Molten Salts and Isotope SeparationFrederic LantelmeUniversite Pierre et Marie Curie, Laboratoire PECSA, UMR 7195, 4 place Jussieu, F-75252Cedex 05, PARIS

Reprint requests to F. L.; E-mail: frederic.lantelme@upmc.fr

Z. Naturforsch. 68a, 39 – 47 (2013) / DOI: 10.5560/ZNA.2012-0105Received September 21, 2012 / published online February 15, 2013

Dedicated to Professor Alfred Klemm on the occasion of his 100th birthday

The work on molten salts and isotope separation performed over the years at Universite Pierreet Marie Curie and at College de France is critically reviewed. This research, closely related toA. Klemm’s pioneering contributions, leads among other things to the discovery of the effect nowcalled the ‘Chemla effect’, after the late Professor Marius Chemla. These studies of ionic motions inmelts, and liquids in general, have greatly benefitted from recent advances in molecular simulations.Some recent results of such simulations – molecular dynamics (MD) and Brownian dynamics (BD)– as well as of related theoretical work are discussed.

Key words: Transport Number; Ionic Mobility; Isotope Effect; Diffusion Coefficient; MolecularDynamics; Fused Salt.

1. Introduction

The origin of the interest in molten salt in the groupat Universite Pierre et Marie Curie in Paris lies in theresearch works performed in Professor Joliot Curie’slaboratory at College de France to produce separatedisotopes. Indeed, since the discovery that chemical el-ements can consist of several isotopes attempts werecarried out to produce separated isotopes.

Apart from the various forms of electromagneticseparation, the main techniques are based on statisticalprocesses such as diffusion, chemical exchange, dis-tillation, thermal diffusion, and ionic migration. Thelast technique was extensively studied, especially forthe elements which have no easily obtainable gaseouscompounds. In the 20s of the previous century, sev-eral experiments were carried out to enrich isotopesby ionic migration in solutions, enclosed in agar gel toavoid mixing by convection [1]. At that time, no sep-aration was detected by the existing methods. In fact,an isotope effect was present, but it was too small. Thiswas proved later when mass-spectrometric and activa-tion analysis methods became available. According tothe kinetic theory, the very low value of the isotope ef-fect in aqueous solution was attributed to the solvationeffect, which drastically reduces the relative mass dif-ference of moving particles.

Taking this fact into account, Klemm [2, 3] sug-gested that it should be easier to obtain isotope sep-aration by carrying out experiments in media wherethe ions do not move with a solvation atmosphere. So,he started his research by studying migration in a solidsalt crystal. For this purpose he chose a crystal of silveriodide, which exhibits a not too small ionic conductiv-ity. He was able to show that the heavy isotope of silverenriched toward the anode.

This successful experiment opened the way to a largenumber of determinations of mass effect in ionic crys-tals. However, though ionic crystals give large isotopeeffects, the separation yields were low due to the gen-erally low conductivity of crystals. Later, Klemm [4]extended his research to molten salts and was able todetermine the difference in the mobilities of lithium orpotassium isotopes in their fused chlorides.

It is our purpose to describe briefly researches car-ried out to determine the migration isotope effects invarious media, with a survey of the attempts to pro-duce separated isotopes. Then, the contribution of themeasurements of isotope effects to the physicochemi-cal properties of ionic liquids will be examined. A fun-damental description at the atomic scale by molecu-lar dynamics calculation will be carried out to obtaina valuable insight into the structure and the thermody-namic and kinetic properties of the liquid state.

© 2013 Verlag der Zeitschrift fur Naturforschung, Tubingen · http://znaturforsch.com

40 F. Lantelme ·Molten Salts and Isotope Separation

2. Ionic Migration and Isotope Effect

2.1. Mass Effect

The isotope effect in ionic migration is described bythe ratio of the mobilities of two isotopes, u1 and u2.Separation takes place when the mobility ratio differsfrom unity

u1

u2= 1+ ε .

Since ε is generally much smaller than 1, it may bewritten

ε =∆uu

,

where ∆u = u2− u1 and u is the mean mobility of theisotope mixture:

u = γ1u1 + γ2u2 with γ1 + γ2 = 1 .

