Heat Properties of Polylactic Acid Biocomposites after Addition of Plasticizers and Oil Palm Frond Microfiber H )

Received: 29th May 2020 Revised: 14th July 2020 Accepted: 28th July 2020 Online: 31 August 2020 Polylactic acid (PLA) is a biopolymer that can replace thermoplastic polymers such as polypropylene (PP) in various applications due to strength, young modulus, biocompatibility, biodegradability, good clarity, oil resistance, and oxygen barrier ability. However, PLA has some drawbacks, including brittle, high glass transition temperature (Tg), and low degradation and crystallization rates. Therefore, modification is needed with the addition of nucleating agents and plasticizers to overcome these limitations of PLA. This research aims to study the effect of plasticizers and microfibril cellulose of oil palm frond (OPF) on thermal stability and to review the crystallization kinetics of PLA biocomposites. Polyethylene glycol and triacetin were used as plasticizers. Thermal analysis was performed using Thermal Gravimetry analysis (TGA) and Differential Scanning Calorimetry (DSC). The crystallization kinetics study was analyzed using a modified Avrami model under non-isothermal conditions. PLAP4000 has better thermal stability than PLAP200 and PLAG with Tonset and T respectively, which are close to pure PLA. All types of plasticizers influenced decreasing the Tg value in the range of 27-42%, whereas OPF microfiber addition contributes to a Tg reduction of 37-55 %.Crystallization kinetic study was informed for heterogeneous and simultaneous nucleation mechanisms with an n value range of about 2-3 for PLAP4000 and PLAOP4000.The crystallization rate was multiplied 4-9-fold for PLAOP200 and 2-3-fold for PLAOP4000.


Introduction
The substitution of fossil-based polymers such as polypropylene and polyethylene with polymers that are easily biodegradable in the environment such as polylactic acid and polyhydroxy butyrate is becoming very important, amid issues of sustainability and a sustainable green industry movement. These fossilbased thermoplastic polymers are widely used in various applications, so their use and management must be controlled because they cannot be biodegradable in the environment. Polylactic acid (PLA) is a biopolymer that has the potential to replace thermoplastic polymers such as polypropylene (PP) for several applications, because it has good strength and firmness, with 2 times the tensile strength and 2.5 times the young modulus, higher than PP [1]. It is also biocompatible, biodegradable, good transparency, good oil resistance, and oxygen barrier ability [2, 3 , 4 , 5 ]. In connection with these properties, PLA can be applied to packaging and health materials, as well as automotive components [2, 3 , 4 ]. Besides, the PLA manufacturing process has advantages in the heating process ' s effectiveness compared to other biopolymers and is more energy-efficient than fossilsourced polymers [2]. PLA, which is synthesized by fermentation of molasses from biological sources such as sugarcane and corn is believed to be more economical and affordable [6]. However, through the fermentation process, the PLA obtained produced different molecular weights and crystal structures. PLA is polymorphic, which has three dimensions of the main crystal structure, which are orthorhombic), and (antiparallel helices arrangement) [ 7 , 8, 9 ].
(orthorhombic) (parallel The polymorph nature of the PLA requires control during the heating and cooling process. It affects the crystal structure formed, which has an impact on changing its mechanical and physical properties. PLA has several limitations, including brittleness, high glass transition temperature (Tg), which is close to room temperature ranging from 56 -65°C , low rates of degradation and crystallization [2, 4 , 8, 10]. Efforts are being made to improve the properties of PLA through intramolecular and intermolecular modifications. Effective modifications include the addition of nucleating agents, plasticizers, and a combination of both [2, 4 , 6, 11].
Modification with plasticizers aims to increase the elasticity of PLA. The plasticizer mechanism in PLA is to insert plasticizers between the PLA molecular chains, thereby decreasing the rotational energy of the C-C bonds, which results in a decrease in Tg [12]. Some plasticizers can be used in PLA, both low and high molecular weights, including glycerol, triacetin, polyethylene glycol, lactic acid oligomers, and plasticized starch [6,13 ]. The addition of plasticizers with low molecular weight, such as citrate esters, glycerol, and glucose monoesters, can increase (ductility) and impact resistance [ 14 ]. The ease of molecular chain mobility due to plasticization, significantly affects PLA ' s thermal characteristics, especially Tg and crystallization temperature ( Tc ). The addition of plasticizers, both low and high molecular weight, can reduce the Tg of PLA [6, 14 , 15 , 16, 17 , 18].
Some studies state an increase in Tc, which shows a more regular crystal structure [ 19 , 20]. Zubir et al. [11], Choi et a\. [ 14 ] and Septevani and Bhakri [12] emphasized that plasticizers with low molecular weight have the potential to migrate, thereby reducing the elasticity of PLA over a while. Meanwhile, the plastic composition that is too high will reduce the mechanical properties of PLA. Another modification is the addition of a nucleating agent to accelerate the formation of nuclei, one of which is by strengthening natural fibers. Apart from being a nucleating agent, oil palm frond (OPF) microfiber can also be used as a reinforcing agent, thereby increasing the mechanical properties of PLA composites. Several studies stated that there was a decrease in Tg of PLA with the addition of microfiber by about 3 % [21], 5 % [22] to 15 % [ 23 ] compared to pure PLA. The addition of 10% MFC ( microfibril cellulose) was able to increase the crystallinity of PLA up to 32 % and decrease the cold crystallization temperature ( Tcc ) [22,24 ]. Apart from increased crystallinity, the addition of MCC ( microcrystalline cellulose) from oil palm empty fruit bunches also improved the heat stability of PLA [ 25 ].
In thermoplastic polymers such as PLA, thermal analysis is indispensable because it affects the choice of production processes, handling, and storage. Modifications with the addition of nucleating agents and plasticizers will affect the thermal characteristics of PLA composites, primarily if the heating and cooling strongly influence the microstructure. In this research, a study of the effect of 3 types of plasticizers is glycerol triacetate (GTA) and polyethylene glycol (PEG) with low molecular weight, and PEG with high molecular weight. Also, as a nucleating agent, microfibers from oil palm frond (OPF) pulp were added. The mixing process generally uses an injection process, while in this study, the mixing was carried out by casting with a solvent casting. Therefore, it is necessary to do a thermal analysis because of additives and differences in processes. This study aimed to study the effect of plasticizer and OPF microfiber on thermal characteristics and a review of crystallization kinetics on PLA composites.

