Concentration dependence of the transient effects in monomer—excimer kinetics

J. Photochem.

Photobiol.

A:

Chem.,

57

(1991)

351-360

351

Concentration dependence of the transient monomer-excimer kinetics+* w Renliang Department

Xu and Mitchell of

Chemistry

and

effects

in

A. WinnikS Erindale

College,

University

of

Toronto,

Toronto,

Ontario

M5S

IAI

(Canada)

(Received

February 12, 1990)

Abstract Transient effects in pyrene monomer-excimer kinetics were investigated by fluorescence decay studies. The results show that, for methyl 4-(1-pyrenebutyrate), the effective capture radius R’ for the reaction in toluene in smaller than that in cyclohexane and, more surprisingly, the mutual diffusion coefficient D, in cyclohexane (but not toluene) displays a negative concentration effect.

1. Introduction The monomer-excimer transformation of ordered and amorphous systems such polymers. The use of the method derives

is a useful probe in luminescence studies as micelfes, phospholipid membranes and from the fact that excimers are formed in

a diffusion-controlled process [l]. Factors which affect the local friction (“microviscosity”) in a system act directly on the diffusion of the reactants, and this in turn affects the rate of excimer formation. Of the various chromophores which form excimers, pyrene, because of its long singlet lifetime, is the species most commonly employed. Diffusion-controlled reactions provide the richest information when studied at short times. According to the theory of diffusion-controlled processes [Z-l], the redistribution of reactants at early times appears in the rate expression as a timedependent rate coefficient (k,(t)), and the time dependence of this term provides information on the mutual diffusion coefficient (Dm) of the reactants and the effective capture radius R’ characterizing the reaction. This “transient effect” is normally difficult to study, especially in the case of excimers, where excimer dissociation to monomer complicates the theoretical description of the reaction rate [5, 61. A simple approach to this problem has been proposed by Martinho and Winnik [7] in terms of a convolution relationship between the monomer and excimer decay curves. With this method we can evaluate the transient contribution to the kinetics of excimer formation and obtain values for the mutual diffusion coefficient and reactive radius. In this way, the temperature dependence of D, has been evaluated for methyl 4-(1-pyrenyl)butyrate (1) in toluene +Transient effects in diffusion-controlled reactions no. 8. “This paper is dedicated to Professor Paul de Mayo to honour the occasion of his retirement. Canada is losing the services of an eminent photochemist. RAuthor to whom correspondence should be addressed.

lOlO-6030/91/$3.50

0 Elsevier Sequoia/Printed

in The Netherlands

352 [7] and for oligomeric polystyrenes containing the pyrene derivative on the end of the chain [S, 91. Here, we examine the kinetics of excimer formation for 1 in cyclohexane and in toluene at room temperature (22 “C). We obtain the curious result that the magnitude of the transient effect (parameter b in eqn. (6), see below) increases with the concentration of I in cyclohexane, but not in toluene, implying a concentration dependence of D,. This kind of effect is common for polymers in this concentration range, but not for small molecules. For polymers, the thermodynamics of the solvent-polymer interaction can have a large effect on the osmotic forces associated with local concentration fluctuations [lo]. For small molecules, determination of the diffusion coefficients at low concentration is much more difficult, but we expect these effects to be small.

2. Materials

and methods

4(1-Pyrenyl)butyric acid methyl ester was prepared by esterification of pyrenebutyric acid with methanol and purified by chromatography and recrystallized. Toluene and cyclohexane (Aldrich) were purified by fractional distillation. The concentration range for eyclohexane solutions was from 1.3 X lop2 M to 7X 10V4 M; for toluene solutions, from 1.3 x lo-' M to 2X 10T3 M. All solutions were degassed by a five-cycle freeze-pump-thaw process, and sealed in Pyrex tubes at a vacuum better than 1 x lo-' Torr. The fluorescence decay curves were obtained using a home-built single-photon timing apparatus [7]. The excitation wavelength was 345 nm; the monomer fluorescence was obtained at 376 nm and the excimer fluorescence at 520 nm. The &function convolution method was used to analyse the decay curves [ll]. The reference curves were obtained using degassed solutions of 2,5-bis(5-reti-butyl-2-benzoaxazolyl)thiophene (BBOT) in ethanol (T= 1.47 ns) for excimer and (p-bis(5-phenyl(oxazol-2-yl)benzene) (POPOP) in cyclohexane (T= 1.1 ns) for monomer decay curves. The reference solution was measured before and after each data collection. A criterion that the weighted maximum channel position from the reference decay curve was not shifted by more than 0.1 channel during the data measurement was adopted to ensure the stability of the apparatus and the reproducibility of the data.

