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Chapter 7

Radiation and the Crystals of Polyethylene and Paraffins 1

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G. Ungar and A. Keller

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School of Materials, University of Sheffield, Sheffield S10 2T7, United Kingdom H.H. Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, United Kingdom The modes in which crystallinity in polyethylene and its n-alkane oligomers is disrupted by ionizing radiation are described. The "polyethylene" mode differs essentiallyfromthe "paraffin" mode: in the former cross-links are randomly distributed through the crystal lattice, while in the latter a separate liquid phase emerges and becomes the preferential location for new cross-link formation. Efficient radiation energy transfer over micron distances across the crystal must occur in n-alkanes. The change-over from the "paraffin" to the "polyethylene" mode is gradual and occurs in the chain length region of 80-90 C-atoms. The role and the nature of the radiation-induced columnar liquid crystalline phase in polyethylene is also discussed.

Ample evidence exists that irradiation-produced cross-links in solid polyethylene are primarily located in the non-crystalline phase (for a review see réf. [I]). Nevertheless, at high absorbed doses crystallinity is reduced and eventually lost at 2 - 3 Grad. Thus, e.g. high density polyethylene becomes transparent as refractive index fluctuations vanish. While such high doses seem almost out of reach for gamma irradiation, the loss of crystallinity due to electron beam damage at equivalent irradiation levels poses serious problems to electron microscopists since diffraction contrast rapidly fades during observation of polyethylene and other organic crystals. In the following we summarize our past work and present new results on radiation-induced changes to the crystal lattice and the mechanism of lattice destruction in polyethylene and its model compounds, n-alkanes. The work which has lead to the recognition of a previously unsuspected long-range active site migration in alkane crystals is also covered.

0097-6156/91/0475-0101$06.00/0 © 1991 American Chemical Society

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

RADIATION EFFECTS ON POLYMERS

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Effect of Cross-Linking on the Crystal Lattice of Polyethylene

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Loss of Crystallinity. Figure 1 shows the crystallinity of bulk linear polyethylene, slowly crystallized (s) and quenched (q), as a function of absorbed gamma radiation. While crystallinity is seen to decrease steadily, the dose dependence of melting temperature is more complex, as illustrated in Figure 2 [2]. Hexagonal Mesophase and the Pressure-Dose Superposition. Melting proceeds in two stages for highly irradiated polyethylene: in the first transition orthorhombic (o) crystals transform into the so-called "hexagonal phase" (h) which, as recently recognized, is a columnar liquid crystal (Ungar, G. Polymer, submitted) with the characteristic two-dimensional order [3]. Only in the second transition is the isotropic melt (I) attained. The dose dependence of the o-h transition temperature is marked by dashed lines in Figure 2, and the isotropization temperature Qi-l and the direct ο-I melting) by full lines. The crystal lamellae in the three samples in Figure 2 differ in their thickness, this being largest in the slowly crystallized bulk (ca. 30 nm) and smallest in the solution-grown single crystals (ca. 11 nm). The hexagonal phase turns out to be of the same type as that occurring in unirradiated polyethylene subjected to hydrostatic pressures above 4 kbars [4]. In fact it was found that pressure and irradiation act in synergism to bring about the hexagonal mesophase. This is illustrated in Figure 3 which shows the dependence of transition temperatures (o-l, o-h and h-l) on irradiation dose for three different pressures for bulk polyethylene irradiated at 85°C [5]. As pressure increases, the triple point is seen to move to lower doses. Similarly, in a p-T diagram, the triple point moves to lower pressures as irradiation dose increases; consequently, at around 500 Mrad, the hexagonal phase becomes stable at 1 bar. In qualitative terms, the reason behind the dose-pressure superposition effect described above is the following. Irradiation-induced cross-links significantly increase the free enthalpies of both the crystal, G , and the isotropic liquid, G,. The free enthalpy of the mesophase, G , is also affected to some extent, but the behaviour of G and G, is dominant, as shown below. The increase in G is due to the substantial lattice strain energy - a calculation by Guiu and Shadrake [6] puts it as high as 2.5xl0" J per cross-link (compare with a heat of fusion of 2.2x10" for a molecule of n-alkane ΟοΗ ). On the other hand, the increase in G, is due to the reduction in configurational entropy upon network formation. A schematic free enthalpy - temperature diagram for irradiated polyethylene is shown in Figure 4. G °, G ° and G,° (bold lines) refer to zero dose, while thinner lines correspond to irradiation doses 1 to 5. G ° is taken as reference and thus coincides with the abscissa axis. The free enthalpy curves are drawn in such a way that their intersections outline the transition temperature - dose behaviour (dashed lines) qualitatively similar to that observed (cf. Figure 2 and Figure 3, bottom). The similarity becomes readily apparent if the free enthalpy diagram is rotated clockwise by 90 degrees. In terms of the diagram in Figure 4, the effect of pressure is to increase the free enthalpies of all three phases, according to the relationship dG = Vdp - SdT, with V, S, p and Τ being, respectively, specific volume and entropy, pressure and temperature. Pressure exerts the largest effect on raising G„ which can again be 0

