QSPR models for predicting the adsorption capacity for microplastics of polyethylene, polypropylene and polystyrene

Abstract

Microplastics have become an emerging concerned global environmental pollution problem. Their strong adsorption towards the coexisting organic pollutants can cause additional environmental risks. Therefore, the adsorption capacity and mechanisms are necessary information for the comprehensive environmental assessments of both microplastics and organic pollutants. To overcome the lack of adsorption information, five quantitative structure–property relationship (QSPR) models were developed for predicting the microplastic/water partition coefficients (log K_d) of organics between polyethylene/seawater, polyethylene/freshwater, polyethylene/pure water, polypropylene/seawater, and polystyrene/seawater. All the QSPR models show good fitting ability (R² = 0.811–0.939), predictive ability (Q²_ext = 0.835–0.910, RMSE_ext = 0.369–0.752), and robustness (Q_cv² = 0.882–0.957). They can be used to predict the K_d values of organic pollutants (such as polychlorinated biphenyls, chlorobenzene, polycyclic aromatic hydrocarbons, antibiotics perfluorinated compounds, etc.) under different pH conditions. The hydrophobic interaction has been indicated as an important mechanism for the adsorption of organic pollutants to microplastics. In sea waters, the role of hydrogen bond interaction in adsorption is considerable. For polystyrene, π–π interaction contributes to the partitioning. The developed models can be used to quickly estimate the adsorption capacity of organic pollutants on microplastics in different types of water, providing necessary information for ecological risk studies of microplastics.

Introduction

Microplastics, defined as plastics with particle size < 5 mm, have become one of the most prominent global environmental pollution problems^1,2. They may originate directly from industrial and personal products, or from the degradation of large-size plastics³. For environmental management, we can ban the direct sources of microplastics to a certain extent. However, the wide application of plastic products in daily life makes hundreds of millions of tons of plastic waste, which definitely become the precursors of microplastics, be discharged into the environment each year⁴. As a result, microplastics have been detected in waste water^5,6, natural water^7,8, and even in drinking water⁹. At present, the pollution of microplastics has become a persistent environmental problem that needs to be urgently addressed. Therefore, comprehensive and accurate assessment of their environmental risks (e.g., environmental behavior and ecotoxicity) is particularly important for developing effective environmental policies.

Previous studies proved that the large specific surface area makes microplastics show high adsorption capacity to the coexisting organic pollutants, such as polycyclic aromatic hydrocarbons¹⁰, polychlorinated biphenyls¹¹, etc. Some ionizable organic pollutants (e.g., antibiotics) also can be adsorbed on microplastics¹². The adsorption interaction may further alter the behavior and toxicity of both microplastics and organic pollutants, such as inevitably change the distribution of organic pollutants between the environmental phase and the microplastic phase¹³, or affect the structures and properties of microplastics and organic pollutants and subsequently affect their environmental transformations. More importantly, more organic pollutants can be carried by microplastics into organisms because of the adsorption, which may increase the bioconcentration of chemicals and cause increased toxicity^14,15. Thus, quantitative measurement of the adsorption for organic pollutions on microplastics is necessary for assessing the environmental risk of both microplastics and organic pollutants in a more comprehensive and accurate way.

Generally, equilibrium partitioning coefficient of organic pollutants between microplastics and water (K_d) is used to represent the adsorption capacity. It can be determined through adsorption equilibrium experiment¹¹. Previous studies^12,16 indicate that the composition and property of both microplastics and water environment media can affect the determined K_d value. Thus, the specific environmental condition should be considered for measuring the K_d values, which will greatly increase the amount of experimental work. However, the present research on microplastics is still in its infancy, and the adsorption data is scarce, which will certainly limit their further research on microplastics and their risk assessment. Therefore, there is an urgent need for a fast and accurate method to obtain the K_d values at different adsorption conditions.

Quantitative structure–property relationship (QSPR) has been proved to be reliable for quickly predicting the properties of chemicals^17,18. Especially, the polyparameter linear free energy relationship (pp-LFER) models based on Abraham descriptors were widely employed to predict the partitioning of chemicals between two phases and explore the partition mechanisms^19,20. For example, many researchers predicted the adsorption capacity of polymers with large size (e.g., used for equilibrium passive samplers) based on pp-LFER²¹. However, the large difference in polymer size may limit the application of these already developed models to the prediction of the adsorption capacity for microplastics^22–24. A few studies established pp-LFER models of log K_d under corresponding experimental conditions based on their measured experimental values^25–27. While, the lack of experimental values of Abraham descriptors for many nonpolar chemicals will affect the construction and application of pp-LFER model^20,28. In order to expand the application range, different descriptors that can be theoretically calculated (e.g., quantum chemical descriptors²⁹) may be selected to build the K_d prediction models. In addition, some ionizable organics such as antibiotics can also be adsorbed by microplastics. The distribution of dissociation species varies under different pH conditions, which will lead to different apparent K_d values. Thus, the molecular dissociation under certain pH values should be involved in the development of QSPR predictive models.

In this study, we thus collected K_d values for the three most frequently detected microplastics, including polyethylene (PE), polypropylene (PP) and polystyrene (PS) in different waters, and employed the n-octanol/water distribution coefficient at special pH condition (log D), and six quantum chemical descriptors to establish new QSPR models. The main purpose is to develop a more practical computational method that can quickly predict the adsorption capacity of microplastics towards organic pollutants in water environments with different pH values.

