Structure-Property Relations in Polymers - American Chemical Society

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20 Probe Spectroscopy, Free Volume Concepts, and Physical Aging of Polymer Glasses 1

2

1

2

2

J. E. Kluin , H. Moaddel , M. Y. Ruan , Z. Yu, , A. M. Jamieson , R. Simha , and J. D. McGervey 2

1

1

2

Department of Physics and Department of Macromolecular Science, Case Western Reserve University, Cleveland, OH 44106

Many properties of polymeric materials can be interpreted by using the free volume concept. Our particular efforts in this area have utilized the Simha—Somcynsky theory, which enables the computation of a free volume function from the experimental equation-of-state of the polymer. In recent years several groups have investigated the possibility of applying spectroscopic techniques as a direct probe of the structural disorder (free volume) in polymers. We review these efforts, which include fluorescence spectroscopy, electron spin reso nance spectroscopy, and positron annihilation lifetime (PAL) measure ments. We describe in detail the application of PAL analysis to investigate free volume changes in situ in bisphenol A polycarbonate subjected to mechanical deformation.

TFHE F R E E properties

V O L U M E C O N C E P T IS C E N T R A L

o f p o l y m e r i c materials.

τ ο T H E INTERPRETATION o f many

The term

"free volume, "

a p p l i e d to

amorphous polymers, refers to the difference between the total v o l u m e o f the material ( V ) a n d the v o l u m e o c c u p i e d b y the component molecules ( V V = V —V f

o c c

o c c

):

, where V denotes free v o l u m e . T h e idea that V plays a major f

f

role i n d e t e r m i n i n g the molecular m o b i l i t y o f the p o l y m e r i c matrix has b e e n w i d e l y a p p l i e d to interpret various b u l k p h e n o m e n a . Examples i n c l u d e the temperature dependence o f the viscoelastic relaxation times ( I ) o f p o l y m e r liquids [viz. the W i l h a m s - L a n d e l - F e r r y ( W L F ) equation] a n d the physical aging p h e n o m e n o n i n the mechanical properties o f p o l y m e r glasses 0065-2393/93/0236-0535$06.25/0 © 1993 American Chemical Society

In Structure-Property Relations in Polymers; Urban, M., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1993.

(2).

536

STRUCTURE-PROPERTY RELATIONS IN POLYMERS

Nevertheless, although the free v o l u m e concept can be d e f i n e d quite p r e cisely, its i m p l e m e n t a t i o n as a quantitative measure o f the structural disorder i n polymers is a challenging p r o b l e m . I n this regard, w e note that a statistical mechanical description o f the b u l k p o l y m e r i c state b y S i m h a and Somcynsky ( 3 ) incorporates a free v o l u m e function, h(P,

T), where h is the fractional

free v o l u m e , p is the pressure, a n d Γ is the temperature. T h e free v o l u m e function can be c o m p u t e d f r o m the experimental equation-of-state

o f the

p o l y m e r i c l i q u i d , and, therefore, explicitly incorporates b o t h entropie a n d enthalpic contributions to the structural disorder. I n glass, the free v o l u m e


depends o n t h e r m a l history a n d the corresponding free v o l u m e function, that quantitative connections can b e made v i a the S i m h a - S o m c y n s k y theory between p r e s s u r e - v o l u m e - t e m p e r a t u r e ( P V T ) data for the glass a n d the t i m e evolution o f mechanical properties d u r i n g isothermal physical aging ( 5 ) .

Several investigations have explored the possibility that techniques

spectroscopic

can be used to probe directly the free v o l u m e i n p o l y m e r i c

materials. Y u et al. ( 6 )

u t i l i z e d the c i s - t r a n s

conversion o f

substituted

stilbenes, w h i c h were dispersed i n the p o l y m e r i c matrix a n d m o n i t o r e d b y the change i n U V absorption. T h e ease o f interconversion decreases w i t h increas i n g size o f substituent

groups ( 6 ) .

