**3.2.3 Rotational dynamics of polar probes in binary solvents**

Binary mixtures of polar solvents represent an important class of chemical reaction media because their polarity can be controlled through changes in composition. In a binary mixture, altering the composition of one of the ingredients can lead to a change in solubility, polarizability, viscosity and many other static and dynamic properties. Yet, it is often found that the dielectric properties of polar mixtures depart significantly from what one might expect on the basis of ideal mixing. In hydrogen-bonding systems, such as alcohol-water mixtures, intermolecular correlations are strong, and consequently, the dielectric properties of the mixture are usually not simply related to those of the separated components. Recently, the properties of some binary solutions were studied using theoretical calculations and molecular dynamics (MD) simulations (Chandra and Bagchi, 1991; Chandra, 1995; Skaf and Ladanyi, 1996; Day and Patey, 1997; Yoshimori et al., 1998; Laria and Skaf, 1999). The results showed that the dynamical features of binary solutions are very much different from those of neat solutions, and the dynamics can be strongly affected by the properties of the solute probe. The binary mixtures show exotic features which pose interesting challenges to both theoreticians and experimentalists. Amongst them, the extrema observed in the composition dependence of excess viscosity (Qunfang and Yu-Chun, 1999; Pal and Daas, 2000) and the anomalous viscosity dependence of the rotational relaxation time (Beddard et al., 1981) are significant. The anomalous features in the complex systems arise from specific

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

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

Binary mixtures of polar solvents represent an important class of chemical reaction media because their polarity can be controlled through changes in composition. In a binary mixture, altering the composition of one of the ingredients can lead to a change in solubility, polarizability, viscosity and many other static and dynamic properties. Yet, it is often found that the dielectric properties of polar mixtures depart significantly from what one might expect on the basis of ideal mixing. In hydrogen-bonding systems, such as alcohol-water mixtures, intermolecular correlations are strong, and consequently, the dielectric properties of the mixture are usually not simply related to those of the separated components. Recently, the properties of some binary solutions were studied using theoretical calculations and molecular dynamics (MD) simulations (Chandra and Bagchi, 1991; Chandra, 1995; Skaf and Ladanyi, 1996; Day and Patey, 1997; Yoshimori et al., 1998; Laria and Skaf, 1999). The results showed that the dynamical features of binary solutions are very much different from those of neat solutions, and the dynamics can be strongly affected by the properties of the solute probe. The binary mixtures show exotic features which pose interesting challenges to both theoreticians and experimentalists. Amongst them, the extrema observed in the composition dependence of excess viscosity (Qunfang and Yu-Chun, 1999; Pal and Daas, 2000) and the anomalous viscosity dependence of the rotational relaxation time (Beddard et al., 1981) are significant. The anomalous features in the complex systems arise from specific

et al., 1999; Dutt and Raman, 2001).

ZH theories, do not agree well.

**3.2.3 Rotational dynamics of polar probes in binary solvents** 

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 aggregate.

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 formation of hydrogen bond with the solvent mixture.

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 unique to the binary solvent mixtures.

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

Rotational Dynamics of Nonpolar and Dipolar

**1.0 1.5 2.0 2.5 3.0 3.5 4.0**

**1.0 1.5 2.0 2.5 3.0 3.5 4.0**

τ

qualitatively mimics the observed profile, with the *<sup>r</sup>*

η**(mPas)**

η**(mPas)**

**0**

**0**

higher *<sup>r</sup>* τ

(Inamdar et al., 2009)

points being different.

The linear variation of the *<sup>r</sup>*

**40**

**80**

**120**

τ**r(ps)**

**160**

**200**

**<sup>240</sup>** C466

**40**

**80**

**120**

τ**r(ps)**

**160**

**200**

C440

Molecules in Polar and Binary Solvent Mixtures 215

Slip+DF

**0**

**0**

τ

in the DMSO rich zone than the corresponding isoviscous point in the water rich

**40**

**80**

**120**

τ**r(ps)**

**160**

**200**

**240**

C151

**50**

**100**

**150**

τ**r(ps)**

**200**

**250**

**300**

C450

**1.0 1.5 2.0 2.5 3.0 3.5 4.0**

**1.0 1.5 2.0 2.5 3.0 3.5 4.0**

η**(mPas)**

from pure water to the composition of the

τ

being slightly larger in the post peak

Slip

τ vs.η

at isoviscous points

GW Slip+DF

Expt

Stick

Stick+DF

η**(mPas)**

Stick+DF

Slip GW Slip+DF

Expt

Stick

GW Slip

Slip GW Slip+DF

as a function of

features in the binary mixture could be different. The dual values of *<sup>r</sup>*

Fig. 10. Plot of rotational reorientation time with viscosity along with theoretical profile including the viscous and the dielectric contribution for C440, C450, C466 and C151 probes