In order to compare the efficiency of various experi-ments, Klemm introduced the notion of mass effect:

µ =∆u/u

∆m/m,

where ∆m is the mass difference, and m is the meanmass of the isotopes. According to the simplest kineticmodel, the drift velocity of a particle should be pro-portional to the reciprocal of the square root of themasses, u1/u2 = (m2/m1)1/2, which for ∆m/m� 1,gives µ ≈−0.5. µ values close to this figure have occa-sionally been obtained, but generally the measured val-ues are much lower (absolute µ values are considered).

2.2. Migration in Aqueous Solutions and Crystals

Migration in aqueous solutions was the method usedin the earliest attempts to separate isotopes. A quite so-phisticated device was described [5] to separate the twopotassium isotopes 39K – 41K. Latter, a simpler methodwas proposed by the team of College de France [6].It consisted of a paper strip impregnated with an elec-trolyte (NaCl solution 0.04%). A spot containing tworadioisotopes 22Na and 24Na (periods: 22Na: 2.6 years,24Na: 14.8 h) was placed in the centre of the strip(Fig. 1). To avoid a too large spreading of the spotby diffusion, the migration time was reduced by using

Fig. 1. Migration on a paper strip [6]. A, B – electrolysiscompartments filled with NaCl solution; C, D – glass rods;E – Geiger–Muller detector. The tube is filled with carbontetrachloride.

a very high electric field: a voltage of 5000 V was ap-plied between the electrodes at a distance of 40 cm. Inorder to keep the radioactive spot at the same place dur-ing the experiment, the paper ribbon was rolled up ontwo glass rods and could thus easily be moved. Themigration distance was 280 cm for a duration of 1 h45 min. The radioactive analysis showed that 22Na mi-grated more rapidly than 24Na; the distance betweenthe centres of gravity of the spots corresponding to thetwo isotopes was 5.8 mm.

A similar experiment was carried out to measure therelative mobilities of lithium isotopes [7]. This elementhas only two stable isotopes, 6Li and 7Li. Their abun-dance in natural salts is 7.5 and 92.5%, respectively.The paper ribbon was now impregnated with a solutionof ammonium nitrate (10%). Moreover, in this case therelative mass difference was large enough and the useof a moving strip was not necessary. The analysis ofthe lithium spot was carried out by the isotopic di-lution technique using a mass spectrometer speciallybuilt by Chemla in his laboratory. With the same ex-perimental device, the 22Na and 24Na migration wasmeasured again. The following results were obtained:µNa22−Na24 = −0.023 and µLi6−Li7 = −0.024. As ex-pected, due to the solvation process, the values weremuch smaller than the values predicted by the kinetictheory.

As pointed out in the introduction, to avoid the per-turbing solvation effect, Klemm studied the electromi-gration in the solid state. He was able to show that inan AgCl crystal the heavy isotope, 109Ag, was enrichedtoward the anode. Using radioactive tracers, Chemlastudied the diffusion of various ions in NaCl and KClmonocrystals [8, 9]. The chlorides of radioactive ele-ments were deposited by sublimation at the surface of

F. Lantelme ·Molten Salts and Isotope Separation 41

the crystals. An electrical field was applied by pressingthe crystal between two platinum electrodes. Accord-ing to the experiments, the device was maintained ata temperature ranging from 570 to 750 ◦C. After a fewhours the crystal was cut in sections of 33 µm witha microtome. In general, the measured mass effectswere quite close to the theoretical value; for examplein NaCl µNa22−Na24 = −0.46. However, notwithstand-ing this interesting value, migration did not appear asa valuable technique to produce separated isotopes dueto the low conductivity at solid state.

2.3. Ionic Migration in Fused Salts

Following the successful enrichment in 1947 oflithium and potassium in their fused chlorides [4],many experimental papers have appeared on ionic mi-gration in fused salts [10]. Since then, the process hasbeen applied to other isotope mixtures. The melt elec-trolysis was generally carried out in a counter-currentflow device. The anodic and cathodic compartmentswere connected through a tube filled with an inert ma-terial, such as a fine grain zirconium powder.

A simple and efficient method, analogous to theelectrophoresis on paper, was proposed to obtaina rapid determination of the isotope effect [11, 12].The porous support needed to avoid convection mix-ing was an asbestos strip calcined beforehand andthen immersed in a molten salt, generally a mix-ture NaNO3 – KNO3; the strip (50×1.5 cm, thick-ness 0.3 mm) was introduced into an electricallyheated glass tubing (Fig. 2). The impregnation was25 mg/cm2. For an applied voltage of 700 V, the cur-rent was 100 mA at 300 ◦C. An advantage of the tech-nique was the short duration of the experiment, whichlasted a few hours. The ribbon was cut in 5 mm slicesto determine the migration distance of the studiedisotopes.

