" A.M. Ange"" Gwen2
and D.
Argonne National Laboratory Argonne, Illinois
I I
Simple Two-Dimensional Magnetic Disc Models of Ionic Liquids
Insight into the nature of processes occurring in the different forms of matter may often be obtained from the study of physical models. We have recently developed two diierent types of models each with certain advantages to represent the situations occurring in ionic liquids where particles of opposite charge attract and repel one another. Models based on magnetic forces have been described previ~usly,~ but have been limited by the use of metal magnets. By employing highly magnetized, elastomer-bonded materials, new types of models have become available which possess many desirable features due to the light weight and flexibility of these material^.^ Model 1
This model is similar to the earlier ones made by floating magnets on water. While quite detailed observations can be made with this type of model,3 we have used it chiefly as a means of demonstrating the fine and subtle effects of the balance of forces in fixing equilibrium configurations. The model was constructed by attaching small (I/( in. diameter) discs, cut from a pre-magnetized plastic sheet magnetized through its thickness, to larger ('/$-I in. diameter) discs of cork sheet, which are thick enough in.) to float the units on water. Discs with the fields in the same direction repel one another, and vice versa (Fig. 1). Provided the discs float at the
' On leave from Melbourne University, Australia. 'Based on work performed under the auspices of the U. S. Atomic Energy Commission. DIETZEL,A., AND DEEQ,E.,Glasstechn. Bw., 30, 282 (1957). Z n n z ~ c s ~J.,, "Physics of Non-Crystalline Solids," North-Holland Publishing Co., Amsterdam, 1964. 'The material referred to is available oommereidly under the general name of Plastiform, a product of Leymsnn Corporation Magnetics Division, and is a. rubber-bonded barium ferrite composite in which the ferrite particles have been oriented during processing to give a high strength permanent magnetic material which can, however, be easily machined, cut with scissors, and bent into any required shape.
'
same level, the force exerted by one "like-charged ion" on another is essentially a radial repulsion whose magnitude approximately depends on the square of the separation of the cork discs except a t close approach. By altering the size of the cork disc, one effectively changes the "potential" of the "ion" thus simulating the effect of changing ionic radius on the strength of the interactions. I n practice, limitations are set both on the strength and the variability of the "ionic interactions" by the ability of the cork disc to float the relatively dense magnetic material and by the surface tension of the float medium. (This can, of course, be reduced by suitable surface-active additives.) The latter has the effect of overcoming the repulsion between "weak" l i e charged "ions" through the reduction in surface energy obtained on contact. We have found this model both instructive and amusing when used in the following manner. A ' / r in. wide strip of I/,, in. Plastiform strip is wrapped around the outside of a 6 in. diameter Petri evaporating dish, about one inch from the bottom and cemented in place. This establishes a radially uniform magnetic field in the horizontal plane. The dish is filled with water (or other medium) to a level about one eighth of an inch below the top of the strip. "Ions" of one "charge" type are repelled toward the center of the dish, and thus the system is stabiliued with respect to wall effects. The svmmetrical arranaements assumed bv different numbers of "lie-charged ions" may be Htudied by adding "ions" sequentially. The existence of potential energy wells, e.g., in the center of Figure 2a, and energy barriers opposing a change from one stable configuration to another (Fig. 2a) may be easily demonstrated. It is also easy to show the formation of l'complex" configurationswith different symmetries on introduction of ions of opposite "charge," as well as the energy
Figure 2.
,,.10"s."
Figure 1.
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lo1 Alternative stable symmetry groups for mutually repulsive
barriers opposing a change from one symmetrical configuration to another. For instance, Figure 3, a, b, and c, shows the two dimensional analogues of the conversion of a tetrahedral complex (here triangular) to an octahedral complex (here, a square). Some insight into the details of the mechanism of the transformation can be gained by observing that the triangular group first distorts to a configuration of maximum energy (LLactivated complex?") before an additional "ligand" becomes bound and the resultant symmetrical configuration becomes energetically favored.
-~ =-
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Figure 3. Stager in conversion of triangular "complex ion" to square "complex ion."