Methodology
This research consists of raw materials preparation, synthesis of PLA biocomposites, thermal analysis of PLA biocomposites, and a review of crystallization kinetics of PLA biocomposites.

Material
Oil palm frond fiber was obtained from the PTPN VIII Sukamaju plantation, West Java . Processing fiber into pulp through a sulfate (kraft) process was carried out at the Center for Pulp and Paper (BBKK) Bandung. PLA (polylactic acid ) D 3001 semicrystalline was obtained from Natureworks, USA, with a specific gravity of 1.24 g / cm 3 and a melt flow rate of 22 g / 10 min. The plasticizers used were GTA (glycerol triacetate) and PEG (polyethylene glycol) with low and high molecular weight. GTA pro analysis was obtained from Wako Pure Chemical Industries Ltd with a density of 1.157 -1.165 g / cm 3 and a molecular weight of 218.2 g / mol. The PEG used had a low molecular weight of 190 -200 g / mol (PEG 200) with a density of 1.157 -1.165 g / cm 3 , while the high molecular weight was 3500 -4500 g / mol (PEG 4000 ) with a density of 1.2 g / cm 3 . The PEG 200 and PEG 4000 pro analyzes were obtained from Merck, Indonesia. The materials used for the pulp bleaching process were sodium chloride 25 % solution in water, and glacial acetic acid 100% pro analysis obtained from Merck Indonesia. Meanwhile, for the PLA composite manufacturing process, 99 % dichloromethane (DCM), 96 % ethanol, and 90 % acetone were used technically purchased from Frisconina.

Bleaching of oil palm frond pulp
OPF pulp with 10 g oven-dry weight was added 600 mL of distilled water. Sodium chloride and glacial acetic acid as delignification agents were added to the mixture, 16 mL and 0.8 mL, respectively. The bleaching process was carried out in a water bath at 8o°C for 1 hour with periodic stirring every 15 minutes. The lighter colored pulp was then filtered and washed with distilled water until the pH is neutral, odorless, and clean. The bleached pulp yield was then referred to as OPF. The bleached OPF pulp ' s chemical composition was 4.53 % lignin, 9.22 % hemicellulose, and 86.25 % cellulose.