η

binary mixture when the viscosity reaches its peak is in accordance with the SED theory, though it does not account for the large curvature in the profile. The theoretical SED stick line shows a sharp hairpin profile. Incorporation of the dielectric friction contribution

viscosity DMSO rich zone. The fact, that a continuum theory without the consideration of any molecular features could reproduce the gross features of the observed profile of *<sup>r</sup>*

is noteworthy. The experimentally observed profile bent upwards yields considerably

zone. This is also reproduced by the theoretical models qualitatively. The pronounced difference in the rotational reorientation times at the isoviscous points can be explained only on the basis of solvation. It is possible that at the isoviscous points the microstructural

in the DMSO rich zone are also due to the contributions of dielectric friction at these two

Expt

Stick+DF

Stick

Stick Expt

Stick+DF

Fig. 9. The molecular structures of (a) C440, (b) C450, (c) C466, (d) C151, (e) F27, (f) FNa and (g) SRB.

viscosity peak point. The viscosity of DMSO is slightly more than twice that of water. At about 40% mole composition of DMSO, the solvent mixture has a maximum value of viscosity of 3.75 m Pas which is 1.87 times that of DMSO and nearly 4 times that of water. From the viscosity profile it may be seen that there are four distinct compositions of DMSO for which the viscosity is nearly the same and as per hydrodynamic theory the friction experienced by a rotating probe molecule is expected to be the same.

Fig. 10 (a and b) represent the variation of *<sup>r</sup>* τ with η along with theoretical profile including the viscous and the dielectric contribution for all the probes, which clearly indicates a nonhydrodynamic behavior. The rotational reorientation time of a solute in a solvent is in a way an index of molecular friction. Experimentally obtained results of all the probes under study show a hairpin profiles bent upwards. The reorientation times gradually increases as a function of viscosity up to the peak viscous value and interestingly these values further increase even after the solvent mixture exhibits reduction in viscosity after the peak value. Thus all the probes exhibit different rotational reorientation values for isoviscous points. Note that, reorientation times are longer in the DMSO region compared to the water rich zone. The studies of the rotational diffusion of the dye molecules in binary solvents showed that the rotational relaxation time does not necessarily scale linearly with viscosity when the solvent composition is changed. These observations have been interpreted as a manifestation of solvent structure on time scales similar to or longer than the time scale of solute rotation or as resulting from a change in the dielectric friction through the solvent mixture. In some cases these observations have been interpreted as a breakdown of the hydrodynamic approximation. The rotational diffusion studies of the dye molecule oxazine 118 in two binary solvent systems as a function of temperature showed a nonlinear dependence of the rotational diffusion on the solvent viscosity when the solvent composition is changed (Williams et al., 1994).

ONa O O

Fig. 9. The molecular structures of (a) C440, (b) C450, (c) C466, (d) C151, (e) F27, (f) FNa and

viscosity peak point. The viscosity of DMSO is slightly more than twice that of water. At about 40% mole composition of DMSO, the solvent mixture has a maximum value of viscosity of 3.75 m Pas which is 1.87 times that of DMSO and nearly 4 times that of water. From the viscosity profile it may be seen that there are four distinct compositions of DMSO for which the viscosity is nearly the same and as per hydrodynamic theory the friction

> τ with η

the viscous and the dielectric contribution for all the probes, which clearly indicates a nonhydrodynamic behavior. The rotational reorientation time of a solute in a solvent is in a way an index of molecular friction. Experimentally obtained results of all the probes under study show a hairpin profiles bent upwards. The reorientation times gradually increases as a function of viscosity up to the peak viscous value and interestingly these values further increase even after the solvent mixture exhibits reduction in viscosity after the peak value. Thus all the probes exhibit different rotational reorientation values for isoviscous points. Note that, reorientation times are longer in the DMSO region compared to the water rich zone. The studies of the rotational diffusion of the dye molecules in binary solvents showed that the rotational relaxation time does not necessarily scale linearly with viscosity when the solvent composition is changed. These observations have been interpreted as a manifestation of solvent structure on time scales similar to or longer than the time scale of solute rotation or as resulting from a change in the dielectric friction through the solvent mixture. In some cases these observations have been interpreted as a breakdown of the hydrodynamic approximation. The rotational diffusion studies of the dye molecule oxazine 118 in two binary solvent systems as a function of temperature showed a nonlinear dependence of the rotational diffusion on the solvent viscosity when the solvent

(e) (f) (g)

experienced by a rotating probe molecule is expected to be the same.

COONa

O

(H5C2)2N N<sup>+</sup>

along with theoretical profile including

SO3Na

SO3 - (C2H5)2

(g) SRB.

COOH

Fig. 10 (a and b) represent the variation of *<sup>r</sup>*

composition is changed (Williams et al., 1994).

