Influence of CO₂ on the rheology of melts from the Colli Albani Volcanic District (Italy): foidite to phonolite

Abstract

In this study, the influence of CO₂ on the rheology of silica poor and K-rich melts from highly explosive eruptions from the Colli Albani Volcanic District (Italy) (CAVD) is measured for the first time. The investigated melts range from foidite to tephri-phonolite to tephrite from the CAVD to a phonolite from the Vesuvius (Italy) with CO₂ concentrations up to 0.50 wt%. Viscosity and calorimetric measurements are performed in the glass transition range T_g between 600 and 780 °C. Although nominally anhydrous, the investigated melts contain H₂O concentrations up to 0.23 wt%. The data exhibit a decrease in viscosity of approx. 10^0.40 Pa s for the phonolitic composition with ~ 0.07 wt% CO₂ and a T_g reduced by approx. 14 °C. For the tephritic composition, T_g is approx. 5 °C lower and has a viscosity reduced by 10^0.25 Pa s for the sample containing ~ 0.5 wt% CO₂. Calorimetric measurements of the tephri-phonolite show lowered onset of T_g by approx. 6 °C for the melt with ~ 0.11 wt% CO₂ and T_g of the foidite appears not to be influenced by a CO₂ concentration of ~ 0.37 wt% CO₂. However, these tephri-phonolitic and foiditic melts foamed during calorimetric measurements preventing a reliable measurement. It would appear that most of this overall drop in viscosity is caused by the small amounts of H₂O in the melts with CO₂ slightly reducing the viscosity or having no effect on viscosity. Additionally, it is shown that the reduction in viscosity decreases with an increasing degree of the depolymerisation for the investigated melts. Consequently, the explosive style of the CAVD eruptions is mainly caused by crystals and bubbles which form and rise during magma storage and ascent which increases the magma viscosity whereas the CO₂ in the melt slightly reduces the viscosity.

Introduction

Rheology of melts plays a key role in magmatic processes. It influences mass transfer, crystallisation processes, nucleation, forming and exsolution of bubbles, the speed of ascent in the volcanic vent and finally the eruptive style. Rheology is affected by melt composition and its volatile content, temperature, pressure, crystal and bubble content as well as oxygen fugacity (i.e. Webb et al. 2007; Chevrel et al. 2013; Di Genova et al. 2014; Campagnola et al. 2016; Klein et al. 2018; Kolzenburg et al. 2018). Among the volatile components in magmatic systems, CO₂ is the most important one after H₂O (Nowak et al. 2003). In many geological settings with mainly explosive volcanic eruptions, magmas get “flushed” with CO₂ by the entrainment of a CO₂-rich gas from deeper levels of the magmatic systems or by the assimilation of a CO₂-rich host material, i.e. the Colli Albani Volcanic District, Italy (Freda et al. 2011), Mt. Somma-Vesuvius, Italy (Bruno et al. 1998), Popocatépetl volcano, Mexico (Goff et al. 2001) or Merapi volcano, Indonesia (Troll et al. 2012). An enrichment of CO₂ in magma results in changes in the rheological behaviour with a decrease in density, changes in chemistry and mineral assemblage and the formation of bubbles and/or crystals. Hence, CO₂ is often assumed to trigger volcanic eruptions (Blythe et al. 2015; Caricchi et al. 2018). Blythe et al. (2015) pointed out that the viscosity of a melt strongly determines the carbonate assimilation rate when a magma interacts with the carbonate wall rock. In contrast, the influence of CO₂ on melt viscosity is poorly investigated as shown below.

Adding CO₂ to polymerised liquids such as NaAlSi₃O₈ (Brearley and Montana 1989) or KAlSi₃O₈ (White and Montana 1990) decreases the viscosity at high pressure. In contrast, Brearley and Montana (1989) detected no influence of CO₂ on the viscosity of the more depolymerised liquid NaCaAlSi₂O₇. Viscosity studies on a K-rich silicate melt by Bourgue and Richet (2001) exhibit a reducing effect of CO₂ on the viscosity within the first 3 wt% CO₂ added. They also measured a linearly decreasing density of the melt with increasing CO₂ concentration at room temperature. Morizet et al. (2007) inferred viscosity from calorimetric measurements of the glass transition temperature T_g of CO₂ bearing jadeitic and phonolitic melts. They concluded there is little or no influence of dissolved CO₂ on viscosity at temperatures near the glass transition because they saw no systematic variations in T_g. Seifert et al. (2013) did experiments on the relaxation times for basaltic, phonolitic and rhyolitic glasses and showed a reduction in relaxation time with increasing CO₂ content for the basaltic melt but no changes for the other compositions. As a consequence, they deduce CO₂ decreases the viscosity of basaltic melts but does not affect the other SiO₂ rich melts. Di Genova et al. (2014) investigated rheological features of natural hydrous and H₂O-CO₂-bearing trachybasaltic and latitic compositions. They showed a decrease in viscosities for volatile bearing melts and found a stronger decrease in H₂O-CO₂-bearing melts than for hydrous ones. The glass transition temperature was reduced by ~ 25 K with the addition of any amount of CO₃²⁻ up to 1900 ppm CO₂. In contrast, the heat capacities are not affected by those volatiles. A study by Robert et al. (2015) on a remelted natural basalt confirms the effect of CO₂ slightly reducing viscosity in the presence of up to 1 wt% H₂O.

The present study investigates the influence of CO₂ on rheological properties of three synthetic equivalents of the Colli Albani Volcanic District (CAVD) and a fourth sample equivalent to the “white pumice” phonolite from the Vesuvius AD 79 eruption (WPVe series) (Iacono Marziano et al. 2007). To minimise crystallisation and structural changes during experimental runs, all CAVD glasses are made with half the amount of Fe in the natural sample. Fe²⁺ is replaced by Mg²⁺ and Fe³⁺ by Al³⁺. Glasses of the CAVD are of the foiditic composition from the Pozzolane Rosse event after Freda et al. (2011) (PR-0.5Fe series) and a tephri-phonolitic one from the Pozzolane Nere event after Campagnola et al. (2016) (PN-0.5Fe series). A further tephritic glass is synthesised by subtracting 4 mol% KAlSi₂O₆ from the Pozzolane Rosse composition (PR-Leu-0.5Fe series) to investigate the rheology of the residual PR-0.5Fe melt after crystallisation of leucite which is a characteristic phenocryst in the pyroclastic products of the CAVD (i.e. Giordano et al. 2006; Freda et al. 2011).

