VOL. 4. NO. 11
SOVIET PHYSICS - SOLID STATE
KABA SS62
0201
,,'"
CERTAIN PECULIARITIES OF COMPRESSIBILITY
OF MOLECULAR CRYSTALS
S. S. Kabalkina
Institute of High - Pressure Physics. A cademy of Sciences. USSR. Moscow
Translated from Fizika Tverdogo Tela. Vol. 4. No. 11.
pp. 3124- 3128 . November. 1962
Original article submitted June 12. 1962
Data on the linear and volum e compressibility of lin ear polyphenyls (biphenyl. terphenyl. and
quaterphenyl) are give n. from wh ich the following conclusion is drawn: The compressibility of
a molecular crystal depends on the ratio of van der Waals and covalent bonds in its structure;
the higher the statistical weight of van der Waals bonds. the more compressible the crystal.
From this st andpoint a molecular crystal is anisotropic whenever the molecule's shape differs markedly from spherical. or when the crystal contains hydrogen bonds.
It is well known that twO types of interaction occur
molecular crystals: covalent interaction between
atoms of one molecule a nd weak van der Waals interaction between molecules. Obviously. the intermolecular
distances are shortened first under high pressure. Hence.
it is natural to assume that th e compressibility of any
member of the class of substa nces under consideration in
the 1-15.000 kgl cm 2 pressure ran ge depends on the numb er of van der Waals bonds in its Structure or. more precisely. the numeri cal ratio of covalent and van der
Waals bonds in the unit cell. However. the numerous
data on the compressibility of organic substances. obtained by Bridgman [1.2]. cannot be used to illustrate
this hypothesis. The explanation must be sought in the
fortuitous choice of subje cts for investigation. which included purely mo ecular crystals without hydrogen bonds
and crystals with hydrogen bonds; nearly all compounds
differed in type of crystal structure and had molecules
of different configuration.
In order to ascert ain the fa ctors determining the
compressibility of molecular crystalS. we decided to
study the effect of high pressure on the structure of a
series of isomorphous hydrocarbons. The following linear
polyphenyls: biphenyl. terphenyl. and quaterphenyl.
whose molecules have geometr ically similar configurations and ioentical structures with equal parameters~.,e..
and B [3.4.5). were chosen as subjects for investigation.
The parameter ~ decreases by about 4.2 A on passing
from terphenyl to biphenyl or from quaterphenyl to terp eny.
The investigation was conducted in a special highpressure x-ray camera [6] in copper radiation. Powder
patterns of biphenyl. terphenyl. and quaterphenyl at
various pressures are shown in Figs. 1. 2. and 3. Results
of the x- ray investigation of polyphenyls at pressures up
in
to 10.000-12.000 kg/cm Z are shown in Figs. 4, 5. 6, and
7, The functions a(p) and b(p) are given in the first two.
c(p) in Fig. 6. and (~VIV)(p) in Fig, 7. [The functions
c(p) and (~V I V)(p) are given for biphenyl and terphenyl.]
A ccording to the data obtained, the compounds under investigation have identical linear compressibilities ~a/ a
== 5.4 ± 0.20/0 and ~b Ib == 3.0 ± 0.20/0 at p == 10,000 kg
per cm 2 ; however, ~c I c is equal to 2.2 % for biphenyl
and 1.40/0 for terphenyl at p == 10,000 kglcm 2• The quantity ~c I c was determined by using the fact that the parameter ~ decreases by the same amount ~c in biphenyl
and terphenyl under pressure. It follows from Fig. 6 that
~c == 0.20 ± 0.01 A at p == 10.000 kg/cm 2• Reliabledata
on (~c I c)(p) could not be obtained for quaterphenyl,
since. in this case, the change in c due to pressure p
2
== lO.000kgl cm is of the same order of magnitude as the
error in determining ~ at the given .,e.
