J . Phys. Chem. 1986, 90, 1973-1977
1973
Conclusions Temperaturedependent changes in the proton NMR line widths of TRDX as it passes through a premelt solid phase between 365 and 378 K indicate the activation of substantial motion of the molecules in the crystal lattice. The line widths are dominated by field-dependent line broadening terms in this phase. Dipoledipole couplings do not contribute significantly to the width of the observed resonance in this regime. These results can be explained if, in the premelt phase, TRDX undergoes the virtually free rotation of a plastic crystal and limited molecular diffusion, making it in effect a “crystal liquid”.
an N M R spectrum which is extremely narrow. Such a low second moment below the the melting point indicates that substantial movement of TRDX molecules occurs among the lattice sites. Similar motion has been observed previously for c y ~ l o h e x a n e ’ ~ at temperatures 40 K below its melting point, but well above the range of its plastic crystalline phase. The line widths observed for TRDX depend on magentic field strength (Figure 2). Our discussion and calculations thus far have assumed that only dipole-dipole interactions contribute to the second moments. Contributions to the line width from field-dependent interactions are present. The ratio of the line widths at the two fields investigated is shown in Figure 4 as a function of temperature. In this region the ratio of line widths at the two fields is constant and approximately 4.4, the value expected if all the line width were linearly dependent on the field. Thus, the previous calculations underestimate the amount of motion present in this phase. The TRDX molecules are clearly extremely mobile at temperatures just below the melting point.
Acknowledgment. This work was supported in part by the Air Force Office of Scientific Research (AFOSR-80-0285) to T.B.B. The N M R spectrometers were obtained with grants from the National Science Foundation (Grant DMR-8308270) and the PHS (Grant GM2761601Sl). Registry No. TRDX, 13980-04-6.
Absorption of Gaseous Iodine by Polythiophene Films and Powders H. Reiss* and Dai-uk Kim Department of Chemistry and Biochemistry, University of California at Los Angeles, Los Angeles, California 90024 (Received: October 24, 1985)
Further determinations of the “reversible” absorption isotherms of iodine (vapor) in both polythiophene films and powders are performed. The films exhibit isotherms of iodine uptake vs. iodine pressure which, at low pressures, are concave downward at low temperatures and concave upward at higher temperatures. This behavior is interpreted in terms of hole-electron equilibria. At a pressure of about 0.68 torr all film isotherms exhibit a discontinuous slope to saturation. The powder isotherms followed those for the film up to the discontinuity, do not exhibit the discontinuity, and continue to absorb iodine as the pressure is increased. By mixing helium into the iodine vapor, we demonstrate that the discontinuity occurs when the total gas pressure is in the neighborhood of 0.68 torr. The phenomenon is explained in terms of a electromechanical instability caused by the formation of a Schottky diode at the film-substrate interface.
I. Introduction Recently, a study of absorption isotherms for iodine in polythiophene films was published as a Letter.’ The isotherms, though preliminary, exhibited some remarkable features. In particular, the absorption process proved to be reversible within experimental error. Furthermore, over long ranges of iodine pressure, at all studied temperatures, iodine uptake appeared to depend linearly on iodine pressure. At very low pressures, there were departures from this behavior such that the isotherm was concave downward (at low pressures) at lower temperatures and concave upward at higher temperatures. One of the most remarkable features was a sharp discontinuity in slope (at all temperatures), to a slope of zero, indicating some sort of saturation. The discontinuity appeared to occur at about the same level of iodine pressure, independent of temperature. Curves of this shape cannot be explained by a saturation phenomenon of the sort that occurs in, say, simple Langmuir-type absorption. Langmuir isotherms are continuous to saturation, and curved, exhibiting linear behavior only at the very lowest pressures. Furthermore, the level of saturation is independent of the temperature, whereas in the I,-polythiophene isotherms the saturation level decreases with increasing temperature. Figure 1 of the present paper, which is based on new and more thorough data (in particular the masses of the films are known), illustrates examples of these kinds of isotherms. Polythiophene is a conducting polymer and I*, an electrically active dopant, behaves as an acceptor.*s3 The ultimate goal of our studies has
been the utilization of thermodynamics (equilibria associated with the isotherms) to infer details of the mechanisms of ionization of dopants as well as ionization e n e r g i e ~ . ~The curvatures of the isotherms at low pressures may be related to ionization. We will have more to say about this later. A particularly remarkable feature of Figure 1 is that the discontinuity which occurs in the slope of the isotherms, at every temperature, seems to always occur at a pressure of about 0.68 torr, independent of temperature. The same behavior was observed in the isotherms of ref 1 where the discontinuities, like the isotherms themselves, were shown to be reversible and reproducible. As a result we undertook further measurements in which an inert gas (helium) was mixed into the iodine vapor. Two sets of experiments of this type were performed, one with the helium pressure maintained at 0.375 torr and the other with helium pressure at 0.60 torr. The results of these investigations are exhibited in Figure 2, superimposed upon the isotherms of Figure 1. The startling fact is that the isotherms, in the presence of helium, are identical with those obtained in the absence of helium until the total gas pressure is about 0.68 torr. This is true, independent of the temperature. For example, with 0.375 torr of helium, the discontinuities in the slopes of the curves occur in the neighborhood 0.29 torr of iodine pressure. With 0.60 torr of helium, the discontinuities occur in the neighborhood of 0.08 torr of iodine pressure. These isotherms were obtained (as explained in the next section) by using thin films of polythiophene electrodeposited over a thin
(1) Kim, D.; Reiss, H. J . Phys. Chem. 1985.89, 2728. ( 2 ) Waltman, R. J.; Bargan, J.; Diaz, A. F. J . Phys. Chem. 1983.87, 1459.
