A Comparative Review on Biodegradation of Poly(Lactic Acid) in Soil, Compost, Water, and Wastewater Environments: Incorporating Mathematical Modeling Perspectives

Abstract

As the demand for environmentally friendly materials continues to rise, poly(lactic acid) (PLA) has emerged as a promising alternative to traditional plastics. The present review offers a comprehensive analysis of the biodegradation behavior of PLA in diverse environmental settings, with a specific focus on soil, compost, water, and wastewater environments. The review presents an in-depth comparison of the degradation pathways and kinetics of PLA from 1990 to 2024. As the presence of different microorganisms in diverse environments can affect the mechanism and rate of biodegradation, it should be considered with comprehensive comparisons. It is shown that the mechanism of PLA biodegradation in soil and compost is that of enzymatic degradation, while the dominant mechanisms of degradation in water and wastewater are hydrolysis and biofilm formation, respectively. PLA reveals a sequence of biodegradation rates, with compost showing the fastest degradation, followed by soil, wastewater, accelerated landfill environments, and water environments, in descending order. In addition, mathematical models of PLA degradation were reviewed here. Ultimately, the review contributes to a broader understanding of the ecological impact of PLA, facilitating informed decision-making toward a more sustainable future.

1. Introduction

Bioplastics, derived from renewable resources such as plant-based materials, are emerging as a sustainable alternative to conventional plastics [1]. Figure 1 illustrates the anticipated growth in global bioplastic production, from 2.18 million tonnes in 2023 to 7.43 million tonnes by 2028, driven by an increasing demand and advancements in bioplastic materials [2]. There are multiple studies that ascertain the importance of biodegradable polymers as promising materials given the environmental issues [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]. Advanced bioplastics encompass such materials as PLA, polyhydroxyalkanoates (PHAs), poly(butylene succinate) (PBS), polyamides (PAs), and polypropylene (PP). PLA contributes 31.0% (cf. Figure 1) of production capacity, and thus, stands out as a prime candidate for an in-depth study due to its significant presence and potential environmental benefits [22]. The field of biodegradable polymers is rapidly evolving, with a multitude of recently synthesized polymers and the identification of several microorganisms and enzymes, which are capable of breaking them down [4,5,6,7]. Intense environmental pollution caused by synthetic polymers has become a critical issue in developing countries. Accordingly, efforts have been directed toward addressing this concern by incorporating biodegradability into commonly used polymers through slight structural modifications [4]. Because of its highest production capacity (cf. Figure 1), PLA is an optimal candidate for scholarly investigation among bioplastics.

PLA is a synthetic polyester, which is produced from renewable resources, such as corn, by different methods, e.g., ring-opening or polymer condensation. PLA’s monomer, lactic acid, exists in two forms: L-lactic acid and D-lactic acid. As shown in Figure 2a, depending on the monomer isomers used in the polymerization process, PLA can acquire three stereochemical forms: PLLA (from L-lactic acid), PDLLA (combination of L-lactic acid and D-lactic acid), and PDLA (from D-lactic acid) [7,8,23]. D-lactate exhibits an amorphous structure, whereas L-lactate possesses a crystalline structure. It was shown that amorphous structures are prone to a significant degradation compared to crystalline domains [9,10] for two primary reasons. First, in the amorphous domains polymer chains are not densely packed like those in crystalline ones (Figure 2b), allowing degrading agents to penetrate easier. Second, as shown in Figure 2b, amorphous domains possess a larger surface area, resulting in an increased exposure to the surrounding environment and greater water absorption, which can accelerate the hydrolysis process [11].

Biodegradation is a natural phenomenon involving the conversion of long chains into simpler chemical compounds such as CO₂, H₂O, or CH₄. The specific mechanisms vary depending on the environment. In general, factors affecting the biodegradation behavior of PLA include its molecular weight, structure, stereochemistry, catalysts, temperature, pH, and the degree of crystallinity [11,12,13,14,15,16]. Among these factors, the degree of crystallinity plays a key role in the degradation process as it increases during PLA decomposition [9,16,17,18], which will be discussed in detail below. However, variations exist under different conditions, and the information regarding the effect of specific characteristics in various environments during biodegradation is scarce. It remains unclear which characteristic dominates over the others and reveals itself as a primary controlling factor. The literature extensively discusses the biodegradation behavior of PLA in various environments, including soil, water, compost, and simulated landfills [11,15,19,24,25,26,27,28,29,30]. Although there is no well-established conclusion regarding the ranking of biodegradation rates in those environments, there are indications that PLA biodegrades most rapidly in compost, followed by wastewater, soil, landfills and water, respectively [6,7,16,19].

There exists a consensus regarding PLA and its blends’ properties, even though some studies suggest that PLA is fully biodegradable, while some factors challenge this conclusion. First, studies have shown that there are indications that micro/nano-plastics, which are harmful to the environment and marine animals, can result from PLA and its blends’ biodegradation [5,31]. In addition, biodegradable polymers degrade only under certain conditions (temperature, humidity, light, oxygen availability, and microorganisms) [30,32,33,34,35]. For example, PLA is not biodegradable in freshwater and seawater at low temperatures [32,36,37,38,39]. There are two primary reasons for this: (i) The hydrophobic nature of PLA, which does not easily absorb water [40,41,42]. In aqueous environments, the lack of hydrophilicity diminishes the hydrolysis process, which is crucial for the initial breakdown of PLA into smaller, more degradable fragments. (ii) Resistance to enzymatic attack; the enzymes that degrade PLA are not prevalent or active under typical freshwater and seawater conditions [39,43,44]. The microbial communities in these environments may not produce the necessary enzymes in sufficient quantities or at the required activity levels to effectively breakdown PLA. Additionally, the relatively stable and crystalline domains of PLA can further resist enzymatic degradation.

The present article provides a literature review covering the above two subjects from 1990 to 2024. This review also elucidates significant gaps in the literature related to PLA. First, the survey reveals several reviews on the degradation behavior of polyesters such as polyethylene terephthalate (PET) [45,46,47,48,49,50,51,52,53,54,55], whereas the information on PLA—despite its equal prevalence in the industry—remains relatively scarce and is not yet comprehensive, highlighting the need for a further review and additional research efforts. Second, while several existing reviews on PLA primarily concentrate on its synthesis and properties, such as physical and mechanical properties, processability, and compostability [56,57,58,59,60,61,62,63,64,65], there is a lack of information on its biodegradability. By shifting the focus towards the degradation mechanisms and kinetics of PLA, the present review offers a comprehensive analysis that not only enhances the understanding of the environmental impact of PLA but also points at the future research directions. This perspective is essential for advancing the development of sustainable materials and addressing the issue of plastic waste. The present review aims at the comprehensive understanding of PLA biodegradation mechanisms under diverse environments, coupled with mathematical modeling. It also covers the degradation process of micro/nano-plastics, which can differ from that of bulk polymers.

2. Biodegradation of PLA

From a physical perspective, polymer degradation can be either heterogeneous or homogeneous, also known as the surface and bulk polymer degradation, respectively. Chemically, polymer degradation can occur in three different ways: (a) scission of the main chains, (b) scission of the side chains, and (c) scission of the intersecting chains [66]. PLA degradation primarily involves the scission of ester bonds in the main chains. Moreover, various natural factors induce polymer degradation, including oxidation, photodegradation, thermolysis, hydrolysis, biodegradation, and enzymolysis [42]. Nevertheless, among the various degradation methods, biodegradation has attracted the greatest attention, which is also in focus in the present review.

