Structure and Properties of Glassy Polymers - American Chemical

Chapter 23

Vacancy Spectroscopy of Polymers Using Positronium Yasuo Ito

Downloaded by EAST CAROLINA UNIV on December 30, 2017 | http://pubs.acs.org Publication Date: January 28, 1999 | doi: 10.1021/bk-1998-0710.ch023

Research Center for Nuclear Science and Technology, The University of Tokyo, Tokai, Ibaraki 319-11, Japan

Characteristics of the methods of estimating vacancies in polymers from the lifetime and intensity of ortho-positronium (o-Ps) are described. From quantum mechanical consideration and from recent experimental results it can be shown that o-Ps is "a seeker and digger" of holes especially in rubbery states leading to significant overestimation of the size of vacancies. In glassy states the vacancy information will be less affected by o-Ps. Although this active nature of o-Ps might look undesirable for direct measurements of vacancies, it can be used to gain additional information about the polymer. Examples of o-Ps spectroscopy applied to the detection of glass transitions, probing sorption sites, probing vacancies in conditioned polymers, and detection of crystallization sites are presented. The o-Ps spectroscopy data are also compared with gas permeation data. In the sorption studies, the oPs lifetime and intensity respond in contrastingly different ways for Langmuir-type and Henry-type sorptions. In all these examples o-Ps brings forth unique information suggesting the usefulness and powerfulness of "vacancy spectroscopy" using o-Ps.

+

It is well recognized that the positron (e ) is a sensitive probe of vacancy type defects in metals and semiconductors since it can be easily trapped in sites where positive ions are missing. A standardized method like the trapping model isfrequentlyused to extract

334

©1998 American Chemical Society

Tant and Hill; Structure and Properties of Glassy Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1999.

335 information about the size and number of the defects. Similarly positronium (Ps), a neutral particle composed of an e and e" pair, has also been noted as a unique indicator of vacancies especially in insulators like polymers and oxides (2). However due to the lack of quantitative knowledge about the behavior of Ps with regard to vacancy characteristics, it has taken some time for Ps to be adopted as a practical laboratory tool. A general reference of positron and positronium spectroscopy can be found, for example, in (/) and (2), respectively. Quite recently a simple model describing the relationship between the Ps lifetime and the size of vacancies was developed (3,4), and spectroscopy of vacancies using Ps is becoming morefrequentas can be seenfromthe fact that the related topics occupy approximately 40% of the presentations of PPC-5 (Int. Workshop on Positron and Positronium Chemistry) (5). There are still fundamental problems to be studied before Ps can be used as a mature analytical tool, but there are already various excellent works in that direction. This article describes the information o-Ps gives concerning the vacancy characteristics in glassy polymers.


+

Formation and annihilation of Positronium +

When positrons, either from β -decay radioisotopes or from nuclear reactions in accelerator facilities, are injected and stopped in polymers, they undergo a sequence of processes including formation and trapping of Ps into vacancies and eventually are annihilated emitting gamma-rays. Ps can be formed with a probability which depends on the physical and chemical conditions of the substance. There are two sub-states of Ps depending on the e and e" spin configuration: para-positronium with the spins antiparallel (p-Ps, S=0) and ortho-positronium with the spins parallel (o-Ps, S=l). The former annihilates rapidly with the mean lifetime τ i~0.12 ns and composes the shortest lived component of the annihilation spectrum (see Figure 1). The lifetime of o-Ps is 140 ns in vacuum, but in condensed media it is substantially reduced to several ns due to the overlap with electrons from the surrounding molecules. This annihilation mode, called the "pick-off" annihilation, constitutes the main part of the o-Ps lifetime and is important with regard to the measurement of the vacancy size. The lifetime, τ 3, and its intensity, I3, of this component are the quantities that can be measured with high accuracy, and it is customary to use these quantities to study behaviors of o-Ps. The intermediate component with τ ^0.5 ns is attributed to the annihilationfrombare e and from compounds containing e or Ps. In addition to the lifetime measurement there are methods to measure the momentum of annihilating pairs, but for the sake of simplicity we will not deal with them in this article. +

2

+

+



336

1e+5 -

f 1e+4 c (Ο

1

1e+3 -

â Ο)

,

ο ie+2 -

Ο

100

200

300

400

500

channel number (50.1 ps/ch) Figure 1. An example of the positron lifetime spectrum in polymers; a polycarbonate. The abscissa is the channel number of the pulse height analyzer and is proportional to time, and the ordinate is the logarithm of the count at each channel. The spectrum is composed of three exponential decay component as shown by the dotted lines, and the longest lived one is the o-Ps annihilating in vacancies.


