The Organic Rankine Cycle (ORC) systems [1,2] employ the organic working fluid as an energy carrier, facilitating the transformation of low-grade thermal energy into high-grade electrical energy. The ORC system presents numerous advantages, such as a straightforward design, ease of maintenance, high safety, and environmental sustainability. ORC technology [3] is based on the principles of the Rankine cycle, utilizing organic substances with low boiling points as the working fluid. The lower boiling points of these organic compounds enable their heating via low-temperature heat sources, facilitating the generation of high-pressure steam for the expansion machine to perform work, ultimately leading to power output. Different from the traditional water vapor Rankine cycle power generation technology, ORC technology can mainly be applied to medium and low temperature heat source conditions. In the ORC, the working fluid functions as a thermal carrier and is pivotal in influencing the efficacy of the the variable temperature heat source [4]. The choice of working fluid in ORC systems is one of the critical and significant issues investigated by researchers and scholars.

Hydrocarbons (HC), hydrofluorocarbons (HFC), hydrochlorofluorocarbons (HCFC), and chlorofluorocarbons (CFC) are potential working fluids suitable for ORC systems [5]. In the selection of an appropriate working fluid, it is crucial to prioritize not only the achievement of high cycle efficiency within the ORC system but to address considerations related to environmental protection and safety. Recent research has extensively examined the physical property parameters of ORC systems. However, in response to increasingly stringent environmental protection standards, the international community has designated R113 and R11 refrigerants previously employed in the initial phases of ORC development as phased out working substances. This decision is attributed to their high global warming potential (GWP) and ozone depletion potential (ODP), despite their favorable energy conversion efficiency [6,7]. In alignment with the amendments stipulated in the Montreal Protocol, developed nations have pledged to phase out refrigerants possessing high global warming potential within the period from 2019 to 2036 [8]. As a result, a new generation of working fluids, known as the fourth generation, has been developed. This includes compounds such as R1233zd(E) and R1336mzz(Z) [9,10], which are intended to replace hydrofluorocarbon (HFC) fluids.

Traditionally, experimental data on the thermal physical properties of working fluids are recorded or plotted in thermodynamic properties diagrams or tables for query. With the development of computers, experimental data on the physical properties of working fluid are fitted using computers according to the developed physical properties model formula. Where, some of the fluid physical property models have been developed specifically for one or some fluids, such as the IAPWS-95 [11] and IAPWS-IF97 [12] formulas for water and water vapor, and the GERG-2004 [13] and GERG-2008 [14] formula for natural gas mixtures. Some are developed for multiple or one class of fluids, such as Helmholtz energy equation of state and Modified Benedict-Webb-Rubin (MBWR) state equation [15,16], etc. These thermophysical property models have been developed into computer software, among which the more popular ones include NIST REFPROP [17,18], CoolProp [19] and Helmholtzmedia [20], etc. The use of working mass physical properties calculation and query software to obtain working mass physical properties is the most widely used method in the industry. Take the Helmholtz energy equation of state as an example, which is established using two binary functions, whose the two independent variables are independent state parameters: temperature and density; two dependent variables are non-dimension ideal gas construction Helmholtz energy and non-dimension residual contribution to Helmholtz energy. All thermodynamic property parameters can be obtained by the analytic derivatives of these two dependent variables. In practice, temperature and density are selected as their non-dimensional relative values to the critical temperature and critical density. This method fits the Helmholtz energy function entirely on the basis of experimental data, focusing on the macroscopic experimental data fitting, without the study of microscopic particles, and can not predict the thermal physical property parameters of the new working medium. Accordingly, the Helmholtz energy equation of state for R1336mzz(Z) [21] has been developed and applied to the NIST REFPROP. This is the most mature and accurate model for calculating the thermal physical properties of R1336mzz(Z) in industry. Furthermore, molecular dynamics (MD) simulations are also frequently employed to investigate the thermophysical properties of refrigerants. Although the quantum thermodynamic microscopic nature of temperature is not well defined, molecular dynamics gives a classical thermodynamic definition of temperature at the microscopic scale. The 26th General Conference on Weights and Measures (CGPM, Conférence Générale des Poids et Mesures) held by the Bureau International des Poids et Mesures (BIPM) in 2018 revised the International System of Units (SI, Système International d’Unités) [22], in which the Boltzmann constant was defined as a fixed value, establishing a fixed relationship between temperature and energy, and the dimension of temperature was derived from energy. Therefore, the relationship between the dynamic energy of microscopic molecules and the macroscopic temperature is fixed and clear. This definition clarified the microscopic nature of temperature in classical thermodynamics and improved the theoretical basis of molecular dynamics. In classical physics, molecular dynamics can link the microscopic motion of molecules with the macroscopic thermodynamic properties, and the study of the microscopic motion of molecules is helpful to predict the macroscopic thermophysical properties of new organic working fluids. Khan et al. [23] use dynamics simulation to study the macroscopic thermodynamic properties of R1336mzz(Z), and the simulation results were compared with NIST REFPROP. The results were almost identical, which also proved that molecular dynamics simulation is a quite accurate and mature method to study R1336mzz(Z) fluid.