3. Kinetic

expressions

The formation of an intermolecular M illuminated by incident light can ML

M*+M

1

-

k](I)

the

kM

I

k,

probe

monomer

(1)

D superscript

* indicates

the first electronically excited singlet state, k, and monomer (M*) and excimer (D*) lifetimes, and k,(t) for the excimer formation and dissociation processes scheme only k,(t)is assumed to be time dependent and is

k, are reciprocals of the excited and k_l are the rate coefficients respectively.

excimer D* from a fluorescence described as

D*

k-1

M where

be

In the

above

353 given by the approximation

theory [4]

k,(t) = 4VTtOTR

of

CR

partially

{1+

diffusion-controlled

pR exp(x2t)

reactions

at

the

first-order

erfc(xt1’2)}

(2)

where

and

(y =u”~)

erfcti)

= p

2

= s Y

exp( -Z’)

dZ

With D,=D,+D,* (=W w h ere D is the translational diffusion coefficient); NA is Avogadro’s number and R is the radius of the spherical reaction volume. The parameter p (= (kAR)/D,) measures the efficiency of excimer formation, where k is the collision or intrinsic rate constant and AR is the thickness of the spherical shell where the reaction is assumed to take place. In eqn. (2), the second term in the brace can be asymptotically expanded exp(y2)

erfc(y)

If y (=xfl”) longer, and

k,(t) =

1 = 79’4

l-

+

+ $

is much greater than we neglect the higher

4vD,N,R’

1000

unity, order

R’

1+

(n-D,#”

+ G 8~

+....

(5)

>

for example terms, then

y=

10, i.e.

at time

4rD,N,R’

or

(f-5)

1000

=

t= 100/x’

where

is an effective distance of reaction. Thus the data fitting should start after t = 100/x2 where the maximum effect of the transient term (b/~i’~) would be (PRll0~“~). At much longer times, i.e. t =b210h, the transient term becomes much less than unity, and the rate constant will reach a steady state value k,(t)(,,

o5= kl’ =

““4;roAR’

(8)

The general solution for eqn. (1) is very complicated and not practically applicable [5]. However, since the excimer is created from the excited monomer with a rate coefficient k,(t), and deactivated by a single exponential decay function with the reciprocal lifetime of AY (= k- 1 + k,), the excimer concentration at time l can be expressed as a convolution (denoted by 8) of these two processes when the extent of excimer dissociation is sufficiently small

P*lr =k~(~)MfM*l, @ exp( -A#) = Wl~kI(BHM*lo 0

exp{--A,@- 0)) de

(9)

354 This expression is rigorously correct if k,(t) is independent of time. Martinho [7] originally proposed this expression by analogy with the case of a time-dependent k,(r). Subsequent theoretical analyses have shown that when excimer dissociation is extensive, dissociation, leading to eqn. (6) must be modified because of the effect of excimer excimer reformation, on the time dependence of k,(t) [12, 131, In a region where the transient effect is negligible and k,(t) =kl’, eqn. (9) can be reduced to a time-independent form whose solution for a &pulse of exciting light is well known [l] [M*],=

P*l,

e

{(AZ --A,)

1

~I’[MIW*IO

=

Az-

exp( - AIt) + (~4, - AI) exp( - A&I

{exp(

Al

-

hf)

- exp(

-

W))

(10) (11)

with A1.2 = 3fW A,=k,‘[M]

+Ay)

--A,)*

+ I@,

+kM;

+

4kl’k_

l[M]}‘n]

A,=k,+k_,

(12) (13)

Thus by incorporating the time dependence of the monomer decay [M*], into the convolutional fitting of eqn. (9), three parameters, i.e. an amplitude, the transient term To obtain individual b ( =R’l(rrD,)l’Z) and the decay coefficient A,, can be obtained. we need to combine the b value with another independent values of R’ and D,, kl’ (eqn. (8)). Two routes can be determination of the steady state rate constant employed to obtain kl’ values from the amplitudes and the decay rates of the double exponential fitting of eqn. (10) or eqn. (11). The first is based on the sum of the two exponential decay constants (A, + A2) as a function of the sample concentration h,+hZ=k~+kD+-k_,+kl’[M]

