Oil Adsorption Kinetics of Calcium Stearate-Coated Kapok Fibers

This study used a simple and efficient dipping method to prepare oleophilic calcium stearate-coated kapok fibers (CaSt2-KF) with improved hydrophobicity. Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), and scanning electron microscopy (SEM) confirmed the deposition of calcium stearate particles on the surface of the kapok fibers. This led to higher surface roughness and improved static water contact angle of 137.4°. The calcium stearate-coated kapok fibers exhibited comparable sorption capacities for kerosene, diesel, and palm oil. However, the highest sorption capacity of 59.69 g/g was observed for motor oil at static conditions. For motor oil in water, the coated fibers exhibited fast initial sorption and a 65% removal efficiency after 30 s. At equilibrium, CaSt2-KF attained a sorption capacity of 33.9 g/g and 92.5% removal efficiency for motor oil in water. The sorption kinetics of pure motor oil and motor oil in water follows the pseudo-second-order kinetic model, and the Elovich model further described chemisorption. Intraparticle diffusion and liquid film diffusion were both present, with the latter being the predominant diffusion mechanism during motor oil sorption.


Introduction
Oil remains as one of the most valuable resources in this rapidly evolving human life having various domestic, recreational, and industrial applications. Catering to the need for oil entails a growing demand for storage and transport [1]. These activities have led to accidental and intentional oil releases in large bodies of water, resulting in billions of tons of discharged oil [2]. As extensive negative environmental and economic impacts persist from the effects of oil pollution, immediate mitigation to lessen the damages is deemed necessary [2,3]. Oil spill remediation techniques include chemical [4], direct combustion [5], bioremediation [6], and physical remediation methods [7]. The most appropriate approach is selected based on several factors such as location, quantity, type of spilled oil, etc. Aside from these factors, the consequences of inducing secondary pollution should be considered. These challenges continue the call for efficient and cost-effective technologies to recover oil in polluted waters [7,8].
Sorbents have been proven to have excellent oil removal efficiency and manageability. Inorganic sorbents, such as perlite, fly ash, exfoliated graphite, and other synthetic sorbents,

Material Characterizations
Scanning electron microscopy (SEM, JEOL JIB-4000 Plus) was performed to evaluate the surface morphology of CaSt 2 -KF. Surface area analysis was done using Brunauer-Emmett-Teller Method (BET, Quantachrome Instruments NOVA 2200e Surface Area and Pore Analyzer). The chemical composition and surface functional groups were determined using X-ray diffraction analysis (XRD, Shimadzu XRD-6100), energy dispersive X-ray analysis (EDX, JEOL JIB-4000 Pl), and Fourier transform infrared spectroscopy (FTIR, ThermoScientific Nicolet iS50). Static water contact angles were obtained using a digital microscope (Dino-Lite AM2111-0.3MP USB). Measurements were performed three times in randomized areas at room temperature with~10 µL water droplet volume.

Oil Sorption and Reusability Experiments
Raw-KF and CaSt 2 -KF were weighed and immersed in 25 mL of motor oil. After 30 min, the fibers were removed, drained to remove residual oil, and then weighed. Reusability tests were performed by subsequent squeezing and immersing in model oil multiple times. The oil sorption capacity (q) was calculated using Equation (1): where m f is the weight of the oil-ridden fiber and m i is the weight of the dry fiber. According to previous studies, tests beyond 30 min are not feasible since sorption of petroleum products usually achieves saturation before this time, and actual oil spill events also require fast removal durations to prevent oil desorption and degradation of sorbent [38][39][40].

Pure Oil Sorption
The pure oil sorption of CaSt 2 -KF was performed based on literature [41]. In a 150 mL beaker, 0.1 g of CaSt 2 -KF was immersed in 100 mL of motor oil. The fibers were retrieved at specific time intervals (10 s-30 min), drained for 30 s without squeezing, and then weighed. The process was repeated until the equilibrium or maximum sorption capacity was obtained. The sorption capacities at each time interval (q t ) were calculated using Equation (1).

