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tris(hydroxymethyl)aminomethane
J. Phys. Chew. Solids Vol. $4, No. 2, pp. 171-181, Printed in Great Britain.
1993
0022-3697/93 S6.00 + 0.00 0 1993 Pergamon Press Ltd
MISCIBILITY AND MOLECULAR INTERACTIONS IN PLASTIC PHASES: BINARY SYSTEM PENTAGLYCERIN/ TRIS(HYDROXYMETHYL)AMINOMETHANE M. BARRIO,t J. FONT,? D. 0. L&SZ,t J. MUNTASELL,t J. LL. TAMARIT,t P. NEGRIER,$. N. B. CHANHS and Y. HAGET$ TDepartament de Fisica i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Diagonal 647,08028 Barcelona, Spain and fLaboratoire de Cristallographie et de Physique Cristalline, URA 144 au CNRS, Universitt Bordeaux I, 351 tours de la Liberation, 33405 Talence Cedex, France (Received 30 January 1992; accepted 27 September
1992)
Abstract-The phase diagram of the plastic crystals pentaglycerin (PG) and tris(hydroxymethyl)aminomethane has been established by means of thermal analysis and X-ray powder diffraction from room temperature to the liquid state. The binary system is characterized by two eutectoid invariants corresponding to solid to plastic phase transitions and by one eutectic invariant corresponding to the melting process. The phase diagram exhibits a demixing region in the plastic state as a consequence of the difference between the disordered high-temperature forms of the pure compounds. The determination of the solubility boundaries in the plastic state shows a narrow two phase domain (about 0.13 in molar fraction). The evolution of the volume occupied by a molecule in the molecular alloys in the plastic phases can be interpreted taking into account the different intermolecular interactions in these phases and by geometrical effects. Keyworrls: Plastic crystal, phase diagram, molecular alloy, solid solution, plastic phase miscibility.
1. INTRODUCTION of the highly orientational disordered phases stable just below the melting point (form I) are generally referred to as plastic or ODIC (orientationally disordered crystalline phase) crystals. Plastic were first recognized by crystals Timmermans [ 1,2] as characteristically containing approximately spherical molecules and showing a low entropy of fusion (AS < 2SR, where R is the gas constant). The high rate of molecular reorientation and the large amplitudes of thermal libration found in the ODIC phase result in a high symmetry crystal in phase I (usually f.c.c. or b.c.c.) [3]. In addition, the symmetry elements of many plastic crystals are incompatible with those of their constituent molecules if this is regarded as stationary [4,5]. Such apparent discrepancies between lattice and molecular symmetries provide one of the reasons to assume that the molecules, even if not literally rotating, are dynamically disordered in orientation. Then, orientationally disordered crystals have the three-dimensional periodicity characteristic of the crystal and the isotropy properties characteristic of the liquid [6]. This paper reports the study of the binary phase diagram between two plastic crystals, tris(hydroxymethyl)aminomethane (TRIS) and pentaglycerin Crystals
(PG) [‘i’l(Fig. 1) from room temperature to 473 K (liquid state for both compounds). This study was undertaken, within a more general framework about the syncrystallization problem, to gain information about the molecular alloys formed in solid crystalline and plastic crystal phases and the influence of intermolecular hydrogen bonding in their formation. 2. EXPERIMENTAL
2.1. Thermal analysis The thermal measurements have been carried out by means of a heat flux differential scanning calorimeter. The differential signal was obtained by means of two thermoelectric modules of great sensitivity (TN0 SI SP [8]) connected in opposition. The sensitivity is about 140mV W-’ at room temperature. The temperature was measured with a Pt-100 R calibrated probe. The data acquisition and treatment was described elsewhere [9]. The scanning rate used was about 1 k min-i. The samples (mass about 10 mg) were hermetically sealed in order to avoid sublimation. 2.2. D@raction
at constant temperature
X-ray measurements were performed by means of a powder Siemens D-500 vertical diffractometer with 171
M. BARRIOet al.
172
a, I
WlOH
-C-c&OH I
T
C&OH -C-
C&OH
C&OH
d&OH
(a)
(W
Fig. 1. Molecules of PG (a) and TRIS (b).
an Anton Paar temperature camera, whose characteristics have been described previously [9]. The goniometer speed used was 2/5”(2fI) min-‘. CsCl was used as internal standard. The samples were re-covered by a mylar sheet to avoid possible sublimation of the powder during the measurement. Lattice parameters were obtained by a leastsquares refinement method [lo]. 2.3. Dzjiiaction as a function of continuous heating Powder diffraction analysis as a function of the continuous evolution of the temperature was performed with a Guinier-Simon camera. The experimental conditions were the same as in previous works [ll]. 3. RESULTS 3.1. Pure compounds Both pure compounds were purchased from Aldrich Chemical Company with purities of 99/9 + % and 99% for TRIS and PG, respectively, and additional purification was performed by a drying process at 333 K. 3.1.1. Crystallographicresults (a) Pentaglycerin The crystal structure at room temperature of PG was determined as body centered tetragonal(14) with Z = 2 [12, 131 (hereinafter referred to as Q phase). Between about 357K and the melting point (about 470 K) PG forms a plastic crystal phase (hereinafter referred to as C,) the structure of which is face centered cubic (Z = 4) [14]. Our study by X-ray powder diffraction at room temperature gave lattice parameters: a = 6.052 (2) A and c = 8.872 (3) A. These values have been already published by us [ 151 and are near those appearing in the bibliography [12, 141.The PG structure is characterized by the presence of strong intermolecular hydroxyl hydrogen bonds in the layers parallel to the (001) plane and weak interlayer bonds due to van der Waals forces [12]. The cubic lattice parameter for the plastic phase has been measured in this work at two temperatures,
363 K and 408 K, giving the values 8.876 (8) A and 8.942 (10) A, respectively. These results match the previously reported values in the literature [14]. We want to emphasize that the plastic X-ray diffraction patterns show only three visible lines (( 11l), (200) and (222)) with considerable background scattering; this fact and the very rapid fall-off in intensity with increasing reflection angle are due to the highly structure disorder. This usual fact in structural studies of plastic crystals justifies the high margin of error given for the cell parameters [14, 16-201. (b) Tris(hydroxymethyl)aminomethane The unit cell and space group of TRIS at room temperature was reported earlier by Rose and Van Camp [21] with an incorrect space group. The crystal structure has been fully determined by Elierman and Rudman [19], who give a Pn2,a space group with Z = 4 for the solid phase (hereinafter referred as 0). The reported lattice parameters for this orthorhombic phase are given in Table 1 together with our refinement by X-ray powder diffraction. The structure of TRIS in the low temperature phase has been described as layers of molecules approximately perpendicular to the c-axis (83”). Within each layer the three OH groups are connected by strong hydrogen bonds whereas one of the amine hydrogen atoms is weakly hydrogen-bonded to the atom of a molecule in an adjacent layer [19,22]. At about 407 K TRIS transforms to a plastic phase. This phase (hereinafter called C,) was found to be body centered cubic (Im3m) with Z = 2 in a detailed single crystal study [19]. The formation of a b.c.c. lattice in the ODIC phase, rather than a f.c.c. as was found in the other compounds of this series [ 13, 14,16, 18,20,23], has been interpreted in terms of the ellipsoidal shape of this molecule. This assumption is reinforced by the rule proposed by Rudman for pseudo-spherical tetrahedral molecules, which establishes that the crystal structures of both ordered and orientationally-disordered phases are controlled by equal-sphere closest-packing principles [24]. In the powder diffraction pattern of the high temperature phase of TRIS only one (by X-ray diffraction at constant temperature) or two (by the Guinier-Simon technique) lines appear. In the last technique the second reflection is not detected due to the presence of the mylar sheet peak. In [14] the authors pointed out the existence of only one reflection and due to the lack of information about the experimental device and conditions used in that work, any explanation can be induced. The literature reported data and our results are summarized in Table 1.
