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Temperature dependence of solvation dynamics in a micelle. 4-Aminophthalimide in Triton X-100
Chemical Physics Letters 385 (2004) 357–361 www.elsevier.com/locate/cplett
Temperature dependence of solvation dynamics in a micelle. 4-Aminophthalimide in Triton X-100 Pratik Sen, Saptarshi Mukherjee, Arnab Halder, Kankan Bhattacharyya
*
Physical Chemistry Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India Received 18 November 2003 Published online: 25 January 2004
Abstract Solvation dynamics of 4-aminophthalimide (4-AP) is studied in a Triton X-100 (TX) micelle at three different temperatures. The average solvation time hss i has been found to be 800, 400 and 110 ps at 283, 303 and 323 K, respectively. This corresponds to an activation energy of 9 1 kcal mol1 . The observed temperature dependence is in qualitative agreement with recent computer simulations on the solvation dynamics in micelles. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction In bulk water, solvation dynamics occurs in sub-picosecond time scale [1–3]. The very fast solvation dynamics in bulk water is due to intermolecular vibrations and librations and the process involves negligible activation energy [1–3]. In the case of water molecules confined in complex organized assemblies and in biological macromolecules, solvation dynamics exhibits a component in 100–1000 ps time scale [4–25]. According to a phenomenological model the slow component of solvation dynamics arises because of an exchange of the water molecules between the ÔboundÕ and the ÔfreeÕ forms [17]. In the limit of very high binding energy (i.e. jDG0bf j), the slow component of solvation (sslow ) is given by [6,17,19] sslow 1=kbf ;
ð1Þ
where the rate constant for bound-to-free interconversion kbf is, kbf ¼ ðkB T =hÞ expðEa =RT Þ:
ð2Þ
Very recently, Bagchi and co-workers [18–21] carried out very detailed computer simulation of solvation dynamics of the cesium counter ion in an anionic micelle. *
Corresponding author. Fax: +91-33-2473-2805. E-mail address: [email protected] (K. Bhattacharyya).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.12.115
According to them, the slow component of solvation dynamics arises because of hydrogen bonding of the water molecules with the polar head groups (PHG) of the micelle [20,21]. They introduced an energy criterion that a water–PHG hydrogen bond exists if the pair energy between a water molecule and a PHG is less than 6:25 kcal mol1 [20]. They found that the average solvation time increases from 20 to 40 ps as the temperature decreases from 350 to 300 K [18]. In the present work, we report on the temperature dependence of the solvation dynamics of 4-aminophthalimide (4-AP) in Triton X-100 (TX) micelles. The main reason for studying the solvation dynamics in TX micelle instead of a cationic micelle (CTAB) or an anionic micelle (SDS) is the following. According to the structural studies (small angle X-ray and neutron scattering), a micelle consists of an essentially ÔdryÕ core containing the hydrocarbon chains which is surrounded by a hydrated peripheral shell made up of the polar head groups and considerable amount of water [26,27]. This hydrophilic shell is called the Stern Layer for an ionic micelle (e.g., CTAB and SDS) and a palisade layer for neutral micelle (such as, TX). The thickness of the hy for the ionic micelles [27] while for drated layer is 6–9 A [26]. Since the TX the thickness of this layer is 25 A in length, in case of solvation probe 4-AP is about 8 A TX it is totally enclosed inside the hydration layer while
358
P. Sen et al. / Chemical Physics Letters 385 (2004) 357–361
O N H
H
N O H
Scheme 1. Structure of 4-AP.
for anionic micelle a considerable part of the probe sticks out of the hydration layer of the micelle into the bulk water.
Emission Intensity (a.u.)
500 400 300 200 100 450
500
550
600
650
Wavelength (nm)
2. Experimental 4-Aminophthalimide (4-AP, Kodak, Scheme 1) was purified by repeated recrystallization from methanolwater mixture. Triton X-100 (Aldrich) was used as received. The steady-state absorption and emission spectra were recorded in a Shimadzu UV-2401 spectrophotometer and a Perkin–Elmer 44B spectrofluorimeter, respectively. For lifetime measurements, the samples were excited at 405 nm using a picosecond diode laser (IBH Nanoled-07). The emission was collected at a magic angle polarization using a Hamamatsu MCP photomultiplier (2809U). The time correlated single photon counting (TCSPC) set up consists of an Ortec 935 QUAD CFD and a Tennelec TC 863 TAC. The data are collected with a PCA3 card (Oxford) as a multi-channel analyzer. The typical FWHM of the system response is about 100 ps. The temperature was maintained using a circulator bath (Neslab, Endocal). From the reported binding constant of 4-AP with TX [28] in 100 mM TX, nearly 85% of the probe (4-AP) molecules remain bound to the micelle. In this work, the concentration of TX was kept at 100 mM for all the three temperatures.
