Calculating Compound Dependent Gas-Droplet Distributions in Aerosols of Propylene Glycol and Glycerol from Electronic Cigarettes

Abstract

Aerosols created by electronic cigarettes are suspensions of liquid droplets in a gas phase. All of the volatile or semi-volatile compounds in the system will partition between both phases; among these compounds are the “e-liquid” constituents plus the degradation products such as formaldehyde produced during “vaping”. This partitioning affects deposition in the respiratory tract and optimal analytical method design. Theory can be used to predict the particle- vs. gas-phase distribution of each compound as a function of the composition of the aerosol droplets, temperature, and the vapor pressure of the compound. As an example, even at the highest total particulate matter (TPM, μg/m³) levels for e-cigarette aerosols, formaldehyde as CH₂O will be mostly in the gas phase; two important adducts of formaldehyde will be mostly in the aerosol droplets even at the lowest TPM levels.

1. Introduction

An aerosol created by an electronic cigarette (e-cigarette) is a collection of liquid particles suspended in a gas phase; the same can be said about tobacco smoke. For any chemical i of interest (e.g., acrolein, benzene, nicotine, propylene glycol, glycerol, etc.) that possesses some volatility (i.e., a non-zero vapor pressure), a portion of i will be in the gas phase. If there are aerosol droplets present, then some dissolution of i into the droplets will occur. The gas/particle partitioning distribution equilibrium for i is then

$$i_{\text{gas}}=i_{\text{particle}}$$ (1)

The fraction of i in the gas phase is denoted f_g,i. A predictive understanding of f_g,i values is important because: 1) f_g,i affects how a chemical is deposited in the respiratory tract (RT): when f_g,i ≈ 1, then i will tend to be deposited to surfaces mostly from the gas phase; when f_g,i is close to zero, then i will tend to be deposited to surfaces mostly by deposition of the aerosol particles; and 2) f_g,i affects the design of chemical analysis protocols for an aerosol (e.g., collection and analysis of just the gas phase will suffice when f_g,i ≥ 0.9).

The science of gas/particle partitioning has been successfully applied to tobacco smoke (Pankow et al., 1997; Pankow 2001; Pankow et al. 2004). This work provides an outline of its application to e-cigarette aerosols by consideration of the particular liquid properties of propylene glycol and glycerol, the primary constituents of e-cigarette aerosols.

The gas/particle coefficient K_p,i (m³/μg) is defined (Pankow, 1994)

$$K_{\text{p},i}\left({\text{m}}^3/\text{μg}\right)=\frac{c_{\text{p},i}(\text{μg}/\text{μg})}{c_{\text{g},i}\left(\text{μg}/{\text{m}}^3\right)}$$ (2)

where c_p,i (μg/μg) is the concentration within the particle phase, and c_g,i (μg/m³) is the concentration in the gas phase. For partitioning into liquid particles (Pankow, 1994)

$$K_{\text{p},i}\left({\text{m}}^3/\text{μg}\right)=\frac{RT}{{10}^6\overline{\text{MW}}{\zeta }_i{p}_{\text{L},i}^{\text{o}}}$$ (3)

where: R = gas constant (8.2 × 10⁻⁵ m³-atm/mol-K); T = temperature (K); $\overline{\text{MW}}$ (g/mol) = mole-average molecular weight of the absorbing liquid phase; ζ_i (dimensionless) = mole-fraction-scale activity coefficient in the liquid phase; and $p_{\text{L},i}^{\text{o}}$ is the vapor pressure (atm) of pure liquid i at temperature T. The presence of presence of $\overline{\text{MW}}$ in Equation (3) is due to the role of mole fraction in determining the volatility of i from a mixture of n₁ + n₂ +n₃ +… moles of different constituents:

$$\overline{\text{MW}}=\frac{n_1{\text{MW}}_1+n_2{\text{MW}}_2+n_3{\text{MW}}_3+\dots }{n_1+n_2+n_3+\dots }$$ (4)

The MW of propylene glycol (PG) is 76.1 g/mol, the MW of glycerol (GL) is 92.1 g/mol. For an equi-volume (≈ equi-molar) mixture of PG+GL having only a few percent total other constituents, $\overline{\text{MW}}\approx 84$ g/mol.

