A neutron diffraction and computer modeling study of the interatomic structure of phosphoric acid

Article abstract of DOI:10.1063/1.477824

Wide angle neutron diffraction in combination with H/D substitution was used to determine the inter- and intramolecular structure of 100% phosphoric acid (H₃PO₄, PA). From radial distribution functions g_HH(r), g_HX(r), and g_XX(r) (where X is either O or P) the hydrogen bonds were found to be characterized by a very short O...H distance (1.54 A). Within a molecule, the orientation of an OH group was found to be preferably in one of the three O-P-O planes. In the interpretation of the radial distribution functions, use was made of preliminary results of molecular dynamics simulations. Temperature effects on the structure of PA were only found in the hydrogen bond structure, which becomes somewhat less well defined when heating up from room temperature to 60°C. Polyphosphates could not be detected, probably due to the small degree of polymerization.

Full text of DOI:10.1063/1.477824

A neutron diffraction and computer modeling study of the interatomic structure of
phosphoric acid
R. Hans Tromp, Stephane H. Spieser, and George W. Neilson
Citation: The Journal of Chemical Physics 110, 2145 (1999); doi: 10.1063/1.477824
View online: http://dx.doi.org/10.1063/1.477824
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 4
22 JANUARY 1999
A neutron diffraction and computer modeling study of the interatomic
structure of phosphoric acid
R. Hans Trompa)
Van ‘t Hoff Laboratory, University of Utrecht, Padualaan 8, 3584CH Utrecht, The Netherlands
Stephane H. Spieser
Department of Crystal and Structural Chemistry, University of Utrecht, Padualaan 8, 3584CH Utrecht,
The Netherlands
George W. Neilson
H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
͑
Received 21 July 1998; accepted 22 October 1998͒
Wide angle neutron diffraction in combination with H/D substitution was used to determine the
inter- and intramolecular structure of 100% phosphoric acid ͑H PO , PA͒. From radial distribution
3
4
functions gHH(r), gHX(r), and gXX(r) ͑where X is either O or P͒ the hydrogen bonds were found
to be characterized by a very short O...H distance ͑1.54 Å͒. Within a molecule, the orientation of an
OH group was found to be preferably in one of the three O–P–O planes. In the interpretation of the
radial distribution functions, use was made of preliminary results of molecular dynamics
simulations. Temperature effects on the structure of PA were only found in the hydrogen bond
structure, which becomes somewhat less well defined when heating up from room temperature to
60 °C. Polyphosphates could not be detected, probably due to the small degree of polymerization.
©
1999 American Institute of Physics. ͓S0021-9606͑99͒50904-5͔
I. INTRODUCTION
liquid state, about 15% of P atoms are in the dimer mol-
ecules ͑pyrophosphoric acid͒.9 Consequently, some H O
2
Phosphoric acid ͑PA, main component H PO or ortho-
should be present which is formed in the polymerization re-
action:
3
4
phosphoric acid͒ is an important basic chemical; in economic
terms it accounts for the greatest expenditure on inorganic
acids, and in amount produced it is second only to sulphuric
2
H PO →H P O ϩH O.
͑1͒
3
4
4
2
7
2
1
acid. It is therefore remarkable that very little work has been
Unfortunately, however, as will be shown below, the amount
of polymerization is not sufficient to be observable with neu-
tron scattering. At room temperature, 100% PA is a syrupy
published concerning its interatomic structure. In the past,
neutron diffraction has been applied to reveal the crystal
2
structure, and concentrated solutions of PA in water were
liquid, which has a tendency to turn into crystalline H PO .