PLA depolymerases, in particular, fall into two enzyme groups [67]: type I, which is protease-based [68,69,70], and type II, which is lipase (cutinase)-based [71,72,73]. Type I depolymerases are specific to PLLA, while type II depolymerases exhibit preference for PDLA. True lipases contain a lid that obstructs PLA access to the catalytic amino acid within the active cavity, affecting their function. In contrast, cutinase-type enzymes lack this lid, and the geometry of their active sites plays a crucial role in catalysis. Accordingly, cutinase-type enzymes within the lipase family are likely classified as type II PLA depolymerase [67]. Table 1 lists three types of microorganisms that can degrade PLA: actinomycetes (filamentous bacteria), bacteria, and fungi. It appears that the primary factor affecting the biodegradation process is the activity level of microorganisms. Therefore, any factor that enhances microbial activity can accelerate the rate of biodegradation. Various factors contribute to increasing microbial activity and, consequently, the rate of biodegradation [74,75,76,77,78,79,80,81].

2.1. Biodegradation in Soil and Compost by Enzymatic Mechanism

Biodegradation of PLA in soil is a complex process affected by microorganisms, enzymes, and environmental conditions. The biodegradation rate can vary depending on the burial depth, with aerobic degradation typically occurring at lower depths and anaerobic degradation at greater depths [82]. Research indicates that enzymatic degradation is a predominant mechanism of PLA biodegradation in soil (see Table 1). Enzymatic degradation begins with the attachment of microorganisms to the PLA’s surface, followed by a breakdown of ester bonds through microbial enzymes. This hydrolysis generates lactic acid monomers as shown schematically in Figure 3. This process includes four steps. First, is substrate binding, in which the enzymes cover the polymer structure (Figure 3a). Second, a nucleophilic attack occurs and the double-bond oxygen (ester bond of PLA) transfers to the single one by the oxygen present in the enzyme (Figure 3b). Third, the right-hand-side PLA bonds with the H atom of the enzyme (protonation in Figure 3c). Finally, the oxygen hole that remained from the previous stage (see Figure 3d) is replaced by a water molecule (hydrolysis in Figure 3e) and the oxygen terminus of the enzyme returns to its structure. This process continues until there is no more PLA left to hydrolyze [83].

Table 1. Studies of PLA degradation in different environments.

Microorganism	Substrate	Mechanism	Secreted Enzyme	T (°C)	pH	Biodegradation Criteria	Ref.
In soil and compost
Actinomycetes
Amycolatopsis sp. 1 strain HT32	PLLA	Enzymatic	Protease	30	7	%TOC 2 = −72.5 (20 days)	[68]
Bacillus stearothermophilus	PDLA		Lipase	58	7	%TOC~−62.5 (20 days)	[69]
Amycolatopsis sp. strain 3118	PLLA	Enzymatic	Protease	30	7	%WL 3 = 9.2 (11 days)	[70]
Pseudonocardia alni AS4.1531(T)	PLLA	Enzymatic	Protease	30	8	%WL = 71.6 (8 days)	[84]
Pseudonocardia sp. RM423	PLLA	Enzymatic	Protease	30	7	%WL = 0.4 ± 0.2 (7 days)	[85]
Amycolatopsis sp. strain KT-s-9	PLLA	Enzymatic	Protease	30	7	-	[67]
Amycolatopsis sp. strain 41	PLLA	Enzymatic	Protease, Lipase	30	6	-	[67]
Amycolatopsis sp. strain K104-1	PLLA	Enzymatic	Protease	37	9.5	%RA 4~200 (7 days)	[86]
Amycolatopsis thailandensis PLA07	PLLA	Enzymatic	Protease	25–37	6–10	-	[74]
Amycolatopsis strain SCM_MK2-4	PLLA	Enzymatic	Protease	30	7	EA 5~ 0.05 U/mL 6 (7 days)	[75]
Actinomadura strain T16-1	PLLA	Enzymatic	Protease	70	10	EA = 46 ± 2 U/mL (6 days)	[76]
Laceyella sacchari LP175	PLLA	Enzymatic	Protease	50	9	EA = 5.07 ± 0.25 U/mL (4 days)	[77]
Bacillus brevis	PLLA	Enzymatic	Protease	58	6.9	-	[78]
Other Bacteria
Geobacillus thermocatenulatus	PLLA	Enzymatic	Esterase	60	7	-	[67]
Pseudomonas geniculata WS3	PLA	Enzymatic	Protease	30	7	%WL~85 (30 days)	[19]
Serratia plymuthica	PLA	Biofilm	Lipase	24	7.5	%WL < 10 (6 months)	[79]
Arthrobacter sulfonivorans	PLA	Biofilm	Amylase, Lipase	24	7.5	%WL < 10 (6 months)	[79]
Fungus
Clitocybe sp (Clit)	PLA	Enzymatic	Cellulase	12.5	7	%WL < 10 (6 months)	[79]
Laccaria laccata (Lac)	PLA	Enzymatic	Cellulase	12.5	7	%WL < 10 (6 months)	[79]
Aspergillus oryzae RIB40	PDLLA	Enzymatic	Cutinase	20–80	8	-	[71]
Trichoderma viride	PLLA	Enzymatic	Cutinase	-	-	-	[72]
In liquid culture medium
Actinomycetes
Amycolatopsis orientalis IFO12362	PLLA	Enzymatic	Protease	30, 40	7	600 mg/L water-soluble TOC	[80]
Kibdelosporangium aridum	PLLA	Enzymatic	Protease	30	6–7	>97% degradation in 14 days	[81]
Saccharothrix waywayandensis	PLLA	Enzymatic	Protease	30	7–8	>95% degradation in 4 days	[87]
Paenibacillus amylolyticus strain TB-13	PDLA, PLLA	Enzymatic	Lipase	45–55	10	-	[88]
Fungus
Tritirachium album ATCC 22563	PLLA	Enzymatic	Protease, Lipase	30	7	76% degradation in 14 days	[89]
Cryptococcus sp. strain S-2	PLLA	Waste water	Cutinase	37	7	-	[73]

¹ Singular species; ² total organic carbon; ³ weight loss; ⁴ relative activity of the enzyme; ⁵ enzyme activity; and ⁶ the amount of enzyme that produces a certain amount of enzymatic activity per milliliter.

Table 1. Studies of PLA degradation in different environments.

Microorganism	Substrate	Mechanism	Secreted Enzyme	T (°C)	pH	Biodegradation Criteria	Ref.
In soil and compost
Actinomycetes
Amycolatopsis sp. 1 strain HT32	PLLA	Enzymatic	Protease	30	7	%TOC 2 = −72.5 (20 days)	[68]
Bacillus stearothermophilus	PDLA		Lipase	58	7	%TOC~−62.5 (20 days)	[69]
Amycolatopsis sp. strain 3118	PLLA	Enzymatic	Protease	30	7	%WL 3 = 9.2 (11 days)	[70]
Pseudonocardia alni AS4.1531(T)	PLLA	Enzymatic	Protease	30	8	%WL = 71.6 (8 days)	[84]
Pseudonocardia sp. RM423	PLLA	Enzymatic	Protease	30	7	%WL = 0.4 ± 0.2 (7 days)	[85]
Amycolatopsis sp. strain KT-s-9	PLLA	Enzymatic	Protease	30	7	-	[67]
Amycolatopsis sp. strain 41	PLLA	Enzymatic	Protease, Lipase	30	6	-	[67]
Amycolatopsis sp. strain K104-1	PLLA	Enzymatic	Protease	37	9.5	%RA 4~200 (7 days)	[86]
Amycolatopsis thailandensis PLA07	PLLA	Enzymatic	Protease	25–37	6–10	-	[74]
Amycolatopsis strain SCM_MK2-4	PLLA	Enzymatic	Protease	30	7	EA 5~ 0.05 U/mL 6 (7 days)	[75]
Actinomadura strain T16-1	PLLA	Enzymatic	Protease	70	10	EA = 46 ± 2 U/mL (6 days)	[76]
Laceyella sacchari LP175	PLLA	Enzymatic	Protease	50	9	EA = 5.07 ± 0.25 U/mL (4 days)	[77]
Bacillus brevis	PLLA	Enzymatic	Protease	58	6.9	-	[78]
Other Bacteria
Geobacillus thermocatenulatus	PLLA	Enzymatic	Esterase	60	7	-	[67]
Pseudomonas geniculata WS3	PLA	Enzymatic	Protease	30	7	%WL~85 (30 days)	[19]
Serratia plymuthica	PLA	Biofilm	Lipase	24	7.5	%WL < 10 (6 months)	[79]
Arthrobacter sulfonivorans	PLA	Biofilm	Amylase, Lipase	24	7.5	%WL < 10 (6 months)	[79]
Fungus
Clitocybe sp (Clit)	PLA	Enzymatic	Cellulase	12.5	7	%WL < 10 (6 months)	[79]
Laccaria laccata (Lac)	PLA	Enzymatic	Cellulase	12.5	7	%WL < 10 (6 months)	[79]
Aspergillus oryzae RIB40	PDLLA	Enzymatic	Cutinase	20–80	8	-	[71]
Trichoderma viride	PLLA	Enzymatic	Cutinase	-	-	-	[72]
In liquid culture medium
Actinomycetes
Amycolatopsis orientalis IFO12362	PLLA	Enzymatic	Protease	30, 40	7	600 mg/L water-soluble TOC	[80]
Kibdelosporangium aridum	PLLA	Enzymatic	Protease	30	6–7	>97% degradation in 14 days	[81]
Saccharothrix waywayandensis	PLLA	Enzymatic	Protease	30	7–8	>95% degradation in 4 days	[87]
Paenibacillus amylolyticus strain TB-13	PDLA, PLLA	Enzymatic	Lipase	45–55	10	-	[88]
Fungus
Tritirachium album ATCC 22563	PLLA	Enzymatic	Protease, Lipase	30	7	76% degradation in 14 days	[89]
Cryptococcus sp. strain S-2	PLLA	Waste water	Cutinase	37	7	-	[73]

