J. Chem. Thermodynamics 2002, 34, 205–227
doi:10.1006/jcht.2001.0900
Available online at http://www.idealibrary.com on
Heat capacities, third-law entropies and
thermodynamic functions of SiO2 molecular
sieves from T = 0 K to 400 K
Juliana Boerio-Goates,a Rebecca Stevens, Ben K. Hom,
Brian F. Woodfield
Department of Chemistry and Biochemistry, Brigham Young University,
Provo, UT 84602, U.S.A.
Patrick M. Piccione, Mark E. Davis,
Division of Chemistry and Chemical Engineering, California Institute of
Technology, Pasadena, CA 91125, U.S.A.
and Alexandra Navrotsky
Thermochemistry Facility, Department of Chemical Engineering, University
of California at Davis, Davis, CA 95616, U.S.A.
Four zeolitic polymorphs of SiO2 , ∗ BEA, FAU, MFI, and MTT, have been studied by
adiabatic heat capacity calorimetry in the temperature interval from appproximately 20 <
(T /K) 6 400 K. From numerical fits of the heat capacities, thermodynamic functions
including the entropy, enthalpy increment, and Gibbs free energy function of all four
phases have been obtained. At T = 298.15 K, the standard molar heat capacities of the
four phases are C op,m = (44.21 ± 0.08) J · K−1 · mol−1 , (45.34 ± 0.08) J · K−1 · mol−1 ,
(45.70 ± 0.08) J · K−1 · mol−1 , (45.97 ± 0.08) J · K−1 · mol−1 for ∗ BEA, FAU, MFI, and
MTT, respectively.
A maximum at T = 365 K was observed in the heat capacity of MFI that has been
attributed to the monoclinic–orthorhombic structural phase transition previously studied
by x-ray and solid state nmr experiments. The enthalpy of transition 1tr H was found
to be (134.8 ± 0.5) J · mol−1 while the entropy of transition 1tr S was (0.385 ±
0.001) J · K−1 · mol−1 . These small values are consistent with the subtle, displacive nature
of the transition.
The heat capacities of three of the polymorphs (FAU, MFI, and MTT) are greater
than that of crystalline quartz over the entire temperature region of this study, while that
of ∗ BEA drops below that of crystalline quartz for T > 240 K. In addition, the excess
heat capacity relative to crystalline quartz of all four polymorphs is greater than that
exhibited by amorphous quartz for T < 200 K. Since amorphous forms of a substance
a To whom correspondence should be addressed (E-mail: [email protected]).
0021–9614/02
c 2002 Elsevier Science Ltd. All rights reserved.
206
J. Boerio-Goates et al.
have higher heat capacities at low temperatures than their crystalline counterparts, this
c 2002 Elsevier Science Ltd. All rights reserved.
result is unexpected. KEYWORDS: SiO2 ; molecular sieves; thermodynamics; heat capacity; entropy
1. Introduction
Zeolites are porous, crystalline materials that contain silicon and aluminum, tetrahedrally
bonded to oxygen, in complex, extended framework structures. (1) Cations such as sodium,
potassium, magnesium and calcium can be present, as needed, to maintain electrical
neutrality. Water can be found in zeolites with varying amounts depending upon the method
of preparation and handling, the nature and number of cations, and the Al/(Al + Si) ratio.
Zeolites are of great practical importance because they can be used as heterogeneous
catalysts and as separation agents because of the chemical reactivity and size selectivity
made possible by the open framework structures. (1)
While zeolites are found in nature, novel synthetic methods have been developed that
allow one to tailor the size, shape, and chemical reactivity of the pores and channels. (2)
These synthetic techniques usually employ an organic structure-directing template that is
then burned off at high temperatures, leaving the inorganic framework behind. The extent to
which these synthetic techniques rely on thermodynamic stabilization or favorable kinetic
effects is not well understood. (2)
Our research groups from California Institute of Technology, University of California,
Davis, and Brigham Young University have collaborated to provide experimental thermochemical and thermodynamic data to shed light on the question of whether there is a thermodynamic driving force that stabilizes these structures. This paper reports heat capacity
measurements from 14 6 (T /K) 6 400 made at Brigham Young University on four polymorphs of pure SiO2 which have zeolitic frameworks. Since they contain no aluminum,
these materials are referred to as molecular sieves rather than zeolites.
The SiO2 polymorphs include ∗ BEA( zeolite beta), FAU (faujasite), MFI (ZSM-5 or
silicalite), and MTT (ZSM-23). Structural details for these frameworks can be found on
the Internet at the site maintained by the Structure Commission of the International Zeolite
Association. (3) The particular polymorphs were chosen because they represent a range
of structural features observed in zeolites. In particular, they span the entire range of
molar volumes observed for pure SiO2 molecular sieves; this parameter has been shown
in previous work to correlate well with the enthalpies of formation of molecular sieves. (4)
Only the heat capacity of MFI has been reported previously. (5)
From the temperature dependence of the heat capacities, thermodynamic functions for
each polymorph (third-law entropy, enthalpy increment, and Gibbs free energy function)
have been calculated. Measurements of the enthalpies of formation of these polymorphs
at T = 298.15 K have been published elsewhere. (4) A detailed interpretation of the
thermodynamic stability of pure silica molecular sieves, based upon free energies of the
framework polymorphs relative to those of the dense phases of SiO2 will be presented
separately. (6)
Heat capacities of SiO2 molecular sieves
207
This work represents the first systematic study of the low-temperature heat capacities
of pure SiO2 molecular sieves. However, the heat capacities and entropies of a number of
natural zeolite samples have been reported. (7–13) The analysis of the heat capacity of the
natural zeolites is hindered by several factors. These include variation in the Al/(Al + Si)
ratio and in the extent of Al/Si mixing on tetrahedral sites, the nature and number of
cations present, and the amount of adsorbed water and the nature of its binding to the
zeolite. The uncertainties associated with these factors complicate the interpretation of the
role of framework characteristics (e.g., densities, pore, and channel sizes) in determining
the thermodynamic stability of zeolites.
It is appropriate to acknowledge in this issue of the Journal, dedicated to Dr P. A. G.
O’Hare, the extremely careful and painstaking work done by him and his colleagues on
these materials. Their papers (7–12) illustrate the extensive corrections that must be made to
the primary heat capacity data of natural zeolites in order to put the results on a consistent
chemical basis for comparison.
By contrast, the pure SiO2 materials offer a number of simplifications. They are
more hydrophobic so water adsorption is minimized. Because the pure SiO2 samples
contain essentially no Al ions, they need no cations for charge compensation and have
no residual entropies associated with Al/Si disorder. In principle, then, measurements on
these materials provide a more direct route to understanding the effect of framework and
structural characteristics on thermodynamic stabilities.
