The S tructure of L iquid H ydrogen Peroxide

The S tructure of L iquid H ydrogen Peroxide By J. T. R a n d a ll, M.Sc. Communication from the Staff of the Research Laboratories of The General Electric Company Limited, Wembley, England ( Communicated by R. H. Fowler, F.R.S. Received 21 October 1936) Much work of recent years, particularly th a t of Debye, Stew art, and Prins, has given support to the idea of structure in liquids; th a t, although atomic or ionic m otions obviously take place, there are certain interatom ic distances which on the average rem ain constant. One of the least indirect methods of approach is th a t of X -ray diffraction, and the present paper is an account of a Fourier analysis of the p attern of hydrogen peroxide. The general expression for the intensity of scattering of X -rays by any arrangem ent of atom s was first worked out by Debye (1915): V 4 1 / l + cos226»\v v s h w ^ m 2c4M 2 srpq 1 where I 0 is the intensity of the incident beam, R the distance from specimen to point of observation. (1 + cos2 26)12, subsequently abbreviated to P, is the polarization factor, 26 being the scattering angle. are the scattering powers of atom s p and q, a distance The exact form of the expression depends entirely on the sum m ation of the interference effects between the various atoms. For a monatomic liquid where the num ber of atom s lying between radii r and + is represented by 4:7rr*g(r)dr, it has been shown th a t (1) reduces to 7 - N i«^ pf { i+ S? nr r)- p)b^ dr} (2) p being the m ean density of the liquid in atom s per c.c. and N the number of irradiated atom s in the specimen. This expression is th a t which was later deduced by Zernike and Prins (1927). Another expression essentially similar to (2) was later developed by Debye and Menke (1930) in connexion with their work on liquid mercury. Strictly, equation (2) can only be used for monatomic liquids. There are liquids, however, containing more th a n one kind of atom, to which equation (2) applies approxim ately; water, examined by Bernal and Fowler (r 933), is an example. The two hydrogen protons are here embedded in the [ 83 ] G2

84 J. T. Randall oxygen ion and the molecule m ay be treated from the scattering point of view as a simple spherical unit. A nother type of example is potassium chloride where the scattering powers of the two ions are identical. In hydrogen peroxide the protons are again em bedded in the oxygens and the liquid m ay be regarded approxim ately as a system of OH groups. The question of th e existence of molecules will be considered later. W ith regard to the technique of application of (2), it has been usual to determ ine by trial and error a function which when inserted in (2) leads to an expression for I closely similar to the observed intensity curve. As Zernike and Prins pointed out, this m ay be avoided by the application of F ourier inversion to (2). A c4 T W riting P for (1 + cos2 20) j2 and k for (2) becomes I / k P - p P i sm<sr 7 477 r2[g{r) p\ ------ o sr say. Then 4:7rr[g(r) />] sin srdr. (3) Now if F(x), an odd function of x, is represented by H(m) is given (Batem an 1932) by 2 f 0 H(m) = - sin n j 0 sin mxh(m)dm, Applying this m ethod of Fourier inversion to equation (3) we have 2 r 477r[^(r) p] = sd>(s) sin rsds, nj 0 2r C00 or 47rr2g(r) = 47rr2p-\ sin rsds, 7TJo 0(s) may be determined from the experimental scattering curve, as will be shown later, and consequently (5) m ay be solved, the resulting curve of 47Tr2g(r) against r giving directly both interatom ic distances and numbers of neighbours. Expressions (2) and (5) may only be applied to the types of liquid already referred to, e.g. sodium, argon, water, hydrogen peroxide. The problem of a molecular liquid w ith effectively more th an one kind of atom (4) (5)

Structure of Liquid Hydrogen Peroxide 85 is much more complicated, and cannot usefully be form ulated in precisely this way, as each kind of atom involves its own distribution function. For m any molecular liquids, however, it would be sufficient to fix the molecular centres of gravity. For example, the determ ination of the positions of the carbon atom s in carbon tetrachloride determines the distribution of chlorine atom s, since the tetrahedral nature of the molecule is accurately known. I f any attem p t is m ade to determ ine molecular centres of gravity in this way / 2 in equation (2) m ust be replaced by F 2 the molecular structure factor. For hydrogen peroxide equation (2) becomes, for the scattering intensity per molecule, /1 Sm^OH 2 P kf0h l / 1+1, ( 6) where g{r) is now the molecular distribution function. I t is clear therefore th a t in order to obtain g(r) for molecules one m ust make use of the internal structure of the molecule. This is frequently known from other work. F ig. 1 The Penney-S utherland m odel for a hydrogen peroxide molecule 100. H ydrogen peroxide is a rather close-packed liquid, as m ay be shown from density considerations, and it appeared doubtful w hether the m ethod of equation (6) would throw any more light on its structure th an the method involved in equation (5), which assumes the liquid to be a spatial arrangem ent of OH groups. The fact th a t hydrogen peroxide is molecular does not really enter in, since all the scattering units are identical in nature. If the Fourier analysis of equation (5) were sufficiently accurate, the molecular nature of the liquid would show up in the radial distribution curve. Each OH group should then have one neighbour a little nearer to it than the rest. A ctually our analysis does not resolve the two peaks. Penney and Sutherland (1934) have carried out an analysis of the wavefunctions of the individual molecule, and their results suggest the skew model of fig. 1 with the angles 6 and (f>in the neighbourhood of 100 ; the hydrogen protons are situated at H and H. Penney and Sutherland, taking