3
3
4
studied by x-ray diffraction. No data appear to be available
The crystals melt at 42.4 °C. Below this temperature the liq-
uid is probably metastable, although in principle the small
degree of polymerization could correspond to a state that has
a free energy which is lower than that of the crystalline
on pure PA in the liquid state, the focus of the work pre-
sented here. From a scientific point of view, PA offers an
opportunity to study a hydrogen bonded system in a highly
acidic environment. Many other liquids structured by O–H
hydrogen bonds have now been studied with neutron diffrac-
1
H PO . H PO contains PO tetrahedra, that in the crystal
3
4
3
4
4
turn out to be deformed due to the strong double bond char-
acter of one of the P–O bonds, rendering the covalent struc-
4
5
6
7
tion, such as water, glycerol, methanol, and glucose, none
of which, however, is highly acidic. High acidity implies a
weak covalent O–H bond. Anticipating the results of this
work, such a weak O–H bond is possibly reflected by a
relatively large O–H bond length and the consequent short-
ening of the hydrogen bond, in accordance with literature
reports of gaseous and crystalline organic acids.8
ture close to OϭP–͑OH͒ . The H atoms on three of the four
3
corners of tetrahedra form hydrogen bonds with neighboring
tetrahedra.
In this work the combination of wide angle neutron dif-
fraction and isotopic substitution of the H atoms by D atoms
was applied to obtain detailed information on the hydrogen
PA can be considered as hydrated phosphorus pentoxide
bonds and spatial arrangement of the PO tetrahedra in liquid
4
(
P O ). 100% PA is P O in the fully hydrated state and
2 5 2 5
PA. Three samples, isotopically distinct with respect to the H
atom, give different neutron diffraction patterns. Processing
these patterns results in the partial radial distribution func-
tions gHH(r), gHX(r), and gXX(r). ‘‘X’’ denotes any atomic
species different from H, i.e., O and P. These radial distribu-
tion function make possible a direct comparison of the crys-
talline structure and the structure in the liquid. The effective-
ness of neutron diffraction to determine interatomic structure
corresponds to 72.4% P O ͑w/w͒. Systems with a higher
2
5
P O content are often called super- or polyphosphoric acid.
2
5
‘
‘Poly’’ refers to the presence of polymeric phosphates
H͑HPO ͒ OH (nϾ1). Interestingly, even in 100% PA in the
3
n
a͒Future address as of 1/9/99: NIZO, Kernhemseweg 2, P.O. Box 20,
710 BA Ede, The Netherlands. Electronic mail: Tromp@nizo.nl
6
0021-9606/99/110(4)/2145/6/$15.00
2145
© 1999 American Institute of Physics
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1

2146
J. Chem. Phys., Vol. 110, No. 4, 22 January 1999
Tromp, Spieser, and Neilson
is strongly enhanced when combined with computer model-
ing. This is particularly the case where isotopic substitution
cannot be applied, e.g., for O and P in PA. In the present
work, by molecular dynamics ͑MD͒ attempts were made to
reproduce by simulation the experimental radial distribution
functions. Often, potentials of interaction between molecules
are not known in sufficient detail to reach complete repro-
ducibility. However, the modeling results enable one to in-
terpret features of the radial distribution functions in terms of
intra- and intermolecular contributions and to decompose
gHX(r) and gXX(r) in contributions from gHO(r), gHP(r),
1
bH
2
SXX͑Q͒Ϫ1ϭ
ͩ
͓b F ͑Q͒
2
2
M
D
c b b ͑b Ϫb ͒ b Ϫb
X
X
D
H
M
M
D
2
b
M
2
D
Ϫb F ͑Q͔͒Ϫ
͓b F ͑Q͒
M
H
D
bHϪb
D
2
D
Ϫb F ͑Q͔͒
ͪ
,
͑5͒
͑6͒
H
in which c b ϭc b ϩc b ,
X
X
O
O
P
P
1
SHX͑Q͒Ϫ1ϭ
͕
c b ͓SHO͑Q͒Ϫ1͔
O O
gOO(r), g (r), and gOP(r). It is stressed that it is not the
PP
c b
X
X
purpose of this work to test or improve potentials or MD
methods. Instead, the MD results are used as a guide for
interpretation of the neutron diffraction results.
