J. Phys. Chem. 1982, 86, 4046-4055
4048
Crystal Structures of the Three Phases of (NH3C3H8NH3)MnC14 and a Hydrogen-I Nuclear Magnetic Resonance Investigation of Its Phase Transitions Joseph C. Crowley, Harold W. Dodgen, and Roger D. Wlllett' Department of Chemlstty, Washington State University, Pullman, Washlngton 99164 (Received: August 18, 1981; I n Flnal Form: h4ay 26, 1982)
The compound (NH3C3H,NH3)MnC14 undergoes two first-order structural phase transitions at 305 and 336 K. The crystal structures of each of the three phases have been determined by X-ray diffraction techniques. Each phase contains a layered Perovskite structure separated by the organic cations. Phases I (space group Imma) and I11 (space group Pnma) differ only by the presence of a twofold disorder of the cation in phase I (the high-temperature phase). The disorder involves a reorientation motion about the long axis of the cation by f40°. Phase I1 (space group Fmmm) involves changes both in the nature of the bridging between the Mn and C1 atoms and in the nature of the hydrogen bonding between the organic cation and the MnCl network. The organic cations are also disordered between two equivalent sites in this phase, but the reorientation angle is only k2Oo. The difference in reorientation angles in phase I and I1 is related to the differences in the hydrogen-bonding schemes of the two phases. The second moment of the broad-line lH NMR spectrum shows a gradual decrease from 78 to 336 K, at which point it shows a discontinuous narrowing, correspondingto the phase I1 phase I transition. It is shown that the disorder is dynamic in phase I and that the data are not incompatible with a dynamic disorder in phase 11.
-
I. Introduction Salts of the general type (C,H2,+lNH3)2MC14and NH3(CH2)nNH3MC14, with M = Mn, Fe, Cu, and Cd, are of much current interest, from both magnetic and structural points of view. In particular, attention has been drawn to the roles of hydrogen bonding and of the thermal motion of the alkylammonium groups in inducing structural phase transition^.'-^ These compounds have a pronounced two-dimensional structure, in which parallel sheets of corner-sharing MC16 octahedra, distorted octahedra, or discrete tetrahedra are held together by alkylammonium groups. The cationic portions of these organic chains occupy the cavities of the MCl, layers and the chains themselves extend out from the layers. They are bonded to the layers at one or both ends, respectively, by hydrogen bonding between the NH, groups and the chlorine atoms bordering the cavities.'-13 Schematic drawings of these two types of compounds are given in ref 9. Initially, interest in these compounds centered on their two-dimensional magnetic behavior. This phenomenon was first studied by Koppen et al.I4 Further work was done by van Amstel and de Jongh,15who investigated the (1)G.Chapius, H. Arend, and R. Kind, Phys. Status Solidi A , 31,449 (1975). (2)G.Heger, D.Mullen, and K. Knorr, Phys. Status Solidi A , 31,455 (1975). (3)R. Kind, S. Plesko, J. Roos, Phys. Status Solidi A , 47,233(1973). (4) R. Kind and J. Roos, Phys. Reu. B , 13,45 (1976). (5)G.Chapius, R. Kind, and H. Arend, Phys. Stutus Solidi A , 36,285 (1976). (6) R. D.Willett and E. F. Riedel, Chem. Phys., 8, 112 (1975). (7)M. Couzi, A. Daoud, and R. Perret, Phys. Status Solidi A, 41,271 (1977). ( 8 ) H.Arend, K. Tichy, K. Baberschke, and F. Rys, Solid State Commun., 18,999 (1976). (9)R. Blinc, M. Burgar, B. Lozar, J. Seliger, J. Slak, V. Rutar, H. Arend, and R. Kind, J. Chem. Phys., 66,278 (1977). (10)K. Knorr, I. R. Jahn, and G. Heger, Solid State Commun.,15,231 (1974). (11)H.Arend, R. Hoffman, and F. Waldner, Solid State Commun., 13, 1629 (1973). (12)J. Petzelt, J.Phys. Chem. Solids, 36, 1005 (1975). (13)E.Peterson and R. D. Willett, J . Chem. Phys., 56,1879 (1972). (14)J. Koppen, R. Hamersams, J. V. Lebesque. and A. R. Miedema. Phys. Lett. A , 26,376 (1967). 0022-365418212086-4046$01.25/0
magnetic properties of (CH3NH3)2MnC14, and reviewed by de Jongh and Miedema.16 More recently, research has been concerned with the phase transitions which these types of compounds exhibit. The existence of phase transitions in these compounds was first published by Arend et al."*" in 1973 and 1974. Subsequent work has included crystallographic structure determinations, NMR, NMR-NQR, Raman spectroscopy, and group theoretical analyses of the t r a n s i t i o n ~ . ~ - ~ ~ItJhas & ~been found that the motion of the aliphatic group in any of the disordered phases consists mainly of a reorientation of the group about its long axis between two or more equivalent positions and that there are two types of hydrogen-bonding schemes possible. One scheme entails two hydrogen bonds to nonbridging chlorine atoms and one bond to a bridging chlorine (this will be labeled the 2nb,lb scheme). The other involves two bonds to bridging chlorine atoms and one bond to a nonbridging chlorine5 (to be labeled the lnb,2b scheme). Structural phase transitions in PDAMnCl, (where PDA stands for the 1,3-propylenediammoniumcation) were first observed by Arend et a1.*'using DTA and hot stage polarizing microscopy. Two discontinuous phase transitions were observed, occurring at about 305 and 336 K. A neutron diffraction study of the room-temperature structures of PDAMnCl, and PDAFeCl, was published by Willett and ReideP in 1975. However, in 1978, Kind et aL3 showed that the refinement of the structure of PDAMnCl, had probably been carried out in the space group (15)W. D. van Amstel and L. J. de Jongh, Solid State Commun., 11, 1423 (1972). (16)L. J. de Jongh and A. R. Miedema, Adu. Phys., 23, 1 (1974). (17)H.Arend, R. Hoffman, and J. Felsche, Ferroelectrics, 8, 413 (1974). (18)S.Marcelja, J. Chem. Phys., 60,3599 (1974). (19)R. D. Willett, J. Chem. Phys., 41,2243 (1964). (20)J. P. Steadman and R. D. Willett, Inorg. Chim. Acta, 4, 367 (1970). (21)G.L. Ferguson and B. Zaslow, Acta Crystallogr.,Sect. B, 27,849 (1971). (22)W.Depmeier, Acta Crystallogr., Sect. B, 32,303 (1976). (23)R. Kind, S.Pleako, and J. Roos, Hela Phys. Acta, 50,601(1977). (24)M. J. Tello, M. A. Arriandiaga, and J. Fernandez, Solid State Commun., 24,299 (1977).