3. Results
Fig. 1. Emission spectra of 4-AP in 100 mM TX-100.
3.2. Time-resolved studies The fluorescence decays of 4-AP in the 100 mM TX micelles are found to be markedly dependent on the emission wavelength at all the three temperatures. For example, at 283 K, at the blue end (450 nm) the fluorescence decay of 4-AP is biexponential with two decay components of 530 ps (65%) and 5300 ps (35%), while at the red end (600 nm) the decay of time constant 5040 ps is preceded by a distinct rise with a time constant of 160 ps. Fluorescence decays of 4-AP in 100 mM TX micelles at 283 K are shown in Fig. 2. At 323 K, at the blue end (450 nm) the fluorescence decay of 4-AP in TX micelle is biexponential with two decay components of 260 ps (60%) and 3350 ps (40%), while at the red end (600 nm) 4-AP exhibits a decay component of 2080 ps and a distinct growth component of 100 ps. Following the procedure prescribed by Maroncelli and Fleming [29], the time-resolved emission spectra (TRES) were constructed using the parameters of best fit to the fluorescence decays and the steady-state emission spectrum. The TRES of 4-AP in 100 mM TX micelles at 283 K are shown in Fig. 3. The solvation dynamics is described by the decay of the solvent correlation function CðtÞ, defined as,
3.1. Steady-state spectra The absorption spectrum of 4-AP in 100 mM TX micelles at all the three temperature remains unchanged and exhibits an absorption maximum at 373 nm. The emission intensity of 4-AP in water is very low with a quantum yield of 0.01 [28]. However, in presence of 100 mM TX, the emission intensity increases about three times and exhibits a blue shift to 530 nm [14]. This indicates that the probe molecules experience a less polar micellar environment as compared to that in bulk water (Fig. 1). The emission maximum of 4-AP remains unaltered with the variation of temperature from 283 to 323 K.
Fig. 2. Fluorescence decays of 4-AP in 100 mM TX-100 at 283 K at (i) 450, (ii) 500 and (iii) 600 nm.
P. Sen et al. / Chemical Physics Letters 385 (2004) 357–361
namics of 4-AP in 100 mM TX at 303 and 323 K are found to be very different than that at 283 K. In a solution of 100 mM TX at 303 K, the decay of CðtÞ for 4-AP, is found to be biexponential with one component of 80 ps (40%) and another 620 ps (60%), with an average solvation time, hss i ¼ 400 50 ps. At 323 K, the decay of CðtÞ is found to be single exponential with a time constant 110 50 ps (Fig. 4, Table 1). The total Stokes shift is observed to be 600 50 cm1 for all the three temperatures.
t Normalized Intensity
1.0 0.8 0.6 0.4 0.2 0.0 15000
20000
25000
4. Discussion
-1
Wavenumber (cm ) Fig. 3. Time resolved emission spectra of 4-AP in 100 mM TX-100 at 283 K at 0 ps (j), 150 ps (s), 600 ps (N) and 4000 ps (r).