¹ Singular species; ² total organic carbon; ³ weight loss; ⁴ relative activity of the enzyme; ⁵ enzyme activity; and ⁶ the amount of enzyme that produces a certain amount of enzymatic activity per milliliter.

Eventually, the lactic acid (LA) monomers serve as carbon and energy sources for microorganisms. The metabolic breakdown of lactic acid by microorganisms ultimately produces carbon dioxide and water, marking the completion of the biodegradation process [83]. As listed in Table 1, the most common microorganisms for the biodegradation of PLA in soil are actinomycetes [75,77,84,86,87,90]. Research has demonstrated that PLA can undergo degradation in both aerobic and anaerobic environments, particularly under thermophilic conditions. The rapid chemical hydrolysis process is notably accelerated at higher temperatures, facilitating PLA degradation [27,28,29,91].

The primary factors affecting the biodegradation of PLA in soil are temperature and depth of burial [82,92,93]. In Figure 4A–C, the weight loss of PLA films buried at different temperatures (37 °C, 45 °C, and 50 °C) in compost and soil is illustrated. Temperature significantly affects the degradation process in soil; however, it does not have a noticeable effect in compost [93]. Figure 4D–M depict the appearance of PLA buried at depths of 20 cm and 40 cm in soil, respectively. Biodegradation under higher-depth conditions (anaerobic) primarily involves bulk hydrolysis. The PLA degradation via hydrolysis intensifies with greater soil depth due to variations in humidity and microbial activity [82].

2.2. Biodegradation in Liquid Media

In PLA-based solid polymer matrices, hydrolytic degradation typically occurs through two distinct mechanisms: surface or heterogeneous reactions, and bulk or homogeneous erosion [94,95,96]. Figure 5 shows the fundamental differences between these mechanisms. Surface degradation tends to be faster than bulk erosion, with heterogeneous degradation progressing faster in the interior of amorphous poly(D,L-lactic acid) compared to its surface.

2.2.1. Hydrolytic Degradation in Freshwater

According to the literature, in the freshwater environment, in which there is no microorganism, the degradation mechanism is hydrolytic degradation. The hydrolytic degradation of PLA occurs in two ways: random chain scissions and autocatalytic hydrolysis. Several studies demonstrate that the autocatalytic hydrolysis is the dominant mechanism of hydrolytic degradation [6,16,94,97,98,99] (see

Table 2. Studies of PLA degradation in water.

Materials and Condition	Mechanisms	Key Findings	Ref.
Materials: PLA Environment: Water	▪ Cleavage of ester groups due to moisture exposure; freshwater with no microorganisms (random chain scissions or non-catalytic hydrolysis) ▪ Decrease in molecular weight and formation of soluble oligomers ▪ Production of carboxylic acid end groups (-COOH) that catalyze further reactions (autocatalytic hydrolysis)	▪ Chain cleavage favored in amorphous regions ▪ Heterogeneous (surface) degradation by random chain scissions, and homogeneous (bulk) by autocatalytic hydrolysis	[6,94]
Materials: Crystalline, semi-crystalline, and amorphous PLA. Environment: HPLC 1-grade water Temperatures: 45, 65, 75, and 85 °C under an unbuffered condition	▪ Non-catalytic and autocatalytic hydrolysis ▪ Water-induced crystallization	▪ Higher crystallinity leads to slower degradation compared to amorphous and partially crystalline samples ▪ Lower temperature reaction rates may approach those at higher temperatures, highlighting the interplay between phase structures and environmental temperature in hydrolytic degradation	[16]
Materials: PLA Environment: Water Temperatures: 140–180 °C Condition: water/PLA ratio up to 50% of PLA by weight	▪ Non-catalytic and autocatalytic hydrolysis	▪ More than 95% of PLA can be hydrolyzed to water-soluble LA within 120 min (at 160–180 °C) ▪ The kinetic constants are highly influenced by reaction temperature, for both high and low initial PLA concentrations	[97]
Materials: PLA Environments: Water, water/ethanol Temperature: 40 °C	▪ Non-catalytic and autocatalytic hydrolysis ▪ Water-induced crystallization	▪ Accelerated hydrolytic degradation in 50% ethanol, achieving a maximum degradation rate of 0.023 per day due to increased water sorption and optimal swelling ▪ Significant crystallization during hydrolysis, consistent with the Avrami equation	[98]
Materials: PLA Environments: Water, and saturated solutions of water with maritime salt and sugar together Temperature: 20 °C	▪ Non-catalytic hydrolysis ▪ Water-induced crystallization	▪ A total of 2.5% water absorption after 8 weeks; most absorption occurred in the first 3–4 days, related to the hydrolysis process	[99]

¹ High-performance liquid chromatography.

). According to the autocatalytic hydrolysis, each hydrolysis step produces a carboxylic acid end group of the short chains. These -COOH groups in the end chains can further catalyze the reaction [16,97]. The autocatalytic hydrolysis is a temperature-independent process [16], while the random chain scission could significantly be enhanced by raising the temperature. For example, the measured concentration of decomposed PLA in a batch system of PLA/water in different ratios is in the 140–180 °C range [69]. The dependence of the ratio ${\displaystyle \frac{{\gamma }_{PLA}}{{\gamma }_{PLA}^0}}$ (${\gamma }_{PLA}$ and ${\gamma }_{PLA}^0$ are the PLA concentrations at times t > 0 and t₀ = 0) on time reveals that the rate of PLA decomposition tremendously increases at high temperatures in 50 min [97]. It can be seen that the initial concentration of PLA does not affect the rate of degradation at high temperatures. The results are consistent with the results of the other study conducted in the 45–85 °C temperature range [16], in which the lowest time of hydrolytic degradation was 120 h at 85 °C.