0 1982 American Chemical Society
Three Phases of (NH3C3H6NH,)MnCI,
The Journal of Physical Chemistry, Vol. 86, No. 20, 1982 4047
TABLE I: Positional Parameters and Site Symmetries of the Non-Hydrogen Atoms of PDAMnC1, In Each of Phases 1-111 site symmetry, (no. equiv positions, Wyckoff notation) (site position) [refined positional parameters]= phase I (Imma)
phase I11 (Pnma)
2 / m , (4a)
2 / m , (8c)
1, (4a)
(0, 0,O) [O.O, O.O,O.O]
(0, 1/4, 1 / 4 ) tO.0, 0.25, 0.251
( O , O ,0)
Cl(1a)
2, (8g) u / 4 , Y 7 1/41 [0.25. 0.01361 (9), 0.251
222, ( 8 f ) (114, 1 / 4 , 1/41 [0.25, 0.25, 0.251
Cl(1b)
same as Cl(1a) same as Cl(1a) same as Cl(1a) m , (8h) (0, Y , 2 ) [O.O, 0.13026 (9), -0.0446 ( 2 ) ] m . (8h)
m m , (8h) (O,Y,O) [O.O, 0.23068 (5), 0.01 m , (16m) (0, Y9 2 ) [O.O, 0.38061 (3), 0.21708 ( 7 ) ] m , (160)
(x, Y , 2 ) [-0.01458 ( 8 ) , 0.12979 (3), -0.04645 ( S ) ] 1, (8d)
(0; Y, 2’)
(x, Y, 0)’ (xi
(x, Y9 2 )
[0.024 (2), 0.1190 (5), 0.520 (f1)1 l)]
[0.2283 (3), 0.3685 (l), 0.0109 ( 5 ) ]l
[-0.033 (3), 0.1861 (5), 0.435 (2)l . ,m m , (4e) (0,114,Z) [0.037 (2), 0.25, 0.527 ( 2 ) ]
[0.3033 (3), 0.4350 (l), -0.0140 (511 . ..
Mn
Cl(2)
N
C(2)
a
phase I1 ( F m m m )
m m , (8g) (x, 112, 0)
[0.2189 (5), 0.50, 0.0138 ( 6 ) ]
[O.O, O.O,O.O] 1, (8d) (x, Y , 2 ) [0.26715 (7), 0.01449 (3), 0.23221 ( 7 ) ] same as Cl(1a) same as C1( l a ) same as Cl(1a) 1, ( 8 d )
[0.0240 (4), 0.1196 (l), 0.5207 (3)1 . ,1, ( 8 d ) (x, Y3 2 )
[-0.0362 (4), 0.1854 ( l ) , 0.4335 (4)] m, ( 4 ~ ) (x, 1/49 2 ) [0.0353 (6), 0.25, 0.5278 ( 6 ) ]
Standard deviations in the least significant figures are given in parentheses.
of the high-temperature phase. The phase transition sequence was then studied3 by using 35Cl NQR, deuteron NMR-NQR, and a variety of other techniques. The results of these studies may be summarized as follows: (1) Extinction axes of phase I1 are rotated 45O about the axis perpendicular to the layers with respect to the axes in phases I and I11 (based on hot stage polarizing microscopy experiments). (2) Phases I and III contain only one type of bridging and one type of nonbridging chloride ion, while in phase I1 the bridging chloride ions are split into two inequivalent types (based on 3sCl NQR experiments). (3) The average position of the planar 1,3propylenediammonium ion (henceforth PDA) is the same in phases I and 111,but its orientation is rotated 45O about the normal to the layer in phase I1 (based on 2HNMR experiments). Phases I and I1 were shown to contain dynamically disordered PDA cations. (4) The space groups of the phases were deduced to be as follows: phase I, Imma; phase I1,Fmmm; and phase 111,Pnma. The relation of the phases to one another can be further elucidated by examining the relationships of the space groups of each of the phases to the space group of an imaginary -parentn phase, of which all the observed space groups are subgroups. Kind et al.3 have shown the fictitious parent phase to be of the space group P4/mmm. In the parent phase, there would be no preferential of hydrogen-bonding scheme, and the PDA ion would be disordered about eight equivalent positions, corresponding to a hindered eightfold rotation about the long axis of the ion. It was shown that there are at least two possible descent-of-symmetrypaths which originate with P4/mmm and that the space group of phase 11lies on a different path than do the space groups of phases I and 111. Thus, while the symmetry elements of the space group of phase I1 form neither a subgroup of those in phase I nor a supergroup of those in phase 111, such a group-subgroup relationship is observed between the space groups of phases I and 111. Landau% has shown that a second-order phase transition
is possible only when the space group of the low-temperature phase is a subgroup of that of the high-temperature phase, and then only if the low-temperature space group is obtainable from the high-temperature space group by the loss of a single symmetry element. The two phase transitions in PDAMnCl, would, therefore, be expected to be first-order transitions, in agreement with the experimental results previously described. The two descent-of-symmetry paths from P4/mmm correspond to the two possible hydrogen-bondingschemes. The path on which Fmmm lies favors two hydrogen bonds to bridging chlorine atoms and one bond to a nonbridging chlorine. The path on which Imma and Pnma lie favors a hydrogen-bonding scheme in which there are two bonds to nonbridging chlorihe atoms and one bond to a bridging chlorine. The two paths also correspond to two major sets of space groups-those in which d bridging chlorine atoms are equivalent and those in which the bridging chlorines are divided equally into two crystallographically different types of bridging chlorine atoms. The space groups Imma and Pnma belong to the former set and Fmmm to the latter. This is evident upon examination of Table I, in which the site symmetry of each of the atoms in each of the three phases is given. In section 11, the crystal structure of each of the three phases is reported. Section I11 reports the results of the theory of broad-line NMR, as applicable to a rigid molecule undergoing twofold dynamic disorder, and the results of an experimental study of ND3(CH2),ND3MnC1, using broad-line proton NMR. 11. S t r u c t u r e Determination of t h e Three Phases of PDAMnCl, Crystal Growth and Data Collection. Crystals of PDAMnCl, were initially grown at room temperature as (25) L. D. Landau and E. M. Liftshitz, “Statistical Physics”, Addison-Wesley, Reading, MA, 1958, Chapter 14.