R1336mzz(Z) [24] exhibits an Ozone Depletion Potential (ODP) of 0, a Global Warming Potential (GWP) of merely 2, is non-combustible, and demonstrates excellent compatibility with commonly utilized lubricating oils. It is considered one of the most promising working fluids for ORC applications, garnering significant scholarly attention [9,24] Molés et al. [25] conducted comparative experiments between R245fa and the novel working fluid R1336mzz(Z) within an ORC system. The findings indicated that the system employing R1336mzz(Z) achieved a higher thermal efficiency than the system using R245fa, with efficiency improvements ranging from −0.3% to 17%. Li et al. [26] and Tanaka et al. [27] conducted in-depth studies on the saturated vapor pressure and density of R1336mzz(Z), respectively. Other physical parameters, such as critical temperature [28], viscosity [29], and thermal conductivity [30], have been investigated experimentally. In a study by Hu et al. [31], MD simulations were utilized to examine the energy storage characteristics of refrigerants, specifically R1234yf, in conjunction with metal-organic framework (MOF) nanoparticles. This research underscores the utility of molecular dynamics in analyzing both physical and thermodynamic properties. The homogeneous condensation, thermal properties, and structural characteristics of R450A, R513A, and R515A were examined utilizing the MD method [32,33]. In contrast, the majority of research concerning the physical properties of R1336mzz(Z) has primarily concentrated on experimental measurements, with a significant paucity of studies analyzing its physical property parameters at the nanoscale.

The thermal physical properties of the working fluid are recognized as critical prerequisites for its processing. In ORC systems, the lubricating oil inevitably interacts with the refrigerant, resulting in notable alterations to the thermal physical properties of refrigerant upon mixing, which subsequently impacts system performance [34,35]. Consequently, it is imperative to investigate the interactions between HFC refrigerants, such as R1336mzz(Z) and lubricating oil. Polyol Ester Oil (POE) [36] is one of the most extensively utilized lubricants in refrigeration and heat pump systems, primarily due to its remarkable thermal stability and lubricative properties. POE demonstrates compatibility with a variety of refrigerants characterized by low GWP. POE lubricants have high temperature stability, high lubricity, economic friendliness, and is widely used in engine and low temperature heat engine mechanical structure lubrication. Lubricants are used in heat engines to lubricate mechanical structures. The working fluid in the ORC expands and does work in the turbine, and is condensed by the pump pressure back to the high pressure state, while the lubricant is the lubrication of the mechanical structure, and the working fluid is inevitably mixed with the lubricating oil in every link. The fundamental composition of POE comprises polyols and ester compounds synthesized from organic acids, with polyols functioning as the principal constituents of POE oil. Pentaerythritol esters (PEC) are the most frequently used polyols, extensively applied in lubricants for refrigeration and air conditioning systems due to their superior lubrication properties and thermal stability [37].

This study aims to bridge the existing research gap concerning the interaction mechanisms between the fourth-generation refrigerant R1336mzz(Z) and lubricating oil at the nanoscale by utilizing molecular dynamic simulation to explore the interactions between R1336mzz(Z) and PEC. Additionally, it examines the variations in physical properties within pure R1336mzz(Z) and the mixed system of R1336mzz(Z)/PEC. The findings provide theoretical support for the application and optimal design of R1336mzz(Z) in practical ORC systems.

All molecular simulations were conducted using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package [38,39]. Figs. 1 and 2 depict the molecular structures of R1336mzz(Z) and PEC, with PEC serving as the primary component of the POE. ORC systems working condition necessitates that OPE exhibits both high thermal stability and low volatility. Although longer PEC chains generally confer enhanced thermal stability and reduced volatility, they also tend to exhibit decreased solubility [40]. Consequently, for this simulation, PEC with medium-long chain lengths was selected. Medium-long chain PEC are typically characterized by ester side chains containing between six and ten carbon atoms. Within this range, PECs exhibit an optimal balance of properties, offering effective lubrication performance while maintaining appropriate viscosity and thermal stability [41]. As shown in Fig. 2, we select PEC9 with the number of ester side chain C atoms of 9. We use CVFF force fields [42] for refrigerant R1336mzz(Z) and PEC9. The interaction between the atoms is described by the Lennard-Jones 12-6 potential as Formula (1).(1)E=4ε((εr)12−(σr)6)where, ε and σ represent the characteristic energy and van der Waals radius, respectively. The detailed parameters of the LJ potential of each atom are shown in Table 1. The arithmetic combining rule is adopted for the interaction parameters between atoms. In addition, the cutoff for the electrostatic part of the potential and the van der Waals force is 10.0 Å. The long-distance electrostatic force and van der Waals interactions are treated by the particle-particle-particle-grid (PPPM) [43] method with a RMS accuracy of 10−4.

