- Email: [email protected]
Reaction model of the dimer photoinitiation reaction in diacetylene crystals
\‘olumc
95. number
REACTION
MODEL OF THE DIMER PHOTOINITIATION
11. GROSS. W. NEUMANN
OCII~IWI
REACTION
IN DIACETYLENE
CRYSTALS
and H. SIXL
Ph.rsikalischc~r Itrsrirrr I. TkiI 3. LiniwrsinFr Snrrrgarr.
I
IS March 1983
CHEMICAL PHYSICS LETTERS
6
Pfaffenwakiring
1962: in finzl form 29 December
57. D- 7000 Snrtrgart
80. Wesr Gerrnan~
1961
Z\ 1m1tk1cslcutcllion of the primary reactions in the solid-state polymerization
of discetylene crystals is presented. It of the dimer initiation reaction st low tempemfor Itrc linc;tr imensir_\ dependence ZIPhi.& temperatures. The model involves 3x1elecrronicrtll~ excited triplet
JL‘L’~WI~IS fL?r Itlc IIIICS and
i-
c\pcrimrnrzdly
J,, .
1 I;t’=(‘-(‘=(‘K
observed non-linear intensity
(1)
dependence
preferentially with the photophysical and photochemical primary process of the polymerization reaction. III this paper we present a reaction model of the primary physical and chemical processes in the photopolymerization reaction of diacetylene crystals. The corresponding kinetic equations are solved and discussed. The resulting non-linear UV-intensity dependence of the dimer initiation reaction at low temperatures is compared with the optical absorption experiments. The rate constants involved in the dime; reaction and the quantum yield of the tow-temperature reaction are deduced from the experiment.
2. Reaction
lkc SI~0~t-ch3in dima. lrinicr. tr’lranler interndi3rrs. c‘lc’.of lfiis rstr3ordirm-y reaction have ban slrtbili/etl ai low ienlper;lIures and have been 31131~/cd bg optical 1-81 311d ESR si>ectroscopy [5]. l’our ph~~roprodurr series have been identified [6] : 111cdir3dical DR,, srrics (with 1
cxhr'n~
AC,,
series (wirh 11b 2). the dicarbene
scrirs (with II Z 7) and the stable otigomer SO,, series (wirb II 2 3). AI short chain length the DR,l iulerruediares are predominant -and are the only ones 10 be disc’usscd in this paper, since we are concerned Ut;,
5s-l
model
The individual steps of the low-temperature polymerization reaction used in our model calculation are show11 schematically in Gg. 1 by example of the DR series. The initiation reaction is a two-step reaction previously proposed by Neumann and Sk1 [7] _ The first step of this reaction involves an electronic excitation of a monomer molecule M by absorption of one photon. in this way a metastable reactive transdiradical configuration M* is produced [7,8] _In a second step the central carbon atoms of the adjacent molecule must rotate in place into the position most appropriate for the chemical reaction to the dimer molecule_ This “molecular shear” [l] is accomplished 0 009-26 14/83/0000-0000/S
03.00 0 1983 North-Holland
Volume 95, number 6
CHEMICAL PHYSICS LI~-II-ERS
R~ ,~.~,
R- °%, "
R,
R,
--K,
%'%'R
R,
• "0 O
R.
R . e"~". .
"R
---K,
vibr. "R
electr. R,..
~ "
"-..K,
"
R-.:e'R
odd.
@
"
"R
%'R
R.
R. o..
~l .o. R
%'R
{> R-~
"-..=
.~-R
'~
R-,i''R
DR 2 ground
,
odd.
"
t> R-,i ' - R
,',
t~
os
R . e"
"\R ~x~.
DR1
R~-
st
-°- R
excited store
-R
,,,
st
R.
R~e.~
R. -
R"let*
RLe
exc.
R.
R ~o.~,
18 Maxch 1983
R
R-o~"°-R
'~-R
~'" DR 3
stote
dirodicol
intermediotes
Fig. l. Schematic reaction model of the photopolymerization ieaction in diacetylene crystals. Diradical (DR) series.
by a vibrational e x c i t a t i o n ~ . A t l o w t e m p e r a t u r e s this e x c i t a t i o n is p e r f o r m e d only via internal conversion processes following p h o t o e x c i t a t i o n o f the m o n o m e r molecules. In the high-temperature limit above T 200 K thermal vibrations o f the molecules provide file p r o p e r m o t i o n s o f the molecules, resulting in a change o f the mechanism. A very preliminary i n t e r p r e t a t i o n o f the p h o t o initiation reaction [9], using two electronically excited states in the dinaer reaction M* + M* --~ M2, also leads t o a quadratic intensity d e p e n d e n c e , b u t is not in a c c o r d with the low activation energies ( o f 0 . 2 5 - 0 . 3 eV p e r molecule [ 1 0 ] ) o f the thermal addition r e a c t i o n processes. T h e alternative possibility, using t w o vibrationally e x c i t e d states ~1 + ~ ~ M2, is excluded, due t o t h e high activation energy ( o f ~1 eV [ 8 , 1 1 ] ) o f the purely thermal p o l y m e r i z a t i o n reaction. Only the c o m b i n a t i o n M* + ~ --> M2, which is used in our model, accounts for t h e e x p e r i m e n t a l observations. T h e m o s t essential p h o t o p h y s i c a l p r i m a r y processes involved in the two-step p h o t o i n i t i a t i o n reaction at l o w t e m p e r a t u r e s are shown schematically in the energy level scheme o f fig. 2. In the triplet mechanism the M* state is i n t e r p r e t e d t o be the S = 1 lowest triplet state T 1 . A n alternative singlet m e c h a n i s m with S 1 = M* is discussed in the a p p e n d i x . Photoe x c i t a t i o n o f the m o n o m e r diacetylene m o l e c u l e s i n t o t h e singlet S I s t a t e is p e r f o r m e d by a 3 0 8 nm e x c i m e r laser pulse.
