Shock-induced electrical activity in polymeric solids. A mechanically

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3040

Graham

The Journal of Physical Chemistry, Vol. 83, No. 23, 1979

Shock-Induced Electrical Activity in Polymeric Solids. A Mechanically Induced Bond Scission Model R. A. Graham Sandia Laboratories, Albuquerque, New Mexico 87185 (Received June 11, 1979) Publication costs assisted the U.S. Department of Energy

When polymeric solids are subjected to high-pressure shock loading, two anomalous electrical phenomena, shock-induced conduction and shock-induced polarization, are observed. The present paper proposes a model of mechanically induced bond scission within the shock front to account for the effects. An experimental study of shock-induced polarization in poly(pyromel1itimide) (Vespel SP-1) is reported for shock compressions from 17 to 23% (pressures from 2.5 to 5.4 GPa). Poly(pyromel1itimide) is found to be a strong generator of such polarization and the polarization is found to reflect an irreversible or highly hysteretic process. The present measurements are combined with prior measurements to establish a correlation between monomer structure and strength of shock-induced polarization; feeble signals are observed in the simpler monomer repeat units of poly(tetrafluoroethy1ene) and polyethylene while the strongest signals are observed in more complex monomers of poly(methy1 methacrylate) and poly(pyromel1itimide). It is also noted that there is an apparent correlation between shock-induced conduction and shock-induced polarization. Such shock-induced electrical activity is also found to be well correlated with the propensity for mechanical bond scission observed in experiments carried out in conventional mechanochemical studies. The bond scission model can account for characteristics observed for electrical activity in shock-loaded polymers and their correlation to monomer structure. Localization of elastic energy within the monomer repeat unit or along the main chain leads to the different propensities for bond scission and resulting shock-induced electrical activity.

Introduction Two anomalous electrical phenomena have been observed in polymers subjected to high-pressure, shock-wave loading. The first of these phenomena occurs in shockloaded samples on which electrodes are placed and to which no electrical potential difference is applied. Under such conditions, currents are observed in external circuits connecting the electrodes when the samples are shock loaded a t pressures greater than some critical stress. The form of the current pulse indicates that it is produced by a bulk polarization with a relaxation time of typically to s. Such a phenomenon has not been successfully described in terms of equilibrium thermodynamic properties. This phenomenon is called shock-induced polarization. The second anomalous phenomenon is the substantial increase in electrical conduction in polymer samples subjected to shock loading. Such shock-induced conduction does not appear explicable in terms of properties of states in thermodynamic equilibrium. Studies of both shock-induced polarization and shock-induced conduction have been summarized in several recent Shock-induced polarization was first reported by Hauver4i5in poly(methy1 methacrylate) (PMMA) and polystyrene, Recent work on PMMA has been reported by de Icaza Herrera and c o - w ~ r k e r s . ~Novitskii -~ et al.1° have reported single experiments on a variety of polymers. Other investigations of Yakushev and Novitskii and their co-workers are reported in the review of Mineev and Ivanov.' Unfortunately, most of the work on polymers reported in this review is not available outside the Soviet Union and is given in only fragmentary form in the review. Similar shock-induced polarization and shock-induced conduction measurements have been reported in ionic crysta1s.l It is the object of this paper to report a study of shockinduced polarization in poly(pyromellitimide), PPMI

(Vespel SP-l), and to draw attention to correlations between monomer structure and shock-induced polarization, shock-induced conduction, and the propensity for bond scission in mechanochemical studies. A model to describe such shock-induced electrical activity and its dependence on monomer structure is proposed based on mechanically induced bond scission and charged species displacement. Following a brief exposition of the phenomenological theory of bulk polarization currents, the experimental procedures and results of the present work will be presented. Systematic behavior of shock-induced electrical activity and bond scission among a variety of polymers will be examined and a model for shock-induced electrical activity will be proposed. Finally, the credibility and implications of the proposed bond scission model will be discussed.

Polarization Currents Allisonll and Horiel* have derived an expression for the shock-induced current pulse in an external electrical short circuit connected to electrodes of a one-dimensional sample subjected to shock loading which produces a shock-induced polarization of the form P(t) = P:e-t/r. Here P,(t) is the stress-induced polarization, P,O is the initial value of the stress-induced polarization, t is time, and T is a relaxation time for the stress-induced polarization. If the sample is electrically insulating and does not exhibit dielectric relaxation, the short circuit current pulse accompanying a steady shock wave moving a t velocity, U , is i(t)to - -

P,OA

+ A U.S. Department of Energy facility. 0022-3654/79/2083-3048$0 1.OO/O

(C 1979 American Chemical Society

Shock-Induced Electrical Activity in Polymeric Solids

The Journal of Physical Chemistry, Vol. 83, No. 23, 1979 3049

Summary of Experiments and Results o n Poly(pyrome1litimide)‘ TABLE I: _____ _______-__ U,,,b U,c :u 10-~i~,f ~ o - ~ pi,’ A , ~ k m / s km/s km/s u/U GPa A 1g m 2 pC/m2 expt ~

_

~~

_

0.609 0.671 0.792 0.805 0.907 1.090

1536 1542 1541 1567 1568 1537

_

_

_____

~

3.25 3.33 3.54 3.71 4.04

_______I_

0.539 0.592 0.695 0.705 0.792 0.942

0.166 0.176 0.197 0.199 0.213 0.234

2.50 2.80 3.5 3.55 4.18 5.42

0.55 1.14 2.2 3.3 4.2 (5.5y’

