Optical and electrical effects during polymerization anddepolymerization in liquid sulfur: indications for thenonuniformity model for covalent liquids

G. C. Vezzoli, P. J. Kisatsky, L. W. Doremus, and P. J. Walsh

The polymerization and depolymerization of liquid sulfur refers, respectively, to the processes of chaingrowth and chain scission promoted by changing thermodynamic conditions. These structural transitionscause major optical and electrical consequences, including: (1) color change from yellow to orange to red,(2) peaked high angle and low angle scattering and minimum in transmission of He-Ne laser light at thestructural changes, (3) a decrease in the current induced by a pulsed ruby laser above the polymerizationtemperature Tp compared with below Tp, (4) two changes in the sign of the temperature coefficient of re-sistance in the vicinity of Tp and the depolymerization temperature Td, and (5) superlinear current-volt-age characteristics above Td. The data are interpreted as being suggestive of the structure of a liquidbeing better described by a nonuniformity rather than random network model.

1. Introduction

In the liquid state sulfur is well known to undergospontaneous polymerization. The polymerizationtemperature Tp 1590C is pinpointed from carefulstudies of the dependence of viscosity on tempera-ture. Sulfur melts to a mobile liquid; however, Geelreports that the viscosity decreases slightly with in-creasing temperature until about 1540C, above whichit sharply rises and continues to increase during thepolymerization process, eventually reaching a maxi-mum value about three to four orders of magnitudegreater than at T < Tp. Bacon and Fanelli2 reportthat the viscosity increases by a factor of 2000 overthe very narrow thermal range and achieves a maxi-mum value at about 1871C. They report also thatthe viscosity heating curve closely follows the viscosi-ty cooling curve. The temperature of maximum vis-cosity was placed at about 1700C by Eisenberg3 who,together with Tobolsky,4 presented a unified theoryon the ring z=± chain equilibrium polymerization ofsulfur. The abrupt rise in the viscosity of liquid sul-fur is attributed by Gee1 to the simultaneous rise inthe concentration and in the chain length of the poly-mer until achieving a maximum chain length of about106 atoms.

P. J. Walsh is with Fairleigh Dickinson University, Departmentof Physics, Teaneck, New Jersey 07666; the other authors are withFeltman Research Laboratory, Picatinny Arsenal, Dover, New Jer-sey 07801.

Received 14 March 1975.

A .sharp peak in the heat capacity vs temperature(at atmospheric pressure) is reported at 1590C byLewis and Randall,5 by Braune and Moller6 and byWest,7 indicating a criterion for a second-order phasetransformation. Meyer8 et al. have reported a dis-continuous peak at 1600C in the shift rate of the ab-sorption edge of liquid sulfur (a shift rate change of10 A per degree Kelvin) at 0.6 optical density.

Electrical resistance measurements of liquid sulfuras a function of temperature were reported by Vezzo-li9 and showed two reversals in the sign of the tem-perature coefficient of resistance (negative to positivedp/dT at 1660C and positive to negative at 1920C).In a more sophisticated study using ultrapure sulfurthe turning points were reported by Vezzoli10 to be164.50 C and 1920C. Both studies showed a sharpdecrease in resistance at 212-2141C.

The present research was undertaken to determinethe following: (1) whether the structural changes inliquid sulfur were associated with simple optical ef-fects such as color changes, relative reflectance, andscattering, (2) an elucidation of the probable cause ofthe two changes in the sign of the temperature coeffi-cient of resistance (i.e. whether these changes indi-cated polymerization and depolymerization directly),(3) whether under conditions of gross thermodynam-ic disequilibrium radiative recombination can beachieved (and detected) due to chain bonding, (4) thetemperature corresponding to the turning points inthe viscosity curve and the kinetic dependence of theviscosity effects, and (5) whether the data cast lighton the general structure of the liquid state.

February 1976 / Vol. 15, No. 2 / APPLIED OPTICS 327

11. Experimental Procedure

Starting material consisted of orthorhombic sulfurof 99.999% purity contained by a fused silica glasstube of dimensions ranging from 1.27 cm i.d. by 1.91cm o.d by 25.4 cm height to 2.2 cm i.d. by 2.54 cm o.d.by 15.2 cm height.

The turning points in the viscosity vs temperaturecurve were obtained through the use of a chemicalbalance technique. A 20-g weight was suspended bya 0.25 mm manganin wire from the left arm of thebalance into liquid sulfur, which was heated in a lab-oratory oven manufactured by the Grieve Corpora-tion (model LO 200C). Heating rates varied from0.10C to 3C per min and cooling rates varied fromnormally 0.20C per min to 50'C per min under theapplication of a stream of ultrapure helium vapor.Sufficient counterweight was utilized to cause theweight to rise (or fall) through a fixed distance, whichwas measured by the indicator of the chemical bal-ance. A calibrated and insulated chromel alumelthermocouple and two platinum electrodes, whichwere fed through a two-hole ceramic tube, were im-mersed in the liquid at the center point of the regiontraversed by the 20-g weight. The thermal gradientin this region was observed to be less than 0.500C.By measuring the time required for the weight to tra-verse the specified region as a function of tempera-ture, a simple method was afforded for measuringviscosity and in particular the turning points of theviscosity vs temperature curve. These turningpoints, as mentioned earlier, are assumed to repre-sent the inception of polymerization and the temper-ature of maximum chain length.

Electrical resistance measurements as a function oftemperature were accomplished by immersing two0.5 mnm platinum electrodes insulated by a two-holeceramic feed-through and (of 1-mm spacing) into the.liquid sulfur. Electrical current was measured atconstant source voltage, which was supplied by aKeithley 240A dc source capable of 1200-V output.Current was recorded by a Gould Brush 240 chart re-corder connected to the output of a Keithley 160 dig-,ital multimeter on a nanoampere scale. In this man-ner electrical current changes of 0.1 nA could be sta-bly and reproducibly detected, measured, and re-corded. Temperature was measured by a chromel al-umel thermocouple positioned between the elec-trodes and calibrated by the boiling point of waterand the melting point of sulfur. Heat was suppliedthrough a Thermolyne hot plate from which a fur-nace was fabricated using ceramic refractory bricksand transparent glass blocks.

Optical effects in the visible range were measuredby an EGG photomultiplier and model 58511 mono-chromator arrangement as well as by a conventionalEGG Light Mike, and in the ir range by a gold-dopedgermanium detector and an EGG ir detector. Irra-diation was supplied by a He-Ne laser and a Koradpulsed ruby laser.

