dielectric aspects of the hydrogen-bond interaction

The influence of hydrogen-bonding on dielectric parameters and, therefore, the study of hydrogen-bonding by dielectric methods, can be summarized in terms of four variables: concentration, temperature, frequency, and electric field strength. Each of these variables can be the means in suitable circumstances of acquiring significant information on the occurrence and character of hydrogen-bonding. It seems appropriate to comment briefly on two of these factors whose role has frequently been considered and to give somewhat more attention to the others.

Mansel Davies University College of Wales

Aberystwyth, U. K.

Concentration

Dielectric Aspects

of the Hydrogen-Bond hteraCti0n

I n respect to structure the appropriate low-frequency dielectric function is the molar polarization (P) as this provides the means of evaluating the molecular electric dipole moment (p). The well-known Debye relation for the low frequency permittivity (eo) expresses this in a way which is strictly valid only for the dilute gaseous state

V is the volume occupied by a gram mole (N) of molecules and a is the sum of. their electronic and atomic polarizahilities. More immediately acceptable for the liquid state, and therefore also applicable to solutions, are modified versions of this relation due to Onsager, Kirkwood, and Frohlich. The Onsager relation for a pure liquid may be written for nl = refractive index in the far infrared

This, as also the original Debye equation, contains the molar concentration (1/V) as a principal term. Accord- ingly, as the concentration is varied for a compound, HA, either in the gaseous or solution states, a ready means is available to detect hydrogen bonding of the form

La 2HA == (HA).

ha,

as p (obs) will vary with concentration except in the un- likely circumstance that 2[p(m0nomer)]~ = [p(dimer)I2. In those cases where p(dimer) = 0 a rather direct esti- mate of the equilibrium constant K,, = kLl/kn is pos- aible (1).

More generally, hydrogen bonding between molecular species X and Y in solution is most immediately as- sessed in terms of the dielectric increment Aro = to- (solution) - ro(solvent), where eo is the low frequency permittivity of the medium. In a nonpolar solvent S,

and for molar concentration Cx of the molecules X, an increment

As0 = ksx.Cx.pxg

will he found in dilute solution where px is the effective electric moment of X in tbat solvent. Similarly for CY and py2; and if Y is added to a solution of X in S, the increment in ro it then induces will only be

if no interaction between X and Y occurs. If a complex (X-Y) is formed, initial addition of Y to the X solution will give increments of the form

where pxy is the effective moment of the new (X-Y) species (see Fig. 1). These relations, which can give

Figvre 1 . Dielectric increments, Am = M (lolutionl - ro (solvent1 ploned .agoinst molar concentrotion for dilute solutions (<1M) of polor molecules X and Y disrolved separately in solvent 5. (11 represents addition of Y to o $olutlon of X with its complete ionversion to the (hydrogen bonded) complex XY; (2) reprasenb the partial (equilibrim) formotion; X + Y ;;: XY.

pXY and the ready possibility of evaluating the equilibrium constant (KxY) for X + Y XY have been ex- ploited in a number of studies (#). Both these factors, pXY and Kxu are of major significance in evaluating the hydrogen-bonding which may be present in (X-Y) ; and the temperature variation of KxY gives the all-important enthalpy of the H-bond formation.

Temperature

Temperature is important as a variable in at least three ways. As already indicated, it gives a basis for the deduction of enthalpy changes-but this, thanks to the operation of the Boltzmann factor, is one of its almost invariable characteristics. More significant is its use in relation t.o the Debye or Onsager equations to provide one of the most reliable methods of evaluating p. A4easurements a t one temperature lead to only if the factors a (Debye) or n12 (Onsager) are known. This is where appreciable uncertainty can enter into the evalua-