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The Journal of Physical Chemistry, Vol. 86,No. 20, 1982
Crowley et al.
TABLE 11: Structural and Crystallographic Parameters of PDAMnCl, in Each of Phases 1-111" phase I
phase I1
phase I11
lattice constants 10.254 (2) 7.198 (2) 7.174 (1) b, A 19.020 (3) 18.891 (3) 18.867 (3) 7.361 (1) 7.398 (2) 10.382 (2) c, '4 calcd density, g cm-3 1.802 1.805 1.805 not measured not measured obsd density, g cm-3 1.83 (ref 6 ) Imma Fmmm space group Pnma molecules/unit cell 4 4 8 32-63 >63 < 32 temp range of phase, "C temp at which data were collected, "C 70 40 23 crystal dimensions, mm 0.208 X 0.250 X 0.108 0.374 X 0.258 X 0.316 0.273 X 0.191 X 0.200 $ , b des 15.99 15.83 16.95 40 not applicable 20 des Standard deviations in the least significant figures are given in parentheses. Puckering angle. Reorientation angle. a> A
a
TABLE 111: Rms Thermal Amplitudes of Vibration" for NH,(CH,),NH,MnCl, in Phases 1-111
Mn C1( l a ) Cl( 2a) N C(1) C(2)
0.024 0.032 0.049 0.090 0.044
0.032 0.051 same as C1( l a ) 0.037 0.036 0.036
0.027 0.040 0.045 0.077 0.041
0.021 0.026 0.025 0.036 0.033 0.029
0.024 0.046 0.032 0.025 0.030 0.025
0.022 0.034 0.028 0.033 0.032 0.027
0.019 0.023
0.024 0.035
0.021 0.027
same as C1( l a ) 0.038 0.038 0.039
0.024 0.029 0.027
0.034 0.036 0.036
" U ( x z )= rms thermal amplitude in x z plane (in the layer), U ( y )= rms thermal amplitude parallel to the y direction (normal to the layer), and U ( x y z )= rms thermal amplitude averaged over all directions. described in ref 8. Recrystallization was carried out within the temperature range of the phase being studied, in order to obtain untwinned crystals. This procedure was mandated by the nature of the phase transitions, both of which involve a 45' rotation of crystallographic axes. Because the rotation can be either clockwise or counterclockwise, the in-plane axes of a crystal which is brought through a phase transition will be a random mixture of the true axes. In numerous attempts and various techniques of heating, we were unable to heat a single crystal through a phase transition without the crystal becoming twinned. These heating attempts were tried on crystals in both phases I1 and I11 and on both nondeuterated and partially deuterated (full deuteration of NH, groups) samples. Data collection was carried out by using the full circle automated Picker diffractometer at Washington State University, with Mo K a radiation (A = 0.71069 A). The standard deviation, u, of the intensity of each reflection was calculated by using u = [TC + BC + (0.0302]1/2,where TC is the total count, BC is the background count, and I is the net count. A 8-28 step scan was used for all data collection, with 36 steps of 0.05' per reflection. Three standards were measured every 50 reflections during the data collection for each phase. The atomic scattering factors used in the data refinement were obtained from the "International Tables of X-ray Crystallography" (ref 26). All three phases of PDAMnCl, belong to the orthorhombic crystal class. All have one long axis, which lies perpendicular to the MnCl, plane and parallel to the axis of the propylenediammonium (PDA) ion, and two shorter axes, which lie within the MnC1, plane. Lattice constants for each of the three phases were determined by a least-squares fit of 12 accurately centered reflections and are given in Table 11, dong with the crystal dimensions and calculated densities. (26) "International Tables of X-Ray Crystallography", Vol. 111, Kynoch Press,Birmingham, England, 1962.
For all structure refinements, the data were corrected for absorption (p = 23.65 cm-') and for linear decay of standards, and, at the end of the least-squares refinement, a correction for isotropic extinction was included. A local program library, utilizing the programs ORXFLS3, ORFFEQ, ORTEP2, and FORDAP, was used for all calculations. To aid comparison of the three structures, we will give the values of $ and $o for each phase if applicable. The puckering angle, $, is the deviation from 180' of the dihedral angle formed between the planes fitted through adjacent metal-[C1(l)lr units. The reorientation angle, $o, is defined as the angle which the planar PDA ion makes with the mirror plane which it intersects. The atoms Cl(1) (Cl(1a) and Cl(1b) for phase 11) are bridging chlorine atoms; Cl(2) are nonbridging chlorine atoms. 1. Structure of Phase III. Data for phase I11 were collected at a temperature of 23 "C, out to 28 = 60' (1512 reflections, of which 1189 had intensity greater than 3u). Systematic extinctions were observed (Okl,k + 1 = 2n + 1, and hOO, h = 2n + l),which indicated either the centric space group Pnma or its noncentrosymmetric subgroup Pn2,a, with 2 = 4. A statistical analysis of the reflection data indicated a centric space group; a satisfactory leastsquares refinement in Pnma confirmed this choice. The lattice constants, given in Table 11, are a = 7.1740 (12) A, b = 19.020 (3) A, and c = 7.3614 (11)A. The final residual (R = CllFol - ~ F c ~ ~ /was ~ ~0.051; F o the ~ ) final weighted residual (WR = {(C(IF,I- IF,1)2/.2)/C(F,2/.2))1/2 was 0 . 0 4 2 . Since the space groups Pnma and Imma are identical with the exception of a mirror plane along the average position of the PDA ion ( x = 0), all non-hydrogen atoms were initially placed in the positions proposed by Willett and Reidel," with the mirror plane removed. The least-squares refinement moved the atoms slightly off of these initial positions. Hydrogen atoms were located by using a difference Fourier map; their positional parameters refined satisfactorily. The final positional parameters of all non-hydrogen atoms are given in Table I, pertinent thermal parameters are in Table 111, and bond lengths and
Three Phases of (NH,C,H,NH,)MnCl,
The Journal of phvsical Chemlstty, Vol. 86, No. 20, 1982 4049
TABLE IV: Bond Distances and Angles for Phase I11 of PDAMnCl, at 23 "Ca atoms
distances, A
atoms
Mn-Cl(1) Mn-Cl(1') Mn-Cl( 2)
2.5830 ( 6 ) Cl(1)-Mn-Cl(li) 2.5982 ( 6 ) Cl(1)-Mn-Cl(1U) 2.4932 ( 8 ) Cl(1)-Mn-C1( 2k Cl(l)-Mn-Cl(2 ) N-C(l) 1.473 ( 4 ) N-C(l)-C(B) C(l)-C(2) 1.501 ( 4 ) C(l)-C(2)-C(liv) N-Cl(2v) 3.321 ( 2 ) C(l)-N-C1(2") N-Cl(1') 3.294 ( 3 ) C(l)-N-Cl(lu,) N-C1(2VL) 3.204 ( 2 ) C(l)-N-C1(2"') i, ( 1 / 2 - x , - y , - I ( - x , -Y, -2); iv, ( x , ( x , Y, 1 + 2 ) . (a I
(b)
(C)
Flguo 1. Projection of the N-H...CI hydrogen-bonding scheme onto the MnCI, plane In each of the three phases of PDAMnCI,: (a) phase 111, (b) phase 11, (c) phase I.