Fig. 2. Migration on an asbestos strip [11]. 1 – electrical fur-nace; 2 – asbestos strip; 3, 4 – electrolysis compartmentsfilled with fused salt; 5, 6 – conducting electrodes; 7 – iso-tope spot.

Fig. 3. Counter-current device for the production of separatedlithium isotopes in LiBr – KBr mixture [18]. 1 – anodic com-partment; 2 – cathodic compartment; 3 – diaphragm; 4, 5 –graphite electrodes; 6 – anodic bromine outlet; 7 – brominetank; 8 – junction tubing; 9 – boiler; 10, 11 – inlet tubings;12 – cathodic bromine outlet; 13 – condenser; 14 – electricalfurnace.

As expected, these set of experiments showed thatfused salts were a more favourable medium to produceseparated isotopes. For example, the mass effects forthe 22Na and 24Na couple were, µNa22−Na24 =−0.023,in aqueous solutions, and µNa22−Na24 = −0.11, infused NaNO3 – KNO3. Nevertheless, these values re-main smaller than those obtained in crystals.

2.4. Production of Separated Isotopes

The only techniques suitable for a practicable sep-aration are counter-current processes in which the el-ementary effect is repeated many times in a contin-uous manner [13 – 15]. The isotopic ions migratingin the electric field move counter-current to the sup-porting medium; then the ions can be allowed tomove over a very large distance, although the whole

42 F. Lantelme ·Molten Salts and Isotope Separation

Fig. 4. Diffusion apparatus [23]. A – silica capillary, B – alu-minium basket, C – Pyrex rod, D – micro-motor, E – saltwith tracers, F – Pyrex needle, G – syringe, H – salt bath, I– Pyrex container, J – argon inlet, K – electrical furnace, L –thermocouple, M – preparation of N2O5 atmosphere, HNO3on P2O5.

process takes place over short distances. Of course,this procedure cannot be used with materials in thesolid state although they exhibit a favourable separa-tion coefficient. It may be used with aqueous solu-tions, but the efficiency remains very low. So, mostof the experiments were carried out using fusedsalts.

A special effort was devoted to the separation oflithium isotopes. Indeed, the light isotope 6Li is valu-able as the source material for the production of tri-tium and as an absorber of neutrons in nuclear fusionreactions. 7Li is used as a part of the molten lithiumfluoride in molten salt reactors.

An interesting way was provided by migration inlithium chloride or bromide [16, 17]. However, somedifficulties appeared when the laboratory techniquewas to be extended toward a large scale production of

separated isotopes. At high temperature, the salt meltsare very corrosive, and it was not possible to maintainthe migration process for a long enough time to achievea high enrichment.

A well-known procedure to obtain a salt bath atlower temperatures is to use a eutectic mixture. At firstglance, this idea seems to be quite unrealistic: indeed,the counter-current technique, which is efficient to sep-arate isotopes having very similar physicochemicalproperties, should first rapidly separate the two com-ponents of the salt mixture. However, an attempt wascarried out to study the separation of lithium isotopesin a eutectic mixture LiBr – KBr [18, 19]. The resultwas very surprising. After a few hours, the salt com-position in the glass tubing reached a constant valueclose to the eutectic composition. No separation be-tween lithium and potassium was observed, but theisotope separation still continued with a progressive7Li enrichment in the anodic compartment whereasthe proportion of 6Li increased on the cathodic side.Moreover, not only the lithium isotopes separated, butit was observed that the potassium isotopes separatedas well, the heavy isotope concentrated also in theanodic compartment and the lighter one toward thecathode.

This unexpected behaviour opened the way towarda more practicable design for the production of sepa-rated isotopes. An apparatus with an automatic recy-cling of the bromine was built with large glass tubing(Fig. 3). This apparatus was able to work properly forabout one month. With this procedure, a few grams ofnearly pure 7Li were produced.

2.5. The Chemla Effect

The strange failure of the counter-current techniqueto separate the components of a salt mixture was notrestricted to the mixture LiBr – KBr, but was also ob-tained with the mixture LiBr – NaBr. Moreover, thisbehaviour was not specific to the bromide salts. It wasrapidly shown that a similar effect occurred in the mix-ture LiNO3 – KNO3 [20].

