J. MATER. CHEM., 1991, 1(3), 401-407 40 1 Radiation Chemical Yields and Lithographic Performance of Electron-beam Resists based on Poly(methy1styrene-co-chlorostyrene) Richard G. Jones,*' Philip C. Miller Tate' and David R. Brambleyb 'Centre for Materials Research, Chemical Laboratory, University of Kent at Canterbury, Canterbury, Kent CT2 7NH, UK bAdvanced Lithography Research Initiative, Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX1 1 OQX, UK Copolymers of methylstyrene and chlorostyrene cross-link when irradiated with 20 keV electrons and hence act as negative-working electron-beam resists. eMethylstyrenelgchlorostyrene and pmethylstyrenelpchlorosty-rene copolymers have been prepared by a free-radical mechanism over the entire composition range and the lithographic performance of the materials has been evaluated.Radiation chemical yields for cross-linking and chain scission have also been estimated. None of the materials undergoes significant chain scission upon irradiation. In contrast to the corresponding methylstyrene/chloromethylstyrene copolymer systems, the resist sensitivities maximize at compositions containing ca. 30% chlorostyrene. A cross-linking mechanism involving an excited-state charge-transfer interaction of adjacent methylstyrene and chlorostyrene chain units is proposed. The copolymers of optimal composition display sufficiently high lithographic sensitivities and contrasts to commend their application as electron-beam resists. Keywords: Lithography; Electron-beam resist; Polflmethylstyreneco-chlorostyrene) ; Copolymer The use of substituted polystyrene derivatives as negative- working electron-beam resists has been well established for more than a decade.Polystyrene itself was demonstrated to be a high-resolution resist when the technology was compara- tively young, but it lacks sensitivity to the electron beam and does not display the high lithographic contrast obtainable from comparably sensitive positive-working resists based on poly(methy1 methacrylate). However, the aromatic structure imparts a high dry-etch durability to resists of this class, which, together with their good film-forming capability, has caused their use in the manufacture of application-specific VLSI devices and in mask-making to endure.It was soon recognised that polychlorostyrene displayed a 10-fold greater sensitivity than polystyrene.' This has been attributed* simply to the increased likelihood of cleavage of the weaker aromatic carbon-chlorine bond when compared with the aromatic carbon-hydrogen bond. Another property to be considered in this context is the greater electron capture cross-section of the chlorine atom. It is important to recognise, however, that the mechanisms of energy transfer from the incident beam to the resist are too complex to allow a simple quantitative analysis of sensitivity in these terms alone. Ring substitution with a chloromethyl group further enhances the inherent sensitivity by at least a factor of four, again owing to a weaker carbon-chlorine bond but further aided by the resonance stability of the resulting benzyl radical.Unfortu- nately, both polychlorostyrene and polychloromethylstyrene undergo significant chain scission upon irradiation.* This suppresses the inherent sensitivity and, worse still, leads to a reduced contra~t.~ However, it has been shown many times that it is not necessary to have a chlorine content as high as one atom per monomer unit in order to realise useful improve- ments in resist sensitivity4*' and lower chlorine contents permit such improvements without greatly compromising lithographic contrast and resolution. Although both exper- imental and commercial resists consisting of either partially chlorinated or chloromethylated polystyrene have been pro- duced, far better overall performance has been achieved from materials that are essentially copolymers of methylstyrene and chloromethylstyrene, usually containing ca.10-20% of the latter. The radiation chemical processes leading to cross-linking in these resists are now well understood.6 Such resists can be produced in a variety of ways. These include non-specific chlorination of polymethyl~tyrene,~ site-specific monochlorination of polymethylstyrene' and through copolymerization of a methylstyrene with chloromethylstyr- ene.'p9 The first two methods have the advantage that the precursor polymer can be synthesized by an anionic mechan- ism to produce a narrow molecular-weight distribution, a feature which enhances the attainable contrast con~iderably.