Oil-In-Water Sorption
Oil-in-water sorption of CaSt 2 -KF was performed based on literature [42]. The oilin-water mixture was prepared by placing 4 mL of motor oil and 100 mL distilled water in a 150 mL beaker at a minimal agitation rate of 200 rpm. 0.1 g of CaSt 2 -KF was placed on the oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 • C for 24 h to remove sorbed water, and the oil-ridden fibers were reweighed. The sorption capacities at each time interval (q t ) Polymers 2023, 15, 452 4 of 15 were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): where m i,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt 2 -KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively. Pseudo-Second Order (PSO) Intraparticle Diffusion (IPD) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(qe − qt) vs. t, where qe (g/g) and qt (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves plotting t/qt vs. t, obtaining the pseudo-second-order rate constant k2 [39,42]. Additionally, the initial sorption rate h can be calculated using Equation (3): Elovich kinetic model is used to evaluate the initial sorption rate and rate constant which describes the activation energy and extent of chemisorption [41,43].
Diffusion mechanisms were further evaluated using intraparticle diffusion and liquid film diffusion models. Intraparticle diffusion refers to the transport of oil from the liquid phase towards both pore and surface diffusion. Pore diffusion is expected to be rate-limiting when the intercept I or boundary layer effect is zero upon plotting qt vs. t 1/2 .
2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively. Table 2. Summary of linear and nonlinear equations of kinetic models and their parameters.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-First Order (PFO) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(q e − q t ) vs. t, where q e (g/g) and q t (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k 1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves plotting t/q t vs. t, obtaining the pseudo-second-order rate constant k 2 [39,42]. Additionally, the initial sorption rate h can be calculated using Equation (3): Elovich kinetic model is used to evaluate the initial sorption rate α and rate constant β which describes the activation energy and extent of chemisorption [41,43].
Diffusion mechanisms were further evaluated using intraparticle diffusion and liquid film diffusion models. Intraparticle diffusion refers to the transport of oil from the liquid phase towards both pore and surface diffusion. Pore diffusion is expected to be rate-limiting when the intercept I or boundary layer effect is zero upon plotting q t vs. t 1/2 . A higher intercept means having surface diffusion as rate-limiting in the sorption process. The intraparticle diffusion rate constant k d may also be obtained [41,44]. To further evaluate surface sorption, liquid film diffusion modeling was performed. Liquid film diffusion refers to the transport of oil from the liquid bulk towards the film surrounding the surface of the fibers. Linear plotting of ln(1 − F) vs. t, where F is the fractional attainment of equilibrium (F = q t /q e ), generates the liquid film diffusion rate constant k fd . A zero intercept suggests that liquid film diffusion would be rate-limiting [44,45].  Figure 1 shows the SEM images and water contact angle measurement of the modified kapok fibers. The hollow tubular structure was maintained after coating with CaSt 2 , as seen in Figure 1a,b. The cross-sectional image in Figure 1b shows an oval-shaped lumen and a thin fiber wall. The fibers exhibited an inner diameter in the range of 20-22 µm, which is consistent with the previously reported values from raw-KF [26]. Figure 1c shows randomly dispersed plate-like calcium stearate particles embedded on the fiber surface. The coating appears to be non-uniformly distributed, considering the presence of dense aggregations of CaSt 2 and bare fiber surfaces. Nevertheless, the addition of CaSt 2 particles provided surface roughness on the previously smooth waxy layer of raw-KF. The unaffected hollow lumen structure of the fibers and the added surface roughness from the CaSt 2 particles provide effective space for oil sorption in the fiber assembly. The increase in surface roughness increases the surface area that anchors oil particles on the fiber surface during sorption and improves oil retention, especially during the extraction of the sorbent from the remediated media [25,46,47]. Surface area analysis using BET showed that modification increased the surface area of raw-KF (0.355 m 2 /g). CaSt 2 -KF exhibited a surface area of 7.024 m 2 /g.