2. Experimental
SAMPLE PREPARATION
∗ BEA
(zeolite beta) and MFI (ZSM-5) were synthesized at the California Institute of
Technology using gel techniques that are described here only in generalities. Specific
details can be found in reference 6. A source of silica was dissolved in water using fluoride
ion as the mineralizing agent and then mixed with an organic structure-directing agent. The
reaction mixtures were maintained near T = 400 K for several days in a sealed Teflon-lined
container. The reaction mixture was cooled to room temperature and the precipitate was
filtered, then washed with water and acetone. Each sample was calcined near T = 800 K
to remove the occluded organic material.
Fluoride ion was used as the principal mineralizing agent since F− ions are known
to produce materials containing fewer silanol (Si–O–H) defect groups. (14) In addition,
materials synthesized with F− are more hydrophobic than those synthesized in hydroxide
media. (14)
The MTT sample was synthesized at Chevron Research and Technology Co. using
techniques similar to those described above and kindly provided by Dr Stacey Zones.
This material showed some black and brown specks that were attributed to incompletely
calcined organic material. Increasing the temperature of calcination, however, did not
remove the colored material.
High-silica faujasite (FAU) (Tosoh 390 HUA), prepared by the Tosoh Chemical Co.,
Japan, was kindly provided by Dr John Cook of Tosoh U.S.A.
208
J. Boerio-Goates et al.
TABLE 1. Details of the calorimetric experiments on four pure-silica molecular sieves
Sample
BEA
FAU
MTT
MFI
SiO2 · 0.005H2 O
SiO2 · 0.026H2 O
SiO2 · 0.007H2 O ·
SiO2 · 0.006H2 O
composition
0.027C· 0.005
Si3 N4
Sample
4.4370
3.1225
4.4537
5.0136
1.26276
1.27292
1.32986
1.37509
mass g−1
Mol He/10−5
Contribution
T /K
per cent
T /K
per cent
T /K
15
22
15
11
15
13
25
23
25
30
25
28
per cent
T /K
per cent
of sample to
15
C p at
25
27
70
14
70
10
70
15
70
14
400
21
400
16
400
24
400
22
selected T
SAMPLE CHARACTERIZATION
Powder x-ray diffraction patterns were collected at room temperature on a Scintag XDS
2000 diffractometer. The diffractometer was equipped with a liquid nitrogen cooled Ge
detector, and it employed Cu Kα radiation with λ = 1.5418 Å in a Bragg–Bretano
geometry. In each case, only a single zeolite phase was observed.
The MTT specimen was also analyzed by Galbraith Laboratories, Inc., Knoxville, TN
for F, C, N, H to determine the nature of the impurity that remained following calcination.
The chemical analysis gave the following results: 34 · 10−6 F and 0.32 mass per cent C,
0.26 mass per cent N, <0.5 mass per cent H. The nonzero C content is commensurate with
a slightly incomplete calcination, but the nitrogen content is unexpectedly high.
The water content of the calorimetric samples was determined using thermogravimetric
techniques. Approximately 15 mg samples of zeolite were subjected to a heating rate of
10 K · min−1 in a TA Instruments 951 Analyzer ( TA Instruments, New Castle, DE) up to
T = 1073 K. For ∗ BEA, FAU, and MFI, the amount of water present in the dehydrated
samples was calculated by taking the difference of the mass losses at T = 1073 K and
at T = 493 K, the temperature to which the samples were dried before loading into
the calorimeter. Buoyancy corrections, based on an experiment conducted with a 15 mg
specimen of Pt, were applied. For MTT, the water content was calculated by taking the
difference between the mass loss observed during the TGA experiment, and the amount of
C and Si3 N4 determined by elemental analysis. The compositions of the polymorphs with
respect to water, and for MTT with C and Si3 N4 are given in table 1.
The FAU sample was prepared by dealumination of an aluminosilicate faujasite. Material from this same synthesis was used in the thermochemical studies of Petrovic et al. (15)
Spectrochemical analyses performed at that time showed that the sample contained 0.119
mass per cent Al, 0.005 mass per cent Ca, 0.001 mass per cent Mg, 0.013 mass per cent Na,
Heat capacities of SiO2 molecular sieves
209
and analysis by TGA showed a 3.97 mass per cent loss attributed to water. Our TGA analysis showed a loss on heating to T = 1073 K of only 1.7 mass per cent, with the difference
for the interval between 493 6 (T /K) 6 1073 being 0.77 mass per cent. If one assumes
that the only difference between the two samples was the amount of water adsorbed initially, the corresponding change on the composition of the metal impurities from those
reported by Petrovic et al. (15) is negligible.
CALORIMETRIC MEASUREMENTS
The heat capacity measurements were made in the large-sample adiabatic cryostat at
Brigham Young University. The apparatus and its electronic components have been
described in detail elsewhere. (16) Sample temperatures are measured using a 25-
Rosemont platinum resistance thermometer (SN 4253) (Rosemount Inc., Aerospace
Division, 1256 Trapp Road, Eagan, MN 55121, U.S.A.). The thermometer was calibrated
on ITS-90 by the manufacturer over the range 13.8 6 (T /K) 6 523, and the calibration
was checked in-house by comparison with an independently calibrated germanium
thermometer and at higher temperatures by measurement of the triple point of sodium
sulfate dodecahydrate. Temperatures are believed to reproduce the ITS-90 to ±0.016 K
for 13.8 < (T /K) 6 40 K, and to ±0.005 K for 40 < (T /K) 6 523.
Prior to loading into the calorimeter, each sample was heated in a vacuum oven to
T = 493 K and, while still hot, placed into an argon-filled glove box in which the water
vapor level is below 1·10−6 . Inside the glove box, the zeolite was loaded into a gold-plated
copper calorimeter with internal volume of 10.48 cm3 . The calorimeter was positioned
inside the loading chamber, which was closed up and transported to a glass vacuum
line. The loading chamber and calorimeter were evacuated to about p = 1 mPa, and
the calorimeter was sealed under a helium atmosphere by pressing a gold gasket onto
the stainless steel knife-edge of the calorimeter. The sample masses and moles of helium
exchange gas used for each set of experiments are given in table 1.
The quantity of sample is smaller than typically used in this calorimeter and the
percentage of the measured heat capacity due to the sample is correspondingly small.
Representative values are given in table 1.
The temperature increment 1T associated with each heat capacity measurement is
approximately 0.1 ∗ T for T < 50 K, and 5 K for T > 50 K. Some measurements have
been made with smaller increments in the transition region of MFI to determine the details
of the heat capacity curve. Curvature corrections have been applied to all measurements,
but their effect was observed to be negligible.
