Dielectric Properties of Bisphenol A Polycarbonate and Its Tethered

May 13, 2013 - BSC, Inc., 3046 Player Drive, Rapid City, South Dakota 57702, United States ... Finally, computer studies of the model compounds, 4,4â€...
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Dielectric Properties of Bisphenol A Polycarbonate and Its Tethered Nitrile Analogue John T. Bendler,† David A. Boyles,‡ Charles A. Edmondson,§ Tsvetanka Filipova,‡ John J. Fontanella,*,§ Mark A. Westgate,§ and M. C. Wintersgill§ †

BSC, Inc., 3046 Player Drive, Rapid City, South Dakota 57702, United States Department of Chemistry, South Dakota School of Mines and Technology, Rapid City, South Dakota 57701, United States § Physics Department, U.S. Naval Academy, Annapolis, Maryland 21402, United States ‡

S Supporting Information *

ABSTRACT: The relative permittivity and dielectric strength have been determined for a bisphenol A polycarbonate (BPAPC), in which a cyanoethyl group has been substituted for one of the geminal dimethyl groups. The new material (CN-PC) has a glass transition temperature that is 19 K higher than that for BPA-PC. In addition, the dielectric strength of CN-PC, 405 V/μm, is somewhat smaller than that for BPA-PC, 620 V/μm. The relative permittivity was determined from 10 to 105 Hz over a wide temperature range and at pressures up to 0.25 GPa. While the real part of the relative permittivity at 103 Hz and room temperature for BPA-PC is about 3, that for CN-PC is found to be greater than 4. Correspondingly, the γ relaxation region in CN-PC is very strong. For the γ relaxation, a strong increase in peak height as temperature increases and a strong decrease in peak height as pressure increases are observed. A relaxation is found at temperatures higher than the γ relaxation. This process is labeled as the β relaxation because it appears to be related to the β relaxation in BPA-PC in that the strength and position depend on the history of the material. The effects of pressure on the γ relaxation for both CN-PC and BPA-PC are quite large and similar to those previously seen for the γ relaxation in a fluorinated tetraaryl bisphenol A polycarbonate (DiF p-TABPAPC). In fact, the activation volume is found to be approximately the same for all three BPA-PC-based materials despite wide variations in both peak position and peak height. Finally, computer studies of the model compounds, 4,4′-diphenylpentanenitrile and diphenyl carbonate, were carried out. Both provide insight into the nature of the γ relaxation with the latter yielding an activation volume in approximate agreement with the experimental values.

1. INTRODUCTION Bisphenol A polycarbonate (BPA-PC) was used in high quality capacitors for many years. One of the drawbacks of the use of BPA-PC is the small value of about 3 for the real part of the relative permittivity, ε′.1 One approach that has been taken recently to increase ε′ is to make structural/chemical modifications in order to add dipoles to BPA-PC. For example, several of the authors have recently reported results for a fluorine-substituted, polycarbonate-based material, fluorinated tetraaryl bisphenol A polycarbonate (DiF p-TABPA-PC).2,3 That work was only partly successful because the increase in ε′ at room temperature relative to BPA-PC was only about 10% though the breakdown strength remained quite high. In addition, the low-temperature γ process loss maximum at 104 Hz in BPA-PC shifted from about 220 to 310 K in DiF pTABPA-PC.2 This shift of the γ loss peak to higher temperature is associated with an increase in the activation energy of the γ process, which in turn is likely caused by increased steric interactions of the ortho-substituted fluorine atoms on the aromatic rings next to the carbonate unit.2 Such an upward temperature shift in the γ process (accompanied by a © XXXX American Chemical Society

simultaneous increase in loss peak magnitude) is undesirable because it leads to greater dielectric loss in the polymer at room temperature. Because theoretical and experimental evidence indicates the presence of cooperative rotation between neighbor carbonate groups and phenyl rings within a polycarbonate chain4,5 as well as the onset of strong steric hindrance resulting from phenyl ring substitutions ortho to the carbonate, it seemed worthwhile to add a new dipole to the polycarbonate molecule at a location so as to minimize intramolecular steric interferences between the dipole and either the carbonate or the phenyl units, and thereby avoid increasing the activation energy of the γ process. In addition, cyano groups were selected as the new dipole addition to the BPA-PC structure because the dipole moment of the cyano group, −CN, is nearly 4 times larger than the dipole of the fluoro group, −F, and could result in a larger enhancement in orientational permittivity over that found for Received: February 1, 2013 Revised: May 1, 2013

A

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DiF p-TABPA-PC.6 It was recognized that a drawback to choosing the −CN dipole over −F is the larger size of −CN and therefore its greater likelihood for steric interference with neighbors. An attempt was made to minimize this anticipated steric problem by attaching the CN dipole to the backbone quaternary carbon via a flexible ethane-1,2-diyl spacer unit (see Figure 1), but it was later realized that strong dipole−dipole

undertaken to study possible intramolecular CN−ring interactions. (The important question of the influence of intermolecular effects on the dipole rotation barrier is discussed below in connection with an estimate of the activation volume. Without doubt, intermolecular forces will increase the barrier heights, often by factors of 2−3.) The model compound chosen was 4,4′-diphenylpentanenitrile (DPPN) shown in Figure 2.