Modification of Kapok Fibers with Calcium Stearate
The intraparticle diffusion rate constant kd may also be obtained [41,44]. To further evaluate surface sorption, liquid film diffusion modeling was performed. Liquid film diffusion refers to the transport of oil from the liquid bulk towards the film surrounding the surface of the fibers. Linear plotting of ln(1-F) vs. t, where F is the fractional attainment of equilibrium (F = qt/qe), generates the liquid film diffusion rate constant kfd. A zero intercept suggests that liquid film diffusion would be rate-limiting [44,45]. Figure 1 shows the SEM images and water contact angle measurement of the modified kapok fibers. The hollow tubular structure was maintained after coating with CaSt2, as seen in Figure 1a-b. The cross-sectional image in Figure 1b shows an oval-shaped lumen and a thin fiber wall. The fibers exhibited an inner diameter in the range of 20-22 µm, which is consistent with the previously reported values from raw-KF [26]. Figure 1c shows randomly dispersed plate-like calcium stearate particles embedded on the fiber surface. The coating appears to be non-uniformly distributed, considering the presence of dense aggregations of CaSt2 and bare fiber surfaces. Nevertheless, the addition of CaSt2 particles provided surface roughness on the previously smooth waxy layer of raw-KF. The unaffected hollow lumen structure of the fibers and the added surface roughness from the CaSt2 particles provide effective space for oil sorption in the fiber assembly. The increase in surface roughness increases the surface area that anchors oil particles on the fiber surface during sorption and improves oil retention, especially during the extraction of the sorbent from the remediated media [25,46,47]. Surface area analysis using BET showed that modification increased the surface area of raw-KF (0.355 m 2 /g). CaSt2-KF exhibited a surface area of 7.024 m 2 /g. The coating also rendered the fibers more hydrophobic with a static water contact angle of 137.4°, as seen from Figure 1d. This value improves 129° for raw-KF obtained from a previous study [27]. The hydrophobicity of CaSt2-KF is proven further by a simple The coating also rendered the fibers more hydrophobic with a static water contact angle of 137.4 • , as seen from Figure 1d. This value improves 129 • for raw-KF obtained from a previous study [27]. The hydrophobicity of CaSt 2 -KF is proven further by a simple surface wettability test as seen in Figure 2, which shows the high selectivity of the fibers to oil as it readily adsorbed onto the surface of the fibers upon contact. The CaSt 2 -KF also maintained its buoyancy despite being ridden with oil on the water surface, which is essential in oil spill remediation. surface wettability test as seen in Figure 2, which shows the high selectivity of the fibers to oil as it readily adsorbed onto the surface of the fibers upon contact. The CaSt2-KF also maintained its buoyancy despite being ridden with oil on the water surface, which is essential in oil spill remediation.   [48]. These are the only characteristic peaks from raw-KF, as seen in Figure 3b. Cellulose in kapok fibers may be amorphous and crystalline. The amorphous cellulose components in kapok fibers are found primarily on the outer wall of the fibers, while crystalline components are in the inner wall [48,49]. The presence of CaSt2 on kapok fibers is indicated by the diffraction peaks at 2 = 5.58 and 9.10°, which were observed from the XRD pattern of synthesized CaSt2 powders from Figure 3c. CaSt2 powders were prepared with the same process of CaSt2-KF sans the kapok fibers. The diffraction peaks at 2 = 5.63, 7. 48, 9.36, 11.18, 13.18, an 15.28° shown in Figure 3c represent the crystalline bilayers of CaSt2 [50]. The broadening of some peaks in the spectra of CaSt2-KF in Figure 3a may have been influenced by the amorphous components of kapok fibers and the presence of nonuniform coating [48]. The FTIR spectra of CaSt2-KF and raw-KF can be seen in Figure 4a and b, respectively. The presence of the broad -OH-stretching vibration peak at 3328 cm −1 and C-O stretching vibration peak at 1032 cm −1 in both spectra represents the waxy cutin and cellulosic  surface wettability test as seen in Figure 2, which shows the high selectivity of the fibers to oil as it readily adsorbed onto the surface of the fibers upon contact. The CaSt2-KF also maintained its buoyancy despite being ridden with oil on the water surface, which is essential in oil spill remediation.   [48]. These are the only characteristic peaks from raw-KF, as seen in Figure 3b. Cellulose in kapok fibers may be amorphous and crystalline. The amorphous cellulose components in kapok fibers are found primarily on the outer wall of the fibers, while crystalline components are in the inner wall [48,49]. The presence of CaSt2 on kapok fibers is indicated by the diffraction peaks at 2 = 5.58 and 9.10°, which were observed from the XRD pattern of synthesized CaSt2 powders from Figure 3c. CaSt2 powders were prepared with the same process of CaSt2-KF sans the kapok fibers. The diffraction peaks at 2 = 5.63, 7. 48, 9.36, 11.18, 13.18, an 15.28° shown in Figure 3c represent the crystalline bilayers of CaSt2 [50]. The broadening of some peaks in the spectra of CaSt2-KF in Figure 3a   The FTIR spectra of CaSt2-KF and raw-KF can be seen in Figure 4a and 4b, respectively. The presence of the broad -OH-stretching vibration peak at 3328 cm −1 and C-O stretching vibration peak at 1032 cm −1 in both spectra represents the waxy cutin and surface wettability test as seen in Figure 2, which shows the high selectivity of the to oil as it readily adsorbed onto the surface of the fibers upon contact. The CaSt2-K maintained its buoyancy despite being ridden with oil on the water surface, which sential in oil spill remediation.   [48]. These are the only characteristic peaks from raw-KF, as seen in Figu Cellulose in kapok fibers may be amorphous and crystalline. The amorphous cell components in kapok fibers are found primarily on the outer wall of the fibers, while talline components are in the inner wall [48,49]. The presence of CaSt2 on kapok fib indicated by the diffraction peaks at 2 = 5.58 and 9.10°, which were observed fro XRD pattern of synthesized CaSt2 powders from Figure 3c. CaSt2 powders were pre with the same process of CaSt2-KF sans the kapok fibers. The diffraction peaks at 2 = 7.48, 9.36, 11.18, 13.18, an 15.28° shown in Figure 3c represent the crystalline bilay CaSt2 [50]. The broadening of some peaks in the spectra of CaSt2-KF in Figure 3a may been influenced by the amorphous components of kapok fibers and the presence of uniform coating [48]. The FTIR spectra of CaSt2-KF and raw-KF can be seen in Figure 4a and 4b, re tively. The presence of the broad -OH-stretching vibration peak at 3328 cm −1 and stretching vibration peak at 1032 cm −1 in both spectra represents the waxy cutin = 15.60 and 22.33 • refer to the crystalline components of cellulose [48]. These are the only characteristic peaks from raw-KF, as seen in Figure 3b. Cellulose in kapok fibers may be amorphous and crystalline. The amorphous cellulose components in kapok fibers are found primarily on the outer wall of the fibers, while crystalline components are in the inner wall [48,49]. The presence of CaSt 2 on kapok fibers is indicated by the diffraction peaks at 2

