Low-temperature Structural Dynamics of Isatin in Dimethyl Sulfoxide (DMSO) Using Dielectric Spectroscopy

Abstract Structural and dynamical properties of heterocyclic organic compound isatin in the solution state with DMSO has been studied in the frequency region of 10 MHz to 50 GHz over the temperature range of 273.15–298.15 K using time domain reflectometry. High- and low-frequency relaxation has been observed for Isatin + DMSO. The high-frequency relaxation peak is due to free DMSO molecules while low-frequency relaxation peak is attributed to isatin. Dielectric permittivity, static dielectric constant, relaxation time, dipole moment, correlation factor along with thermodynamical parameters have been calculated. Molecular interaction has been discussed broadly under solute–solute, solute–solvent, and solvent–solvent category.


Introduction
Heterocyclic compounds are an important class of organic compounds having wide range of biological and pharmacological applications and show different biological properties. 1,2Isatin (1Hindole-2, 3-dione), also known as indenedione and indole quinone, is one such biologically active heterocyclic moiety.
Therefore, in the present study, we focus on the concentration and temperature dependence of structural and dynamical properties of isatin in the solution state in DMSO.As DMSO is a dipolar aprotic molecule with an extremely large dipole moment of 3.95 D, it has strong nonideal physicochemical behaviors in aqueous and other solutions.The anomalous behaviors of DMSO are attributed to its tendency to form intermolecular associations with itself and with other molecules. 13,14any attempts have been made previously [15][16][17][18][19][20] to investigate large number of heterocyclic organic compounds but no study has been found, which gives insights into the structural behavior of isatin and DMSO below room temperature (273.15K) through dielectric spectroscopy and thermodynamical properties.Therefore, the main purpose of the present work is to study the structural behavior of isatin in the DMSO environment through dielectric and thermodynamical properties using time-domain reflectometry technique in the frequency region of 10 MHz to 50 GHz at different temperatures ranging from 298.15 K to 273.15 K.

Materials
Isatin and DMSO were purchased from Hi Media Laboratories Pvt. Ltd.Mumbai, India and used without purification.

Measurements
Tektronix Digital Serial Analyzer model no.DSA8300 sampling mainframe along with the sampling module 80E10B has been used to obtain complex spectra using time domain reflectrometry (TDR) technique details about the experimental techniques is given in Kabara et al. 21Cole et al. 22 Lin 23 and Kumbharkhane. 24

Result and discussion
Dielectric dispersion and absorption curves for the Isatin þ DMSO system at various temperatures here only spectra at two temperatures i.e. low and high temperatures are shown) and concentrations are depicted in Figure 1.The spectra show that there is a gradual decrease in dielectric permittivity for all the studied concentrations and the loss peaks shift toward lower frequency side.Two relaxation processes were observed for studied systems.The faster process i.e. high-frequency process, which is assigned to the DMSO molecule and less dependent on solute molecule.While slower process i.e. low-frequency process is fully dependent on the solute concentration i.e. isatin molecule.
The process can be described by S. Havriliak-Negami equation 21 using least square fit method.
Figure 1.Permittivity spectra at temperatures 273.15K and 298.15 K; the spectra show decrease in permittivity with increasing temperature over all the used concentrations.
Equation ( 1) is the general form of S. Havriliak-Negami equation.For two relaxation processes we use Equation ( 2), the parameters used in Equation ( 2) are the relaxation strengths De 1 ¼ e 1À e 2 and De 2 ¼ e 2À e 1 for low-frequency and high-frequency process respectively. 21