CORRECTIONS TO THE HEAT CAPACITY MEASUREMENTS FOR IMPURITIES
The SiO2 molecular sieves are much less hygroscopic than the aluminosilicate zeolites and
all of the four samples were found to have water contents of less than one mass per cent
after drying to T = 493 K. The commercial FAU sample had the largest water content
with 0.77 mass per cent H2 O. Given the small amount of water present in these materials,
we have chosen not to apply corrections to our heat capacity measurements. This decision
was based not only on considerations of the amount of water, but also on an uncertainty of
210
J. Boerio-Goates et al.
what heat capacity values to use for the water. It is known that there may be more than one
type of water in the zeolite cage: some water molecules are tightly bound to framework and
may be associated with cations, while more loosely bound water may be simply present in
the open cages. (13, 17) From the results of Johnson et al. (10) on analcime and dehydrated
analcime, which contain cations, one could calculate an effective contribution of water to
the heat capacity of aluminosilicate zeolites, but contributions arising from the two types
of water cannot be separated. Since our samples have, at worst, only trace amounts of
cations, the nature of the water adsorbtion to the solid may be very different from that
present in the analcime. Hemingway and Robie (13) have also shown that the effective
contribution of zeolitic water changes with overall water content, becoming more ice-like
as the concentration of water increases. The results they cite are for water concentrations
much higher than those found in our samples, and there is no systematic trend in the
variation with water content. Therefore, lacking definitive values for the contribution of
water appropriate for our samples, we have chosen not to correct any of the samples for
these small amounts of water. As part of our ongoing project, we intend to investigate
systematically the effect of water on the heat capacity of these polymorphs and can make
more appropriate contributions at that time, if they are warranted.
The original heat capacity results for MTT have been corrected for the 0.32 mass per cent
of C using the heat capacity of graphite (18) and for the 0.26 mass per cent of N assuming
it to be present as Si3 N4 . (16)
ESTIMATES OF THE UNCERTAINTIES OF THE MEASUREMENTS
Measurements of the standard molar heat capacity of synthetic sapphire (NIST SRM-720)
were performed in separate experiments in order to assess the accuracy of the heat capacity
measurements obtained from this apparatus. The values obtained in these measurements
agree with those reported in table 2 of Archer (19) to within ±0.02 · C p for 13 6 (T /K) <
25; ±0.005 · C p for 25 6 (T /K) < 30; ±0.002 · C p for 30 6 (T /K) < 40; ±0.001 · C p
for 40 6 (T /K) < 250; ±0.0015 · C p for 250 6 (T /K) < 300; and ±0.001 · C p
for 300 6 (T /K) < 400. In each of the above ranges, our deviations are within the
uncertainties quoted by Archer for his values. (19)
Because of the relatively small contribution of the molecular sieve to the (sample
+ empty calorimeter) experiments and the additional uncertainty associated with the
adsorbed water, the uncertainty in the molar heat capacities of the zeolites will be larger
than those deviations cited above for the NIST standard sapphire measurements. We
estimate that the uncertainties are ±0.05 · C p for (T /K) 6 25, ±0.01 · C p for 25 6
(T /K) < 50; and ±0.002 · C p for 50 6 (T /K) < 400. As discussed below, problems with
helium exchange gas limit the reliability of our results below T = 25 K, except for FAU.
3. Results and discussion
The molar heat capacities of ∗ BEA, FAU, MFI, and MTT are reported in tables 2 to 5,
respectively. An additional significant figure beyond those justified based on the uncertainties are given in the tables for the sake of those who might wish to perform additional
Heat capacities of SiO2 molecular sieves
211
TABLE 2. Experimental heat capacities of the ∗ BEA polymorph of SiO2
C p,m
C p,m
C p,m
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
19.477
0.5706
133.67
22.903
285.47
42.858
20.971
1.2003
138.75
23.795
290.64
43.498
22.533
2.2485
143.84
24.614
290.74
42.312
24.641
2.6805
148.93
25.435
295.81
43.878
26.998
3.2166
154.03
26.252
295.98
43.974
29.448
3.7019
159.14
26.973
300.98
44.513
32.137
4.2056
164.25
27.838
301.14
44.460
35.076
4.8547
169.37
28.519
306.16
45.004
38.284
5.3739
174.49
29.295
306.30
45.044
41.848
6.0201
179.62
30.117
311.34
45.461
45.233
6.6781
184.75
30.838
311.46
45.446
49.447
7.4712
189.89
31.585
316.62
45.983
53.868
8.3301
192.63
31.940
321.80
46.370
54.984
8.6065
195.03
32.249
326.98
46.843
58.374
9.2328
197.77
32.618
332.16
47.346
60.065
9.6214
200.17
32.935
337.35
47.628
62.963
10.187
202.91
33.234
337.89
47.617
64.650
10.539
208.06
33.958
342.52
48.231
67.622
11.195
213.21
34.623
343.33
48.287
69.341
11.425
218.36
35.323
347.71
48.668
72.354
12.014
223.52
36.008
348.51
49.027
74.094
12.257
228.67
36.634
352.85
49.023
78.906
13.031
233.83
37.177
353.68
49.276
83.757
13.870
238.99
37.829
357.97
49.569
88.643
14.743
244.14
38.491
358.86
49.588
93.559
15.641
249.30
39.006
364.04
50.082
98.504
16.565
254.47
39.596
369.23
50.379
103.48
17.467
259.63
40.183
374.41
50.765
108.47
18.359
264.79
40.867
379.58
51.361
113.47
19.242
269.96
41.370
384.77
51.544
118.50
20.206
275.13
41.832
389.95
51.907
123.55
21.083
280.30
42.285
395.15
51.953
128.60
21.997
398.84
51.953
numerical calculations on the results. Plots of the heat capacities as a function of temperature are shown in figure 1. In the region from 25 6 (T /K) < 250, the heat capacities of
212
J. Boerio-Goates et al.
60
40
30
15
Cp,m /(J . K –1 . mol –1)
Cp,m /(J . K –1 . mol –1)
50
20
10
10
5
0
10
0
0
50
100
150
200
T/K
20
30
T/K
250
300
40
350
50
400
FIGURE 1. The experimental heat capacities of the four pure silica molecular sieves as a function of
temperature: , ∗ BEA; H, FAU; , MTT; , MFI. The results for FAU, MTT, and MFI have been
shifted by (2, 4, and 8) J · K−1 · mol−1 , respectively, from the values given in tables 2 to 5. The solid
curves, —, represent heat capacities calculated from equation (1) with the parameters in table 6. The
inset shows an expanded view of the low-temperature results.
•
all four polymorphs are very similar. To distinguish the curves in figure 1, the results for
−1
FAU, MTT, and MFI have been shifted by (2, 4, and 8) J · K−1 · mol , respectively, from
the values given in the tables. Below T = 25 K, the heat capacity curves of ∗BEA, MFI,
and MTT diminish rapidly, with a temperature dependence reminiscent of a glass transition. This behavior is shown as an inset to figure 1. Above T = 250 K, the heat capacity
results begin to diverge, most notably in MFI where a slight structural transition has been
reported.