6.312 6.335 6.253 6.380 6.320 6.360

1.229 1.176 1.184 1.241 1.193 1.226

1.0 2.1 4.1 6.0 7.6 9.0

remarks small deflection signal better early-time resolution better early-time resolution 2.0-mm thick, unbacked impactor

a Samples are 37-mm diameter rod stock poly(pyromel1itimide) (PPMI) manufactured by the DuPont Co. under the trade name Vespel SP-1. Initial density is 1.425 Mg/m3. Longitudinal ultrasonic wave speed is 2.39 km/s, shear wave speed is 0.985 km/s, and the calculated bulk sound speed is 2.10 km/s. Ultrasonic wave speeds were determined by I. J. Fritz. u,, is the measured impact velocity. Impact conditions are OFHC copper on PPMI. U is the shock velocity determined from the measured thicknesses and the current pulse durations from the samples. u is the particle velocity in the PPMI sample determined graphically by applying conditions of continuity of stress and particle velocity a t the impact interface for the measured U , u,, data, and stress-particle velocity data for OFHC copper as published in ref 18. e u is the longitudinal component of stress calculated from u = p,,Uu. f ii is the experimentally observed jump in current upon impact. P 1 is the specimen thickness. A is the charge-collecting area taken to the center of the insulating ring. ’ Pi = $ / A U ( l - u / U ) . See eq 3. Peak not fully resolved. ii estimated based o n minimum in current relative to that of experiment 1568. J

where tois the transit time of the wave through the thickness of sample, A is the charge collecting area of the electrode, u is the particle velocity imparted by the shock, and a is the ratio of the compressed-to-uncompressed permittivity. Two special cases are of interest. The solution in the limit as 7 03 is that of an elastic piezoelectric in the uncoupled approximation. (See, e.g., Davison and Graham,3 Graham,13 and Graham et al.14) For t = 0, the solution is reduced to

-

where ii is the current observed immediately after impact. From eq 2 it is apparent that, in addition to the mechanical parameters which are subject to independent measurement, the volume or stress dependence of the permittivity must be known to establish values for a and thereby permit determination of the polarization from ii. If the material remains electrically insulating and does not exhibit dielectric relaxation, the form of the current pulse can be used to determine a value for a. Unfortunately, both conduction and dielectric relaxation (which are not included in the derivation of eq 1) are known to occur under shock loading3 and it is difficult to distinguish among the various relaxation processes. With this in mind, it is convenient to define an effective shock-induced polarization computed from the initial current as (3) This effective polarization can then serve as a relative measure of polarization among various materials and, when data describing permittivity become available, the true polarization can be determined. It is generally believed that CY > 1;hence, Pi < P,O, (The general usefulness of eq 3 to characterize various polarization phenomena is noted by Davison and Graham.3) Experimental Procedures and Results Shock-induced polarization measurements were carried out on poly(pyromellitimide, PPMI (Vespel SP-l), manufactured and supplied by the Dupont Co. The material is available in both rod and plate form; the present experiments used 35-mm diameter by 6-mm thick disk samples machined from 37-mm diameter rod. Our measured density of 1.425 mg/m3 is the same as that reported for

film of the same composition which is sold under the trade name Kapton,15and the same as that previously reported for Vespel SP-1.16 Both major faces of the samples were plated with goldover-chrome electrodes and a guard-ring configuration was constructed on one electrode with a sand-blasted insulating ring 0.1 mm wide. In this configuration the diameter of the inner electrode was nominally 12 mm and the guard ring was 12-mm wide. A guard ring of this width, which is twice the thickness, ensures that the electrical and mechanical conditions are one dimensional throughout the volume in which the properties are being sampled. The inner electrode is connected to a 50-3 coaxial cable and the outer electrode is connected to the ground electrode with a resistor whose resistance is chosen to maintain the same resistancearea product on both inner and guard-ring electrodes. Shock loading was carried out with a smooth bore compressed gas gun which accelerates a projectile to a preselected velocity and permits precise alignments between an impactor on the projectile and a sample attached to the muzzle end of the barrel. Such a technique has been utilized in extensive studies of piezoelectrics.13J4J7 Typical “tilt” or misalignment of the impacting surfaces is 250 prad. In the present case an impactor of oxygen-free highconductivity (OFHC) copper was utilized. In order to determine the pressure and compression imparted to the sample from the measured impact velocity, the pressureparticle velocity relationship must be known. The data of McQueen et a1.18 were used to characterize the copper and wave transit time measurements from the shock-induced current pulses were used to specify the properties of the PPMI. In one experiment the thickness of the impactor was chosen to be sufficiently small (2.0 mm) that a decompression wave from the copper impactor-vacuum interface would propagate into the sample before the initial loading wave fully traversed the sample. This experiment provides a measure of the reversibility of the polarization phenomena. The active sample electrodes were connected to an electrically terminated Tektronix 7903 oscilloscope through 14 m of low-loss coaxial cable (Andrew 7/8-in. Heliax, H5-50). This arran ement provides a measure of current into a 5 0 4 load wit an electronic rise time limited by that of the preamplifier, about 2 ns. The conditions of each experiment and a summary of results are shown in Table I. Experiments were carried out at pressures from 2.5 to 5.4 GPa, values corresponding

-a

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The Journal of Physical Chemistry, Vol. 83, No. 23, 1979

Graham

TABLE 11: Summary of Investigations of Shock-Induced Polarization in Polymers -

.------~---___~--I--___-___-__-__I___

_ I _ _

compress., author

% remarks poly(methy1 methacrylate) (PMMA) Eichelberger and Hauver (ref 4 ) 25-38 full electrode samples Hauver (ref 5) 16.5->40 guard ring samples de Icaza Herrera et al. (ref 6, 8, 9), Altuglas guard ring samples 13-27 Yakushev et al. (ref 1 9 ) 35? full electrode, relaxation only polystyrene (PS) Eichelberger and Hauver (ref 4 ) 22-35 full electrode Hauver (ref 5 ) 29-42 guard ring Mineev and Ivanov (ref 1) 30 polarization independent of molecular weight Nylon Eichelberger and Hauver (ref 4 ) , Zytel 101, Nylon 616 32 full electrode Novitskii et al. (ref l o ) , Kaprolon-B full electrode 30 epoxy ((2-7) Eichelberger and Hauver (ref 4 ) 25-39 full electrode polyethylene Hauver (ref 20) guard ring 30 Novitskii et al. (ref 1 0 ) full electrode -33 polypropylene Novitskii et al. (ref 1 0 ) full electrode 33 poly( tetrafluoroethylene) (Teflon) Bloomquist (ref 21) full electrode 19 Novitskii et al. (ref 1 0 ) 36 full electrode, negative Pi poly(ethy1ene terephthalate) (PET) Novitskii et al. (ref 10) 33 full electrode poly( butyl methacrylate) (PBMA) Novitskii et al. (ref 1 0 ) full electrode 33 plasticated poly(viny1 chloride) Novitskii et al. (ref 1 0 ) 33 Pi = 9.8 X lo-’ C/m2,dibutyl phthalate plasticizer vinylplast ( ? ) Novitskii et al. (ref 1 0 ) 33 Pi = 7.9 x C/m’, unspecified plasticizer 5