͖
ϩc b ͓SHP͑Q͒Ϫ1͔ ,
P
P
and
1
2
2
2 2
SXX͑Q͒Ϫ1ϭ
͕
c b ͓S ͑Q͒Ϫ1͔ϩc b ͓S ͑Q͒Ϫ1͔
O O P P
OO PP
2
2
X
c b
X
II. THEORY
ϩ2c 2c b b ͓SOP͑Q͒Ϫ1͔
͖
.
͑7͒
O
P O P
Neutron diffraction combined with isotopic substitution
uses the fact that the nuclei of isotopes of the same chemical
element interact with the neutron in different ways, i.e., they
have different neutron scattering lengths. In general, interfer-
ence patterns in the intensity of neutron diffraction reflect the
spatial arrangement of the diffracting atoms. Therefore, as-
III. EXPERIMENTAL PROCEDURE AND DATA
ANALYSIS
A. The samples
Natural PA and deuterated PA (D PO ) were prepared
3
4
1
suming the different isotopes, in the present case H and D
in identical ways by dissolving an excess of P O ͑Merck,
2
5
are chemically identical, the difference of the neutron dif-
fraction patterns of two isotopically distinct samples reflects
the spatial distribution around the substituted atomic species.
The static differential cross section of diffraction per
atom is extracted from the total cross section after correction
for absorption, incoherent scattering, multiple scattering, and
container scattering and is expressed by
extra pure͒ in natural water and in 99.8% deuterium oxide
Merck͒, respectively. The excess relative to 100% PA was
͑
determined by titration with 0.1000 M NaOH solution. Extra
solvent was added to bring down the concentration to as
close to 100% as possible. The two concentrations obtained
this way should differ by less than 1% in the number of
31
atoms per unit volume. The P nuclear magnetic resonance
͑
NMR͒ spectrum of the two types of PA showed quite dif-
ferent quantities of pyrophosphoric acid ͑dimeric PA͒, corre-
sponding to a much larger difference in P O content. A
F͑Q͒ϭ
c c b b ͓S␣␤͑Q͒Ϫ1͔,
␣ ␤ ␣ ␤
͑2͒
͚
␣
,␤
2
5
possible explanation is the slow establishment of the equilib-
rium molar weight distribution in polyphosphoric acid after
different thermal histories of the two samples. Because titra-
tion is considered the most reliable way to determine the
concentration, no effort was taken to reconcile titration and
NMR results. Total neutron scattering cross sections turned
out to be consistent with similar atomic number concentra-
tions. The sample of mixed isotopic composition was made
by combining natural and deuterated PA in weighted quan-
tities corresponding with a final composition of 48.7% H and
51.3% D.
in which c␣ is the atomic fraction of species ␣, b␣ is its
neutron scattering length, and S␣␤(Q) is the structure factor
of the spatial correlations of atomic species ␣ and ␤. From
F(Q) for three different H/D ratios, i.e., F (Q), F (Q), and
D
H
F (Q), ͑where M denotes a mixture of H and D͒, three
M
structure factors are obtained:
1
1
SHH͑Q͒Ϫ1ϭ
ͩ
͓F ͑Q͒
D
2
H
c ͑b Ϫb ͒ b Ϫb
M
H
D
M
1
ϪF ͑Q͔͒Ϫ
͓F ͑Q͒ϪF ͑Q͔͒
ͪ
,
M
D
H
B. The experiment
bDϪb
H
The neutron scattering experiment was carried on
SANDALS of the ISIS Facility at the CLRC Rutherford
Appleton Laboratory, Oxon, UK. This time-of-flight instru-
ment has detector angles between 4° and 36°. The Q range
͑
3͒
1
bDϩbH
SHX͑Q͒Ϫ1ϭ
ͩ
͓F ͑Q͒
D
2
c c b ͑b Ϫb ͒ b Ϫb
Ϫ1
H
X
X
H
M
D
M
used was from 0.5 to 40 Å . To contain the sample a flat
3
.5ϫ3.5ϫ0.1 cm TiZr sample cell was used. Data were col-
bDϩb
M
H
ϪF ͑Q͔͒Ϫ
͓F ͑Q͒ϪF ͑Q͔͒
ͪ
,
lected at room temperature ͑Х25 °C͒, where the liquid phase
is metastable, and 60.0 °C. A temperature of 60 °C was cho-
sen to probe the structure well above the melting temperature
M
D
H
bDϪb
͑
4͒
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J. Chem. Phys., Vol. 110, No. 4, 22 January 1999
Tromp, Spieser, and Neilson
2147
TABLE I. Coefficients of F(Q)s in Eqs. ͑3͒, ͑4͒, and ͑5͒. Units are
Ϫ1
millibarn
.
