9507
J. Phys. Chem. 1992, 96, 9507-9512 Nz, = N1,OkU - l/ak-'(l/a = NI,o(!)(~ - l/W1(l/a' By induction Nx,k
= Nl,O(kl)(l - l / a k - ' + ' ( l / a P 1
For both Z >> 1 and k Poisson distribution Nx,k/Nl,O
(4415)
>> x, this can be approximated to the (xP1/(x- I)!) exp(-x)
where A = (x) = k/Z. Registry No. c-Caprolactam, 105-60-2.
References and Notes (1) Suematsu, K.; Okamoto, T.Colloid Polym. Sci. 1992,270,405,421. (2) Suematsu, K.; Okamoto, T.J. Phys. SOC.Jpn. 1992, 61, 1539. (3) (a) Carothers, W. H. Chem. Reo. 1931,8,353. (b) Flory, P. J. J. Am. Chem. Soc. 1940,62, 2255. (c) Kotliar, A. M.J. Polym. Sci. 1981, 16, 367. (4) (a) Brubaker, M.
M.;Coffman, D. D.; McGrew, F. C. US Patent
2,339,237, 1944. (b) Beste, L. F.; Houtz, R. C. J. Polym. Sci. 1952.8, 395. (c) Han, M.J.; Kang, H. C.; Choi, K. B. Mucromolecules 1986, 19, 1649.
(5) (a) Vert, M.;Chabot, F.; LeRay, J.; Chritel, P. Mukromol. Chem. Suppl. 1981,5,30. (b) Dayte, K. V.; Raje, H. M.J. Appl. Polym. Sci. 1985, 30,205. (c) Muhlebach, A.; Economy, J.; Johnson, R. D.; Karis, T.;Lyerla, J. Mucromolecules 1990. 23, 1803. (6) Carmichael, J. B.; Winger, R. J . Polym. Sci. 1965, 3, 971. (7) Stem, M. D.; Tobolsky, A. V. J . Chem. Phys. 1946,14, 93.
(8) (a) Grever, G. Mukromol. Chem. 1957, 22, 183. (b) Grever, G.; Oechmann, W. Mukromol. Chem. 1961,44228. (9) Catcheside, D. G.; Lea,D. E.; Thoday, J. M. J. Genet. 1945,47,113. (10) Alberts, B.; Bray, D.; Lewis, J.; Rail, M.; Roberts, K.; Watson, J. D. Moleculur Biolom of the Cell; Kyoikusha: Tokyo, 1985. (11) Flory, P. J. Chem. Rev. 1946,39, 137. (12) Tobolsky, A. V., Eisenberg, A. J. Am. Chem. SOC.1%9,8/, 2302: 1960,82,289. (13) Lertola, J. G. J. Polym. Sei. Part A,: Polym. Chem. 1990,28,2793. (14) Kondepudi, D. K.; Pojman, J. A.; Mansour, M.M.J. Phys. Chem. 1989, 93, 593 1. (1 5) Pojman, J. A.; Garcia, A. L.; Kondepudi, D. K.; Van den Bnxck, C. J. J. Phys. Chem. 1991,95, 5655. (16) (a) Kuhn, W. Kolloid 2.1934,68,2. (b) Jacobson, H.; Stockmaya, W . H. J. Chem. Phvs. 1950.18, 1600. (17) Zjmm, B. H.; Stockmayer, W. H., J . Chem. Phys. 1949, 17, 1301. (18) Fuman, M. J. Chem. Phys. 1955, 23, 1656. (19) lmoto, M.Kuguku 1960, 15, 540 (in Japanese). (20) Hoshino, K. Nihonkugukkuishi 1940, 61, 475 (in Japanese). (21) Mattes, A. Mukromol. Chem. 1951, 5, 197; 1954, 13, 90. (22) Kruissink, C. A.; Van der Want, G. M.; Staverman, A. J. J . Polym. Sci. 1958, 30, 67. (23) Hermans, P. H.; Heikens, D.; Van Velden, P. F. J. Polym. Sci. 1958, 30, 81. (24) (a) Wiloth, F. Kolloid 2.1955, 144, 58. (b) Wiloth, F. Kolloid 2. 1958,160,48. (c) Wdoth, F. Z . Phys. Chem. N.F., 1%7,11,78. (d) Wiloth, F. Mukromol. Chem. 1959.30, 189. (25) Ogata, N. Mukromol. Chem. 1959,30, 212. (26) Meggy, A. B. J. Chem. Soc. 1953,796. (27) Spoor, H.; Zahn, H. 2.A w l . Chem.1959,168, 190. (28) Andrews, J. M.;Jones, F. R.; Semlyen, J. A. Polymer 1974, IS, 420. (29) See The Merck Index; Merck & Co.: Inst. 1976; p 59.