Methods

Sample preparation

Volatile-free base glasses were made of powdered and previously dried metal oxides and carbonates. They were melted at 1600 °C at ambient pressure and atmosphere for 1 h and subsequently grinded and mixed for 20 min. This procedure was repeated before the glass was finally melted for the third time for 4 h. The glasses were quenched by dipping the crucible with the melt in water at ambient temperature. The base glasses are than powdered and dried at 500 °C for 20 h to avoid adsorption of H₂O. The sample powder is filled into Au₇₅Pd₂₅ capsules and welded at approx. 500 °C. For the CO₂- bearing melts, the powdered base glass is mixed with silver oxalate Ag₂C₂O₄ as the source of CO₂ loaded into the capsules and welded at room temperature. The experiments are performed in an internally heated pressure vessel (IHPV) with an intrinsic oxygen fugacity $f_{{{\text{O}}_{{\text{2}}} }}$  = NNO + 3 at 1250 °C and approx. 250 MPa for 46 or 70 h (for a detailed description of the IHPV see Schanofski et al. 2019). The melts are quenched with a cooling rate of ~ 150 °C s⁻¹ previously determined in similar studies (Benne and Behrens 2003).

Density

Based on Archimedes’ principle, the sample is weighed in air and in distilled H₂O with a wetting agent to reduce the surface tension of H₂O using a Mettler Toledo Excellence XP/XS analyse balance. The calculation of the density ρ follows the equation

$$\rho = \frac{A}{{A - B}} \times \rho _{{{\text{H}}_{{\text{2}}} {\text{O}}}}$$

(1)

with A: sample weight in air, B: sample weight in distilled H₂O and $\rho _{{{\text{H}}_{{\text{2}}} {\text{O}}}}$: density of the H₂O at ambient temperature after Bigg (1967). The density of every glass is measured 10 times.

Fourier transform infrared spectroscopy (FTIR)

Contents of CO₂ and H₂O are determined by FTIR spectroscopy in the mid-infrared (MIR) range of 1200–4000 cm⁻¹ and in the near-infrared (NIR) range of 2000–6000 cm⁻¹, respectively. Measurements are done with a Bruker Hyperion 3000 IR microscope and a coupled Bruker Vertex 70 FTIR spectrometer. A tungsten lamp, a MCT detector cooled by liquid nitrogen and a KBr beam splitter together with a Globar light source and a CaF₂ beam splitter are used to collect the MIR and NIR spectra, respectively. 100 scans in transmission with 4 cm⁻¹ spectral resolution are collected for each spectrum with a spot size of 50 × 50 µm. Samples are double polished and have a thickness of 100–190 µm for the MIR spectra and 200–250 µm for the NIR spectra.

Colorimetric micro-determination of the iron species

The colorimetric method of Wilson (1960) and Schuessler et al. (2008) was used to determine the Fe speciation. Each sample is powdered and 5–15 mg are dissolved in hydrofluoric acid (HF). Upon addition of 2:2′bipyridyl to the solution, a reddish Fe(II)-bipyridyl-complex is built by the Fe²⁺. This complex has an intensive absorption band at ~ 523 nm in an UV/VIS spectrum. Hydroxylamine hydrochloride (H₄NOCl) is then used to reduce Fe³⁺ to Fe²⁺ to measure the total Fe content Fe_tot. Comparison of the intensities at ~ 523 nm of the unreduced and reduced solutions provides the ratio of Fe²⁺ to the total Fe content Fe²⁺/Fe_tot. The UV/VIS measurements are performed at an AvaSpec-UV/VIS/NIR spectrometer from Avantes and the AvaSoft software Version 8.3.

Micropenetration technique

Viscosity η is measured using the micropenetration technique with a Netzsch TMA 402 dilatometer in the range 10^8.5–10^13.5 Pa s. The calibration of the temperature is done with the melting points of Bi (268.02 °C), Zn (417.02 °C), Al (659.02 °C), NaCl (800.05 °C) and Ag (951.09 °C). The DGG1, a Na₂O-CaO-SiO₂ float glass from the Deutsche Glastechnische Gesellschaft, is measured as a standard glass to determine the precision of the dilatometer. A total error of ± 0.06 log₁₀ Pa s (1σ) is assessed for the measurements. Samples with parallel surfaces are double polished and have a thickness of 1.5 mm. A sphere of a single crystal of Al₂O₃ with a diameter of 1 mm is forced into the discs with 0.1–1.5 N. Depending on the expected viscosity, the measurements are performed for 30 min up to 6 h in a temperature range of 600–780 °C. The penetration rate of the sphere into the glass disc is used for the calculation of the viscosity by:

$$\eta = \frac{{0.1875~Ft}}{{r^{{0.5}} l^{{1.5~}} }}$$

(2)

with F: the applied force, t: time, r: radius of the indent sphere, l: distance of indent (Pocklington 1940; Tobolsky and Taylor 1963; Dingwell et al. 1992). As this equation assumes that both the thickness of the sample and the radius of the sphere is much greater than the penetration distance, both F and t are chosen such that l < 80 µm in all of the measurements.