(14)

Here the slope of the plot yields the time-independent rate constant kl’. The second method is based on both the amplitude ratio B ( = (A, - Al)/(Az --A,)) and the decay constants (A, and AZ) of the double exponential fitting of eqn. (10) k , -_ Al-&+(A*--MI)B 1

[MI(l +B)

of the excited monomer lifetime which can be In eqn. (15) kM is the reciprocal determined either from the A, values in dilute solution (kM= A,)c_-o) or from the difference between the intercept of the (A, + AZ) vs. C plot ( =kM + kD f k-,) and A, (=k,+ k-,). The second method is also a test for the concentration dependence of an error in the value of kl’ when the concentration is so k I’, but it will introduce low that the numerator and the denominator of eqn. (15) are very small. For an apparatus equipped with a flash lamp with a pulse width of a few nanoseconds, the measured fluorescence curve is related to the sample decay under a d-pulse of excitation I(r) and the lamp profile L(f) by I

I-‘(t)

=L(t)

@I(t)

=

s

L(t - @)I( 0) de

(16)

0

We use eqn. (17) for our data are measured with the same

reduction procedure: lamp profile, eqns.

since monomer and excimer decays (9) and (16) lead to the expression

355

ZEp(t)

=_4k~(t)Z~p(t)

c3

exp( -Ayt)

HereA is a normalization constant.

(17)

factor

related

to the solution

concentration

and the instrument

4. Results 4.1. Cyclohexane solution Double exponential fitting was performed on both the monomer and excimer decay curves according to eqns. (10) and (11) respectively. A linear plot of the sum of the decay rate (A, +- AZ) vs. monomer concentration (Fig. 1) gave the steady state kl’ of 4.93 x 10’ s-l and 5.09~ 10’ s-l from the excimer decay and rate constants monomer decay respectively. Calculation following eqn. (15) gave ki’ values at each individual concentration as shown in Table 1; these are in agreement with the values obtained from Fig. 1. The convolution fitting of eqn. (17) gave values of the transient term b and the decay rate A,. In the convolution fitting, it was found that the fitted b values and A, values were dependent on the channel number (C,) from which the fitting was started. If Cf was located at the neighbourhood of the lamp centroid, the fitting residue (2) was very large. 2 values showed a sudden drop after 2-3 channels from the lamp centroid entering a plateau region. This decrease in 2 value was chosen as the criterion to judge the correct Cr value where the higher order terms of eqn. (5) would vanish but the transient term would still be large enough (approximately 20%) for effective fitting. Figure 2 shows typical fitted results with the measured data. By combining eqn. (6) and eqn. (S), the values of R’ and D, could be obtained from

10

I

I

I

w-4

I

r-

CJY

0

8

2 -iii

6

x + x"

4

cr c H

0

2.Y

/ 2 0

I

I

4

8

C/10-3M

0

I

12

-2.9 16

0

120

Time

240

360

480

(nsl

Fig. 1. Plot of the sum of the two decay rates (A, +ha) from the double exponential fitting of the monomer fluorescence decay (diamonds, measured at A, = 376 nm) and excimer fluorescence decay (squares, measured at A,,=520 nm) US. the solution concentration of 1 in cyclohexane at 22 “C. The excitation wavelength was 345 nm. The full line shows the linear least-square fitting results. (A, + h2)monomcr = 2.50 X lo-* + 5.09[M] and (Al + Az)excimcr = 2.27 X lo-* + 4.93[M] (unit, ns-I). Fig. 2. Time-dependent fit of 1 in cyclohexane at 22 “C according to eqn. (17). Ce3.32~ lop3 M. The points on the top curve represent the measured excimer decay function. The lower curve is the measured monomer decay function. The top full line shows the fitted result using A,=0.0187 ns-’ and b =0.504 ns lR. The weighted residue (WR) is defined by (I,,, -Z,,r)/ Zmea I’*. The inset is the autocorrelation of the weighted residue.

