1 Introduction

Chemical weapons use chemical substances that can cause incapacitation, harm, or death in some living organisms. They are classified as weapons of mass destruction since they are effective against a large population indiscriminately. The effects of chemical weapons on humans, their acuteness, and severity depend largely on the chemical agents, which are often classified according to the physiological effects they produce into the following categories [1]:

  • Nerve agents, often organophosphorus compounds such as sarin.

  • Vesicants (blistering agents), e.g., mustards or arsenicals.

  • Blood agents such as cyanides.

  • Choking agents, which include phosgene gas and chlorine gas.

  • Riot control agents, for example, lachrymators, often referred to as teargases.

  • Psychomimetic agents such as lysergic acid diethylamide (LSD).

  • Toxins, i.e. compounds synthesized by living organisms.

Throughout history, many attempts have been made to ban the use of chemical weapons during warfare. Possible reasons why the use of chemical weapons, in particular, was deemed illegitimate during warfare, unlike the use of many other weapons, are discussed in the literature [2, 3]. Despite several attempts to ban them with international agreements, incidences of the use of chemical weapons against groups of people or individuals have been reported around the world. Furthermore, since 1915, the toxicity of chemical warfare agents has increased by a factor of 1000 [4]. Considering these and many other factors, the need for research and development of detection devices, protective measures, treatment, decontamination, and methods for safe liquidation has emerged. For this reason, knowledge of the properties of chemical substances that are used as weapons is fundamental.

This work focused on nerve agents, most of which are organophosphorus compounds. These compounds penetrate biological barriers and can be rapidly absorbed through different routes, including inhalation, oral, and percutaneous routes. The acute neurotoxicity of organophosphorus nerve agents is generally attributed to their effect on cholinergic nerve transmission, specifically irreversible inhibition of acetylcholinesterase (AChE, EC 3.1.1.7) through phosphorylation of the serine group in the active center of the enzyme. Symptoms depend on the dose, duration of exposure, and method of absorption and may include miosis, sweating, fasciculations, seizures, bradypnea, and bronchospasm. The common cause of death is suggested to be respiratory failure [5]. Some organophosphorus compounds are commercially available and are widely used in industry, agriculture, medicine, and pharmacology [6], thus leading to professional, accidental, or suicidal intoxications. Treatment for organophosphorus nerve agent poisoning includes administering an antidote such as atropine [7].

Given the high toxicity of organophosphorus nerve agents, research is commonly performed with simulant molecules, which possess similar molecular structures and physical properties but are less toxic. A list of suitable simulants for chemical warfare agents was presented, e.g., by Lavoie et al. [8]. For the purposes of this work, the list was reviewed, and four simulants were chosen based on their similarity, availability, hazardous properties, and relative abundance of the literature data. Three of the simulants, trimethyl phosphate, triethyl phosphate, and dimethyl methylphosphonate, were chosen directly from the list, while the fourth one, diethyl methylphosphonate, was chosen by reviewing additional literature.

An experimental and theoretical study of the thermodynamic properties of the simulants was performed in this work. The phase behavior was checked with a heat–flux differential scanning calorimeter. Vapor pressures were determined using a static method in the total temperature range of 238–363 K; temperature ranges for individual compounds vary according to their volatility. A Tian–Calvet type calorimeter was used to determine the liquid heat capacities, while the ideal gas heat capacities were calculated using a combination of quantum chemistry and statistical thermodynamics. The R1SM [9] approach was used, which combines the rigid rotor–harmonic oscillator (RRHO) model, one-dimensional hindered rotor (1-D HR) model for symmetric internal rotations and mixing model for contributions of various conformers. The experimental and theoretical results were simultaneously correlated with the data in the literature, and the parameters of the Clarke and Glew equation [10] were obtained.

2 Experimental and Theoretical Part

2.1 Materials

All the compounds were purchased from Sigma‒Aldrich, and according to the certificates of analysis, the purities of all the compounds except for triethyl phosphate (unspecified method) were determined using gas–liquid chromatography (GLC). In this work, additional purity analysis was performed using GLC. Table 1 provides general information on the compounds studied.