Figure 1. Molecular structure of the cyano-substituted polycarbonate, CN-PC.

and dipole−ring forces are also present (see below) and likely reduced the final value of ε′ below that expected from the model. Schmidhauser and Longley7 were the first to synthesize the CN-PC polymer of Figure 1 with the objective of studying its gas transport properties. They did not report electrical measurements. Schmidhauser and Longley were surprised to discover that, in spite of the sizable side group, the CN-PC was more dense at room temperature than BPA-PC (1.24 g/cm3 vs 1.20 g/cm3), and they attributed the greater density, improved packing, reduced gas permeability, and lower specific free volume to enhanced polar interactions between the chains. A prior study of CN-substituted polycarbonates by Banucci8 examined the consequences of replacing one and then both BPA methyl groups with CN. Banucci noted large thermal and mechanical effects produced by the CN substitutions, and he, too, attributed the thermal/mechanical property modifications to enhanced polar attractions between the chains. The results reported below further support the conclusions of Schmidhauser/Longley and Banucci, namely that strong polar interactions exist between the CN-PC chains in the glassy state. Section 2 presents ab initio quantum SCF results for internal barriers to CN rotation in a model compound related to CNPC. While an outline of the synthesis of CN-PC is given in the Supporting Information, some further details of sample preparation are given in section 3 along with details of the electrical measurements. The results and discussion are found in section 4. In the course of these studies of the electrical properties over a wide range of temperatures and pressures, it was found that the low-temperature γ relaxation region is complex, and the position, shape, and intensity depend upon the history of the material. A characterization of the thermal history dependence of the γ relaxation in CN-PC is presented. In addition, high-pressure studies of the γ relaxation region (for both CN-PC and BPA-PC) along with computational estimates of the activation volume were carried out. Finally, the results of dielectric breakdown studies are reported.

Figure 2. Molecular structure of the model compound 4,4′diphenylpentanenitrile (DPPN), indicating the bond around which the CN dihedral is varied in the energy map of Figure 3.

Hartree−Fock calculations were carried out using STO-3G basis set with Gaussian 09 to determine the energy surface for complete rotation of the CN group around the axis indicated.9 Figure 3 shows the calculated energy profile for rotation of CN

Figure 3. Energy map for rotation of the CN group in the isolated, vacuum state model compound 4,4′-diphenylpentanenitrile (DPPN). The minimum-energy trans geometry is shown on the left, and the cis (transition state) geometry is shown on the right-hand side.

along with the two lowest energy minima. Surprisingly, the large CN group is seen to interfere with the phenyl rings even though the rings are three carbons removed. The barrier to CN rotating past the phenyl ring is about 7 kcal/mol (0.303 eV), nearly twice the barrier to phenyl ring rotation itself in BPAPC.4 The lowest energy conformation of DPPN is for the CN dipole in the trans configuration (see the left conformation in Figure 3) to the quaternary carbon, also being the most distant location of the CN from the backbone. The highest energy conformation occurs when the CN group is cis to the quaternary carbon (see the right conformation in Figure 3), corresponding to its closest approach to the polymer backbone. In addition, two intermediate energy minima (geometries not shown) are found with the CN group gauche to the quaternary carbon (Figure 3 shows these two minima at 90° and 270°). Thus, in spite of the spacer group separating the CN dipole from the quaternary carbon, appreciable steric interaction occurs upon CN rotation in the isolated model compound and much greater interference can be expected in the bulk polymer.

2. SCF CALCULATIONS FOR A MODEL COMPOUND The new CN dipole in CN-PC is attached to the quaternary carbon on the polymer backbone using a flexible ethane-1,2-diyl spacer unit (see Figure 1), and so the new dipole is a significant distance from the carbonate group and was initially also expected to avoid contact with the aromatic rings. When the experimental dielectric results (see below) indicated significant dipole hindrance to reorientation, molecular calculations were B

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3. EXPERIMENTS The synthesis of the CN-PC is described in the Supporting Information. All materials were prepared using the techniques described there. Nonetheless, as will become apparent, small differences in the electrical relaxation spectrum are observed for the as-prepared samples. These differences may be attributed to small variations that occur during the film-casting process. For example, one factor that could cause small differences in the electrical properties is solvent evaporation rate which, in turn, depends on sample thickness. Because the casting was done at room temperature and atmospheric conditions, there are also small variations in temperature, humidity, etc. The films were prepared for measurement by evaporating aluminum electrodes onto the surfaces to form a parallel plate capacitor. Complex conductance measurements were then performed using a CGA-85 capacitance measuring assembly, which operates at 17 frequencies from 10 to 105 Hz. (This instrument is a prototype for the bridges that are currently available commercially from Andeen-Hagerling, Inc., Cleveland, OH.) The equivalent parallel capacitance, C, and conductance divided by the angular frequency, G/ω, were measured. The system is accurate to about 10 aF in both C and G/ω. Two different systems were used to vary the temperature. Some measurements were carried out in vacuum from 5.5 to 350 K in a Precision Cryogenics CT-14 dewar, and the temperature was controlled using a LakeShore Cryotronics DRC 82C temperature controller. Other measurements were carried out at atmospheric pressure in flowing nitrogen gas using a Novocontrol sample holder and Quatro temperature controller. That system operated from 123 to 523 K. In both cases, the temperature is held constant to within 0.01 K, and the accuracy is estimated to be about 0.05 K. The high-pressure experiments were carried out using equipment described elsewhere.11 For the present experiments, Fluorinert FC-770 was used as the pressure transmitting fluid and the temperature was controlled by an on−off controller. Because of the large mass of the pressure vessel, the temperature remained constant to within about 0.1 K while the pressure data were taken. The accuracy of the temperature is estimated to be about 0.5 K. In each case, the sample was equilibrated at each pressure for 30 min with pressures decreasing from the highest pressure. The pressure was estimated to be accurate to within 0.0004 GPa (4 bar). The data were transformed to the complex relative permittivity as follows. First, geometrical measurements were made and ε′ was calculated at 1000 Hz and room temperature using the usual equation for a parallel plate capacitor ε′ =