With the proper choice of disc size and magnetic field strength one can show the existence of a maximum coordination number above which the "charge" on the central "ion" is insufficient to "neutralize" or overcome the mutual repulsions of the "ligands." Forced approach of an extra "ligand" in this case causes the "dissociation" of the complex before the new "ligand" can be accepted, demonstrating the sort of mechanism one might suppose is operative in exchange of radioisotopes among complex ions. Aggregations of these "ions" in approximately equal numbers, have a definite cohesive energy, but the interaction energies are insufficient to show more than a weak tendency to particular symmetry groupings when the aggregate is agitated to simulate thermal motion. Model 2
I n thii model one achieves stronger interactions and therefore a closer approach to the actual situation in ionic liquids. With thii model, however, it is not possible to observe the very subtle balance of forces seen in Model 1. I n Model 2 the "positive" and "negative" potentials are generated by wrapping a in. wide, in. thick Plastiform strip around in. thick cork discs of ' / r 3 / 4 in. diameter, giving a considerable range of "ionic radius ratios." Depending on the side of the tape facing out, one obtains a "positive" or "negative" field directed radially out from the center of the disc (Fig. 4). Because the magnetic strips may come into touching contact in this model, the interaction energies are stronger than in Model 1, and an assemblage of "positive" and "negative" "ions" has a very considerable cohesive energy. An ordered close packed arrangement of these "ions" requires vigorous agitation before "melting" to a disordered "liquid" phase occurs. The strength of the interactions can he controlled by changing the degree of magnetization, or the thickness (or numher) of the strips around a given cork disc. Thus the relative potentials of given types of ions, e.g., K+ and C1- ions may be simulated.
Figure 4.
We have measured (by balance weighings) the attractive and repulsive forces exerted by pairs of these "ions" on one another and have found the forces to vary approximately as the inverse sixth power of the separation of the centers, for the range of sizes of discs employed. Pairs of particles interacting coulombically should, of course, exert forces porportional to the inverse square of the separation of centers. The observed r-6 behavior may, however, be just what is required to simulate an ionic melt, since, as Stillinger, Kirkwood, and Wojtowicz point out,=the overlapping of the long range coulomb forces in an assembly of ions causes the pair interaction potential to fall off much more rapidly than r-%being in fact an r-6 function for the Debye-Hiickel case. In principle these "ions" may also be floated on water or other such medium as in Model 1, but we find that "like-charged ions" on close approach tend to jump out of the horizontal plane in order to find positions of attractive potentials. This tendency can be repressed by placing a cover-plate over the model, but then the wetting of the cover plate by water causes problems. We have found it more satisfactory to observe the behavior of these "ions" on polished, low friction Teflon sheets. Thus we have built a model involving some 140 "ions" of different types, which are loosely confined in a 12 in. diameter glass dish between a in. Teflon sheet base and a '/4 in. clear plastic cover-plate (see Fig. 6). The dish is mounted on a Cenco-Meinzer sieve shaker by which a vigorous shaking action simnlating thermal motion of the ions may be imparted to the model. While the motion obtained from this particular shaker is not ideal, having a steady rotation component, it still has been possible to observe a number of interesting effects. Most of the "ions" used simulated C1- and K + ions in size, but a few smaller "ions" with higher "charge density" were added. These were made with three sucessive layers of magnetic tape and can he taken to simulate Ca++ ions. The effect of the magnetic ribbon on the distribution of the discs is seen in the contrast between Figure 5, which shows an agitated assembly of cork discs without magnetic tape wrapping and Figure 6a. The numbers and diameters of the discs in each case are the same. In addition to the expected observation that "ions" tend to surround themselves with nearest neighbors of opposite "charge," the point most clearly demonstrated by the model is the tendency of the first coordination "TILLINQER, F. H., JR., KIRKWOOD, J. G., A N D WOJTOWICZ, P. J., J . C h m . Phys., 32, 1837 (1960). Volume 43, Number 4, April 7 966
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shell "ions" to occur in either triangular or square arrangements and to shun intermediate configurations. This phenomenon, a consequence of the mutual repulsions of "like-charged ions," is particularly marked for the nearest neighbors of the smaller "ions" with higher charge density. We refer to these arrangements in the following discussion as the two dimensional analogues of tetrahedral and octahedral groupings in a three dimensional model.
