Energetic Characterization of 3-D Printed Acrylonitrile Butadiene Styrene Fuels for Hybrid Rocket Propulsion Applications

Abstract

Hybrid rocket technologies are gaining recognition as eco-friendly alternatives to traditional propulsion systems. Utah State University’s Propulsion Research Laboratory has developed a High-Performance Green Hybrid Propulsion (HPGHP) technology, leveraging 3D-printed ABS fuel for reliable, low-energy ignition. Among tested materials, only ABS shows suitable electrical-breakdown properties for arc ignition. Unfortunately, due to the proprietary formulations in commercial ABS blends, and its limited use as a rocket-propellant, related composition and combustion data are limited. This study uses spectroscopic evaluation and bomb calorimetry to estimate material compositions, enthalpies of formation, and combustion energies for multiple commercially available 3-D print feed stock ABS types, finding minimal differences amongst the samples tested. Based on these test results, “representative” ABS properties including chemical formula, mean molecular weight, enthalpy of formation, and Higher Heating Value, is recommended. Follow-on tests with 5 alternative, commonly used, 3D-printable thermoplastic feed stocks demonstrate that ABS has significantly higher energy content. This result supports ABS’s advantages and utility as a conveniently fabricated hybrid rocket fuel.

1. Introduction

A recent European Space Agency study [1,2] highlighted the need to lower production, operational, and transport costs by reducing propellant toxicity and explosion risks. With stricter regulations and costly requirements for hydrazine use—including storage, transport, servicing, and cleanup—hydrazine is becoming less viable. Developing a non-toxic, stable “green” propulsion system is crucial for the SmallSat industry’s growth. Both NASA [3] and the USAF [4] are pursuing alternatives to hydrazine.

Hybrid rockets are emerging as environmentally sustainable alternatives to traditional propellants. Compared to liquid and solid systems, hybrids offer notable safety and handling benefits, with single fluid flow paths making them as simple as hydrazine monopropellant systems but delivering better performance. Their built-in safety makes them especially suitable for ride-sharing spacecraft and positions them well in the growing commercial space market. Current considerations for hybrid propulsion include sounding rockets [5,6], orbital insertion stages for nano launchers and SmallSats [7], and surface launch technology for sample return missions from the Moon, Mars, and beyond [8].

Over the last decade, Utah State University’s Propulsion Research Laboratory has created advanced hybrid propulsion systems offering a safer, eco-friendly alternative to hydrazine. Their High-Performance Green Hybrid Propulsion (HPGHP) system can be started, stopped, and restarted easily [9], and multiple units ranging from 5 to 1600 N thrust have been built and tested [10]. The HPGHP thruster technology uses 3D-printed Acrylonitrile Butadiene Styrene (ABS) fuel, the printed ABS exhibits useful electric-breakdown properties; under an inductive potential, arcing pyrolyzes the material, enabling reliable arc-ignition and efficient operation. Refs. [11,12] attempted to reproduce this phenomenon with various 3-D printed and extruded fuel materials. Only a few printed materials, notably ABS, showed the necessary arcing properties, while none of the extruded materials did. These results suggest that 3-D printing is crucial for low-energy arc-ignition, likely due to the FDM grain structure and ABS’s electromechanical characteristics.

Thus, because of the advantages of arc-ignition, ABS is the preferred material for HPGHP applications. As a widely used thermoplastic that is known for its durability and versatility, ABS serves in plumbing, structural uses, and can last underground for decades. Its compatibility with FDM printing [13] allows easy fabrication into various shapes. Using 3-D printing, it is possible to embed complex high-surface area flow paths within the hybrid fuel grains [14,15]. These internal flow paths increase burn rates and combustion efficiency, enabling much shorter motor aspect ratios than those possible with conventional casting methods for solid propellants like hydroxyl terminated polybutadiene (HTPB).

ABS has gained popularity as a hybrid propellant and has been studied extensively in recent years. Notable works by Casse et al. [16], and Fabiana et al. [17], have advanced understanding of ABS combustion through combined numerical and experimental research. Despite this progress, ABS remains uncommon as a rocket fuel due to the lack of a thermodynamic database, which makes internal ballistics predictions challenging. In particular, data on its standard enthalpy of formation is scarce, hindering accurate motor performance and plume analysis.

Whitmore et al. [18] provide early analytical estimates using group-addition methods, but only for a single, assumed ABS formulation and without experimental validation. The study showed that the ABS enthalpy of formation and combustion properties will vary widely depending on the ratio of the various co-polymers that make up the ABS polymer. For plume contamination research, basic chemical properties like co-polymer mass, mole fractions, molecular weights, and enthalpy must be measured or estimated. Commercially available ABS formulations, including 3-D printing feed-stock compositions are proprietary and undisclosed. Thus, no widely accepted enthalpy value is available.

This work builds on the previously published work of Ref. [19] and specifically focuses on the bulk properties rather than the molecular characteristics of ABS. Understanding the bulk properties requires knowledge of the relative proportions of Acrylonitrile, Butadiene, and Styrene, the three copolymers constituting ABS. Accurate determination of these proportions enables calculations for the material’s enthalpy of formation, molecular weight, and non-stoichiometric chemical formulae, all essential bulk properties for predicting key combustion characteristics relevant to propulsion applications. The resulting engineering model for ABS is intended to be suitable for broad propulsive use.

This work used Fourier transform Infrared Spectroscopy (FTIR) to determine the copolymer compositions of various commercial 3D printing ABS feedstocks. Based on these proportions, material properties such as enthalpy of formation, chemical formulae, and molecular weights were estimated. These values enabled hybrid combustion calculations using gaseous oxygen, and combustion heats from analysis were validated against bomb calorimetry, supporting the accuracy of ABS identification and enthalpy estimates.

2. Materials and Methods

This section covers the thermochemical properties of an ABS polymer, including its chemical structure, molecular weight, enthalpy of formation, and combustion energy. To assess these properties, FTIR spectroscopy and bomb calorimetry were used. The section also outlines the tested ABS samples and explains the lab procedures and analytical methods used for the thermochemical assessments.

2.1. Thermo-Chemical Analysis of ABS Fuel Material

ABS [19] is a type of terpolymer made from three monomers: acrylonitrile, butadiene, and styrene. To produce ABS, acrylonitrile and styrene are first copolymerized to form styrene-acrylonitrile (SAN), then butadiene gas is added to the SAN mixture. Figure 1 shows the chemical structure of the constituent copolymers and Equation (1) shows the corresponding chemical formulas for the constituent ABS co-polymers [20],

$$\begin{array}{ccc}acrylonitrile& & C_3{H}_{3}N\\ polybutadiene& =& {\left(C_4{H}_6\right)}_n\\ styrene& & C_8{H}_8\end{array}$$

(1)

In Equation (1) the subscript on the butadiene entry indicates that ABS is made from polybutadiene, with n being the polymer chain length. Polybutadiene [21] is a clear-to-pale yellow, viscous liquid at room temperature. Depending upon the polymerization method, the butadiene monomers can be bonded in one of three configurations: (1) 1,2 vinyl, (2) 1,4 trans, and (3) 1,4 cis, with 1,4 cis being the most common allotrope in ABS formulations. The bond structure of butadiene copolymers primarily impacts mechanical properties: acrylonitrile enhances chemical resistance, butadiene boosts impact resistance and energy content, and styrene increases stiffness for easier machining. Combustion properties are rarely emphasized by commercial vendors, except when burn retardants are occasionally added. Commercial FDM feed-stock formulas are proprietary, and their co-polymer ratios vary by brand. Most ABS contains 21–27% acrylonitrile, 12–25% butadiene, and 54–63% styrene molar proportions.

