28 October 1996

EISEVIER Physics Letters A 222 ( 1996) 19% 198

Intermolecular ordering of hydrogen-bonded

S. Sarkar, R.N. Joarder

PHYSICS LETTERS A

liquid glycerol

Department of Physics, Jadavpur University, Calcutta 700 032, Indiu

Received 23 May 19%; accepted for publication 3 1 July 1996 Communicated by J. Flouquet

Abstract

Analysis of X-ray diffraction data on trihydric H-bonded liquid glyceroloshows that at room temperature on the average

each glycerol monomer has 6.5 hydroxyl neighbors at a distance of 2.95 A. The comparison of intermolecular X-ray and neutron pair correlation function curves and the number of H-bonds per monomer suggests the possibility of parallel orientational correlation among the neighboring molecules and the combined analyses via X-ray and neutron data show that this possibility is not ruled out.

PACS: 61.25

1. Introduction

Liquid glycerol is a trihydric liquid alcohol con- mining three hydroxyl groups and is able to form H-bonds with neighboring molecules in the liquid state. Since there is no general method for the analy- sis of the diffraction data of such complex liquids, we have no clear and conclusive evidence about the intermolecular ordering in liquid glycerol. In the present study, we have first tried to find the number of neighboring molecules associated with each glyc- erol monomer in the liquid state, using available X-ray diffraction data. We then compute the real space total pair correlation functions from X-ray and neutron diffraction data available in the literature and compare them to identify the intermolecular atom- atom radial distribution functions. Finally, we have tried to test a model of parallel orientational correla-

Neutron diffraction data [2] at 296 K are available up to k= 16 A-‘.

It is now quite well-known that an isolated glyc- erol molecule is capable of exhibiting several alter-

_y a

tion of neighboring glycerol monomers in the liquid state. X-ray diffraction data [l] at 300 K is available for the momentum transfer k = 0.2 to 9.0 A-‘. Fig. I. Structure of the D-glycerol molecule.

0375~9601/%/$12.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PII SO375-9601(96)00612-3

196 S. Sarkar. R.N. Joarder / Physics Letters A 222 (1996) 195-l 98

Table 1

Structural parameters of liquid glycerol

Parameters Neutron scattering X-ray scattering

(296 K) 131 (250- 350 K)

rc [c2 (A) 1 S92 1.559

rc,c, (8) 1.506 1.532

rco (A) I .366 1.439, 1.424, 1.358

rco (A) I .090 _

;

28.6 31.6”

34.1” _

:,e

- 20.6 - 9.0”

112.8” _

9 109.3” _

Jr 112.3” I 10.94”

native isomeric forms in equilibrium at room temper- ature. In the X-ray scattering measurements [l], the single elongated molecular conformation observed in the crystal [2] was shown to persist in the liquid. Neutron scattering [3] assumes more general molecu- lar conformational options which can be represented as in Fig. 1 and the intraparameters are listed in Table 1.

2. Intermolecular association and ordering

For either X-ray or neutron scattering, the total structure function, H(k), is given by

H(k) =H,(k) +HJk)* (1)

where H,,,(k) is the intramolecular structure function and H,,(k) is the intermolecular structure function. The latter function contains all information about the intermolecular correlations in the liquid accessible from the diffraction experiment and can be obtained from the experimental H(k) using the above equa- tion. If the intermolecular linking is through H-bonds then the X-ray H,(k) function would be dominated by OH.. . OH terms particularly at moderate to large k. To find the number of H-bonded OH * . . OH interactions involving neighboring molecules at dis- tances rOH .,, OH, we have followed Narten and Habenschuss’ method of analysis [4]. We calculate the structure function for only OH . * . OH interac- tion using the relation

HP “‘O”(k) =nf,‘H(k)jo(kroH . ..OH)

Xexp( -hi” ...0Hk2/2)9 (2)

where fOH(k) is the scattering factor for the OH group treated as a single scattering unit and A is the rms deviation. There is good agreement between the experimental X-ray kH&k) and the calculated kHfH .“OH(k>, for rOH OH = 2.95 .k and n = 6.5 for large k data (Fig. 2). The analysis is not very convincing due to the absence of large k data. We, however, see that the real space version of Eq. (2) is more convincing. Thus the Fourier inversion of the function H,(k) is given by

1 g(r) = 1 + -

/ km”“kHd( k)

2rr’pr 0 sin kr m( k) dk,

(3) where p is the density of liquid glycerol, m(k) is the modification function [5]. The function g(r) is mainly of use in identifying the peak locations of the dominant atom-atom correlations. The most striking feature of the plot of g<,r) (Fig. 3) is the presence of a strong peak at 2.95 A which must be ascribed to H-bonded hydroxyl groups. This peak is almost com- pletely resolved and well described by a peak com- puted for 6.5 OH . . . OH interactions.

