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. 2023 Sep 18;8(39):36604–36613. doi: 10.1021/acsomega.3c06428

Thioflavin-T: A Quantum Yield-Based Molecular Viscometer for Glycerol–Monohydroxy Alcohol Mixtures

Puspal Mukherjee 1,*, Sintu Ganai 1,*
PMCID: PMC10552499  PMID: 37810704

Abstract

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Molecular rotor dye thioflavin T (ThT) is almost nonfluorescent in low-viscosity solvents but highly fluorescent when bound to amyloid fibrils. This unique property arises from the rotation of the dimethylaniline moiety relative to the benzothiazole moiety in the excited state, which drives the dye from an emissive locally excited state to a twisted intramolecular charge-transfer state. This process is viscosity-controlled, and therefore, we can use the quantum yield of ThT to assess the viscosity of the environment. In this study, we have investigated the quantum yield of ThT (φThT) in various compositions of six alcoholic solvent mixtures of glycerol with methanol, ethanol, n-propanol, iso-propanol, n-butanol, and tert-butanol. We have proposed an empirical model using φThT as a function of the mole fraction of glycerol to estimate the interaction parameters between the components of the solvent mixtures. This analysis allowed us to predict the extent of nonideality of the solvent mixtures. The Förster–Hoffmann- and Loutfy–Arnold-type power law relationship was established between the quantum yield of ThT and bulk viscosity for solvent mixtures of methanol, ethanol, n-butanol, and tert-butanol with glycerol, and it was found to be similar in nature in all the four mixtures. Applying this knowledge, we proposed a methodology to quantify and predict the bulk viscosity coefficient values of several compositions of n-propanol–glycerol and iso-propanol–glycerol mixtures which have not been previously documented.

1. Introduction

Thioflavin-T (ThT, Scheme 1) is a well-established marker for β-amyloid fibrils which are associated in a wide range of protein disorder diseases like Alzheimer’s, Parkinson’s, and prion diseases.1–4 Thioflavin-T exhibits weak fluorescence emission in water, but upon binding with amyloid fibrils, it undergoes a remarkable enhancement in emission intensity.1–4 ThT selectively binds to DNA, RNA, and enzymes, and the same type of drastic fluorescence increase has been observed in the ThT–biomolecule complex.5–9 Such an increase in emission intensity is not only unique to ThT. It belongs to a class of dyes known as molecular rotors.1,10–13 Molecular rotor dyes experience internal rotation in the excited state, which controls their emissive properties.1,10–13 In the ground state, the dihedral angle between the benzothiazole and dimethylaniline moiety around the C–C bond of ThT is approximately 37°.1,14–16 The relative orientation of those two moieties around the C–C bond changes in the excited state.1,14–18 Upon excitation, ThT molecules populate a locally excited (LE) state which has a similar geometry like ground state, and the fluorescence emission of ThT primarily originates from this state.1,14–18 Subsequently, ThT undergoes a twisting motion of the dimethylaniline moiety with respect to the benzothiazole fragment, resulting an angle of ∼90°.1,14–18 Significant charge redistribution within the molecular framework accompanies this motion, and therefore, this process is known as twisted intramolecular charge transfer (TICT).1,14–20 The TICT state is a dark nonemissive state of ThT.1,14–20 The LE to TICT conversion is generally considered to be barrierless and ultrafast in nature, and any external factor that hinders this channel leads to an increase in the fluorescence intensity of ThT.1,17,18,21–23

Scheme 1. Chemical Structure of Thioflavin-T.