~ However, they both have their disadvantages.The former results in main-chain as well as substituent methyl chlori- nation, thus enhancing undesirable radiation-induced chain- scission reactions, and the latter is restricted to maximum degrees of chlorination of CQ. 20%. Nonetheless, it has recently been demonstrated" that the presence of 20% or more of o-methylstyrene units in a range of chlorinated polymethyl- styrene resists enhances their lithographic performance by suppressing chain scission. The mechanism of this effect is not entirely clear but is postulated as being due to a steric interaction of the chain and the ortho methyl group which raises the energy of chain-centred benzylic radicals, thus inhibiting their formation.Another possible explanation involves intramolecular hydrogen-atom abstraction from an adjacent ortho methyl group by any benzylic radicals formed at chain-centred a-carbon atoms, thus offering a deactivation pathway as an alternative to Q-scission. Preparations based on the copolymerization of methyl- styrenes with chloromethylstyrene have the advantage of enabling the synthesis of materials with the content of chlor- ine-containing units continuously variable from 0-100%. Backbone chlorination is precluded, although the molecular weights and polydispersities are confined to those attainable: through free-radical polymerization. This limits the resist contrast but it has been advocated by Ledwith et al.as a method of achieving substituent positional specificity for investigations of the radiation chemistry of such materials.' It was subsequently applied in lithographic studies of copoly- mers of o-, rn-and p-methylstyrene with chloromethylstyrene.9 Chloromethylstyrene monomer is only available commercially as vinyl benzyl chloride (VBC), a 2: 1 mixture of the rneta and para isomers. Complete positional specificity of the chlor- omethyl substituents was not therefore achieved. Copolymers of methylstyrene and chlorostyrene are not so constrained as all three isomers of monochlorostyrene are readily available. The poly(o-methylstyrene-co-p-chlorostyrene)and poly(p-methylstyrene-co-p-chlorostyrene)systems that are the subject of this paper have been chosen for study to elucidate further the mechanisms of radiation-induced chain scission and cross- linking in chlorine-containing styrene-based resists.Experimental Materials p-Methylstyrene (pMS) and o-methylstyrene (oMS) were sup- plied by Lancaster Synthesis and p-chlorostyrene (pCS) by Koch-Light Laboratories. The monomers were distilled at 40-50 "C under reduced pressure prior to use. Polymerizations were carried out in stoppered boiling tubes. A total of 6 cm3 of monomers together with 10cm3 of dry toluene and an appropriate amount of 2,2'-azobis(isobutyronitri1e) were deaereated with dry argon for 15 min before the tubes were immersed for ca. 5 h in a water bath maintained at a tempera- ture of 70 "C.Polymers were precipitated in a large excess of methanol, reprecipitated from toluene solution, filtered and dried at 80 "C. With one exception, all copolymer yields were maintained within the range 14-25%. Apparatus and Procedures Copolymer compositions were established from NMR spectra obtained using a JEOL JNM-GX270 spectrometer operating at 67.8 MHz. Chemical shifts were relative to TMS. Peak-area measurements were achieved using inverse-gated decoupling with a 5 s pulse delay. Monomer reactivity ratios were estimated by curve-fitting to the feed composition- polymer composition data using non-linear regression analysis in accordance with the 'terminal' model of monomer reactivity. Molecular weights were obtained as linear polystyrene equivalents using HPLC equipment supplied by Polymer Laboratories and equipped with a 5 pm PLgel dual column bank of lo4 and 500A.Glass transition temperatures were determined using a Perkin-Elmer DSC-7 differential scanning calorimeter.Thin films of the polymers ca.0.5 pm thick were spin-coated from 10% solutions in chlorobenzene