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236 E L E C T R I C A L P R O P E R T I E S OF HIGH P O L Y M E R S f irs t four, essentially nonpolar polymers, tan 6 was about 2. 5 (±0. 5) X 10~5 and for the polar materials , about an order of magmtude larger. At 4 . 2 i t was confirmed that e' is independent of V from 40 to 1000 Hz. Hara et a l . (100) also have examined the dielectric properties of PS and poly-p-chlorostyrene. A classical bridge and a calorimetric method were used by Bobo and Perr ier (101) to determine tan 6 at 500 Hz for Mylar ( P E T ) , Teflon ( P T F E ) , and Kapton (PI) at 4 . 2 ° , 770, and 2930K. Also, he obtained the ac and dc dielectric strengths for P T F E , nylon, P E , P E T , P V C , PI , micaceous and kraft papers, P T F E - P I mix, and P T F E - g l a s s in liquid He at 4 . 2 ° K , and in both liquid and gaseous N2 at 770K. Conduction Conduction in Liquids and Solutions This I S a complicated and extensive field,, and our review only samples it. The Russians are quite active in this field; for example, Barabanov et a l . (103) found by a series of viscometric, turbidometric, and electrochemical techmques that solutions in ketones of copolymers of methyl methacrylate with (RCH):(CR') , (where R ' may be H, C I , CN, or CH3 and R may be H or Ph or NO2) had the following features: If a low molecular weight e lec- trolyte (e .g . , chloroacrylic acid, K C I A A , or Et4NBr) is added as a third component, the size of the polymer coil is much less than when m a benzene solution with no third component. F r o m light scattermg, the presence of the third component, with specific effects for each copolymer and solvent, leads to new conforma- tions. When ternary copoljmiers (obtained by neutralization of the bmary copolymers by K O H , NaOH, and LiOH) were dissolved in Me2CO-MeOH, the polymer's salt groups dissociated to a greater extent than its acid groups and the mtrmsic viscosity was inde- pendent of the ratio of acid/salt , the type of metal ion, and the degree of substitution of the acid. In a subsequent paper (104), radiotracer techmques were used to show that, at sufficiently high concentrations, divalent B a and Sr 10ns (from MAA salts) become structure-forming agents in the solution. Conductance
CONDUCTION 237 measurements before and after ultrasonic agitation indicated supra- molecular structures. Budtov (105) gave a theory of ionic mobility in dilute polymer solutions. Hydrodynamic interactions and solvation of the chams by the ions are included, along with a discussion of the effect of e'. Data are said to corroborate the theory. Conductivity as a function of T and concentration c was measured by Sazhin and Shuvaev (106) for PS/benzene, PS-oMS/dioxane, P(p-ClSty)A)enzene, and PMMA/ benzene. The ionic mobility m a concentrated solution was said to be U = a exp (-AH*/kT ) [T7 ]c , where [rj] is the intrmsic viscosity. When e' (polymer) is larger than e' (solvent) there is a competition between the tendency to mcrease o by enhancing lomc dissociation (as c I S increased) and to decrease it due to the increase in v i s - cosity. Using a system of matched cel ls , one containing an aqueous solution of DNA and NaCl and the other only NaCl of the same con- ductance, Hanss et a l . (107) demonstrated that a nonlinear effect exists, in their case, indicated by the presence of the third har- monic of the input frequency. The amplitude A(3V) was propor- tional to V^c and decreased as the ionic strength mcreased. Other experiments indicated that the nonlmear effect depends upon the conformation of the polymer. Watson and Schneider (108) have described some new experi- ments and theoretical ideas related to the beautiful crossed- electron-beams techmque that Watson conceived some years ago. Two examples that are typical of the method are treated. One is the "charge-up characteristic" that leads to a fully developed space-charge-limited ( S C L ) distribution. The other is the decay from a steady state (SOLD) . After certain fluid mechamcal complications are allowed for, data and theory agree very well . The method gives, as one of its parameters, the average charge- c a r r i e r mobility. They quote a value of 2. 8 x 10~6 cm2/v sec for a siloxane fluid (DC-550), As a rather unusual application, for liquids, Dansas and Sixou (109) have applied the Bucc i -Fieschi technique of ionic thermo- currents ( ITC) to 2-ethylhexan-l-ol (EHO) and to tr icresy l phosphate ( T C P ) . Initial fields of about 5 k v / c m and warming rates of 0.1150/sec gave an asymmetrical peak near -50OC for T C P and a simple peak near - 1 0 7 ° and with AH* = 1.12 eV for EHO. In closing this topic, it is worthwhile to note a study in which Morant (110) found that anomalous charging and discharging
