**3.2.2 Rotational dynamics of polar probes**

The rotational dynamics studies using polar solutes in polar solvents have shed lights on concepts such as dielectric friction and solute-solvent hydrogen bonding. In addition to viscous drag, polar-polar interaction between a polar solute and a polar solvent gives rise to an additional retarding force often termed as dielectric friction. This arises because of the inability of the solvent molecules, encircling the polar solute probe, to rotate synchronously with the probe. The result of this effect is the creation of an electric field in the cavity, which exerts a torque opposing the reorientation of the probe molecule. Under such circumstances, the observed friction, which is proportional to the measured reorientation time, has been explained as a combination of mechanical and dielectric frictions. However, many experimental investigations of reorientation dynamics have indicated that there is another source of drag on a rotating probe molecule due to hydrogen bonding between the solute and the solvent molecules. A solute molecule can form hydrogen bond with the solvent molecule depending on the nature of the functional groups on the solute and the solvent which enhances the volume of the probe molecule. This further impedes the rotational motion and thus the observed reorientation time becomes longer than that observed with the bare solute molecule.

Molecular structures of the three coumarin dyes chosen under the category of polar probes are shown in Fig. 7. The reorientation times of C522B, C307 in alcohols and alkanes and C138 in alcohols (Mannekutla et al., 2010) are summarized in Tables 6 and 7. The τ*<sup>r</sup>* values obtained in alkanes clearly show that C522B rotates faster compared to C307. In alcohols, it is interesting to note that, the probe C138 rotates faster almost by a factor of 1:2 from propanol to decanol compared to C522B and C307, respectively. In other words, C138 experiences a reduced mechanical friction i.e., almost same as C522B and twice as C307 from propanol to decanol. This is because C307 shows greater interaction owing to its greater polarity.

Fig. 7. Molecular structures of (a) C522B, (b) C307 and (c) C138

Rotational Dynamics of Nonpolar and Dipolar

alcohols follow the trend: *C CB C* 307 522 138

relaxation in alkanes may be expected.

Fig. 8. Plots of

and C307

τ*r* vs η

Fig. 8 gives a typical plot of

*rr r*

alkanes. For biphenyl a nonlinearity was observed in the plot of

 τ> ≥ .

ττ

τ*r* vs η

Molecules in Polar and Binary Solvent Mixtures 211

The normalized rotational reorientation times (at unit viscosity) are smaller in alkanes compared to alcohols, which indicates that the probes C522B and C307 rotate faster in alkanes compared to alcohols. The reorientation times of the three probes thus obtained in

with the stick and slip lines. Note that the experimentally measured reorientation times lie between slip and stick hydrodynamic in case of alcohols. However, in alkanes we observe, as the size of the solvent molecule becomes equal to and bigger than the size of the solute molecule, the probe molecule experiences a reduced friction. Benzler and Luther (1977) measured the reorientation time of biphenyl (*V*=150 Å3) and *p*-terphenyl (*V*=221 Å3) in *n*-

from tetradecane, in case of *p*-terphenyl. Singh [24] studied reorientation times of the probe neutral red (*V*=234 Å3) which experienced a reduced friction from tetradecane to hexadecane following subslip behavior. C522B (223 Å3) and C307 (217 Å3) have nearly identical volumes as compared to neutral red and *p*-terphenyl and thus a similar rotational

for the three coumarins in alcohols (○), and alkanes (•) in case of C522B

for all the three probes in alcohols and in alkanes along

τ*r* vs η

from decane and


a Viscosity data is from Inamdar et al., 2006

Table 6. Steady-state anisotropy (*<r>*), fluorescence lifetime (τ*<sup>f</sup>*) and rotational reorientation time (τ*<sup>r</sup>*) of coumarins in alcohols at 298K (the maximum error in the fluorescence life times is less than ±50 ps) (Mannekutla et al., 2010)


a Viscosity data is from Inamdar et al., 2006

Table 7. Steady-state anisotropy (*<r>*), fluorescence lifetime (τ*<sup>f</sup>*) and rotational reorientation time (τ*<sup>r</sup>*) of coumarins in alkanes at 298K for C522B and C307 (the maximum error in the fluorescence life times is less than ±50 ps) (Mannekutla et al., 2010)

The probes C522B and C138 have shown coincidentally similar interactions. In C138, aminomethyl group being free contributes more to the charge separation through resonance- whereas in C522B this resonance contribution is sluggish, comparatively. However, the presence of -CF3 in C522B increases the charge separation, which leads to better interaction with the hydrogen bonding solvents. Replacement of -CF3 by cyclic alkyl group in C138 would not have any great contribution towards its polarity. Hence, the presence of two different groups with contradicting properties leads to the coincidental similarities in reorientation dynamics of C522B and C138.