Scheme 1

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Binding with amyloid fibrils and other biomolecules prevents the internal rotation of ThT and, thus, increases the fluorescence intensity. Macromolecular hosts can also impose spatial restrictions, and a similar phenomenon has been observed when ThT interacts with micelles, cellulose nanocrystals, and cyclodextrin or cucurbit[n]uril compounds.24–27 The viscosity of the medium becomes the governing factor for ThT emission in liquid media, as the molecular rotation is significantly controlled by the presence of viscous drag.1,24,28,29 Several studies have explored the effect of viscosity on the excited-state dynamics of the molecular rotors, and they have been used as viable viscosity sensors in biological systems.30–33 Singh et al. have studied the excited-state dynamics of ThT using ultrafast spectroscopy in aqueous solutions, amyloid fibrils, in an acetonitrile–ethylene glycol mixture and inside the AOT reverse micelle.28,34–36 Amdursky et al. have studied the temperature dependence of fluorescence properties of ThT in glass forming liquids.37 The enhancement of ThT fluorescence intensity with viscosity has been very prominently shown in deep eutectic solvents by Gautam et al. and in ionic liquids by Singh et al.38,39 Stsiapura et al. have shown that in low-viscosity solvents like water and ethanol, the charge-transfer process influences the dynamics of TICT formation.40 A temperature-dependent study of ThT and auramine O in n-propanol, n-butanol, and n-pentanol has found direct correlation between viscosity and steady-state fluorescence properties.41 Such studies along with many others have illustrated the influence of viscosity of the medium on the rate of LE → TICT transition and the barrierless characteristics of the excited-state potential energy surface. Since LE → TICT transition involves significant charge transfer, solvent polarity influences this process.37,40–42 For example, Stsiapura et al. have recorded transient absorption spectroscopic data for ThT in 12 different solvents at room temperature and explored static and dynamic solvation effects on the charge-transfer rate based on Marcus theory.42 Solvation dynamics can control the process, but the overall excited-state lifetime of ThT is shorter than the solvent relaxation time in most of the solvents.37,40–42 There are other reports that suggest the existence of multiple TICT states along with conical intersections in the potential energy surface (PES) of the first singlet excited state. Specifically, Mukherjee et al. have demonstrated that a second TICT state can be formed via rotation of the dimethylamine moiety of ThT, and this process contributes to the excited-state dynamics significantly in chlorinated solvents like chloroform and dichloromethane.43 Ghosh and Palit have suggested the involvement of triplet state of ThT in the excited-state dynamics.44 All the studies agree to the fact that all the TICT states are nonemissive, whereas the LE state is the only emissive state of ThT.

The preceding discussion highlights that the photophysical properties of ThT can be used to quantify the viscosity of the surrounding medium. Commonly, bulk viscosities are measured by capillary-based methods. While Ostwald’s viscometer is generally used for teaching purposes, Cannon-Ubbelohde-type capillary viscometers are used for accurate viscosity values.45,46 Rolling ball-type viscometers are also used for the measurement of liquid viscosities.47 Apart from these common experimental methods, the bulk viscosity of pure liquids has been measured using acoustics spectroscopy.48,49 Molecular rotors have also been used to sense viscosity changes in various biomolecular environments.50,51 Molecular rotors do not actually encounter bulk viscosity. Instead, the viscous drag imposed on the fragmental rotation is by the solvation shell around the molecule.34–44 This is known as microviscosity, and molecular rotor dyes sense the microviscosity around them. The composition and properties of the solvation shell can be different from the bulk composition, especially in solvent mixtures, in confined environments, or in a system having dynamic heterogeneity.34–44 Therefore, quantification of the environmental viscosity by observing photophysical quantities is not straightforward. There are some examples of estimation of viscosity in cells and other biological systems.30–33 However, these types of studies have been mostly carried out in confined spaces and sometimes involve designing complicated molecules.30–33 We wanted to explore whether a common photophysical property like fluorescence quantum yield can be quantitatively related/calibrated to bulk viscosity in the liquid phase and be used to estimate the unknown viscosity of a binary solvent system. ThT is a perfect candidate for that purpose because its photophysics is well established; it only shows emission from the LE state, and therefore, its emission spectrum is free from contribution of radiative transitions from other TICT states. The easiest way to vary viscosity is either to study a large range of solvents or to use solvent mixtures where one component has a high viscosity. However, the nonpolar and chlorinated solvents were to be avoided due to the unusual photophysical responses of ThT in them. We therefore decided to undertake a study on binary mixtures of glycerol and monohydric alcohols, namely, methanol, ethanol, n-propanol, iso-propanol, n-butanol, and tert-butanol. As both components of the binary mixtures are alcohols, any sudden changes in the bulk properties are not expected. Since glycerol has very high viscosity compared to the others, the variations of viscosity in these mixtures are enormous. In the following sections of this report, we outline a methodology for predicting the unknown bulk viscosity of n-propanol–glycerol and iso-propanol–glycerol mixtures by simple measurement and analysis of ThT quantum yield along with the determination of the solvent interaction parameter of the constituents of the binary solvent mixtures.

2. Experimental Section

2.1. Materials

HPLC-grade methanol, n-propanol, iso-propanol, n-butanol, and tert-butanol were purchased from Spectrochem, India. Ethanol was purchased from Himedia, and molecular biology-grade glycerol was purchased from Merck, India. All the solvents apart from glycerol were distilled prior to use. Thioflavin-T (ThT) was purchased from SRL, India, and recrystallized twice from ethanol. The concentration of ThT was kept below 10 μM in all of the experiments to avoid any aggregation-induced effect.

