**iii. Rotational reorientation times of Exalite 428 (E428)**

E428 is the largest probe studied so far in literature. In alcohols the τ*<sup>r</sup>* values for E428 increase linearly with η from methanol to butanol and follows slip boundary condition, and from pentanol to decanol a large deviation from the linearity is observed resulting in subslip behavior (Fig. 6). However, in alkanes the measured reorientation times, clearly follow slip hydrodynamics up to tridecane, whereas in higher alkanes pentadecane and hexadecane

Rotational Dynamics of Nonpolar and Dipolar

0

0

1500

3000

τr/ ps

4500

**Stick**

**Slip**

800

1600

τr/ ps

2400

Molecules in Polar and Binary Solvent Mixtures 205

**Stick**

**Slip**

0.0 0.7 1.4 2.1 2.8

η/ mPa s

0 3 6 912

η/ mPa s

Fig. 6. Plot of rotational reorientation times of E428 as function of viscosity in (a) alkanes and (b) alcohols. The symbols (○,●) represent experimentally measured reorientation times. The stick and slip lines calculated using hydrodynamic theory are represented by solid lines. GW and DKS quasihydrodynamic theories are represented using the symbols Δ and respectively.

Fig. 5. Plot of rotational reorientation times of E417 as function of viscosity in (a) alkanes and (b) alcohols. The symbols (○,●) represent experimentally measured reorientation times. The stick and slip lines calculated using hydrodynamic theory are represented by solid lines. GW and DKS quasihydrodynamic theories are represented using the symbols Δ and respectively.

**Stick**

**Slip**

0.0 0.7 1.4 2.1 2.8

**Stick**

**Slip**

η/ mPa s

0 3 6 912

η/mPa s

Fig. 5. Plot of rotational reorientation times of E417 as function of viscosity in (a) alkanes and (b) alcohols. The symbols (○,●) represent experimentally measured reorientation times. The stick and slip lines calculated using hydrodynamic theory are represented by solid lines. GW and DKS quasihydrodynamic theories are represented using the symbols Δ and respectively.

0

0

1100

2200

τr/ ps

3300

**(b)**

600

1200

τr/ ps

1800

**(a)**

Fig. 6. Plot of rotational reorientation times of E428 as function of viscosity in (a) alkanes and (b) alcohols. The symbols (○,●) represent experimentally measured reorientation times. The stick and slip lines calculated using hydrodynamic theory are represented by solid lines. GW and DKS quasihydrodynamic theories are represented using the symbols Δ and respectively.

Rotational Dynamics of Nonpolar and Dipolar

hydrogen bonds are ruptured and others are formed.

among the solvent molecules leading to supramolecular structures.

alcohols, at 25±50 C

Molecules in Polar and Binary Solvent Mixtures 207

Table 4. List of normalized rotational diffusion parameters of neutral nonpolar solutes in

with hydrogen bridges in temporary microcrystalline structures. These structures are in fact not stable, and at a given instant each of these has a finite length. At each instance some

The first dispersion region is connected with the molecules in these microcrystalline structures. The dielectric relaxation process involves the breaking and reforming of the hydrogen bonds with the orientation of dipole moment, and the rate of breaking off is a determining factor for the relaxation time. In order to check whether there is any dielectric friction on these large nonpolar probes in alcohols, we have also calculated dielectric friction contribution to the rotating probe molecule. The dipole moment values in the excited states were obtained using solvatochormic shift method (Inamdar et al., 2003; Nadaf et al., 2004; Kawski et al., 2005). It is noted that summing up the contribution due to hydrodynamic and dielectric friction will not affect the subslip trend exhibited by the rotational reorientation times. Hence, we attribute this unhindered faster rotation due to strong hydrogen bonding

There are several reports in literature where the reorientation times of neutral nonpolar solutes have been measured as a function of solute size and the transition from slip to stick hydrodynamics has been observed experimentally. Ben-Amotz and Drake (Ben-Amotz and Drake, 1988) have reported the rotational dynamics of the neutral large sized probe BTBP (*V*=733 Å3) in series of alcohols and alkanes, and observed that rotational correlation times followed stick boundary condition. Though, BTBP contain the electronegative groups like - O and –N, which are capable of forming hydrogen bond with any solvent, they attributed, stick condition to its volume which is much larger than that of all the solvent molecules studied. Later, Roy and Doraiswamy (Roy and Doraiswamy, 1993) have studied the rotational dynamics of series of nonpolar solutes, which do not contain any electronegative groups like -O or –N. They observed transition towards the stick boundary condition on increasing the solute size from BMQ (*V* = 325 Å3) to QUI (*V* = 639 Å3). It is clear from the above two findings that a stick transition arises due to increase in the solute size, when compared to that of the solvent. Thus, one can expect stick or superstick behavior in case of exalites (E404, E417 and E428) as these are larger than QUI by a factor of 1.1, 1.3 and 1.6, respectively. The present situation, where the largest probe E428 follows subslip in alcohols