In some experiments ultrapure helium vapor wascontinuously passed over the molten sulfur sample,

and the resulting electrooptical characteristics fromthese experiments were essentially the same as in ex-periments that did not utilize the helium flow.

The possibility for piezoelectric effects was studiedusing a lead zirconate titanate piezoid (PZT 5A) con-nected to 0.25 mm platinum wire with a high-temper-ature solder that melted above 2300C. The piezoidstudy was conducted to determine whether thepulsed ruby laser caused a pressure wave that wecould measure in the sulfur sample and to determineif the drastic viscosity changes, which occur duringpolymerization and depolymerization, could cause achange in the stress applied to the piezoid.

Ill. Results and Discussion

A. Scattering, Reflectance, and TransmissionExperiments

The scattering at approximately right angles of aHe-Ne laser (6328 A) shows a sharp peak at thestructural transition temperature in liquid sulfur.Figure 1 shows this peak at 1660C and a small secon-dary peak at 170°C and corresponds to the first cool-ing cycle on a virgin sample. The turning points inthe resistance trace (see current) occur at 1740C and1690C. The inset to the figure shows a small peak at1730C upon heating after many cycles. Figure 2shows three such effects at 176°C, 170°C, and 166°C.

SCATTEREDLIGHT (Hc le)

Fig. 1. Chart recording showing temperature in degrees Celsius,radiation, in arbitrary units, and current in nanoamperes:displaying a sharp maximum in scattered light intensity at reversalin (da)/(dT) characteristic of the chain breakdown and ring for-

mation when cooling through T2C and Tjc.

328 APPLIED OPTICS / Vol. 15, No. 2 / February 1976

t

1;t�

ZI

2IIt

IitII

TEMPERATURE 2mv/di + 26'C

Fig. 2. Temperature, radiation, and cur-rent as in Fig. 1: showing three scatteringpeaks probably corresponding to the struc-tural effects of long chain breakdown (peakat 1760C) and ring formation (peak at1660 C). The peak at 1760 C coincides ap-

proximately with the current reversal atT2c.

At

:_0

s M.

zI'L

1.

1 _C7

- i85% 184%C 182'C

i 1111

J175C~ qlll I

- Z ERO

M -

in - -.1 .. . - ..

Fig. 3. Wavelength, radia-tion, and current: showingscattering peak at 1820Ccoincident with reversal insign of (da/dT) at minimumcurrent of 10.5 nA. Belowabout 1800C the monochro-mator was set on an automat-ic scan from 3000 A to 8000 A.The middle trace shows thenonzero photomultiplier out-put when the monochromatorgrating passes through the

- 6328 A region.I a--

Figure 3 shows the effect at about 1820C and corre-sponds to the tenth cooling cycle and a more obliqueangle of laser beam incidence than in Figs. 1 and 2.The most prominent effect at 1660C is at too low atemperature and is too steeply peaked to indicate asimple following of the viscosity peak. Furthermorethe effects are not examples of differences in relativereflectance characteristics of two equilibrium phasesand appear more explicable in terms of scattering orabsorption due to density or index of refractionchanges. Since the scattering is in the increasing di-rection for both rising and falling temperature we arenot involved with a property such as enthalpy whosesign is dependent on whether we are heating or cool-ing through a transition.

Figure 4 gives a plot of relative reflectance vs tem-perature for near normal (10-15°) incidence of aHe-Ne laser. In the experiments corresponding tothe figure, the thermocouple was placed in the centerof the liquid. A thermocouple placed in the liquidbut near the front wall where the laser was incidentindicated about a 10° gradient. Thus the true tem-peratures corresponding to effects that cause peaks

shown in Fig. 4 are probably in the 184-1941C range.The furnace was then rebuilt to reduce the lateralgradient to less than 1C. The results shown in Figs.1-4 may not be completely characteristic of scatter-ing phenomena and may be also partially due to sam-ple absorption and the consequent change in reflec-tion of the transmitted beam from the furnace walls.Figure 5 gives the direct data on transmission vs tem-perature for heating and cooling. The data indicatea minimum in transmission at a temperature of about167°, which is the approximate temperature at whichthe-temperature coefficient of resistance changes signfrom negative to positive. The transmittance onboth sides of the minimum is approximately the sameand the valley of the trace in Fig. 5 occurs during avery short temperature range, less than 10C.

Photon scattering at centers of structural transfor-mations are due to a number of effects that are sub-stantially a result of mismatch of indices of refractionof two phases at their interface, which itself consti-tutes an inhomogeneity. Adiabati6 density fluctua-tions lead to scattering, and the change in density en-ters the scattering relationship as a squared term.11

February 1976 / Vol. 15, No. 2 / APPLIED OPTICS 329

1 70C I 66C

-- 4

-

S.C,

CR Cen c:, ;up> O7-sm z

ZERO -

-L

H

9;I

0Z;Z"

l

(a) RVOLTS OUTPUT

OF PHOTO-MULTIPLIER

TUBE

110

100

R1.2(a)

(b)

90

80

70F

60F

112'C

-7 _Th

-6 0.0 \ I

R j-5 VOLTS

-4 0.7 192'C

-3 I 'I I

-2 0.6 I400 500

TEMPERATURE (K) i_1 194°C "V

| 1374

C

SAMPLERUN I

-o05u 4'u 0

40

30 I-

20

10

100 200 1

SAMPLE 1, IRUN 2 rI

* . I

1, I00 / Iroes 187 C

I

00

0

300 400

4o1

300

200

RI .1(o)

1O

350 400 450 500

TEMPERATURE ( K)

Fig. 4. Relative reflectance R (in arbitrary units) of liquid sul-fur under near normal incidence (He-Ne laser) vs temperature

in K.(a) The effect of melting is a large decrease in the relative re-flectance because significantly more light is transmittedthrough the mobile yellow liquid. Inset shows reflectance in

liquid state giving peak at 186-192°.(b) Reflectance in liquid state during melting and polymeriza-tion. Peak appears to be at 186-1941C apparently at tempera-

ture where the viscosity 77 peaks.