Table 1 Studied materials
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2.2 Phase Behavior Study

The phase behavior was studied using a heat-flux differential scanning calorimeter (TA Q1000, TA Instruments, USA). Specifically, glass transitions or melting temperatures of the samples were aimed at being identified in the temperature range of 183 K to 298 K. All measurements were carried out using a continuous method with a cooling and heating rate of 2 K·min−1. Samples of approximately 5 to 10 mg were placed in hermetically sealed aluminum pans, while an empty pan was used as a reference. The temperature and enthalpy calibrations of the apparatus were previously performed using 1,3-difluorobenzene, n-octane, indium, tin, distilled and demineralized water, naphthalene, and benzoic acid [11].

2.3 Heat Capacity Measurements

A Microcalvet calorimeter (SETARAM, France) was used to determine the liquid heat capacities. The instrument is equipped with a 3D sensor in which the sample and the reference cell are surrounded by Peltier elements. To reach temperatures lower than 273 K, an additional water thermostat was used. The experiments were performed in continuous mode with a constant heating rate of 0.3 K·min−1. Several cycles were performed by alternating the heating and cooling modes, and the results were averaged. A three-step procedure was employed, where the reference cell was always empty while the measurement cell was empty, filled with the reference substance (synthetic sapphire, NIST SRM 720), and filled with the sample. Based on the testing experiments with benzophenone, benzoic acid, naphthalene, and benzothiazole, the combined expanded uncertainty of the measured heat capacity data was estimated to be \(U_{{\text{c}}} (C_{{p,{\text{m}}}}^{0} ) = 0.006C_{{p,{\text{m}}}}^{0}\) [12].

Initially, the liquid capacities of TMP, TEP and DMMP were measured in the temperature range from 228 K to 362 K. However, a noticeable sample loss was observed in all three experiments, which was attributed to the use of an EPDM (ethylene-propylene-diene polymer) seal that was proven to be chemically incompatible with the organophosphorus compounds. Therefore, the heat capacity of the DEMP was measured using a Viton sealing, with which no significant sample loss was observed. Given these observations, measurements of the heat capacities of DMMP and TMP were repeated with Viton sealing in a shorter temperature range of 243 K (shortened because of the glass transition of Viton sealing at approximately 235 K) to 353 K (shortened to reduce mass loss through evaporation). The measurements with Viton sealing were in excellent agreement with the measurements with EPDM sealing if they were evaluated against the final sample mass. Measurement of the heat capacities of TEP, where the relative sample loss was lower than the experimental uncertainty, was thus not repeated but was only evaluated with respect to the final mass.

2.4 Theoretical Calculations

The ideal-gas thermodynamic properties of the simulants were calculated using a combination of quantum chemical and statistical thermodynamics methods to evaluate their consistency with the experimental measurements. First, all the stable conformers were found, and their relative energies, moments of inertia, and molecular vibrational frequencies were calculated. In the second step, potential energy profiles of the methyl tops were obtained for a relaxed rotation. These quantum chemical calculations were performed in Gaussian 16 [13] using density functional theory (DFT) at the level of theory B3LYP/6-311+G(d,p) with D3 empirical dispersion correction [14]. Harmonic vibrational frequencies were scaled by a double-linear factor [9], which is by (0.9948 − 1.35·10−5 ν/cm−1) below 2000 cm−1 and by 0.960 above 2000 cm−1.

The ideal gas thermodynamic properties of each stable conformer were subsequently calculated in the rigid rotor–harmonic oscillator (RRHO) approximation with one-dimensional hindered rotor (1-DHR) corrections for methyl rotations. The bulk properties were ultimately evaluated using the mixing model, resulting in the R1SM approach described in detail by Štejfa et al. [9].