Volume 46, Number I, January 1969 / 17

tion of @-and especially so for some hydrogen-bonded species. The instance of the carboxylic acid dimers may be mentioned: according to the value of a(dimer) thought to be appropriate the value of ~(dimer) estimated in solution (1) can vary from 0.0 to 1.6 D. It is probable that the value p(dimer) = 0 is essentially correct (3): a gas-phase evaluation in which P(dimer) is plotted against 1/T gives both a(dimer) and p(dimer) explicitly. The same instance may serve to illustrate a certain arbitrariness in the concept of the molecular dipole moment. In condensed phases (solution, liquid, or solid) this arises not only from uncertainties in a (or n12) but also from the inescapable fact that all that can be directly measured is the product of the molecular moment (p) with the resultant moment formed by it and its environment ( j i ) or

,2 (oh) = ,'p = g #'

where g is Kirkwood's structural factor (4). At present, g has rarely been evaluated independently. This emphasizes the greater significance of gas phase values where g = 1.00. The gas-phase p (dimer) = 0 for the carboxylic acids is accompanied by an unusually large a value, i.e., an unusually large a (atomic) value. This means that the molecule in its ground vibrational state has a zero moment but that there are many vibrations in the far infrared of smaU amplitude ot a few with large amplitude and, when activated, these are equivalent to an appreciable moment. The molecule is thus readily distorted from its symmetric zero-moment configuration. I n this sense the zero moment depends upon the frequency a t which one observes the molecule, but this is perhaps an academic point as one has to cross from the microwave region well into the infrared (with say v = 3 X 101° Hz, or D = 1 cm-' as the crossing point), before these vibrations are encountered.

The third use of temperature is in relation to dielectric absorption where it can partly replace frequency as a variable: measurements a t one frequency over a range of temperature are equivalent to those over a range of adjacent frequencies a t one temperature. And the use of frequency provides much further insight into hydrogen-bonding conditions. Frequency

As a polar molecule in any medium and specifically in the liquid phase will take a finite time to reorient in the direction of the applied field, it is not difficult to find a frequency so high that the molecules have no opportun- ity to reorient and the permittivity falls to a value characteristic of a nonpolar material: this fall of r with frequency from ro (at zero or low frequency) to r, (where dipole reorientation can no longer occur) is the dispersion of the permittivity and is itself an adequate reason for abandoning the term "dielectric constant" for r. Again we follow Debye who showed the conse- quences of the simplest representation of the decay of polarization in time when the orienting electric field is removed: p(t) = p(0)e-" = p(0)e-"/'. The dipole relaxation time (r sec) is clearly the reciprocal of the first-order rate-coefficient (k sec-I). Debye deduced (6)

( t o - e m ) e' = e , + - 1 + w2rs

(1)

w is the angular frequency of measurement = 2rv (rad sec-I), s' is the frequency dependent permittivity and s" is the dielectric loss factor whose measurement immediately defines T (or = 1 for the maximum value eW(max) = (eo - rm)/2). General rate-theory relations will apply to ( l /r) so.that we have

(I/?) = wexp (-AH'IRT)

Empirically one can use the Arrhenius version: uo = A, AH* = AHA*. Alternatively, Eyring gives

v0 = (kTIh) exp (AS=*/R)

But Eyring's is an inappropriate model for molecular dipole rotation and an obviously more apposite and ex- perimentally better justified one is Bauer's, which may be reduced to

no = (kT/2 4'"exp (ASn'IR)

where I is the moment of inertia of the (rigid) reorient- ing dipoles

AHA* = AHB* + 'IIRT = AHE* + RT

These relations provide the means of studying the rate and activation energy of dipole reorientation and its influence by hydrogen bonding. An extensive literature exists on these studies and only some aspects can be picked out for mention (6).