356 TABLE

Kinetic

1

parameters

of excimer

k,

(M-l

1.25 x lo-’ 7.77 x 10 -3 5.52 x 1O-3 3.32~10-~ 1.34x 10-3 7.18 x 1O-J -+O

ns-l)a

formation

for methyl pyrenebutyrate

4

b (ns”‘)

0.0191 0.0190 0.0187 0.0187 0.0185 0.0178 0.0182

0.652 0.505 0.544 0.504 0.451 0.440 0.445

D, (10-h

(ns-‘)

4.85 4.80 4.97 5.37 5.01 4.47

(1) at 22 “C in cyclohexane

R’ (A)

x2

9.55 8.05 8.46 a.04 7.46 7.33 7.43

0.99 1.05 1.20 1.11 1.19 1.20

cm2 s-‘)

4.82 8.09 7.70 8.10 8.73 8.88 8.87

“Computed according to eqn. (15) by taking kM= 4.24 X 10e3 ns-I; the average of kl =5.00 M-l ns-’ is calculated by excluding the value 4.47; k,. A_37hnm=5.09 M-r ns-’ and k,. A_520,,,=4.93 ’ nsK’ computed according to eqn. (14).

0.70

I

0.60

-

0.50

- I

0.40

-

I

I

II

I

10

‘I 0

7 a

0.30 0

I

1

I

4

8

12

6 16

0

C/10-3M Fig. 3. Uncertainty range of the b values of the fitted transient of 1 dissolved in cyclohexane at 22 “C.

4

8

12

16

C/10-3M term at different

concentrations

Fig. 4. Concentration dependence of the mutual translational diffusion coefficient of 1 in cyclohexane at 22 “C. The full line is from the linear least-square fitting, D, (cm’ s-l) =8.87X lo-“(1 - 18C).

b and kl’. The results are listed in Table 1. However, even in the 2 plateau, b values gradually decreased to a plateau as Cf changed. Figure 3 shows the uncertainty ranges of the b values at different concentrations. The exponential term A, also exhibited a minor variation with concentration. From the plot of D, vs. the monomer concentration (Fig. 4, D, = 8.87 X lo-’ (1 - 18C(M)) = 8.87 x IO-” (1 - 6OC(g ml- ‘))) the diffusion second virial coefficient and the mutual diffusion coefficient at infinite dilution were estimated. Furthermore, from eqn. (6) an effective reaction distance R’ at zero concentration was obtained (R’(C -+ 0) = 7.27 A). 4.2.

Tohene solution we obtained the concentration Following the same data analysis procedure, dependence for the sum of the decay rates at different wavelengths as shown in Fig. 5. Figure 6 shows the fitted results. A similar variation of b values was observed when

357 IO”

10

0

T 7%

x +

-x

IO4

8

lo3 6

lo2 4

3.5 0

2

-3.5 0

4

a

12

0

16

C/10-3M

120

240

Time

Ins)

360

480

Fig. 5. Plot of the sum of the two decay rates (Al+ A*) from the double exponential fitting of the monomer fluorescence decay (diamonds, measured at & = 376 nm) and excimer fluorescence decay (squares, measured at A,,=520 nm) US. the solution concentration of 1 in toluene at 22 “C. The excitation wavelength was 345 nm. The full line shows the linear least-square fitting and (A, + AZ)excimer=2.78 X lo-‘+3.48[M] (unit, results. (A, + &Imonomer= 2.79 X lo-* + 3.73[M] nss’). Fig. 6. Time-dependent fit of I in toluene at 22 “C according to eqn. (17). C= 6.40 x 10p3 M. The points on the top curve represent the measured excimer decay function. The lower curve is the measured monomer decay function. The top full line shows the fitted result usingA,=0.0223 of ns-’ and b = 0.156 nsl”. WR is defined by (I,,, --Zca,)lImeal/z . The inset is the autocorrelation the weighted residue. TABLE Kinetic

2 parameters

of excimer

C (M)

k, (M-l

1.26x lo-’ 8.54 x 10 -’ 6.40 x lo--7 2.11 x 1o-A Average

3.43 3-61 3.36 27.8 3.46

formation

for methyl

pyrenebutyrate

(1) at 22 “C in toluene

A, (ns-‘)

b (ns”‘)

0.0223 0.0235 0.0223 0.0230 0.0228

0.154 0.165 0.156 0.148 0.156

ns-‘)= 1.19 1.17 1.19 1.44

“Computed according to eqn. (15) by taking kM = 5.00~ 10e3 ns-‘; the average excluding the value 27.8; k,.h_97hnm=3.73 M-r ns-r and k,,A_-520nm=3.48 M-’ according to eqn. (14). D,=14.1~10-” cm’s_‘; R’=3.28 A. Cr changed.