Results and discussion

QSPR models for the adsorption of PE

Three QSPR models of log K_d were developed for the adsorption of PE in seawater, freshwater and pure water, respectively:

$$\begin{array}{cc}\hfill \text{Seawater:}log{K}_{\text{d}}& =\left(0.725\pm 0.058\right)\times logD+\left(-36.236\pm 9.034\right)\times {\epsilon }_{\alpha }\hfill \\ \hfill & +\left(-23.169\pm 4.501\right)\times {\epsilon }_{\beta }+\left(17.856\pm 2.572\right)\hfill \\ \hfill \end{array}$$ 1

$$\text{Freshwater:}log{K}_{\text{d}}=\left(0.667\pm 0.047\right)\times logD+\left(1.714\pm 0.302\right)$$ 2

$$\text{Pure}\text{water:}log{K}_{\text{d}}=\left(0.449\pm 0.041\right)\times logD+\left(0.265\pm 0.115\right)\times M_{\text{w}}^{\prime }+\left(1.855\pm 0.302\right)$$ 3

where log D is the n-octanol/water distribution coefficient at special pH value, ε_α is the covalent acidity, ε_β is the covalent basicity and M′_w is the relative molecular mass. As shown in Williams plot for model (3) (Fig. S1 of the Supplementary Information, S1), 17α-ethinyl estradiol obtained an absolute SR value (− 3.392) larger than 3 and it was diagnosed as an outlier. Structural analysis showed that 17α-ethinyl estradiol is significantly different from other compounds due to its acetylene group and steroidal ring (unsaturated benzene ring connects with saturated six-membered ring). Such discrepancy may be the main cause of predictive inaccuracy. After removing it, the following model was yielded:

$$\text{Pure}\text{water:}log{K}_{\text{d}}=\left(0.486\pm 0.035\right)\times logD+\left(2.420\pm 0.199\right)$$ 4

The statistical parameters of the developed QSPR models are presented in Table 1. For the models (1), (2) and (4), R² = 0.868, 0.903 and 0.811, Q² = 0.868, 0.903 and 0.811, and RMSE = 0.826, 0.686 and 0.612, respectively. The statistical results indicate that the models have high goodness-of-fit. As shown in Table S1, all the VIF values (1.000–1.204) are less than 10, indicating there is no multicollinearity for the three models. The fitting plots (Fig. 1) state a good consistence between the experimental and predicted log K_d values. As shown in Fig. 2, the distributions of predictive errors show no dependence on experimental log K_d values. Thus, the developed models have no systematic error, which is also proved by BIAS = 0.000–0.001 (Table 1).

Table 1.

Statistical parameters of the regression models and simulated external validation.

	N	R2	Q2	RMSE	BIAS	MAE	MPE	MNE
Model (1)	37	0.868	0.868	0.826	0.000	0.695	1.643	− 1.678
Training set	26	0.857	0.857	0.880	0.000	0.748	1.634	− 1.437
Test set	11	0.902	0.892	0.752	− 0.102	0.664	1.230	− 1.074
Model (2)	24	0.903	0.903	0.686	0.000	0.502	1.044	− 1.983
Training set	17	0.896	0.896	0.732	0.000	0.511	1.059	− 1.895
Test set	7	0.947	0.910	0.661	0.036	0.467	0.970	− 0.998
Model (3)	48	0.800	0.800	0.641	0.000	0.463	2.175	− 1.801
Model (4)	47	0.811	0.811	0.612	0.001	0.470	1.469	− 1.721
Training set	33	0.804	0.804	0.671	0.000	0.522	1.442	− 1.671
Test set	14	0.854	0.835	0.471	− 0.081	0.3838	0.953	− 0.536
Model (5)	35	0.939	0.939	0.381	− 0.003	0.282	1.069	− 0.706
Training set	25	0.945	0.945	0.396	0.000	0.307	0.968	− 0.697
Test set	10	0.898	0.874	0.369	0.047	0.228	0.792	− 0.646
Model (6)	28	0.837	0.837	0.791	0.000	0.634	1.703	− 1.610
Training set	20	0.829	0.829	0.853	0.000	0.669	1.585	− 1.593
Test set	8	0.859	0.843	0.714	0.092	0.654	0.903	− 0.697

Figure 1.

Fitting plots of experimental and predicted log K_d by models (1), (2) and (4).

Figure 2.

Distributions of prediction errors of log K_d calculated by models (1), (2) and (4).

For the simulated external validation, the redeveloped QSPR models (S1–S3) based on 70% experimental data and the same descriptors in model (1), (2) and (4) show similar fitting performance (including R², Q², RMSE and MAE) and regression coefficients with the models developed by the whole dataset (Table 1). Thus, the models are statistically stable. As the training subsets are randomly assigned, there is no casual correlation. The predictive performance of each rebuilt model to the test set (30% subset, shown by the superscript of b in Table 2) are listed in Table 1. The values of Q², RMSE and MAE indicate excellent predictive quality of the developed QSPR models. The results of leave-one-out cross validation (Q²_CV = 0.882–0.940) also show a good robustness and internal predictivity.

Table 2.

