**1.1 Steady-state and time resolved fluorescence**

Fluorescence measurements can be broadly classified into two types of measurements: steady-state and time-resolved. Steady-state measurements, the most common type, are those performed with constant illumination and observation. The sample is illuminated with a continuous beam of light, and the intensity or emission spectrum is recorded as function of wavelength. When the sample is first exposed to light steady state is reached almost immediately. Because of the ns timescale of fluorescence, most measurements employ steady-state method. The second type of measurement is time-resolved method which is used for measuring intensity decays or anisotropy decays. For these measurements the sample is exposed to a pulse of light, where the pulse width is typically shorter than the decay time of the sample. The intensity decay is recorded with a high-speed detection system that permits the intensity or anisotropy to be measured on the ns timescale.

## **1.2 Fluorescence anisotropy**

The photoselection of fluorescent probe by polarized light offers the opportunity to study some relevant processes occurring at molecular level in heterogeneous systems. The fluorescence, emitted from the samples excited with polarized light, is also polarized. This polarization is due to the photoselection of the fluorophores according to their orientation relative to the direction of the polarized excitation. This photoselection is proportional to the square of the cosine of the angle between the absorption dipole of the fluorophore and the axis of polarization of the excitation light. The orientational anisotropic distribution of the excited fluorophore population relaxes by rotational diffusion of the fluorophores and excitation energy transfer to the surrounding acceptor molecule. The polarized fluorescence emission becomes depolarized by such processes. The fluorescence anisotropy measurements reveal the average angular displacement of the fluorophore, which occurs between absorption and subsequent emission of a photon. The degree of polarization, *P*, and steady state fluorescence anisotropy *r*, are thus respectively given by equations (Lakowicz, 2006)

$$P = \frac{I\_{\parallel \parallel} - I\_{\perp}}{I\_{\parallel \parallel} + I\_{\perp}} \tag{2}$$

$$r = \frac{I\_{\parallel \parallel} - I\_{\perp}}{I\_{\parallel \parallel} + 2I\_{\perp}} \tag{3}$$

where || *I* and *I*⊥ represent the fluorescence intensities when the orientation of the emission polarizer is parallel and perpendicular to the orientation of the excitation polarizer, respectively. The fluorescence anisotropy (*r*) is a measure of the average depolarization during the lifetime of the excited fluorophore under steady-state conditions. A steady-state observation is simply an average of the time-resolved phenomena over the intensity decay of the sample. But the time resolved measurements of fluorescence anisotropy using ultrafast polarized excitation source (laser) give an insight into the time dependent depolarization. The time dependent fluorescence anisotropy decay, *r(t)*, is defined as