Differential scanning calorimetry (DSC)

Heat capacities are measured with the Netzsch DSC 404C differential scanning calorimeter. The samples are heated to the approximate temperature at which the viscosity is 10⁹ Pa s (T_g⁹) which is in the temperature range of 730–800 °C, depending on the chemical composition. Measurements are performed with a constant heating- and cooling rate of 20 °C min⁻¹. To erase the thermal history of the glasses, only the second calorimetric run of each sample is used for the determination of the glass transition temperature T_g. Measurements are done in a Pt crucible against an empty Pt crucible and calibrated with a single sapphire crystal with the data of Robie et al. (1978) from 20 to 1000 °C. Measured discs of the WPVe and PR-Leu-0.5Fe series as well as the CO₂-free samples of the PN-0.5Fe and PR-0.5Fe series were double polished with parallel faces. During their first calorimetric runs, the discs of CO₂-bearing samples of the PN-0.5Fe and PR-0.5Fe series foamed and raised the lid of the crucible. Hence, these samples were subsequently crushed to coarse fragments before their measurements.

The configurational heat capacity C_p^conf is determined from the scanning data and is the difference between the relaxed heat capacity of the melt and that of the glass at the same temperature just above the glass transition (C_p^conf = C_pl  − C_pg).

The liquid heat capacity (C_pl) is directly given by the heat capacity curve. To extrapolate the heat capacity of the glass (C_pg) to a higher temperature, the unrelaxed glass data are fitted by the Maier–Kelley equation:

$$C_{{{\text{pg}}}} = a + bT + cT^{{ - 2}}$$

(3)

with a, b, c as parameters and T: temperature in Kelvin (Maier and Kelley 1932). The unrelaxed C_pg is extrapolated to approx. 150 °C to the temperature at which the relaxed C_pl has been determined.

Results

The results of the electron microprobe analysis of the chemical compositions of the investigated melts are listed in Table 1 as well as the chemical compositions calculated with the atomic analysis of the electron microprobe and the Fe ratio Fe²⁺/Fe_tot received from the colorimetric micro-determination. All melts are metaluminous by the definition: (Na₂O + K₂O) < Al₂O₃ < (CaO + MgO + Na₂O + K₂O) in mole fraction (Shand 1927). Fe²⁺/Fe_tot ranges from 0.33 (PR-0.5Fe_0.2) to 0.51 (samples within the PN-0.5Fe series) (Table 1). The degree of polymerisation of the melt structure is given by γ = (Na₂O + K₂O + CaO + MgO + FeO)/(Na₂O + K₂O + CaO + MgO + FeO + Al₂O₃ + Fe₂O₃) in mole fraction (Toplis et al. 1997; Webb et al. 2007) and seen in Table 1. The most depolymerised melts are those of the PR-Leu-0.5Fe series (γ = 0.72), followed by the PR-0.5Fe series (γ = 0.68‒0.70) and the PN-0.5Fe series (γ = 0.59‒0.60). The melts of the WPVe series have the highest degree of polymerisation (γ = 0.55). All melts are nominally anhydrous (H₂O < 0.50 wt%). The WPVe and PR-Leu-0.5Fe series are crystal free. The PN-0.5Fe and PR-0.5Fe series contain up to 4 vol% crystals with a mean aspect ratio (= major axes/minor axes) of 1.29 and grain sizes from 2 to 4 µm (Table 2) that formed during the IHPV runs. All CO₂-free glasses are bubble free. The CO₂-bearing samples of the WPVe and the PN-0.5Fe series contain up to 3 vol% spherical bubbles (Table 2). Raman spectroscopy identified the gases in the bubbles as molecular CO₂ with characteristic peaks at 1286 and 1390 cm⁻¹ (Schrötter and Klöckner 1979) (for the Raman spectra see Fig. A1 in Appendix A). The crystals as well as the bubbles are unconnected in the crystal and bubble bearing glasses. All glasses are checked for homogeneity by the FTIR. The CO₂-bearing melts of the PR-0.5Fe series showed little variations of the CO₂ concentration within the samples. Thus, the CO₂ concentration of these melts are determined after their viscosity and heat capacity measurements and given in Table 2.

Table 1 Chemical compositions of the investigated melts

Table 2 Conditions during IHPV runs, water concentration c(H₂O) determined by FTIR, concentration of the carbon ion c(CO₃²⁻) determined by FTIR, total carbon concentration c(CO₂)^total measured by carbon sulphur (CS) analysis and density ρ. All errors are 1σ for evaluations in this study, errors of absorptions coefficients of ε₃₅₅₀ and ε₁₄₂₅ from the literature are 2σ (see references). The crystals in the melts of the PN-0.5Fe and PR-0.5Fe series have grain sizes ranging from 2 to 4 µm and a mean aspect ratio (= major axes/minor axes) of 1.29

Density

The densities are shown in Table 2. The WPVe series has the lowest densities with 2.47–2.48 g cm⁻³, followed by the PN-0.5Fe series with 2.57–2.60 g cm⁻³. The PR-0.5Fe and the PR-Leu-0.5Fe series have similar densities, ranging from 2.70–2.73 to 2.71–2.74 g cm⁻³, respectively. Within each series of the investigated melts the density appears to decrease with increasing CO₂ concentration (Fig. 1A). This decrease in density is, however, within the error of the density of the volatile-free glasses.

Fig. 1

A Densities of the investigated melts as a function of CO₂ concentration; B T_g¹² vs CO₂ concentration for the WPVe and PR-Leu-0.5Fe series; C B_e/S^conf vs CO₂ content for the WPVe and PR-Leu-0.5Fe series. Symbols for the melt series are the same for the three panels

FTIR spectroscopy

The relation between the concentration of a species and the IR-absorbance is given by the Lambert–Beer-law:

$$c_{i} = \frac{{M_{i} \times A_{j} }}{{d \times \rho \times \varepsilon _{j} }} \times 100$$

(4)

with c_i: concentration of the species i in wt%, M_i: molar mass of the species i, A_j: peak height of the absorbance of the band j, d: thickness of the sample in cm, ρ: density of the sample in g l⁻¹, ε: absorption coefficient in l mol⁻¹ cm⁻¹ (i.e. Stolper 1982; Thibault and Holloway 1994; Behrens et al. 2009).

