Enhancing melt strength and crystallization kinetics in polylactide: Influence of chain topology

Enhancing melt strength and crystallization kinetics in polylactide: Influence of chain topology Ainhoa Fern´ andez-Tena a , Mercedes Fern´ andez a,* , Aleida J. Sandoval b , M. Itxaso Calafel a , Amaia Aguirre c , Nora Aranburu a , Gonzalo Guerrica-Echevarria a , Maria Laura Di Lorenzo d , Alessandra Longo d,1 , Juan Francisco Vega e,* , Alejandro J. Müller a,f,** a POLYMAT and Department of Advanced Polymers and Materials: Physics, Chemistry and Technology, Faculty of Chemistry, University of the Basque Country UPV/ EHU, Paseo Manuel de Lardizabal 3, 20018 Donostia-San Sebasti´ an, Spain b Laboratorio de Procesamiento de Alimentos, Departamento de Tecnología de Procesos Biol´ ogicos y Bioquímicos, Universidad Sim´ on Bolívar, Aptdo. 89000, 1080A Caracas, Venezuela c POLYMAT and Department of Applied Chemistry, University of the Basque Country UPV/EHU, Tolosa hiribidea 72, 20018 Donostia-San Sebasti´ an, Spain d National Research Council (CNR), Institute of Polymers, Composites and Biomaterials (IPCB), c/o Comprensorio Olivetti, Via Campi Flegrei 34, 80078, Pozzuoli, Italy e BIOPHYM, Department of Macromolecular Physics, Instituto de Estructura de la Materia (IEM-CSIC), c/Serrano 113bis, 28006 Madrid, Spain f IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain ARTICLE INFO Keywords: Polylactide Crystallization kinetics Long chain branching Computational rheology FT rheology LAOS ABSTRACT The generation of long-chain branches (LCB) in biobased and biodegradable polylactide (PLA) by adding different amounts of a chain extender is studied. The rheological and calorimetric behavior have been used to determine the effect of LCB presence and their topology on PLA melt strength and crystallization behavior. Rheological modeling of linear and non-linear viscoelastic shear and extensional properties identified several possible branched structures. Moreover, remarkable differences were observed for the different topologies regarding the intrinsic non-linear parameters and the intra-cycle elastic and viscous non-linearities. Differential scanning calorimetry and polarized light optical microscopy measurements revealed a significant increase in the nucleation density and rate of PLA with increasing the amount of LCB, albeit they provoke a decrease in the growth rate due to a reduction in chain diffusion. Nevertheless, overall crystallization rate values revealed a predominant effect of nucleation over crystal growth. The introduction of LCB within the chains is highly beneficial as they increase nucleation, crystallinity, and elongational viscosity, thus improving the properties of biodegradable PLA. 1. Introduction Poly(lactic acid) or polylactide (PLA) is a thermoplastic aliphatic polyester derived from renewable resources such as corn starch, sugar cane, and other renewable biomass products and waste [1]. Due to its competitive processing costs and its good mechanical and physical properties [2] (e.g., high modulus, high strength, transparency, and barrier properties), the development of biodegradable products based on PLA has received increasing attention from both academia and industry and now represents >10 % of the biomass-based consumer products market, emerging as a promising substitute for petroleumderived polymers in a wide range of commodity and engineering applications [3], such as packaging, textiles, construction and automotive [1]. Furthermore, due to its biocompatibility, non-toxic characteristics, and biodegradability, PLA could also be a promising candidate for biomedical applications, such as drug delivery, blood vessels, tissue engineering, and scaffolds [4,5]. The increasingly urgent need to reduce dependence on petroleum-based materials certainly opens up market opportunities for this environmentally friendly polymer. This requires overcoming certain drawbacks described for PLA, which may limit its * Corresponding authors. ** Correspondence to: A. J. Müller, POLYMAT and Department of Advanced Polymers and Materials: Physics, Chemistry and Technology, Faculty of Chemistry, University of the Basque Country UPV/EHU, Paseo Manuel de Lardizabal 3, 20018 Donostia-San Sebasti´ an, Spain. E-mail addresses: [email protected] (M. Fern´ andez), [email protected] (J.F. Vega), [email protected] (A.J. Müller). 1 Present address: National Research Council (CNR), Institute of Polymers, Composites and Biomaterials (IPCB), Via Paolo Gaifami 18, 95126, Catania (CT), Italy. Contents lists available at ScienceDirect International Journal of Biological Macromolecules journal homepage: www.elsevier.com/locate/ijbiomac https://doi.org/10.1016/j.ijbiomac.2024.136783 Received 14 June 2024; Received in revised form 14 October 2024; Accepted 20 October 2024 International Journal of Biological Macromolecules 282 (2024) 136783 Available online 28 October 2024 0141-8130/© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC license ( http://creativecommons.org/licenses/bync/4.0/ ). production and use in different applications. These limitations are mainly due to PLA’s low melt strength and slow crystallization rate, making its processability difficult and reducing thermal resistance [4]. The melt strength of a polymer is mainly determined by the degree of chain entanglement, which increases with molecular weight (MW), molecular weight distribution (MWD), and long chain branching (LCB). PLA typically has a moderate molecular weight, MW <200 kg/mol, and a strong tendency to undergo hydrolysis at temperatures above the melting point, further decreasing molecular weight and, thus, rheological properties [5]. It is, therefore, necessary to keep the molecular weight at high levels to compete with conventional polymers such as polypropylene (PP) and polystyrene (PS) (MW ~ 240–800 kg/mol) for acceptable rheological and processing performance. Among the many attempts that have been made to increase the strength of polymer melts, modifying polymers to obtain branched structures capable of maintaining a high molecular weight has proven to be an effective approach to solving this problem [6]. LCB significantly improves the physical strength of polymer melts. Even for small amounts, significant changes in the melt’s rheological, thermal, and mechanical properties have been reported [7,8]. Thus, various types of multi-functional monomers, including multi-functional alcohol, isocyanates, phenyl phosphites, and epoxides, are reported to be used to enhance melt strength, although in some cases, chain extension, rather than LCB formation, dominates [9]. Especially relevant is the use of multi-functional styrene-acrylic epoxide chain extenders under the trade name Joncryl®. Such extenders have proven to be very useful in improving melt strength and viscosity, restoring molecular weight, and controlling degradation over a wide range of processing temperatures and for various polymers [10], including proven efficacy in PLA. In particular, ADR grade 4368 has been shown to act as a chain extender that improves PLA’s viscoelastic and rheological properties [11,12] and could also accelerate the crystallization rate [10,13,14]. Several works report that branching structures can significantly improve the crystallization of PLA since grafting points can act as nucleating sites [13], increasing the nucleation rate and density [13–17]. Nevertheless, a detrimental effect of branches on the primary nucleation of PLA has also been reported [18]. Moreover, there are discrepancies in how branches affect the secondary nucleation and overall crystallization of PLA [13,14,19]. It has also been observed that branched polymers with different topologies (star, combs, H-shaped, hyper-branched…) could affect the crystallization of PLA differently. Liu et al. [17] concluded that H-shaped branches were the most effective chain structures for improving the nucleation of PLA. Nouri et al. [15] observed that hyper-branched PLAs display the fastest overall crystallization rate. Star-like PLAs and, finally, comb-like structures showed the lowest crystallization rate, albeit all of them displayed a faster crystallization rate than their linear homolog. Indeed, few works cover the effect of branches on PLA’s nucleation, growth, and overall crystallization kinetics [13,17,19,20]. In those works, nucleation is only studied qualitatively (through direct PLOM observations), and spherulitic growth rate (G) vs. crystallization temperature (T c ) plots are not always provided. Therefore, the study of the generation of long-chain branching by the addition of Joncryl® and, in particular, the effect that different concentrations and branching topology produce on melt strength and desired crystallization properties is of great interest to develop the potential of PLA in those applications that require melt processing and dimensional stability. Taking this challenge as the main objective, this work will address the structural changes produced by reactive extrusion using Joncryl®ADR as a chain extender in a commercially available PLA and their effects on PLA’s elongational behavior and crystallization. The products obtained were fully characterized by several methods, using size-exclusion chromatography (SEC), differential scanning calorimetry (DSC), wide-angle X-ray scattering (WAXS), and rheological methods in linear and non-linear regimes. Using low concentrations of Joncryl® resulted in subtle structural modifications. At the same time, a higher amount was sufficient to substantially modify the initial product, resulting in a branched structure with strain-hardening properties and a significant increase in the crystallization rate. The article is organized into two parts. First, an experimental rheological study assisted with computational calculations based on reptation concepts is presented. This part of the work includes experimental data combining extensional, linear, and non-linear shear rheology. Relevant information about the existence of the LCB structures and the quantitative information on chain topology and chain fractions have been obtained in detail for the first time by combining computational modeling and experimental data. Then, we address the non-linear flow of linear and branched topologies using the specific signature of the large amplitude oscillatory shear (LAOS) test [21]. This approach has allowed us to understand better molecular architecture’s effect on the PLA’s flow properties. The data are analyzed by Fourier Transform Rheology (FTR), which allows for quantitative assessment of the nonlinear response intrinsic to the polymer structure. The interpretation in terms of the well-known non-linear elastic behavior (stiffening-softening) and non-linear viscous behavior (thickening-thinning) is investigated by the stress signal decomposition (SD) methodology coupled with Chebyshev polynomials [22]. Our results and analysis revealed the existence of different molecular architectures, even in a PLA sample with the smallest amount of chain branching, for the first time. Moreover, the second part of the work is devoted to a thorough investigation of the effects of LCB on PLA crystallization. Primary nucleation, secondary nucleation, and overall crystallization kinetics were studied in detail by DSC and polarized light optical microscopy (PLOM). Thermal transitions and crystallization kinetics revealed a strong influence of LCBs on the crystallization of PLA. The separate impact of LCB on primary nucleation and crystal growth has been obtained. 