F (Q)
F (Q)
F (Q)
H
D
M
SHH(Q)
SHX(Q)
SXX(Q)
0.0126
Ϫ0.0056
0.0016
0.0137
0.0015
Ϫ0.0010
Ϫ0.0263
0.0041
0.0074
͑42.4 °C͒ of the crystalline phase. Temperatures higher than
60 °C would cause serious corrosion of the sample container.
Even at 60 °C, there was some H formation after several
2
hours. This tended to slightly inflate the sample cell and
change its thickness by a few percent. In the data analysis
this was taken into account by a simple scaling factor. At
FIG. 1. Structure functions of liquid 100% phosphoric acid at 25 °C.
SHX(Q)ϭ0.823SHO(Q)ϩ0.182SHP(Q)
ϩ0.298SOP(Q)ϩ0.033SPP(Q).
and
SXX(Q)ϭ0.673SOO(Q)
25 °C no corrosion was observed.
C. Data analysis
which is equal to the average number of atoms of species ␤
within a shell of inner radius R and outer radius R around
an average atom of species ␣.
The raw scattering data were normalized on the monitor
count, corrected for background and container scattering, put
on the absolute intensity scale by comparison with the scat-
tering of a vanadium slab of known thickness, and corrected
for absorption and multiple scattering with the CORAL suite
1
2
D. Computer modeling
For the molecular modeling, MD simulations were un-
dertaken with the GROMOS 87 software package. In a previous
study12 new force field parameters, as well as starting struc-
tures of the current liquid system were established. The sys-
tem consisted of 160 molecules of H PO ͑1280 atoms͒ in a
1
0
of programs. The contribution of incoherent scattering
shows a slow Q and scattering angle dependence mainly due
to the presence of light hydrogen atoms and was removed by
3
4
fitting a seventh order polynomial to the high Q part ͑above
Ϫ1
rectangular box of dimension 27.6ϫ27.6ϫ27.6 Å. Each MD
simulation was 500 ps with a time step of 1 fs. A cutoff for
nonbonded interactions was employed with a short range and
a long range truncation of the van der Waals and Coulomb
interactions of 1.1 Å, which were calculated during
neighbor-list generation every 5 fs. The temperature was
controlled by weak coupling to a bath of 300 K with a time
constant of 0.1 ps. The pressure was also controlled by weak
coupling with a time constant of 2.0 ps and kept constant at
1
0 Å ͒ of the total differential cross section and subtracting
the fit result. Except at the lowest angles, differential cross
sections of all detector banks ended up satisfactorily similar.
The lower angle detectors ͑below 10°͒ were not included in
the analysis. The three differential cross sections per atom
F (Q), F (Q), and F (Q) were substituted into Eqs. ͑3͒,
H
D
M
͑4͒, and ͑5͒, and used to calculate SHH(Q), SHX(Q), and
SXX(Q). The coefficients of F (Q), F (Q), and F (Q) are
H
D
M
given in Table I. The coefficients in Eq. 3 are larger by an
average factor of 5, which means that SHH(Q) contains the
highest statistical error.
