I2
-
J. Phys. Chem. 1987, 91, 195-203 21
which is trivially shown to be concerted via a totally symmetric coordinate. It is interesting to note that if the next step is of the form12 H2 + I HI H +
+
then it is only concerted (see mechanism iii in Figure 6 ) if G, = C, = Gn precluding a Ch transition state. It is still possible, however, that a Cz structure (IH,) is an intermediate in a two-step mechanism for the H2 I reaction. Other radical mechanisms have been proposed,I3 but the above examples should suffice to show how the symmetry rules can be applied to the individual steps. It is interesting to note that Anderson and co-workers14 have recently shown using trajectory calculations that both mechanism i and the composite (ii) and (iii) mechanisms are involved. The bimolecular concerted process (mechanism i) occurs with moderately vibrationally excited I2 (0 < u < 90) and H2 ( u = o).
+
Conclusions
We have attempted to show how a practical implementation of the classical selection rule stage is sufficient to (i) generate the symmetry-allowed pathways for a given R,P pair, and (ii) uniquely define the transition-state symmetry for each pathway. If the details of the normal coordinates are also known, it is possible to deduce directly the actual structure of the transition state. In (13) Sullivan, J. H. J . Chem. Phys. 1967, 46, 73. (14) Jaffe, R. L.; Henry, J. M.; Anderson, J. B.J . Am. Chem. SOC.1976, 98, 1140. (15) Jahn, H. A.; Teller, E. Proc. R.SOC.London 1937, A l d l , 220.
195
addition, we have shown how the classical selection stage also dictates that for a concerted inversion of a chiral molecule, the transition state must be achiral. This is not a trivial result, even though it appears intuitively obvious. The examples discussed in this paper have been chosen to illustrate the utility of the procedure for relatively simple reactions, but spanning a range of types of concerted reactions. The mechanisms that are generated have also been determined intuitively, and most are well-known. However, the tris(bidentate) inversion example generates (neglecting the dissociative mechanisms here, as they are multistep), in addition to the Bailar twist and Ray-Dutt twists, two less familiar mechanisms: the pushthrough twist and the cross-over twist. For the specific case of the tris(che1ate) structure, these are energetically unviable, but there is absolutely no reason why other D3systems (e.g., without a central metal atom at the origin) cannot exploit these mechanisms. It is important to appreciate this point, for it is only in the secondary stage in which the energetics is explicitly included that the actual structure (as distinct from symmetry) is taken into account. All four mechanisms are significant for a D3inversion; however, for certain D3 structures, certain of these mechanisms may become energetically unviable. We are currently working on other inorganic isomerizations, and the classical selection procedure generates, in addition to postulated mechanisms currently in the literature, new mechanisms which are energetically viable. The procedure is predictive, and if the present results are familiar, it is important to appreciate that we have purposely chosen systems that are relatively simple in order to highlight the principal features of the approach. Further studies highlighting this ability to generate previously overlooked mechanisms for inorganic systems will be published elsewhere.
Complex Formation in Pyrosulfate Melts. 3. Density and Conductometric Measurements of the System V20,-K2S207 in the Temperature Range 350-490 OC Gerard Hatem,’” Rasmus Fehrmann,lbMarcelle Caune-Escard,lPand Niels J. Bjerrum*lb Chemistry Department A, Technical University of Denmark, DK-2800 Lyngby, Denmark, and Laboratoire de Dynamique et Thermophysique des Fluides, associe au CNRS, Universite de Provence, Centre de St. - JerSme, F-13397 Marseille. Cedex 4, France (Received: April 14, 1986; In Final Form: August 21, 1986)
Densities of the molten VZO5-KzSzO7system were measured at 11 different compositions in the mole fraction range Xv20s = 0-0.399 and in the temperature range 360-490 OC. For each composition the measurements were fitted to an equation of the form p = A(X) B(X)(t - 450). Furthermore, all the measured data were fitted to a general polynomial p = x&42 + C?B,,,(t- 450)m. Excess molar volumes were calculated for the examined composition range. Maximum deviation from ideality was found around Xv,o, = 0.3-0.4 indicating complex formation in the melt. The specific conductivities of the solid and molten VZO5-K2SzO7system were measured at 15 different compositions in the composition range XvzoJ= 0-0.5266 and in the temperature range 350-480 OC. For each composition in the examined temperature range the specific conductivity was expressed by equations of the form K = A(X) B(X)(t - 450) + C(x)(t - 450)2 + D(x)(t - 450)3. Finally all conductivity measurements were fitted to a general polynomial of the type K = x&4,,P+ x y B m ( t - 450)m. The activation energy of the equivalent conductivity of the potassium ions in the melt was also calculated for the given compositionsand a large increase was found at increasing mole fractions of Xvzos. This effect is probably due to polymerization in the melt. Furthermore, the experimental molar conductivity of the melt was found at all compositions and compared with theoretical values. The large negative deviations between theoretical values and experimental values are most probably due to complex formation in the melt. The combined results of the two methods are in agreement with the concept of complex formation at the compositions 2K2S207:1V205 and 1K2S207:1V205.These two compositions correspond to maximum concentrations of the likely species, dimeric (VOz)2(S04)2S207eand polymeric (V02S04),”-, respectively.
+
+
Introduction
This work constitutes a part of a series of investigations carried out in order to characterize molten systems related to the sulfuric acid catalyst. The molten V205-K2S207system investigated here (1) (a) Laboratoire de Dynamique et Thermophysique des Fluides, Universite de Provence. (b) Chemistry Department A, Technical University of Denmark.
is considered a realistic model of the oxidized form of the catalyst. Nevertheless reliable fundamental data such as the density and the conductivity as well as the Phase diagram of this system are not available in the literature. Previously2 the densities of the molten KHS04-KzS207system and very dilute solutions of V205in this melt (i.e., Xv20s< 0.04) (2) Hansen, N. H.; Bjerrum, N. J. J. Chem. Eng. Data 1982, 26, 13.