Experimental and predicted log K_d values of organic compounds and the values of the selected molecular descriptors in models (1), (2), (4), (5) and (6).

No	Organic compounds	Log Kd a		Log D	εα	εβ	π	Refs
		Exp.	Pred.
For the adsorption of PE in seawater
1	2,4,4′-trichlorobiphenylb	6.150	5.490	5.690	0.252	0.317		11
2	2,4′,5-trichlorobiphenyl	6.000	5.473	5.690	0.251	0.321		11
3	2,2′,3,5′-tetrachlorobiphenyl	5.890	5.444	6.340	0.259	0.329		11
4	2,2′,5,5′-tetrachlorobiphenyl	5.900	5.497	6.340	0.257	0.329		11
5	2,4,4′,5-tetrachlorobiphenyl	6.660	6.112	6.340	0.246	0.321		11
6	2,3′,4,4′-tetrachlorobiphenylb	6.690	6.048	6.340	0.247	0.322		11
7	2,2′,4,5,6′-pentachlorobiphenyl	6.190	6.160	6.980	0.248	0.336		11
8	2,3,3′,4,4′-pentachlorobiphenylb	6.970	6.561	6.980	0.243	0.325		11
9	2,3′,4,4′,5-pentachlorobiphenyl	7.000	6.634	6.980	0.242	0.324		11
10	3,3′,4,4′,5-pentachlorobiphenyl	7.780	6.920	6.980	0.235	0.322		11
11	3,3′,4,4′,5,5′-hexachlorobiphenyl	8.840	7.450	7.620	0.231	0.327		11
12	2,2′,3,4′,5,6-hexachlorobiphenyl	6.790	6.624	7.620	0.248	0.336		11
13	2,2′,3,4,4′,5′-hexachlorobiphenylb	7.250	6.686	7.620	0.246	0.335		11
14	2,2′,4,4′,5,5′-hexachlorobiphenylb	7.650	6.682	7.620	0.248	0.334		11
15	2,3,3′,4,4′,5-hexachlorobiphenyl	7.860	7.135	7.620	0.238	0.329		11
16	2,2′,3,3′,4,4′,5-heptachlorobiphenyl	7.940	7.137	8.270	0.245	0.338		11
17	2,2′,3,4,4′,5,5′-heptachlorobiphenyl	7.940	7.271	8.270	0.243	0.335		11
18	Dichlorodiphenyltrichloroethaneb	4.986	5.534	5.440	0.238	0.330		32
19	Pentachlorobenzene	5.220	4.876	5.220	0.246	0.339		33
20	Hexachlorobenzene	4.630	5.669	5.860	0.234	0.344		33
21	Phenanthreneb	4.440	4.999	4.350	0.254	0.294		33
22	Fluoranthene	5.520	6.403	4.930	0.226	0.296		33
23	Anthracene	4.770	6.275	4.350	0.230	0.276		33
24	Pyreneb	5.570	6.413	4.930	0.236	0.279		33
25	Chrysene	6.390	6.398	5.520	0.243	0.287		33
26	Benzoapyrene	7.170	7.800	6.110	0.226	0.271		33
27	Dibenzanthraceneb	7.870	7.645	6.700	0.235	0.283		33
28	Benzo[g,h,i]perylene	7.610	8.656	6.700	0.230	0.246		33
29	Pentadecafluorooctanoic acid	2.695	2.673	4.000	0.307	0.300		13
30	Dioctyl phthalate	4.993	6.636	8.390	0.283	0.305		13
31	Trimethoprim	0.811	1.500	0.730	0.280	0.291		12
32	Sulfadiazineb	0.797	0.424	− 1.510	0.275	0.274		12
33	Oxytetracycline	0.623	− 1.055	− 5.590	0.245	0.258		34
34	α-Hexachlorocyclohexane	2.410	2.797	4.260	0.254	0.386		33
35	β-Hexachlorocyclohexane	2.040	3.512	4.260	0.237	0.382		33
36	γ-Hexachlorocyclohexane	2.330	2.879	4.260	0.257	0.378		33
37	δ-Hexachlorocyclohexaneb	2.080	3.175	4.260	0.244	0.386		33
For the adsorption of PE in freshwater
38	2,4,4′-trichlorobiphenyl	5.350	5.509	5.690				11
39	2,4′,5-trichlorobiphenyl	5.110	5.509	5.690				11
40	2,2′,3,5′-tetrachlorobiphenyl	4.920	5.943	6.340				11
41	2,2′,5,5′-tetrachlorobiphenylb	5.010	5.943	6.340				11
42	2,4,4′,5-tetrachlorobiphenylb	5.890	5.943	6.340				11
43	2,3′,4,4′-tetrachlorobiphenyl	6.170	5.943	6.340				11
44	3,3′,4,4′-tetrachlorobiphenyl	6.620	5.943	6.340				35
45	2,2′,4,5,6′-pentachlorobiphenyl	5.610	6.370	6.980				11
46	2,3,3′,4,4′-pentachlorobiphenyl	6.350	6.370	6.980				11
47	2,3′,4,4′,5-pentachlorobiphenyl	6.360	6.370	6.980				11
48	3,3′,4,4′,5-pentachlorobiphenylb	6.940	6.370	6.980				11
49	3,3′,4,4′,5,5′-hexachlorobiphenyl	8.780	6.797	7.620				11
