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Ion transport in free and supported nitrobenzene aliquat nitrate liquid membrane ion-selective electrodes
Journal of Membrane Science, 4 (1979) 379-394 o Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
379
ION TRANSPORT IN FREE AND SUPPORTED NITROBENZENE ALIQUAT NITRATE LIQUID MEMBRANE ION-SELECTIVE ELECTRODES I. BULK ELECTRICAL PROPERTIES INCLUDING ION ASSOCIATION AND DIELECTRIC CONSTANT DALE E. MATHIS and RICHARD
P. BUCK
William Rand Kenan Jr. Laboratories of Chemistry, Chapel Hill, North Carolina 27514 (U.S.A.)
The University
of North
Carolina,
(Received August 21, 1978)
Summary A controlled-thickness thin layer cell and wide-band cross correlator bridge have been used to characterize ion transport in free liquid and supported ion exchange membranes. The base system of Aliquat nitrate in nitrobenzene was measured, and transport parameters were used to establish properties of supports: cellulose triacetate, PVC-acrylonitrile, polypropylene and Teflon. From DC to 0.5 MHz impedance measurements, geometrical capacitance, electrical relaxation time constants and dielectric constants were determined over a range of temperatures and membrane loadings. Depression of dielectric constant with loading and temperature coefficients are reported. Conductivities were analyzed classically to yield equivalent conductances of ions, transference numbers and ion pairing constants. Temperature coefficients gave transport enthalpy and thermodynamic quantities. Data from supported membranes gave direct measures of void volumes of inert membrane supports, and clear evidence for cases of membrane solubilization by entrapped solvents.
Introduction The utility of ion selective electrodes as species-selective activity sensors in analytical chemistry has been extensively demonstrated. Electrodes responsive to different ions can be constructed in a variety of formats using many ion sensitive materials. The liquid ion exchanger-based electrodes are particularly important because of their versatility. They can be used to measure ion activities which cannot be measured using insoluble, conducting salts or ion sensitive glasses. At the same time, this general applicability means that liquid ion exchanger-based electrodes are more susceptible to ion interferences. Although some liquid ion exchange systems have recently been superseded by neutral carrier electrodes with superior selectivity and sensitivity specifications, e.g. Cal+ electrode [ 11, this has not been the case for anion-selective liquid ion exchanger electrodes. The Aliquat 3365, tricaprylmethyl ammonium-based ion exchange electrodes have been the most successful sensors of this kind,
380
and often exhibit Nernstian slopes over more than five orders of magnitude of activity for anions. The supported Aliquat-based systems are examples of successful electrode formats, and are worthy of detailed study from a practicsl perspective. Coljious scientific literature is concerned with various aspects and applications of the same Aliquat-nitrobenzene ion exchanger systems studied in this work. It would be difficult and unnecessary to give a comprehensive review. It is, however, instructive to cite those studies which form a fundamental data base against which the results of this work can be compared. The relevant papers of this type can be roughly divided into two categories: conductance studies of tetraalkyl ammonium salts in nitrobenzene, and electrode construction formats based on the Aliquat ion exchangers with their characteristic responses and applications. Both categories are considered in turn. Bulk electrical properties of electrolytes in nitrobenzene as solvent at 25°C have been thoroughly investigated in three early papers. Ion association constants and limiting conductances for several tetraalkyl ammonium salts in nitrobenzene have been measured by Taylor and Kraus [2] and by Witschonke and Kraus [ 31. The work of Fuoss and Hirsch [ 41 considered several other symmetrical ammonium salts, but also included an evaluation of ionic radii as well. The Aliquat ion is not considered in any of these studies and has not been investigated previously. The lack of formal literature concerning the solution behavior of Aliquat salts has in no way discouraged their use as ion exchangers in liquid membrane electrodes. Applications of Aliquat-based sensors include detection and measurement of inorganic anions [ 51, anionic detergents [6] and amino acids [7]. Even Fe(III) has been measured by forming the FeCl, salt of the exchanger [ 81. Aliquat membranes have been used with good results as coated wire electrodes for several of the above applications [ 91. While this list is not comprehensive, it demonstrates the utility of this ion exchange agent. Widespread applicability of the Aliquat-based ion exchanger electrodes makes it important that the properties of membranes containing Aliquat salts be well understood. Since the ingredients of these membranes are inexpensive and easily obtained, electrodes can be readily prepared by laboratory workers using commerical barrels, liquid ion exchangers and support materials. For this reason, users should know what effects can be expected on ion activity measurements when parameters such as exchanger concentration and composition of support materials are varied. In addition, Aliquat-nitrobenzene membranes exhibit anomalous responses when used immediately following construction. This conditioning phenomenon warrants investigation. The observations, as exemplified in Fig.1, are three-fold: (1) preliminary calibration curves are SuperNemstian; (2) electrode responses are noisy, and (3) there is a monotonic shift in the value of E” toward more negative potentials. After several hours of use in aqueous media, classical anion responses are obtained and sensors can be used for quantitative measurements. This conditioning effect on response might be caused by water
381
-LOG
(a)
Fig. 1. Potentiometric response at 2 X 10m4 M Aliquat nitrate nitrobenzene membrane to aqueous KNO, at 25°C as a function of electrode lifetime. 0, newly fabricated; x , 6 hours later; 0, 24 hours later.
uptake in the exchanger solution, by changes in the support void volume through partial solubilization of some supports in nitrobenzene, or by increasing surface rates of ion exchange due to hydrating of the support surface. It is necessary to measure these possible changes in the bulk and surface properties of ion sensitive membranes as they are used, because the effects are not presently included in the idealized models for responses of these systems. In particular, we will demonstrate quantitatively the extent of each of these proposed effects in this and the following paper. A more general reason for studying the electrical properties of the Aliquat systems in nitrobenzene is to obtain a deeper understanding of factors relevant to improved responses and design of new sensors. In addition, our investigations add to the data against which theoretical prediction and models can be evaluated in the general context of ion transport in artificial membranes. Experimental Reagents Aliquat 3368 was obtained from General Mills and converted to the nitrate form by repeated equilibration with concentrated aqueous KN03. It was then washed with distilled, deionized water and dried over molecular sieves. Reagent grade nitrobenzene used for this study was further purified by washing repeatedly with aqueous 0.1 M NazCOJ and then with distilled, deionized water. The solvent was then vacuum distilled off of Linde 3A molecular sieves. Freshly distilled nitrobenzene prepared in this way has a specific conductance less than 0.02 micro-Siemenicm.