OH O O

Cl Cl

Fig. 10. Plot of rotational reorientation time with viscosity along with theoretical profile including the viscous and the dielectric contribution for C440, C450, C466 and C151 probes (Inamdar et al., 2009)

The linear variation of the *<sup>r</sup>* τ as a function of η from pure water to the composition of the binary mixture when the viscosity reaches its peak is in accordance with the SED theory, though it does not account for the large curvature in the profile. The theoretical SED stick line shows a sharp hairpin profile. Incorporation of the dielectric friction contribution qualitatively mimics the observed profile, with the *<sup>r</sup>* τ being slightly larger in the post peak viscosity DMSO rich zone. The fact, that a continuum theory without the consideration of any molecular features could reproduce the gross features of the observed profile of *<sup>r</sup>* τ vs.η is noteworthy. The experimentally observed profile bent upwards yields considerably higher *<sup>r</sup>* τ in the DMSO rich zone than the corresponding isoviscous point in the water rich zone. This is also reproduced by the theoretical models qualitatively. The pronounced difference in the rotational reorientation times at the isoviscous points can be explained only on the basis of solvation. It is possible that at the isoviscous points the microstructural features in the binary mixture could be different. The dual values of *<sup>r</sup>* τ at isoviscous points in the DMSO rich zone are also due to the contributions of dielectric friction at these two points being different.

Rotational Dynamics of Nonpolar and Dipolar

including viscous contribution for F27

**General conclusion and summary** 

probes up to a radius of 6.3 Å in alkanes.

dielectric frictions using NZ and ZH theories, do not agree well.

bonding.

Molecules in Polar and Binary Solvent Mixtures 217

Fig. 11. Plot of rotational reorientation time with viscosity along with theoretical profile

valuedness of τr at isoviscous points near the organic solvent rich zone were attributed to different contributions of dielectric friction at these compositions and to strong hydrogen

In this article, an attempt has been made to understand solute-solvent interactions in various situations using the powerful fluorescence spectroscopic techniques. The interesting observation of faster rotation of nonpolar probes in alcohols compared to alkanes can be attributed 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. Presumably the exalite molecules will be located mainly in these solvophobic regions and thus, can rotate more freely in these gaps and experience reduced friction due to 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. Also, the largest probe E428 following subslip trend in alcohols is surprising. 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. The experimental results indicate that DKS theory also holds well even for larger

In case of polar probes, a faster rotation of the probes is observed for C522B and C138 in alcohols compared to C307. In spite of the distinction in structure a coincidental similar rotational reorientation times is observed in case of 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. Experimentally and theoretically obtained

Beddard et al. (1981) reported different rotational relaxation times of the dye cresyl violet in ethanol water mixture by varying the ethanol water composition i.e., at the same viscosity but at different compositions. The observed re-entrance type behavior of the orientational relaxation time when plotted against viscosity could not be explained only in terms of nonideality in viscosity exhibited in a binary mixture. Beddard et al. also reported that the reentrance behavior is strongly dependent on the specific interaction of the solute with the solvents. This is because in a system where solute interacts with few different species in a binary mixture in a different manner, its rotational relaxation will depend more on the composition than on the viscosity of the binary mixture. The role of specific interaction on the orientational dynamics has often been discussed in relation to changing boundary conditions (Fleming, 1986). We find that the orientational relaxation time of the probe molecules when plotted against the solvent viscosity does indeed show re-entrance. Our study here re-affirms that for a solute dissolved in a binary mixture, its rotational relaxation will depend more on the composition than on the viscosity of the binary mixture and thus the re-entrant type behaviour is strongly dependent on the interactions of the solute with the two different species in the solvent.

The rotational dynamics of two kinds of medium sized three dyes-Fluorescein 27(F27) and Fluorescein Na(FNa) (both neutral but polar), and Sulforhodamine B(SRB) (anion) has been studied in binary mixtures comprising of 1-Propanol and water at room temperature using both steady-state and time resolved fluorescence depolarization techniques. Alcohols have both a hydrogen-bonding -OH group and a hydrophobic alkyl group. The latter affects the water structure. The objective in studying two neutral and an anion dyes is to compare and contrast the rotational dynamics as a function of charge. A nonlinear hook-type profile of rotational reorientation times of the probe (*τr*) as a function of viscosity (*η*) is observed for all three dyes in this binary system, with the rotational reorientation times being longer in organic solvent rich zone, compared to the corresponding isoviscous point in water rich zone. This is attributed to strong hydrogen bonding between the solute and propanol molecules.

The increase in viscosity as 1-propanol is added to water is sharp with the peak value of 2.70 mPa s being reached at about 30% mole composition of 1-propanol. The viscosity of 1 propanol is 1.96 mPa s, the decrease after the post peak point is linear but gradual. The dielectric friction contribution in water, amides, and dipolar aprotics is minimal while it goes on increasing in alcohols (Krishnamurthy et al, 1993).