These workers w e r e able to

further

demonstrate that the fraction o f trans isomers f o r m e d decreases u p o n anneal i n g i n the glassy state (6). These observations are consistent w i t h the idea that the stilbene derivative probes a subset o f the distribution o f free v o l u m e sites whose lower l i m i t is d e t e r m i n e d b y the molecular v o l u m e o f the probe, glass. B y covalently attaching the stilbene moiety to the p o l y m e r at different locations, Y u et al. ( 6 ) were further able to show that the free v o l u m e at chain ends is larger than that i n the interior o f the chain. A particular feature o f the stilbene probes is that a reasonably accurate estimation o f the v o l u m e swept out d u r i n g the c i s - t r a n s conversion can be made ( 6 ) . Fluorescence fluorescence

probes have b e e n

investigated by several groups.

The

anisotropy that is a measure o f the rotational diffusive m o t i o n o f

the probe is f o u n d to be strongly dependent o n the probe size as w e l l as o n the molecular m o b i l i t y o f the p o l y m e r matrix i n w h i c h it is located. I f the probe is large, the

fluorescence

anisotropy is sensitive to the free v o l u m e o f

the matrix i n w h i c h it is dispersed (7, 8). T h u s , the temperature o f the (7,

8).

fluorescence

dependence

anisotropy is described b y an equation o f the W L F type

T h i s observation is consistent

w i t h an expression for the

rotational correlation time, T , o f the f o r m (7, c

T = c

T exp(BV /V ) c

0

m

probe

8)

f


(1)

20.

KLUIN ET AL.

537

Physical Aging of Glasses

w h e r e τ® is the correlation t i m e o f a freely rotating probe, V

is the probe

v o l u m e , a n d β is a system-dependent constant. I f Β a n d V

temperature

m

m

are

independent, T s h o u l d exhibit W L F behavior characteristic o f the p o l y m e r c

host. H o w e v e r , w h e n the probe is small, its rotational m o t i o n is also i n f l u e n c e d b y sub-glass-transition temperature (sub-T ) m o t i o n (7, 8). g

I n a p r e l i m i n a r y way, M e y e r has explored the potential o f

fluorescence

anisotropy to f o l l o w free v o l u m e changes d u r i n g isothermal physical aging o f a p o l y m e r glass ( 9 ) .

T h e anisotropy o f diphenylanthracene dispersed i n

p o l y (vinyl acetate) ( P V A c ) was isothermally m o n i t o r e d at T — 2, after a g

shallow q u e n c h f r o m above T . T h e anisotropy increased w i t h aging t i m e Downloaded by GEORGE MASON UNIV on June 6, 2014 | http://pubs.acs.org Publication Date: May 5, 1993 | doi: 10.1021/ba-1993-0236.ch020

g

consistent w i t h an increase i n T due to the collapse o f free v o l u m e . H o w e v e r , c

taking ratios o f the p o l a r i z e d a n d d e p o l a r i z e d emission, is not sufficient to effectively m o n i t o r the comparatively small changes i n free v o l u m e that accompany isothermal physical aging deep i n the glassy state. A g a i n , it is anticipated that the probe monitors a subset o f the free v o l u m e distribution state that depends o n probe size, V . m

L i k e w i s e , the spectral l i n e w i d t h of electron spin resonance ( E S R ) probes dispersed i n polymers shows a temperature dependence d e t e r m i n e d b y the mobility o f the matrix. Specifically, the E S R spectrum o f nitroxide probes shows a collapse associated w i t h the point at w h i c h the m e a n rotational relaxation frequency becomes equal to the spin resonance

frequency. A

correlation has b e e n n o t e d between the temperature at w h i c h this occurs (T

5 0 G

) a n d the glass-transition temperature (JO,

II).