2.2. Methods

The UV–visible spectra were recorded in a Shimadzu UV-1900 commercial spectrophotometer, and the fluorescence spectra were recorded in an Agilent Cary Eclipse spectrofluorimeter. All of the measurements were performed in quartz cuvettes of 1 cm path length. ThT solutions were prepared by thoroughly dissolving recrystallized ThT in pure solvents, followed by filtration to remove any undissolved particles. ThT dissolved in n-butanol was used as the reference in quantum yield measurements.14,42 All the steady-state absorption and emission spectra of ThT in pure solvent and solvent mixtures were recorded under the same experimental conditions. Fluorescence quantum yields were calculated using eq 1.

2.2. 1

In eq 1, φThT and φref are the quantum yields of ThT in a particular medium and ThT in n-butanol, respectively. IThT and Iref are the integrated area of emission for AThTλex and Arefλex are the absorbance indexes at the excitation wavelength of ThT in a medium and n-butanol, respectively. ni and nref are the refractive indexes of the solvent and n-butanol. φref was taken from refs (14) and (42). In order to prevent any artifacts caused by variations in excitation wavelengths, the same excitation light of 400 nm was used in all cases. The background Raman scattering from the solvent medium was removed from the emission spectra of ThT for the quantum yield calculations. To estimate the error in the quantum yield value measurements, we have repeated the experiments in a few randomly selected compositions for each of the solvent mixtures and found the maximum error in quantum yield estimation to be ±2%. Refractive index measurements of the n-propanol–glycerol mixture and iso-propanol–glycerol mixture were performed on a commercial Abbe refractometer (Atago, Japan). For reference, we used the refractive index value of pure water at room temperature. Experiments involving tert-butanol were performed keeping the room temperature at 30 °C since tert-butanol can freeze at lower temperatures. All other experiments were performed at 25 °C.

3. Results and Discussion

Considering the deliberations presented in the Introduction Section, it is reasonable to infer that the emission spectra of ThT in alcoholic solvents are primarily the radiative decay of population from the LE state of the molecule which can help us correlate the emissive property with a bulk solvent property. We, therefore, measured the absorption and emission spectra of ThT in the various compositions of the solvent mixtures, namely, methanol–glycerol, ethanol–glycerol, n-propanol–glycerol, iso-propanol–glycerol, n-butanol–glycerol, and tert-butanol–glycerol. The representative absorption spectra are shown in Supporting Information Figure S1. The fluorescence emission spectra of ThT in various compositions of the solvent mixtures mentioned are presented in Figure 1. In each case, we recorded the spectra in nine different compositions along with the pure solvents. The intensity of the emission spectra of ThT is inherently controlled by the viscosity of the solvent medium as highlighted in the Introduction Section. Glycerol has a viscosity of 950 cP at room temperature, which is tremendously high compared to the viscosity of methanol (0.6 cP), ethanol (1.105 cP), n-propanol (1.97 cP), iso-propanol (2.098 cP), n-butanol (2.568 cP), and tert-butanol (3.155 cP).52–54 Therefore, the viscosity of the solvent mixtures studied varied over a wide range, and the change in the intensity of the emission spectra of ThT in these mixtures is distinctly noticeable, as depicted in Figure 1. We would like to point out here that the gradual increase in the intensity of emission spectra with increasing glycerol mole fraction in the mixture was observed in all the cases, and no sudden unique feature appeared. In Figure 1, the emission spectra of ThT in glycerol are shown in the inset since the intensity is very high compared to others. The steady-state absorption and emission spectra recorded in pure solvents was found to match with previous reports.15,40,43

Figure 1.

Figure 1

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Emission spectra of thioflavin T in different compositions of the solvent mixtures: (a) methanol–glycerol, (b) ethanol–glycerol, (c) n-propanol–glycerol, (d) iso-propanol–glycerol, (e) n-butanol–glycerol, and (f) tert-butanol–glycerol. XGly indicated the mole fraction of glycerol. The spectra of ThT in pure glycerol are shown in the inset of (a). The excitation wavelength in all of the cases is 400 nm.

The emission spectra shown in Figure 1 are not corrected for their absorbance at excitation wavelength, and therefore, their intensity should not be directly compared. Moreover, we are reiterating that the tert-butanol–glycerol mixture was studied at 30 °C instead of 25 °C unlike the other solvent mixtures. Nonetheless, Figure 1 shows the trend in the increase of fluorescence intensity and, in turn, medium viscosity.