2.2.2. Biodegradation in Wastewater and Landfills

The biodegradability of polylactic acid (PLA) is often assessed based on its behavior during aerobic composting. However, PLA-containing waste is commonly disposed of in anaerobic municipal landfills. Degradation is almost impossible to occur in landfills naturally [56] as hydrolysis is the first step of biodegradation [100]. However, there are some studies on PLA biodegradation in wastewater. PLA degradation during anaerobic sludge digestion was investigated to elucidate the impact of temperature on its biodegradation [101]. It was observed that when the degradation temperature exceeds the glass transition temperature (T_g) of PLA, anaerobic biodegradation accelerates. This could be attributed to an increased accessibility of the amorphous part of the polymer to microorganisms at higher temperatures. The glass transition temperature is related to the macromolecular movements in the amorphous phase of the polymer. The higher the T_g is, the higher the energy necessary for chain motion in the amorphous state. An increase in T_g can be attributed to a decrease in the content of the amorphous phase [101]. Conversely, when the degradation temperature is below the T_g of PLA, anaerobic biodegradation slows down [102,103].

The mechanism of PLA biodegradation in sludge is microbial degradation, which is controlled by the formation of biofilm on the surface of PLA. Biofilms play a significant role in accelerating the biodegradation of PLA through their abundance and hydrolytic activity [94]. The presence of biofilms on the surface of PLA provides a conducive environment for microbial colonization and enzymatic activity. [104,105,106,107,108,109]. The abundance of biofilms increases the surface area available for microbial attachment and enzymatic degradation of PLA, leading to enhanced biodegradation rates. Additionally, biofilms’ hydrolytic activity, facilitated by enzymes produced by microorganisms within the biofilm, contributes to the breakdown of PLA into smaller fragments that are readily biodegraded by microorganisms [104,105]. Biofilms pose multiple threats to synthetic polymeric materials, including coating surfaces. Biofilms also contaminate adjacent environments like water with released microorganisms, enhancing the leaching of additives and monomers from the polymer matrix, absorbing water and microbial filaments into the polymer matrix, leading to swelling and heightened conductivity [110].

Table 3. Studies of PLA degradation in wastewater and landfills.

Materials and Condition	Mechanisms	Key Findings	Ref.
Materials: PLA Environment: wastewater Temperatures: 36, 56 °C	▪ First, hydrolysis, followed by biofilm formation and enzymatic degradation.	▪ Microorganism settlement on the surface of PLA fibers and material erosion over 4 weeks. ▪ Effective biodegradation of PLA requires processing temperatures above Tg.	[101]
Materials: PLA Environment: wastewater sludges from dairy, rice vermicelli and coconut milk factories in soil Temperatures: 37 °C	▪ Accelerated enzymatic reaction by adding activated sludge to soil.	▪ Complete degradation of PLA sheets was found after 15 days. ▪ Synergistic action of the microbial consortium in sludge.	[102]
Materials: PLA Environment: digested sludge Temperatures: 50, 65 °C	▪ Anaerobic biodegradation of amorphous part of the polymer (accessible by microorganisms).	▪ Accelerated degradation above Tg.	[103]
Materials: PLA Environments: activated sludge Temperature: 20 °C	▪ First, hydrolysis, followed by biofilm formation and enzymatic degradation.	▪ Bacterial adhesion to the polymer surface after 7 days. ▪ Identification of Aeromonas genus, typical for activated sludge.	[105]
Materials: PLA Environments: mixture of landfill soil and sludge Temperature: 61 °C	▪ Hydrolytic degradation, followed by formation of pores, cracks, and irregular roughness, and enzymatic degradation.	▪ Weight loss of 90% after 90 days. ▪ Decrease in decomposition temperature.	[28]
Materials: semi-crystalline PLA Environments: accelerated landfill condition Temperature: 21, 35 °C	▪ No direct biological degradation of PLA under the anaerobic conditions.	▪ At 21 °C, biodegradation takes 100+ years. ▪ At 35 °C, less than 40% biodegradation occurs after 170 days. ▪ Additional data on time/temperature history experienced in landfills will be needed.	[27]
Materials: semi-crystalline PLA Environments: landfill Temperature: 35, 55 °C	▪ Hydrolytic degradation, followed by enzymatic degradation	▪ No biodegradation at 35 °C due to high degree of crystallinity after 60 days. ▪ Readily biodegradable under thermophilic conditions (55 °C).	[29]

summarizes PLA degradation mechanisms in wastewater and landfills of recent studies. While numerous studies have explored the biodegradation of PLA in various environments, like industrial compost, activated sludge, home compost, and cultivated soil, there is notably less work on PLA degradation in aquatic settings, particularly in seawater and freshwater [36,41,104,111,112,113,114]. This gap in knowledge highlights the significant deficiency in understanding PLA’s degradability in natural aquatic environments such as lakes, rivers, ponds, and marine ecosystems. Considering that there is an abundant effective biofilm on a PLA film, there are two notable observations during its degradation process. First, degradation leads to an increase in carboxylic acid chain ends, which are known to accelerate ester hydrolysis through autocatalysis. Second, only soluble oligomers within the aqueous medium surrounding such a matrix are able to escape. Early in the degradation process, soluble oligomers near the surface can be leached out, while they remain trapped in the deeper zones [16,96].

3. Mathematical Modeling of PLA Biodegradation Linked to the Experiments

The experimental approach employed to quantify biodegradation aims at measuring carbon dioxide (CO₂) as a final product. This is performed via standard test methods such as ISO 14855 [115] for composting conditions, or ASTM 5988 for soil environments. In these methods, the CO₂ emanating from biodegradation can be trapped by metal hydroxides like potassium hydroxide (KOH) or barium hydroxide (Ba(OH)₂). For example, if KOH is used as a trap, potassium carbonate (${{\mathrm{K}}_2\mathrm{C}\mathrm{O}}_3$) forms according to the following reaction:

$${2\mathrm{K}\mathrm{O}\mathrm{H}\left(\mathrm{a}\mathrm{q}\right)+\mathrm{C}\mathrm{O}}_2\left(\mathrm{g}\right)={{\mathrm{K}}_2\mathrm{C}\mathrm{O}}_3\left(\mathrm{aq}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$$

(1)

By subsequently titrating the carbonate with hydrochloric acid (HCl), the following reaction would occur:

$${{\mathrm{K}}_2\mathrm{C}\mathrm{O}}_3\left(\mathrm{aq}\right)+2\mathrm{H}\mathrm{C}\mathrm{l}\left(\mathrm{a}\mathrm{q}\right)=2\mathrm{K}\mathrm{C}\mathrm{l}\left(\mathrm{a}\mathrm{q}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)+{\mathrm{C}\mathrm{O}}_2\left(\mathrm{g}\right)$$

(2)

The sum of reactions (1) and (2) yields Equation (3). As a result, the number of moles of CO₂ released from biodegradation is equal to half of the moles of HCl used to titrate the entire trap (KOH), as per Equation (4). Then, the degree of biodegradation can be calculated using Equation (5):

$$2\mathrm{K}\mathrm{O}\mathrm{H}+2\mathrm{H}\mathrm{C}\mathrm{l}\left(\mathrm{a}\mathrm{q}\right)=2\mathrm{K}\mathrm{C}\mathrm{l}+{2\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$$

(3)

$$\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f} {\mathrm{C}\mathrm{O}}_2={\displaystyle \frac{\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s} \mathrm{o}\mathrm{f} \mathrm{H}\mathrm{C}\mathrm{l}}{2}}$$

(4)

$$\%\mathrm{biodegradation}={\displaystyle \frac{\mathrm{e}\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{v}\mathrm{e}\mathrm{d} {\mathrm{C}\mathrm{O}}_2}{\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} {\mathrm{C}\mathrm{O}}_2}}\times 100$$

(5)

where the predicted mass of CO₂ is the amount expected from complete biodegradation.

The second approach is to measure the number average molecular mass (M_n) of the specimens extracted from different environments using Gel Permeation Chromatography (GPC), which provides insights into the molecular degradation of the material.