2. Experimental part 2.1. Materials A highly stereoregular PLA containing <1 % D-isomer counits and with a melt flow index of 8 g/10 min (210 ◦C/2.16 kg), grade name L175, was kindly provided by Total Corbion (The Netherlands). Joncryl® ADR-4400 multi-functional reactive polymer was kindly provided by BASF (Germany). It has a molar mass of M w =7.1 kg/mol, glass transition temperature (T g ) of 65 ◦C, and epoxy equivalent weight of 485 g/mol. 2.2. Sample preparation Before processing, the plain polymers were dried in an oven at 60 ◦C under vacuum overnight. Blends and neat PLA were processed using a Thermo Haake MiniLab twin-screw extruder operating in batch mode at 180 ◦C and 100 rpm, with a mixing time of 4 min, sufficient to attain plateau torque value. 2.3. Characterization methods 2.3.1. Size-exclusion chromatography (SEC) measurements The molar mass and branching degree of the polymers were analyzed by Size-Exclusion Chromatography detection (SEC/TD). The equipment was composed of an LC20 pump (Shimadzu) coupled to a DAWN Heleos multiangle (18 angles) light-scattering laser photometer equipped with a He – Ne laser (λ =658 nm), an Optilab Rex differential refractometer (λ =658 nm), and Viscostar differential viscometer (all from Wyatt Technology Corp., USA). The equipment used three columns in series (Styragel HR2, HR4, and HR6, with pore sizes from 10 2 to 10 6 Å). The analyses were performed at 35 ◦C, and THF was used as the mobile phase at a flow rate of 1 mL/min. The polymers were diluted in HPLC-grade THF at 4 mg/mL concentrations, and the dn/dc employed was 0.042 A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 2 mL/g. 2.3.2. Fourier transform attenuated total reflection infrared spectroscopy (FTIR-ATR) Fourier Transform Infrared Spectroscopy analyses were conducted using a PerkinElmer FTIR Spectrum 100 spectrometer equipped with a PerkinElmer ATR accessory with a diamond crystal. Each spectrum is an average of 16 individual scans, recorded with a resolution of 4 cm −1 . FTIR-ATR spectra were used to validate the reaction between PLA and Joncryl®, with results detailed in the SI file as Fig. S1. 2.3.3. Rheological characterization Large amplitude (LAOS) and small amplitude (SAOS) dynamic oscillatory shear in linear and non-linear regimes and transient shear measurements were performed with a strain-controlled ARES-G2 Rheometer (TA Instruments) using a parallel plate geometry with 25 mm of diameter and a spacing gap of approximately 0.8 mm. Good reproducibility was obtained using the same thermal treatment consisting of melting the sample for 3 min at T =185 ◦C before the experiments at the temperature of interest. Before measurements, samples were dried at 75 ◦C for 24 h in a vacuum oven. All measurements were performed in an N 2 atmosphere to avoid degradation during the experiments. 2.3.3.1. Dynamic shear viscosity in the SAOS regime. The dynamic shear viscosity in the SAOS (small amplitude oscillatory shear) regime was studied from frequency sweep tests ranging from 0.1 to 100 Hz at a small strain amplitude within the linear viscoelastic regime and temperatures from 155 to 185 ◦C. The master curves were obtained using the timetemperature superposition principle [23,24] (Fig. S2a and Fig. S2b). The data were shifted along the frequency axis, and the horizontal shift factors for all PLA samples were fitted with the Arrhenius functions: aT=Ea R(1 Tref −1 T), with T ref =175 ◦C. An activation energy of flow increasing slightly from PLA to PLA1.5 was obtained (Fig. S2c). 2.3.3.2. Elongational test. The transient elongational flow was performed in the classic strain-controlled ARES Rheometer (Rheometric Scientific) coupled with the extensional viscosity fixture (EVF). The sample sheets were cut into pieces with a width of 10 mm, length of 18 mm, and thickness of 0.8 mm. Constant strain rates of 0.1, 0.3, and 1 s −1 at 175 ◦C were applied. A pre-elongation for 3 s was performed before the measurements to ensure no slipping between the sample and the fixtures. The presence of the chain extender Joncryl® at the lower concentrations of 0.5 and 1 % did not significantly improve the deformation behavior of PLA, while for PLA1.5, strain hardening was observed (Fig. S3). Thus, the elongational viscosity curves obtained for PLA0.5 and PLA1 did not offer a significant difference with respect to the linear PLA sample and were not included in the experimental data set for modeling the rheological-structural relationship. The strain hardening curves of the PLA1.5 sample were analyzed to deduce the most probable branching topologies. 