onto 3 int silicon wafers using a Headway EC-101 spinner, and prebaked at 120°C for 30 min. The wafers were cut into quadrants for density measurements and lithographic assessments of the resists. Film thicknesses before and after exposure were measured using a Taylor Hobson Talystep. Film densities were deter- mined by calculation from the film thicknesses, the areas of the quadrants and their masses before and after resist removal.Masses were measured to 10 pg accuracy. Lithographic assessment was accomplished using a Cam- bridge Instruments EBMF-2 electron-beam lithography tool operating at 20 kV accelerating potential. Exposed resists were developed in methyl isobutyl ketone (MIBK) for 60s, rinsed in isopropyl alcohol for 30 s and dried in a stream of nitrogen. Sensitivities were estimated as the dose correspond- ing to 50% thickness remaining after development (D:.').All thicknesses were normalised to the original spun thickness. 7 1 in=2.54 cm J. MATER. CHEM., 1991, VOL. 1 Lithographic contrasts (y) were calculated from D:.' and the gel dose (D:)using Radiation chemical yields were determined in accordance with the method described by Hartney' and using the approxi- mations to radiation dose and gel fraction developed by Novembre and Bowmer." This involves obtaining a best fit of Inokuti's equation [eqn.(2) below] to the lithographic data by minimising the sum of the squared differences between normalised thicknesses remaining (assumed equivalent to the gel fraction) and those values of gel fraction generated by the equation, over an array of possible Gs and Gx values: 1 -g=A-3(A2A+4Ag[1 -(1 +Ay/Q)-']/y +4g2A[1 +Ay/B]-@+')) (2) where g is the gel fraction, A =Gs/Gx, j7=l/(Mw/Mn-l), A = A+2g, y= 1.04 x 10-6GxMnr,r is the radiation dose in Mrad, Gsand Gx are the radiation chemical yields for scission and cross-linking, respectively, M,and Mw are the number- and weight-average molecular weights respectively.There are a number of considerations pertinent to the application of Hartney's method for the determination of G values and the reader is referred to the original paper2 for clarification. Results Reactivity ratios were calculated from the data of Fig. 1 and 2 which show the variations in the compositions of the copolymers with those of the feedstocks for the pCS/oMS and pCS/pMS series respectively. For the pCS/oMS system with pCS designated as monomer A, rA= 1.406+0.075 and rB= 0.353 & 0.014 (rArB =0.496). Similarly for the pCS/pMS system rA=0.919 & 0.055 and rB =0.543 +0.030 (rArB =0.499). The lat- ter pair of values compares favourably with those reported in the Polymer Handbook12 (rA= 1.150, rg=0.610).These figures indicate that in both cases pCS is the preferred monomer but that the copolymer structures are essentially statistical. The relevant physical and lithographic properties of the two series, together with those of polystyrene, are presented in Table 1.The reasonable substitution of normalised film thickness for gel fraction in Inokuti's equation relies upon uniform gelation occurring throughout the thickness of the film and also upon complete removal of the soluble fraction 1 .o h c 0.8 .-4-E .c-0.6 Y L Q)E5 0.L 9. K.-v)u Q 0.2 0.0 0-0 0.2 0.L 0.6 0.8 1.o pCS in feed (mol fraction) Fig. 1 Composition plot for pCS/oMS copolymers J.MATER. CHEM., 1991, VOL. 1 Table 1 Physical and lithographic properties of pCS/MS copolymer resists pCS(%) M, M, M,/M, 7JK D,"/pC cm-' D:.'/pC cm-' y G, Gx C/(Mrad/pC cm-') (I/R0.') M,/106 Mrad-' OMS 0 7700 11300 1.5 402 405 638 2.5 0.00 0.05 2.12 0.07 8 16000 27700 1.7 412 28.1 pCS/oMS 46.6 2.3 0.05 0.32 2.05 0.38 14 16400 30000 1.8 412 21.1 32.1 2.7 0.05 0.44 2.08 0.50 19 23600 43900 1.9 41 1 11.4 16.9 2.9 0.00 0.56 2.09 0.64 23 24000 44400 1.9 410 10.9 17.2 2.5 0.04 0.51 2.17 0.60 28 24100 46600 1.9 408 9.2 14.3 2.6 0.09 0.62 2.18 0.69 35 6300 10100 1.6 398 46.0 73.0 2.5 0.00 0.59 1.98 0.69 54 7300 12300 1.7 398 40.0 63.5 2.5 0.00 0.53 2.02 0.63 73 8700 14600 I .7 397 37.0 61.0 2.3 0.05 0.49 2.03 0.55 87 10100 17500 1.7 400 36.5 62.0 2.2 0.13 0.43 2.00 0.46 PCS 100 10700 18100 1.7 402 40.0 69.5 2.1 0.18 0.40 2.04 0.39 0 34100 58000 1.7 388 48.6 77.:MS 2.5 0.02 0.09 2.18 0.10 PCSlPMS 3 17100 29400 1.7 386 18.1 28.8 2.5 0.02 0.47 2.04 0.58 3 15900 26900 1.7 386 15.0 23.5 2.6 0.10 0.64 2.14 0.74 9 15500 26200 1.7 388 12.5 19.9 2.5 0.11 0.75 2.17 0.88 28 39600 69500 1.8 396 3.9 6.1 2.6 0.03 0.85 2.21 1.07 47 41400 74800 1.8 398 4.0 6.2 2.6 0.00 0.73 2.39 0.90 64 42900 78200 1.8 40 1 4.4 6.7 2.7 0.02 0.75 2.17 0.88 80 46900 82700 1.8 406 4.4 6.5 3.0 0.09 0.75 2.24 0.83 0 41200 70900 1.7 357 97 styrene 155 2.5 0.02 0.04 2.03 0.04 spun polymer films may differ significantly from those of bulk 1.o samples, a series of density measurements were made on some of the spun samples.Fig. 3 shows a plot of density against composition for the copolymers of the pCS/pMS series. Even oa .