h

Q

D

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In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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100

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3 60

V·. \ \

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X(%)

\ \ \

AO

\

^ " " ^

\ \

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Fig. 1 Full lines: X-ray crystallinity (after Hermanns and Weidinger) vs. dose for as-irradiated bulk polyethylene (s = slowly crystallized, q = quenched). Dashed lines: crystallinityfromheat of fusion.

HO

0

500

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dose(Mrad) Fig. 2 Melting (full lines) and orthorhombic - hexagonal transition temperature (dashed lines) vs. dose for slowly crystallized (o) and quenched bulk (o) and for single crystals grown at 85 °C (Δ) (Reproduced with permissionfromref. 2. Copyright 1980 IPC Business Press). In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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RADIATION EFFECTS ON POLYMERS

,οο' Ο

'

'

:

ΙΟΟ 2 0 0 3 C O

1

1

4θΟ 5 0 0

'

1

1

1

6 0 0 7 0 0 8 0 0 9CC D O S E / M rad

Fig. 3 ο-Ι, ο-h and h-I transition temperatures vs. dose, measured at hydrostatic pressures of 1 bar, 1.60 kbar and 2.20 kbar (slowly crystallized bulk polyethylene, gamma irradiation at 85°C) (Reproduced with permission from ref. 5. Copyright 1985 IPC Business Press).

Fig. 4 Schematic free enthalpy vs. temperature diagram for irradiated polyethylene. With increasing dose (denoted 0 to 5) the transition temperatures follow the dashed lines (cf. Figures 2 and 3). In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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traced to the reduction in entropy, similar to the effect of network formation. Thus pressure helps shift the triple point to lower irradiation doses, as observed. It should be noted, however, that the synergistic effect of hydrostatic pressure is only present because the columnar mesophase is a high-entropy low-volume phase ft 5,7]. The Nature of the Mesophase. It had been postulated that there is considerable conformational disorder in the hexagonal phase in polyethylene [8]. NMR and IR spectroscopies are the appropriate techniques for the determination of the type and amount of conformational defects. Unfortunately neither technique is well suited for high pressure studies, so that the pressure-induced hexagonal phase has not been examined by these methods. Fortunately, the obstacle does not arise in the case of irradiated polyethylene. Thus a temperature dependent Fourier-transform IR study was carried out at atmospheric pressure on slowly crystallized (s) and quenched (q) bulk polyethylene samples irradiated with 800 Mrad at 85°C [7]. The DSC thermograms of these samples, displaying the double melting endotherms, are shown in Figure 5. There are two common types of conformational defects in long hydrocarbons, the gauche-trans-gauche sequence (GTG and GTG*) and the gauche-gauche (GG) sequence, which have distinct localized IR-active vibration modes [9]. These give rise to absorptions at 1306 cm" and 1352 cm' , respectively. Figure 6 shows the temperature dependence of the 1306 cm" absorbance (GTG+GTG*). Sample sO has not been irradiated and acts as reference. It melts directly into the isotropic liquid and the one-step increase in the 1306 cm" absorption illustrates this. On the other hand, the double endotherm melting of irradiated samples s800 and q800 (Figure 5) is mirrored also in a two-step increase in the 1306 cm" absorbance (Figure 6). In contrast, the behaviour of the 1352 cm" absorbance (GG defects) is quite different. Here the defect concentration increases in only one step, simultaneously with the second endotherm, i.e. the h-m transition [7]. The implication is that no GG defects are present in the hexagonal phase, but there is a considerable amount (3 to 4 in every 100 C-C bonds) of GTG or GTG* defects (for details see ref. [7]). This difference in the temperature dependence of the two defect bands can be easily understood if it is assumed that all the defects responsible for the 1306 cm" absorption in the hexagonal phase are of the GTG* type. The latter defects (socalled kinks) do not alter the overall trajectory of the all-trans chain (see Figure 7), and could thus be incorporated within the hexagonal array of essentially extended chains (or columns) with little energetic penalty. On the other hand, GG defects would bend the chain by ca. 90 degrees and would not be viable in a lattice of any kind. The formation of the hexagonal phase in polyethylene is promoted by the incorporation into the crystal lattice of any constitutional defect and not just cross-links. Thus a high concentration of methyl branches [2] or chlorine substituents [10] in ethylene-propylene or ethylene-vinylchloride copolymers can by itself induce the h phase. Furthermore, even in low propylene content orthorhombic EP copolymers, much lower irradiation doses are required for h phase formation than in the case of pure polyethylene [11]. 1