Cd ε0A

ε″ = ε′ tan δ = ε′

G ωC

(2)

The dc dielectric strength was measured using a Hippotronics model HD140 Auto A, ac/dc hipot tester. The samples were immersed in a Fluorinert FC-770 high dielectric strength fluid to suppress surface events that were not indicative of the bulk dielectric properties. The sample was placed on a polished conducting steel ground plane. The upper electrode was a 1 cm diameter tool steel post ∼75 mm in length. The weight of the post was used to establish a consistent contact pressure between the electrodes and the sample. The edge of the cylindrical electrode post was radiused in accordance with ASTM D3755 test procedure in order to minimize the probability of edge breakdown during testing. The face of the electrode was polished to a mirror finish with 0.1 μm polish compound to minimize the probability of a breakdown event being initiated by the surface texture of the electrode. A voltage ramp rate of 500 Vdc/s was used throughout the test. The Hippotronics hipot tester was set to trigger at a current of 1 mA for all tests. The applied voltage at breakdown was converted to an electric field using the measured sample thickness. The cumulative probability for failure was estimated using the median rank approximation.12 A Weibull two-parameter probability distribution αW

P(E b) = 1 − e−(E b / E0)

(3)

was fit to the experimental data. P(Eb) is the cumulative probability of failure for a given electric field, Eb. E0 is the characteristic field (that will be referred to in this paper as the dielectric strength) and is the electric field corresponding to a 63.2% probability of failure. The exponent αW is a shape parameter that is related to the spread in observed values.

4. RESULTS AND DISCUSSION Figure 4 is a plot of the cumulative probability of failure as a function of applied electric field. The dielectric strength of the material, E0, is 405 V/μm. This value is somewhat smaller than the dielectric strength observed for purified BPA-PC.1 The Weibull shape parameter, αW, is 6. The figure represents collective results for four different as-prepared samples. When analyzed individually, the samples showed a significant variation

(1)

ε0 is the permittivity of free space, A is the area of the electrodes, and d is their separation (the thickness of the sample). The value at 296 K, 1 bar, and 1000 Hz for CN-PC was found to be ε′ = 3.79 ± 0.03. This is about 25% higher than the value for BPA-PC.1 The real part of the relative permittivity was calculated at other temperatures, pressures, and frequencies by multiplying the ratio of the capacitances (CT,P,f/C296,1,1000) by 3.79. This procedure is based on the assumptions that thermal expansion is insignificant in the case of temperature variation and that isothermal bulk modulus is not important for reduction of the variable pressure data. Finally, the imaginary part of the relative permittivity, ε″, at all temperatures, pressures, and frequencies was calculated using

Figure 4. Cumulative probability of failure as a function of the applied electric field in CN-PC. The solid squares represent experimental dielectric breakdown events. The solid line is Weibull two-parameter fit. The thickness of the sample is t. C

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in fit parameters. The experimentally determined dielectric strength depends on many factors, some of which are not indicative of the bulk properties of the material. The observed variation from sample to sample in this material is not well understood at the present time. Thus, all breakdown events in all samples were included as a single data set in Figure 4. The results for ε′ and ε″ vs temperature at 104 Hz in vacuum for CN-PC (sample 1) are shown in Figure 5. (The data were

Figure 5. Real (open circles) and imaginary (filled circles) parts of the relative permittivity at 104 Hz for as-prepared CN-PC (sample 1). (The data were taken from the lowest temperatures to the highest temperature.)

taken from the lowest temperatures to the highest temperature.) Comparisons of these results for CN-PC with those for purified BPA-PC1 are shown in Figure 6a,b. As is apparent from Figure 5, the relaxation/conductivity spectrum for CN-PC is composed of three relaxations (labeled α, β, γ as temperature decreases) accompanied by a rapidly rising signal as temperature increases. The rapidly rising signal is due to the dc (presumably ionic) conductivity, and neither that nor the α relaxation will be considered further in this paper. The results for a sample (sample 2) where the β relaxation is stronger than that for the sample shown in Figures 5 and 6 (sample 1) are plotted in Figure 7. The data for two frequencies are plotted in Figure 7: 10 and 104 Hz. It is clear that the height of the γ relaxation increases strongly as frequency/temperature increases. This is the same behavior that is exhibited by the γ relaxation in BPA-PC1 or DiF p-TABPA-PC.2 As will be seen, this peak is well-defined in that the peak position varies very little from sample to sample or when the thermal history of the sample changes. This can be seen by comparison of Figures 5 and 7, for example. However, some variation in broadening and peak height is observed. Certainly the peak heights for the γ relaxation in Figures 5 and 7 are different, the peak height in Figure 5 being almost 0.11 while that in Figure 7 is less than 0.08. As indicated above, the differences seen between sample 1 (Figure 5) and sample 2 (Figure 7) are not due to chemical differences (the chemical compositions are identical) but are the result of variations in the film-forming conditions. On the other hand, as can be inferred from Figure 7, the peak height of the β relaxation does not increase with frequency/ temperature as does the γ relaxation. Rather, the peak height of the β relaxation decreases as temperature increases. Also, the β relaxation is not well-defined in that it changes position and strength with the history of the sample. In fact, it is straightforward to make the β relaxation disappear by thermal cycling. Figure 8 shows results for a sample (sample 3) that is