These results encouraged a lot of experiments whichshowed that this effect was fairly common in bi-nary molten salt systems consisting of two monovalentcations with a common anion. It was even observed ina system with a common cation: LiCl – LiNO3 [21].This important phenomenon was named the Chemlaeffect [22].

F. Lantelme ·Molten Salts and Isotope Separation 43

Fig. 5. Ionic diffusion coefficients and electrical mobilities,LiNO3 – KNO3 mixtures [20].

This behaviour is in contradiction with the classicaltheory of the particle motion in liquid state, and its in-terpretation was of crucial importance to reach a betterunderstanding of the nature of ionic liquids. Of course,it was evident that, at the constant composition (calledthe critical composition) reached during the counter-current experiments, the two cations have exactly thesame mobility.

The stable situation concerning the concentration ofthe mixture components implies that, in mixtures richin heavier cations, the mobility of the heavier cationshould be larger than that of the lighter one; the reverseshould be obtained on the other side of the critical com-position. To check this assumption, measurements ofionic mobilities were carried out by Chemla’s group. Inorder to obtain an accurate determination of the ionicmotion, the capillary technique (Fig. 4) was used tomeasure the aptitude of ions to move in the melt. Theself-diffusion coefficient of the different componentsof the salt mixture was accurately measured [23, 24].The self- (or tracer) diffusion of the potassium andsodium ions were measured using radioactive tracers,42K (period 12.4 hours), 22Na (period: 2.6 years), andthe stable isotope 6Li. In nitrate melts, the diffusion ofthe anions was followed by 15NO−3 . The concentrationof stable isotopes was determined by use of the isotopicdilution technique.

The results were again very surprising: in the wholeconcentration range of the mixture LiNO3 – KNO3, thelithium ions moved faster than the potassium ions, incontradiction with the expected crossing (Fig. 5). Theaccuracy of the experiment left no doubt about this re-

Fig. 6. Apparatus for the measurement of transport num-bers [20]. A – Pyrex container, B – platinum sheet, C – Pyrextube, D – porous plug, E – tantalum wire, F – equilibrationtubing, G – device used to equilibrate the salt level in the twocompartments, H – electrical furnace, I – thermocouples, J –nitric acid inlet, K – boiler, L – condensation column.

sult, the displacements of potassium and lithium weremeasured simultaneously in the same experiment, andthe ratio of the diffusion coefficients was obtained witha great accuracy, around 1%. Of course, it was thensuspected that for a given ion i, the diffusion coefficientDi and the electrical mobility ui could exhibit a differ-ent behaviour, notwithstanding the Nernst–Einstein re-lation, which states that the ratio Di/ui should be con-stant: Di/ui = kBT/ei [25] (T is the absolute tempera-ture; kB Boltzmann’s constant, and ei the charge of themoving ion).

An accurate knowledge of the ionic electrical mo-bility was needed. It was obtained from the transportcoefficients of the melt components measured by theclassical Hittorf technique [26]. In order to avoid hy-drodynamic flows, the anodic and cathodic compart-ments were separated by a porous plug, and a spe-cial apparatus was built to maintain the same salt levelin the two compartments [27, 28] (Fig. 6). The ionic

44 F. Lantelme ·Molten Salts and Isotope Separation

mobilities were deduced from the ionic transport num-bers and from the equivalent conductivity Λ of themelt. The results are shown in Figure 5. Now, theChemla effect was clearly explained: In lithium richmixtures, the lithium ions moved faster than the potas-sium ones, and in potassium rich mixtures, the potas-sium ions moved faster than the lithium ones. The mo-bility of the lithium ions decreased more rapidly thanthat of the potassium ions when the potassium concen-tration was increased.

In order to investigate the system used by Chemlafor the isotope separation, the same determinationswere carried out in the LiBr – KBr mixtures [29]. Thesame effect as in nitrate melts was obtained. A moremarked crossing was observed, whatever the tempera-ture; the mobility of the lithium ions decreased muchmore rapidly than that of the potassium ions. However,surprisingly, as already obtained for the nitrate melts,the diffusion measurements did not show any crossing,the lighter ions moved always faster than the heavierones in the whole concentration range [30].