S=O
S=1
singlet
triplet
$1
j--]-~" " -, ISC M" ota
2~
,/ /
i
s
vibr. ~
o
I
is' M
¢
Fi~ 2. Energy-level scheme. Interpretation and pathways of the generation and decay of ..Mand M*.
The radiationless processes (1) a n d (2) form file basis for the two-step l o w - t e m p e r a t u r e chemical reaction. T h e first step o f t h e dimer initiation is the D R 1 f o r m a t i o n , which is best r e p r e s e n t e d b y t h e m e t a s t a b l e triplet T I state M* [8]. T h e intrinsic lifet i m e o f M* is s u p p o s e d t o be o f the o r d e r o f m s t o /as. M* is p r o d u c e d by i n t e r s y s t e m crossing via p a t h (1) f r o m t h e p h o t o e x c i t e d S 1 state. T h e S 1 state is s u p p o s e d t o be p r e d o m i n a n t l y deactivated nonradiat ively - i a p a t h ( 2 ) p r o d u c i n g vibrational m o d e s p r o m o t i n g the a d d i t i o n reaction o f the dimer init i a t i o n in t h e second reaction step. T h e same m o d e s are also required in t h e subsequent single-step 585
18 ?.larch 1983
CHEMICAL PHYSICS LETTERS
Valutn~ 95. number 6
chain propagation reactions to the trimer, tetramer molecules. etc. as shown in fig. 1. At temperatures above 2300 K the %! states are produced thermally_ The crucial time for the dimer formation is given by the shortest decay time of the two states % and Xi’. At low remperarures this may be the decay time + of tbe \~ibrational excitation, which is expected to be shorter than the electronic lifetime r*. In contrast 11)the low-temperature esperiments. the situation is reversed ztt hi&er temperatures_ due to the permanent presence of thermal phonons. The temperatureindependrnt dimer formation time of =50-100 ns in the csperiments of Niederwald et al. (lo] reflects the hietinie r* of the hl‘ state. From fluorescence nie3surenicnts [lo] 3 lifetime of the St state
initial concentrations [M*(f = 0)] and [a(t = O)] are dependent on the laser-pulse intensity_ In the experiments under consideration the average penetration depth x0 of the laser light is much smaller than the crystal thickness d. Therefore, following the Lambert-Beer absorption law the absorbed photon density n and consequently [M*] and [G] become dependent on the penetration depth x following n(x) = (~V/X~)
N= A / 0
e-“l-re,
n(x) dx _
(3)
n(s) is normalized to the total number N of photons absorbed in the crystal. A is the homogeneously irradiated surface of the crystal. Provided the laser pulse time is shorter than the lifetimes r* and? of the M* and %l states. we obtain the following initial (t = 0) concentration profiles: [M*(s_o)]
= [p*l@* +pF] )z(_X)=C* 32(x)
(4a)
and [KI(X. O)] = [o$/(p*
+$)I
,2(X) = PU(X) .
(4b)
p* and j? are the intersystem-crossing and interna& conversion population probabilities of the M* and % states, (Yis the number of excited % states obtained in one relaxation process.
4. Low laser intensity 3. Kinetical equations At’tci hiscr-pulse cscitation the kinetic equations 01‘the tiipkt mechanism of the low-temperature dimer initiation reaction are given by
d]\l’]Jd/ d]3].~dr J~M~j!tlr k’=
j+-
= =
/?*(>I-] lilti]
=k,[M‘]
+]hl*]
.
[a]
.
(211) 0)
[.Gj _
(Zc)
md I? = Ii? are the first-order non-chemical tlcc:t~~constants d the hl’ nttd ti molecules. k2 is the s~co~lr!-o~-dc~rate constant of the chemical dimer initiation resction. In eq. (2b) the term k2[M*] [a] 113sbeen omitted. This accounts for the very effective non-chemical &cay of the vibrational excitation. The
In this situation the second term of eq. (Za) is neglected with respect to the first term since the dimer reaction is quadratically dependent on the light intensity_ hloreover the first term becomes unimportant (see also section 5). because dimers Mz are only formed within very short times given by ? 4 T* _ During the time of dirtier formation the concentration [M*] therefore remains almost constant and the solutions of eqs. (2a) and (2b) are given by illi*@. r)] = c* rz(_Y))
(5a)
and [n(x)
r)] = f? Jl(X) emzr
The dimer concentration by
.
(Sb) then follows from eq. (2)
[M,(x)1=
jk2Pl’kIf%x, 01
4
[Mz(x)l = f
dt
1 e+ dt = (k#)
c*&zz(x) _
(6)
0 In an optical absorption experiment the total concentration of the dimer molecules is measured. It is given by
tMzl =A y
lh$(x)l
ax
(74
0
= (x-,/k) c*c’
s
d(x)
k,[M*(x, 01 t&x, f)l dr
0
0
= k,c*~n’(x)
18 hlarch 1983
CHEMICAL PHYSICS LETTERS
Volume 95. number 6
dx
= k2i%*zz2(x)esp[(k21E)
X
semGr exp[(Ji?/~)
Fzz(x)]
Fn(x)
e-zr]
dt
0 = C* II(X) { 1 - esp [-(&/Q
Fez]
3-
(9)
The total concentration [M,] is finally given by integration overx [see eq. (7a)]. Using eq. (3) we obtain
0 =
(k#)
c*EN2/2x~
-
0)
Therefore the concentration of dimer molecules produced by one laser pulse at low laser intensity and low temperatures turns out to be quadratically dependent on the absorbed light quanta N.
