concentraconcentra-tion was brought in contact with the leading ion zone. During the experiment the terminator migrated into the separation chamber and replaced the leading electrolyte. After the leading electrolyte had left the separation chamber, the terminating ion zone

was

collected. The pH and/or conductivity was measured and compared with the theoretical values.

2. PH AND TEMPERATURE IN A CAPILLARY COLUMN

Several authors (26, 35, 48, 53) reported the use of capillary tubes for isotachophoretic experiments. Everaerts (52) and Routs (73) showed some separation of weak acids and attempted to give a quantitative interpretation of the results: In this kind of analysis it is necessary to know the pH-values of the zones, in order to be able to calculate the net charges and therefore the net mobilities of the acid ions.

2 1 Experimental

A capillary apparatus was constructed to measure the pH differences between the leading and terminating zones. This apparatus is depicted in Fig. 3.1. It consists of six parallel capillary tubes, which are coupled to specially constructed electrode vessels. The inner/outer diameters of the capillary tubes were 0.45/0.75 mm. The cathode compartment consisted of a plexiglass block (Fig. 3.1a), containing six reservoirs (2) for the terminating electrolyte.

Fig. 3.1 A 8 C D

I

I I

a} TOWARDS ANODE

) I

I

I

/,\\

A 8 C D

I I I I

TOWARDS CATHODE

The electrode compartment of the capillary apparatus.

b)

a Terminator block: 1. cathode. 2. reservoir for terminating electrolyte. 3. capillary

b Leading electrolyte block: 4. anode. 5. polyethylene tube. 6. membrane. 7. compartment for leading electrolyte 8. capillary

The anode compartment (Fig. 3.1bl was a reservoir for the leading electrolyte. To prevent hydrostatic flow and to diminish the influence of electroendosmotic flow a cellulose acetate membrane (6) was placed over the anode vessel. The membrane was stretched by an exactly fitting polyethylene tube (5).

A Baird-Atomic voltage supply, model 1512, delivered a constant voltage of 5 kV. A constant voltage meant, however, a decrease of the current when the terminator migrated into the capillary. Therefore the voltage drop per em in the leading ion zone decreased and as a consequence the zone velocity also decreased. This fact made it difficult to estimate how far the zone boundary had migrated in the capillary. In each experiment one of the terminator reservoirs was, therefore, filled with 0.02M picric acid. The yellow colour of this compound gave a visible indication of the zone boundary.

When the terminator had moved into the leading electrolyte vessel, the current was switched off and the liquid from two capillaries was collected and its pH measured. Then the pH of the content of the next two tubes, and

fin~.tiiY of all five tubes together, was determined. The results were averaged, together with those of a second identical experiment. The standard deviation was found to be less than 0.03 pH units. The pH in these experiments was measured by a digital pH meter (Philips).

22 The shape of the terminator concentration boundary

Approximately 5% of the capillary content at the terminator side was discarded bofore the pH-measurement was made. The reason was that the concentration boundary existing between the two »parts» of the terminator, the one in the electrolyte compartment and the one in the capillary, is neither sharp nor immobile. This in turn is due to three reasons:

a) During the filling procedure of the terminator compartment there will always occur some mixing with the leading electrolyte in the capillary. When the terminator reservoir was filled with a solution of dyestuff to estimate the magnitude of this effect, the leading electrolyte in the capillary mixed with the dyestuff over a distance of 3 to 7 mm.

b) Terminating ions will diffuse from the electrode compartment into the capillary during the experiment. This effect can be estimated with the

Einstein-Srnoluchowski equation:

2

<x > = 2Dt (3.1)

2

cm2 <x> mean square distance of diffusion

D diffusion coefficient cm2sec- 1

t time sec

Assume that the concentration of the terminator in the capillary is much smaller than in the reservoir. If Dis 10-5 cm2 sec- 1 and the analysis time is two hours,

<

x 2

>

is equal to 0.14 cm 2. The root-mean-square distance is 0.12cm.

c) Electrophoretic migration of the terminating ions will cause the concentration boundary to move, for which Macinnes and Longsworth (12) derived the following equation:

T' -T" I B B f

e=

.