Miscibility and molecular interactions
173
Table 1. Lattice parameters for phases 0 and C, of TRIS a(A)
Parameters b(A)
c(A)
T(K)
Reference
8.844 (1) 8.807 (6)
7.794 (1) 8.872 (7)
8.795 (1) 7.709 (7)
295 Room temp.
[191
Phase 0 G
8.853(3) 7.804(2) 8.800(3)
293
6.852 (6) 6.83 6.888 (8)
408 408
t251t This work v91 1241 This work
tThe lattice parameters in [25] are given according to the Pna2, space group.
3.1.2.
Thermodynamic results
plane), while TRIS (R = -NH,) forms a layered structure with weak hydrogen bonds between layers. In the ODIC phase, those compounds with the exception of R = -NH,(TRIS), crystallize in a f.c.c. lattice with four molecules per unit cell. For all these compounds there is one molecule per lattice point, and thus, by comparing the site symmetry and the intrinsic molecular symmetry, the molecules must be highly disordered with pseudo-spherical symmetry [4, 51. TRIS forms a b.c.c. unit cell with Z = 2. There is a significant number of ODIC materials that form b.c.c. cells [3,29-311. The common feature of the molecules forming a b.c.c. lattice is that there are intermolecular interactions between these molecules due to a distortion from sphericity or as a result of bonding interaction (as hydrogen bonding which occurs in TRIS producing an ellipsoidal rather than a spherical molecule). Thus, the plastic state of TRIS differs from the other pseudospherical compounds of the series because of the more extensive remaining hydrogen bonding. This fact is coherent with the rotational activation energy in the plastic phase of 5 1.6 kJ mol-’ [32], while it is of the order of 4-9 kJ mol-’ in plastic phases without important remaining hydrogen bonding. A vibrational spectra study of TRIS has confirmed that the anisotropy of the hydrogen bonds in the low temperature phase (strong in the layers and weak between layers) became isotropic (weak in and between layers) in the ODIC state [33]. The fact that the hydrogen bonding plays a dominant role in the ODIC state is unusual because in most of the plastic phases the molecules rotate quite easily while their centers of mass remain fixed in the lattice. On the contrary for PG and according to [34], all the hydrogen bonds are broken at the transition temperature,
(a) Pentaglycerin The temperature and enthalpy variation of the solid to plastic phase transition are, respectively, 357.5 +_ 1.0 K and 21.3 + 1.0 kJ mol-’ and, for the melting process 471.7 f 1.0 K and 5.1 &-0.3 kJ mol-’ for the corresponding parameters. Some significant differences can be observed between these values and those previously reported by us [9, 151. These differences may be attributed to the purity of the original pure compound. (b) Tris(hydroxymethyl)aminomethane The TRIS has been subjected to many thermodynamic studies [19,26-281. The characteristic values of solid-solid phase transition obtained from the literature are shown in Table 2 together with the respective parameters of the melting process. Our results are 406.8 f 1.0 K and 34.0 f 1.7 kJ mol-’ for the temperature and enthalpy variation of the transition, and 442.7 +_ 1.0 K and 3.7 +_0.2 kJ mol-’ for the liquefaction process. In Table 2 we can compare these values with those of the bibliography. 3.1.3. Comparison of the structure of the pure compounds and the role of the hydrogen bonds. When comparing the structure of the poly(hydroxymethyl) compounds, TRIS becomes of special interest. Most of these compounds are tris(hydroxymethyl) with the general formula R-C(CH,OH),, where R is -CH,OH, -COOH, -C,H,, -CH,, -NO,, -NH,. The R = -CHX compound (PG) is tetragonal with only van der Waals bonding between strongly hydrogen-bonded layers (parallel to the 001
Table 2. Temperatures and enthalpy variations for the phase 0 to phase C, and the phase C, to liquid transitions of TRIS TO-.,,
AH,.+,,
6)
(kJ mol-‘)
408 404407 407.3 406.7 406.8
34.2 32.93 33.4-34.0 34.0 + 1.7
TCl-L (K) 44546 439-442 446.0 442.7 f 1.0
AH,,-, (kJ mol-‘)
Reference
3.0 2.97 3.7 & 0.2
;:A; This work
M. BARRIOet
174
permitting molecular vibration and rotation in the ODIC phase. The different bond scheme between PG and TRIS produces some important geometric considerations. The column occupied by a molecule in the unit cell (V/Z) in the ordered low temperature phases is 152.0 A’ and 162.5 A’ for TRIS and PG, respectively (at room temperature); due to the fact that the two isolated molecules have a similar volume (the volume increments of the atomic combinations -NH, and - CH, used for calculating the packing coefficient are 19.7 A’ and 23.5 A’, respectively [35]) it is obvious that the hydrogen bonds pull the molecules closer in TRIS. If one compares the same relationship in the plastic phase (163.4A’ and 178.8 A’ for TRIS and PG, respectively at 408 K) two consequences can be obtained. (1) These two values are always greater than their respective values in the ordered phase and then, the bonds in the ODIC phase become weaker. (2) The values in the plastic phase keep the same order than in the ordered phase and, thus in spite of the similarity in the molecule volume, the plastic phase of TRIS must have stronger bonds than the respective plastic phase of PG, in agreement with the infrared spectroscopy and NMR measurements previously mentioned. 4. MOLECULAR
ALLOYS
The samples have been prepared from the melt of the two pure compounds in the desired proportion and slow cooling from the liquid phase to room temperature. 4.1. Crystallographic
study
4.1.1. Difraction as a function of continuous heating. The Guinier-Simon X-ray camera allows us to follow on film the continuous evolution of the diffraction pattern of the samples vs temperature, and then to know the phases coexisting in equilibrium at each temperature. In Fig. 2b we give the Guinier-Simon pattern corresponding to the sample X = 0.3 molar fraction of PG. The successive domains may be described as: l l
l l
l l l
existence of a disappearance about 350 K; existence of a disappearance about 387 K; existence of a disappearance existence of a
two phase domain [0 + Q]; of Q and appearance of Cr at two phase domain [0 + Cd; of C2 and appearance of C, at two phase domain [0 + C,]; of 0 at 394 K; one phase domain C,;
l l
al.
beginning of melting at 430 K; and end of melting at about 435 K.
Figure 2c is relative to the sample X = 0.4 and, as temperature rises, one meets successively: existence of a two phase domain [0 + Q]; disappearance of Q and appearance of C, at about 343 K; existence of a two phase domain [0 + Cd; disappearance of C, and 0 phases and appearance of the C, phase at 381 K; existence of one phase domain C,; appearance of Cr phase at 413 K; existence of a two phase domain [C, + Cj; disappearance of C, and appearance of the liquid [L] phase at the same temperature of 427 K; existence of a two phase domain [L + C,]; and end of the melting at about 433 K. These experimental results support the existence of three eutectic phenomena, whose temperatures will be determined more accurately by thermal analysis (next section). The three eutectic invariants correspond to equilibria: the three phase P+Q+Gl, [0 + C, + CJ and, finally [C, + C, + L]. The diffraction pattern of the sample X = 0.5 has been also recorded by Guinier-Simon technique (see Fig. 2d). At about 352 K we detected the change from [0 + Q] to [0 + C,] and subsequently at 387 K the change from [0 + C,] to [C, + CJ. At 408 K the C, phase disappears and the C, phase remains until the melting process, which takes place between 434 and 440 K. The Guinier-Simon pattern obtained for the sample X = 0.8 (see Fig. 2e) shows a two phase domain [0 + Q] which changes to another [0 + C,] at about 344 K and at 368 K the 0 phase disappears and at any moment one cannot observe the C, phase. At about 447 K the melting process starts and it ends at about 455 K. To determine the solubility boundaries of the different two phase domains we have performed isothermal X-ray diffraction at several temperatures; the results are shown below. 4.1.2. Study at 293 K. To determine the limit of the solid solutions at 293 K accurately, we have analysed the evolution of the reflections of each phase in function of the concentration. In Fig. 3 we depict the evolution of the (111) and (022) reflections corresponding to the orthorhombic phase (0) vs concentration. From the analysis of the evolution of the Bragg angles we can conclude that the solubility boundary of TRIS in PG is fraction of PG), i.e. the &(r=293K) = 0.015 (molar molecular alloy TRIS~,985PG,,,,,.