angles are in Table IV. A list of observed and calculated structure factors for this and the two other phases is available. (See paragraph at end of text regarding supplementary material.) In this phase, the hydrogen-bonding scheme consists of two bonds to nonbridging chlorines, C1(2), and one bond to a bridging chlorine, Cl(1). The PDA ion occupies an ordered position in this phase, the hydrogen bonding creating a distortion of the cavities in the octahedral layer,
/ ~
angles, de 92.09 (1 87.91 ( 1 90.93 ( 2 89.07 ( 2 113.1 ( 2 ) 109.8 (3) 105.53 ( 5 96.0 ( 1 ) 110.91 ( 6
+ 2 ) ; ii, ( - I / ~ + x, y , 1 / 2 - 2); iii, - Y,
2);v,
(1/2
+ x , Y,
- 2 ) ; vi,
as seen in Figure 1. The hydrogen-bonding scheme 1 causes the f&iliar puckering, or "washboard" effect, of the MnCb plane normal to the c direction in which tipping of the MnC& octahedra causes raising and lowering of alternate rows of bridging chlorine atoms parallel to the axes. A small rotation of the octahedra about the normal to the layer also occurs in this phase. The bridging chlorine atoms occupy positions which are alternately 0.275 A above and below the plane defined by the manganese atoms and are all chemically equivalent. The resultant puckering can be seen in Figures 2 and 3 and involves a puckering angle, $, of 16.95". 2. Structure of Phase 11. Data for phase I1 were collected at 40 "C out to 28 = 55" (664 reflections, of which
Flguro 2. Stereoscopic illustration of the PDA ion, its environment, and the N-H...CI hydrogen bonding in phase 111 of PDAMnCI,.
Flguro 3. Stereoscopic view of the unit cell content of the phase 111 of PDAMnCI,.
4050
Crowley et ai.
The Journal of Physical Chemistry, Vol. 86,No. 20, 1982
Flgure 4. Stereoscopic illustration of the PDA ion, its environment, and the N-He * 43 hydrogen bonding in phase I I of PDAMnCI,.
621 had intensity greater than 317). Systematic extinctions were observed (hkl, h k = 2n 1 or k 1 = 2n + 1or both), which indicated either the centric space group Fmmm or one of ita noncentric subgroups Fmm2 or F222, with 2 = 8. As in the solution of phase 111, the centric space group was chosen, with satisfactory results. The lattice constants for this phase are a = 10.254 (2) A, b = 18.867 (3) A, and c = 10.382 (2) A. The final residual obtained was R = 0.031; the final weighted residual was WR = 0.033. The hydrogen atoms were located on a difference Fourier map, which was calculated by using only low-angle data (20 < 35O), and were included in the least-squares refinement. The positional parameters of the hydrogens refined satisfactorily. The two short crystallographic axes of this phase can be obtained by rotation of 4 5 O of the short axes of phases I and III about the long axis, with a resultant increase from 7 to 10 A. Simultaneous with this rotation is the splitting of the bridging chlorines into two crystallographically different types of bridging chlorines, and a rotation of the average position of the PDA ion by 4 5 O about the long axis. In the solution of this phase, the Mn-C1 network was put into the only position in the Fmmm unit cell which would allow for two distinct bridging chlorine atoms, a single type of manganese, and a single type of nonbridging chlorine. These restrictions on the positions of the Mn-Cl network were obtained from a previous NMR-NQR study of the ~ompound.~ The mean position of the organic chain was located, by Fourier synthesis, on a mirror plane and was later moved off the mirror to allow for proper bonding lengths and angles to the hydrogen atoms. The resultant disorder imposed on the chain was confirmed by the flattening of the difference map and by the fact that bond angles and lengths became more reasonable after the disorder was introduced. The reorientation angle of the PDA chain, &, is 20°. The final refined atomic parameters for this phase are given in Table I, pertinent thermal parameters in Table 111, and bond lengths and angles in Table V. The hydrogen-bonding scheme exhibited by the intermediate phase is particularly interesting. Kind et al. had predicted the use of the lnb,2b scheme., However, the actual scheme is intermediate in nature between the 2nb,lb and lnb,2b hydrogen-bonding schemes, being closer to the 2nb,lb scheme, and is represented as such in Figure 4. One NH, H atom has a hydrogen bond to a bridging chlorine Cl(1b) only (2.47 A), one NH3 H atom has a hydrogen bond to Cl(2) only (2.52 A), while the third NH3 H atom bonds to both a Cl(2) (2.43 A) and a Cl(1a) (2.81 A). Two indications of the weak hydrogen bond to Cl(1a) are the position of H(3) and the thermal parameters of Cl(1a).
+
+
+
TABLE V : Bond Distances and Angles for Phase I1 of PDAMnCl, at 40 'Ca atoms distances, A atoms angles, deg Mn-Cl(1a) Mn-Cl(1b) Mn-Cl(2) N-C( 1 ) C(l)-C(2) N-C1(2",) N-Cl(lbLV) N-Cl(2) a
i,
(x,
'/z
2.5635 ( 5 ) 2.6210 ( 6 ) 2.4877 (8) 1.471 ( 4 ) 1.493 ( 4 ) 3.337 ( 2 ) 3.358 ( 3 ) 3.180 ( 2 )
Cl(1b)-Mn-Cl(2) Cl(lb)-Mn-C1(2') N-C(1)-C(2) C(1)-C(2)-C(lE) C(l)-N-C1(2") C(1)-N-Cl(lbN) C(l)-N-CI(B)
90.10 ( 3 ) 89.90 ( 3 ) 110.5 ( 3 ) 106.7 ( 4 ) 100.4 ( 1 ) 92.0 ( 2 ) 115.8 ( 1 )
- x, y , - 2 ) ;ii, (x, y , 1 - 2);iii, (-x, y , 2);iv, - y , ' / z - 2).