This explains why large scattering effects occur atcritical points such as the lambda point in the molarheat capacity of helium, a second-order transition oc-curring between 1.7-2.4 K.12 Light scatter will resultfrom variations in density, changes in concentration,and changes in the anisotropy tensor.13 The peakedoptical effects in sulfur are suggestive of some type ofactivated transitory state. This state may possiblybe the condition at which the average polymer chainlength is approximately equal to the wavelength ofthe incident radiation allowing constructive interfer-ence of waves scattered by the forming polymer. Weassume a chain similar to that of fibrous sulfur hav-ing 10 atoms per one helical turn of 13.8 A and allowa factor of two to account for self-coiling of chains.(The factor is noncritical and can vary by an order ofmagnitude.) The He-Ne wavelength in angstroms

would then be about equal to a chain of about 104atoms, which is achieved in sulfur between 160-170°C. This corresponds, in general, fairly well withthe temperature values for the optical peaks (about1600 C); however, the interpretation at this point isstill speculative.

In the above context, peaked optical scatteringwould only occur over a very small thermal region ATwhere the average chain length was about equal tothe monochromatic wavelength of the laser. The pe-riodicity might then represent the average distancebetween polymeric diradically terminated chainends, where the anisotropic structural region of an

34K unpaired electron spin may act as a preferential scat-

tering site or perturbation. The magnitude of thescattered light is directly related to the spatial Fouri-er component of the perturbation,1 4 and motion ofthe perturbation due to aperiodic oscillation fromthermal agitation and also due to diffusion can leadto a Doppler broadening A'y.15 (We were unable tostudy any line broadening at these peaks because inthe experiments where a monochromator was utilizedthe scan was not sufficiently rapid and the resolutionof the instrument not sufficiently narrow to be suitedto measuring any Ay.) In addition, if the scatteringsite is anisotropic, the scattered radiation from a po-larized incident beam can be depolarized. Since the

data). ItlyI

v S i ~~~~~~, L iW

IIIIII1. 7 .11111 1 1 1 1

X f HeA~~~~~i

Fig. 5. Transmission of He-Ne laser vs temperature showingminimum at transition temperature on heating and cooling (raw

data).

330 APPLIED OPTICS / Vol. 15, No. 2 / February 1976

-

Fig. 6. Color of sulfur upon heating to temperatures up to 2060 C.Note change from orange to red between 155-164 0 C during

polymerization.

scattering effect is of such a transient nature we wereunable to measure polarization effects. The Ay is aRayleigh broadening and is expected in liquid sulfurduring polymerization from either a fluctuation inthe strain tensor or the effect of rotational Brownianmotion or the elastic vibrations of quasi-linear mole-cules in the fields of neighboring molecules. 15 In liq-uid sulfur from comparison with other polymers it isdoubtful that the line broadening (using convention-al excitation sources such as the Hg line) for the nor-mal Rayleigh scattering exceeds 100 cm' except per-haps at the optical peaks accompanying the transi-tion. References 14 and 15 give a theoretical treat-ment of Rayleigh scattering and of the effects of an-isotropy.B. Color Changes Due to Polymerization andDepolymnerization

Figure 6 shows, in black and white, an indication ofthe color changes in sulfur at temperatures from990C in the solid state through the polymerizationrange and eventually to 2060C, which is above the de-polymerization temperature. A gradual transition incolor from yellow to orange to red is apparent in theexperiment, with the most dramatic change occurringbetween 155-1640C, during which polymerization istaking place. Any color change associated with de-polymerization is far more subtle and appears to be aslightly deeper reddening. Upon cooling (Fig. 7) thecolor changes are even less distinct, but a slight or-ange texture becomes apparent when cooling from167C to 1400C. The color film and indoor lightingutilized in this study caused a loss of some of the redtones in favor of orange, as compared with the unaid-ed eye and when judged according to standards.This was, in turn, passed on to the black and white

pictures used in the text. The results indicate thatincreasing chain concentration causes a general red-dening of the liquid and hence a greater porportion ofthe intensity of the He-Ne laser line will be reflectedat temperatures above the polymerization point thanbelow it.

A color picture (see cover) was taken of liquid sul-fur exposed to a thermal gradient covering the rangeof 2580C at which the sulfur is a deep blood red liq-uid to about 1400C where sulfur is orange. The tem-perature at the lower interface between the blood redsulfur and the bright red sulfur is 192-1951C, and thetemperature at the red-orange interface is about1660C. The viscosity increases abruptly in the or-ange-red boundary as measured by free fall experi-ments through the thermal gradient. There is no in-dication with increasing or decreasing temperature,however, that any color change in the form of a singu-

HEATN

Fig. 7. Color of sulfur upon cooling from 1960 C to 140'C. Thereis only very slight color change upon cooling through the viscosity

maximum.

10

5

SULFUR SAMPLE 2 RUN 2

% CURRENTI NCREASE

- WHILE04- 0- l I COOLING

157'C \

0 100 200 300 400TEMPERATURE *- T () T-(O)

500 K

PHOTO CURRENT AT 800 V/mm FIELD

Fig. 8. Current in nA due to pulsed ruby laser irradiation vs tem-perature in K upon heating and cooling.

February 1976 / Vol. 15, No. 2 / APPLIED OPTICS 331

.11:

IJ

L.

c-

11

4.

1

6I1 g

! 2

I J

f

E 4 600f~

I- o

.ez

12.0 IGO 180 IC

1 .

120 240 260 180

TEMPERATURE (0

C)-_

,00 120 140 160 IH0

TEMPERATURE (0

C)

200(-C)

Iz I

ge *

Ia - e

2 30 ; . 5

a 2

120

260(-t)

Fig. 9. Middle: current induced by pulsed ruby laser vs temper-ature (upon cooling). Note major change at about 1600C. Fieldcurrent at constant source voltage is also plotted, and turningpoints are shown at 1701C and 1560C, corresponding to T2C andT1c, the temperatures corresponding to the change in the sign of(da)/(dT). Top: change in temperature, as measured by chromelalumel thermocouple, due to irradiation with unfocused pulsedruby laser. Bottom: voltage change across PZT 5-A piezoid

showing large variation from 170'C in 1590 C.

larity (increasing reddening then decreasing redden-ing) accompanies any of the optical reflectance, scat-tering, and transmittance data. Increasing polymerconcentration causes a deeper reddening, and at veryhigh temperatures liquid sulfur becomes black. In-creasing the temperature causes the orange-red in-terfacial region to propagate toward the positioncoordinates of higher temperature.