293 K -344 ~368
Lo+a1
KK-
,=
[otc,l [c&l
-447K +455 K =
4;!fLl [LI
(e) X=0.8
293 K -
101 -357
K -
K,l
-472
K-
,.(f)
X=l
CL1
(PG)
Fig. 2. Guinier-Simon pattern corresponding to the pure compounds TRIS (a) and PG (r) and to the samples X = 0.3 (b), X = 0.4 (c), X = 0.5 (d) and X = 0.8 (e). The reflections that do not disappear in the pattern of TRIS correspond to SiO, used to seal the Lindeman capillary [I 11.
175
M. BARRIOet
176
al. 10.40’
9.13 r 0
(111)
.6
PG
Fig. 3. Variation of the Bragg angles (0(O)) with the concentration for the (111) and (022) reflections corresponding to the orthorhombic cell at 293 K.
Fig. 4. Variation of the Bragg angles (O(O)) with the concentration for the (110) and (112) reflections corresponding to the tetragonal cell at 293 K.
solubility boundary SW,= 293Kj, that in this case corresponds to the solid solution TRIS,,M PG,,,94. The lattice parameter values of the solid solutions are given in Table 3.
Figure 4 shows the evolution of the Bragg angle of the (110) and (112) reflections corresponding to the tetragonal lattice as a function of the molar concentration of PG. In a similar way we can establish the
Table 3. Lattice parameters of the unit cells for the pure compounds and their alloys at 293 K Parameters Form
X 0 (TRIS) 0.01 0.015 (S&J 0.94 (S,) 0.95 1 (PG)
8.853 (3) 8.842 (3) 8.847 (4) 6.059 (2) 6.059 (2) 6.052 (2)
[Ql
CLQ
b&
a(A)
7.804 (2) 7.810 (4) 7.813 (4)
V/Z&?
152.0 (1) 152.1 (2) 152.4 (2) 162.2 (1) 162.2 (I) 162.5 (1)
8.800 (3) 8.810 (4) 8.818 (5) 8.837 (3) 8.838 (3) 8.872 (3)
aIA1
8.70 -
6.66 -
6.60 TRIS
I
1
.2
A
‘B .6
I I I I x I .s
PO
Fig. 5. Evolution of the Bragg angles O(“) (a), and lattice parameter f.c.c. C, phase at 363 K.
lwlii
a@),
.7
.B
.9
PG
(b), vs concentration for the
Miscibility and molecular interactions Table 4. Cubic lattice parameters corresponding to the f.c.c. C, phase at 363 K x 0.77 (S,) 0.80 0.90 0.95
1 (PC+)
a(A)
Table 5. Lattice parameters and volume occupied by one molecule for the pure compounds and their alloys at 408 K
W(A)
8.814 (9) 8.820 (10) 8.847 (10) 8.860 (10) 8.876 (8)
177
X
171.2 (6) 171.5 (6) 173.1 (6) 173.9 (6) 174.8 (5)
Study at 363 K. The crystallographic investigation at 363 K has been performed in order to determine the solubility of TRIS in PG and the value obtained will be helpful in determining the phase diagram. Figure 5a and b shows the evolution of the Bragg angles of the (111) cubic reflection and the cubic lattice parameter, respectively, vs concentration. The evolution of the (111) cubic reflection allows us to determine the solubility boundary of TRIS in PG at 363 K to be SB(T_363Kj = 0.77. In Table 4 we give the values of the lattice parameters of the molecular alloys. From Fig. Sb we can observe that a cubic parameter (and thus the unit cell of molecular alloys) decreases when the concentration of PG diminishes. 4.1.4. Study at 408 K. Because of the fact that the pure compounds crystallize in the ODIC state in different space groups, the existence of a demixing region in the plastic phase becomes necessary. In Fig. 6a we depict the evolution of the (110) reflection corresponding to the b.c.c. cells in function of the concentration. From it we can establish the solubility boundary at 408 K to be SAo.=408Kj= 0.39 4.1.3.
0 (TRIS) 0.1 0.2 0.3 0.35 0.39 (S,) 0.52 (S,) 0.60 0.70 0.80 0.90 1 (EC)
Form El; ;$;
141 [C,l Gl t”cj E; Gl
a(A) 6.888 (8) 6.914 (8) 6.952 (8) 6.971 (8) 6.997 (8) 7.010 (8) 8.842 (10) 8.860 (11) 8.881 (11) 8.904 (10) 8.923 (11) 8.942 (10)
ww 163.4 (5) 165.3 (6) 168.0 (6) 169.4 (6) 171.3 (6) 172.3 (6) 172.8 (6) 173.9 (6) 175.1 (6) 176.5 (6) 177.6 (6) 178.8 (5)
molar fraction of PG. Figure 6b shows the lattice parameters of these cubic alloys. The same study is shown for the other phase [C,] present at 408 K in Fig. 7a and b. The values of the lattice parameters at 408 K for the pure compounds, their alloys and the limit solid solutions are in Table 5. In this case the solid solution limit corresponds to a PG concentration of 0.52, i.e. S,,,=,,, = 0.52. 4.2. Thermal analysis To obtain the characteristic temperatures from the experimental heat flux calorimeter signals we used the “shape factor methods” [36,37]. The determination of the crystalline solid-plastic and plastic-liquid equilibrium temperatures has been developed in a previous work [15]. The idea is to consider that the isothermal phenomena of melting and solid-solid transition are detected in an apparent temperature range due to the experimental device.
[__ T
8.96 -
7:
=A@ 1 I
TRIS
.2
4
-
2s
Ii--r
I
A
.a
II
PQ
Fig. 6. Evolution of the Bragg angles O(O), (a) and lattice parameter a@), (b), vs concentration for the b.c.c. C, phase at 408 K.
M. BARRIO et al.
178
8.55
3
Fig, 7. Evolution of the Bragg angles s(O), (a) and lattice parametera(&, (b), vs concentration for the f-cc. C, phase at 408 K.
In Fig. 8 we depict the characteristic thermograms corresponding to several samples. The two eutectoid invariants at 345.7 f 1.0 K and 384.7 + 1.0 K are clearly shown in this figure and, in addition, these
373
T(K)
temperature values (accurately determined) agree with those previously determined by the Guinier-Simon technique (with a higher margin of error).
4
Fig. 8. Character&tictl~ermogramsfor the pure cmnp~~ds and severa sampbs for the solid-s&d phase transitions.
Miscibility and molecular interactions
179
Table 6. Characteristic temperatures for the different phase transitions in the PG/TRIS samples x
T,, 00
0 (TRIS) 0.01 0.025 0.05 0.10 0.20 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.75 0.80 0.85 0.90 0.95
1 W)
345.0 f 1.5 345.6 + 1.0 346.0 + 1.O 346.5 + 1.0 346.8 + 1.0 345.9 + 1.5 346.4 _+1.O 345.3 + 1.0 347.3 * 1.3 345.9 + 1.0 345.6 f 1.2 344.0 + 1.5 344.8 + 1.2 345.1 k 1.3 344.7 + 1.4 (348.8 + 1.1) (357.5 * 1.0)
Tfi.iti I (W
r, (W (406.8 f (396.8 f 383.2 f 384.6 f 384.5 f 384.7 f 385.1 f 384.6 + 384.4 + 384.7 f 384.8 f 385.4 +
380.7 &-5.0 364.1 f 5.0 351.3 + 5.0 350.5 _+1.6 353.7 * 1.4 355.2 f 1.4
1.O) 3.2) 1.0
1.1 1.0 1.2 1.3 1.0 1.0 1.0 1.0 1.4
Tenis,, r WI 404.3 f 403.7 + 402.8 + 399.2 + 395.1 * 392.0 + 388.9 f 387.2 f
1.2 1.2 1.1 1.4 1.3 1.2 1.1 1.2
Ts WI 442.7 _+1.0 440.9 f 1.2 440.2 _+1.2 437.2 + 1.2 434.2 If: 1.3 431.6 f 1.5 431.7 f 1.3 431.6+ 1.2 431.5 f 1.2 432.5 & 1.5 434.0 f 1.3 438.3 + 1.2 443.9 * 1.3 445.7 f 1.2 449.8 & 1.7 455.4 f 1.3 460.3 f 1.2 463.2 f 1.0 471.7 f 1.0
T, 6) 442.7 f 441.7 f 440.2 f 437.7 f 435.4 + 434.9 f 434.2 + 433.2 f 436.7 k 439.5 f 444.5 f 449.3 f 454.0 * 456.8 + 460.2 + 464.3 * 467.2 f
1.2 1.1 1.2 1.4
1.3 1.2 1.3 1.2
1.1 1.1 1.4 1.2 1.2 1.5 1.3 1.3 1.1
T,,: Invariant eutectoid [0 + Q + C,]. The values noted by 0 are out of the invariant. Ttish ,: Change from [0 + Cd to [Cd for 0.70 Q X d 0.80 and to [Cd for 0.85 Q X C 0.95. T,: Invariant eutecoid [0 + C, + C,]. The values noted by 0 are out of the invariant. Tbish *: End of the transition [0 + C,] to [C,]. T,: Beginning of the melting process (solidus). T,: End of the melting process (liquidus).