-0 though the plot is not perfectly linear, it is reasonable to c. E estimate the density of a given copolymer by way of a linear c-interpolation between the points corresponding to the homo- 0 0.6 E polymers since the direct measurement technique is tedious v L and of limited accuracy. This method has been employed for (u both series of copolymers. The calculated values of C deviateg0.L significantly from 2 and by interpreting the lithographic data n in terms of absorbed radiation dose (R) rather than charge .-c dose (D),this has been taken into account.(I)0 Q. 02 The final column of Table 1 is the reciprocal of the reactivity of the resist, where R0.5is the absorbed energy dose in Mrad corresponding to D:.'. RO.' is employed rather than the / absorbed radiation dose at the gel point, Ro, as the former I I I I 1 00 02 OL 06 08 10 may be more accurately determined, so giving rise to less pCS in feed (mol fraction) experimental scatter when correlated with other parameters. Fig. 2 Composition plot for pCS/pMS copolymers The reciprocal reactivity (1 /RO.'MW)is an excellent indication of the intrinsic sensitivity of a resist in that it provides a by the developing solvent.Neither increased immersion time numerical parameter which increases with increasing suscepti- in MIBK nor a post-development bake at 120 "Cfor 30 min, bility to cross-linking by radiation. It is independent of which was applied to a few samples taken at random, had Tany measurable effect on thickness remaining after develop- 1l5 ment. Hence, the necessary conditions are met and the use of normalised film-thickness measurements as a measure of gel fraction for use in the Inokuti equation is justified. These observations are also in accordance with those published recently regarding free volume in resist layers, in which polystyrene was used for purposes of compari~on.'~ The dose conversion factor, C, referred to in Table 1, is used to convert the charge dose of the incident electron beam in pC cm-2 to the equivalent absorbed energy dose in Mrad in accordance with the method of ref.11. C depends on the density of the resist film and also upon its thickness and for a wide range of polymers of this type it can be approximated to 2 if the 00 c2 OL 36 oe 1c film thickness is of the order of 0.5 pm and its density is pCS in polymer (mol fraction) ca. 1.1 g cmA3. However, bulk poly-p-chlorostyrene has a den- Fig. 3 Variation of the density of spun films with composition in the sity significantly greater than this, and since the density of pCS/pMS copolymer series 404 molecular weight and therefore is determined solely by poly- mer chain microstructure.Its correlation with radiation chemi- cal yields has previously been reported for the chlorinated polymethylstyrenes.lo A typical characteristic exposure curve is shown in Fig. 4. The radiation chemical yields, together with the number- and weight-average molecular weights, completely determine the theoretical response of the polymer to the radiation by way of Inokuti’s model. It is this response that is represented by the line on the figure. The different representation depicted in Fig. 5, in accordance with the Charlesby-Pinner eq~ation,’~ is more revealing: s +,/s =Gs/2Gx+9.65 x 105/MwGxr (3) where s (= 1 -g) is the soluble fraction. Here the Inokuti fit is almost linear (theory predicts that it should be linear for materials with a polydispersity of 2) but the deviation of the data points from the theoretical curve follows a distinctive pattern; rather than being randomly distributed about the curve they appear to follow a contour defined by two intersecting curves which are