Investigation of Key Components in Class A Foam for Synergistic Wetting and Adhesion: A Molecular Dynamics Simulation Case

Abstract

To enhance the fire suppression performance of Class A foam, this study identifies sodium dodecyl sulfate (SDS) as the primary foaming agent and develops a high-efficiency foam system comprising primary and auxiliary foaming agents, wetting agents, and foam stabilizers. It interprets these macroscopic findings at the molecular level through molecular dynamics simulations. Sixteen formulations were designed using orthogonal experiments and evaluated in terms of surface tension, viscosity, wetting performance, and foam expansion ratio. The results demonstrated that the formulated systems exhibited superior foaming characteristics compared to conventional aqueous film-forming foam (AFFF), while other physicochemical properties were inferior. Two high-performing foam systems were further investigated using molecular dynamics simulations. Analysis of the spatial concentration distributions, diffusion coefficients, and the hydrogen-bonding networks of water molecules revealed 14.3% and 14.2% increases in the peak values of the radial distribution function (RDF) for the two systems modified with auxiliary foaming agents, respectively. The auxiliary foaming agents exhibited synergistic effects with SDS, enhancing its water activation capability. The incorporation of wetting agents reduced the water diffusion coefficients by 4.7% and 21.9%, indicating that sodium bis(2-ethylhexyl) succinate sulphonate (T) interferes less with the primary foaming agent than alcohol ethoxylate (AEO). The selected formulations also demonstrated 4.4% and 3.5% reductions in water hydrogen bonding compared to SDS-only solutions, indicating decreased molecular cohesion and improved water activation. By integrating physicochemical evaluation with molecular simulation, the optimized formulation was determined to be SDS (primary foaming agent), sodium fatty alcohol ether sulfate (auxiliary foaming agent), alcohol ethoxylate (wetting agent), lauryl hydroxysultaine (foam stabilizer), and ethylene glycol butyl ether (cosolvent).

1. Introduction

Class A foam, according to NFPA standards, refers to firefighting foam formulated for Class A combustibles, which are materials sustaining combustion on or below their surfaces, including vegetation, wood, textiles, paper, rubber, and certain plastics. It is typically composed of wet foam, specifically water-based foam solutions [1,2,3]. The dominant extinguishing agent in Class A foam is water, with foam generation relying on specialized surfactants within the solution. Fire suppression mechanisms involve three coordinated actions: (1) liquid-phase cooling through foam drainage retention, (2) oxygen deprivation via cohesive foam blanket formation, and (3) the attenuation of thermal radiation flux [4,5]. Foam degradation begins with gravitational drainage and progresses to structural collapse as reduced stability causes film rupture and bubble coalescence [6]. This phenomenon is mainly caused by Laplace pressure gradients driving gas through bubble membranes, with smaller bubbles shrinking faster due to thermodynamic instability until they collapse via Ostwald ripening [2,7].

Class A foams are formulated with foam-generating compounds and auxiliary solubilizing surfactants, wherein hydrocarbon surfactants constitute the formulation cornerstone. Contemporary fluorocarbon surfactants, notably perfluorooctane sulfonate (PFOS), demonstrate exceptional interfacial activity and thermal resilience. These properties endow fluorinated fire-suppressing formulations with advanced filmogenesis kinetics, spontaneous substrate coverage, flame quenching efficacy, and flashover suppression capacity [8,9,10,11]. PFOS, however, exhibits recalcitrance to both biotic and abiotic degradation as a prototypical organofluorine ecotoxicant. The absence of fluorocarbon surfactants imposes intrinsic limitations in achieving multifunctional performance parameters. This technological impasse necessitates the engineering of advanced fire-suppression colloids through the strategic integration of hydrocarbon-based amphiphiles with zwitterionic co-surfactants in synergistic aqueous systems [12,13,14,15]. The current strategies for replacing fluorocarbon surfactants mainly include the following. The first approach is to replace long-chain fluorocarbon surfactants with short-chain ones (C4–C6). For instance, 3M has introduced a commercially available, eco-friendly foam extinguishing agent formulated with short-chain fluorocarbon surfactants. However, its fire suppression performance is inferior to that of traditional foam extinguishing formulations. In addition, short-chain fluorocarbon surfactants still carry potential environmental and health risks [16,17]. The second strategy is the use of silicone-based surfactants. Studies by Sheng et al. have shown that incorporating silicone surfactants significantly improves both the foaming capacity and foam stability of the blended system [10]. The third approach is to use currently popular bio-based surfactants like rice protein and Gleditsia (soap pod) extracts [18,19]. The fourth strategy involves the formulation of blended systems based on hydrocarbon surfactants. For instance, Jia et al. developed a fluorine-free foam extinguishing agent using a ternary system of Silok8141/SDS/isobutanol, which showed significant cooling and fire suppression effects [20]. In terms of foaming agent performance tests, Zhang et al. observed that blending SDS, alkyl polyglucoside, and sodium dodecylbenzenesulfonate led to superior foaming performance compared to each surfactant used individually [21]. Liu et al. concluded that using long-chain betaine as a stabilizer in a short-chain betaine system imparted viscoelastic surfactant properties to the composite foamer, reducing liquid drainage, strengthening the foam film, and enhancing foam stability via synergistic effects [22]. In investigating the effect of gas type on foam strength and flow behavior in tight carbonates, Alvinda et al. found that zwitterionic surfactants based on amido amine oxide and sulfobetaine exhibited excellent foaming performance under reservoir conditions of 90 °C and 13.8 MPa [23]. Sun et al. demonstrated that multi-surfactant systems outperform single-surfactant systems in foam volume, stability, and surface adsorption, clearly highlighting the benefits of compounding [24].