In Table characteristic analysis.
6 we give all the experimental temperatures recorded from thermal
4.3. Phase diagram
narrow third two phase domain [C, + CJ between the plastic phases. In Table 8 we give the solubility domains at different temperatures determined by X-ray powder diffraction at constant temperature.
Taking into account the temperatures measured by thermal analysis and the X-ray diffraction patterns as a function of continuous heating and together with the solubility boundaries determined by X-ray diffraction at different temperatures, we propose the phase diagram drawn in Fig. 9 from room temperature to the liquid state. 5. DISCUSSION AND CONCLUSIONS
The phase diagram PG/TRIS highlights the repercussion of the dimorphism [38] of the two pure components in the syncrystallization problem [39]. Due to this factor four different crystalline forms are implicated, producing a phase diagram with a relative high degree of complexity. The determination of the phase diagram has been made possible by the use of the different techniques in a specific and complementary way as calorimetry and X-ray powder diffraction both at constant and as a function of the temperature. The main characteristics of this diagram are the existence of one eutectic and two eutectoid invariants, the characteristic temperatures and concentrations which are summed up in Table 7. On the other hand, we can note the existence of two wide two phase domains [0 + Q] and [0 + CL!,] and a
Fig. 9. Phase diagram of the binary system PG/TRIS. ( x ) Heat flux differential scanning calorimeter. (0) Guinier-Simon technique. (A) Solubility boundaries determined by X-ray powder diffraction at constant temperature.
M. BARRIOet al.
180
Table 7. Characteristic temperature and concentration values corresponding to the invariants present in the phase diagram
x Invariant Eutectoid T,, Eutectoid Fe2 Eutectic T,,
M
E
0.02 0.02 0.35
0.82 0.45 0.38
Table 8. Solubility boundaries at different temperatures determined by X-ray diffraction at constant temperature T(K)
Form
Solid solution domain
0 C* C, C,
o
293 363 408
It is obvious that the miscibility in the plastic phase may be only partial due to the different space groups of the unit cells of the pure compounds; then for a given temperature there are three domains: two domains of miscibility where solid solutions (i.e. molecular alloys) PG, TRIS, _ x are formed and one demixing domain where two limit solid solutions SA and SBcoexist. From a crystallographic point of view, this fact gives rise to a continuous variation of the crystalline parameters from X = 0 to X,, and from Xsr, to X = 1 (corresponding to the b.c.c. and f.c.c. alloys, respectively). Moreover, and from a thermodynamic point of view, two curves of the Gibbs energy (one for each phase) are needed to account for the stability of all the molecular alloys [40,41]. In closing, TRIS and PG are clearly not isomorphic in the plastic phase. Our studies of the miscibility in the plastic phases in binary systems formed by two “plastic molecules” allowed us to analyse the competitivity between the incidence of their differences in shape and size and the incidence of the differences in
N 0.92 0.68 0.425
Temperature (K) 345.7 + 1.0 384.7 + 1.0 431.6 + 1.2
their chemical nature. These studies allow also to analyse the role of the molecular interactions in the mixed crystals structures. In Fig. 10 we draw the values of the volume occupied by a molecule (V/Z) in the molecular alloys in the ODIC state (at 408 K). The evolution of the V/Z vs concentration can be interpreted taking into account the difference in the intermolecular interactions in the C, and C, plastic phases and by geometrical effects. The increasing of the lattice parameter of the molecular alloys observed for the C, plastic phase can be associated to two facts. On the one hand, the volume occupied by a PG molecule is larger than a TRIS molecule and, on the other, the PG molecules (according to [35]) do not have the ability to form hydrogen bonds as occurs in the plastic phase of TRIS. For the C, molecular alloys the behaviour of the evolution of V/Z can be interpreted in a similar way. The introduction of TRIS molecules that occupy a smaller volume than PG molecules would produce a diminution of the unit cell. In addition, the TRIS molecule keeps hydrogen bonds in its plastic phase. Then, the possibility to keep these intermolecular interactions has to be taken into account when these types of molecules are introduced in another unit cell. At any rate, it should be underlined that the investigation of the molecular packing in disordered solid solutions is, strictly speaking, impossible without studying the short-range order; therefore, the geometrical model of molecular alloys, built only on the basis of the data on size and shape of molecules and on unit cell dimensions, should be used with extreme caution. Thus, studies of the different molecular motions on molecular alloys in plastic phases would be of interest.
Acknowledgements-This work was performed within the framework of a “Reseau Europeen de Laboratoires sur les Alliages Molbulaires” (REALM). The authors are grateful to every REALM member who has given help in the development of this study whenever needed. This project was supported by a CICYT grant (reference PB89-0281CO3-02). REFERENCES
Fig. 10. Volume occupied by a molecule (V/Z) in the molecular alloys in the ODIC state at 408 K.
1. Timmermans J., J. Bull. Sot. Chem. Belg. e 17 (1935). 2. Timmermans J.,. J. Chim. Phys. 35, 331 (1938).
Miscibility and molecular interactions 3. Parsonage N. K. and Staveley L. A. K., Dborder in Crystals (The International Series of Monographs on Chemistry). Clarendon Press, Oxford (1978). 4. Dunning W. J., J. Phys. Chem. Solids 18, 21 (1961). 5. Staveley L. A. K., Ann. Rev. Phys. Chem. 13,351 (1962). 6. Gray G. W. and Winsor P. A., Liquid Crystals and Plastic Crystals. Ellis Horwood, Chichester (1974). 7. The IUPAC names are (2-hydroxymethyl-2 methyl1,3propanediol) for PG and (2-amino-hydroxymethyl1,3 propanediol) for TRIS. 8. Van der Graaf F., Research in Calibration and Application Errors of Heat Flux Sensors, p. 79. American Society for Testing Materials (1976). 9. Barrio M.,-Font J., Lopez D. O., Muntasell J., Tamarit J. LI., Chanh N. B. and Haget Y., J. Chitn. Phys. 87, 1835 (1990). 10. AFMAIL, computer program, Bordeaux. 11. Barrio M., Font J., Lopez D. O., Muntasell J., Tamarit J. LI., Chanh N. B. and Haget Y., J. Phys. Chem. Solids 52, 666 (1991). 12. Elierman D., Lippman R. and Rudman R., Acta Cryst. B39, 263 (1983). 13. Chandra D., Barret C. S. and Benson D. K., Ado. X-Ray 29, 305 (1986). 14. Doshi N., Furman M. and Rudman R., Acta Cryst. B39, 143 (1973). 15. Barrio M., Font J., Muntasell J., Tamarit J. LI., Chanh N. B. and Haaet Y.. J. C/rim. Phvs. 87. 255 (1990). 16. Sake Gowda I?. S. and Rudman R., J. ?hem. k’hys.‘77, 4671 (1982). 17. Armoureaux J. P., Sauvajol J. L. and Bee M., Acta Cryst. A37, 97 (1981). 18. Sake Gowda D. S. and Rudman R., J. Chem. Phys. 77, 4666 (1982). 19. Elierman D. and Rudman R., J. Chem. Phys. 72, 5656 (1980). 20. Sake Gowda D. S., Federlin N. and Rudman R., J. Chem. Phys. 77, 4659 (1982). 21. Rose H. A. and Van Camp A., Anals. Chem. 27, 1356 (1955). 22. Rudman R., Elierman D. and La Placa J., Science 200, 531 (1978).