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In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

RADIATION EFFECTS ON POLYMERS

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Fig. 5 DSC thermograms of the two bulk polyethylene samples s and q, gamma-irradiated with 800 Mrad at 85°C (Reproduced from ref. 7. Copyright 1986 American Chemical Society.)

80

100

120 Τ CO

K0

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Fig. 6 Temperature dependence of the 1306 cm" GTG/GTG* band intensity for bulk polyethylene irradiated with 800 Mrad (samples s and q) and for unirradiated sample s. The curves in the diagrams are normalized to the same intensity in the melt and displaced vertically by 0.2 units for clarity (Reproduced from ref. 7. Copyright 1986 American Chemical Society.)

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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Effect of the Mesophase on Irradiation Response. In the context of irradiation effects, the importance of the h phase is in its high molecular mobility compared to the crystalline state. The cross-linking efficiency (G-value) of the mesophase is expected to be nearer that of the amorphous (or isotropic liquid) phase than that of the crystal. This expectation is clearly corroborated by experiments on nalkanes. There it was found [2] that the cross-linking efficiency in the "rotator" phase, which is in many respects similar to the h phase in polyethylene, is at least as high as in the liquid. The intervention of the h phase may account for the following two observations concerning the final loss of crystallinity at high irradiation doses: (i) that the lifetime of thick crystal is somewhat longer than that of thin ones, and (ii) that the final loss of crystallinity is preceded by a steep drop in melting Qi-m) temperature (Figure 2). The proposed interpretation of both effects is that accelerated crosslinking commences as the o-h transition temperature approaches the irradiation temperature and molecular mobility increases. From Figure 2 it is clear that this approach occurs at a lower dose for thinner crystals, since the o-h transition temperature is lower. Such dependence of T _ on lamellar thickness is simply a thermodynamic consequence of the lower surfacefreeenergy of the hexagonal mesophase, σ \ compared to that of the orthorhombic crystal, a °. The transition temperature for lamellae of thickness / is given by [12]: 0

h

β

c

Γ

h

h

2(ν°σ ° - v o ) 1 β

e

where T ° is the equilibrium transition temperature of infinitely thick lamellae, v° and v are specific volumes of the two phases, and Ah is the transition enthalpy per unit mass. We note that no change in / takes place upon the transition as the polymer is densely crosslinked at radiation doses in question. t