238 E L E C T R I C A L P R O P E R T I E S OF HIGH P O L Y M E R S currents in nonpolar dielectrics may be due to charge storage on the walls of the test cel l rather than associated with the volume of the liquid. An appropriate metal screen can greatly reduce such "polarization' currents. Ionic Conduction m Solids The olefin oxide polymers exhibit a surprising effect. Smce they contam no unsaturated bonds and are relatively hydrophobic, one would expect them to be tjrpical polymeric msulators with a ~ 10-17 n - l / c m - 1 . Indeed, PMO (-CHgO-) , the f i r s t member of the series , does have a conductivity of the expected magmtude, but P E O , PtriMO, and PtetraMO have conductivities that are larger by six to nine decades. After demonstrating that the con- duction process is intrmsic ( i . e . , not primari ly due to impurities, including water), Binks and Sharpies (111) developed a new theoretical model for charge transport in these systems. The idea I S that a proton is removed from one of the CHg groups, leaving a negative group, CH~ behmd, and becomes weakly attached to the ether oxygen on an adjacent cham. In the presence of an external field, these protons wil l be able to migrate from one - O - to another if there is sufficient segmental mobility to bring the groups into positions favorable for a transfer. In PMO, the segmental mobility at 25°C is low since T â = 180°C; thus it has a much lower a than P E O , for which Tg = 63^^. As an independent check on the theory, they were able to observe a reverse voltage of 1.7 V cor - responding to H"*" + e~ H* . Direct-current conductivities of poly-benzyl-L-glutamate ( P B L G ) , nylon 66, and DNA were inves- tigated by Miyoshi and Saito (112) as examples of H-bonded solids. Adsorption of either polar (HgO, CHgOH) or nonpolar (CgHg) so l - vents increases o and decreases AH*. Disagreements between data and various hjrpotheses are discussed, and new mechanisms are proposed. Seanor (113) studied conduction in nylon 66 and saw three tem- perature regions: (I) below 80OC, (11) 80 to 110° , and (III) near or above 120° . In I , a continued to decrease over long times, with negligible gas evolution; m I I , o was relatively constant, with slight gas evolution; and in HI, a continuous decrease was again seen, with gas evolution corresponding to about half of the amount expected if all of the conduction were protomc. He concludes
CONDUCTION 239 that below region i n , o is mainly electronic, but in region HI con- duction involves both electrons and protons. Along similar lines, Fava and Horsfield (115) mvoked an electronic contribution to a because thermally activated ion hopping models did not fully de- scribe the behavior during the curing of epoxy resins. The effects of stretchmg on cr and other properties of P T F E were investigated by Yamaguchi and Ota (117). In some cases a was doubled after stretching. Kossman (118) measured the decay of current j , following a 4-kV rectangular pulse, m ebonite and several inorganic materials (including glass) and found that Curie's law applied, i . e . , j = at"". A rather unusual type of experiment was performed by Uemura and Furuya (120). Natural and butyl rubbers were made conducting by adding different amounts of carbon black and subsequently heating them. Then the "noise" current was measured and found to be a linear function of the resistance. A hysteresis phenomenon was observed in plots of noise current versus impressed current. Nonohmic Behavior (NOB) In electric fields of about 1 M V / m or more it is the rule, rather than the exception, that nonohmic effects appear in polymers. Some of the previously listed references ( e . g . , 107, 108, 111) could have been placed in this category, as could some of those listed under space charge effects and under a number of other topics. NOB I S of obvious technological importance in devices that use thm f i lms , since only a few volts potential difference may cor- respond to very large field intensities. Not so obvious perhaps, I S the fact that NOB is potentially useful as a means of probing the local structure of the material . Thin cast f i lms and biaxially oriented films of PS, 0. 