PCS 5412-O
181
23. Elierman D. and Rudman R., Acta Cryst. B35, 2768 (1979). 24. Rudman R., Solid State Comman. 29, 785 (1979). 25. Kendi E., Z. Krist. 160, 139 (1982). 26. Murril E. and Breed E., Thermochim. Acta 1, 239 (1970). 27. Arvidson K. and Westrum E. F. Jr., J. Chem Thermodyn. 4, 443 (1972). 28. Laugt M., Pelous’E., Teisseire M. et Guion J., Calorim. Anal. Therm. 16. 470 (1985). 29. Dolling G., Powell B. ‘M. and Sears V. F., Mol. Phys. 37, 1859 (1979). 30. Drifford M., Rousson R. and Weulersse J. M., Can. J. Phys. 56, 1353 (1978). 31. Newton M. G., Pantaleo N. S., Galobardes M. and Pinnick H. W., J. appl. Cryst. 11, 194 (1978). 32. Wasylishem R. E., Barron P. F. and Doddrell, Aust. J. Chem. 32, 905 (1979). 33. Schroetter S. and Bougeard D., Dynam. Mol. Cryst. 46, 213 (1987). 34. Benson D. K., Burrows R. W. and Webb J. D., Solar Energy Mat. 13, 133 (1986). 35. Kitaigorodsky A. I., Molecular Crystals and Molecules. Academic Press, New York (1973). 36. Courchinoux R., Chanh N. B., Haget Y., Tauler E. and Cuevas-Diarte M. A., Thermochim. Acta lu), 45 (1988). 37. Courchinoux R., Chanh N. B., Haget Y., Clavet T., Estop E. and Cuevas-Diarte M. A., J. Chim. Phys. 86, 561 (1989). 38. Mondieig D., Haget Y., Muntasell J., Labrador M., Estop E., Calvet T. and Cuevas-Diarte M. A., Meeting on Disorder in Molecular Crystals, P-13, Garchy, France, 5-7 July (1989). 39. Haget Y., Bonpunt L., Cuevas-Diarte M. A. and Oonk H. A. J., Meeting on Disorder in Molecular Crystals, P-10, Garchy, France, 5-7 July (1989). 40. Oonk H. A. J., Van der Linde P. R., Haget Y., Bonpunt L., Chanh N. B. and Cuevas-Diarte M. A., J. Chim. Phys. 88, 329 (1991). 41. Haget Y., Oonk H. A. J. and Cuevas-Diarte M. A., 16”“” Journies d’Etude des Equilibres entre Phases, P-35, Marseille, France, 21-22 March (1990).
1993
0022-3697/93 S6.00 + 0.00 0 1993 Pergamon Press Ltd
MISCIBILITY AND MOLECULAR INTERACTIONS IN PLASTIC PHASES: BINARY SYSTEM PENTAGLYCERIN/ TRIS(HYDROXYMETHYL)AMINOMETHANE M. BARRIO,t J. FONT,? D. 0. L&SZ,t J. MUNTASELL,t J. LL. TAMARIT,t P. NEGRIER,$. N. B. CHANHS and Y. HAGET$ TDepartament de Fisica i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Diagonal 647,08028 Barcelona, Spain and fLaboratoire de Cristallographie et de Physique Cristalline, URA 144 au CNRS, Universitt Bordeaux I, 351 tours de la Liberation, 33405 Talence Cedex, France (Received 30 January 1992; accepted 27 September
1992)
Abstract-The phase diagram of the plastic crystals pentaglycerin (PG) and tris(hydroxymethyl)aminomethane has been established by means of thermal analysis and X-ray powder diffraction from room temperature to the liquid state. The binary system is characterized by two eutectoid invariants corresponding to solid to plastic phase transitions and by one eutectic invariant corresponding to the melting process. The phase diagram exhibits a demixing region in the plastic state as a consequence of the difference between the disordered high-temperature forms of the pure compounds. The determination of the solubility boundaries in the plastic state shows a narrow two phase domain (about 0.13 in molar fraction). The evolution of the volume occupied by a molecule in the molecular alloys in the plastic phases can be interpreted taking into account the different intermolecular interactions in these phases and by geometrical effects. Keyworrls: Plastic crystal, phase diagram, molecular alloy, solid solution, plastic phase miscibility.
1. INTRODUCTION of the highly orientational disordered phases stable just below the melting point (form I) are generally referred to as plastic or ODIC (orientationally disordered crystalline phase) crystals. Plastic were first recognized by crystals Timmermans [ 1,2] as characteristically containing approximately spherical molecules and showing a low entropy of fusion (AS < 2SR, where R is the gas constant). The high rate of molecular reorientation and the large amplitudes of thermal libration found in the ODIC phase result in a high symmetry crystal in phase I (usually f.c.c. or b.c.c.) [3]. In addition, the symmetry elements of many plastic crystals are incompatible with those of their constituent molecules if this is regarded as stationary [4,5]. Such apparent discrepancies between lattice and molecular symmetries provide one of the reasons to assume that the molecules, even if not literally rotating, are dynamically disordered in orientation. Then, orientationally disordered crystals have the three-dimensional periodicity characteristic of the crystal and the isotropy properties characteristic of the liquid [6]. This paper reports the study of the binary phase diagram between two plastic crystals, tris(hydroxymethyl)aminomethane (TRIS) and pentaglycerin Crystals
(PG) [‘i’l(Fig. 1) from room temperature to 473 K (liquid state for both compounds). This study was undertaken, within a more general framework about the syncrystallization problem, to gain information about the molecular alloys formed in solid crystalline and plastic crystal phases and the influence of intermolecular hydrogen bonding in their formation. 2. EXPERIMENTAL
2.1. Thermal analysis The thermal measurements have been carried out by means of a heat flux differential scanning calorimeter. The differential signal was obtained by means of two thermoelectric modules of great sensitivity (TN0 SI SP [8]) connected in opposition. The sensitivity is about 140mV W-’ at room temperature. The temperature was measured with a Pt-100 R calibrated probe. The data acquisition and treatment was described elsewhere [9]. The scanning rate used was about 1 k min-i. The samples (mass about 10 mg) were hermetically sealed in order to avoid sublimation. 2.2. D@raction
at constant temperature
X-ray measurements were performed by means of a powder Siemens D-500 vertical diffractometer with 171
M. BARRIOet al.
172
a, I
WlOH
-C-c&OH I
T
C&OH -C-
C&OH
C&OH
d&OH
(a)
(W
Fig. 1. Molecules of PG (a) and TRIS (b).