We have performed additional measurements on ∗ BEA at very low temperatures 0.5 6
(T /K) 6 50 in another cryostat and found that the anomalous behavior in the heat capacity
is associated with the presence of the helium exchange gas. In measurements without the
Heat capacities of SiO2 molecular sieves
213
TABLE 3. Experimental heat capacities of the FAU polymorph of SiO2
C p,m
C p,m
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
14.591
15.670
17.005
18.720
20.425
20.430
22.178
22.249
24.152
24.551
27.104
29.955
33.042
36.449
40.331
44.520
48.801
53.192
57.603
57.682
62.257
63.676
66.908
68.252
72.989
77.776
82.606
87.480
92.389
97.329
102.30
107.28
112.29
117.32
122.36
127.42
132.48
137.56
142.65
147.74
152.84
157.95
0.6322
0.7920
1.0046
1.3411
1.6564
1.5477
1.9215
1.9442
2.3881
2.3481
2.8323
3.3965
3.9999
4.6894
5.4270
6.1924
6.9901
7.8533
8.6689
8.7013
9.5979
9.9089
10.401
10.791
11.731
12.584
13.565
14.474
15.404
16.360
17.202
18.210
19.185
20.093
20.993
21.896
22.751
23.644
24.522
25.271
26.167
27.011
163.06
168.19
173.31
178.44
183.57
188.71
190.15
193.85
195.24
198.99
200.39
205.53
210.68
215.83
220.98
226.14
231.30
236.46
241.62
246.80
251.96
257.12
262.29
267.45
272.62
277.79
282.96
288.13
289.06
293.30
294.24
298.48
299.41
303.65
304.59
308.83
309.76
314.94
320.11
325.28
330.46
335.65
27.831
28.644
29.424
30.204
30.952
31.652
31.917
32.396
32.668
33.093
33.323
34.072
34.771
35.429
36.142
36.846
37.515
38.179
38.877
39.440
40.223
40.774
41.384
42.060
42.526
43.116
43.670
44.240
44.122
44.801
44.757
45.378
45.292
45.919
45.787
46.444
46.436
46.966
47.524
48.007
48.522
49.034
C p,m
T
K
J · K−1 · mol−1
340.84
342.66
342.99
344.77
346.02
347.56
348.58
349.96
351.19
352.44
353.75
355.12
356.38
357.30
358.93
360.26
362.13
364.11
365.38
366.95
369.29
370.48
371.75
374.47
375.55
376.53
379.66
380.60
381.29
384.85
385.64
386.05
390.04
390.66
390.77
395.21
395.48
395.66
398.86
49.362
49.619
49.710
49.820
49.943
49.976
50.186
50.437
50.343
50.436
50.592
50.736
50.843
50.938
51.012
51.483
51.344
51.507
51.873
51.713
51.950
52.262
52.264
52.410
52.912
52.644
52.757
53.023
52.923
53.016
53.143
53.230
53.248
53.507
53.422
53.492
53.544
53.712
53.686
214
J. Boerio-Goates et al.
TABLE 4. Experimental heat capacities of the MFI polymorph of SiO2
C p,m
C p,m
C p,m
C p,m
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
15.343
16.936
18.507
0.2054
0.3606
0.4839
174.62
179.74
184.87
30.029
30.774
31.550
300.94
301.40
302.32
46.039
46.117
46.197
369.87
370.17
370.62
52.247
52.027
51.639
20.113
22.032
24.628
27.443
30.235
0.7527
1.9790
2.5628
3.1229
3.6731
187.37
190.00
192.62
195.14
197.76
31.910
32.279
32.669
33.056
33.434
306.12
306.56
307.49
311.29
311.72
46.609
46.611
46.677
47.145
47.202
371.66
372.26
372.70
373.74
374.34
51.273
51.330
51.096
51.452
51.192
33.300
4.1752
200.28
33.804
312.67
47.248
374.78
51.376
36.724
40.603
43.258
4.8167
5.5599
6.0310
202.90
208.04
213.19
34.157
34.849
35.567
316.90
322.07
327.25
47.780
48.366
48.937
375.09
375.82
376.42
50.871
51.094
51.222
44.801
47.977
6.3040
6.8677
218.34
223.49
36.290
36.943
332.43
337.61
49.464
50.086
376.86
377.90
51.038
51.141
52.324
7.6832
228.64
37.608
342.78
50.694
378.95
52.132
56.814
8.5093
233.79
38.265
343.51
50.798
380.00
51.166
59.153
61.383
64.884
8.9153
9.3948
10.013
238.95
240.27
244.11
38.936
39.183
39.562
347.96
349.15
351.30
51.339
51.579
51.966
380.28
381.04
382.08
51.296
51.214
51.056
69.511
10.918
245.49
39.805
354.33
52.418
383.12
51.267
74.266
79.067
83.911
88.793
93.709
98.653
11.846
12.757
13.696
14.655
15.604
16.563
249.27
250.65
254.43
255.81
259.59
260.97
40.153
40.403
40.794
41.025
41.434
41.568
354.58
357.69
358.61
359.50
359.76
360.22
52.429
52.841
53.033
53.288
53.349
53.413
384.16
385.48
390.68
395.86
399.17
51.554
51.576
51.744
52.001
51.860
103.62
108.61
113.62
118.64
123.68
128.74
17.522
18.436
19.459
20.425
21.397
22.305
264.75
266.14
269.91
271.30
275.08
276.47
42.076
42.226
42.659
42.794
43.195
43.334
361.26
361.84
362.30
363.34
363.92
364.38
53.635
53.717
53.538
53.641
54.027
54.096
133.81
138.88
143.96
149.06
154.16
23.199
24.093
24.982
25.880
26.749
280.25
281.64
285.42
286.81
290.58
43.732
43.903
44.354
44.455
44.866
364.67
365.42
365.99
366.46
367.50
53.978
54.235
53.944
53.746
53.429
159.26
164.38
169.50
27.553
28.407
29.198
291.98
295.76
297.15
45.035
45.472
45.568
368.07
368.55
369.59
53.597
53.101
52.415
Heat capacities of SiO2 molecular sieves
215
TABLE 5. Experimental heat capacities of the MTT polymorph of SiO2
C p,m
C p,m
C p,m
C p,m
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
T
K
J · K−1 · mol−1
14.497
15.188
16.281
17.819
19.431
21.147
23.193
25.381
27.713
30.240
33.112
36.307
39.834
43.826
48.119
48.262
52.488
52.618
57.070
61.600
66.234
70.940
75.705
80.517
85.372
90.265
95.191
100.14
105.12
110.11
115.13
120.16
125.20
130.26
135.33
140.41
141.42
145.50
146.41
150.59
151.51
0.2518
0.2576
0.4359
0.6777
0.9666
1.8851
2.3360
2.8360
3.2080
3.6648
4.1911
4.7750
5.3960
6.1299
6.9050
6.9243
7.7250
7.7655
8.7589
9.5741
10.484
11.431
12.360
13.292
14.276
15.245
16.203
17.208
18.178
19.171
20.111
21.047
21.997
22.942
23.838
24.723
24.963
25.622
25.806
26.490
26.602
156.62
161.73
166.84
171.96
177.09
182.21
187.35
191.88
192.16
192.48
196.95
197.24
197.62
202.10
202.38
202.76
203.15
207.24
207.52
207.91
208.11
212.39
212.67
213.26
217.54
217.82
218.41
222.69
222.97
223.57
227.84
228.12
228.72
233.00
233.28
233.88
238.15
238.44
239.04
239.32
243.31
27.486
28.329
29.135
29.956
30.777
31.569
32.325
32.950
32.890
33.086
33.589
33.631
33.858
34.303
34.384
34.576
34.520
34.987
35.063
35.299
35.196
35.699
35.734
35.906
36.418
36.464
36.597
37.108
37.159
37.260
37.789
37.811
37.983
38.449
38.475
38.527
39.109
39.164
39.297
39.259
39.730
243.60
244.19