2.6. Polyionic Displacements

The above observations soon appeared not tobe limited to the two systems LiBr – KBr andLiNO3 – KNO3, and the large generality of this be-haviour encouraged the scientific community to digdeeper into the mechanism of particle motions in ionicliquids. The first idea put forward came from the sur-prising deviation from the Nernst–Einstein relation. Itwas generally assumed that, at least for alkali halides,the ions are fully ionized in crystals or fused crystals.Thus, the charge of the moving alkali ions should bethe electron charge e. However, the particle motionin condensed media should take into account the ef-fect of interactions between the particle and its envi-ronment. For example, the Debye–Huckel theory in-dicates that ions moving in a solvent are surroundedby a hydration shell which has a drag effect on the ionmotion. This shell arises from the electrostatic inter-action between the ion and the dipoles of the solventmolecules; this interaction slows down the ion mo-tion; a similar behaviour must occur in ionic liquids, allthe more so since the cation–anion interaction is quitestronger than the ion–dipole interaction. The ion mo-tion can be described as the ion moving surroundedby its ‘hydration shell’. But now the shell is madeof charged particles, so the effect of the shell is also

to change the apparent charge of the moving particle,ei 6= e.

To illustrate this mechanism, it has been pro-posed [20] to calculate the statistical proportion ofthe ion displacements attributed to ‘free’ ions andto ‘group motions’ such as that of anion–cationpairs [AC]0 or more generally of groups such as[AxCy](y−x)+. The calculation was performed basedon the deviations from the Nernst–Einstein relation byusing the diffusion coefficients and the ionic mobilitiesdeduced from the Hittorf experiments, called externalmobilities (measured with respect to the wall of thecontainer). This description, known as the polyionicmodel, has the advantage of providing a simple illus-tration of the charged particle motion in an ionic envi-ronment. An example of the results for the nitrate sys-tem is given in Table 1.

Some points should be emphasized. Firstly, the pairproportion (or associate motion) increases stronglyfrom potassium to lithium; this effect illustrates the in-fluence of the electrostatic interactions, which dependsdirectly on the size of the ion: the smaller the ion thelarger the anion–cation interaction.

Secondly, the potassium ions do not attract the an-ions very much. Thus, in potassium rich mixtures, theanions are more available for associate cations thanin lithium rich mixtures; this behaviour explains theChemla effect: the proportion of associated motion in-creases when the salt mixture becomes potassium rich,this trend is much more marked for the smaller ions(lithium) than for the larger ones (potassium).

Thirdly, the association effect depends also on thestructure of the melt. As the temperature increases thequasi-lattice structure vanishes and the particles of op-posite sign tend to associate more freely, the liquidstructure approaches that of the gaseous state, whichis mainly made of neutral anion–cation pairs. On theother side, at low temperature, the association shoulddecrease, the particles remaining in their own quasi-lattice; it is well known that in crystals the particle mo-tion nearly obeys the Nernst–Einstein equation, show-ing that the associated motions remain small. This ten-dency is illustrated by the results in Table 1, whichshow that the proportion of free-motion particles in-creases for decreasing temperature. This trend explainsthe shift in the concentration of the mobility crossing-point as the temperature varies. A similar calculationwas done for the bromide mixtures and led to the sameconclusions.

F. Lantelme ·Molten Salts and Isotope Separation 45Ta

ble

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tage

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6317

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107

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226

350

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40.6

LiN

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59.4

6416

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3910

75

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185

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18.5

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81.5

747

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163

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43.0

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M=

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Fig. 7. Time evolution of the percentage of ions remainingin a shell around a moving ion; LiCl – KCl eutectic, 1570 K,solid line with, dotted line without Coulomb forces [35].

3. Molecular Dynamics Calculations

3.1. Simple Ionic Salts, Alkali Halides

The experimental observations previously describedencouraged the scientific community to dig moredeeply into the intimate mechanism of particle motionin purely ionic media. To obtain a more concise viewof the transport properties in ionic liquids, the idea ger-minated to calculate ab initio the properties of a col-lection of charged particles. However, at least for al-kali halides, the Coulomb interactions are the dominantforces acting on the particles. The effect of these longrange forces can be easily taken into account by themethod described by Ewald [31]. The particle notionwas deduced from the integration of Newton’s equa-tion step by step in a computer program.

