The Group of Thermooptical Spectroscopy of Dr. M. Proskurnin

Thermal Lens Spectroscopy as Tool for Fundamental Analytical Chemistry

Determination of Stability Constants by Thermal Lens Spectrometry

Nowadays, several hundred papers are devoted to various applications of thermooptical spectrometry. Nevertheless, much less number of studies are devoted to the application of this method for studying fundamental—kinetic and thermodynamic—parameters of analytical reactions at the nanogram level of reactants. The use of thermooptical spectroscopy may be a sufficiently promising approach to solving this problem because this method is highly sensitive and non-destructive and uses all the variety and the experience gathered by conventional spectrophotometry. This study shows the possibilities of thermal lensing for studying thermodynamics and kinetics of complexation and redox reactions at the level of nanogram concentrations of reactants and the use new regularities for improving the performance characteristics of the analytical procedures.

Thermal lens spectroscopy as a tool of fundamental analytical chemistry

Thermal Lens Spectroscopy as a Tool for Fundamental Analytical Chemistry

The parameters measured by thermal lensing changes in the chemistry of analytical reactions when changing to trace amounts that can (and should) be studied by thermal lensing:
  • Reagent ratios
    • pH
    • analytical reagents
    • reductants/oxidants
  • Thermodynamics of interaction
  • Kinetics of Interaction
  • Selectivity
  • Sensitivity

Fundamental Parameters Measured by Thermal Lensing

  • Kinetics
    • Rate constants for homogeneous (redox and chelation)
    • Rate constants for heterogeneous reactions (sorption)
    • Activation Energy
    • Van’t Hoff Temperature Coefficients
    • Orders (pseudo-orders)
    • Rates of competing reactions
  • Thermodynamics
    • Stability constants
    • Standard redox potential
    • Acidity Constants
    • Solubility Constants
    • Distribution Coefficients
    • Sorption Constants, Langmuir equation coefficients
    • Changes in Gibbs Free Energy
    • Isosteric heats of sorption
    • Changes in Gibbs Free Energy
    • Sorption Constants, Langmuir equation coefficients

Determination of Equilibrium Constants

The data obtained show that the conditions of thermal lens measurements provide higher reliability and precision of measurements of equilibrium (chelate stability, acid–base, and other) constants compared to conventional spectrophotometry and potentiometry. In more detail it can be summarized as follows:

  • The reproducibility of thermal-lens measurements (at concentrations of n × 10–6 M and below) including coefficients of correlation of reagent-saturation curves is higher compared to spectrophotometry (more dilute solutions), and e.g. no significant oxidation of such an unstable complex as [Cu(Phen)2]+ occurs in the time of thermal-lens measurements.
  • Using low concentrations of reactants, it is possible to increase the effect of the competing reaction of the metal and decreases the possibility of other side processes.
  • In general, the studied system is simplified and more closely fits the approximation of ideal solutions. This increases the precision of measurements of stability constants.
  • Under the same conditions, the sensitivity ratio of thermal lensing to conventional spectrophotometry for the measurements of equilibrium constants is higher than in the case of analytical measurements of concentrations (calibration curves), as the effect of blank signal is less significant to the final results.
As a result, this makes it possible to determine equilibrium constants, including stepwise constants of chelates, for which traditional methods are inapplicable. For instance, this is the case of chelates of transition metals with 1,10-phenanthroline (see Table 1). For copper(I) with 2,9-dimethyl-1,10-phenanthroline stepwise constants were found for the first time. Also, more accurate determination of constants allowed us to explain seeming contradiction between stability constants of copper(I) 1,10-phenanthroline and 2,9-dimethyl-1,10-phenanthroline chelates: from the new data they are almost the same as expected from theory.
Table 1. Equilibrium constants found by thermal lensing (P = 0.95; n = 7)
System Medium Concentration level, mol/L Experimental constants
Iron(II) tris-(1,10-phenanthrolinate) Water n × 10–8– n × 10–6 logb3=21.3 ± 0.3 logK1=6.8 ± 0.5 logK2=6.8 ± 0.5 logK3=7.2 ± 0.5
Copper(I) bis-(2,9-dimethyl-1,10-phenanthrolinate) Water–ethanol (9 : 1) n × 10–6– n × 10–5 logK1=7.8 ± 0.5 logK2=7.4 ± 0.5 logb2=16.0 ± 0.5
Bismuth(III) iodide Water n × 10–8 – n × 10–7 logK1=6.2 ± 0.7 logb2=13.2 ± 0.5 logb3=18.5 ± 0.8 logb4=24.2 ± 0.7 logb5=27 ± 1 logb6=29.5 ± 0.9
Copper(I) bis-(1,10-phenanthrolinate) DMSO – acetonitrile (9:1) n × 10-6 logK1=5.9 ± 0.3 logK2 = 5.4 ± 0.3 logb2=11.3 ± 0.5
Copper(I) bis-(1,10-phenanthrolinate) Water n × 10-6 logK1=6.8 ± 0.4 logK2=9.0 ± 0.5 logb2=15.8 ± 0.9
2,9-dimethyl-1,10-phenanthroline Water n × 10–6 – n × 10–5 logKa=5.85 ± 0.05
Copper(II) diethyldithiocarbamate Water–ethanol (1 : 3) n × 10-7 logb2=12.6 ± 0.4
Nickel(II) diethyldithiocarbamate Water–ethanol (1 : 3) n × 10-6 logb2=16.4 ± 0.6
Cobalt(II) diethyldithiocarbamate Water–ethanol (1 : 3) n × 10-6 logb2=19.3 ± 0.7
Nickel(II) dimethylglyoximate Water–ethanol (1 : 4) n × 10-6 logb2=17.0±0.3