382
Instrumentation
The admittance measuring instrument used in this study was built in the lab with the same configuration as that described by Bentz et al. [lo] but including the broad band modifications developed by Mathis and Buck [ll] . A Haake model FK2 thermocirculator was used to thermostat an oil bath in which the impedance cell was immersed for measurements. The impedance cell constructed in this lab used parallel-face platinum disk electrodes with an area of 0.193 cm2 sealed in a Teflon shroud. The two-electrode configuration employed variable spacing control in which the driven electrode was mounted on a micrometer tip, much as Hubbard and Anson [12], to allow adjustment of the cell thickness for polymer measurements. The entire cell was Teflon lined to eliminate leaching of cell walls as a source of test sample contamination. Polymer
samples
The following polymer support materials were obtained from Gelman: Metricel GA-8 (0.2 micron cellulose triacetate), Metricel Acropore AN450 (0.45 micron PVC-acrylonitrile copolymer) and Metricel # 61757 (10.0 micron polypropylene). FGLP01300 (0.2 micron Teflon) was obtained from Millipore. Procedure The “in-phase” and “out-of-phase” (quadrature) admittances of pure, dry Aliquatrnitrobenzene solutions were measured from about 3 Hz to 560 KHz at quarter decade intervals for nine Aliquat nitrate concentrations, from lo-‘M to pure nitrobenzene, and four temperatures: 20, 25, 30, and 35°C. These experiments were repeated after saturating each ion exchanger solution with water. To avoid perturbing the solution concentrations, water saturation was achieved by first equilibrating distilled, deionized water with an aliquot of sample solution and then equilibrating the rest of the sample solution with the pre-equilibrated water. Effects of polymer support on the electrical properties of the ion exchangers were studied by measuring admittances of polymer discs saturated with known concentrations of ion exchanger solution which had been secured between the planar surfaces of the platinum electrodes in the impedance cell. Calculations
Frequency dependent “in-phase” and “out-of-phase” admittances were converted into Real and Quadrature (out of phase) impedances and displayed as an impedance plane plot. Calculated parameters were determined as follows: C,
Geometric capacitance was determined by interpolating the value of the quadrature admittance corrected for stray, or parasitic, cell capacitance at o max corresponding to C, = YQ/w (YQ is the quadrature component of the admittance). A plot of log YQ vs. log w used for interpolation is shown in Fig. 2.
383
LOG
(f)
Fig. 2. Plot of log YQ vs. log f (Hz) used to determine C, for pure nitrobenzene at 25°C.
Ei3
fv
24 ilo R,
(JO Tel Wmax
Activation energy for ion transport calculated as 1.987 times the slope of a plot of ln,R, vs. l/T” (K). The fraction of the macroscopic polymer disc volume occupied by voids (not occupied at all) and experimentally defined as the ratio of R, for pure ion exchanger to R, of the same solution occluded in the polymer. C,/8.84 X IO-l4 F/cm, the dimensionless dielectric constant. Equilibrium constant for ion pair formation calculated from conductance data by the method of Fuoss and Shedlovsky [13]. Limiting salt conductance at infinite dilution was also determined by the method of Fuoss and Shedlovsky (cm’/ohm-equiv.). High frequency resistance was determined from the width of a least squares circle fit to the impedance plane data and corrected for the parallel conductance of pure solvent. Experimental impedance plane plots are shown in Fig. 3. Specific,conductance, l/R,. R, X C,,the time in seconds for the system to relax to l/e of its equilibrium value after an electrical perturbation. Angular frequency at which the quadrature impedance is a maximum or alternatively, the frequency at which the real impedance is half R, .
384
2’
(Mfl-cm)
Fig. 3. Impedance plane plot of -2” 0, 20”; +, 25”; 0, 30” ; x , 35°C.
vs. 2’ for purified nitrobenzene at four temperatures:
The following additional symbols have been used: f
Frequency in Hertz; o /2n = f. Subscript 0 indicates infinite dilution. Absolute charge (coulombs). Distance (cm). Gas constant. Absolute temperature, unless otherwise specified. Single ion transference numbers. Molar volume. Quadrature admittance. Imaginary and real components of impedance.
X+, X_ Single ion conductances. 4
Ik T L tV
YQ
Z”, 2’
Results and discussion I. Geometric capacitance and dielectric cons tan ts Results of impedance measurements on dry Aliquat nitrate-nitrobenzene solutions are presented in Table 1 for a range of Aliquat concentrations at four temperatures. These data serve as the basis for calculated values of KA and E, which are given later. Note that the geometric capacitance values become more unreliable as concentration increases, because the relative magnitudes of the quadrature admittance to real admittance is becoming smaller. At concentrations greater than 4 X 10e4 A4 the quadrature admittance can no longer be resolved in the accessible frequency range and therefore, C,, K , and r,l could not be determined. The value of K 25 determined for pure nitrobenzene of 36.0 + 0.5 agrees with the accepted value of 34.8. The small (+3.5%) error may be caused by
385 TABLE1 Bulk properties of dry Aliquat nitrate in nitrobenzene Aliquat
Temp.
cont.
(C”)
R, (ohm-cm)
0.0
20.0 25.0 30.0 35.0
60.2M 55.6 46.9 38.5
1.6x 1O-s
20.0 25.0 30.0 35.0
4.0x 10-s
.
K
7el
a0
%
0.0166 0.0178 0.0213 0.0260
3.231t.03 36.5k.3 3.19+.05 36.0+.5 3.13k.06 34.8t.7 2.94e.06 33.2t.7
194 177 147 113
2.45M 2.29 2.14 2.02
0.409 0.437 0.467 0.495
3.16k.15 3.08k.19 2.96k.16 2.87t.20
35.7k1.7 34.8*2.1 33.4*1.8 32.4*2.2
7.74 7.05 6.33 5.80
20.0 25.0 30.0 35.0
0.922M 0.857 0.804 0.747
1.09 1.17 1.25 1.34
3.1Ok.13 2.94k.08 2.88t.10 2.76k.10
35.0?1.4 33.2+0.9 32.5*1.3 31.1+1.1
2.86 2.52 2.32 2.05
8.0x 10-s
20.0 25.0 30.0 35.0
0.452M 0.419 0.392 0.371
2.21 2.39 2.55 2.67
3.08k.19 2.96k.22 2.82k.27 2.792.34
34.8%2.2 33.5+2.5 31.9+3.1 31.5+3.8
1.39 1.24 1.11 1.04
2.0x 1o-4
20.0 25.0 30.0 35.0
0.184M 0.170 0.157 0.146
5.45 5.90 6.39 6.87
2.99i.19 2.86k.04 2.67k.15 2.52k.11
33.8%2.1 32.3+0.5 30.1*1.7 28.551.3
0.550 0.486 0.419 0.368
4.0x lo-'
20.0 25.0 30.0 35.0
93.7K 87.1 81.4 76.5
10.7 11.5 12.3 13.1
2.40+.21 2.26+.31 2.12k.15 1.98k.28
27.1+2.3 25.5i: 3.5 24.0*1.6 22.4i3.2
0.225 0.197 0.173 0.151
8.0x lo-*
20.0 25.0 30.0 35.0
48.3K 45.2 42.2 39.1
20.7 22.1 23.7 25.6
2.0x 1o-3
20.0 25.0 30.0 35.0
21.2K 19.6 18.5 17.2
42.2 51.0 54.0 58.1
1.0x 10-2
20.0 25.0 30.0 35.0
5.52K 5.15 4.72 4.35
181 194 212 230