337 Ps formation in polymers is not completely understood. Basically Ps can be formed in two ways. In the course of thermalization (energy loss) in polymers e passes through an energy region, called the Ore gap, where e can efficiently pick up an electronfromthe molecule M to form Ps as, +

+

+


e* +M

--»Ps* + M-

0)

Since the Ps binding energy (Ip =6.8 eV in vacuum) is smaller than the ionization energy of the molecule, IM, this is an endothermic reaction and there is an energy threshold (Eth=lM-Ip) for e below which Ps formation is not possible. In this epithermal process the nascent Ps has an energy ranging up to several eV, i.e. the Ps is a hot atom. This takes place in a special space region, called the "short track" (6), where the e energy loss process is almost ending accompanied by an exceptionally high density of energy deposition. It can be shown by a crude estimation that approximately 1 mole/dm of ion pairs are formed in the short track. In such an environment it is difficult for the hot Ps to survive reaction with the positive ions, and Ps is most probably oxidized to bare e+ (or electron transfer) as; 8

+

e

+

3

Ps*+M

+

--»

+

e +M

(2) +

The next possible way of Ps formation is the recombination of e with one of the excess electrons produced in the short track (Ps formation by the spur process). +

e + e -» Ps

(3)

This process is quite akin to geminate recombination in radiation chemistry and indeed many experimental results show excellent parallelism between the data of Ps formation and radiation chemistry (7,8). The main part of Ps we observe in polymers appears to comefromreaction (3), but if the epithermal Ps via reaction (1) survive the oxidation reaction (2) it will also show up. The energetics of Ps formation via the spur process are given by, -E + - E . + Ep ^ Ip e

c

s

(4)

8

where E's are the energy levels, measured from the vacuum level, of the precursors and the product. In polymers e and e* may be sitting on certain energy levels +


338 corresponding to their work functions. It is difficult to estimate Ep since we do not know to which state in the vacancy Ps is formed at first. We suggested before (9JO) that in polymers where there are many different holes Ps may be resonantly formed into virtual levels in them. The level is higher the smaller the vacancy size, and hence there can be a critical hole size below which Ps formation is not possible. This critical size is dependent on the energy levels Ee+ and E , and hence there can be an interplay between the energy levels and the hole size. When the energy level of e" becomes lower (E . takes a larger negative value), the critical hole size must be shifted to a larger one and eventually for a fixed hole population the number of holes available for Ps formation becomes smaller. Indeed it is a well recognized fact that molecules with large electron affinity lead to a smaller Ps formation probability (11). This effect can sometimes lead to a negligibly small Ps formation probability as in Kapton (12). e

c


c

How Positronium Sees Polymers +

Ps is a neutral light particle composed of e and e". Since it is a free radical it may undergo reactions with paramagnetic species and electron acceptors via oxidation, compound formation, and spin exchange reactions. +

o-Ps + X -> e , PsX, p-Ps

(5)

The rate of this reaction is expressed by a pseudo-first order reaction as λ =k[X]. In diamagnetic substances, however, Ps feels strong repulsive force based on the Pauli's exclusion principle. Hence in crystals Ps will exist in interstitial sites as a Bloch wave, but in substances having density fluctuation it is trapped in open space. Describing the Ps state in the interstitial or in the trapped states by a spherical potential well with infinite height, its zero-point energy is given as, 2

2

2

Eo = π h /4meR = 0.188 / R

2

(Eo : eV, R: nm)

(6)

where R is the radius of the well and η% is the static mass of the electron. It must be noted that, due to the small mass (=2 nie) of Ps, Eo is as large as several eV for R normally found in polymers. An important consequence of the high zero-point energy is that Ps can expand the size R with the energy required to do so compensated by the decreased Eo. A well known example is the "Ps bubble" in liquids which Ps creates by pushing aside the surrounding molecules and is self-trapped by virtue of the lowered Eo.