Figure 6. (a) Real part of the relative permittivity at 103 Hz for asprepared CN-PC (sample 1: open circles) and purified BPA-PC (filled circles). (b) Imaginary part of the relative permittivity at 103 Hz for asprepared CN-PC (sample 1: open circles) and purified BPA-PC (filled circles).

Figure 7. Imaginary part of the relative permittivity at 10 and 104 Hz for as-prepared CN-PC (sample 2).

initially heated from room temperature to 493 K (open squares). This temperature is above the glass transition temperature. In order to reduce the effects of geometry that may change with temperature, the representation is tan δ rather than ε″. The open triangles represent cooling from 493 to 123 K, and the filled circles represent the final heat from 123 K to room temperature. For comparison, the corresponding data (now at 103 Hz) for the sample shown in Figure 5 (as-prepared sample 1) are also plotted in Figure 8. The heat treatment causes a significant broadening on the high temperature side of the γ relaxation. However, results at 10 Hz (not shown) exhibit a shoulder on the high temperature D

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Figure 9. Zero-shifted (0.015 from each previous plot) tan δ vs temperature at 102 Hz for an as-prepared CN-PC (sample 4). The letters designating the temperature scans are located at the beginning of the temperature scan. Also, the open symbols are associated with increasing temperature and the filled symbols designate decreasing temperature. (a) The as-prepared sample 4 was cooled to 123 K, and the open triangles represent the initial data run (from 123 to 373 K). (b) The filled triangles represent data for decreasing temperature after the initial data run. (c) The open squares are the data for increasing temperature after (b). The sample was removed from the cell, heated in vacuum to 473 K, and transferred quickly in situ to a glovebox where it was quenched to 77 K, warmed to room temperature (in the glovebox), removed from the glovebox, loaded into the cell, and then data run (d) was begun. (d) After the thermal treatment described in the previous sentence, the sample was cooled to 123 K, and the open circles represent the data from 123 to 473 K. The sample remained at room temperature in flowing nitrogen for 3 days, and then the sample was cooled to 123 K. The open deltas are the data as the sample was warmed from 123 to 373 K. The filled squares are the data as the sample was cooled from 373 to 123 K. The sample again remained at room temperature in flowing nitrogen for 3 days, and then the sample was cooled to 123 K. The open diamonds are the data as the sample was heated from 123 to 473 K. Finally, the filled diamonds represent the data as the sample was cooled from 473 to 123 K.

Figure 8. Plot of tan δ vs temperature at 103 Hz for the γ relaxation region in CN-PC. The open circles are as-prepared sample 1. The remaining data are for as-prepared sample 3: the open squares are the initial heat from room temperature to 493 K, the open triangles are cooling from 493 to 123 K, and the filled circles are the final heat from 123 K to room temperature. (The data for temperatures above about 420 K are not shown.)

side of the γ relaxation, indicating a shift of at least a portion of the β relaxation to lower temperatures. However, the shifted relaxation is very weak. To learn more about the β relaxation, further thermal cycling experiments were carried out, and the results for tan δ at 100 Hz are shown in Figure 9. The letters designating the temperature scans are located at the beginning of the temperature scan. Also, open symbols are associated with increasing temperature and filled symbols designate decreasing temperature. All of the data are for a different, single sample (sample 4). Each data run is shifted vertically by 0.015 from the previous run. The bottom three traces (a−c) follow the protocol of Figure 8 with one important exception. The highest temperature reached in the initial data run (trace a for sample 4) shown in Figure 9 was only 373 K as opposed to 473 K for the data shown in Figure 8 (samples 1 and 5). 373 K is almost 70 K lower than Tg. Nonetheless, traces b and c show the same change in the relaxation spectrum (vanishing or shifting of the β relaxation and broadening and decrease in the peak height for the γ relaxation) as observed in Figure 8. Consequently, Figure 9 shows that “annealing” effects (redistribution of the dipoles) take place well below the glass transition temperature. Other experiments showed that the “annealing” effects could be observed as low as 110 K below Tg. Of most interest is the subsequent data, trace d. After data run c, the sample was removed from the cell, heated in vacuum to 473 K, transferred quickly in situ to a glovebox where it was quenched to 77 K, warmed to room temperature (in the glovebox), removed from the glovebox, loaded into the cell, and then data run d was begun. Trace d shows that, in general, the initial relaxation spectrum is restored. The β relaxation reappears though it is now somewhat stronger and the position is shifted slightly. Also, the γ relaxation is as sharp and strong as it was initially (data run a). The subsequent data runs, e−h, were up and down runs to and from 373 and 473 K. Both cycles resulted in a broadened and weakened γ relaxation. Interestingly, a weakened and shifted β relaxation was also observed in traces e−h. This is not surprising as no special attempt was made to cool quickly. These results suggest that the β relaxation observed in the present work for CN-PC is related to the β relaxation in BPAPC. This relaxation has been mentioned by Floudas et al.,13