(M)
(fiSiemen/cm) M/cm)
(C,/C, vat)
(@I
an error of less than 0.1 pf in the stray capacitance determined for the empty impedance cell and is therefore acceptable in this study. The temperature dependence of K determined for pure nitrobenzene follows a typical exponential law [ 141 and a least squares analysis of log K vs. 2’ for our results and
386
literature data gives the following coefficients: log
K (!!‘)fit
=
(-2.15
log K ( T)exp = (-2.74
f .05) X 1O-3 T (“C) + (1.593 + 0.005) * .47) X 103 T(C)
+ (1.62 ? 0.01)
(1) (2)
Agreement between intercepts is good, but the slopes are not within experimental error. Rather than a systematic error, the small data set and the narrow temperature range studied may be responsible. Capacitance measurements are not restricted to pure nitrobenzene and so dielectric constants can also be obtained for the ion exchanger solutions. Data for pure solvent are-more accurate than corresponding electrolyte solution values because the resistance of pure solvent is maximum and capacitive admittance can be resolved at lower frequencies. Despite uncertainties in the dielectric measurements on Aliquat nitrate solutions, previously unreported trends are evident. Table 2 lists the coefficients from the linear regression analysis for the equation 1OgK
=AT+B
(3)
TABLE 2 Coefficients
of log K = AT + 3
Cont. (M)
A x 10” (“C-l)
B
0.0 0.0 1.6 4.0 8.0 2.0 4.0
-2.15+ 0.05 -2.74* 0.46 -2.88* 0.17 -3.26 f 0.35 -3.02+ 0.45 -5.06* 0.28 -5.495 0.12
1.593+ 1.62 f 1.61 + 1.61 ? 1.60 f 1.63 * 1.54 +
(Lit.) (Exp.) x 1O-S x 10-s x lo-” x lo-’ x lo-’
Correlation coefficient .005 .Ol .Ol .Ol .Ol .Ol .Ol
0.999 0.972 0.995
0.988 0.978 0.997 0.999
for all Aliquat solutions measured. Although this relationship has not been widely verified for dilute ionic solutions, all of the correlation coefficients are close to unity. The zero temperature intercepts are unaffected by Aliquat concentration but the temperature coefficients increase with salt concentration. This result suggests an increased activation barrier for solvent dipole structure breaking as the local electric fields increase with ionic strength. Although it is not surprising that the addition of point charges should have this effect, a viscosity increase by addition of viscous Aliquat salt may also be involved. II. Conductance The AC techniques for frequency-dependent impedance measurements can give information on both AC and, in the limit, DC steady state conductances of electrolyte solutions and membranes. Efficiency depends on the reversibility of the contacting electrodes. For blocking platinum electrodes used in this study, only the AC conductivities can be computed from the so-
387
called infinite frequency resistance. The latter appears in series with the capacitance of the blocking electrodes in the equivalent circuit of the electrolyte/ membrane cells used here. The real admittance is not frequency-dependent and, unlike dielectric constants, can be determined for concentrated electrolytes. When the conductance is significantly less than the reactance of the series double layer capacitance of the blocking platinum electrodes, the conductivity can be computed with an accuracy determined by the AC instrument. In this study, conductivity values are accurate within 3%. Conductance data for dry and wet bulk ion exchanger electrolyte solutions are presented in Tables 1 and 3, respectively. Values at four temperatures were used to determine activation energies of ionic transport as a function of exchanger concentration and water uptake. These results are reported in Table 4 according to the relationship (5= (3’ exp (-&JR
T)
(4)
Each was experimentally determined by the equivalent method of measuring the slope of a plot of In, R, vs. l/T as shown in Fig. 4. TABLE 3 Bulk properties of wet Aliquat nitrate in nitrobenzene Temp. (“C)
20.0
25.0
30.0
35.0
Aliquat cont. (M)
R,(ohm-cm) o0 (clS/cm)*
R, (ohm-cm) oD (d/cm)
R,(ohm-cm) o. (d+xn)
R,(ohm-cm)
2.0 x lo-’
0.200M (5.00)
0.185M (5.41)
0.173M (5.78)
0.162M (6.17)
4.0 x lo-’
98.8K (10.1)
91.8K (10.9)
85.4K (11.7)
79.7K (12.5)
8.0 x 1O-4
50.OK (20.0)
46.5K (21.5)
43.6K (22.9)
40.9K (24.4)
2.0 x 1o-3
21.4K (46.7)
20.OK (50.0)
18.7K (53.5)
17.6K (56.8)
1.0 x 1o-2
o0 W/cm)
5.88K
5.47K
5.11K
4.85K
(170)
(183)
(196)
(206)
*uO values given in parentheses.
III. Equivalent conductivities and ion pairing thermodynamics Values of KA and A0 for wet and dry solutions, calculated from a computer-optimized Shedlovsky analysis of the concentration-dependent conductances, are given in Table 5. The Shedlovsky plots for this analysis are shown in Fig.5. A few percent variation between KA and A0 at 25°C for wet vs. dry solutions can be observed, but this variability is thought to be caused by in-
389
TABLE 5 KA and A, values for Aliquat nitrate in nitrobenzene State (wet or dry)
Temp. (“C)
dry
20.0 25.0 30.0 35.0 25.0
dry dry dry wet
1
3
28.2 30.3 32.3 34.4 29.1
131 133 120 108 140
5
7 ACSF*
9
11
13
(~10~)
Fig. 5. Shedlovsky plot used to determine A., and KA at four temperatures. 0, 20” ; X , 25”; 0, 30”; l, 35°C. S is the Shedlovsky function and F* is the square mean salt activity coefficient.
From analysis of limiting salt conductances of Aliquat nitrate at 25”C, A,-,25 = 30.3. (h-25), was measured as 22.6 for nitrate ions in nitrobenzene [ 151. Thus, for the Aliquat cation, (x+*5)o = Ao-(x-*5)o
= 7.7
(5)
The corresponding transference numbers of these ions are: (t+25),, = (X+25),, /A0 = 0.25 for the Aliquat cation (t-*5)*
= (x-2S)o /A, = 0.75 for the nitrate ion
A Wilke-Chang
(6a) (6b)
plot of (X+25),, vs. v- O-6[ 161 for a homologous series of
Fig.6.
Wilke-Chang
plot
of data in Table
6.
spherically symmetric quaternary ammo&urn ions, using data compiled by Taylor and Kraus [ 171 is shown in Fig.G._The limiting conductance of the Aliquat cation is plotted at the values of V determined by the empirical relationship: V (A3) = 1.33 X mass (g)
(7)
The validity of this relationship is demonstrated in Table 6. The fact that the specific conductivity of the Aliquat cation lies on the Wilke-Chang line asserts the spherical symmetry of the molecule in spite of its asymmetric substitution. A Wilke-Chang plot was chosen instead of the classical Stokes radius analysis because the former yields the expected zero intercept. Both plotting methods assert the spherical symmetry of the Aliquat cation. Comparison of KA’~ values for Aliquat nitrate and tetrabutyl ammonium TABLE
6
Data for Wilke-Chang
plot
Cation
Mass
1.33
(Et),N+
130 186 242 298 452
172.7 247.1 321.5 396.0 600.6
(Pr), N’ (Bu),N+ (Pe),N+* (Cap),MeN’
*Pe = Pentyl.