The addition of an appropriate amount of wetting agent is conducive to improving the fire extinguishing performance of foam fire extinguishing agent for solid fires, especially to make it more effective for solid fires prone to deep fires, such as timber, fabric stacks, etc. Liao et al. compounded SDS with iso-octanol ethoxylated ether (JFC) and found that the solution had excellent wetting ability for coal dusts of different particle sizes, and infrared analyses were performed on the solution, which was attributed to the ability of JFC to significantly increase the proportion of hydrophilic functionality on the surface of coal dust with SDS. JFC and SDS can significantly increase the proportion of hydrophilic functional groups on the surface of coal dust [25]. Zhdanova et al. studied the effect of wettability on fire extinguishing agents and concluded that when extinguishing combustibles of a certain thickness, solutions with lower surface tension penetrate deeper and are more effective in cooling [26]. Foam adhesiveness governs its residence time on combustible surfaces, the uniformity of surface coverage, and the efficacy of secondary flame inhibition. Wang et al. demonstrated that foam formulations with elevated viscosity attach more easily to combustible substrates, decreasing the fuel–air interface and consequently hindering further oxidation of the burning fuel [27]. Nevertheless, foaming ability is strongly controlled by gas–liquid viscosity; in viscous media, bubbles tend to distort, elongate, and fragment into microbubbles during foam generation, and the associated increase in viscosity significantly impairs foamability [28,29].

However, the physicochemical properties alone cannot fully reveal the underlying mechanisms of foam performance. With the development of science and technology, many scholars have introduced molecular dynamics simulations into the study of foam [30,31,32,33]. Molecular dynamics simulations allow us to study the molecular aggregation patterns of surfactants at interfaces from a molecular point of view in order to explain the micro-mechanisms of surfactants [34]. From the perspective of hydrogen bonding, Xiao et al. found that the hydrogen bonding between surfactant molecules and water promotes the adsorption of surfactant at the gas–liquid interface, reduces the interfacial tension, and enhances the foaming ability and stability; at the same time, the stable hydrogen-bonding network structure makes the gas–liquid interface more elastic, which can effectively resist the external interference, reduce the risk of foam rupture, and slow down the bubble merger due to the Marangoni effect [35]. By comparing the interactions and hydrogen bonding numbers of the water–SDS, alkyl glycoside (APG1214)–bituminous coal, and water–bituminous coal systems, Sun et al. found that SDS and APG1214 were more readily adsorbed on the surface of the bituminous coal, with reduced cohesion between water molecules and increased activity compared to water [36]. In summary, numerous fluorine-free foam alternatives have emerged, accompanied by a deeper understanding of foam generation and stabilization mechanisms. However, the aspects of foam wettability and adhesion have received comparatively little attention. It is urgently necessary to design more efficient formulation systems specifically targeting Class A fires by addressing foam wettability and adhesion, employing novel technologies and innovative approaches to expand this field.

In this study, SDS was proposed as the primary foaming agent, with the auxiliary foaming agent, foam stabilizer, wetting agent, and co-solvent listed in

Table 1. Sources and components of experimental materials.