2.1.1. Analyses of ABS Samples Using Fourier Transform Infrared Spectroscopy (FTIR)

Accurate combustion analysis necessitates the estimation of the molar concentrations of the ABS constituent co-polymers. Fourier Transform Infrared (FTIR) spectroscopy [22] was performed to identify potential differences among four different industrial ABS formulations. The FTIR analysis reveals the types of functional groups found in the samples and provides an approximate measure of their relative molar amounts. The specific technique used for this analysis was Attenuated Total Reflection (ATR) [23]. In ATR, the sample is placed on a germanium reflective crystal, pressure is applied, and an IR beam creates an evanescent wave that interacts with the sample. Where the sample absorbs energy, the IR signal is attenuated, then detected and processed into an IR spectrum by the FTIR spectrometer. Figure 2 shows a functional schematic of the ATR imaging accessory.

The four materials analyzed were: (1) Stratasys ABSPlus-340 print stock (ABS-Plus, https://support.stratasys.com, Minnetonka, MN, USA), (2) Generic Natural color pellets (Generic, https://stemfinity.com, Boise, ID, USA), (3) Makerbot Natural ABS feed-stock (ABS-R, https://store.goengineer.com, New York, NY, USA), and (4) Bambu Labs^® black print stock (Bambu, https://stemfinity.com, Shenzhen, China). The NASA Marshall Space Flight Center’s (MSFC, Huntsville, AL, USA) Chemical Analysis Group, in collaboration with the Utah State University’s Propulsion Research Laboratory (PRL) analyzed the ABS-Plus, Generic, and ABS-R materials. Whitmore previously reported these results. [24]. The USU Materials Physics group, collaborating with the PRL, performed FTIR analysis of the Bambu feed stock. The USU PRL also duplicated the Generic ABS analysis to compare FTIR methods. For later reference, the MSFC Generic ABS analysis is labeled as Generic-1, while the USU PRL Generic ABS analysis is labeled as Generic-2 to differentiate the groups. Data and conclusions from FTIR experiments will be presented later in the Results section of this paper, Section 3.1.

2.1.2. Using FTIR Spectrum to Estimate the Molar Proportions of Constituent Co-Polymers

By applying the Beer–Lambert law [25] and performing a least-squares linear-regression analysis, and the co-polymer compositions of the various samples were estimated. For this analysis, the FTIR spectra are compared to reference spectra for acrylonitrile, butadiene, and styrene, using a linear curve-fit model of the form,

$${\mathbb{A}}_{ABS}\left(n\right)=a·{\mathbb{A}}_{C_3{H}_{3}N}\left(n\right)+b·{\mathbb{A}}_{C_4{H}_6}\left(n\right)+c·{\mathbb{A}}_{C_8{H}_8}\left(n\right)$$

(2)

In Equation (2), $\left\{{\mathbb{A}}_{C_3{H}_{3}N}\left(\lambda \right), {\mathbb{A}}_{C_4{H}_6}\left(\lambda \right), {\mathbb{A}}_{C_8{H}_8}\left(\lambda \right)\right\}$ are the absorbances of acrylonitrile, butadiene, and styrene co-polymers at wavenumber λ. The parameters {a, b, c} are linear fit coefficients, and ${\mathbb{A}}_{ABS\left(\lambda \right)}$, is the least-squares estimate of ABS absorbance at wave number n. These coefficients are optimized to minimize the squared error between the measured ABS spectrum and the model across all wavenumbers. Normalizing {a, b, c} estimates the molar proportions of each co-polymer in the ABS sample; dividing each by its molecular weight yields the mass fractions.

2.1.3. FTIR Spectrum Curve Fit Error Analysis

Although the authors acknowledge that Equation (2) offers only a simplified representation of the intricate chemical structure present in the processed materials, it serves as an effective engineering model for evaluating relative differences among the tested samples. The coefficients obtained from fitting Equation (2) are inherently approximate; therefore, it is essential to provide an evaluation of the accuracy associated with each estimated coefficient {a, b, c} alongside their estimated values. The following analysis presents this assessment usung Hamming’s method [25].

First writing the curve fit equation in matrix form as

$${\left[\begin{array}{c}{\mathbb{A}}_1\\ ⋮\\ {\mathbb{A}}_m\end{array}\right]}_{ABS}=\left[\begin{array}{ccc}{\mathbb{A}}_{C_3{H}_3{N}_1}& {\mathbb{A}}_{C_4{H}_{6_1}}& {\mathbb{A}}_{C_8{H}_{8_1}}\\ ⋮& ⋮& ⋮\\ {\mathbb{A}}_{C_3{H}_3{N}_m}& {\mathbb{A}}_{C_4{H}_{6m}}& {\mathbb{A}}_{C_8{H}_{8_m}}\end{array}\right]·\left[\begin{array}{c}a\\ b\\ c\end{array}\right]$$

(3)

and making the symbolic substitutions, with m spectrum data points,

$$\begin{gathered} Y=H·X, \mathrm{where} \\ Y={\left[\begin{array}{c}{\mathbb{A}}_1\\ ⋮\\ {\mathbb{A}}_m\end{array}\right]}_{ABS}, H=\left[\begin{array}{ccc}{\mathbb{A}}_{C_3{H}_3{N}_1}& {\mathbb{A}}_{C_4{H}_{6_1}}& {\mathbb{A}}_{C_8{H}_{8_1}}\\ ⋮& ⋮& ⋮\\ {\mathbb{A}}_{C_3{H}_3{N}_m}& {\mathbb{A}}_{C_4{H}_{6_m}}& {\mathbb{A}}_{C_8{H}_{8_m}}\end{array}\right], X=\left[\begin{array}{c}a\\ b\\ c\end{array}\right] \end{gathered}$$

(4)

Then if the Mean Square curve fit error is Ψ², calculated from the squared residual between the Normalized FTIR spectrum and the curve fit model, ${\Psi }^2={\left[\hat{Y}-Y\right]}^T·\left[\hat{Y}-Y\right]$, then the covariance of the estimated parameters is the matrix

$$Cov\left[X\right]={\left[H^{T}H\right]}^{-1}·{\Psi }^2$$

(5)

The diagonal elements of Cov[X] are the associated variances of the curve fit parameters {a, b, c}.

2.1.4. Selecting the Proper Reference Spectra

To calculate the mole fractions of acrylonitrile, butadiene, and styrene in ABS accurately, selecting the correct reference spectra is essential. The following sub-sections illustrate these choices.

Acrylonitrile

Acrylonitrile is an essential monomer in ABS plastic production, polymerized with styrene and butadiene to form ABS’s unique structure. Polyacrylonitrile (PAN), which consists only of acrylonitrile units, is not involved in ABS manufacturing. Instead, the raw acrylonitrile also reacts directly with other components to create ABS, integrating acrylonitrile chains with styrene and butadiene [26]. Figure 3 compares the absorption spectra of acrylonitrile monomer [27] and PAN [28]. Both spectra display two main peaks at approximately 1410/cm and 2230/cm. However, the prominent monomer peak near 960/cm is absent in PAN due to its saturated backbone. The origin of the extra “soft peaks” observed in PAN on Figure 3 is unclear; they might be due to the conversion from the original data, changes from transmittance to absorbance, or possibly artifacts introduced in the published spectrum.