Thermodynamic Analysis of Scanning Calorimetric Transitions Observed for Dilute Aqueous Solutions of ABA Block Copolymers N. M. Mitchard, A. E. Beezer,' J. C. Mitchell, J. K.Armstrong? B. Z. Chowdhry,+ S. Leharne? and G. Bucktod Chemical Laboratory, The University of Kent at Canterbury, Canterbury, Kent, CT2 7NH, U.K, (Received: April 8, 1992; In Final Form: July 18, 1992)
Dilute aqueous solutions of a series of poly(oxyethylene)-poly(oxypropylene)-poly(oxyethylene) block polymers have been shown to undergo phase transitions. A high-sensitivity differential scanning calorimetric (HSDSC) study of these block copolymers has enabled the thermodynamic parameters for the phase transitions to be obtained. The thermodynamic parametera are all dependent on poly(oxypropy1ene) content of the polymer and not on poly(oxyethy1ene) content or total polymer molecular mass. The importance of the poly(oxypropy1ene) in determining the aqueous solution phase properties of these polymers is further emphasized by the positive value for the heat capacity change from pre- to postphase transition. A positive heat capacity change is characteristic of "melting" of water ordered by exposad nonpolar groups. The work reported in this paper shows that the thermodynamic parameters describing the polymer phase transitions can be derived from basic thennodynamic principles and from consideration of the poly(oxypropy1ene) content. The theoretical analysis described in this paper also predicts that these polymers should undergo a second phase transition at high temperature and indeed these transitions have been detected by HSDSC.
Iatroduction
Previous work by Rassing et al.5 and Gilbert et a1.6 and our own investigation of P237 (P237 consists of 70% ethylene oxide (Eta) and 304%Propylene Oxide (pro) (p237; aveWetotal molar M1.t 7700 of which MI for E t 0 = 5390 and Mr for Pro = 2310)) by NMR3 show that the temperature associated with the phase transition is related to the properties of the hydrophobic portion of the molecule. The observed positive heat capacity H(OCH~-CH~)a-(OCHMeCH~)~-(O-CH2-CH2)oOH chanae for the ore- to DostDhaSC transition M related to. as noted by P&lov,8 "&e gradA melting of water ordered by the expo~urc and therefore have distinct hydrophilic and hydrophobic regions. Of non-polar groUP***" (see refs 7-1 By altering the size and ratio of the two regions it is possible to It was suggestedlZ that the thermodynamic parameters dealter the solution properties of the polymers and so to affect the scribing the phase transitions could be fitted to equations of the physicochemical characteristics of the phase transitions. form X,, = aMr(Pro) bMr(Eto) (1) iSchool of Biological and Chemical Sciences, Greenwich University, London SEI8 6PF, UK. wherex is a thermodynamic f U l W h Such as enthalpy Or e n m y tSchool of Pharmacy, University of London, Brunswick Square, London WClN 1AX. UK. change and a and 6 are constants. This functional form requires
I,,
p ~ b ~ ~ t i o n sit1was -4 that in dilute solutions of poloxamers, poly(oxyethy1ene)-poly(oxypropy1ene)-poly(oxyethylene), ABA block copolymers undergo reversible phase transitions. The poloxamers have the general formula
+
0022-3654/92/2096-9507$03.00/00 1992 American Chemical Society
Mitchard et al.
9508 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 TABLE I: Cbmctwbtia of t k Polos8" Stpdied mly(oxyethy1ene) content (%) 40 50 70 80 poloxamer PI84 E35 P407 P338 P237 P308 P207 P238 P188 Pl08 36 30
EXCES8 Cpf/kJ/K/mol)
1
A
t
I\
I\
TEMPERATURE (K) Figure 2. High-sensitivity DSC scam for the poloxamer 8 series. The poloxamers represented are, from the low-temperature end, P338, P238, P308,P188,and P108.