Water is certainly a hydrogen-bonded liquid, but it is (among other features) remarkable for showing appar- ently zero influence of hydrogen-bonding in many dielectric aspects. First, when the correct value of nlz = c, = 4.5 is inserted in Onsager's equation for the pure liquid, p(H,O) varies from 1.83 D at O°C to 1.76 D at 50°C, while @(HzO vapor) = 1.83 D. This "normality" is not surprising in one sense: the (X-H) bond length displacement in most hydrogen-bonds is a t most some few per cent: in the absence of a drastic change in charge distribution the "bond dipole moment" [a concept of only limited validity] will change to only the same extent. Remarkably, the whole of the dipole dispersion of water fits very closely the <elations (1) and (2). This means the dipole reorientation process is defined by a single rate coefficient: and this despite the unquestioned presence of aggregates of differing molecular complexity. Furthermore, if ~(298'K) = 6.8 X

sec is used with Debye's relation for a spherical molecule of radius r in a medium of viscosity q

the value r(H20) = 1.3: k is deduced, in comparison with the value of 1.4 A for r(HgO) from b (van der Waals) or from the crystal density. However, this is a coincidence, best forgotten. The activation energy AHe* is 3.Qn kcal mole-' for liquid HzO, which com- pares with AH*(q) = 4.2 kcal mole-' for its viscosity. These value are somewhat larger than those for non- hydrogen-bonded liquids (7). However, AHB*(T) for D,O liquid is -4.3 kcal mole-'. This larger value for D20 almost immediately rules out any contribution to the H-bond energy in water from proton-tunnelling, which would lead to weaker bonding in D20.

Especially interesting is a comparison of the data for water and ice near O0C, given in the table. It is seen that there is almost smooth continuity in t o , but 7

changes dramatically and AHB*(~) = 13.5 kcal mole-I

18 / Journol of Chemiml Education

Dielectric Parameters for Liquid Water and Ice . X , ~ + ~ .

' Supercooled liquid.

for HzO ice; and AHs*(r) = 13.7 kcal mole-' for D20 ice again firmly excludes proton-tunnelling.' These features show that at low frequencies the total molecular dipole moment is as well able to reorient in ice as in water but the activation energy is about three times as large. What do these observations amount to? A reasonable very brief summary appears to be that molecular dipole reorientation in water and in ice occurs by individual hydroxyl groups rotating from one H bonded position to another

In the liquid it is plausible to suggest that this can occur by the breaking (on average) of approximately one H- bond, in ice perhaps an average of three such bonds must be broken. The ice-lattice provides four bonds per HzO molecule, and a minimum energy demand is that this reorients by keeping one bond fixed and rotating about it. The situation is not quite that simple as such reorientation will originate at defects in the lattice and, statistically, less than three bonds per molecule need be broken (8).

Perhaps the.most interesting water system, dielectrically speaking, is that of the "gas hydrates" or, as better describes their structure, the ice clathrates. In these crystals foreign ("guest") molecules (G) are en- trapped in well-defined cavities which form part of a number of alternative cubic ice lattices. Two common types have ideal compositions G . 5.8 H20; G. 17 H,O. In the latter (structure I1 ice-clathrates) all the guest molecules are in essentially spherical cavities which can accommodate molecules whose van der Waals diameters do not much exceed 6.7 A. Tetrahydrofuran

CH1-CHI

I ? CH-CH1

ice clathrate (mp 5.1°C) is in this category and the two dipole relaxations which can he studied in it are of im- mediate interest in terms of hydrogen-bonding. David- son and coworker established the character of the water molecule reorientation in these ice-like lattices. I t conforms very closely to the simple Debye pattern as is shown by the plot of e" against e' introduced by Cole and Cole on the basis of the relation obtained by elimi- nating w r between eqns. (1) and (2)

That is, as a significant factor in the H-bond energy.