Styrene

Similarly, in the polymerization of ABS the raw acrylonitrile monomer reacts directly with the other components. The polymer polystyrene is not a constituent component of ABS. Figure 4 compares the IR absorbance spectra of the styrene monomer [29] to that of polystyrene [30]. Again, notice the absence of strong peaks at low wavenumbers in the polystyrene spectrum, which is a result of its saturated backbone.

Butadiene

Polybutadiene, and not the butadiene monomer, is a key component in ABS plastic. ABS is produced by polymerizing styrene and acrylonitrile with polybutadiene, which adds toughness and impact resistance. Figure 5 shows that the IR spectrum of (cis 1–3) polybutadiene [31] lacks the strong peak at 750–760/cm seen in the (1–3) butadiene monomer [32], due to its saturated polymer backbone. Higher-frequency variations in the plotted results likely stem from differing sampling methods used by the original authors of these data.

2.1.5. Using Mole-Fractions to Calculate ABS Properties of Combustion

Mole fractions from Section 2.1.2 are used to estimate ABS’s equilibrium combustion characteristics with NASA’s Chemical Equilibrium with Applications (CEA, (FCEA2 V2, 5/21/2004)) program [33,34,35]. CEA, developed at NASA Glenn Research Center, is an industry standard software package for calculating chemical equilibrium compositions and thermodynamic properties of mixtures. It can also determine theoretical rocket performance parameters like thrust, specific impulse, and characteristic velocity. Detailed results from CEA calculations will be discussed in Section 3.2.

Using the CEA program GUI, Ref. [35] the thermodynamic and transport properties of the reactants are typically inserted using the standard program database libraries; however, because ABS is not a conventional propellant, its properties are not included. Thus, ABS thermodynamic and transport properties must be entered manually to the program. For this manual entry the user specifies the enthalpy of formation and the fundamental chemical formula. Ref. [34] (pp. 8–9) explains the process for performing these entries to the program. Ref. [33] (pp. 19–20) show the process by which these external data entries are used for the equilibrium calculations.

2.2. Bomb Calorimeter Testing for ABS Enthalpies of Combustion

To complement the previously presented test results and analyses, a series of bomb calorimetry experiments were conducted. Bomb calorimetry offers a direct and reliable approach to experimentally determine the enthalpy of combustion for candidate ABS feedstocks. Enthalpy values from calorimetry will be compared with those calculated using FTIR co-polymer mass fraction and CEA analysis. Results from the calorimetry testing campaign will be discussed in detail in Section 3.3.

Besides the four ABS materials tested in FTIR—ABS-Plus, Generic, ABS-R, and Bambu—three additional commercial feedstocks were evaluated. These additional materials were, (1) Toner-Plastics Natural Color ABS, (Toner, https://tonerplastics.com, East Longmeadow, ME, USA), (2) Atomic Filaments Black ABS (Atomic, https://atomicfilament.com/, Kendallvile, IN, USA), and (3) IC3D Black ABS (IC3D, https://www.ic3dprinters.com, River Heights, UT, USA). Finally, after completing ABS bomb calorimetry tests, other 3D printing materials were also tested to compare their combustion performance with ABS.

2.2.1. Bomb Calorimetry Test Apparatus

A Parr Instruments (Moline, IL, USA) 6200 Isoperibol Calorimeter [36] was used for precise calorific measurements. This device records heat release during combustion at constant volume in pressurized oxygen, with a temperature resolution of 0.0001 °C and accuracy of ±0.1%. Figure 6 shows a simplified schematic of the calorimeter apparatus. The setup includes a stainless-steel vessel, water jacket, ignition circuit, and digital controls. Procedures followed ASTM D240 [37,38] with minor changes for solid polymeric fuels. Calorimeter calibration using benzoic acid tablets gave a heat-capacity constant of about 8932.1 J/K.

2.2.2. Bomb Calorimetry Test Procedures

For each test, a 1 g sample was placed on a nickel combustion dish with a nickel-chromium fuse wire. The bomb was sealed, filled with oxygen to 20 atm, and submerged in a 2000 g water jacket. After stabilizing for 10 min, the sample was ignited by energizing the fuse wire for 3 s. Jacket water temperature was recorded every 30 s until it plateaued. Afterwards, the bomb was depressurized, disassembled, and cleaned of residue.

2.2.3. Bomb Calorimeter Analysis Methods

The energy content of fuel is expressed as its higher heating value (HHV). The total heat released was determined from the bomb’s heat capacity, temperature increase during combustion, and the fuse’s heat contribution.

$$\Delta Q=C_{bomb}·\Delta T-e_{wire}·\Delta L_{Fuse}$$

(6)

In Equation (6), C_bomb is the heat capacity of the bomb calorimeter, from calibration, ΔT is the water bath temperature increase, ΔL is the burned wire length, and e_wire is the energy per unit length (about 9.6 J/cm). As described in the previous paragraph, the bomb calorimeter operates at a constant volume, and for accurate comparison to the FTIR/CEA data, the data must be adjusted to account for the work action within on the bomb chamber during combustion. Thus, the total change in enthalpy is calculated by

$$\Delta H=\Delta Q+P·V$$

(7)

In Equation (7), P is the internal bomb pressure after combustion, and V is the bomb reactor internal volume, approximately 342 cm³.

The Parr Instruments Company (Moline, IL, USA) 6200 calorimeter used in these tests cannot directly measure combustion pressure inside the chamber, so post-combustion internal pressure was estimated using ideal gas analysis. Here, the initial pressures before and after combustion are related to the number of gaseous (n) moles, the universal gas constant (R_u = 8314.46 J/kg-K), and the internal bomb gas temperatures (T),

$$P_1·V=n_1·R_u·T_1{P}_2·V=n_2·R_u·T_2$$

(8)

Since the initial mass oxygen in the bomb is calculated by,

$$M_{ox}={\displaystyle \frac{V·P_1}{\frac{R_u}{M_{w_{ox}}}·T_1}}$$

(9)

and number of initial gaseous moles of O₂ is

$$n_1={\displaystyle \frac{M_{ox}}{M_{w_{ox}}}}={\displaystyle \frac{V·P_1}{R_u·T_1}}$$

(10)

Similarly, the number of post-combustion gaseous moles is calculated by

$$n_2={\displaystyle \frac{M_{ox}+M_f}{M_{w_{comb}}}}={\displaystyle \raisebox{1ex}{$\left(V·\frac{P_1}{\frac{R_u}{M_{w_{ox}}}·T_1}+M_f\right)$}\!\left/ \!\raisebox{-1ex}{$M_{w_{comb}}$}\right.}$$

(11)

In Equation (11), M_wcomb is the molecular weight of the combustion products. Finally, using Equation (8) the post-combustion pressure is solved for,

$$P_2=P_1·{\displaystyle \frac{n_2·\left(T_1+\Delta T\right)}{n_1·T_1}}$$

(12)

The test sample HHV is subsequently calculated by dividing the work-adjusted total heating u by the mass of the fuel sample, M_f,

$$HHV={\displaystyle \frac{\Delta Q+P_2·V}{M_f}}=u+{\displaystyle \frac{P_2·V}{M_f}}$$

(13)

3. Results

This section summarizes results from FTIR and bomb calorimetry tests. Chemical formulas, molecular weights, and enthalpies of formation for each ABS sample are determined using FTIR data. With these values, CEA calculates rocket performance parameters and combustion enthalpies for ABS burned with gaseous oxygen. CEA’s Higher Heating Values are compared to bomb calorimetry findings, and presented statistical analysis evaluates material performance quantitatively.