2.3.3.3. Transient non-linear shear. Experimental start-up flow curves were performed at different applied shear rates in the 0.01 to 50 s −1 range at T =175 ◦C. Entangled polymers are expected to give a very rich response, which depends on the time scale of the applied flow and the relaxation times of the chains. The response can be very complex in the case of branched polymers, as the branches and the backbone have different relaxation times [25]. 2.3.3.4. Large amplitude oscillatory shear (LAOS). The non-linear dependence of the stress response on strain was evaluated from strain sweep tests in the MAOS (medium amplitude oscillatory shear) and LAOS (large amplitude oscillatory shear) regimes at T =175 ◦C and different frequencies from 0.05 to 5 Hz. Before applying quantitative analytical techniques, the obtained data can be represented in the form of Lissajous-Bowditch (L-B) curves, allowing a visual inspection of the non-linear response of materials subjected to large deformations. Fig. S4 shows the data measured at each imposed frequency; (a) the elastic Lissajous–Bowditch curves represent the periodic stress response at steady state plotted against strain, σ (t)vs γ(t),and (b) the viscous Lissajous–Bowditch curves represent the stress as a function of strain rate, σ (t)vs ˙γ(t). The elliptical shape of the curves accounts for the viscoelastic behavior so that the non-linear flows simultaneously cause distortions of the elastic and viscous paths. The closed-loop plots showed no significant differences among the samples studied at low deformations. However, when strong elastic non-linearity occurs at high deformations, the Lissajous stress versus strain rate curves showed a double loop for neat PLA, PLA0.5, and PLA1.0, which was not observed for the PLA1.5 sample. This self-intersect phenomenon has been reported in many LAOS analyses of various systems and constitutive models [26]. Physically, such strong elastic non-linearity would correspond to a non-linear viscoelastic shear stress overshoot in which existing stress is unloaded more quickly than new deformation is accumulated. This rationalization of the LAOS response has been tested in various molecular configurations and microstructures, such as polymer solutions, polymer melts, soft glassy materials, and other structured fluids [27]. However, the interpretation of the presence of secondary flows has been limited to the study of specific materials, generally related to the absence of long-chain branching in polymer melts. However, secondary loops have also been observed for star-polymer networks [27]. Regarding the behavior of the PLA samples of the present study, the presence of secondary flows will not be considered a decisive result since they were only found for the highest strains and frequencies, where the effect of certain flow instabilities cannot be ruled out. Therefore, the study of the different structures in these samples will be approached by applying different calculations to the LAOS data using the discrete Fourier transformation methodologies (see Supporting Information, section S5). 2.3.4. Polarized light optical microscopy (PLOM) The spherulitic nucleation and growth were measured using polarized light optical microscopy (PLOM). To that end, isothermal measurements were performed in an Olympus BX51 PLOM (Tokyo, Japan) equipped with an Olympus SC50 digital camera and a Linkam-15 TP-91 hot stage. Films with around 10 μ m were prepared by melting the samples between two glass slides. Measurements were conducted as follows: first, the thermal history of the material was erased by keeping the sample at 200 ◦C for 3 min. Then, samples were cooled down to a selected crystallization temperature (T c ) at 50 ◦C/min and maintained at that T c while spherulites appeared and grew. This protocol was repeated at several T c s for each sample. The nucleation kinetics was determined by counting the number of active nuclei that appeared in a specific area at a selected T c as a function of time. It was assumed that each spherulite grew from a single active nucleus. Similarly, the spherulitic growth kinetics of each sample were determined by measuring the radius of the spherulites as a function of time at different T c s. The spherulitic growth rate (G) could be calculated from the radius versus time plots at each T c . At least three spherulites were measured for each reported G value. 2.3.5. Differential scanning calorimetry (DSC) Calorimetric studies were conducted in a Perkin Elmer DSC800 calorimeter (Waltham, MA, USA) under an ultrahigh-purity nitrogen atmosphere with a 20 mL/min flow. Indium and tin standards were used to calibrate the equipment, and sample amounts around 2 mg were used for each measurement. 2.3.5.1. Non-isothermal DSC measurements. First, the thermal history of the samples was erased by maintaining the samples at 200 ◦C for 3 min. A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 3 Then, samples were cooled down to 25 ◦C at 20 ◦C/min, kept at 25 ◦C for 1 min, and then heated to 200 ◦C at the same rate. From the recorded cooling and heating scans, the melting (T m ), cold crystallization (T cc ), and crystallization (T c ) peak temperatures, as well as the enthalpies of the corresponding transitions, were determined. For the calculation of the degree of crystallinity (X c ) of each sample, a value of 107 J/g was considered as the melting enthalpy of 100 % crystalline PLA [28], which corresponds to the melting enthalpy of 100 % crystalline PLLA in the α ′ -crystal form. This value was chosen considering that the temperature range at which PLA crystals grow in the current work is typical of the α ′ -modification. 