Modification of Kapok Fibers with Calcium Stearate
Polymers 2023, 15, x FOR PEER REVIEW surface wettability test as seen in Figure 2, which shows the high selectivity of to oil as it readily adsorbed onto the surface of the fibers upon contact. The CaS maintained its buoyancy despite being ridden with oil on the water surface, w sential in oil spill remediation.   [48]. These are the only characteristic peaks from raw-KF, as seen in Cellulose in kapok fibers may be amorphous and crystalline. The amorphou components in kapok fibers are found primarily on the outer wall of the fibers, w talline components are in the inner wall [48,49]. The presence of CaSt2 on kapo indicated by the diffraction peaks at 2 = 5.58 and 9.10°, which were observed XRD pattern of synthesized CaSt2 powders from Figure 3c. CaSt2 powders were with the same process of CaSt2-KF sans the kapok fibers. The diffraction peaks a 7. 48, 9.36, 11.18, 13.18, an 15.28° shown in Figure 3c represent the crystalline CaSt2 [50]. The broadening of some peaks in the spectra of CaSt2-KF in Figure 3a been influenced by the amorphous components of kapok fibers and the presen uniform coating [48]. The FTIR spectra of CaSt2-KF and raw-KF can be seen in Figure 4a and 4 tively. The presence of the broad -OH-stretching vibration peak at 3328 cm − stretching vibration peak at 1032 cm −1 in both spectra represents the waxy    Figure 3a. The diffraction peaks at 2 = of cellulose [48]. These are the only ch Cellulose in kapok fibers may be am components in kapok fibers are found talline components are in the inner w indicated by the diffraction peaks at XRD pattern of synthesized CaSt2 pow with the same process of CaSt2-KF san 7. 48, 9.36, 11.18, 13.18, an 15.28° show CaSt2 [50]. The broadening of some pe been influenced by the amorphous co uniform coating [48].  Figure 3c represent the crystalline bilayers of CaSt 2 [50]. The broadening of some peaks in the spectra of CaSt 2 -KF in Figure 3a may have been influenced by the amorphous components of kapok fibers and the presence of non-uniform coating [48]. surface wettability test as seen in Figure 2, which shows the high selectivity of the fibers to oil as it readily adsorbed onto the surface of the fibers upon contact. The CaSt2-KF also maintained its buoyancy despite being ridden with oil on the water surface, which is essential in oil spill remediation.   [48]. These are the only characteristic peaks from raw-KF, as seen in Figure 3b. Cellulose in kapok fibers may be amorphous and crystalline. The amorphous cellulose components in kapok fibers are found primarily on the outer wall of the fibers, while crystalline components are in the inner wall [48,49]. The presence of CaSt2 on kapok fibers is indicated by the diffraction peaks at 2 = 5.58 and 9.10°, which were observed from the XRD pattern of synthesized CaSt2 powders from Figure 3c. CaSt2 powders were prepared with the same process of CaSt2-KF sans the kapok fibers. The diffraction peaks at 2 = 5.63, 7.48, 9.36, 11.18, 13.18, an 15.28° shown in Figure 3c represent the crystalline bilayers of CaSt2 [50]. The broadening of some peaks in the spectra of CaSt2-KF in Figure 3a may have been influenced by the amorphous components of kapok fibers and the presence of nonuniform coating [48]. The FTIR spectra of CaSt2-KF and raw-KF can be seen in Figure 4a and b, respectively. The presence of the broad -OH-stretching vibration peak at 3328 cm −1 and C-O stretching vibration peak at 1032 cm −1 in both spectra represents the waxy cutin and cellulosic The FTIR spectra of CaSt 2 -KF and raw-KF can be seen in Figures 4a and 4b, respectively. The presence of the broad -OH-stretching vibration peak at 3328 cm −1 and C-O stretching vibration peak at 1032 cm −1 in both spectra represents the waxy cutin and cellulosic components of the kapok fibers [26,51,52]. The peaks at 2915 cm −1 and 2848 cm −1 belong to the asymmetric and symmetric -CH-stretching vibrations, which may be associated with the cellulose and plant wax [25,53]. The spectra of CaSt 2 -KF in Figure 4a showed an increase in intensity for the peaks at 2915 cm −1 and 2848 cm −1 , indicating the presence  [52]. Plant wax is also characterized by the peaks at 1734 cm −1 and 1370 cm −1 corresponding to C=O stretching vibrations and C=O acetyl group stretching at 1240 cm −1 . These peaks correspond to the aliphatic aldehydes, esters, and ketones of plant wax [53,54]. CaSt 2 -KF showed a decrease in intensity for these peaks, which indicates the possible deesterification of kapok fibers due to the presence of NaOH in the CaSt 2 solution [47]. The skeletal C=C stretching vibrations at 1594 cm −1 , 1504 cm −1 , and 1460 cm −1 of lignin and -CH-stretching vibrations at 1425 cm −1 are all present in raw-KF. However, only the peak at 1504 cm −1 remained for CaSt 2 -KF. The other peaks were masked by the addition of new pronounced COO-asymmetric stretching vibration peaks at 1575 cm −1 and 1540 cm −1 and COO-symmetric stretching vibration peaks at 1465 cm −1 and 1420 cm −1 corresponding to CaSt 2 [50,52]. The decrease in the intensity of peaks attributed to plant wax and lignin in the spectra of CaSt 2 -KF may have exposed the cellulosic structure of the kapok fibers as indicated by the strong and broad -OH group peak. This -OH group has the potential to chemically bond with the CaSt 2 coating [55]. As shown in the schematic in Figure 5, CaSt 2 is composed of a Ca 2+ ion head and two long alkyl chain tails. An ionic or dipole-dipole interaction between the positive Ca 2+ of the coating and negative -OH of the cellulose exposed on the fiber surface may have occurred during the modification of the kapok fibers. The presence of CaSt 2 on the kapok fiber surface is further confirmed by the appearance of Ca element through the EDX analysis from Figure 4c. The low amount of Ca may be due to the irregular coating of CaSt 2, as seen from the SEM images. Nevertheless, the surface analysis showed that calcium stearate successfully anchored onto the surface of the kapok fibers. components of the kapok fibers [26,51,52]. The peaks at 2915 cm −1 and 2848 cm −1 belong to the asymmetric and symmetric -CH-stretching vibrations, which may be associated with the cellulose and plant wax [25,53]. The spectra of CaSt2-KF in Figure 4a showed an increase in intensity for the peaks at 2915 cm −1 and 2848 cm −1 , indicating the presence of CaSt2 [52]. Plant wax is also characterized by the peaks at 1734 cm −1 and 1370 cm −1 corresponding to C=O stretching vibrations and C=O acetyl group stretching at 1240 cm −1 . These peaks correspond to the aliphatic aldehydes, esters, and ketones of plant wax [53,54]. CaSt2-KF showed a decrease in intensity for these peaks, which indicates the possible deesterification of kapok fibers due to the presence of NaOH in the CaSt2 solution [47]. The skeletal C=C stretching vibrations at 1594 cm −1 , 1504 cm −1 , and 1460 cm −1 of lignin and -CHstretching vibrations at 1425 cm −1 are all present in raw-KF. However, only the peak at 1504 cm −1 remained for CaSt2-KF. The other peaks were masked by the addition of new pronounced COO-asymmetric stretching vibration peaks at 1575 cm −1 and 1540 cm −1 and COO-symmetric stretching vibration peaks at 1465 cm −1 and 1420 cm −1 corresponding to CaSt2 [50,52]. The decrease in the intensity of peaks attributed to plant wax and lignin in the spectra of CaSt2-KF may have exposed the cellulosic structure of the kapok fibers as indicated by the strong and broad -OH group peak. This -OH group has the potential to chemically bond with the CaSt2 coating [55]. As shown in the schematic in Figure 5, CaSt2 is composed of a Ca 2+ ion head and two long alkyl chain tails. An ionic or dipole-dipole interaction between the positive Ca 2+ of the coating and negative -OH of the cellulose exposed on the fiber surface may have occurred during the modification of the kapok fibers. The presence of CaSt2 on the kapok fiber surface is further confirmed by the appearance of Ca element through the EDX analysis from Figure 4c. The low amount of Ca may be due to the irregular coating of CaSt2, as seen from the SEM images. Nevertheless, the surface analysis showed that calcium stearate successfully anchored onto the surface of the kapok fibers.