For accurate information about the H-position, analysis of neutron diffraction data is necessary. For this analysis the X-ray scattering factors are replaced by the neutron scattering lengths of the nuclei. The r-weighted total neutron pair correlation function d(r) is obtained according to the relation

d(r)=4vpr[g(r)-11.

s,, :w. i : , I 1’ 1 I

\I

-0.5 I 1 , 1 I 1 I ’ 0 2 4 6 8 11

k(A-‘)

Fig. 2. (- - -) experimental &f&k) (data provided by Dr.

Soltwisch). (- ) calculated J&“” ‘_““(k) for r = 2.95 A

and n = 6.5.

(4)

3

S. Sarkar. R.N. Joarder/ Physics Letters A 222 (1996) 195-198 197

1.6 ,

0.8 z %I

0.4

-0.4 , I , / , I , I , (

0 2 4 6 8 10 r(A)

Fig. 3. ( -_) g(r) obtained for (X-ray) experimental k.&(k).

(0) g(r) calculated for r = 2.95 A and n = 6.5.

This function $hows a clear hydrogen-bonded OD peak at 1.7 A (Fig. 4). This peak confirms the expected behavior and shows that the H-bonding in glycerol has similar characteristics to that exhibited by deuterated water and other associated organic liquids [6]. For comparison we show in the same graph the X-ray diffraction results. Both curves show at 2.8 to 3.0 A a small peak or hump which clearly signifies the positions of neighboring O-O atoms arising from a linear H-bond between two neighbor- ing molecules. This is likely because the DD and CD correlations from the methyl groups will not exhibit any spatial correlations due to the absence of specific association. Two clear humps on either side of the main peak in both X-ray and neutron data probably reflect the carbon skeleton of the glycerol molecule. For further information to give unambiguous assign- ments of individual features in d(r) curves probably H/D isotopic substitution would be necessary.

A clear feature of d(r) is the regular periodicity of N 4.5 A in the oscillations for large values of r (> 8 A>. It seems that the contributions from a large number of partial g(r) terms are sufficiently com- plex in this region to average out and give features which effectively represent the overall packing of the molecules. In this sense, the oscillatory behavior is an indication of the correlation function for molecu- lar centers. The fact that three or more orders are visible up to 20 A indicates that despite the flexibil- ity of each molecular unit, the distribution exhibits significant structural ordering.

3. Whether a parallel orientational correlation is plausible

The comparison of the X-ray and neutron d(r) curves and the number of H-bonds per monomer extracted above suggest that a parallel orientational correlation among the neighboring glycerol molecules is plausible. To test this we follow the method of analysis of Egelstaff et al. [7] to study the parallel orientational correlation of two neighboring glycerol monomers. For parallel orientational correlation be- tween neighboring molecules the molecular structure factor is given by

4 k) = F,( k)&( k)

2 d%(k) +[W) -F,"wl~dk. (5)

c

where S,(k) is the center structure factor, F,(k) is the molecular form factor, Fzu(k) is the uncorrelated form factor of the neighboring molecule, R, is a correlation distance. Using X-ray data we have cal- culated the center structure factor S,(k) using an iterative method and which is plotted in Fig. 5. We observe that the function has a double peak, whose nature is similar to that observed in other H-bonded liquids like water and methanol. Using the above S,(k) we compute the neutron molecular structure factor, a(k), and compare it with experimental neu- tron data [3] (Fig. 5). It is interesting to note that the overall agreement between the two curves is not bad.

0 2 4 i-(i)

6 8 10

Fig. 4. r-weighted total pair correlation function d(r): (- ) X-ray result. (- - -) neutron result.

198 S. Sarkar, R.N. Joarder/Physics Letters A 222 (1996) 195-198

0.16 -

_zO.lO - ”

0.05 -

0.00 , ** I , I ) I , I , 0 0 2 0 6 8

k Ii;‘,

Fig. 5. Total structure for neutron diffraction: (- - -) Calculated

for parallel orientation, (*I experimental data [3]. ( -) F,(k)

[31.

So the possibility of a parallel orientational correla- tion between two neighboring glycerol molecules in the liquid state is not ruled out. It is, however, too early to draw any conclusion from such incomplete data as we have here. The computer simulation [8] suggests a more complex ordering for liquid glycerol at room temperature.

4. General remarks

Information about the intermolecular association is obtainable from the moderate to high k region of X-ray diffraction data [6]. Since such high k data are not available, it is difficult to be accurate concerning the intermolecular association of glycerol monomers

at room temperature. We suggest from our analysis of X-ray data [ 1 I at T = 300 K that on average each glycerol monomer has 6.5 hydroxyl neighbors from other molecules within a well defined intermolecular OH. . . OH distance of 2.95 A.

The intermolecular ordering of liquid glycerol is not simple. The parallel orientational correlation be- tween two glycerol molecules in the liquid state is not conclusive although it is a plausible model de- duced from the information in the present analysis.

Acknowledgement

The authors gratefully acknowledge the financial supports of CSIR, Govt. of India and IUC-DAEF, Indore, India. They also thank Dr. Soltwisch for sending X-ray data on liquid glycerol.

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