CðtÞ ¼
mðtÞ mð1Þ ; mð0Þ mð1Þ
ð3Þ
where mð0Þ, mðtÞ and mð1Þ are the peak frequencies at time 0, t, and 1, respectively. The decay of CðtÞ of 4-AP in 100 mM TX at 283 K, is found to be biexponential with one component of 150 ps (30%) and another 1080 ps (70%), with an average solvation time, hss i ¼ 800 100 ps (Fig. 4, Table 1). The solvation dy-
1.0
359
1.0
The most important observation of the present work is the marked decrease in the average solvation time by almost eight times from 800 100 ps at 283 K to 110 50 ps at 323 K. Assuming an Arrhenius dependence (Eq. (2)) of the rate constant (¼ hss i1 ), the activation energy (Ea ) for the solvation may be evaluated from the slope of the plot of logarithm of hss i1 against (1/T) (Fig. 5). The magnitude of Ea is obtained as 9 1 kcal mol1 . It may be noted that the temperature dependence of solvation dynamics detected in this work is in qualitative agreement with that observed in the molecular dynamics simulation carried out by Pal et al. [18]. However, the magnitude of temperature dependence detected in this work is higher than that reported in the simulation. It
0.8
0.8
0.6
24
0.4 0.2 0.0
0.4
23 0
100
200
300
400
ln (1/<τ s >)
C(t)
0.6
0.2
22
21
0.0 0
1000 2000 3000 4000
Time (ps)
20 0.0030
Fig. 4. Decay of response function, CðtÞ of 4-AP in 100 mM TX-100 at 283 K (j), at 303 K (s), and at 323 K (N). The points denote the actual values of CðtÞ and the solid line denotes the best fit to an exponential and/or biexponential decay.
0.0033
0.0036
-1
1/T (K ) Fig. 5. Plot of ln(1=hss i) against 1=T .
Table 1 Decay parameters of CðtÞ of 4-AP in the presence of 100 mM TX-100 at different temperatures Temperature (K)
Dma (cm1 )
a1
s1 (ps)
a2
s2 (ps)
hss ib (ps)
283 303 323
600 600 600
0.30 0.40 1.00
150 80 110
0.70 0.60 –
1080 620 –
800 100 400 50 110 50
a b
50 cm1 . hss i ¼ a1 s1 þ a2 s2 .
360
P. Sen et al. / Chemical Physics Letters 385 (2004) 357–361
should be emphasized that the simulation deals with solvation of an ion (cesium) which is much smaller in than that of the solvation probe, size (diameter ¼ 3.6 A) 4-AP (8 A). Also the structure of the anionic micelle studied by simulation is different from that of the TX micelle. The activation energy (9 1 kcal mol1 ) determined in this work is higher than the hydrogen bond energy between two water molecules in bulk water (5.5 kcal mol1 ) [20]. However, it should be noted that according to computer simulations [20] hydrogen bond energy of interfacial water molecules forming one or two hydrogen bonds with PHG of a micelle is 13–14 kcal mol1 , i.e., 7–8 kcal mol1 stronger than a water– water hydrogen bond. Though, as noted earlier, the simulations [20] were carried out on an anionic micelle having a different structure, the activation energy (9 1 kcal mol1 ) determined in the present work is very close to the difference in between the water–micelle and water–water (7–8 kcal mol1 ) hydrogen bond energies [20]. Thus, it appears that the rate determining step in micellar solvation is removal of water molecules from the interfacial region to bulk water. This is consistent with the earlier phenomenological model [17]. Several authors reported that the hydration number (i.e., the number of water molecules per molecule of surfactant) changes with rise in temperature [30–32]. Streletzky and Phillies [32] studied the temperature dependence of structure and hydration of TX micelle using quasi-elastic light scattering spectroscopy. According to them, the hydration number of TX micelle increases from 6 to 16 with increase in temperature from 283 to 323 K [32]. If the eightfold decrease in average solvation time from 283 to 323 K in TX micelle were due to solely changes in hydration number and structure of TX micelles, the solvation time should not involve any activation barrier and should not display a linear Arrhenius plot. The linearity of the Arrhenius plot (Fig. 5) suggests the changes in structure and hydration number have a minor role in the observed temperature dependence of solvation dynamics. In a recent work, it has been proposed that slow solvation dynamics of a probe in the water pool of a microemulsion (reverse micelle) involves self-diffusion of the probe [13]. The self-diffusion of the probe is manifested in the time-dependent change in spectral width. No such time dependent change in the emission spectral width is observed in the present work.
5. Conclusion This work shows that solvation dynamics of 4-AP in TX micelles exhibit marked temperature dependence. The activation energy of the slow component of solvation dynamics is found to be 9 1 kcal mol1 . This is
very close to the difference between the water–micelle and water–water hydrogen bond energy as reported in a recent simulation [20]. The role of temperature dependent change in the structure and hydration number of TX micelles appears to be minor.