5. High laser intensity In this situation the first term of eq. (?a) is neglected with respect to the second term. Eq. (2a) then may be written in the form
dIM*(x, r)l = -kz [A&, [hl*Cr, 01
t)] dr = -kz Fn(x) eekr dt. @a)
This general equation is also valid for the situation of low laser intensity yielding the quadratic intensity dependence (7b) for reasons given in the introduction of section 4. fn the limiting situation of high photon intensities, we obtain [M,] = c* N - (c*/F) (Ii&)
x&I ,
(11)
representing a linear intensity dependence_ The quantum yield $J~ of the dimer initiation reaction in this case (for N + 00) is G2 = [M2]/N=c*
(12)
and therefore is identical with the monomer diradical M* yield.
Integration finally leads to [M-(x, r)] = C* )z(x) exp [(k@)
Fn(x) (emzf - l)] _
(8b) The dimer concentration by
then follows from eq. (2%)
6. High-temperature mechanism In contrast to the two-quantum mechanism described in our reaction model of the low-temperature photodirnerization process, the formation of a polymer chain under the action of UV light at room temperature is usually considered to be the result of a single one-quantum chain-initiation event, followed by thermally activated chain growth [8,15,16]. In this high-temperature regime above WOO K the a states become thermally activated and independent of time. Consequently the change of M by UV excitation is 587
\‘itlunw
CHEMICAL
91. IIUI~I~IX 6
then ncpligible.
In this situation
(30) is substituted
PHYSICS
18 March
LETTERS
19S3
by 80_
lhll = 3 X 10~1/cn13 is the concentration of the monocV [ 101 is the activax11er IIlolectllcs. AE = 0 25-0.3 tion ewrgy itt analogy to the thern~ally activated addition reactions Xl,, + Cl - M,,, , of the diradical reacIi011 iIttcrInediates (see fig. 1). Eqs. (?a)-(2) then IctiuCc 10
initid dependence
60_
4o_
dependence o1
(14a)
0
20
40
NORMALIZED tl(M,]/&
=
/il[>lj
c-AE!kT[hl-]
_
(14b)
‘l‘he s~~lutioIis of tiiis I’irst-order linear system of cqualions xc ~~btaitied ai1:11~1gc~slyto tlte low-temperature i;IlctIl;Itiort. They arc given by lal’cl)l
= C* !\; csp-
k;,,,f)
(1%)
;111tI
= c- (kI/k,,,,)
jhlgr)]
x
11
csp(
k,,,,:)]
IS11 ,-.J*:‘IA-T A’ _
(15b)
I‘11c clccay :IOLIIisc times of hl’ a11d hl, are therefore id~ntiial. I‘lw linal diIiicI~ concent ration at I - m is Ii~ic’:~il~t!epeiident oIt the light inIeitsity in the wltoie iiitcnsil\f regime with 3 misiimni quantum yield $3, = 1.‘. which is ol~laincd wly for k‘ 4 ktot.
Oplii;ll ;tlxa~~ptioli spectroscopy is perlbntied \\ ~tii ;I ~;Iii;Il~lc tcmpmtt1re ctyoslat (Oxfort Instru~licllls. (‘I’ 204) in 3 coIiventioI1al optical absorption sl~~~tI~mc’tcr (l’hilips Sl’ S-30). The II~onunIer crysI;115;IIL*III~~uIttcd with the (100) cleavage plane perylldicular IO tlw indicatt light. The dinner photo~IIiIi:lli~~I~IcxIi~m is pcrfomlcd \viIh one pulse of an cxcitiicr 13sc’r (Lanibd;l Physics EhlC 100) with waveIcn~IlI .:Os 11111(r;e(‘l). Tltc laser pulse hits been at. IcIrIIatc~I using quartz gray filters. l:ig. 3 shows the intensity dependence of the inte*‘IA 3 * 51, optical ;ihsorl~tion of the dimer diradicztl pliot0*~roduct with zero-l~liinion transition at 421 nni.
60
80
100
UV-INTENSIN
Fig.. 3. Nornxdized intensity dependence of the dimcr diradiCA absorption. The c&xiatrd curves have been fitted to the espcrimental points applying cq. (10). The normalization is given in the tes 1.
The non-linear dependence has been fitted using eq. (IO). The normalized axes correspond to 6 X lOI4 photons per niniZ (N/.4 = 100) and to a concentration of 5 X 10’ 2 dimers per nun2 ([Mz]/A = 100). The number of photons is obtained using a (Gentcc ED 500) joulen~eter. The diIner concentration has been evaluated by integration of the optical absorption spectra. applying [ 61 [&I
= (1.6 X 1012/nsfl~OD
dii .
(16)
The optical density OD is directly Ineasured in the esperinlents, )I z 1 is the refractive index and f z 1 is the oscillator strength of the optical transition. it low laser power a quadratic intensity dependence is absented in contrast to the linear intensity dependence at high laser power. The calculated curve is fittedJo the esperirnental points using the paranieters kxo~*/k2F= 2.1 X 10t1/nun2 andc* = Q = 0.01. Therefore the quantunl yield of the dimer fortnation process is given by one dimer Inolecule per 100 photons. This is also in agreement with our ESR esperinients and is within the order of nlagnitude expected for the triplet quantum yield in diacetylene n~olecules. According to eqs. f 11) and (1’) the maxinnnn dimer quantuIn yield is obtained only at high intensities. independent of the laser power. The second parameter relates the first-order decay
\‘olume 95. number
CHE!dKAL
6
rate constant k to the second-order constant k2 by
chemical
k2 = 4.8 X IO-ls
Z _
cm2 X (c*/t?)xo
PHYSICS
rate
(17)
A detailed analysis of the rate constants kt, k* and ?; is only possible by nano- and picosecond timeresolved optical experiments of both the luminescence decay and the dimer absorption transients.