Those two methods are very time-consuming and would take months or years to complete. Hence, developing mathematical models is essential to reduce the time of measuring the degradation rate for PLA and its different compositions. The first experimental approach is linked to the biodegradation model (see Section 3.2), and the second one (M_n) is linked to the hydrolytic degradation model (see Section 3.1). Moreover, there are other models of PLA degradation such as the atomistic modeling of water diffusion in hydrolytic biomaterials [116], multi-scale modeling using the Cellular Automata (CA), and kinetic Monte Carlo modeling (KMC) [117]. However, the following mathematical models are the most used in the literature.

3.1. Hydrolytical Degradation Model

Measuring the degradation rate in water media is a time-consuming process. Therefore, the development of mathematical models to predict the rate of degradation has drawn significant attention [24,25,26,116,117,118,119,120,121]. The earlier mathematical models were developed using the diffusion–reaction systems (zero-order kinetics) for drug release developed in applications [122,123]. The models are based on the hydrolysis of degradable polymers. They have been developed considering the molecular mass changes in a polymer as a function of the ester bond concentration. Reference [118] introduced some modifications, resulting in a comprehensive mathematical model for biodegradable polymer degradation (cf. Figure 6 illustrates the one-dimensional situation). Equation (6) expresses the rate of chain scissions as a combination of non-catalytic reaction (the rate coefficient k₁) with the end scissions and the autocatalytic reaction (the rate coefficient k₂), which is catalyzed by the carboxylic acid end groups. The short chains are considered as the products of polymer hydrolysis. The diffusion of the short chains is assumed to be the controlling step in the degradation process. Therefore, Ref. [90] took into account the diffusion process, and the corresponding model can predict the ester bound concentration in the polymers, the monomer concentration (see Equation (9), in which diffusion of monomers affects the total rate of chain scissions), and the volumetric degree of crystallinity (see Equation (7), showing how it affects ester bond concentration).

$${\displaystyle \frac{\mathrm{d}\mathrm{R}}{\mathrm{d}\mathrm{t}}}={\mathrm{k}}_1{\mathrm{C}}_{\mathrm{e}}+{\mathrm{k}}_2{\mathrm{C}}_{\mathrm{e}}{\mathrm{C}}_{\mathrm{m}}^{\mathrm{n}}$$

(6)

where R is the number of chain scissions, C_e is the ester bond concentration, C_m is the monomer concentration, k₁ is the non-catalytic reaction coefficient of the hydrolysis reaction, k₂ is the autocatalytic reaction coefficient of the hydrolysis reaction, and n is the degree of dissociation of the acid end group.

The reduction in the ester bond concentration can be written as

$${\displaystyle \frac{\mathrm{d}{\mathrm{C}}_{\mathrm{e}}}{\mathrm{d}\mathrm{t}}}=-{\displaystyle \frac{\mathrm{d}\mathrm{R}}{\mathrm{d}\mathrm{t}}}-\omega {\displaystyle \frac{\mathrm{d}{\mathrm{x}}_{\mathrm{C}}}{\mathrm{d}\mathrm{t}}}$$

(7)

in which $\omega$ is the crystalline polymer chain concentration.

According to the Avrami equation for crystallization, the degree of crystallinity depends on time t as

$${\mathrm{x}}_{\mathrm{C}}-{\mathrm{x}}_{\mathrm{C}0}=1-\exp \left[-{\left({\mathrm{k}}_{\mathrm{C}}\mathrm{t}\right)}^{{\mathrm{n}}_{\mathrm{A}}}\right]$$

(8)

where x_c0 is the degree of crystallinity at the beginning, and x_C is the current degree of crystallinity, n_A is the Avrami exponent coefficient, and k_c is the rate-responsible factor in the Avrami law.

The incorporation of the Fikian diffusion generalizes Equation (6) as the following species balance equation:

$${\displaystyle \frac{\mathrm{d}{\mathrm{C}}_{\mathrm{m}}}{\mathrm{d}\mathrm{t}}}={\displaystyle \frac{\mathrm{d}\mathrm{R}}{\mathrm{d}\mathrm{t}}}+{\mathrm{d}\mathrm{i}\mathrm{v}}_{\mathrm{x}\mathrm{i}}\left[{\mathrm{D}\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}}_{\mathrm{x}\mathrm{i}}\left({\mathrm{C}}_{\mathrm{m}}\right)\right]$$

(9)

in which D is the effective diffusion coefficient, which depends on the porosity p through a linear relation D = D₀(1 + αp), in which α is the porosity coefficient, and D₀ is the intrinsic diffusion coefficient. Accordingly, the following dimensionless parameters correspond to the problem at hand:

$${\overline{\mathrm{C}}}_{\mathrm{e}}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{e}}}{{\mathrm{C}}_{{\mathrm{e}}_0}}},{\overline{\mathrm{C}}}_{\mathrm{m}}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{m}}}{{\mathrm{C}}_{{\mathrm{e}}_0}}},{\overline{\mathrm{X}}}_{\mathrm{i}}={\displaystyle \frac{{\mathrm{X}}_{\mathrm{i}}}{\mathrm{l}}},\overline{\mathrm{t}}=\left({\mathrm{k}}_2{\mathrm{C}}_{{\mathrm{e}}_0}^{\mathrm{n}}\right)\mathrm{t},{\overline{\mathrm{k}}}_1={\displaystyle \frac{{\mathrm{k}}_1}{{\mathrm{k}}_2{\mathrm{c}}_{{\mathrm{e}}_0}^{\mathrm{n}}}},{\overline{\mathrm{D}}}_0={\displaystyle \frac{{\mathrm{D}}_0}{{\mathrm{C}}_{{\mathrm{e}}_0}^{\mathrm{n}}{\mathrm{k}}_2{\mathrm{l}}^2}}$$

(10)

whereas the dimensionless governing equations take the following form:

$${\displaystyle \frac{\mathrm{d}{\overline{\mathrm{C}}}_{\mathrm{m}}}{\mathrm{d}\overline{\mathrm{t}}}}={\overline{\mathrm{k}}}_1{\overline{\mathrm{C}}}_{\mathrm{e}}+{\overline{\mathrm{C}}}_{\mathrm{e}}{\overline{\mathrm{C}}}_{\mathrm{m}}^{\mathrm{n}}+{\overline{\mathrm{D}}}_0\mathrm{div}\left\{1+\mathrm{\alpha }\left[1-\left({\overline{\mathrm{C}}}_{\mathrm{m}}+{\overline{\mathrm{C}}}_{\mathrm{e}}\right)\right]\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{d}\left({\overline{\mathrm{C}}}_{\mathrm{m}}\right)\right.\}$$

(11)

$${\displaystyle \frac{\mathrm{d}{\overline{\mathrm{C}}}_{\mathrm{e}}}{\mathrm{d}\overline{\mathrm{t}}}}=-\left({\overline{\mathrm{k}}}_1{\overline{\mathrm{C}}}_{\mathrm{e}}+{\overline{\mathrm{C}}}_{\mathrm{e}}{\overline{\mathrm{C}}}_{\mathrm{m}}^{\mathrm{n}}\right)$$

(12)

Eventually, the dimensionless Equations (11) and (12) were solved using the finite element method (FEM) [118]. The degradation behavior is controlled by the interplay between the reaction and diffusion processes. For the lower values of the reaction-rate coefficient k₁, the diffusion process controls degradation, while at higher values of k₁, the degradation process is kinetically controlled (see Figure 7).