.',
360
Transition Temperature (/K)
7
+ " 270
ZOO
290
300
310
320
350
340
360
360
370
TEMPERATURE (K) Figure 1. High-sensitivity DSC scans for the poloxamer 7 series. The poloxamers represented are, from the low-temperature end, P407,P237, and P207.
that the thermodynamic parameter be linearly dependent on the molecular mass of poly(oxypropy1ene) and of poly(oxyethy1ene) content. This has been shown not to be the case2s4and all thermodynamic parameters show a dependence on poly(oxypropy1ene) content alone. It is the aim of the work reported in this paper to show that the thermodynamic parameters for the phase transitions can be calculated from their dependence on the poly(oxypropy1ene) content of the poloxamer.
Methods The poloxamers studied were donatad by IC1 (Cleveland, U.K.) and are described in Tables I and 11. The purity of the samples was established by the presence of a single elution peak after gel permeation chromatography. Solutions, at a concentration of 5 mg ~ m - were ~ , prepared by dissolution of the polymers in phosphate buffer at pH 7.2 (0.03 MI. The polymers studied are surface active agents and therefore they were dissolved by gentle stirring in order to avoid the creation of foam. These solutions were then equilibrated for 1 h before the HSDSC scans were run. All poloxamer samples were prepared in phosphate buffer solution as described above: constant pH and ionic strength was ensured through the use of this buffer. The effect of added electrolytes and their concentrations will be discussed in a future paper. Although the nonionic poloxamers will not be affected by pH, a pH of 7.2 was chosen because of the poloxamers' use in drug targeting systems. The solution-phase HSDSC measurements were conducted in a Microcal M C 2 microcalorimeter (Microcal, Amherst, MA). The calorimeterand data acquisition were controlled by dedicated software, DA2 (Mi&, Amherst, MA). The calorimetric scans were conducted at a rate of I K min-I, and calibration was by use of the method of electrical substitution. Heating (and cooling) scans were conducted over the range lodo K h-l. The scans did not show any hysteresis and the transitions are not kinetically limited. Results .ed Dbcllseioll All investigations were performed at a fmed concentration of 5 mg ~ m - ~Studies . of phase transitions of these polymers as a function of concentration will be publishedL3subsequently, although investigationsof partial molar volume and of molar mass indicate the presence of only monomeric species at the studied concentration.
320
-
+ + +
+ 4-
300 -
+ t
6
280 900
1,900
1,400
2,400
M,of
2,900
3,400
3,900
Pro
Figwe 3. Transition temperature maxima for poloxamer phase traneitions. The transition temperature maxima for the poloxamers is dependent on the poly(oxypropy1ene) content. Delta H (/kJ/mol) 250 1
I
200 -
+++
+
150 I
900
1,400
+ +
1,900
I
2,400
M, of
2,900
3,400
3,900
Pro.
Elgm 4. Phase transition cnthalpica for the poloxamer phase transitions. The transition enthalpy for the poloxamers is dependent on the poly(oxypropylene) content.
The thermograas for the four series of poloxamersare displayed in Figures 1 and 2, and the derived thermodynamic parameters are displayed in Table 11. These phase transitions have been shown to be associated with the 'melting" of water associated with the hydrophobic, poly(oxypropylene), portion of the molecule.14 The dependence of the thermodynamic parameters on the poly(oxypropy1ene) content can be seen in Figures 3 and 4, where the thermodynamic parameters are plotted against the poly(oxypropy1ene) relative molecular mass (M,). No relationship is found between the thermodynamic parameters and total molecular mass or polyoxyethylene content. Although there is a dependence of the thermodynamic parameters on pdy(oxypr0pyIene) content of the poloxamer, it is pasible that the correlation could be improved in two ways: first, by
HSDSC Study of ABA Block Copolymers
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9509
TABLE II: Tbcrmadp.mic Parmetem for the Sdutioa-PhUc Tnnritim of Pdouwrs polywd/ poloxamer Mr dupenity pro0 EtO. T,/K W mol-’ 4Ooo 5000 lo00 P108 349.7 42 6680 328.7 1670 8350 67 P188 8640 10800 185 317.1 1.3 2160 P238 148 10800 312.4 2700 P308 13500 11200 P338 302.8 1.4 2800 14OOO 158 4620 319.5 1980 128 P207 6600 5390 306.9 1.2 2310 7700 193 P237 8750 297.7 12500 1.5 3750 226 P407 2400 307.0 4650 1.2 2250 186 P235 1740 P184 1160 313.7 2900 149
AKnI
kJ mol-’
kJ mol K-I
241 299 247 319 420 234 318 423 322 217
2.5 5.6 13.7 14.6 21.8 8.9 19.5 32.5 19.0 12.6
T@C 17.0 11.8 10.8 9.5 6.3 13.3 8.7 6.4 8.7 11.3
See text for definitions.