. Biocomposite Film Preparation
The PLA biocomposite manufacturing process went through several stages: raw material preparation, mixing, and molding. The solvent exchange process was carried out in 2 stages, first, using 96 % ethanol stirred with pulp for 1 hour, followed by acetone stirring for 1 hour. PLA was dissolved with DCM and added 10% (w / w) of plasticizer then stirred for 60 minutes. As much as 10% (w / w) of OPF pulp was added to the PLA solution and plasticizer, then stirred again for 15 minutes. After the mixing process, the solution was spread out on a teflon mat and dried at room temperature for 24 hours. PLA films were molded using a hot press at 170°C for 30 seconds at a pressure of 1 MPa. Film sheets were cut with 5 x 5 mm dimensions for testing thermal properties using DSC and TGA. The test samples were coded, as shown in Table 1. where w is the weight fraction of PLA in the composite, AHm is the melting enthalpy of the biocomposite obtained at the second heating stage, while AHm°is the melting enthalpy for PLA which has a degree of crystallinity of 100% with a value of 93 W / g [26].

Overview of Non-Isothermal Crystallization Kinetics
The crystallization kinetics of the PLA system with the addition of plasticizer and OPF was carried out in non-isothermal conditions. This condition was chosen because, in real conditions, the biocomposite manufacturing process is carried out through a continuous process, including injection molding, blow molding, and extrusion. The crystallization kinetics analysis stage was heating from a temperature of 25°C to 200°C with a heating rate of 40°C/ min. Then the samples were held at 200°C for 5 minutes, followed by cooling from 200°C to o°C with set cooling rates of 5 , 10, and i 5°C/ min. Kinetics analysis was carried out at the cooling (exothermic) process stage. The crystallization kinetics analysis approach used the Avrami model [ 27 , 28]. Based on the assumption that total crystallization is linear with the energy released during the crystallization process, the relative crystallization degree (X( t)) can be described by equation 2

Morphological analysis of OPF pulp fibers
OPF pulp fiber morphological analysis was carried out using Field Emission Scanning Electron Microscope (FE-SEM) -Quattro S Thermo Fisher Scientific. The OPF pulp fibers were placed in a step without coating, then analyzes were carried out at magnifications of 100, 500 , and 1000 times by scanning electrons at 2 kV.

.1. Thermal Gravimetry Analysis (TGA)
TGA analysis using the TGA 4000 Perkin Elmer. A test sample of 10 mg was placed in a ceramic crucible in a combustion chamber flowing with nitrogen gas. The test sample is heated from 25°C to 500°C with a heating rate of io°C / min.

.2. Differential Scanning Calorimetry ( DSC)
The characterization of the thermal properties of the PLA biocomposite was carried out using the DSC 4000 Pyris 1 Perkin Elmer, which was equipped with a cooler. The results of the DSC analysis are the thermal parameters of polymer, including Tg (glass transition temperature), Tm ( melting temperature), Tcc (cold crystallization temperature), Tc (crystallization temperature), melting enthalpy and crystallization enthalpy.
The DSC analysis stages included heating from -25°C to 250°C with a heating rate of io°C / min. Then the samples were held at 250°C for 1 minute. Then cooled from 250°C to -25°C with a cooling rate of io°C / min. Samples were held at -25°C for 1 minute. Then the samples were heated again from -25°C to 250°C with a heating rate of io°C / min. The results obtained are used to determine the degree of crystallization of the biocomposite using equation 1. (2) X(t) is the volume fraction of the polymer that crystallizes at time t, AHC is the crystallization enthalpy during the time interval dt (heat flow), t is the measured time during the crystallization process, 00 is the time when crystallization ends. The crystallization kinetics parameters use the relative crystallization degree relationship with a constant from the Avrami model and are described by equation 3 . The modification of Avrami model for nonisothermal process is at t which has a relationship with temperature and cooling rate as described in equation 5 [ 29 ], where T is the temperature at the time of crystallization t, T0 is the temperature at the beginning of crystallization, while 0 is the velocity cooling down.
Calculation of Avrami constants K and n by connecting the log graph [-In (l-X(t))] with log t so that the results K as the intercept and n as the slope.