50	2,2′,3,4′,5,6-hexachlorobiphenyl	6.180	6.797	7.620				11
51	2,2′,3,4,4′,5′-hexachlorobiphenylb	6.890	6.797	7.620				11
52	2,2′,4,4′,5,5′-hexachlorobiphenyl	7.040	6.797	7.620				11
53	2,3,3′,4,4′,5-hexachlorobiphenyl	7.170	6.797	7.620				11
54	2,2′,3,4,4′,5-hexachlorobiphenyl	6.920	6.797	7.620				35
55	2,2′,3,4′,5′,6-hexachlorobiphenylb	6.240	6.797	7.620				35
56	2,2′,3,3′,4,4′,5-heptachlorobiphenylb	7.290	7.230	8.270				11
57	2,2′,3,4,4′,5,5′-heptachlorobiphenyl	7.390	7.230	8.270				11
58	Ciprofloxacin	1.741	0.914	− 1.200				12
59	Trimethoprim	0.923	1.967	0.380				12
60	Sulfadiazine	0.792	1.234	− 0.720				12
61	Amoxicillinb	0.924	0.240	− 2.210				12
For the adsorption of PE in pure water
62	2,2′,5-trichlorobiphenylb	4.900	5.185	5.690				36
63	2,4,4′-trichlorobiphenyl	5.400	5.185	5.690				36
64	2,4′,5-trichlorobiphenyl	5.301	5.185	5.690				37
65	2,2′,4,4′-tetrachlorobiphenyl	5.083	5.501	6.340				37
66	2,2′,5,5′-tetrachlorobiphenyl	5.500	5.501	6.340				36
67	2,2′,3,5-tetrachlorobiphenyl	5.500	5.501	6.340				36
68	2,3′,4,4′-tetrachlorobiphenylb	5.900	5.501	6.340				36
69	2,2′,4,5,5′-pentachlorobiphenyl	6.200	5.812	6.980				36
70	2,3,3′,4′,6-pentachlorobiphenylb	6.100	5.812	6.980				36
71	2,3′,4,4′,5-pentachlorobiphenyl	6.400	5.812	6.980				36
72	2,3,3′,4,4′-pentachlorobiphenyl	6.300	5.812	6.980				36
73	2,2′,4,5′,6-pentachlorobiphenylb	5.019	5.812	6.980				37
74	2,2′,4,4′,5,5′-hexachlorobiphenylb	6.400	6.123	7.620				36
75	2,2′,3,4,4′,5′-hexachlorobiphenyl	6.600	6.123	7.620				36
76	2,2′,3,3′,4,5-hexachlorobiphenylb	6.600	6.123	7.620				36
77	2,2′,3,3′,4,4′-hexachlorobiphenyl	6.500	6.123	7.620				36
78	2,2′,3,4′,5,5′,6-heptachlorobiphenyl	7.100	6.439	8.270				36
79	2,2′,3,4,4′,5,5′-heptachlorobiphenylb	7.000	6.439	8.270				36
80	2,2′,3,3′,4,4′,5-heptachlorobiphenyl	6.900	6.439	8.270				36
81	Chlorobenzeneb	3.080	3.703	2.640				30
82	Benzene	2.190	3.387	1.990				30
83	Toluene	2.910	3.654	2.540				30
84	Ethyl benzoate	2.810	3.548	2.320				30
85	Naphthaleneb	3.770	3.961	3.170				30
86	2-Methylanthracene	5.000	4.797	4.890				36
87	1-methylphenanthrene	4.700	4.797	4.890				36
88	9,10-Dimethylanthraceneb	5.300	5.064	5.440				36
89	3,6-dimethylphenanthrene	5.200	5.064	5.440				36
90	Phenanthrene	4.300	4.534	4.350				36
91	Anthracene	4.300	4.534	4.350				36
92	Oxytetracycline	1.176	− 0.068	− 5.120				34
93	Phenylalanine	3.519	1.798	− 1.280				38
94	Cyclohexane	3.880	3.965	3.180				30
95	Hexane	4.500	4.019	3.290				30
96	Carbamazepineb	2.281	3.514	2.250				39
97	3-(4-methylbenzylidene)camphor	4.726	5.297	5.920				39
98	Triclosanb	3.711	4.685	4.660				39
99	Sulfamethoxazole	2.845	2.653	0.480				40
100	Propanololb	3.362	3.684	2.600				40
101	Sertraline	3.522	4.991	5.290				40
102	p,p'-DDT	5.590	5.720	6.790				41
103	o,p'-DDT	5.760	5.720	6.790				41
104	p,p'-DDD	4.890	5.273	5.870				41
105	o,p'-DDD	4.940	5.273	5.870				41
106	p,p'-DDE	5.770	5.336	6.000				41
107	o,p'-DDE	5.620	5.336	6.000				41
108	p,p'-DDMUb	5.370	5.093	5.500				41
For the adsorption of PP in seawater
109	2,3-dichlorobiphenylb	4.980	4.332	5.050		0.321		13
110	2,4′-dichlorobiphenyl	4.980	4.411	5.050		0.317		13
111	2,4,4′-trichlorobiohenyl	5.090	4.873	5.690		0.317		13
112	2,2′,5,5′-tetrachlorobiphenyl	5.090	5.137	6.340		0.329		13
113	2,2′,3,5′-tetrachlorobiphenyl	5.140	5.133	6.340		0.329		13