T h e subscript 5 0 G

indicates that the transition temperature is d e f i n e d w h e n the E S R line w i d t h equals 50 gauss. M e y e r ( 9 ) has investigated isothermal changes at T — 7 i n the l i n e w i d t h g

o f the nitroxide probe, 4-(2-bromoacetamide)-2, 2, 6, 6-tetramethyl-l-oxylpiperidine ( B R O M O ) , dispersed i n P V A c following a q u e n c h f r o m the e q u i l i b r i u m melt. A t this temperature, B R O M O is i n the motionally restricted region w h e r e a " b i m o d a T spectrum is observed ( I I ) .

A s the sample

annealed

(physical aging), a small increase was observed ( 9 ) i n the position o f the high-field peak o f the derivative spectrum, f r o m w h i c h an increase w i t h aging t i m e o f the average rotational correlation t i m e T times i

a

> 1 h , w e observed ( 9 ) d l o g 7 /d c

log f

a

c

was d e d u c e d . A t aging

= constant. S u c h behavior

can b e rationalized b y free v o l u m e arguments used b y Struik ( 2 ) a n d a p p l i e d to an equation o f the f o r m o f equation 1, p r o v i d e d the instantaneous free v o l u m e is far f r o m b o t h the initial q u e n c h a n d the final e q u i l i b r i u m values. H o w e v e r , as i n

fluorescence

anisotropy, the l i n e w i d t h variations that w e

observe d u r i n g physical aging i n the glassy state are exceedingly small (9), v o l u m e changes i n the glass. I n addition, the probe again locates i n a p o r t i o n o f the free v o l u m e distribution that depends o n the probe size.


538


A n alternative approach using fluorescence probe spectroscopy is to m o n i t o r the increase i n emission intensity, F , that occurs w h e n the m o b i l i t y o f the p o l y m e r i c host matrix decreases. T h i s increased emission intensity occurs because o f a decrease i n nonradiative deexcitation mechanisms. A n equation has b e e n p r o p o s e d (12) that relates the emission intensity to the matrix free v o l u m e : F/F

0

= exp(feV /V ) m

H e r e F is the emission intensity o f a freely rotating probe, V is the molar v o l u m e o f the probe, a n d b is a system-dependent constant. W e have studied (13) the emission intensity o f auramine Ο dispersed i n P V A c i n the l i q u i d a n d glass states. T h e fluorescence intensity shows a change i n temperature coefficient at T that is consistent w i t h that anticipated b y free v o l u m e concepts a p p l i e d to e q 2. F o l l o w i n g a q u e n c h into the glass state f r o m the melt, a time-dependent isothermal increase i n fluorescence was observed (2, d log i = constant. A g a i n , using arguments given b y Struik, this behavior appears to be consistent w i t h equation 2, p r o v i d e d w e are far f r o m e q u i l i b rium ( I , 13). Similar observations have b e e n made for other p r o b e - p o l y m e r combinations (14, 15). M o s t interestingly, a recent c o m m u n i c a t i o n (16) describes the observation o f nonlinear responses (asymmetry) i n the isother m a l emission o f probes dispersed i n polystyrene a n d p o l y (methyl methaery late) following a two-stage t h e r m a l conditioning, w h i c h consisted o f a q u e n c h into the glass at T — T i , f o l l o w e d b y a single temperature j u m p to T — T > T — T T h e shapes o f the fluorescence relaxation curves are reported (16) to d e p e n d o n the direction a n d magnitude o f the j u m p i n a fashion similar to the w e l l - k n o w n behavior f o u n d i n the b u l k specific v o l u m e (17, 0


