A MAGNETIC MODEL OF POLYELECTROLYTE INTERACTION B. E. CONWAY The Chester Beatty Research Institute, London, England
A
NUMBER of properties of polyelectrolytes and their solutions must be envisaged as arising from electrostatic interactions of various kinds; thus intramolecular and intermolecular interactions, as well as interactions between the polymeric ions and their counterions, are possible. The degree of over-all extension of flexible polyelectrolytes, and hence their viscosity, has been ascribed (1) to the mutual effects of the ionized groups on the polymer; and various osmotic, conductance, viscosity, and titration effects have been ascribed to interactions occurring between the polyion and its counter-ions (2-5). These interactions are all determined fundamentally by a force law (operating between charges e and e') of the form:
Figure 1. Diagram of Arrsnpment of Magnetsin Cork.
If a flexible line of magnets of the same orientation representing a fully charged particle is put in the water bath it assumes an approximately linear configuration, Figure 2. Upon insertion of "counter-ions," the "charges" become neutralized and the model folds up into a compact, approximately circular mass (Figure 3). where F is the force between the charged groups a t a Removal of the 'Lconnter-ion"magnets one by one causes distance r, in the solution of dielectric constant D. An a reversal of the process and the coil again expands. exactly similar law holds for magnetic interactions, so I n the contracted condition the model is the analogue it should be possible to construct a magnetic model that represents the electrostatic situation in polyelectrolyte solutions by means of magnets floating on water with their axes supported vertically in corks. As magnets are necessarily dipolar, isolated poles which mould exactly simulate electric charges cannot readily be obtained without complicated screening arrangements. However, if the magnets are all aligned with their like poles above the water and if the distance betvveen them is small compared with their length, the diagonal heteropolar interactions (attractions) are relatively small. Thus for magnets 10 cm. long and 2 em. apart the repulsive forces between the like ends are about 25 times greater than the diagonal attractive by Regulaion: "Counter-ion." Fully forces, and the model approximates a system of isolated Figure 2. Chain Fvlly Extended Dissociated like poles or like charges. Models of polyelectrolyte molecules may be con- of the uncharged parent polymer or perhaps more structed by floating a number of magnets in small exactly of the polyelectrolyte in excess of neutral salt. corks as in Figure 1 and joining them together a t a I n observing the model it is of interest to note that the small distance of separation by means of thread (for counter-ion charges not only diminish the repulsive flexible polyelectrolytes), very fine wire (semiflexible interaction down the chain, hut may also give rise to polyelertrolytes), or stiffer wire for rigid polyelectro- local allractions between two or three adjacent polymeric lytes. A string of 15 to 20 magnets in corks is sufficient charge units on a given chain, pulling these centers to demonstrate the general principles of polyelectrolyte nearer together than they might otherwise be. This behavior. Counter-ions may be represented by iso- is exactly the behavior that is observed in viscosity lated floating magnets of opposite polarit,y. experiments (14, 15) where the polymer salt is found to Owing to the nature of the medium and to the lack have a much smaller effective volume in the presence of any effective Brownian motion, magnets of opposite of excess neutral salt than has the parent uncharged sign are attracted close to one another immediately. polymer acid or polymer base. .77
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"Counter-iom- Ar.oci.ted;
Chain. Fully Contraoted
The magnetic model may not a t first appear to be a faithful reproduction of conditions existing in aqueous polymer solutions. The main objection, that of the absence of Brownian motion, has already been mentioned. The immediate tendency for magnets of opposite sign to undergo association is reminiscent of the behavior of strong electrolytes in media of low dielectric constant, and this model for aqueous solutions would a t first sight appear to he misleading. Hower-er, it has been demonstrated both experimentally in conductance and osmotic studies (5,4,5)and theoretically in calculations ( 6 ) , that considerable counter-ion association with the polymeric ion occurs. This arises not on account of the low dielectric constant of the medium-for in the dilute solutions used experimentally it can be little helou. the static value of 78 for water-but from the fact that the electrostatic potential energy of ions near the polyion is unusually large, i.e., several times greater than 1iT owing to the high charge density on the polyion ( 7 , 8 ) , and that as a consequence the distribution of ions betreen the polymer interface and the solution is significantly in favor of making the ions remain very near the polpion.