-

-

-

-

-

-

to volume compressions of from 17 to 23%. Ultrasonic wave speed measurements were carried out at atmospheric pressure by I. J. Fritz. A typical current pulse is shown in Figure 1. Figure l a shows the pulse for the full wave transit time while Figure l b shows an expanded time scale for the time immediately following impact. The pulses are characterized by a rapid increase to an initial value upon impact, followed by a relaxation over a period of perhaps 100 ns and an approximately exponentially increasing current which reaches a peak at wave transit time. Better time resolution is achieved in the present work than in prior work but the wave shapes generally correspond to what has been observed on other polymers and can be well described by eq 1. The present work generally shows a sharper relaxation early in time which was not previously discerhable due to limited resolution. The rise time of the current pulse upon impact of between 10 and 25 ns is larger than can be accounted for by the tilt or by electronic rise times of cables and oscilloscopes. Considering the typical tilt achieved in our facility, \here is some evidence that the rise time of the polarization is in the range of about 5-10 ns. Nevertheless, this point cannot be fully resolved until more detailed studies of rise times are carried out. As has been noted for other polymers, shock-induced polarization in PPMI appears to have a threshold compression before the onset of polarization. In the particular sample configuration used here, the experiment at the smallest volume compression is at the limit of accurate detectability of the current pulse. Experiments on much thinner samples are required for more detailed study of the threshold for the effect. At a compression of 23% the polarization of 9 X C/m2 for PPMI is substantial but weak by piezoelectric standards; for example, this polarization is about 0.5% of that of X-cut quartz at a compression of 1% . If the change in polarization of PPMI with compression is taken for data

above the threshold, it is roughly 0.5% of the linear piezoelectric stress constant of X-cut quartz which is 0.171 C/m2. The decompression experiment with the thin impactor (Table I, experiment 1537) furnished what was perhaps the most interesting result of the present work. When the decompression wave arrived at the sample input electrode from the copper impactor free surface, the perturbation in current was only 3% even though the stress was reduced by about 20%. This observation provides direct evidence for an irreversible or highly hysteretic physical process controlling the shock-induced polarization. Discussion of Results The observed shock-induced polarization of PPMI follows a pattern similar to those observed in prior investigations of other polymers. In order to develop a systematic picture of this electrical activity, it is important to consider the collected data. Although most of the work is fragmentary, the summary given in Table I1 indicates that a significant body of data is available. The principal detailed work is that of Hauver5 on poly(methyl methacrylate) (PMMA) and polystyrene (PS) which was reported in 1965 and the more recent work on PMMA by de Icaza Herrera et al.6-9 Early exploratory work of Eichelberger and Hauver4 is of interest. The measurements of Novitskii on a variety of polymers are of considerable significance.1° There has been considerable work in the Soviet Union by Yakushev, Novitskii, and co-workers, but it is not available for distribution outside that country and the review by Mineev and Ivanovl gives very limited information on the work. All the prior data were taken with explosive loading except that of Bloomquist, which was taken under conditions similar to those of the present work. Most of the data shown in Table I1 are taken on samples without guard rings and would be expected to be influenced by two-dimensional contributions. There is only a single datum point each for Teflon, Nylon 6/6, poly-

The Journal of Physical Chemistry, Vol. 83,

Shock-Induced Electrical Activity in Polymeric Solids

No. 23, 1979 3051

X -CUT Q'JARTZ, DIEZOELECTRIC

A

62

0 A

e G U A R D - R I N G SAPUPLES FULL-ELECTRODE SAhlPLES

4 0.5

OG

1.0

2.0

1.5

TIME, ys

tb

i

t(

-

- PPIMI PRESENT WORK

.

10-6

F t t t TIME,

ns

I!'-"

Flgure 1. Accurate tracings from original oscilloscope records of current-time pulses from impact-loaded poly(pyromel1itimide)(Vespel SP-1) are shown. The upper trace (a, experiment 1567) shows the full pulse duration while the lower trace (b, experiment 1568) shows the early-time portion of the pulse on an expanded time scale. The vertical scale of the lower trace does not include a calibration factor of about 1.10. Because of improved time resolution, the present work shows more detail on the early-time relaxation than shown previously.

TABLE 111: Equation-of-State Data o n Polymers of Carter and Marshz3 U = a t bu, km/s ~

-~~

~~

b

range of u,' km/s

1.186

2.59

1.52

0.3-2.9

1.140

2.67

1.69

0.8-2.6

1.046 1.192 0.954

2.34 2.69 2.86

1.58 1.51 1.57

0.7-2.8 0.4-2.8 0.7-3.2

2.151 0.904 1.414

1.68 2.86 2.66

1.79 1.49 1.48

0.6-2.8 0.7-3.2 0.6-2.2

P,,,

-

polymer PMMA ( R o h m and Haas 11) Nylon 616 (Polypenco 101) polystyrene (Styrolux) epoxy (Epon 8 2 8 ) polyethylene (Marlex EMN 6 0 6 5 ) Teflon (DuPont) polypropylene (Avisuh) PPMI (Meldin PI)

a,

Mg/m3 km/s

a The maximum particle velocities correspond to those required t o induce polymorphic phase transitions.