5 to 5 Mm in thickness, were used by Burmester and Caldecourt (121) in a study of charge transport versus applied field, up to 2 MV/cm. Two techniques were used: current flow in a circuit with an applied voltage source, and decay of static charge placed on the surface of a f i lm. The conclusions of this paper are rather surprising: When E > 8 V/Um the current density is j = aE^- 5, but below about 0. 8 v A i m the PS f i lm "appears to be nonconducting instead of Ohmic ." Kryszewski et a l . (122) studied PS under some rather different
240 E L E C T R I C A L P R O P E R T I E S O F HIGH P O L Y M E R S conditions (liquid electrodes of 0.1 M aqueous NaCl, Nal, or Nal plus Ig), and they too reported NOB. The main point of this paper, however, was to look for photoinjection of holes by UV irradiation. The experiments also included copoly(vinyl chloride-vinylidene chloride) and copoly(acrylonitrile- 2-vinylpyridine). No hole in- jection was observed. Gregor and Kaplan (123) produced thin f i lms by the electron bombardment of epichlorohydrin vapor and concluded from their NOB that both tunneling and electron emission are involved, with the latter predominating at 2 5 ° C . It was reported by Kaska et a l . (124) that important deviations from Ohm's law, observed m dry samples of poly(N-chloroalkoxy- methylcaproamides), suggest that charge c a r r i e r s are injected from the electrodes and that j - V characterist ics may be inter- preted by space-charge-limited-current theory. Space-Charge Effects Often closely associated with NOB and semiconduction, several papers in which space charge is mentioned are discussed under other categories; e .g . , in reference 108, S C L C is the prime basis of the analysis. Beck (125) made an interesting study of conduction m varnish fi lms deposited on Pt and F e electrodes from aqueous solutions of an acrylate-based model adhesive. F o r f i lms of about 10 ^Ì m thickness, the log j versus log V plot mdicates a slope near one below 1 V / a m and near five above 10 V / i i m : however, a model Beck developed predicts V = V Q - A(j + J Q " ⢠^'^'^ * ® agree with this. In the model, the f i lm is treated as a weakly acidic ion-exchanger, and for E > 10 V / u m , the protons (corresponding to a 1 ppm dissociation of the COOH groups) are very mobile so that the field produces a charge separation. At the anode, protons are evolved by H2O (m film) -* 2H+ + 2e ^ho^, and COO" ions may be attached there. Near the cathode, there is a protonic (gegenion) space charge. Maser (126) considered conduction through f i lms in which lomc space charge is maintained in a potential barr ier m such a way that electron injection can occur by a thermally activated process at the metal electrodes. A general solution was derived for the steady-state current and then discussed for two explicit barr ier
CONDUCTION 241 shapes that approximate limiting practical extremes of the d i s tr i - butions of the ions. A detailed model of SC effects that result from the trapping in insulating materials of thermalized irradiation electrons was given by Monteith and Hauser (127). F o r a uniform distribution of electron-trapping sites (below the energy level for charge transfer), the rate of charge accumulation and decay is a function of '''^Aj.