114	3,3′,4,4′-tetrachlorobiphenyl	5.630	5.358	6.340		0.318		13
115	2,3′,4,4-tetrachlorobiphenyl	5.260	5.277	6.340		0.322		13
116	2,3′,4,4′,5-pentachlorobiphenylb	5.710	5.708	6.980		0.324		13
117	2,3,3′,4,4′-pentachlorobiphenylb	5.770	5.690	6.980		0.325		13
118	2,2′,3,4′,5-pentachlorobiphenyl	5.510	5.526	6.980		0.334		13
119	2,2′,3,5′,6-pentachlorobiphenylb	5.260	5.577	6.980		0.331		13
120	2,3,3′,4′,6-pentachlorobiphenyl	5.630	5.538	6.980		0.333		13
121	2,2′,4,5,5′-pentachlorobiphenylb	5.510	5.594	6.980		0.330		13
122	2,2′,3,3′,4,6′-hexachlorobiphenylb	6.190	5.994	7.620		0.335		13
123	2,3,3′,4,5,6-hexachlorobiphenylb	6.060	5.993	7.620		0.335		13
124	2,2′,4,4′,5,5′-hexachlorobiphenyl	6.190	6.013	7.620		0.334		13
125	2,2′,3,4,4′,5-hexachlorobiphenyl	5.770	5.977	7.620		0.335		13
126	2,2′,3,3′,4,4′-hexachlorobiphenyl	5.450	5.930	7.620		0.338		13
127	2,2′,3,4′,5,5′,6-heptachlorobiphenylb	5.730	6.448	8.270		0.336		13
128	Pentachlorobenzene	4.500	4.098	5.220		0.339		33
129	Hexachlorobenzene	5.010	4.489	5.860		0.344		33
130	Phenanthrene	4.000	4.314	4.350		0.294		33
131	Fluorantheneb	4.790	4.720	4.930		0.296		33
132	Anthracene	4.290	4.678	4.350		0.276		33
133	Pyrene	4.800	5.038	4.930		0.279		33
134	Chrysene	5.510	5.344	5.520		0.287		33
135	Benzoapyrene	6.100	6.079	6.110		0.271		33
136	Dibenz[a,h]anthracene	7.000	6.294	6.700		0.283		33
137	Benzo[g,h,i]perylene	6.690	7.006	6.700		0.246		33
138	Trimethoprim	0.594	1.663	0.730		0.291		12
139	Sulfadiazine	0.853	0.299	− 1.510		0.274		12
140	α-Hexachlorocyclohexane	2.690	2.474	4.260		0.386		33
141	β-Hexachlorocyclohexane	2.180	2.554	4.260		0.382		33
142	γ-Hexachlorocyclohexaneb	2.580	2.633	4.260		0.378		33
143	δ-Hexachlorocyclohexane	2.230	2.483	4.260		0.386		33
For the adsorption of PS in seawater
144	Pentachlorobenzene	5.100	4.070	5.220			1.138	33
145	Hexachlorobenzeneb	5.280	4.545	5.860			1.204	33
146	Phenanthrene	5.390	5.190	4.350			1.518	33
147	Fluorantheneb	5.910	5.528	4.930			1.553	33
148	Anthracene	5.610	5.560	4.350			1.616	33
149	Pyrene	5.840	6.437	4.930			1.794	33
150	Chryseneb	6.630	6.146	5.520			1.661	33
151	Benzo[a]pyrene	6.920	7.347	6.110			1.924	33
152	Dibenz[a,h]anthracene	7.520	7.267	6.700			1.847	33
153	Benzo[g,h,i]perylene	7.150	5.540	6.700			1.388	33
154	4-Fluorobenzoic acid	2.134	1.771	− 0.940			1.112	16
155	Trimethoprim	0.863	2.566	0.730			1.164	12
156	Sulfadiazine	0.833	1.874	− 1.510			1.193	12
157	α-Hexachlorocyclohexane	3.190	3.297	4.260			1.024	33
158	β-Hexachlorocyclohexaneb	2.630	3.515	4.260			1.082	33
159	γ-Hexachlorocyclohexane	3.010	3.416	4.260			1.056	33
160	δ-Hexachlorocyclohexane	2.800	3.221	4.260			1.004	33
161	Perfluoropentanoic acid	2.432	0.835	1.540			0.628	16
162	Perfluorohexanoic acidb	1.760	1.181	2.220			0.655	16
163	Perfluoroheptanoic acid	1.731	1.492	3.110			0.654	16
164	Perfluorodecanoic acid	2.669	2.480	5.780			0.663	16
165	Pentadecafluorooctanoic acid	3.220	2.055	4.000			0.719	16
166	Heptadecafluorooctanesulfonamide	2.147	2.963	5.800			0.789	16
167	Perfluoro-1-octanesulfonyl fluorideb	2.792	3.233	6.890			0.758	16
168	Perfluoroundecanoic acid	2.752	2.992	6.670			0.715	16
169	Perfluorododecanoic acidb	2.720	3.308	7.550			0.715	16
170	Pentacosafluorotridecanoic acidb	3.162	3.558	8.440			0.697	16
171	Perfluorotetradecanoic acid	3.088	3.904	9.330			0.704	16