propylene, poly(ethy1ene terephthalate), poly(buty1 methacrylate), and the plasticated poly(viny1 ch1oride)s. Other work of interest is that for polymer films by Champion and Benedick22which incIudes polarization contributions due to adhesive material. Data from the present and prior investigations on well-defined polymers are summarized in Table I1 and plotted in Figure 2. The polarization is plotted over a four-decade log scale against a linear compression scale. Much of the data were originally reported in terms of pressure and we have computed the corresponding volumes by using shock-compression data of Carter and Marsh,23 as summarized in Table 111. For the PPMI used in the present work, we have used shock velocities determined from the duration of the polarization current pulses. It should be recognized that the polarieation shown in Figure 2 is the effective polarization, Pi,of eq 3. Hauver's

POLY PROPYLENE

IPOLYETHYLENE

i

TEFLON

.A5

O.'lO

@.I15

L.:O

0.25

0.30

0.135

04!@

C Oh1PRESS I ON

Figure 2. The effective shock-induced polarization from the present measurements and from prior measurements on other polymers are shown as a function of the compression on a semilogarithmic scale. The polarizations seem to be characterized by three different response regions: (1) a subthreshold region below compressions of about l o % , (2) a strong generation region, and (3) a saturation region above compressions of about 30%. The shock-induced polarizations are generally weaker than those for the piezoelectric effect and from similar anomalous shock-induced polarizations observed in ionic crystals.

data5 on P,O were converted to Piby using initial dielectric constants of 2.78 for PMMA and 2.56 for p o l y ~ t y r e n e . ~ ~ We have not included polarization data above the phase transitions detected by Carter and Marsh23because the extreme current pulse distortions, which likely involve shock-induced conduction, lead to unrealistically large polarization values. The data of de Icaza Herrera have not been plotted. They generally agree with those of Hauver5 at the lower compressions but appear to give a much lower saturation polarization. This may be due to the method of loading which was not sufficiently planar to stress the full guard-ring area. The observed polarizations range over at least three orders of magnitude from to C/m2. The polarization is generally weaker than that observed in ionic crystals for which polarizations from to about 3 X C/m2 have been observed. The data on volume dependence of observed polarization are limited and most were not obtained under equivalent conditions; nevertheless, there are common features of interest. The sign of the polarization initially induced at low pressure is the same for all the polymers studied and indicates a net orientation of dipoles from negqtive to positive along the shock direction. In every case in which the polarization has been investigated over a range of compressions, it is apparent that the polarization is highly nonlinear with compression and there appear to be three characteristically different response regions. These regions can be described as (1) a subthreshold region, (2) a strong-generation region, and (3) a saturation region. The subthreshold region has not been investigated and values for the critical compression above which significant polarization is observed have not been determined. Nev-

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The Journal of Physical Chemistry, Vol. 83,

No. 23, 1979

Graham

TABLE IV: Shock-Induced Polarization in Polymers

-

polymer PMMA

shoe k-induced polarization

monomer repeat unit

strong

H

I I 1

H H-C-H

I -c-cI

O//c\o

I I H

H-C-H

PPMI

strong

Nylon 6/6

strong t o modest

0

--N-(CH216-N-C

I epoxy

modest

poly(ethy1ene terephthalate)

modest

polystyrene

modest

-(CH214-

I1C -

I

H t '

-c-c-

Ai

polypropylene

feeble

H

H

I

1

I

1

-c-c-

I

/

H H--C-H

I

H

polyethylene

feeble

Teflon

feeble

H

I

\ i

-c-c-

I

F

ertheless, extrapolation of the existing data indicates typical thresholds of detectability between about 10 and 15% compression. It is clear that the observed polarization does not extend monotonically through zero compression. In the strong-generation region, which is typically in the range of about 15-3070 compression, the polarization is a strong function of compression. Changes in polarization of an order of magnitude result from changes in total compression of less than 10%. On the basis of the available data, the saturation polarization region appears to be characteristic of compressions greater than about 30-4070. An important characteristic of the shock-induced polarization which has only been investigated in the present work is the irreversible or highly hysteretic response to unloading. In interpreting this result, however, it should be recognized that the observation is limited to a single experiment and the unloading wave is highly dispersive due to strong nonlinearity in the pressure-volume response of polymers. For this reason the effective unloading rate within the sample decreases as time progresses and is not as severe as the initial loading. In order to look for evidence of systematic behavior among the various polymers, we have grouped them in terms of the magnitude of their polarizations as feeble,

I

F

modest, or strong and displayed the different monomer repeat units in Table IV. The difference between feeble and strong polarization is substantial, amounting to some three orders of magnitude. The difference between modest and strong polarization is an order of magnitude or less. Since the data are generally not available on the different polymers over common compression ranges, some extrapolation is necessary to make this comparison. In the present comparison we have evaluated the polarizations at a compression of 25%, As more data are obtained, the relative polarization scale can be made more quantitative but further refinements are not warranted on the basis of the present data. Examination of the monomer units associated with characteristic shock-induced polarizations is best brought out by inspection of the polymers with feeble polarizations. These monomers are very simple and composed of a limited number of constituents. The clearest cases here are Teflon and polyethylene which have no side groups. Polypropylene has a single CH3 side group and the polymer exhibits the strongest polarization of the feeble generators. Thus, feeble shock-induced polarizations are observed in the monomers with the simpler monomer structures. On the other hand, the polymers which exhibit strong shock-induced polarizations, PPMI and PMMA, are quite

The Journal of Physical Chemistty, Vol. 83, No. 23, 1979 3053

Shock-Induced Electrical Activity in Polymeric Solids

TABLE V : Mechanochemistry of Selected Polymers mechanical degradation vibromilling polymer PMMA PS PET PEB