The height of the FTIR-absorption bands related to the carbon species is determined by subtracting the spectrum of the CO₂-free glass from that of the CO₂-bearing sample scaled to the same thickness. As shown in Fig. 2A, the residual spectrum of the PR-Leu-0.5Fe series shows a doublet at approx. 1510 and 1425 cm⁻¹, caused by the asymmetric stretching vibration of CO₃²⁻ (Blank and Brooker 1994; Botcharnikov et al. 2006). To quantify the concentration of the CO₃²⁻ species, the absorbance at approx. 1425 cm⁻¹ is used since the doublet is assumed to be symmetric (Dixon and Pan 1995) and the absorbance at 1510 cm⁻¹ could be overlapped by a vibration mode of H₂O molecules (Botcharnikov et al. 2006) and hence falsify the evaluation of the carbon concentration. For this PR-Leu-0.5Fe series, the composition-dependent absorption coefficient ε₁₄₂₅ is calculated using the absorbance normalised by the thickness of the glass chip and density and the total carbon content determined by the carbon sulphur (CS) analysis (Table 2). The value for ε₁₄₂₅ is 324 ± 12 (2σ) l mol⁻¹ cm⁻¹ (see Fig. B1 in Appendix B) being in good agreement with that calculated for Ca-rich silicate glasses from Dixon and Pan (1995) with ε₁₄₂₅ = 335 l mol⁻¹ cm⁻¹.

Fig. 2

A MIR spectra of the CO₂-bearing melt PR-Leu-0.5Fe_1.3 (continuous line) and the corresponding CO₂-free spectra normalised to the thickness of the CO₂-bearing one (dashed line). The residual spectrum is the result of the subtraction of the CO₂–bearing minus the CO₂-free spectra whose absorbance at ~ 1425 cm⁻¹ is used for the determination of the concentration of CO₃²⁻; B MIR spectra of the CO₂-bearing melt WPVe_1.1 (continuous line) and the corresponding CO₂-free spectra normalised to the thickness of the CO₂-bearing one (dashed line). The residual spectrum is the result of the subtraction of the CO₂-bearing minus the CO₂-free spectra. Besides the CO₃²⁻ doublet at 1425 and 1510 cm⁻¹ a peak at 2350 cm⁻¹ exists indicating the presence of molecular CO₂ in this melt

The FTIR spectra of the WPVe and the PN-0.5Fe series show the doublet of CO₃²⁻ and an extra peak at approx. 2350 cm⁻¹ as shown in Fig. 2B. This extra peak is caused by the asymmetric stretching vibration of CO₂ molecules (Blank and Brooker 1994). Since the Raman spectrum (Fig. A1 in Appendix A) attests to the presence of molecular CO₂ in the bubbles, it is assumed that this extra peak arises from the substance in the bubbles. The CO₂ species in the presented melts is assumed to be dissolved as CO₃²⁻ only since Fine and Stolper (1986), Thibault and Holloway (1994), Behrens et al. (2009), Shishkina et al. (2014) as well as Schanofski et al. (2019) detected no molecular CO₂ in their bubble-free basaltic, Ca-rich leucititic, phono-tephritic, mafic melts as well as phonolitic and foiditic melts, respectively. Therefore, the CS analysis overestimates the total amount of CO₂ in these samples and is not reliable for the determination of ε₁₄₂₅ for these melts (an example of the falsified determination of ε₁₄₂₅ is given in Fig. B2 in Appendix B). Due to the underestimations of the absorption coefficients of the bubble bearing melts and the inhomogeneity in CO₂ distribution of the CO₂-bearing melts of the PR-0.5Fe series, ε₁₄₂₅ values of 245 l mol⁻¹ cm⁻¹ (Schanofski et al. 2019), 296 l mol⁻¹ cm⁻¹ and 334 l mol⁻¹ cm⁻¹ (calculated after Dixon and Pan 1995) are used for the determination of the CO₃²⁻ content for the WPVe, PN-0.5Fe and the PR-0.5Fe series, respectively. Determined concentrations of CO₃²⁻ are listed in Table 2.

In the NIR spectra, weak absorbances at approx. 3550 cm⁻¹ are caused by the fundamental OH stretching mode (Stolper 1982; Ohlhorst et al. 2001; Behrens et al. 2009). A two-tangent baseline is used to determine the peak height at 3550 cm⁻¹. There is no evidence of molecular H₂O in the glasses, since there is no absorbance peak at approx. 5200 cm⁻¹ which is in agreement with previous studies (i.e. Stolper 1982; Behrens et al. 2009) who observed the OH⁻ groups to be the predominant H₂O species in H₂O bearing glasses with total H₂O content < 0.5 wt%. For the calculation of the total amount of H₂O, values for the absorption coefficients ε₃₅₅₀ are taken from other surveys since they strongly depend on melt composition. Stolper (1982) calibrated an absorption coefficient ε₃₅₅₀ for variable compositions ranging from basaltic to albitic to rhyolitic and found it to be the same within error and is 67.0 ± 6.7 l*mol⁻¹*cm⁻¹. Behrens et al. (2009) found ε₃₅₅₀ for a phono-tephritic glass to be 63.9 ± 5.4 l*mol⁻¹*cm⁻¹. For the measurements of the H2O contents of the melts in this study, ε₃₅₅₀ = 67.0 ± 6.7 l*mol⁻¹*cm⁻¹ and ε₃₅₅₀ = 63.9 ± 5.4 l*mol⁻¹*cm⁻¹ are used for the WPVe and PR-0.5Fe series as well as for the PN-0.5Fe and PR-Leu-0.5Fe series, respectively. The melts contain H₂O concentrations up to 0.23 wt% (Table 2) due to the reduction of Fe³⁺ in the samples by hydrogen following the reaction Fe₂O₃ + H₂ $\to$ 2FeO + H₂O (Brearley and Montana 1989; Botcharnikov et al. 2006; Behrens et al. 2009) during sample preparation in the IHPV. An additional possibility for H₂O entry into the samples could be adsorbed H₂O on the Ag₂C₂O₄ dissolved during the experimental run in the IHPV.

