**3. Experimental methods**

The experimental techniques used for the investigation of rotational reorientation times mainly consist of steady-state fluorescence spectrophotometer and time resolved fluorescence spectrometer employing time correlated single photon counting (TCSPC).

#### **3.1a Steady-state measurements**

For vertical excitation, the steady-state fluorescence anisotropy can be expressed as (Dutt et al., 1999; Lakowicz, 1983)

$$r < r \implies \frac{I\_{\parallel \perp} - GI\_{\perp}}{I\_{\parallel \perp} + 2GI\_{\perp}} \tag{35}$$

where || *I* and *I*<sup>⊥</sup> denote the fluorescence intensities parallel and perpendicular polarized components with respect to the polarization of the exciting beam. G (= 1.14) is an instrumental factor that corrects for the polarization bias in the detection system (Inamdar et al., 2006) and is given by

where the first term represents the mechanical contribution and the second the dielectric

Alavi and Waldeck theory (Alavi and Waldeck, 1991a), proposes that it is rather the charge distribution of the solute than the dipole moment that is used to calculate the friction experienced by the solute molecule. Not only the dipole moment of the solute, but also the higher order moments, contribute significantly to the dielectric friction. In other words, molecules having no net dipole moment can also experience dielectric friction. AW theory has been successful compared to NZ and ZH theories in modeling the friction in nonassociative solvents (Dutt and Ghanty, 2003). The expression for the dielectric friction

0

0 ( 1) (2 1) *DF <sup>P</sup> <sup>D</sup>* ε

4 2 1 ( )! 3 1 ( )!

*i j L iL j ji*

θ

= × + +

ε

<sup>−</sup> <sup>=</sup> <sup>+</sup>

max 11 1 1

*L LM <sup>P</sup> akT* == = = *L LM*

<sup>2</sup> (cos ) (cos )cos

*M qq P P M*

where ( ) *MP x <sup>L</sup>* are the associated Legendre polynomials, *a* is the cavity radius, *N* is the number of partial charges, *qi* is the partial charge on atom *i*, whose position is given by

continuum like the NZ and vdZH theories, it provides a more realistic description of the

The experimental techniques used for the investigation of rotational reorientation times mainly consist of steady-state fluorescence spectrophotometer and time resolved fluorescence spectrometer employing time correlated single photon counting (TCSPC).

For vertical excitation, the steady-state fluorescence anisotropy can be expressed as (Dutt et


<sup>−</sup> < >=

*I GI*

*I* and *I*<sup>⊥</sup> denote the fluorescence intensities parallel and perpendicular polarized components with respect to the polarization of the exciting beam. G (= 1.14) is an instrumental factor that corrects for the polarization bias in the detection system (Inamdar et

⊥ ⊥

*r*

*i j M M*

*NN L L*

*ji L M*

*L L*

*r r*

*a a*

  2

 τ

+ −

 θ

*<sup>j</sup> <sup>i</sup>* . Although the AW theory too treats solvent as a structureless

φ

+ (35)

(33)

(34)

contribution.

where

( , , *iii r* θ φ), and φ *ji* = − φ φ

electronic properties of the solute.

**3.1a Steady-state measurements** 

al., 1999; Lakowicz, 1983)

al., 2006) and is given by

where ||

**3. Experimental methods** 

**iii. The Alavi and Waldeck theory (AW)** 

according to this model is given by (Alavi and Waldek, 1991a)

τ

$$G = \frac{I\_{HV}}{I\_{HH}}\tag{36}$$

where *HV I* is the fluorescence intensity when the excitation polarizer is kept horizontal and the emission polarizer vertical and *IHH* is the fluorescence intensity when both the polarizers are kept horizontal.

### **3.1b Time-resolved fluorescence measurements**

The fluorescence lifetimes of all the probes were measured with time correlated single photon counting technique (TCSPC) using equipment described in detail elsewhere (Selvaraju and Ramamurthy, 2004). If the decay of the fluorescence and the decay of the anisotropy are represented by single exponential, then the reorientation time τ*<sup>r</sup>* is given by (Lakowicz, 1983)

$$\pi\_r = \frac{\pi\_f}{(r\_0/-1)}\tag{37}$$

where *r0* is the limiting anisotropy when all the rotational motions are frozen and τ*<sup>f</sup>* is the fluorescence lifetime.

In case of a prolate-ellipsoid model, the parameter *stick f* is given by (Anderton and Kauffman, 1994)

$$f\_{\rm stick} = \frac{2(\rho^2 + 1)\left(\rho^2 - 1\right)^{3/2}}{3\rho\left[\left(2\rho^2 - 1\right)\ln\left\{\rho + \left(\rho^2 - 1\right)^{1/2}\right\} - \rho\left(\rho^2 - 1\right)^{1/2}\right]}\tag{38}$$

where ρ is the ratio of major axis (*a*) to the minor axis (*b*) of the ellipsoid. This expression is valid for stick boundary condition.