2.3.5.2. Isothermal measurements. The overall crystallization kinetics were studied using isothermal DSC experiments. The measurements were performed according to the procedure proposed by Müller et al. [29,30]: first, the thermal history of the samples was erased by keeping them at 200 ◦C for 3 min. Then, samples were quenched at 60 ◦C/min to a selected T c, and the isothermal crystallization was conducted until it reached saturation. Finally, samples were heated to 200 ◦C at 20 ◦C/min. The experiment was repeated for several T c values. The apparent melting points were determined from heating runs performed immediately after isothermal crystallization, from T c to complete melting. These values were used to carry out the Hoffman-Weeks [31] extrapolation and, thus, calculate the equilibrium melting temperature (T m 0 ). 2.3.6. Wide-angle X-ray scattering (WAXS) A Philips X’pert PRO automatic diffractometer was used to collect the X-ray powder diffraction patterns at room temperature. The equipment operated at 40 kV and 400 mA, in theta-theta configuration, with a secondary monochromator with Cu-K α radiation (λ =1.5418 Å) and a PIXcel solid state detector (active length in 2θ =3.347◦). Data were collected between 5 and 70◦2θ (step size =0.026◦and time per step = 180 s) during a total data collection time of 30 min. A variable divergence slit, which provided a constant 8 mm area of sample illumination, was used. 3. Results 3.1. Rheological characterization 3.1.1. Topological characterization: computational linear and non-linear rheology Chain reactions occur in polyesters such as PLA due to bridging the hydroxyl or carboxyl end groups with functional compounds such as Joncryl®. The reaction result is due to epoxide ring-opening events in the Joncryl® molecule and the production of covalent connections via PLA’s hydroxyl/carboxyl end groups [32]. Initially, the reaction may result in an extension of the PLA chains, producing a fraction of the material with a higher molecular weight than the parent PLA. When more PLA chains are involved in the reaction, LCB topologies (stars or Hshaped) arise, which may eventually produce even more complicated structures (combs or dendrimers). SEC results clearly show that the amount of Joncryl® increases the molecular weight. Fig. 1 compares the absolute molar mass versus the elution time for the samples under study. As can be appreciated, except for neat PLA, none of the samples present a monotonous decrease of the molar mass with the elution time; on the contrary, molar masses increase at long elution times, and this effect is more pronounced as the amount of Joncryl increases. This non-ideal elution, also known as anomalous elution, has been reported for branched polymers [33]. Sometimes, this behavior is attributed to the anchoring of branched polymer chains in the pores of the columns, resulting in a later elution together with smaller polymer chains [33]. In addition, branching leads to the contraction of the polymer chains; therefore, when a branched and a linear polymer have the same hydrodynamic volume, the branched polymer presents a higher molar mass. This indicates that when analyzing branched polymers by SEC, a dispersion of polymer chains of different molar masses might elute together [34,35]. The emergence of an asymmetric SEC trace towards the high-M w side of the distribution is accompanied by an increase in M w values (see Table 1). Fig. 2 (left panel) depicts the fit of the experimental SEC traces to typical peak functions. In the case of the neat PLA material, the fit indicates a log-normal distribution, with an average molecular weight M w of roughly 65 kg/mol and a polydispersity index of D =M w /M n =1.3. A multipeak fit approach yields interesting results in the remaining samples. The PLA0.5 distribution clearly shows a percentage (w =0.20) with a larger molecular weight than neat PLA, which amounts to 140 kg/mol on average (Scheme 1A). Chain structure becomes more complicated in the case of PLA1.0, which has a third population (w =0.05) with a molecular weight of around 260 kg/mol. The linear chain population of the initial PLA almost vanishes when the polymer is melt processed with 1.5 % Joncryl® (PLA1.5), and new populations with molecular weights of 270 kg/mol (w =0.18) and 512 kg/mol (w =0.05) arise. Table 2 displays the fractional content, average M w , and D values for each fraction in the different samples. Considering the M wi values of the different MWD nodes, the data in Table 2 show that branched species may emerge (on average) for Joncryl® contents >1 %. In fact, the second node appears to be made up of linear molecules with an average length double that of the neat PLA sample. The third and fourth nodes are almost certainly branched. The branching structure in these nodes might be symmetric or asymmetric stars, H-shaped or comb-like, and dendritic (Scheme 1C and D). In a very simple scenario, the third node, with a M w of about 260–270 kg/mol, might be made up of symmetric stars with four branches of 65 kg/mol