Acknowledgements Thanks are due to Department of Science and Technology of India (DST), the ÔFemtosecond Laser FacilityÕ and to Council of Scientific and Industrial Research (CSIR) for generous research grants. P.S. thanks DST and A.H. thanks CSIR for awarding fellowships. K.B. thanks Professor B. Bagchi for many illuminating discussions.
References [1] B. Bagchi, Annu. Rep. Prog. Chem. Sect. C 99 (2003) 127. [2] R. Jimenez, G.R. Fleming, P.V. Kumar, M. Maroncelli, Nature 369 (1994) 471. [3] N. Nandi, S. Roy, B. Bagchi, J. Chem. Phys. 102 (1995) 1390. [4] N. Nandi, K. Bhattacharyya, B. Bagchi, Chem. Rev. 100 (2000) 2013. [5] K. Bhattacharyya, Acc. Chem. Res. 36 (2003) 95. [6] S.K. Pal, J. Peon, B. Bagchi, A.H. Zewail, J. Phys. Chem. B 106 (2002) 12376. [7] N.E. Levinger, Curr. Opin. Coll. Interface Sci. 5 (2000) 118. [8] X.J. Jordanides, M.J. Lang, X. Song, G.R. Fleming, J. Phys. Chem. B 103 (1999) 7995. [9] P. Dutta, P. Sen, A. Halder, S. Mukherjee, S. Sen, K. Bhattacharyya, Chem. Phys. Lett. 377 (2003) 229. [10] E.B. Brauns, M.L. Madaras, R.S. Coleman, C.J. Murphy, M.A. Berg, Phys. Rev. Lett. 88 (2002), 158101-1. [11] L. Frauchiger, H. Shirota, K.E. Uhrich, E.W. Castner Jr., J. Phys. Chem. B 106 (2002) 7463. [12] S. Sen, D. Sukul, P. Dutta, K. Bhattacharyya, J. Phys. Chem. B 106 (2002) 3763. [13] P. Dutta, P. Sen, S. Mukherjee, A. Halder, K. Bhattacharyya, J. Phys. Chem. B 107 (2003) 10815. [14] A. Dutta, D. Mandal, S.K. Pal, S. Das, K. Bhattacharyya, J. Mol. Liq. 77 (1998) 121. [15] S.K. Pal, D. Sukul, D. Mandal, S. Sen, K. Bhattacharyya, Chem. Phys. Lett. 327 (2000) 91. [16] K. Hara, H. Kuwabara, O. Kajimoto, J. Phys. Chem. A 105 (2001) 7174. [17] N. Nandi, B. Bagchi, J. Phys. Chem. B 101 (1997) 10954. [18] S. Pal, S. Balasubramanian, B. Bagchi, J. Chem. Phys. 117 (2002) 2852. [19] S. Balasubramanian, S. Pal, B. Bagchi, Phys. Rev. Lett. 89 (2002), 115505-1. [20] S. Pal, S. Balasubramanian, B. Bagchi, J. Phys. Chem. B 107 (2003) 5194. [21] S. Pal, S. Balasubramanian, B. Bagchi, Phys. Rev. E 67 (2003) 061502. [22] J. Faeder, M.V. Albert, B.M. Ladanyi, Langmuir 19 (2003) 2514. [23] S. Senapati, M.L. Berkowitz, J. Chem. Phys. 118 (2003) 1937. [24] C.D. Bruce, S. Senapati, M.L. Berkowitz, L. Perera, M.D.E. Forbes, J. Phys. Chem. B 106 (2002) 10902. [25] D.A. Panatano, D. Laria, J. Phys. Chem. B 107 (2003) 2971. [26] H.H. Paradies, J. Phys. Chem. 84 (1980) 599.
P. Sen et al. / Chemical Physics Letters 385 (2004) 357–361 [27] S.S. Berr, J. Phys. Chem. 91 (1987) 4760. [28] G. Saroja, A. Samanta, Chem. Phys. Lett. 246 (1995) 506. [29] M. Maroncelli, G.R. Fleming, J. Chem. Phys. 86 (1987) 6221.
[30] L.S. Romsted, J. Yao, Langmuir 12 (1996) 2425. [31] L.S. Romsted, J. Yao, Langmuir 15 (1999) 326. [32] K. Streletzky, G.D.J. Phillies, Langmuir 11 (1995) 42.