Before further exploration, it is necessary to discuss the shift in the spectra. The excited-state deactivation process of ThT involves the formation of the TICT state from the LE state, which is viscosity-controlled.1,14,15,18,40 However, the excitation from the ground to the excited state and the subsequent deactivation process of the molecules are also influenced by the polarity of the medium.40–42 The dielectric constant of the solvents studied ranged from 10.9 (tert-butanol) to 46.5 (glycerol).55 To examine the effect of this variation, the spectral shifts of ThT were recorded. Table 1 presents the observed absorption, emission maxima, and Stokes shift of ThT in various compositions of glycerol–alcohol solvent mixtures. Figure 2 represents the variation of these maxima as a function of the mole fraction of the glycerol content in those mixtures. In each of the solvent mixtures, with increase in glycerol content, the absorption and emission maxima of ThT showed a bathochromic shift. From Figure 2a, we can see that the largest range of shift in absorption maxima with increase in glycerol content in the mixture was found in a methanol–glycerol mixture, whereas a largest range of shift for emission maxima was observed in the ethanol–glycerol mixture (Figure 2b). The Stokes shift values are also similar and varied within ∼2800 to ∼3200 cm–1. These small changes in spectral parameters showed that the extent of influence of polarity on the excited-state properties of ThT is small or similar in the solvent mixtures studied here. So, we can safely assume that viscosity is the major and primary factor of changes in emission spectra.

Table 1. Absorption Maxima, Emission Maxima, Stokes Shift Values, and Quantum Yield of Thioflavin-T in Six Glycerol–Monohydroxy Alcohol Solvent Mixtures along with the Known Values of Bulk Viscosity of the Mixtures.