decreasing the molecular weight distributionof the samples studied and second by increasing the poly(oxypropy1ene) content. As the poly(oxypropy1ene) content of the poloxamer decreases there is an increase in the transition half-width. This increases the error associated with the determination of the phase transition enthalpy because of the greater temperature range over which the base line is undetermined during the transition. More recently, study of the solution properties of poloxamers by isothermal calorimetry13shows that structural rearrangement of the poloxamer occurs in solution for up to 40 h after dissolution. The short equilibration time prior to the HSDSC scans reported in this paper may contribute to the reported correlations.
Delta Cp UkJlmollK) 101
Theoretical Anrlystp of the T h e d p r m i c Parameters
-2
In calculating the thermodynamic properties of a phase transition for any molecule, the most important and yet the most difficult piece of information to obtain is the heat capacity change associated with the pre- to postphase transition. The problems encountered in determining the pre to posttransition heat capacity change are twofold: first, the base line cannot be determined during the phase transition; second, the fact that water is liquid over a narrow temperature range means that baselines are short, making accurate heat capacity-temperature correlation difficult. Spline base-line analysis was used to predict the transition base lines and then the pre- to posttransition heat capacity change was calculated from the transition enthalpy using the following relationship
ACp = 6AH/6T
(2)
where ACp is the heat capacity change and AH is the enthalpy change.
ReLtioaship between Heat Capacity and Poly(oxypropylene) Content The systems under observation are not ideal and, as with all polymers, there is a molecular weight distribution. The heat capacity change is dependent on the degree of conformational change (i.e., the ratio of poloxamer in the pre- to posttransitional states) and this will be dependent on the molecular weight distribution. Due to the nonideal systems being studied a modified form of eq 2 was used:
ACpc= A 4 H / A T (3) where AC; is the heat capacity change, A@ is the experimental transition enthalpy and AT is the temperature range over which the transition ocws. The values of AC; have been plotted against the relative molecular mass of poly(oxypropy1ene) for the polymers studied (Figure 5). The results show a direct dependence of the heat capacity change on the poly(oxypropy1ene) content of the poloxamer and the linear relationship can be represented by and equation of the form AC’ = Cp” + Cp*Mr (4) where Cp”is the limiting heat capacity when the relative molecular mass of the poly(oxypropy1ene) tends to zero, Cp* is the dependence of the heat capacity on poly(oxypropy1ene) content, and M,is the poly(oxypropy1ene) relative molecular mass. The main
a84-
2-
“Y 0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
M,
of Pro Figure 5. Heat capacity change for poloxamer phase transitions. The change in heat capacity for the pre- to postphase transition is linearly dependent on the poly(oxypropy1ene) content.
consequence of the dependence of the heat capacity on the poly(oxypropy1ene) relative molecular mass is that the other thermodynamic parameters that describe the phase transitions are also only dependent on the poly(oxypropy1ene) relative molecular mass. It is therefore possible to predict these thermodynamic parameters for any poloxamer. The graph of the transition heat capacity change versus the poly(oxypropy1ene) relative molecular mass (Figure 5 ) lends further support to the importance of the poly(oxypropy1ene) content, because, as the relative molecular mass of the poly(oxpropylene) decreases the calorimetric heat capacity becomes less positive. At a poly(oxypropy1enc) relative molecular maa of approximately 700 the heat capacity change for a transitionwould be zero; this therefore, defines a polymer relative molecular maas for which no phase transition would be observable; i.e., below a relative molecular maw of 700 the polymer will not undergo a phase transition which implies that solvation is favorable at all temperatures. Indeed, ~chmolka~~ points out that,above a relative molecular mass of about 750, poly(oxypropy1ene) changes from beiig water soluble to being relatively insoluble in water,
Relatiomhip between Enthalpy .nd Poly(oxypmpykne) Content If it is assumed that the heat capacity of the transition is independent of the temperature, which is clearly not the aue but will not deet the final calculation, then it is paesible to determine the value of the enthalpy change between pre and posttransition states at all temperatures. The following (Kirchoff) equation is Used
where @(T) is the enthalpy difference at temperature T, -( is the enthalpy difference at the transition temperature and 7& is the transition temperature. The dependence of the transition enthalpy, @(0, on temperature is displayed in Figure 6. The values of A!H( and AC; are experimental results, and therefore the value of A,H( T )
n)
3)
Mitchard et al.