M , change, ora (1) (2) 0.12 0.095

7.7 1.1

ultrasonicC E S R ~0,1017 min-’ y , 1 0 6 min-’ 1.3

15.0 5.3

high-press. sheard 01, min-’ 0.38 0.34e

0.055f 3.8 x

0.08

shock-induced polarizn strong modest modest feeble

where Mw is the molecular weight. Detection of A M , is through viscosity measurements. Casale p is the number of paramagnetic centers per gram broken per minute. Butyagin e t al., ref 30. and Porter, ref 28, p 120. y is the number of bonds broken per minute as determined by radical scavengers. Casale and Porter, ref 29, p 526. Shear a t pressure of 5 GPa. Determined from molecular weight changes. Larsen and Drickamer, ref 31. e Substantial Polypropylene is more sensitive to shear gel formation indicates considerable secondary reactions. f Reference 29, p 344. degradation than polyethylene. Teflon is said t o be very insensitive t o mechanical degradation. a 01

= M;‘AM,At-‘,

complex. They contain a large number of constituents and generally have large side groups or a large number of relatively massive components in the main chain. Poly(buty1 methacrylate) is not shown in Table IV due to lack of space but it is complex and exhibits a strong polarization. In the modest polarization group we find monomer units of intermediate complexity. It is perhaps noteworthy that they all have a single benzene ring. The polarizations observed for the plasticated polyvinyls of Table I1 are obtained on samples of essentially unknown composition. The relatively large polarizations of these materials do not seem to fit in well with the other polymers and suggest that the addition of the plasticizer, dibutyl phthalate, significantly enhances the propensity for shock-induced polarization. Further, there are indications that there is a correlation between shock-induced conduction and shock-induced polarization. Teflon is recognized as the best insulator available under high-pressure shock loading and both high and low density polyethylene remain good insulators at pressures of 30 GPa.25 These polymers are the weakest generators of shock-induced polarization. On the other hand, investigations on a PPMI film, Kapton H, show that the material becomes highly conductive above a pressure of about 9 GPa.26 Single experiments on films of TFE and F E P Teflon, Kel F, and Halar (a CTFE copolymer) show that their resistances remain high for situations in which Kapton becomes highly conductive. Mylar (a P E T film) displays an intermediate sensitivity to shock-induced conduction. Thus, on the basis of the available data, shockinduced conduction and shock-induced polarization appear to be well correlated; this suggests that a common phenomenon is responsible for shock-induced electrical activity in polymers. The limited shock velocity, particle velocity data as well as the ultrasonic wave speed data indicate that Vespel SP-1 has significantly different stress-volume properties than the similar polymer, Melden PI, used for shock-compression studies by Carter and Marsh.23 The present data indicate that an anomalous stiffening is occurring over the range of compression studied. Nevertheless, the data are limited and firm conclusions cannot be drawn until more data are in hand. Although there are insufficient data to distinguish specific molecular groups directly responsible for the electrical activity, the overall correlation is sufficiently promising to suggest seeking the physical mechanism responsible for the correlation. A bond scission model appears to be physically realistic, to be well correlated with monomer structure, and to be supported by independent mechanochemical studies. It also explains the correspondence between shock-induced conduction and shock-induced po-

larization. The definition of a “complex” monomer will become clearer as the model is developed.

Mechanochemistry Mechanochemistry, the initiation and acceleration of chemical reaction under the action of elastic energy,27is a well-developed pragmatic science for polymers and there is considerable progress toward developing a physical basis for observations. Interest in mechanochemistry in polymers stems from both the salubrious and deleterious effects of mechanical action in processing and degrading polymers through mechanically induced bond scission. An excellent review by B ~ t y a g i nsummarizes ~~ the principal mechanochemical effects while the comprehensive two-volume book by Casale and Porter28s29organizes and summarizes almost 1500 references to work in the field. The mechanochemistry literature can be used to anticipate the mechanical effects of shock loading and even the most casual examination of the literature reveals evidence that bond scission is to be expected under shock loading. Detailed examination of the data on mechanical degradation of various polymers subjected to the same degradation process in a common study are even more revealing. The mechanochemistry literature indicates that many polymers are sensitive to mechanically induced bond scission and it has been demonstrated that the most favorable conditions for such bond scission are those under which there is a maximum concentration of mechanical energy per unit time. The shock wave provides such conditions and ButyaginZ7suggests that shock waves should be uniquely efficient in causing bond scission processes. Mechanochemical data are available on polymers of interest from vibromilling, ultrasonic irradiation, and highpressure shearing. A summary of mechanochemical effects observed in various polymers by the same investigator in a given investigation is given in Table V, along with the corresponding magnitude of shock-induced polarization. The molecular weight change rate measurements used to deduce mechanically induced bond scissions due to vibromilling show the propensity for bond scission in order of decreasing sensitivity as PMMA, PS, PET. This is the same order shown for the propensity for shock-induced polarization. ESR measurements of radical species in vibromilled samples show that PMMA is much more sensitive to bond scission than polyethylene. The same tendency is shown in the shock-induced polarization of these polymers. Similarly, radical scavenger measurements in ultrasonic irradiation experiments show PMMA more sensitive to bond scission than PS. The high-pressure shear measurements also show PMMA the most sensitive to bond scission with PS less sensitive and PE much less sensitive. Although

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The Journal of Physical Chemistry, Vol. 83, No. 23, 7979

quantitative values are not given, it is reported that polypropylene is more sensitive to degradation by shear than polyethylene and Teflon is reported to be very insensitive to mechanical degradation. Again, these bond scission sensitivities fall in the same order as the propensity for shock-induced polarization. Based on the data outlined above on mechanochemical studies, all six polymers for which data are available show the same relative propensity for bond scission as for shock-induced polarization. Such a correlation, and the observed connection between shock-induced polarization and shock-induced conduction, are consistent with the occurrence of shock-induced bond scission and defect displacement in the stress gradient accompanying the shock.