3.1. FTIR Testing Campaign and Associated Analyses

3.1.1. Comparing the FTIR Spectra for the Various ABS Samples

Portions of the FTIR data to be presented here were originally published by Whitmore (2022, [39]) and Whitmore and Brewer (2017, [40])). This report includes the original data and results from additional test samples. Also, the presented analysis is considerably more detailed. To reduce noise in FTIR spectra, each ABS material (ABS-Plus, Generic1, Generic2, ABS-R, and Bambu) was tested several times and the results averaged. Figure 7 shows the mean absorbance spectra by wavenumber, with key peaks labeled. The spectra are very similar, although USU PRL tests span a wider range than MSFC tests.

Table 1. ABS Sample Correlation Indexes, r_c.

Material	ABS-Plus	Generic-1	ABS-R	Bambu	Generic-2
ABS-Plus	1.000	0.931	0.951	0.905	0.901
Generic-1	0.931	1.000	0.950	0.925	0.905
ABS-R	0.951	0.950	1.000	0.911	0.905
Bambu	0.905	0.925	0.911	1.000	0.964
Generic-2	0.901	0.905	0.905	0.964	1.000

lists correlation coefficients, calculated using the simple Pearson method,

$$r_c\left(x,y\right)={\displaystyle \frac{\sum _{i=1}^n\left[\left(x_i-\overline{x}\right)·\left(y_i-\overline{y}\right)\right]}{\sqrt{\sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}·\sqrt{\sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}}$$

(14)

Equation (11) uses parameters {x, y} to represent absorbances across all wavenumbers for each data set, with the “bar” denoting sample means. Correlation coefficients exceed 90%, indicating minimal chemical composition variation among ABS materials. The differences between Generic-1 and Generic-2 are primarily due to different testing instruments.

3.1.2. Curve Fitting of the FTIR Data to Reference ABS Spectra

As described earlier in Section 2.1.3 the choice of reference spectra has a critical influence upon the accuracy of associated curve fits and the resulting compositional mole fractions. As examples of the least squares data fits, Figure 8 compares the best fit and measured spectra for the Bambu material with Figure 8a using all monomer reference values for the reference spectra [27,29,31], Figure 8b using all polymer reference values [28,30,32], and Figure 8c using the monomer (Acrylonitrile), polymer (Butadiene), and monomer (styrene) reference spectra.

Table 2. Curve Fit Statistics and Species Mole Fraction Estimates for Bambu Material, using Monomer and Polymer-based Reference Spectra.

Case	Reference Spectra	Mole Fractions, %	Fit Correlation Coefficient
Acrylonitrile	Monomer [27]	26.63	0.4511
Butadiene	Monomer [31]	−23.65
Styrene	Monomer [29]	98.02
Acrylonitrile	Polymer [28]	−98.18	0.420
Butadiene	Polymer [32]	−335.95
Styrene	Polymer [30]	−137.77
Acrylonitrile	Monomer [27]	24.01	0.865
Butadiene	Polymer [32]	35.40
Styrene	Monomer [29]	40.59

shows the associated curve fit correlation coefficients as well as the estimated molar proportions for each member of the ABS terpolymer.

Note that the first two table entries, using either all monomer or all polymer reference spectra give very poor fit correlations, less than 50%; whereas the fit using the previously described monomer-polymer-monomer reference spectra, give a significantly higher correlation, approximately 87%. Similarly, the curve-fit overlays of Figure 8 exhibit poor comparisons for the first two cases, and a significantly better comparison for the final case. More significantly, the first two examples produce physical nonsensical mole fraction ratios, producing negative values for several of the subspecies. These data comparisons strongly suggest that the appropriate reference spectra to use for these correlations are the monomer reference spectra for Acrylonitrile [27] and Styrene [29] and the polymer [32] reference spectrum for Butadiene. This result supports the earlier discussion regarding the appropriate reference spectra selection.

3.1.3. Error Analysis of the Fitted Spectra

Using this derived knowledge,

Table 3. Co-Polymer Mole Fraction Estimates for Each of the 5 Tested ABS Materials.

Material	Acrylonitrile		Butadiene		Styrene		Curve Fit RMSE %
	Mole Frac. %	RMS Uncertainty %	Mole Frac. %	RMS Uncertainty %	RMS Mole Frac. %	Uncertainty %
ABS-Plus	23.77	3.11	34.60	1.03	41.63	3.12	7.79
Generic-1	24.32	2.90	30.95	0.96	44.73	2.91	7.27
ABS-R	28.39	3.06	41.09	1.02	30.52	3.07	7.66
Bambu	24.01	3.04	35.40	1.01	40.59	3.05	7.61
Generic-2	26.53	2.86	31.50	0.96	41.97	2.88	7.17
Mean, μ	25.40	-	34.71	-	39.89	-	-
RMS Uncertainty	-	3.00	-	0.99	-	3.01	7.50

presents the monomer mole fractions and estimated uncertainties for five ABS materials, determined by least squares curve-fitting using the monomer-polymer-monomer reference spectra method. Equation (15) provides the covariance information matrix from Equation (5), which depends solely on the reference spectra used.

$${\left[H^{T}H\right]}^{-1}=\left[\begin{array}{ccc}0.1595& -0.0123& -0.2164\\ -0.0123& 0.0176& -0.0187\\ -0.2164& -0.0187& 0.1608\end{array}\right]$$

(15)

The mole fraction uncertainties are calculated using the square root of the product of Ψ² and the diagonal elements of [H^TH]⁻¹.

3.1.4. Presentation of FTIR Curve Fit Results

Table 3 shows the co-polymer mole fraction estimates (%) per subspecies using Equation (2), alongside their measurement uncertainty. Table 3’s last column presents the curve uncertainty as the root mean square, derived from the square root of Ψ². The final rows in Table 3 report the mean mole fractions and total RMS uncertainty for each monomer, averaged across all material samples.

3.1.5. Mean Co-Polymer Mole and Mass-Fractions for Each ABS Test Material

The average mole fractions from Table 3 are used to determine the molecular weights for each test material, which are then applied to find the mass fractions of each monomer. These results are shown in

Table 4. Co-Polymer Mole and Mass Fraction Estimates for Each of the 5 Tested ABS Materials.