Rotational Dynamics of Nonpolar and Dipolar

Molecules in Polar and Binary Solvent Mixtures 189

resolve because, unlike in solids, the spatial relationship between the molecules are not fixed on time scales that can be accessed using structural measurements such as X-ray diffraction or multidimensional NMR spectrometry. Intermolecular interactions in the liquid phase are more complex than those in gas phase because of their characteristic strength, the property that gives rise to the liquid phase and at the same time prevents a simple statistical description of collisional interactions from providing adequate insight (Fleming, 1986). Regardless of almost three and a half decades of continuous investigation, the details of solute-solvent interactions, particularly in polar solvent systems, remain to be understood in detail. Most investigations of intermolecular interactions in solution have used a "probe" molecule present at low concentration in neat or binary solvent systems. Typically, a short pulse of light is shone to establish some non-equilibrium condition in the ensemble of probe molecules, with the object of the experiment being to monitor the return to equilibrium. These studies have included fluorescence lifetime, molecular reorientation (Eisenthal, 1975; Shank and Ippen, 1975; von Jena and Lessing, 1979a; Sanders and Wirth, 1983; Templeton et al., 1985; Blanchard and Wirth, 1986; Templeton and Kenney-Wallace, 1986; Blanchard, 1987, 1988, 1989; Blanchard and Cihal, 1988; Hartman et al., 1991; Srivastava and Doraiswamy, 1995; Imeshev and Khundkar, 1995; Dutt, et al., 1995; Chandrashekhar et al., 1995; Levitus et al., 1995; Backer et al., 1996; Biasutti et al., 1996; Horng et al., 1997; Hartman et al., 1997; Laitinen et al., 1997; Singh, 2000; Dutt and Raman, 2001; Gustavsson et al., 2003; Dutt and Ghanty, 2004; Kubinyi et al., 2006), vibrational relaxation (Heilweil et al., 1986, 1987, 1989; Lingle Jr. et al., 1990; Anfinrud et al., 1990; Elsaesser and Kaiser, 1991; Hambir et al., 1993; Jiang and Blanchard, 1994a & b, 1995; McCarthy and Blanchard, 1995, 1996) and timedelayed fluorescence Stokes shift (Shapiro and Winn, 1980; Maroncelli and Fleming, 1987; Huppert et al. 1989, 1990; Chapman et al., 1990; Wagener and Richert, 1991; Fee et al., 1991; Jarzeba et al., 1991; Yip et al., 1993; Fee and Maroncelli, 1994; Inamdar et al., 1995) measurements. Of these, molecular reorientation of molecules in solution has been an important experimental and theoretical concept for probing the nature of liquids and the interactions of solvents with molecules. This has proven to be among the most useful because of the combined generality of the effect and the well-developed theoretical framework for the interpretation of the experimental data (Debye, 1929; Perrin, 1936; Chuang and Eisethal, 1972; Hu and Zwanzig, 1974; Youngren and Acrivos, 1975; Zwanzig and Harrison, 1985). Though, the effect of solute-solvent interactions on the rotational motion of a probe molecule in solution has been extensively studied, these interactions are generally described as friction to probe rotational motion and can be classified into three types. The first category includes short-range repulsive forces, which dominate intermolecular dynamics during molecular collisions. These interactions are present in all liquids and lead to viscous dissipation, which is well described by hydrodynamic theories (Fleming, 1986). The second category includes long-range electrostatic interactions between a charged or dipolar probe and polar solvent molecules. As the solute turns, the induced solvent polarization can lag behind rotation of the probe, creating a torque, which systematically reduces the rate of rotational diffusion. This effect, termed dielectric friction, arises from the same type of correlated motions of solvent molecules, which is responsible for the time dependent Stokes' shift (TDSS) dynamics of fluorescent probes (van der Zwan and Hynes, 1985; Barbara and Jarzeba, 1990; Maroncelli, 1993). The third category includes specific solute-solvent interactions. Hydrogen bonding is probably the most frequently encountered example of this kind. Strong hydrogen bonds will lead to the formation of

$$r(t) = \frac{I\_{\parallel \perp}(t) - I\_{\perp}(t)}{I\_{\parallel \perp}(t) + 2I\_{\perp}(t)}\tag{4}$$

where || *I t*( ) and *I t*( ) <sup>⊥</sup> are the fluorescence intensity decays collected with the polarization of the emission polarizer maintained parallel and perpendicular to the polarization of the excitation source, respectively. For a fluorophore in a sample solvent, the fluorescence depolarization is simply due to rotational motion of the excited fluorophore and the decay parameters depend on the size and shape of the fluorophore. For spherical fluorophores, the anisotropy decay is a single exponential with a single rotational correlation time and is given by (Lakowicz, 2006)

$$r(t) = r\_0 \exp(-t \mid \pi\_I) \tag{5}$$

where 0*r* is the initial anisotropy (anisotropy at time t=0 or anisotropy observed in the absence of any depolarizing processes) and *<sup>r</sup>* τ is the rotational correlation time. The initial anisotropy 0*r* is related to the angle (θ) between the absorption and emission dipoles of the fluorophore under study as

$$r\_0 = \frac{2}{5} \left( \frac{3\cos^2(\theta) - 1}{2} \right) \tag{6}$$

where the value 0*r* can vary between 0.4 and –0.2 as the angle (θ) varies between <sup>0</sup> 0 and <sup>0</sup> 90 respectively. The rotational correlation times *<sup>r</sup>* τ of the fluorophore is governed by the viscosity ( ) η , temperature ( ) *T* of the solution and the molecular volume ( ) *V* of the fluorophore. This is given by Stokes-Einstein relation (Fleming, 1986) as shown below:

$$
\sigma\_r = \frac{\eta V}{kT} \tag{7}
$$

where *k* is the Boltzmann constant.

The relation between the steady-state anisotropy (*r*), initial anisotropy ( <sup>0</sup>*r* ), rotational correlation time ( *<sup>r</sup>* τ ) and fluorescence lifetime ( *<sup>f</sup>* τ ) is given by Perrin equation as follows (Lackowicz, 1983)

$$\frac{r\_0}{r} = 1 + \frac{\pi\_f}{\pi\_r} \tag{8}$$

The Perrin equation is very useful in obtaining the correlation time without the measurement of polarization dependent fluorescence decays [ || *I t*( ) and *I t*( ) <sup>⊥</sup> ]. The theory developed for more complicated shapes of the fluorophore show that a maximum of five exponentials are enough to explain the fluorescence anisotropy decay (Steiner, 1991).