subslip behavior is observed. It is interesting to note that, all the three probes rotate much faster in alcohols compared to alkanes. This can be explained as due to large interstitial gaps that may be formed in the solvent medium and because of the possible elastic nature of the spatial H-bonding network of large alcohol molecules constituting a supramolecular structure. The elasticity of the spatial network is a driving force for solvophobic interaction, which is important for the larger probes. Presumably these exalite molecules will be located mainly in these solvophobic regions. The probe molecules, thus, can rotate more freely in these gaps as they experience reduced friction due to a decreased viscosity at the point of contact. This actual viscosity is highly localized and cannot be measured easily. In such a situation the coupling parameter *C* can be much smaller than *Cslip* predicted by slip hydrodynamic boundary condition. One of the plausible reasons is also due to the Brownian motion, which results from the fluctuating forces in the liquid, is behind and diffusive process.

Ben-Amotz and Scott (1987) opined that processes, which are slow compared to solvent fluctuations, would see the full spectrum of the fluctuations and thus the shear viscosity of the solvent. For example, the fluctuations in *n*-alcohols occur roughly on the 100 ps/mPa s time scale – precisely the time scale of the Debye absorption in these solvents. On the other hand, processes, which are extremely fast, do not experience Brownian fluctuating force and are not viscously damped. Thus one expects a reduction in microscopic friction for probe molecules, which diffuse at a rate comparable to or faster than the solvent fluctuations. This is exactly the type of effect, which could explain the faster rotational diffusion of exalites in *n*-alcohols than in *n*-alkanes. Further, the subslip behavior observed for these probes in polar solvents indicates the existence the nonhydrodynamic forces and the straightforward relation between the probe size and the nature of their behavior may not be appropriate.

Table 3 and 4 contain selected data for various neutral solute molecules (including exalites), whose rotational times in alkanes and alcohols have been measured experimentally. There are many reports on rotational diffusion of small neutral molecules which follow subslip behavior. Garg and Smyth (1965) have attributed these alcohol molecules to be associated


Table 3. List of normalized rotational diffusion parameters of neutral nonpolar solutes in alkanes, at 25±50 C

subslip behavior is observed. It is interesting to note that, all the three probes rotate much faster in alcohols compared to alkanes. This can be explained as due to large interstitial gaps that may be formed in the solvent medium and because of the possible elastic nature of the spatial H-bonding network of large alcohol molecules constituting a supramolecular structure. The elasticity of the spatial network is a driving force for solvophobic interaction, which is important for the larger probes. Presumably these exalite molecules will be located mainly in these solvophobic regions. The probe molecules, thus, can rotate more freely in these gaps as they experience reduced friction due to a decreased viscosity at the point of contact. This actual viscosity is highly localized and cannot be measured easily. In such a situation the coupling parameter *C* can be much smaller than *Cslip* predicted by slip hydrodynamic boundary condition. One of the plausible reasons is also due to the Brownian motion, which

Ben-Amotz and Scott (1987) opined that processes, which are slow compared to solvent fluctuations, would see the full spectrum of the fluctuations and thus the shear viscosity of the solvent. For example, the fluctuations in *n*-alcohols occur roughly on the 100 ps/mPa s time scale – precisely the time scale of the Debye absorption in these solvents. On the other hand, processes, which are extremely fast, do not experience Brownian fluctuating force and are not viscously damped. Thus one expects a reduction in microscopic friction for probe molecules, which diffuse at a rate comparable to or faster than the solvent fluctuations. This is exactly the type of effect, which could explain the faster rotational diffusion of exalites in *n*-alcohols than in *n*-alkanes. Further, the subslip behavior observed for these probes in polar solvents indicates the existence the nonhydrodynamic forces and the straightforward relation between the probe size and the nature of their behavior may not be appropriate. Table 3 and 4 contain selected data for various neutral solute molecules (including exalites), whose rotational times in alkanes and alcohols have been measured experimentally. There are many reports on rotational diffusion of small neutral molecules which follow subslip behavior. Garg and Smyth (1965) have attributed these alcohol molecules to be associated

Table 3. List of normalized rotational diffusion parameters of neutral nonpolar solutes in

alkanes, at 25±50 C

results from the fluctuating forces in the liquid, is behind and diffusive process.


Table 4. List of normalized rotational diffusion parameters of neutral nonpolar solutes in alcohols, at 25±50 C

with hydrogen bridges in temporary microcrystalline structures. These structures are in fact not stable, and at a given instant each of these has a finite length. At each instance some hydrogen bonds are ruptured and others are formed.