. Morphology of OPF pulp fiber
The bleached OPF pulp has long fiber morphology with a high aspect ratio, as shown in Figure 1 (a). Figures  1 (b) and 1 (c) show that the fiber diameter ranges from 10-30 pm. According to Zimmermann et al. [ 30 ], fibers with a diameter of less than 50 pm with a millimeterscale length are called microfibrils.
PEG. This is because PEGs with higher molecular weight can be said more stable binds to the PLA polymer chain arrangement. Plasticizers with high molecular weight have longer polymer chains, so they are not easily decomposed [12]. Apart from that, it can also act as a protective layer to inhibit the permeability of volatile substances [ 31 ]. Quiles-Carrillo et al. [ 32 ] explained that the decrease in Tonset could be caused by the evaporation of the plasticizer and the low molecular weight. On the other hand, the GTA plasticizer has two Tonsets, as shown in Figure 2 (a) and two decomposition peaks shown in Figure 2 (b). The PLAG Tonset is at 135.96°C and 353.33°C , while the peaks of decomposition are at 157.82°C and 376.69°C . These results may occur because GTA is not evenly dispersed in the PLA matrix, resulting in a separate decomposition of the plasticizer from the PLA matrix decomposition. Zubir et al. [11] explained that the incompatible phase difference between plasticizer and PLA resulted in two decomposition peaks. When viewed from the ease of dispersion or the effect of plasticizers on the mobility of the PLA polymer chain arrangement, PEG-based plasticizers are easier to disperse than GTA plasticizers.
The parameters of the thermal stability of PLA biocomposite obtained from the TGA and DTG analysis can be seen in Table 2, with observations only at the second peak for PLAG. The measured parameters in Table 2 obtained from the TGA thermogram include initial decomposition temperature (T 0 ), decomposition peak temperature ( Tmax ), and final decomposition temperature ( Tt ). Meanwhile, the DTG thermogram states the differential weight loss against temperature changes includes the temperature when the weight loss reaches 5 % (T 5 ), 50 % (T 50 ), and 95 % (T 95 ), and char residue at 450°C . There was a decrease in Tonset, To, Tmax, Tt for all types of plasticizers. The reduction may be due to the plasticizer coating the surface and breaking down polymer interactions, particularly low molecular weight [12,17 ]. PLAP200 has the most reduction compared to PLAG and PLAP 4000 . The observation on T 5 shows that PLAG decomposes faster than PLAP, then increases again after T 50 and T 95 . This indicates partial evaporation of GTA at the onset of heating [ 32 ].
In contrast, PLAP 4000 provides better thermal resistance than PLAG and PLAP200 for all decomposition points (T 5 , T 50 , T 95 ) and char residue, which shows a higher value than PLA, PLAG, and PLAP200. In this sense, PLAP has a broader range of processing, application, and storage temperatures than PLAG so that it can be processed and stored at temperatures above 200°C. The manufacturing process of PLA composites is in the temperature range of 170 -I8O°C. c.

. Characterization of thermal stability properties of PLA biocomposite through TGA analysis
The heat stability characteristic of PLA biocomposite is expressed by weight loss in temperature units obtained from TGA and DTG analysis. Figure 2(a) and Figure 2 (b) show that the type of plasticizer affects the thermal stability of PLA biocomposites. The PEG-based plasticizer produces one decomposition peak, just like the pure PLA depicted in Figure 2 (b). However, there is a decrease in the initial decomposition temperature ( Tonset ) of PLAP200 and PLAP 4000 compared to pure PLA, which are 11.5 % and 2%, respectively. The lower molecular weight PEG produces PLA with lower thermal resistance, compared to the higher molecular weight  The weight-loss parameters for temperature are presented in Table 2, where the Tonset for PLAOG is only shown at the second peak. The DTG data review shows that To, Tmax, and Tt with the addition of OPF have decreased in value compared to pure PLA and plasticized PLA. A similar trend occurred in plasticized PLA composites with the addition of OPF for T 5 and T 50 where PLAOG had the lowest T 5 value then increased when it reached T 50 compared to PLAOP. However, when it reached T 95 , PLAOP 4000 increased instantaneously with the char residue obtained reaching 0.43 %. In this case, PEG 4000 has the ability as a compatibilizer and plasticizer simultaneously [ 35 ]. Char residue of PLA composites with the addition of OPF, has a higher value than pure PLA and plasticized PLA. This shows that the carbon atoms in PLA are converted to gas, while the OPF microfibers become carbon.  However, this decrease can also be attributed to the low dispersed OPF microfibers in PLA despite the presence of plasticizers. These results differ from studies conducted by Haafiz et al. [ 25 ] and Safdari et al. [ 35 ], which showed an increase in thermal stability after adding micro and nanofibers to the PLA due to good dispersion, thus suppressing the mobility of the PLA chain. The same trend also occurs in the plasticized PLA / OPF system, where PLAOP 4000 gives a higher Tonset value than PLAOP200, while PLAOG produces two Tonsets, as shown in Figure 3 (a) and Figure 3 (

