Introduction

Membrane processes are one of the most feasible options for water shortage alleviation and water supply augmentation1,2. The essence of membrane science is the process of mass and energy transfer. The key parameters water fluxes Jw, solute fluxes Js and the mass transfer coefficient k can express the mass transfer effect of membrane3,4. However, there is still a lack of energy parameter that can accurately express the energy transfer efficiency. The lack of such key parameters hinders a good understanding of the relationships among membrane operation/performance and energy consumption efficiency.

Researchers have analyzed the relationship between energy conversion efficiency and membrane from various aspects such as electrochemistry, thermodynamics, and external power source5,6,7,8,9, but there is still no parameter that can express the membrane performance by using the energy transfer efficiency. At present, the FO process is considered a low-energy desalination technology by using the current method to calculate the energy consumption10,11,12. But, current researches confirm that the main reason for the lower water flux is the concentration polarization (CP) in the FO process13,14,15. However, CP of energy consumption should not be neglected under FO mode. The main reason for the result is that the current energy principle uses exogenous energy as the total energy. The existence of knowledge gaps makes it impossible to analyze energy consumption using existing formulas, which leads to the inability to scientifically express the energy transfer efficiency of membrane. Therefore, it is important to establish a novel key parameter to express the energy transfer efficiency of the membrane.

Analyzing the energy transfer efficiency of membrane is aimed at saving energy consumption. There are various efforts to reduce energy consumption such as the optimization of monomer16,17, introduction of additives18, thermal post-treatment19 and use of osmotically driven membrane processes [i.e., forward osmosis (FO) and pressure retarded osmosis (PRO)]. Here, how to evaluate a certain modification method of the membrane is a relatively more effective strategy is very important. At present, the evaluation indicators for membrane modification methods mainly focus on such parameters as water permeability A, volumetric flux of water Jv, and structural parameter S20,21,22. But, the evaluated results might be wrong.

When we introduce a set of data and analyze the current evaluation parameters, it is easy to verify why the conclusion might be incorrect. In one example (Method 1), two different types of highly hydrophilic materials such as silica nanoparticles (SiNPs) and zwitterionic polymers were used to modify polyamide thin-film composite membranes23. The value of water permeability, A decreased from 5.778 L/m2-h-bar to 4.556 L/m2-h-bar. In another example (Method 2), amine functionalized multi-walled carbon nanotubes was used as an additive in an aqueous solution of 1,3-phenylendiamine to enhance the FO membrane performance24. The A value was increased from 3.1 ± 0.04 L/m2-h-bar to 4.47 ± 0.24 L/m2-h-bar. These data show that Method 1 has a negative effect on the water permeability, while Method 2 could enhance the water permeability. However, comparing the A values between the two modified can be very confusing or misleading. As far as we know, similar to parameter A, the current membrane parameters are all characterizing parameters that cannot be used to evaluate the improvement in energy consumption and performance of the modified membranes. However, the aforementioned confusing/misleading can be extended to the diverse pristine membranes with different values of the parameters. Hence, there are scientific knowledge gaps: (1) Whether a method has a positive or negative effect on the modification of the membrane performance that cannot be identified by the current parameters; (2) The parameters cannot express how much a modified method can change the membrane performances.

In fact, researchers are more concerned about which the research ideas can be used to achieve the perfect membrane performance. To the best of our knowledge, there is no research that can scientifically guide how to improve membrane performance through data analysis. Researchers need to use an evaluation system to analyze the relative advantages and disadvantages of current modification methods and screen out the research direction with relatively promising development. Finally, researchers need to make a judgment on the research value of self-study modified membrane method through evaluation system. However, when a membrane modification method lacks evaluation system, all modification methods are relatively isolated points. When the research method is independent of other researches, then its scientific significance will be greatly weakened.

In order to fill the key knowledge gaps in the membrane science mentioned above, this article will achieve the following goals: (1) construct a bridge between membrane performance and energy; (2) use an novel evaluation system to evaluate the effect of modification methods on energy transfer efficiency; (3) use data to verify that modifying the support layer is a more effective method than modifying the active layer; and (4) use the evaluation system to provide optimized research routes for future membrane modification methods.