X1 X2 absorption maxima in cm–1 (in nm) emission maxima in cm–1 (in nm) Stokes shift in cm–1 quantum yield of ThTa viscosity (cP)b,c
Glycerol (1) + Methanol (2)
0.000 1.000 24073.18 (415.4) 21186.44 (472.0) 2886.74 0.0005 0.6
0.058 0.942 24026.91 (416.2) 21164.02 (472.5) 2862.89 0.0012 1.8
0.122 0.878 23969.32 (417.2) 21097.05 (474.0) 2872.27 0.0018 4.8
0.192 0.808 23934.9 (417.8) 21008.40 (476.0) 2926.50 0.0022 7.7
0.270 0.730 23877.75 (418.8) 20898.64 (478.5) 2979.10 0.0030 13
0.357 0.643 23843.59 (419.4) 20768.43 (481.5) 3075.15 0.0041 28
0.454 0.546 23809.52 (420.0) 20682.52 (483.5) 3127.0 0.0063 58
0.564 0.436 23775.56 (420.6) 20597.32 (485.5) 3178.24 0.0082 130
0.689 0.311 23741.69 (421.2) 20554.98 (486.5) 3186.71 0.0128 250
0.833 0.167 23707.92 (421.8) 20533.88 (487.0) 3174.04 0.0200 630
1.000 0.000 23707.92 (421.8) 20576.13 (486.0) 3131.79 0.0963 950
Glycerol (1) + Ethanol (2)
0.000 1.000 23900.57 (418.4) 21276.6 (470.0) 2623.98 0.0013 1.23
0.082 0.918 23866.35 (419.0) 21164.02 (472.5) 2702.33 0.0021 2.81
0.167 0.833 23820.87 (419.8) 21008.4 (476.0) 2812.46 0.0026 6.28
0.255 0.745 23820.87 (419.8) 20876.83 (479.0) 2944.04 0.0034 13.70
0.348 0.652 23798.19 (420.2) 20811.65 (480.5) 2986.54 0.0048 29.01
0.444 0.556 23775.56 (420.6) 20746.89 (482.0) 3028.67 0.0063 59.24
0.545 0.455 23764.26 (420.8) 20639.83 (484.5) 3124.42 0.0089 115.76
0.651 0.349 23741.69 (421.2) 20597.32 (485.5) 3144.37 0.0129 214.68
0.762 0.238 23730.42 (421.4) 20576.13 (486.0) 3154.29 0.0221 374.08
0.878 0.122 23696.68 (422.0) 20576.13 (486.0) 3120.55 0.0373 605.47
1.000 0.000 23707.92 (421.8) 20576.13 (486.0) 3131.79 0.0963 950.0
Glycerol (1) + n-Propanol (2)
0.000 1.000 23900.57 (418.4) 20898.64 (478.5) 3001.93 0.0024  
0.103 0.897 23866.35 (419.0) 20811.65 (480.5) 3054.69 0.0029  
0.205 0.795 23832.22 (419.6) 20790.02 (481.0) 3042.20 0.0038  
0.306 0.694 23809.52 (420.0) 20746.89 (482.0) 3062.64 0.0057  
0.407 0.593 23798.19 (420.2) 20725.39 (482.5) 3072.80 0.0070  
0.507 0.493 23764.26 (420.8) 20661.16 (484.0) 3103.10 0.0108  
0.607 0.393 23730.42 (421.4) 20639.83 (484.5) 3090.59 0.0148  
0.706 0.294 23707.92 (421.8) 20618.56 (485.0) 3089.36 0.0203  
0.805 0.195 23696.68 (422.0) 20597.32 (485.5) 3099.36 0.0304  
0.903 0.097 23674.24 (422.4) 20554.98 (486.5) 3119.26 0.0440  
1.000 0.000 23707.92 (421.8) 20576.13 (486.0) 3131.79 0.0963  
Glycerol (1) + iso-Propanol (2)
0.000 1.000 23957.83 (417.4) 20898.64 (478.5) 3059.19 0.0027  
0.105 0.895 23889.15 (418.6) 20833.33 (480.0) 3055.82 0.0038  
0.208 0.792 23866.35 (419.0) 20833.33 (480.0) 3033.02 0.0050  
0.311 0.689 23832.22 (419.6) 20790.02 (481.0) 3042.20 0.0073  
0.413 0.587 23798.19 (420.2) 20725.39 (482.5) 3072.80 0.0106  
0.513 0.487 23764.26 (420.8) 20703.93 (483.0) 3060.32 0.0138  
0.612 0.388 23752.97 (421.0) 20682.52 (483.5) 3070.45 0.0209  
0.711 0.289 23719.17 (421.6) 20618.56 (485.0) 3100.61 0.0286  
0.808 0.192 23696.68 (422.0) 20597.32 (485.5) 3099.36 0.0415  
0.905 0.095 23685.46 (422.2) 20554.98 (486.5) 3130.47 0.0540  
1.000 0.000 23696.68 (422.0) 20576.13 (486.0) 3120.55 0.0963  
Glycerol (1) + n-Butanol (2)
0.000 1.000 23889.15 (418.6) 20876.83 (479.0) 3012.33 0.0043 2.57
0.122 0.878 23854.96 (419.2) 20855.06 (479.5) 2999.90 0.0058 4.78
0.239 0.761 23820.87 (419.8) 20790.02 (481.0) 3030.85 0.0081 8.90
0.350 0.650 23786.87 (420.4) 20746.89 (482.0) 3039.98 0.0110 16.52
0.455 0.545 23775.56 (420.6) 20703.93 (483.0) 3071.62 0.0141 30.56
0.556 0.444 23741.69 (421.2) 20682.52 (483.5) 3059.17 0.0197 56.24
0.653 0.347 23719.17 (421.6) 20682.52 (483.5) 3036.64 0.0260 102.83
0.745 0.255 23707.92 (421.8) 20661.16 (484.0) 3046.76 0.0334 186.66
0.834 0.166 23696.68 (422.0) 20639.83 (484.5) 3056.85 0.0471 336.12
0.919 0.081 23696.68 (422.0) 20618.56 (485.0) 3078.13 0.0637 600.13
1.000 0.000 23696.68 (422.0) 20576.13 (486.0) 3120.55 0.0963 950.0
Glycerol (1) + tert-Butanol (2)
0.000 1.000 23889.15 (418.6) 20920.5 (478.0) 2968.65 0.0050 3.15
0.126 0.874 23866.35 (419.0) 20855.06 (479.5) 3011.29 0.0077 8.22
0.246 0.754 23854.96 (419.2) 20811.65 (480.5) 3043.31 0.0122 18.72
0.358 0.642 23820.87 (419.8) 20768.43 (481.5) 3052.44 0.0171 37.85
0.465 0.535 23798.19 (420.2) 20725.39 (482.5) 3072.80 0.0240 69.04
0.566 0.434 23741.69 (421.2) 20703.93 (483.0) 3037.76 0.0292 115.12
0.661 0.339 23741.69 (421.2) 20682.52 (483.5) 3059.17 0.0358 177.45
0.752 0.248 23707.92 (421.8) 20639.83 (484.5) 3068.08 0.0429 255.31
0.839 0.161 23685.46 (422.2) 20597.32 (485.5) 3088.13 0.0479 345.77
0.921 0.079 23674.24 (422.4) 20597.32 (485.5) 3076.92 0.0520 444.00
1.000 0.000 23696.68 (422.0) 20576.13 (486.0) 3120.55 0.0780 544.03
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a

The maximum error associated with the measurements ±2%.

b

Viscosity data are taken from refs (56)–60.

c

The viscosity values of glycerol–n-propanol and glycerol–iso-propanol mixtures are not reported in the literature and estimated using our proposed methodology in the next section.

Figure 2.

Figure 2

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(a) Absorption and (b) emission maxima of thioflavin T as a function of the mole fraction of glycerol in different glycerol–monohydroxy alcohol solvent mixtures. Gly indicates glycerol.