In the earlier reaction–diffusion models, the autocatalytic nature of the hydrolysis reactions and the degree of crystallinity were not taken into account [122,123]. Also, in Wang’s model [118] and the early analytical models, several important factors were not taken into account during the polymer degradation process. These include the change in the concentration of ester bonds, the formation of oligomers (which are hydrolysis products consisting of short chains), the diffusion of these oligomers to the outside environment, and the degree of crystallization [118]. Later, the authors of Ref. [24] neglected diffusion because it is supposedly suppressed by crystallinity. Additionally, they included oligomer concentration due to degradation in Equations (6)–(12). Finally, the authors of Ref. [16] extended the model of Ref. [24] by incorporating a detailed description of crystallinity during degradation. Because the effect of crystallinity on PLA hydrolysis is complex, Ref. [16] introduces a three-phase structure model including mobile amorphous fraction (MAF), crystalline fraction (CF), and rigid amorphous fraction (RAF), as per Equations (13)–(15) defining these fractions:

$${\mathrm{x}}_{\mathrm{c}}={\displaystyle \frac{\mathsf{\Delta }{\mathrm{H}}_{\mathrm{m}}-\sum \mathsf{\Delta }{\mathrm{H}}_{\mathrm{c}}}{\mathsf{\Delta }{\mathrm{H}}_{\mathrm{m}}^0}}$$

(13)

$${\mathrm{x}}_{\mathrm{M}\mathrm{A}\mathrm{F}}={\displaystyle \frac{\mathsf{\Delta }{\mathrm{C}}_{\mathrm{p}}}{\mathsf{\Delta }{\mathrm{C}}_{\mathrm{p}}^0}}$$

(14)

$${\mathrm{x}}_{\mathrm{R}\mathrm{A}\mathrm{F}}=1-{\mathrm{x}}_{\mathrm{M}\mathrm{A}\mathrm{F}}-{\mathrm{x}}_{\mathrm{C}}$$

(15)

where ΔH_m is the enthalpy of fusion found using the integration of the heat flux in the melting region, ΔH_c is the exothermic peak enthalpy, Δ${\mathrm{H}}_{\mathrm{m}}^0$ is the melting enthalpy of 100% crystalline PLA (139 J/g) (calculated in Ref. [124]), Δ$\mathrm{C}$_p is the measured heat capacity change at glass transition temperature (T_g) of a specimen, and $\mathsf{\Delta }{\mathrm{C}}_{\mathrm{p}}^0$ is the heat capacity change of 100% amorphous PLA.

Furthermore, Ref. [16] investigated the effect of crystallinity (CF, MAF, and RAF) on the hydrolytic degradation of PLA at 45 °C to 85 °C. The authors of Ref. [16] evaluated the model for certain values of the molecular mass and degree of crystallinity to correlate the ester bond concentration with the entire amorphous fractions (MAF and RAF) by treating the crystalline fraction as non-hydrolysable. They rewrote Equation (12) in the following form:

$${\displaystyle \frac{\mathrm{d}{\mathrm{R}}_{\mathrm{s}}}{\mathrm{d}\mathrm{t}}}={\mathrm{k}}_1{{\mathrm{C}}_{\mathrm{e}}+\mathrm{k}}_2^{\prime }{{\mathrm{C}}_{\mathrm{e}}\mathrm{C}}_{{\mathrm{H}}^{+}}$$

(16)

where R_s is the total molar concentration of chain scissions, k₁ is the rate coefficient for non-catalytic hydrolysis, ${\mathrm{K}}_2^{\prime }$ is the rate coefficient for the autocatalytic hydrolysis, and ${\mathrm{C}}_{\mathrm{e}}$ is the total concentration of the ester bonds of the long chains in both MAF and RAF, which can be calculated as

C_e = C_e0 − C_ol − ω (x_C − x_C0)

(17)

Here, C_e0 is the ester units in MAF and RAF before hydrolysis, C_ol is the total concentration of the ester units in all the oligomers and monomers (of a length less than 8 units), ω is the total concentration of the ester bonds in the crystalline phase, x_C is the crystallinity at time t, x_C0 is the crystallinity at time t = 0, and ${\mathrm{C}}_{{\mathrm{H}}^{+}}$ is the concentration of carboxylic acid end groups (which are the catalysts of hydrolysis) of the short chains defined as

$${\mathrm{C}}_{{\mathrm{H}}^{+}}={\mathrm{k}}_{\mathrm{a}}{\left({\displaystyle \frac{{\mathrm{C}}_{\mathrm{o}\mathrm{l}}}{\mathrm{m}(1-{\mathrm{X}}_{\mathrm{C}})}}\right)}^{0.5}$$

(18)

in which k_a is the acid disassociation coefficient of carboxylic end groups and m is the average degree of polymerization. Hence, Equation (16) could be presented as

$${\displaystyle \frac{\mathrm{d}{\mathrm{R}}_{\mathrm{s}}}{\mathrm{d}\mathrm{t}}}={\mathrm{k}}_1{\mathrm{C}}_{\mathrm{e}}+{\mathrm{k}}_2{\mathrm{C}}_{\mathrm{e}}{\left({\displaystyle \frac{{\mathrm{C}}_{\mathrm{o}\mathrm{l}}}{1-{\mathrm{X}}_{\mathrm{C}}}}\right)}^{0.5}$$

(19)

in which k₂ is defined as

$${\mathrm{k}}_2={\displaystyle \frac{{\mathrm{k}}_2^{\prime }{\mathrm{k}}_{\mathrm{a}}^{0.5}}{{\mathrm{m}}^{0.5}}}$$

(20)

The number average molecular mass (M_n) is calculated by adding up the weights of all the polymer chains in a specimen (in both its amorphous and crystalline parts) excluding the oligomers that might dissolve in the hydrolysis solution. This total molecular mass is then divided by the sum of the total number of all chains before hydrolysis (${\mathrm{N}}_{{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{i}\mathrm{n}}_0}$) and cleaved chains (R_s), excluding oligomers as per

$${\mathrm{M}}_{\mathrm{n}}={\displaystyle \frac{{(\mathrm{C}}_{\mathrm{e}0}+\omega {\mathrm{X}}_{\mathrm{C}0}-{\mathrm{C}}_{\mathrm{o}\mathrm{l}}){\mathrm{M}}_0}{{\mathrm{N}}_{{\mathrm{c}\mathrm{h}\mathrm{a}\mathrm{i}\mathrm{n}}_0}+{\mathrm{R}}_{\mathrm{s}}-\left(\frac{{\mathrm{C}}_{\mathrm{o}\mathrm{l}}}{\mathrm{m}}\right)}}$$

(21)

The authors used four different PLA specimens, specifically, amorphous PLA film (PLA–Q), fully crystallized film (PLA–MC–C), and partially crystallized films (PLA–MC–A and PLA–MC–B), to evaluate the model predictions for them. Figure 8 depicts the predicted dependences of M_n on the hydrolysis time at different temperatures. The data presented by symbols is contrasted with the curves of the model predictions based on Equation (21). The results reveal that among PLA specimens with varying degrees of crystallinity, there is only minimal variation in terms of the normalized M_n at lower temperatures (see Figure 8a–c). Additionally, there is no substantial difference in M_n at higher temperatures (Figure 8d).

The model of Ref. [16] is based on the assumption that crystals present a non-hydrolysable component within a polymer system. This simplification facilitates the assessment of the rate coefficients for both non-catalytic (k₁) and autocatalytic (k₂) mechanisms for hydrolysable RAF and MAF. Non-catalytic hydrolysis of PLA involves breaking ester bonds upon exposure to water, while the autocatalytic hydrolysis is accelerated by the carboxylic acid chain ends of oligomers. The incorporation of these rate coefficients improves the accuracy of the prediction of hydrolysis behavior, enabling the precise calculation of the degradation trends in time.

3.2. Biodegradation Model

PLA biodegradation under standards ISO 14855 (for aerobic biodegradability) and ISO 11734 [125] (for anaerobic biodegradability) can take several months and years, respectively. Accordingly, there has been considerable interest in the development of mathematical models capable of facilitating studies of the necessary factors required for designing biodegradable devices. Under composting conditions, the biodegradation rate can be linked to the mineralization of monomers. It was demonstrated that under controlled composting conditions, the degradation of solid carbon to carbon dioxide follows a first-order reaction [126,127,128,129,130].