86 J. T. Randall /^oh = ^h2o/2 cos53, obtain /i = 2 x 10~18e.s.u. favourably with the experim ental value of 2*13 x 10_18e.s.u. Bernal, in th e discussion on this paper, suggested th a t th e m olecular stru ctu re p ro posed would be likely to lead to the form ation of tetrahedral groups very similar to those shown by Bernal and Fowler (1933) to exist for water. E x per im en ta l R esults and Calculations for H ydrogen P e r o x id e Hydrogen peroxide cannot be obtained commercially in concentrations higher than 30 % and it is necessary to carry out careful distillation in order to obtain the pure m aterial. Merck s 30 % peroxide was distilled according to the m ethod given in P artington s Inorganic C hem istry, p. 298. Some considerable care is necessary, owing to the highly explosive nature of the concentrated liquid, and the whole of the distillation apparatus was protected by strong m etal gauze. Several distillations were carried out to remove w ater and the resultant liquid was colourless and oily in appearance. A sm all quantity of the pure liquid was collected in an extremely thin glass capillary tube of about l'o m m. diam eter, and sealed off. In order to obtain accurate results of X -ray scattering out to large values of sin 0/A, photographs were taken using Cu-Ka and Mo-Ka radiations. The copper radiation enables the scattering at com paratively small angles to be obtained accurately, and the molybdenum radiation achieves the same result for the large angles. Fig. 2 shows a the microphotom eter curve using Cu-Ka, and b the curve obtained when using Mo-Ka. The longer wave-length curve a shows two maxima. The main peak a t an equivalent spacing of 2-95 A is accompanied by a weak outer band, and it is difficult to estim ate the precise position of this. An approxim ate equivalent spacing is 1*40 A. In addition the broad shelf on the inner side of the main peak should be noticed. <p(s) is obtained from the experimental scattering curve as follows. The m icrophotom eter record of the X -ray scattering is transform ed into a density curve and plotted against sin 0/A. Subject to well-known limitations, this curve is equivalent to the intensity-sin 0/A curve, as yet on an arbitrary scale, and comprises both th e coherent and incoherent scattering. Use is now made of the fact th a t the scattering curve approaches t h e / 2 curve at large values of sin 0/A. To reduce the experimental scattering curve to absolute values th e steps are now (1) Correct the density-sin 0/A curve for absorption in the specimen and lack of polarization in the X -ray beam.

on September 5, 2018 Structure of Liquid Hydrogen Peroxide 87 Downloaded from http://rspa.royalsocietypublishing.org/ (2) Calculate the values of / 2 (coherent plus incoherent)* and plot the sum against sin OjX. Const, x 20 F ig. 2 a, M icrophotom eter record of scattering by hydrogen peroxide using Cu-Ka rad iatio n ; b, M icrophotom eter record of scattering by hydrogen peroxide using M o-ka radiation. 0 01 0-2 0-3 0-4 0-5 0-6 07 08 0-9 10 sin 0/A -> F ig. 3 a, Corrected scattering curve for hydrogen peroxide reduced to absolute scale; b,/ 2 curve per m olecule including incoherent scattering. (3) A djust the scale of the intensity curve so th a t it fits t h e / 2 curve a t large values of sin OjX (fig. 3) and from the difference between the ordinates * Using In tern atio n al Tables for th e D eterm ination of Crystal S tru ctu re, vol. 2, and Com pton and Allison, X -rays in Theory and E x p erim en t, p. 782.

88 J. T. Randall o b tain ( I/kP-f2). (I/kP-/ 2) / / 2, which is equal to is th en calculated. The integration of s<fi(s) sin rs ds is then carried out graphically for each value of r and the final curve of 4nr2g{r) r is plotted. The curve of s<p(s) against sin d/a. (=5/477-) is shown in fig. 4. 4nr2p was calculated from a density of 1*465 and is equal to 0*52 for r 1. 0*1 0*2 0*3 0-4 0-5 0-6 F ig. 4 s<f>(s) curve for hydrogen peroxide plotted against sin 0/A ( = s/4tt). T h e Structure of H ydrogen P ero x id e There is no reason to suppose th a t the mean OH distance determined here will differ very m arkedly from the value of 2*8 A found in crystals. Density considerations show im mediately th a t an openwork structure, such as the tetrahedral co-ordination arrangem ent suggested for water, cannot hold, unless a very much smaller OH radius than has so far been observed is accepted. Although the structure of solid hydrogen peroxide has not been completely determined, a recent exam ination (Feher and K lotzer 1935) has shown the unit cell to be tetragonal and of size 4*02 A, c = 8*02 A,