The first dispersion region is connected with the molecules in these microcrystalline structures. The dielectric relaxation process involves the breaking and reforming of the hydrogen bonds with the orientation of dipole moment, and the rate of breaking off is a determining factor for the relaxation time. In order to check whether there is any dielectric friction on these large nonpolar probes in alcohols, we have also calculated dielectric friction contribution to the rotating probe molecule. The dipole moment values in the excited states were obtained using solvatochormic shift method (Inamdar et al., 2003; Nadaf et al., 2004; Kawski et al., 2005). It is noted that summing up the contribution due to hydrodynamic and dielectric friction will not affect the subslip trend exhibited by the rotational reorientation times. Hence, we attribute this unhindered faster rotation due to strong hydrogen bonding among the solvent molecules leading to supramolecular structures.

There are several reports in literature where the reorientation times of neutral nonpolar solutes have been measured as a function of solute size and the transition from slip to stick hydrodynamics has been observed experimentally. Ben-Amotz and Drake (Ben-Amotz and Drake, 1988) have reported the rotational dynamics of the neutral large sized probe BTBP (*V*=733 Å3) in series of alcohols and alkanes, and observed that rotational correlation times followed stick boundary condition. Though, BTBP contain the electronegative groups like - O and –N, which are capable of forming hydrogen bond with any solvent, they attributed, stick condition to its volume which is much larger than that of all the solvent molecules studied. Later, Roy and Doraiswamy (Roy and Doraiswamy, 1993) have studied the rotational dynamics of series of nonpolar solutes, which do not contain any electronegative groups like -O or –N. They observed transition towards the stick boundary condition on increasing the solute size from BMQ (*V* = 325 Å3) to QUI (*V* = 639 Å3). It is clear from the above two findings that a stick transition arises due to increase in the solute size, when compared to that of the solvent. Thus, one can expect stick or superstick behavior in case of exalites (E404, E417 and E428) as these are larger than QUI by a factor of 1.1, 1.3 and 1.6, respectively. The present situation, where the largest probe E428 follows subslip in alcohols

Rotational Dynamics of Nonpolar and Dipolar

**3.2.2 Rotational dynamics of polar probes** 

the bare solute molecule.

polarity.

Molecules in Polar and Binary Solvent Mixtures 209

been evidenced that the GW theory correctly predicts the observed results for a solute with ~2.5 Å radius. Therefore, the GW model is adequate for very small solutes that show subslip behavior, viz., I2 and NCCCCN (Goulay, 1983). Though, DKS theory is found to be in good agreement with the experimentally observed trend up to decane in case of E404 and up to nonane for E428, a better agreement is found in alkanes for E417. It has been noted that the rotational reorientation times in alkanes is reproduced quantitatively for solutes with radius up to 4.2 Å only, beyond which the theory tends to show poor agreement with experimental values [93]. Our experimental results are indicative of the fact the DKS theory also holds well even for larger probes up to a radius of 6.3 Å in

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

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

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

τ*<sup>r</sup>* values

C138 in alcohols (Mannekutla et al., 2010) are summarized in Tables 6 and 7. The

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

alkanes and brings out the subtle variations in the observed data.

is surprising in the light of above studies. In such a situation the microscopic friction of the solvent molecules reduces well below the macroscopic value, which may result from either dynamic or structural features of the macroscopic solvation environment-giving rise to faster rotation in hydrogen bonding solvents.

On the other hand, rotational reorientation times of these exalite nonpolar probes bequeath interesting results following slip boundary condition in alkanes. It is observed from the Table 5 that there is a difference in slope for the two solvent types. Therefore, it is evident that the rotational reorientation times of these exalites are shorter in alcohols than alkanes of comparable viscosity. This difference is an indication of nonhydrodynamic effects in one or both of the solvents. It is unlikely that nonhydrodynamic behavior resulting from frequency dependence of the solvent friction occurs in alkanes on the 100 ps to 1 ns time scale (Hynes, 1986). These times are much longer than dynamic memory effects in the solvent arising from molecular collisions. These collisional events manifest themselves in the viscoelastic relaxation time, which for an *n*-alkane is estimated to lie in the subpicosecond to single picosecond time domain (Hynes, 1986).


\* Second entry for solute is a slope of the best fit line made to pass through the origin.