Experiments showed that in certain concentration ranges of metal iodides, the short-term signal fluctuations experience a sharp increase due to the formation of colloidal substances, which affect thermooptical properties of water and, thus, the thermal lens effect. From this behaviour, we estimated the solubility constants of copper(I), lead(II), and tin(II) iodides; pKs= 10.7 ± 0.3, 7.6 ± 0.1, and 8.3 ± 0.2 (P = 0.95; n = 6), respectively, which is in a good agreement with existing data.

Kinetics at the Nanogram Level

A combination of thermal lensing and analytical kinetics is a standalone problem. Another direction of our group is devoted to this problem (see the page
"Hyphenation of Thermal Lensing with Kinetic Measurements on the results in this direction). In this paper, we limit ourselves to the new kinetic effects appearing in thermal lensing of well-known analytical reactions. It was found that the rate of formation of the chelate of iron(II) with 1,10-phenanthroline at pH 0–2 decreases significantly, which is not observed at the spectrophotometric level. Under these conditions, the time of attaining of the constant is about 1.5 h. From thermal-lens data, the rate constants of formation and dissociation of iron(II) tris-(1,10-phenanthrolinate) at the level of 10–8 mol/L (Table 2). Thermal-lens data are characterized by higher precision than spectrophotometry.
Table 2. The general scheme of formation and dissociation of iron(II) tris-(1,10-phenanthrolinate) and determined rate constants
n×10–6– n×10–4 mol dm–3
Thermal lensing
n×10–8– n×10–6 mol dm–3
k1, min–1 (2.9±0.1)×10–3 (3.00 ± 0.05)×10–3
k-1, min–1 (2.0 ± 0.1)×10–2 (2.00 ± 0.05)×10–2

It is demonstrated that thermal-lens studies of kinetics at nanogram level allows the discrimination of processes that overlap in the case of conventional photometry. For instance, it is possible to discriminate reversible decomposition of diethyldithiocarbamate complexes of transition metals and irreversible oxidation of diethyldithiocarbamic acid (see Table 3). The changes in the reaction conditions were used for enhancing the selectivity and sensitivity of analytical reactions at the nanogram level both in the batch and flow conditions.
Table 3. Rate constants of the decomposition of cobalt(II) diethyldithiocarbamate (8.5×10–6М), calculated from thermal-lens experiments (biexponential decomposition), T = 293 K. l = 488.0 nm, Р = 60 mW. Water–ethanol solutions 3 : 1.(n = 10)
pH kt, min-1 kt, min–1
2.0 0.7 ± 0.4 (1.1 ± 0.2) × 10-3
2.4 1.0 ± 0.5 (9 ± 3) × 10-4
2.7 1.4 ± 0.7 (9 ± 3) × 10-4