h

t

Destruction of Crystallinity in n-Paraffins Phase Separation Upon Gamma-Irradiation. Although n-alkanes are often considered and studied as models for polyethylene, they behave quite differently from their polymer counterpart regarding the mode of crystallinity destruction on irradiation. We have investigated this phenomenon in some detail, both by applying ^Co gamma-irradiation [13] and electron microscope beam [14-16]. In addition to samples of polyethylene with different crystal morphologies, the materials studied included n-alkanes of different chain lengths, rangingfrom20 to 94 C-atoms, as well as a long-chain α,τσ-dicarboxy-n-alkane with ca. 100 Catoms, denoted DPE. The latter was obtained by ozone degradation of polyethylene single crystals, and is not as strictly monodisperse as n-alkanes. An illustration of the difference in irradiation behaviour between paraffin and polyethylene crystals is given in Figure 8, where changes in the unit cell parameters a and b are plotted as a function of gamma irradiation dose received at 40°C [13]. The crystal lattice in both polyethylene single crystals (the same is true for the bulk) and in the long chain diacid becomes greatly distorted. This is attributed mainly to cross-link formation in the lattice. The unit cell increases in the a direction, meaning that hexagonal symmetry (with a/b=/3), is approached.

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

RADIATION EFFECTS ON POLYMERS

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Fig. 7 Conformations of a GTG* and a GG defect, linked to an ail-trans chain at either side. (Reproduced from ref. 7. Copyright 1986 Amer. Chem. Soc). 8-5·

PESC 80-

/

0

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dose(Mrad)

Fig. 8 Change in unit cell parameters a and b with dose of gamma irradiation. SC: polyethylene single crystals grown at 85°C; DPE: dicarboxylic acid; C*: n-tetracontane (Reproduced with permission from ref. 13. Copyright 1980 IPC Business Press).

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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In contrast, the unit cell in n-tetracontane (C^H^) does not change at all, until crystallinity is completely lost around 2 Grad. Still shorter paraffins behave in this respect like ΟοΗ . The diffraction linewidth parallels the change in lattice spacings: in n-alkanes C^H^ and shorter, where spacings do not change, the lines remain sharp. This indicates that the crystal lattice, although reduced in overall amount, remains largelyfreeof defects. It also means that the phase separation is on a large scale: small crystalline domains would cause line broadening; on the other hand, point defects (isolated Angstrom-scale regions of disorder), while leaving sharp diffraction peaks, would not produce an amorphous halo with a discrete scattering maximum. To help understand the difference in radiation response of crystal lattices in polyethylene and paraffins, it is instructive to compare the melting thermograms of the irradiated samples described above. Figure 9 shows thermograms of unirradiated and irradiated DPE (polyethylene behaves similarly) and paraffin C^Hgj. The difference in melting behaviour of these two compounds is as striking as the difference in dose dependence of their lattice parameters (Figure 8). The endotherm of the 800 Mrad irradiated DPE remains sharp but the melting point is substantially reduced (by >20°C). On the other hand, the "peak melting temperature" in equally irradiated paraffin is reduced by only 8°C., but the endotherm is substantially broadened. The shape of the latter is typical of twophase melting of an impure compound where the impurities are soluble in the liquid but insoluble in the solid phase.

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Further Evidence for Phase Separation. X-ray diffractograms of irradiated paraffins show the appearance of a diffuse peak, characteristic of the amorphous phase, superimposed on the crystalline diffraction pattern - see Figure 10. As either dose or temperature is raised the diffuse halo increases at the expense of the crystalline reflections. The change with temperature is fully reversible. All this is evidence that phase separation occurs in irradiated C W with the two phases being (i) pure perfect crystal and (ii) a liquid containing the bulk of irradiation products. For Ο,Η^ it turns out that the uncrosslinked, or "monomer" fraction, as measured by GPC, coincides almost exactly with crystallinity at room temperature as determinedfromthe heat of fusion (Ungar, G.; Stejny, J.; Keller, Α., unpublished results). Thus the liquid phase at room temperature is almost entirely made up of cross-linked material. The combination of GPC values for the cross-linkedfractionand the shapes of the thermograms in Figure 9 (bottom) allows one to construct an equilibrium binary phase diagram uncrosslinked - crosslinked C^H^, which realistically describes the phase separation (liquidus curve) for different doses and temperatures - see Figure 11. Recent high-resolution solid-state C NMR spectra of gamma-irradiated Ο,,Η^ and Q X H M by Toriyama et al [17] indeed confirm that a mobile phase is produced by irradiation. While there is general agreement between these authors and ourselves on the main issues, their interpretation of the mobile phase differs somewhatfromours: they regard it as being confined to isolated "glassy islands", containing only a few molecules, and dispersed within the crystal lattice. It may be argued, however, that such amorphous occlusions are likely to produce severe m