9510 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992
(a)
(a) 2,000
Delta H (lkJlmollk)
1,000
2m t--. \
-..._
0
-
I
1,000
-
-2,000
t-
-P207
-3,000 200
260
’.._P2S7 300
-P407
360
P2S8
400
460
-P184
600
660
600
-6 200
300
260
1 360
400
460
600
660
600
Temperature (K)
Temperature (K)
(b)
(b) Dqltr H (IkJIMol) 1,000I
1
31s 2
5-
-1
\-....
-2t -
I
2,000 200
I 260
300
360
400
460
600
660
600
Temperature (K)
Figure 6. Theoretical enthalpy change for poloxamer phase transitions.
for a poloxamer at its transition temperature will be independent of the assumption that the heat capacity is invariant with respect to temperature. The relationship between the transition enthalpy and the temperature can be represented by the following equation s&
AH“ + ~
x M- T(AC,” ,
+ AC,,M,)
(6)
where AH“ is the transition enthalpy at 0 K and zero poly(oxypropylene) content and AEP reprcaents the dependence of the heat capacity on poly(oxypropy1ene) content at 0 K. If in eq 6 temperature is replaced by the phase transition temperature maxima then the phase transition enthalpies can be calculated. Relrtioasbip between Entropy md Poly(oxypropylene)
Content The relationship between entropy and the heat capacity is described by the following equation: 4 C p / T = S@/ST
(7)
By assuming, as before, that C; is invariant with temperature, it is possible to use the following equation to describe the relationship betwen the entropy of the phase transition and the temperature @(T). ANT) =
Wa)+ 4c;
In (a/T) (8) At the phase transition temperature the value of the Gibbs free energy is zero and so it follows that
@(ne)= w(a)/a
(9)
and by substitution for C; from eq 3, eq 8 can be expressed as @(T) =
4H(n)/n+ AC; In (a) - AC;
In ( T )
(10)
-3
t
-4‘ 200
-p108
P238
..’ P308
-PS38\
--la8
1 260
300
360
400
460
600
660
600
Temperature (K) Figure 7. Theoretical entropy change for poloxamer phase transitions.
The results for the dependence of the phase transition entropies on temperature are plotted in Figure 7,and the resulting data can be fitted to the equation @(T) = ASo
+ AS*M, + (AC,” + AC,*M,) In (T)
(11)
If the value of Tis replaced by the experimental p l y e transition temperatures, T,, then the phase transition entropy, @(7&), can be calculated. Relrtio&ip between Gibbs Free Energy and Poly(oxypr0pykae) content Having derived equations that predict the effect of temperature on M and AS it is now possible to predict the effect of temperature on Gibbs free energy, AG, of the system because
AG=AH-TAS
(12)
By substituting eqs 6 and 11 into eq 12 the following equation is obtained:
4 G ( T ) = Lwo + A P M , - T(AC,,” + ACp*Mr)T(ASo + AS*M,) + (AC,” + AC,*M,) In ( T ) (13) The dependence of Gibbs free energy on temperature, for the poloxamers under study, is displayed in Figure 8. From these graphs it can be seen that the value of GG(T) is equal to zero at two discrete temperatures for each poloxamer. The low-temperature value, is equivalent to the measured experimental phase transition temperature, T,, and the high-temperaturevalue, Po,represents a theoretically predicted temperature at which the poloxamers should undergo a second phase transition. The experimental phase transition temperatures, T,, and the calculated values, are plotted in Figure 9 and, as can be seen,
a,
a,
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9511
HSDSC Study of ABA Block Copolymers
(a)
n
Delta Q (/kJ/Mol) 600 I
-P ~ O T
1
-.-PZST
-P~OT
-
~2as - P P ~
1%
e
400
300
2
1
A
3
3 0 5 P c
E
z
z
Temperature (K)
Delta Q (/kJ/mol)
300 1
-
20
t
-ctoo
60 200
- - P250
-Po0
260
300
--.-Psoo
360
1
-Pi350
400
460
600
Temperature (K) Figure 8. Theoretical Gibbs free energy change for poloxamer phase transitions. 420
-
400
-
\
360
I
L* J 1,400 1,000 2,400 2.000 9,400 3,000 M,of Pro
280 000
Flgm 9. Calculated transition temperature maxima for poloxamer phase transition: (+) Experimental low-temperature phase transitions. (-) Theoretical low-temperature phase transitions. (*) Experimental hightemperature phase transitions. (-) Theoretical high-temperature phase transitions.