2.5 Vapor Pressure Measurements

Vapor pressure measurements were carried out by the static method, primarily using the STAT6 apparatus. A detailed description of the apparatus can be found in [15], and only a brief overview follows. The apparatus is constructed of stainless-steel tubing and pneumatically operated all metal valves. The pressure is measured simultaneously using two capacitance diaphragm gauges, which differ in their upper limits of 133 Pa and 1333 Pa. An internal temperature controller keeps the temperature of the manometric membranes constant at a value of 318 K. Calibrations were performed by the manufacturer, and a relative uncertainty of the pressure readings of less than 0.05% was determined. The sample container was immersed in a Lauda liquid bath thermostat, which regulates the temperature between 233 and 308 K. The sample temperature was measured using a platinum resistance thermometer with an uncertainty of less than 0.02 K.

Due to the low volatility of TMP and TEP and the limited amount of data in the literature for these compounds, their vapor pressures were also determined at elevated temperatures using the STAT8 apparatus [16]. The construction of the STAT8 apparatus is very similar to that of STAT6, except for the use of an air thermostat, a single capacitance diaphragm gauge, and a thermistor element with a temperature measurement uncertainty lower than 0.01 K. The expanded uncertainty of the measurements at both apparatuses is Uc(p/Pa) = 0.005p/Pa + 0.05 [17].

2.6 Simultaneous Treatment of Vapor Pressures and Related Thermal Data (SimCor Method)

In the SimCor method, the selected experimental vapor pressure data were correlated simultaneously with the difference in the heat capacities between the ideal gas and liquid, \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0} = C_{{p,{\text{m}}}}^{0} ({\text{ig}}) - C_{{p,{\text{m}}}}^{0} ({\text{l}})\), where \(C_{{p,{\text{m}}}}^{0} ({\text{ig}})\) and \(C_{{p,{\text{m}}}}^{0} ({\text{l}})\) were obtained theoretically and from calorimetric measurements, respectively. For an exact treatment, a description of the pVT behavior of the gaseous phase would be needed, which can hardly be determined experimentally for the given compounds. In some cases, pVT behavior (in the form of virial coefficients) is estimated using an empirical method, which typically requires critical temperature and pressure. These are again unavailable, and the use of estimated values in the virial-coefficient estimation method would ultimately lead to large uncertainties in the pVT correction to \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0}\). Therefore, \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0}\) was correlated only at temperatures where p < 1 kPa, where the nonideality of the gaseous phase has a negligible impact on \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0}\).

The SimCor method was described in detail previously [18] and was used in our laboratory to develop recommended vapor pressure and thermophysical data for several groups of crystalline and liquid compounds (see, e.g., Mahnel et al. [19] and references therein). The Clarke and Glew equation [10] with four parameters was used within the SimCor procedure to describe the vapor pressures and the derived thermal properties, which corresponds to a linear temperature dependence of \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0}\). The Clarke and Glew equation has the following form:

$$\begin{aligned} R\ln \frac{p}{{p^{0} }} & = - \frac{{\Delta_{{\text{l}}}^{{\text{g}}} G_{{\text{m}}}^{0} (\theta )}}{\theta } + \Delta_{{\text{l}}}^{{\text{g}}} H_{{\text{m}}}^{0} (\theta )\left( {\frac{1}{\theta } - \frac{1}{T}} \right) + \Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0} (\theta )\left[ {\frac{\theta }{T} - 1 + \ln \left( {\frac{T}{\theta }} \right)} \right] \\ & \quad + \left( {\frac{\theta }{2}} \right)\frac{{\partial \Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0} }}{\partial T}(\theta )\left[ {\frac{T}{\theta } - \frac{\theta }{T} - 2\ln \left( {\frac{T}{\theta }} \right)} \right],\end{aligned}$$
(1)

where p0 = 100 kPa is the reference pressure, θ = 298.15 K is the reference temperature, R is the molar gas constant, and \(\Delta_{{\text{l}}}^{{\text{g}}} G_{{\text{m}}}^{{0}}\) and \(\Delta_{{\text{l}}}^{{\text{g}}} H_{{\text{m}}}^{0}\) are the standard molar vaporization Gibbs energy and enthalpy, respectively. Note that Eq. 1 is derived under the ideal gas assumption. Its parameters can be used to evaluate vapor pressure at any temperature within the validity range of the equation, but the thermal properties \(\Delta_{{\text{l}}}^{{\text{g}}} H_{{\text{m}}}^{0}\) and \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0}\) can be identified with the adjustable parameters only at low vapor pressures. At high vapor pressures, they should be evaluated through the Clapeyron equation.