Theoretical framework

The first objective of the study is to establish a new parameter of membrane performance - energy transfer efficiency (φ). The most important concern of membrane science is how much effective energy can remain after a certain amount of initial total energy passes through the membrane. Therefore, we provide the following formula to define this parameter.

$$\varphi =\frac{{E}_{1}}{{E}_{0}}$$
(1)

where, φ as the membrane energy transfer efficiency (φ = E1/E0) to express the energy transformation property of the membrane. E0 is defined as the initial total energy of the fluid. J. E1 is defined as the remaining energy of the fluid after passing through the membrane. Therefore, the following derivation will revolve around how to turn E0 and E1 into measurable and computable parameters, ultimately leading to the numerical expression of φ. The process of derivation of the following formula follows the principle of simple and easy to obtain.

The total energy of a membrane module can be attributed to the total initial pressure that the solution has before it transports across the membrane. The remaining energy after a certain quantity of water (m1) passing through the membrane is the effective energy contained by m1 (e.g., it is available energy for m1 to move through the chamber downstream of the membrane). The initial total pressure ΔP is the sum of the pressure generated by the salt concentration difference and the external pressure. ΔP as the initial total pressure, there are generally three cases: (1) there is both external pressure and the pressure difference caused by salt concentration, and ΔP is the sum of the two; (2) there is only external pressure and the pressure generated by salt concentration difference is zero. In this case, ΔP is equal to external pressure; (3) there is only the pressure caused by salt concentration difference and the external pressure is zero. In this case, ΔP is equal to the external pressure caused by salt concentration.

When a certain pressure is applied to a fluid, a fluid potential energy is generated. When this pressure is equal to the total initial pressure, the corresponding total initial energy generated by the resulting acting fluid is E0, J. Assuming that E0 is the total energy before mass m0 transport across the membrane, the initial total energy could be assumed to be potential energy or kinetic energy. The purpose of the E0 formula is to calculate the value of the initial total energy, so the subsequent research is to obtain its value more effectively and simply.

$${E}_{0}={m}_{0}{gh}=\frac{1}{2}{m}_{0}{v}_{0}^{2}$$
(2)

where m0 is the total mass of water before transporting across the membrane, kg; g is acceleration of gravity, m/s2; h is an imaginary head that makes m0 have an initial total energy of E0, m. Obviously, h corresponds to the total pressure difference (including both mechanical and osmosis pressure) between the two chambers of the membrane; and v0 is the fluid velocity corresponding to the initial kinetic energy, m/s. When water m1 passed through the membrane, the total energy contained by m1 can be determined as:

$${E}_{1}=\frac{1}{2}{m}_{1}{v}_{1}^{2}$$
(3)

where E1 is defined as the effective energy contained by m1, which is essentially the residual energy after m1 across the membrane, J; m1 is the quantity of water transporting across the membrane, kg; and v1 is the permeate water flux (= flow rate) after m1 crossing the membrane, L/m2 h. Under different conditions, E1 will have different formulas to calculate its value. Notice that:

$${m}_{0}={\rm{\rho }}{V}_{0}=\rho {v}_{0}{St}$$
(4)
$${m}_{1}=\rho {V}_{1}=\rho {v}_{1}{St}$$
(5)

where V0 is the total volume of water before crossing the membrane, m3; and V1 is the water volume after m1 crossing the membrane, m3; S is the area of the membrane, m2; and t is time for m1 to pass through the membrane, s. Combining Eqs. (3) and (5) leads to the following equation:

$${E}_{1}=\frac{1}{2}\rho {v}_{1}^{3}{St}$$
(6)

Under salt-free condition, term v1 is AΔP with ΔP (There is only external pressure and the pressure generated by salt concentration difference is zero, ∆P is equal to external pressure). Thus, Eq. 6 becomes:

$${{E}_{1}=E}_{R}=\frac{1}{2}\rho {(A\triangle {\rm{P}})}^{3}{St}$$
(7)

where ER is the effective energy after pure water m1 crosses the membrane under the RO mode, J. Under the FO mode or PRO mode (salt condition), Jv is the water permeability of the FO or PRO system, m/s; thus, we have:

$${{E}_{1}=E}_{F}=\frac{1}{2}{m}_{1}{J}_{v}^{2}=\frac{1}{2}\rho {J}_{v}^{3}{St}$$
(8)

where EF is the effective energy after pure water m1 crossing the membrane under the FO mode or PRO mode, J. Obviously, E0/St, ER/St and EF/St can be considered as energy values per unit area (m2) and per unit time (s), J/m2-s.