By scanning the laser beam across the interpene-trating interfacial orange - red zones, scatteringpeaks and transmission minima were consistently ob-served using the photomultiplier tube, and the en-hanced scattering was even apparent to the unaidedeye. Thermocouple measurements indicated an av-erage temperature of about 172 h5°C for the scatter-ing peaks obtained by moving the laser beam as com-pared with the 166-182°C for the scattering peaksobtained by varying temperature at a constant laserposition. The former phenomenon is not a geometri-cal effect because vertical movement of the detectorcaused no change in the scattering peak; however,vertical movement of the entire furnace, such thatthe boundary region no longer was coincident withthe laser, caused the scattering to decrease sharply.

When a sample was removed from the gradient

furnace and the tube held in air for a few seconds, itwas consistently noticed that the red polymer regionat the base of the tube rose to the top of the tubewithout losing its integrity. When the red regionreached the top of the tube it spontaneously trans-formed to the orange octameric liquid phase. Thiseffect was attributed to the lower density of the redphase which maintains its integrity because it is ap-parently an immiscible phase as compared with theorange phase. The red phase transforms to the or-ange phase at the top of the tube because of thestrong forces at the sulfur-air interface and their ac-tion on a supercooled phase to reduce the free energy.

C. Current Induced by Pulsed Laser

A plot of the laser-induced current measured bythe digital ammeter-Brush recorder combination isshown in Fig. 8 as a function of increasing and de-creasing temperature; a sharp transition is observedat the polymerization temperature. Thermocouplemeasurements indicated a temperature rise of about1PC during laser irradiation; calculations indicatethat a 1.0-1.8 0 C rise in temperature would be reason-able. The use of a PZT 5-A piezoid was unable todetect any pressure wave caused by the pulse of laserlight. However, since the laser light is pulsed and isof very high intensity and moderate power, the in-duced current is probably not a conventional photocurrent; and we refer to it simply as a laser-inducedcurrent or LIC. From the previous sections it is rea-sonable that above the polymerization point Tp lessabsorption of red light should occur. Figure 8 showsthat the fall-off in the LIC is of the order of 85%above the polymerization temperature. Figure 9 alsoshows the change in the LIC upon cooling throughthe polymerization transition, and also gives thechange in the field current at constant voltage (800V), giving the two changes in the sign of the tempera-ture coefficient of resistance at about 1580 C and1700C. The figure also shows that portion of thechange in the temperature (about 1C) due to thepulsed laser, which the thermocouple was capable ofdetecting. The laser pulse lasts only of the order ofnanoseconds; however, our only recording instrumen-tation, which was capable of detecting tenths of na-noamperes, was incapable of nanosecond time re-sponse. Hence, the results may not be absolute inmagnitude but are definitely consistent in trend.The temperature-induced piezoid voltage changeshown in Fig. 9 will be discussed later.

D. Current-Voltage CharacteristicsThe current-voltage (I-V) characteristics are given

in Fig. 10 at steady-state temperatures varying fromroom temperature through the melting point and po-lymerization range to above the depolymerizationvalue. At fields of 300 V/mm the curves begin toshow slight superlinearity above the polymerizationtemperature (curve E at 1750 C) and considerable su-perlinearity becomes evident at 2360 C (curve H). Itshould be noted that curve F represents a higher re-sistance than curve E (1750C). This nonsemicon-

332 APPLIED OPTICS / Vol. 15, No. 2 / February 1976

.6

A 6O , , , ,, , , _-

16,

J

/236'C

H/

50 2

c i; ^ tz ~~~~~~~~~~~~~~~~~~~~~~~175 C

2.0-

30 DARK CURRENT

oo 200 300 2.0 52, 60 70 0

ELECTRiC FIELD IN VOLES PER MILLIMETER

Fig. 10. Current in nA vs voltage in volts at several tempera-tures ranging from 240 C to 258°C. Note the superlinearity be-ginning at about 1980C and the inversion of curves E and F due

to reversals in the sign of (da)/(dT).

ductor-like phenomenon is due to the reversal in thesign of the temperature coefficient of resistance inthe polymerization region. The increasing resistanceduring polymerization and the simultaneous incep-tion of superlinearity are apparently indications ofcompeting processes that will be treated quantita-tively in a later publication. Under high electricfield conditions (104-105 V/cm), liquid sulfur under-goes a switching to a high conductance phase. Thiswas observed using 1-mm spacing electrodes as wellas in experiments using thin sulfur liquid films (1-10 im) in a tungsten boat configuration. Figure 11gives I-V curves at temperatures of 1660C and about1780C. The inset shows bona fide reversible switch-ing from a high impedance to a high conductancestate. The curve at 1660C, just above the polymer-ization point, shows two separate high conductanceregimes, perhaps suggestive to two types of conduc-tion processes. Scattered indications were also ob-served for further transitions at higher electric fieldsfrom high to low conductance states similar to a phe-nomenon reoprted for liquid selenium at high tem-peratures.'6 The current-voltage characteristicsbear some resemblance to the I-V curves for liquidchalcogen alloys and for some amorphous semicon-ductors.'6

E. Resistance vs Temperature Characteristics

The turning points in the resistance vs tempera-ture characteristics for liquid sulfur are indeed veryunusual. During the temperature interval fromabout 1660C to 1860C in the up-temperature direc-tion, and about 180-159°C in the down-temperature

direction, the temperature coefficient of resistancebehaves opposite to a conventional semiconductormaterial, namely increasing with increasing tempera-ture.

We have been unable to describe the data quanti-tatively by simply assuming that the dc conductivityarises from the diradically terminated chain ends.During the polymerization interval, although the av-erage chain length increases, the concentration of thelong polymer and of the opened rings also increases.Thus no direct mechanism for a turning point in theresistance vs temperature characteristics arises fromdiradical contributions. The turning points in theresistance data can be described quantitatively if thebackground dc conductivity is ascribed to the closedring material whose concentration begins to be sharp-ly reduced' at the polymerization transition. How-ever, from comparison of the activation energy ofcrystalline ring sulfur (1.3 eV) with that of liquidchain sulfur (0.5 eV) and from considerations of theinsulating properties of closed molecular rings, itdoes not seem plausible to us that the ring speciescan be responsible for the dc conductivity of liquidsulfur. Therefore, the unusual property of increas-ing resistance while the temperature is also increas-ing does not appear to involve the temperature de-pendence of carrier concentration.