361
Temperature dependence of solvation dynamics in a micelle. 4-Aminophthalimide in Triton X-100 Pratik Sen, Saptarshi Mukherjee, Arnab Halder, Kankan Bhattacharyya
*
Physical Chemistry Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India Received 18 November 2003 Published online: 25 January 2004
Abstract Solvation dynamics of 4-aminophthalimide (4-AP) is studied in a Triton X-100 (TX) micelle at three different temperatures. The average solvation time hss i has been found to be 800, 400 and 110 ps at 283, 303 and 323 K, respectively. This corresponds to an activation energy of 9 1 kcal mol1 . The observed temperature dependence is in qualitative agreement with recent computer simulations on the solvation dynamics in micelles. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction In bulk water, solvation dynamics occurs in sub-picosecond time scale [1–3]. The very fast solvation dynamics in bulk water is due to intermolecular vibrations and librations and the process involves negligible activation energy [1–3]. In the case of water molecules confined in complex organized assemblies and in biological macromolecules, solvation dynamics exhibits a component in 100–1000 ps time scale [4–25]. According to a phenomenological model the slow component of solvation dynamics arises because of an exchange of the water molecules between the ÔboundÕ and the ÔfreeÕ forms [17]. In the limit of very high binding energy (i.e. jDG0bf j), the slow component of solvation (sslow ) is given by [6,17,19] sslow 1=kbf ;
ð1Þ
where the rate constant for bound-to-free interconversion kbf is, kbf ¼ ðkB T =hÞ expðEa =RT Þ:
ð2Þ
Very recently, Bagchi and co-workers [18–21] carried out very detailed computer simulation of solvation dynamics of the cesium counter ion in an anionic micelle. *
Corresponding author. Fax: +91-33-2473-2805. E-mail address: [email protected] (K. Bhattacharyya).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.12.115
According to them, the slow component of solvation dynamics arises because of hydrogen bonding of the water molecules with the polar head groups (PHG) of the micelle [20,21]. They introduced an energy criterion that a water–PHG hydrogen bond exists if the pair energy between a water molecule and a PHG is less than 6:25 kcal mol1 [20]. They found that the average solvation time increases from 20 to 40 ps as the temperature decreases from 350 to 300 K [18]. In the present work, we report on the temperature dependence of the solvation dynamics of 4-aminophthalimide (4-AP) in Triton X-100 (TX) micelles. The main reason for studying the solvation dynamics in TX micelle instead of a cationic micelle (CTAB) or an anionic micelle (SDS) is the following. According to the structural studies (small angle X-ray and neutron scattering), a micelle consists of an essentially ÔdryÕ core containing the hydrocarbon chains which is surrounded by a hydrated peripheral shell made up of the polar head groups and considerable amount of water [26,27]. This hydrophilic shell is called the Stern Layer for an ionic micelle (e.g., CTAB and SDS) and a palisade layer for neutral micelle (such as, TX). The thickness of the hy for the ionic micelles [27] while for drated layer is 6–9 A [26]. Since the TX the thickness of this layer is 25 A in length, in case of solvation probe 4-AP is about 8 A TX it is totally enclosed inside the hydration layer while
358
P. Sen et al. / Chemical Physics Letters 385 (2004) 357–361
O N H
H
N O H
Scheme 1. Structure of 4-AP.
for anionic micelle a considerable part of the probe sticks out of the hydration layer of the micelle into the bulk water.
Emission Intensity (a.u.)
500 400 300 200 100 450
500
550
600
650
Wavelength (nm)
2. Experimental 4-Aminophthalimide (4-AP, Kodak, Scheme 1) was purified by repeated recrystallization from methanolwater mixture. Triton X-100 (Aldrich) was used as received. The steady-state absorption and emission spectra were recorded in a Shimadzu UV-2401 spectrophotometer and a Perkin–Elmer 44B spectrofluorimeter, respectively. For lifetime measurements, the samples were excited at 405 nm using a picosecond diode laser (IBH Nanoled-07). The emission was collected at a magic angle polarization using a Hamamatsu MCP photomultiplier (2809U). The time correlated single photon counting (TCSPC) set up consists of an Ortec 935 QUAD CFD and a Tennelec TC 863 TAC. The data are collected with a PCA3 card (Oxford) as a multi-channel analyzer. The typical FWHM of the system response is about 100 ps. The temperature was maintained using a circulator bath (Neslab, Endocal). From the reported binding constant of 4-AP with TX [28] in 100 mM TX, nearly 85% of the probe (4-AP) molecules remain bound to the micelle. In this work, the concentration of TX was kept at 100 mM for all the three temperatures.