Material	Acrylonitrile		Butadiene		Styrene
	Mole Frac. %	Mass Frac. %	Mole Frac. %	Mass Frac. %	Mole Frac. %	Mass Frac. %
ABS-Plus	23.77	16.90	34.60	25.06	41.63	58.06
Generic-1	24.32	16.93	30.95	22.00	44.73	61.11
ABS-R	28.39	21.81	41.09	32.18	30.52	46.02
Bambu	24.01	17.18	35.40	25.82	40.59	57.00
Generic-2	26.53	18.82	31.50	22.77	41.97	58.42
Mean, μ	25.40	18.33	34.71	25.57	39.89	56.12
Std. Dev. σ	2.00	2.10	4.05	4.02	5.46	5.85
Student-t Conf. Interval (95%)	2.48	2.61	5.02	4.99	6.77	7.26

. The bottom three rows of Table 4 lists the ensemble means, standard deviation, and student-t mean variations (95% confidence for 4 degrees-of-freedom) across all materials studied. When comparing calculated sample standard deviations with the propagated uncertainties from the formal error analysis of Table 3, Acrylonitrile and Styrene show the highest projected mole fraction uncertainties (3.00% and 3.01%), while Butadiene has the lowest (0.99%). However, standard deviations for the material ensemble data set are highest for Styrene (5.46%) and Butadiene (4.05%), with Acrylonitrile at 2.00%. The Student-t confidence intervals for the ensemble are Styrene 6.77%, Butadiene 5.02%, and Acrylonitrile 2.48%. The ensemble data set shows mean curve fit variability slightly exceeding formal error analysis uncertainties.

Equation (16) provides a quantitative comparison of the co-polymer mole fractions between the Bambu and Generic-1 material samples, illustrating the material differences in a more rigorous manner.

$$\begin{gathered} \Delta {\mathbb{M}}_{frac}=\left({\displaystyle \frac{\sqrt{{\left({\mathbb{M}}_{Bambu}-M_{Generic}\right)}_{Acrylonitrile}^2+{\left({\mathbb{M}}_{Bambu}-M_{Generic}\right)}_{Butadiene}^2+{\left({\mathbb{M}}_{Bambu}-M_{Generic}\right)}_{Styrene}^2}}{\frac{1}{2}\left[{\left({\mathbb{M}}_{Bambu}+M_{Generic}\right)}_{Acrylonitrile}+{\left({\mathbb{M}}_{Bambu}+M_{Generic}\right)}_{Butadiene}+{\left({\mathbb{M}}_{Bambu}+M_{Generic}\right)}_{Styrene}\right]}}\right)= \\ {\displaystyle \frac{100·\sqrt{{\left(24.01-24.32\right)}^2+{\left(35.40-30.95\right)}^2+{\left(40.59-44.73\right)}^2}}{\frac{1}{2}·\left[\left(24.01+24.32\right)+\left(35.40+30.95\right)+\left(40.59+44.73\right)\right]}}=6.1\% \end{gathered}$$

(16)

Based on this calculation the co-polymer compositions for the two materials differ by around 6%. Similar results are observed for the other materials tested. These minor variations shown by Table 4 and Equation (16) could reflect small differences in material composition. or simply result from random variability, but the limited sample size prevents definitive conclusions.

3.2. Calculating the Enthalpies of Formation Using FTIR Results

The mean molar fractions from Table 3 and Table 4 can be used to estimate the chemical formula and the associated enthalpies of formation (ΔH_f) for each of the tested ABS samples. Table 5 presents a calculation example using the mean material composition from Table 3 and Table 4 (row 6), with mole fractions of 25.4% acrylonitrile, 34.71% butadiene, and 39.89% styrene. Table 5 also lists the enthalpy contributions for each of the ABS copolymers including ΔH_f, ΔQ_p, and the net enthalpy contribution of each monomer, according to its mole fraction.

It must be noted that ABS polymerization is highly exothermic; thus, combustion requires breaking these bonds, reversing the energy released during polymerization. This effect means the combustion products retain less energy. Since ABS forms by copolymerization, its enthalpy of polymerization varies, typically between 71 and 85 kJ/mol, as reported by Hu et al. [41] and online by Refs. [42,43]. The total enthalpy of ABS is lower than the sum of its monomers, with each monomer’s net enthalpy calculated by subtracting ΔQ_p from ΔH_f. The chemical formula and molecular weight (Mw) of the ABS material are determined using the mole fractions of the co-polymers. When bond energy is included in the calculation, the net enthalpy contribution for the Bambu ABS is 66.285 kJ/mol (0.9068 kJ/g). Without considering bond energy, the estimated ΔH_f is 137.928 kJ/mol (1.8598 kJ/g), which is over 70% higher than the actual enthalpy value.

Table 5. Example Enthalpy of Formation Calculation for Mean ABS Composition from Table 3.

Monomer	Chemical Formula	Mw g/mol	ΔHf Monomer kJ/g-mol	ΔQp Polymer kJ/g-mol	Net ΔHf kJ/g-mol	Mole Fraction	Mass Fraction	Net Enthalpy Contribution kJ/g-mol
Acrylonitrile	C3H3N	53.06	172.62 [44]	72.4	100.22	0.2540	0.1826	25.456
Butadiene	C4H6	54.09	104.10 [45]	69.8	34.30	0.3471	0.2544	11.906
Styrene	C8H8	104.15	146.91 [46]	72.8	74.11	0.3989	0.5630	29.563
ABS Total	C5.3416H6.0358 N0.254	73.799				1.000	1.000	66.924
Net Enthalpy Contribution kJ/g			0.9068

Table 5. Example Enthalpy of Formation Calculation for Mean ABS Composition from Table 3.

Monomer	Chemical Formula	Mw g/mol	ΔHf Monomer kJ/g-mol	ΔQp Polymer kJ/g-mol	Net ΔHf kJ/g-mol	Mole Fraction	Mass Fraction	Net Enthalpy Contribution kJ/g-mol
Acrylonitrile	C3H3N	53.06	172.62 [44]	72.4	100.22	0.2540	0.1826	25.456
Butadiene	C4H6	54.09	104.10 [45]	69.8	34.30	0.3471	0.2544	11.906
Styrene	C8H8	104.15	146.91 [46]	72.8	74.11	0.3989	0.5630	29.563
ABS Total	C5.3416H6.0358 N0.254	73.799				1.000	1.000	66.924
Net Enthalpy Contribution kJ/g			0.9068

Estimating the Associated Uncertainties in the Enthalpies of Formation

Uncertainties in enthalpy of formation, molecular weight, and chemical formulas are estimated using a Monte Carlo simulation with mole fraction uncertainties modeled as Gaussian noise.

Table 6. Enthalpy, Molecular Weight, and Chemical Formula Error Analysis from Ensemble Data Set.

Parameter	ΔHf (Molar) kJ/g-mol	ΔHf (Mass) kJ/g	Mw g/mol	Monomer Mass Fractions (%)			Chemical Formula
				C3H3N	C4H6	C8H8
ABS-Plus	66.50 ± 1.16	0.8904 ± 0.024	74.71 ± 1.17	23.77 ± 3.11	34.60 ± 1.03	41.63 ± 3.12	C5.431H6.123N0.237 C±0.112 H±0.114 N±0.025
Generic-1	68.12 ± 1.02	0.894 ± 0.022	76.25 ± 1.08	24.32 ± 2.90	30.95 ± 0.96	44.72 ± 2.91	C5.548H6.617N0.243 C±0.104 H±0.107 N±0.023
ABS-R	65.11 ± 1.16	0.943 ± 0.025	69.03 ± 1.17	28.39 ± 3.06	41.09 ± 1.02	30.52 ± 3.07	C4.934H5.758N0.284 C±0.110 H±0.107 N±0.024
Bambu	66.25 ± 1.11	0.894 ± 0.023	74.13 ± 1.15	24.01 ± 3.04	35.40 ± 1.01	40.59 ± 3.05	C5.381 H6.090N0.240 C±0.110 H±0.111 N±0.024
Generic-2	68.50 ± 0.98	0.916 ± 0.022	74.81 ± 1.09	26.53 ± 2.86	31.50 ± 0.96	41.97 ± 2.88	C5.411 H6.042N0.266 C±0.105 H±0.106 N±0.023
Mean, μ	66.92	0.907	73.80	25.4	34.71	39.89	C5.342H6.036N0.254
Std. Dev. σ	1.071	0.023	1.133	3.00	0.99	3.01	C±0.108 H±0.109 N±0.239
95% Student-t conf. Interval	1.33	0.018	1.40	-	-	-	-

shows results from 2500 test cases, including mean values and standard errors for molar and mass-based enthalpies, molecular weights, mole fractions (from Table 3), and non-stoichiometric chemical formulas for ABS materials. Rows 6 and 7 display ensemble means and standard deviations for each parameter.