Viscosity

The measured viscosities at a given temperature of all melts are given in the supplementary material (Appendix C). Due to the narrow temperature range applied in this study the statistical analysis needs to fit a straight line through the measured viscosity data which is given by the Arrhenian Equation

$$\log _{{10}} ~\eta = A + \frac{{B \times 10^{4} }}{T}$$

(5)

with η: viscosity in Pa s, A and B as: fit parameters and T: temperature in Kelvin. All fit parameters are listed in Table 3.

Table 3 Fit parameter for the Arrhenian Equation (Eq. 5), T_g¹² and fragility m (Eq. 7) calculated with the viscosity data

The CO₂–bearing samples WPVe_1.1 and WPVe_1.2 contain < 1 vol% spherical bubbles and show bubble growth and rise at temperatures > 700 °C, and therefore these data are not shown.

Einstein (1906) developed a formula for the effect of suspended isolated spheres on melt viscosity:

$$\eta _{{{\text{rel}}}} = ~\frac{{\eta _{{{\text{eff}}}} }}{{\eta _{{{\text{melt}}}} }} = 1 + f \times \varphi$$

(6)

with η_rel: relative viscosity, η_eff: effective viscosity of the dilute suspension in Pa s, η_melt: viscosity of the pure suspending liquid in Pa s, f: constant that is 1 for spherical bubbles (Taylor 1932) and φ: bubble fraction.

For the CO₂-bearing samples, the influence of the present bubbles on viscosity is < 0.01 log₁₀ Pa s and hence negligible. As seen in Fig. 3A, the viscosities of the CO₂-free melts of the WPVe series agree with each other within the measurement error of 0.06 log₁₀ Pa s. At a temperature of 650 °C, the viscosities of the samples WPVe_0.1 and WPVe_0.2 are 12.42 and 12.37 log₁₀ Pa s, respectively. The viscosities of the CO₂-bearing samples, having the same CO₂ content, are about 0.4 log₁₀ Pa s lower at this temperature, namely 12.01 log₁₀ Pa s for WPVe_1.1 and 11.96 log₁₀ Pa s for WPVe_1.2. The glass transition temperature T_g¹² for the CO₂-bearing melts is approx. 14 °C lower with respect to that of the CO₂-free samples of this series (see Fig. 1B and Table 3).

Fig. 3

Viscosity data of all melts investigated in this study as a function of inverse temperature for: A the CO₂ free and CO₂-bearing melts of the WPVe series, B the CO₂ free PN-0.5Fe and PR-0.5Fe melts and C the CO₂ free and CO₂-bearing melts of the PR-Leu-0.5Fe series. The measured temperature range in °C is given at the top of the figure

The CO₂-bearing melts of the PN-0.5Fe and the PR-0.5Fe series disintegrated during heating before reaching the temperature of measurement. It is assumed, that gases in existing or forming bubbles in the PN-0.5Fe series and PR-0.5Fe series, respectively, expand und lead to the fragmentation of these melts. Therefore, only the viscosities of the CO₂-free melts are investigated.

As illustrated in Fig. 3B, the viscosity of PN-0.5Fe_0.1 is approx. 0.1 log₁₀ Pa s higher than those of PN-0.5Fe_0.2 over the whole temperature range i.e. at 700 °C the viscosity is 11.25 log₁₀ Pa s and 11.13 log₁₀ Pa s, respectively. The viscosities of the CO₂-free samples of the PR-0.5Fe series are additionally shown in Fig. 3B. At a temperature of 700 °C, the viscosity of PR-0.5Fe_0.1 is 10.18 log₁₀ Pa s and that from PR-0.5Fe_0.2 is 10.11 log₁₀ Pa s differing by 0.07 log₁₀ Pa s.

Figure 3C shows the viscosities of the PR-Leu-0.5Fe series. The viscosity data of the CO₂-free samples agree with each other, i.e. at 650 °C the viscosities for PR-Leu-0.5Fe_0.1 and PR-Leu-0.5Fe_0.2 are 11.41 and 11.39 log₁₀ Pa s, respectively, what is within the error of measurements. The viscosities of the samples with a CO₂ concentration of ~ 0.30 wt% (PR-Leu-0.5Fe_1.1), ~ 0.40 wt% (PR-Leu-0.5Fe_1.2) and ~ 0.50 wt% (PR-Leu-0.5Fe_1.3) are 0.18, 0.22 and 0.25 log₁₀ Pa s lower, respectively, compared to the CO₂ free PR-Leu-0.5Fe_0.2. The glass transition temperature T_g¹² of the CO₂-bearing melts decreases by approx. 5 °C with respect to PR-Leu-0.5Fe_0.2 (see Fig. 1B and Table 3).

Fragility

Using the viscosity data, the fragility m is calculated by

$$m = \frac{{B \times 10^{4} }}{{T_{g}^{{12}} }}$$

(7)

with B: fit parameter from the Arrhenian fit (Eq. 5) and T_g¹²: temperature at which the viscosity is 10¹² Pa s in Kelvin (Toplis et al. 1997; Webb 2011).

As demonstrated in Table 3, the PR-Leu-0.5Fe series has the highest fragilities (38.7–41.2) whereas the fragilities of all other melts for which viscosity measurements are possible, are nearly the same (25.5–28.7).

The Vogel-Fulcher-Tamann Equation (VFT Equation)

$$\log _{{10}} \eta = A_{{{\text{VFT}}}} + \frac{{B_{{{\text{VFT}}}} }}{{T - C_{{{\text{VFT}}}} }}$$

(8)

with A_VFT: constant, B_VFT and C_VFT: parameters and T: temperature in Kelvin (i.e. Toplis et al. 1997), can be used to force a curve in the fit to the viscosity data. This requires setting the constant A_VFT to − 4 (see Kleest et al. (2020) for a discussion). Corresponding to the VFT Equation (Eq. 8), the fragility m_VFT is then:

$$m_{{{\text{VFT}}}} = \frac{{B_{{{\text{VFT}}}} }}{{T_{g}^{{12}} \left( {1 - {{C_{{{\text{VFT}}}} } \mathord{\left/ {\vphantom {{C_{{{\text{VFT}}}} } {T_{g}^{{12}} }}} \right. \kern-\nulldelimiterspace} {T_{g}^{{12}} }}} \right)^{2} }}$$

(9)

The constant A_VFT, the parameters B_VFT and C_VFT as well as the fragilities using Eq. 9 are given in the supplemental material (Appendix D).