244.47
248.47
248.76
249.35
249.63
253.93
254.51
254.79
259.08
259.68
259.96
264.25
264.84
265.13
269.41
270.01
270.29
274.58
275.18
275.46
279.75
280.35
280.63
284.92
285.52
285.80
290.09
290.69
290.97
291.95
292.57
295.26
295.87
296.15
297.03
297.57
300.43
301.04
301.32
39.819
39.886
39.842
40.371
40.429
40.530
40.414
41.044
41.172
41.058
41.622
41.775
41.752
42.329
42.384
42.365
42.868
42.953
42.939
43.345
43.442
43.451
43.896
44.024
44.033
44.539
44.500
44.596
45.128
45.092
45.115
45.175
45.310
45.614
45.675
45.693
45.725
45.886
46.174
46.270
46.281
302.21
302.75
306.21
307.38
307.92
311.39
312.55
313.10
317.66
317.73
318.27
322.84
322.90
323.44
328.02
328.09
328.64
333.19
333.27
333.82
337.41
338.37
338.44
338.99
342.40
343.56
343.62
344.17
347.58
348.73
348.80
349.35
352.76
357.94
363.11
368.30
373.47
378.65
383.83
389.02
394.20
46.258
46.425
46.916
46.842
46.955
47.409
47.426
47.554
47.887
48.000
48.075
48.415
48.506
48.835
48.958
49.046
48.914
49.387
49.490
49.711
49.926
49.890
49.940
50.000
50.358
50.269
50.373
50.344
50.783
50.691
50.820
50.860
51.299
51.711
52.120
52.554
53.063
53.534
53.851
54.199
54.475
216
J. Boerio-Goates et al.
1.5
1.0
0.5
0.0
– 0.5
– 1.0
a
50
100
150
200
250
300
350
400
b
100* ∆Cp,m /(J . K –1 . mol –1)
1
0
–1
50
100
150
200
250
300
350
400
c
1
0
–1
50
100
150
200
250
300
350
400
d
1
0
–1
50
100
150
200
T/K
250
300
350
400
FIGURE 2. The deviations of the experimental heat capacities of the four molecular sieves from the
fitted curves as a function of temperature. Fitted curves have been calculated using equation (1) with
the parameters given in table 6. a, , ∗ BEA; b, H, FAU; c, , MTT; d, , MFI. The deviations are
plotted as 100 · 1C p,m where 1C p,m = {C p,m (expt) − C p,m (fit)}/C p,m (fit). Experimental points
in the vicinity of the phase transition in MFI are not included in this figure.
•
exchange gas, the heat capacity curve is similar to that of FAU. Our interpretation, based
on these additional results, is that the exchange gas has condensed into the cavities and
channels of ∗ BEA, MFI, and MTT and is no longer facilitating thermal conduction. The
energy put into the calorimeter during a heating pulse is not distributed throughout the
entire sample, and the heat capacity value that is obtained is too small. Additional results
on these zeolites below T = 25 K will be published at a later time.
In modeling the heat capacity of other rigid inorganic materials, we have found that the
combination of a Debye function and an Einstein function often does a satisfactory job of
fitting the heat capacity results from our apparatus. (20, 21) The heat capacities of the four
molecular sieves exhibited a temperature dependence from 50 6 (T /K) 6 175 that was
nearly linear and which could not be adequately represented by this set of fitting functions,
Heat capacities of SiO2 molecular sieves
217
nor with the addition of the T and T 2 terms which are sometimes included to model the
C p − Cv contribution.20,21 However, we found that if we added a Schottky function, we
could improve the fit over the temperature range 25 6 (T /K) 6 250 dramatically for all
four data sets. The fitting equation is given by using
C p,m = n · D(θ D /T ) + m · E(θ E /T ) + n S · S(θ S /T ),
(1)
where D(θ D /T ) represents a three-dimensional Debye heat capacity; E(θ E /T ) represents
a one-dimensional Einstein heat capacity function; and S(θ S /T ) is a two-level Schottky
heat capacity function with the degeneracies of both levels set equal to one. Six parameters,
n, θ D , m, θ E , n S , and θ S are varied by the computer algorithm to obtain the best fit. Even
with the Schottky function, however, we found that the data above T = 250 K showed
deviations from the fit that were systematic and larger than our estimated experimental
uncertainty.
Fits that were more satisfactory for obtaining the thermodynamic functions could be
obtained, however, by optimizing the six parameters using data from 25 6 (T /K) 6 250 K
in one calculation. Then, the parameters obtained for the Schottky function in the low
temperature fit were fixed, and a new set of Debye and Einstein parameters were obtained
from a data set encompassing the temperature region, 150 6 (T /K) 6 400. The two
versions of equation (1) were joined at a temperature, TS , which was taken as that
temperature in which the absolute values of the heat capacity and its first and second
derivatives with temperature calculated from the two fits showed the best agreement. The
fitting coefficients in the two temperature regimes and TS are given in table 6 for each
molecular sieve.
At this time, we attribute no physical significance to the physical phenomenon that
gives rise to the excess heat capacity modeled by the Schottky function. We adopt
the functional form of equation (1) because it adequately represents the temperature
dependences of the heat capacity of all four polymorphs. The goodness of fit can be seen in
figure 2, where the deviations of the experimental points from the curves fitted using these
parameters is plotted as 100 · 1C p,m . The deviation function 1C p,m has been defined as
{C p,m (expt) − C p,m (fit)}/C p,m (fit). Above T = 50 K, the precision in 1C p,m is generally
±0.004; below 50 K, the scatter is greater because of the relatively small contribution of
the sample to the calorimetric measurements.
There are two advantages in this approach to fitting the heat capacity results over the
more conventional procedure that uses orthogonal polynomials. One is associated with the
ability of these functions to be extrapolated into temperature regions where no data exist,
and the other lies in their ability to be interpolated in regions where additional contributions
to the heat capacity may be present.