Oil Sorption Capacity
Various oils were utilized to evaluate the sorption performance of the modified kapok fibers. The maximum sorption capacities of CaSt2-KF in different oils are higher than those of raw-KF in Figure 6. CaSt2-KF showed a maximum sorption capacity of 52.07, 60.63, 68.00, and 86.55 g/g in kerosene, diesel, palm oil, and motor oil, respectively. Oil viscosity significantly influenced the sorption performance of the modified and raw kapok fibers. CaSt2-KF exhibited the highest sorption capacity for motor oil, which has the highest viscosity, as listed in Table 1. Low viscosity oils like kerosene and diesel rapidly form a film around the smooth surface of the raw kapok fibers and penetrate the internal lumen. However, low viscous oils can also easily escape or desorb [16]. High viscosity oils like palm oil and motor oil are more likely to be anchored onto the surface. Penetration is still possible for high viscosity oils, but the rate would be slower [37]. In this case, the highly viscous oil is entrapped within the fiber assembly through the effect of stronger capillary bridging. The additional surface roughness provided by calcium stearate particles rendered the surface with greater adhesion to highly viscous oils [8,26,56].

Oil Sorption Capacity
Various oils were utilized to evaluate the sorption performance of the modified kapok fibers. The maximum sorption capacities of CaSt 2 -KF in different oils are higher than those of raw-KF in Figure 6. CaSt 2 -KF showed a maximum sorption capacity of 52.07, 60.63, 68.00, and 86.55 g/g in kerosene, diesel, palm oil, and motor oil, respectively. Oil viscosity significantly influenced the sorption performance of the modified and raw kapok fibers. CaSt 2 -KF exhibited the highest sorption capacity for motor oil, which has the highest viscosity, as listed in Table 1. Low viscosity oils like kerosene and diesel rapidly form a film around the smooth surface of the raw kapok fibers and penetrate the internal lumen. However, low viscous oils can also easily escape or desorb [16]. High viscosity oils like palm oil and motor oil are more likely to be anchored onto the surface. Penetration is still possible for high viscosity oils, but the rate would be slower [37]. In this case, the highly viscous oil is entrapped within the fiber assembly through the effect of stronger capillary bridging. The additional surface roughness provided by calcium stearate particles rendered the surface with greater adhesion to highly viscous oils [8,26,56].

Oil Sorption Capacity
Various oils were utilized to evaluate the sorption performance of the modified kapok fibers. The maximum sorption capacities of CaSt2-KF in different oils are higher than those of raw-KF in Figure 6. CaSt2-KF showed a maximum sorption capacity of 52.07, 60.63, 68.00, and 86.55 g/g in kerosene, diesel, palm oil, and motor oil, respectively. Oil viscosity significantly influenced the sorption performance of the modified and raw kapok fibers. CaSt2-KF exhibited the highest sorption capacity for motor oil, which has the highest viscosity, as listed in Table 1. Low viscosity oils like kerosene and diesel rapidly form a film around the smooth surface of the raw kapok fibers and penetrate the internal lumen. However, low viscous oils can also easily escape or desorb [16]. High viscosity oils like palm oil and motor oil are more likely to be anchored onto the surface. Penetration is still possible for high viscosity oils, but the rate would be slower [37]. In this case, the highly viscous oil is entrapped within the fiber assembly through the effect of stronger capillary bridging. The additional surface roughness provided by calcium stearate particles rendered the surface with greater adhesion to highly viscous oils [8,26,56].