who described the β relaxation in BPA-PC as “a process which depends strongly on annealing”. Similar observations for the β relaxation in BPA-PC were made recently by several of the authors.1 Next, the isochronal data for the γ relaxation were analyzed. Typical results for an “annealed” sample (sample 5) are shown in Figure 10. The as-prepared sample 5 had been heated to 323 K in vacuum before taking data as temperature decreased. The peak position, Tmax, and the peak height were determined by

Figure 10. ε″ vs temperature for CN-PC (sample 5) at 10 Hz (squares), 103 Hz (triangles), and 105 Hz (hexagons). E

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Table 1. Best-Fit Arrhenius Parametersb for the γ Relaxation in CN-PC, DiF p-TABPA-PC, and BPA-PCa

fitting the empirical double asymmetric sigmoidal function (DAS) ε″ = y0 +

ADAS −(x − xC + w1/2)/ w2

1+e ⎛ ⎞ 1 ⎜1 − ⎟ ( /2)/ − x − x − w w C 1 3 ⎠ ⎝ 1+e

log(τpreTmax(s)) CN-PC sample 1 sample 3 sample 5 DiF p-TABPA-PCc BPA-PCd BPA-PCe

(4)

to the data. (Equation 4 is used as a six-parameter smoothing function.) ADAS is the amplitude, y0 is the offset, xC is the center, and w1, w2, and w3 are width parameters. (For best-fit curves that are similar to those found for CN-PC in the present work, see Figure 4 of ref 2 where the best-fit curves and data are shown for the γ relaxation in DiF p-TABPA-PC.) In this case, x = T. For each frequency, both Tmax and the peak height were determined numerically using the DAS function and best-fit parameters. An Arrhenius plot of the results is shown by the

−13.76 −13.60 −13.83 −15.6 −14.9 −15.1

ETmax, eV (kcal/mol) 0.478 0.485 0.482 0.66 0.46 0.45

(11.0) (11.2) (11.1) (15.2) (10.6) (10.4)

a The uncertainty in log(τ (s)) and the derivative is estimated to be about 5%. An extra decimal place is shown for CN-PC in order to distinguish between the samples. bτpreTmax is the pre-exponential and ETmax is the activation enthalpy in eq 5. cReference 2. dPurified sample from ref 1. eCommercial sample from ref 1.

the filled circles in Figure 11, where T is the temperature at which the experiment was carried out. The results are similar to those for both BPA-PC1 and DiF p-TABPA-PC2 in that the isochronal and isothermal data give rise to Arrhenius plots that are greatly displaced from one another. Typical isothermal high-pressure data are shown in Figure 12. The isothermal analysis procedure described in the previous

Figure 11. Logarithm of the peak frequency vs reciprocal temperature (Arrhenius plot) for the γ relaxation in CN-PC. The open circles and squares represent log( f) vs 1000/Tmax for vacuum data in the dewar (sample 5) and atmospheric pressure in the pressure vessel (sample 6), respectively. The filled circles and squares represent log( f max) vs 1000/ T for vacuum data in the dewar (sample 5) and atmospheric pressure in the pressure vessel (sample 6). Figure 12. Conductance divided by the angular frequency vs the logarithm of the frequency at 237 K and 0.25 GPa (open squares), 0.15 GPa (filled circles), and 0.05 GPa (open circles) for sample 6.

open circles in Figure 11. Because the behavior is approximately Arrhenius, the equation τ = τpre z exp(Ez /kBT )

(5)

paragraph was also carried out for the high-pressure data. The points shown in Figure 13 are the results of that analysis. It was found that the isotherms in Figure 13 exhibited slight curvature. Consequently, the quadratic

was best-fit to the data where Ez is the activation enthalpy, τpre z is the pre-exponential, z = Tmax (indicating that the isochronal data were analyzed), and the frequency was transformed to a relaxation time, τ, using 2πfτ = 1. This best-fit procedure was also carried out for the samples for which the data are shown in Figure 8 (sample 1 and decreasing temperature for sample 3). The best-fit parameters for the 3 samples are listed in Table 1, and the average values of the Arrhenius parameters are about ETmax = 0.48 eV (11.1 kcal/mol) and log(τpreTmax (s)) = −13.7. The activation enthalpy and the pre-exponential for the γ relaxation in BPA-PC and Di-F p-TABPA-PC are also listed in Table 1 for comparison. While the activation enthalpy for CNPC is slightly larger than that for BPA-PC, the value is a great deal smaller than that for Di-F p-TABPA-PC. Some isothermal results were also analyzed for sample 5. In this case, eq 4 was used where x = f and f is the applied frequency. Next, z = fmax and f max is the frequency where ε″ has its maximum value. An Arrhenius plot of the results is shown by

log(fmax ) = log(fmax ,0 ) + AP + BP 2

(6)

was best-fit to the data. The values of −A = (∂ log(τ)/∂P)P=0 are listed in Table 2. Because the results for CN-PC are approximately Arrhenius (see Figure 11), a meaningful activation volume can be calculated using13,14 ⎛ ∂ ln τ ⎞ ⎟ ΔV * = kBT ⎜ ⎝ ∂P ⎠T