8. High-temperature
experiments
In the high-temperature limit (above ~200 K) the dimer diradicals are not stable and react to the trimer, tetramer, etc. and finally to the polymer. The total quantum yield of the photopolymerization reaction Q is then determined by the number of monomer molecules which react to the polymer upon absorption of one photon. As a consequence, it is therefore dependent on the photoinitiation process (with quantum yield I$,) and on the thermal chain propagation reaction to an average chain length of II by Q=f$-,,2_
LETTERS
18 March 1983
As discussed above, the total quantum yield Q is also dependent on the polymer chain length JZ, which from preliminary esperiments is strongly temperature dependent_ A detailed investigation of the temperature dependence of c$? and JI is in progress.
Acknowledgement This work has been supported by the Stiftung Volkswagenwerk and by the Deutsche Forschungsgemeinschaft. We are grateful to Dr. H. Niederwald for valuable information and to W. Tuffentsammer for sample preparation.
Appendix In a singlet mechanism with hi* = S, at low temperatures the M states are formed directly from the hi* states. The kinetic equations after laser-pulse escitation are then given by
(18)
d[M*]/dr
In the room-temperature experiments of Hersel [ 131, Battacharjee and Pate1 [ 141 and of Niederwald [lo], using different experimental techniques, linear intensity dependencies are obtained according to our model of section 6. Representative values of Q ranging from =O.Ol to 0.1 are evaluated. Even with JZ = IO’, representing the !owest limit of the chain length [ 12,151, a very low quantum yield 9, for the room-iempenture dimer initiation process ranging from 10m4 to 10e3 is deduced. In our low-temperature experiments, I.$, = 0.01 is obtained, which is one to two orders of magnitude larger than the corresponding room-temperature values. A drastic reduction of the dimer quantum yield at high temperatures may be explained only by a corresponding reduction of the M* lifetimes, which may be induced by both trapping of M* escitons at unreactive lattice sites and by thermally activated radiationless Tt + Su or Tt --f Sr or S, + Su transitions. Therefore the masimum quantum yield is obtained only when energy is not transferred to unreactive lattice sites. Optimal conditions are given in very pure monomer crystals at zero conversion, where the photon energy is not captured by polymer filaments.
d[M]/dr=
= -k* [hl*] - k2 [M*] [Mi] , ctk*[M]
-z
[a]
,
and d[hlz]/dr
= k2[M*]
Assuming?
@ii] _
iAl)
< r* we obtain
[M] = ct(k*/i) [?vl*] _ Eqs. (Al) d[hl*]/dr=
(AZ)
then reduce to -k*[M*]
- okl(k*/k)
[M*12
and d[M,]/dr
= ak2(k*/k’) [M*] 2 _
(AS)
The solutions of (A3) are obtained analogously to the procedure discussed in the paper. In the low-intensity limit we obtain a quadratic intensity depcndence [M2]=
(k,/4~xoA)Na.
(A4)
The M* decay and M2 rise times are given by r* and 7*/Z. In the high-intensity limit a linear intensity dependence
5s9
Volume 95. number 6
CHEBIICAL
is obtained.
The quantum yield of 1 can be reduced only by non-chemical bimolecular reactions, e.g. by singlet-singlet annihilation processes, which become important at high laser intensity.
References [ I ] G. Wcgncr. ?.lakromol Chem. 134 (1970) 219; 154 (1972) 35. I?] R.11. Baughman and R.R. Chance. in: Synthesis and properties ol~lou-dimensional marerials. eds. J.S. Miller and A. l
1 Il. _%I. \V. llrrsel and 11.C. \\‘olf.Chem. Phys. Letters 53 (1978139.
1 C. Uubrck. 11. Six1 and KC. Wolf. Chem. Phys. 32 (1978) 231;
C. Buheck. W. Neumann and H. Sixl. Chem. Phyr 48 (1980) 269: <‘. Bubcck. \\‘. Herscl. 11. SixI and J. Waldmann, Chem. l’hys. 51 (1980) 1:
590
PHYSICS
LETTERS
18 hlarch 1983
R.A. Huber. M. Schwoerer. H. Benk and H. Si.1. Chem. Phyr Letters 78 (1981) 416. [ 61 H. Gross and H. Sk-l. Chem. Phys. Letters 91 (1982)
[7] [ 81
[ 91 [I-O]
262: H. $ross.Thesis, Universitit Stuttgart (1983). W. Neumann and H. Sill. Chem. Phys. 58 (1981) 303. R.R. Chance and G.N. Pate& J. Polym. Sci. Polym. Phys. Ed. 16 (1978) 859. W. Neumann and H. siul, Chem. Phys 50 (1980) 273. H. Niederwald. H. Eichele and hf. Schwoerer, Chem. Phys. Letters 72 (1980) 242;
H. Niederwald. Thesis. Universitiit Bayreuth (1982). [ 1 l] A.R. McGhie. P.S. Kalayanaraman and A.F. Garito.
J. Polym. Sci. Polym. Letters Ed. 16 (1978) 335.
[ 121 R. Mondong and H. Bfissler. Chem. Phys. Letters 78 (1981) 371.
[ 131 W. Hersel. Thesis, Universitst Stuttgart (1981). [ 141 H.R. Battacherjee and G.N. Pate]. 1. Photochem.
16 (1981) 85. [ 151 R.R. Chance, G.N. Pate]. E.A. Turi and Y.P. Khanna, J. Am. Chem. Sot. 100 (1978) 1307; V. Enkelmann, R.J. Leyrer and G. Wegner. Makromol. Chem. 180 (1979) 1787. [ 161 R.H. Baughman, J. Chem. Phyr 68 (1978) 3110.