(3) Frommer, J. E.; Chance, R. R. In Encyclopedia of Polymer Science and Engineering, Grayson, M., Kroschitz, J., Eds.; Wiley: New York,in press. (4) Reiss, H.; Murphy, W. D. J. Phys. Chem. 1985, 89, 2596.
0022-3654,I86,12090-1973S01.50 I O I
0 1986 American Chemical Societv -
1974 The Journal of Physical Chemistry, Vol. 90, No. 9, 1986
Reiss and Kim
m e
FILM
POWDER
+ -
'7
'I
'I
P R E S S U I 'TORR
Figure 1. Absorption isotherms for iodine in a polythiophene film (0.24 rmol) at five temperatures. Uptake in rmole and iodine pressure in torr. Reversibility is indicated by separate runs (circles and squares).
P
0
1,
I
-
9
I
- --
-fb
.
.-
i
PRESSURE TORR
J
y&
-% IOC
p"-70C
-
-* I
Figure 3. Absorption isotherms for a powder sample containing 0.24 @molof polythiophene. Filled circles correspond to powder. The open circles are the 30, 40, and 50 "C isotherms of Figure 1. The powder isotherms do not show the discontinuities in slope, but, at pressures lower than that corresponding to the discontinuity,are identical with the film isotherms.
layer of gold supported by a glass cover slip. In order to test the generality of the phenomena, we also measured the absorption isotherms, using bulk (in the form of powder) polythiophene. The polymers in the powder were synthesized in the laboratory of Professor F. Wudl at the University of California, Santa Barbara. These polymers contained 44 monomer units (thiophene) and had an iodine atom attached to the last unit in the chain. The powder sample was weighed and selected to have the same mass as the corresponding film (see next section). Absorption isotherms obtained with powder are exhibited, in Figure 3, and are plotted over the isotherms appearing in Figure 1 . It is apparent that the isotherms obtained with powder are identical with those obtained with film until the pressure of the discontinuity is reached. The powder isotherms do not exhibit the discontinuity and continue to higher pressures with the same straight line slopes. Thus, the discontinuity is a property of the film alone and needs to be explained. We examine this question in the later sections of this paper.
a prior deposit of gold (7.5 nm) had been laid down. The I, did not react with the gold at the temperatures of the measurements. In the previous measurements1 the masses of the polythiophene films were not known. In the present study they were determined by weighing the gold coated coverslips before polythiophene deposition and determining the weight of the entire assembly (coverslip, gold, and polythiophene) after deposition. The difference between the initial and final weights was assumed to represent the mass of the film. The isotherms were determined by suspending the films in an all quartz microbalance (sensitivity, 0.1-0.2 pg) in a vapor of the pure 12 at a controlled temperature. The 1, pressure was measured by optical absorption (sensitivity 0.01 torr), and the uptake of I, by the film was determined by measuring the weight change on the microbalance. Isotherms were also obtained on bulk, powdered samples of polythiophene, prepared in the laboratory of Professor F. Wudl at the University of California, Santa Barbara. The polymers in this powder contained 44 thiophene units, the last unit containing an iodine atom. As indicated in the previous section, enough powder was used so that the resulting sample had approximately the same weight as the corresponding film. The sample was held in a small quartz container which could be attached to the balance. The times required to equilibrate the powder with iodine vapor ranged from 20 to 30 min. Also, as indicated in section I, film isotherms were obtained in the presence of helium, at 0.375 and 0.60 torr. In each case it was determined that helium by itself was not absorbed by the film (at least not within the precision of measurement).