X mass
Vii* (a3)
V-.6 X 10’
(A+),
171.5 247.4 323.0 396.6
4.56 3.66 3.12 2.76 2.15
16.2 13.3 11.7 10.0 7.7
391
nitrate may appear contradictory because the former was found to be 133 whereas the latter ion has a smaller spherical radius but a KA’~ of only 40 [ 181 Apparently the dominant radius for Aliquat is determined by the methyl group. An effective radius less than the mean size of the dapryl group is also suggested from the enthalpy values. The temperature dependence of KA for dry exchanger solutions given in Table 4 gives the following values for the thermodynamic quantities of ion pair formation for Aliquat nitrate in nitrobenzene; AG” = -2.88
+ 0.03 Kcal/mole
(8)
AH” = -2.53
f 0.75 Kcal/mole
(9)
AS” = +1.16 * 2.50 Cal/degree-mole
(10)
A large uncertainty in AS” does not invalidate a small magnitude for this quantity. This result suggests that the nitrobenzene solvent sphere, which must be removed prior to ion pair formation, is very loosely coordinated. The value of AH” is more reliable, and can be used to estimate the separation distance of charge centers in the ion pair from the following relationship: p=
AH” =
00
s
(-$/K
r’)dr
(11)
r=IP
where g is the value of the unit charge, K is the dimensionless dielectric constant of the solvent and r is the separation between charge centers. This analysis for Aliquat nitrate gives a value of 3.6 A for the ion pair nuclear separation distance when K = 34.8. However, it has been shown in this study that K decreases dramatically with Aliquat salt concentration. Because AH” was determined using concentrations from 10e4 to 10e2 M, it is not valid to use the K for pure solvent in this calculation. Assuming an intermediate dielectric constant of 22.4 (25°C for 2 X 10m4 M), a more likely value of 5.9 A is obtamed for r. Since the radius of nitrate ion is about 2 A, a radius of about 3.9 _&for Aliquat cation is indicated. This value is near the radius of tetramethyl (3.47 A) and tetraethyl (4.0 A) ammonium cations. It therefore appears that during ion pair formation, nitrate can approach the charged nitrogen center as closely as the single methyl group permits. IV. Support void volumes and reactivity in nitrobenzene Numerical values of Ea2’, f, and K 25, experimental and calculated, for four commonly used polymer membrane support materials impregnated with 2 X 10e4 M ion exchanger (to swamp out any effects of fixed sites) are reported in Table 7. Activation energies for ionic transport of Aliquat nitrate in Acropore and polypropylene are the same, within experimental error, as that for unsupported solutions. This result means that bulk properties of the ion exchanger are not influenced by occlusion in these polymer supports. The GA-8 (cellulose triacetate) support gave a significantly larger transport
392
TABLE
I
Polymer
support
Polymer
data
Composition
Pore
-5
K*s(exp.)
~*~(calc.)
Kzs(polymer)
0.40 k.04
3.08 i.43
21.8 il.1
17.9 t1.2
7.5
0.36 t.04
2.55 +.25
12.8 * .7
14.2 k1.3
-4
0.10 ‘.Ol
2.58 t.09
7.4 .7
5.3 i.4
2.3
t
1.4 t.1
2.3 t.2
2.0
f,
(Kcal/mole)
size M&rice1 GA-8
cellulose triacetate
0.2 v
Acropore AN450
pvcacrylonitrile
0.45
Metricel 61757
polypropylene
10 IJ
Millipore FGLPOl300
Teflon
0.2 Jl
Ir
.Ol
activation energy. In addition, during the experiment the polymer membrane changed irreversibly from opaque’to clear and became brittle. Repeated washing with methanol to remove the exchanger did not restore the original opacity. These observations are interpreted, in agreement with the literature, to mean that this polymer is partially solubilized and its pores partially collapsed in nitrobenzene. The increased value of E, is thought to occur by interaction of the exchanger with solvated polymer, and the large uncertainty is attributed to non-steady state measurements, since the polymer is degrading during the experiment. A value for E, could not be obtained for the Teflon support because of its large thermal coefficient of expansion and very low void volume. When the temperature was raised, polymer expansion significantly perturbed the void volume and decreased the amount of ion exchanger in the polymer. Empirical dielectric constants for polymer supports impregnated with Aliquat nitrate ion exchanger are also reported in Table 7. Predicted values were calculated using the sum of the volume-fraction-weighted dielectric constants of the pure components as follows: x25 calculated = f& 25
(Aliquat-nitrobenzene)
+ (l-
fv)~ 25(polymer)
(12)
Experimental and predicted values of K are in good agreement for the nonreactive supports, acropore and polypropylene. This result is consistent with the lack of interaction between the polymer and the exchanger in these supports because of the complete failure of eqn. (12) when applied to the other polymer supports. Polymer GA-8 is anomalous in that the experimental values are significantly higher than predicted. The value for Teflon is controlled entirely by the polymer because of its low void fraction. Conclusions Solutions of Aliquat 3368 nitrate in nitrobenzene have been shown to be weakly associated liquid ion exchangers in which the bulk electrical proper-
393
ties are unaffected by equilibration with water. Variation of conductance with Aliquat salt concentration, or “loading”, follows the square root of concentration dependence typical in largely dissociated ionic solutions. Increased loading of the ion exchanger causes very pronounced depression of the solution dielectric constant. This observation has possible fundamental effects on ion selectivity. For example, it has been shown previously that the selectivity of dissociated liquid membrane ion selective electrodes is independent of membrane loading except when the ion exchange constant is influenced by the bulk properties of the ion exchange agent or solvent [ 191. A further property which strongly influences selectivity, as shown by Stover and Buck [20], is the degree of association, a loading-dependent parameter which can significantly influence selectivity ratios for ions of different size. It is expected that a reduction of the membrane dielectric constant will generally enhance existing selectivity of the larger ion [ 211. This conclusion together with the findings of this paper suggest that the selectivities of this sensor should be improved by increasing membrane loading. The enhancement of selectivity by increased membrane loading may be obtained at the expense of an increased limit of detection when exchanger partitioning is controlling the potentiometric response at low sample ion concentration [ 221. This result, however, is not always the case, and in a later paper we will demonstrate how the limit of detection may actually be improved by increasing the ion exchanger concentration. Potentiometric response times are a second property of ISE’s* which can be controlled by the properties of the membrane. In this case, bulk electrical relaxation has been shown to be about 0.2 ms for pure solvent, which is the slowest possible value. Rapid relaxation is consistent with the expected values of limiting conductance for Aliquat nitrate relative to other tetraalkylammonium nitrate salts. Short relaxation times indicate that the potentiometric response time of these sensors is controlled by ionic diffusion through an unstirred layer of solution at the membrane surface [23] or slow interfacial kinetics. It has been shown here that the use of polymer materials inert to the membrane solvent as a support medium does not affect the electrical properties of the bulk exchanger solution. Rather, these heterogeneous systems can be modeled simply as a polymer lattice with voids filled by exchanger, and their electrical properties calculated from the weighted properties of the pure components. Lack of interaction between exchanger and support has been demonstrated only for inert polymers with appreciable void fractions, and this principle probably cannot be successfully applied to low void fraction membranes. Useful support materials need only be inert to membrane solvent, wettable by the membrane solvent, and hydrophobic. Transport enthalpy discriminates inert membrane supports from those which are degraded by solvents. It has also been shown that changes in the ion exchange solution because of water uptake do not affect transport parameters in free liquid and inert support *WE
= ion selective
electrode.
394
effects, time dependent interfacial rates, and hydration layers are investigated in Part II of this series [24] .