0022-3654/87/2091-0195$01.50/00 1987 American Chemical Society
196
The Journal of Physical Chemistry, Vol. 91, No. I , I987
have been measured, while the densities of .the molten V2OsK2S207system are completely lacking (including the catalytically important mole fraction range Xv20s= 0.20-0.33). The variation of the conductivity of K&O7 (and some other alkali pyrosulfates) in the temperature range 400-600 O C has been reported3 while only one paper4 has dealt with the conductivity of the solid and molten V205-K2S207systems. However, only four compositions (corresponding to the molar ratio K / V = 1, 2, 3, and 5) were investigated and only a few measurements were performed in the liquidus range. Furthermore the K2S2O7 used was probably not very pure since it was obtained by dehydrating K H S 0 4 at 450 OC-a method that usually leadss to a mixture of pyrosulfate and hydrogen sulfate. Several studieP9 of the phase diagram of the V2OS-K2S2O7 binary system show marked discrepancies. This is demonstrated by the variation in the values published for the liquidus temperature at Xv,05 = 0.5, namely 590,6 4908 and 430 O C 9 Also the composition of the eutectic is very uncertain and values of 92: 85,7 90,* and 7S9 mol % K2S2O7 have been proposed. A number of different compounds are claimed6-" to be formed in the V20s-K&07 system and characterized by molar ratios of K2S2O7/V2O5 of 1, 1.25, 1.5, 2, 3, and 6. The compounds with the composition 3K2S207-V205, 2K2S2O7.V2O5,and K2S207-V205 are probably9 the so-called pyrosulfovanadates K3V02S04S207, K4(V02)2(S04)2S20,, and KV02S04, respectively. The large discrepancy may be caused either by the use of impure K2S2O7 (contaminated by K H S 0 4 as mentioned earlier), or by open cell measuring systems giving rise to decomposition due to evaporation or reactions with the atmospheric moisture. Further the experimental difficulties involved in the study of these viscous and deeply colored melts are severe. As shown in this work (and work in progress) conductometric measurements can avoid these difficulties and can be useful for phase studies of such melts. Only a few papers have been concerned with the species present in the molten V,O5-K,S2O7 system. Thus,S it has been shown that molten K&O7 contains the S2O7,- ion and that the decomposition reaction S2072-~=tS042-+ SO3is not important below about 450 "C. In the molten V2O5-K2S2O7system dilute with respect to V20s (Le., Xv,os < 0.05) spectrophotometric, cryoscopic, and potentiometric investigations12 at 410-450 O C have shown that the monomeric complexes V02S04-and a solvated form of this, V02S04S2073-,are most probably present in the melt. The presence of V02S04- in the melt is also supported by electrochemical investigation~l~ at 430 O C . Regarding the species present in melts more concentrated with respect to vanadium (Le., Xv,05 = 0-0.5) no investigations have been reported so far. However, recent calorimetric i n v e s t i g a t i o n ~ ~performed ~J~ at 400-450 OC showed that possibly dimeric and polymeric species like (V02)(S0,)2S20,4-and (V0,S04)," are formed in the important (3) Kostin, L. P.; Shligerskaya, L. G.; Makarevich, N. A. I m . Vyssh. Uchebn. Zaoed. Khim. Khim. Tekhnol. 1975, 18(7), 1015. (4) Dubinin, V. G.; Illarionov, V. V.; Maslennikov, B. M. Kinet. Katal. 1972, 13, 454.
( 5 ) Fehrmann, R.; Hansen, N . H.; Bjerrum, N. J. Inorg. Chem. 1983,22, 4009. (6) Bazarova, Zh. G.; Boreskov, G. K.; Kefeli, L. M.; Karakchiev, L. G.; Ostankowich, A. A. Dokl. Akad. Nauk SSSR 1968, 180, 1132. (7) Hahle, S.; Meisel, A. Kinet. Katal. 1971, 12, 1276. (8) Maslennikov, B. M.; Illarionov, V . V.; Gubareva, V. N.; Bushuev, N. N.; Tavrovskaya, A. Ya.; Leneva, Z. L. Dokl. Akad. Nauk. SSSR 1978,238, 1411. (9) Glazyrin, M. P.; Krasil'nikov, V. N.; Ivakin, A. A. Zh. Neorg. Khim. 1980, 25, 3368. (10) Boreskov, G . K.; Illarionov, V. V.; Ozerov, R. G.; Kil'disheva, E. V. Zh. Obshch. Khim. 1954, 24, 23. (1 1) Gubareva, V. N.; Illarionov, V. V.; Maslennikov, B. M.; Bushuev, N. N.; Leneva, Z. L.; Mikhailova, I. M.; Vilina, V. Yu.; Krasil'nikova, I. G. Tr. Nauchn.-lssled. Inst. Udobr. Insektofungits. 1977, 230, 23. (12) Hansen, N . H.; Fehrmann, R. F.; Bjerrum, N. J. Inorg. Chem. 1982, 21, 744. (13) Durand, A.; Picard, G.; Vedel, J. J. Elecrroanal. Chem. 1981, 127, 169. (14) Fehrmann, R.; Gaune-Escard, M.; Bjerrum, N. J. Inorg. Chem. 1986, 25, 1132. (15) Fehrmann, R.; Jeanne, P.; Gaune-Escard, M.; Bjerrum, N. J., to be
submitted for publication.
Hatem et al.
Figure 1. Conductivity cell made of borosilicate glass: A, standard taper joint with stem; B, melt reservoir; C, cell compartment; D, capillary tube; E, gold electrode plate; F, gold wire; G, glass sealed gold foil; H, gold wire.
mole fraction range Xv201= 0.2-0.5 (a range of particular interest in studies of the catalyst). The present work involves some of the few methods that can be used for high-temperature studies of these very dark and viscous melts. It is undertaken in order to acquire both fundamental data for the V2O5-K2S2O7system and at the same time to throw light on the possible complexes involved in the reaction mechanism for the oxidation of SO, to SO3 by 0,.