2288
The following result is depicted in Fig. 7. The substances under investigation have different volume compressibilities; at p == 10,000 kgl cm 2 • ~ vi V for biphenyl
is 8.6% larger than for terphenyl. This leads to the following conclusion: All other conditions being equal
(geometrically similar molecules of identical structure),
the substance with larger molecules is less compressible.
The functions (~V I V)(p) for naphthalene and anthracene
(Bridgman's data [2] and ours) are shown in Fig, 8. Xray powder patterns of naphthalene and anthracene at
various pressures are shown in Figs. 9 and 10. As is evident from Fig. 8. ~vlv for naphthalene is about 220/0
higher than for anthracene at p == 10,000 kg/ cm 2 , which
once more confirms the above assertion.
This fact may be explained quite simply in the case
of linear pOlyphenyls. Analytically it can be shown
through the expression
(fc
Vo
m
2289
CO M P RESSIBILITY OF MOLECULAR CRYSTALS
, 1963
'I f.~ "";"'''~ ~"."
•
~
...... __ .•.'..........
21~~~~~~.>'~
:. . . .,. . . "\,. "
-1-......
..........
~':--~
~
..
~
··:,l.l~·1
."0,
3
Fig. 1. Powder patterns of biphenyl, taken at various pressures on one film.
Pressure..e (kg/ cm 2 ): 1) 1 (before compression); 2) 12,600; 3) 11,900; 4)
11,40 0; 5) 1 (after removal of pressure).
j
I
Fig. 2. Powder patterns of terphenyl, taken at various pressures on one film.
Pre ssure..e (l<g/ cm 2): 1) 1 (before compression); 2) 8300; 3) 6000.
5, 6, a nd
firsr two,
unctions
Fig. 3. Powder patterns of quaterphenyl, taken at various pressures on one
film. Pressure.E (kg/ cm 2): 1) 1 (before compression)! 2) 8000; 3) 11,200;
4) 1 (after removal of pressure).
L ~rphe nyl.]
under inies t::.a/ a
100 kg
ph enyl
['he quanI the paJiphe nyl
g. 6 that
able data
enyl,
lie p
,de as the
b,A
a. A
'6~
5.0
The subne combiphenyl
the fol -
5.
1.4 '---'---',_
.
.1..-...1.--'--'---'Z or 6 8 10 12
p'10'~ kg/ cm 2
~qual
ructure),
)tessible,
nhracene
8. x~ ne at
5 is evi,r 22,,/0
2, which
the case
own
Fig. 4. Dependence of parameter
on pressure for biphenyl (I), terphenyl (2), and quaterphenyl (3).
II V
-- =
V
aL---'---'---'----'8---'O---''--'?
, If 6
1 I..
P'10'~kg/ cm 2
~
!in
t:.b·
6.c
q
- - t - - - t - - - t - cot 81t'
u
be"
';v .... c~..)c inic crystals) that the difference in /::" V/ V
Y.llt;.:;s for biphenyl and terphenyl is almost wholly determined by the difference in their /::"c! c values. The lat-
Fig. 5. Dependence of parameter
on pressure for biphenyl (1), terphenyl (2), and quaterphenyl (3).
.£ .
ter follows from the fact that the first two terms (6.a/ a
and /::"b/ b) are identical for both compounds, whereas.
the term cot ec.e is very small (cot 81th :1:0.2,,/0 at p
= 10,000 kg/ cm2 ; + for biphenyl, and - for terphenyl).
Let us assume that the decrease of parameter ~ due to
pressure..e may be expressed as the sum /::"c = /::"co + /::"cl'
..
~
2290
S. S. KAI3ALKINA
it ·,
~, 'K.
c,fI
V'
0
r
t2
to
t:.
8
.
.
~.
c
•
;:
"
\. ~
,-
.~.::.r~::'~\:~.
o - I
"
"
~
Fig. 7. Dependenceof~VIVonpres­
sure for biphenyl (I) and terphenyl
(II). Experimental points: 1) biphenyl (our data); 2}terphenyl (our
data); 3) terphenyl ('Bridgman's
data).