n>

13

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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DPE

i

Temperature ( ° C )

Fig. 9 Top: DSC melting traces of an unirradiated and an irradiated (800 Mrad at 85°C) sample of degraded polyethylene (dicarboxy-n-alkane). Bottom: DSC traces of an unirradiated and two irradiated (500 and 800 Mrad at 40-45 Q samples of n-C H . Thermograms are normalized to the same sample mass (Reproduced with permission from ref. 13. Copyright 1980 IPC Business Press). o

40

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In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

7. UNGAR & KELLER

Crystals of Polyethylene and Paraffins



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19°

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Fig. 10 Series of X-ray powder diffractograms of gamma-irradiated Ο,Η^ (800 Mrad) recorded at increasing temperatures.

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TCC)

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Fig. 11 Binary phase diagram for partially cross-linked Ο,Η^ constructed after DSC curves and GPC data for the 219 and 500 Mrad samples. X is the weight fraction of cross-linked paraffin, X (the liquidus) is the composition of the liquid in equilibrium with the solid. The latter contains no cross-links as judged from the absence of any lattice distortion. Details of the construction will be described elsewhere. T

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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lattice strain which could only be released by rejection of the underlying chemical defect (e.g. cross-link) into a completely separate phase. Indeed, our X-ray diffractograms already show a distinct amorphous halo for paraffins irradiated to comparable doses (90 Mrad). Even if full phase separation did not occur in asirradiated crystals, it would have certainly taken place after melting and recrystallization (see above). However, the NMR spectra of recrystallized irradiated alkanes reportedly did not differfromthe spectra of the crystals prior to melting [17]. We have found no evidence for phase separation either in polyethylene or in DPE. Here the cross-links are distributed through the crystal lattice resulting in a uniformly depressed melting point. Melting is of the "homophase" type (Figure 9, top) rather than "heterophase" as in shorter paraffins (Figure 9, bottom). Primary or Secondary Phase Separation. The phase separation between crosslinked and uncrosslinked paraffin, described in the preceding section, has been established "post mortem", and it is not clearfromthe experimental evidence presented how this separation came about. It is certain that, mobility permitting, cross-links tend to be excludedfromthe crystal lattice of shorter paraffins. This tendency has been demonstrated on mixtures of n-alkane 0> Η and the model "H-shaped" molecules of l,l,2,2-tetra(tridecyl)ethane, which contains two 27 Catoms chains linked in the middle [18]. The "H" molecules did not co-crystallize with either the orthorhombic (o) or the rotator phase (Ungar, G.; Stejny, J; Keller, Α., unpublished results). According to the above, even if cross-links had initially formed at random throughout the crystal, phase separation could have occurred subsequently. It should be noted, however, that in the case of polyethylene or DPE crystals no amount of annealing could eliminate radiation-induced lattice distortions: once formed, the cross-links have always remained within the crystals. 7

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Irradiation in the Electron Microscope. In order to elucidate the origin of phase separation in irradiated paraffins, we resorted to electron microscope (EM) experiments [14-16]. The advantage of EM is in its provision for simultaneous irradiation and monitoring, both of the appearance of the crystals in diffraction contrast, and of the changes in lattice spacings and distortions using electron diffraction. 100 keV electrons were used. The beam current density and specimen temperature were accurately controlled and measured. The main question posed originally was answered early on in the course of EM experiments. The emergence of the second phase in the form of radiationinduced amorphous domains was visualised with remarkable clarity in images of paraffin crystals like those in Figure 12. The oval "holes" in the thin crystals are in fact non-diffracting amorphous droplets which appear at an early stage of irradiation. With increasing dose these droplets grow in size but not in numbers. Their growth is at the expense of the crystal which, otherwise, remains relatively free of defects. The time-scale of EM irradiations was considerably shorter (minutes to hours) than that of gamma irradiation (weeks to months), and observable phase separation on a micron scale (Figure 12) often became established in a matter of one or a few seconds. Thus molecular segregation subsequent to cross-link formation