(7)

The activation volumes at each temperature are also listed in Table 2. The average value of ∼36 cm3/mol is relatively large compared with other secondary relaxations below Tg.15 For example, ΔV* for the sub-Tg relaxation in poly(ethylene oxide) is on the order of 4 cm3/mol.16 In fact, 36 cm3/mol is more typical of values observed for relaxation associated with the F

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reorienting species is the same (or at least similar) in both cases. This may explain the similar activation volumes because similar species would be expected to produce a similar volume change as the dipole reorients between the equilibrium position and the saddle point. On the other hand, the relaxation process may be more difficult in the case of Di-F p-TABPA-PC (as reflected in the peak position or activation enthalpy) because of steric interference between the ortho F-substituents on the rings and the neighbor carbonyl oxygen. Finally, because of the similarity in activation volumes for CN-PC and Di-F p-TABPA-PC, the effect of pressure on the γ relaxation in BPA-PC was also studied. Because a detailed analysis of the atmospheric pressure γ relaxation in BPA-PC has been given elsewhere1 and the effect of pressure is qualitatively similar to that shown in Figures 12 and 13 for CN-PC, only the numerical results are given. Specifically, the resultant values of (∂ log(τ)/∂P)P=0 are listed in Table 2 along with the activation volumes. As has been pointed out, the activation enthalpy for BPA-PC is slightly smaller than that for CN-PC. (This is reflected in a slightly lower peak position for BPA-PC.) However the strength of the relaxation in BPA-PC is at least a factor of 6 smaller than that for CN-PC. Nonetheless, the values of the activation volumes for BPA-PC, 36 and 45 cm3/ mol at 231 and 203 K, respectively, are approximately the same as those for both CN-PC and Di-F p-TABPA-PC. In an attempt to understand the high-pressure results for the γ process, computer studies of the small-molecule model compound diphenyl carbonate (DPC) in vacuum were carried out. A few remarks concerning the relevance of small-molecule studies which do not include intermolecular effects are appropriate. First, all studies of the γ relaxation in BPA-PC agree that both carbonate group motion and phenyl ring motion are involved,1,4,5,13,14,20,21 and DPC is the smallest subunit of BPA-PC that contains both groups. Second, prior work of Jones et al.22,23 comparing structures found using ab initio methods, either Hartree−Fock or density functional, show excellent agreement between small molecule, vacuum ab initio geometries and single crystal X-ray structures for BPA-PC and several model compounds. Third, it has long been recognized that the structure of dense liquids and glasses is chiefly controlled by short-range, steep, repulsive interactions between molecules and that the long-range attractive forces act essentially as a background effect renormalizing the cohesive energy and overall bulk density.24−26 The Weeks−Chandler− Anderson24 (WCA) method, for example, successfully splits the intermolecular energy into a short-range repulsion plus a weak, long-range attraction, treating the latter as a perturbation. For these reasons one may expect changes in molecular shape and volume to correlate with changes in local structure and packing in the liquid and glass. Three conformations of DPC are found computationally and observed experimentally.4,20−23 The trans−cis conformer is the most polar and highest energy conformation, but it is assumed to be less than 10% of all carbonates in the glass, and may be difficult to convert to the extended trans−trans form.20,21 We consider only interconversions of trans−trans conformers in the following. The trans−trans anti and trans−trans syn conformations are similar in energies and geometries.4 A steepest descent energy path between the two conformational states was studied using the SCAN option of Gaussian 09, and the energy variation along the path is displayed in Figure 14 as a single aromatic ring−carbonate dihedral angle is varied.

Figure 13. Logarithm of the frequency of the peak maximum vs pressure for the γ relaxation in CN-PC (sample 6). The approximate temperatures are 232 K (filled squares), 237 K (open squares), 242 K (filled circles), 248 K (open circles), 253 K (filled trianges), 259 K (open triangles), 265 K (filled diamonds), and 271 K (open diamonds).

Table 2. Pressure Variation of the Relaxation Time and Activation Volumea for the γ Relaxation in CN-PC, DiF pTABPA-PC, and BPA-PCb T (K) 232 237 243 248 253 259 265 297 304 311 203 231

(∂ log(τ(s)))/(∂P) (GPa−1) CN-PC 9.03 7.43 7.60 6.91 6.41 6.17 6.16 DiF p-TABPA-PCc 6.2 6.4 6.2 BPA-PC (purified) 11.6 8.2

ΔV* (cm3/mol) 40.1 33.7 35.3 32.8 31.0 30.6 31.2 35 37 37 45 36

a ∂ log(τ (s))/∂P is the pressure derivative of the relaxation time. ΔV* is the activation volume calculated using eq 7. bThe uncertainty in log(τ (s)) and in the derivative is estimated to be about 5%. c Reference 2.