Experimental Section Materials. Pure and dry K2S207 was obtained by thermal decomposition of K2S208(Merck, Pro Analysi, maximum 0.001% N) as earlierI2 described. The V205used was from CERAC (pure (99.9%)). All handling of chemicals was performed in gloveb o ~ e s ' ~ 9with ' ~ atmospheres of nitrogen or argon dried continuously to around 5 ppm H20. Prior to use the K2S207was kept in sealed ampules, or possibly briefly exposed to the dry atmosphere of the glovebox. Density Measurements. The densities of the molten V2O5K&O7 system were obtained after the Archimedian principle by measuring the mass of a spherical platinum bob dipped into a quartz crucible containing the liquid. The crucible was contained in a tube of quartz in an atmosphere of dry argon; the temperature difference between top and bottom of the crucible did not exceed 4 "C. The volume of the bob was obtained by measuring the mass of the bob in water and in air. The volume of the bob at the measuring temperature ( t "C) was obtained from the equation
+
V, = Vooc(l 0.2554 X 10-4t
+ 0.0104 X
lo%*)
(1)
The mass of the bob was measured to an accuracy of 10.5mg, and since the measured masses were of the order of 1 g the relative error of the mass determination was around 0.05%. The volume of the bob was ca. 0.5 cm3. The variation in the temperature of the melt during the experiments was within about *2 O C (because of the vertical temperature gradient). After each series of
Complex Formation in Pyrosulfate Melts measurements the weight of the content of the crucible was estimated and a mass loss of up to 1.5% was observed. The mass loss was most probably due to the decomposition of K&O7 to SO3and K,SO,. Measurements at higher temperatures than ca. 480 OC were not performed due to the increasing decomposition of the melt at higher temperatures. Conductivity Measurements. The borosilicate glass cell used for measuring the conductivity is shown in Figure 1. It consists of two compartments (C) of 12-mm tubing connected through a I-mm4.d. capillary tube (D) giving rise to a measured resistance of at least 700 Q . The cell further consists of a neck (A) of 8-mm tubing with a standard taper joint on top making it convenient for the addition of materials. The widening of the compartment at (B) to around 17 mm facilitates mixing of the components of the melt without the danger of forcing the melt into the stem (A). The electrodes which are sealed into the bottom of the cell are made of gold, since gold is probably the only metal inert to the melt. Each consists of a plate (4 X 4 mm) (E) connected to a gold wire (1 mm) (F), which is welded to a gold foil (G). The foil has a thickness of not more than about 15 bm in order to secure a vacuum-tight seal when fused into the borosilicate glass tube leading through the bottom of the chamber. Outside the cell the foil is connected to a gold wire (1 mm) (H) leading to the measuring device. In the drybox, the cell was filled with chemicals through the taper joint. The cell was thereafter evacuated and closed by sealing the stem (A). Up to seven different compositions could be measured with each cell by addition of chemicals through the stem. The stem was cut open in the drybox and thereafter sealed again. After the cell was filled it was placed in an aluminum block furnace as earlier describedL6with temperature regulation to within f0.1 OC. The components of the melt could be mixed well by mechanically rocking the furnace. The temperature of the melt was measured by a controlled chromel-alumel thermocouple placed directly at the capillary tube. The melt was usually equilibrated at the highest measuring temperature during 1-3 days. Before the resistance was measured, the melt was flushed several times through the capillary tube in order to secure a homogeneous liquid in the measurement region. This was done manually by taking the cell holder with the cell out of the furnace for a short while. The resistance of the cell was measured until it became constant. The temperature was reduced in steps of 5 OC down to the lowest measuring temperature and the resistance was measured each time. Finally the cell was reheated to the initial measurement temperature and an observation of a resistance almost identical with the initial measured resistance (Le., better than f l % ) was used as a criterion for accepting the series of measurements. The resistance was measured at 2 kHz with a precision better than 0.1% by using a Wheatstone bridge as described previo~sly.'~ It was found that measurements at other frequencies (e.g., up to 12 kHz) gave almost identical values for the resistance. In all four different cells were used. Cell constants of the order of 300 cm-I (relative accuracy *OS%) were determined in a thermostat at room temperature by using 0.1 dema! KC1 standard solution as described in the literature.Is The cell constant was not corrected for the temperature dependency since the estimated error resulting from ignoring this at the highest measuring temperature was only around 0.1%. General Considerations
The density and specific conductivity of molten V 2 0 5in the extrapolated liquid state below the melting point of 670 OC was found by extrapolation of the data of Pantony and Vasu.I9 A least-squares fit of their data gave for t OC the expressions pf = 3.453 - 1.702 X IO-% and K , = 4919 exp(-10933/t + 273.2) for the density and conductivity respectively, of molten V2OS. (16) Andreasen, H. A,; Bjerrum, N. J.; Foverskov, C . E. Rev. Sci. Instrum. 1977,48, 1340. (17) Poulsen, F. W.; Bjerrum, N. J. J . Phys. Chem. 1975,79, 1610. (18) Jones, G.; Bradshaw, B. C . J . Am. Chem. SOC.1933,55, 1780. (19) Pantony, D. A,; Vasu, K. I. J . Inorg. Nucl. Chem. 1968,30, 433.
The Journal of Physical Chemistry, Vol. 91, No. 1 , 1987 197 Density. The density was obtained from the expression pf
= Am/vf, g/cm3
(2)
where pf is the density at the temperature t , Am is the mass difference in grams of the bob in air and in the melt, and V, is the volume of the bob at the temperature t calculated from eq 1.
The excess molar volume V : of the melt at the temperature t and the composition XK2s207 is given by
where Mv20,and MK2s20, are the molar masses of V205 and K2S2O7, respectively, p , and pf,K2S20,are the measured densities at the temperature t of the melt and of molten K2SZO7, respectively, and pf,vzoIis the density of V205 in the extrapolated liquid state at the temperature t. Conductometry. The conductivity of ionic melts is usually related exponentially to the temperature K = A e-E.IRT (4) where K is the conductivity, A , a constant, E , is the energy necessary to promote the ionic migration (the so-called activation energy), and R and T have their normal meanings. The equivalent conductivity A of a conducting species present in the molar concentration C is given by the equations A = (K/C)1000
(5)
The experimental molar conductivity, Aexptlat a given composition and temperature is expressed by (7) where K is the measured specific conductivity and P 'is the molar volume of the melt calculated from the composition and the measured density of the melt. In order to discuss possible complex formation in molten salts, Aexptlshould not be compared with the figure obtained by simple addition of the molar conductivities of the components making up the melt, but rather be compared with Acalcdobtained from the equationZo Acaicd
= XIAI + X2A2
x1x2A1
(AI
< A2)
(8)
where XI and X 2 are the mole fractions and A I and A2 the molar conductivities of the components, respectively.
Results and Discussion Density Measurements of the Molten V205-K2S207System at 360-490 "C. The experimental densities and temperatures of the V2OS-K2S2O7system are given in Table I. It should be noted that for some compositions and temperatures the density measurement have been checked for reproducibility after measurements at other temperatures. Attempts to measure the densities at higher mole fractions of V 2 0 5failed due to the very slow rate of dissolution of V2OSand the apparently very high viscosity of these melts. Stirring or agitation of the melt was not possible. Table I includes only measurements of the V20,-K2S20, system in the liquid region determined by the conductometric measurements described later. It is noted that the lowest temperature for which results could be obtained for molten K&O7 is 417 f 2 O C in good agreement with the melting point of 418.8 OC found previous1y.l2 In Table I1 the measured densities for the V,05-K2S20, system are expressed by the linear equation p = A ( X ) + B ( X ) ( t - 450 ( 2 0 ) Electrochemistry of Fused Salts; Delimarskii, Iu, K., Markov, B. F., Eds.; English Edition, The Sigma Press: Washington, DC, 1961.
198 The Journal of Physical Chemistry, Vol. 91, No. 1, 1987
Hatem e t al.