^aThe unit of K_d is kg/L; ^b The compounds used for test subset in simulated external validation.

Williams plots were employed to test the application domain of the QSPR models (1), (2) and (4). The calculated alert value h^* are 0.324, 0.250 and 0. 128, respectively. As shown in Fig. 3, there are three (oxytetracycline, sulfadiazine and δ-hexachlorocyclohexane), and one (2,2′,3,3′,4,4′,5-heptachlorobiphenyl) compounds located at the right side of h^* for models (1) and (4), respectively. As their absolute SR values are < 3, these chemicals are not diagnosed to be outliers. In summary, these results indicate the developed QSPR models have excellent generalization capabilities in their descriptor matrix. Given the molecular structures for developing models, QSPR model (1) can be used to predict the log K_d values of organics including polychlorinated biphenyls, antibiotics, polycyclic aromatic hydrocarbons, chlorobenzenes, perfluorinated compounds and hexachlorocyclohexanes between PE and sea water; model (2) can be employed for predicting the log K_d values of polychlorinated biphenyls and antibiotics between PE and fresh water; model (4) can be performed to predict the adsorption of PE in pure water towards organic pollutants such as polychlorinated biphenyls, antibiotics, polycyclic aromatic hydrocarbons, chlorobenzenes, aromatic hydrocarbons and aliphatic hydrocarbons.

Figure 3.

Williams plots for the applicability domain of models (1), (2) and (4). The h_i refers to the verse leverage value. (a) oxytetracycline; (b) sulfadiazine; (c) δ-hexachlorocyclohexane; (d) 2,2′,3,3′,4,4′,5-heptachlorobiphenyl.

The n-octanol/water distribution coefficient at special pH value (log D) was selected for all the three log K_d predictive models for PE in seawater, freshwater and pure water. The experimental log K_d values significantly correlate with log D, which yields positive correlation coefficients (0.725, 0.667 and 0.486) in models (1), (2) and (4). Thus, the organic pollutants with high hydrophobicity will prefer to be adsorbed onto the PE. For example, hydrophobic polychlorinated biphenyls (PCBs) with large log D values exhibit higher log K_d values than ionizable organic pollutants (e.g., antibiotics). This is because the hydrophobicity of PE itself makes hydrophobic interaction as the main mechanism in the adsorption of PE towards organic pollutants. The same adsorption mechanism was also confirmed by Hüffer et al. who established prediction model based on the log K_ow values of seven organic compounds³⁰.

For the adsorption of PE in seawater, ε_α and ε_β, which respectively represents covalent acidity and covalent basicity, were also selected. The quantum chemical descriptor of ε_α shows a negative contribution to the log K_d values, suggesting that organic pollutant with large ε_α value prefers to dissolve in water, leading to a decrease in log K_d. That means the surface of PE has a weaker H-accepting ability to organic pollutants than water at the adsorption interface³¹. Similarly, the log K_d values increase with decreasing ε_β, indicating that the H-donating ability of the PE surface is also weaker than water. It follows that hydrogen bond interaction is also an important mechanism for the interactions between PE and organic pollutants in sea water.

Compared with fresh water and pure water, the high salinity of seawater can enhance the dipole–dipole and dipole–induced dipole interactions in the system, which can make hydrogen bonds form easily. As a result, ε_α and ε_β play more important role in the log K_d value of PE for seawater. In brief, the distribution behavior of the studied organics between PE and water is mainly affected by the hydrophobic interaction. For the adsorption in seawater, hydrogen bond interaction is another important driving force.

QSPR model for the adsorption of PP

A QSPR model of log K_d was yielded for the adsorption of PP in seawater:

$$\text{Seawater:}log{K}_{\text{d}}=\left(0.751\pm 0.035\right)\times logD+\left(-19.323\pm 2.072\right)\times {\epsilon }_{\beta }+\left(6.735\pm 0.663\right)$$ 5

Values of R², Q², and RMSE are 0.939, 0.939 and 0.381, respectively. Thus, the model (5) show great goodness of fitting and can explain 94% variability of the whole dataset. The nonlinearity of model (5) has been proved by the VIF values (1.034 for both descriptors, Table S1). As shown in Fig. S2, the predicted log K_d values show good consistence with their experimental values. The Fig. S3 and BIAS value (− 0.003) proved that there is no dependence of predictive errors on experimental log K_d values.

For the simulated external validation, the regression coefficients (R² = 0.945, RMSE = 0.396 and MAE = 0.307) and statistical parameters of the training subset are similar to that of the whole dataset (Table 1 and model S4). Thus, model (5) is statistically stable and there is no casual correlation. As shown in Table 1, the high prediction quality of the developed QSPR model can be proved by the predictive performance of the new model (Q² = 0.874, RMSE = 0.369 and MAE = 0.228) to the test subset. Furthermore, model (5 has good robustness and internal predictive ability (Q²_CV = 0.957). The Williams plot for the applicability domain of model (5) (Fig. S4) shows that there are two compounds (sulfadiazine and γ-hexachlorocyclohexane) located at the right side of h^* (0.257). While, these two compounds yield absolute SR values < 3, indicating they are not outliers. Thus, model (5) can be used to predict the log K_d values of PE in seawater towards the organics including polychlorinated biphenyls, chlorobenzenes, hexachlorocyclohexanes, polycyclic aromatic hydrocarbons and antibiotics.