We measured the quantum yield (φThT) of ThT using the procedure described in the Experimental Section. To calculate the quantum yield values, we needed a refractive index for each experimental composition of solvent mixtures. The refractive index values of exact compositions of the methanol–glycerol solvent mixture used in this study at 25 °C are reported in the literature.56 For ethanol–glycerol, n-butanol–glycerol, and tert-butanol–glycerol mixtures, the refractive index values are reported in several compositions but not at the exact compositions of the mixtures prepared by us.57–60 To estimate the values at our experimental compositions, we fitted the reported data using a second-order polynomial equation and evaluated the required values from it. The literature values along with the estimated refractive indexes are reported in Supporting Information Table S2. Despite conducting an extensive literature search, we could not find any existing reports on refractive index values for n-propanol–glycerol and iso-propanol–glycerol mixtures. Therefore, we measured the refractive index values of those two solvent mixtures at our experimental compositions, which are reported in Supporting Information Table S3. These measured values were used for quantum yield calculation.

The calculated values of φThT are listed in Table 1. To validate our measurements, we compared the values in pure solvents with the reported values and found them to be comparable.1,15,40,41 φThT gradually increased with increasing concentration of glycerol in each mixture, which correlates with the increase in fluorescence emission intensity shown in Figure 1. However, the specific variation pattern differs for each case, and φThT exhibits a nonlinear relationship with the glycerol concentration across all systems. In Figure 3, we have shown the variation of log φThT vs mole fraction of glycerol (XGly) for each system. The trend of log φThT also showed a nonlinear dependence on XGly, indicating the nonideality of the solvent mixtures. The nonideality originates from a specific interaction between the components of the mixture.56–60 Since φThT is a direct manifestation of viscosity of the medium, we followed the Grunberg–Nissan model for liquid mixture viscosity to quantitatively analyze the variation of φThT.61,62 The simplest approach would be to model φThT of the solvent mixtures to be a linear combination of the values in pure components, but it only works for ideal cases. Grunberg–Nissan developed an empirical model to estimate the viscosity of solvent mixtures.61,62 It follows an Arrhenius type of mixing model with the incorporation of a solvent–solvent interaction parameter.61,62 As per the proposition of the Grunberg–Nissan model, this interaction coefficient depends on temperature but does not change with the composition of the mixture. In the case of viscosity, the interaction coefficient can be directly related to the activity coefficients of the pure components via Raoult’s law.61,62 Thus, it can be used to estimate the deviation of the solvent mixture from ideality. Similarly, we propose that the quantum yield of ThT in any composition of a specific binary solvent mixture can be modeled as follows

3. 2

Figure 3.

Figure 3

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Plot of variation of logφThT against the mole fraction of glycerol in (a) methanol–glycerol, (b) ethanol–glycerol, (c) n-propanol–glycerol, (d) iso-propanol–glycerol, (e) n-butanol–glycerol, and (f) tert-butanol–glycerol solvent mixtures. XGly indicated the mole fraction of glycerol. The black lines indicate fitting using eq 4.

Here, log φ12, log φ1, and log φ2 are the quantum yields of ThT in the mixture, in pure component 1, and in pure component 2, respectively; x1 and x2 are the mole fractions of components 1 and 2 in the mixture, and δ is the interaction parameter. This interaction parameter δ may depend on temperature but is assumed to not change with the composition of a particular binary solvent mixture. We can rewrite eq 2 by substituting x2 with 1-x1 as follows

3. 3

Equation 3 offers the advantage of using only x1 to fit the data of log φ12. We used eq 3 to fit the data of log φThT against XGly, and the fitting curves along with the fitting equations are also shown in Figure 3. The interaction parameters for each of our experimental systems are reported in Table 2, and these values indicate the extent of interaction between the two components of the binary mixture. Generally, to predict deviation from ideally of liquid mixtures, excess thermodynamic quantities are measured.56–60 Spectroscopic properties such as solvatochromic shift were also used to predict synergistic or preferential interactions.63 However, estimation of the solvent–solvent interaction using quantum yield data is rare. Since the concentration of ThT is extremely low compared to the solvents, the overall system will be negligibly perturbed. Therefore, the modeling proposed here can represent deviation from ideality. The δ parameters found from this analysis showed that the interaction is highest between ethanol and glycerol, followed by n-propanol–glycerol. Interestingly, the only positive δ value was shown by the tert-butanol–glycerol mixture, which signifies that the nature of the interaction is opposite in this case. Based on the discussion on the available models of nonideality, it may be concluded that a positive δ value means negative deviation from ideality and a negative δ parameter means positive deviation from ideality.61,62 Accordingly, we can say that the binary mixtures of glycerol with methanol, ethanol, n-propanol, iso-propanol, and n-butanol showed positive deviation from ideality, whereas a mixture of glycerol with tert-butanol showed negative deviation from ideality. To check whether these mixtures actually deviate from ideality and their nature of interaction, we have used the measured refractive index values of the n-propanol–glycerol and iso-propanol–glycerol mixtures and calculated the excess molar refractivity values as per the method given in Supporting Information Scheme S1. We found that both the mixtures showed positive deviation from ideality as predicted by our model. The maximum deviation from ideality occurs for composition with a mole fraction around 0.5 in each case (Supporting Information Figure S2). We cannot, however, compare the interaction parameters obtained from our analysis to the excess molar refractivity as the two physical parameters depend on different properties of the medium, but it validates that our model can successfully predict the positive and negative deviation from ideality. This observation can be validated from previous thermodynamic studies also.56–60 So, our proposed model of ThT quantum yield can successfully estimate the degree of solvent–solvent interaction and can predict nonideality without any help from excess thermodynamic property measurements.