(2)

f

m

g

a

g

g

g

2

v

T h e preponderance o f the p r e c e d i n g evidence indicates that fluorescence a n d E S R probes are i n d e e d sensitive to free v o l u m e effects i n p o l y m e r i c materials. H o w e v e r , the i m p l e m e n t a t i o n o f these techniques as a quantitative measure o f the small changes i n free v o l u m e associated w i t h isothermal physical aging is difficult because o f uncertainties w i t h regard to probe size variations (6-10), poor sensitivity ( 9 ) , a n d possible temperature dependence o f the parameters Β a n d b i n eqs 1 a n d 2, respectively (13-16). T h e positron lifetime m e t h o d offers the possibility o f avoiding some, i f not a l l , o f these difficulties. This experiment involves b r i n g i n g the p o l y m e r into contact w i t h a radioactive positron source, typically N a . Positrons e m i t t e d into the poly m e r i c matrix b e c o m e t h e r m a l i z e d a n d suffer several possible fates (19-21): (1) annihilation as free positrons (e + e~~ —> hi); (2) b o n d i n g o f an electron o f opposite spin to f o r m parapositronium ( p - P S ) and subsequent self-annihila tion (e + p - P s —> h v ) , a n d (3) b o n d i n g o f an electron o f parallel spin to f o r m orthopositronium (o-Ps) a n d t h e n annihilation b y " p i c k - o f f ' o f a matrix electron (e + e~o-Ps; o-Ps + > h v ) . T h e lifetimes associated 2 2

+

+

+


20.

KLUIN ET AL.

539


w i t h these processes can be measured b y measuring the time intervals between the detection o f the high-energy 7 ray released w h e n the positron is e m i t t e d and the low-energy g a m m a rays released o n annihilation. T h e t i m e intervals are quite distinct: τ e+ +

e~->

p-Ps -> hv; a n d τ

e~-> hv.

χ

= 120 ps, for e + e~-> hv; τ

3

-

+

1 0 0 0 - 2 5 0 0 ps for e +

O f particular interest is the observation

~ 400 ps for

2

é?~-> o-Ps, o-PS +

+

(19-20)

that the relatively

long-lived species o-Ps can become trapped i n regions o f l o w electron density (i.e., a 'hole') a n d that the p i c k - o f f annihilation rate o f o-Ps is very sensitive to the size o f the hole.


A variety o f studies o f o-Ps annihilation characteristics

i n polymers

confirm that they are sensitive to p h e n o m e n a associated w i t h changes i n matrix free v o l u m e

(20-24). T h e s e

the temperature coefficient o f τ changes

3

at T

g

studies i n c l u d e observations o f changes i n (20,

21, 24) a n d

reports

i n the relative fraction o f o-Ps annihilation events,

(22-24) i

3

, during

isothermal physical aging i n the glass following a q u e n c h f r o m above T . g

F o c u s i n g o n o u r o w n efforts i n this area, w e have c a r r i e d out an extensive study o f o-Ps annihilation i n p o l y (vinyl acetate) ( P V A c ) , a p o l y m e r whose P V T relationships have b e e n extensively characterized b o t h i n the l i q u i d a n d glassy states (25). F u r t h e r m o r e , f r o m these data, the S i m h a - S o m c y n s k y free v o l u m e function has b e e n c o m p u t e d i n the melt [h(P, well-specified histories [h(P,

T, tj]

(25,

other polymers (20, 21), w e observe (23)

that τ

T)] a n d for glasses o f

Consistent w i t h studies o n

26). 3

increases w i t h temperature

a n d exhibits a discrete change to a larger temperature coefficient at T . O n g

the other h a n d , 1 Because Z

3

3

exhibits ( 2 4 ) a b r o a d shallow m a x i m u m centered o n T . g

is a measure

reasonable to assume that I A l s o , w e can relate τ

3

o f the probability o f formation o f o-Ps, it is 3

is proportional to the n u m b e r density o f holes.

to the v o l u m e o f a hole. W e utilize an equation

p r o p o s e d b y N a k a n i s h i et al. ( 2 7 ) , following a m o d e l developed b y T a o

(19)

for a spherical hole w i t h radius R a n d a surface electron layer o f thickness Δ β . T h e lifetime o f a t r a p p e d o-Ps atom has b e e n shown by q u a n t u m mechanical arguments to be (19,

τ

where R

0

3

= 0.5[1

-

R/R

0

27)