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

2

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Fig. 12 Examples of droplet formation in n-alkane crystals irradiated in EM: (a and b) crystals of C^H^ exposed to an electron current density 0.022 A/m (a) and 0.56 A/m (b). (c): crystal of QQH^ exposed to electron current 0.56 A/m . An exposure of 1 Coulomb/m (1 C/m ) has been estimated to correspond to an absorbed dose of 25 Mrad for 10 nm thick crystals [22]. (Reproduced with permissionfromref. 16. Copyright 1991 Pergamon Press).

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7-1

b —*—0

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Fig. 13 Dose dependence of unit cell parameters a and b for paraffin QgH^ (Δ), Ο,Η,Β (Χ) and C^H^ (ο) irradiated at room temperature. Electron current density 0.1 A/m . The new spacings corresponding to a=8.4A and &=4.9A appearing at around 100 C/m are those of the hexagonal rotator phase (Reproduced with permissionfromref. [14]. Copyright 1980 IPC Business Press). 2

2

(secondary segregation) cannot account for the observed phase separation. Cross­ links and, possibly, other defects must actually be forming in situ within the newly created droplets. As shown in Figure 12, the lower the dose rate the larger the scale on which phase separation occurs. Extrapolation to the very low dose rates of gamma irradiation would thus suggest a very thorough spatial separation between the pure alkane and irradiation products, as indeed observed. Since the initial energy deposition is random, a highly mobile active intermediary must exist in irradiated paraffin crystal, capable of intermolecularly traversing the lattice over micron distances and inducing cross-linking in the liquid. The rate of this migration is estimated [14] to be at least ten orders of magnitude higher than the diffusion rate of alkyl radicals within a polyethylene crystal [19-21]. Thus the active species in question cannot be alkyl radicals, which are commonly perceived as precursors of cross-links (also see below). The nature of the active migrating species still remains unknown, but we have accumulated by now a reasonable amount of information which might, in combination with other techniques, at least narrow the choice of likely candidates. As has been shown, the distinction between the behaviours of paraffins on the one hand and polyethylene and DPE on the other is very clear in the case of gamma irradiation. However, this distinction is more blurred in electron irradiation, as illustrates in Figure 13. At one end, for paraffin C^H^, the unit cell parameters hardly change at all on irradiation. At the other end, in the long alkane QMH^, and also in DPE and in polyethylene, the lattice gradually distorts as in In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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gamma irradiation of these same materials. However, ΟοΗ shows an intermediate behaviour: the lattice parameters change up to a point, and then remain constant. Here the effect of irradiation temperature is very important: if it is raised from 25°C to 60°C., QoHgj behaves like C^H^ at 25°C., i.e. negligible distortion occurs. Alternatively, at sub-zero temperatures Ο,Η^ behaves like polyethylene. Additionally, the following general rule was found to apply to electronirradiated hydrocarbon compounds: the lack of sizeable change in lattice parameters is invariably accompanied by the observation of distinct nondiffracting droplets. Thus, e.g., at room temperature droplets are seen in C^H^ (Figure 12) but not in ΟοΗ . On the other hand, large droplets occur in Ο,Η^ at 60°C. It should be noted, however, that even at temperatures very close to the melting point no droplets of the above type are seen in C^H^. The effect of the three explored variables, viz. temperature, dose rate and chain length, on the extent to which phase heterogeneity does ("paraffin-like" behaviour) or does not occur ("polyethylene-like" behaviour) is summarized in Table I. Long-Range Active Site Migration. Most of the observed features of paraffin irradiation can be rationalized in terms of the following description: (1) The active sites in question can, under certain conditions, move rapidly and over large distances across the orthorhombic crystal lattice common to both paraffins and polyethylene. (2) Disorder, such as that found in the liquid or even in the "rotator" phase of n-alkanes, appears to inhibit the migration, as suggested by recent experiments [16]. (3) The active species terminate with formation of cross-links, but this termination occurs mainly upon the arrival at an existing liquid droplet. (4) Diffusion of the active species is thermally activated; its rate increases with temperature. In Figure 14 we present a schematic illustration of the droplet formation in paraffin crystals. At the inception of irradiation the concentration of active sites increases uniformly throughout the lattice, producing occasional cross-links. Where cross-links are sufficiently abundant to raise the free energy above a critical value, the crystal will melt locally and the embryo droplet will form. This now serves as a sink for incoming active sites within a given capture radius, determined by the sites' diffusion rate. Thus the active site concentration in the vicinity of a droplet is kept low; no cross-links and hence no new droplets form in the crystal once the initial population is established. The droplet separation will be determined by their capture radius, i.e. by the sites' diffusion rate. This, in turn, 82