95. number
REACTION
MODEL OF THE DIMER PHOTOINITIATION
11. GROSS. W. NEUMANN
OCII~IWI
REACTION
IN DIACETYLENE
CRYSTALS
and H. SIXL
Ph.rsikalischc~r Itrsrirrr I. TkiI 3. LiniwrsinFr Snrrrgarr.
I
IS March 1983
CHEMICAL PHYSICS LETTERS
6
Pfaffenwakiring
1962: in finzl form 29 December
57. D- 7000 Snrtrgart
80. Wesr Gerrnan~
1961
Z\ 1m1tk1cslcutcllion of the primary reactions in the solid-state polymerization
of discetylene crystals is presented. It of the dimer initiation reaction st low tempemfor Itrc linc;tr imensir_\ dependence ZIPhi.& temperatures. The model involves 3x1elecrronicrtll~ excited triplet
JL‘L’~WI~IS fL?r Itlc IIIICS and
i-
c\pcrimrnrzdly
J,, .
1 I;t’=(‘-(‘=(‘K
observed non-linear intensity
(1)
dependence
preferentially with the photophysical and photochemical primary process of the polymerization reaction. III this paper we present a reaction model of the primary physical and chemical processes in the photopolymerization reaction of diacetylene crystals. The corresponding kinetic equations are solved and discussed. The resulting non-linear UV-intensity dependence of the dimer initiation reaction at low temperatures is compared with the optical absorption experiments. The rate constants involved in the dime; reaction and the quantum yield of the tow-temperature reaction are deduced from the experiment.
2. Reaction
lkc SI~0~t-ch3in dima. lrinicr. tr’lranler interndi3rrs. c‘lc’.of lfiis rstr3ordirm-y reaction have ban slrtbili/etl ai low ienlper;lIures and have been 31131~/cd bg optical 1-81 311d ESR si>ectroscopy [5]. l’our ph~~roprodurr series have been identified [6] : 111cdir3dical DR,, srrics (with 1
cxhr'n~
AC,,
series (wirh 11b 2). the dicarbene
scrirs (with II Z 7) and the stable otigomer SO,, series (wirb II 2 3). AI short chain length the DR,l iulerruediares are predominant -and are the only ones 10 be disc’usscd in this paper, since we are concerned Ut;,
5s-l
model
The individual steps of the low-temperature polymerization reaction used in our model calculation are show11 schematically in Gg. 1 by example of the DR series. The initiation reaction is a two-step reaction previously proposed by Neumann and Sk1 [7] _ The first step of this reaction involves an electronic excitation of a monomer molecule M by absorption of one photon. in this way a metastable reactive transdiradical configuration M* is produced [7,8] _In a second step the central carbon atoms of the adjacent molecule must rotate in place into the position most appropriate for the chemical reaction to the dimer molecule_ This “molecular shear” [l] is accomplished 0 009-26 14/83/0000-0000/S
03.00 0 1983 North-Holland
Volume 95, number 6
CHEMICAL PHYSICS LI~-II-ERS
R~ ,~.~,
R- °%, "
R,
R,
--K,
%'%'R
R,
• "0 O
R.
R . e"~". .
"R
---K,
vibr. "R
electr. R,..
~ "
"-..K,
"
R-.:e'R
odd.
@
"
"R
%'R
R.
R. o..
~l .o. R
%'R
{> R-~
"-..=
.~-R
'~
R-,i''R
DR 2 ground
,
odd.
"
t> R-,i ' - R
,',
t~
os
R . e"
"\R ~x~.
DR1
R~-
st
-°- R
excited store
-R
,,,
st
R.
R~e.~
R. -
R"let*
RLe
exc.
R.
R ~o.~,
18 Maxch 1983
R
R-o~"°-R
'~-R
~'" DR 3
stote
dirodicol
intermediotes
Fig. l. Schematic reaction model of the photopolymerization ieaction in diacetylene crystals. Diradical (DR) series.
by a vibrational e x c i t a t i o n ~ . A t l o w t e m p e r a t u r e s this e x c i t a t i o n is p e r f o r m e d only via internal conversion processes following p h o t o e x c i t a t i o n o f the m o n o m e r molecules. In the high-temperature limit above T 200 K thermal vibrations o f the molecules provide file p r o p e r m o t i o n s o f the molecules, resulting in a change o f the mechanism. A very preliminary i n t e r p r e t a t i o n o f the p h o t o initiation reaction [9], using two electronically excited states in the dinaer reaction M* + M* --~ M2, also leads t o a quadratic intensity d e p e n d e n c e , b u t is not in a c c o r d with the low activation energies ( o f 0 . 2 5 - 0 . 3 eV p e r molecule [ 1 0 ] ) o f the thermal addition r e a c t i o n processes. T h e alternative possibility, using t w o vibrationally e x c i t e d states ~1 + ~ ~ M2, is excluded, due t o t h e high activation energy ( o f ~1 eV [ 8 , 1 1 ] ) o f the purely thermal p o l y m e r i z a t i o n reaction. Only the c o m b i n a t i o n M* + ~ --> M2, which is used in our model, accounts for t h e e x p e r i m e n t a l observations. T h e m o s t essential p h o t o p h y s i c a l p r i m a r y processes involved in the two-step p h o t o i n i t i a t i o n reaction at l o w t e m p e r a t u r e s are shown schematically in the energy level scheme o f fig. 2. In the triplet mechanism the M* state is i n t e r p r e t e d t o be the S = 1 lowest triplet state T 1 . A n alternative singlet m e c h a n i s m with S 1 = M* is discussed in the a p p e n d i x . Photoe x c i t a t i o n o f the m o n o m e r diacetylene m o l e c u l e s i n t o t h e singlet S I s t a t e is p e r f o r m e d by a 3 0 8 nm e x c i m e r laser pulse.