+

(l/2ir)sin(2'TTR/R )]"

= R + Δ β . It was s h o w n (27)

0

(3)

1

that e q 3, w i t h Δ Κ = 0.1656 n m

gives good agreement w i t h the o-Ps lifetimes i n molecular solids such as zeolites, w h e r e hole sizes have b e e n i n d e p e n d e n d y estimated. I n polymers containing a distribution o f hole sizes, w e expect to find a distribution o f o-Ps lifetimes. H o w e v e r , typically it is possible only to estimate an average o-Ps lifetime (23),

( τ ) , w h i c h therefore yields an average hole v o l u m e (v ) 3

{

=

( 4 / 3 ) i r B , w h e r e R is the average hole radius c o m p u t e d v i a e q 3. W e have 3


of

540


related the positron results to the free v o l u m e fraction v i a the equation (4)

h = Cl (v ) 3

{

w h e r e C is a coefficient that depends u p o n the rate o f formation o f o-Ps i n holes. W e d e t e r m i n e d C b y c o m p a r i n g the o-Ps parameters versus h(P, T) c o m p u t e d f r o m P V T data at Γ = T v i a the S i m h a - S o m c y n s k y theory (25). I n previous w o r k , w e f o u n d that the temperature dependence o f the product i ( V > for P V A c is i n excellent agreement w i t h that o f the theoreti cal h for temperatures Τ > T , i n support o f our hypothesis. A t h i g h temperatures, Γ > T 4- 60 °C the p r o d u c t i < V > exhibited a positive devia tion f r o m the theoretical H. W e speculate that this may be due to the fact that the smaller free v o l u m e sites relaxed too fast to be sampled b y the o-Ps (23). B e l o w T , a quantitative comparison is r e n d e r e d difficult because o f the physical aging p h e n o m e n o n . H o w e v e r , the free v o l u m e values c o m p u t e d f r o m the τ a n d i appear to be o f the correct order o f magnitude (23). W e note that to obtain a detailed interpretation o f certain features of the o-Ps data, specifically the existence o f isofree v o l u m e states i n the glass p r o d u c e d b y distinct t h e r m a l histories, w h i c h differ i n Z a n d , it w i l l clearly be necessary to incorporate a treatment o f the free v o l u m e distribution into the theoretical interpretation o f o-Ps annihilation. Recently it was demonstrated (S. Vleeshouwers, private c o m m u n i c a t i o n , 1992) that a two-dimensional ( 2 D ) M o n t e C a r l o simulation o f a process o f hole nucleation a n d hole cluster formation o n a lattice, i n w h i c h the total fractional hole free v o l u m e is set equal to the S i m h a - S o m c y n s k y value at each temperature, reproduces the m a x i m u m observed i n the temperature dependence o f I i n P V A c . E s s e n tially, the increase i n I w i t h temperature b e l o w T is because o f an increase i n the n u m b e r o f holes (hole nucleation). A b o v e T , the n u m b e r o f holes decreases w i t h temperature because o f hole clustering. g

3

f

g


g

3

f

g

3

3

3

f

3

3

g

g

O u r emphasis i n this report is the application o f positron lifetime spectroscopy to the investigation o f changes i n the free v o l u m e o f p o l y m e r i c solids p r o d u c e d b y mechanical deformation. I n o u r initial efforts w e focused o n the engineering thermoplastic b i s p h e n o l A polycarbonate. T o enable these experiments, a miniature l o a d c e l l was constructed to p e r f o r m i n situ positron lifetime measurements u n d e r well-specified strains (28).

Experimental Details Positron Lifetime Spectrometer. T h e positron annihilation fifet i m e spectroscopy system consists o f a v a c u u m chamber, B a F a n d C s F 7-ray detectors, and a fast fast-coincidence detection system, based o n E G & G O r t e c nuclear instrumentation modules ( N I M ) modules. D a t a were collected o n a personal c o m p u t e r analyse ( P C A ) m u l t i c h a n n e l analyzer (Tennelec). U n i f o r m sample temperature is maintained b y a temperature controller 2


20.