there is good agreement between the theoretical and experimental data. By entering the theoretical values of into eqs 6 and 11, the values for the phase transition enthalpy, & H ( G ) , and phase transition entropy, A$(%),can be calculated for any polmmer. The calculated values for the enthalpy and entropy of the poloxamer phase transitions correlate well with the experimental data. The deviation at low poly(oxypropy1ene) content is caused by inaccuracies in the experimental determination of the phase transition enthalpies due to base-line extrapolation.
-
1s-
10
-
5 -
0 -
-5.
~
200 220 240 2 6 0 2 8 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 4 0 0 4 2 0 4 4 0 4 6 0 4 8 0 6 0 0
260 200
25
1
I
1
I
I
I
I
I
I
I
J. Phys. Chem. 1992,96,9512-95 17
9512
the poly(oxyethy1ene) content appears not to be involved in the transitions reportedhere. That this cannot be wholly true is evident from the nonconformity with this analysis of polymer L62 which contains only 20% of poly(oxyethy1ene). Studies of a wider range of block copolymers of differing A/B proportions is currently in progress. The calculation performed in this paper is similar to calculations that have been conducted on the aqueous solution phase transitions of proteins.'** The work on protein phase transitions predicted that there should be a lower temperature phase transition, known as cold denaturation. The predicted temperature at which cold denaturation occurs for most proteins is well below the freezing temperature of water; however, by the use of supercooled water and techniques such as salting out, to destabilize the protein, it has been possible to measure cold denaturation for a few proteins. With the poloxamer block copolymers it is possible to measure the analogous phase transition, the low-temperature phase transition, without needing to force the experimental conditions. The high-temperature phase transitions for the poloxamers of high ply(oxypropy1ene) relative molecular mass also OCCUT in the liquid phase of water at atmospheric pressure. By chemically altering the structure of the poloxamers it will be possible to manipulate their solution properties and understand
the effect that the introduction of other groups, such as ionic groups, will have on the poloxamer solution properties.
R
W NO. (EO)(PO) (block CopOlWCr), 106392-12-5.
References rad Notes (1) Mitchard, N. M.;&ezer, A. E.; Rces, N. H.; Mitchell, J. C.; Lebarne, S.;Chowdhry, B. Z.; Buchon, G. J. Chem. Soc., Chem. Commun. 1990,900. (2) Mitchard, N. M. Ph.D. Thais, University of London, 1990. (3) Beem,A. E.;Mitchell, J. C.; Rees, N. H.; Armstrong, J. K.; Chowdhry, B. Z.; Leharne, Buckton, G. J . Chem. Res. 1991, 254. (4) Beezer, A. E.; Mitchard, N. M.;Mitchell, J. C.; Armstrong, J. K.; Chowdhry, B. 2.;Lehame, S.;Buckton, 0. J. Chem. Res. 1992,236.