We take advantage of the ability to extrapolate in calculating the contributions to the
thermodynamic functions below T = 25 K for ∗ BEA, MFI, and MTT and below T = 15 K
for FAU. The interpolation feature is used, as discussed below, for the analysis of the
thermodynamics of the MFI phase transition.
o , and 8o =
The standard molar thermodynamic functions, C op,m , 10T Hmo , 10T Sm
T
T
o
o
(10 Sm − 10 Hm /T ) have been calculated from these fits at smoothed temperatures,
assuming that the molar entropy at T = 0 K is zero. The results of the calculations are given
218
J. Boerio-Goates et al.
TABLE 6. Parameters used to calculate smooth values of the heat capacity
of the pure silica molecular sieves from equation (1)
∗ BEA
FAU
0.880182
0.772792
MFI
MTT
Low temperature
n mol−1
θD
K−1
306.025
m mol−1
1.237037
θ E K−1
671.0703
n S mol−1
0.637764
θ S K−1
86.40593
Ts K−1
165
285.1369
1.059682
565.9032
0.494978
85.18686
137
1.052377
370.5717
1.178857
719.4484
0.817107
98.39438
165
0.97997
340.1407
1.148572
667.6218
0.697831
90.04602
163
High temperature
n mol−1
θD
1.624448
K−1
498.3392
m mol−1
θ E K−1
1.28492
1253.209
n S mol−1
θ S K−1
0.637764
86.40593
1.572717
480.9437
1.410729
1192.773
0.494978
85.18686
1.17863
377.6457
1.414703
878.3706
0.817107
98.39438
1.720786
512.3952
1.382753
1297.031
0.697831
90.04602
in tables 7 through 10 for ∗ BEA, FAU, MFI, and MTT, respectively. The uncertainties in
the derived thermodynamic functions at T = 298.15 K are estimated to be 0.004 · J where
J is the particular thermodynamic function.
An other method to calculate the thermodynamic functions below T = 25 K was tested.
We took one or two data points from each polymorph immediately above the region where
adsorption of the exchange gas takes place and estimated a simple-T 3 contribution. In all
four polymporphs, and for all the thermodynamic functions, the two methods lead to values
of the thermodynamic functions that differ by less than 0.1 per cent at T = 298.15 K. Since
we consider the thermodynamic functions J to have an uncertainty given by 0.004∗ J at
that temperature, these differences are not considered significant.
PHASE TRANSITION IN MFI
A reversible phase transition in MFI (silicalite, ZSM-5) has been observed by both x-ray
and solid state nmr diffraction techniques. (22–27) The transition temperature, as detected
by changes in x-ray powder patterns, has been reported to be a function of the Si/Al
ratio. Samples with a low Al content exhibit the transition temperature in the range
317 6 (T /K) 6 325; increasing Al content decreases the transition temperature. (22) Solid
state 29 Si magic angle spinning nmr experiments on materials with low Al content report
the transition to occur at still higher temperatures, 355 6 (T /K) 6 365 K. (24) According
to another study, (26) changes in the nmr spectrum occur over the entire temperature range
of their measurements, 153 6 (T /K) 6 403 with the most dramatic change occurring
Heat capacities of SiO2 molecular sieves
219
TABLE 7. Standard molar thermodynamic functions of ∗ BEA. ( p o = 0.1 MPa).
o − 1T H o /T )
8om = (10T Sm
0 m
T
K
C op,m
−1
J · K · mol−1
o
10T Sm
o /T
10T Hm
J · K−1 · mol−1
J · K−1 · mol−1
8om
−1
J · K · mol−1
0
5
10
15
20
25
30
35
40
45
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
273.15
280
290
298.15
300
320
340
360
380
400
0
0.00751
0.12965
0.75219
1.7588
2.8051
3.7867
4.7336
5.6855
6.6560
7.6390
9.5910
11.473
13.289
15.073
16.852
18.637
20.421
22.188
23.919
25.597
27.208
28.734
30.179
31.568
32.911
34.212
35.477
36.707
37.903
39.067
40.198
41.296
41.635
42.360
43.392
44.208
44.390
46.285
48.049
49.683
51.195
52.590
0
0.00249
0.02893
0.17974
0.52978
1.0356
1.6347
2.2897
2.9837
3.7090
4.4614
6.0274
7.6482
9.2994
10.968
12.648
14.338
16.036
17.740
19.448
21.156
22.860
24.556
26.239
27.908
29.562
31.199
32.820
34.424
36.012
37.583
39.138
40.675
41.156
42.196
43.701
44.915
45.189
48.115
50.975
53.768
56.495
59.157
0
0.00187
0.02302
0.14627
0.41995
0.79324
1.2112
1.6469
2.0920
2.5451
3.0053
3.9409
4.8835
5.8213
6.7503
7.6714
8.5871
9.4989
10.407
11.311
12.208
13.095
13.971
14.831
15.676
16.504
17.317
18.113
18.895
19.662
20.416
21.155
21.880
22.106
22.593
23.292
23.853
23.979
25.315
26.601
27.838
29.028
30.172
0
0.00062
0.00591
0.03346
0.10983
0.24239
0.42355
0.64283
0.89171
1.1642
1.4561
2.0865
2.7648
3.4782
4.2176
4.9765
5.7506
6.5369
7.3332
8.1375
8.9485
9.7648
10.585
11.408
12.233
13.058
13.883
14.707
15.529
16.350
17.168
17.983
18.795
19.050
19.604
20.408
21.062
21.210
22.800
24.374
25.929
27.467
28.985
220
J. Boerio-Goates et al.
TABLE 8. Standard molar thermodynamic functions of FAU. ( p o = 0.1 MPa).
o − 1T H o /T )
8om = (10T Sm
0 m
T
K
C op,m
−1
J · K · mol−1
o
10T Sm
o /T
10T Hm
J · K−1 · mol−1
J · K−1 · mol−1
8om
−1
J · K · mol−1
0
5
10
15
20
25
30
35
40
45
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
273.15
280
290
298.15
300
320
340
360
380
400
0
0.00815
0.12441
0.66905
1.5435
2.4845
3.4158
4.3506
5.3035
6.2716
7.2454
9.1804
11.094
13.007
14.929
16.849
18.743
20.582
22.342
24.045
25.746
27.364
28.915
30.413
31.866
33.280
34.660
36.006
37.320
38.600
39.846
41.057
42.232
42.594
43.370
44.471
45.341
45.535
47.549
49.414
51.136
52.721
54.178
0
0.00270
0.02942
0.16650
0.47473
0.92026
1.4568
2.0522
2.6952
3.3756
4.0868
5.5792
7.1382
8.7444
10.387
12.060
13.755
15.465
17.182
18.900
20.618
22.331
24.037
25.732
27.416
29.087
30.744
32.387
34.017
35.633
37.234
38.820
40.392
40.884
41.948
43.490
44.734
45.015
48.019
50.958
53.832
56.640
59.382
0
0.00203
0.02320
0.13424
0.37379
0.70185
1.0767
1.4774
1.8959
2.3282
2.7713
3.6786
4.6014
5.5324
6.4696
7.4117
8.3560
9.2987
10.235
11.160
12.076
12.982
13.874
14.751
15.614
16.462
17.296
18.116
18.922
19.716
20.496
21.264
22.019
22.254
22.761
23.491
24.076
24.208
25.604
26.951
28.247
29.494
30.693
0
0.00067
0.00622
0.03226
0.10094
0.21840
0.37900
0.57480
0.79923
1.0474
1.3155
1.9007
2.5369
3.2120
3.9177
4.6480
5.3987
6.1663
6.9476
7.7400
8.5413
9.3496
10.163
10.981
11.802
12.625
13.448
14.272
15.095
15.917
16.738
17.556
18.373
18.630
19.187
19.999
20.658
20.807
22.414
24.007
25.585
27.146
28.689
Heat capacities of SiO2 molecular sieves
221
TABLE 9. Standard molar thermodynamic functions of MFI. ( p o = 0.1 MPa).