3 Results and Discussion

3.1 Phase Behavior

The phase behavior of the compounds studied was studied between 183 K and 298 K, but no phase transitions were observed. No published data on the solid–liquid transitions of dimethyl methylphosphonate (DMMP) or diethyl methylphosphonate (DEMP) were found while Saini et al. [20] reported glass transition temperatures of trimethyl phosphate (TMP) and triethyl phosphate (TEP) at 138 K and 137 K, respectively. Moreover, two different crystal phases of TMP were observed [21]. Unfortunately, the conditions of their preparation, as well as their melting temperatures, were unspecified. Depending on the equipment used, cooling with liquid nitrogen might be used. It can be concluded that the simulants studied hardly crystallize under common conditions and that they exhibit glass transitions well below 183 K.

3.2 Liquid Heat Capacity

Liquid heat capacities measured with the Microcalvet calorimeter are presented in Table 2. No published values were found for comparison. Since the simulants studied have distinct molar masses, it is more relevant to compare their specific heat capacities, as in Fig. 1. These values lie within a reasonable range between 1.5 and 2 J·K−1·g−1 at ambient temperature. Phosphonates exhibit detectably larger specific heat capacities than phosphates. TMP and DMMP seem to exhibit minima on the liquid heat capacity curve, which can occur in the region (close) above the melting temperature depending on the structure of the compound [22].

Table 2 Experimental liquid heat capacities \(C_{{p,{\text{m}}}}^{0}\) in J·K−1·mol−1 at p = 100 ± 5 kPa
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Fig. 1
figure 1

Comparison of the specific liquid heat capacities of the simulants. ▲, TMP; , TEP; , DMMP; , DEMP

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3.3 Ideal Gas Thermodynamic Properties

The most stable conformers of the simulants at the B3LYP-D3/6-311+G(d,p) level of theory are illustrated in Fig. 2. Lists of stable conformers for each compound with corresponding relative electronic energies and dihedral angle coordinates can be found in Tables S1 to S4 in Supporting Information (SI). TMP and DMMP were found to have coincidently 3 conformers, of which the third has a much higher relative energy. TEP and DEMP have 42 and 16 conformers, respectively, at this level of theory. The conformer labels are written in the clockwise direction, and the dihedral labels are cis (c) ≈ 0°, gauche (g) ≈ 60°, anti-gauche (g′) ≈ − 60°, and trans (t) ≈ 180°. Following the previous study on TEP [23], dihedral angles O–P–O–C are given first by uppercase letters, followed by P–O–C–C dihedral angles in lowercase letters for TEP and DEMP.

Fig. 2
figure 2

Optimized molecular structures obtained at the B3LYP-D3/6-311+G(d,p) level of theory

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The conformational space of TMP has previously been discussed a few times. The conformer TGG was initially calculated to be 4.2 kJ·mol−1 more stable than GGG at a low level of theory (HF/6-31G(d)) [21]. However, negligible changes in conformational equilibria with temperature, as proven by liquid Raman and IR spectra, indicated that the difference in enthalpy between them must be much lower [21]. A later study [24] suggested that GGG is more stable than TGG based on new calculations at several higher levels of theory. The conformer with CS symmetry discussed in [24], which exhibited a very low barrier to conversion to TGG, was found to be unstable at the B3LYP-D3/6-311+G(d,p) level of theory in this work. To our knowledge, the conformer TTT has so far been discussed only within an NMR study [25].