KLUIN ET AL.

541


( m o d e l 805, L a k e Shore Cryogenics) using two diode sensors that m o n i t o r the temperature at two different surface areas a n d control fluctuations i n temper ature d u r i n g data acquisition to w i t h i n ± 0 . 0 4 °C. T o o p t i m i z e the t i m e resolution f u n c t i o n a n d the detecting efficiency o f the system, a cylindrical cesium fluoride crystal (1.5 X 1.5 in.) was u s e d as a scintillator to detect the 1 . 2 7 - M e V g a m m a ray that functions as the positron " b i r t h " signal a n d a conical b a r i u m fluoride crystal (0.8 X 1 X 1 in.) to detect the 0 . 5 1 1 - M e V g a m m a ray that serves as the " d e a t h " signal. T h e w i n d o w s o f the constant fraction differential discriminators, w h i c h select the energy ranges o f the g a m m a rays, w e r e set using a sodium-22 positron source w i t h a polycarbonate sample. F o r a 1 5 - μ Ο sample o f N a , the count rate was about 300 counts/s. T h e source, w h i c h contained u p to 30 μΟί o f N a C l , was deposited o n a t h i n a l u m i n u m foil (1.7 m g / c m ) w i t h i n an area o f diameter « 2.5 m m . T h e foil was t h e n f o l d e d into a 7 - m m square shape a n d sand w i c h e d between two rectangular pieces (1 X 1.3 X 0.4 c m ) o f the polycar bonate sample. T h e time resolution f u n c t i o n i n each case was d e t e r m i n e d i n the process o f c o m p u t e r fitting o f the data a n d was c o m p a r e d w i t h i n d e p e n dent measurements using the p r o m p t g a m m a rays o f C o . F o r C o the f u l l w i d t h at half m a x i m u m ( F W H M ) was consistently less than 230 ps. T i m e calibration was done b y several methods. O n e m e t h o d , w h i c h was based o n the r a n d o m coincidence rate, showed that the channel w i d t h o f the m u l t i c h a n n e l analyzer was 10.3 ps. T o test this result, w e observed the g a m m a rays f r o m the decay o f B i a n d f o u n d a m e a n lifetime of 182 ± 5 ps for the 570-keV level o f P b , w h i c h agreed w i t h the p u b l i s h e d lifetime o f 186 ps.


2 2

2 2

2

6 0

6 0

2 0 7

2 0 7

Data Analysis of Positron Annihilation Lifetime Spectra. E a c h positron annihilation lifetime ( P A L ) spectrum was fitted to a s u m o f four exponentially decaying functions convoluted w i t h the resolution function. T h e fitting was b y means o f the p r o g r a m Patfit-88. T h e resolution f u n c t i o n is approximated as the sum o f three Gaussian functions whose statistical weights a n d f u l l widths at h a l f m a x i m u m ( F W H M ) are d e t e r m i n e d b y the fitting p r o g r a m to be those that give the best fit to the data. A f t e r the resolution function has b e e n d e t e r m i n e d for one lifetime spectrum w i t h a given s o u r c e - s a m p l e assembly, the function is assumed to be the same for all subsequent lifetime spectra as l o n g as the assembly remains i n place. T h e resolution f u n c t i o n consistently h a d a F W H M o f about 230 ps, w h i c h is e q u a l to that f o u n d f r o m the C o source. W h e n a n e w sample is i n t r o d u c e d , the resolution f u n c t i o n is again f o u n d f r o m the fitting procedure; m i n o r changes i n the tail of the f u n c t i o n are sometimes f o u n d , probably because o f a change i n scattering f r o m one detector to the other w h e n the geometry changes slightly. A f t e r the resolution f u n c t i o n is d e t e r m i n e d f r o m analysis o f the initial r u n o n a sample, the parameters to be c o m p u t e d i n each subsequent analysis are the position τ for the starting point o f each exponential decay, the four intensities ( I , Z I , J ) , a n d the four decay constants (reciprocals o f the 6 0

0

s

1 ?