membranes. Conditioning Acknowledgement
This work was supported by National Science Foundation Grant CHE7500970-A01 and CHE77-20491. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
D. Ammann, M. Giiggi, E. Pretsch and W. Simon, Anal. Letters, 8 (lo), (1975) 709. E.G. Taylor and C.A. Kraus, J. Am. Chem. Sot., 69 (1947) 1731. C.R. Witschonke and C.A. Kraus, J. Am. Chem. Sot., 69 (1947) 2472. E. Hirsch and R.A. Fuoss, J. Am. Chem. Sot., 82 (1960) 1018. C.J. Coetzee and H. Freiser, Anal. Chem., 41 (1969) 1128. T. Fujinaga, S. Okazaki and H. Freiser, Anal. Chem., 46 (1974) 1842. M. Matsui and H. Freiser, Anal. Letters, 3 (1970) 161. R.W. Cattrall and Pui Chin-Poh, Anal. Chem., 47 (1975) 93. H. James, G. Carmack and H. Freiser, Anal. Chem., 44 (1972) 856. A.J. Bentz, J.R. Sandifer and R.P. Buck, Anal. Chem., 46 (1974) 543. D.E. Mathis and R.P. Buck, Anal. Chem., 48 (1976) 2033. A.T. Hubbard and F.C. Anson, Anal. Chem., 36 (1964) 723. R.M. Fuoss and T. Shedlovsky, J. Am. Chem. Sot., 71 (1949) 1496. G. Akerlof, J. Am. Chem. Sot., 54 (1932) 4125. C.R. Witschonke and C.A. Kraus, J. Am. Chem. Sot., 69 (1947) 2472. B.L. Karger, L.R. Snyder and C. Horvath (Eds.), Introduction to Separation Science, John Wiley and Sons, New York, 1973, p. 78. E.G. Taylor and C.A. Kraus, J. Am. Chem. Sot., 69 (1947) 1731. CR. Witschonke and C.A. Kraus, J. Am. Chem. Sot., 69 (1947) 2472. F. Conti and G. Eisenman, Biophys. J., 6 (1966) 227. F.S. Stover and R.P. Buck, Biophys. J., 16 (1976) 753. P.R. Danesi, G. Scibona and B. Scuppa, Anal. Chem., 43 (1971) 1892. N. Kamo, N. Hazemoto and Y. Kobatake, Talanta, 24 (1977) 111. W. Morf, E. Lindner and W. Simon, Anal. Chem., 47 (1975) 1596. D.E. Mathis, F.S. Stover and R.P. Buck, J. Membrane Sci., 4 (1979) 395.
379
ION TRANSPORT IN FREE AND SUPPORTED NITROBENZENE ALIQUAT NITRATE LIQUID MEMBRANE ION-SELECTIVE ELECTRODES I. BULK ELECTRICAL PROPERTIES INCLUDING ION ASSOCIATION AND DIELECTRIC CONSTANT DALE E. MATHIS and RICHARD
P. BUCK
William Rand Kenan Jr. Laboratories of Chemistry, Chapel Hill, North Carolina 27514 (U.S.A.)
The University
of North
Carolina,
(Received August 21, 1978)
Summary A controlled-thickness thin layer cell and wide-band cross correlator bridge have been used to characterize ion transport in free liquid and supported ion exchange membranes. The base system of Aliquat nitrate in nitrobenzene was measured, and transport parameters were used to establish properties of supports: cellulose triacetate, PVC-acrylonitrile, polypropylene and Teflon. From DC to 0.5 MHz impedance measurements, geometrical capacitance, electrical relaxation time constants and dielectric constants were determined over a range of temperatures and membrane loadings. Depression of dielectric constant with loading and temperature coefficients are reported. Conductivities were analyzed classically to yield equivalent conductances of ions, transference numbers and ion pairing constants. Temperature coefficients gave transport enthalpy and thermodynamic quantities. Data from supported membranes gave direct measures of void volumes of inert membrane supports, and clear evidence for cases of membrane solubilization by entrapped solvents.
Introduction The utility of ion selective electrodes as species-selective activity sensors in analytical chemistry has been extensively demonstrated. Electrodes responsive to different ions can be constructed in a variety of formats using many ion sensitive materials. The liquid ion exchanger-based electrodes are particularly important because of their versatility. They can be used to measure ion activities which cannot be measured using insoluble, conducting salts or ion sensitive glasses. At the same time, this general applicability means that liquid ion exchanger-based electrodes are more susceptible to ion interferences. Although some liquid ion exchange systems have recently been superseded by neutral carrier electrodes with superior selectivity and sensitivity specifications, e.g. Cal+ electrode [ 11, this has not been the case for anion-selective liquid ion exchanger electrodes. The Aliquat 3365, tricaprylmethyl ammonium-based ion exchange electrodes have been the most successful sensors of this kind,
380
and often exhibit Nernstian slopes over more than five orders of magnitude of activity for anions. The supported Aliquat-based systems are examples of successful electrode formats, and are worthy of detailed study from a practicsl perspective. Coljious scientific literature is concerned with various aspects and applications of the same Aliquat-nitrobenzene ion exchanger systems studied in this work. It would be difficult and unnecessary to give a comprehensive review. It is, however, instructive to cite those studies which form a fundamental data base against which the results of this work can be compared. The relevant papers of this type can be roughly divided into two categories: conductance studies of tetraalkyl ammonium salts in nitrobenzene, and electrode construction formats based on the Aliquat ion exchangers with their characteristic responses and applications. Both categories are considered in turn. Bulk electrical properties of electrolytes in nitrobenzene as solvent at 25°C have been thoroughly investigated in three early papers. Ion association constants and limiting conductances for several tetraalkyl ammonium salts in nitrobenzene have been measured by Taylor and Kraus [2] and by Witschonke and Kraus [ 31. The work of Fuoss and Hirsch [ 41 considered several other symmetrical ammonium salts, but also included an evaluation of ionic radii as well. The Aliquat ion is not considered in any of these studies and has not been investigated previously. The lack of formal literature concerning the solution behavior of Aliquat salts has in no way discouraged their use as ion exchangers in liquid membrane electrodes. Applications of Aliquat-based sensors include detection and measurement of inorganic anions [ 51, anionic detergents [6] and amino acids [7]. Even Fe(III) has been measured by forming the FeCl, salt of the exchanger [ 81. Aliquat membranes have been used with good results as coated wire electrodes for several of the above applications [ 91. While this list is not comprehensive, it demonstrates the utility of this ion exchange agent. Widespread applicability of the Aliquat-based ion exchanger electrodes makes it important that the properties of membranes containing Aliquat salts be well understood. Since the ingredients of these membranes are inexpensive and easily obtained, electrodes can be readily prepared by laboratory workers using commerical barrels, liquid ion exchangers and support materials. For this reason, users should know what effects can be expected on ion activity measurements when parameters such as exchanger concentration and composition of support materials are varied. In addition, Aliquat-nitrobenzene membranes exhibit anomalous responses when used immediately following construction. This conditioning phenomenon warrants investigation. The observations, as exemplified in Fig.1, are three-fold: (1) preliminary calibration curves are SuperNemstian; (2) electrode responses are noisy, and (3) there is a monotonic shift in the value of E” toward more negative potentials. After several hours of use in aqueous media, classical anion responses are obtained and sensors can be used for quantitative measurements. This conditioning effect on response might be caused by water
381
-LOG
(a)
Fig. 1. Potentiometric response at 2 X 10m4 M Aliquat nitrate nitrobenzene membrane to aqueous KNO, at 25°C as a function of electrode lifetime. 0, newly fabricated; x , 6 hours later; 0, 24 hours later.
uptake in the exchanger solution, by changes in the support void volume through partial solubilization of some supports in nitrobenzene, or by increasing surface rates of ion exchange due to hydrating of the support surface. It is necessary to measure these possible changes in the bulk and surface properties of ion sensitive membranes as they are used, because the effects are not presently included in the idealized models for responses of these systems. In particular, we will demonstrate quantitatively the extent of each of these proposed effects in this and the following paper. A more general reason for studying the electrical properties of the Aliquat systems in nitrobenzene is to obtain a deeper understanding of factors relevant to improved responses and design of new sensors. In addition, our investigations add to the data against which theoretical prediction and models can be evaluated in the general context of ion transport in artificial membranes. Experimental Reagents Aliquat 3368 was obtained from General Mills and converted to the nitrate form by repeated equilibration with concentrated aqueous KN03. It was then washed with distilled, deionized water and dried over molecular sieves. Reagent grade nitrobenzene used for this study was further purified by washing repeatedly with aqueous 0.1 M NazCOJ and then with distilled, deionized water. The solvent was then vacuum distilled off of Linde 3A molecular sieves. Freshly distilled nitrobenzene prepared in this way has a specific conductance less than 0.02 micro-Siemenicm.