No

Table

is computed

2, D,

concentration using

dependence the

average

was value

observed

for

the

is calculated by ns-’ computed

b value.

Thus,

in

of b.

5. Discussion 5.1.

The steady state value kl' When the fluorescence decay profiles of 1 in cyclohexane and toluene in terms of Birks’ model [l], excellent fits to eqns. (lo), (11) and (14)

are examined are obtained.

358 The essential conclusion to be drawn from these fits is that the transient contribution to the excimer formation kinetics is small, and that these data provide precise and meaningful values of kI’. From this analysis we obtain k,’ = (5.00 + 0.20) x IO9 M-l s-l for 1 in cyclohexane and kI’ =(3.45 &0.10)x 10’ M-l s-l for 1 in toluene. We were surprised by these results, since we expected kI’ to be larger in the less viscous solvent (toluene). From eqn. (8) (103kI’ = 471_N,D,R’), we expect kI’ to decrease with increasing solvent viscosity (qO) because D, is proportional to 70- ‘. This leads to the conclusion that R’ is smaller for excimer formation in toluene than in cycIohexane. 5.2. Time-dependent

k,(t)

Although the contribution of the transient effect to the excimer formation kinetics is small, its presence and the magnitude of its effect can be determined by simultaneous analysis of the monomer and excimer decay profiles. In the application of eqn. (17) we must be careful in choosing the detection wavelength. The fluorescence intensity measured should be entirely from the excimer emission. Any residue from the monomer emission will lead to an error in the resolved b value. For example, although the monomer emission intensity at A0 =500 nm has only 1% of its peak value (A,= 376 nm), this small amount still causes an increase in b value of about 20% when compared with the measurement performed at ho=520 nm where the monomer emission intensity is only approximately 0.1% of the peak value. Thus, in choosing AO= 520 nm as a compromise between the fluorescence intensity and the interference from monomer emission, the experimental error limit in determining the b value will be a few per cent. When we fitted our experimental data to eqn. (17), we set k,(t) =n(l +bt-“‘), and determined the optimum value of b as described above. D, and R’ were then calculated by combining eqns. (6) and (8). This analysis confirms the result that R’ (cyclohexane) is larger than R’ (toluene). Experiments in toluene indicate that b, D, and R’ are independent of the concentration of 1. For experiments in cyclohexane, b varies with the concentration of 1, which leads to the very surprising conclusion that D, and R’ depend on concentration in this solvent. 5.3.

The concentration

dependence

of D

Although the concentration dependence of the mutual diffusion of polymers is well known [lo, 14, 151, such a result for small molecules is not anticipated. Few data are available, at least in the concentration range of these experiments. Values of D for small molecules in solution are commonly measured by pulsed field gradient nuclear magnetic resonance (NMR) [16]. Although this method is simple, convenient and reliable, it requires higher concentrations than those (lop3 to lo-* M) employed here. For large molecules in dilute solution, the concentration (C) dependence of the mutual diffusion coefficient is described by the expression [lo] D=D,(l+k,C+.._.)

with DO=kgTlfo, f=f,(l

(18)

and

the

friction

coefficient

+ kfC + . ...)

The concentration coefficient k, is always negative depending on the relative magnitude macromolecules, as described by the second k,=2A2M-kkf-v

f varying

with

concentration (1%

whereas kD can be positive or positive, of the thermodynamic interaction between virial coefficient A2 and the friction effects (20)