Notice that for a membrane system ρgh = ∆P. Thus, from Eq. (1), we have:

$${v}_{0}^{2}=\frac{2\triangle {\rm{P}}}{\rho }$$
(9)

Combining Eqs. (2, 7, and 9), we have:

$${E}_{0}=\frac{1}{2}{m}_{0}{v}_{0}^{2}={m}_{0}\frac{\triangle {\rm{P}}}{\rho }=\rho {v}_{0}{St}\frac{\triangle {\rm{P}}}{\rho }=\triangle {\rm{P}}\sqrt{\frac{2\triangle {\rm{P}}}{\rho }}{St}$$
(10)

The energy transfer efficiency of the membrane is the more energy that can be transferred through the membrane, the better the membrane performance in terms of the energy transfer efficiency. Therefore, the energy transfer efficiency of membrane is determined by the key parameters: E0 and E1. Let’s define a parameter, φ as the membrane energy transfer efficiency (φ = E1/E0) to express the energy transformation property of the membrane. By combining Eqs. (5) and (9), φ can be expressed as follows:

$$\varphi =\frac{{E}_{1}}{{E}_{0}}=\frac{\frac{1}{2}\rho {v}_{1}^{3}{St}}{\triangle {\rm{P}}{St}\sqrt{\frac{2\triangle {\rm{P}}}{\rho }}}=\frac{{\rho }^{\frac{3}{2}}{v}_{1}^{3}}{{2}^{\frac{3}{2}}{\triangle {\rm{P}}}^{\frac{3}{2}}}$$
(11)

The parameters involved in this equation are all measurable and calculable; thus, this equation provides sufficient information about the membrane energy transfer efficiency. This parameter φ is the basic parameter of this paper, and parameters such as E0 and E1 are used to effectively obtain the value of parameter φ. Therefore, the derivation direction of these formulas is practical, measurable and computable. Now, let’s analyze the numerical change of parameter φ under the RO, FO, or PRO mode. Under the RO mode (v1 = A), Eq. (11) becomes:

$${\rm{\varphi }}={\varphi }_{R}=\frac{{{v}_{1}^{3}\rho }^{\frac{3}{2}}}{{{2}^{\frac{3}{2}}\triangle {\rm{P}}}^{\frac{3}{2}}}=\frac{{\rho }^{\frac{3}{2}}{A}^{3}}{{{2}^{\frac{3}{2}}\triangle {\rm{P}}}^{\frac{3}{2}}}$$
(12)

where \({\varphi }_{R}\) is the membrane energy transfer efficiency under the RO mode. Under the FO (\({v}_{1}={J}_{v}\)) or PRO mode (\({v}_{1}={J}_{v}\)), we have:

$${\rm{\varphi }}={\varphi }_{F}={\varphi }_{P}=\frac{\frac{1}{2}{m}_{1}{v}_{1}^{2}}{\frac{1}{2}{m}_{0}{v}_{0}^{2}}=\frac{{\rho }^{\frac{3}{2}}{J}_{v}^{3}}{{2}^{\frac{3}{2}}{\triangle {\rm{P}}}^{\frac{3}{2}}}$$
(13)

When the initial reference points of the two membrane processes are different, it is difficult (or even impossible) to use the existing parameters in the current literatures to evaluate which method improves the membrane performance more effectively. The initial benchmark values must be consistent (or at least transformable) when comparing the effects of different methods on the performance of the modified membranes. Therefore, in this study, we propose a new parameter θ –the energy transfer efficiency ratio– to compare the effective energy of the modified membrane with that of the pristine membrane as follows:

$$\theta =\frac{{E}_{1m}}{{E}_{1p}}=\frac{\frac{1}{2}{m}_{1m}{v}_{1m}^{2}}{\frac{1}{2}{m}_{1P}{v}_{1P}^{2}}=\frac{\rho {v}_{1m}{St}}{\rho {v}_{1P}{St}}\times {(\frac{{v}_{1m}}{{v}_{1P}})}^{2}={\left(\frac{{v}_{1m}}{{v}_{1P}}\right)}^{3}{or}\theta =\frac{{E}_{1m}}{{E}_{1P}}=\frac{\frac{{E}_{1m}}{{E}_{0}}}{\frac{{E}_{1P}}{{E}_{0}}}=\frac{{\varphi }_{1m}}{{\varphi }_{1P}}$$
(14)