In a recent study, it was suggested that the degradation of polymers can be divided into two main steps [25]. First, the primary degradation, in which the long chains are cleaved to oligomers. Second, ultimate degradation, in which microorganisms can assimilate the short chains and release carbon dioxide, water, and biomass as the final products. As shown in Figure 9, the total carbon content in a polymer is considered as readily (C_r), moderately (C_m), and slowly (C_s) hydrolysable carbons. According to the model of Ref. [25], the curve of carbon dioxide production includes two branches corresponding to the growth and stationary phase [130]. Later, the model of Ref. [130] was modified by adding an additional phase (the lag phase) to the curves [25].

Beginning with the first-order kinetic model, there are three separate kinetics equations, namely

$${\displaystyle \frac{\mathrm{d}{\mathrm{C}}_{\mathrm{r}}}{\mathrm{d}\mathrm{t}}}=-{\mathrm{k}}_{\mathrm{h}\mathrm{r}}{\mathrm{C}}_{\mathrm{r}}$$

(22)

$${\displaystyle \frac{\mathrm{d}{\mathrm{C}}_{\mathrm{m}}}{\mathrm{d}\mathrm{t}}}=-{\mathrm{k}}_{\mathrm{h}\mathrm{m}}{\mathrm{C}}_{\mathrm{m}}$$

(23)

$${\displaystyle \frac{\mathrm{d}{\mathrm{C}}_{\mathrm{s}}}{\mathrm{d}\mathrm{t}}}=-{\mathrm{k}}_{\mathrm{h}\mathrm{s}}{\mathrm{C}}_{\mathrm{s}}$$

(24)

where k_hr, k_hm, and k_hs are rapid, moderate, and slow hydrolysis rate coefficients. The intermediate carbon, then, will be consumed to mineralize as per Equations (25) and (26):

$${\displaystyle \frac{\mathrm{d}{\mathrm{C}}_{\mathrm{a}\mathrm{q}}}{\mathrm{d}\mathrm{t}}}={\mathrm{k}}_{\mathrm{h}\mathrm{r}}{\mathrm{C}}_{\mathrm{r}}+{\mathrm{k}}_{\mathrm{h}\mathrm{m}}{\mathrm{C}}_{\mathrm{m}}+{\mathrm{k}}_{\mathrm{h}\mathrm{s}}{\mathrm{C}}_{\mathrm{s}}{–\mathrm{k}}_{\mathrm{a}\mathrm{q}}{\mathrm{C}}_{\mathrm{a}\mathrm{q}}$$

(25)

$${\displaystyle \frac{\mathrm{d}{\mathrm{C}}_{\mathrm{T}}}{\mathrm{d}\mathrm{t}}}=-{\mathrm{k}}_{\mathrm{a}\mathrm{q}}{\mathrm{C}}_{\mathrm{a}\mathrm{q}}$$

(26)

with k_aq being the mineralization rate coefficient of water-soluble carbon into carbon dioxide.

After solving the equations analytically, the following equation can be derived to plot the CO₂ concentration versus time:

$${\mathrm{C}}_{\mathrm{T}}-\mathrm{t}=\left[\begin{array}{c}{\mathrm{C}}_{\mathrm{aq}0}{(1-\mathrm{e}}^{-{\mathrm{k}}_{\mathrm{a}\mathrm{q}}\left(\mathrm{t}-\mathrm{C}\right)})\\ +\left[{\mathrm{C}}_{\mathrm{r}0}\left(1-{\displaystyle \frac{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}}{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}-{\mathrm{k}}_{\mathrm{h}\mathrm{r}}}}{\mathrm{e}}^{{-\mathrm{k}}_{\mathrm{h}\mathrm{r}}\left(\mathrm{t}-\mathrm{C}\right)}+{\displaystyle \frac{{\mathrm{k}}_{\mathrm{h}\mathrm{r}}}{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}-{\mathrm{k}}_{\mathrm{h}\mathrm{r}}}}{\mathrm{e}}^{{-\mathrm{k}}_{\mathrm{a}\mathrm{q}}\left(\mathrm{t}-\mathrm{C}\right)}\right)\right]\\ +\left[{\mathrm{C}}_{\mathrm{m}0}\left(1-{\displaystyle \frac{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}}{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}-{\mathrm{k}}_{\mathrm{h}\mathrm{m}}}}{\mathrm{e}}^{{-\mathrm{k}}_{\mathrm{h}\mathrm{m}}\left(\mathrm{t}-\mathrm{C}\right)}+{\displaystyle \frac{{\mathrm{k}}_{\mathrm{h}\mathrm{m}}}{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}-{\mathrm{k}}_{\mathrm{h}\mathrm{m}}}}{\mathrm{e}}^{{-\mathrm{k}}_{\mathrm{a}\mathrm{q}}\left(\mathrm{t}-\mathrm{C}\right)}\right)\right]\\ +\left[{\mathrm{C}}_{\mathrm{s}0}\left(1-{\displaystyle \frac{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}}{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}-{\mathrm{k}}_{\mathrm{h}\mathrm{s}}}}{\mathrm{e}}^{{-\mathrm{k}}_{\mathrm{h}\mathrm{s}}\left(\mathrm{t}-\mathrm{C}\right)}+{\displaystyle \frac{{\mathrm{k}}_{\mathrm{h}\mathrm{s}}}{{\mathrm{k}}_{\mathrm{a}\mathrm{q}}-{\mathrm{k}}_{\mathrm{h}\mathrm{s}}}}{\mathrm{e}}^{{-\mathrm{k}}_{\mathrm{a}\mathrm{q}}\left(\mathrm{t}-\mathrm{C}\right)}\right)\right]\end{array}\right]$$

(27)

Figure 10 illustrates the agreement between the model prediction and experimental data for the cumulative percentage C-CO₂ over the testing time for the PLA biodegradation under composting conditions [25].

To sum up the mathematical models,

Table 4. A comparison of the developed mathematical models on PLA degradation.

Aspect	Hydrolytic Degradation Model	Biodegradation Model
Purpose	Predict degradation rate of PLA and its mechanism in water media.	Facilitate study of biodegradable devices and degradation under composting conditions.
Key Mechanisms	Hydrolysis involving non-catalytic and autocatalytic reactions influenced by molecular concentration.	Two stages: primary degradation (cleaving long chains to oligomers) and ultimate degradation (microbial assimilation).
Main Equations	Ester bonds’ scission rate (first-order equation) $({\displaystyle \frac{\mathrm{d}\mathrm{R}}{\mathrm{d}\mathrm{t}}}={\mathrm{k}}_1{\mathrm{C}}_{\mathrm{e}}+{\mathrm{k}}_2{\mathrm{C}}_{\mathrm{e}}{\mathrm{C}}_{\mathrm{m}}^{\mathrm{n}}) -$ Equation (6).	Hydrolysable carbon $({\displaystyle \frac{\mathrm{d}{\mathrm{C}}_{\mathrm{T}}}{\mathrm{d}\mathrm{t}}}=-{\mathrm{k}}_{\mathrm{a}\mathrm{q}}{\mathrm{C}}_{\mathrm{a}\mathrm{q}}) -$ Equation (26).
Modeling Approach	Incorporates diffusion and crystallinity, utilizes finite element method for model solving.	Utilizes first-order kinetics; focuses on mineralization of carbon dioxide production.
Predictions/Outcomes	Controls degradation by reaction and diffusion interplay; predicts normalized molecular weight $({\mathrm{M}}_{\mathrm{n}}$) changes over time.	Cumulative CO2 production correlates well with experimental data under composting conditions.
Strengths	Comprehensive model by including temperature and crystallinity as influencing factors.	Straightforward experimental validation by either gas analyzer or titration method.
Drawbacks	Indirect experimental validation, which increases error probability using Equation (21).	Models are based on first-order kinetics, potentially oversimplifying complex degradation processes.

shows a comparison between two main models (biodegradation and hydrolytic models) together.