'.
.
+
0
+Toff
8
6
6 8 W n
p 10-; kgl cm 2
o
'0
6
"
/"
,oy
I
• -Z
6-J
2
Fig. 6. Dependence of parameter ~
on pressure for biphenyl (1) and terphenyl (2).
I
V
A V 0/.
0 _,
+ -2
A-J
2
II
6
P 70
8
10
it
-! kgl cm 2
Fig. 8. Dependence of 6.V Iv on pressure for naphthalene (I) and anthracene (II). Experimental points: 1)
naphthalene (our data); 2) anthracene (our data); 3) Bridgman's data
for naphthalene and anthracene.
~
f: . .~:!.: :~.: '~:'H:ij' ~ ··~\""I .
Fig. 9. Powder panerns of naphthalene, taken at various pressures on one film. Pressure £
(kgl cm 2): 1) 1 (before compression); 2) 9300; 3) 8700; 4). 8100; 5) 1 (after removal of
pressure).
Fig. 10. Powder panerns of anthracene, taken at various pressures on one film.
Presswe £ (kg I cm2);" 1) 1 (before compression); 2) 6200; 3) 9300; 4) 10,000; 5)
1 (after removal of pressure).
where ~Co corresponds to the shortening of ~ caused by
cm 2 ) the unit cell parameters and volumes in biphenyl,
the approach of adja cent molecules, and 6.cl is the change terphenyl, and quaterphenyl change only on account of
in ~ resulting from shortening of the distance between
shortening of the ' distances between molecules; the latatoms of one molecule. Identic"l packing in polyphenyls ter maintain their shape and dimensions unchanged (redetermines the identity of van der Waals interaction of
sult of covalent bond strength). This conclusion follows
the molecules (identical atoms located at equal disfrom the fact that at a given £ the parameter ~ detances from one another interact), and hence equal 6.eo
creases by the same amount 6c in biphenyl and terphenyl.
values at the given £. The laner may not be said of 6.~
So, in the case of polyphenyls,identical vim der
values, which cannot be equal in different polyphenyls
Waals interactions exist between molecules, the number
owing to the difference in size of the molecules. Exof covalent bonds in the unit cell increases from biperiment showed that at high pressures (1-15,000 kgl
phenyl to quaterphenyl, and the ratio of van der Waals
to coval
is th e m
of van d
compres
same pa
anthrac
of van d
general
pressibil
the rati
conditio
metrica
pend on
Fro
cular cr
1.
ferent
may be
molecu
normal
Th
graphit
is an in
do not
the cry
gligibl
permit
2.
to the
sional
along s
in othe
exist).
chains
vestiga
sure th
tion pe
along t
I
.
"
/
presthra: 1)
thradata
~oy l.
, of
atreows
eoyl.
ber
Is
COMP lHiS SI 13ILITY O F M O LECULAR CRYSTALS
to covalent bonds ch.:mges accord ingly. I3iphenyl. wh ich
is the most compressible. has a high statistical \Veight
of van del' Waals bonds; quaterphcnyl. which is the least
compressible . has the lowe st \Ve ight of such bonds. The
same pattern is observed in the case of naphthalene and
anthracene. the first of \Vhich has a higher per centage
of van der Waals bonds and higher compr essibility. The
general conclusion is th is: The linear and volume compressibiliti of a m ol ecul ar crystal are determined by
the ratio of van der Waa ls and covalent bonds; other
cond itions being equal (identical structure and geometrical sim ilarity of the molecules), their values depend on the size of the molecule.
From this standpoint the compressibility of a molecular crysta l is anisotropic in th e following ca ses.