« where I S the material's dielectric relaxation time e'/<^ and is a characteristic time for the release of electrons from traps. The authors say that for P E T , T ^ J / T ^ l and that theory and ex- periment are in reasonably good agreement. Semiconduction and Other Electronic Processes It appears that there are sti l l some major difficulties in establishmg a realist ic quantitative theoretical description of semiconduction m macromolecular systems. At least the old misconception, prevalent a few years ago, that a material that has a conductivity about half- way (on a log scale) between those of conductors and msulators is a semiconductor, has almost died. Some of the theoretical difficul- ties are discussed by Halperin (128). F o r example, there is the paradox of the Mott-Twose prediction (for a one-dimensional random potential, the electron states are localized and hence o should be zero) which is in direct contradiction with transport theory and perturbation theory, both of which predict a nonzero a if the F e r m i level does not he within the energy gap and if the disorder is sufficiently small . McCubbin (129) took polymethylene as the main example for an mtramolecular band theory calculation. It was suggested that traps arise from the disorder-induced distribution of gap states and that this may determine the drift mobility. It was stated that a formally exact (even if qualitative) description of the eigen func- tions in each energy band would be as helpful in the study of dis- ordered systems as numerical results for ban gaps are. A question that required examination was: If the f irs t conduction band of P E is 3 eV above the valence edge, why is no intrinsic optical absorp- tion observed for X ~ 200 nm? Experiments involving dichroism were suggested. Changes in the work function <p and in the potential difference AV between a f i lm of P E and a glass-covered electrode, when O2
242 E L E C T R I C A L P R O P E R T I E S OF HIGH P O L Y M E R S or I2 vapor is absorbed, were measured by Margulis and Boguslavskii (130). It appears that physisorption of these mole- cules occurs with the formation of dipoles on the surface with the negative ends outward. They said that this should increase <p. A semi-empirical molecular orbital model, previously used to discuss the iomzation potentials of paraffins, was applied by Gurney (131) to estimate the shift in effective hole mass m* between P E and P P . He thought, due to a relatively small value for m*, that holes should dominate conduction processes. Hopping between chams was predicted to be difficult. The probability of tunneling should show a strong dependence on hole momentum and therefore on T and E . The importance of the interfaces in spherulitic bulk specimens was emphasized. Szymanski (132) studied charge c a r r i e r trapping in a series of p-polyphenyls and found that trap depths gradually decrease as one goes to larger molecular weights. In agreement with McCubbm (129) and Gurney (131), the traps appeared to be related to the barr i er s between the molecules. A series of conductivity measure- ments by Manecke et a l . (133) on some very complex polyporphyra- zines gave values between 5. 5 x 10-5 and 10-4 Q - 1 cm~^ (roc) with the decrease occurring as the aromatic character of nitriles of the original reactants decreased. In some experiments, metal ions occurred as polychelates and it appears that a = cr(i,r), where I is the ionization potential of the metal ion, and r its ionic radius. Measurements of thermal emf indicated hole conduction. Solutions, in 1,2-dichloroethane, and pressed-powder samples of an iodine complex with poly(vmylpyridme) were studied by Sazhin and Vasilenok (134). Measurements of a, u v and E S R spectra were made. F o r the solid a ~ 10"'Ì to 10"^ roc and there were 10^^ - ^ unpaired spins/g. Activation energies were in the range 14 to 29 kcal /mol . The evidence was interpreted to mean that conduction in the solid was due to holes and electrons with a negligible ionic contribution and that o for the solutions was ionic. Semiconduction in linear acetylenic polyammes, [ X - ( N R ) - (CH2)-CECR']j^ where R is (a) Ph or (b) a-naphthyl; R ' is (c) - C H 2 - or (d) - C E C - C H 2 - ; and X is (e) - N P h - or (f), was studied by Korshak et a l . (137). There was a 27-fold variation m a; the maximum when R, R ' , and X were (b), (d), and (f); and the mini - mum when they were (b), (c), and (f). However, not every com- bmation was observed. F o r the polymer with the minimum a (2. 6 x 10-4 roc) , 2AH* was the maximum found (9. 0 eV) . E S R and IR spectra were also observed.