S=O
S=1
singlet
triplet
$1
j--]-~" " -, ISC M" ota
2~
,/ /
i
s
vibr. ~
o
I
is' M
¢
Fi~ 2. Energy-level scheme. Interpretation and pathways of the generation and decay of ..Mand M*.
The radiationless processes (1) a n d (2) form file basis for the two-step l o w - t e m p e r a t u r e chemical reaction. T h e first step o f t h e dimer initiation is the D R 1 f o r m a t i o n , which is best r e p r e s e n t e d b y t h e m e t a s t a b l e triplet T I state M* [8]. T h e intrinsic lifet i m e o f M* is s u p p o s e d t o be o f the o r d e r o f m s t o /as. M* is p r o d u c e d by i n t e r s y s t e m crossing via p a t h (1) f r o m t h e p h o t o e x c i t e d S 1 state. T h e S 1 state is s u p p o s e d t o be p r e d o m i n a n t l y deactivated nonradiat ively - i a p a t h ( 2 ) p r o d u c i n g vibrational m o d e s p r o m o t i n g the a d d i t i o n reaction o f the dimer init i a t i o n in t h e second reaction step. T h e same m o d e s are also required in t h e subsequent single-step 585
18 ?.larch 1983
CHEMICAL PHYSICS LETTERS
Valutn~ 95. number 6
chain propagation reactions to the trimer, tetramer molecules. etc. as shown in fig. 1. At temperatures above 2300 K the %! states are produced thermally_ The crucial time for the dimer formation is given by the shortest decay time of the two states % and Xi’. At low remperarures this may be the decay time + of tbe \~ibrational excitation, which is expected to be shorter than the electronic lifetime r*. In contrast 11)the low-temperature esperiments. the situation is reversed ztt hi&er temperatures_ due to the permanent presence of thermal phonons. The temperatureindependrnt dimer formation time of =50-100 ns in the csperiments of Niederwald et al. (lo] reflects the hietinie r* of the hl‘ state. From fluorescence nie3surenicnts [lo] 3 lifetime of the St state
initial concentrations [M*(f = 0)] and [a(t = O)] are dependent on the laser-pulse intensity_ In the experiments under consideration the average penetration depth x0 of the laser light is much smaller than the crystal thickness d. Therefore, following the Lambert-Beer absorption law the absorbed photon density n and consequently [M*] and [G] become dependent on the penetration depth x following n(x) = (~V/X~)
N= A / 0
e-“l-re,
n(x) dx _
(3)
n(s) is normalized to the total number N of photons absorbed in the crystal. A is the homogeneously irradiated surface of the crystal. Provided the laser pulse time is shorter than the lifetimes r* and? of the M* and %l states. we obtain the following initial (t = 0) concentration profiles: [M*(s_o)]
= [p*l@* +pF] )z(_X)=C* 32(x)
(4a)
and [KI(X. O)] = [o$/(p*
+$)I
,2(X) = PU(X) .
(4b)
p* and j? are the intersystem-crossing and interna& conversion population probabilities of the M* and % states, (Yis the number of excited % states obtained in one relaxation process.
4. Low laser intensity 3. Kinetical equations At’tci hiscr-pulse cscitation the kinetic equations 01‘the tiipkt mechanism of the low-temperature dimer initiation reaction are given by
d]\l’]Jd/ d]3].~dr J~M~j!tlr k’=
j+-
= =
/?*(>I-] lilti]
=k,[M‘]
+]hl*]
.
[a]
.
(211) 0)
[.Gj _
(Zc)
md I? = Ii? are the first-order non-chemical tlcc:t~~constants d the hl’ nttd ti molecules. k2 is the s~co~lr!-o~-dc~rate constant of the chemical dimer initiation resction. In eq. (2b) the term k2[M*] [a] 113sbeen omitted. This accounts for the very effective non-chemical &cay of the vibrational excitation. The
In this situation the second term of eq. (Za) is neglected with respect to the first term since the dimer reaction is quadratically dependent on the light intensity_ hloreover the first term becomes unimportant (see also section 5). because dimers Mz are only formed within very short times given by ? 4 T* _ During the time of dirtier formation the concentration [M*] therefore remains almost constant and the solutions of eqs. (2a) and (2b) are given by illi*@. r)] = c* rz(_Y))
(5a)
and [n(x)
r)] = f? Jl(X) emzr
The dimer concentration by
.
(Sb) then follows from eq. (2)
[M,(x)1=
jk2Pl’kIf%x, 01
4
[Mz(x)l = f
dt
1 e+ dt = (k#)
c*&zz(x) _
(6)
0 In an optical absorption experiment the total concentration of the dimer molecules is measured. It is given by
tMzl =A y
lh$(x)l
ax
(74
0
= (x-,/k) c*c’
s
d(x)
k,[M*(x, 01 t&x, f)l dr
0
0
= k,c*~n’(x)
18 hlarch 1983
CHEMICAL PHYSICS LETTERS
Volume 95. number 6
dx
= k2i%*zz2(x)esp[(k21E)
X
semGr exp[(Ji?/~)
Fzz(x)]
Fn(x)
e-zr]
dt
0 = C* II(X) { 1 - esp [-(&/Q
Fez]
3-
(9)
The total concentration [M,] is finally given by integration overx [see eq. (7a)]. Using eq. (3) we obtain
0 =
(k#)
c*EN2/2x~
-
0)
Therefore the concentration of dimer molecules produced by one laser pulse at low laser intensity and low temperatures turns out to be quadratically dependent on the absorbed light quanta N.