or asymmetric stars with two branches of 65 and one of 140 kg/mol (Scheme 1B). A comb-like molecular structure with 4 branches of 65 kg/mol and a 260 kg/mol Fig. 1. RI raw data (continuous line) and molar mass evolution determined by SEC/MALS for the samples under study. Table 1 Molecular properties of the samples under study. Sample Mn (kg/mol) Mw (kg/mol) D Mw/Mn PLA 51.7 65.1 1.3 PLA0.5 58.6 71.3 1.2 PLA1.0 72.1 91.6 1.3 PLA1.5 93.4 131.2 1.4 A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 4 backbone would also be a feasible topology for the fourth node, which has a very high M w of 512 kg/mol (Scheme 1D). A Cayley tree (2 generations) with 9 segments of around 60 kg/mol could also be a possible topology for this highly branched node of the MWD, see Scheme 1. As it is well known, the rheological properties of polymers in both the linear and non-linear regimes are extremely sensitive to the polymers’ macromolecular architecture and topology. These molecular characteristics are defined mainly by M w and D, but especially by the LCB. The presence of LCB is highly desirable since it improves processing by increasing shear thinning behavior in shear and strain hardening in extension [36,37], both of which are beneficial for various applications. The rheological properties of the PLA molecules in the systems under study should then reflect the existence of the newly created species, regardless of their topology. We have used the branch-on-branch (BoB) rheology software to model polymer rheology using the molecular ensemble provided by the SEC trace and, in a first approach, the molecular populations mentioned above [38–40]. BoB employs algorithms based on the extended tube model to calculate the rheological response of polymer melts, encompassing both linear and non-linear regimes, irrespective of polymer architecture. This method establishes a connection between molecular structure and rheological properties. The chemical characteristics of monomers are effectively captured by two key parameters: one representing the entanglement length (entanglement molar mass, M e ) and a time scale (entanglement relaxation time, τ e ). In the initial phase of the calculation, a macromolecular ensemble is generated, retaining the chain connectivity and molar mass. This step is derived from examining the chemical reaction scheme and analyzing experimental GPCLS data (Table 2). The algorithm’s accuracy has been verified through validation with experimental data from model polymers of diverse chemistries and architectures [40]. The model parameters, including the dynamic dilation exponent α =1, reflecting the entanglement features’ behavior with dilution, and p 2 =1/40, connected to the fraction of tube diameter the branch point traverses on average during each segment/branch retraction time, have been determined based on their optimal performance across different polymeric chemistries and architectures [40]. Considering different values for α and p 2 may lead to variations in the chosen values of M e and τ e . Therefore, we adhere to the original results from Das’s work, which have undergone testing across a wide range of materials [40]. We should adhere to the fundamental principle of the reptation theory, which is to uphold the universality of polymer relaxation mechanisms. The numerical ensembles of polymer molecules were constructed using the above assumptions for the various populations derived from the MWD multifit approach. To study the effect of modest weight fractions of highly branched species, we created 40,000 molecules. Then, Fig. 2. LEFT: SEC traces with deconvolution of the samples under study. The gray bars indicate the approximate location of the peaks corresponding to each fraction. RIGHT: Experimental linear viscoelastic response at 175 ◦C of each sample (symbols – squares, G’, circles, G" and triangles, | η * |). Solid lines represent the computed rheological response of the samples with parameters in Table 2 and the discussed topology in the text. Dashed lines represent the computed response for symmetric stars (b, c) and Cayley (d) molecules. Dotted lines represent the behavior of linear PLA. A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 5 using the BoB software, the discrete distributions of molecules of different molar masses with the assumed topology were directly used to determine rheological parameters. The computations require the density, taken as ρ =1.16 g/cm 3 , and the two chemistry-dependent quantities, M e and τ e . Unfortunately, literature reports on fundamental properties like M e or C ∞ of PLAs seriously disagree. In fact, the literature data for M e for PLA are variable, between 4000 and 10,500 g/mol. [41]. Thus, we have used the experimental linear response of neat PLA sample to determine both M e and τ e . The best fit obtained for the linear PLA sample gives values of M e =4500 g/mol and τ e =6.5 ×10 −7 s. The value of M e is well within the most accepted value of entanglement molecular weight of PLA [42], and the τ e value describes well the value of the crosspoint moduli, G x =G’ =G”. Table 2 (right panel) shows the findings of the computed linear rheological properties compared to the experiments at T =175 ◦C for all the samples using the same set of M e , τ e parameters. The behavior of the linear PLA sample is represented by the dotted lines in all figures. In