TABLE I: Experimental Densities (g/cm3) and Temperatures ("C) of the Molten V2O3-KS2O, System Xv20s,mole fraction measd temp 0.000 0.054 0.102 0.125 0.150 0.154 0.198 0.210 362 374 383 385 387 388 391 392 394 396 399 400 400 406 408 408 408 409 410 412 414 41 5 417 418 419 419 419 420 42 1 423 424 427 429 43 1 43 1 432 433 435 436 436 437 439 440 44 1 442 443 444 444 446 447 448 448 449 449 452 452 454 455 456 458 459 460 461 462 462 464 465 466 467 470 472 472 473 474 475
0.300
0.336
0.399
2.305 2.223 2.288 2.281 2.279 2.215 2.235 2.428 2.419 2.272 2.264 2.435 2.420 2.417
2.200 2.223 2.261 2.262 2.267 2.164 2.364
2.406 2.417
2.356 2.186
2.218
2.099 2.217 2.216
2.127
2.218 2.223 2.392 2.159 2.168
2.257 2.251 2.252 2.243
2.094
2.120 2.1 15 2.1 12
2.089
2.402 2.408 2.408
2.336 2.341
2.205 2.192
2.148 2.153 2.144 2.147
2.234 2.244
2.193 2.196 2.384 2.204
2.087
2.385 2.389
2.146
2.112 2.141
2.244 2.153
2.1 11
2.310
2.372
2.230 2.244 2.173
2.104 2.142 2.141 2.235
2.186 2.197
2.31
2.189
2.079 2.079
2.368 2.385 2.181
2.292 2.220
2.131 2.133
2.136
2.188 2.218
2.140 2.138
2.07 1 2.071
2.309 2.166
2.355
2.098 2.128 2.167 2.094 2.124 2.119 2.373
2.129 2.064
2.121 2.205
2.351
The Journal of Physical Chemistry, Vol. 91, No. 1 , 1987 199
Complex Formation in Pyrosulfate Melts TABLE I (Continued)
Xvzol,mole fraction
measd temp
0.000
0.054
0.102
0.125
0.150
0.154
0.198
0.210
0.300
0.336
0.399
2.294
476 480 482 483 486 486
2.342 2.116
2.209 2.368
2.106 2.1 11
TABLE 11: Linear Density Emations and Excess Molar Volumes of the Molten V,O,-KS,O,
mole fracn
A(x),b
vzos ( x )
dcm'
0.000
2.080 (1) 2.106 (1) 2.137 (1) 2.147 (2) 2.187 (2) 2.183(5) 2.238 (2) 2.228 (1) 2.315 (3) 2.370 (1) 2.387 (2)
0.054 0.102 0.125 0.150 0.154 0.198 0.210 0.300 0.336 0.399
-0.650 -0.617 -0.709 -1.009 -0.835 -1.160 -0.590 -0.843 -1.102 -0.871 -0.712
(27) (54) (28) (50) (54) (24) (52) (37) (15) (35) (58)
'For the measured temperature ranges consult Table I. b p = A(X)
TABLE III: Values of Coefficients in the Empirical Polynomial' for Densities of the Molten V90,-K,S20, Svstemb
4,
A,,
4,
g/cm3 g/cm'
g/cm'
g/cm3
2.0813
0.1393
4.918
-10.981
+
+
' p = A,
Az,
A,X
A#
+
A$
4,
104B1, g/
g/cm3 (cm'deg)
SD, g/cm3
6.547
-8.935
0.012
+
A N
+
Bl(t
-
System'
excess molar vo1: cm3/mol
SD, dcm'
430 "C
475 o c
0.001 0.003 0.003 0.005 0.004 0.010 0.003 0.005 0.003 0.003 0.006
0.000 -0.329 (167) -1.14 (16) -1.49 (26) -2.85 (20) -2.86 (49) -4.03 (14) -3.52 (24) -5.58 (13) -6.79 (12) -5.81 (23)
0.000 -0.521 (172) -1.13 (17) -0.828 (271) -2.65 (21) -1.94 (52) -4.48 (15) -3.44 (24) -5.27 (13) -6.97 (12) -6.34 (24)
+ B ( X ) ( t - 450).
CCalculatedon the basis of eq 3.
2 -25
450).
bTemperature range: The upper limit is 490 "C and the lower limit is obtained from Table I. Mole fraction range 0.000 6 Xv,o, Q 0.3999.
"C); as discussed previously21 this equation gives a more satisfactory representation of the measured data than the usually employed equation p = A(X) B(X)t. p is the density in g/cm3, t is the temperature in OC,A(X) is the density at the composition Xvzo3at 450 OC, and B ( X ) is the density change per degree at the composition Xvzo5.The standard deviations for the densities are rather high, reflecting the experimental difficulties concerned with these melts of high viscosity. Table I1 also lists the values of the excess molar volume of the melt a t 430 and 475 OC calculated from eq 3. In eq 3 the densities of the melt at different compositions are taken from Table I1 and the density of V205in the extrapolated liquid state is calculated as described under General Considerations. As an example the densities at 430 and 475 O C of the molten V205-K2S207system as a function of the composition are shown in Figure 2 . The full-line curves are made on the basis of the general polynomial given in Table 111. On the right axis is shown the excess molar volumes at 430 and 475 OC at different compositions of the melt. The dashed curves are calculated from eq 3 also by using densities obtained from the general polynomial given in Table 111. It can be seen that the excess molar volume most probably has a maximum around Xvzo5= 0.33.This might reflect the formation of a complex in solution obtaining the maximum concentration at the molar ratio V205:K2SZ07 of 1:2 as will be discussed later. For general use an empirical equation for the density at all temperatures and compositions in the ranges investigated here is also calculated. Values of densities of molten V205 in the extrapolated liquid state have also been included in the calculations. The equation is of the form p = C&4,$" CyB,(t 450)", and the most satisfactory values of n and m were found to be 4 and 1, respectively. The calculated coefficients, A , and
+
+
(21) Andreasen, H. A.; Bjemm, N. J.; Hansen, N. H. J . Chem. Eng. Data 1980, 25, 236.
xv205
Figure 2. Upper curves: Density isotherms for the molten KzSZO7-VzOS system. Lower curves: Excess molar volume isotherms for the molten K2S2O7-V2O5system. The half-filled circle represents a coincidence of
a filled and an open circle.
B,, are given in Table 111. It should be noted that the standard deviation is higher when this general equation is applied instead of the equation given in Table 11. However, from the general equation and the equation of Table I1 for pure K2S207at 430 O C , deviations from the work of Hansen and Bjerrum2 of only 0.2% and 0.5% are found, respectively. Conductivity Measurements on t h e Vz05-KzSz0,System in the Temperature Range 350-480 O C . The conductivity of the V205-K2S207system at 15 different compositions in the mole fraction range Xvzos= 0-0.5 and the temperature range 350-480 O C has been measured as shown in Table IV. For each value of Xvzo3the experimental data could be expressed by the polynomial K = A ( X ) B ( X ) ( t - 450) C(X) ( t - 450)2 D(X) ( t - 450)3 where K is the conductivity in 9-'cm-' and t is the temperature in OC. In Table V the coefficients are given for the different compositions along with the standard deviations. It is
+
+
+
200 The Journal of Physical Chemistry, Vol. 91, No. I, 1987
Hatem et al.