Figure 2. A Cole-Cole I2 versvs 6') plot of the dielectric absorption for the ice-lonice in lhe tetrohydrofurm ice-clathrote. The frequencies for individual poinh ore shown: tX (rnw.1 is found n e w 15.0 kHz 7 = '/SF X 15.000 = 10.6 X lO-'sec.

i.e., a semi-circle: (x - a)a $. y2 = rZ. The THF-clathrate, Figure 2, gives for the single

process by which all its water molecules reorient: 7 =

10.2 X sec a t 199.7'K, AH=* = 8.6 * 0.5 kcal mole-'. The appreciable decrease in the activation energy from that in normal ice (13.5 kcal mole-') probably reflects the longer ?-bonds of the clathrate cubic lattice (2.78 A: cf., 2.76 A in ice) and the departures from the geometry of tetrahedral coordination of (H20) molecules in the clathrate, leading to a variety of significantly non- linear (0-H---- 0 ) groupings. These aspects, and also the behavior of water molecules in the various crystal forms of ice, have been discussed by Davidsou (9).

More unusual is the behavior of the cyclic ether molecule (C4HsO) within the ice cavity. I t could be ex- pected that this molecule would hydrogen-bond with one of the many (0-H) groups forming the walls of the cavity. The facts are very different: the THF molecule is able to reorient as completely and as rapidly in its ice cage at 88°K as it would in most solvents a t room temperature. The relevant factors are: T = 11 X 10-l2 sec, AHa* = 0.40 2 0.05 kcal mole-'. This very low activation energy (cf., in benzene solution AHe* - 2.0 kcal mole-') emphasizes the great rotational freedom of the THF molecule in its cage. Similar results have been found for other molecules, some even more lia- ble to H-bonding, e.g., acetone. This surprising state of affairs does not.mean that there is no significant interaction between C4Ha0 and H20. What it emphasizes is that in the pseudo-spherical field of the ice-clathrate cage the guest molecule encounters a very smooth local energy contour: thus the guest molecule finds only an insignificant harrier to rotation from any supposed at- tachment to one site on the cage wall to adjacent ones. Clearly, the cage also has adequate volume for the guest molecule to rotate.

This situation is repeated in other clathrates (10). In the pquinol lattice the cage has two of its faces formed by hexagonal arrays of hydroxyl groups. Within these cages some typical activation enthalpies for guest-molecule rotations are, in kcal mole-': HCl < 1; SO, < 1; HCN = 1.4; HCOOH = 3.6. I n all these instances the low frequency permittivity led to a dipole moment matching that for the guest in the gaseous or dilute (benzene) solution: for HCOOH, p (clathrate) = 1.8 D, the value for the monomer molecule in benzene. Nevertheless, the increased activation term for. (HCOOH) implies significantly larger variations in the local field, some of which are

Volume 46, Number I , January 1969 / 19

probably due to steric factors and some to localized hydrogen-bonding forces. These features are clearly of general relevance to molecular motion in hydrogen- bonding solvents.

Some other examples showing the character of H-bonding in the solid state may be quoted. In the long-chain secondary alcohols Meakins found a com- paratively low-frequency absorption (urn., < 1MHz) which disappeared more rapidly than the concentration decreased as the alcohol was diluted by solid solution in a hydrocarbon. As the crystalline alcohol shows a larger permittivity than the liquid a t the freezing point, the indications are that a chain association of (0-H) groups already present in the liquid is extended by their further alignment in the solid. There is much evidence suggesting that the strong dipolar absorption is then the result of a reversal of such an array without much move- ment of the rest of the molecule

This secondary alcohol absorption has an activation energy - 6 kcal mole-', which also suggests that H-bond rupture may be a major feature of the rate process. Significantly, the similar absorption in the primary alcohols has an activation energy of 15 kcal mole-'. Very probably the reason for this notable increase is the head-to-head strncture of the primary alcohols giving a double array of hydroxyl groups

On this simple basis one can at least represent two H-bonds being formed per hydroxyl group: the activation energies imply some such situation.