all samples with Joncryl®, a clear shift of the viscoelastic fingerprint to lower frequencies is obtained. As the amount of Joncryl® increases, so does the shift to lower angular frequencies. Interestingly, despite the simplicity of the assumptions we made for the topology of the created species, the consistency between the experimental findings and the model (solid lines) is excellent. From the results of this computational exercise, some interesting conclusions can be drawn: (1) For a low Joncryl concentration (0.5 %), the existence of branched species is deemed unnecessary to account for the observed linear viscoelastic behavior. Initially, we applied the model assuming solely linear species (depicted by the solid line in Fig. 2b, right panel). This calculation replicates the viscoelastic response that would be expected if a percentage of high molecular weight material (w =0.2), with twice the molecular weight of the original PLA, is present. This result implies that a low Joncryl® content does not inherently lead to the presence of LCB. However, an alternative scenario where the second node of the distribution comprises symmetric 3-star structures (branches of approximately 47 kg/mol) also reproduces the rheological response observed within the experimental frequency window (depicted by the dashed line in Fig. 2b, right panel). Consequently, the possibility of a small fraction of branched species cannot be conclusively ruled out. The additional fraction of either linear or branched molecules retards the linear response by approximately five times compared to that of the neat PLA sample. (2) LCB occurs when the Joncryl® content is 1 % or greater. According to linear rheology, asymmetric star branches are most likely created first. When a topology with four symmetric branches is considered, the calculated linear rheology does not reach the experimental low-frequency zone (dashed lines in Fig. 2c, right panel). It should be emphasized that, in this case, the G’ function allowed us to distinguish between the two selected choices of branch structures. In this scenario, the presence of only 5 % of that asymmetric star species causes the rheological response to be delayed by one frequency decade compared to the neat PLA sample. (3) For a 1.5 % Joncryl content, asymmetric star molecules and a minor fraction of H-shaped or comb-like structures are still produced. This is significant since it has been demonstrated in the literature that stars LCB topology is insufficient to impose a Scheme 1. Possible structures between PLA and Joncryl® (Joncryl is multi-functional, but in this scheme, a functionality of 3 is considered for each molecule). Table 2 Multipeak fit results obtained for the samples under study. Each node is a lognormal function with the indicated M w and polydispersity index (M w /M n ). Sample M w1 [kg/ mol] D 1 M w2 [kg/ mol] D 2 M w3 [kg/ mol] D 3 M w4 [kg/ mol] D 4 PLA 65 1.3 – – – – – – PLA0.5 65 (w = 0.8) 1.2 140 (w = 0.20) 1.2 – – – – PLA1.0 65 (w = 0.80) 1.2 130 (w = 0.15) 1.1 256 (w = 0.05) 1.2 – – PLA1.5 65 (w = 0.15) 1.2 90 (w = 0.62) 1.1 270 (w = 0.18) 1.3 512 (w = 0.05) 1.1 The weight fraction of each component is indicated in brackets. A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 6 strain-hardening feature on the sample, as the behavior observed in extensional flow is similar to that of linear polymers [43,44] [43,44] instead, the topology should be comb-like or even branch-on-branch (dendritic or Cayley tree) [45]. A Cayley tree fraction (2 generations, as in Scheme 1D) with segments around 60 kg/mol gives rise to undistinguishable linear rheology (dashed lines in Fig. 2d, right panel). The effect of this type of comb or branch-on-branch species is enormous in this scenario. When compared to the linear PLA, the presence of star molecules (22 %) and comb-like or Cayley tree molecules (5 %) delays the linear rheology of the sample by more than two decades (Fig. 2d, right panel). Extensional properties should be explored in this case to discriminate between the different topologies. Using the same molecular ensembles and material parameters, it is also possible to compute the non-linear viscoelastic properties in shear and extensional start-up experiments. The comparison between the experimental and computational results can be observed in Fig. 3. Fig. 3a shows the transient shear viscosity obtained in experiments at 175 ◦C for PLA0.5, PLA1.0 and PLA1.5 samples at shear rates between 0.05 and 20 s −1 . The effect of LCB, in this case, is clearly seen, as it induces a strong shear thinning in PLA1.5 (combs/Cayley branches) but only slightly affects PLA1.0 (star branches). On the contrary, the PLA0.5 sample remains closely Newtonian in the shear rate range explored. Moreover, with the assumed topological constraint, the computational model nicely captures the experimental behavior. Fig. 3b shows the experimental results obtained from start-up uniaxial extension measurements in the case of PLA1.5 sample at two different strain rates and 175 ◦C. As expected, the strain hardening behavior is clear in this case, likely due to the branch-on-branch structures present (5 % of comb/Cayley molecules). Interestingly, considering only a 5 % high-M w fraction of comb molecules, the computation model agrees very well with the experiments (solid lines). This is not the case of the Cayley tree model, for which the strain hardening factor is much lower (dotted lines) than in the case of comb molecules, especially for the highest strain rate of 1 s −1 . This result has turned out to be very interesting, as it means that the combination of experiments and rheological modeling may help to discriminate among different possible branched structures in the samples. 