. Thermal characteristics of PLA biocomposites through DSC analysis
DSC analysis provides information about the parameters of the thermal properties of PLA biocomposites, including Tm, Tc, and Tg, along with their energy. One of the weaknesses of PLA is that the high Tg value reaches 59.73°C , as presented in Table 3 . The decrease in Tg value occurred with the addition of a plasticizer even up to 42.84 % in the PLAP200. The peak of Tg widens, and there is a point shift for PLA with the addition of a plasticizer, as shown in Figure 4  α α plasticizer chain, making PLA more flexible [12, 17 , 18, 35 ]. Semicrystalline PLA is unique. At a certain point during the endothermic process, it undergoes selfnucleating before melting occurs, which is known as cold crystallization, as shown in Figure 4 (a). A similar event occurred in PLAG, although the point shift occurred due to the decrease in Tg.
However, with the PEG plasticizer, there was a reduction in the area on the PLAP 4000 , as indicated by a decrease in the AHCC value in Table 3 . There was even no cold crystallization peak formation on the PLAP200. In this case, PEG can accelerate the crystal formation process in PLA. Cold crystallization formationindicate a slow crystallization process and amorphous PLA [ 23 ]. On the other hand, the sloping AHCC shows higher PLA crystallization, and the absence of Tcc indicates that PLA has crystallized in a certain order, which means that PEG functions as a crystal nucleating agent [20,24 ]. The endothermic curve of pure PLA yielded two peaks, indicating that there was a melting of different crystal structures (regular and irregular) after cold crystallization (shown as arrows in Figure 4 (a).) This suggests that to obtain a regular crystal structure from irregular crystals requires a slower reorganization process [20,22]. As explained by Salas-Papayanopolos et al. [18], there is a reorganization of unstable ' crystals into a more stable . The addition of a plasticizer gave different results, where only one peak was formed, which referred to the formation of one type of crystal. These results also indicate that there is no crystal phase separation [ 17 ]. The melting point (Tm) values decrease considerably, reaching 31.8 %; 42.8 %; and 27.3 % for PLAG, PLAP200, and PLAP 4000 , respectively, compared to pure PLA. This reduction in Tm contributes to the determination of the process production, application, distribution, and storage of PLA biocomposites in synergy with the decomposition temperature. Figure 4 (b) shows that the PLAP200 and PLAP 4000 produce exothermic curves with sharp peaks while PLA and PLAG are extensive. These results indicate that PLA and PLAG did not undergo a complete crystallization process. Therefore, PLA requires a nucleating agent to accelerate crystallization because PLA tends to undergo slow crystallization. The results presented in Figure 4 (b) and Table 3 show that PEG plasticizer can be a nucleating agent compared to GTA. The degree of crystallization (Xc) also increased for PLA with PEG plasticizers, both with low and high molecular weights. This may be because of the ease of insertion of molecules between the PLA polymer chains. Increasing chain mobility resulted in a decrease in Tg and Tcc, which contributed to an increase in the crystallization rate [ 17 ].  The addition of OPF to the PLA matrix did not significantly affect the thermal properties of PLA biocomposites. Even there was an increase in Tg in PLAO and PLAOG, as presented in Table 3 . In contrast to the PLAOP200 and PLAOP 4000 biocomposites, the Tg value decreased by 55.5 % and 37.5 %. Meanwhile, similar characteristics to PLA occur in PLAO and PLAOG, where a cold crystallization occurs, and two peaks form on the endothermic curve (shown by arrows in Figure 5 (b)). Different results occurred in PLAOP200 and PLAOP 4000 were no cold crystallization occurred, and one peak was formed on the endothermic curve. This is because OPF cannot accelerate the arrangement of the orderly crystal structure in PLAO and PLAOG. The addition of OPF to PLA and plasticized PLA caused a decrease in the degree of crystallization (Xc) compared to pure PLA. According to Safdari et al. [ 35 ], cellulose fibers to PLA can inhibit polymer chain mobility and crystal growth, thereby increasing stiffness, increasing in Tg value and decrease in Xc, if it is not adequately dispersed. and PLAOG show broad peaks like PLA, but for the PLAOP200 and PLAOP 4000 , the exothermic curve peaks are narrower. In this case, OPF can still act as nucleating agent for PLA with PEG plasticizers. PEG still contributes to the dispersion ability of OPF in the PLA matrix. Apart from being a plasticizer, PEG also functions as a compatibilizer, so that it has a better effect on the formation of PLA crystals compared to GTA. The crystallization peaks during the exothermic process are getting sharper, suggesting that there is a surface interaction between cellulose and PLA [ 23 ], thereby increasing the nucleus-forming free area and encouraging crystallization [ 24 ].
Analysis of the crystallization kinetics using the Avrami model can determine the value of the constant K, which shows the total crystallization rate and the value of n, which shows the formed crystals geometry.
The crystallization process of PLA biocomposite through the Avrami model was obtained by connecting the stratified logarithmic graph of relative crystallization. The logarithmic of the temperature function in the non-isothermal crystallization process. The results of the graph plots are presented in Figure 6 for each cooling rate. Figure 6 presents a linear line showing that the Avrami model fits a PLA biocomposite system at all cooling rates.