Table 2. Interaction Parameter δ in eq 2 and the Slope α in eq 5 for Six Glycerol–Monohydroxy Alcohol Mixtures.

solvent mixture δ α
glycerol + methanol –0.1074 0.502
glycerol + ethanol –0.6985 0.495
glycerol + n-propanol –0.6465 0.49–0.50 (predicted range)
glycerol + iso-propanol –0.2652 0.49–0.50 (predicted range)
glycerol + n-butanol –0.3530 0.491
glycerol + tert-butanol 0.5068 0.489
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The key aspect of this study was to establish a relationship between φThT values and the bulk viscosity of the solution. The viscosity coefficients for our experimental compositions of the methanol–glycerol mixture were obtained from a previous report and were directly used for calculations.56 However, in the case of the ethanol–glycerol, n-butanol–glycerol, and tert-butanol–glycerol mixtures, viscosity coefficients were reported, but not specifically for the compositions studied here.57–60 Hence, for these two cases, we applied the Grunberg–Nissan model to the available data and estimated the viscosity values according to our requirements.61,62 A detailed analysis is provided in Supporting Information Scheme S2 and Figure S3. After conducting an extensive literature search, we discovered a lack of published data on the viscosity for the n-propanol–glycerol and iso-propanol–glycerol mixture. Consequently, this presented a unique opportunity for us to predict the bulk viscosity at various compositions of these two solvent mixtures based on the φThT measurements.

Generally, the quantum yield of a molecular rotor has a power law relationship with viscosity commonly referred as the Förster–Hoffmann equation.1,18,64 In this model, the power varies between 1/3 to 2/3. Loutfy and Arnold in their seminal work checked the validity of the model for molecular rotor dye over a large range of temperatures and in solvents comprising low to high viscosity.64 They found the equation to be valid. If the measurement is performed at a constant temperature, then simply we can write

3. 4

Here, φ is the quantum yield of the molecular rotor, η is the viscosity coefficient, and B and α are the solvent- and probe-dependent constants. For ThT, we can write eq 4 taking logarithm in each side as

3. 5

In eq 5, ηbulk signifies the bulk viscosity of the solvent mixture. This equation establishes a linear relationship between log φThT and log ηbulk with an intercept log B and slope α. Accordingly, we plotted log φThT against log ηbulk for the four binary mixtures for which viscosity was reported, i.e., methanol–glycerol, ethanol–glycerol, n-butanol–glycerol, and tert-butanol–glycerol mixtures. These plots are listed in Figure 4. Here, it should be mentioned that the parameter log B is the same for pure solvents and different compositions of solvent mixture as all the solutions of ThT are homogeneous in nature. The first observation was that if we exclude the data point of pure glycerol in each of these four systems, the rest of the points follow a linear trend. The reason may be the excessively high viscosity of pure glycerol compared to the mixtures. While there may be other causes related to excited-state dynamics, they are beyond the scope of this discussion here. Nonetheless, we fitted the data points excluding the point corresponding to pure glycerol, and parameters of the fit are reported in both the figure and Table 2. Perhaps, the most significant and intriguing finding is that the slope value (α) ranged only between 0.489 and 0.502. Considering the intrinsic error associated with the measurements, α values are extremely close to one another. It is to be noted that the experiment of tert-butanol–glycerol mixtures was performed at 30 °C, and still, we got a similar value for α. This fascinating finding suggests that the dependence of α on the solvent is minimal for the ThT and glycerol–monohydroxy alcohol mixture.

Figure 4.