an Anton Paar temperature camera, whose characteristics have been described previously [9]. The goniometer speed used was 2/5”(2fI) min-‘. CsCl was used as internal standard. The samples were re-covered by a mylar sheet to avoid possible sublimation of the powder during the measurement. Lattice parameters were obtained by a leastsquares refinement method [lo]. 2.3. Dzjiiaction as a function of continuous heating Powder diffraction analysis as a function of the continuous evolution of the temperature was performed with a Guinier-Simon camera. The experimental conditions were the same as in previous works [ll]. 3. RESULTS 3.1. Pure compounds Both pure compounds were purchased from Aldrich Chemical Company with purities of 99/9 + % and 99% for TRIS and PG, respectively, and additional purification was performed by a drying process at 333 K. 3.1.1. Crystallographicresults (a) Pentaglycerin The crystal structure at room temperature of PG was determined as body centered tetragonal(14) with Z = 2 [12, 131 (hereinafter referred to as Q phase). Between about 357K and the melting point (about 470 K) PG forms a plastic crystal phase (hereinafter referred to as C,) the structure of which is face centered cubic (Z = 4) [14]. Our study by X-ray powder diffraction at room temperature gave lattice parameters: a = 6.052 (2) A and c = 8.872 (3) A. These values have been already published by us [ 151 and are near those appearing in the bibliography [12, 141.The PG structure is characterized by the presence of strong intermolecular hydroxyl hydrogen bonds in the layers parallel to the (001) plane and weak interlayer bonds due to van der Waals forces [12]. The cubic lattice parameter for the plastic phase has been measured in this work at two temperatures,
363 K and 408 K, giving the values 8.876 (8) A and 8.942 (10) A, respectively. These results match the previously reported values in the literature [14]. We want to emphasize that the plastic X-ray diffraction patterns show only three visible lines (( 11l), (200) and (222)) with considerable background scattering; this fact and the very rapid fall-off in intensity with increasing reflection angle are due to the highly structure disorder. This usual fact in structural studies of plastic crystals justifies the high margin of error given for the cell parameters [14, 16-201. (b) Tris(hydroxymethyl)aminomethane The unit cell and space group of TRIS at room temperature was reported earlier by Rose and Van Camp [21] with an incorrect space group. The crystal structure has been fully determined by Elierman and Rudman [19], who give a Pn2,a space group with Z = 4 for the solid phase (hereinafter referred as 0). The reported lattice parameters for this orthorhombic phase are given in Table 1 together with our refinement by X-ray powder diffraction. The structure of TRIS in the low temperature phase has been described as layers of molecules approximately perpendicular to the c-axis (83”). Within each layer the three OH groups are connected by strong hydrogen bonds whereas one of the amine hydrogen atoms is weakly hydrogen-bonded to the atom of a molecule in an adjacent layer [19,22]. At about 407 K TRIS transforms to a plastic phase. This phase (hereinafter called C,) was found to be body centered cubic (Im3m) with Z = 2 in a detailed single crystal study [19]. The formation of a b.c.c. lattice in the ODIC phase, rather than a f.c.c. as was found in the other compounds of this series [ 13, 14,16, 18,20,23], has been interpreted in terms of the ellipsoidal shape of this molecule. This assumption is reinforced by the rule proposed by Rudman for pseudo-spherical tetrahedral molecules, which establishes that the crystal structures of both ordered and orientationally-disordered phases are controlled by equal-sphere closest-packing principles [24]. In the powder diffraction pattern of the high temperature phase of TRIS only one (by X-ray diffraction at constant temperature) or two (by the Guinier-Simon technique) lines appear. In the last technique the second reflection is not detected due to the presence of the mylar sheet peak. In [14] the authors pointed out the existence of only one reflection and due to the lack of information about the experimental device and conditions used in that work, any explanation can be induced. The literature reported data and our results are summarized in Table 1.
Miscibility and molecular interactions
173
Table 1. Lattice parameters for phases 0 and C, of TRIS a(A)
Parameters b(A)
c(A)
T(K)
Reference
8.844 (1) 8.807 (6)
7.794 (1) 8.872 (7)
8.795 (1) 7.709 (7)
295 Room temp.
[191
Phase 0 G
8.853(3) 7.804(2) 8.800(3)
293
6.852 (6) 6.83 6.888 (8)
408 408
t251t This work v91 1241 This work
tThe lattice parameters in [25] are given according to the Pna2, space group.
3.1.2.
Thermodynamic results
plane), while TRIS (R = -NH,) forms a layered structure with weak hydrogen bonds between layers. In the ODIC phase, those compounds with the exception of R = -NH,(TRIS), crystallize in a f.c.c. lattice with four molecules per unit cell. For all these compounds there is one molecule per lattice point, and thus, by comparing the site symmetry and the intrinsic molecular symmetry, the molecules must be highly disordered with pseudo-spherical symmetry [4, 51. TRIS forms a b.c.c. unit cell with Z = 2. There is a significant number of ODIC materials that form b.c.c. cells [3,29-311. The common feature of the molecules forming a b.c.c. lattice is that there are intermolecular interactions between these molecules due to a distortion from sphericity or as a result of bonding interaction (as hydrogen bonding which occurs in TRIS producing an ellipsoidal rather than a spherical molecule). Thus, the plastic state of TRIS differs from the other pseudospherical compounds of the series because of the more extensive remaining hydrogen bonding. This fact is coherent with the rotational activation energy in the plastic phase of 5 1.6 kJ mol-’ [32], while it is of the order of 4-9 kJ mol-’ in plastic phases without important remaining hydrogen bonding. A vibrational spectra study of TRIS has confirmed that the anisotropy of the hydrogen bonds in the low temperature phase (strong in the layers and weak between layers) became isotropic (weak in and between layers) in the ODIC state [33]. The fact that the hydrogen bonding plays a dominant role in the ODIC state is unusual because in most of the plastic phases the molecules rotate quite easily while their centers of mass remain fixed in the lattice. On the contrary for PG and according to [34], all the hydrogen bonds are broken at the transition temperature,
(a) Pentaglycerin The temperature and enthalpy variation of the solid to plastic phase transition are, respectively, 357.5 +_ 1.0 K and 21.3 + 1.0 kJ mol-’ and, for the melting process 471.7 f 1.0 K and 5.1 &-0.3 kJ mol-’ for the corresponding parameters. Some significant differences can be observed between these values and those previously reported by us [9, 151. These differences may be attributed to the purity of the original pure compound. (b) Tris(hydroxymethyl)aminomethane The TRIS has been subjected to many thermodynamic studies [19,26-281. The characteristic values of solid-solid phase transition obtained from the literature are shown in Table 2 together with the respective parameters of the melting process. Our results are 406.8 f 1.0 K and 34.0 f 1.7 kJ mol-’ for the temperature and enthalpy variation of the transition, and 442.7 +_ 1.0 K and 3.7 +_0.2 kJ mol-’ for the liquefaction process. In Table 2 we can compare these values with those of the bibliography. 3.1.3. Comparison of the structure of the pure compounds and the role of the hydrogen bonds. When comparing the structure of the poly(hydroxymethyl) compounds, TRIS becomes of special interest. Most of these compounds are tris(hydroxymethyl) with the general formula R-C(CH,OH),, where R is -CH,OH, -COOH, -C,H,, -CH,, -NO,, -NH,. The R = -CHX compound (PG) is tetragonal with only van der Waals bonding between strongly hydrogen-bonded layers (parallel to the 001
Table 2. Temperatures and enthalpy variations for the phase 0 to phase C, and the phase C, to liquid transitions of TRIS TO-.,,
AH,.+,,
6)
(kJ mol-‘)
408 404407 407.3 406.7 406.8
34.2 32.93 33.4-34.0 34.0 + 1.7
TCl-L (K) 44546 439-442 446.0 442.7 f 1.0
AH,,-, (kJ mol-‘)
Reference
3.0 2.97 3.7 & 0.2
;:A; This work
M. BARRIOet
174
permitting molecular vibration and rotation in the ODIC phase. The different bond scheme between PG and TRIS produces some important geometric considerations. The column occupied by a molecule in the unit cell (V/Z) in the ordered low temperature phases is 152.0 A’ and 162.5 A’ for TRIS and PG, respectively (at room temperature); due to the fact that the two isolated molecules have a similar volume (the volume increments of the atomic combinations -NH, and - CH, used for calculating the packing coefficient are 19.7 A’ and 23.5 A’, respectively [35]) it is obvious that the hydrogen bonds pull the molecules closer in TRIS. If one compares the same relationship in the plastic phase (163.4A’ and 178.8 A’ for TRIS and PG, respectively at 408 K) two consequences can be obtained. (1) These two values are always greater than their respective values in the ordered phase and then, the bonds in the ODIC phase become weaker. (2) The values in the plastic phase keep the same order than in the ordered phase and, thus in spite of the similarity in the molecule volume, the plastic phase of TRIS must have stronger bonds than the respective plastic phase of PG, in agreement with the infrared spectroscopy and NMR measurements previously mentioned. 4. MOLECULAR
ALLOYS
The samples have been prepared from the melt of the two pure compounds in the desired proportion and slow cooling from the liquid phase to room temperature. 4.1. Crystallographic
study
4.1.1. Difraction as a function of continuous heating. The Guinier-Simon X-ray camera allows us to follow on film the continuous evolution of the diffraction pattern of the samples vs temperature, and then to know the phases coexisting in equilibrium at each temperature. In Fig. 2b we give the Guinier-Simon pattern corresponding to the sample X = 0.3 molar fraction of PG. The successive domains may be described as: l l
l l
l l l
existence of a disappearance about 350 K; existence of a disappearance about 387 K; existence of a disappearance existence of a
two phase domain [0 + Q]; of Q and appearance of Cr at two phase domain [0 + Cd; of C2 and appearance of C, at two phase domain [0 + C,]; of 0 at 394 K; one phase domain C,;
l l
al.
beginning of melting at 430 K; and end of melting at about 435 K.