11. Experimental Section
111. Discussion of the Curved Portions of the Isotherms
The method of measurement has been described before.' PoIythiophene films were prepared in the oxidized state by electrodeposition from a solution in which the solvent was acetonitrile. The films were subsequently electroreduced to the neutral, unoxidized state. They were supported on glass coverslips on which
As we have mentioned, and as is apparent from Figure 1, the isotherms in the lower pressure regime are not only curved but also make a transition from being concave downward at lower temperatures to concave upward at higher temperatures. As is well-known,2 the polymer in the film undergoes configurational
---+-ST
I ti
PRfSSURE T O R R
Figure 2. Absorption isotherms for iodine in the same polythiophene film used for Figure 1, but in the presence of partial pressures of helium amounting to 0.375 and 0.600 torr, indicated by filled circles and triangles, respectively. Isotherms at only four temperatures are plotted, and the open circles and squares are again the data of Figure 1. Note that the discontinuities in slope all occur at about the same total pressure of the ambient gas
Gaseous Iz Absorption by Polythiophene
The Journal of Physical Chemistry, Vol. 90, No. 9, 1986 1975
changes as electrically active dopant is added. Such configurational changes, if they lead to changes in the binding energy, can of course result in curved isotherms. In the case of the concave upward isotherms, the binding energy would have to be increased as dopant is added. Carried to the logical extreme, this would lead to a kind of catastrophe in which it would be difficult to rationalize the linear character of the isotherms in the regime of higher pressures. As an alternative, we might investigate the possible effects of the “ionization” equilibria which lead to the p-type conductivity of the iodine doped polymer. At the outset, we have to realize that concave upward isotherms are possible only when “association” equilibria are involved. The extreme example of this would involve a phase transition in which large clusters of a new phase are produced. Then at the pressure of the transition the isotherm would actually become vertical in the two phase region (essentially infinitely concave upward). Good candidates for such association equilibria involving iodine are processes like 312
-
213-
+ 2e+
-
(1)
(where e+ is a valence band hole) and
13-
+ I,
I,-
(2) since I,- and I,- are known stable species. The process in eq 1, by itself, would not lead to a concave upward isotherm because the number of product “molecules” (four) exceeds the number of reactant molecules (three). However, in eq 2, two reactant molecules produce only one product molecule, and this could lead to concave upward behavior. We could, of course, invoke higher states of I, association than I> 1. In eq 22 a is the surface charge density on the plates. We need a value for a. The easiest way to find this value (consistent with the model) is to realize that the potential ~ . potential is to be set equal to between the plates is 4 ? ~ a l / This @. The result is the relation a
=~@/4al
(23)
The force (of attraction) per unit area between, and normal to, the plates is
Typically, for organic materials, Ygf is of the order of 20 to 30 dyn cm-I. Assuming 0 = 4’ and ygf = 24 dyn cm-’ gives
9 = 0.058 dyn cm-l
(14) Suppose the film is of thickness 1 and area A so that its constant (incompressible) volume is approximated by V = A1
(15)
when it is subjected to an ambient pressure p so that 1 is reduced by dl, the work performed will be -pA dl. This work is applied to increasing A and must therefore equal DW specified by eq 12. Thus -PA d l = 7 dA (16) or, using eq 15, we have P =Y/l
as the condition of balance. We return to a modified version of this relation below. Now the key point in the model we wish to develop is the following. The semiconducting film lies on a metal base (gold). When it is doped p-type with iodine, it could therefore form a Schottky junction9 with the gold. Using depletion layer theory
where, in the last step, eq 23 has been used. The spreading force (dyn cm-’) y,,due to the mutual repulsion of the like charge within the plates is 711 = (au/aA)aA,, = - ~ T L T ‘ I / K
(25)
In carrying out the differentiation in eq 25, we have to bear in mind that a = constant/A. The magnitude of y e may be comparable to that of y.lo Therefore, in a truly quantitative theory it should not be neglected. However, the value of 7 which we quote in eq 14 is based on the assumption of reasonable, but absolutely arbitrary, values for 0 and ygf. Thus in the present crude analysis there is no justification for complicating the issue by replacing 7 by 7 yll,and we avoid this embellishment.
+
(9) Grove, A. S. Physics and Technology of Semiconductor Deoices; Wiley: New York, 1967; p 267. (IO) y,,is really an electrocapillarity effect which acts to reduce the surface tension to 7 + y , , . We must estimate its magnitude. Substituting eq 23 gives -XIS2
(7) Shirakawa, H.; Ikeda, S. Synrh. M e [ . 1980, I , 175. (8) Adamson, A. W. Physical Chemistry of Surfaces; Wiley: New York, 1976; 3rd ed, p 340.
=,r and using the parameters in eq 20, setting I equal to the nominal value 3 cm, gives y = -0 036 dyn cm-l.
X
1977
J . Phys. Chem. 1986, 90, 1977-1979
7
\
0.8-
0 3
\ r\
0.6-
r
t!
E
0.4-
0 0
+-.-----0
200
_i
_ _ . _ I 1
400
800
600
PRESSURE (DYNESICM
1000
')
Plot of eq 27 as 1 (cm) vs. p (dyn cm-2),exhibiting the instability which initiates at p = 938 dyn cm *. Figure 4.