It has been found that organic resins reflect an in-crease in resistance during polymerization accompa-nying increasing viscosity and eventual conversion tosolid dielectrics.'7 However, we believe that sinceliquid sulfur above 1590C is an elemental polymer,the generally suspected electrolytic type conductionand the accompanying theoretical treatments are notcogent. The conductivity data for liquid sulfur fitvery closely to the general band theory for electronicconduction.'0"18 The conductance can be conven-tionally written

a = J/E = njejuj

where n, e, and refer to the number, charge, andmobility of carrier type j in unit volume. It appearsto us that the turning points in resistance at T, andT2 can be explained in terms of the dependence ofcarrier mobility on the structure of the polymer.

ma I1.0

T - 1781C

10 V0.5

T-1661C

10 20 30 40 VOLTS

Fig. 11. High field current-voltage characteristics showing strongsuperlinearity at 1660C and switching at 1780 C.

February 1976 / Vol. 15, No. 2 / APPLIED OPTICS 333

Fig. 12. Chart recording of temperature in C upon heating andthe radiation detected by Light Mike. Note sharp peak at 198°Cwhere current reverses trend. A second peak is shown at about214-2280C. ILM = intensity of radiation detected by Light Mike;

iF = field current.

This is to suggest that the coiling, intertwining, ndincreased van der Waals bonding act as enhancedcarrier scattering sites during polymerization. Sinceelectric field magnitude was not extremely large inthe temperature dependence experiments (800 V/mm), we shall neglect the field dependence of theconductivity and mobility. Since there is no evi-dence of depletion of carriers during polymerization,we suggest that the mobility is curtailed by latticescattering, the term taken in the broadest sense ofthe scattering due to aperiodicity in potential. Weassume that this aperiodicity is maximuml during thepolymerization process, just as the optical scatteringpotential is maximum at the polymerization inter-face. The scission of long chains accompanying de-polymerization probably causes decreased carrierscattering because of the lesser chain intertwining,and increased conduction because of additionalcharge transport sites at broken bonds, thus promot-ing the reversal back to a negative temperature coef-ficient of resistance.

It is untenable that the turning points in the resis-tance vs temperature data are due to impurity phe-nomena because the changes in the sign of the tem-perature coefficient of resistance at T, and T2 occur

upon heating and cooling. The average values uponheating for T, and T2 for ten different samples andten cycles for each sample were Tlh = 168 -t90C andT2h = 189 4120C, compared with Tic = 161 100Cand T2c = 180 A10'C upon cooling. In addition, noclearcut rate dependence for T, and T2 was estab-lished except that at the highest heating and coolingrates the average deviations for Ti and for T2 werelargest. In general the virgin' sample yielded essen-tially the same values for T, and T2 as the samplethat was cycled many times. We would expect impu-rity effects to reflect less temperature reversibilityand less general reproducibility in cycling. Thevalues of T, and T2 agree well with the temperaturesfor the color change zones given in Sec. III.

The carrier scattering process during polymeriza-tion can be further complicated by the thermally in-duced Brownian motion that the quasi-linear sulfurchains undergo. The mathematical formalism forthe electrical conductivity of even a homogeneoussimple liquid through the correlation function is ex-tremely complex19 and is not treated herein for thecomplicated ring-chain equilibrium in liquid sulfur.The mathematical abstraction' 9 is a generalization of

::: .!: 1 Ss9~,

- IIl-; o

t .. : , : E :

Fd- I .---- --!T u~~ ''''"~I I 5 '-'t''''.'4.,,

Co_.n (.....I tuac ! -)E

Fig. 13. Chart recording of temperature in C upon coolingand detected radiation. Note radiation activity begins atabout 220-2241C, and large peak is observed at 1760C, wherethe current undergoes a reversal in trend at T2 C. Light Mike

was positioned 2.5 cm in front of a square opening in the

furnace.

334 APPLIED OPTICS / Vol. 15, No. 2 / February 1976

ea&-f-

Fig. 14. Chart recordings of temperature, detected radia-tion, and current, showing maxima at (a) 1870C correspond-ing to Tjh = 190'C and (b) 170'C where T1 h = 172 0C. Inthese experiments a converging lens was utilized between

the gold doped Ge detector and the sample.

the Einstein relation connecting the carrier mobilityto the diffusion constant for the inhomogeneoussemiconductor.

F. Additional Optical Effects

In this section we want to simply present some pre-liminary data on optical effects detected duringstructural transitions without use of incident visiblelight. Figures 12 and 13 show optical peaks detectedby a Light Mike corresponding roughly to the tem-peratures of reversals in the sign of (da)/(dT). InFig. 12 the heating rate was about 12'C per min andan optical output or burst is observed at 1980 C but,due to the thermal gradient, is believed to correspondto about 1880C. Just prior to the radiation burst acurrent reversal from increasing current to decreas-ing current with rising temperature is observed (39.4nA - 39.3 nA - 39.6 nA) indicating the change in(du)/(dT) at Tlh.

Figure 13 shows that upon cooling at about 20C permin optical activity begins to be detected at about ameasured 2240C, which is believed to correspond toabout 2120C. A large radiation burst in the same di-rection as in the heating experiment is observed cen-tered at 176°C (probably 1680C) during which (da)/(dT) changes sign at T2c.

It should be pointed out that the Light Mike be-came heated from the furnace during these experi-ments because proximity to the sample seemed ad-

visable as it was believed that any optical burstwould be of a small magnitude. This caused theelectronics of the Light Mike to heat up, which prob-ably accounts for some or most of the rise in thebackground radiation trace upon heating. The LightMike was withdrawn 13 cm from the furnace to in-sure that it remained cool, and the effects shown inFigs. 12 and 13 were observable sometimes aschanges in the magnitude and/or sign of the slope ofthe trace and sometimes as small bursts.

Figures 14(a) and (b) show other forms of the ef-fect given in Figs. 12 and 13. These effects were notobserved using photomultiplier tubes, sensitive to thevisible; however the optical anomalies occur at tem-peratures at which structural phenomena are knownto occur and correspond quite well with T, and T2.The cause of the optical burst is not established andmay be related to scattering or to an unusual emis-sion phenomena.

Figure 15 shows another anomalous effect that wasgenerally observed at between 194-2221C while man-ually scanning with an ir monochromator and usingan EGG infrared detector. The optical bursts shownin the figure were of very small magnitude comparedwith the optical effects mentioned earlier and wereobserved at about 1.3-1.4 gim. The explanation ofthe phenomena is unestablished at present but maypossibly be associated with anomalous resistancebreaks, which are occasionally observed at 212-214'C

g

I.