Material	Molecular Formula	Source	Function
Sodium dodecyl sulfate (SDS)	C12H25NaO4S	Tianjin Yongda Chemical Co.	Primary foaming agent
Sodium lauryl ether sulfate (AES)	C16H33SO6Na	Shandong Yusuo Chemical Technology	Auxiliary blowing agent
Lauryl glucoside (APG1214)	C16H32O6	Shandong Yusuo Chemical Technology	Auxiliary blowing agent
Lauryl hydroxy sulfobetaine (LHSB)	C17H37NO4S	Shandong Yusuo Chemical Technology	Foam stabilizing agent
Cocamidopropyl betaine (CAB-35)	C19H38N2O3	Shandong Yusuo Chemical Technology	Foam stabilizing agent
Fatty alcohol polyoxyethylene ether glucoside (AEG050)	(C6H11O5)m (C2H4O)nO C12H25	Shandong Yusuo Chemical Technology	Foam stabilizing agent
Disodium lauryl citrate sulfosuccinate (PEG-5)	C42H76O23S2Na	Shandong Yusuo Chemical Technology	Foam stabilizing agent
Alcohol ethoxylate (AEO)	C26H54O8	Shandong Yusuo Chemical Technology	Wetting agent
Sodium bis(2-ethylhexyl) sulfosuccinate (AOT)	C20H37O7SNa	Jiangsu Haian Petrochemical Plant	Wetting agent
Sodium dodecylbenzene sulfonate (LAS)	C18H29NaO3S	Tianjin Yongda Chemical Co.	Wetting agent
Sodium dioctyl sulfosuccinate (T)	C20H37O7SNa	Shandong Yusuo Chemical Technology	Wetting agent
Ethylene glycol monobutyl ether (BCS)	C6H14O2	Zhengzhou Yinfeng Reagent	cosolvent
Diethylene glycol monobutyl ether (DEBCS)	C8H18O3	Zhengzhou Yinfeng Reagent	cosolvent

. An orthogonal experimental design was adopted to establish the test matrix. Foam concentrates were prepared and diluted with water at a 1:99 ratio to obtain foam solutions, which were subsequently evaluated for foam expansion ratio (foaming capacity), surface tension, viscosity, and wetting time. Formulations exhibiting surface tension ≤ 30.0 mN/m and wetting time ≤ 20.0 s were selected as optimal candidates. A molecular model of the preferred formulation was constructed using Materials Studio 2023 to analyze the radial distribution function (RDF) between surfactants and water molecules, compare the mean square displacement (MSD) of water, and assess hydrogen bonding interactions. The formulation with the best overall performance was then identified based on these molecular-level analyses.

2. Experimental and Methods

2.1. Materials

All chemical reagents were of analytical grade and used as received. Their sources, functions, and molecular formulas are listed in Table 1.

2.2. Formulation of Foam Concentrate

Taking the preparation of 100 g of foam concentrate as an example, the operation of the experimental process is described in the following specific steps. (1) Weigh and add the main blowing agent, auxiliary blowing agent, co-solvent, and 30 g of deionized water into the beaker in turn, and mix thoroughly for 30 min. (2) Weigh the foam stabilizing agent and wetting agent, mix them evenly on the weighing paper, and add them slowly to the beaker, stir for 90 min, and then add the remaining deionized water to a total weight of 100 g and continue stirring for 30 min. (3) Bottle and label the well-mixed foam fire extinguishing agent liquid concentrate for storage. Figure 1 shows a flow chart of the preparation of the liquid concentrate.

Using the orthogonal test method, the chemical components of the main blowing agent, auxiliary blowing agent, foam stabilizing agent, and wetting agent were screened.

Table 2. Orthogonal experimental design for compound formulation of foam concentrate.