382
Instrumentation
The admittance measuring instrument used in this study was built in the lab with the same configuration as that described by Bentz et al. [lo] but including the broad band modifications developed by Mathis and Buck [ll] . A Haake model FK2 thermocirculator was used to thermostat an oil bath in which the impedance cell was immersed for measurements. The impedance cell constructed in this lab used parallel-face platinum disk electrodes with an area of 0.193 cm2 sealed in a Teflon shroud. The two-electrode configuration employed variable spacing control in which the driven electrode was mounted on a micrometer tip, much as Hubbard and Anson [12], to allow adjustment of the cell thickness for polymer measurements. The entire cell was Teflon lined to eliminate leaching of cell walls as a source of test sample contamination. Polymer
samples
The following polymer support materials were obtained from Gelman: Metricel GA-8 (0.2 micron cellulose triacetate), Metricel Acropore AN450 (0.45 micron PVC-acrylonitrile copolymer) and Metricel # 61757 (10.0 micron polypropylene). FGLP01300 (0.2 micron Teflon) was obtained from Millipore. Procedure The “in-phase” and “out-of-phase” (quadrature) admittances of pure, dry Aliquatrnitrobenzene solutions were measured from about 3 Hz to 560 KHz at quarter decade intervals for nine Aliquat nitrate concentrations, from lo-‘M to pure nitrobenzene, and four temperatures: 20, 25, 30, and 35°C. These experiments were repeated after saturating each ion exchanger solution with water. To avoid perturbing the solution concentrations, water saturation was achieved by first equilibrating distilled, deionized water with an aliquot of sample solution and then equilibrating the rest of the sample solution with the pre-equilibrated water. Effects of polymer support on the electrical properties of the ion exchangers were studied by measuring admittances of polymer discs saturated with known concentrations of ion exchanger solution which had been secured between the planar surfaces of the platinum electrodes in the impedance cell. Calculations
Frequency dependent “in-phase” and “out-of-phase” admittances were converted into Real and Quadrature (out of phase) impedances and displayed as an impedance plane plot. Calculated parameters were determined as follows: C,
Geometric capacitance was determined by interpolating the value of the quadrature admittance corrected for stray, or parasitic, cell capacitance at o max corresponding to C, = YQ/w (YQ is the quadrature component of the admittance). A plot of log YQ vs. log w used for interpolation is shown in Fig. 2.
383
LOG
(f)
Fig. 2. Plot of log YQ vs. log f (Hz) used to determine C, for pure nitrobenzene at 25°C.
Ei3
fv
24 ilo R,
(JO Tel Wmax
Activation energy for ion transport calculated as 1.987 times the slope of a plot of ln,R, vs. l/T” (K). The fraction of the macroscopic polymer disc volume occupied by voids (not occupied at all) and experimentally defined as the ratio of R, for pure ion exchanger to R, of the same solution occluded in the polymer. C,/8.84 X IO-l4 F/cm, the dimensionless dielectric constant. Equilibrium constant for ion pair formation calculated from conductance data by the method of Fuoss and Shedlovsky [13]. Limiting salt conductance at infinite dilution was also determined by the method of Fuoss and Shedlovsky (cm’/ohm-equiv.). High frequency resistance was determined from the width of a least squares circle fit to the impedance plane data and corrected for the parallel conductance of pure solvent. Experimental impedance plane plots are shown in Fig. 3. Specific,conductance, l/R,. R, X C,,the time in seconds for the system to relax to l/e of its equilibrium value after an electrical perturbation. Angular frequency at which the quadrature impedance is a maximum or alternatively, the frequency at which the real impedance is half R, .
384
2’
(Mfl-cm)
Fig. 3. Impedance plane plot of -2” 0, 20”; +, 25”; 0, 30” ; x , 35°C.
vs. 2’ for purified nitrobenzene at four temperatures:
The following additional symbols have been used: f
Frequency in Hertz; o /2n = f. Subscript 0 indicates infinite dilution. Absolute charge (coulombs). Distance (cm). Gas constant. Absolute temperature, unless otherwise specified. Single ion transference numbers. Molar volume. Quadrature admittance. Imaginary and real components of impedance.
X+, X_ Single ion conductances. 4
Ik T L tV
YQ
Z”, 2’
Results and discussion I. Geometric capacitance and dielectric cons tan ts Results of impedance measurements on dry Aliquat nitrate-nitrobenzene solutions are presented in Table 1 for a range of Aliquat concentrations at four temperatures. These data serve as the basis for calculated values of KA and E, which are given later. Note that the geometric capacitance values become more unreliable as concentration increases, because the relative magnitudes of the quadrature admittance to real admittance is becoming smaller. At concentrations greater than 4 X 10e4 A4 the quadrature admittance can no longer be resolved in the accessible frequency range and therefore, C,, K , and r,l could not be determined. The value of K 25 determined for pure nitrobenzene of 36.0 + 0.5 agrees with the accepted value of 34.8. The small (+3.5%) error may be caused by
385 TABLE1 Bulk properties of dry Aliquat nitrate in nitrobenzene Aliquat
Temp.
cont.
(C”)
R, (ohm-cm)
0.0
20.0 25.0 30.0 35.0
60.2M 55.6 46.9 38.5
1.6x 1O-s
20.0 25.0 30.0 35.0
4.0x 10-s
.