I

5OII

I

r I5I

I" c: O

TEP.

TEMP.

RADLATION

RADIATJON

RADIATION-4 CURRENT1.0 nA/dt,

Fig. 15. Temperature in 0C, detected radiation, and cur-rent in nA, showing radiation effect at about 1.4 um at T2 h

- 194°C. Inset figures show small radiation effects at2120C.

February 1976 / Vol. 15, No. 2 / APPLIED OPTICS 335

212'C -,C _

TEST PUISE

r

I

IIIII

III

II

II

IIIiI

E. .C. PHOTO.MLLTIPLIEOR ATRIGIH ANGLE

130.131

128

124

125

127

128CURRENT -

Fig. 16. Chart recording of temperature in OC, pulsed radiationand dc field current plus superimposed laser-induced current innA. Note two reversals in current direction at 170'C and 1560 C.Over this temperature range the voltage across the piezoid showedthe same variation trend as the current through the probes. How-ever, at temperatures above 1700 C, the piezoid voltage showed notemperature variation even though the probe current changed by

the same amount as over the 170-156 0 C range.

and were reported earlier.9-10 This is near the calcu-lated temperature region where the weight composi-tion of the polymer begins to exceed that of the rings.

G. Effects Detected With PiezoidThe PZT 5-A (lead zirconate titanate) piezoid,

having a time constant of over 250 sec, was posi-tioned 1 mm from the platinum current leads andpicked up a potential of several hundred microvoltsfrom the potential applied to the sample through thecurrent probes. Since the viscosity of sulfur changessharply with temperature, it was speculated that dur-ing a sudden viscosity change an effect detectable bya piezoid may occur while the pressure is redistribut-ing itself through a new pgh (the acceleration due togravity g and the height of h are constant, but thedensity p is changing). In Fig. 16 our best piezoidtrace is shown and remains constant until T2C isreached, which signifies the change in the sign of(d)/(dT); below T2C the piezoid trace behaves simi-larly to the current trace. The center channel of Fig.16 displays spikes that are due to a pulsed ruby laserincident on an EGG photomultiplier tube. No effectis apparent on the piezoid trace at each laser pulse.However, at temperatures below 161'C the laser-in-duced current on channel 3 is prominently shown ac-companying each laser spike on channel 2. Appar-ently, when the sulfur is highly viscous at tempera-tures above the polymerization point, the piezoiddoes not display a current variation as shown in

channel 3. This may be partially due to the high re-sistance of the polymer, which interferes with pickup,or to a decrease in the ability of the molten phase toact as a good pressure transmitting medium becauseof its very high viscosity. The same general effect isshown in Fig. 9.

H. Viscosity vs Temperature Data and ColorCorrelation

Experimental data on the viscosity of liquid sulfurvs temperature are shown in Fig. 17 under equilibri-um conditions and using a 20 C per min heating andcooling rate. Data indicate (curve A) that under ap-proximate equilibrium the viscosity of liquid sulfurincreases abruptly between 159-1600C and continuesto rise until reaching a maximum at about 186 +4C.The viscosity cooling curve (curve B) shows a maxi-mum at about the same temperature. Curves C, D,and E in Fig. 17 show a maximum at about 177 +51Cand are achieved by heating and cooling at the rate ofabout 2C per min. The change in the position ofthe maxima due to heating rate may account forsome of the discrepancy in the literature regardingthe temperature of maximum viscosity. This shift inthe depolymerization temperature due to heating and

300'

280.

. 700 POISE

..

T!I I. 5

T6IMAX)

AUP-TEMP 176 5

BDOWN.TEMP 176 5

CUP-TEMP 178 * 2

DUPTEMP 186 i 4

E D N-TEMP 187 t 3

R +

HEATING RATE Ra T

2-/MIN 163

162

STEADY STATE 159

X3'/MIN

166I72168I71

175

.22

-20

-18

16

-14

-12

*10

9

rS E

5* *

8

*26

-2

14O 160 180 200TEMPERATURE (C)

VISCOSITY DATA

Fig. 17. Relative viscosity vs temperature for heating andcooling at about 20C/min and for approximate equilibriumconditions. R and R2 refer to the changes in the tempera-ture coefficients of resistance at T1 and T 2 and occur be-tween the temperatures of minimum and maximum viscosi-ty. The rate dependence of the viscosity maximum may ex-plain some of the differences reported in the literature forthe temperature of maximum viscosity. The magnitude ofmaximum viscosity of approximately 700 P is calculatedthrough a spherical approximation and is consistent with

the 103 given by others.

336 APPLIED OPTICS / Vol. 15, No. 2 / February 1976

Wi l l

e

1;..7

6It:1.

I

2I

gA1

-

.

cooling rate is a result of the kinetic dependence ofthe ring - chain (octamer polymer) reactions.The positions marked R, and R2 on each curve referto the conditions for the sign reversals in the temper-ature coefficients of electrical resistance and weretreated in Sec. III. E. It appears that the change inthe sign of the temperature coefficient of resistance isnot a direct invariant point identifying the inceptionof polymerization and depolymerization. Instead,the changes in resistance appear to delineate a cer-tain stage in the polymerization condition where thecompeting processes change their degree of domi-nance. However, the temperature at the currentprobes may not be exactly the same as the averagetemperature of the region through which the viscosi-ty is being measured. The average value of the tem-perature of maximum viscosity is about 1860C, whichis about the same as the average value of T 2h, thus itappears attractive to suspect that the beginning ofthe chain scission process promotes a decreased car-rier scattering and causes the temperature coefficientof resistance to reverse sign. Presently, it is not cer-tain whether the carrier scattering at a given temper-ature is proportional to the chain length (and its in-escapable coiling) or to the temperature derivative ofthe chain length. If the latter were the case, thenthis may explain why the resistance is increasing withthe largest slope (vs temperature) during the regionwhere the viscosity vs temperature curve is steepest.

The cause of the increased viscosity during poly-merization is not simply the increase in average chainlength but the intertwining and coiling of the chainsand the resultant increase in secondary or Van derWaals bonding. Thus the process causing the highviscosity is not directly the process causing the colorchange and optical scattering, reflectance, and trans-mission effects. The change in body color at the oc-tamer polymer transition is, due to a change in se-lective absorption (by the chain molecules), transmit-ting the orange-red end of the visible spectrum.Even after the viscosity decreases above 1880C, thecolor of the liquid sulfur becomes more red, indica-tive of a higher polymer concentration even thoughthere exists lesser intertwining.