s.;
( 5 ) Rassing, J.; McKenna, W. P.; Bandyopadhyay, S.;Eyring, E. M. J. Mol. Liq. 1984,27, 165. (6) Gilbert,J. C.; Washington, J. C.; Davis, M.C.; Hadgraft, J. Inr. J. Pharm. 1981,40,93. (7) Privalov, P. L.; Gill, S.J. Adu. Protein Chem. 1989, 39, 191. (8) Privalov, P.L. Annu. Rev. Btophys. Chem. 1989,18,47. (9) FrPnLs, H. S.; Evans, M.W. 1.Phys. Chem. 1945,30, 507. (10) Glew, D. G. N. J. Phys. Chem. 1%2,66,605. (11) Nemethy, G.; Scheraga, H. A. J . Chem. Phys. 1%2,36, 3382. (12) Vadnere, M.;Amidon, G.; Lindendaum, S.;Haslam, J. M. Inr. J. Pharm. 1984, 22, 201. (13) Irwin, J. J.; Beezcr, A. E.; Mitchell, J. C.; Buckton, G.; Chowdhry, B. Z. J. Phys. Chem. Submitted for publication, 1992. (14) Schmolka, I. R. J . Am. Oil. Chem. Soc. 1977,54, 110.
Deactlvatlon of Excited S p e c k by Mffu8lon-Contrdled Quenchlng In Clusters of Reversed Micelles Mats Almgren* and Ragnar J6bnnwon Department of Physical Chemistry, University of Uppsala, S- 751 21 Uppsala, Sweden (Received: April 9, 1992; In Final Form: July 21, 1992)
Kinetic models for the deactivation of excited spacies by quenching in clusters of micelles are prcaented and tested experhmtally by measurement of phosphorescence deactivation in clusters of AOT-water reversed micelles having an H20/AOT molar ratio of 12.5 in dodecane. Models were devised for a random walk of quenchers in compact clusters, in open and ramified clusters (fractal clusters), and also a model especially adapted for very small clusters. Experimental studies under these conditions gave consistent results for the walk frequency, k,,, for which a value of (2-4) X lo5 s-l was obtained. Similar values were obtained with several different probtquencher pairs, which supports the proposed fusion-fission mechanism for the transport between the micelles. The rate constant k, reflects the rate of fusion of the micelles.
IntrodlK!tim It is well recognized that discrete water droplets persist in the phase of the AOTalkane-water systems up to very high droplet concentration and temperature. In fairly dilute solutions a critical demixing into two phases occufs with increase in water content or tempemture, favored by long alkyl tails of the solvent oil. Strong evidence has been gathered by several techniques that clusters of droplets form on approach to this phase boundary,as also when the droplet concentration is increased, and a strongly temperature-dependent percolation threshold is approached. The conclusion drawn from neutron scattering rneasurements'J is that the microemulsionconsistS of dosed r e v d micelles, which cluster together when the critical line is approached. This is c o n f i e d by electric conductivity measurements which display percolative transition of the cond~ctivity.*~Maitra et al.5 concluded that the miceHes retain their closed structure although they form infinite clusters due to strong interbplet interactions. Earlier results from dynamic light scattering measurements performed by Zulauf et a1.6 indicated a dramatic increase in the Stokes radii as T, was approached, which, as pointed out by Kotlarchyk et al.,'.' could be related to the correlation of clusters of micelles. To whom correspondence should be a d d r d .
We recently reportedthat small clusters of AOT-water r e v d micelles were present rather far from the phase separation limit with both dodecane and isooctane as bulk solvent? The evidence came from the deactivation kinetics of long-lived excited states (>lo M). The decay curves showed three well-separated time regions. First, a very quick deactivation on a time scale of about 10-30 ns occurs in the micelles which contain quenchers. Deactivation due to quenchers present in the same cluster as the excited state, but in other micelles, required about 1-5 p. F i i y , a very slow deactivation process could be observed, presumably involvihg a migration of p r o k and quenchers between different clusters. In the interpietation of these results, the Infelta-Tachiya9JO model for deactivation in micella was C0"ented with a term for the intracluster process, assumed characterized by a first-ordarquenching umstant, k,for the interadon of a quencher and an excited state on the same cluster, analogous to kq for the intramicelle pmcas but about 2 orders of magnitude slower. The intracluster quenching process involves a transfer of quenchex and excited probe from micelle to micelle until they meet and react. The special considerations needed for small and polydispersed clusters were also discussed. In this work, the rate of diffusional quenching in compact, fractazandsmallclus~isdeacribed~tically.Expgimental results for the deactivation of long-lived excited species by
OO22-3654/92/2096-95 12$03.OO/O Q 1992 American Chemical Society