The exclusive use of the lnb,2b bonding scheme is prohibited in the structure of this phase for two reasons. First, it would necessitate an increase in the angle which the N-C(l) bond subtends with the normal to the MnC1, plane. Because of the presence of the mirror plane passing through the central carbon atom, this leads to a compression of the PDA chain, distorting the otherwise tetrahedral N-C(l)-C(Z) and C(l)-C(2)-C(l') bond angles. The latter is clearly energetically unfavorable. More importantly, such a hydrogen-bonding scheme would lead to contacts between the CH2 groups and Cl(2) which are much shorter than van der Waals contact distances. Thus, the PDA chain in this phase has a reorientation angle of only 20°, as opposed to the 45O reorientation angle expected for full implementation of the lnb,2b hydrogenbonding scheme. The observed hydrogen-bonding scheme, together with the position and motion of the PDA ion, creates a "dimpling" of the MnC1, layer in which one-fourth of the bridging chlorines are raised above the plane defined by the metal atoms, one-fourth are depressed below that plane, and half are held in the plane. This is caused by alternate clockwise and counterclockwise rotation of the octahedra about the a axis. Each Cl(2) atom participates in two short hydrogen bonds, on each from adjacent PDA ions. This force tends to tip the MnC1, octahedra back and forth along the direction of the a axis. There are two disordered hydrogen bonds to each Cl(1b) atom from H(2) hydrogens, lifting these chlorine atoms out of the plane. These bonds reinforce the tipping force that the hydrogen bonds to Cl(2) atoms have on the MnCI, octahedra. The Cl(1b) atoms occupy positions which are alternately above and below the plane by about 0.365 A. Each Cl(1a) atom participates in four weak hydrogen bonds to H(3) atoms, which exert equal forces in opposite directions along the 2, y, and z directions. As a result, the Cl(1a) atoms are restrained rigorously in the MnC1, plane. The dimpling of the MnC1, plane, which involves a puckering angle of
The Journal of Physical Chemlstry, Vol. 86, No. 20, 1982 4051
Three Phases of (NH3C3H,NH,)MnCi,
Flgure 5. Stereoscopic view of the unit cell content of phase I1 of PDAMnCI,.
-
Flgure 6. Stereoscopic illustration of the PDA ion, Rs environment, and the N-H. .Ci hydrogen bonding in phase I of PDAMnCI,.
15.99', can be seen in Figures 4 and 5. In Figure 1,note that the distortion of the octahedral cavities, which was present in phase 111, is absent in this phase because of the disorder of the PDA ion. 3. Structure of Phase I. Crystallographic data for phase I were collected at 70 "C, out to 28 = 50' (504 reflections, of which 432 had intensity greater than 3a). The observed systematic extinctions (hkl, h + k 1 = 2n + 1; hkO, h = 2n 1)indicated either the centric space group Imma or ita noncentric subgroup I2ma. As in phases I1 and 111, the centric space group was chosen. The lattice constants were found to be a = 7.198 (2) A, b = 18.891 (3) A, and c = 7.398 (2) A. Because of the great similarity of the space groups and lattice constants of phases I and 111, all atom positions were initially set to the same positions as the final refined values of the atoms in phase 111. The final residual obtained from the leastsquares refinement was R = 0.048; the weighted residual was WR = 0.058. The hydrogen atoms were located by means of a Fourier map calculated by using low-angle data (28 < 35O). The positional parameters of the hydrogen atoms attached to the nitrogen and central carbon (C(2)) atoms refined satisfactorily. Large amplitudes of vibration of C(1) prevented refinement of the positions of hydrogen atoms attached to this carbon. Therefore, these hydrogen atoms were placed in the same positions as the finalrefined values of the corresponding atoms of phase 111. The final atomic parameters of the molecule in phase I are given in
+
+
Table I, thermal parameters in Table 111, and pertinent bond lengths and angles in Table VI. In this phase, the PDA ion is again presumed to be dynamically disordered about the mirror plane on which the time-averaged position of the ion sits. The reorientation angle, &, is 40'. The PDA chain is no longer planar in this phase, as evidenced by the large thermal root mean square (rms) amplitudes of vibration normal to the chain axis, U(xz),of the end carbons (C(l), in Table 111). The chain is undergoing a twisting motion which moves the C(1) atoms out of the plane defined by the nitrogen and central carbon (C(2)) atoms. It is this motion which did not allow refinement of the positional parameters of the hydrogens attached to C(1). The hydrogen-bonding scheme of this phase is the Same as that of phase I11 (i.e., the 2nb,lb scheme), except that the bonding is disordered across a mirror plane, along with the PDA ion (compare Figure 1, a and c). This hydrogen-bonding scheme, along with the dynamic disorder of the PDA ion, creates a puckering of the MnC14 plane in which all Cl(1) atoms are chemically equivalent and are moved alternately above and below the plane by about 0.257 A. The resultant puckering of the plane, which involves a puckering angle of 15.83' is evident in Figures 6 and 7. The distortion of the octahedral cavities, which is present in phase I11 and absent in phase 11, is again absent in this phase because of the disorder of the PDA ion, as can be seen in Figure 1.
4052
Crowley et al.
The Journal of Physical Chemktty, Vol. 86,No. 20, 1982
Figure 7. Stereoscoplc vlew of the unit cell content of phase I of PDAMnCI,.
TABLE VI: Bond Distances and Angles for Phase I of PDAMnCl, at 70 “C
atoms
distances, A
atoms
angles, deg
Mn-Cl(1) Mn-Cl(2)
2.5933 (5) 2.483 ( 2 )
N-C(l) C(l)-C(2) N-Cl(2fv) N-Cl(1’) N-Cl(Zv)
1.47 ( 2 ) 1.48 (2) 3.44 (1) 3.44 (1) 3.236 ( 9 )
Cl(l)-Mn-Cl(l!) Cl(l)--Mn-Cl(lll) C1( 1)-Mn-Cl(2) Cl(l)-Mn-C1(2i) N-C(1)-C(2) C(1)-C(2)-C(liii) C(l)-N-C1(2iv) C(1)-N-Cl(1i) C(l)-N-C1(2”)
87.88 ( 2 98.12 (2 89.80 ( 5 90.20 (5 114 (1) 110 (1) 104 (1) 95.2 (8) 110.6 (6)
i, (-x, y ,
y,
’ A - 2);v,
2 ) ; ii,
(x, - y ,
(x, Y, 1 +
2 ) ; iii,
(x,
‘i2 - y,
2 ) ; iv,
t x,
2).