3.3. Calculating the Properties of Combustion

The average chemical formulas and enthalpies of formation from Table 6 (Row 6) were utilized, together with CEA, to estimate theoretical equilibrium combustion characteristics. This analysis assumes that ABS fuel combusts with gaseous oxygen (GOX) at various oxidizer-to-fuel (O/F) ratios and a combustion efficiency of 100%. The combustion chamber pressure (Pc) is varied over typical hybrid motor operating ranges, specifically from 50 psia (345 kPa) up to 500 psia (3450 kPa) in increments of 50 psi.

Figure 9 presents several critical parameters as functions of the O/F ratio: (a) combustion flame temperature (T₀), (b) ratio of specific heats (γ), (c) molecular weight (M_w), (d) specific heat at constant pressure (Cp_comb), (e) specific heat at constant volume (Cv_comb), and (f) specific enthalpy of combustion (Δh_comb). In these graphs Δh_comb represents the total heat released per unit mass during the reaction minus the initial enthalpy of reactants, which are at standard conditions (298 K). The vertical, dashed, red line on these plots marks the stoichiometric O/F ratio, approximately 2.97.

Using the data of Figure 9, Figure 10 replots Δh_comb for stoichiometric conditions (O/F = 2.97) versus combustion chamber pressure, including the mean trend-line and error lines accounting for the variability of the mean enthalpy of formation from Table 6. Here the calculations are based on the extremal enthalpy of formation values, i.e.,

$$\left[\begin{array}{c}{\left(\Delta H_f\right)}_{min} ={\left(\Delta H_f\right)}_{mean}-\sigma \left(\Delta H_f\right)\\ {\left(\Delta H_f\right)}_{mean}\\ {\left(\Delta H_f\right)}_{max} ={\left(\Delta H_f\right)}_{mean}+\sigma \left(\Delta H_f\right)\end{array}\right]=\left[\begin{array}{c}66.88-1.07={\displaystyle \frac{65.81 \mathrm{kJ}}{\mathrm{mol}}}\\ {\displaystyle \frac{66.88 \mathrm{kJ}}{\mathrm{mol}}}\\ 66.88+1.07={\displaystyle \frac{67.95 \mathrm{kJ}}{\mathrm{mol}}}\end{array}\right]$$

(17)

In Figure 10, the solid black symbols denote the calculated enthalpy (Δh_comb), determined using the mean enthalpy of formation (66.88 kJ/mol) across nine different combustor pressure levels. The solid black line represents a polynomial curve fitting these data points. Dashed black lines indicate the enthalpy calculated with the upper (67.95 kJ/mol) and lower (65.81 kJ/mol) enthalpy of formation values from Equation (16) throughout the pressure range. The solid blue symbol is the calorimeter test condition. For all calculations, the ABS chemical formula is maintained at the mean value from Table 6 (C_5.343H_6.038N_0.253). When combustion pressure is about 500 psia, the greatest difference between the average and extreme curves is below 0.5%. The data shows that compositional uncertainties of around 6% from FTIR analysis have a decreasing impact on combustion enthalpy results.

Notably, in Figure 10, Δh_comb demonstrates a slight decrease as chamber pressure increases, which is attributed to the reduced heat capacity of combustion products at elevated pressures. Additionally, the solid red symbol shown in Figure 10 corresponds to the combustion enthalpy (32.49 kJ/mol) at a chamber pressure of approximately 28 atmospheres (41 psia). This pressure aligns with the estimated post-test condition for the bomb calorimeter data discussed in the following section, where the significance of this data point will be addressed in detail.

3.4. Bomb Calorimeter Testing Campaign and Associated Analyses

The average higher heating value (HHV) for each material was determined based on five repeated tests, with the standard deviation reflecting the consistency of the results. For the constant-volume correction that accounts for the work done in the bomb chamber during combustion, a stoichiometric is used to calculate the molecular weights. For GOX/ABS combustion at 20 atm, CEA analysis estimates the mean molecular weight as 26.75 g/mol. As an example,

Table 7. Summary of Bomb Calorimeter Tests Fir Toner Plastics ABS Sample.

Parameter	Sample Mass, g	ΔT Bomb, °C	P Final, atms	ΔQ, kJ	u, MJ/kg	HHV, MJ/kg
Test 1	0.970	3.70	26.86	33.011	34.032	34.992
Test 2	0.960	3.80	26.84	33.892	35.304	36.273
Test 3	0.970	3.80	26.87	33.894	34.942	35.902
Test 4	0.970	3.70	26.86	33.002	34.022	34.982
Test 5	0.970	3.70	26.86	33.016	34.997	34.997
μ	0.968	3.74	26.86	33.363	34.468	35.429
σ	0.0045	0.055	0.010	0.4838	0.612	0.615
95% Conf. Intvl.	0.0047	0.057	0.011	0.5073	0.642	0.645

shows the complete set of test outcomes for the Toner ABS test sample. Identical calculations were performed for each of the other six material samples.

The authors note that internal bomb combustion is likely not stoichiometric, resulting in excess post-burn oxygen. However, variations in assumed molecular weight minimally affect the final HHV calculations. Figure 11 shows this result with a 200-run Monte Carlo Analysis of the Toner-Plastic ABS bomb data, where molecular weight fluctuates randomly by a standard deviation of 20% around a mean of 26.76 g/mol. Figure 11 presents scatter plots: Figure 11a shows input molecular weights, Figure 11b displays calculated post-burn bomb pressure, and Figure 11c illustrates calculated HHVs. Even though the 20% error in M_w yields an estimated post-burn pressure of 28 atms (412 psia) with a standard deviation of 6.7 atms (24% error); the mean HHV is 35.4 MJ/kg, with a standard deviation of 0.24 MJ/kg (<0.7% error) is significantly less. To address errors from non-stoichiometric combustion, this HHV error value is root-summed-squared with the experimental HHV sample standard deviation in Table 7, Row 7. The 95a% Student-t confidence intervals are calculated using the RRS value. A similar procedure was followed for each of the materials listed in Section 2.2.

Table 8. Summary of Bomb Calorimetry Test Results.