Bond Scission and Charged Species Displacement It is well known that shock loading of solids produces defects in copious q ~ a n t i t i e s .Although ~ it is not difficult to establish that such defects are produced, there has been little progress in determining particulars, especially during the submicrosecond time scale of the experiment. Creation and displacement of cation defects within the shock front have been shown to be the cause of shock-induced polarization in ionic A similar process provides a credible model for shock-induced polarization in solid polymers. For polymers, however, the mechanochemical studies indicate that the defects are the result of mechanically induced bond scissions. The bond scission model for shock-induced polarization follows from the known sensitivity of polymers to mechanical degradation and from the relative sensitivity of different polymers to mechanical degradation. The strain rates within a shock front are of the order of lo8 s-l; stresses and compressions are large, and the typical stress gradient of about 300 GPa/mm is probably the highest encountered under any conditions. The severity and uniqueness of shock deformation is well demonstrated by observations of shock-induced p o l y m e r i z a t i ~ n , ~enhancements ~-~~ in rates of phase transformations of over six orders of magn i t ~ d e ,and ~ ~ by ! ~the ~ unique defect structures induced in shock-loaded solid^.^ The unique aspect of the present proposal, however, is its mechanical character. The initial temperatures and pressures of the present experiments are not sufficient to significantly alter reaction rates. The effects are purely mechanical, and are a direct result of the stress gradient in the shock front. The magnitudes of the stresses involved are significant but modest by shockloading standards. As indicated schematically in Figure 3, it is proposed that early in the shock deformation process a critical stress threshold is exceeded above which bond scission is significant. Such scission will, in general, result in both chain shortening as chains are scissioned and formation of primary radicals as side groups and shorter chain segments are separated from the main chain. Because of mass motion within the front, primary highly reactive radicals may possibly be expected to encounter unreacted sites and cause further secondary scissions. As a result of the bond scissions, an ensemble of electrically charged species is present. This process is transient and recombinations will likely be significant. The charged species are located within a large stress gradient which will displace the various species. Polarization results from a net relative displacement of negatively and positively charged species. It should be recognized that the entire process occurs within the shock front and is completed within a few nanoseconds. The polarized state is not in thermodynamic

Graham

1

BOND S C I S S I O N S

A

DEPOLYMERIZATION

\

RADICAL FORMATION

S E C O N D A ~ Y SCISSIONS

I

CHARGED SPECIES

RECOMBINATION 1 SELECTIVE DISPLACEMENT ( NET I

DIPOLE MOMENTS

Figure 3. Schematic diagram of the proposed bond scission model for shock-induced polarization. The process of bond scission and charged species displacement occurs within the shock front whose rise time is thought to be less than a few nanoseconds.

equilibrium and will relax toward that state. The relaxation times are those of the defects which are typically quite long compared to molecular relaxation processes and it is not difficult to justify relaxation times of s or longer. In the bond scission model the sensitivity of a monomer to mechanical scissions and the ease of displacement of the defect determines its ability to produce shock-induced polarization. The resulting polarization is

P: = pN

(4)

where p is the magnitude of the dipole moment representing a statistical average of a large ensemble, and N is the number of such moments per unit volume. For a singly charged defect the dipole moment is ea, the product of the electronic charge and the relative displacement distance. In the absence of other data, it is difficult to separate the contribution of the number of dipoles and their displacement. Nevertheless, we can estimate quantities by assuming that the displacement of a singly charged defect is of the order of a monomer repeat unit, say 1-10 A. The observed maximum polarization of PMMA of about C/m2 for a monomer molecular weight of 100 indicates that there is about one dipole per lo3 to lo4 monomers. This estimate will vary directly as the assumed separation distance. Such a low dipole density indicates that the process is credible. It appears that the observed features of shock-induced polarization, such as a critical compression threshold, a saturation at large compression, and irreversibility, can be readily fit into the framework of the present bond scission model. The correlation of monomer structure with the polarization strongly suggests the more complex polymers are more sensitive to bond scission. This propensity can be explained in terms of the likelihood of mechanical energy becoming localized, thus stressing local bonds and exceeding the bond strength. This view is discussed in more detail by ButyaghZ7 The most uncertain aspects of the bond scission model are the polymer characteristics and conditions which control or influence the relative displacement of the charged species in the stress gradient of the shock front. Support for this concept comes from the Soviet cation displacement modell which describes shock-induced polarization in 13 different ionic crystals. In this model cation vacancies are produced due to mechanical yielding; thus, the thresholds are the respective Hugoniot elastic limits. Because of the

Shock-Induced Electrical Activity in Polymeric Solids

simpler character of the crystal, the defects are well defined and the correlation of the shock-induced polarization with cation radius, independent of anion, clearly identifies the effect as one of cation displacement. The data indicate cation relative displacement distances of about 1 to 10 lattice spacing. Thus, the cation displacement model for shock-induced polarization is similar to the present bondscission model in assigning the basic action to mechanical effects. The cation displacement provides strong support for displacement of defects over lattice dimensions due to stress gradients within the shock front. Summary In the present paper, a systematic association between electrical activity (shock-induced polarization and shockinduced conduction) in shock-loaded polymers and the complexity of the monomer repeat unit is demonstrated. From prior mechanochemical studies, it appears that the severe stress gradient in a shock front could reasonably be expected to cause bond scission. The prior mechanochemical studies also show that the propensity for mechanical bond scission observed for various polymers has the same tendency as the propensity for shock-induced electrical activity. On these bases, a model for such activity has been proposed whereby mechanically induced bond scission leads to formation of electrically charged species which are relatively displaced in the stress gradient of the shock front. Prior observations of cation displacements in ionic crystals over lattice distances reinforces the credibility of the displacement of the charged species. The bond scission and charged species displacement model has the appropriate features to explain the observed threshold and relaxation, the irreversible nature of the phenomenon, and the presence of a saturation. The creation of charged molecular defects can account for the connection between shock-induced polarization and shock-induced conduction and their joint association with complex monomer repeat units. The proposed bond scission process most likely results from local elastic nonequilibrium processes directly influenced by the monomer structure. Accordingly, the definition of a “complex monomer” relates to its propensity to localize or trap elastic energy, thereby causing transient stressing of a bond. Such an effect is well illustrated by the absence of local mass discontinuities in the simple monomers of Teflon and polyethylene which provide little opportunity for localization of energy, are insensitive to bond scission, and exhibit feeble electrical activity. Theoretical elastic vibrational studies of monomer repeat units to identify propensity for localization of elasticenergy are of immediate interest. Thequestion of entanglement of polymer chains may complicate such an investigation. Because the proposed effects occur in subnanosecond times and thus lie outside the range of electronic experimental resolution, optical probes should provide the most effective means of following the kinetics of the process within shock fronts. Shock-induced polarization provides a simpler and more direct probe of shock-induced electrical activity than similar measurements of shock-induced conduction. Thus, it appears that e v e n though the correlation between shockinduced polarization and shock-induced conduction must be more carefully examined, shock-induced polarization studies should prove the more productive. Shock-induced polarization measurements provide a simple and effective probe of a shock-induced disequilibrium thermodynamic process which should be used in further study of the association of monomer structure with threshold compression, maximum rate of change of polar-