### **3.2 Fluorescent probes used in the study**

#### **Nonpolar probes**

A variety of the nonpolar fluorescent probe molecules have been studied extensively in the recent past. Most of the nonpolar probes so far studied have the radii of 2.5 Å to 5.6 Å (Inamdar et al., 2006) and a transition towards stick boundary condition is evident with increase in size of the solute. Most of the medium sized neutral nonpolar molecules rotate faster in alcohols compared to alkanes, which is in contrast to that of smaller neutral solutes. It is also noted that the quasihydrodynamic description is adequate for small solutes of 2-3 Å radius in case of GW theory whereas, the DKS model with experimental value in alcohols fail beyond the solute radius of 4.2 Å. Our earlier work on rotational dynamics of exalite probes E392A (*r* = 5.3 Å), and E398 (*r* = 6.0 Å), yielded striking results (Inamdar et al., 2006), in that, these large probes rotated much faster than slip hydrodynamics and followed subslip trend in alcohols.

The quest to understand the influence of size of solute on rotational dynamics is continued with three nonpolar solutes viz., Exalite 404 (E404), Exalite 417 (E417) and Exalite 428 (E428), which may further fill the gap between the existing data. These probes have an anistropic shape and a dipole emission along their long rod-like backbones. The rod like or cylinder shape is a macromolecular model of great relevance. A number of biopolymers including

Rotational Dynamics of Nonpolar and Dipolar

**3.2.1 Rotational dynamics of non-polar probes** 

Eqn. (4.43), are tabulated in Table 1 and 2, respectively.

Fig. 2. Molecular structures of (a) E404, (b) E417 and (c) E428

0.0

Fig. 3. Absorption and Fluorescence spectra of E404

0.5

Absorbance

1.0

**(c)**

Molecules in Polar and Binary Solvent Mixtures 201

were excited at 375 nm and the emission was monitored from 403-422 nm from alkanes to alcohols for Exalites. All the solvents (Fluka, HPLC grade) were used without further purification. The concentration of all the solutions was kept sufficiently low in order to

The molecular structures of the non-polar probes exalite 404 (E404), exalite 417 (E417) and exalite 428 (E428) chosen for the study are shown in Fig.2.The absorption and fluorescence spectra of the probes in methanol are shown in Fig.3. These probes are approximated as prolate ellipsoids (Inamdar et al., 2006) with molecular volumes 679, 837 and 1031 Å3,

300 400 500

λ /nm

τ

*<sup>r</sup>*) calculated using

Fluorescence

reduce the effects of self-absorption. All the measurements were performed at 298 K.

respectively, for E404, E417 and E428. The rotational reorientation times (

some polypeptides, proteins, nucleic acids and viruses, under certain conditions exhibit the typical rod-like conformation and their hydrodynamic properties can therefore be analyzed in terms of cylindrical models. Surprisingly, not much is studied about the motion of these highly anisotropic rod-like molecules in liquids, neither experimentally nor by any simulation studies. These exalite dyes have found applications in many areas of research. When pumped by XeCl-excimer laser, Ar+ and Nd:YAG laser, provide tunable lasers in the ultraviolet-blue range (Valenta et al., 1999). E428 has been used to generate circularly polarized light in glassy liquid crystal films (Chen et al., 1999). Exalites are mixed with plastic scintillators (PS) to form new scintillaors, which are for superficial and diagnostic applications (Kirov et al., 1999).

### **Polar probes**

Rotational diffusion of medium-sized molecules provides a useful means to probe solutesolvent interactions and friction. By modeling this friction using various continuum-based theories (NZ, AW and ZH) one can get better insight into the nature of solute-solvent interactions. In order to understand the effect of polar solvents on the reorientational dynamics of the polar solutes, one must unravel the effects of mechanical friction, dielectric friction and specific short-range solute-solvent interactions. To address this issue, rotational dynamics of three polar laser dyes: coumarin 522B (C522B), coumarin 307 (C307) and coumarin 138 (C138) having identical volumes and distinct structures have been carried out in series of alcohols and alkanes. These coumarins are an important class of oxygen heterocycles, which are widespread in plant kingdom and have been extensively used as laser dyes. Their chemical structures can be looked upon as arising out of the fusion of a benzene ring to pyran-2-one, across the 5- and 6-positions in skeleton. In the present coumarins, the two free substituents at 6 and 7 positions, ethylamino and methyl for C307 in comparison with the analogous model substrate C522B wherein, there is no free substituent rather they are joined by ends to obtain piperidino moiety. These two probes are looked upon as polar due to the presence of electron donating amino group and electron withdrawing CF3 group. In C138, this CF3 group is replaced by an alkyl group making it less polar compared to C522B and C307.