Static dielectric constant (e i )
Figure 2 shows the variation in the values of static dielectric constant ðe i ) for both the relaxation processes (i ¼ 1 for low-and 2 for high-frequency process) as a function of concentration and temperature.For low-frequency process, static dielectric constant decreases toward higher temperature over all the concentrations.This decrease in the values of e 1 toward room temperature may be due to the decrease in the effective dipole-dipole antiparallel alignment and as a result relaxation time decreases.However, nonlinear variations in the values of static dielectric constant e 1 (c) have been detected.A sudden decrease in the e 1 (c) at 0.2265 M concentration is noticed over all the measured temperature.Decrease in the values of static dielectric constant is due to the decrement in the effective dipole-dipole antiparallel alignment at this concentration only.This decrement in the dipole-dipole alignment occurs because isatin is able to make stable complex with the DMSO molecules at lower isatin concentration where few DMSO molecules are interacting with isatin through dipole-dipole antiparallel interaction as shown in Figure 2 while the remaining DMSO molecules are involved in the self-association, 25 which form dimers of DMSO.Further increase in the values of static dielectric constant e 1 (c) toward higher concentration clearly indicates that the relaxation in the low-frequency region is mainly due to an increment of the effective dipole-dipole antiparallel alignment of isatin molecules (Figure 2).This can be clearly observed from the correlation factor g 1 (Table 2), which decreases with concentration leading to strong evidence of the antiparallel alignment of dipoles.
The study has also extended toward lower temperature to understand the structural dynamics at low temperature.From the obtained data it has been noticed that e 1 (T) increases toward low temperature over all the used concentrations.Increase in the values of static dielectric constant by lowering the temperature increases the effective dipole-dipole antiparallel alignment of isatin, which may form isatin dimers as shown in Figure 3 associated with DMSO that are brought into contact more closely. 20,26he concentration dependence of the high-frequency static dielectric constant e 2 (Figure 2), decreases linearly with the DMSO concentration up to 0.2265 M for measured temperatures and then increases for the rest of the concentrations.This decrease can be associated with the cooperative relaxation of self-associated DMSO or the formation of stable complex of DMSO.Shikata and Venkataramanan 27,28 also reported similar association/dissociation of DMSO in its pure state and also in solution.Above 0.2265 M there was found to be a sudden increase in the values of high-frequency static dielectric constant that could be due to increased dipole-dipole antiparallel alignment of DMSO-DMSO molecules or the formation of DMSO dimers. 28lso, high-frequency static dielectric constant was found to be temperature dependent, which was found to be increasing toward lower temperature for all the used concentrations.This gives a clear evidence of the formation of complex of DMSO molecules (self-association) and can be correlated with the higher relaxation time s 2 toward low temperature.

Dielectric relaxation time (s i )
Dielectric relaxation time for the low-frequency process was observed to be increasing linearly with isatin concentrations in the temperature region 298.15-288.15K but show anomalous behavior at lower temperature as shown in Figure 4.The relaxation time calculated for DMSO in its pure liquid state for low-frequency process at room temperature (298.15K) was 20 ps, 27 which agrees well with the relaxation time measured (20.8 ps) in this work.As isatin is able to form stable but antiparallel complex with DMSO molecules and are interacting with isatin at lower concentration with reduced correlation, there was found to be a small hindrance to the rotational motion of isatin dimers associated with DMSO molecules, which lowers the relaxation time at lower concentration.As isatin concentration increases, the number of complexes formed that gives increment in dipole-dipole antiparallel alignment thereby increases the hindrance to the molecular reorientation for isatin dimers associated with DMSO, which results in higher relaxation time.So, in the high concentration region, solute-solute interaction i.e. dimers of isatin molecules are more dominant than the DMSO-isatin interaction.The anomalous behavior of relaxation was found in the low temperature (283.15-273.15K) and at low concentration (0.2265 M) where dielectric relaxation time abruptly decreases and then increases for the further increase in the isatin concentration.At this concentration and at all temperatures there may be reduced cooperativity due to the dissociation of dimers taking place into monomers, which offers lower steric hindrance to the molecular reorientation isatin dimers associated with DMSO as a result of which the relaxation time decreases.But further increase in the isatin concentration makes the environment more cooperative for the formation of isatin dimers where the system was observed to be more complex with isatin molecules that can be attributed to the cooperative relaxation, which increases toward higher concentrations for all temperatures.High-frequency relaxation time does not seem to be affected more at room temperature except a slight increase toward higher concentration.This may be due to irrotationally bound DMSO molecules to isatin dimers or more clearly it can said that DMSO molecules are locked by isatin dimers.Toward lower temperature and up to 0.2265 M concentration there was found to be a decrease in the high-frequency relaxation time; this could be due to the dissociation of DMSO dimers into monomers, which reduces the orientational correlation as a result of which the relaxation time decreases, but for higher concentration in the low temperature region the relaxation time was almost independent of the concentration.This suggests that toward higher DMSO concentration and lower temperature, a number of irrotationally bound DMSO molecules to isatin dimers are lesser due to the formation of DMSO dimers.