Many polar molecules of approximately spherical shape rotate in t,he crystal form stable below their melt- ing points. One such group consists of camphane de- rivatives, and activation energies for molecular reorientation in the solids include the following values (kcal mole-'): camphene, 2.5; camphor, 2.1; horny1 chloride, 2.8; iso-borneol, 5.8. The higher value for iso-borne01 is certainly related to the interaction between the hydroxyl groups; and detailed changes with temperature of its dielectric absorption show the in- cidence of this interaction (11): at -20°C the interaction suffices to tie all the molecules rigidly together and the permittivity (eo = 2.58) then becomes equal to the optical value (nd = 2.55).

One of the most interesting features which should be "seen" dielectrically, when it occurs, is that of proton- - + jumping: (X-H---Y)-(X---H-Y.) Dipole moment measurements suffice to show when such intra-molecular ionization plays an important part in the structure. Thus the pyridine complexes of a sequence of carboxylic acids have the moments (1 2)

However, such "static" values show that the proton has jumped (e.g., in pyridine-trichloracetate), without catching it, frequency-wise, in the act of jumping. To ohsewe the jump-frequency dielectrically, favorable conditions must he established: the energy difierence between the alternative positions of the hydrogen must be small and the barrier between them must also be low; in the solid phase where such a process is likely to be cooperative (i.e., to entrain a large number of jumps in different molecules) a net change in dipole polarization must occur-although it will not necessarily arise owing to symmetry features. It should he emphasized that a t present (March, 1968) no proton-jumping appears to have been clearly established as the source of an absorption process in the dielectric region (10-"10" Hz), and this despite numerous explorations in a number of laboratories. I t is probably a sound conclusion that the jumping process is far less frequent than much of the literature implies. However, there are reasons why it may not readily be seen even when it might occur. The symmetry aspect can be illustrated

/o---H-0 \

,o-H---0

R-C A )C-R * R-C a B ,C-R

\c-H---o \o---H-~

by the zero dipole polarization difference for A cr B: then, the absorption may be narrower than is usual for dipolar absorptions, and its frequency may be beyond that (8 = 3 cm-') usually reached in dielectric studies, i.e., i t may occur in the far infrared region only now be- coming generally accessible.

Some specific results should be mentioned: the sodium salt of (calf-thymus) desoxyrihonucleic acid (DNA) has been studied and found to have only two dielectric-type absorpt,ions (IS): one due to conduc- tivity and the other B Debye-type absorption with T = 3 X 10-l2 see, both thought to be due to the presence of water. The latter relaxation time is less than that for liquid water at the same temperatures (T = 10 X sec a t 20') and implies, if nothing else, that the water molecules in DNA have unusual freedom of reorientation. In Rochelle salt, the dispersion of the (ferro-electric) permittivity is of especial interest: the very high values, ro - loa, it has been suggested are at least partly due to proton-jumping in a hydrogen- bond. The high-frequency dielectric absorption has been described (14) as of a Debye-type, with some dis- tributions of relaxation times about a mean value. However, the opinion has also been expressed that it is actually narrower in frequency than a Debye process: this means it partakes of a resonance character. This, if confirmed, would certainly establish it as abnormal and as arising from a dipole transition having a specific (resonance) frequency. A similar absorption is said to he present in the analogous (and simpler) case of potassium hydrogen succinate (IS)

20 / Journol o f Chemical Education

If furtber study codfirms them imtacea an important (and rather direct) insight into the field conditiorm of theee hydrogen bonds will be available.

It is clear that dielectric hrpt iorm provide a manu cf meamring rates of molecular pmceaxa involving a dipole moment change, e.g., dipole mrientation, ion jumping, eta. Accordingly, it ahould be pmsible, in suitable ci-ces to measure the rate at which a hydmgen-bond is formed. A situation of the geatost inter& in that of the (reylar helix) + (random coil) t d t i o n in the synthetic polypeptidm which simulate, in this reversible confirrurational c h g e , the usually imvemiile denaturation of pmteim. The helix, e.g., in poly (+enryl-~-glutamate) (PBLG) hss 3.4 mono r uni6 per spiral turn, eaeb unit adding - 1.5YP the ** of the rigid helix wtmm dluneter is -18 Each unit is held in p h dong the spird , a bydmgen bond, c N - H - - O - D 3 formed C

tween groups on one t- with those of 6e next turn. Dieledric studies (16) have quantitatively confirmed the helix structure in mlution and dm shown (from chaweu in A- and T ) how the trdormation to the random coil can be detected I t can take p b on c h g e of mlvent, acidity of the medium, or temperature.