The rotational diffusion studies of the following two sets of structurally similar molecules dyes: (i) coumarin-440 (C440), coumarin-450 (C450), coumarin 466 (C466) and coumarin-151 (C151) and (ii) fluorescein 27 (F27), fluorescein Na (FNa) and sulforhodamine B (SRB) 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 influence molecular reorientation due to possible hydrogen bonding with the solvent mixture. The spectroscopic properties of fluorescein dyes are well known with the dyes having applications ranging from dye lasers to tracers in flow visualization and mixing studies. SRB has been used to measure druginduced cytotoxicity and cell proliferation for large-scale drug-screening applications (Koochesfahani and Dimotakis, 1986; Dahm et al., 1991; Karasso and Mungal, 1997; Voigt, 2005). Both F27 and FNa are neutral polar molecules each containing one C = O group, F-27 has two Cl and FNa has two Na groups. The anionic probe SRB possesses N (C2H5), N+ (C2H5) groups and sulfonic groups SO3Na and SO-3 at positions 3, 6, 4′ and 2′, respectively.

The laser grade nonpolar probes Exalites (E404, E417 and E428), nonpolar probes (i) coumarin derivatives (C522B, C307 and C138) and (ii) F27, FNa and SRB (all from Exciton Chemical Co., USA) were used as received. For steady-state experiments, all the samples

some polypeptides, proteins, nucleic acids and viruses, under certain conditions exhibit the typical rod-like conformation and their hydrodynamic properties can therefore be analyzed in terms of cylindrical models. Surprisingly, not much is studied about the motion of these highly anisotropic rod-like molecules in liquids, neither experimentally nor by any simulation studies. These exalite dyes have found applications in many areas of research. When pumped by XeCl-excimer laser, Ar+ and Nd:YAG laser, provide tunable lasers in the ultraviolet-blue range (Valenta et al., 1999). E428 has been used to generate circularly polarized light in glassy liquid crystal films (Chen et al., 1999). Exalites are mixed with plastic scintillators (PS) to form new scintillaors, which are for superficial and diagnostic applications (Kirov et al., 1999).

Rotational diffusion of medium-sized molecules provides a useful means to probe solutesolvent interactions and friction. By modeling this friction using various continuum-based theories (NZ, AW and ZH) one can get better insight into the nature of solute-solvent interactions. In order to understand the effect of polar solvents on the reorientational dynamics of the polar solutes, one must unravel the effects of mechanical friction, dielectric friction and specific short-range solute-solvent interactions. To address this issue, rotational dynamics of three polar laser dyes: coumarin 522B (C522B), coumarin 307 (C307) and coumarin 138 (C138) having identical volumes and distinct structures have been carried out in series of alcohols and alkanes. These coumarins are an important class of oxygen heterocycles, which are widespread in plant kingdom and have been extensively used as laser dyes. Their chemical structures can be looked upon as arising out of the fusion of a benzene ring to pyran-2-one, across the 5- and 6-positions in skeleton. In the present coumarins, the two free substituents at 6 and 7 positions, ethylamino and methyl for C307 in comparison with the analogous model substrate C522B wherein, there is no free substituent rather they are joined by ends to obtain piperidino moiety. These two probes are looked upon as polar due to the presence of electron donating amino group and electron withdrawing CF3 group. In C138, this CF3 group is replaced by an alkyl group making it less

The rotational diffusion studies of the following two sets of structurally similar molecules dyes: (i) coumarin-440 (C440), coumarin-450 (C450), coumarin 466 (C466) and coumarin-151 (C151) and (ii) fluorescein 27 (F27), fluorescein Na (FNa) and sulforhodamine B (SRB) 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 influence molecular reorientation due to possible hydrogen bonding with the solvent mixture. The spectroscopic properties of fluorescein dyes are well known with the dyes having applications ranging from dye lasers to tracers in flow visualization and mixing studies. SRB has been used to measure druginduced cytotoxicity and cell proliferation for large-scale drug-screening applications (Koochesfahani and Dimotakis, 1986; Dahm et al., 1991; Karasso and Mungal, 1997; Voigt, 2005). Both F27 and FNa are neutral polar molecules each containing one C = O group, F-27 has two Cl and FNa has two Na groups. The anionic probe SRB possesses N (C2H5), N+

The laser grade nonpolar probes Exalites (E404, E417 and E428), nonpolar probes (i) coumarin derivatives (C522B, C307 and C138) and (ii) F27, FNa and SRB (all from Exciton Chemical Co., USA) were used as received. For steady-state experiments, all the samples

3 at positions 3, 6, 4′ and 2′, respectively.

**Polar probes** 

polar compared to C522B and C307.

(C2H5) groups and sulfonic groups SO3Na and SO-

were excited at 375 nm and the emission was monitored from 403-422 nm from alkanes to alcohols for Exalites. All the solvents (Fluka, HPLC grade) were used without further purification. The concentration of all the solutions was kept sufficiently low in order to reduce the effects of self-absorption. All the measurements were performed at 298 K.