359

Here, v is rhe partial specific volume of the solvent and M is its molecular weight. In a good solvent, AZ is positive, reflecting a net repulsive interaction between solute molecules. For polymers in a 0 solvent, where by definition A*= 0, kD is negative. D will be independent of concentration when AZM= (k,+ v). Many examples of polymer diffusion with positive, negative and zero k,--, values are known. For small molecules, we expect ko “0, because AZ, M and k, are expected to be small. Our result for 1 in cyclohexane shows a relatively large negative value of k, (- 60 ml g-l), especially when compared with, for example, polystyrene (M= lo4 g mol-‘) end-labelled with pyrene (k, = - 5 ml g-‘) [17]. In this instance, the D and kD values deduced from transient effects in pyrene excimer formation studies are essentially identical to those determined unambiguously by dynamic light scattering on unlabelled polystyrene of the same molecular weight [18], indicating that pyrene as a substituent on the polymer makes a negligible contribution to the diffusion parameters of the polymer. For polystyrene of low molecular weight in cyclohexane (0 temperature, 34.5 “C), A*=O. Because the entropy of mixing of polymers and solvents is so much smaller than that of two small molecules, polymer solubility is limited to cases where A2 is positive or only slightly negative. It is thus possible, in principle, that A, for 1 in cyclohexane is more negative than A Z for polystyrene. In accord with our data, it is worth noting that the limiting solubility of pyrene in cyclohexane (X=0.01, X is the mole fraction) is eight times smaller than that in toluene (X=0.08) at 22 “C [19]. We finish this paper with a brief comparison of the D values for 1 obtained here with those obtained for pyrene itself by Heumann [ZO] from picosecond studies of the transient effect in excimer formation. His values for a series of solvents (Fig. 7) yield a linear plot of D US. Q_ To compare 1 with pyrene, we assume that D scales with M-l’*. For toluene, our scaled D value falls on the line, whereas, for cyclohexane, it is the scaled zero concentration value that fits with Heumann’s data. We take this as further support that the concentration dependence of D for 1 in qclohexane is real and that the Do value is meaningful.

--a I cn cu E u ‘p 0 -r-i

1.5-

l-

o.!i-

1

0 O-

I

I

I

0

1

2

3

77-l

(

4

103Pa-is-i)

Fig. 7. Diffusion coefficient (0) of pyrene as a function of the reciprocal of the solvent viscosity. The diamonds are taken from Heumann [20] with the full line showing the linear fitting. The squares are from the present study (D=O.SD,) after a square-root the molecular weight difference between 1 and pyrene.

molecular weight scaling for

360 Acknowledgments

the

The authors thank NSERC sample of 1 used in these

Canada for financial experiments.

support

and Mr.

M. Strukelj

for

References 1 J. B. Birks, Rep. Prog. Phys., 38 (1975) 903. 2 Ii. M. Noyes, in G. Porter (ed.), Progress in Reaction Kinetics, Vol. 1, Pergamon, Oxford, 1961, p. 129. Vol. 2, Wiley, New York, 1975. 3 J. B. Birks, Organic Molecular Photophysics, C. F. H. Tipper and R. G. Compton (eds.), Comprehensive 4 A. S. Rice, in C. H. Banford, Chemical Kinerics, Vol. 25, Elsevier, New York, 1988. W. D. Weixelbaumer, J. Burbaumer and H. F. Kauffmann, J. Chem. Phys., 83 (1985) 1980. K. Sienicki and M. A. Winnik, .I. Chem. Phys., 87 (1987) 2766. J. M. G. Martinho and M. A. Winnik, J. Phys. Chem., 91 (1987) 3640. J. M. G. Martinho, K. Sienicki, D. Blue and M. A. Winnik, J. Am. Chem. Sot., 110 (1988) 7773. 9 M. Strukelj, M.Sc. Thesis, University of Toronto, Toronto, 1988. Harper and Row, New York, 1971. 10 H. Yamakawa, Modem Theory of Polymer Solution, 11 M. Zuker, A. G. Szabo, L. Bramall, D. T. Krajcarski and B. Selinger, Rev. Sci. Insrrum., 56 (1985) 14. J. P. Pinhero and J. M. G. Martinho, submitted to J. Phys. Chem. 12 M. N. Berberan-Santos, 13 N. Agmon and A. Szabo, J. Chem. Phys., 92 (1990) 5270. 14 A. Z. Akcasu, Polymer, 22 (1981) 1169. 15 C. W. Pyun and M. Fixman, J. Chem. Phys., 41 (1964) 937. 19 (1987) 1. 16 P. Stilbs, Prog. Nucl. Magrz. Reson. Spectrosc., 17 M. Strukelj, J. M. G. Martinho, M. A. Winnik and R. P. Quirk, Macromolecules, in the press. I8 (1985) 1461. 18 K. Huber, S. Bantle, P. Lutz and W. Burchard, Macromolecules, 19 C. L. Judy, N. M. Pontikos and W. E. Acree, Jr., J. Chem. Eng. Data, 32 (1987) 60. 2. Natwforsch. Teil A, 36 (1981) 1323. 20 E. Heumann,