	1	2	3	4	5	6
Proportion/%	Primary Foaming Agent (15)	Auxiliary Foaming Agent (5)	Wetting Agent (4)	Foam Stabilizing Agent (5)	Cosolvent (20)	Deionized Water (51)
1#	SDS	AES	AEO	LHSB	BCS	/
2#	SDS	APG12	AOT	CAB35	DEBCS	/
3#	SDS	AES	T	AEG	BCS	/
4#	SDS	APG12	LAS	PEG	DEBCS	/
5#	SDS	AES	AOT	AEG	DEBCS	/
6#	SDS	APG12	AEO	PEG	BCS	/
7#	SDS	AES	LAS	LHSB	DEBCS	/
8#	SDS	APG12	T	CAB35	BCS	/
9#	SDS	AES	T	PEG	DEBCS	/
10#	SDS	APG12	LAS	AEG	BCS	/
11#	SDS	AES	AEO	CAB35	DEBCS	/
12#	SDS	APG12	AOT	LHSB	BCS	/
13#	SDS	AES	LAS	CAB35	BCS	/
14#	SDS	APG12	T	LHSB	DEBCS	/
15#	SDS	AES	AOT	PEG	BCS	/
16#	SDS	APG12	AEO	AEG	DEBCS	/

shows the composition of the proposed 16 groups of foam fire extinguishing agent formulations, and the additions of each substance in the table are in percentage.

2.3. Surface Tension

Tests were carried out using the platinum plate method, and the surface tension of the foam solution of the compounding system was determined using a QBZY-3 fully automatic surface tension meter (from Shanghai Fangrui Instrument Co., Ltd., Shanghai, China). In order to minimize the effect of experimental errors, three measurements were conducted on the fire extinguishing agent formulations, and the average value was taken.

2.4. Viscosity

A DV-1 digital display rotational viscometer was chosen to measure the viscosity of the surfactant-mixed foam solution. The viscosity of the solution to be tested was less than 15 mPa-s, so the rotor selected was No. 0, and the rotational speed was set at 60 rpm. After wetting the rotor and rotor protection frame with the solution to be measured, 20–30 mL of the test solution was added to ensure that the rotor was completely submerged, and the measurement was started. After the reading stabilized, the viscosity value was recorded.

2.5. Wetting Time

The test was carried out using the cotton disc immersion method. Cotton discs were made of 30 mm diameter canvas No. 202. During the test, the immersion clamp was rinsed with a small amount of the foam solution to be measured. The position of the sliding bracket of the planar three-pronged arm on the handle of the submerged clamp was adjusted so that the center of the clamped cotton cloth disc was about 40 mm from the liquid surface. The submerged clamp was opened for about 6 mm so that the cotton cloth disc was kept nearly vertical. The submerged clamp was used to hold the cotton cloth disc and immerse it in the foam solution to be tested. When the lower end of the cloth disc touched the solution, the stopwatch was started immediately, the same planar three-pronged arm was placed on the mouth of the beaker, and the submerged clamp was opened. When the cloth disc started to automatically sink, the stopwatch was stopped. The same foam solution was used to continuously repeat the measurement a total of 10 times, and the arithmetic average of the 10 measurements was taken as the result of the wetting time measurement of the foam solution.

2.6. Foam Multiplier

The standard compressed air jet method was used for testing. The foaming process is shown in Figure 2. The measurement of foaming and foam expansion ratio is as follows. Start the compressed air foam system, and adjust the pressure of the inlet pipe and the pressure-resistant tank pressure to ensure that the foam solution outlet flow rate reaches 11.4 ± 0.4 L/min. Weigh the dialysate tester (m₁): weigh dialysate tester 1 using balance 1, and weigh dialysate tester 2 using balance 2. After spraying foam and reaching stability, place the foam outlet horizontally in front of the foam collector so that the distance from the front end of the foam outlet to the top of the foam collector is 2.5 ± 0.3 m. Spray foam and adjust the height of the foam outlet so that the foam hits the center of the foam collector. After the spraying reaches stability, receive the foam with the dialysate tester 2, scrape the level of the overflowing foam with the dialysate tester, wipe it off, weigh the foam (m₂), and calculate the foam multiplicity F according to the following formula:

$$F=\mathsf{\rho }V\left(m_2-m_1\right)$$

(1)

where F is the foam expansion ratio; ρ is the density of the foam solution in grams per milliliter (g/mL), taken as ρ = 1.0 g/mL; V is the volume of the foam receiving tank in milliliters (mL); m₁ is the mass of the dialyzer in grams (g); and m₂ is the mass of the dialyzer after it is filled with foam, in grams (g).