Reusability
The reusability of CaSt 2 -KF and raw-KF sorbents was investigated by multiple cycles of immersion and squeezing in various model oils. The sorption capacity per cycle is referenced from the initial mass of the fibers. Reusability test results can be seen in Figure 7. CaSt 2 -KF attained sorption capacities of 38.70, 45.23, 61.12, and 77.61 g/g after five sorption cycles for kerosene, diesel, palm oil, and motor oil, respectively, at 30 min each cycle. These values are higher than that of raw-KF. Consequent squeezing may result in deformation of the hollow lumen, increased compaction of the fiber assembly, and trapped residual oil inside the fibers. The decrease in available spaces for oil uptake decreases the sorption capacity over multiple cycles [26,47]. High percent retention (>89%) for highly viscous oils was observed for CaSt 2 -KF and raw-KF. However, a decrease in retention was seen for low viscous oils, where CaSt 2 -KF exhibited ≥75% retention after five sorption cycles. The improved surface roughness in CaSt 2 -KF may have hindered these oils from easily escaping the fiber assembly compared to raw-KF with a smooth surface [16,57].

Reusability
The reusability of CaSt2-KF and raw-KF sorbents was investigated by multiple cycles of immersion and squeezing in various model oils. The sorption capacity per cycle is referenced from the initial mass of the fibers. Reusability test results can be seen in Figure 7. CaSt2-KF attained sorption capacities of 38.70, 45.23, 61.12, and 77.61 g/g after five sorption cycles for kerosene, diesel, palm oil, and motor oil, respectively, at 30 min each cycle. These values are higher than that of raw-KF. Consequent squeezing may result in deformation of the hollow lumen, increased compaction of the fiber assembly, and trapped residual oil inside the fibers. The decrease in available spaces for oil uptake decreases the sorption capacity over multiple cycles [26,47]. High percent retention (>89%) for highly viscous oils was observed for CaSt2-KF and raw-KF. However, a decrease in retention was seen for low viscous oils, where CaSt2-KF exhibited ≥75% retention after five sorption cycles. The improved surface roughness in CaSt2-KF may have hindered these oils from easily escaping the fiber assembly compared to raw-KF with a smooth surface [16,57].

Pure Oil Sorption
Considering the excellent performance of CaSt2-KF for sorption of motor oil in static conditions, kinetic modeling was done to estimate the sorption mechanism. Figure 8 shows the experimental data obtained and the nonlinear fitted models. The kinetic parameters and applicability indicators for both linear and nonlinear fitting of models are presented in Table 3. The system fitted best for the pseudo-second-order kinetic model having the highest R 2 (0.9989), lowest 2 (1.1979) values, and closest qe, 60.6061 g/g for linear and 58.7719 g/g for nonlinear, to the experimental qe (59.6887 g/g). The agreement to this model suggests that both physical and chemisorption are present during oil sorption. The Elovich kinetic model further describes the heterogeneous nature of pseudo-second-order kinetics [58]. The system exhibited high R 2 (0.9318) and low 2 (6.3266) values for this model, suggesting that chemisorption may be the rate limiting step [41,59].

Pure Oil Sorption
Considering the excellent performance of CaSt 2 -KF for sorption of motor oil in static conditions, kinetic modeling was done to estimate the sorption mechanism. Figure 8 shows the experimental data obtained and the nonlinear fitted models. The kinetic parameters and applicability indicators for both linear and nonlinear fitting of models are presented in Table 3. The system fitted best for the pseudo-second-order kinetic model having the highest R 2 (0.9989), lowest where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively.  1979) values, and closest q e , 60.6061 g/g for linear and 58.7719 g/g for nonlinear, to the experimental q e (59.6887 g/g). The agreement to this model suggests that both physical and chemisorption are present during oil sorption. The Elovich kinetic model further describes the heterogeneous nature of pseudo-second-order kinetics [58]. The system exhibited high R 2 (0.9318) and low oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): , 100%

Linear Form Nonlinear Form Parameters
( where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-First Order (PFO) Pseudo-Second Order (PSO) ] Polymers 2023, 15, x FOR PEER REVIEW 10 of 15  The diffusion mechanisms were also estimated using intraparticle diffusion and liquid film diffusion models. The mass transfer mechanism varies during different stages of oil sorption, and diffusion models determine which stage is rate-limiting. The stages of sorption include (1) external mass transfer from liquid bulk to fiber surface; (2) liquid film diffusion; and (3) intraparticle diffusion [41,60]. The external mass transfer is rapid, as seen in Figure 8, which is therefore not rate-limiting. Upon modeling, both intraparticle diffusion and liquid film diffusion models do not pass through the origin. Neither can be assumed as the sole rate-limiting step [61]. The intraparticle diffusion model has shown a non-zero intercept (I), indicating the presence of a boundary layer effect. The large I  oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-Second Order (PSO) Intraparticle Diffusion (IPD) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(qe − qt) vs. t, where qe (g/g) and qt (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves plotting t/qt vs. t, obtaining the pseudo-second-order rate constant k2 [39,42]. Additionally, the initial sorption rate h can be calculated using Equation (3) oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): ( where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-First Order (PFO) Pseudo-Second Order (PSO) Elovich ln ln 1 ln 1 Intraparticle Diffusion (IPD) Liquid Film Diffusion (LFD) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(qe − qt) vs. t, where qe (g/g) and qt (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves  oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): , 100% ( where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-First Order (PFO) Pseudo-Second Order (PSO) Elovich ln ln 1 ln 1 Intraparticle Diffusion (IPD) Liquid Film Diffusion (LFD) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): , 100% ( where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-First Order (PFO) Pseudo-Second Order (PSO) Elovich ln ln 1 ln 1 Intraparticle Diffu- Liquid Film Diffusion (LFD) The diffusion mechanisms were also estimated using intraparticle diffusion and liquid film diffusion models. The mass transfer mechanism varies during different stages of oil sorption, and diffusion models determine which stage is rate-limiting. The stages of sorption include (1) external mass transfer from liquid bulk to fiber surface; (2) liquid film diffusion; and (3) intraparticle diffusion [41,60]. The external mass transfer is rapid, as seen in Figure 8, which is therefore not rate-limiting. Upon modeling, both intraparticle diffusion and liquid film diffusion models do not pass through the origin. Neither can be assumed as the sole rate-limiting step [61]. The intraparticle diffusion model has shown a non-zero intercept (I), indicating the presence of a boundary layer effect. The large I indicates that surface diffusion is rate-limiting compared to pore diffusion. Liquid film diffusion exhibited a higher R 2 (0.9236) than the intraparticle diffusion model (R 2 = 0.7139), suggesting that surface sorption may be the predominant diffusion mechanism for the system. Surface sorption is advantageous in reusability since desorption requires minimal energy [44].