Dipole moment
In order to provide deep insight into structural dynamics, we have calculated the dipole moment using the Cavell's equation 29,30 (Equation (3)): Parameters used in Equation ( 3) are well explained in Bottcher 30 and Barthel and Buchner. 31l 2 eff (effective dipole moment) is connected to the 'gas-phase dipole moment' l 0 (in the absence of orientational correlations) via where g i is an empirical factor, which indicates the correlation between dipoles.g i ¼1 implies that there is no orientational correlation between dipoles, and g i >1 means a tendency toward parallel alignment and g i <1 indicates there is antiparallel alignment.Let us see the solute contribution (i ¼ 1 for low frequency process) that Depends on both the polarizability and reaction field factor which was assumed to be independent of concentration c.
l was calculated by using Equation (3). 32able 2 indicates dipole moment variation, which was observed to be decreasing with increasing isatin concentration over all measured temperatures.This decrease may be due to the formation of antiparallel dipole-dipole correlation between isatin molecules toward higher concentration.The observed systematic weak decrease in l eff /(1 À af) with an increased concentration c indicates that isatin molecules are closer to each other, and a slight tendency toward dipole antiparallel alignment may emerge, according to energetic convenience.
Also, l eff (T) over all used concentrations was observed to be increasing toward lower temperature.This could be due to an increase in the induced isatin-isatin interaction.At low concentration and temperature, the screening of isatin molecules by DMSO molecules increases and the interaction between isatin molecules are screened.Therefore, at lower solute concentrations the isatin-DMSO interaction is more dominant than that of isatin dimers at higher solute concentration and therefore the value of l eff /(1 À af) is found to be higher toward lower temperatures.

Correlation factor g i
In addition to the dipole moment, we have estimated the maximum value of correlation factor g 1 in order to have insights into the magnitude of these antiparallel alignments.
g 1 ¼1 implies that there is no orientational correlation between dipoles.g 1 >1 shows a tendency toward parallel alignment and g 1 <1 shows a tendency toward anti-parallel alignment.
The values of correlation factor 'g 1 ' gives orientational correlation between a molecule and its nearest neighbors, which was calculated for all used concentrations and temperatures and were found to be far less than unity (Table 2).Departure of g 1 far less than unity supports the formation of multimers and molecular association due to short range ordering interactions in the solution.This suggests that as the concentration of the solute increases, the antiparallel molecular dipole alignment increases, thereby reducing the effective dipole moment of the solute.
The changes in the correlation factor g 1 are due to the changes in the correlation factor of DMSO due to the weakening of the DMSO layer around isatin via a growth of isatin-induced interaction at higher concentration and more probability of DMSO dimers or DMSO complex formation.This can be well studied by obtaining a number of DMSO molecules per isatin molecules.However, at 298.15 K, we notice that the number of DMSO molecules per isatin molecules decreases from 9.5 (0.11 molÁL À1 ) to 1.9 (0.45 molÁL À1 ) DMSO molecules around isatin molecules, which departs g 1 value from 1.These results suggest that as the concentration of isatin increases, antiparallel molecular dipole correlations increases thereby reducing the effective dipole moment of isatin molecules.
Apart from the concentration effect, it has been noticed that temperature also plays a vital role in changing the effective dipole moment.As the number of DMSO molecules per isatin molecules decreases toward lower temperature over all measured concentrations, the g 1 value is found to fluctuate or is observed to be slightly increased that gives a clear indication of the screening of isatin molecules or induced isatin interaction, which increases the isatin-isatin interaction (the formation of dimers) and as a result of which the effective dipole moment increases.
Concentration and temperature dependence of the relaxation time can be well described in terms of molar fraction of the solute, X as where a, b, and c parameters of Equation ( 6) along with the regression coefficient R 2 and relaxation time at infinite dilution s 1 (X!0) are displayed in Table 1.From the intercept at the origin, the relaxation time s 1 at infinite dilution was obtained.These values are used for calculating rotational dynamic parameters such as effective volume of rotation discussed in Section 4.6.