The Journal of Physical Chemistry, Vol. 83,

No. 23, 1979 3055

ization with compression,and saturation polarization. The correlation between shock measurements and more conventional mechanochemical studies is of interest and mechanochemical studies should provide the basis for predicting shock-induced electrical activity. Conversely, shock-induced polarization may provide a method for predicting the propensity for polymers to undergo mechanical degradation. Bond scissions within the shock front are expected to cause local release of energy and local increases in thermal energy which should be reflected in wave speeds of shockloaded polymers. The present data on PPMI are insufficient to investigate this point but a hint of such an effect is shown in the data. Sheffield and B l o o m q ~ i s have t~~ noted a discontinuity in the U,u relation of shock-loaded PMMA at a compression in the vicinity of the proposed threshold for shock-induced polarization. In a contemporary investigation, Bloomquist and Sheffield40have investigated the possibility of measuring the temperature of shock-loaded solids. Their measurements on PMMA and epoxy show anomalous increases in temperature at threshold compressions consistent with those for shock-induced polarization. Thus, their measurements provide tentative additional support for a mechanically induced bond scission. Descriptions of the state of shock-compressed matter have traditionally been based on concepts of either a “benign shock’ or a “catastropic shock’. In the benign shock concept the shock transition is considered to carry the material from one equilibrium thermodynamic state to another in a manner analogous to quasi-static compression. In the catastropic shock concept the shock transition is considered to be a source of considerable lattice disorder which introduces a disequilibrium defect state. In this case, the shock transition carries matter into a nonequilibrium thermodynamic state in which defects have a substantial if not overriding influence on material response. Such nonequilibrium thermodynamic processes may not have a counterpart in other environments. The model proposed in the present work is clearly framed within the catastropic shock concept and it should be noted that most shock-induced electrical response measurements indicate the need for such a concept. In fact, correlation of electrical response measurements to shock-induced defects provides a very sensitive and effective probe of the mechanical deformation processes occurring within shock fronts, clearly demonstrates the nonequilibrium character of such deformations, and provides a quantitative basis for distinguishing between shock deformation and related static deformation. Prior suggestions that shock-induced polarization result from elastic rotation of electric dipole^',^^^^^^^ are based on the benign shock concept. Key considerations not justified in prior work involve questions of relaxation time of polarized states, rotation without bond scission, and support of the proposed process from independent sources. Harris’ lattice distortion model involves similar consideration^.^^

Acknowledgment. The author is pleased to acknowledge the excellent technical work of G. T. Holman, Jr., discussions with D. D. Bloomquist and s.A. Sheffield, and review of the manuscript by S. A. Sheffield and J. G. Curro. This work was sponsored by the U.S. Department of Energy under Contract DE-AC04-76-DP00789. References a n d Notes (1) V. N. Mineev and A. G. Ivanov, Sov. Phys., Usp., 19, 400 (1976). (2) W. J. Murri, D. R. Curran, C. F. Petersen, and R. C. Crewdson in “Advances in High Pressure Research”, Vol. 4, R. H. Wentorf, Jr., Ed., Academic Press, New York, 1974, p 1.

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The Journal of Physical Chemistry, Vol. 83, No. 23, 1979

(3) L. Davison and R. A. Graham, Phys. Rep., accepted for publication. (4) R. J. Eichelberger and G. E. Hauver in "Les Ondes De DBtonation", Editions du Centre National de la Recherche Scientifique, 15, Quai AnatoleFrance-Paris, VIP, 1962, p 363. (5) G. E. Hauver, J . Appl. Phys., 36, 2113 (1965). (6) M. de Icaza Herrera, A. Migault, and J. Jacquesson, C . R. Acad. Sci. Paris, 284, 503 (1977). (7) M. de Icaza Herrera, A. Migault, and J. Jacquesson, C . R . Acad. Sci. Paris, 264, 531 (1977). (8) M. de Icaza Herrera, Thesis, University of Poitiers, France, 1976, in French. (9) M. de Icaza Herrera, A. Migault, and J. Jacquesson in "High Pressure Science and Technology", Vol. 11, K. D. Timmerhaus and M. S. Barber, Ed., Plenum Press, New York, 1979, p 870. (10) E. Z. Novitskii, A. G. Ivanov, and N. P. Khokhlov in "Combustion and Explosion, Proceedings Third All-Union Symposium on Combustion and Explosion", Nauka, Moscow, 1971, p 579, in Russian. (11) F. E. Allison, J. Appl. Pbys., 36, 2111 (1965). (12) Y. Horie, Brit. J . Appl. Pbys. ( J . Phys. D), 1, 1183 (1968). (13) R. A. Graham, Phys. Rev. B , 6, 4779 (1972). (14) R. A. Graham, F. W. Neilson, and W. B. Benedick, J . Appl. Phys., 36, 1775 (1965). (15) Dupbnt Company, Bulletin H-2, Electrical Insulation Products Division, Dupont Film Department. (16) G. A. Bernier and D. E. Kline, J . Appl. Polym. Sci., 12, 593 (1968). (17) R. A. Graham, J . Appl. Pbys., 48, 2153 (1977). (18) R. G. McQueen, S. P. Marsh, J. W. Taylor, J. N. Fritz, and W. J. Carter in "High-Velocity Impact Phenomena", R. Kinslow, Ed., Academic Press, New York, 1970, p 293. (19) V. V. Yakushev, 0. K. Rozanov, and A. N. Dremin, Sov. Phys. JETP, 27, 213 (1968). (20) G. E. Hauver, Proc. Symp. Detonation, 5tb, 387 (1970). (21) D. Bloomquist, private communication.