CONDUCTION 243 Vanzura and Krasnec (138) investigated a 9:1 mixture of fluorene and caffeine before and after heating for 5 min at 120Oc in a closed s i l ica crucible. The following resistivities (0 cm) were obtained- flu caf 9f:lc before heat 1.2 x 10l6 2 x lO^'^ 3.2 x 10^6 after heat ? � 6.1 x 10^3 The 500-fold mcrease in a is probably due to the formation of a complex. According to Gregor (139) Schottky emission dominates the conduction process in poly(divinyl benzene) fi lms 10 to 30 nm thick. In high fields the fi lms are non-Ohmic. Kuhn et a l . (141) have measured the ionization potentials I and electron affinities A for a number of phthalates. This study was in conjunction with their investigation of high-field Schottky effects in P E T (Mylar) and dimethyl terephthalate (DMT). It was found that Ijj-^i = 0. 03 eV and Aj-jjyjrp = 0. 64 eV; the other compounds have s imi lar values- 1(9. 57-10.13) and A(0. 55-0.77). They feel that their data supports the hypothesis that o for P E T is due to Schottky effects. This is not in agreement with some earl ier ideas by Amborski [ J . Polym. Sci . 62, 331 (1962)]. O'Dwyer (144) explored a new possibility for steady-state current flow in a dielectric with blocking electrodes at high field intensity. A model is considered in which charge injection from the electrodes is negligible and the charge carr i er s responsible for steady-state conduction arise by collision ionization within the dielectric. This mechanism is referred to as "double charge ejection. " Curves for voltage, field, and current versus position (all in dimensionless form) are presented for (1) an Ohmic contact (E = 0, regardless of the current injected), and (11) a strongly blocking contact for which the injected current is zero, independently of E . A polyurethane synthesized by Klopffer and Rabenhorst (145) from b i - and tri-functional isocynates and N, N bis(j3-hydroxyethyl)- p-dimethylammoaniline (BHDA) was reported to exhibit hole con- duction. The hypothesis is that BHDA m the polymer acts as an electron donor and that upon doping with B r , stable radical cations are formed which permit conduction by holes. As evidence, Seebeck coefficients, spectroscopic data, and the concentration dependence of a were discussed.
244 E L E C T R I C A L PROPERTIES OF HIGH POLYMERS A new technique that employs low-energy electrons (<30 eV) to avoid barrier limitations at the injecting electrodes was developed by Tantraporn (146) and used to measure electron transport m thin films of polymerized silicone oil. The essence of the tech- nique was to compare the voltage drop across an electron collector before and after the deposition of an insulating film. Thicknesses up to 67 nm were used, and it was found that the effective mobility of about 10~11 cm2/v sec was nearly mdependent of the incident energy. Schnakenberg (147), by a canonical transformation of the small polaron theory, investigated conduction by polaromc impurity hopping m both polar lattices and in amorphous substances. Photoelectric and Other Quantum Mechamcal Effects The photoconductivity of PS was discussed by Ofran et al. (148). The photocurrent yield increased in spectral regions where the fluorescent quantum yield increased. At wavelengths longer than 140 nm there was very little photocurrent. It made no significant difference whether the exciting radiation was applied at the positive or negative electrode. Lakatos and Mort (149) demonstrated that for poly-N-vinyl carbazole(PVK) films on substrates of Au, Cu, and Al the photo- emission thresholds for hole injection were 1.28, 1. 48, and 1. 53 eV, respectively. Relative to the vacuum level, the valence band edge of PVK was reported to be 6.1 + 0.4 eV. (cf. ref. 122). Equations to describe transient currents in insulators for the limiting cases (i) of strong photoexcitationâso that j is S C L â and (11) weak light pulsesâso that j is electrode-limited, were discussed by Weisz et al. (150). Thermally Stimulated Currents (TSC) or Ionic Thermocurrents (ITC) A discussion of theoretical relations that are supposed to be valid for any type of trapping, as related to the process of TSC of a semiconductor, was given by Krumberg (151). Kryszewski et al. (152) mvestigated TSC for several poljrmers (PE, PS, PVC, PVF) and found that crystallinity caused an en- hancement of the effect. Their films were polarized by contact