For the adsorption of PP in sea water, log D and ε_β were also selected in model (5). Thus, hydrophobic interaction and hydrogen bond interaction also play determining roles in the adsorption. However, unlike the log K_d predictive model of PE in seawater, the ε_α representing the covalent acidity is not selected in model (5). Such dissimilarity may come from the addition of methyl groups in the PP structure that reduces the difference of H-accepting ability between the microplastics and water, consequently resulting in a negligible contribution of ε_α in the adsorption of PP.

QSPR model for the adsorption of PS

For the adsorption of PS in seawater, the experimental log K_d values of 28 organic pollutants (of which 14 are ionizable compounds) were used to established predictive model:

$$\text{Seawater:}log{K}_{\text{d}}=\left(0.357\pm 0.062\right)\times logD+\left(3.766\pm 0.384\right)\times \pi +\left(-2.080\pm 0.540\right)$$ 6

As shown in Tables 1 and S1, the obtained statistical parameters (R² = Q² = 0.837) prove a good regression performance and the calculated VIF values (1.000 for both descriptors) prove no multicollinearity of model (6). Meanwhile, the favorable consistence between the experimental and predicted log K_d values was observed in Fig. S5. The pattern of predictive errors shown in Fig. S6 reveals no systematic error for model (6), which is also verified by BIAS = 0.000 (Table 1).

Based on the training subset (70%), similar regression coefficients and statistical parameters of the new model (S5) were obtained (Table 1). The comparable statistics were also received for the test set. Moreover, Q²_CV value (0.898) of the leave-one-out cross validation was obtained, higher than the acceptable criteria. Thus, model (6) has satisfactory robustness and internal predictive ability. As shown in the Fig. S7 of Williams plot, three compounds (fluoranthene, chrysene and pentacosafluorotridecanoic acid) with ׀SR׀ < 3 locate at the right side of h^* (0.321), indicating that they are not outliers. In conclusion, model (6) can be employed for predicting the adsorption carrying capacity (log K_d) of PS for organic pollutants (especially for ionizable organic pollutants) within the application domain in seawater. In previous study²⁰, the influence of dissociation on log K_d for ionizable organic pollutants was not considered in the construction of predictive models. In fact, the physicochemical properties (e.g., hydrophobicity) of various dissociation species are quite different, which may significantly affect the partition of ionizable organic pollutants between PS and seawater. Therefore, the predictive models established without considering the effect of pH on the distribution of dissociation species is only applicable to predict log K_d values under the experimental water pH. However, the QSPR model (6) constructed in this study can expand the predictive application to various pH values. Limited by the number of ionizable compounds and pH range used for model construction, the developed models are more suitable for the pH range of natural waters (6–9).

The presence of log D in model (6) proves that hydrophobic interaction also can enhance the adsorption of organics on PS in seawater. In addition to log D, π was also selected. The experimental log K_d values positively correlate with π (3.766) in the QSPR model, indicating that chemicals with larger π value preferred to be adsorbed onto PS in seawater. As shown in Tables 2 and S2, the organic compound, which contains strong π–electron conjugation in the structure, generally has a large π value. Thus, it can be inferred that the π − π interaction also contributes to the adsorption for PS. The phenyl groups in the PS structure produce higher π–π interactions with organic chemicals than PE and PP, thus yielding higher log K_d values (Table 2). For example, the log K_d value of phenanthrene onto PS (5.50) is much higher than that on PE (4.440) and PP (4.000) in sea water. In brief, hydrophobic interaction and π–π interaction play important roles in the adsorption of PS in sea water.

Materials and methods

Collection of experimental K_d values

In order to improve the predictive accuracy, the properties of microplastics and water environment media were considered by screening and classifying the experimental data used for modeling. For the adsorption of organic pollutants on PE, 37, 24 and 48 experimental K_d values were collected for seawater, freshwater, and pure water, respectively. For the adsorption of PP and PS in seawater, 35 and 28 experimental K_d values were selected, respectively. All these collected data are listed in Table 2. The unit of all K_d values was unified to kg/L. As the value of K_d is quite large, its logarithmic form (log K_d) was used for developing QSPR models. Experimental conditions for determining K_d values are shown in Table S3. Molecular structures for all organic pollutants, including polychlorinated biphenyls, polycyclic aromatic hydrocarbons, aromatic hydrocarbons, chlorobenzenes, hexachlorocyclohexanes, aliphatic hydrocarbons, antibiotics and perfluorinated compounds, are shown in Table S2.

Molecular structural parameters

Based on the previous studies^20,30, hydrophobic interaction, hydrogen bond and π-π interaction may play important roles in the adsorption of microplastics towards organic pollutants. Thus, the n-octanol/water distribution coefficient at special pH value (log D), molecular mass (M′_w = M_w/100) and six quantum chemical descriptors were calculated for developing QSPR models (Table S4). Six selected quantum chemical descriptors include molecular volume (V′ = V/100), the ratio of average molecular polarizability and molecular volume (π = α/V), the most positive atomic charge on H atom (qH⁺), the most negative atomic charge (q⁻), covalent acidity (ε_α = E_LUMO − E_HOMO-water), and covalent basicity (ε_β = E_LUMO-water − E_HOMO) where E_HOMO refers to the highest occupied molecular orbital energy and E_LUMO stands for the lowest unoccupied molecular orbital energy. For non-dissociable compounds, the n-octanol/water distribution coefficients are the same for the different pH values. While for the ionizable organics, different log D values for the relevant experimental conditions were obtained from SciFinder⁴². The values of M_w, V, π, q⁺, q^–, E_HOMO and E_LUMO were extracted from the Gaussian output files.