2.7. MD Simulation Details

Molecular dynamics simulations were carried out using Materials Studio 2023 [37]. Since the COMPASS force field is applicable to organics [36], all studies in this paper are based on the COMPASS force field for computational simulation. The surfactant and water molecules were first subjected to force field assignment, followed by the construction of individual mixed-solution boxes using the Amorphous Cell module [38]. Then, Geometry Optimization and Anneal were performed on the boxes using the Forcite module to obtain the lowest energy and most stable molecular structure configuration. After the optimization was completed, molecular dynamics simulations were carried out under the Dynamics module of Forcite using NPT (1 atm) and NVT system synthesis in turn to ensure that the system entered the calculation stage in thermodynamic equilibrium to obtain reliable statistical results [37]. The specific parameters of the simulations are as follows: the simulation accuracy is medium; charges are set to force field assigned; the simulation method is set to PPPM for electrostatic and atom-based for van der Waals [33]; the thermostat is set to Nosé [34]; the temperature is set to 298 K; the time step is 1 fs; the total simulation duration is 300 ps; and the total number of steps is 300,000 steps.

3. Results and Discussions

3.1. Selection of Critical Foam Components Guided by Physicochemical Parameters

The results of the tests on the foaming multiplicity and various physical property parameters of the 16 groups of compounded foam solutions are presented in

Table 3. Test results of foaming multiplicity and physical property parameters of 1% foam solution.

Group	Foaming Multiplicity	Surface Tension (mN/m)	Viscosity (mPa·s)	Wetting Time (s)
AFFF	2.1	19.81	0.99	/
1#	8.4	29.33	1.5	7.8
2#	4.8	28.37	1.6	14.44
3#	7.3	29.47	1.4	6.62
4#	5.35	31.9	2	9.44
5#	5.6	31.8	1.8	4.97
6#	5.5	32.17	1.6	9.94
7#	5.1	32.2	1.8	6.16
8#	4.74	30.63	1.3	6.62
9#	5.33	32.1	2	4.53
10#	4.6	32.27	1.7	11.97
11#	7.01	31.1	1.8	9.73
12#	4.92	29.73	1.5	5.18
13#	4.3	31.17	1.7	7.06
14#	4.96	30.9	1.86	4.25
15#	5.95	31.17	1.6	8.50
16#	7.8	31.7	1.69	6.69
Average	5.73	31	1.68	7.74

. They are also compared with the relevant physical and chemical properties of AFFF, which is commonly used in the market [39]. It can be seen that the foam expansion ratio of the compounded solutions is much larger than that of AFFF. The foam expansion ratios of 1#, 3#, 11#, and 16# all exceed 7, which shows very strong foaming performance.

In terms of surface tension, the surface tension of the compound solution was basically the same but still significantly higher than that of the AFFF aqueous solution, indicating that the AFFF aqueous solution has higher surface activity. Among them, the 1#, 2#, 3#, and 12# foam solutions meet the requirement of surface tension ≤ 30 mN/m. The viscosities of these four compound solutions were less than the average value of 16 groups of solutions of 1.68. From the table, it can be concluded that the average viscosity of the compounded solution with DEBCS as the co-solvent is 1.82, which is higher than the average value of BCS of 1.54. This means that DEBCS is more suitable to act as a co-solvent for the compounded system.

None of the four compliant foam solutions contained LAS, and the surface tension and viscosity of the LAS-added compounded solutions were higher than the average values. The foaming performance was lower than that of the other compounded solutions. From the comparison of the four solutions that met the requirements, the foaming multiplicities of 2# and 12# with AOT were 4.8 and 4.92, which were lower than the average value, and the foaming performance was not good; the foaming multiplicities of 1# and 3# foam were 8.4 and 7.3, which were much higher than the average value; the foaming multiplicity of 1# foam was larger than that of 3# foam, showing better foaming performance. In terms of wetting time, the wetting time of 3# foam was 6.62 s, slightly stronger than that of 1# foam, at 7.8 s. Therefore, the 1# and 3# foams were selected for further molecular dynamics simulation.

3.2. Molecular Modeling of Key Components in Foam Formulations

The surfactant molecules and water molecules involved in the compounding solution were modeled as follows. The length of the AES carbon chain was taken as 12, and the length of the ethylene oxide chain (EO) was taken as 2; the length of the AEO carbon chain was taken as 12, and the length of EO was taken as 7; and the length of the AEG carbon chain was taken as 12, and the length of EO was taken as 2. For a more intuitive demonstration, orthogonal boxes containing ten active-agent molecules were constructed using the Amorphous Cell module by setting the x-axis and y-axis of the boxes to 40 Å, and the z-axis was not fixed. A cubic box containing 1000 water molecules was constructed. The ball-and-stick model of the modeling result is shown in Figure 3.