At isoviscous points there are two different *τr* values and this duality results from different values of dielectric frictions at the isoviscous points (Fig. 11). It is seen that both the neutral dyes F27 and FNa clearly produce the hook-type profile bent upwards and qualitatively mimic the nonhydrodynamic behavior. The reorientation times gradually increase as a function of viscosity up to the peak viscous value. τr values decrease after the solvent mixture exhibits a reduction in viscosity after the peak value. Note that the reorientation times are longer in propanol rich region compared to the water rich zone. In case of SRB though it exhibits hook type profile, surprisingly τr values longer in water rich zone in the beginning and later probe rotates faster in the intermediate viscous region. In propanol rich zone SRB shows similar τr values as those of water rich zone. This may be due to both amino groups of SRB are ethylated and the rotational diffusion of this dye was slightly more rapid than predicted. Theoretical models mimic this trend qualitatively, though GW & DKS models invariably predict a reduced friction and illustrate a hairpin - bending downwards. Thus, these models underestimate the friction experienced by the probe. The dual

Beddard et al. (1981) reported different rotational relaxation times of the dye cresyl violet in ethanol water mixture by varying the ethanol water composition i.e., at the same viscosity but at different compositions. The observed re-entrance type behavior of the orientational relaxation time when plotted against viscosity could not be explained only in terms of nonideality in viscosity exhibited in a binary mixture. Beddard et al. also reported that the reentrance behavior is strongly dependent on the specific interaction of the solute with the solvents. This is because in a system where solute interacts with few different species in a binary mixture in a different manner, its rotational relaxation will depend more on the composition than on the viscosity of the binary mixture. The role of specific interaction on the orientational dynamics has often been discussed in relation to changing boundary conditions (Fleming, 1986). We find that the orientational relaxation time of the probe molecules when plotted against the solvent viscosity does indeed show re-entrance. Our study here re-affirms that for a solute dissolved in a binary mixture, its rotational relaxation will depend more on the composition than on the viscosity of the binary mixture and thus the re-entrant type behaviour is strongly dependent on the interactions of the solute with

The rotational dynamics of two kinds of medium sized three dyes-Fluorescein 27(F27) and Fluorescein Na(FNa) (both neutral but polar), and Sulforhodamine B(SRB) (anion) has been studied in binary mixtures comprising of 1-Propanol and water at room temperature using both steady-state and time resolved fluorescence depolarization techniques. Alcohols have both a hydrogen-bonding -OH group and a hydrophobic alkyl group. The latter affects the water structure. The objective in studying two neutral and an anion dyes is to compare and contrast the rotational dynamics as a function of charge. A nonlinear hook-type profile of rotational reorientation times of the probe (*τr*) as a function of viscosity (*η*) is observed for all three dyes in this binary system, with the rotational reorientation times being longer in organic solvent rich zone, compared to the corresponding isoviscous point in water rich zone. This is attributed to strong hydrogen bonding between the solute and propanol

The increase in viscosity as 1-propanol is added to water is sharp with the peak value of 2.70 mPa s being reached at about 30% mole composition of 1-propanol. The viscosity of 1 propanol is 1.96 mPa s, the decrease after the post peak point is linear but gradual. The dielectric friction contribution in water, amides, and dipolar aprotics is minimal while it

At isoviscous points there are two different *τr* values and this duality results from different values of dielectric frictions at the isoviscous points (Fig. 11). It is seen that both the neutral dyes F27 and FNa clearly produce the hook-type profile bent upwards and qualitatively mimic the nonhydrodynamic behavior. The reorientation times gradually increase as a function of viscosity up to the peak viscous value. τr values decrease after the solvent mixture exhibits a reduction in viscosity after the peak value. Note that the reorientation times are longer in propanol rich region compared to the water rich zone. In case of SRB though it exhibits hook type profile, surprisingly τr values longer in water rich zone in the beginning and later probe rotates faster in the intermediate viscous region. In propanol rich zone SRB shows similar τr values as those of water rich zone. This may be due to both amino groups of SRB are ethylated and the rotational diffusion of this dye was slightly more rapid than predicted. Theoretical models mimic this trend qualitatively, though GW & DKS models invariably predict a reduced friction and illustrate a hairpin - bending downwards. Thus, these models underestimate the friction experienced by the probe. The dual

the two different species in the solvent.

goes on increasing in alcohols (Krishnamurthy et al, 1993).

molecules.

Fig. 11. Plot of rotational reorientation time with viscosity along with theoretical profile including viscous contribution for F27

valuedness of τr at isoviscous points near the organic solvent rich zone were attributed to different contributions of dielectric friction at these compositions and to strong hydrogen bonding.