TABLE I V Specific Conductivity, K (Q-'cm-I), of the V20rKZS20, System at Different Molar Fractions, XVpgand Temperatures, t ( " C ) t K A: Xv20J 0.0000 425.0 426.5 430.0 43 1.O 431.5 435.0 436.0 440.0 441.5 446.0 446.5 450.5 45 1.O 451.5 455.0 456.5 460.5 461.5 466.0 466.5 466.5 470.5 471.5 475.0 476.0 476.5
0.248 0 0.248 8 0.258 0 0.2600 0.258 3 0.267 8 0.268 0 0.277 8 0.278 3 0.287 9 0.288 0 0.298 0 0.300 4 0.298 3 0.307 6 0.308 7 0.318 3 0.3188 0.328 8 0.329 0 0.329 5 0.339 1 0.339 5 0.349 0 0.350 3 0.349 8
B: Xv, 420.5 425.5 430.5 433.0 441.0 446.0 450.5 455.5 460.5 466.0 470.0 475.5
c: 420.5 425.5 430.5 435.5 441.0 446.0 450.5 455.5 460.5 465.5 470.5 475.5
0.222 6 0.2136 0.231 9 0.235 8 0.250 9 0.260 5 0.269 0 0.279 8 0.289 6 0.299 5 0.309 6 0.3200 XV2,, = 0.1112 0.1720 0.1803 0.1889 0.197 3 0.206 2 0.215 3 0.224 2 0.233 2 0.242 5 0.251 7 0.261 1 0.270 6
D: Xv, 420.5 425.5 430.5 435.5 441.0 446.0 450.5 455.5 460.5 466.0 470.5 475.5
= 0.0480
= 0.1494 0.148 9 0.1568 0.1648 0.173 1 0.181 5 0.190 1 0.198 5 0.207 3 0.215 9 0.224 9 0.233 9 0.243 0
t
K
'
E: Xv20s= 0.201 1 420.5 426.0 430.5 436.0 440.5 446.0 450.5 455.5 460.5 466.0 470.5 475.5
0.1273 0.1348 0.1423 0.150 1 0.1582 0.166 2 0.1744 0.1827 0.191 1 0.1996 0.208 4 0.2167
F: Xv205= 0.2589 381.0 391.0 401.0 411.0 421.0 426.0 43 1.O 436.0 441.0 446.0 451.0 456.0 461.0 466.0 47 1.O 476.0
0.045 17 0.054 38 0.064 86 0.076 50 0.088 80 0.095 17 0.101 8 0.108 7 0.1158 0.1230 0.1305 0.1396 0.1480 0.1562 0.165 2 0.1747
G: Xv20s= 38 1.O 391.5 401.0 411.0 421.5 426.0 43 1.O 436.0 441.5 446.5 45 1.5 456.5 461.5 466.5 471.5 476.0
0.3000 0.031 85 0.039 20 0.048 09 0.058 03 0.068 93 0.074 63 0.073 21 0.086 97 0.093 47 0.1000 0.1068 0.1138 0.121 0 0.1287 0.1369 0.1447
H: Xv,os = 0.3352 397.0 401.5 411.5 421.5 427.0 431.5 437.0 442.0 446.5 452.0 456.0 461.5 466.5 471.5 477.0
0.033 50 0.037 45 0.046 12 0.055 72 0.060 89 0.066 25 0.071 78 0.077 69 0.083 67 0.089 90 0.096 38 0.1030 0.1098 0.1168 0.1240
noted that the third-degree polynomial employed gives rise to standard deviations close to the uncertainty in the measurement of K, indicating that a satisfactory fit has been obtained.
t
K
I: Xv205= 0.3628 351.0 361.0 371.5 381.0 391.0 391.0 4 10.0 411.5 421.0 426.5 431.5 436.5 441.5 446.5 451.5 456.5 461.5 466.5 471.5 476.5
0.008 612 0.01223 0.01671 0.022 04 0.028 52 0.028 89 0.043 44 0.044 33 0.053 58 0.058 57 0.063 80 0.069 70 0.075 51 0.08 1 32 0.087 36 0.093 42 0.099 88 0.106 3 0.1130 0.1194
J: XvloJ = 0.3968 38 1.O 0.01689 391.5 401.0 411.5 421.0 427.0 43 1.O 436.5 441.5 446.5 451.0 457.0 461.5 467.0 47 1.5 476.5
0.022 3 1 0.028 72 0.036 18 0.044 56 0.049 11 0.05401 0.058 98 0.064 25 0.069 65 0.075 29 0.081 12 0.087 15 0.093 26 0.099 77 0.1064
K: Xvzos= 0.4257 351.0 361.0 370.5 381.0 391.0 401.0 41 1.0 421.0 426.0 43 1.O 436.0 441.0 446.0 45 1.O 456.0 461.0 466.0 47 1.O 475.5
0.003 678 0.005 637 0.008 227 0.01 164 0.01 5 84 0.020 97 0.027 04 0.034 7 1 0.038 67 0.042 92 0.047 15 0.051 93 0.056 88 0.061 59 0.067 09 0.072 73 0.078 60 0.085 40 0.093 01
t
K
L: Xvlos = 0.4509 352.0 361.0 37 1.O 38 1.O 391.5 401 .O 411.5 421.5 426.5 43 1.O 437.0 442.0 447.0 452.0 456.5 461.5 466.5 471.5 477.0
M: Xv, 351.0 361.5 372.0 38 1.5 411.5 427.0 432.0 437.0 442.0 447.0 452.0 457.0 462.0 467.0 472.0 477.0
0.003 640 0.005 449 0.008 083 0.01 1 37 0.015 55 0.020 49 0.026 53 0.033 42 0.037 20 0.041 18 0.045 42 0.049 95 0.054 56 0.059 47 0.064 54 0.069 8 1 0.075 17 0.080 86 0.086 72 = 0.4752 0.003618 0.005 529 0.008 020 0.01 1 18 0.025 75 0.035 77 0.039 45 0.043 45 0.047 79 0.052 27 0.057 01 0.061 98 0.067 22 0.072 59 0.078 26 0.083 98
N: Xv20s= 0.4988 381.5 411.5 426.5 431.5 436.5 441.5 446.5 451.5 456.5 461.5 466.5 471.5 476.5
0.01086 0.024 23 0.033 60 0.037 12 0.040 86 0.044 89 0.049 06 0.053 45 0.057 95 0.062 72 0.067 75 0.073 10 0.078 44
0:Xv20J= 0.5266 351.0 362.0 371.0 38 1.O 391.0 401.0 411.5 421.0 426.0 43 1.O 437.0 441.5 447.0 45 1.5 456.5 461.5 467.0 47 1.5 476.5
0.003 617 0.005 638 0.007 804 0.01090 0.01469 0.019 29 0.024 78 0.030 9 1 0.034 29 0.037 90 0.041 76 0.045 86 0.050 12 0.054 60 0.059 30 0.064 11 0.069 23 0.074 49 0.079 84
In Figure 3 are plotted the values from Table IV together with the respective curves determined by the polynomials defined in Table V. For clarity not all of the compositions are included in
The Journal of Physical Chemistry, Vol. 91, No. 1, 1987 201
Complex Formation in Pyrosulfate Melts TABLE V Coefficients for Empirical Equations' for the Specific Conductivity for Different Compositions, XvpS, of the V205-KzS20, Systemb xv209 IO~B(X), IO~C(X), ~ o ~ D ( x ) , A(X), em-' Q-' cm-l Q-I cm-l SD, mole fracn i2-I em-' deg-l deg-' deg-' R-' em-' 1.9935 1.831 2.555 0.001 1 0.0000 0.296343 2.1412 3.976 0.0480 0.267 847 -36.566 0.004 1 0.1112 0.222953 1.8274 2.528 -3.603 0.00031 0.1494 0.197301 1.7269 2.684 -1.019 0.00039 0.2011 0.173267 1.6632 2.367 -3.373 0.00047 1.5741 0.2589 0.129555 5.870 1.196 0.00031 0.3000 0.104 184 1.4142 5.395 0.128 0.0019 0.3352 0.087930 1.2584 3.749 -1.370 0.00042 0.3628 0.085 272 1.2074 3.762 -0.638 0.00028 0.3968 0.073 523 1.1297 4.031 -0.621 0.00040 0.4257 0.060 791 1.0680 5.689 0.741 0.00047 0.4509 0.057 668 4.435 0.9738 1.067 0.000 28 0.4752 0.055 076 0.9443 4.754 0.471 0.000 12 0.4988 0.052059 0.8835 4.220 0.149 0.000 05 0.5266 0.053 097 0.8932 4.328 0.356 0.00021
I
I
I
1
I
\. \
\
\*
" K = A ( X ) + B ( X ) ( t - 450) + C(X) (t - 450)2 + D(X) (t - 450)3. For the measured temperature ranges consult Table IV.