Irrotationally bound DMSO molecules (Z ib )
Irrotationally bound DMSO molecules to isatin (Z ib ) is an effective number that may be taken as a measure of the relative strength of solute-solvent interactions at a given temperature.
From Table 2 the correlation factor for higher isatin concentration was found to be smaller and we can define the apparent concentration of DMSO as: where g 2 (0) is the correlation factor for DMSO.Therefore, c app DMSO c ð Þ corresponds to the apparent concentration of the DMSO molecule.From Cavell's equation ( 3) we obtain the apparent concentration of the DMSO molecule.
For obtaining the value of f 2 , 29 here we considered a 2 ¼ 8 Å 3 i.e. polarizability of DMSO molecule and the radius of DMSO molecule is r ¼ 2.93 Å.Now, comparing the values of c app DMSO c ð Þ with the analytical DMSO concentration c DMSO c ð Þ of the solution, we can calculate irrotationaly bound DMSO molecules Z ib as: Equation ( 9) represents the number of DMSO molecules irrotationally bound to the isatin molecule.Table 2 shows that at lower solute concentration the effective number of irrotationally bound DMSO molecules (Z ib ) are more but toward higher concentration Z ib decreases more rapidly.This may be due to the increase in isatin-isatin interaction 20,26 through DMSO so that the number of DMSO molecules gets irrotationally bound or effectively locked by the isatin molecule.Toward lower temperature, Z ib decreases because at lower temperature DMSO molecules forms self-association i.e. the formation of DMSO dimers taking place, which reduces the number of monomers forming association with isatin.

Effective volume of rotation V eff
From the measured relaxation time s 1 it is possible to calculate the effective volume of rotation and the viscosity g for the studied system using Stockes-Einstein-Debye equation: 30 Table 2 shows the V eff values calculated by using Equation (10).Here, we have calculated V m (molar volume) at room temperature, which was found to be 99.954Â 10 À30 m 3 .
Effective volume of rotation (V eff ) for the low-frequency process was found to be greater than the molecular volume V m .V eff was observed to be linearly increasing with concentration in the high-temperature region (298.15 and 293.15 K) but showed nonlinear behavior toward lower temperatures.A linear increase in V eff values in the high-temperature region is the clear indication of the formation of dimers of isatin.
Larger effective volume V eff than the molar volume Vm is the indication of deviation from structural geometry due to induced interaction in such a way that the dipole moment toward lower temperature increases.Decrease in the values of effective volume toward lower temperature at 0.2265 M concentration reveals that there may be reduced correlation between DMSO and isatin molecules due to the association of DMSO dimers.But for the rest of the concentrations there was found to be an increase in the effective volume toward lower temperatures.