3. Results
Fig. 1. Emission spectra of 4-AP in 100 mM TX-100.
3.2. Time-resolved studies The fluorescence decays of 4-AP in the 100 mM TX micelles are found to be markedly dependent on the emission wavelength at all the three temperatures. For example, at 283 K, at the blue end (450 nm) the fluorescence decay of 4-AP is biexponential with two decay components of 530 ps (65%) and 5300 ps (35%), while at the red end (600 nm) the decay of time constant 5040 ps is preceded by a distinct rise with a time constant of 160 ps. Fluorescence decays of 4-AP in 100 mM TX micelles at 283 K are shown in Fig. 2. At 323 K, at the blue end (450 nm) the fluorescence decay of 4-AP in TX micelle is biexponential with two decay components of 260 ps (60%) and 3350 ps (40%), while at the red end (600 nm) 4-AP exhibits a decay component of 2080 ps and a distinct growth component of 100 ps. Following the procedure prescribed by Maroncelli and Fleming [29], the time-resolved emission spectra (TRES) were constructed using the parameters of best fit to the fluorescence decays and the steady-state emission spectrum. The TRES of 4-AP in 100 mM TX micelles at 283 K are shown in Fig. 3. The solvation dynamics is described by the decay of the solvent correlation function CðtÞ, defined as,
3.1. Steady-state spectra The absorption spectrum of 4-AP in 100 mM TX micelles at all the three temperature remains unchanged and exhibits an absorption maximum at 373 nm. The emission intensity of 4-AP in water is very low with a quantum yield of 0.01 [28]. However, in presence of 100 mM TX, the emission intensity increases about three times and exhibits a blue shift to 530 nm [14]. This indicates that the probe molecules experience a less polar micellar environment as compared to that in bulk water (Fig. 1). The emission maximum of 4-AP remains unaltered with the variation of temperature from 283 to 323 K.
Fig. 2. Fluorescence decays of 4-AP in 100 mM TX-100 at 283 K at (i) 450, (ii) 500 and (iii) 600 nm.
P. Sen et al. / Chemical Physics Letters 385 (2004) 357–361
namics of 4-AP in 100 mM TX at 303 and 323 K are found to be very different than that at 283 K. In a solution of 100 mM TX at 303 K, the decay of CðtÞ for 4-AP, is found to be biexponential with one component of 80 ps (40%) and another 620 ps (60%), with an average solvation time, hss i ¼ 400 50 ps. At 323 K, the decay of CðtÞ is found to be single exponential with a time constant 110 50 ps (Fig. 4, Table 1). The total Stokes shift is observed to be 600 50 cm1 for all the three temperatures.
t Normalized Intensity
1.0 0.8 0.6 0.4 0.2 0.0 15000
20000
25000
4. Discussion
-1
Wavenumber (cm ) Fig. 3. Time resolved emission spectra of 4-AP in 100 mM TX-100 at 283 K at 0 ps (j), 150 ps (s), 600 ps (N) and 4000 ps (r).
CðtÞ ¼
mðtÞ mð1Þ ; mð0Þ mð1Þ
ð3Þ
where mð0Þ, mðtÞ and mð1Þ are the peak frequencies at time 0, t, and 1, respectively. The decay of CðtÞ of 4-AP in 100 mM TX at 283 K, is found to be biexponential with one component of 150 ps (30%) and another 1080 ps (70%), with an average solvation time, hss i ¼ 800 100 ps (Fig. 4, Table 1). The solvation dy-
1.0
359
1.0
The most important observation of the present work is the marked decrease in the average solvation time by almost eight times from 800 100 ps at 283 K to 110 50 ps at 323 K. Assuming an Arrhenius dependence (Eq. (2)) of the rate constant (¼ hss i1 ), the activation energy (Ea ) for the solvation may be evaluated from the slope of the plot of logarithm of hss i1 against (1/T) (Fig. 5). The magnitude of Ea is obtained as 9 1 kcal mol1 . It may be noted that the temperature dependence of solvation dynamics detected in this work is in qualitative agreement with that observed in the molecular dynamics simulation carried out by Pal et al. [18]. However, the magnitude of temperature dependence detected in this work is higher than that reported in the simulation. It
0.8
0.8
0.6
24
0.4 0.2 0.0
0.4
23 0
100
200
300
400
ln (1/<τ s >)
C(t)
0.6
0.2
22
21
0.0 0
1000 2000 3000 4000
Time (ps)
20 0.0030
Fig. 4. Decay of response function, CðtÞ of 4-AP in 100 mM TX-100 at 283 K (j), at 303 K (s), and at 323 K (N). The points denote the actual values of CðtÞ and the solid line denotes the best fit to an exponential and/or biexponential decay.