The structures of all the molecules were optimized at B3LYP/6-31G(d,p) level using Gaussian 09 program package⁴³, and confirmed to be local minima by vibrational frequency analyses with the same method. For the ionizable compounds, all dissociation species may exist under the experimental pH conditions were optimized. The apparent value of each quantum chemical descriptor at special pH value can be calculated as:

$$X_{\text{pH}}=\sum {\alpha }_i{X}_i$$ 7

where X stands for the quantum chemical descriptor, α_i is the fraction of each dissociation species under the experimental pH conditions (Table S3), which can be calculated through the pK_a values of the ionizable compounds (Table S5).

Model development and validation

The initial prediction model can be expressed as follows:

$$log{K}_{\text{d}}=dlogD+v{V}^{\prime }+m{M}_{\text{w}}^{\prime }+a{\epsilon }_{\alpha }+b{\epsilon }_{\beta }+p\pi +f{q}^{+}+e{q}^{-}+g$$ 8

where d, v, m, a, b, p, f and e are fitting coefficients, and g is a regression constant. The model development and variable filtration were performed by multiple linear regression (MLR)⁴⁴ with a step-wise algorithm embedded in soft package SPSS 21.0. The statistical parameters squared correlation coefficient (R²) and root-mean-square error (RMSE) were calculated to characterize the fitting performance and predictive squared correlation coefficient (Q²) was used to represent the predictive ability of the developed QSPR models⁴⁵. Statistically, the values of R² and Q² should be > 0.5. The larger value of Q² indicates the predictive ability of model is stronger. The collinearity of the employed parameters was assessed by the variance inflating factor (VIF) values. The calculation details for all statistical parameters were listed in the Text S1.

The statistical robustness and predictive ability of the developed models were verified by the simulated external validation and leave-one-out cross validation⁴⁶. The data set was randomly divided into a 70% training set and a 30% test subset^25,29 (shown in Table 2). Based on the training set, a new model was rebuilt with the same descriptors selected by the whole dataset. Subsequently, log K_d values in the test subset were predicted and evaluated by the new models. The values of R², Q² and RMSE of the simulated external validation were calculated to estimate the predictive performance⁴⁷. To assess the model robustness, cross-validated correlation coefficients (Q²_CV) were calculated with Weka 3.8.0⁴⁸.

Outliers and application domain

The Williams plot was performed to visualize the application domain and determine the outliers^49,50, where the leverage value (h_i) was set as horizontal coordinate and standardized predictive residuals (SR) was set as vertical coordinate. Hat-matrix was used to calculate the h_i values⁵¹. When the absolute value of SR is larger than 3, the relevant compound was designated as outlier and should be removed. Warning value (h^*) is defined as h* = 3p/n⁵¹, where p and n are the number of descriptors and compounds in the developed model, respectively. If h_i > h^*, the compound is far away from the descriptor-matrix center. Thus, the Williams plot also can be used to describe the distribution of chemicals in the whole descriptor matrix.

Conclusions

QSPR models were established for predicting the adsorption capacity of organic pollutants on PE in seawater, freshwater and pure water, on PP in seawater and on PS in seawater. The statistical results and application domain validations indicate the satisfactory goodness-of-fit, robustness and predictive ability of the predictive models. The constructed models have two significant advantages: (1) the descriptors used in the models are not dependent on experimental values and can be simply obtained based on the structure of organic pollutants; (2) the models can be used to predict the log K_d values of ionizable compounds at various pH values.

Based on the descriptors selected in the predictive models, main adsorption mechanisms between microplastics and organic pollutants were explored. For all the systems studied here, hydrophobic interaction has been proved to be an indispensable factor for the adsorption. Hydrogen bond interaction and π–π interaction are also considerable mechanisms for the adsorption onto PE and PP in sea water and the adsorption onto PS in sea water, respectively. Thus, this study provides us feasible tools to rapidly and easily predict the adsorption capacity of organic pollutants onto different microplastics in various waters, and also reveals the possible adsorption mechanisms. It will be helpful for further investigation of the environmental risks of both microplastics and their coexisting organic pollutants. Of course, the application scope of the predictive models constructed in this study is still limited as the limitation of experimental data. Therefore, it is still necessary to develop QSPR models for other types of microplastics in the further, or develop predictive method that does not depend on experimental data.

Author contributions

Conceptualization and design of study, X.W. and H.Y.; data curation, M.L., Y.W, and J.L.; calculations, data analysis, and validation, M.L.; writing—original draft preparation and editing, X.W. and M.L.; writing—review, discussion, X.W., H.Y. and G.M.; funding acquisition, X.W.

Competing interests

The authors declare no competing interests.

Supplementary information

is available for this paper at 10.1038/s41598-020-71390-3.