K
7el
a0
%
0.0166 0.0178 0.0213 0.0260
3.231t.03 36.5k.3 3.19+.05 36.0+.5 3.13k.06 34.8t.7 2.94e.06 33.2t.7
194 177 147 113
2.45M 2.29 2.14 2.02
0.409 0.437 0.467 0.495
3.16k.15 3.08k.19 2.96k.16 2.87t.20
35.7k1.7 34.8*2.1 33.4*1.8 32.4*2.2
7.74 7.05 6.33 5.80
20.0 25.0 30.0 35.0
0.922M 0.857 0.804 0.747
1.09 1.17 1.25 1.34
3.1Ok.13 2.94k.08 2.88t.10 2.76k.10
35.0?1.4 33.2+0.9 32.5*1.3 31.1+1.1
2.86 2.52 2.32 2.05
8.0x 10-s
20.0 25.0 30.0 35.0
0.452M 0.419 0.392 0.371
2.21 2.39 2.55 2.67
3.08k.19 2.96k.22 2.82k.27 2.792.34
34.8%2.2 33.5+2.5 31.9+3.1 31.5+3.8
1.39 1.24 1.11 1.04
2.0x 1o-4
20.0 25.0 30.0 35.0
0.184M 0.170 0.157 0.146
5.45 5.90 6.39 6.87
2.99i.19 2.86k.04 2.67k.15 2.52k.11
33.8%2.1 32.3+0.5 30.1*1.7 28.551.3
0.550 0.486 0.419 0.368
4.0x lo-'
20.0 25.0 30.0 35.0
93.7K 87.1 81.4 76.5
10.7 11.5 12.3 13.1
2.40+.21 2.26+.31 2.12k.15 1.98k.28
27.1+2.3 25.5i: 3.5 24.0*1.6 22.4i3.2
0.225 0.197 0.173 0.151
8.0x lo-*
20.0 25.0 30.0 35.0
48.3K 45.2 42.2 39.1
20.7 22.1 23.7 25.6
2.0x 1o-3
20.0 25.0 30.0 35.0
21.2K 19.6 18.5 17.2
42.2 51.0 54.0 58.1
1.0x 10-2
20.0 25.0 30.0 35.0
5.52K 5.15 4.72 4.35
181 194 212 230
(M)
(fiSiemen/cm) M/cm)
(C,/C, vat)
(@I
an error of less than 0.1 pf in the stray capacitance determined for the empty impedance cell and is therefore acceptable in this study. The temperature dependence of K determined for pure nitrobenzene follows a typical exponential law [ 141 and a least squares analysis of log K vs. 2’ for our results and
386
literature data gives the following coefficients: log
K (!!‘)fit
=
(-2.15
log K ( T)exp = (-2.74
f .05) X 1O-3 T (“C) + (1.593 + 0.005) * .47) X 103 T(C)
+ (1.62 ? 0.01)
(1) (2)
Agreement between intercepts is good, but the slopes are not within experimental error. Rather than a systematic error, the small data set and the narrow temperature range studied may be responsible. Capacitance measurements are not restricted to pure nitrobenzene and so dielectric constants can also be obtained for the ion exchanger solutions. Data for pure solvent are-more accurate than corresponding electrolyte solution values because the resistance of pure solvent is maximum and capacitive admittance can be resolved at lower frequencies. Despite uncertainties in the dielectric measurements on Aliquat nitrate solutions, previously unreported trends are evident. Table 2 lists the coefficients from the linear regression analysis for the equation 1OgK
=AT+B
(3)
TABLE 2 Coefficients
of log K = AT + 3
Cont. (M)
A x 10” (“C-l)
B
0.0 0.0 1.6 4.0 8.0 2.0 4.0
-2.15+ 0.05 -2.74* 0.46 -2.88* 0.17 -3.26 f 0.35 -3.02+ 0.45 -5.06* 0.28 -5.495 0.12
1.593+ 1.62 f 1.61 + 1.61 ? 1.60 f 1.63 * 1.54 +
(Lit.) (Exp.) x 1O-S x 10-s x lo-” x lo-’ x lo-’
Correlation coefficient .005 .Ol .Ol .Ol .Ol .Ol .Ol
0.999 0.972 0.995
0.988 0.978 0.997 0.999
for all Aliquat solutions measured. Although this relationship has not been widely verified for dilute ionic solutions, all of the correlation coefficients are close to unity. The zero temperature intercepts are unaffected by Aliquat concentration but the temperature coefficients increase with salt concentration. This result suggests an increased activation barrier for solvent dipole structure breaking as the local electric fields increase with ionic strength. Although it is not surprising that the addition of point charges should have this effect, a viscosity increase by addition of viscous Aliquat salt may also be involved. II. Conductance The AC techniques for frequency-dependent impedance measurements can give information on both AC and, in the limit, DC steady state conductances of electrolyte solutions and membranes. Efficiency depends on the reversibility of the contacting electrodes. For blocking platinum electrodes used in this study, only the AC conductivities can be computed from the so-
387
called infinite frequency resistance. The latter appears in series with the capacitance of the blocking electrodes in the equivalent circuit of the electrolyte/ membrane cells used here. The real admittance is not frequency-dependent and, unlike dielectric constants, can be determined for concentrated electrolytes. When the conductance is significantly less than the reactance of the series double layer capacitance of the blocking platinum electrodes, the conductivity can be computed with an accuracy determined by the AC instrument. In this study, conductivity values are accurate within 3%. Conductance data for dry and wet bulk ion exchanger electrolyte solutions are presented in Tables 1 and 3, respectively. Values at four temperatures were used to determine activation energies of ionic transport as a function of exchanger concentration and water uptake. These results are reported in Table 4 according to the relationship (5= (3’ exp (-&JR
T)
(4)
Each was experimentally determined by the equivalent method of measuring the slope of a plot of In, R, vs. l/T as shown in Fig. 4. TABLE 3 Bulk properties of wet Aliquat nitrate in nitrobenzene Temp. (“C)
20.0
25.0
30.0
35.0
Aliquat cont. (M)
R,(ohm-cm) o0 (clS/cm)*
R, (ohm-cm) oD (d/cm)
R,(ohm-cm) o. (d+xn)
R,(ohm-cm)
2.0 x lo-’
0.200M (5.00)
0.185M (5.41)
0.173M (5.78)
0.162M (6.17)
4.0 x lo-’
98.8K (10.1)
91.8K (10.9)
85.4K (11.7)
79.7K (12.5)
8.0 x 1O-4
50.OK (20.0)
46.5K (21.5)
43.6K (22.9)
40.9K (24.4)
2.0 x 1o-3
21.4K (46.7)
20.OK (50.0)
18.7K (53.5)
17.6K (56.8)
1.0 x 1o-2
o0 W/cm)
5.88K
5.47K
5.11K
4.85K
(170)
(183)
(196)
(206)
*uO values given in parentheses.
III. Equivalent conductivities and ion pairing thermodynamics Values of KA and A0 for wet and dry solutions, calculated from a computer-optimized Shedlovsky analysis of the concentration-dependent conductances, are given in Table 5. The Shedlovsky plots for this analysis are shown in Fig.5. A few percent variation between KA and A0 at 25°C for wet vs. dry solutions can be observed, but this variability is thought to be caused by in-
389
TABLE 5 KA and A, values for Aliquat nitrate in nitrobenzene State (wet or dry)
Temp. (“C)
dry
20.0 25.0 30.0 35.0 25.0
dry dry dry wet
1
3
28.2 30.3 32.3 34.4 29.1
131 133 120 108 140
5
7 ACSF*
9
11
13
(~10~)
Fig. 5. Shedlovsky plot used to determine A., and KA at four temperatures. 0, 20” ; X , 25”; 0, 30”; l, 35°C. S is the Shedlovsky function and F* is the square mean salt activity coefficient.
From analysis of limiting salt conductances of Aliquat nitrate at 25”C, A,-,25 = 30.3. (h-25), was measured as 22.6 for nitrate ions in nitrobenzene [ 151. Thus, for the Aliquat cation, (x+*5)o = Ao-(x-*5)o
= 7.7
(5)
The corresponding transference numbers of these ions are: (t+25),, = (X+25),, /A0 = 0.25 for the Aliquat cation (t-*5)*
= (x-2S)o /A, = 0.75 for the nitrate ion
A Wilke-Chang
(6a) (6b)
plot of (X+25),, vs. v- O-6[ 161 for a homologous series of
Fig.6.
Wilke-Chang
plot
of data in Table
6.
spherically symmetric quaternary ammo&urn ions, using data compiled by Taylor and Kraus [ 171 is shown in Fig.G._The limiting conductance of the Aliquat cation is plotted at the values of V determined by the empirical relationship: V (A3) = 1.33 X mass (g)
(7)
The validity of this relationship is demonstrated in Table 6. The fact that the specific conductivity of the Aliquat cation lies on the Wilke-Chang line asserts the spherical symmetry of the molecule in spite of its asymmetric substitution. A Wilke-Chang plot was chosen instead of the classical Stokes radius analysis because the former yields the expected zero intercept. Both plotting methods assert the spherical symmetry of the Aliquat cation. Comparison of KA’~ values for Aliquat nitrate and tetrabutyl ammonium TABLE
6
Data for Wilke-Chang
plot
Cation
Mass
1.33
(Et),N+
130 186 242 298 452
172.7 247.1 321.5 396.0 600.6
(Pr), N’ (Bu),N+ (Pe),N+* (Cap),MeN’
*Pe = Pentyl.
