## 3 Results and Discussion
### Degree of PS Degradation in Ocean, Determined from Rate Constant of ST Formation  
Various chemical species possibly derived from artificial sources have been detected in the nature. Figures 4 and 5 show typical TIM-GC/MS chromatograms of analytical samples by extraction of sand and pebble in each sampling site far from industrial area. Figure 4 shows the chromatogram of an extraction sample of sand from Waikiki beach at Oahu, Hawaii in 1975 and Figure 5 shows the chromatogram of an extraction sample of pebbles by Showa base, Antarctic Continent in 1984. Compared with the mass fragments of each standard sample, Peak 1 was identified as SM, 3 as diethyl phthalate, 4 as SD\({}_{1}\), 5 as SD\({}_{2}\), 8 as bisphenol A, 9 as ST. 2 as diphenyl added as a surrogate and 6 as phenanthrene added as an internal standard and Un means unknown chemicals. SM has been shown a breakdown product formed by cinnamon mold flora and possibly may be present in oceans as a single contaminant [25]. However, the other styrene oligomers are not naturally present in ocean. Considering the constant ratio of SM:SD:ST, the authors concluded that SOs have been shown to be the degradation products of PS from land-based sources. The chemical contamination generated from PS had already been present in the n  
Figure 4: TIM-GC/MS chromatograms of the sample extracted from sand in Waikiki beach, Hawaii, 21\({}^{\circ}\)16’ N, 158\({}^{\circ}\)8\({}^{\prime}\) E, Date: 25 March 1975. [PERSON] et al. [26] estimated total waste plastics inflow in 2010 into world oceans to range from 4.8 to \(12.7\times 10^{6}\) MT. However, in all these computations [3; 4; 5; 6; 26], there has always been considerable margin for error. There is really virtually no completely relivable information on the quantities of plastics that have undergone degradation and sedimented to the ocean floor. The rate of ST formation was thought same as the rate of PS decomposition at ambient temperatures in oceans and on beaches since PS decomposition at low temperature, 30-150 \({}^{\circ}\)C, give ST as the dominant product [22]. The decomposition rate, \(k\), of PS (basically the same as the formation rate of ST) was found to be \(S_{t}=P_{0}[1-exp(-kt)]\approx P_{0}kt\), where \(k\left(\min^{-1}\right)=9.850\times 10^{-6}\ exp(-5029/T)\) where \(P_{0}\) is the initial amount of purified PS in a flask, \(t\) the reaction time and \(T\) the temperature in Kelvin. Rate of ST formation was \(6.15\times 10^{-13}\) min\({}^{-1}\). Converting the unit of rate into annual rate, the annual decomposition rate, \(k\), of PS was given as \(k\left(\text{year}^{-1}\right)=5.177\ exp(-5029/T)\) where \(P_{0}\) is the amount of PS in the ocean, \(t\) time in years since 1950 and \(T\) the temperature in Kelvin. The ST rate was \(3.233\times 10^{-7}\) year\({}^{-1}\) at 30 \({}^{\circ}\)C. One MT PS decomposed at a rate of 0.3 g per year at 30 \({}^{\circ}\)C. PS production of seven percent in the total plastics production [2]. [PERSON] et al. assumed three percent of the total plastic consumption as plastic inflow to the ocean [26]. The cumulative amounts of PS and SOs in the ocean were simulated as shown in Figure 6.  
The simulation was conducted by using three differential equations (Equations (1) through (3)). The production share of PS at seven percent and inflow ratio at three percent were assumed to be constant during 1950 to 2050. \[w(t)=1.50\times 10^{6}+4.845\times 10^{4}t^{2.107} \tag{1}\]  
\[\frac{dP(t)}{dt}=3.150\times 10^{3}+101.7t^{2.107}-3.232\times 10^{-7}P(t) \tag{2}\]  
\[\frac{dS(t)}{dt}=3.232\times 10^{-7}P(t) \tag{3}\]  
where \(w(t)\) (MT) is the annual plastic production at the eclipsed year \(t\) since 1950, \(P(t)\) (MT) is the cumulative amount of PS accumulated in the ocean at eclipsed year since 1950, \(t\), \(S(t)\) (MT) is the total amount of SOs in the ocean at the year \(t\). Equation (1) is a fitting result to the statistical data of global plastic production [1; 2].