Communications to the Editor (22) A. R. Champion and W. B. Benedick, Rev. Sci. Instrum., 39, 377 (1968). (23) W. J. Carter and S. P. Marsh, private communication. (24) G. E. Hauver, private communication. (25) A. R. Champion, J. Appl. Phys., 43, 2216 (1972). (26) R. A. Graham, Bull. Am. Pbys. Soc., 24, 711 (1979). (27) P. Yu. Butyagin, Russ. Chem. Rev., 40, 901 (1971). (28) A. Casale and R. S. Porter, "Polymer Stress Reactions", Voi. 1, Academic Press, New York, 1978. (29) A. Casale and R. S. Porter, "Polymer Stress Reactions", Vol. 2, Academic Press, New York, 1979. (30) P. Yu. Butyagin, A. A. Berlin, A. E. Kalmanson, and L. A. Blyumenfekl, Rubber Cbem. Techno/., 33, 942 (1960). (31) H. A. Larsen and H. G. Drickamer, J. Phys. Chem., 61, 1643 (1957). (32) G. A. Adadurov, I. M. Barkalov, V. I. Gol'danskii, A. N. Dremin, T. N. Ignatovich, A. M. Mikhailov, V. L. Tal'roze, and P. A. Yampol'skii, Polym. Sci. USSR, 7, 196 (1965). (33) L. V. Al'tshuler, I.M. Barkalov, I.N. Dulin, V. N. Zubarev, T. N. Ignatovich, and P. A. Yampol'skii, H/gbEnergy Cbem., 2, 73 (1968). (34) L. V. BabarB, S. V. Pershin, and V. V. Yakovlev in "Proceedings, Second All-Union Symposium on Combustion and Explosion", L. N. Stesik, Ed., 1971, p 305, in Russian. (35) I.Yu. Tsarevskaya, V. A. Kargin, V. N. Zubarev, V. I.Gol'danskii, P. A. Yampol'skii, and T. V. Fremel' in "Proceedings, Second AlCUnion Symposium on Combustion and Explosion", L. N. Stesik, Ed., 1971, p 301, in Russian. (36) P. A. Yampol'skii in "Proceedings, Second All-Union Symposium on Combustion and Explosion", L. N. Stesik, Ed., 1971, p 293, in Russian. (37) A. N. Dremin and 0. N. Breusov, Russ. Cbern. Rev., 37, 392 (1968). (38) G. E. Duvall and R. A. Graham, Rev. Mod. Phys., 49, 523 (1977). (39) S. Sheffield and D. Bloomquist, private communication. (40) D. Bloomquist and S. Sheffleld, private communication. (41) P. Harris, J . Appl. Phys., 36, 739 (1965).

COMMUNICATIONS TO THE EDITOR Chemical Oscillations during the Uncatalyzed Reaction of Aromatic Compounds with Bromate. 2. A Plausible Skeleton Mechanism

Sir: Koros and Orb6n1i2have recently reported oscillations when a number of aromatic compounds are oxidatively brominated by acidic bromate even without the metal ion catalysts previously thought necessary for such oscillating systems. These compounds can all be regarded as derivatives of phenol or aniline. All3 have a hydrogen attached to oxygen or nitrogen whose abstraction would generate a resonance stabilized free radical. All have a t least one free ortho position subject to bromination by Br, or HOBr. All have OH or NH, substituents and have at least one free ortho or para position so that oxidation could generate quinone or quinone imine structures. Investigations conducted to date have revealed very diverse behavior of different reacting s y ~ t e r n s . Thus, ~ various quinones, brominated derivatives, and oxidatively coupled products have been observed. However, these uncatalyzed oscillatory reactions are all controlled by bromide ion, and the critical bromide concentration is close to that observed during catalysis by metal ions.5 Although the detailed chemistry of any system will depend upon the organic substrate, we believe the oscillations observed with at least the polyphenolic compounds can be explained by the skeleton mechanism shown in Scheme I. In that scheme, HAr(OH), is an aromatic compound containing at least two phenolic groups, HAr(0H)O. is the radical obtained by hydrogen atom abstraction, HArO, is the related quinone, BrAr(OH), is the brominated derivative, and Ar2(0H)4is the coupling product. 0022-3654/79/2083-3056$01 .OO/O

Scheme I

+ Br- + 2H+ + HBrO, + HOBr HBrO, + Br- + Hf 2HOBr Br03- + HBrO, + H+ -+2Br0,. + HzO BrOz. + HAr(OH), HBrO, + HAr(0H)O. 2HBr0, Br0,- + HOBr + H+ HOBr + HAr(0H)O. + Br. + HArO, + H 2 0 Br. + HAr(0H)O. Br- + HAr02 + H+ HOBr + Br- + H+ + Br, + HzO Br2 + HAr(OH)z BrAr(OH), + Br- + H+ (K9) HOBr + HAr(OH), BrAr(OH), + H 2 0 (K10) Br0,-

-

-

-

-

-

Steps K1 to K5 involve inorganic chemistry identical with that already demonstrated for metal-ion catalyzed bromate oscillations5 except the organic substrate replaces reduced metal ion for the 1-equiv reduction of the Br02. radical in step K4. If the system contains sufficient bromide ion, the stoichiometry of net reaction A is generated by the sequence K1 + K2. Br0,0 1979 American

+ 2Br- + 3H+

Chemical Society

-

3HOBr

(A)