Molar free energy of activation ðDF s iÞ
The molar free energy of activation DF si measured in the temperature range 298.15-273.15K has been evaluated using dielectric relaxation as an Eyring's rate process. 33 and where DF si , DH si , and DS si are respectively the molar free energy of activation, molar enthalpy of activation, and molar entropy of activation for the dipolar orientation given in Equations ( 11) and (12).The values of enthalpy of activation were calculated by calculating the slope of log(Ts i ) vs. inverse temperature i.e. 1000/T as shown in Table 3.
Table 3 indicates that, for low-frequency process molar free energy of activation was found to be in the range of 2-3 kcal mol À1 , which is suggested for the cooperative relaxation.Such variations in free energy of activation are mainly attributed to isatin being weakly associated with DMSO molecules.
For high-frequency process, free energy DF s2 was found to be in the range of 1-2.5 kcal mol À1 as shown in Table 3, which was found to increase with the increase in the isatin concentration.Lower free energy is associated with the free rotation of monomers of DMSO.With the increase in the concentration there was found to be an increase in the value of molar free energy of activation DF si , which could be due to very weakly induced intermolecular H-bonding taking place between isatin and monomeric DMSO molecules or the formation of DMSO dimers.Due to the formation of such H-bond with the monomeric DMSO, there was found to be lesser hindrance to the molecular motion of induced intermolecular H-bonded DMSO molecules.As a result, the relaxation time for high-frequency process was very small of the order of 2-5 ps.But, a slight increase in DF s2 toward lower temperature supports for the slight increase in the strength of H-bonding between solute and monomers of DMSO molecules due to which s 2 increases.

Molar enthalpy of activation DH s i
Here, molar enthalpy of activation for low-frequency process at lower concentration was found to be 4.1087 kcal mol À1 , which can be attributed to the association of dimers of isatin molecules or strong H-bonded network.But the reduction in the value of enthalpy at 0.2265 M concentration from 4.1087 to 2.7410 kcal mol À1 is the clear indication of dissociation of DMSO dimers into monomers 27,34 due to the presence or addition of new isatin molecules.For all the studied concentrations, the nature of enthalpy of activation was found to be decreasing except at 0.3398 M concentration which may be due to lesser hindrance to the rotation of DMSO molecule on increasing isatin concentration that is well matched with the relaxation time for the corresponding concentration.Gradual increase in the enthalpy for further increase in the isatin concentrations may be due to the characteristics of rotation of DMSO associated with the isatin dimers.Positive values of enthalpy for low-frequency process suggest that the reaction is endothermic.
For high-frequency process, the values of molar enthalpy of activation at low isatin concentration (high DMSO concentration) were observed to be 7.5670 kcal mol À1 .Such an activation enthalpy is a characteristic of rotation of DMSO associates i.e. the rotation of DMSO dimers or rotation of DMSO associated with isatin.The magnitude of association was found to be lower for 0.2265 M isatin concentration, which indicates weakening of association but as the concentration increases further the values of activation enthalpy increases as more energy is needed for the rotation of strongly associated complex or due to the rotation of DMSO dimers.Further increase in the isatin concentration or decrease in the DMSO concentration suddenly decreases the activation enthalpy to 2.32 kcal mol À1 .This could be due to the formation of dissociation of DMSO dimers or very weak interaction between isatin and DMSO taking place.Positive values of enthalpy suggest that the reaction is endothermic.Values of molar enthalpy of activation are as shown in Table 3.