X mass
Vii* (a3)
V-.6 X 10’
(A+),
171.5 247.4 323.0 396.6
4.56 3.66 3.12 2.76 2.15
16.2 13.3 11.7 10.0 7.7
391
nitrate may appear contradictory because the former was found to be 133 whereas the latter ion has a smaller spherical radius but a KA’~ of only 40 [ 181 Apparently the dominant radius for Aliquat is determined by the methyl group. An effective radius less than the mean size of the dapryl group is also suggested from the enthalpy values. The temperature dependence of KA for dry exchanger solutions given in Table 4 gives the following values for the thermodynamic quantities of ion pair formation for Aliquat nitrate in nitrobenzene; AG” = -2.88
+ 0.03 Kcal/mole
(8)
AH” = -2.53
f 0.75 Kcal/mole
(9)
AS” = +1.16 * 2.50 Cal/degree-mole
(10)
A large uncertainty in AS” does not invalidate a small magnitude for this quantity. This result suggests that the nitrobenzene solvent sphere, which must be removed prior to ion pair formation, is very loosely coordinated. The value of AH” is more reliable, and can be used to estimate the separation distance of charge centers in the ion pair from the following relationship: p=
AH” =
00
s
(-$/K
r’)dr
(11)
r=IP
where g is the value of the unit charge, K is the dimensionless dielectric constant of the solvent and r is the separation between charge centers. This analysis for Aliquat nitrate gives a value of 3.6 A for the ion pair nuclear separation distance when K = 34.8. However, it has been shown in this study that K decreases dramatically with Aliquat salt concentration. Because AH” was determined using concentrations from 10e4 to 10e2 M, it is not valid to use the K for pure solvent in this calculation. Assuming an intermediate dielectric constant of 22.4 (25°C for 2 X 10m4 M), a more likely value of 5.9 A is obtamed for r. Since the radius of nitrate ion is about 2 A, a radius of about 3.9 _&for Aliquat cation is indicated. This value is near the radius of tetramethyl (3.47 A) and tetraethyl (4.0 A) ammonium cations. It therefore appears that during ion pair formation, nitrate can approach the charged nitrogen center as closely as the single methyl group permits. IV. Support void volumes and reactivity in nitrobenzene Numerical values of Ea2’, f, and K 25, experimental and calculated, for four commonly used polymer membrane support materials impregnated with 2 X 10e4 M ion exchanger (to swamp out any effects of fixed sites) are reported in Table 7. Activation energies for ionic transport of Aliquat nitrate in Acropore and polypropylene are the same, within experimental error, as that for unsupported solutions. This result means that bulk properties of the ion exchanger are not influenced by occlusion in these polymer supports. The GA-8 (cellulose triacetate) support gave a significantly larger transport
392
TABLE
I
Polymer
support
Polymer
data
Composition
Pore
-5
K*s(exp.)
~*~(calc.)
Kzs(polymer)
0.40 k.04
3.08 i.43
21.8 il.1
17.9 t1.2
7.5
0.36 t.04
2.55 +.25
12.8 * .7
14.2 k1.3
-4
0.10 ‘.Ol
2.58 t.09
7.4 .7
5.3 i.4
2.3
t
1.4 t.1
2.3 t.2
2.0
f,
(Kcal/mole)
size M&rice1 GA-8
cellulose triacetate
0.2 v
Acropore AN450
pvcacrylonitrile
0.45
Metricel 61757
polypropylene
10 IJ
Millipore FGLPOl300
Teflon
0.2 Jl
Ir
.Ol
activation energy. In addition, during the experiment the polymer membrane changed irreversibly from opaque’to clear and became brittle. Repeated washing with methanol to remove the exchanger did not restore the original opacity. These observations are interpreted, in agreement with the literature, to mean that this polymer is partially solubilized and its pores partially collapsed in nitrobenzene. The increased value of E, is thought to occur by interaction of the exchanger with solvated polymer, and the large uncertainty is attributed to non-steady state measurements, since the polymer is degrading during the experiment. A value for E, could not be obtained for the Teflon support because of its large thermal coefficient of expansion and very low void volume. When the temperature was raised, polymer expansion significantly perturbed the void volume and decreased the amount of ion exchanger in the polymer. Empirical dielectric constants for polymer supports impregnated with Aliquat nitrate ion exchanger are also reported in Table 7. Predicted values were calculated using the sum of the volume-fraction-weighted dielectric constants of the pure components as follows: x25 calculated = f& 25
(Aliquat-nitrobenzene)
+ (l-
fv)~ 25(polymer)
(12)
Experimental and predicted values of K are in good agreement for the nonreactive supports, acropore and polypropylene. This result is consistent with the lack of interaction between the polymer and the exchanger in these supports because of the complete failure of eqn. (12) when applied to the other polymer supports. Polymer GA-8 is anomalous in that the experimental values are significantly higher than predicted. The value for Teflon is controlled entirely by the polymer because of its low void fraction. Conclusions Solutions of Aliquat 3368 nitrate in nitrobenzene have been shown to be weakly associated liquid ion exchangers in which the bulk electrical proper-
393
ties are unaffected by equilibration with water. Variation of conductance with Aliquat salt concentration, or “loading”, follows the square root of concentration dependence typical in largely dissociated ionic solutions. Increased loading of the ion exchanger causes very pronounced depression of the solution dielectric constant. This observation has possible fundamental effects on ion selectivity. For example, it has been shown previously that the selectivity of dissociated liquid membrane ion selective electrodes is independent of membrane loading except when the ion exchange constant is influenced by the bulk properties of the ion exchange agent or solvent [ 191. A further property which strongly influences selectivity, as shown by Stover and Buck [20], is the degree of association, a loading-dependent parameter which can significantly influence selectivity ratios for ions of different size. It is expected that a reduction of the membrane dielectric constant will generally enhance existing selectivity of the larger ion [ 211. This conclusion together with the findings of this paper suggest that the selectivities of this sensor should be improved by increasing membrane loading. The enhancement of selectivity by increased membrane loading may be obtained at the expense of an increased limit of detection when exchanger partitioning is controlling the potentiometric response at low sample ion concentration [ 221. This result, however, is not always the case, and in a later paper we will demonstrate how the limit of detection may actually be improved by increasing the ion exchanger concentration. Potentiometric response times are a second property of ISE’s* which can be controlled by the properties of the membrane. In this case, bulk electrical relaxation has been shown to be about 0.2 ms for pure solvent, which is the slowest possible value. Rapid relaxation is consistent with the expected values of limiting conductance for Aliquat nitrate relative to other tetraalkylammonium nitrate salts. Short relaxation times indicate that the potentiometric response time of these sensors is controlled by ionic diffusion through an unstirred layer of solution at the membrane surface [23] or slow interfacial kinetics. It has been shown here that the use of polymer materials inert to the membrane solvent as a support medium does not affect the electrical properties of the bulk exchanger solution. Rather, these heterogeneous systems can be modeled simply as a polymer lattice with voids filled by exchanger, and their electrical properties calculated from the weighted properties of the pure components. Lack of interaction between exchanger and support has been demonstrated only for inert polymers with appreciable void fractions, and this principle probably cannot be successfully applied to low void fraction membranes. Useful support materials need only be inert to membrane solvent, wettable by the membrane solvent, and hydrophobic. Transport enthalpy discriminates inert membrane supports from those which are degraded by solvents. It has also been shown that changes in the ion exchange solution because of water uptake do not affect transport parameters in free liquid and inert support *WE
= ion selective
electrode.
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effects, time dependent interfacial rates, and hydration layers are investigated in Part II of this series [24] .
membranes. Conditioning Acknowledgement
This work was supported by National Science Foundation Grant CHE7500970-A01 and CHE77-20491. References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
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