Structure of Liquid Hydrogen Peroxide 89 with 4 molecules to the cell. The volume of the cell is therefore roughly 128 A3 and the volume per OH group is 16 A3, a small value suggestive of close packing. - I ti ^ / i \ \ 0 10 2-0 3-0 4 0 5-0 r in angstrom s F ig. 5 The curve shows th e radial distribution of m atter in hydrogen peroxide. Curve a represents the m ean density. A face-centred close-packed arrangem ent of OH groups giving the requisite density of 1*465 leads to an OH diam eter of 3*0 A and the volume per OH group is then 19*055 A3. The actual volume per OH group calculated from VOH = M /2Nd is 19* 14 A3, and it m ay be assumed from this th a t the structure should approxim ate closely to th a t of face-centred close packing.

90 J. T. Randall A body-centred close packing leads to an OH diam eter of 2*9 A, and the volume per group is then 19-25 A3. The value of 2-9 A is nearer the accepted OH diam eter and only the Fourier analysis can decide between the two types of packing. Turning now to fig. 5, where 4rrr2g(r) is p lo tted of interest, it is seen th a t there are two pronounced peaks where the curve exceeds the mean density represented by curve a. These peaks are at 3-0 and 4-25 A, and their shapes enable us to estim ate the areas beneath with fair accuracy. T able I Analysis of R adial D en sity Curve fo r H ydrogen P e r o x id e Position of peak in A 3-0 4-25 Observed num ber of neighbours 11-92 6-12 Calculated num ber of neighbours 12-0 6-0 The area under a peak of this curve gives directly the num ber of neighbours at any particular distance, and the results given in Table I agree very closely w ith the calculations for face-centred cubic packing. There can be little doubt of this result; although an error in the peak position of 0-1A m ight conceivably be possible, an error of several units in the area is very unlikely. The Fourier analysis of liquid hydrogen peroxide has therefore led to a close-packed structure of the face-centred cubic type, and it is of some interest th a t the OH group appears to have its radius 0-1A greater than in water, for example. The general chemical instability of the pure substance would suggest rather weaker binding forces and the greater group radius is not inconsistent w ith this observation. T h e D ipo le Moment As already mentioned in the introduction, the Penney-Sutherland model of H 20 2 illustrated in fig. 1 appears to be the only reasonable one, with regard to the OH orientations, to account for the observed dipole moment of 2-13 x 10~18. In addition to earlier observations recent work on the R am an Effect (Simon and Feher 1935) has given evidence in support of this model. I t is therefore of interest to examine the position anew as a result of th e X -ray determ inations.

Structure, of Liquid Hydrogen Peroxide 91 In fig. 6 a is outlined a face-centred cubic cell, and the directions of the OH bond m ost likely to fit in w ith such a structure are indicated by arrows. Taking any pair of OH groups in contact it is clear th a t the angles are as shown in fig. 6 b, and 6 and 0 are both equal to 90. F ig. 6 a, Proposed orientation of OH directions in close-packed m odel; b, isolated case of single molecule 0 = <^ = 7t/2. Hence B ut from which /% 2o3 2/tOHcos45. ^ oh = /% 2o/2 cos = 2 x 0*602 X ^ 18 /% 2o, 1-9x0-707 x 10-18 2-2 x 10-18 e.s.u. 0-602

92 J. T. Randall This value is only 5 % greater th an the observed figure of 2-13 x 10-18e.s.u., and the agreement of the proposed model w ith regard to size of OH group, observed density and dipole mom ent, can be regarded as satisfactory. Summary An X -ray investigation of the structure of liquid hydrogen peroxide has been carried out, using a modified form of the Debye-Menke Fourier Analysis method. This m ethod enables not only the interatom ic positions to be determ ined, but also the num ber of neighbours of any given atom or ion. The structure of liquid hydrogen peroxide is essentially th a t of cubic close-packing and the radial distribution curve fixes the type as face-centred. This determ ination has been used to fix the directions of the OH bonds and it is found th a t the Penney-Sutherland model is the m ost probable one. The angles 6, (j), of the skew model are determ ined as n/2 rather than 100, and this gives a dipole m om ent of 2-23 x 10_18e.s.u. compared with the experim ental value of 2T3 x 10_18e.s.u. R E F E R E N C E S B atem an 1932 P artial Differential E quations of M athem atical Physics, p. 206. (Camb. U niv. Press.) B ernal and Fow ler 1933 J. Chem. Phys. 1, 515. Debye 1915 A n n. P hys., Lpz., 46, 809. D ebye and Menke 1930 Phys. Z. 31, 797. Feher, F. and K lotzer, F. 1935 Z. Elektrochem. 41, 850. P enney and S utherland 1934 Trans. Faraday Soc. 30, 398. Simon, A. and Feher, F. 1935 Z. Elektrochem. 41, 290. Zernike and P rins 1927 Z. Phys. 41, 184.