0 L,
1
I
I
I
I
I
01
02
03
04
05
6
Figure 4. Conductivity isotherms for the molten K2S20,-V205 system.
TEMPERATURE ('0
Figure 3. Conductivity of the K2S2O7-V2O5system for the following different compositions;Xv20; A, 0.0000; B, 0.0480; C, 0.1 112; D, 0.1494; E, 0.2011; F, 0.2589; G, 0.3000; H, 0.3352, J, 0.3968; 0, 0.5266. For clarity the data for some of the measured compositions, Le., I, K, L, M, and N of Table IV. are not shown.
this figure. It is seen that the conductivity decreases with decreasing temperature as should be expected and that it decreases drastically with increasingly amounts of V2O5 added to the melt. Another way of presenting the data is shown in Figure 4. The conductivity is here plotted vs. the composition of the melt. For simplicity only two curves are shown representing the conductivities at 430 and 415 O C . The data points are calculated by using the polynomials of Table V. A steep decrease of the conductivity is observed when increasing amounts of V205are added to the melt. However, around the composition Xv,05= 0.33 the curve shows a "break" and from Xv205= 0.4 the conductivity decreases less and less steeply toward the mole fraction value Xv20sof around 0.5. At this composition the melt most probably becomes saturated, since further addition of V205 results in the visible presence of solid V2O5 in the cell. The observation that the resistance at this composition becomes immeasurably large (probably caused by a blocking of the capillary tube by a poor conducting solid) indicates also that the melt is saturated with respect to V2O5. As will be discussed later; the break at the molar ratio V205:K2S207 = 1:2 and the presence of the saturation point near V205:K2S207 = 1:l indicate that complexes might be formed to a maximum extent at these compositions. Applying eq 4 to the measured conductivities given in Table IV for pure molten K&07 gives rise to a straight-line relationship (within the experimental error) of In K vs. 1/T. From the slope of the line a value of 29.4(2) kJ/mol can be calculated for E, and from the intercept a value of 39.6(14) Q-' cm-' for the constant
A,. These values deviate rather much from values of around 23.0 kJ/mol and 19.2 9-' cm-' found for E , and A,, respectively, by applying literature data3 in the same way. However, the conductivity measured previously3for K2SZ07is in general 20% higher than the values found by us. This is probably caused by contamination by K H S 0 4 of the commercial K2S207used. It has been shown2that a commercial analytical grade K2SZO7 consisted of more than 60% KHS04. Furthermore, extrapolation of the conductivity dataz2for molten KHSO, in the temperature range 21 1-300 O C to the temperature region of molten K&O7 (Le., above 419 "C) shows that an appreciably higher conductivity (around three times as high) should be expected compared to pure K2SzO7. This indicates that contamination of K2S20, by KHS04 indeed may give rise to an increased conductivity of the melt. Returning to the V205-K2Sz07system, the only paper4 dealing with the conductivity seems also to be based on melts contaminated by K H S 0 4 since the K2S2O7 used was obtained by dehydrating K H S 0 4 at 450 OC-a doubtful5 method of synthesis. Thus, calculations based on the diagram given in ref 4 show that the conductivity at 450 "C for the composition Xv20s= 0.17 (K/V = 5) is around 25% higher than found by us. However, the values = 0.25 and 0.50 are around 5 times for the conductivity at Xv205 lower while the conductivity at Xv20!= 0.33 compares well with our value. The earlier results thus indicate that there is a pronounced maximum for the conductivity in the composition range XVloJ= 0.25-0.50. In any case it is clear that there is a large discrepancy between our results and the results published earlier on the V2O5-K2S2O7system. The values of In K and 1/ T have been calculated for all the data in Table IV. There are three branches in the In K vs. 1 / T relationship most probably representing liquid, liquid + solid, and solid state of the mixture in the cell. By identifying these different phases the curves enable us to estimate the liquidus point and the melting points of solids formed in the binary V205-K2S207 system. For some compositions the temperature range studied was not sufficiently large to obtain results for the solid state and, for Xv20s lower than 0.2589, only data for the liquid state were examined. Further conductometric measurements in the K2S207-richregion (22) Rogers, S.E.: Ubbelohde, A. R. Tram. Faraday SOC.1951,46, 1051.
202 The Journal of Physical Chemistry, Vol. 91, No. I , 1987
Hatem et al.
TABLE VI: Values of Coefficients in the Empirical Polynomial' for Specific Conductivitiesof the Molten VZOsK&O7 Systemb
0.29728
+
= A,, A,X Xv201S 0.5266. ' K
-0.67683
0.60039
-5.16572
16.83730
-14.93280
1.4715
+ Az$ + AJ3 + A@ + A# + B,(t - 450) + B,(r - 450)2. bTemperature range:
2.5592
0.0070
410-480 OC. Mole fraction range 0.000 S
TABLE VII: Experimental' and CalculatedbMolar Conductivities and Percent Deviation between These Values at Different Mole Fractions of V205in the Molten V2OrK2S2O7 System; ParametersCfor the Temperature Dependency of the Equivalent Conductivity of the Potassium Ion hex
*LlCd.