2. Phase Distributions

The parameter TPM (total particulate matter, μg/m³) gives the total mass of suspended particulate matter per m³ in the gas+particle aerosol system. The product c_p,iTPM(μg/m³) then gives the mass of i in the particle phase per m³ of the gas+particle aerosol system. Because the volume of the gas phase portion of most aerosols is only slightly less than the gas+particle volume, c_g,i (= mass of i in the gas phase per m³ of gas) is negligibly slightly less than the mass of i in the gas phase per m³ of gas+particle aerosol system. This means that, both c_g,i and c_p,iTPM essentially have the same units, and we can write that the total concentration of i in the aersosol system is (Pankow, 1994; 2001)

$$T_i=c_{\text{g},i}+c_{\text{p},i}\text{TPM}$$ (5)

The fraction of i in the gas phase is then

$$f_{\text{g}i}=\frac{c_{\text{g.}i}}{T_i}=\frac{c_{g,i}}{c_{\text{g,}i}+c_{\text{p.}i}+c_{\text{p.}i}\text{TPM}}=\frac{1}{1+K_{\text{p},i}\text{TPM}}$$ (6)

and the fraction of i in the particle phase is

$$f_{\text{p,}i}=\frac{c_{\text{p.}i}\text{TPM}}{T_i}=\frac{c_{\text{p.}i}\text{TPM}}{k_{\text{g.}i}+c_{\text{p.}i}\text{TPM}}=\frac{K_{\text{p.}i}\text{TPM}}{1+K_{\text{p.}i}\text{TPM}}$$ (7)

At temperature T, for neutral compounds that are not ionizable (e.g., acetaldehyde, acrolein, benzene, etc.), for each particular i in the e-cigarette system, there will not be large aerosol-to-aerosol variability in K_p,i. This is because most e-cigarette aerosols are compositionally dominated by PG and/or GL. The polarity and MW properties of PG and GL similar, so neither $\overline{\text{MW}}$ nor ζ_i will vary much with e-cigarette aerosol composition. However, introduction of significantly varying amounts of water (MW = 18.0 g/mol) will lead to some variability in K_p,i for a particular compound, due to changing $\overline{\text{MW}}$ and ζ_i values.

For nicotine, protonation in PM converts the free-base form Nic to NicH⁺, i.e. (Pankow 1997; Pankow 2001; Pankow, 2003):

$$\text{Nic}+{\text{H}}^{+}={\text{NicH}}^{+}$$ (8)

In the particle phase, both Nic and NicH⁺ will be present, and the fraction in the free-base form can vary: 0 < α_fb < 1. In the gas phase, essentially only the Nic form is present. The value of K_p for the free-base form is denoted K_p,fb (Pankow et al.,1997). Like the K_p,i value for a neutral compound, K_p,fb values for nicotine will not vary significantly for e-cigarette aerosols when the PM is mostly PG and/or GL. The K_p that governs partitioning of total nicotine will vary with α_fb according to (Pankow et al.,1997; Pankow 2001; Pankow, 2003):

$$K_{\text{p}}=\frac{c_{\text{p}}}{c_{\text{g}}}=\frac{c_{\text{p,fb}}/{\alpha }_{\text{fb}}}{c_{\text{g}}}=\frac{c_{\text{p,fb}}/c_{\text{g}}}{{\alpha }_{\text{fb}}}=\frac{K_{\text{p,fb}}}{{\alpha }_{\text{fb}}}$$ (9)

Among different neutral compound forms, for a particular aerosol, the K_p,i value (K_p,fb in the case of nicotine) is determined by ζ_i and $p_{\text{L},i}^{\text{o}}$. Both PG and GL are polar compounds, so ζ_i values for polar species like monomeric formaldehyde (CH₂O), acetaldehyde, acrolein, the aldehyde flavor chemical benzaldehyde, and nicotine can be expected to be close to unity. Benzene is not polar, so ζ_benzene > 1. Benzene is, however, is polarizable, so ζ_benzene is not very large, ~14 (Opris, 1981). For the non-polar C₁₀ flavor chemical limonene, it can be expected that ζ_i > 1. Table 1 provides some example calculations for expected K_p,i values. For most compounds in the table, it is assumed that ζ = 1.

Table 1.

Estimated K_p,i Values at T = 298.15 K for Gas/Particle Partitioning of Example Compounds to 1:1 Propylene Glycol:Glycerol with $\overline{\text{MW}}\approx 84$ g/mol. Measured or Estimated Pure-Compound Liquid Vapor Pressure Values $p_{\text{L},i}^{\text{o}}$ are for T = 298.15 K. Assumed Activity Coefficient Values ζ_i are Given.