Differential scanning calorimetry (DSC)

The extrapolated parameters of the Maier–Kelley-Fit (Eq. 3) of the studied melts are listed in Table 4 together with the heat capacities of the glasses (c_pg) and liquids (c_pl) and the configurational heat capacity C_p^conf. C_p^conf is lowest for the WPVe series (10.35–12.42 J mol⁻¹ K⁻¹), followed by the PN-0.5Fe series (13.76–16.38 J mol⁻¹ K⁻¹). The PR-0.5Fe series has a similar C_p^conf (20.70–26.3 J mol⁻¹ K⁻¹) to the PR-Leu-0.5Fe series (25.31–26.93 J mol⁻¹ K⁻¹).

Table 4 All values measured or derived from the DSC data: fit parameters a, b and c from the Maier–Kelley fit (Eq. 3), glassy and liquid heat capacities c_pg and c_pl, respectively, configurational heat capacity C_p^conf, configurational entropy S^conf, the B_e parameter (Eq. 11), T_g^Onset and the mean value for the shift factor K^Onset of each melt series (Eq. 10)

Figure 4 shows is a positive correlation between C_p^conf and the degree of depolymerisation expressed by γ which is in agreement with previous studies from Giordano and Russell (2017) and Russell and Giordano (2017) who demonstrated that C_p^conf diminishes with increasing SiO₂ content. An increase of SiO₂ increases the degree of polymerisation and hence a lower re-ordering of the structure in the melt is required at the glass transition range resulting in lower C_p^conf.

Fig. 4

Configurational heat capacity C_p^conf as a function of γ: the higher the degree of polymerisation the lower C_p^conf

The fragmentation of the CO₂-bearing glasses of the PN-0.5Fe and PR-0.5Fe series prevented viscosity measurements, however, the calorimetric data can be used to estimate the viscosities. Scherer (1984) postulated a relation between viscosity in the glass transition range and the cooling-rate during calorimetric measurements:

$$\log _{{10}} \eta \left( {T_{g}^{{{\text{Onset}}}} } \right) = K_{{{\text{Onset}}}} - \log \left| q \right|$$

(10)

with η:– viscosity in Pa s, T_g^Onset: temperature at the beginning of the glass transition range, defined by the extrapolated glassy heat capacity via the Maier–Kelley fit (Eq. 3) and the rapid increase in heat capacity, K_Onset: shift factor of 11.3 and q: cooling rate in °C s⁻¹.

K_Onset is calculated for each sample for which viscosity data are available. The average of K_Onset (øK_Onset) for each melt series is used for further investigations of the CO₂-bearing melts and is listed in Table 4 as well as T_g^Onset.

K_Onset varies from 11.56 ± 0.05 for the PR-0.5Fe series to 11.86 ± 0.10 for the WPVe series. K_Onset is assumed to be independent of the chemical composition (Stevenson et al. 1995). However, Stevenson et al. (1995) argued that K_Onset slightly decreases with increasing agpaitic index ((Na₂O + K₂O)/Al₂O₃ in mol. fraction). As seen in Fig. 5 showing øK_Onset of each series vs SiO₂ concentration, øK_Onset slightly increases with increasing SiO₂ content. Conventionally implicating a more polymerised melt with increasing SiO₂ content, this observation agrees with that from Stevenson et al. (1995) treating the agpaitic index as an indication of the degree of polymerisation of a melt.

Fig. 5

Average of the shift factor K_Onset of each melt series vs SiO₂

The CO₂-bearing melts of the WPVe and PN-0.5Fe series contain bubbles of < 1 vol% and 3 vol%, respectively. Based on Eq. 6, the influence of bubbles on viscosity is < 0.01 log₁₀ Pa s for the WPVe melts and 0.01 log₁₀ Pa s for the PN-0.5Fe melts which is within the measurement error of 0.06 log₁₀ Pa s.

The calorimetrically determined viscosities are shown in Fig. 6, presented as the difference in log₁₀ η at T_g^Onset between the CO₂-free and the CO₂-bearing samples of each series vs CO₂ concentration. For the WPVe, the PN-0.5Fe as well as for the PR-Leu-0.5Fe series, the CO₂-bearing melts have lower viscosities at T_g^Onset than the CO₂-free melts.

Fig. 6

The viscosity differences of the CO₂ bearing and CO₂-free melts of each series at T_g^Onset from DSC measurements vs CO₂ concentration. Numbers in rectangles next to the intrapolated lines of each melt series are γ as a value of the degree of polymerisation. The viscosity drop decreases with increasing γ and hence with increasing degree of depolymerisation

The viscosity of the WPVe_1.1 sample decreases by 0.39 log₁₀ Pa s and the WPVe_1.2 sample has a viscosity drop of 0.60 log₁₀ Pa s with respect to the CO₂-free WPVe_0.1 melt. In contrast to the results of the viscosity measurements, the viscosities of the CO₂-bearing melts of the WPVe series differ by 0.21 log₁₀ Pa s at T_g^Onset.

The viscosity of the CO₂-bearing melts with approx. 0.10 to 0.12 wt% CO₂ of the PN-0.5Fe series decreases by approx. 0.27 log₁₀ Pa s in comparison to PN-0.5Fe_0.1 at T_g^Onset.

The PR-Leu-0.5Fe_1.1 sample with a CO₂ concentration of ~ 0.30 wt% has a viscosity diminished by 0.26 log₁₀ Pa s and the viscosities of PR-Leu-0.5Fe_1.2 and PR-Leu-0.5Fe_1.3 with an increased CO₂ content up to ~ 0.50 wt% CO₂ are reduced up to 0.46 log₁₀ Pa s at T_g^Onset with respect to the PR-Leu-0.5Fe_0.1 sample.