113
0-1cmfmol-1
XV20J' mole fracn
430 OC
0.0000 0.0480 0.1112 0.1494 0.201 1 0.2589 0.3000 0.3352 0.3628 0.3968 0.4257 0.4509 0.4752 0.4988 0.5266
31.1 (2) 27.2 (5) 21.4 (1) 18.2 (1) 15.1 (1) 10.3 (1) 7.76 (20) 6.25 (5) 5.99 (4) 4.94 (5) 3.85 (5) 3.64 (3) 3.44 (2) 3.23 (2) 3.28 (2)
475
0-l
o c
42.9 (3) 38.4 (5) 31.3 (2) 27.3 (2) 23.4 (1) 18.0 (1) 14.5 (2) 12.0 (1) 11.4 (1) 9.94 (6) 8.57 (6) 7.89 (5) 7.53 (4) 7.00 (4) 7.05 (4)
cm2 mol-'
430 "C 31.1 (13) 28.2 (13) 24.6 (12) 22.5 (11) 19.9 (11) 17.1 (10) 15.3 (9) 13.8 (9) 12.7 (9) 11.4 (8) 10.3 (8) 9.42 (74) 8.61 (70) 7.86 (67) 7.02 (63)
475 OC 42.9 (14) 38.9 (13) 34.0 (12) 31.1 (12) 27.5 (11) 23.7 (10) 21.1 (10) 19.1 (9) 17.5 (9) 15.7 (8) 14.3 (8) 13.1 (8) 11.9 (7) 10.9 (7) 9.74 (66)
430 0.0 -3.5 -13.0 -19.1 -24.1 -39.8 -49.3 -54.7 -52.8 -56.6 -62.6 -61.3 -60.0 -58.9 -53.3
deviation,d % OC 475
ELK+>
oc
0.0 -1.3 (0) -7.9 (3) -12.2 (5) -14.9 (6) -24.1 (10) -31.3 (15) -37.2 (18) -34.9 (18) -36.7 (19) -40.1 (23) -39.8 (24) -36.8 (22) -35.8 (23) -27.6 (19)
(2) (6) (9) (13) (23) (32) (36) (38) (40) (49) (48) (49) (50) (48)
1o - ~ A ~ , ~ + ,
kJ mol-'
Q-' cmz mol-'
31.2 33.2 37.3 40.0 43.5 55.3 61.8 64.5 63.5 69.3 78.1 76.1 74.5 71.8 70.0
3.24 (3) 4.23 (16) 7.09 (6) 10.06 (9) 15.20 (17) 88.78 (76) 215.6 (57) 294.2 (43) 247.5 (43) 575.5 (91) 2141 (24) 1501 (22) 1141 (14) 715.0 (65) 578.4 (67)
(3) (13) (3) (4) (5) (5) (16) (9) (11) (11) (9) (11) (9) (7) (8)
'Calculated on the basis of the equations given in Tables 111 and V and eq 7. bCalculated on the basis of conductivities of the initial compounds, K2S2O7and V z 0 5 , and the equation given in Table 111 and eq 8. CCalculatedon the basis of eq 5 and 6. d[102(A,,,,l - Acalcd)]/Acalcd.
are in progress, and the phase diagram for the whole composition range XvZo5 = 0-0.5 will be obtained. For general use an empirical equation for the conductivity-as for the density-can be. calculated on the basis of the conductivity at all the measured temperatures and compositions in the liquidus range of the V205-K2S207system. The equation is of the form K = z y B , ( t - 450)" and the satisfactory n and m values were found to be 5 and 2, respectively. The values of the calculated coefficients A , and B, are given in Table VI together with the standard deviation. Appropriately the standard deviation is higher when this general equation is applied compared to the use of the more specific equations of Table V. On the basis of the measured conductivities and the densities from the general polynomial (Table 111) and under the assumption that K+ is carrying all the current the equivalent conductivity of the potassium ion hK+can be calculated by applying eq 5. This has been done for each composition in the composition range XvzOs = 0-0.5 and for those temperatures above the liquidus temperatures. The values of In hK+show a linear relationship with the reciprocal of the absolute temperature at each composition indicating the correctness of the assumption that the potassium ion carries the major part of the current. From the slope and intercept of these lines the value of EbK+and AAK+can be calculated for each composition via eq 6 as shown in Table VII. A remarkable increase in the activation energy for migration of the potassium ion is observed when increasing amounts of VzOs are added to the melt. Furthermore, both parameters possibly have maxima around XvZo5 = 0.33 and 0.42. Complex Formation. The earlier investigation^'^^'^ and investigations in p r o g r e s ~ on ' ~ the ~ ~ dilute ~ and more concentrated solutions of Vz05in KzSzO7 show that VzOs probably transforms to V(V) complexes of the so-called pyrosulfovanadate type by the strong exotermic dissolution process. This type of complex formation in the melt may also gain support from the isolation9 of the potassium pyrosulfovanadates KV02S04,K4(V0z)2(S04)zSzO7, and K3V02S04S207 from the molten binary system. Also the very recent isolation and i d e n t i f i ~ a t i o nof ~ ~the , ~ ~lower valence
These complexes are expected to be formed to a maximum extent in the binary V205-K2SZ07system at the compositions Xv20s= 0.25, 0.33, and 0.50, respectively. On the basis of recentI4Js calorimetric measurements, complexes seem to be formed to a maximum extent at XvzoJ= 0.33 and 0.50, corresponding probably to the dimer complex (V02)z(S04)2S2074and most reasonably polymer complexes formulated as (VOzS04),"-. No indication of any significant concentration of the third complex, Le., = 0.25. V02S04Sz073-,was found at the composition XvzOJ The present investigation of the density and the conductivity of the molten binary V2O5-KZSZO7system also indicates that a drastic change of the structure of the melt occurs at XvZo5 = 0.33 and in addition that the change is terminated at around XvzOs= 0.50 where the melt becomes saturated with respect to VzO5. These observations are in accordance with the formation of complexes indicated in eq 10 and eq 11 where the latter complexes most probably are polymeric accounting for the high viscosityz6 of the melt. The increasing and high energy of activation for the migration of the potassium ions observed in the melt as the composition approaches saturation is in accordance with the increase in viscosity at higher concentrations of VzO5. The energy of activation for the viscosityz6also seems to approach a maximum close to Xvz0,= 0.5. Further support for a strong interaction between the two components of the melt is also obtained from
(23) Hatem, G.; Fehrmann, R.; Gaune-Escard, M.; Bjerrum, N. J., to be submitted for publication. (24) Fehrmann, R.; Krebs, B. Paptheodorou, G. N.; Berg, R. W.; Bjerrum, N. J. Inorg. Chem. 1986, 25, 1571.