. Overview of PLA Biocomposite Crystallization Kinetics
The crystallization kinetics of PLA biocomposites was carried out through the Avrami model approach, which explains the crystallization mechanism or the total solidification of thermoplastic polymers. Total crystallization includes the process of nucleation and crystal growth [ 27 , 28]. The discussion on kinetics is more focused on PLA biocomposite with PEG plasticizer and the addition of OPF. The DSC analysis results show a much different change, especially in the crystallization process (exothermic conditions), compared to GTA plasticized PLA. The DSC analysis results showed that the PEG plasticizer and OPF microfibers were effective as nucleating agents. However, the effect can only be explained by the analysis of crystallization kinetics.   reported by Ding et al. [ 36 ], in which the presence of cellulose in PLA composites gave an increase in K value because cellulose was effective as a crystal nucleating agent.
The value of n is an integer number between 1-4 , where the value of n between 2-3 indicates the threedimensional crystal growth dimension, while the n value <1 and n > 3 indicates 2-dimensional crystal [ 27 , 28].
Besides showing the dimension of crystal growth, the value of n can describe the mechanism of crystal growth. The value of n < 2 describes the mechanism of crystal growth homogeneously and simultaneously. The values of n = 2 -3 are heterogeneous and simultaneous, while more n > 3 are homogeneous and sporadic [ 4 , 37 , 38 , 39 ]. Table 4 shows the results of n values between 2-3 on the PLAOP200, PLAP 4000 , and PLAOP 4000 . These results explain that the crystallization mechanism that occurs is heterogeneous crystallization and simultaneous crystallization with 3 -dimensional crystals formed. Whereas in PLA, only with a speed of 5°C/ min, which results in n at a value of 2-3 . This shows that the crystallization of PLA is slow because, with a cooling rate of more than that, the value of n is 1 -2. Different results were also obtained for the PLAP200, which resulted in a value of n > 3 , which indicates that the crystals formed were denser. These results indicate that the crystallization process at a rate of 5 -i 5°C/ min is too slow for the PLAP200. Thus, PEG plasticizers can be said to be very effective as nucleating agents and increase the crystallization rate of PLA, which is generally between 1-3°C/ min [8].

. Conclusions
The addition of plasticizers and microfibers from OPF affected the thermal resistance properties of PLA biocomposites. PLAP 4000 has better thermal resistance compared to PLAP200 and PLAG with Tonset and T values reaching 349.17°C and 374.68°C , respectively, approaching pure PLA. The addition of OPF reduces the thermal stability of all plasticized PLA, both with GTA and PEG. The crystallinity analysis of the DSC analysis showed that PEG has the ability as a nucleating agent better than GTA with the formation of an endothermic peak, a decrease in Tcc, and an increase in Tc in the max -