Even more striking in SC~WIUS'II merit finding (18) of an h r p t i o n near 1 M B . which uises from the rate at which individual units are able to move into position and form the hydmge.n-bond which loch them into the spiral (see Ei(lure 3). The rate coefficient for this important &p, deduced fmm the frequency of the dielectric h r p t i o n to which it gives rise, is h X 10' see-I.

Such individual rates ue far too rapid for measurement by any chemical method. The evaluation of activation enthdpiea and entmpim for such p- will pmvide information of the greatest biomolecular interent.

Basically, the dielectric h r p t i o n a p p m because there is a change in the effective molecular dipole moment when the mndom coil goen to the h e l i As an increase in the moment occurs on formation of the helix, the latter is favored, and its formation promoted, by an electric field (&) : a dipole G) at an angle 8 to E hss the electrid field energy - Gain 8, this d@ng when fi increasas. huthermore, the helix cMias its own intense I d electric field from the p-ee of the dipoles oripted in the direction of its axis: this meaas that as eoon as a turn or two of the helm are formed the field m created wiU significu~tly pronbte the formation of further turns. This is an important aspect of the formation of the helix with its low confiyrational entropy from the tandomly wiled chain. Finally, as the next paragraphs wiU show, a strong electric field (as in present in the helid atructure) can dso promote a (reversible) protomjumping p-

This p- could well be involved in the traasmission of ow impulaoe in such protein and nucleic acid structures ss contain helid polypeptidm.

Tbe final variable in them dielectric studim is the electric field strength (&). Tbe normal working fields (up to 100 V cm-3 produee suab small cbangm in dipolar energy (pE << kT) that their effeeta are strictly proportional to the field ntmngth. In exceea of 10' V em-' small departures from the lineor rssponse be- come detdable, in the aenw that mme &I of eventual "dipole aatumtion" (i.e., complete dipole orientation) may appear. Debye, Battoher, and othm (6) have treated this nonlinearity for rigid polar moleculm, but

Piek-w and his students, who have studied thme &ecb for ova thirty yeam, have established (17) featma far more in- tercsting and molecularly rev* than the non- liwuity fmmaatumtion. The obmrvatio~ on 1- p e n b l mqy be quoted as t y p i d for by@ b o d liquids. Figwe 4 compared the "cl.asi- 4'' nonlineu effect as trp'tdy o k e d in diethyl ether, with the very much krger and more involved behavior in the alcohol. U&g Ae - [e (at high field strength) - (at lor field

be proportional to the dipole concentration in ether solutions. For pentanol the effect initially leads to an increase in permittivity before a decrease appears at higher concentrations and i t reaches a value about a hundred times that for diethyl ether. It is the concentration (and solvent) influence which is most significant. The principal factor which has been introduced to give a quantitative account of the observations is the shift of the hydrogen-bond proton under the influence of the applied field (see Fig. 5). This is an in- duced intra-molecular ionization and produces a large

increase in the effective dipole moment of the sol- " 1 b-&,n ute. From the symme-

Z try of the various multi- mers the indications are

I A 1 A.DH that the dipole effect is 0- n -------- 0 at a maximum for the

dimer and this also is the basw of the maximum in \R (Ar/EZ) as the concentra-

Figure 5. The ( 0 - H I bond length tion increases. Accord- and the energy voriotion with position of the H atom in an ( 0 - H - - 0 1

ing to Piekara's analysis bond in an dcoho~. of the data the effective

moment of the ionized dimer is 13 D, and the energy difference for the internal ionization (Au, Fig. 4) is 2.3 kcal mole-'; in the absence of strong fields, Au is estimated to be of the order of 18 kcal mole-'. The simultaneous measuremelit of the ordinary molar polarization and of the high-field effect (Ae/E2) offers the means for a more detailed analysis of the molecular equilibria in such cases zu the alcohols and, more importantly, a quantitative assessment of the (especially, electric field) conditions within the H- bond becomes possible.