111. NMR Study of NDa(CH2)3ND3MNC14 1 . NMR of Motionally Narrowed Lines. The second
moment of a resonance line is defined as
l:(H
- Ho)21(H - Ho)
d(H - Ho)
M2 =
This equation, however, is restricted to systems in which there is no motion of the internuclear vectors. We have derived an equation for the second moment of a molecule which is undergoing a specific type of thermal motion. The particular type of motion considered here is that in which a molecule reorients between two equivalent orientations as a rigid unit. The molecule reorients through an angle 2d0,such that each vector, Fjk, assumes orientations &dofrom its average position. (The do so defined is identical with the 4o defined in the description of the crystal structures given in section 11.) With the z axis defined as the reorientation axis, Bj[ is defined as the angle between the z axis and Fjk. No internuclear vectors change magnitude, no new interactions are gained, and no old ones are lost. The key to this derivation is to use the following sequence of steps. First, calculate the thermal average of the term (3 cos2 8 l ) ,then square this term, and finally take the powd&-average of [ ( 3 cos2 Bik UthermSlaverage]2. This results in the following expression:
(1)
S_:I(H - Ho)d(H - Ho) where Ho is the center of the peak and I(H - Ho) is the intensity at point H - He Van Vleck2’ has shown that the second moment of a resonance line for a single crystal, in which the resonating molecular unit is rigid and occupies an ordered position, is
Substitution of eq 4 into eq 2 gives
k>j
[I In eq 2, N is the number of nuclei in the elementary dipole-interaction cell which are in resonance and the subscripts j and k run over the N nuclei. The angle between the internuclear vedor (7;k)and the magnetic field vector is and g, 8, and I have their usual definitions. dutowsky et al.% have shown that the second moment of a powdered crystalline sample is given by (3) k>j
(27)J. H.van Vleck, Phys. Rev., 74, 1168 (1948). (28)H.S. Gutowsky and G. E. Pake,J. Chem. Phys., 17,972(1949).
+ 3(sin2 8jk”
cos 240
+ cos2 8;k”)2]
(5)
For those internuclear vectors which have no motion, the value 4ois zero. It can be seen that substitution of do = Oo into eq 5 yields Gutowsky and Pake’s equation for the second moment of a powdered static ~ r y s t a l eq , ~ 3. Details of the derivation are given in Appendix A (supplementary material). By comparing 5 and 3, one can see that the contribution to the second moment by a particular ijkis reduced by a factor, Rjk = [ I + 3(sin2 ejkficos 240 + cos2 8jk”)2]/4for a powder sample. In the special case Bjk” = ~ / 2 Rik , = ‘I4 for O0 = ~ / and 4 Rjk = 1for rpo = ~ / 2 For . n-fold hmdered rotation with Fjk perpendicular to the axis of rotation, (29)H.S.Gutowsky and G. E. Pake,J. Chem. Phys., 18,162(1950).
The Journal of Physical Chemlsby, Vol. 86, No. 20, 1982 4053
Three Phases of (NH3C3H,NH3)MnCI,
I X
TABLE VII: Results of Nonlinear Least-Squares Fits of Broad-Line NMR Data at Selected Temperaturesa phase temp, "C I11 I11 I1
I
-196 7 23 70
H,,G
W,,G
W,,G
Hd,G
3.26 3.36 2.87 1.83
8.09 4.98 4.41 3.15
5.79 4.37 4.47 5.42
4.32 4.32 4.86 3.10
H, = contact shift, H, = dipolar splitting, W ,= line width of C(1) proton resonance line, W ,= line width of protons attached to C(2).
Gutowsky and PakeN have shown that Rp = l/q for n 1 3 and R = 1 for n = 2. The reorientation of a pair of nuclei atout an axis is, in theory, always distinguishable from the hindered rotation of the pair except in the above special cases. 2. Experimental Results. A temperature-dependent proton NMR study has been carried out on a powdered sample of ND3(CHJ3ND3MnC14,in order to determine the magnitude of the motion of the PDA ion in each of the three phases of the compound. The ammonium proton sites were deuterated by recrystallization of undeuterated PDAMnC14 from D20. The phase transitions in the deuterated compound have been reported3 to occur at about 22 and 63 OC. The derivative of the absorption curve was measured by using the apparatus described by B l o ~ m q u i s t . ~The ~ magnetic field was varied and the frequency was held constant. For all but the data taken a t liquid-nitrogen temperature (77 K), data points were recorded every 0.0315 G. At liquid-nitrogen temperature, the broad resonance line required data points to be recorded every 0.0630 G. The observed derivative spectra showed a substantial asymmetry, making precise location of the center of resonance difficult. The source of the asymmetry is assumed to be a paramagnetic contact interaction which is substantially larger for the C(1) protons than the C(2) protons. The observed asymmetry, whatever its source, will lead to overestimation of the second moments of absorption spectrum when calculated via direct integration using eq 1. In order to obtain a more precise estimation of the second moment, we fitted the experimental derivative spectrum to a model, and the second moment was calculated for the model. The model used the following assumptions: (1) The contributions of each CH2 proton could be represented by a doublet, arising from dipolar splitting, Hd. (2) The C(1) and C(2) protons are offset from each other by an amount H,, the paramagnetic contact shift. Mathematically, doublets are represented by a sum of two Gaussian functions, and the total spectrum as the weighted sum of two pairs of doublets 2
I(H)=
2
C C C&H&ij,wi) is1 j=l
(6)
where the sum i runs over the two types of CH2 groups (type 1 = C(l) protons, type 2 = C(2) protons) and the sum of j runs over the two peaks of the dipolar doublet. The weighting factor ci, to be applied to each Gaussian function, is given by ni/N where ni is the number of protons of the i-th type and N is the total number of protons in resonance. Here g(H,Hij,WJ is a normalized Gaussian function (30)H.S.Gutowsky and G.E.Pake, J. Chem. Phys., 16,1164(1948). (31)D.R.Bloomquist, R. D.Willett, and H. W. w e n , J. Am. Chem. SOC., 103, (1981). (32)G. E.Pake and E. M. Purcell, Phys. Reu., 74, 1184 (1948).