A conformational study of TEP [23] was previously performed that identified 35 stable conformers, all with relative energies below 12.5 kJ·mol−1. Ten of the conformers were derived from the GGG cluster (identical to conformer 1 of TMP), and 25 were derived from the GGT cluster (conformer 2 of TMP). We located one additional minima for each of the clusters plus five conformers derived from clusters unstable in the case of TMP (GGG′ and TG′G) or unconsidered in [23] (TTT). As in the case of TMP, the conformer with the TTT cluster exhibited a relative energy considerably higher than that of all the other conformers. Due to the large number of TEP conformers and the narrow span of their relative energies, the conformer stability rankings presented in [23] and obtained in this work are not equal. As in the case of n-alkanes [9], the D3 correction employed in our calculations makes gauche dihedral angles slightly more favorable, changing, e.g., the most stable conformer.

For DMMP, six stable conformers were theoretically identified first [26]. Later, the occurrence of a sole conformer (TG) was derived from the IR spectra of the gaseous phase by the same authors [27]. In this work, three stable conformers were found, and TG was the least stable. Considering the currently obsolete methods used for calculations [26] that were also used for the interpretation of spectra [27], disagreement with the current study is not considered crucial. A recent study [28] theoretically identified the same three DMMP conformers as we did (four are listed by the authors, but two of them are mirror images). Subsequently, only two more stable species (GG and GG′) were reported to be present under the experimental conditions and were treated as two species [28] despite the very low energy barrier between them (< 0.8 kJ·mol−1).

In the case of DEMP, a total of nine conformers were identified; however, comprehensive listings and descriptions were provided for only seven of them based solely on their energies, dipole moments, and moments of inertia. [29]. Without any information about their structure, discussion of the correspondence with our extended set of 16 stable conformers seems futile.

The rotations of the methyl groups were treated in the 1-D HR approximation, assuming that they are uncoupled mutually as well as from other modes of intramolecular motion. The potential energy profiles of the individual rotating tops were calculated with a 5° step and fitted with the Fourier expansion, which provided the rotational parameters listed in Table S5 in the SI. For TEP and DEMP, the lowest energy conformer was used to determine the rotational energy profiles, which could be appropriately described with the cos(3φ) term. In the case of TMP, the lowest energy conformer adopts C3 symmetry, which means that all three methyl rotations would yield identical profiles. Therefore, the second most stable conformer was used for calculation of the rotational profiles, and since their rotational barriers are low and noticeably close, the use of the same set of parameters for the most stable conformer was considered to introduce negligible errors. For DMMP, the rotations of the methyl tops were found to be coupled with the other internal rotations. During methyl rotation, the two most stable conformers transform into each other with a low rotational barrier that practically corresponds to free rotation at ambient temperatures. Thus, a unique set of Fourier expansion parameters was assigned to each of the three stable conformers. The rotational profiles also required additional Fourier expansion terms to appropriately describe this behavior.

The rotational barriers of methyl tops bound to oxygen or phosphorus were found to be noticeably lower than common for alkyl chains [9]. Finally, overall ideal gas heat capacities, entropies, and thermal enthalpies were calculated using the R1SM approach [9]. Table 3 lists the calculated ideal gas thermodynamic properties. A comparison of the ideal gas heat capacities is shown in Fig. 3.

Table 3 Ideal-gas thermodynamic properties at p = 100 kPa, in J·K−1·mol−1
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Fig. 3
figure 3

Comparison of ideal gas heat capacities calculated using the R1SM approach. ━, TMP; , TEP; , DMMP; , DEMP

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3.4 Vapor Pressure

The vapor pressures of TMP, TEP, DMMP, and DEMP were measured with the STAT6 apparatus in the temperature ranges of 243–308 K, 274–308 K, 238–308 K, and 248–308 K, respectively. Different temperature ranges were chosen because of differences in the volatility of the substances. Additionally, the vapor pressures of TMP and TEP were measured using the STAT8 apparatus in the temperature ranges of 283–349 K and 288–363 K, respectively. The experimental vapor pressure data, including their deviations from the correlation equation, are listed in Tables 4 and 5. The vapor pressures of individual substances are graphically compared in Fig. 4. Over the entire temperature range of the experiments, the vapor pressures of DMMP were the highest, while the vapor pressures of TEP were the lowest. The vapor pressures of TMP and DEMP were very close in the experimental temperature range.