339 It is not an established understanding that Ps does the same in solids, but, as will be made clear later in this article, there is a good reason to expect that Ps can "dig" holes in rubbery polymers. However in glassy polymers Ps will not be able to dig with the same ease. Another consequence of the high zero-point energy is that Ps may "seek" larger holes. In polymers the size of holes is normally of the order of R ^ O . l nm and, according to equation 6, a slight change in R of about 0.2% leads to an energy shift larger than thermal. Thus Ps is not able to move into smaller holes but is preferentially transported to larger ones, if any. Good evidence that Ps is "digging and seeking" holes is found in our recent work on the solids of low molecular weight compounds, where o-Ps was found to be in a large vacancy as if the solid is in a super-cooled liquid state (13). The lifetime of o-Ps is several ns in polymers. This time scale is faster than most of the segmental motions and Ps will see the polymer chains as almost static even in the rubbery polymers. Ps will probe this static vacancy distribution with its "digging and seeking" flaw character. The vacancy information brought forth by Ps must be received with a precaution, but we still expect the information is valuable. As will be discussed later it is also possible to use the "digging and seeking" nature of Ps as an active probe. Once o-Ps is confined in a hole it stays there colliding many times on the wall until an electron, having anti-parallel spin to the e spin, in the wall meets e and is annihilated (pick-off annihilation). Theoretically the rate of this pick-off annihilation is proportional to the overlap integral of the e wave function with those of external electrons. In a simple but useful model a spherical potential well is assumed for the hole and the external electrons are dealt with as an electron layer pasted over the wall with a thickness Δ R. The o-Ps lifetime is then given as (3)\ +

+

+

τ pick-off = 0.5 [1-R/(R+A R)+sin(2 π R/(R+A R))/2 π ]

ns

(7)

where Δ R=0.166 nm was found to give τ i k-off agreeing well with the experimental τ 3 values (4). Thus equation 7 gives a simple means to calculate the size of the hole, vp», from the measured τ value through vp=4 π R /3. Due to the "digging and seeking" nature it is not guaranteed that v thus obtained represents the intrinsic hole size. This issue must be examined separately. The o-Ps lifetime is the sum of the chemical reaction term and the pick-off term. pC

3

3

8

Pg

IIτ

3

=λ

3

~~ λ ρ^.^

+k[X]


(8)

340 It must be noted that the experimental τ value can be equated to the pick-off term via equation 7 only when one is certain that the chemical reaction term is not playing an important role. Quite often the chemical reaction term can not be neglected. Examples are found in the dependence of τ on electron affinities of the acid anhydride moieties of polyimides (12), reduction of o-Ps lifetime and intensity in baked and carbonized polymers (Tanaka, K., Yamaguchi Univ., unpublished data.). In these cases τ no longer represents the hole size through equation 7. 3

3


3

The o-Ps intensity I3 is the fraction of positrons that formed Ps and are trapped in the holes. From many evidences it appears to be correlated with the number of the holes, but no quantitative relationship between them is derived yet. One will easily understand the difficulty considering the complicated processes of Ps formation and trapping into holes. In a most crude case, however, it is assumed that I3 is proportional to the number of holes. In such a case the free volumefractionv is equated to a product of the size of the o-Ps hole, vpg, and I as Vf=a · vp, · I , where a is the proportionality factor (14). In some reports it is claimed that this simple treatment works well. This is probably because all the complicated factors related to Ps formation and trapping processes and the "digging and seeking" nature are rounded off in the proportionality factor. However it is not mature to generalize this kind of treatment since we do not know the details of the processes leading to I . f