glass transition for polymers such as poly(propylene oxide)17,18 (PPG) or poly(dimethylsiloxane−ethylene oxide) copolymer19 (PDMS-EO). However, it has been pointed out2 that the large value of ΔV* for the γ relaxation in Di-F p-TABPA-PC is perhaps not surprising considering that the activation volume associated with the α relaxation in a related material, BPA-PC, is among the largest for any material, being nearly 400 cm3/ mol.14 Consequently, the large value of ΔV* for the γ relaxation in CN-PC is also not surprising. However, what is surprising is that, as can be seen in Table 2, the values of ΔV* for the γ relaxation in CN-PC and Di-F p-TABPA-PC are about the same. This occurs despite the large difference in peak positions (also reflected in the activation enthalpies). For example, the 103 Hz relaxation in CN-PC (E ≈ 0.48 eV or 11.1 kcal/mol) occurs at about 230 K while that for Di-F p-TABPA-PC (E ≈ 0.66 eV or 15.2 kcal/mol) occurs at about 280 K (Figure 4 or 15 of ref 2). One interpretation of this result is that the G

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To estimate the energy change for a volume strain of 11%, consider the continuum elastic expression for the energy of a volume strain ε: ΔE =

1 2 1 Bε ≅ (5 × 109 N/m 2)(0.11)2 ≅ 1.4 kcal/mol 2 2 (9)

taking the bulk modulus B of BPA-PC as 5.0 × 10 N/m and using the molar volume of BPA-PC of 211 cm3/mol. Thus, a volume strain of 11% increases the activation enthalpy by a factor of 2.4 over the vacuum result in Figure 14. An independent Monte Carlo integration method for estimating the volume change per BPA-PC monomer unit associated with passage of a phenyl ring through a coplanar carbonate configuration is described in the Appendix. Lastly, it is useful to comment on the contributions of the carbonate dipoles and CN dipoles to the experimental permittivity of CN-PC polymer. First, consider the glassy state BPA-PC itself. The refractive index of glassy BPA-PC has been carefully measured by LeGrand and co-workers and is 1.588,27 so n2 = ε∞ ≅ 2.52, and using the molar volume 211 cm3 given above, the density of carbonate dipoles is easily found. The carbonate dipoles associated with the trans conformations are each about 0.2 D, so that even for completely free, liquid-like, 180° carbonate rotations (using, for example, the Onsager equation for the dielectric constant of a polar liquid28), the trans carbonate conformations alone of BPA-PC cannot explain the large permittivity of ε′ ≈ 3.0 found experimentally. A possible explanation is that cis−trans dipoles also occur in reasonable abundance and partially reorient in the applied field, contributing with relaxation strength Δε′ ≅ 0.5. For CN-PC, the experimentally measured permittivity at room temperature is ≈4.0. On the other hand, using the experimental bulk density ρ = 1.24 g/cm3,6,7 and the dipole moment of a CN group μCN ≅ 4 D, the Onsager equation for a freely rotating dipolar liquid28 predicts a static permittivity of about εOnsager ′ ≈ 17 or a hypothetical relaxation strength ΔεCN ′ ≅ 14. Comparing measured and predicted permittivities for CN-PC indicates that only about 1/10 of the CN dipoles are able to rotate in the glass, or more likely, most are severely restricted in their rotational freedom. While the focus of this paper is the science of CN-PC and BPA-PC, a few comments concerning the applicability as capacitor materials are appropriate. While ε′ for CN-PC represents an improvement over that for BPA-PC, the rather large loss associated with the γ relaxation must be considered. The upper limit of loss for useful capacitors is usually taken to be tan δ ≈ 0.01. In order to evaluate the loss for the present materials, the values of ε″ must be divided by ε′. Of course, ε′ varies with frequency and temperature (and pressure), but a reasonable approximation is to use ε′ ≈ 4. With this in mind, results for an annealed sample such as that shown in Figure 10 show that CN-PC meets the loss requirement in the vicinity of room temperature for frequencies below about 103 Hz. The extra loss due to the β relaxation for the as-prepared material, such as that shown in Figure 6b, also represents a concern. However, in the present paper, it was shown how to eliminate the β relaxation, namely by thermal annealing. Finally, the breakdown strength for the as-prepared CN-PC is lower than that for BPA-PC, and this is a very important factor because the energy density varies as the square of the electric field. However, it is clear that impurities strongly affect the breakdown strength.1 While care was taken in the preparation 9

Figure 14. Energy path from anti to syn conformations of DPC as one phenyl ring−carbonate dihedral angle is varied from 0 to 360°.