where E1m and E1P are the effective energy of the modified and pristine membrane, respectively, J ; v1m and v1p are the permeate water flux after crossing the modified and pristine membrane, respectively, m/s; \({\varphi }_{1m}\) and \({\varphi }_{1P}\) are the membrane energy coefficient of the modified and pristine membrane, respectively, unitless. Under the same initial process conditions, the value of the modified membrane parameter v1p and the value of the pristine membrane parameter v1m could be measured. Here, as long as we can measure the values of these two parameters, then we can obtain the value of the evaluation system θ. The definable conditions of parameters v1m and v1p determine the applicable range of parameter θ. However, the measurement of the two parameters is not conditionally limited. Hence, this novel evaluation system θ could be applicable to any type of water treatment membrane (MF, UF, RO etc).

Under the RO mode, we have:

$$\theta ={\theta }_{R}=\frac{{E}_{1m}}{{E}_{1P}}={(\frac{{A}_{m}}{{A}_{P}})}^{3}$$
(15)

where θR is the energy transfer efficiency ratio under the RO mode; and Am and AP are the water permeability of the modified and pristine membrane, respectively, m3/m2-s-bar. Under FO or PRO mode, we have:

$$\theta ={\theta }_{F}={\theta }_{P}=\frac{{E}_{1m}}{{E}_{1P}}={(\frac{{J}_{{vm}}}{{J}_{{vP}}})}^{3}$$
(16)

where θF and θP are the energy transfer efficiency ratios of the FO and PRO mode, respectively; and Jvm and JvP are the water permeability of the modified and pristine membrane, respectively, m/s. The derivation process of the above formula accords with the basic fluid dynamics equations25.

Results and discussion

Energy transfer efficiency of membranes with different structures and operational modes

From Table 1, the similarity and difference between energy expression parameter φ and current parameters A and Jv for different conventional membranes and modes are analyzed. Parameters A and Jv are similar to the energy parameter φ to express the membrane performances. The larger the values of A, Jv and φ are, the better the membrane performance is. As shown in Columns 3 A and 6 A, Parameters A and φ represent the same sequence of membrane performance from good to bad: Asymmetric TFC hollow fiber > Positively charged hollow fiber > doubled-skinned flat-sheet membrane > TFC hollow fiber > TFC flat-sheet membrane and commercial asymmetric flat-sheet membrane > Symmetric flat-sheet membrane. The parameter φ shows the same trend of change as A and Jv do. For instance, under FO or PRO mode, the commercial asymmetric flat-sheet membrane (Jv = 18.30 L/m2 h, φF = 4.368 × 10−23 or φP = 3.408 × 10−22) has a better membrane performance than the TFC flat-sheet membrane (Jv = 15.79 L/m2 h, φF = 2.905 × 10−23 or φP = 1.967 × 10−22), while the φR and A values of the two membranes were the same under the RO mode (Table 1). Hence, the membrane performance can be expressed by the energy transfer efficiency, but under different process conditions, the values of the energy transfer efficiency will be different.

Table 1 Membrane energy transfer efficiency coefficients affected by different membrane structures and operational modes
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However, parameter φ has its own unique function. Parameter φ, as an energy expression parameter, can reflect the relationship between different membranes and energy. In the absence of salt, the φR values of conventional membranes range from 9.892 × 10−27 to 2.245 × 10−21. Under the FO or PRO mode, the range for parameter φF/P is still very low (2.540 × 10−24 ～ 5.020 × 10−22). These results demonstrate that the energy consumption of the membrane is huge. Thus, it is very important to find ways to improve the energy transfer efficiency and to establish an evaluation system for the methods of modifying the membrane.

In this study, the energy transfer efficiency is calculated by analyzing two key parameters instead of building a conventional model. First, let’s analyze the knowledge bottleneck existing in conventional research. This kind of research mainly through the establishment of theoretical model, analysis of the energy consumption of the membrane, calculation of energy transfer efficiency. The core problem in establishing this theoretical model is that the membrane structure is complicated, which makes it impossible to describe the specific fluid mass transfer route. The main idea to solve this research is to simplify the model through theoretical assumptions and use exogenous energy consumption as the energy consumption of the membrane. The theory assumes a simplified model, which causes the theoretical model to be far away from the internal structure of the actual membrane, such as the two typical theories of mass transfer theory—the solution-diffusion model and the pore flow model26,27,28,29. One theory assumes that the membrane has no pores and is homogeneous, while the other assumes that the pores in the membrane are square. Hence, the energy consumption using such models is not only due to the large difference between the internal resistance structure of the membrane and the actual situation, but also because different models will have different results, so the final energy transfer efficiency of the membrane is not of universal practical significance. When researchers use exogenous energy consumption to analyze energy consumption, they ignore the salt concentration difference with large energy (Table 1). Due to the complex structure of membrane, the energy theory of membrane is still a black-box nature. Therefore, there are still some key knowledge gaps in the analysis of fluid energy transfer efficiency by conventional methods.