Butler (9,11) suggested that for desoxyribonucleic acid the abnormally high viscosities of polyelectrolyte solutions of Jhite concentrations compared with their intrinsic viscositiesand also the marked shear dependence in these more concentrated solutions-could be explained by postulating that local ionic interaction occurs in the salt-free polyelectrolyte solution (cf. 18). The reason for this effect is the tendency for counterions to attempt to complete their "Debye-Hiickel" ionic atmospheres by locally utilizing segments of the polymeric anions, no other simple ions of opposite charge being available. This would give rise to a spectrum of local interactions varying in strength throughout the polymer solution, and could explain its weak gel-like behavior. Examination of the behavior of the model readily demonstrates that this kind of interaction is possible. If a highly charged pair of model polymer particles is taken, introduction of one or two counter-ions is enough to cause local attraction where segments of the polymeric ions and a counter-ion happen to he sufficiently near to one another. The bulk of the polymeric ions are still repelled from one another hut the beginnings of a network formation are easily discerned (Figure 4). The local interactions are weak and are the result of a balance of local short-range attractive forces between one counter-ion and several charges on the polymeric anions that are nearby, and more general repulsive forces between the remainder of the polymer charges a t greater distances. Locally, the attractive forces are seen to be greater than the repulsive forces. Thus, for example, if two counter-ions of charge e are a t distances in a straight line of rl and TZ from unshielded polymer segments of charge e in two chains, the repulsive force between these two segments u-odd be
if the counter ions aere not present. Owing to their presence, however, these give rise to an attractive force on the polymer segments in an opposite direction of
Figure 4. Local Assoriation of Tar. Cheina Throvgh a Shared
"Counter-ion-
The magnetic model therefore simulates the conditions in polyelectrolyte solutions more accurately than might a t first have been supposed. It will be of interest to consider other -properties in the light of the behavior of the model. From the dependence of the reduced specific viscosity on concentration of a volvelectrolvte (10) " . . and the effects of salts and shear on this dependence, Conway and ~
per ion. For any real positive values of rl and rz the attractive forces because of the counter-ions are greater than repulsive forces between the segments. The net attrartive force demonstrated by the model is precisely similar to the Debye-Hiickel attractive force causing ionic interaction in solutions of simple strong electrolytes, and to the attractive forces in ionic crystals. By introducing counter-ions of greater valence, i.e., two or three magnets together, much stronger attractive forces are observed (Figure 5 ) and the behavior is the analogue of gelation, which can be induced experimentally in polyacrylate solutions by Ca or Ba ions (16). It is clear that the strong interaction brought about by the divalent counter-ions in this case must also occur to a diminished but significant extent when
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the divalent ions are replaced by their equivalent of monovalent ions. Such effects have been discussed by Butler and Conway ( 1 1 ) and Conway and Butler (9). By applying a small shearing force to the model in which int,erpolymer interactions of this kind exist, it
Figure 5.
stronger Local Associetion of Th...
Sharsd Polyvalent "Countel.-ion"
chains. The net attractive effect between similar chain elements depends on the diameter of the magnet "counter-ions" and is naturally greater the smaller the diameter of the associating "counter-ion," or the greater its valence. I n real solutions the local associating effect of counter-ions might be expected to be dependent on their ionic radii or, probably more correctly, upon their Stokes radii (IS). The weakness of the model is mainly that no Brownian motion is occurring (though this can be simulated by stirring the water in which the models are floated) ; the general behavior observed must occur to a greater or lesser extent in real solutions where a proportion of ions a t any instant will be relatively fixed near the polymeric ions. Experiment suggests that this proportion is not negligible and the interactions demonstrated by inspection of the model may be expected also to occur in real solutions.