5. High laser intensity In this situation the first term of eq. (?a) is neglected with respect to the second term. Eq. (2a) then may be written in the form
dIM*(x, r)l = -kz [A&, [hl*Cr, 01
t)] dr = -kz Fn(x) eekr dt. @a)
This general equation is also valid for the situation of low laser intensity yielding the quadratic intensity dependence (7b) for reasons given in the introduction of section 4. fn the limiting situation of high photon intensities, we obtain [M,] = c* N - (c*/F) (Ii&)
x&I ,
(11)
representing a linear intensity dependence_ The quantum yield $J~ of the dimer initiation reaction in this case (for N + 00) is G2 = [M2]/N=c*
(12)
and therefore is identical with the monomer diradical M* yield.
Integration finally leads to [M-(x, r)] = C* )z(x) exp [(k@)
Fn(x) (emzf - l)] _
(8b) The dimer concentration by
then follows from eq. (2%)
6. High-temperature mechanism In contrast to the two-quantum mechanism described in our reaction model of the low-temperature photodirnerization process, the formation of a polymer chain under the action of UV light at room temperature is usually considered to be the result of a single one-quantum chain-initiation event, followed by thermally activated chain growth [8,15,16]. In this high-temperature regime above WOO K the a states become thermally activated and independent of time. Consequently the change of M by UV excitation is 587
\‘itlunw
CHEMICAL
91. IIUI~I~IX 6
then ncpligible.
In this situation
(30) is substituted
PHYSICS
18 March
LETTERS
19S3
by 80_
lhll = 3 X 10~1/cn13 is the concentration of the monocV [ 101 is the activax11er IIlolectllcs. AE = 0 25-0.3 tion ewrgy itt analogy to the thern~ally activated addition reactions Xl,, + Cl - M,,, , of the diradical reacIi011 iIttcrInediates (see fig. 1). Eqs. (?a)-(2) then IctiuCc 10
initid dependence
60_
4o_
dependence o1
(14a)
0
20
40
NORMALIZED tl(M,]/&
=
/il[>lj
c-AE!kT[hl-]
_
(14b)
‘l‘he s~~lutioIis of tiiis I’irst-order linear system of cqualions xc ~~btaitied ai1:11~1gc~slyto tlte low-temperature i;IlctIl;Itiort. They arc given by lal’cl)l
= C* !\; csp-
k;,,,f)
(1%)
;111tI
= c- (kI/k,,,,)
jhlgr)]
x
11
csp(
k,,,,:)]
IS11 ,-.J*:‘IA-T A’ _
(15b)
I‘11c clccay :IOLIIisc times of hl’ a11d hl, are therefore id~ntiial. I‘lw linal diIiicI~ concent ration at I - m is Ii~ic’:~il~t!epeiident oIt the light inIeitsity in the wltoie iiitcnsil\f regime with 3 misiimni quantum yield $3, = 1.‘. which is ol~laincd wly for k‘ 4 ktot.
Oplii;ll ;tlxa~~ptioli spectroscopy is perlbntied \\ ~tii ;I ~;Iii;Il~lc tcmpmtt1re ctyoslat (Oxfort Instru~licllls. (‘I’ 204) in 3 coIiventioI1al optical absorption sl~~~tI~mc’tcr (l’hilips Sl’ S-30). The II~onunIer crysI;115;IIL*III~~uIttcd with the (100) cleavage plane perylldicular IO tlw indicatt light. The dinner photo~IIiIi:lli~~I~IcxIi~m is pcrfomlcd \viIh one pulse of an cxcitiicr 13sc’r (Lanibd;l Physics EhlC 100) with waveIcn~IlI .:Os 11111(r;e(‘l). Tltc laser pulse hits been at. IcIrIIatc~I using quartz gray filters. l:ig. 3 shows the intensity dependence of the inte*‘IA 3 * 51, optical ;ihsorl~tion of the dimer diradicztl pliot0*~roduct with zero-l~liinion transition at 421 nni.
60
80
100
UV-INTENSIN
Fig.. 3. Nornxdized intensity dependence of the dimcr diradiCA absorption. The c&xiatrd curves have been fitted to the espcrimental points applying cq. (10). The normalization is given in the tes 1.
The non-linear dependence has been fitted using eq. (IO). The normalized axes correspond to 6 X lOI4 photons per niniZ (N/.4 = 100) and to a concentration of 5 X 10’ 2 dimers per nun2 ([Mz]/A = 100). The number of photons is obtained using a (Gentcc ED 500) joulen~eter. The diIner concentration has been evaluated by integration of the optical absorption spectra. applying [ 61 [&I
= (1.6 X 1012/nsfl~OD
dii .
(16)
The optical density OD is directly Ineasured in the esperinlents, )I z 1 is the refractive index and f z 1 is the oscillator strength of the optical transition. it low laser power a quadratic intensity dependence is absented in contrast to the linear intensity dependence at high laser power. The calculated curve is fittedJo the esperirnental points using the paranieters kxo~*/k2F= 2.1 X 10t1/nun2 andc* = Q = 0.01. Therefore the quantunl yield of the dimer fortnation process is given by one dimer Inolecule per 100 photons. This is also in agreement with our ESR esperinients and is within the order of nlagnitude expected for the triplet quantum yield in diacetylene n~olecules. According to eqs. f 11) and (1’) the maxinnnn dimer quantuIn yield is obtained only at high intensities. independent of the laser power. The second parameter relates the first-order decay
\‘olume 95. number
CHE!dKAL
6
rate constant k to the second-order constant k2 by
chemical
k2 = 4.8 X IO-ls
Z _
cm2 X (c*/t?)xo
PHYSICS
rate
(17)
A detailed analysis of the rate constants kt, k* and ?; is only possible by nano- and picosecond timeresolved optical experiments of both the luminescence decay and the dimer absorption transients.