Since p I is a pressure, applied in the same direction as p , it should be added to the left side of eq 17. We obtain
or p = 'y/l.- ~ @ ~ / 8 7 1 '
(27)
Using the values of y, K , and @ listed in eq 14 and 20 we may use eq 27 to calculate p vs. I or I vs. p . Figure 4 exhibits the plot of p in dyn cm-2 vs. I in cm, obtained in this manner. This interesting curve exhibits an infinite slope at p = 938 dyn ern-,, or 0.71 torr, where I = 3.1 X cm. Furthermore, at values cm, I decreases as pressure decreases. of I less than 3.1 X This clearly indicates a mechanical instability in which, as the pressure is increased, the film collapses away from the compressive stress! Of course, the collapse cannot continue indefinitely since the elastic component of the film's viocoelastic behavior (which has not been considered in the theory thus far) will act to prevent this catastrophe.
Nevertheless, the occurrence of the instability is strongly indicated. The fact that it occurs at p = 0.71 torr, close to the pressure at which the discontinuity in slope appears in Figures 1 and 2, is, of course, a result of the magnitudes of the various parameters we have chosen. However, these magnitudes are not unreasonable and demonstrate that the theory is viable. If the film collapses to another thickness, discontinuously at the pressure of the instability, this is accompanied, according to eq 24, by an abrupt change in p I . It is well-known that a solute with a positive partial molar volume will exhibit an increase in partial vapor pressure upon an increase in external pressure. At constant partial vapor pressure this implies a reduction in solubility. This could be one reason for the discontinuous saturation appearing in the isotherms of Figures 1 and 2. Another possibility could involve the reorientation of rodlike polymer molecules from a configuration in which they are oriented with their long axes perpendicular to the gold surface to one in which the long axes are parallel to that surface. This is almost a requirement if the "spreading" of the film is to take place in the manner assumed by the above theory. Such a liquid-crystallike transition could result in a phase in which the solubility of I, was decreased. Our model does not entirely explain the approximate independence of the discontinuity in slope from temperature or I2 content. Off-hand one might expect 9 and other parameters to depend on both temperature and iodine content. Perhaps these parameters are not too sensitive (relative to the overall phenomenon) to these variables, or possibly the changes due to temperature are partly compensated by changes due to iodine content. The resolution of this problem will have to await further studies. Acknowledgment. This work was supported by N S F Grants C H E 82-07432 and DMR 84-21383. The authors are grateful to Drs. L. Warren and D. P. Anderson of the Rockwell International Science Center who prepared the polythiophene films and measured their masses. We also acknowledge the assistance of Professor F. Wudl of the University of California, Santa Barbara, who together with his co-workers prepared the polythiophene powder. Registry No. I,, 7553-56-2;polythiophene, 25233-34-5.
A Noniterative Solution of the WLMB Integral Equation for the Electrical Double Layer Pedro J. Colrnenares and Wilrner Olivares* Grupo de Qdmica TeBrica, Departamento de Quimica, Facultad de Ciencias, Uniuersidad de Los Andes, MCrida 51 01, Venezuela (Received: October 19, 1985)
The WLMB integral equation is solved for the electrical double-layer problem by using the noniterative method. The analytical series expression obtained for the contact potential gives values that fare very well with the Monte Carlo data for a 1-1 electrolyte in the restricted primitive model (RPM).
Lovett et al.' and independently Wertheim, introduced an integral equation for the one-particle distribution function of inhomogeneous systems. The characteristics of this equation were studied for the planar interacting electrical double layers by Olivares and McQuarrie3 and for one charged interphase by Blum et aL4 and Colmenare~.~For the electrical double-layer problem this equation can be written as (1) Lovett, R.;Mou, C.; Buff, F. J . Chem. Phys. 1976, 65, 570. (2) Wertheim, M . S . J . Chem. Phys. 1976.65, 2311. (3) Qlivares, W.; McQuarrie, D. A. J . Phys. Chern. 1980, 84, 863. (4) Blum,L.; Hernando, J.; Lebowitz, J. J . Phys. Chem. 1983,87,2825. ( 5 ) Colmenares, P. J. Thesis for Assistant Professor, Universidad de Los
Andes, MErida, Venezuela,
1984.
O022-3654/86/2090-1977$01.50/0
d In gi(x) dx -2aipj~x+R j=i
(r,x,xd J" gj(x2)rdCij"8x2 dx, d r -
max[O,x-R]
Ix-x~l
d W ) &ziedx (1) where pi is the particle density of ionic species i , gi(x) is the particle-wall distribution function. and C," is defined by pzizje2
Cijo(r,x,x2)= C,(r,x.x2)+ (2) tr where C,(r,x,x2)is the direct two-particle inhomogeneous cor0 1986 American Chemical Society