2

3


542


mean lifetimes T , T T , T ) for the exponential functions. T h e source c o m ponent (J , T ) results f r o m positrons that are annihilated before they reach the sample; almost all o f these stop i n the a l u m i n u m foil covering the source. F r o m the k n o w n foil thickness we calculate that i n our experiments about 7 % o f the positrons were annihilated i n the foil. T h e positron lifetime i n the a l u m i n u m foil is k n o w n to be T = 180 ps; hence the values o f I a n d T can be i k e d i n the curve fitting procedure. S

S

1 ?

2

3

s

s

s

s

T h e p r o g r a m Patfit-88 determines the r e m a i n i n g seven parameters, after subtracting the k n o w n source components. T h e starting t i m e £ , the three mean lifetimes, and two intensities are varied; the t h i r d intensity is t h e n d e t e r m i n e d b y r e q u i r i n g the s u m o f the intensities to be equal to 100%. Because o f the m u l t i c o m p o n e n t nature o f the P A L spectrum, several distinct choices can be made i n c o m p u t i n g the fit parameters, w h i c h w i l l result i n systematic differences i n the r e p o r t e d τ a n d I values. F o r example, d u r i n g physical aging experiments, the two shortest lifetimes show variations that appear to be r a n d o m ; therefore, to m i n i m i z e the effects o f the r a n d o m fluctuations o n the values o f τ a n d I , these two lifetimes are h e l d at their m e a n values i n a subsequent analysis o f all o f the curves. A l s o , theoretically, m e a n lifetime is k n o w n to be 125 ps. I n addition, the intensity o f p-Ps must be proportional to that o f o-Ps (I = 0.331 ). Generally, it is not possible to obtain a good fit b y k e e p i n g τ fixed at 125 ps a n d using a reasonable intensity for this component. Therefore, Ι o r τ can be allowed to vary, positron state i n the polymer. C l e a r l y , it follows that an unambiguous description o f the o-Ps decay component requires specification o f the p a r a m eters for the p-Ps a n d e decays.


0

3

3

3

3

x

3

1

λ

1

+

Sample Preparation. T h e b i s p h e n o l A polycarbonate specimens used i n this investigation were typical c o m m e r c i a l materials obtained f r o m Bayer A G C o m p a n y ( L e v e r k u s e n , G e r m a n y ) . T h e glass-transition tempera ture was d e t e r m i n e d to be 150 °C b y a differential scanning calorimeter ( D S C ) at a heating rate o f 20 ° C / m i n . Because the p r i n c i p a l a i m o f this investigation is to characterize changes o f free v o l u m e i n the p o l y m e r glass, each aging experiment the annealing temperature was at T 4- 5 °C. O n e h o u r was r e q u i r e d to increase the temperature o f the sample f r o m r o o m temperature to the annealing temperature, w h e r e it was h e l d for 30 m i n to erase the p r i o r t h e r m a l history to e q u i h b r i u m . A f t e r q u e n c h i n g to the measuring temperature (cooling rate 2 ° C / m i n ) a n d a further equilibration p e r i o d o f 20 m i n , the temperature o f the entire sample was u n i f o r m a n d stable. F o r our study o f the temperature dependence o f the positron spec t r u m (29), w e likewise took 1 h to increase the temperature to T + 5 °C, g

g


20.

KLUIN ET AL.