IV. Implications and Conclusions

For many years glass scientists have embraced theZachariasen 2 0 random-network model, or a hybridthereof, for the structure of glasses. The basic modelseems appealing because glasses are derived from liq-uids, and liquids were normally thought to be homo-geneous since phase transitions were not observed inthe liquid state. (Although two immiscible liquids ofdifferent composition were well known to exist underequilibrium conditions, the notion of pressure andtemperature causing major structural transitions inan elemental liquid was virtually unheard prior to thelast decade.)

To our knowledge the first paper that presented aviable alternative to the random network model wasauthored by Roy,21 in which he proposed the meta-

stable immiscibility and nonuniformity model.Since the germination of the concept, many otherstudies have indicated the existence of immiscibleseparate phases in a glass. This approach leads to asingle and/or diphasic nonuniform structure for mostglasses other than simple ionic glasses. It is not gen-erally realized that a single phase does not have to bestructurally or compositionally homogeneous in itsentirety. The immiscibility of the liquids fromwhich glasses are formed, and the resulting nonuni-formity, is given as the first step leading to the crys-tallization of some compositions. The nonuniform-ity model seems to be applicable to the chalcogenidememory glasses whereby a high power electrical pulsegenerates enough heating to cause a phase separationof a filament.

Recent work has shown unequivocally that tem-perature and pressure induce changes in the struc-ture of and coordination number of liquids as evi-denced through viscosity and x-ray diffraction pat-terns of products quenched from diversified pres-sure-temperature (p-T) conditions,22 and also shownin situ by neutron diffraction in liquid tellurium,23

differential thermal analysis (DTA) in liquid sulfur,2 4

and very recently by differential scanning calorime-try in liquid bismuth.25 Boundaries have been ob-served (and are plotted on a p-T diagram) that iden-tify the inception or a critical stage in the liquid statereaction, such as the polymerization of sulfur. Theexistence of these boundaries is generally observedby DTA or by electrical resistance techniques. Thereaction boundary is not identical to an equilibriumphase transformation boundary in the solid-state,and in covalently bonded liquids is statistical in na-ture due to the statistical kinetics of the scission andthe formation of a covalent band.

Sulfur, for example, displays an equilibrium con-centration of rings and chains at any temperatureabove the liquidus., 34 The ring and chain configu-rations constitute, in a sense, two liquids. Even dur-ing the polymerization of liquid sulfur the ring con-figuration as well as short chain diradicals arepresent in the liquid. In liquid tellurium the princi-pal coordination number changes from two to threeto greater than five as temperature is raised in theliquid state.23 In addition, the Hall coefficient andtemperature coefficient of resistance reverse sign.26

This means that the most probable configuration forthe greater portion of the liquid volume at a particu-lar temperature has a certain characteristic coordina-tion. However, this does not preclude the existenceof different (less probable and less prevalent) liquidspecies at the same temperature. Johnson27 was ableto successfully describe in mathematical terms theresistance vs temperature curve of liquid telluriumincluding the minima at 670°C by assuming a mix-ture of a semiconductive component and a metallicdissociated component with a Boltzmann probabilitygoverning the dissociation of a chain bond.

The above discussion coupled with the narrowscattering, reflectance, and transmission peaks

February 1976 / Vol. 15, No. 2 / APPLIED OPTICS 337

suggests that liquid sulfur does not adhere to a ran-dom network structural model but is better describedby a nonuniformity two-liquid (octamer and poly-mer) model. The grounds for this suggestion arethat two liquid species are essentially always presentin the thermal range under consideration and thatthe polymerization and depolymerization transitionsappear to occur through a process resembling solid-state transitions. The peaks in optical data occurover too narrow a temperature range to be due simplyto the viscosity change and are probably due to mis-match of indices of refraction and fluctuations indensity. The octamer - polymer transition proba-bly proceeds according to a nucleation and growthprocess occurring at an inhomogeneity or nonunifor-mity positional neighborhood and may involve theformation of an activated transient nonequilibriumstate. The activated state has properties differentfrom both the reactant and product phases, whichmay explain the peaked optical data at the transition.The interfacial region (orange-red) occurs over atemperature range of a few degrees and identifies anonuniformity region from which the polymerizationreaction is growing. This region occurs at a tempera-ture at least 71C higher than the temperature forspontaneous polymerization and apparently is char-acterized by a polymer chain of critical length whoseproperties and concentration give rise to the red bodycolor. Another strong indication of the nonuniform-ity (or unmixing of more than one liquid) is the re-port of quenching different solid-state phases de-pending on the pressure-temperature conditionswhere the sample was held. This has been common-ly observed in sulfur2 83 0 and in tellurium. 2 2 This in-dicates that different regions of the p-T liquid fieldare characterized by different local structural or-dering from which a different solid phase can bequenched metastably.

Actually, the idea of phases of different molecularstructure in the liquid state was suggested much ear-lier by Bridgman,31 who reported that, with respectto viscosity, a molecule in the liquid state behavesand functions as a unit. The extension of this inter-pretation can envision different structural units cor-responding to major viscosity changes. In the samesense, the Andrade3 2 theory suggests that viscosity isa measure of a temporary "freezing-together" of mol-ecules in the liquid state into larger aggregates, whichhave a more nearly crystalline character over a shortrange. Structural transitions in the liquid state arethus far more compatible with a nonuniformity rath-er than random network model. The applicability ofsuch .phenomena as nucleation and growth33 to theliquid state over a limited spatial range is in keepingwith the transitions observed in the chalcogen liq-uids, sulfur, and tellurium and is compatible with theproperties of materials intermediate between thesolid and molten phase such as liquid crystals. Theoptical data appear to be in best agreement with thistype of interpretation.

In summary, the support we have found for the

nonuniformity model in liquid sulfur can be listed asfollows:

(1) above 1590C, sulfur consists of a mixture of aring and chain concentration;

(2) the red polymeric phase, formed at tempera-tures above 1660C, does not mix with the orangephase, even when the red phase is moved into a tem-perature region below 1660C where the orange phaseis stable, (instead the red phase maintains its integri-ty);

(3) the orange-red interpenetrating interface is anonuniformity that preferentially scatters the He-Nelaser light and acts as the nonuniformity from whichthe major part of the phase change proceeds. At thisinterface, the rate of increasing polymer chain lengthand increasing polymer concentration per fraction ofdegree temperature increase is apt to be largest.