However, the present study uses two key parameters E0 and E1 to calculate the energy transfer efficiency value, which effectively avoids the above drawbacks. The values of the two parameters are independent of the energy transfer process. Therefore, the energy transfer efficiency calculated by this method is independent of how and in what form the energy is transferred. Because only the residual energy of the fluid after passing the membrane is the effective energy, the fluid energy that the fluid bounces back from the membrane and the energy that remains in the membrane are invalid energy. When the initial total energy is determined, the remaining energy of fluid is the larger, and the energy transfer efficiency of the membrane is the higher. The method developed in this study for calculating energy transfer efficiency is not only simple and practical, but also universal because the values of this parameter can be calculated via measurable data, making the method be objectivity and reliable.

Using energy parameters to evaluate the effects of modifying membranes’ active layers

There is rapid growth in studying FO membranes30,31,32 and FO-based applications33,34,35,36,37,38,39,40,41. The FO membrane includes two layers-an active layer and a support layer. Significant efforts have been made to improve the active layer by focusing on: surface hydrophobicity42,43, membranes pore structure44, internal concentrative concentration polarization45, surface roughness46 and pore size distribution47. So far, the modified membranes are evaluated on the basis of water/salt permeability coefficients; limited information is available on how the modifications would affect energy transfer efficiency of the membranes. Herein, we found that modifying the characteristics of the active layer with different strategies (four shown in Table 2) may affect the energy parameters (φ and θ) under the RO, FO, and PRO mode. Below, parameters φ and θ use the data to show the influence of the modified activated layer on the energy transfer efficiency.

Table 2 Energy parameters affected modifying the active layer of the membranes and operational modes
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There are two kinds of modification methods for expression parameters evaluation: (1) Evaluation of different methods for modifying the properties of the same membrane; (2) Evaluation of the different methods for modifying the properties of the different membranes. In the first case, using the current parameter evaluation will not produce wrong conclusions, which are consistent with the evaluation results of the evaluation system. Fixed the pristine membrane, the values of all parameters (A, Jv, φ and θ) are in the same order from small to large. (Table 2). For example, when the initial membrane is TFC2 (control), the A value rises from 3.1 ± 0.04 L/m2 h bar to 4.47 ± 0.24 L/m2 h bar, the corresponding θR increases from 2.214 × 10−22 to 6.620 × 10−22, and when Jv increases from 11.43 L/m2 h to 32.8 L/m2 h, the corresponding θF rises from 1 to 23.76, and the corresponding θP rises from 1 to 12.84.

In the second case, the results of modification methods evaluated by expression parameters (A, Jv and φ) apparent parameters and evaluation parameter (θ) are quite different. Under RO mode, the φR and A values of the modified membranes have the following order: TFC4−3 > TFC1-1 and TFC1-2 > TFN 2-3 > TFC3-3 > TFN5-3, and the θ of the modified membranes have the other following order: TFC3-3 (39.68) > TFN5-3 (11.80) > TFC4-3 (4.184) > TFN 2-3 (2.990) > TFC1-1 (0.4902) and TFC1-2 (0.4902); Under FO mode, the φR values of the modified performance of membranes from the best to the worst were as follows: TFC3-3 > TFN2-3 > TFN5-3 > TFC4-3, and the θ values of the modified membranes from large to small were as follows: TFC3-3 (23.76) > TFN5-3 (6.785) > TFC4-3 (3.980) > TFN2-3(2.974); Under PRO mode, the φP values from high to low were as follows: TFN2-3 > TFC3-3 > TFC4-3 > TFN5-3, and the θ values of the modified membranes from high to low were as follows: TFN 2-3 (17.84) > TFC3-3 (12.84) > TFC4-3 (5.136) > TFN5-3 (3.279). What are the reasons for this? Is it related to the inability of expression parameters to evaluate the modification method?