CONDUCTION 245 with electrodes at -lOflOC and subsequently warmed at a constant rate with no applied voltage; currents of a few nanoamps were generated. If the films were irradiated with UV during polariza- tion, larger currents were observed. It was thought that the electrons were trapped at fissures and other structural imperfec- tions . Although it appears to not have yet been applied to polymers, Zhdan et al. (153) have reported a new modification of TSC, which they call TCD (thermostimulated capacitor discharge), that might prove useful in studies of polymers. Dielectric Strength E j , Experiments to clarify the mechanism of dielectric breakdown in polymers, and in particular to try to distinguish between electro- mechamcal, intrinsic, and thermal breakdown theories, were reported by Blok and LeGrand (154, 155). The presence of elec- tromechanical thinning was confirmed by two types of evidence: First , Eb IS significantly larger for a polymer (PE) that is encap- sulated (electrodes and all) withm a hard glassy material (e.g., epoxy); and second, optical birefringence measurements show that small, localized regions of high shear deformation precede break- down. By using a 35 percent carbonate 65 percent dimethysiloxane block copolymer ( i .e . , with glassy segments and rubbery segments) they showed that there is a residual deformation, which for this particular copolymer persists for several seconds, subsequent to the removal of a high field. Their data suggest that the bire- fringence IS proportional to the square of the applied field. Along similar lines to the work of Blok and LeGrand, a study by Toyoda (156) mdicates that the tensile strength s(kg/cm2) is related to Eb(V/cm) by the equation s = 7.7Ebexp(Eb/3). Vershimn and Trippel (157) presented a curve that suggests a correlation between bulk resistance and the energy of streamer formation. The data were based on P E , PlB, PVC, PVAlc, PMMA, PS, P T F E , paraffin, and rosin. In a paper by Artbauer (158), E^j is considered as an extreme value related to the molecular dielectric relaxation time. Re- sults similar to experimental values are said to be obtained. A study of Ejj versus molecular weight M for PS and related polymers was reported by Kolesov and Geifman (159). It was
2 4 6 E L E C T R I C A L PROPERTIES OF HIGH POLYMERS found that E^j increases as M increases in the range 1 0 ^ to 1 0 ^ g/moL Their interpretation is that structural changes (as M in- creases) result in a decrease in the mean free path of the elec- trons . Bobo et aL ( 1 6 0 ) measured E^j at 4 . 2 0 K and S O Q O K for the following polymers and conditions. The umts are MV/cm. I n m IV V VI T(°K) Conditions* PET PA(Nylon n) P T F E TFErHEP PI (HI-V Layer) 3 0 0 i n T . O . 2 . 7 2 . 6 3 . 0 2 . 0 3 . 1 3 2 3 0 0 i n C . L . 5 . 8 3 . 7 4 . 2 2 . 5 4 . 4 5 . 7 4 . 2 Liquid He 2 . 0 2 . 1 1 . 1 2 . 2 2 . 3 2 . 0 4 . 2 V L X 3 . 3 2 . 9 2 . 7 3 . 1 3 . 8 3 . 8 4 . 2 VHZ 4 . 0 2 . 5 3 . 2 3 . 9 4 . 0 5 . 0 4 . 2 VLXC 4 . 1 4 . 3 3 . 7 3 . 9 5 . 0 5 . 2 Beard and Orman (161) determined that for cured epoxide is virtually independent of the original epoxide resin and the curing agent, provided both are pure and the casting has a minimal amount of dissolved air. Limiting strengths appear to be about 10 MV/cm. The effects of complexes involving metal ions (Fe-+, Cu+''", Co"* ,Ì Ni"*"*", and Zn"""*" were also studied. The effects of artificial defects in epoxy molding resin were studied by Leu (162). One of the parameters studied was gas buildup in the defects. Bobrovskaya and Ryabov (163) measured the time to failure t£ versus E in alternating fields and direct fields. Usually tf decreases as E mcreases toward the limiting value of about 40 kV/cm. In an ac field tf increases as T mcreases, but in a dc field it decreases (at constant E ) . * T . O. IS transformer oil (5 x 10^1 fi cm and E ^ = 30 KV/mm); C . L . IS a creosote liquid (2 x 108 CI cm and E^^ = 25 kV/mm); V L X IS vacuum (10~7 Torr), low impedance voltage source; VHX IS for vacuum, high impedance voltage source; and VLXC is for V L X with an 8-um coating film of sjmthetic varnish on the poljrmer films which were 50 um thick. Pol3mier rv is tetrafluoroethylene- hexafluoropropylene copolymer (Teflon F E P ) and V is the polyimide Kapton.