-.

c' - c"

F

s

(3.2) 8 8

'a

the migration distance of the zone em boundary

T' B transport number of 8 in the cathode reservoir

T" _B transport number of B in the capillary

c' B concentration of Bin the cathode reservoir molcm- 3 c" _B concentration of B in the capillary mol cm- 3

f quantity of charge through the capillary

c

F Faraday's constant

c

s

cross-sectional area cm2

40. 10-5 cm2

v-

1sec-1 and 20. 10-5 cm2

v-

1

sec-

1, respectively, at

infinite dilution. If the concentrations of Band P in the terminator vessel are 0.01M and in the capillary 0.001M, Ti:J and Ts will be 0.685 and 0.672, respectively, in accordance with equation (2.50). An analysis time of two hours with a current of 100 pA will give a value of

le

equal to 0.07 mm. The boundary between the leading electrolyte and the terminator has, in the same time interval, covered a distance of 3.6 meters. It is clear that ₁₈ is negligible compared to the migration distance of th,e isotachophoretic front.

2.3 Results

In the first series of experiments a solution of 0.014M histidine and 0.01M HCI was used as a leading electrolyte. Eleven different weak acids were used as terminators. They are listed in Table 3.1 together with their pK and mobility values at infinite dilution;:.. (first six columns). The pH-values of the terminating zones were measured and compared to the theoretically calculated values (last two columns).

In the next series of experiments the leading electrolyte consisted of 0.01M HCI and, as counter-ion benzidine at a pH of 3.35. The reasons for the choice of benzidine as counter-ion were:

1. the possibility to check the equations for a divalent counter-ion

2. the pK values of most weak acids are within the buffering region of benzidine

3. the fact that benzidine is buffering at low pH and therefore can be used to test the validity of the equations, even when a relatively large amount of the current is carried by H+.

On the other hand benzidine is not very stable, is only slightly soluble in water and is poisonous.

The experimentally determined pH values in the benzidine system (Table 3.2) do not agree with the theoretical values as closely as in the histidine system, *Most of the pK and mobility data are taken from literature (88-91)

TABLE 3.1

The theoretical and experimental values of pH and the calculated net mobility (m₈₂1 in an isotachophoretic system with histidine-HCI as leading electrolyte. The experimental values were obtained from metiSUrements in a capillary apparatus at 25°C. The pK and mobility data used for the theoretical calculations are listed in the first columns.

ION SPECIES _{pKB21 pKB22} pKB23 mB21 mB22 mB23 mB2 pHtheor. pHexp.

cm2

v-

1sec-1 • 105 chloride 78 78 5.75. 5.75 oxalate 1.23 4.19 40 73 72 5.76 5.78 tartrate 2.98 4.34 39 64 62 5.79 5.80 formate 3.75 56 56 5.79 5.81 citrate 3.08 4.74 6.40 38.5 55 70 56 5.82 5.81 succinate 4.16 5.61 40 60 52 5.85 5.81 malonate 2.83 5.69 40 58 51 5.85 5.83 acetate 4.75 41 39 5.89 5.87 a-hydroxybutyrate 3.65 39 36 5.89 5.87 phosphate 2.12 7.21 12.67 38 55 69 34 5.87 5.87 carbonate 6.37 10.25 44.5 72 23 6.39 6.41

but in most cases the deviation is not very large. The discrepancy between theory and practice is largest for the low conductive zones, such as acetate, a-hydroxybutyrate and carbonate.

TABLE 3.2

Theoretical and experimental values of the pH and the calculated net mobility (m₈₂1 of different terminators in an isotachophoretic system, with benzidine-HCI as leading electrolyte. The experimental values were obtained from measurements in a capillary apparatus, at a temperature of 26°C.

ION SPECIES _pHexp.

chloride 3.35 3.35 oxalate 3.56 3.42 formate 3.97 3.85 succinate 3.65 3.62 tartrate 3.60 3.75 phosphate 3.60 3.70 citrate 3.78 3.74 malonate 4.16 4.00 acetate 4.47 4.20 a:·hydroxybutyrate 4.44 4.19 carbonate 5.36 4.80

24 Temperature measurements on the capillary tube

mB2 cm2v-\ec-1 x 105 78 46 35 35 33 32 28 21 15 14 4

As Everaerts (52) pointed out, the heat production is different in each zone as a result of the different voltage gradients. The evolution of heat in a zone, and thus its temperature (73), has a linear relationship with the specific resistance of the zone, when the current is constant throughout the system. The temperature difference between the zones can be detected by a thermocouple. An example is given in Fig. (3.2). The step-height of an acid is 51