It was found that the interference from cobalt, nickel and copper on the interaction of iron(II) with 1,10-phenanthroline changes significantly when moving from microgram to nanogram concentrations of the reactants. And it is noteworthy that nickel, which is traditionally considered the strongest interfering element due to the highest stability constant of its chelate with 1,10-phenanthroline (Table 4), shows much weaker interference at the nanogram level. As a result, the selectivity to nickel increases by the factor of 3–4 (compared to a 2–2.5-fold increase in the cases of copper and cobalt, see Table 4). This results from the fact that the nickel(II) chelate is the most inert among considered, and it has not enough time to form at the level of n × 10 M at the sample-preparation stage (20–25 min). It Rate constants of the decomposition of cobalt(II) diethyldithiocarbamate (8.5 × 10–6 М), calculated from thermal-lens experiments (biexponential decomposition), T = 293 K. l = 488.0 nm, Р = 60 mW. Water–ethanol solutions 3 : 1.(n = 10)proven by the measurements of the same solutions 24 h after preparing the solutions (Table 4), which show that the interference from nickel is more significant.
Table 4. The interference (mol : mol) from cobalt, nickel, and copper on the determination of iron(II) (1.8×10–7 mol/L) with 1,10-phenanthroline (5 ×10–5 mol/L).
Element logb3 Spectrophotometry Thermal lensing
after 20 min after 20 min after 24 h
Ni 24.3 10–15 45–50 15–20
Co 19.9 20–25 45–50 40–45
Cu 20.8 20–25 45–50 40–45

Changes in the Selectivity

Thermal lensing is known to be a NONSELECTIVE spectroscopic method; thus, the problems of decreasing the blank and providing the purity of reagents and solvents for analytical thermal lensing are of prime importance. However, the selectivity of thermal lens procedures CAN change, and even improve, compared to spectrophotometric determination as a result in the change of interaction at the nanogram level, which should be taken into account in developing thermal-lens procedures. Apart from the examples on the interference from nickel on the determination of iron(II) with 1,10-phenanthroline, the following examples can be given.


It is known that Pb, Sn, Cu, and Sb are the most interfering elements on the spectrophotometric determination of bismuth with iodide due to the formation of difficultly soluble compounds and decreases in the row Pb >> Cu(I) > Sn = Sb (Table 5), which is in good concordance with the solubility constants of corresponding iodides. However, under the same reaction conditions, thermal lens determination of bismuth is much more selective. This effect can be accounted for the fact that the precipitates of difficultly soluble iodides are not formed, and the selectivity becomes determined by the light absorption of corresponding complex iodides. The selectivity row changes to Cu(I) > Sn > Pb > Sb (Table 5), which is in good concordance with the stability constants for the corresponding chelates.
Table 5. Selectivity of spectrophotometric and thermal-lens determination of bismuth

Changes in the Sensitivity

It is common opinion that sensitivity parameters of thermal lensing (limits of detection and determination) are primarily determined by the instrumental sensitivity of the instrumentation (pump laser power and the optical-scheme design) and thermooptical parameters of the medium. However, a change in the chemical interaction on a decrease in the concentration level can also affect the sensitivity.

More favourable conditions of carrying out the reaction at the trace level.

For instance, the determination limit of spectrophotometric determination of bismuth is 600 ng/mL, while thermal lensing is characterized by the value of 0.5 ng/mL. Thus, we observe a 1200-fold growth in the sensitivity because in the case of thermal lensing (higher excess amounts of ascorbic acid, lower concentrations of iodide), the effect of formation of free iodine is negligible, and the determination limit is improved substantially.

An increase in the completeness of the analytical reaction at the nanogram level.

For instance, in the case of thermal lens determination of some phenols in aqueous solutions by azo-coupling with p-nitrophenyldiazonium, when changing from conventional spectrophotometry to thermal lensing, the actual slope of the calibration plot increases by the factor of 100, while the theory of thermal lens effect predicts a 35–40-fold growth only.


These examples illustrate that thermal lensing can be applied for determining various fundamental thermodynamic and kinetic parameters of the processes in question, and the accuracy and precision of such determinations is rather advantageous compared to conventional methods. As a whole, the development of procedures of thermal-lens determination shows that a decrease in the concentrations of reactants affects not only the sensitivity but also the selectivity of the determination. This direction of development of thermal lens spectrometry seems rather important for analytical chemistry because it combines both basic and applied research, which undoubtedly expands the possibility of the methods at the trace level.
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