With the help of Professor Singer’s group at RoyalHolloway College [32], we have initiated a program tocalculate by the molecular dynamics (MD) techniquethe behaviour of a set of charged particles [33, 34]. Thegood agreement between the experimental and calcu-lated properties proved the validity of the model. Thistool provided a suitable means for examining the struc-ture of the ionic medium at a microscopic scale and themechanism of ionic motion at very short times [35]. Ata time scale of around 10−13 s, it was shown that theparticles oscillated in a quasi lattice structure. The os-cillating motion rapidly vanished and then, after about2 ·10−12 s, the mean square displacement of the ionprovided a correct value of the macroscopic (experi-mental) diffusion coefficient. So we have carefully ex-amined the behaviour of the ions during this cruciallapse of time. For example, the presence of the anionsin a shell surrounding a cation was followed (the shellradius corresponds to the first minimum of the anion–cation radial distribution function). At very short time,

46 F. Lantelme ·Molten Salts and Isotope Separation

Tabl

e2.

Cut

-off

radi

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.800

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the

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atio

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Cat

ion

Li+

K+

146

.18

48.1

544

.21

42.8

646

.11

52.1

347

.87

27.0

720

.80

229

.63

29.6

329

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323

.33

50.0

050

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33.5

916

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646.

718.

567.

949.

4443

.94

56.0

630

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25.7

64

5.09

4.83

5.56

6.35

4.44

45.4

554

.55

36.3

618

.18

55.

795.

566.

024.

767.

7848

.00

52.0

024

.00

28.0

06

2.78

2.55

3.01

1.98

4.44

45.8

356

.17

20.8

433

.33

81.

851.

851.

850.

783.

3350

.00

50.0

012

.50

37.5

09

1.04

0.93

1.16

1.19

1.11

46.4

455

.56

33.3

422

.22

∗ Ang

les

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etr

iple

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atio

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69

100% of the ions remained in the shell; whereas at longtime the surrounding structure vanished (Fig. 7). Aftera time long enough to reach the macroscopic mean dis-placement of the cation (≈ 2 ·10−12 s), the anion re-maining in the shell were considered as being involvedin the motion. The results in Table 2 show that most ofthe particles moved either freely or coupled with a par-ticle of opposite sign, the paired displacements beingmore important for the lithium ions than for the potas-sium ions Thus, everything happens as if the motiondescribed in the polyionic displacement model camefrom associated species, the life-time of which wasaround 2 ·10−12 s, long enough to affect the particlemotion, but too short to be considered as long livingmacroscopic species.

The application of statistical mechanics to the re-sults of computer simulation provided a valuable toolfor a better understanding of particle motions in ionicliquids. For example, to illustrate the influence of theCoulomb forces on the particle motion, the behaviourof the same set of particles was examined withoutthe presence of these electrostatic forces. The curvesin Figure 7 show clearly that now the influence ofthe surrounding atmosphere vanished rapidly. The dif-ference was most important for the smallest cation(lithium).

Moreover, the migration isotope effect was stud-ied by varying the mass of the moving particles. It isknown that for dilute gases, or to a lesser extent forionic solids, the transport coefficients are roughly pro-portional to the reciprocal of the square root of themass of the moving particles. In ionic liquids, it wasshown that at very short times the particle motion canbe described by a unique function if the time is scaledas t/m1/2. However, this effect, which corresponds toGraham’s law, vanished quite abruptly according toa collision–dissipation process [36]; the time evolutionof this dissipation is quite well described by the Brow-nian motion approximation [37]. This mechanism wascarefully interpreted in the frame of a perturbation the-ory, the parameter introduced in this theory being pro-portional to the reciprocal of the square root of themasses [38].

4. Conclusion

The research work initiated by Professor Klemm forproducing separated isotopes by migration in moltensalts was the starting point of experiments leading to

F. Lantelme ·Molten Salts and Isotope Separation 47

a better understanding of fused media. The presentpaper shows his pioneering work concerning the de-scription of ionic motion in liquids. These experimentshave open the way to a large number of investigations.Firstly, the Brownian dynamics model was applied to

the study of concentrated solutions and, latter, molecu-lar dynamics calculations were extended to the study ofvarious melts of industrial interest (nitrates, fluoridessilicate with multivalent cations . . . ). These investiga-tions are described in the literature [39, 40].

[1] J. Kendall, Phys. Rev. 21, 389 (1923).[2] A. Klemm, Naturwiss. 32, 69 (1944).[3] A. Klemm, Z. Naturforsch. 2a, 9 (1947).[4] A. Klemm, H. Hintenberger, and P. Hoernes, Z. Natur-

forsch. 2a, 245 (1947).[5] A. K. Brewer, S. L. Madorsky, and J. W. Westhaver,

Science 104, 156 (1946).[6] A. Bonnin, M. Chemla, and P. Sue, Comptes rendus

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