The following takes the evaluation result of parameter A as an example: in Method 1, two additional different types of highly hydrophilic materials (i.e., silica nanoparticles (SiNPs) and zwitterionic polymers) can modify polyamide thin-film composite membranes23. The A value was decreased 5.778 L/m2 h bar to 4.556 L/m2 h bar; in Method 2, amine functionalized multi-walled carbon nanotubes were used as additive in aqueous solution of 1,3-phenylendiamine to enhance the FO membranes performance48. The A value increased from 1.12 L/m2 h bar to 3.82 L/m2 h bar. These data show that method 1 has a negative impact on the parameter A, while method 2 has a positive impact on the parameter A. However, up comparing the value of parameter A of method 1 and the value of parameter A of method 2 of the modified membrane, it is interesting note the wrong conclusion regarding utilization of parameter A. Hence, the result demonstrates that the current parameters are unable to evaluate membrane modification methods.

It is well-known that the performances of the different pristine membranes are different (i.e., inconsistent). Thus, only after removing the influences of the different pristine membranes can eliminate the error. Therefore, the evaluation system takes the energy transfer efficiency of different pristine membranes as the denominator, and the energy transfer efficiency of different modified membranes as the numerator, and calculates the values. Using the energy transfer efficiency ratio of the pristine membrane θ as a benchmark, the criteria can be established as follows: (1) for the modification of a single membrane: if θ = 1, no improvement; if θ < 1, a negative improvement; and if θ > 1, a positive improvement effect on the energy transfer efficiency of the membrane; (2) for comparison between different modification methods: a larger θ value indicates more improvement. Therefore, parameter θ can be used as an evaluation system to analyze the influence of different methods on the energy transfer efficiency.

The maximum energy transfer efficiency of the modified activation layer can reach 39.68 times of that of the pristine membrane, while the minimum energy transfer efficiency of the modified activation layer is only 0.4902 times. These results show that modified activation layer is an effective way to reduce energy consumption, but there is still a lot of room for improvement.

Using energy parameters to evaluate the effects of modifying membranes’ supporting layers

Various studies have been explored to optimize the support layers by incorporating hydrophilic polymer49, inorganic nano-particles50,51, pore forming agents52,53 into the membrane substrate, or by altering the coagulation bath during the membrane formation54, and so on. However, these two knowledge gaps remain in the research as follows: (1) how much influence do the modified support layers have on the energy consumption of the membranes; (2) what is the energy transfer efficiency of the support layers modified by different strategies?

Analyzing the impact on the energy transfer efficiency of the same pristine membrane, the trends of the characterization parameter (e.g., A, Jv and φ) and evaluation parameter (θ) are consistent (Tables 2, 3). The differences between Tables 3, 2 are analyzed below.

Table 3 Energy parameters affected modifying the support layer of the membranes and operational modes
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Table 3 shows that the energy transfer efficiency is effectively improved by modifying the supporting layer in the RO mode, FO mode, and PRO mode. By comparing the data in Tables 2, 3, it is shown digitally for the first time that the modified support layer has greater potential to improve the energy transfer efficiency of the membrane than the modified active layer. The maximum θ values of the influence of the modified activation layer on the energy transfer efficiency in the RO mode, FO mode, and PRO mode are 39.68, 23.76 and 17.84, respectively (Table 2). The maximum θ values of the modified support layer are 1.969 × 104, 3.278 × 104, and 1.652 × 104 in the RO mode, FO mode, and PRO mode, respectively. The results further prove that the support layer has more influence on the fluid transfer than the active layer54. Therefore, these results indicate that the modified support layer has greater potential to improve the energy transfer efficiency of the membrane than the modified activation layer.