1. The s ape of the molecule differs conside rably
fro m spherical . a nd hence its dime nsions in different directions are different. Accordingly. the ratio of van der
Waals and covalent interactions will be different in different crystallograph ic directions. Normal paraffins
may be given as the first example. The molecule has
an el ongated shape; its length is many times its transverse dim ensions. According to x-ray data (ours [6.7]
for n-C 30 HG2' n-C 32H66' and n-C34,H70; Muller's [8] for
n-Cz3H48 and n-C z9 H60 ) the compressibility along the
mol ecule ' s long axis is from %0 to %0 that in the plane
norm al to this axis.
The se cond example consists of the layer structures,
graphit e, and boron nitride. In this case, the molecule
is an infinite layer in which van der Waals interactions
do not occur. X-ray investigations [9. 10] showed that
the crysta l' s compressibility parallel to the layer is negligible . and existing experimental accuracy does not
permit its m easurement.
2. CompreSSibility anisotropy also occurs in structures with intermolecul ar hydrogen bonds. which lead
to th e form ation of ch ains. ribbons, infinite two-dimension al networks. etc. Naturally, the compressibility
along such cha in s and networks should be much less than
in other dir ections (where ordinary van der Waals bonds
exist). Urea is an example of a structure containing
chains of molecules with hydrogen bonds. An x-ray investigation [11] showed that under high hydrostatiC pressure the urea crystal is compressed mainly in the direction perpendicular to the chains. The compressibility
along the chains, b. c/ c, is from %to
the compres-
%
2291
sibility b. a/ a. Another example is pent aerythritol. Hydroge n bonds unite the molecules into layers parall el to
the ab plane. the distance between layers being 3.5 A.
Our investigation showed that the compressibility b.c/ c
is 4-5 times the compreSSibility b.a/ a (at p = 10.000
kg/ cm Z, b.c/ c = 4.40/0 and b.a/ a = 1.00/0).
Still another example is tartaric acid. Hydrogen
bonds between molecules are concentrated mainly in
the (020) planes. In conformity with this, Bridgman' s
results [13J showed that the compressibility b. b/ b is 5
to 6 times the compressibilities b.a/ a and b.c/ c.
In conclusion, I thank Corresponding Member, AN
SSSR. L. F. Vereshchagin for interest in the work and a
discussion of the results.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
LITERA TURE CrrED
P. W. Bridgman, Proc. Am. Acad. Arts. Sci .. 76, 3,
83 (1948).
P. W. Bridgman, Proc. Am. Acad. Arts. Sci .. 76. I,
19 (1945).
J. Dhar, Indian J. Phys.. 2,43 (1932).
L. W. Pickett, Proc. Roy. Soc .. A142, 333 (1933).
H. Romer. Z. phys. Chem .. B23. 226 (1933).
s. S. Kabalkina and L. F. Vereshchagin. DAN SSSR,
143, 818 (1962) [Soviet Physics - Doklady. Vol. 7.
p. 310].
s. S. Kabalkina, DAN SSSR, 125. 114 (1959).
s. S. Kabalkina and Z. V. Troitskaya, Zhurnal
strukt. !<hun.,~, 27 (1961).
A. Muller, Proc. Roy. Soc., 178.227 (1941).
s. S. Kabalkina and L. F. Vereshchagin, DAN SSSR,
131. 300 (1960) [Soviet Physics - Doklady. Vol. 5,
p. 373].
s. S. Kabalkina and L. F. Vereshchagin, DAN SSSR.
134, 330 (1960) [Soviet Physics - Doklady. Vol. 5.
p. 1065J.
s. S. Kabalkina, ZhFKh. 35, 276 (1961).
P. W. Bridgman, Proc. Am. Acad. Arts Sci., 64. 51
(1929).
All abbreviations of periodicals in the above bibliography
are letter-by-letter transliterations of the abbreviations as
given in the original Russian journal. Some or all of thi~
periodical literature may well be available in En~lish translation. A complete list of the cover-to-cover English translations
appears at the ba~k of this issue.