The Fourier transformation of S␣␤(Q) results in the ra-
dial distribution function g␣␤(r), given by
1
bar. Coordinates were stored every 0.1 ps. Calculations of
the radial distribution function were carried out using Eq.
10͒:
͑
͗
N r,⌬r
͒
͘
͑
g͑r͒ϭ
͑10͒
1
ϱ
M͑ N͒␳V͑r,⌬r͒
2
1
2
g␣␤͑r͒ϭ1ϩ
͵
͓S␣␤͑Q͒Ϫ1͔sin͑Qr͒Q dQ,
2
␲ r␳
0
in which N(r,⌬r) is the number of atoms found in a spheri-
cal shell of radius r and thickness ⌬r concentric with a ref-
erence atom, M is the number of time steps, N is the total
number of atoms, and V(r,⌬r) is the volume of a spherical
shell of radius r and thickness ⌬r.
͑
8͒
Ϫ3
where ␳ is the atomic number density of PA ͑ϭ0.0916 Å
Ϫ3
at 25 °C, and 0.0902 Å at 60 °C͒. The transformation was
carried out using an iteration routine11 which finds a fit to the
experimental S␣␤(Q) that gives minimum noise and no
structure in g␣␤(r) below a cutoff distance of 1 Å in gHH(r)
and 0.7 Å in gHX(r) and gXX(r).
IV. RESULTS
Quantitative interpretations of peak areas in g␣␤(r) can
be made by calculating the running coordination number
Figure 1 shows the partial structure factors SXX(Q),
SHX(Q), and SHH(Q) at room temperature. The high Q
structure present in SXX(Q) and SHX(Q), and nearly absent
in SHH(Q), is due to the strong intramolecular interference in
the first two. The partial radial distribution functions gXX(r),
gHX(r), and gHH(r) at 25 and 60 °C are shown in Figs. 2, 3,
␤
␣
n (R ,R ):
1
2
R
2
␤
␣
2
n ͑R ,R ͒ϭ4␲␳c
␤
͵
g␣␤͑r͒r dr,
͑9͒
1
2
R
1
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2148
J. Chem. Phys., Vol. 110, No. 4, 22 January 1999
Tromp, Spieser, and Neilson
FIG. 2. The radial pair distribution function gHX(r)͓ϭ0.823gHO(r)
ϩ0.182gHP(r)͔ at room temperature ͑bold full line͒ and at 60 °C ͑bold
dashed line͒ of liquid 100% PA. Interconnected circles: MD simulation of
the gHX(r) used for interpretation, thin line: gHO(r) of water at room tem-
perature. ͑3͒ H–O correlation through hydrogen bond in water. For other
features see Table II.
FIG. 4. The radial pair distribution function gHH(r) at room temperature
͑bold full line͒ and at 60 °C ͑bold dashed line͒ of liquid 100% PA. Thin line:
gHH(r) of water at room temperature. ͑1͒ intramolecular HH correlation in
water, ͑2͒ HH correlation through a hydrogen bond in water. For other
features, see Table II.
respect to the hydrogen bonding, the length of which is over-
estimated by 0.2 Å. However, the main features in the ex-
perimental data are also found in the MD results, a fact
which assists in their interpretation. After comparing simu-
lation and experiment, it is found that the shape of the
double-peaked feature between 2.5 and 3.5 Å is largely due
to intramolecular H–O correlations. These correlations are
between an H atom on the one side and the three O atoms on
and 4, respectively. Table II gives an overview of the promi-
nent features in these functions and, where useful, their inte-
gral calculated according to Eq. ͑9͒.
A. The function gHX„r…
The function
gHX(r)͓ϭ0.823gHO(r)ϩ0.182gHP(r)͔
͑Fig. 2͒ clearly shows the H–O correlation due to hydrogen
bonding at 1.55 Å ͑room temperature͒ and 1.58 Å ͑60 °C͒.