Molar Entropy of activation DS s i
Table 3 shows that the values of molar entropy of activation for low-frequency process were found to be less positive than in the case of high-frequency process.Positive entropy is the indication of less ordered structure.This indicates that the presence of small percentage of isatin at lower concentration changes the structural alignment due to the formation of complexes with DMSO molecules.Toward higher isatin concentration entropy again reduces and becomes less positive which indicates comparatively more order structure due to the isatin dimers formation.When isatin concentration increases to 0.2265 M, molar entropy suddenly changes to negative which indicates orderly structure that could be due to the structural alignment of dimers of isatin and also due to the association of DMSO dimers.Further increase in the isatin concentration increases the association or the formation of complex between isatin dimers as a result of which molar entropy increases and becomes positive.
For high-frequency process, the values of molar entropy of activation were found to be more positive than that of the low-frequency process indicating that the environment of the system is noncooperative for the activated process and the activated state is less stable and disordered than the normal state.Here, the dipole of monomers formed at different concentrations are aligned in such a way that the system was observed to be in more disordered state.The higher values of molar entropy toward lower concentrations may be due to the less ordered structure due to the formation of DMSO dimers.Molar entropy of activation seems to be lower toward higher concentrations of isatin, which makes the system comparatively more ordered due to the dissociation of dimers into monomers.

Conclusion
In this work, we have provided information regarding the concentration dependence of structural dynamics of Isatin þ DMSO in the temperature region of 298.15-273.15K by using dielectric spectroscopy in the GHz region.The dielectric spectra reveal two relaxation modes, the low-frequency relaxation and the high-frequency relaxation.From the observed dielectric parameters it has been concluded that in the case of low-frequency process, a decrease in the values of static dielectric constant towards higher temperature over all the measured concentrations is due to the decrease in the effective dipole-dipole antiparallel alignment and this is clear from the decreasing correlation factor g 1 and obviously the effective dipole moment l eff /(1 À a 1 f 1 ) toward higher concentration.This will make the structure more ordered at lower concentration but becomes less ordered toward higher concentration, which could be due to the formation of isatin dimers associated with DMSO.Also, temperature has an effect on e 1 (T) values, which increases toward lower temperature for all concentrations that concludes increasing effective dipole-dipole antiparallel alignment between isatin dimmers associated with DMSO molecules thereby increasing the effective dipole moment l eff /(1 À a 1 f 1 ).However, on increasing the isatin concentration e 2 (C) high-frequency dielectric constant decreases initially at lower concentration.This could be due to the structural changes in pure DMSO.But on further increase in concentration, e 2 starts increasing which is a clear evidence that isatin is associated with the DMSO molecule.Also, toward low measured temperature e 2 (T) seems to be increasing.This increase in the values of e 2 suggests strong association between DMSO-DMSO or solvent-solvent molecules.High-frequency static dielectric constant e 2 (c) decreases with an increase in the DMSO concentration (decrease with isatin concentration) over all used temperatures owing to self-association of DMSO, which is correlated with the free rotation of monomers with the relaxation time of around 2-3 ps at room temperature and starts forming association towards lower temperature which is correlated with higher relaxation time s 2 (around 6-8 ps)where the structure was found to be more disordered as entropy is positive at all used concentrations.
The results have been confirmed through DMSO dynamics by a number of DMSO molecules that are locked or frozen or irrotationally bound (Z ib ) by isatin dimers.With increasing solute concentration Z ib decreases due to the dominant solute-solute interaction.Toward lower temperature Z ib decreases for all used concentrations as low temperature affects the reorientational dynamics of solvent due to the formation of large numbers of isatin dimers associated with few DMSO molecules as DMSO at lower temperature are engaged in forming self-complex or say DMSO dimers, which reduces the solute-solvent interaction.

Figure 2 .
Figure 2. Static dielectric constant for low-and high-frequency process as a function of temperature at different concentrations.

Figure 3 .
Figure 3. Dipole moment behavior of isatin at (a) low concentration and (b) at high concentration.

Figure 4 .
Figure 4. Relaxation time for low-and high-frequency relaxation process as a function of concentration and temperature.

Table 2 .
Values obtained and tabulated for various parameters, dipole moment, correlation factor, no. of irrotationaly bound molecules and effective volume as a function of concentration at various temperatures.

Table 1 .
Fit parameters corresponding to the relaxation time of the solute as a function of its molar fraction X for low-frequency process.

Table 3 .
Values of temperature-dependent molar enthalpy of activation for Isatin þ DMSO.