Test Sample	Degrees of Freedom	ΔQ, kJ Mean (μ)	ΔQ, kJ Std. Dev. (σ)	u, MJ/kg Mean	u, MJ/kg Std. Dev.	HHV, MJ/kg Mean	HHV, MJ/kg Std. Dev.
Toner Plastics	4	33.36	0.484	34.47	0.612	35.43	0.678
Atomic Filaments	4	34.25	1.011	34.75	1.218	35.69	1.301
IC3D Black	4	33.00	0.012	34.24	0.324	35.20	0.407
Polymaker Black	4	33.34	0.032	34.32	0.341	35.29	0.402
Generic Natural	4	34.25	0.450	34.40	0.515	35.36	0.554
ABS-R	4	33.03	0.045	34.32	0.261	35.28	0.336
Bambu Labs Black	4	33.39	0.462	34.51	0.580	35.48	0.616
μ	34	33.52		34.43		35.39
σ		0.525	1.294	0.169	1.658	0.163	1.811
95% Conf. Intvl.		0.485	0.444	0.156	0.569	0.150	0.622

presents calorimetry results for the seven materials listed in Section 2.2, including mean values and standard deviations from five samples each. Columns show total heat release, specific internal energy, and work-adjusted HHVs. Rows 8–10 provide ensemble statistics. The bar charts of Figure 12 display mean HHVs with 95% confidence intervals. The minimal variation among data supports FTIR test conclusions that industrially available ABS feed stocks are fabricated using essentially the same monomer ratios (Because ABSPlus is no longer commercially available, the Polymaker (https://shop.polymaker.com, Changshu, China) ABS Black feed stock was substituted here).

3.5. Comparing CEA Calculations to Bomb Calorimeter Test Results for ABS Samples

The CEA calculations were repeated for each ABS material in Table 8 using mass fraction data from the FTIR tests.

Table 9. CEA Enthalpy Calculations using FTIR Mass Fraction Analysis of ABS Materials.

Material	ΔHf (Mass), kJ/g	MH2O, % Concentration	ΔHc (Mass), kJ/g LHV	ΔHc (Mass), kJ/g HHV
Polymaker Black	0.891	24.26	32.54	35.81
Generic-1	0.894	23.99	32.43	35.70
ABS-R	0.944	24.29	32.47	35.87
Bambu	0.894	24.73	32.55	35.88
Generic-2	0.915	24.00	32.33	35.61
Mean, μ	0.907	24.25	32.46	35.77
Std. Dev. σ	0.022	0.300	0.221	0.232
95% Student-t Conf. Interval	0.028	0.373	0.150	0.144

presents the results, including material name, mass fraction, chemical formula, enthalpy of formation enthalpy (by mass), and combustion enthalpies at the stoichiometric O/F ratio. Both the low-heating (LHV) and high-heating (HHV) values are listed. As shown by Equation (18), the LHV is derived from plume specific enthalpy, adjusted for fuel, and not total mass flow rate,

$$\Delta H_{LHV}=C_v·T_0·{\left({\displaystyle \frac{{\dot{m}}_f+{\dot{m}}_{O_2}}{{\dot{m}}_f}}\right)}_{stoich} =C_v·T_0·\left(O/F_{stoich}+1\right)$$

(18)

In Equation (18), flame temperature (T₀) and specific heat (C_v) are taken from CEA analysis and interpolated to the bomb-calorimeter’s post-combustion pressure, which is roughly 28 atm (412 psig). It must also be noted here, because the CEA calculations, which assumed a constant pressure process, are to be compared against the bomb calorimetry data, which result from a constant volume process, C_v and not C_p are used the ΔH_LHV calculation.

The CEA-derived enthalpy ignores the water content in the exhaust plume, treating all water as vapor. Figure 13 shows how plume water content changes with chamber pressure and O/F ratio, based on average monomer fractions from Table 3 and Table 4. At stoichiometric conditions, water ranges from 12% to 13% depending on pressure. For accurate comparison with bomb calorimetry data, the CEA LHV requires adjustment for the latent heat of vaporization of plume water, calculated as follows:

$$\Delta H_{H_{2}O}=M_{H_{2}O}·\left({\displaystyle \frac{{\dot{m}}_{ox}+{\dot{m}}_f}{{\dot{m}}_f}}\right)·L_{H_{2}O}=M_{H_{2}O}·\left(O/F+1\right)·L_{H_{2}O}$$

(19)

In Equation (19), ΔH_H2O is the latent heat adjustment, M_H2O is the exhaust plume water mass fraction, and L_H2O the latent heat of vaporization for water under standard conditions, about 2460 kJ/kg. Adding the calculated enthalpy of vaporization, to the LHV gives the adjusted value for the HHV. The calculated values for HHV can now be accurately compared against the bomb calorimetry data. Table 9 summarizes the results of the CEA Enthalpy Calculations. Figure 14 also presents this comparison graphically as bar charts where the ensemble mean HHV values from the calorimetry tests (a) (from Table 8) are compared against the ensemble mean CEA enthalpy (b), calculated using FTIR mass fraction analysis (from Table 8). The error bars on each bar graph display the 95% Student-t confidence intervals from the tables.

3.6. Comparing the Enthalpies of Combustion to ABS to Alternative Commercially Available 3-D Print Materials

As referenced earlier, because ABS is a thermoplastic suitable for 3-D printing, it offers key advantages over traditional thermoset solid-propellant binders like HTPB. With the rise of 3-D printing; however, many plastics can now be additively manufactured, including Polycyclohexylene Dimethylene Terephthalate glycol (PCTG), Polyethylene Terephthalate Glycol (PETG), Acrylonitrile Styrene Acrylate (ASA), Thermoplastic Polyurethane (TPU), and Polyamide-6 (PA6). These materials have not been evaluated as rocket propellants before. Therefore, bomb calorimetry tests were performed on five commercial 3-D printer feedstocks to address inconsistent energy data among different polymer brands. The alternative commercial feed-stock materials as tested were: (1) PCTG-3DX-TECH (Grand Rapids, MI, USA) (https://www.3dxtech.com/products/max-g-pctg-1?variant=43690859462709&country=US&currency=USD&utm_medium=product_sync&utm_source=google&utm_content=sag_organic&utm_campaign=sag_organic&utm_source=googleads&utm_source=google&utm_medium=cpc&gad_source=1&gad_campaignid=18867142456&gclid=CjwKCAiA1obMBhAbEiwAsUBbIjSGYkNUE2QsSBIxAsFGEtYFUBVmhj90UiN1u1Kh8GcmCKz2n96aQhoCp1EQAvD_BwE, accessed on 12 April 2026), (2) PETG-HF Bambu Labs (https://us.store.bambulab.com/products/petg-hf?srsltid=AfmBOop0FaH1pi8bK4_bhDLzM7Swm-FWfV0nP39dfyKyroKdMlOk7xSv, accessed on 12 April 2026), (3) Polymaker ASA (Changshu, China) (https://polymaker.com/about-polymaker/, accessed on 12 April 2026), (4) Bambu Labs TPU 95A HF (https://www.matterhackers.com/store/l/bambu-lab-tpu-hf-filament-175mm-1kg/sk/MRXC3F21?rcode=PMAX_BAMBUFIL&gad_source=1&gad_campaignid=22167739572&gclid=CjwKCAiA1obMBhAbEiwAsUBbIsX_cfumyfZaKFTIwcaC2ZijLjjKjUE_THRdEaGfuSo6pTVglky6rxoCjpEQAvD_BwE, accessed on 12 April 2026), and (5) SunLu Nylon-6 (https://store.sunlu.com/products/sunlu-nylon-6-glass-fiber-pa6-gf-3d-printer-filament-1kg?currency=USD&variant=50850969387290&utm_source=google&utm_medium=cpc&utm_campaign=Google%20Shopping&stkn=98fc28031836&gad_source=1&gad_campaignid=21543374792&gclid=CjwKCAiA1obMBhAbEiwAsUBbIlKrTVLIIHEhQUiFlMh46pIyh9mDuCh-NeCY4kyFZe7Hq08WJfcrOBoCdqwQAvD_BwE, accessed on 12 April 2026).