represented on the plot as broken lines.This behaviour is observed for nearly all of the materials assessed during the course of this study but, as yet, no explanation can be offered; it may just be an artefact. What is clear, however, is that any lithographic contrast derived from a linear-regression analysis of the almost linear section of the plot between the gel point and the point at which 50% normalised thickness remains can give rise to a value rather different from that derived from Inokuti’s model, which for a material with a polydispersity of 1.8 is 2.45.In the case of the system of Fig. 5, the measured contrast is 2.6. In Table 1, values up to 3.0 are recorded. A limitation of the Inokuti model is that it will always provide a gel dose appropriate to the polydispersity and G values of the resist, c3, ’0 0 .-C L c 0.0 1 3 L 6 10 20 LO 60 106’ 1000 dose/pC cm-‘ Fig. 4 Characteristic exposure curve for the pCS/pMS copolymer containing 28% pCS (the curve has been fitted using the Inokuti equation and derived G values) I pGO II 000 0 05 010 0 15 R-’/M rad-’ Fig. 5 Charlesby-Pinner plot for the system of Fig. 4 J. MATER. CHEM., 1991, VOL.1 and in some cases this can lead to the ‘best fit’ deviating markedly from the data points at the low-dose end of the plot. Another feature that is apparent in Fig. 4 is a point at very high dose (1000 pC cm-*) at which there is a significant soluble fraction and a concomitant loss in resist thickness. This was again observed for the majority of samples and is believed to arise when saturation of cross-linking has been achieved. Under these circumstances, although no further cross-linking occurs (either because all possible sites for cross- linking have undergone reaction or because the rigidity brought about by cross-linking prevents sufficient molecular motion to permit further cross-link formation), scission pro- cesses continue.This can lead only to an increase in the soluble fraction and is a situation that is commonly evident when negative-working resists are exposed to doses some 200 times greater than the gel dose. For a polymer of initial number-average molecular weight of ca. 40 000, this dose would correspond to a cross-link density that would involve about one in two of the repeat units, and is a situation in which the polymer is most unlikely to undergo further cross- linking. However, the point is made more to draw attention to the effect than to explain it, for it has been common practice to normalise resist thicknesses to the thickness remaining after exposure to very high doses rather than to the initial thickness. This can lead only to erroneous analysis of the data. Fig.6 depicts the variation of intrinsic sensitivity with copolymer composition. With the exception of one pCS/oMS copolymer of low pCS content, the intrinsic sensitivities of all of the copolymers are greater than those of either of the relevant homopolymers. Both series follow the same general trend, with the pCS/pMS resists being more sensitive than the pCS/oMS materials of the same pCS content. The plots are asymmetric, with maxima at compositions corresponding to a pCS content of between 25 and 35%. A similar variation has been reported by Whipps” for copolymers of styrene and pCS used as electron-beam resists (the so-called ‘HSN/HRN’ series). Fig. 7 depicts the variation in radiation chemical yields with composition and it is clear that the trends in intrinsic sensitivity arise from a similar trend in Gx values. The corresponding Gs values are small for copolymers containing <75% pCS units and only become significant at even higher pCS contents.Though low, the Gs values appear to reach a minimum of zero at 50% pCS content, and, more significantly, they do not differ greatly between the two copolymer series.? ?Note that Gs values cannot be determined as accurately as Gx values since a small error in film thickness measurement, particularly of the original spun thickness to which all other values are normalised, will lead to a much larger error in Gsthan in G,. > lo 00 0 0 0 0 0 00 c 20 LO 60 80 100 pCS (mol%) Fig. 6 Intrinsic sensitivity uersus composition plots: (0)pCS/pMS system; (0)pCS/oMS system J.MATER. CHEM., 1991, VOL. 1 10 OF3 / \ 0 D 06 G OL C 2G LO 60 80 130 pCS (rnol%) Fig. 7 Radiation chemical yields versus composition plots: (m) G, and (0) G,Gx values for the pCS/pMS system; (0)Gs and (0) values for the pCS/oMS system Fig. 8 and 9 are plots that relate intrinsic sensitivity to the opposing influences of cross-linking and scission in the resists. They are based on derivations from the Charlesby-Pinner equation which have been described elsewhere:" Gx -0.250Gs =4.8 x 105/R0Mw (4) Gx-0.414Gs=8.0 x 10'/RO~S~w Despite the Charlesby-Pinner equation being valid only for polymers of polydispersity 2, to date all negative-working resists that cross-link by a single-stage mechanism correlate with these equations.There is a small degree of scatter, which is apparently not dependent on polydispersity.'O In the case of the present systems, the contribution from Gs is negligible, so the correlation is essentially one of intrinsic sensitivity with Gx. However, the deviation of the data points from the line I ! 1 1 1" c5 13 15 (R0M,)-'/1O6Mrad-' Fig. 8 Correlation of G values with 'gel' intrinsic sensitivity: (0)pCS/ pMS system; (0)pCS/oMS system 22 O6OL I1I ux "2 0,' 0 00 ,' 1 1 00 05 10 (R0.5M,) -'/ 1O6 Mrad-' Fig. 9 Correlation of G values with intrinsic sensitivity: (0)pCS/ pMS system; (C)pCS/oMS system is less pronounced in Fig.9 than in Fig. 8 which is an indication of the greater accuracy in the determination of RO.' as opposed to Ro. This further underpins the previously recommended use of the former in resist sensitivity assessment, despite the theoretical premise that the latter is the more fundamental parameter. Discussion The notable observations from the lithographic results are (i) that, contrary to expectation, both the pCS/oMS and pCS/ pMS systems demonstrate negligible scission over a wide range of compositions, and (ii) the synergy that arises from the mutual incorporation of pCS and MS in these resists. Although there are at least two possible explanations for the absence of radiation-induced chain scission in styrene-based polymers containing a significant amount of ortho methyl groups, no ready explanation is forthcoming for the inhibition of scission in the pCS/pMS system.However, it is now apparent that significant scission is observed to occur only in those substituted polystyrene resists that are sensitized by chloromethyl groups. Thus it is possible that it is the presence of a chloromethyl group on a ring which facilitates the abstraction of the hydrogen atom from the chain a-carbon atom which is required for chain scission to ensue. If chloro- substitution of the ring does not activate the a-carbon atom in a similar way, then there is no reason why radiation- induced chain scission should be greater for the copolymers than for the homopolymers. The Gs values for polystyrene, poly-pMS and poly-oMS are virtually zero, and for poly-pCS it is only 0.18.The enhanced intrinsic sensitivities of the copolymers of both series over those of the relevant homopolymers means that the intrinsic sensitivity of a pCS/pMS resist of ca. 30% pCS content is not significantly less than those of resists based on the corresponding VBC/MS copolymers. The intrinsic sensitivity of the optimal pCS/pMS material (1.07 x Mrad-') is half that of comparable CMS resists [i.e. poly-(pMS-co-VBC) or chlorinated poly-pMS] which is a consider- able improvement over the four-fold to five-fold difference in the intrinsic sensitivities of poly-pCS and poly-VBC. It is possible to produce resists based on VBC which display intrinsic sensitivities approaching 3 x Mrad-but such materials have large Gs values and consequently offer poor contrast.The Inokuti model predicts that contrast is invariant with molecular weight3 so, in theory, the pCS/pMS copolymer resists, as with all similar materials, can be tailored to a particular working sensitivity simply by synthesizing them with the appropriate molecular weight. With the current generation of electron-beam machines there is less emphasis on very high sensitivity than on high resolution, and the D:.' values of ca. 6 pC cm-' demonstrated here are acceptable for many types of production lithography. The predominant limitation to performance will be resist swelling during devel- opment which, as for all solvent-developed negative-working polymeric