o − 1T H o /T )
8om = (10T Sm
0 m
T
K
C op,m
−1
J · K · mol−1
o
10T Sm
o /T
10T Hm
J · K−1 · mol−1
J · K−1 · mol−1
8om
−1
J · K · mol−1
0
5
10
15
20
25
30
35
40
45
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
273.15
280
290
298.15
300
320
340
360
380
400
0
0.00503
0.07525
0.54853
1.5047
2.6047
3.6337
4.5642
5.4429
6.3175
7.2142
9.0885
11.026
12.974
14.910
16.833
18.740
20.626
22.481
24.291
26.043
27.726
29.209
30.776
32.302
33.781
35.209
36.580
37.893
39.145
40.338
41.481
42.601
42.948
43.705
44.802
45.695
45.897
48.071
50.385
53.384
51.168
52.195
0
0.00167
0.01732
0.11786
0.39886
0.85291
1.4204
2.0514
2.7185
3.4100
4.1218
5.6012
7.1474
8.7469
10.387
12.057
13.752
15.463
17.188
18.920
20.656
22.391
24.117
25.831
27.536
29.231
30.914
32.583
34.239
35.878
37.500
39.105
40.691
41.187
42.261
43.814
45.067
45.351
48.382
51.364
54.324
57.159
59.810
0
0.00126
0.01361
0.09694
0.3226
0.6692
1.0790
1.5114
1.9482
2.3849
2.8228
3.7095
4.6160
5.5390
6.4728
7.4128
8.3560
9.3002
10.243
11.182
12.115
13.038
13.946
14.838
15.717
16.583
17.437
18.276
19.100
19.910
20.703
21.480
22.242
22.479
22.989
23.722
24.311
24.443
25.852
27.225
28.590
29.844
30.936
0
0.00042
0.00371
0.02092
0.07623
0.18374
0.34139
0.54006
0.77038
1.0251
1.2990
1.8917
2.5314
3.2079
3.9141
4.6447
5.3954
6.1630
6.9446
7.7381
8.5415
9.3529
10.171
10.993
11.819
12.647
13.477
14.308
15.138
15.968
16.797
17.624
18.449
18.709
19.271
20.091
20.757
20.908
22.530
24.139
25.734
27.314
28.874
222
J. Boerio-Goates et al.
55
Cp,m /(J . K –1 . mol –1)
50
100∗∆Cp,m /(J . K –1 . mol –1)
3
45
2
1
0
40
250
300
50
100 150
350
200
T/K
250
300
350
400
T/K
FIGURE 3. A comparison of the heat capacity of MFI as a function of temperature obtained in this
study with that reported by Johnson et al. in reference 5 in the vicinity of the MFI phase transition:
, Johnson et al. reference 5; , this work. The inset gives a plot of 100 · 1C p,m over the entire
temperature region of both studies, where 1C p,m = {C p,m (Johnson) − C p,m (this study)}/C p,m
(this study).
•
◦
at T = 355 K. (26) Single crystal x-ray diffraction results show that a complicated set
of displacements is associated with the monoclinic–orthorhombic transition, but that the
changes in Si–O–Si bond angles and Si–O bond distances are small. (27)
The phase transition was not observed by Johnson et al. (5) in their thermodynamic
study of MFI (silicalite). However, their adiabatic calorimetric measurements stopped near
T = 350 K. By comparison with our results, shown in figure 3, we conclude that their
calorimetric measurements extended into the onset of the transition, but stopped before
the maximum was reached. Their curve shows an upward trend above T = 325 K
that parallels the increase in our results before the maximum at T = 365 K. But,
since their measurements stopped short of T = 365 K, they were unable to discern the
presence of the transition. A comparison of the two sets of measurements over the entire
Heat capacities of SiO2 molecular sieves
223
4
Cexcess /(J . mol –1 . K –1)
3
2
1
0
250
275
300
325
T/K
350
375
400
FIGURE 4. The excess heat capacity as a function of temperature in the region of the phase transition
in MFI. Cexcess = C p,m (expt)−C p,m (lattice): . The lattice heat capacity has been calculated using
the parameters for MFI given in table 6. The solid curve, —, is obtained from fits with cubic splines
to the excess heat capacities.
•
temperature region is presented as an inset to figure 3. This plot shows 100 · 1C p,m where
1C p,m = {C p,m (Johnson) − C p,m (this study)}/C p,m (this study). The comparison is made
using the smoothed results from both studies.
We have calculated the thermodynamic quantities associated with the monoclinic–
orthorhombic transition by making use of the Debye/Einstein/Schottky fit described earlier.
We obtained an estimate of the lattice heat capacity by fitting the functions of equation (1)
using data outside the transition region and then using the results to interpolate within the
region. The excess heat capacity in the transition region obtained in this manner is plotted
in figure 4. The transition is observed to extend over a very large temperature interval
250 6 (T /K) 6 380 with the maximum at T = 365 K. This transition region is consistent
with spectroscopic results that show significant changes in the 29 Si nmr signal occurring
224
J. Boerio-Goates et al.
2.0
1.5
∆ Cp /(J . K –1 . mol –1)
1.0
0.5
0.0
– 0.5
–1.0
0
50
100
150
200
250
300
350
T/K
FIGURE 5. The heat capacity of molecular sieves and other phases of SiO2 as a function of
temperature, relative to that of quartz. 1C p,m = C p,m (polymorph) − C p,m (quartz). , ∗ BEA;
H, FAU; , MTT; , MFI; , cristobalite; , coesite; ∇, amorphous silica.
◦
•
throughout this interval. (26) The smooth curve in figure 4 is a cubic spline fit to the excess
heat capacity, Cexcess , calculated as C p,m (expt) − C p,m {equation (1)}.