	$\text{log\hspace{0.17em}}{p}_{\text{L},i}^{\text{o}}$ (atm)a	ζi	Kp,i (m3/μg)
compound
formaldehyde related
formaldehyde (CH2O)	0.70	~1	−10.2
hydrate (methanediol)	−3.88c	~1	−5.7
hemiacetal with PGb	−4.93d	~1	−4.6
other compounds
acetaldehyde	0.072	~1	−9.6
acrolein	−0.44	~1	−9.1
benzene	−0.93	~14e	−9.8
diacetyl	−1.12	~1	−8.4
limonene	−2.58f	>1	< −9.0
benzaldehyde	−2.77	~1	−6.8
nicotine	−4.48g	~1	−5.1h

^aBased on Antoine parameters given in the NIST Webbook unless otherwise indicated, http://webbook.nist.gov/chemistry/, accessed September 12, 2016.

^bStructure is HO-CH₂-O-CH₂-CH(OH)-CH₃ or HO-CH₂-CH(O-CH₂-OH)-CH₃.

^cChemSpider, http://www.chemspider.com/Chemical-Structure.71348.html, as predicted using the ACD/Labs Percepta Platform - PhysChem Module, accessed September 27, 2016.

^dUsing the SIMPOL group contribution method of Pankow and Asher (2008).

^eOpris (1981)

^fYaws (1994).

^gBased on equation in Lewis (1994) that gas phase nicotine concentration (g/cm³) = 10^{(−3260/T + 4.47)}.

^hK_p,fb.

Formaldehyde is an important compound in e-cigarette aerosols, with multiple studies showing that that it forms at higher power settings (e.g. Kosmider et al., 2014). Included in Table 1 are three variations of formaldehyde: 1) CH₂O itself; 2) the hydrate methanediol (aka methylene glycol, Winkelman et al., 2002), which likely forms in e-cigarette aerosols; and 3) the hemiacetal with PG, which has been found in e-cigarette aerosols formed at higher power settings (Jensen et al., 2015; hemiacetals with GL are also possible). The reactions converting formaldehyde to methanediol and the hemiacetal of PG are provided in Fig. 1. The vapor pressure values in Table 1 illustrate the ~5 order of magnitude difference in volatility between: 1) CH₂O; vs. 2) methanediol and the hemiacetal of formaldehyde with PG.

Fig. 1.

a. Reaction of formaldehyde with water to form methanediol; b. reaction of formaldehyde with propylene glycol to form a hemiacetal.

Fig. 2 provides curves of f_g,i vs. log $p_{\text{L},i}^{\text{o}}$ for e-cigarette aerosols for several values of log TPM covering the range 7 to 9 as observed elsewhere Pankow et al. 2016), assuming $\overline{\text{MW}}\approx 84$ g/mol and ζ_i ≈ 1. Also provided are curves for tobacco smoke, assuming log TPM values of 7.1 and 7.8 (total PM of ~5 to 25 mg/cigarette, total smoke volume of ~400 mL/cigarette, assuming $\overline{\text{MW}}=100$ g/mol, and ζ_i ≈ 1; Pankow et al., 2004).

Fig. 2.

Fraction in the gas phase of an e-cigarette or tobacco smoke aerosol as a function of the liquid vapor pressure of a pure compound $p_{\text{L},i}^{\text{o}}$ for varying values of total particulate matter (TPM, μg/m³) with ζ_i ≈ 1. For e-cigarettes, log TPM = 7 to 9, with $\overline{\text{MW}}=84$ g/mol; for tobacco smoke, log TPM = 7.1 to 7.8 (corresponds to 5 to 25 mg of total particulate matter in ~400 mL smoke), with $\overline{\text{MW}}=84$ g/mol. For benzene, with ζ = 14, f_g,i would be obtained with an x-axis value equal to $\text{log\hspace{0.17em}}{p}_{\text{L},\text{benzene}}^{\text{o}}+\text{log}(14)=\text{log\hspace{0.17em}}{p}_{\text{L},\text{benzene}}^{\text{o}}+1.15$.

3. Conclusions

The importance of understanding the phase distribution of each chemical of interest in e-cigarette aerosols cannot be overstated. Even at the highest TPM levels for e-cigarette aerosols, formaldehyde as CH₂O will be mostly in the gas phase, but the two adducts considered here will be mostly in the aerosol droplets, even at the lowest TPM levels. For the toxic flavor chemical diacetyl, at log TPM = 7, f_g ≈ 1; at log TPM = 9, f_g < 0.2. Formaldehyde as CH₂O will be delivered to the e-cigarette user mostly from the gas phase, but delivery of methanediol and hemiacetals of formaldehyde will mostly involve deposition of the aerosol droplets.

Highlights.

• Aerosol phase distributions depend on molecular properties and aerosol mass concentration

• Governing properties are vapor pressure, activity coefficient, and molecular weight

• Increasing vapor pressure and decreasing aerosol mass concentration favor the gas phase