To better visualize the synergistic interactions between surfactants, a control group containing only the main foaming agent SDS was introduced and labeled as 0#. Each of the three groups was modeled separately, and the specific modeling details are as follows. Box 0# contained 60 SDS molecules and 3000 H₂O molecules, which was the control group, with a box size of 49.1 × 49.1 × 49.1 Å. Box 1# contained 60 SDS molecules, 10 AES molecules, 10 LHSB molecules, 10 AEO molecules, and 3000 H₂O molecules, with a box size of 51.9 × 51.9 × 51.9 Å. Box 3# contained 60 SDS molecules, 10 AES molecules, 10 AEG molecules, 10 T molecules, and 3000 H₂O molecules, with a box size of 51.8 × 51.8 × 51.8 Å. Molecular dynamics simulations were performed as described above, and the results are shown in Figure 4.

3.3. System Equilibrium Processes

During simulation, variations in temperature and energy over time are generally used as the balance criterion [37]. After the system underwent dynamic simulation in the NPT and NVT ensemble, the resulting density, energy, and temperature curves were determined, as shown in Figure 5, Figure 6 and Figure 7. The density curve from the NPT ensemble simulation increases sharply and stabilizes after 50 ps; fitting the data after 50 ps gives the equilibrium densities, arranged from low to high as 0#1.049 g/cm³, 1#1.056 g/cm³, and 3#1.058 g/cm³. In the NPT ensemble dynamics simulation phase, energy corresponding to the density drops significantly within 50 ps due to model instability, stabilizing around 100 ps. After further optimization in the NVT ensemble, the energy curve decreases slightly, but still converges to a straight line. The system’s temperature exhibits sharp fluctuations only within the first 5 ps, at the system’s initial stage; after 5 ps, the temperature fluctuates between 290 K and 306 K, with the total temperature stabilizing around 298 K. Based on the temperature and energy curves, the system reached an equilibrium state.

3.4. Radial Distribution Function

The degree of aggregation of water molecules and surfactant molecules can be characterized by interatomic RDF. In this study, the degree of diffusion of SDS molecules in water was investigated. Since the hydrophilic group of the SDS molecule is SO4, the SO4 structure in SDS was chosen for RDF calculation with the oxygen atom (O_W) in the water molecule.

The results of the RDF analysis of SO₄ with OW are shown in Figure 8. From the figure, it can be seen that the peaks of all three groups appeared at r = 1.35, and the intensities of the peaks were 2.196, 2.511, and 2.509, respectively. Compared with the 0# solvent without co-propellant, the peak intensities of 1# and 3# increased by 14.3% and 14.2%, which indicates that the interactions between SDS molecules and water molecules in the groups of 1# and 3# were more intense, and it was more likely to form more strongly. This indicates that the interaction between SDS molecules and water molecules is stronger in the 1# and 3# groups, and it is more likely to form stronger hydrogen bonds [40]. The peak intensities of both 1# and 3# are larger than that of the 0# solution with SDS molecules alone, which proves that the co-powdering agent AEG in the compound solution enhances the activation of SDS molecules on water to a certain extent.

3.5. Mean Square Displacement

Mean square displacement (MSD) refers to the average of the squares of the displacements of atoms from their initial positions and can be used to describe the motion of atoms. By calculating the MSD of a water molecule and combining it with the diffusion coefficient (D), it is possible to obtain the diffusion behavior of a water molecule in the presence of a surfactant [37]. The MSD formula is as follows:

$$MSD={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{\left[r_i\left(t\right)-r_i\left(0\right)\right]}^2$$

(2)

D can be calculated from the Einstein equation:

$$D={\displaystyle \frac{1}{6N}}\underset{t\to \infty }{\mathit{lim}}{\displaystyle \frac{d}{dt}}{\sum }_{i=1}^N{\left[r_i\left(t\right)-r_i\left(0\right)\right]}^2$$

(3)

Combining the above equations:

$$D=\underset{n\to \infty }{lim}\left({\displaystyle \frac{MSD}{6t}}\right)={\displaystyle \frac{1}{6}}{K}_M$$