Oil-In-Water Sorption
The mechanism of sorption of motor oil mixed with water by CaSt 2 -KF was also estimated using kinetic models. Figure 9 shows the experimental data obtained, the nonlinear fitted models, and the motor oil removal efficiency by CaSt 2 -KF. The kinetic parameters and applicability indicators for both linear and nonlinear fitting of models were presented in Table 4. The system consistently fitted best for the pseudo-secondorder kinetic model showing the highest R 2 (0.9959) and lowest oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-Second Order (PSO) Intraparticle Diffusion (IPD) Liquid Film Diffusion (LFD) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(qe − qt) vs. t, where qe (g/g) and qt (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves plotting t/qt vs. t, obtaining the pseudo-second-order rate constant k2 [39,42]. Additionally, the initial sorption rate h can be calculated using Equation (3): Elovich kinetic model is used to evaluate the initial sorption rate and rate constant which describes the activation energy and extent of chemisorption [41,43].
Diffusion mechanisms were further evaluated using intraparticle diffusion and liquid film diffusion models. Intraparticle diffusion refers to the transport of oil from the liquid phase towards both pore and surface diffusion. Pore diffusion is expected to be rate-limiting when the intercept I or boundary layer effect is zero upon plotting qt vs. t 1/2 . 2 (0.3625) values. It also produced the closest q e , 34.7222 g/g for linear and 33.8150 g/g for nonlinear, compared to the experimental q e (33.9245 g/g). This is explained by the rapid initial sorption by CaSt 2 -KF, exhibiting a 65.61% removal efficiency after only 30 s [62]. At equilibrium, 92.5% removal efficiency was reached. The system also showed a good fit (R 2 = 0.8659) with the Elovich model, indicating the presence of chemisorption. indicates that surface diffusion is rate-limiting compared to pore diffusion. Liquid film diffusion exhibited a higher R 2 (0.9236) than the intraparticle diffusion model (R 2 = 0.7139), suggesting that surface sorption may be the predominant diffusion mechanism for the system. Surface sorption is advantageous in reusability since desorption requires minimal energy [44].

Oil-In-Water Sorption
The mechanism of sorption of motor oil mixed with water by CaSt2-KF was also estimated using kinetic models. Figure 9 shows the experimental data obtained, the nonlinear fitted models, and the motor oil removal efficiency by CaSt2-KF. The kinetic parameters and applicability indicators for both linear and nonlinear fitting of models were presented in Table 4. The system consistently fitted best for the pseudo-second-order kinetic model showing the highest R 2 (0.9959) and lowest 2 (0.3625) values. It also produced the closest qe, 34.7222 g/g for linear and 33.8150 g/g for nonlinear, compared to the experimental qe (33.9245 g/g). This is explained by the rapid initial sorption by CaSt2-KF, exhibiting a 65.61% removal efficiency after only 30 s [62]. At equilibrium, 92.5% removal efficiency was reached. The system also showed a good fit (R 2 = 0.8659) with the Elovich model, indicating the presence of chemisorption. The rapid initial sorption is governed by external mass transfer diffusion. Meanwhile, both the intraparticle diffusion model and liquid diffusion showed low linearity having a non-zero intercept (I), suggesting that both contribute to the rate-limiting step. Intraparticle diffusion exhibited a higher R 2 (0.8073) than the liquid film diffusion model where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively. Table 2. Summary of linear and nonlinear equations of kinetic models and their parameters.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-First Order Pseudo-Second Order (PSO) Intraparticle Diffusion (IPD) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(qe − qt) vs. t, where qe (g/g) and qt (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves plotting t/qt vs. t, obtaining the pseudo-second-order rate constant k2 [39,42]. Additionally, the initial sorption rate h can be calculated using Equation (3): Elovich kinetic model is used to evaluate the initial sorption rate and rate constant which describes the activation energy and extent of chemisorption [41,43].
Diffusion mechanisms were further evaluated using intraparticle diffusion and liquid film diffusion models. Intraparticle diffusion refers to the transport of oil from the liquid phase towards both pore and surface diffusion. Pore diffusion is expected to be rate-limiting when the intercept I or boundary layer effect is zero upon plotting qt vs. t 1/2 . weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): , 100% ( where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively. Pseudo-Second Order (PSO) Elovich ln ln 1 ln 1 Intraparticle Diffu- Liquid Film Diffusion (LFD) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(qe − qt) vs. t, where qe (g/g) and qt (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves plotting t/qt vs. t, obtaining the pseudo-second-order rate constant k2 [39,42]. Additionally, the initial sorption rate h can be calculated using Equation (3): Elovich kinetic model is used to evaluate the initial sorption rate and rate constant which describes the activation energy and extent of chemisorption [41,43].
Diffusion mechanisms were further evaluated using intraparticle diffusion and liquid film diffusion models. Intraparticle diffusion refers to the transport of oil from the liquid phase towards both pore and surface diffusion. Pore diffusion is expected to be rate-limiting when the intercept I or boundary layer effect is zero upon plotting qt vs. oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): , 100% ( where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively.