I
6'
283
'
303
323
343
T(K)
Flguro 8. Temperature dependence of the second moment of the proton NMR spectrum of PDAMnCI,: (X) calculated from eq 1 , (0) calculated from eq 7.
TABLE VIII: Comparison of Three Methods of Calculating the Second Moment of a Proton NMR Spectrum second moment, G* phase
temp,"(=
I11 I11 I1 I
-196 7 23 70
theoretical exptl eq 5 viaeq 1 viaeq7 19.8 19.8 13.6 6.6
20.7 14.2 12.8 7.2
19.5 13.6 12.0 7.2
with width Wi centered at Hij,with Hij= Ha + (-l)iHd/2 and Ho, = Ho2 + H,. The observed spectrum was fitted to the derivative of this function by a least-squares procedure. The results are given in Table VII. The second moment of the experimental line was then calculated for each temperature calculated by using the following equation: (7) Equation 7 expresses the second moment of a set of overlapping Gaussian lines whose centers and widths are known. The symbol H represents the center of the experimental line and is calculated by using
The results of these calculations are shown in Figure 8, and selected values given in Table VIII. The theoretical value of the second moment for each phase was calculated from eq 5 using structural parameters which were obtained from an X-ray diffraction study of the nondeuterated compound (vide supra). The final refined positional parameters of the heavy-atom (C, N) portion of the PDA ion for each phase, as obtained from the X-ray diffraction investigation, were used to calculate the positions of ideally placed hydrogen atoms. These positions were calculated such that the H-C-H angles on all CH2 groups were 109.5O and the proton-proton distance on a given CH2 group was 1.71 A. Proton-proton interactions with neighboring PDA ions were included in the theoretical calculations for phase 111 because of the ordered and, hence, constant nature of these interactions. Because of the disorder in phases I1 and I, however, no interactions from neighboring PDA chains were considered in the calculations for these phases. The additional twisting motion deduced from the X-ray results of phase I was also ignored.
Crowley et ai.
The Joumal of Physical Chemistry, Voi. 86, No. 20, 1982
4054
TABLE IX: Contributions t o the Second Moment (M,) of the Proton NMR Spectrum for Each of the Three Phases of PDAMnCl, phase I interaction (i-k)a 1-2, 1-3. 1-4: 2-3, 2-4, 1-6 2-5 1-5 2-6
3-4, 5-6 5-3 5-4 6-3 6-4
(ao= 39.8") (Mijkr
ejk", rjk,
1.715 2.952 2.397 2.409 2.952 2.918 2.918 2.379 2.344
deg
Rjk
90 113.8 119.8 119.1 113.4 144.0 144.0 0.0
0.27 0.32 0.36 0.36 0.32 0.64 0.64 1.0 1.0
0.0
phase I11 (ao= 0.0")
phase I1 (& = 19.7")
3.86 0.12 0.45 0.43 0.12 0.12 0.12 0.66 0.72
(Mz)'kr
Bjk",
rjk,A
deg
Rjk
Gd
1.715 2.987 2.446 2.446 2.987 2.959 2.959 2.412 2.411
90 113.8 119.5 119.5 113.8 144.6 144.6
0.70 0.74 0.76 0.76 0.74 0.89 0.89 1.0 1.0
9.82 0.25 0.85 0.85 0.25 0.16 0.16 0.61 0.61
0.0 0.0
(Mikkr
8jk"T
rjk,
A
deg
1.715 2.952 2.394 2.412 2.952 2.965 2.965 2.445 2.394
90 114.5 120.7 119.7 113.9 144.7 144.7
2.778
90
0.0
0.0
Rjk
G
1.0 14.08 1.0 0.36 1.0 1.27 1.0 1.21 1.0 0.36 1.0 0.18 1.0 0.18 1.0 0.56 1.0 0.56
Intermolecular Interactions between Chains A and B 6.60
-0
P
Q. Numbering scheme of the protons of the POA chain as used
in Table IX.
Table I X lists, for each phase and for each protonproton interaction (see Figure 9 for proton numbering scheme), the length of the ijkvector, the value of the reduction factor Rjk, and the contribution of the interaction, (M2)'k, to the second moment. The reduction factor, Rjk,for an interaction is defined as
Bjc,
Rjk
= f/4[1
+ 3(Sin28jk"
COS
240
+ COS2
(9)
The contribution, (M2)jk)of an interaction to the second moment is given by
A comparison of the theoretical calculations and experimentally observed second moments (as calculated directly and by analysis via nonlinear least-squares methods) is given in Table VIII. Excellent agreement is observed between theory and data for phases I and I1 and for phase I11 as measured at liquid-nitrogen temperature. For phase 111, as measured at 7 "C, there is much poorer agreement between the theoretical calculation of the second moment and the second moment of the observed line. This is due to neglect of the torsional motion of the PDA anion, which is quite large in phase I11 as evidenced by the V ( x z )values for N, C(1), and C(2) in that phase. IV. Discussion Important information can be gained from a comparison of the thermal amplitudes of vibration of the molecule in
13.56
1.0
1.04 19.80
the three phases. For the heavy atoms (i.e., Mn, Cl), the rms amplitudes of vibrations increase more or less smoothly with temperature. However, for the atoms in the cation (N, C), the rms amplitudes of vibration are smallest in the intermediate phase. Thus, in going from phase I11 to phase 11, the cation becomes disordered, but the amplitude of vibration about its equilibrium position decreases in magnitude. This has an important consequence with regard to the 'H NMR spectra of phases I11 and 11. With the exception of U(xz) of C(1) in phase I, the thermal parameters of the nitrogen and carbons of the organic chain are essentially equal to each other for any particular phase. Large amplitudes of vibrations are evident along the directions of the two shorter axes, while considerably smaller vibrations are observed normal to the layers. This corresponds to a torsional motion of the PDA ions about their long axes and is consistent with the type of thermal motion involved in the various phases and in the phase transition. Figure 8 shows that the second moment of ND3(CH2)3ND3MnC14decreases linearly with temperature from -196 "C (liquid-nitrogen temperature) to about 63 "C and that no sudden change in second moment, corresponding to the I11 I1 phase transition, is observed in that temperature range. This latter must be reconciled with the observation of a first-order p&e transition by Kind et al.3 The answer lies in the unusual nature of the intermediate phase of this compound. Examination of Figure 2 and Table I11 shows that large thermal vibrations of the PDA chain parallel to the MnC1, plane already exist at room temperature, 10 "C below the low-temperature phase transition of the undeuterated compound. As the temperature of the compound is raised, the torsional motion of the PDA chain increases until, at the transition to phase 11, the chain begins to reorient about ita long axis between two positions which are about 40" apart from each other with a concomitant reduction in torsional motion. Examination of Figures 2 and 4 and Table I11 shows that the torsional motion of the PDA chain (the U(xz)values in Table 111) decreases upon passing from phase I11 to phase 11. Thus, accidentally, the effect of torsional motions of the PDA ion in phase I11 is comparable to the combined effects of torsional and reorientational motion in phase II. At liquid-nitrogen temperature, there is little or no motion of the PDA chain, as evidenced by the excellent agreement of the second moment at this temperature with theoretical calculations. The cadmium analogue of PDAMnCl,, PDACdC14,undergoes only one phase transition. It is a second-order