(25) Fehrmann, R.; Boghosian, S.; Nielsen, K.; Berg, R. W.; Papatheodorou, G. N.; Bjerrum, N. J., to be submitted for publication. (26) Ivanenko, S. V.;Torocheshnikov, N. S.; Saltanova, V. P. Zh. Vses. Khim. Oua. im. D . I . Mendeleeva 1972, 17, 110.
z$4,,P+
compounds KV(SO& and K4(V0)3(S04)sby interaction of SO2 with the melts add to the probability of the existence of vanadium-oxosulfato complexes in the melts. Reactions accounting for the formation of V(V) complexes in accordance with the stoichiometry of the above-mentioned V(V) compounds and the V(V) complexes found in the dilute meltsI2 are v205
-
+ 3s20~~-2 v o z s o 4 s z o 7 3 -
VzO5 + 2Sz072VzO5
(VOz)z(S04)zSz074-
+ S20T 2-
2VOzS04-
(9) (IO) (11)
J . Phys. Chem. 1987, 91, 203-210 the other data presented in Table VII. Here the experimental molar conductivity a t 430 and 475 "C, Acxptl,is obtained from eq 7 by using the measured densities and conductivities. The calculated molar conductivity Amid is obtained from eq 8 by using values of AK2s20,and AVloJcalculated on the basis of the general polynomial for the density (Table 111) and the specific conductivities of molten K2S2O7 and V205 (in the extrapolated liquid stateI9). The percentage difference between Aexptland Acald is also calculated. The very large negative deviation (up to around -60%) suggests20that most probably complexes are formed in the system. Usually20 complex formation is considered to take place for deviations higher than about 5%. The restricted ability for the melt to dissolve more V205when Xv205is 0.5 indicates that V2O5 is probably only soluble in the melt when residual pyrosulfate ions are present. This investigation also indicates that monomeric complexes, VO2SO; and V02S04S207"-,might only be important in melts very dilute with respect to V2O5 and that they might not be formed to any appreciable extent at higher mole fractions of V205 (since no signs-of breaks are found on the density or con-
203
ductivity curves at Xv20s= 0.25). The possible structures of the complexes (V02)2(S04)2S2074and (V02S04),w have been discussed re~ent1y.I~ The former probably contains an oxygen double bridge and bidentate coordinate sulfate and pyrosulfate ions making the coordination number of 6 possible for vanadium. The latter is probably a chain like complex where the vanadium atoms with a coordination number of 4 are linked together with bidentate coordinate sulfate ions. Further evidence for the existence and structures of the species proposed in this paper is being sought through planned NMR, IR, and X-rays investigations on liquids and solids of the V205-K2S207system.
Acknowledgment. This investigation has been supported by the Danish Technical Science Research Foundation, the French National Center of Scientific Research, and the European Economic Communities (EEC) in accordance with contract No. STI-011-J-C(CD). Registry No. V205, 1314-62-1; K2S207,1190-62-1.
Concentration-Dependent Main-Chain Dynamics of Sodium Polyacrylate As Probed by NMR in the Semidilute Regime C. J. M. van Rijn, W. Jesse, J. de Bleijser, and J. C. Leyte* Gorlaeus Laboratories, Department of Physical and Macromolecular Chemistry, University of Leiden, Leiden. The Netherlands (Received: April 15, 1986; In Final Form: August 26, 1986)
Sodium polyacrylate chains exhibit reduced reorientationalmobility in the semidilute regime as probed by frequency-dependent nuclear magnetic relaxation experiments. Nuclear magnetic relaxation rates of deuterons have been measured in aqueous solutions of methylene-deuteriated poly(acry1ic acid) (CD2-PAA). Upon diluting a neutralized solution of CD2-PAA (sodium polyacrylate), a sharp increase of the transverse relaxation rate R2 was observed, whereas the longitudinal relaxation rate R , remained unaffected. It is shown that in the semidilute regime slow motions with correlation times > lo-* s show up irrespective of the fast (internal) motions with correlations times s. The origin of these slow motions is indicated by polyelectrolytetheory; the large correlation times are probably due to the enhanced (electrostatic) stiffness of the CD2-PAA chain in the semidilute regime. In concordance with this idea is the fact that the large correlation times decrease when a simple salt (NaC1) is added to the solution. An implication for the interpretation of counterion relaxation is discussed.
-
Introduction This paper reports a N M R study on dynamic chain behavior of methylene-deuteriated poly(acry1ic acid) (CD2-PA4). Whereas proton relaxation is usually dependent on intra- and intermolecular motion, deuteron relaxation is completely determined by the reorientational motion of the C D bonds in the polyacrylic acid chain. Deuteron relaxation is therefore a particularly suitable source of information on chain dynamics. An interesting topic in polyelectrolyte physics is the relaxation between the stiffness of a polyelectrolyte chain and its dynamic behavior's2 as probed by N M R relaxation. As will be discussed in more detail in other sections, this relation is by no means simple and straightforward. From a sufficiently extended N M R investigation one may obtain values of the spectral density function J ( w ) for the time-dependent process driving the relaxation, at a certain number of frequencies. This set of numerical values may be transformed to a set of correlation times if the functional shape of J(o)is known or assumed. For rotation diffusion models the correlation function reduces to a sum of exponentials and J ( w ) is then represented by a sum of Lorentzians. Under the assumption of rotation diffusion, relaxation rates of a polymer nucleus such (1) Yamakawa, H. Modern Theory of Polymer Solutions; Harper & Row: New York, 1971. (2) Yamakawa, H.; Fujii, M. J . Chem. Phys. 1984, 81, 997.
0022-3654/87/2091-0203$01.50/0
as 2Husually yield more than one correlation time, a typical result being three correlation times. In the next stage of interpretation these correlation times should be related to some representation of (part of) the polymer molecule. For sufficiently long polymer molecules the order of magnitude of the correlation times usually indicates that overall motion of the complete molecule cannot be the motional process involved: the dynamical unit is often considerably smaller than the polymer. Thus one is led to the concept of a dynamical persistence length, Le., the length of polymer chain involved in correlated motion. For flexible polymers in solution it may be expected that this dynamic persistence length corresponds roughly with the conformational persistence length. On relating the correlation times to a prolate Perrin ellipsoid, its short and long semiaxes will be tentatively identified with the thickness and persistence length of poly(acry1ic acid). If as another example the model of a spherical reorienting dynamical unit (with one internal rotation mode) is used, the radius of the sphere will, again tentatively, be identified with the persistence length of the polymer. Comparison with experimental estimates of these lengths should then lead to conclusions on the appropriateness of the motional model. Poly(acry1ic acid) in aqueous solution may be considered an interesting polyelectrolyte model s stem by virtue of the small intrinsic persistence length3 (- 10 ) of the main chain and the
$:
0 1987 American Chemical Society