Figure 2c is relative to the sample X = 0.4 and, as temperature rises, one meets successively: existence of a two phase domain [0 + Q]; disappearance of Q and appearance of C, at about 343 K; existence of a two phase domain [0 + Cd; disappearance of C, and 0 phases and appearance of the C, phase at 381 K; existence of one phase domain C,; appearance of Cr phase at 413 K; existence of a two phase domain [C, + Cj; disappearance of C, and appearance of the liquid [L] phase at the same temperature of 427 K; existence of a two phase domain [L + C,]; and end of the melting at about 433 K. These experimental results support the existence of three eutectic phenomena, whose temperatures will be determined more accurately by thermal analysis (next section). The three eutectic invariants correspond to equilibria: the three phase P+Q+Gl, [0 + C, + CJ and, finally [C, + C, + L]. The diffraction pattern of the sample X = 0.5 has been also recorded by Guinier-Simon technique (see Fig. 2d). At about 352 K we detected the change from [0 + Q] to [0 + C,] and subsequently at 387 K the change from [0 + C,] to [C, + CJ. At 408 K the C, phase disappears and the C, phase remains until the melting process, which takes place between 434 and 440 K. The Guinier-Simon pattern obtained for the sample X = 0.8 (see Fig. 2e) shows a two phase domain [0 + Q] which changes to another [0 + C,] at about 344 K and at 368 K the 0 phase disappears and at any moment one cannot observe the C, phase. At about 447 K the melting process starts and it ends at about 455 K. To determine the solubility boundaries of the different two phase domains we have performed isothermal X-ray diffraction at several temperatures; the results are shown below. 4.1.2. Study at 293 K. To determine the limit of the solid solutions at 293 K accurately, we have analysed the evolution of the reflections of each phase in function of the concentration. In Fig. 3 we depict the evolution of the (111) and (022) reflections corresponding to the orthorhombic phase (0) vs concentration. From the analysis of the evolution of the Bragg angles we can conclude that the solubility boundary of TRIS in PG is fraction of PG), i.e. the &(r=293K) = 0.015 (molar molecular alloy TRIS~,985PG,,,,,.
293 K -344 ~368
Lo+a1
KK-
,=
[otc,l [c&l
-447K +455 K =
4;!fLl [LI
(e) X=0.8
293 K -
101 -357
K -
K,l
-472
K-
,.(f)
X=l
CL1
(PG)
Fig. 2. Guinier-Simon pattern corresponding to the pure compounds TRIS (a) and PG (r) and to the samples X = 0.3 (b), X = 0.4 (c), X = 0.5 (d) and X = 0.8 (e). The reflections that do not disappear in the pattern of TRIS correspond to SiO, used to seal the Lindeman capillary [I 11.
175
M. BARRIOet
176
al. 10.40’
9.13 r 0
(111)
.6
PG
Fig. 3. Variation of the Bragg angles (0(O)) with the concentration for the (111) and (022) reflections corresponding to the orthorhombic cell at 293 K.
Fig. 4. Variation of the Bragg angles (O(O)) with the concentration for the (110) and (112) reflections corresponding to the tetragonal cell at 293 K.
solubility boundary SW,= 293Kj, that in this case corresponds to the solid solution TRIS,,M PG,,,94. The lattice parameter values of the solid solutions are given in Table 3.
Figure 4 shows the evolution of the Bragg angle of the (110) and (112) reflections corresponding to the tetragonal lattice as a function of the molar concentration of PG. In a similar way we can establish the
Table 3. Lattice parameters of the unit cells for the pure compounds and their alloys at 293 K Parameters Form
X 0 (TRIS) 0.01 0.015 (S&J 0.94 (S,) 0.95 1 (PG)
8.853 (3) 8.842 (3) 8.847 (4) 6.059 (2) 6.059 (2) 6.052 (2)
[Ql
CLQ
b&
a(A)
7.804 (2) 7.810 (4) 7.813 (4)
V/Z&?
152.0 (1) 152.1 (2) 152.4 (2) 162.2 (1) 162.2 (I) 162.5 (1)
8.800 (3) 8.810 (4) 8.818 (5) 8.837 (3) 8.838 (3) 8.872 (3)
aIA1
8.70 -
6.66 -
6.60 TRIS
I
1
.2
A
‘B .6
I I I I x I .s
PO
Fig. 5. Evolution of the Bragg angles O(“) (a), and lattice parameter f.c.c. C, phase at 363 K.
lwlii
a@),
.7
.B
.9
PG
(b), vs concentration for the
Miscibility and molecular interactions Table 4. Cubic lattice parameters corresponding to the f.c.c. C, phase at 363 K x 0.77 (S,) 0.80 0.90 0.95
1 (PC+)
a(A)
Table 5. Lattice parameters and volume occupied by one molecule for the pure compounds and their alloys at 408 K
W(A)
8.814 (9) 8.820 (10) 8.847 (10) 8.860 (10) 8.876 (8)
177
X
171.2 (6) 171.5 (6) 173.1 (6) 173.9 (6) 174.8 (5)
Study at 363 K. The crystallographic investigation at 363 K has been performed in order to determine the solubility of TRIS in PG and the value obtained will be helpful in determining the phase diagram. Figure 5a and b shows the evolution of the Bragg angles of the (111) cubic reflection and the cubic lattice parameter, respectively, vs concentration. The evolution of the (111) cubic reflection allows us to determine the solubility boundary of TRIS in PG at 363 K to be SB(T_363Kj = 0.77. In Table 4 we give the values of the lattice parameters of the molecular alloys. From Fig. Sb we can observe that a cubic parameter (and thus the unit cell of molecular alloys) decreases when the concentration of PG diminishes. 4.1.4. Study at 408 K. Because of the fact that the pure compounds crystallize in the ODIC state in different space groups, the existence of a demixing region in the plastic phase becomes necessary. In Fig. 6a we depict the evolution of the (110) reflection corresponding to the b.c.c. cells in function of the concentration. From it we can establish the solubility boundary at 408 K to be SAo.=408Kj= 0.39 4.1.3.
0 (TRIS) 0.1 0.2 0.3 0.35 0.39 (S,) 0.52 (S,) 0.60 0.70 0.80 0.90 1 (EC)
Form El; ;$;
141 [C,l Gl t”cj E; Gl
a(A) 6.888 (8) 6.914 (8) 6.952 (8) 6.971 (8) 6.997 (8) 7.010 (8) 8.842 (10) 8.860 (11) 8.881 (11) 8.904 (10) 8.923 (11) 8.942 (10)
ww 163.4 (5) 165.3 (6) 168.0 (6) 169.4 (6) 171.3 (6) 172.3 (6) 172.8 (6) 173.9 (6) 175.1 (6) 176.5 (6) 177.6 (6) 178.8 (5)
molar fraction of PG. Figure 6b shows the lattice parameters of these cubic alloys. The same study is shown for the other phase [C,] present at 408 K in Fig. 7a and b. The values of the lattice parameters at 408 K for the pure compounds, their alloys and the limit solid solutions are in Table 5. In this case the solid solution limit corresponds to a PG concentration of 0.52, i.e. S,,,=,,, = 0.52. 4.2. Thermal analysis To obtain the characteristic temperatures from the experimental heat flux calorimeter signals we used the “shape factor methods” [36,37]. The determination of the crystalline solid-plastic and plastic-liquid equilibrium temperatures has been developed in a previous work [15]. The idea is to consider that the isothermal phenomena of melting and solid-solid transition are detected in an apparent temperature range due to the experimental device.
[__ T
8.96 -
7:
=A@ 1 I
TRIS
.2
4
-
2s
Ii--r
I
A
.a
II
PQ
Fig. 6. Evolution of the Bragg angles O(O), (a) and lattice parameter a@), (b), vs concentration for the b.c.c. C, phase at 408 K.