Kinetic Model Linear Form Nonlinear Form Parameters
Pseudo-First Order (PFO) Pseudo-Second Order (PSO) Elovich ln ln 1 ln 1 Intraparticle Diffusion (IPD) Liquid Film Diffusion (LFD) The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(qe − qt) vs. t, where qe (g/g) and qt (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves plotting t/qt vs. t, obtaining the pseudo-second-order rate constant k2 [39,42]. Additionally, the initial sorption rate h can be calculated using Equation (3): Elovich kinetic model is used to evaluate the initial sorption rate and rate constant which describes the activation energy and extent of chemisorption [41,43].
Diffusion mechanisms were further evaluated using intraparticle diffusion and liquid film diffusion models. Intraparticle diffusion refers to the transport of oil from the liquid phase towards both pore and surface diffusion. Pore diffusion is expected to be rate-limiting when the intercept I or boundary layer effect is zero upon plotting qt vs. oil-in-water mixture for specific amounts of time (0.5-10 min), drained for 30 s, and then weighed. The fibers were dried at 105 °C for 24 h to remove sorbed water, and the oilridden fibers were reweighed. The sorption capacities at each time interval (qt) were calculated using Equation (1). The removal efficiency (RE) was also calculated using Equation (2): , 100% ( where mi,oil is the weight of motor oil in the oil-in-water mixture.

Kinetic Models
Various kinetic models were used in determining the sorption behavior involved in oil-only and oil-in-water sorption. Table 2 shows the linear and nonlinear equations of the kinetic models used to fit the experimental data from the sorption of motor oil by CaSt2-KF. Model fitting and parameter calculations were conducted using Microsoft Excel. Correlation coefficient (R 2 ) and chi-square square analysis ( 2 ) were used to determine the suitability of the linear and nonlinear fitted models for the system, respectively. The main sorption mechanisms were examined using the pseudo-first-order, pseudosecond order, and Elovich kinetic models. Suitability to the pseudo-first-order model indicates a reversible system wherein physical sorption is the primary sorption mechanism. Linear fitting involves plotting ln(qe − qt) vs. t, where qe (g/g) and qt (g/g) are the sorption capacities at equilibrium and specific time intervals, respectively, t is the immersion time, and k1 is the pseudo-first-order rate constant [39,43]. Meanwhile, the pseudo-second order model indicates both physical and chemisorption in the system. Linear fitting involves plotting t/qt vs. t, obtaining the pseudo-second-order rate constant k2 [39,42]. Additionally, the initial sorption rate h can be calculated using Equation (3): Elovich kinetic model is used to evaluate the initial sorption rate and rate constant which describes the activation energy and extent of chemisorption [41,43].
Diffusion mechanisms were further evaluated using intraparticle diffusion and liquid film diffusion models. Intraparticle diffusion refers to the transport of oil from the liquid phase towards both pore and surface diffusion. Pore diffusion is expected to be rate-limiting when the intercept I or boundary layer effect is zero upon plotting qt vs. The rapid initial sorption is governed by external mass transfer diffusion. Meanwhile, both the intraparticle diffusion model and liquid diffusion showed low linearity having a non-zero intercept (I), suggesting that both contribute to the rate-limiting step. Intraparticle diffusion exhibited a higher R 2 (0.8073) than the liquid film diffusion model (R 2 = 0.7344). Given high magnitudes of I from intraparticle diffusion modeling, surface sorption is still identified as the predominant diffusion mechanism for the system [44].

Conclusions
The potential use of calcium stearate-coated kapok fibers to remove oil in oil-in-water applications was evaluated. As shown by XRD, FTIR, and SEM-EDX analyses, calcium stearate was successfully coated on the kapok fibers. The modified kapok fibers showed improved hydrophobicity with a water contact angle of 137.4 • owing to the roughened fiber surface by calcium stearate particles. CaSt 2 -KF had similar sorption performance for kerosene, diesel, and palm oil and improved sorption capacity for motor oil compared to raw-KF. Greater sorption capacities were observed for high viscosity oils. Consequently, CaSt 2 -KF exhibited ≥ 75% retention after five cycles for all model oils, with improved retention for low viscous oils. Kinetic experiments showed that motor oil only and oilin-water sorption both agreed to pseudo-second-order kinetic model. Chemisorption was also present with high suitability to the Elovich model. Surface diffusion was the predominant diffusion mechanism for both systems. The improved surface properties and sorption performance for pure oil and oil-in-water systems make CaSt 2 -KF a suitable sorbent material, especially for oil-in-water applications.