Table 5. Linear regression results of rotational reorientation of exalites in series of alcohols, alkanes and binary mixture

Thus one would expect rotational times to be well described by the SED relation with the appropriate boundary condition and the solute shape factor (Ben Amotz and Scott, 1987) in *n*-alkanes. The internal mobility also allows the solute molecule to slip better through the surrounding solvent molecules than for a rigid molecular backbone (Alavi et al., 1991b,c). Waldeck et al. (1982) have also argued for the probe DPB, that the slip boundary condition is entirely reasonable for an uncharged nonpolar molecule in nonpolar solvents. E428 is about 5 times larger than DPB and from the Table 3; it is evident that τ*r*/τ*stick* ratio is same for both these probes in alkanes, which suggests the fact that the rotation of these probes can be well explained by slip hydrodynamics. Similarly, the studies of the neutral dye BBOT (Fleming et al., 1977), an approximate prolate top, found that this molecule followed slip boundary condition. It was anticipated that neutrals would not strongly interact with the solvent, and slip boundary condition were thus more appropriate. Others have argued (Porter et al., 1977) that the faster rotation observed for BBOT might also be due to the internal mobility of the dye. This may be one of the possible reasons for the faster rotation observed for the large exalite probes. Both GW and DKS models were tested for a quantitative prediction of τ*<sup>r</sup>* of solutes in alkanes. The GW model predicts very low τ*<sup>r</sup>* values in alkanes as well as in the case of alcohols and fails to satisfactorily explain the observed results. Also, the *C* values are nearly invariant of the size of the solute. It has

is surprising in the light of above studies. In such a situation the microscopic friction of the solvent molecules reduces well below the macroscopic value, which may result from either dynamic or structural features of the macroscopic solvation environment-giving rise to

On the other hand, rotational reorientation times of these exalite nonpolar probes bequeath interesting results following slip boundary condition in alkanes. It is observed from the Table 5 that there is a difference in slope for the two solvent types. Therefore, it is evident that the rotational reorientation times of these exalites are shorter in alcohols than alkanes of comparable viscosity. This difference is an indication of nonhydrodynamic effects in one or both of the solvents. It is unlikely that nonhydrodynamic behavior resulting from frequency dependence of the solvent friction occurs in alkanes on the 100 ps to 1 ns time scale (Hynes, 1986). These times are much longer than dynamic memory effects in the solvent arising from molecular collisions. These collisional events manifest themselves in the viscoelastic relaxation time, which for an *n*-alkane is estimated to lie in the subpicosecond to single

\* Second entry for solute is a slope of the best fit line made to pass through the origin.

E428 is about 5 times larger than DPB and from the Table 3; it is evident that

τ

Table 5. Linear regression results of rotational reorientation of exalites in series of alcohols,

Thus one would expect rotational times to be well described by the SED relation with the appropriate boundary condition and the solute shape factor (Ben Amotz and Scott, 1987) in *n*-alkanes. The internal mobility also allows the solute molecule to slip better through the surrounding solvent molecules than for a rigid molecular backbone (Alavi et al., 1991b,c). Waldeck et al. (1982) have also argued for the probe DPB, that the slip boundary condition is entirely reasonable for an uncharged nonpolar molecule in nonpolar solvents.

is same for both these probes in alkanes, which suggests the fact that the rotation of these probes can be well explained by slip hydrodynamics. Similarly, the studies of the neutral dye BBOT (Fleming et al., 1977), an approximate prolate top, found that this molecule followed slip boundary condition. It was anticipated that neutrals would not strongly interact with the solvent, and slip boundary condition were thus more appropriate. Others have argued (Porter et al., 1977) that the faster rotation observed for BBOT might also be due to the internal mobility of the dye. This may be one of the possible reasons for the faster rotation observed for the large exalite probes. Both GW and DKS models were

*<sup>r</sup>* values in alkanes as well as in the case of alcohols and fails to satisfactorily explain the observed results. Also, the *C* values are nearly invariant of the size of the solute. It has

τ*r*/τ

*<sup>r</sup>* of solutes in alkanes. The GW model predicts very

*stick* ratio

faster rotation in hydrogen bonding solvents.

picosecond time domain (Hynes, 1986).

alkanes and binary mixture

tested for a quantitative prediction of

low τ been evidenced that the GW theory correctly predicts the observed results for a solute with ~2.5 Å radius. Therefore, the GW model is adequate for very small solutes that show subslip behavior, viz., I2 and NCCCCN (Goulay, 1983). Though, DKS theory is found to be in good agreement with the experimentally observed trend up to decane in case of E404 and up to nonane for E428, a better agreement is found in alkanes for E417. It has been noted that the rotational reorientation times in alkanes is reproduced quantitatively for solutes with radius up to 4.2 Å only, beyond which the theory tends to show poor agreement with experimental values [93]. Our experimental results are indicative of the fact the DKS theory also holds well even for larger probes up to a radius of 6.3 Å in alkanes and brings out the subtle variations in the observed data.