-
J. Phys. Chem. 1982, 86, 4055-4001
transition from the space group Pnma to the space group Imma.22 A temperature-dependent proton NMR studyg of PDACdC14has shown the temperature dependence of the NMR spectrum of PDACdCh to be very similar to that which we have observed for PDAMnC14 in the present study. In both compounds, the second moment decreases linearly with temperature until the transition to phase I (63 and 103 “C for PDAMnC14 and PDACdC14, respectively), at which the second moment drops discontinuously to about 60% of its pretransition value. Thus, in the Cd salt the PDA chain undergoes increasing thermal vibrations until, at the high-temperature phase transition, the chain begins to reorient between two equivalent positions, which are about 80’ apart from each other. The higher transition temperature, and the lack of the existence of a phase equivalent to phase I1 of the Mn salt, can be attributed to the longer length of the nonbridging M-Cl (M = Mn or Cd) distance in the Cd salt. This longer distance leads to increased C1-CH2 repulsion forces. In both the low- and high-temperature phases, all bridging chlorines are equivalent. In phase 11,half of the bridging chlorines participate in a Mn-Cl-Mn bond angle of 180° and half form a Mn-C1-Mn bond angle of 164.01 (4)’. The puckering angle, 11, is identical within the experimental error, for phases I and I1 (15.99’ and 15.83’, respectively), in which a dynamic disorder is present. The puckering angle of phase 111,however, is noticeably larger (16.95’). This is a result of the fact that the PDA ion is ordered in this phase, allowing the hydrogen bonding of all PDA chains to act in a concerted manner to distort the lattice. Bond distances and angles, in all phases, are in agreement with those of similar c ~ m p o u n d s ? * ~ J ~In* phases ~ I and 111, the bond lengths and angles of the PDA chain
4055
show little distortion of the ion due to its placement between MnCb sheets or due to the hydrogen-bonding scheme. In phase 11,however, where the hydrogen-bonding scheme becomes distorted, both the N-C(l)-C(B) and C(l)-C(2)-C(l’) bond angles decrease by about 3’ each. This can be explained by examination of the angle fl which the N-C(l) bond makes with the long axis of the ion. This angle is equal in phases I and I11 (32’ and 31.7O, respectively). However, in phase 11, it increases to 33.0°. This increase is necessary in order to accommodate the hydrogen-bonding scheme of phase 11. In phase 11,the PDA ion sits more deeply in the octahedral cavity than in the other phases (0.229 and 0.194 A, respectively), because of the additional weak hydrogen bond to a bridging chlorine atom. The presence of a mirror plane parallel to the MnCb sheets and passing through C(2) requires the N-C(l)-C(Z) and C(l)-C(2)-C(l’) bond angles to decrease with any increase in fl. The distortion of the PDA chain in phase 11, which is evident in Figure 4, causes the interlayer spacing of this phase (9.43 A) to be smaller than that of either phase I or phase I11 (9.45 and 9.51 A, respectively). The PDA ion retains an all-trans confiiation in phases I1 and 111. In phase I, the large value of U(xz)for C(1) implies the introduction of some contribution of a gauche conformation. Acknowledgment. The support of NSF grant CHE77-08610 is gratefully acknowledged. Supplementary Material Available: Tables of the observed and calculated structure factors for the three phases, complete tables of atomic parameters, bond distances, and angles (including hydrogen atoms) for all phases, and detailed derivation of eq 5 (25 pages). See any current masthead page for ordering information.
Transfer Thermodynamics of Benzoic Acid in Aqueous Mixtures of Some Ionic and Nonionic Cosoivents and the Structuredness of Solvents Jayatl Dattat and Klron K. Kundu* Physical Ctmmktry laboratories, Jadavpur Unlvers& Galcutla 700 032,Indk (Received: August 31, 1981; In Final Form: June 3, 1982)
Standard free energies (AG,”) and entropies (AS,’) of transfer of benzoic acid (HBz) from water to aqueous mixtures of some ionic and nonionic cosolvents like LiC1, KBr, dioxane (D), acetonitrile (ACN),propylene glycol (PG), and glycerol (GL) have been determined from solubility measurements at different temperatures. The observed AGt-composition profiles in the salt solutions appear to result from the well-known salting-out effects of the salts, and those in the organic cosolvents are dictated by the combined effects of dispersion and acidbase-type interactions. The observed TASto-composition profiles, as well as those obtained after correcting for the “cavity effect” as estimated tentatively by use of “scaled particle theory (SPT)”, were examined in the light of Kundu et ala’s semiquantitative theory proposed earlier. The latter profies suggest that, while isopropyl alcohol (IPA) behaves as a promoter of the three-dimensional (3D)tetrahedral structure of water and the salts as structure breakers, all the organic solvents induce a structure-breakingeffect right from the initial compositions. Also,the observed graded reduction of the structure-promotingpropensity of IPA in PG and GL systems, resulting from the successive replacement of hydrophobic (CH,) groups by partially hydrophilic (CH,OH) groups in the cosolvents, confirms that structuring and destructuring ability of a cosolvent depends on the ratio of hydrophobicity to hydrophilicity of the cosolvent.
Thermodynamic quantities, especially transfer enthalpies and entropies, of electrolytes and nonelectrolytesoften
provide useful information regarding the structuredness of solvents. It has been observed by various workers14 that (1) S.Rajender and R. Lumry, BiopoZymers, 9, 1125 (1970).
‘Nee Sinha. 0022-3654/82/ 2086-4055$01.25/ 0
0 1982 American Chemical Society