Integration of this peak ͓Eq. ͑9͔͒ gives a value of 0.75͑5͒
hydrogen bonded O atoms to an average H atom, both for
room temperature and 60 °C. Peaks at 0.975 and 2.20 Å are
the intramolecular correlations between H and directly
bonded O, and H and P, respectively. Application of Eq. ͑9͒
the other side of the PO tetrahedron ͑Fig. 5͒. The presence
4
of two maxima indicates that these three O atoms are not
equivalent. This suggests a preferred position of the H atom
near the plane defined by one O–P–O group, consistent with
one O atom at 2.7 Å and two O atoms at 3.2 Å.
O
results in a value for the nH ͑0,1.25͒ of 0.95͑0.10͒, which is
B. The function gXX„r…
within error as expected for one oxygen atom directly bound
to an H atom. MD turns out to give results which do not
accurately reproduce the experimental data, especially with
The function
gXX(r)͓ϭ0.673gOO(r)ϩ0.298gOP(r)
ϩ0.033g (r)͔ ͑Fig. 3͒ is at distances below 3 Å dominated
PP
TABLE II. Overview of features and assignments.
Data set
label in figure͒
Position Areaa
͑Å͒ ͑atoms͒
͑
Assignment
gHX(r) Fig 2͑1͒ 0.975͑5͒ 0.95͑10͒ H–O direct bond
gHX(r)
gHX(r)
gHX(r)
gHX(r)
͑2͒ 1.54͑1͒ 0.75͑15͒ H–O through hydrogen bond
͑4͒ 2.20͑2͒ n.m.b
H–P intramolecular
H–O2 intramolecular
b
c
͑5͒ 2.80͑1͒ n.m.
͑6͒ 3.25͑2͒ n.m.b
H–O3/4 intramolecular
c
gXX(r) Fig. 3͑1͒ 1.54͑1͒ 1.16͑15͒ O–P direct bond
gXX(r)
͑2͒ 2.51͑1͒ 3.8͑2͒
O–O intramolecular and through
hydrogen bond
gXX(r)
gXX(r)
gXX(r)
gXX(r)
͑4͒ 3.7͑1͒
͑5͒ 4.9͑1͒
͑6͒ 5.6͑1͒
͑7͒ 7.1͑2͒
n.m.b
n.m.b
O–P intermolecular
O–O intermolecular
O–P intermolecular
O–O intermolecular
H–H across hydrogen bond
H–H intramolecular and
intermolecular
b
n.m.
n.m.b
b
gHH(r) Fig. 4͑3͒ 1.9–2.6 n.m.
gHH(r)
͑4͒ 2.5–4.2 n.m.b
FIG. 3. The radial pair distribution function gXX(r)͓0.673gOO(r)
ϩ0.298gOP(r)ϩ0.033gPP(r)͔ at room temperature ͑bold full line͒ and at
6
0 °C ͑bold dashed line͒ of liquid 100% PA. Interconnected circles: MD
a
simulation of the intermolecular gXX(r) used for interpretation, thin line:
gOO(r) of water at room temperature. ͑3͒ O–O correlation through hydrogen
bond in water. For other features see Table II.
Calculated by applying Eq. ͑9͒.
n.m.: not meaningful.
Labels of O atoms are in Fig. 5.
b
c
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1

J. Chem. Phys., Vol. 110, No. 4, 22 January 1999
Tromp, Spieser, and Neilson
2149
and 1.58 Å in the temperature range considered here. With a
covalent O–H distance of 0.975 Å and a hydrogen bond
O–O distance of 2.52 Å, it follows that the angle O...H–O is
between 160° and 170°. Values close to 180° should prob-
ably be expected in disordered liquid systems. A strong, lin-
ear hydrogen bond is characteristically found in crystalline
systems between highly electronegative donors and accep-
tors with a large excess of negative charge. A short average
hydrogen bond is therefore in line with the strong acidity of
part of the oxygen atoms of PA. The H–O covalent bond
length seems significantly longer than the values usually
found on SANDALS, such as 0.960͑5͒ in ambient 0.1 M
FIG. 5. Schematic representation of two neighboring H PO molecules in
liquid 100% phosphoric acid, with average distances as observed by neutron
diffraction. Units are Å.