A difference in viscosity of the PR-0.5Fe series is not detectable since the decrease in viscosity is 0.01 and 0.03 log₁₀ Pa s for PR-0.5Fe_1.1 and PR-0.5Fe_1.2 compared to the CO₂ free PR-0.5Fe_0.1 melt which is within the error. However, the CO₂-bearing melts of the PR-0.5Fe series foamed during DSC measurements resulting in an incorrect evaluation of T_g^Onest and consequently to an incorrect calculated viscosity at T_g^Onest. Since the formation of bubbles due to exsolution of volatiles in the melt already occurs during the first calorimetric run, it shifts the glass transition range in the second run to higher temperatures and hence an increased T_g^Onset and diminishes the resulting differences in viscosity of the CO₂-free and CO₂-bearing melts_.

The Adam-Gibbs theory combines the data from viscosity and DSC measurements and enables the calculation of the configurational entropy S^conf:

$$\log _{{10}} \eta = A_{e} + \frac{{B_{e} }}{{\ln ~10~\left[ {S^{{{\text{conf}}}} \left( {T_{{\text{g}}}^{{12}} } \right) + \mathop \smallint \nolimits_{{T_{{\text{g}}}^{{12}} }}^{T} \frac{{C_{{\text{p}}}^{{{\text{conf}}}} }}{T}dT} \right]T}}$$

(11)

with A_e and B_e as constants, T_g¹²: temperature at which the viscosity is 10¹² Pa s in Kelvin (calculated using the Arrhenian Fit Eq. 5), T: temperature in Kelvin and C_p^conf: configurational heat capacity (C_p^conf = C_pl–C_pg; C_pl is directly measured by DSC and C_pg is extrapolated via Eq. 3) (Adam and Gibbs 1965; Richet 1984; Toplis et al. 1997; Webb 2008) which is valid with the assumption of no variations in S^conf at temperatures below T_g¹². The parameter A_e defines the viscosity at infinite temperature and is assumed to be constant for all compositions (i.e. Toplis et al. 1997; Toplis 1998; Giordano et al. 2008). In the present study, A_e is chosen to be − 4.00 log₁₀ Pa s following the Maxwell relation τ = η₀/G (with τ:– relaxation time, η₀ = time-independent Newtonian viscosity and G = elastic shear modulus) with τ₀ = 10^–14 s (τ₀ = vibration frequency at infinite temperature) (Martinez and Angell 2001; Angell et al. 2003) and G_∞ = 10 ± 0.5 GPa (G_∞ = shear modulus at infinite frequency) (Dingwell and Webb 1989). For a detailed discussion of A_e see Kleest et al. (2020) and references therein.

Equation 11 fits both, the parameter B_e and the configurational entropy S^conf and the results are shown in Table 4. S^conf of the WPVe series, the PN-0.5Fe series and the PR-Leu-0.5Fe series are in a similar range (12.49–19.86 J mol⁻¹ K⁻¹), and the PR-0.5Fe series has the highest S^conf (29.07 and 29.27 J mol⁻¹ K⁻¹). The ratio B_e/S^conf indicates the changes of the potential energy barrier to viscous flow (Richet 1984; Toplis 1998; Webb 2005) and the smallest unit moving in a melt structure (Toplis 1998). Figure 1C shows B_e/S^conf as a function of the CO₂ concentration and it is seen that the CO₂-bearing melts have a lower B_e/S^conf than the CO₂-bearing melts which is more pronounced for the WPVe series than for the PR-Leu-0.5Fe series with a drop of 0.51 × 10³ and 0.29 × 10³ K, respectively. Hence, the CO₂-bearing melts needs to overcome a lower energy barrier to viscous flow.

Discussion

As shown in Figs. 1B, 3A and 6, the viscosity of the WPVe series apparently decreases by the addition of CO₂. The H₂O content of 0.12 wt% in the CO₂-free samples rises to 0.17 and 0.18 wt% for WPVe_1.1 and WPVe_1.2, respectively (see Table 2). It is well studied that H₂O reduces the viscosity of a melt as discussed below. Giordano et al. (2008) developed a model to predict the melt viscosity at given temperatures depending on melt composition including the H₂O concentration (subsequently denominated as GRD08). GRD08 is applied to the phonolitic WPVe series to estimate the effect of H₂O on the viscosity. Corresponding to GRD08, an addition of 0.05 and 0.06 wt% H₂O lowers the viscosity by approx. 0.4 log₁₀ Pa s, in the low temperature—high viscosity range as investigated in this study. For the WPVe_1.1 melt, the viscosity decrease determined by the micropenetration technique and the viscosity at T_g^Onset agree with each other and is approx. 0.4 log₁₀ Pa s (Figs. 3A and 6). The viscosities of the WPVe_1.2 melt determined with the micropenetration method plots nearly on those for the WPVe_1.1 melt (Fig. 3A). Corresponding to GRD08, the viscosity drop for WPVe_1.1 and WPVe_1.2 results from the H₂O content wherefore the CO₂ influence appears to vanish. On the other hand, the viscosity difference at T_g^Onset (Fig. 6) is approx. 0.6 log₁₀ Pa s for WPVe_1.2 contrasting to 0.4 log₁₀ Pa s based on GRD08 indicating a combined viscosity reducing the effect of both volatiles H₂O and CO₂. This influence of H₂O seems to be more pronounced at lower temperatures demonstrated by the comparison of the micropenetration viscosity data and the viscosity at T_g^Onset (Figs. 3A and 6).

All CO₂-free samples of the PN-0.5Fe series and PR-0.5Fe series contain microcrystals (Table 2), thus the viscosity of the pure liquid should be less than that measured (i.e. Einstein 1906; Roscoe 1952; Vetere et al. 2010). Klein et al. (2018) established a model for the calculation of the relative viscosity η_rel of crystal-bearing melts considering crystal fraction, crystal volume and shape. By means of the model, the decrease in viscosities of the pure liquid for both series is up to 0.06 log₁₀ Pa s for the maximum crystal fraction of 0.04 in this study, what is within the measurement error.