Using energy parameters to evaluate the effects of modifying membranes’ single factor or structure

For a long time, it has been recognized that modifying the structure of the membranes would mitigate internal concentration polarization (ICP). However, up to now, it is often difficult to evaluate the relative effectiveness of these methods because different strategies were used to modify these membranes due to different structure and chemical properties of the pristine membranes. For example, the value of the structural parameter S is a direct indicator of the ICP55,56,57, which can be determined by using the classical ICP model developed before58. However, simply comparing the Sc values among different methods (Table 4), it would be difficult for one to determine the effectiveness of different modification methods on the membrane properties. As shown in Table 4 and Fig. 1, the relationships among Sc and the energy transfer efficiency of modified membranes can be evaluated, for the first time, via the two energy parameters. Taking the modified membrane parameter S as the numerator and the pristine membrane parameter Sc as the denominator, the change rate of the ratio S/Sc and the regression equations are as follows: (1) hydroxyl functionalized polytriazole-co-polyoxadiazolecopolymers is optimal for promising porous substrates (Fig. 1A: y = 0.9147x−1.862, R2 = 0.9752 under the FO mode; y = 0.8744x−1.179, R2 = 0.9467 under the PRO mode); (2) CaCO3 nanoparticles dispersed in PSf matrix were effectively etched with hydrochloric acid to increase the substrate porosity (Fig. 1B: y = 0.9518 x−2.655, R2 = 0.9981 under the FO mode; y = 1.0558 x−2.717, R2 = 0.9962 under PRO mode); (3) the modified polyvinylidene fluoride high porosity and large amounts of surface membrane pores were prepared with zinc oxide nanoparticles (Fig. 1C: y = 0.9438 x−2.024, R2 = 0.9948 under FO mode; y = 0.8744 x−1.179, R2 = 0.9238 under PRO mode); (4) the modified nanofiber exhibited slightly higher structural parameter than the pre-wetted thin composite membrane (Fig. 1D: y = 1.0016 x−1.747, R2 = 0.9999 under FO mode; y = 0.9976 x−0.455, R2 = 0.9971 under PRO mode); and (5) the addition of disulfonated poly (arylene ethersulfone) hydrophilic-hydrophobic multiblock copolymer in the polysufone substrates enhance hydrophilicity and porosity of membrane (Fig. 1E: y = 0.9348x−1.405, R2 = 0.9072 under FO mode; y = 0.9295x−2.349, R2 = 0.9588 under PRO mode). Therefore, the results show that the model can be unified as θ = a(S/SC)b with a being about 1 and b being negative. The result of reducing ICP by reducing the value of structural parameter S could enhance the membrane energy transfer efficiency, which is consistent with previous studies59,60. Table 4 shows that using the two energy parameters can easily compare the results obtained from different studies. Of the five different modification methods, membranes using nano-CaCO3 particles as sacrificial component has the largest θ and with a steepest improvement in the φ value (Table 4), demonstrating that the method may be the best to mitigate ICP phenomenon among the five methods.

Table 4 Energy parameters affected by structural parameters
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Fig. 1: The relationship between S/Sc and θ for mitigating ICP phenomenon with different methods under FO mode () or PRO mode (▲).
figure 1

(A) In situ mineralization56; (B) chemical-etching57; (C) chemical-etching58; (D) surface modification72; and (E) blending hydrophilic components73.

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Moreover, φ and /or θ can be used to analyze the impact of changing a single factor on the energy transfer efficiency. Figure 2 shows the relationships between the concentration of incorporated nanoparticle and the membranes’ energy transfer efficiency coefficients φ. Adding different nanomaterials can lead to different models (improvement) for φ. Through these models, it is possible to digitally analyze how much the additional nanoparticles. Therefore, these equations indicate the relationship between the physical and chemical properties of membrane and the energy transfer efficiency of the membrane, which opens a window to study how to reduce energy consumption by improving the physical and chemical parameters of the membrane.

Fig. 2: Established formulas to reveal the relationship between nanoparticle concentration and the membrane energy transfer efficiency coefficient under RO (), FO (▲) or PRO mode ().
figure 2

A F-MWCNTs24; (B) NH2-TNTs48; and (C) HNTS69.

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Implications

Herein, the parameter θ has been evaluated under the three modes. However, it could have a wider range of applications. As long as a method affects the fluid (gas, water, and organic phases, etc.) flow rate out of the membrane, which can be evaluated by θ. Under direct contact membrane distillation (DCMD) mode, as shown in Table 5, parameter θ evaluates the optimal method independent of membrane performance. The conclusion further confirms that it is unscientific to screen the optimal method by membrane performance.