Figure 5. Model 2 cork discs without magnetic tope.
(01 Figure 6. Model 2 during agitation. "free volume."
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i 1% "free volurne;'lb)
18%
Figure 6a for instance is a picture of the model taken during agitation, and shows that the small "high charge-density cations" prefer either "tetrahedral" or "octahedral" sites. The degree of distortion from the symmetrical arrangement in these particular pictures is often appreciable. The "coordination numbers" of the "lower charge density cations" appear to be less well defined. The "free volume" in this instance, defined by the dierence between the number of "ions" required to close-pack the available space regularly, and the number of "ions" actually present, is llyoof the total space. I n Fig. 6b the "free volume" has been increased to 18% hy removing "ions," while the intensity of agitation is unchanged. Thus, in effect, a change of pressure at constant temperature has been simulated. I t is noteworthy that the main effect appears to be an increase in number and size of the "holes" with accompanying decrease in "co-ordination number." Although "octahedral" arrangements are less in evidence in Fig. 66 than in Fig. 6 a there are insufficient ions in the model to indicate whether or not "free volume" should be regarded as an important factor in the equilibrium between octahedral and tetrahedral "complexes."
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There is at least a fair degree of accord between the behavior of the model and the behavior of 3d ions in molten chloride solvents as observed in spectral s t u d i e ~ , ~ where either octahedral or t,etrahedral groupings, or, under the right circumstances, equilibria between the two types may be observed. During agitation the lifetimes of the symmetrical groupings may he compared with those of intermediate or different configurations (e.g., linear, and dimeric molecule types). The predominance of the former groups in typical instantaneous photographs is, of course, a reflection of their greater lifetimes. Some idea of the diffusion process may also be obtained, particularly by observing the progressive separation of two marked "cations." I n this model relative motion seems to occur as much by co-operative motion of assemblages of positive and negative "ions" as by individual jumps into holes by the ions under observation. At low agitation rates, the model tends to "crystallize," or at least to show regions of crystal-like order, but the loss of "mobility" usually prevents a completely regular arrangement from being realized. Stopping the motion abruptly ("quenching") leads to rapid contraction to a disordered hut relatively dense aggregate which may be regarded as analogous to the glassy state produced in the quenching of numerous molten salt mixture^.^ Although conditions of polarization are not readily simulated, charge asymmetry may be introduced by adding extra thicknesses of tape at particular points on the perimeter of the "ions." Similarly, first approximation representations of polar molecules with positions of positive and negative charge density may he fabricated. Some interesting effects of "charge density" on miscibility have been observed. An wsortment of neutral particles (cork discs without any magnetic tape), with an initial random distribution among the "ions," are swiftly t h r o m out of "solution" when agitation is commenced. Also, we notice a tendency toward segregation of the high charge density "ions," a situation which may bear some relation to the microphase heterogeneity found in some glass-ceramic systems. We conclude that for purposes of demonstration of cohesive energy and other charge effects these models are quite useful and are certainly diverting. However, they can only be expected to show nearest neighhor interaction effects, and as the interaction energy, radius relations, must be very different from those of real ions, one must be careful not to treat the observed behavior as too closely related to that of real ionic liquids. Finally we note that, in principle, Model 2 could be extended to three dimenions by wrapping thin magnetized sheet around cork spheres, in the manner of manufacture of tennis balls. However, we can offer no solution to the problem of determining the "ionic" distribution pattern or the principal configurations within the bulk of such a three-dimensional model during agitation. 'GRUEN,D. M., AND MCBETH,K. L.,Pure & A p p l . Chem.:6, 23 \ilQfi?l A""..,. THILO, E., WIEKER,C., AND WIEKER,W., Silikaltechn. 15,109