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Table I.

Effect of Chain Length, Irradiation Temperature and Dose Rate on Irradiation Behaviour of n-Alkanes

"Paraffin-type" behaviour

"Polyethylene-type" behaviour Increasing chain length Increasing irradiation temperature Increasing dose rate

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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L

crit.

et X—

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low temp,

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short chains

high dose rate

low dose rate

Fig. 14 Development of concentration profiles of active sites along a space coordinate χ in the lamellar plane of an irradiated paraffin crystal. Broken line marks the critical concentration for droplet formation; dents in c^ mark the droplets. (Reproduced with permission from ref. [15], Copyright 1983 Pergamon Press). will depend on temperature and chain length as already described. Furthermore, it is clearfromthe steady state dynamics of the process that a high dose rate (high input of sites) would result in a high density of droplets (cf. scheme on the left, Figure 14, and observation on C^H^, Figure 12). At this point it is appropriate to mention the revealing experiments by Clough [23] on irradiated mixed crystals of perdeuterated and protiated n-tetracosane. Clear evidence for alkyl radical migration by hydrogen (or deuterium) hopping was obtainedfromthe observation, by mass spectroscopy, of isotopic exchange occurring during irradiation. From the extent of the exchange, or "scrambling", it was deduced that, on average, there are 14.3 hops per radical pair before termination. Assuming random walk, this means an average migration distance of 6.3 Â for an alkyl radical. This is clearly not sufficient to account for the longrange active site migration, producing liquid domains microns apart, described above. It should be remarked that formation of liquid droplets and certain other features of "paraffin-type" irradiation behaviour are not observed in alkanes with 25 or less C-atoms [16]. This has been attributed to the fact that even a relatively low dose of irradiation at ambient temperature induces a phase transitionfromthe ordered crystal to the transient orientationally-disordered and mobile "rotator" crystal. The long-range active site migration is absent in the rotator phase, and it may be that alkyl radical migration by hydrogen hopping becomes the dominant process. It is thus possible that isotopic exchange experiments on an alkane longer In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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than the C^H» used by Clough would show comparatively less scrambling, if the non-radical long-range migration process replaces hydrogen hopping. Active Site Migration in Long and Short Chain Hydrocarbons. Finally, we address the question of why polyethylene and paraffins behave differently. More precisely, why is the long-range active site migration not operative for chains with ca. 90 C-atoms or more? The experimental fact is that the temperature interval of droplet formation decreases with increasing chain length: it is at least 50°C for CzjHx [16], only 20°C for QsH (Ungar, G.; Hill, M.J.; Ogawa, Y., unpublished), and nil for C^H^ [14]. We propose that this convergence is the result of the site diffusion rate being linked to lattice mobility, whose activation energy increases approximately linearly with lamellar thickness (chain length). On the other hand, chain length dependence of melting point of paraffins levels off at higher molecular weights. Hence C H and polyethylene melt before their lattice mobility becomes high enough for efficient radiation energy transfer.