0.0033
0.0036
-1
1/T (K ) Fig. 5. Plot of ln(1=hss i) against 1=T .
Table 1 Decay parameters of CðtÞ of 4-AP in the presence of 100 mM TX-100 at different temperatures Temperature (K)
Dma (cm1 )
a1
s1 (ps)
a2
s2 (ps)
hss ib (ps)
283 303 323
600 600 600
0.30 0.40 1.00
150 80 110
0.70 0.60 –
1080 620 –
800 100 400 50 110 50
a b
50 cm1 . hss i ¼ a1 s1 þ a2 s2 .
360
P. Sen et al. / Chemical Physics Letters 385 (2004) 357–361
should be emphasized that the simulation deals with solvation of an ion (cesium) which is much smaller in than that of the solvation probe, size (diameter ¼ 3.6 A) 4-AP (8 A). Also the structure of the anionic micelle studied by simulation is different from that of the TX micelle. The activation energy (9 1 kcal mol1 ) determined in this work is higher than the hydrogen bond energy between two water molecules in bulk water (5.5 kcal mol1 ) [20]. However, it should be noted that according to computer simulations [20] hydrogen bond energy of interfacial water molecules forming one or two hydrogen bonds with PHG of a micelle is 13–14 kcal mol1 , i.e., 7–8 kcal mol1 stronger than a water– water hydrogen bond. Though, as noted earlier, the simulations [20] were carried out on an anionic micelle having a different structure, the activation energy (9 1 kcal mol1 ) determined in the present work is very close to the difference in between the water–micelle and water–water (7–8 kcal mol1 ) hydrogen bond energies [20]. Thus, it appears that the rate determining step in micellar solvation is removal of water molecules from the interfacial region to bulk water. This is consistent with the earlier phenomenological model [17]. Several authors reported that the hydration number (i.e., the number of water molecules per molecule of surfactant) changes with rise in temperature [30–32]. Streletzky and Phillies [32] studied the temperature dependence of structure and hydration of TX micelle using quasi-elastic light scattering spectroscopy. According to them, the hydration number of TX micelle increases from 6 to 16 with increase in temperature from 283 to 323 K [32]. If the eightfold decrease in average solvation time from 283 to 323 K in TX micelle were due to solely changes in hydration number and structure of TX micelles, the solvation time should not involve any activation barrier and should not display a linear Arrhenius plot. The linearity of the Arrhenius plot (Fig. 5) suggests the changes in structure and hydration number have a minor role in the observed temperature dependence of solvation dynamics. In a recent work, it has been proposed that slow solvation dynamics of a probe in the water pool of a microemulsion (reverse micelle) involves self-diffusion of the probe [13]. The self-diffusion of the probe is manifested in the time-dependent change in spectral width. No such time dependent change in the emission spectral width is observed in the present work.
5. Conclusion This work shows that solvation dynamics of 4-AP in TX micelles exhibit marked temperature dependence. The activation energy of the slow component of solvation dynamics is found to be 9 1 kcal mol1 . This is
very close to the difference between the water–micelle and water–water hydrogen bond energy as reported in a recent simulation [20]. The role of temperature dependent change in the structure and hydration number of TX micelles appears to be minor.
Acknowledgements Thanks are due to Department of Science and Technology of India (DST), the ÔFemtosecond Laser FacilityÕ and to Council of Scientific and Industrial Research (CSIR) for generous research grants. P.S. thanks DST and A.H. thanks CSIR for awarding fellowships. K.B. thanks Professor B. Bagchi for many illuminating discussions.
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