3
4
14
LiCl ͑Ref. 13͒ and 0.950͑5͒ in water at 95 bar. The value
obtained from reactor data,15 0.971͑5͒, is only slightly lower
than that found in PA ͑The more limited Q range of reactor
data may cause truncation errors in the Fourier transform and
affect the peak position͒. It is tentatively suggested that the
strong hydrogen bond in PA stretches to some extent the
covalent H–O, although the small differences found in the
O–H bond length can well be artifacts. Even if no artifacts
play a role, it is not clear whether a longer O–H bond in PA
as compared with water is directly related to high acidity or
just to the difference in the chemical environment. No other
inorganic oxyacids have been studied in the liquid state with
neutron scattering combined with H/D substitution. All neu-
tron scattering data on acidic H–O bond lengths have been
obtained in the crystalline state, where quite long distances
by intramolecular correlations at 1.52 Å ͑O–P͒ and 2.52 Å
͑O–O͒. For the assignment of the features observed at higher
distances we refer to the results of MD. Above 3 Å, MD
reproduces the experimental data reasonably well. Its decom-
position into a contribution from the intermolecular parts of
gOO(r) and gOP(r) ͓g (r) does not contribute to any sig-
PP
nificant extent͔ shows that the peak at 4.9 Å and a weak
feature near 7 Å are probably due to O–O correlations, while
O–P correlations give rise to the peaks at 3.7 and 5.6 Å. In
the range 2.5–3.5 Å, the performance of the MD simulation
is quite poor. This is exactly the range of distances in which
O–O correlations between hydrogen bonded O atoms are
expected. The mismatch is probably caused by the overesti-
mation of the hydrogen bond length and incorrect configura-
tion of the hydrogen bond and has already been observed in
the MD result of gHX(r). Considering the very clear signa-
ture of hydrogen bonding in the experimental gHX(r), an
effect of hydrogen bonding on gXX(r) is anticipated. There-
fore, it is concluded that the hydrogen bonded O–O correla-
tion is hidden under the intramolecular O–O correlation at
8
are found, but an influence of the crystal field cannot be
excluded.
There is a small, but significant, temperature dependence
in gHX(r) ͑Fig. 2͒. At 60 °C the H...O hydrogen bond feature
position is increased by 0.03 Å and appears less pronounced
than in the ambient data. However, the number of hydrogen
bonds has not changed significantly. Correspondingly, as a
result of the less pronounced hydrogen bonding, the intramo-
lecular H–P correlation ͑2.2 Å͒ becomes better defined. The
source of change with temperature of the intramolecular
2.52 Å. On the safe assumption that it is completely due to
O–O correlations this interpretation is confirmed by integra-
tion of the peak, which gives a coordination number
O
O
H–O correlation across the PO tetrahedron ͑between 2.5
n (2.2,3) of 3.8, whereas 3 is expected for an isolated PO
4
4
and 3.5 Å͒ is less obvious: the H–O2 correlation ͑Fig. 5͒
strengthens with temperature, most probably due to weaker
hydrogen bonding. However, the H–O3 and H–O4 correla-
tions do not show any change. A possible explanation is the
presence of some intermolecular H–O correlation in this re-
gion. The effect of intramolecular change may be compen-
sated or moderated by this in some way. Interestingly, in
gXX(r) there is no appreciable temperature dependence. This
tetrahedron. The difference of 0.8 must at least be partly due
to hydrogen bonded O atoms at about 2.5 Å.