Similar results, whose analysis may be simpler than for liquids, are to be found in the solid state. Such features could be of particular importance there. The hydrogen-bonding situation in crystals is frequently of a cooperative character as ferro-electric effects strikingly emphasize: and the regular orientation of dipoles or of ions which is typical of crystal lattices can itself be the

source of electric field strength adequate to promote proton-jumping. The significance of hydrogen-bond interactions in physiologically active molecules has frequently been pointed out (18) and their participation has often been invoked in biomolecular mechanisms, even in the theory of genetic mutation (19).

Literature Cited

(1) POHL, H. A., HOBBS, M. E., AND GROSS, P. M., Proc. N. Y. Acad. Sei., 40, 389 (1940).

(2) S o n c z ~ ~ , L., in "Hydrogen Bonding," (Edi lo~: HADZI, D., AND THOMPSON, H. W.), Pergamon Press, London, 1959.

(3) COOP, L. E., DAVIUSON, N. It., AND SUTTON, L. E., J . Chem. Physics, 6, 905 (1938).

(4) KIRKWOOD, J. G., J . Chem. Physics, 7 , 911 (1939); Trans. Faradav Soc.. 42A. 7 (1946).

(5) For this'and 'othe; theoretical sspects see BOrrcnm, C. J. F., "Electric Polmizatian," Elsevier, Amsterdam, 1952.

(6) See also SMYTH, C. P., "Dielectric Behavioor and Struc- ture," McGraw-Hill, New York, 1955. DAVLRS, M., "Some Electric and Optical Aspects of Molecular Be- haviour," Pergamon, London, 1965.

(7) BRANIN, F. H., AND SMYTA, C. P., J . C h m . Physics, 20,1127 (1952).

(8) BJRRRUM, N., Mat. Fys. Medd. Dansk. Vid. Selsk., 27, 3 119.51). , ~~ ,

(9) DAVIDSON, D. W., in "Molecular Relaxation Processes," Chemical Society (London) Special Publication No. 20, London, 1966.

DAVIES, M., AND WILLIA~S, K., Trans. Fa~aday Soc., 64, 529 (1968).

CLEMETT, C., AND DAVIES, M., Trans. Farad. Soe., 58,1705, 1718 (1962).

DAVIRS. M.. AND SOBCZYK. L.. J. Chem. Soe. (London). 3000 . . (1962). GOUGH, R., PLD. thesis, Univ. df ~ales;'1965.

(13) SORCZYK, L., (Wroclaw), personal communication. (14) AKAO, H., AND SABAKI, T., J. Chem. Physics, 23, 2210

(1955). (15) WADA, A,, J. C h m . Physics, 29,674 (1958); 31,495 (1959);

J . Polymer Sri., 45, 145 (1960). (16) SCHWARZ, G., AND SEELIG, J., Riopolymw~, in press. (17) MALECKI, J., J . Chem. Physics, 36, 2144 (1961). PIEKARA,

A,, J . Chem. Physics, 36, 2145 (1961). PII:KARA, A,, in "Nuclear Magnetic Resonance and Relaxation in Solids," North-Holland Puhl. Ca., Amsterdam, 1965.

(18) D.WIES, M., Chemistry and Industry, 614 (1953); 1191 (1968).

(19) LOWDIN, P. O., Rev. Modern Physics, 35, 724 (1963).

22 / Journol o f Chemical Education

dielectric aspects of the hydrogen-bond interaction

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