(4)

where N is the number of diffusing molecules, r_i(t) and r_i(0) are the position vectors of the molecules at a certain moment t and at t = 0, respectively, and K_M is the slope of the MSD curve. Therefore, it can be concluded that the diffusion coefficient D is one-sixth of the slope of the MSD curve. Figure 9 shows the MSD curves of the three systems as well as the fitted plots, and the R² of the fitted straight lines are all greater than 0.99. From the fitted curves, it can be seen that the K_M of 0#, 1#, and 3# is 0.77, 0.73, and 0.6, respectively, and it can be calculated that the diffusion coefficients D of the three systems are 0.128 × 10⁻⁸ m²/s, 0.122 × 10⁻⁸ m²/s, and 0.1 × 10⁻⁸ m²/s, respectively. Compared with the diffusion coefficient of 0# water molecules, the diffusion coefficients of 1# and 3# water molecules decreased by 4.7% and 21.9%, respectively. The viscosity of the system increased due to the thickening effect of the foam stabilizers AEO and AEG contained in 1# and 3#, resulting in a decrease in the diffusion coefficient compared with that of the single SDS solution. The diffusion coefficient in the 1# system is larger than that in 3#, and its difference from 0# is smaller, which means that AEO has less of an effect on water diffusion compared with T.

3.6. Hydrogen Bond

Hydrogen bonding is a very strong interatomic electrostatic force that manifests in interatomic interactions and has a large effect at the macroscopic level. As the number of intermolecular hydrogen bonds increases, the electrostatic force increases. There are a large number of hydrogen bonds in water molecules, and the addition of surfactants changes the number of hydrogen bonds between water molecules, which can be indirectly determined by the interactions by calculating the number of hydrogen bonds between molecules in a solution system [41]. In this paper, the results of calculating the number of hydrogen bonds between each surfactant and water molecules using the Calculation Hydrogen Bonds module are shown in

Table 4. Number of hydrogen bonds between each surfactant and water molecules.

Group	Molecules Bonded to H2O	Average Number
0#	H2O	9271
	SDS	960
1#	H2O	8863
	SDS	942
	AES	178
	AEO	138
	LHSB	169
3#	H2O	8951
	SDS	933
	AES	185
	T	150
	AEG	145

.

From the table, it can be seen that compared with 0#, the number of hydrogen bonds between water molecules in the 1# and 3# solutions decreased by 4.4% and 3.5%, respectively, which means that the constructed foam system effectively reduced the interaction force of water molecules and enhanced activity. The decrease in hydrogen bonding between water molecules in 1# is larger than that in 3#, which means that the surface tension of 1# should be smaller than that of 3#. This is in line with the results of the surface tension experiment. The number of hydrogen bonds formed between AEO and water molecules in 1# is 8% lower than that of T molecules in 3#, which indicates that T molecules have better wetting performance in the system with SDS molecules as the main blowing agent, and it is consistent with the results of the wettability experiment.

4. Conclusions

In this study, SDS was used as the main blowing agent, aiming to screen out the foam extinguishing agent constructed from the main blowing agent, auxiliary blowing agent, wetting agent, foam stabilizer, and co-solvent, which was highly efficient in extinguishing Class A fires. The proposed surfactants were divided into 16 groups using the orthogonal test method, and the physicochemical properties as well as the foaming multiplicities of each group were tested, from which two groups of composite systems meeting the requirements were selected. The molecular dynamics simulation of the selected systems was carried out in Materials Studio, and the steady state, RDF of water molecules and SDS molecules, diffusion coefficients of water molecules in each system, and the number of hydrogen bonds between each surfactant and water molecules were analyzed. The experimental and simulation results are as follows:

(1) The foaming performance of the foam system was excellent, but only four groups of experiments met the requirement of surface tension ≤ 30, with 1# and 3# showing the most balanced properties overall.

(2) Compared to the 0# solvent without co-propellant, the RDF peak intensities of 1# and 3# increased by 14.3% and 14.2%, which proved that the auxiliary foaming agent AES in the compound solution enhanced the activation of SDS molecules on water.

(3) The MSD analysis of water molecules showed that the diffusion coefficients of 1# and 3# water molecules decreased by 4.7% and 21.9%. This means that the wetting agent decreases the diffusion coefficient of water, and T in 3# has a greater effect on the diffusion of water compared to AEO in 1#.

(4) The number of hydrogen bonds formed between AEO and water molecules in 1# is 8% worse than that of T molecules in 3#. The wetting performance of T molecules is slightly better than that of AEO molecules.

Taken together, the optimal combination of the foam system was determined as the main blowing agent SDS, the co-blowing agent AES, the wetting agent AEO, the foam stabilizing agent LHSB, and the co-solvent BCS.