Figure 4

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Plot of variation of log φThT against log ηbulk for (a) methanol–glycerol, (b) ethanol–glycerol, (c) n-butanol–glycerol, and (d) tert-butanol–glycerol solvent mixtures. The black lines indicate linear fitting excluding the point for pure glycerol.

n-propanol and iso-propanol have a molecular weight and bulk viscosity value between the values of ethanol and n-butanol. So, from this analysis, we can safely assume that for the n-propanol–glycerol and iso-propanol–glycerol mixtures, α will have a similar value. We can use the estimated range of α to predict the bulk viscosity for different compositions of these two mixtures, which is not reported until now. The novelty of idea is that we can make this prediction without measuring the bulk viscosity. Since we do not have the knowledge about the intercept of the line, i.e., log B, we used the reported value of viscosity of pure n-propanol and iso-propanol in eq 5 to modify it as follows

3. 6

Here, φThTi is the quantum yield of ThT in the ith composition of the mixture and φThTPrOH is the same in pure n-propanol or iso-propanol. Similarly, ηbulki is the bulk viscosity of the ith composition of the mixture and ηbulkPrOH is the same for pure n-propanol or iso-propanol. So, we can calculate log ηbulki as

3. 7

We used the value of α = 0.49 and 0.50 and calculated log ηbulki for n-propanol–glycerol and iso-propanol–glycerol mixtures at25 °C. Employing 4, we have estimated the bulk viscosity (ηbulki) for each of the α values for various compositions of n-propanol–glycerol and iso-propanol–glycerol mixtures, which is given in Table 3. In Figure 5, we have shown the variation of log φThTi against logηbulki for α = 0.50 and variation of ηbulki with the mole fraction of glycerol for α = 0.50 in the two mixtures. The procedure discussed here can be employed to determine the bulk viscosity of an unknown composition of n-propanol–glycerol and iso-propanol–glycerol mixtures as well as can be used for other glycerol–monohydroxy alcohol mixtures.

Table 3. Estimated Values of Viscosity Coefficient Using eq 7 for Different Compositions of Glycerol–n-Propanol and Glycerol–iso-Propanol Mixtures.

X1 X2 viscosity (cP) for α = 0.490 viscosity (cP) for α = 0.500
Glycerol (1) + n-Propanol (2)
0.000 1.000 1.97 1.97
0.103 0.897 2.91 2.89
0.205 0.795 5.04 4.94
0.306 0.694 11.41 11.02
0.407 0.593 17.48 16.73
0.507 0.493 42.48 39.95
0.607 0.393 80.90 75.11
0.706 0.294 155.24 142.25
0.805 0.195 354.54 319.57
0.903 0.097 752.39 668.04
Glycerol (1) + iso-Propanol (2)
0.000 1.000 2.10 2.10
0.105 0.895 4.05 4.00
0.208 0.792 6.80 6.64
0.311 0.689 14.80 14.26
0.413 0.587 31.75 30.07
0.513 0.487 54.62 51.17
0.612 0.388 126.95 116.95
0.711 0.289 240.01 218.30
0.808 0.192 514.29 460.70
0.905 0.095 877.93 778.08
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Figure 5.

Figure 5

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Plot of variation of log φThT against predicted log ηbulk using eq 7 and estimated values of ηbulk against XGly (a), (b) n-propanol–glycerol (c) and (d) iso-propanol–glycerol.

4. Conclusions

The experiments and analysis performed in this work demonstrated the variation of quantum yield of ThT (φThT) at different compositions of methanol–glycerol, ethanol–glycerol, n-propanol–glycerol, iso-propanol–glycerol, n-butanol–glycerol, and tert-butanol–glycerol solvent mixtures. With an increasing concentration of glycerol in the mixture, the φThT values increased. We modeled the trend and estimated the deviation from ideality in each of mixtures. The extent of nonideality was found to vary as ethanol > n-Propanol > n-Butanol > iso-Propanol > methanol, whereas tert-butanol showed opposite deviation from ideality. This predictive model can be utilized to forecast the extent of nonideality resulting from solvent–solvent interactions for other binary mixtures too. A linear relationship between log φThT and log ηbulk was established in four mixtures for which bulk viscosity is already known. The inference drawn from the analysis was used to develop our methodology to measure the bulk viscosity of glycerol–monohydroxy alcohol mixtures solely based on the quantum yield measurement. Applying it, we estimated and predicted the viscosity values for the previously unreported n-propanol–glycerol and iso-propanol–glycerol mixtures at several compositions. This analysis holds the potential to be extended to other solvents and biological systems, expanding its applicability and significance.

Acknowledgments

Puspal Mukherjee thanks Netaji Subhas Open University for funding vide project grant number Reg./1291 dated 22/11/2021, and Sintu Ganai thanks Netaji Subhas Open University for funding vide project grant number Reg./1289 dated 22/11/2021.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c06428.

  • Absorption spectra of thioflavin-T in different solvent mixtures; refractive index of binary mixtures of glycerol with methanol, ethanol, n-propanol, iso-propanol, n-butanol, and tert-butanol; and viscosity of ethanol–glycerol, n-butanol–glycerol, and tert-butanol–glycerol mixtures (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao3c06428_si_001.pdf (561KB, pdf)

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