τ

τ

*<sup>r</sup>*) of coumarins in alcohols at 298K (the maximum error in the fluorescence life times

*<sup>r</sup>*) of coumarins in alkanes at 298K for C522B and C307 (the maximum error in the

The probes C522B and C138 have shown coincidentally similar interactions. In C138, aminomethyl group being free contributes more to the charge separation through resonance- whereas in C522B this resonance contribution is sluggish, comparatively. However, the presence of -CF3 in C522B increases the charge separation, which leads to better interaction with the hydrogen bonding solvents. Replacement of -CF3 by cyclic alkyl group in C138 would not have any great contribution towards its polarity. Hence, the presence of two different groups with contradicting properties leads to the coincidental

*<sup>f</sup>*) and rotational reorientation

*<sup>f</sup>*) and rotational reorientation

a Viscosity data is from Inamdar et al., 2006

a Viscosity data is from Inamdar et al., 2006

is less than ±50 ps) (Mannekutla et al., 2010)

time (τ

time (τ

Table 6. Steady-state anisotropy (*<r>*), fluorescence lifetime (

Table 7. Steady-state anisotropy (*<r>*), fluorescence lifetime (

similarities in reorientation dynamics of C522B and C138.

fluorescence life times is less than ±50 ps) (Mannekutla et al., 2010)

The normalized rotational reorientation times (at unit viscosity) are smaller in alkanes compared to alcohols, which indicates that the probes C522B and C307 rotate faster in alkanes compared to alcohols. The reorientation times of the three probes thus obtained in alcohols follow the trend: *C CB C* 307 522 138 *rr r* ττ τ> ≥ .

Fig. 8 gives a typical plot of τ*r* vs η for all the three probes in alcohols and in alkanes along with the stick and slip lines. Note that the experimentally measured reorientation times lie between slip and stick hydrodynamic in case of alcohols. However, in alkanes we observe, as the size of the solvent molecule becomes equal to and bigger than the size of the solute molecule, the probe molecule experiences a reduced friction. Benzler and Luther (1977) measured the reorientation time of biphenyl (*V*=150 Å3) and *p*-terphenyl (*V*=221 Å3) in *n*alkanes. For biphenyl a nonlinearity was observed in the plot of τ*r* vs η from decane and from tetradecane, in case of *p*-terphenyl. Singh [24] studied reorientation times of the probe neutral red (*V*=234 Å3) which experienced a reduced friction from tetradecane to hexadecane following subslip behavior. C522B (223 Å3) and C307 (217 Å3) have nearly identical volumes as compared to neutral red and *p*-terphenyl and thus a similar rotational relaxation in alkanes may be expected.

Fig. 8. Plots of τ*r* vs η for the three coumarins in alcohols (○), and alkanes (•) in case of C522B and C307

Rotational Dynamics of Nonpolar and Dipolar

aggregate.

Molecules in Polar and Binary Solvent Mixtures 213

intermolecular interactions due to structural heterogeneities. In DMSO+water mixture, the partial negative charge on the oxygen atom of the dimethyl sulphoxide molecule forms hydrogen bonds with water molecules, giving rise to a non-ideal behavior of the mixture. The non-ideality of mixtures depends on the nature of interaction between the different species constituting the mixture. Traube suggested that the anomalous behavior of viscosity in binary mixtures arises from the formation of clusters (Traube, 1886). The prominent hydrophilic nature of DMSO renders it capable of forming strong and persistent hydrogen bonds with water through its oxygen atom (Safford et al., 1969; Martin and Hanthal, 1975; De La Torre, 1983; Luzar and Chandler, 1993). This leads to the formation of DMSO-water molecular aggregates of well-defined geometry which are often responsible for the strong nonideal behavior manifested as maxima or minima (Cowie and Toporowski, 1964; Packer and Tomlinson, 1971; Fox and Whittingham, 1974; Tokuhiro et al., 1974; Gordalla and Zeidler, 1986; 1991; Kaatze et al., 1989). The largest deviations from the ideal mixing occur around 33% mole of DMSO, thus suggesting the existence of stoichiometrically well defined 1DMSO:2water complexes. Recently, a number of MD simulations (Vaisman and Berkowitz, 1992; Soper and Luzar, 1992; 1996; Luzar and Chandler, 1993; Borin and Skaf, 1998; 1999) and neutron diffraction experiments have indeed identified the structure of the 1DMSO:2water complex and linked many of the structural and dynamical features of DMSO water mixtures to the presence of such aggregates. Of late, Borin and Skaf (Borin and Skaf, 1998; 1999) have found from MD simulations, another distinct type of aggregate consisting of two DMSO molecules linked by a central water molecule through H-bonding, which is expected to be the predominant form of molecular association between DMSO and water in DMSO-rich mixtures. This H-bonded complex is referred to as 2DMSO:1water