4. Micro/Nano-Plastics (MPs and NPs) of PLA

Microplastics are extremely small pieces of plastic (less than 5 mm) debris in the environment resulting from the disposal and breakdown of consumer products and industrial waste. They are categorized based on their origins into two main types: primary and secondary. Primary microplastics are the intentionally manufactured plastics with micrometer dimensions such as microbeads [131], whereas secondary microplastics originate from fragmentation and breakdown of environmental plastics due to external factors [132]. The term “biodegradable” does not automatically imply 100% environmental friendliness of a polymeric material, necessitating further exploration into their degradation pathways under natural environmental conditions. MPs and NPs, ranging in size from 50 nm to 5 mm, are residual plastic fragments remaining after the bulk plastics’ degradation. Degradation methods encompass biodegradation and abiotic technologies, with a combination often yielding superior results [133,134,135,136]. However, it should be emphasized that plastic degradation generates significant amounts of MPs and NPs. When such materials are ingested by organisms, it can cause physical harm and inflammatory effects, as well as facilitate the entry of various contaminants into the food chain [137]. Moreover, the electric charge, high specific surface area, and hydrophobic nature of MPs make them effective carriers for transporting various pollutants. The adsorption capacity of MPs is affected by such factors as their physicochemical characteristics, the properties of an adsorbed medium, and the chemical nature of contaminants [138].

With the increasing production of PLA, there is an expected rise in its contribution to plastic waste, potentially leading to a similar impact as that of traditional plastics, i.e., placing PLA in the class of novel emerging contaminants. Recently, several studies have been devoted to PLA MPs. Figure 11 ascertains a noticeable surge in such research activity since 2021, highlighting the dynamic nature of PLA MPs on the plastic pollution landscape.

The lack of standardized methods for detecting and quantifying MPs is a significant challenge in assessing their impact on soil environments. Nevertheless, there are systematic approaches available to isolate MPs from environmental samples. In general, there are two main ways to degrade MPs. First, the catalytic degradation of MPs simultaneously with the bulk polymer. Second, catalytic recycling and upcycling plastic wastes into monomers, fuels, and valorized chemicals [139]. Various techniques such as chemical digestion [140], filtration [141], elutriation [142], pressurized fluid extraction [143], density separation [144], electrostatic separation [145], centrifugation [146], ultrasonication [147], and oil extraction [148] are employed for this purpose in separating MPs from soils. Additionally, artificial aging treatments are frequently applied to degrade microplastics. These methods include ultraviolet (UV) weathering, Fenton oxidation, and persulfate oxidation [149,150,151,152,153]. Artificial aging refers to the accelerated exposure of materials to controlled environmental conditions to simulate long-term aging effects [154]. Factors such as elevated temperature and UV radiation play a significant role in the acceleration of the degradation rate [154,155].

Although blending PLA with other biodegradable polymers such as poly(butylene succinate) (PBS) [156], poly(ε-caprolactone) (PCL) [157], polyhydroxyalkanoates (PHAs) [82], and a polysaccharide starch [158] can accelerate PLA degradation, it cannot guarantee not to produce any MPs during the degradation process. Several studies include different blend compositions of PLA, which can alter the degradation level. As a result, products of the degradation process of MPs are not necessarily monomers or oligomers. In each case, there is a different mechanism for PLA MP degradation [31]. It has been shown that the degradation tendency of PLA increases with various additives. Metals and metal oxides, which can provide reactive surface areas [159,160,161,162,163], accelerate the hydrolysis process. For example, TiO₂ nanofillers enhance PLA hydrolysis at the interface of the PLA matrix and nanofillers, and subsequently, facilitate degradation process [164]. Similar results were obtained for montmorillonite clay, SiO₂, and polyhedral oligomeric silsesquioxanes (POSSs) [165,166,167]. ZnO nanoparticles as basic metal oxides can provide a proper surface area for PLA to anchor. As a result, it can absorb hydroxyl ions of water and create a regular degradation pattern, which can avoid producing MPs [168]. There is a novel method to reduce MP amounts during PLA degradation named embedding enzymes via melt extrusion or the casting process. For example, the authors of Ref. [169] embedded lipase into three different polyesters to develop self-degradable polymers.

Table 5. Overview of PLA micro/nano-plastics: characteristics, impacts, and degradation methods.

Aspect	Description/Findings	Ref.
Definition of Microplastics (MPs)	Small plastic pieces less than 5 mm resulting from the breakdown of larger plastics or intentionally manufactured.	[133,134,135,136]
Types of Microplastics	▪ Primary Microplastics: Intentionally manufactured, e.g., microbeads. ▪ Secondary Microplastics: Result from the fragmentation of existing plastics due to environmental factors.	[131]
Challenges in Detection	Lack of standardized methods hinders assessment of MPs’ impact on soil environments; systematic approaches exist for isolation.	[133,134,135]
Degradation Techniques	▪ Physicochemical Methods: Chemical digestion, filtration, elutriation, density separation, etc. ▪ Artificial Aging: Including UV weathering, Fenton oxidation, and persulfate oxidation to accelerate degradation.	[140,141,142,143,144,145,147,148,149,150,151,152,153,170]
Blend Composition Effects	Blending PLA with PBS, PCL, and PHAs can accelerate degradation but may still produce MPs.	[82,156,157]
Additive Effects on Degradation	Additives like metals and metal oxides such as TiO2 nanofillers and ZnO nanoparticles enhance hydrolysis and degradation rates.	[164,168]
Innovative Methods	Embedding enzymes during the melt extrusion or casting process to create self-degradable polymers.	[169]

summarizes and concludes the above materials regarding micro/nano-plastics.

5. Perspectives

Recently, there has been a notable increase in the global consumption of plastic products, leading to a rise in plastic waste production. One promising approach to address this issue is the recycling of plastic waste [171,172,173,174]. According to a review by Atakok et al. (2022) [175], the most commonly aimed subjects related to the production techniques and fibrous materials are the fused deposition modeling (FDM) production method and PLA filaments, respectively [175]. The interest to PLA filaments stems from their easy recycling compared to other filament options. As a result, the use of PLA fibrous materials in subsequent 3D printing processes is affordable as a raw material [176,177,178,179]. Recycled PLA aggregates can be used as fine aggregates in cementitious composites to enhance their physical and mechanical properties and durability [171]. Additionally, they can be used to blend with other bioplastics such as PBS, PCL, and PHAs to achieve desirable properties [180,181,182,183].

6. Conclusions

In this review article, the objective was to assess the degradation behavior of PLA in various environments. Specifically, PLA degradation behavior in compost, soil, water, wastewater, and landfills was considered, and the factors affecting degradation rates were elucidated. Moreover, the corresponding mathematical kinetic-diffusion models of PLA degradation under hydrolytic and enzymatic mechanisms were discussed. The highlights from the review can be listed as follows:

• From a biodegradation viewpoint, PLA demonstrates biodegradability in compost, wastewater, soil, under accelerated landfill conditions, and in water in descending order.
• The primary mechanism driving PLA degradation involves the hydrolysis of ester bonds. This process occurs via autocatalytic hydrolysis in water, facilitated by carboxylic acid end groups of PLA.
• PLA undergoes enzymatic degradation in compost and soil, catalyzed by different enzymes secreted by microorganisms.
• While temperature significantly influences PLA biodegradation under both aerobic (compost) and anaerobic (digested sludge) conditions, degradation occurs at a slower rate in anaerobic environments.
• It should be emphasized that neat PLA cannot be classified as a completely biodegradable polymer, as it generates microplastics (MPs) during biodegradation.
• The generation of PLA MPs is inevitable; however, the utilization of synthetic enzymes, like metal oxides, can significantly reduce MP production.
• To streamline the assessment of PLA degradability, alternative methods such as diffusion–reaction and zero-order kinetic models can be employed, bypassing the time-consuming conventional approaches.

Because of the lack of detailed information on the PLA MP structure and their degradation mechanisms, studies of the factors and mechanism underlying MP degradation and developing the corresponding mathematical models hold great promise for applications.