The additional bomb calorimetry tests were conducted using the same equipment, procedures. As FTIR data on sample composition and molecular weights was unavailable for the alternative materials, constant volume corrections were not performed. For consistency with the ABS samples, specific internal energies (u), equivalent to the Low Heating Values (LHV) are compared, instead of the higher heating values (HHV). Figure 15 presents these results, displaying the ABS ensemble’s specific internal energies alongside those of alternative materials. The repeatability of the subsequent tests matched previous levels; however, ABS consistently produced higher combustion energies compared to the other materials tested.

4. Discussion

This section presents a statistical assessment for both the ABS (Section 3.5) and alternative materials (Section 3.6) test results. Here a Student’s t-test assesses [47] whether any observed differences between the means of these two groups are statistically significant or simply due to random chance, considering the sample means, variances, and sizes. The corresponding t-value is calculated using Welch’s formula [48], Equation (20), where μ and σ represent the sample mean and variance, respectively, for each group, and n indicates the sample count within each dataset. At 95% confidence level is assumed. The associated degrees of freedom for the collected data set are approximated by the Welch–Satterthwaite formula [49], Equation (21),

$$\mathit{t}={\displaystyle \frac{\left|{\mathit{\mu }}_{\mathit{b}\mathit{o}\mathit{m}\mathit{b}}-{\mathit{\mu }}_{\mathit{F}\mathit{T}\mathit{I}\mathit{R}}\right|}{\sqrt{\left(\frac{{\mathit{\sigma }}_{\mathit{b}\mathit{o}\mathit{m}\mathit{b}}^2}{{\mathit{n}}_{\mathit{b}\mathit{o}\mathit{m}\mathit{b}}}\right)+\left(\frac{{\mathit{\sigma }}_{\mathit{F}\mathit{T}\mathit{I}\mathit{R}}^2}{{\mathit{n}}_{\mathit{F}\mathit{T}\mathit{I}\mathit{R}}}\right)}}}$$

(20)

$$D.O.F={\displaystyle \frac{{\left\{\left(\frac{{\sigma }_{bomb}^2}{n_{bomb}}\right)+\left(\frac{{\sigma }_{FTIR}^2}{n_{FTIR}}\right)\right\}}^2}{\left\{\frac{{\left(\frac{{\sigma }_{bomb}^2}{n_{bomb}}\right)}^2}{n_{bomb}-1}\right\}+\left\{\frac{{\left(\frac{{\sigma }_{FTIR}^2}{n_{FTIR}}\right)}^2}{n_{FTIR}-1}\right\}}}$$

(21)

4.1. Statistical Assessment of FTIR/Bomb Calorimetry Results for ABS Samples

Figure 16 presents the outcome of a Student’s t-test comparing the two sets of data from Figure 12: one from bomb calorimetry experiments (35 samples) and the other from FTIR mass-fraction analysis (5 samples). In this comparison, the t-statistic (1.305) falls below the critical value (2.031) for the (equivalent) 37 degrees of freedom, so the null hypothesis is accepted, suggesting there is no significant difference between the data sets. Figure 15 shows that the blue symbol—representing the t-statistics—remains well within the critical range indicated by the dashed red lines. Accordingly, all tested ABS samples are statistically identical, and row seven of Table 4 accurately reflects typical properties for commercial ABS feed stocks. The results from bomb calorimetry support FTIR mass-fraction analysis, confirming the findings presented in Table 4, Table 6 and Table 7.

4.2. Statistical Assessment of Bomb Calorimetry Results, Comparing Mean ABS Result Against the Alternative Materials

When testing alternative materials, only the ASA Polymaker sample (31.92 MJ/kg) had a comparable energy content to the ABS average (34.50 MJ/kg, Table 6). A Student’s t-test performed at the 95% confidence level, resulting in a t-statistic of 5.284, which far exceeded the critical value of 2.446 for the equivalent degrees of freedom. This outcome demonstrates that ABS possesses significantly higher combustion energy relative to ASA. As shown in Figure 17, the t-statistic falls outside the critical range, reinforcing the finding that among all tested 3D print feed-stock alternatives, ABS exhibits the highest energy content.

5. Conclusions

During the past decade ABS has gained popularity as a hybrid propellant and has been studied extensively in recent years. ABS is an affordable thermoplastic with mechanical and thermodynamic properties ideal for hybrid rocket fuel. It is mass-produced for various uses, including plumbing and structural work, and is popular in FDM printing due to its softening near the glass transition temperature rather than having a clear melting point. FDM printing allows for the quick fabrication of ABS fuel grains in multiple shapes and sizes. Notably, FDM-processed ABS exhibits unique electrical breakdown traits, making it suitable for fast, low-energy arc ignition, outperforming other tested 3-D printing materials.

Despite this progress, ABS remains uncommon as a rocket fuel due to the lack of a thermodynamic database, which makes internal ballistics predictions challenging. In particular, data on its standard enthalpy of formation is scarce, hindering accurate motor performance and plume analysis. As ABS is rarely studied as a rocket fuel grain, there is little published data on its standard enthalpy of formation needed for motor performance and plume analysis. Commercial-available ABS formulations, including 3-D printing feed-stock compositions are proprietary and undisclosed. Thus, no widely accepted enthalpy value is available.

Determining the proportions of Acrylonitrile, Butadiene, and Styrene in ABS is crucial for calculating its enthalpy of formation, molecular weight, and chemical formula, important factors for predicting combustion behavior in propulsion. This study uses spectroscopy to analyze commercial ABS compositions and estimate enthalpies, producing an engineering model suitable for various propulsive applications.

Results from combustion property calculations with gaseous oxygen agree with bomb calorimetry measurements, confirming the accuracy of both composition analysis and enthalpy values. Among seven industrial ABS samples, no significant differences were found between data sets. For general-use hybrid rocketry calculations with 3-D printed ABS, a mean enthalpy of formation of approximately 66.92 ± 1.33 KJ/g-mol (0.907 ± 0.018 MJ/kg) is recommended. The mean molecular weight is recommended as approximately 73.80 ± 1.13 g/mol, with the corresponding mean non-stoichiometric chemical formula of C_5.342H_6.036N_0.254. When burned with gaseous oxygen the recommended High Heating Value is about 35.39 MJ/kg ± 0.62 MJ/kg.

Follow-on bomb calorimetry tests demonstrated that ABS possesses more combustion energy compared to five alternative, commercially available 3D printing materials: PCTG, PETG, ASA, TPU, and Polyamide-6. Among these, only ASA had energy levels close to ABS. Statistical analysis using a Student’s t-test confirmed that ABS has significantly higher energy, proving that ABS is more energetic than all tested non-ABS alternatives. The benefits and usefulness of ABS as a hybrid rocket fuel are already well recognized.