The rotational diffusion studies of the following two sets of structurally similar molecules dyes: coumarin-440 (C440), coumarin-450 (C450), coumarin 466 (C466) and coumarin-151 (C151) and fluorescein 27 (F27), fluorescein Na (FNa) and sulforhodamine B (SRB) (Fig. 9) in binary mixtures of dimethyl sulphoxide + water and propanol + water mixtures, respectively. Among coumarins, C466 possess N-diethyl group at the fourth position whereas, other three dyes possess amino groups at the seventh position in addition to carbonyl group. This structure is expected to affect the reorientation times due to the

The photo-physics of fluorescent molecules in solvent mixtures has not been studied as extensively as those in neat solvents. Thus the structure and structural changes in the solvent environment around the solute in the mixed solvents have not been fully understood. It is therefore important to investigate the photophysical characteristics that are

DMSO is miscible with water in all proportions and aqueous DMSO solutions are quite interesting systems, as there exists a nonlinear relationship between the bulk viscosity and the composition of the solvent mixture. In DMSO-water binary mixture, there is a rapid rise in viscosity with a small addition of DMSO to water and viscosity decay profile after the post peak point is gradual. The sharp increase in the viscosity of the binary mixture with increasing DMSO concentration may be attributed to significant hydrogen bonding effects between water and DMSO molecules. Beyond around 15% composition of DMSO, there exist two DMSO compositions for which viscosity is same. This dual valuedness should

τ

) about the

manifest in reasonable mirror symmetry of the rotational reorientation time ( *<sup>r</sup>*

formation of hydrogen bond with the solvent mixture.

unique to the binary solvent mixtures.

Note that the probes experience reduced friction as the size of the solvent increases. A number of probes have been studied (Phillips et al., 1985; Courtney et al., 1986; Ben Amotz and Drake, 1988; Roy and Doraiswamy, 1993; Williams et al., 1994; Jiang and Blanchard, 1994; Anderton and Kauffman, 1994; Brocklehurst and Young, 1995) in alcohols and alkanes, wherein faster rotation of the probe in alcohols is observed compared to alkanes, which has been explained as due to higher free volume in alcohols compared to alkanes with the help of DKS theory. If there were no electrical interaction between the coumarins and alcohols, a faster rotation of the coumarins would have been observed in alcohols compared to alkanes, but an opposite trend has been observed that indicates the presence of electrical friction (Dutt and Raman, 2001). Before evaluating the amount of dielectric friction, the contribution due to mechanical friction must be estimated with a reasonable degree of accuracy. SED theory with a slip hydrodynamic boundary condition is often used to calculate the mechanical friction in case of medium-sized solute molecules. However, in the present study the solvent size increases by more than 5 times in alcohols from methanol to decanol. Hence, DKS quasihydrodynamic theory is found to be more appropriate, when size effect is taken into account as compared with GW. Eqn. 25 is used to calculate Δ*V* in associative solvents like alcohols, because *CDKS* obtained in this manner gave a better agreement with the experimental results (Hubbard and Onsager, 1977; Anderton and Kauffman, 1996; Dutt et al., 1999; Dutt and Raman, 2001).

In summary, a faster rotation of the probes is observed in case of C522B and C138 in alcohols compared to C307. In spite of the distinct structures, almost similar rotational reorientation times are observed for C522B and C138 in alcohols from propanol to decanol. Further studies of dielectric friction in alcohols, the observed reorientation times of these coumarins could not follow the trend predicted by the theories of Nee-Zwanzig and van der Zwan-Hynes. Dielectric frictions obtained experimentally and theoretically using NZ and ZH theories, do not agree well.