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Conclusion There is solid experimental evidence for the existence of two different mechanisms of radiation-induced crystal destruction in hydrocarbon chain systems. The "polyethylene mode" differs essentially from the "paraffin mode": in the former cross-links are randomly distributed through the crystal lattice, while in the latter a separate amorphous phase (liquid or gel) forms and becomes the preferential location for new cross-link formation. Efficient radiation energy transfer over micron distances across the crystal must be invoked to account for the observed features of the "paraffin mode". The nature of the fast and longrange migrating species involved is not yet known, but it is unlikely that they are alkyl radicals. The change-overfromthe "paraffin" to the "polyethylene" mode is gradual and occurs in the chain length region of 80-90 C-atoms, depending on irradiation temperature and dose rate. At high doses the gradual accumulation of cross-links in the crystal lattice of polyethylene induces one-dimensional melting, manifested as a transitionfromthe three-dimensional orthorhombic crystal to a two-dimensionally ordered columnar liquid crystal phase with pseudohexagonai symmetry. Final amorphization follows shortly after this transition, as cross-link formation is enhanced in the mobile columnar phase. The inverse relationship between radiation sensitivity and crystal thickness can be explained by a lower stability of the crystalline relative to the columnar phase in thinner lamellae; hence the dose required to induce the transition decreases with decreasing crystal thickness. Literature Cited 1. 2. 3. 4. 5. 6. 7.

Keller, A. in Developments in Crystalline Polymers; Bassett, D.C., Ed.; Applied Science: London, 1981; p. 37. Ungar, G.; Keller, A. Polymer 1980, 21, 1273. Yamamoto, T.J.Macromol.Sci.-Phys. 1979, B16, 487. Bassett, D.C. In Development in Crystalline Polymers; Bassett, D.C., Ed.; Applied Science: London, 1982; Ch. 2. Vaughan, A.S.; Ungar, G.; Bassett,D.C.;Keller, A. Polymer 1985, 26, 726. Guiu, F.; Shadrake, L.G. Phil. Mag., Ser. A 1980, 42, 687. Ungar, G. Macromolecules 1986, 19, 1317. In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

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8. Tanaka, H.; Takemura, T. Polym. J. (Tokyo) 1980, 12, 355. 9. Maroncelli, M.; Strauss, H.L.; Snyder, R.G. J. Chem. Phys. 1985, 82, 2811. 10. Gomez, M.A.; Tonelli, A.E.; Lovinger, A.J.; Schilling, F.C.; Cozine, M.H.; Davis, D.D. Polym. Prepts., Amer. Chem. Soc. 1989, 30, 317. 11. Marks, B.S.; Carr, S.H. J. Polym. Sci. - Polym. Phys. Ed. 1985, 23, 1563. 12. Marchetti, Α.; Martuscelli, E. J. Polym. Sci. - Polym. Phys. Ed. 1976, 14, 323. 13. Ungar, G. Polymer 1980, 21, 1278. 14. Ungar, G.; Grubb, D.T.; Keller, A. Polymer 1980, 21, 1284. 15. Ungar, G.; Grubb, D.T.; Keller, A.Radiat.Phys. Chem. 1983, 22, 849. 16. Ungar, G.; Hill, M.J.Radiat.Phys. Chem. 1991, 37, 37. 17. Okazaki, M.; Toriyama, K. Chem. Phys. Lett. 1990, in press. 18. Bennett, R.L.; Keller, Α.; Stejny, J. J. Polym. Sci. - Polym. Chem. Ed. 1976, 14, 3021. 19. Seguchi, T.; Tamura, R. Rep. Prog. Polym. Phys. Jpn. 1971, 14, 565. 20. Shimada, S.; Maeda, M.; Kashiwabara, H. Polymer 1977, 18, 25. 21. Grimm, H.J.; Thomas, E.L. Polymer 1985, 26, 27. 22. Grubb, D.T. J. Mater. Sci. 1974, 9, 1715. 23. Clough, R.L. J. Chem. Phys. 1987 87, 1588. R E C E I V E D April 22, 1991

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.