resists, inevitably worsens with increasing molecular weight.However, it has been demonstrated previously,16 through work on related systems, that this effect can be minimised by judicious selection of the developer. The existence of the maxima in the intrinsic sensitivity and Gx uersus composition plots is to be the subject of further investigation. That all the copolymers exhibit a higher intrinsic sensitivity than either of the relevant homopolymers indicates that the radiation-induced cross-linking requires the adjacency of dissimilar chain units and is related to sequence distri- butions. Assuming that this effect operates over and above the cross-linking mechanisms that are inherent to the homo- polymers, it can be rationalised in terms of the involvement CH2-CH-CH,-CH--CH2-CH-CH2-CH-I CH3 c1bIQjCH3 1 pCH,-CH-CH,-CH-I I -CH2-C -CH,-CH-I I -CH-CH,-Scheme 1 of an intramolecular excited-state charge-transfer interaction of adjacent pCS and MS chain units.The following mechanism (Scheme l), in which the charge-transfer complex reacts with a nearby MS unit of another chain to form two comparatively stable benzylic radicals as cross-link precursors, is provision- ally proposed; it is assumed that in the absence of such a reactive pathway, the exciplex would simply deactivate. One of the radicals has been represented as being chain-centred at the or-carbon atom and the other at what was formerly a substituent methyl group. The a-radical is considered to be the more probable structure for the first of these, as proton elimination from the methyl group would result in a mar- ginally less stable radical.Although this less stable structure is the chosen representation for the second radical, depending upon which group (chain methine or substituent methyl) was the most favourably placed for H-atom abstraction, either structure might result. On this basis it is also possible to rationalize the similar behaviour observed by Whipps for the poly( pCS-co-styrene) system. That cross-linking by this mechanism should occur in the vicinity of the track of an electron (either primary or second- ary) depends on three probabilities: (i) the probability (P1) that the electron encounters chlorine atoms of pCS units; (ii) the probability (P2)that the pCS units have adjacent MS units on the same chain with which to form an exciplex, and (iii) the probability (P3) that there are MS units of other chains sufficiently close as to be available for intermolecular hydrogen atom abstraction by the resultant exciplexes within their lifetime.P1 is simply proportional to mA, the mole fraction of chlorostyrene in the copolymer and P3 is similarly pro- portional to mB, the mole fraction of methylstyrene in the copolymer. Pz on the other hand, is compounded from PBAA, PAAB and PBAB, the respective probabilities that a given chlorostyrene unit has a methylstyrene unit to its left, to its right, and on both sides, and is given by P2 =PBAA+PAAB +2PBAB (6) The multiplying factor, 2, of the last term is introduced because there will be twice the probability of exciplex forma- tion if the chlorostyrene unit is bounded by methylstyrene units on both sides.Harwood and Ritchey ”have derived expressions for these sequence probabilities in terms of an index called the run J. MATER. CHEM., 1991, VOL. 1 number (R),which is defined as the average number of both A and B monomer sequences (runs) occurring in a copolymer per 100 monomer units: R(100 mA -R/2) 2(100 mA)2PBAA=PAAB = (7) PBAB =(R/2OOmA)’ (8) P2 =R/1OOmA (9) R and the overall probability of cross-link formation (P= P1P2P3)are given by Assuming that the cross-linking mechanisms inherent to the homopolymers leads to a linearly varying contribution to Gxover the whole composition range, then Gxwill be given by an equation of the form of where K, A and B are constants.For the pCS/pMS system A=0.31 and B=0.09, and for the pCS/oMS system A=0.35 and B =0.05. It is thus possible to determine optimum values of K by the application of a least-squares fitting routine to the data of Fig. 7. The lines represented on Fig. 7 have been determined in this way. The fit is quite acceptable for the pCS/oMS system for which the data points are more abundant. 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