The authors are indebted to Gus Tirellis of the En-gineering Sciences Division for experimental assis-tance and to Matthew Nowak for his patient loan ofspecial apparatus.

This work was supported under DA Project1T0551101A91A with the encouragement and sup-port of John W. Gregorits and G. Sharkoff. The re-lated support under DA Project 1T061102B11A03with the encouragement of B. Zarwyn made the expe-dient progress of this effort possible.

References

1. G. Gee, Trans. Faraday Soc. 48, 515 (1952).2. R. Bacon and R. Fanelli, J. Am. Chem. Soc. 65, 639 (1943).3. A. Eisenberg, J. Chem. Phys. 39, 1852 (1963).4. A. Tobolsky and Eisenberg, J. Am. Chem. Soc. 81, 780 (1959).5. G. Lewis and M. Randall, J. Am. Chem. Soc. 33,476 (1911).6. H. Braune and 0. Moller, Z. Naturforsch 92, 210 (1954).7. E. West, J. Am. Chem. Soc. 81, 29 (1959).8. B. Meyer, M. Gouterman, D. Jensen, T. V. Oomen, K. Spitzer,

and S. Hansen, Adv. Chem. Ser. 110, 53 (1972).9. G. Vezzoli, J. Polym Sci., Part A 8, 1587 (1970).

10. G. Vezzoli, J. Am. Ceram. Soc. 55, 66 (1972).11. A. Einstein, Ann. Phys. (Leipzig) 33, 1275 (1910).12. G. Plazek, Phys. Z. 31, 1052 (1930).13. A. F. Harvey, Coherent Light (Wiley-Interscience, London,

1970), Chap. 4, Sec. 4.14. M. Bertolotti, B. Crosignani, P. DiPorto, and D. Sette, Phys.

Rev. Vol. 157, 146 (1967).15. V. S. Starunov, Dokl. Akad. Nauk, SSSR 153, 1055 (1963);

Sov. Phys.-Dokl. 8, 1205 (1964); also V. S. Starunov Opt.Spektrosk. 18, 300 (1965); Opt. Spectrosc. 18, 165 (1965).

16. F. Mahdjuri, J. Non-Cryst. Solids 8, 992 (1972); A. Regel, A.Andreev, and M. Mhmadaliev, J. Non-Cryst. Solids 8, 455(1972); G. Busch, H. Gunterodt, H. Kunzi, and A. Schweiger,Phys. Lett. 33A, 64 (1970); G. Vezzoli, A. Napier, and L. W.Doremus, J. Non-Cryst. Solids 13, 80 (1973).

17. J. A. Aukward, R. W. Warfield, and M. C. Petree, J. Poly. Sci.27, 199 (1958).

18. R. K. Steunenberg, C. Trapp, R. M. Yonco, and E. J. Cairns,Adv. Chem. Ser. 110, 190 (1972); 0. Watanabe and S. Tamaki,Electrochim. Acta 13, 11 (1968).

338 APPLIED OPTICS / Vol. 15, No. 2 / February 1976

19. See for example R. Kubo, J. Phys. Soc. (Jpn.) 12, 570, 1263(1957); and S. A. Rice and P. Gray, The Statistical Mechanicsof Simple Liquids (Wiley Interscience, New York, 1965),Chap. 7.

20. W. Zachariasen, J. Am. Chem. Soc. 54, 3841 (1932).

21. R. Roy, J. Am. Ceram. Soc. 43, 670 (1960).

22. G. Vezzoli, J. Poly. Sci 11, 1337 (1973).

23. G. Tourand, G. Cabane, and M. Breuil, J. Non-Cryst. Solids 5,676 (1972).

24. G. Vezzoli, F. Dachille, and R. Roy, J. Poly. Sci. A-i, 7, 1557(1969).

25. D. Larson, Grumman Aircraft Corporation; private discussion.26. A. Epstein, H. Fritzsche, and K. Lark Horovitz, Phys. Rev.

107, 412 (1957).27. V. Johnson Phys. Rev. 98,1567(A) (1955).28. S. Geller, Science 152, 644 (1972).

29. C. B. Sclar, L. Garrison, W. Gager, and 0. Stewart, J. Phys.Chem. Solids 27,1339 (1966).

30. G. Vezzoli, F. Dachille, and R. Roy, Science 166, 218 (1969); G.Vezzoli, Ph.D. thesis, Pennsylvania State University (March1969).

31. P. W. Bridgman, The Physics of High Pressure (Belland Sons,London), p. 352-356.

32. E. N. Andrade, Nature 125, 309, 582 (1930).33. We have also observed the preferential scattering of laser light

accompanying a fluid phase transition during the liquid vapor reaction in water. The presence of a rising transparentwater vapor or air bubble causes an instantaneous 25-30% de-crease in transmission and an increase in scattering of theHe-Ne laser. The bubble can be viewed as a type of nuclea-tion region having distinct scattering properties at the inter-face with the host liquid due to mismatch of indices of refrac-tion.

CIE Report on Sports Lighting for Color TV

The International Commission of Illumination (CIE) has just published

Report No. 28 on The Lighting of Sports Events for Color TV Broadcasting.

This report has been prepared by a panel of experts from many countries and

details the standard practice used for lighting sports facilities to accommodate color

television pick up.

The aim of this report is to detail the fundamental principles which

govern the lighting of sports facilities to meet the needs of color television.

It is based on the experience gained over the past several years by the experts in

their various countries.

This report is intended to provide a basis for uniform national standards

since sports activity and TV are international in scope. It also details methods of

evaluating completed installations. It is therefore of value to anyone involved in

the design or use of major sports facilities.

Copies of CIE Report No. 28 may be obtained at a cost of $7.00

each from Mr. Louis E. Barbrow; Secretary, U. S. National Committee, CIE;

% National Bureau of Standards; Washington, D. C. 20234. Payment should

accompany the order and should be made payable to "U. S. National Committee,

CIE." Canadians may obtain copies by sending a check payable to "The Receiver

General of Canada, Credit National Research Council" with their order to

"Publications Distribution Office, National Research Council of Canada, Ottawa,

Ontario, KA R6."

February 1976 / Vol. 15, No. 2 / APPLIED OPTICS 339