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ACKNOWLEDGMENT
This investigation has been supported by grants to can be demonstrated that movement of one polyrnermodel particle can be conveyed to the other interacting the Royal Cancer Hospital and Chester Beatty Research model through the magnetic linkage, provided the speed of motion is not too large. At higher speeds of motion the local interaction is ruptured. The marked dependence of viscosity of nucleic acid on shear a t all but the highest dilutions suggests that this kind of process is in fact occurring (18) and that the high sheardependence at very low rates of shear arises from local electrostatic interactions that are progressively broken with increasing rates of shear. I n addition to the local rupture of interchain interactions by the shearing force, the chains are forced into a configuration in which they are parallel. When this occurs, local attractive interactions are outbalanced by a general repulsion between the similarly charged parallel chains. For comparison, the experimental concentration-dependence of reduced viscosity of polyelectrolytes a t high rates of shear is much diminished, compared with the behavior a t low ~~~~i~~~~ from the ~ ~ i ~~~i~~ ~ i ~cancer h campaign, or zero shear, and the effect of neutral salts is less. the J~~~cofni childs ~ ~~~~d for ~ ~ ~ ~d This suggests that i n t e r p o l ~ ~interactions r are Research. the Anna Fuller Fund. and the National u. w.
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polymer chain necessarily finds itself in an atmosphere of counter-ions at various distances from the charged LITERATURECITED chain, the total charge in this atmosphere being equal ( 1 ) ARNOLD, .- - ..- R., - -. AND J. TH.G . OVERWEEK, Rec. trau. chim., 69, and opposite to that on the polymer chain. Owing to 1YZ (IY5U). the lack of Brownian motion hthe model, this situation (2) H ~ Z E N GJ.A R., , P. F. GRIEGER, AND F. T. WALL,J. Am. is difficult to achiere with the magnets. However, the Chem. Soc. 72,2636 (1950). behavior of the mametic model in an atmosvhere of (31 . , WALL.F. T.. G. S. STENT.AND J. J. ONDREICIN.J. Phus. & olioi id ch'em., 54,979 (i950). counter-ions, qualitatively approximating that existing W., Z . physik. Chem.,A181,249 in real solutions, may be studied by placing the chain of (4) ( 5 ) STRAUSS, U. P., AND R. M. Fuoss, J . Polymer Sci., 4 , 457 magnets among magnets of opposite polarity fixed a t (1949). various positions in the bath (Figure 6). Under these ( 6 ) Faoss, R.M.,A. KATCHALSKY, AND S. LIFSON,PYOC. m. Acad. Sci. U.S., 37, 579 (1951). conditions the local effect of any given counter-ion in ( 7 ) KATC~ALSKY, A.1 Endeauour, 12,90 (1953). effecting association between two chains of the type ( 8 ) KATCHALSKY, A., "Prooeedings of the symposium on shown in ~i~~~~ 4 and 5 is diminished, owing to the mscromolecules, Uppsala, 1953," J. Polymer Sci., in press. simultaneous attractive effects of neighboring counter( 9 ) c,,,~,, B. E,,AND J. A, V. B ~ J , polymer ~ sci., ~ in ~ ions in an opposite direction on the elements of the press.
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480 (10) POUYET, J., J . chim. phys., 48,90 (1951). (11) BUTLER,J. A. V., AND B. E. CONWAY, Nature, 172, 153 (1953). (12) CONWAY, B. E., AND J. A. V. BUTLER, J . Polymer Sn'., 11, 277 (1953). (13) ULICK, H., A. EUCKEN, and K. L. WOLF,H a d u n d Jahrbuch der ehem. Phys., Leipzig, 6, 120 (1933). (14) Fuoss, R. M., Discussions Faraday Soc., 11,125 (1951).
JOURNAL OF CHEMICAL EDUCATION (15) DOTY,P., AND G. EHRLICK, Ann. Rev. Phys. Chem., 3 , 81 (1952). J . Polymer Sci., 7 , 83 (16) WALL,F. T., AND J. W. DRENNAN, (1951). E. J. W., AND J. TH. G. ~ R B E E K "Theory , of (17) VERWEY, the Stability of Lyophohio Colloids," Elsevier Publ. Co., Amsterdam, 1948. (18) LANGWR,I., J . Chem. Phys., 6 , 873 (1938).