Table 4 Experimental vapor pressure of TMP and TEP
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Table 5 Experimental vapor pressure of DMMP and DEMP
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Fig. 4
figure 4

Comparison of vapor pressures of the simulants studied. ▲, TMP, STAT6; , TMP, STAT8; , TEP, STAT6; , TEP, STAT8; , DMMP; , DEMP

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An overview of the literature data on the vapor pressures of the simulants is presented in Table 6, including the temperature and pressure ranges and the method used. It should be noted that some of the reported vapor pressure data exhibit large deviations or uncertainties, especially in the low vapor pressure range. For example, Brozena et al. [30] observed large deviations from the vapor pressure data of TEP at the lower end of the temperature range of differential thermal analysis (DTA) from the other data sets determined in the same study. Butrow et al. [31] used DSC to determine vapor pressures and suggested that this method should be used with caution since the experimental uncertainty increases as the vapor pressure decreases. Kosolapoff [32] noted that vapor pressure data determined using the isoteniscope method at lower temperatures were not trustworthy. These issues, together with additional inconsistencies in the literature data, can be observed when applying the arc method [33] in Fig. 5 and Fig. 6. For this reason, some data points or entire data sets were excluded from simultaneous correlation treatment, as discussed in Sect. 3.5.

Table 6 Literature data overview on vapor pressures
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Fig. 5
figure 5

Arc plot representation of the vapor pressures of TMP (left) and TEP (right). , This work, STAT6; , this work, STAT8; , Evans et al. [34]; , Brozena et al. [30], DTA; ■, Brozena et al. [30], transpiration; , Brozena et al. [30], Knudsen effusion; , Bikelytė et al. [35]. Data points marked with empty symbols were excluded from the simultaneous correlation treatment

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Fig. 6
figure 6

Arc plot representation of the vapor pressures of DMMP (left) and DEMP (right). , This work, STAT6; , Kosolapoff [32]; , Fan and Wang [36]; □,■, Butrow et al. [31], DSC; , Butrow et al. [31], transpiration; , Bikelytė et al. [35]. Data points marked with empty symbols were excluded from the simultaneous correlation treatment

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3.5 Simultaneous Correlation

The experimental and selected literature vapor pressure data were correlated simultaneously with the heat capacity values determined calorimetrically (Sect. 3.2) and theoretically (Sect. 3.3). The Clarke and Glew equation, Eq. 1, was used, the adjusted parameters of which are presented in Table 7.

Table 7 Parameters of Clarke and Glew Eq. 1 derived using the SimCor procedure a
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Graphical representations of the SimCor results are illustrated in Figs. 7 and 8. Due to large deviations from the overall trend, all the data from three references [32, 35, 36] were excluded from the correlation. Additionally, some data points from other references were excluded due to obvious experimental difficulties that led to significant deviations from the trend: isoteniscope measurements [34] below 5 kPa, the whole data set from DTA [30], and DSC measurements [31] below 500 Pa. Although the accepted literature data exhibit an appreciable scatter of approximately 5% from the developed correlation, their inclusion is believed to be more accurate than simple extrapolation towards high temperatures. Moreover, descriptions of the vapor pressures and \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0}\) in the experimental temperature range of this work are not notably affected by their inclusion.