However, the CO₂-free melts of both series show differences in their H₂O concentrations (Table 2). As mentioned above, H₂O affects the viscosity noticeably. Previous studies pointed out a viscosity decreasing effect of H₂O that is larger in the low temperature—high viscosity range than in the high temperature—low viscosity range. This viscosity reducing effect decreases with increasing amounts of H₂O and is more pronounced for more polymerised melts than for less polymerised melts. At 700 °C and in the range of H₂O concentration as presented in this study for the PN-0.5Fe and PR-0.5Fe series, the drop in viscosity is approx. 0.1 log₁₀ Pa s for a shoshonitic melt (Vetere et al. 2007) or up to approx. 0.4 log₁₀ Pa s for melts of the Campi Flegrei (Misiti et al. 2011). Whittington et al. (2000) observed a viscosity decrease of 0.20 log₁₀ Pa s for an anhydrous tephrite (0.01 wt% H₂O) by the addition of 0.12 wt% H₂O. Robert et al. (2013) observed a viscosity decrease of approx. 3 log₁₀ Pa s from a “dry” (0.01 wt% H₂O) to a 0.56 wt% H₂O bearing basaltic andesite at 700 °C.

For the CO₂-free melts of the PN-0.5Fe series, the H₂O contents are approx. the same within the error (Table 2) resulting in similar viscosities (Fig. 3) differing at the very limit of the measurement error. Figure 6 suggests a CO₂-driven viscosity drop for this series at T_g^Onset. Taking into account strong viscosity reducing effect of H₂O, it is not clearly predictable how CO₂ affects these melts.

The differences in viscosity of the CO_2-bearing melts of the PR-0.5Fe series appear to be negligible at T_g^Onset (Fig. 6). As mentioned above, the foaming of the CO₂-bearing melts of the PR-0.5Fe series falsify the results of the calorimetric experiments and consequently, it is not possible to state the effect of the influence of CO₂ on this melt composition.

The viscosities of the CO₂-free melts of the PR-Leu-0.5Fe series agree with each other (Fig. 3C). As a consequence, an increased amount of 0.01 wt% H₂O (Table 2) has no detectable influence on the viscosities of this melt series. A further addition of approx. 0.02 wt% H₂O as found in the CO₂-bearing melts of the PR-Leu-0.5Fe series (Table 2) is assumed also to have a negligible (within the ± 0.06 log₁₀ Pa s error in measurements) effect on viscosity (Table 2). The viscosities of the CO₂-bearing melts with different CO₂ concentrations are within the error of each other (Figs. 3C and 6). The presented data indicate a viscosity decreasing effect by the addition of CO₂ as seen in Figs. 1B, 3C and 6. However, this apparent viscosity drop grazes the extreme end of the precision of the measurements.

Based on the presented data, CO₂ concentrations up to ~ 0.50 wt% result in a slight to negligible decrease in viscosity. The overall observed viscosity drop of the phonolitic, tephri-phonolitic and tephritic melts is mainly caused by their H₂O content with this decrease in viscosity increasing when the degree of polymerisation (γ) increases (Fig. 6).

Geological importance for the PR and PN eruptions

Kleest et al. (2020) showed that the viscosities of the volatile-free melts of the Pozzolane Rosse and Pozzolane Nere event are higher than expected. They also demonstrated a viscosity decrease for the PR melt caused by assimilation of carbonate wall rock due to an enrichment in Ca²⁺, and an additional reduction in melt viscosity following leucite crystallisation.

Based on the results of the present study, an incorporation of small amounts of CO₂ do not affect the melt viscosity to a great extent. In contrast, even a small H₂O content in the melt results in a detectable decrease in viscosity and hence, is more effective.

During the storage of the parental PR and PN magmas, crystal formation reaches fractions up to 60 vol% documented by pyroclastic products (Freda et al. 2011). Kleest et al. (2020) calculated a resulting viscosity increase up to two orders in magnitude for a leucite content of 56 vol% after a model from Caricchi et al. (2007). Additionally, carbonate assimilation reaches values of 15 wt% (Iacono-Marziano et al. 2007) which clearly exceeds the solubility of CO₂ in the PR melt (Schanofski et al. 2019). Consequently, the melt becomes oversaturated in CO₂ resulting in the formation of bubbles as recorded in scoria layers with a vesicularity up to 50% (Giordano et al. 2006). Trolese et al. (2017) found emplacement temperatures of ignimbrites from the PR and PN eruptions of approx. 710 °C and 600–630 °C, respectively, and inferred that magma fragmentation starts at temperatures being approx. 100 °C higher. Since these fragmentation temperatures are near the glass transition for the CO₂ free PR-0.5Fe and PN-0.5Fe melts, the magma on the top of the vent is highly viscous or nearly rigid due to the large crystal content. It is suggested, that a sudden release of bubbles as a consequence of carbonate assimilation or depressurisation in the subjacent less viscous magma forces the magma plug out of the vent leading to magma fragmentation during the eruption and results in a highly explosive eruptive style. Similar findings are discussed by Freda et al. (2011) and Marra et al. (2009) for the PR and PN event and by Cross et al. (2014) for the Albano Maar volcanism, postulating free CO₂ triggering explosive eruptions at the CAVD.

Conclusion

The presented study concerns the viscosities of CO₂-bearing phonolitic, tephri-phonolitic, tephritic and foiditic melt compositions. The carbon is incorporated as CO₃²⁻ in the melts. With the exception for the foiditic melt, for which no data are reliable, the viscosity apparently decreases with the addition of CO₂. However, this drop in viscosity is overshadowed by the decrease in viscosity caused by small H₂O concentrations in the melts. This effect is more pronounced in the more polymerised melts. Although it is difficult to separate the effect of H₂O and CO₂ on the viscosity of theses melts, it would appear that CO₂ results in a small to negligible decrease in viscosity at these high viscosity conditions.