M. BARRIO et al.
178
8.55
3
Fig, 7. Evolution of the Bragg angles s(O), (a) and lattice parametera(&, (b), vs concentration for the f-cc. C, phase at 408 K.
In Fig. 8 we depict the characteristic thermograms corresponding to several samples. The two eutectoid invariants at 345.7 f 1.0 K and 384.7 + 1.0 K are clearly shown in this figure and, in addition, these
373
T(K)
temperature values (accurately determined) agree with those previously determined by the Guinier-Simon technique (with a higher margin of error).
4
Fig. 8. Character&tictl~ermogramsfor the pure cmnp~~ds and severa sampbs for the solid-s&d phase transitions.
Miscibility and molecular interactions
179
Table 6. Characteristic temperatures for the different phase transitions in the PG/TRIS samples x
T,, 00
0 (TRIS) 0.01 0.025 0.05 0.10 0.20 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.75 0.80 0.85 0.90 0.95
1 W)
345.0 f 1.5 345.6 + 1.0 346.0 + 1.O 346.5 + 1.0 346.8 + 1.0 345.9 + 1.5 346.4 _+1.O 345.3 + 1.0 347.3 * 1.3 345.9 + 1.0 345.6 f 1.2 344.0 + 1.5 344.8 + 1.2 345.1 k 1.3 344.7 + 1.4 (348.8 + 1.1) (357.5 * 1.0)
Tfi.iti I (W
r, (W (406.8 f (396.8 f 383.2 f 384.6 f 384.5 f 384.7 f 385.1 f 384.6 + 384.4 + 384.7 f 384.8 f 385.4 +
380.7 &-5.0 364.1 f 5.0 351.3 + 5.0 350.5 _+1.6 353.7 * 1.4 355.2 f 1.4
1.O) 3.2) 1.0
1.1 1.0 1.2 1.3 1.0 1.0 1.0 1.0 1.4
Tenis,, r WI 404.3 f 403.7 + 402.8 + 399.2 + 395.1 * 392.0 + 388.9 f 387.2 f
1.2 1.2 1.1 1.4 1.3 1.2 1.1 1.2
Ts WI 442.7 _+1.0 440.9 f 1.2 440.2 _+1.2 437.2 + 1.2 434.2 If: 1.3 431.6 f 1.5 431.7 f 1.3 431.6+ 1.2 431.5 f 1.2 432.5 & 1.5 434.0 f 1.3 438.3 + 1.2 443.9 * 1.3 445.7 f 1.2 449.8 & 1.7 455.4 f 1.3 460.3 f 1.2 463.2 f 1.0 471.7 f 1.0
T, 6) 442.7 f 441.7 f 440.2 f 437.7 f 435.4 + 434.9 f 434.2 + 433.2 f 436.7 k 439.5 f 444.5 f 449.3 f 454.0 * 456.8 + 460.2 + 464.3 * 467.2 f
1.2 1.1 1.2 1.4
1.3 1.2 1.3 1.2
1.1 1.1 1.4 1.2 1.2 1.5 1.3 1.3 1.1
T,,: Invariant eutectoid [0 + Q + C,]. The values noted by 0 are out of the invariant. Ttish ,: Change from [0 + Cd to [Cd for 0.70 Q X d 0.80 and to [Cd for 0.85 Q X C 0.95. T,: Invariant eutecoid [0 + C, + C,]. The values noted by 0 are out of the invariant. Tbish *: End of the transition [0 + C,] to [C,]. T,: Beginning of the melting process (solidus). T,: End of the melting process (liquidus).
In Table characteristic analysis.
6 we give all the experimental temperatures recorded from thermal
4.3. Phase diagram
narrow third two phase domain [C, + CJ between the plastic phases. In Table 8 we give the solubility domains at different temperatures determined by X-ray powder diffraction at constant temperature.
Taking into account the temperatures measured by thermal analysis and the X-ray diffraction patterns as a function of continuous heating and together with the solubility boundaries determined by X-ray diffraction at different temperatures, we propose the phase diagram drawn in Fig. 9 from room temperature to the liquid state. 5. DISCUSSION AND CONCLUSIONS
The phase diagram PG/TRIS highlights the repercussion of the dimorphism [38] of the two pure components in the syncrystallization problem [39]. Due to this factor four different crystalline forms are implicated, producing a phase diagram with a relative high degree of complexity. The determination of the phase diagram has been made possible by the use of the different techniques in a specific and complementary way as calorimetry and X-ray powder diffraction both at constant and as a function of the temperature. The main characteristics of this diagram are the existence of one eutectic and two eutectoid invariants, the characteristic temperatures and concentrations which are summed up in Table 7. On the other hand, we can note the existence of two wide two phase domains [0 + Q] and [0 + CL!,] and a
Fig. 9. Phase diagram of the binary system PG/TRIS. ( x ) Heat flux differential scanning calorimeter. (0) Guinier-Simon technique. (A) Solubility boundaries determined by X-ray powder diffraction at constant temperature.
M. BARRIOet al.
180
Table 7. Characteristic temperature and concentration values corresponding to the invariants present in the phase diagram
x Invariant Eutectoid T,, Eutectoid Fe2 Eutectic T,,
M
E
0.02 0.02 0.35
0.82 0.45 0.38
Table 8. Solubility boundaries at different temperatures determined by X-ray diffraction at constant temperature T(K)
Form
Solid solution domain
0 C* C, C,
o
293 363 408
It is obvious that the miscibility in the plastic phase may be only partial due to the different space groups of the unit cells of the pure compounds; then for a given temperature there are three domains: two domains of miscibility where solid solutions (i.e. molecular alloys) PG, TRIS, _ x are formed and one demixing domain where two limit solid solutions SA and SBcoexist. From a crystallographic point of view, this fact gives rise to a continuous variation of the crystalline parameters from X = 0 to X,, and from Xsr, to X = 1 (corresponding to the b.c.c. and f.c.c. alloys, respectively). Moreover, and from a thermodynamic point of view, two curves of the Gibbs energy (one for each phase) are needed to account for the stability of all the molecular alloys [40,41]. In closing, TRIS and PG are clearly not isomorphic in the plastic phase. Our studies of the miscibility in the plastic phases in binary systems formed by two “plastic molecules” allowed us to analyse the competitivity between the incidence of their differences in shape and size and the incidence of the differences in
N 0.92 0.68 0.425
Temperature (K) 345.7 + 1.0 384.7 + 1.0 431.6 + 1.2
their chemical nature. These studies allow also to analyse the role of the molecular interactions in the mixed crystals structures. In Fig. 10 we draw the values of the volume occupied by a molecule (V/Z) in the molecular alloys in the ODIC state (at 408 K). The evolution of the V/Z vs concentration can be interpreted taking into account the difference in the intermolecular interactions in the C, and C, plastic phases and by geometrical effects. The increasing of the lattice parameter of the molecular alloys observed for the C, plastic phase can be associated to two facts. On the one hand, the volume occupied by a PG molecule is larger than a TRIS molecule and, on the other, the PG molecules (according to [35]) do not have the ability to form hydrogen bonds as occurs in the plastic phase of TRIS. For the C, molecular alloys the behaviour of the evolution of V/Z can be interpreted in a similar way. The introduction of TRIS molecules that occupy a smaller volume than PG molecules would produce a diminution of the unit cell. In addition, the TRIS molecule keeps hydrogen bonds in its plastic phase. Then, the possibility to keep these intermolecular interactions has to be taken into account when these types of molecules are introduced in another unit cell. At any rate, it should be underlined that the investigation of the molecular packing in disordered solid solutions is, strictly speaking, impossible without studying the short-range order; therefore, the geometrical model of molecular alloys, built only on the basis of the data on size and shape of molecules and on unit cell dimensions, should be used with extreme caution. Thus, studies of the different molecular motions on molecular alloys in plastic phases would be of interest.
Acknowledgements-This work was performed within the framework of a “Reseau Europeen de Laboratoires sur les Alliages Molbulaires” (REALM). The authors are grateful to every REALM member who has given help in the development of this study whenever needed. This project was supported by a CICYT grant (reference PB89-0281CO3-02). REFERENCES
Fig. 10. Volume occupied by a molecule (V/Z) in the molecular alloys in the ODIC state at 408 K.
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