8. High-temperature
experiments
In the high-temperature limit (above ~200 K) the dimer diradicals are not stable and react to the trimer, tetramer, etc. and finally to the polymer. The total quantum yield of the photopolymerization reaction Q is then determined by the number of monomer molecules which react to the polymer upon absorption of one photon. As a consequence, it is therefore dependent on the photoinitiation process (with quantum yield I$,) and on the thermal chain propagation reaction to an average chain length of II by Q=f$-,,2_
LETTERS
18 March 1983
As discussed above, the total quantum yield Q is also dependent on the polymer chain length JZ, which from preliminary esperiments is strongly temperature dependent_ A detailed investigation of the temperature dependence of c$? and JI is in progress.
Acknowledgement This work has been supported by the Stiftung Volkswagenwerk and by the Deutsche Forschungsgemeinschaft. We are grateful to Dr. H. Niederwald for valuable information and to W. Tuffentsammer for sample preparation.
Appendix In a singlet mechanism with hi* = S, at low temperatures the M states are formed directly from the hi* states. The kinetic equations after laser-pulse escitation are then given by
(18)
d[M*]/dr
In the room-temperature experiments of Hersel [ 131, Battacharjee and Pate1 [ 141 and of Niederwald [lo], using different experimental techniques, linear intensity dependencies are obtained according to our model of section 6. Representative values of Q ranging from =O.Ol to 0.1 are evaluated. Even with JZ = IO’, representing the !owest limit of the chain length [ 12,151, a very low quantum yield 9, for the room-iempenture dimer initiation process ranging from 10m4 to 10e3 is deduced. In our low-temperature experiments, I.$, = 0.01 is obtained, which is one to two orders of magnitude larger than the corresponding room-temperature values. A drastic reduction of the dimer quantum yield at high temperatures may be explained only by a corresponding reduction of the M* lifetimes, which may be induced by both trapping of M* escitons at unreactive lattice sites and by thermally activated radiationless Tt + Su or Tt --f Sr or S, + Su transitions. Therefore the masimum quantum yield is obtained only when energy is not transferred to unreactive lattice sites. Optimal conditions are given in very pure monomer crystals at zero conversion, where the photon energy is not captured by polymer filaments.
d[M]/dr=
= -k* [hl*] - k2 [M*] [Mi] , ctk*[M]
-z
[a]
,
and d[hlz]/dr
= k2[M*]
Assuming?
@ii] _
iAl)
< r* we obtain
[M] = ct(k*/i) [?vl*] _ Eqs. (Al) d[hl*]/dr=
(AZ)
then reduce to -k*[M*]
- okl(k*/k)
[M*12
and d[M,]/dr
= ak2(k*/k’) [M*] 2 _
(AS)
The solutions of (A3) are obtained analogously to the procedure discussed in the paper. In the low-intensity limit we obtain a quadratic intensity depcndence [M2]=
(k,/4~xoA)Na.
(A4)
The M* decay and M2 rise times are given by r* and 7*/Z. In the high-intensity limit a linear intensity dependence
5s9
Volume 95. number 6
CHEBIICAL
is obtained.
The quantum yield of 1 can be reduced only by non-chemical bimolecular reactions, e.g. by singlet-singlet annihilation processes, which become important at high laser intensity.
References [ I ] G. Wcgncr. ?.lakromol Chem. 134 (1970) 219; 154 (1972) 35. I?] R.11. Baughman and R.R. Chance. in: Synthesis and properties ol~lou-dimensional marerials. eds. J.S. Miller and A. l
1 Il. _%I. \V. llrrsel and 11.C. \\‘olf.Chem. Phys. Letters 53 (1978139.
1 C. Uubrck. 11. Six1 and KC. Wolf. Chem. Phys. 32 (1978) 231;
C. Buheck. W. Neumann and H. Sixl. Chem. Phyr 48 (1980) 269: <‘. Bubcck. \\‘. Herscl. 11. SixI and J. Waldmann, Chem. l’hys. 51 (1980) 1:
590
PHYSICS
LETTERS
18 hlarch 1983
R.A. Huber. M. Schwoerer. H. Benk and H. Si.1. Chem. Phyr Letters 78 (1981) 416. [ 61 H. Gross and H. Sk-l. Chem. Phys. Letters 91 (1982)
[7] [ 81
[ 91 [I-O]
262: H. $ross.Thesis, Universitit Stuttgart (1983). W. Neumann and H. Sill. Chem. Phys. 58 (1981) 303. R.R. Chance and G.N. Pate& J. Polym. Sci. Polym. Phys. Ed. 16 (1978) 859. W. Neumann and H. siul, Chem. Phys 50 (1980) 273. H. Niederwald. H. Eichele and hf. Schwoerer, Chem. Phys. Letters 72 (1980) 242;
H. Niederwald. Thesis. Universitiit Bayreuth (1982). [ 1 l] A.R. McGhie. P.S. Kalayanaraman and A.F. Garito.
J. Polym. Sci. Polym. Letters Ed. 16 (1978) 335.
[ 121 R. Mondong and H. Bfissler. Chem. Phys. Letters 78 (1981) 371.
[ 131 W. Hersel. Thesis, Universitst Stuttgart (1981). [ 141 H.R. Battacherjee and G.N. Pate]. 1. Photochem.
16 (1981) 85. [ 151 R.R. Chance, G.N. Pate]. E.A. Turi and Y.P. Khanna, J. Am. Chem. Sot. 100 (1978) 1307; V. Enkelmann, R.J. Leyrer and G. Wegner. Makromol. Chem. 180 (1979) 1787. [ 161 R.H. Baughman, J. Chem. Phyr 68 (1978) 3110.