Fig. 7
figure 7

Deviation plot for vapor pressures of TMP (left) and TEP (right). , This work, STAT6; , this work, STAT8; , Evans et al. [34]; , Brozena et al. [30], DTA; ■, Brozena et al. [30], transpiration; , Brozena et al. [30], Knudsen effusion; , Bikelytė et al. [35]. Data points marked with empty symbols were excluded from the simultaneous correlation treatment. Uncorrelated data sets and data points might be partially displayed or out of scale

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Fig. 8
figure 8

Deviation plot for vapor pressures of DMMP (left) and DEMP (right). , This work, STAT6; , Kosolapoff [32]; , Fan and Wang [36]; ■, Butrow et al. [31], DSC; , Butrow et al. [31], transpiration. Data points marked with empty symbols were excluded from the simultaneous correlation treatment. Uncorrelated data sets and data points might be partially displayed or out of scale

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As already mentioned, DMMP is the most volatile of the simulants studied in the experimental pressure range, whereas TEP is the least volatile. Volatility is generally considered to be driven by the molecular mass and strength of intermolecular interactions. In Fig. 9, the vapor pressures at 298 K are plotted as a function of the molar mass for the four simulants studied. The dependence is not only unsmooth but even non-monotonous, with TMP being less volatile than heavier DEMP. It can be concluded that phosphates exhibit stronger intermolecular interactions than phosphonates. Similarly, the same non-monotonous trend was observed for the standard boiling temperatures of the compounds.

Fig. 9
figure 9

Dependence of vapor pressure and vaporization enthalpy on the molar mass of the simulant

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The vaporization enthalpies at 298 K obtained by the SimCor procedure are also shown in Fig. 9. This dependence is monotonous but has a noticeable deviation from linearity. The vaporization enthalpies of phosphonates are lower than those of phosphates, and their dependence on molar mass is less steep than that of phosphates, which again indicates stronger intermolecular interactions in phosphates.

Although some differences between the respective compounds (or the two classes) can be observed in the specific liquid or ideal gas heat capacities, Fig. 10 shows that \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0}\) of all four compounds lie in a narrow range between − 75 J·K−1·mol−1 and − 90 J K−1·mol−1 at 300 K, and exhibit very similar temperature dependencies.

Fig. 10
figure 10

The temperature dependences of the difference in heat capacity between the liquid and ideal gas, \(\Delta_{{\text{l}}}^{{\text{g}}} C_{{p,{\text{m}}}}^{0}\). ▲, TMP; , TEP; , DMMP; , DEMP. The points are the experimental data, and the lines are the SimCor descriptions. Empty points were not correlated because they lie in the region where p > 1 kPa for the given compound; and the unevaluated pVT correction might already be considerable

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4 Conclusions

A thermodynamic study of simulants for chemical warfare weapons was performed. The study consisted of both experimental and theoretical methods. The phase behavior, vapor pressures, and liquid phase heat capacities were determined experimentally, whereas the ideal gas heat capacities were determined using theoretical calculations. The values were then compared with the data from the literature. Using the method of simultaneous correlation, the parameters of the Clarke and Glew equation were derived. On the basis of the obtained results, several conclusions were drawn:

Glass transition or crystallization was not observed for any of the substances at temperatures down to 183 K. The specific liquid heat capacities of the four compounds were found to be in the expected range of 1.5 to 2 J·K−1·g−1 at ambient temperatures, with both phosphonates having higher values than the phosphates. During the calculation of ideal gas thermodynamic properties, we found that the rotational barriers of methyl tops bound to oxygen or phosphorus were noticeably lower than those common in alkyl chains. During the potential energy scan of methyl rotation in dimethyl methylphosphonate, the two most stable conformers transformed into each other with a low rotational barrier, corresponding to a practically free rotation. Thus, a unique set of Fourier expansion parameters was assigned to each of the conformers of dimethyl methylphosphonate.

In compliance with expectations based on the molecular mass, the vapor pressure of dimethyl methylphosphonate was the highest, and the vapor pressure of triethyl phosphate was the lowest over the experimental temperature range. However, the vapor pressures of trimethyl phosphate and diethyl methylphosphonate were very close, and trimethyl phosphate was even less volatile, although it has a lower molar mass than diethyl methylphosphonate. This result reflects differences in the strength of intermolecular interactions between the phosphate and phosphonate groups of the compounds. The derived vaporization enthalpies and standard boiling-point temperatures also support this evidence.