In the first part of the work, the pure refrigerant R1336mzz(Z) was simulated. As shown in Fig. 3a, we build a simulation box containing 2250 R1336mzz(Z) molecules that have periodic boundary changes in the x, y and z directions. Under the initial conditions, all 2250 molecules are arranged repeatedly in a simple cubic structure with an initial velocity of zero. At the beginning of the simulation, the software directly changes the molecular velocity until a specified equilibrium temperature is reached. First, the pure R1336mzz(Z) system is preliminarily equilibrated under the NVT ensemble (constant N, constant V, constant T), and the molecular dynamics process of 500ps is performed at 270, 300, 330, and 360K, respectively. Subsequently, a 3ns system equilibrium process was carried out under the NPT ensemble (constant N, constant P, constant T). The NVT ensemble holds the volume of the simulation box constant until equilibrium is reached. The NPT ensemble continuously adjusts the volume of the simulation box to achieve the specified equilibrium pressure. The temperature is 270, 300, 330, 360 K, and its pressure is set to the saturation pressure at these four simulated temperatures. After the system reaches equilibrium, the relevant parameters are statistically measured within 500 ps, such as radial distribution function (RDF), mean square displacement (MSD), diffusion coefficient. In this simulation system, the timestep is set to 1 fs.

In the second part of the work, in order to reveal the mechanism of interaction between R1336 and lubricating oil, we mixed 8 and 18 PEC9 in 2250 R1336mzz(Z) moleculars systems respectively, to form two mixing systems with different lubricating oil content. This mixing system is shown in Fig. 3b. The same temperature and pressure as the pure R1336mzz(Z) system were simulated. Each system first relaxes 500 ps under the NVT ensemble, then reaches equilibrium within 3 ns simulation time under the NPT ensemble, the timestep of the first 1 ns simulation is 0.1 fs, and the timestep of the second 2 ns simulation is 1 fs, and finally performs data acquisition through the dynamic process of 500 ps.

First, In this section, the simulated density is compared with the date of NIST REFPROP to verify the correctness of the model. Second, the molecular interaction mechanism of R1336mzz(Z) and PEC9 is discussed from four aspects: radial distribution function, mean azimuth-shift, diffusion coefficient, binding energy and solubility parameter. The effect of the addition of PEC9 on the diffusion of R1336mzz(Z) and the change of compatibility between the two at different temperatures were analyzed. This provides a theoretical basis for compatibility between refrigerants and lubricants.

In this study, the interaction mechanism between the fourth-generation refrigerant R1336mzz(Z) and PEC, the principal component of lubricating oil, was investigated using molecular dynamics simulations. Specifically, PEC with a chain length of nine (PEC9) was selected for analysis. The parameters, including the RDF of relevant atomic pairs, MSD, diffusion coefficient, binding energy, and solubility parameter were calculated. A comparative analysis of the diffusion coefficients of R1336mzz(Z) in both pure and mixing systems was conducted. The findings indicate that the incorporation of PEC9 impedes the diffusion of the refrigerant. Furthermore, an analysis was conducted on the variations in binding energy and solubility parameters between the refrigerant and PEC9 across different mixing systems. The findings indicate that the binding energy of the mixed system containing a higher concentration of PEC9 polymer chains is greater than that of systems with fewer polymer chains. Additionally, the binding energy decreases as the temperature rises. The analysis of solubility parameter differences reveals that this difference increases with rising temperature, and the results also indicate that compatibility deteriorates as the PEC9 content increases.

Based on the mechanism of microscopic molecular interaction, the macroscopic thermodynamic parameters such as molar heat capacity at constant volume, molar heat capacity at constant pressure, compression factor and thermodynamic energy can be calculated by molecular dynamics method in future studies. Compared with direct experiments, this is a faster and quite accurate method to obtain hydrodynamic parameters for new mixed working fluids that are not included in physical property calculation software or not developed by traditional thermodynamic property calculation models. Additionally, it is helpful to optimize the efficiency and power of ORC to analyze the thermodynamic properties of the phase transition process of the mixed working medium. The thermodynamic properties of non-azeotropic mixtures used in ORC can also be predicted by molecular dynamics method. The choice of mixing medium in ORC is an important factor affecting its performance. It is a promising innovation direction to combine molecular dynamics prediction of working medium physical properties with ORC thermal cycle simulation. This enables the development of a mature mixture selection scheme for optimizing ORC.