543


2 ° C / m m , w a i t e d 10 m i n f o r t h e r m a l equilibration, a n d a c q u i r e d spectral data for 1 H. F i n a l l y after a further annealing at T + 5 °C w e increased the temperature to obtain positron spectra at temperatures to 2 0 0 °C. g

Results and Discussion Temperature Dependence of τ and I and Fractional Free Volume. T h e temperature dependence o f Z a n d T for polycarbonate is 3

3

3

3

shown i n F i g u r e l a and b . I n F i g u r e l c , w e show the p r o d u c t h/C = Z , 3. T h i s comparison follows u p o n o u r previous study o f p o l y (vinyl acetate) (23) i n w h i c h w e argued that Z is proportional to t h e n u m b e r o f holes p e r unit v o l u m e a n d hence Z (t> > is p r o p o r t i o n a l to the fractional free v o l u m e . Generally, t h e experimental results show behavior similar to that observed earlier (23) for P V A c . A change i n temperature coefficient o f τ is observed near T = 150 °C, w h i c h indicates a n increase i n temperature coefficient o f the hole radius i n the l i q u i d state c o m p a r e d to the glass state. I n addition, Z exhibits a weak m a x i m u m i n t h e glass-transition region. F o r comparison, i n


3

f

3

3

f

3

g

28 -30

«

1

1

0

30

ι

60

ι

90

ι

120

ι 150

ι I

180

t e m p e r a t u r e (C) Figure I. Temperature-dependence of orthopositronium annihilation in polycarbonate: (a) o-Ps intensity, l ; (b) o-Ps lifetime, τ ; (c) apparent free volume fraction, h/C = I ( V ^ ) . These values were extracted by fits in which r was constrained to r = 120 psi. The solid lines are theoretical calculation of the Simha-Somcynsky free volume function. Continued on next page. 3

3

3

1


1

3


"i

1

1

1

1

1

r (b)

2.7

J 170

Ο Ο

Η 150

2.5

2.3 h Downloaded by GEORGE MASON UNIV on June 6, 2014 | http://pubs.acs.org Publication Date: May 5, 1993 | doi: 10.1021/ba-1993-0236.ch020

Ο θ °

2S

.

-I 130

OCT

w

ο >

0)

i—l

Ο

2.1

110

h

H 90

1.9 J

-30

0

1

1

30

60

_l

I

I

L

90

120

150

180

1

Γ

t e m p e r a t u r e (C) 0.16

Ί

1

1

(c) 0.14

h —

Ο =

0.12

Λ

0.10

= theory measurement

h

0.08

0.06

0.04 -30

>ooc& J

ι

0

30

L

60

90

J

I

L

120

150

180

t e m p e r a t u r e (C) Figure 1. Continued


g

1

20.

KLUIN ET AL.

545


F i g u r e l c , the temperature variation of the S i m h a - S o m c y n s k y free v o l u m e fraction for polycarbonate calculated f r o m P V T data (J. E. K l u i n , Z . Y u , J. D. M c G e r v e y , A . M. Jamieson, R. Simha, a n d K . Sommer, u n p u b l i s h e d results) is shown. T h e theoretical f u n c t i o n is arbitrarily matched to the positron values at the glass-transition temperature T = 150 °C. A g a i n , as w e reported g

previously for P V A c (23),

good agreement w i t h theory is observed

for

Τ > T ; as the temperature is l o w e r e d further b e l o w T , increasingly poor g

g

agreement is observed.


Several points should be made here.

1. F r o m analysis (J. E. K l u i n , Z . Y u , J. D. M c G e r v e y , A . M. Jamieson, R. Simha, a n d K . S o m m e r , u n p u b l i s h e d results) of simulated P A S spectra containing m u l t i p l e o-Ps decay c o m p o nents d e r i v e d f r o m hole size distributions p r o d u c e d b y the previously referenced M o n t e C a r l o calculations (S. Vleeshouwers, private c o m m u n i c a t i o n , 1992), w e find that the average o-Ps lifetime < τ > d e r i v e d f r o m typical three-component

fit

3

ting is the n u m b e r average value < τ ) =

Ση^τ^.

3

2. W e find that the corresponding o-Ps intensity I

3

e x p

is always

numerically smaller than the n u m b e r average; that is, J / =

3

e x p

Structure-Property Relations in Polymers - American Chemical Society

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