C. The function gHH„r…
The function gHH(r) represents the radially averaged
spatial correlation of H atoms, which is relatively featureless
͑Fig. 4͒. The shoulder between 1.9 and 2.6 Å on the left hand
slope of the main, intramolecular feature at 3.5 Å is probably
due to correlations across a hydrogen bond ͑Fig. 5͒. In water
this correlation is found at a similar distance ͑2.3 Å͒ ͑Fig. 4͒.
We also note that at 25 °C, some intramolecular structure
between H atoms across the tetrahedron is still resolved: be-
tween 2.6 and 3 Å.
suggests that the PO tetrahedral frame of the PA molecule is
4
not affected by an increase in temperature from 25 to 60 °C.
Consequently, all temperature dependence in the structure of
PA as probed by neutron scattering appears to be due to the
changing interaction of H atoms with their surroundings.
Also, because neither the intramolecular part, or the intermo-
lecular part of gXX(r) is affected by temperature, there is
probably no preferential relative orientation of neighboring
V. DISCUSSION
The results for gHX(r) ͑Fig. 2͒ clearly show that the
hydrogen bonds in PA are shorter, and therefore stronger
than in water ͑1.8 Å͒. By combining the information in
gHX(r) and gXX(r) an average hydrogen bond angle can be
calculated. The length of the hydrogen bond is between 1.55
PO tetrahedra, which otherwise would be destroyed to some
4
extent by increasing the temperature. With respect to tem-
perature effects on gHH(r), changes in the range 1.9–2.6 Å
are consistent with a weaker hydrogen bond at higher tem-
perature. However, they are not very well separable from the
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2150
J. Chem. Phys., Vol. 110, No. 4, 22 January 1999
Tromp, Spieser, and Neilson
effect on intramolecular H–H correlation near 3.5 Å.
A small degree of polymerization established according
to Eq. ͑1͒, is present in 100% PA in equilibrium at room
significantly temperature dependent between 25 and
60 °C, with no significant breaking up of hydrogen
bonds.
9
temperature. As a consequence there should be an H–H
͑2͒ The OH groups have a nonarbitrary orientation relative
correlation peak near 1.55 Å in gHH(r) due to the presence of
water molecules. However, no such peak could be detected.
to the PO tetrahedron to which they are connected. The
H atom is preferentially located near a plane defined by a
set of O–P–O atoms.
4
4
This observation is easily explained: about 15% of P atoms
are expected to be in nonmonomeric phosphate. It can be
calculated that the water content in such a case is 2%͑w/w͒.
This means that the weighting in SHH(r) of intramolecular
HH correlation in water molecules is about 0.005 times that
of PA and polyphosphate taken together and therefore not
strong enough to be observed by neutron scattering. Another
signature of polymerization would be the integral according
to Eq. ͑9͒ of the 1.52 Å peak in gXX(r) ͑intramolecular O–P
correlation͒ being greater than one. The latter follows from
the fact that in polymeric phosphate some O atoms are di-
rectly bound to two P atoms instead of one. Again, however,
the statistical error in the application of Eq. ͑9͒, which is at
least 10%, does not allow an assessment of polymerization,
which would only have an effect of 2%.
͑3͒ PO tetrahedra probably have an isotropically distributed
4
orientation relative to their neighbors.
1
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1
2
3
4
5
͑
6
7
8
͑
9
0
1
VI. CONCLUSIONS
1
1
1
1
2
3
The neutron diffraction results show that in liquid 100%
phosphoric acid:
͑
14
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J. Chem. Phys. 101, 6210 ͑1994͒.
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Y. Guissani, J. Chem. Phys. 107, 2942 ͑1997͒.
͑
1͒ The hydrogen bonds are appreciably shorter than in wa-
ter. About 80% of the H atoms are involved in hydrogen
bonding with an O atom. The hydrogen bond structure is
15
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1