3

3

3

Applications of Positronium as the Probe of Vacancies Glass Transition One of the direct and simplest applications of Ps is the detection of glass transition as illustrated in Figure 2 for polyvinyl alcohol) (15). PALS was measured at various temperatures and the measured o-Ps lifetime τ was converted through equation 7 to the mean size of the holes in which o-Ps is trapped. Evidently there are two slopes, and the crossing point agrees very well with the known value of Tg. The slopes correspond to thermal expansion of v and the expansion coefficients α (v ), which are 6x10" and 4x10' deg" for glassy and rubbery states, respectively, are about one order of magnitude larger than the macroscopic expansion coefficients α (v ). The larger coefficient for vp than for v is not surprising because o-Ps is measuring the expansion of the open spaces itself. If we make a crude assumption that the bulk specific volume VB is the sum of occupied volume andfreevolume (vB=vo+Vf), and that the size of the Ps hole is proportional to the free volume fraction (vp^Vf), it is straightforward to deduce α (vp )/ α (VB)=1/VF. This may explain as a first approximation why the expansion coefficient of the o-Ps hole is larger than the bulk 3

Ps

4

3

Ps

1

B

e

B

s



341

ο •

0.30

Τ increasing direction Τ decreasing direction

Φ

ο χ: (Ο

α.

/

0.25

ι Ο

CO

"Ό 0.20 (Ο

Tg

α:

0

50

100

Temperature

150 °C

Figure 2. Temperature dependence of the size of o-Ps holes obtained from the PALS measurements for polyvinyl alcohol. The crossing point corresponds to the glass transition, Tg.


342 expansion, but the actual situation is a little more complicated. To see this we refer to the data of poly(propylene) (16), for which it is reported that below Tg the values of α (vp ) and a(v ) are 1.7xl0" and 2.2 χ 10" , respectively. The ratio is 8, which may properly be compared with l/v . However above Tg a(vPs) and a(vB) are 1.2 χ 10" and 8.1 χ 10" , and the ratio is 15. This larger ratio for the rubbery state is opposite to the expectationfromthe α (v )/ a (v )=l/v relationship, since VF is larger in the rubbery state. This large a (vp )/ α (v ) ratio for the rubbery state provides an evidence that o-Ps is digging holes with more ease in the rubbery states than in the glassy states. 3

s

4

B

F

2

4

Ps


g

B

F

B

Many data of Tg determined by the o-Ps method agree with those from the conventional methods. A compilation of Tg data obtained from PAL is found in (17). The beauty of the o-Ps method lies in the ease of experiments. Since only the high energy annihilation gamma-rays have to be measured from outside, it is possible to introduce various experimental conditions to the sample polymer. For example τ 3 can be measured in vacuum or by introducing guest molecules as sorption gases, by imposing external pressure, and so on. Sorption Probing sorption states by o-Ps is also promising. In our first report of this research polyimide (6FDA-TMPD, Tg=377°C) and LDPE (Tg=-27°C) were measured by introducing vapors like hexane, cyclohexane, benzene, etc. (18).The experiment was simple as shown in Figure 3. A glassware having two arms connected with a stopcock was used. In one of the arms was placed a positron source (about 0.5MBq of ^NaCl sealed in a Kapton foil) sandwiched by two identical pieces of sample polymer (10x10x1 mm ). In order to ensure efficient diffusion of vapor molecules thin foils of the polymer were used and were stacked together to make thickness of about 0:5 mm, which is necessary to stop all the positrons in the sample. The liquid to be sorbed was put in the other arm. After evacuating the whole system, the stopcock connecting the two arms was opened and PALS measurements were performed. Figure 4 shows an example of the changes of τ and I after introducing benzene as the sorbed molecules, but the basic tendency did not depend on the kind of the vapors used. In polyimide both τ and I3 dropped spontaneously, and then followed their gradual and delayed rise. The spontaneous drop is due to the Langmuir-type sorption in which the vapor molecules fill in the preexisting vacancies. In such conditions o-Ps finds less number and smaller size of vacancies. In LDPE, on the other hand, both τ and I3 simply increased. This result is attributed to the typical Henry-type sorption where the sorbed molecules dissolve into the chains and participate in the micro3

3

3

3

3


343


sample with e

+

source liquid

scintillation detectors

Figure 3. The experimental setup for the PALS measurements of sorption of liquid vapor in polymers. The positron source together with the sample polymer is contained in one arm of the glassware and the liquid to be sorbed is contained in the other arm. The positron lifetime measurement is performed by detecting the gamma-rays emittedfromthe source andfrompositron annihilation in the sample.

polyethylene

CO

c

-

e

CO

c φ

Structure and Properties of Glassy Polymers - American Chemical

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