For each ring of the DPC molecule, there are two rotational pathways to convert the molecule from anti to syn. Either ring can rotate in a clockwise or counterclockwise direction (assuming one is sitting on one of the rings and facing the central carbonate group), thereby passing through either a perpendicular (90°) ring−carbonate configuration or through a coplanar (0°) configuration. The pathway through the perpendicular (90°) ring−carbonate configuration is very low in energy, illustrated by the two small bumps on the energy surface near 180° and 360° in Figure 14. The pathway through the coplanar (0°) configuration is significantly higher in energy (∼0.043 eV or 1.0 kcal/mol), corresponding to the larger maxima in Figure 14 near 60° and 240°. Of equal importance are geometry changes that take place when the molecule passes through the coplanar configuration. The bond angles are significantly distorted as the coplanar configuration is reached. These bond angle distortions momentarily elongate the DPC molecule and have two important consequences: (1) the length of the polymer unit expands by about 0.3 Å, generating local intermolecular and intramolecular strain, and (2) the local strain produced by the bond distortions raises the energy of the transition state. Estimates for the magnitude of each effect are now given. The molecular weight of one monomer of BPA polycarbonate is 254.0 g/mol, and the density of BPA-PC is 1.20 g/cm3 at room temperature. From this it follows that the molar volume is 211.7 cm3/mol. Therefore, the volume of one monomer unit = 351 Å3, and if we model the monomer as a sphere, then the radius of each monomer is roughly 4.38 Å. Assuming that the carbonate−ring expansion of 0.3 Å may be attributed to the monomer as a whole, then the volume of the monomer at the transition point V* will momentarily expand to about V* ≅

4π (4.38 Å + 0.30 Å)3 = 429 Å3 3

(8)

leading to a momentary volume strain of V*/V = 1.22, or 22%. Thus, the volume expansion per mole, ΔV* = V* − V, would be ∼47 cm3. It is perhaps more reasonable to assign the expansion of 0.3 Å to the monomer diameter and not to the radius, in which case the monomer expansion will be roughly 23 cm3/mol (or 11% volume expansion)still of the same order of magnitude as the activation volumes reported above for the low-temperature gamma process. H

2

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activation volume was taken as ΔV* ≃ (254/332) × (V* − Vmin) = 0.76 × (60 cm3/mol) ≈ 45 cm3/mol, similar to the estimate found in the text. In light of the approximate character of the Monte Carlo integration algorithm, numerical agreement is fortuitous, but the order of magnitude and qualitative trend support the idea that the activation volume measured reflects a backbone rearrangement.

of the CN-PC, it could be further purified. Consequently, between thermal annealing and additional purification, it is likely that the loss and electrical energy density in this material could be improved significantly. While consideration is being given to such experiments, attention is currently focused on other materials as they appear to be more promising.

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5. CONCLUSIONS The relative permittivity and dielectric strength have been determined for bisphenol A polycarbonate, in which a cyanoethyl group has been substituted for one of the geminal dimethyl groups. The new material, CN-PC, has a glass transition temperature, Tg = 440 K, that is slightly higher than that for BPA-PC for which Tg = 421 K. In addition, the dielectric strength of CN-PC, 405 V/μm, is somewhat smaller than that for purified BPA-PC, 619 V/μm. A strong γ relaxation region is found, and ε′ for CN-PC at 103 Hz and room temperature is found to be greater than 4 vs 3 for BPA-PC. A relaxation is found at temperatures higher than the γ relaxation and is labeled the β relaxation. This relaxation is thought to be related to the β relaxation in BPA-PC because the strength and position of the associated loss peaks depend on the history of the material. The variations in the as-prepared materials are attributed to the film-casting process, and the β relaxation is found to be very sensitive to thermal cycling. The unusual characteristics often observed for the γ relaxation in BPA-PCbased materialsa strong increase in peak height as temperature increases and a strong decrease in peak height with increasing pressureare observed. High-pressure permittivity measurements were also carried out in BPA-PC. The effects of pressure on the γ relaxation for both CN-PC and BPA-PC are quite large and consistent with results found for the γ relaxation in Di-F p-TABPA-PC. In fact, the activation volume is found to be approximately the same for all three BPA-PC-based materials despite the wide variation in both peak position and peak height. Computer calculations on the model compounds DPPN and DPC have been carried out. The calculations on DPPN give insight into the nature of the reorientation mechanism of the CN dipoles. The results for the activation volume modeled using DPC are in approximate agreement with the experimental values. Finally, comparison of the measured permittivity of the CN-PC glass with a model calculation assuming free CN rotation in the glass suggests that the CN dipoles are severely restricted in their motions.

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ASSOCIATED CONTENT

S Supporting Information *

Synthesis of the CN-PC. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Tel +01 410 293 5507; fax +01 410 293 5508; e-mail [email protected], [email protected] (J.J.F.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the U.S. Office of Naval Research. D.A.B., J.T.B., and T.S.F. gratefully acknowledge financial support by the Department of Defense−Army Research Office (Grant DAAD19-01-1-0482). J.J.F. acknowledges support from JJFontanella LLC.

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REFERENCES

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APPENDIX

Monte Carlo Estimate of the Activation Volume ΔV* Using Gaussian 09

In order to obtain an independent estimate for the activation volume, ΔV*, associated with a coplanar phenyl ring− carbonate configuration, a Monte Carlo surface integration algorithm in Gaussian 09 was employed.9 The volume subroutine in Gaussian 09 has an accuracy of about 10% and is available to estimate the solvent cavity radius for use with the Onsager reaction field model. Monte Carlo surface integration calculations of molecular volume were carried out for p-cumyldiphenyl carbonate, using both the optimized minimum energy geometry and the coplanar transition state geometry, with the results being Vmin = 210 cm3/mol and V* = 270 cm3/mol. Because pcumyldiphenyl carbonate is slightly larger than a BPA-PC repeat unit (Mw = 332 g/mol vs 254 g/mol for BPA-PC), the I

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