Table 5 Parameter θ affected by the modified DCMD performance
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Scientific data alone is often meaningless, and its value needs to be assessed in a system. θ is as an evaluation parameter, which is the link for establishing the comparison of modified methods. The main function of parameter θ as an evaluation parameter is reflected in two aspects: (1) analyze the effect of the modified method on the energy transfer efficiency and its superiority compared with other modified methods; (2) by analyzing the differences of multiple modification strategies, one can identify the future research directions with reasonable theoretical support. The content of the article on how parameters are evaluated for modification methods has been discussed earlier. The following content uses the parameter θ to analyze a series of modified methods for improving the membrane performances, and gives a reasonable scientific research direction. The scientific research should be to choose the research direction with relatively comparative advantages from the big aspects. Furthermore, the shortcomings of researches are looked for from a small aspect, and the advantages of other researches are learned from to supplement its shortcomings. In the following, the parameter θ was utilized to evaluate the modified methods, and give an optimal research direction.

Under the FO /PRO/RO mode, θ as an evaluation parameter analyzes the completely different laws shown by the data, and its difference represents its irreplaceability and new theoretical direction (Table 6). Surprisingly, the data clearly shows the relatively advantageous of several research directions as follows: (1) the modified support layer could be more conducive to improving the energy conversion efficiency than the modified active layer. For example, the maximum θ values of the modified support layer and the modified active layer is 3.278 × 104 (Table 3) and is 39.68 (Table 2), respectively; (2) modifying the structure of the membrane often gives a much higher θ value (The modified structure θ = 39.68, The modified surface hydrophilicity θ = 2.990), and thus, could be the more efficient way to improve the energy transfer efficiency than the modified properties; and (3) the synergistic effect of multiple strategies is better than a single strategy, but the difference is not significant.

Table 6 Influence of modification methods on the energy transfer efficiency ratio
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When the research focuses on the point, we need to analyze the deficiencies of different modification methods and find technical routes for improvement. Pore size is an important characteristic of membrane morphology. Herein, the effect of pore size change on parameter θ was analyzed as shown in Table 7. Firstly, it is the most conventional law that the energy transfer efficiency of membranes with larger pore size increases. Secondly, basic materials play a crucial role in energy transfer efficiency, such as graphene oxide as a new type of membrane material. A nanostrand-channelled graphene oxide ultrafiltration membrane with gold nanoparticles has a best performance of energy transfer efficiency at Table 7. But, the use of metal nanoparticles is not an effective method to improve energy transfer efficiency of a membrane. In Table 7, two more effective methods are provided for us: Method 1 is the supramolecular interaction facilitated block copolymer assembly technology; Method 2 is to enhance the membrane surface porosity and unify membrane pore distribution technology. When designing the modified method obtains an efficient energy transfer of membrane, we can choose to use the above two methods to optimize the membrane pores on the basis that the membrane material is graphene oxide. Here, the provision of this optimization research idea does not indicate a certain feasibility of the operation. Therefore, when there are certain obstacles in the implementation of this route, this parameter θ can be further used to find more optimal research ideas. The more θ values are introduced here, the clearer the relatively scientific direction and the more reasonable research ideas introduced by science can be considered. However, this is a function that the current parameters do not have on the analysis modification method.

Table 7 Parameter θ affected by the modified pore size
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Further studies are needed on the effect of different characteristics of the membrane on the energy transfer efficiency. Indeed, the new energy parameters will offer new tools to answer some important questions.

Hence, the study focuses on the key knowledge gaps in membrane science: (1) there is no parameter to construct the relationship between membrane performance and energy consumption; (2) The lack of evaluation system for modification methods leads to relatively isolated research on modification methods. Therefore, φ, as a novel energy parameter, is established to express the membrane performance, which shows that the energy transfer efficiency of membrane is about 10−23. The expression of φ on the membrane performances is similar to other similar parameters, such as A, Jw, k, etc., but it is expressed from an energy perspective. Based on this, a novel system can digitally evaluate the multiple times that each method improves the energy transfer efficiency of the modified membrane compared to the energy transfer efficiency of the pristine membrane. The system θ was used to analyze the modification methods of the membranes, and it was concluded that the most effective modification method can improve the energy transfer efficiency of the modified membrane to 3.278 × 104 times that of the pristine membrane. However, this still indicates that membrane modification methods need further research to find new optimization strategies. This novel evaluation system θ can compare the influence of different modification methods on the energy transfer efficiency of membranes, and provide data guidance for the optimization route of modification methods in the future. This study not only solves the key knowledge holes existing in membrane science, but also has a good guiding value for the application of membrane science.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.