In the regions where the excess heat capacity is zero, the thermodynamic functions
of MFI reported in table 9 are calculated from the Debye/Einstein/Schottky functions of
equation (1). Within the transition region the excess heat capacity shown by the smooth
curve of figure 4 is included in the calculation of the thermodynamic functions.
The thermodynamic quantities associated with the phase transition, the enthalpy of
transition, 1tr H and entropy of transition 1tr S have been obtained by integrating the
smooth curve shown in figure 4. Given the extended transition region, the values, 1tr H =
−1
(134.8 ± 0.5) J · mol−1 and 1tr S = (0.385 ± 0.001) J · K−1 · mol , are very small.
(The errors to the transition quantities have been estimated by considering the results of
different choices of lattice curves and spline fits.) These small values are consistent with an
interpretation of a subtle, displacive transition that has only minor effects on the average
Si–O–Si bond angle and Si–O bond length. (27) They also explain why the transition was
not detected when the drop calorimetric measurements of Johnson et al. (5) were merged
with their adiabatic calorimetric results. The transition enthalpy we measured would have
represented less than 0.2 per cent of the total enthalpy measured in the Johnson drop
Heat capacities of SiO2 molecular sieves
225
TABLE 10. Standard molar thermodynamic functions of MTT ( p o = 0.1 MPa).
o − 1T H o /T )
8om = (10T Sm
0 m
T
K
C op,m
−1
J · K · mol−1
o
10T Sm
o /T
10T Hm
J · K−1 · mol−1
J · K−1 · mol−1
8om
−1
J · K · mol−1
0
5
10
15
20
25
30
35
40
45
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
273.15
280
290
298.15
300
320
340
360
380
400
0
0.00608
0.10618
0.67747
1.6622
2.6998
3.6504
4.5381
5.4195
6.3289
7.2746
9.2426
11.243
13.233
15.205
17.163
19.102
21.013
22.877
24.681
26.411
28.055
29.701
31.215
32.669
34.073
35.434
36.757
38.045
39.301
40.524
41.715
42.875
43.234
44.003
45.098
45.967
46.161
48.188
50.082
51.848
53.488
55.008
0
0.00202
0.02326
0.15462
0.47936
0.96289
1.5405
2.1703
2.8337
3.5241
4.2400
5.7380
7.3138
8.9452
10.618
12.321
14.048
15.792
17.548
19.310
21.072
22.830
24.581
26.322
28.049
29.761
31.456
33.135
34.798
36.444
38.073
39.686
41.282
41.781
42.861
44.425
45.687
45.972
49.016
51.995
54.908
57.756
60.539
0
0.00151
0.01852
0.12669
0.38314
0.74376
1.1502
1.5712
1.9970
2.4274
2.8646
3.7626
4.6884
5.6322
6.5865
7.5464
8.5089
9.4716
10.431
11.385
12.330
13.262
14.181
15.086
15.973
16.843
17.696
18.533
19.353
20.158
20.949
21.725
22.487
22.724
23.235
23.970
24.560
24.692
26.098
27.454
28.761
30.019
31.231
0
0.000504
0.00475
0.02793
0.09622
0.21913
0.39028
0.59912
0.83667
1.0967
1.3750
1.9762
2.6254
3.3129
4.0313
4.7749
5.5393
6.3209
7.1170
7.9250
8.7428
9.5684
10.400
11.236
12.076
12.917
13.760
14.602
15.444
16.285
17.124
17.962
18.795
19.057
19.626
20.455
21.127
21.278
22.918
24.541
26.138
27.737
29.307
226
J. Boerio-Goates et al.
calorimetric experiments at T = 350 K, and it would contribute increasingly smaller
amounts to the experiments at higher temperatures. The drop calorimetric results have a
root mean standard deviation of 0.51 per cent about the fitting equation for the enthalpy
reported as equation 3 in reference 5. It is unlikely that this excess enthalpy would have
been observable in the scatter of those experiments.
COMPARISON WITH HEAT CAPACITY OF DENSE POLYMORPHS OF SIO2
The heat capacities of the zeolitic polymorphs of SiO2 can be compared with those of the
dense phases of SiO2 . Figure 5 shows the results of that comparison in which 1C p,m
is defined here as C p,m (molecular sieve, cristabolalite, coesite or amorphous silica)–
C p,m (crystalline quartz). Quartz has been taken as the reference for the comparison since
it is the stable phase of SiO2 at this temperature and pressure. The heat capacity results
of Gurvich (28) have been used for quartz. These agree well with what we have been able
to construct of the unpublished data of Westrum on quartz† (29) and the smoothed values
reported by Richet et al. (30) The values for cristobalite and amorphous silica are those of
Richet et al.; (30) those for coesite are from Holm et al. (31)
The most obvious difference apparent in the figure is that the coesite heat capacity
follows a trend relative to quartz that is opposite of those exhibited by the other
polymorphs. The heat capacity of coesite decreases relative to quartz when the others are
increasing and increases when the others are decreasing. Coesite is denser than quartz,
while the other phases are less dense. The decrease in density occurs in the order: quartz,
cristobalite, amorphous silica, MTT, MFI, FAU, and ∗ BEA. (6) There is a slight trend of
the heat capacities at T < 50 K that follows density: the least dense material has the
highest heat capacity in this region, but at higher temperatures the behavior of the heat
capacity becomes more complex. It is of interest to note that the molecular sieves exhibit
an excess heat capacity relative to quartz which is much greater than that of amorphous
silica in the temperature region 25 6 (T /K) 6 200. This is an unexpected result since
amorphous materials are generally characterized by an increase in the heat capacity relative
to crystalline materials in this temperature region, (32) and the molecular sieves exhibit
crystalline rather than glassy behavior. An attempt to explain this observation in terms of
the lattice dynamics of these molecular sieves will be explored in a later paper.
We thank Brian Lang for assistance with the integration of the transition region in the MFI
heat capacity results and for the very low temperature measurements on ∗ BEA. B. K. Hom
and R. Stevens gratefully acknowledge financial support from the Office of Research and
Creative Works at Brigham Young University. P. Piccione and M. E. Davis have received
support from the Chevron Research and Technology Co. and the work of A. Navrotsky on
this project has been funded through NSF grant DMR 97-31782. We thank P. A. G. O’Hare
for a lifetime of valuable contributions to the field of chemical thermodynamics, including
the production of high quality thermodyamic data using many calorimetric techniques, the
mentoring of young thermodynamicists (among them J. Boerio-Goates), and the rigorous
editing of this journal.
†Westrum E. F. Jr, never published his low temperature data on quartz, but distributed it to colleagues. The
authors of reference 29 report both results calculated from a theoretical model and their deviation from Westrum’s
values. Working backwards from the theoretical results and the deviations, we reconstructed Westrum’s results.
Heat capacities of SiO2 molecular sieves
227
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(Received 24 January 2001; in final form 31 May 2001)
RS-09