3.1.2. Structural information provided by the analysis of large amplitude oscillatory shear (LAOS) Large amplitude oscillatory shear (LAOS) tests are widely used to characterize complex fluids due to their ability to capture a very broad spectrum of the viscoelastic response. This is achieved by varying the amplitude and the frequency of the applied strain. In oscillatory experiments in which the strain is controlled under conditions of linear viscoelasticity, i.e., at sufficiently small strains, a sinusoidal strain [γ(t) =γ 0 sin( ω t)] is applied and a stress response is obtained which is also sinusoidal [ σ (t) = σ 0 sin( ω t)], such that the stress amplitude, σ 0 , and the strain amplitude, γ 0 , have a linear relationship. However, if the applied strain increases and exceeds the limit of linear viscoelasticity, the stress function is distorted, and more harmonics, in addition to the fundamentals, are necessary. The complexity of a multi-harmonic response makes it difficult to correlate the non-linear response with the molecular structure, so the focus has been placed on the medium amplitude (MAOS) zone, i.e., in the intermediate zone between the small amplitude (SAOS) and large amplitude (LAOS) regimes, where the non-linear flow is due only to the appearance of the third harmonics. In particular, it has been reported that the third harmonic analysis has been successfully used to identify the response of the LCB versus the linear chain structures, even in those systems where no significant changes in the linear viscoelastic regime were observed [46–49]. 3.1.2.1. Intrinsic non-linearity response in the MAOS regime. The analysis of the non-linear response of MAOS has become considerably more efficient due to the introduction of the new concept of intrinsic nonlinearity. This approach has proven very relevant in the structural characterization of polymers containing LCB. The methodology proposed by Hyun et al. [49] is based on the experimental observation that the third harmonic intensity, I 3/1 ( ω ,γ 0 ) = σ 3 / σ 1 , i.e., the intensity of the third harmonic, σ 3, normalized by the intensity of the fundamental, σ 1, scales quadratically with the strain amplitude, γ 0, in the MAOS regime, I 3/1 ~ γ 0 2 . The slope of 2 has been obtained in experiments and simulations for linear polymers. Still, some branched polymers [49] showed a slope slightly <2, even though the pom-pom constitutive model predicts Fig. 3. Start-up experiments in shear (a) and uniaxial extension (b) for the different samples at the indicated shear and strain rates and T =175 ◦C. The dotted gray line corresponds to the linear viscoelastic envelope. A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 7 that the slope of I 3/1 is 2 for H-shaped branched polymers [50], and also an experimental slope of 2 is obtained for combs and linear PS model polymers [51] and 3-arm star 1,4-cis-polyisoprene [52]. These differences can be explained based on the experimental difficulties in observing slope 2 at very low deformations, where the third harmonic signal is very noisy. Using this scaling relation, a non-linear parameter is defined as Q=I3/1 γ02 . When evaluated at relatively small strains, this parameter Q results in a constant parameter (similar to Newtonian viscosity), which allows to define a zero-strain non-linearity, Q 0 , as limγ0→0Q≡Q0 [46]. The constant value of Q 0 does not mean that nonlinearity disappears but that it remains constant at low strains, so the Q 0 coefficient reflects the inherent non-linear properties of the materials [47]. The quantification of these non-linear coefficients (Q and Q 0 ) for linear and chain-extended PLA is presented in the Supporting Information (see Fig. S6 and Fig. S7). The analysis of I 3/1 as a function of strain amplitude at frequencies from 0.1 to 3 Hz is included in the Supporting Information (see Fig. S7). As can be seen, the slope of I 3/1 is confirmed to be 2 in all cases, and the values of Q 0 have been calculated for the different frequencies, as shown in Fig. S8. In cases where Q 0 was not obtained directly, the possibility of using a Cross-type equation was considered by analogy with the Newtonian viscosity determination. These results show that the MAOS and LAOS regions are very different depending on the Joncryl® content, which agrees with results reported for branched polymers where the frequency dependence of Q 0 is very sensitive to the molecular architecture. Linear, 3-arm star, and comb structures have been described in the MAOS region by different non-linear Q 0 ( ω ) vs De curves according to the relaxation modes of these complex structures [53]. At the lower frequencies (De <1), Q 0 ( ω ) scales quadratically with frequency [Q 0 ( ω ) ∝ ω 2 ], while for the higher frequencies (De >1), it has been experimentally described to scale as Q 0 ( ω ) ∝ ω k , with k −0.35. At De =1, a maximum Q 0 (≡Q 0max ) is reported. The response is even more complex in the case of branched species, and two distinct Q 0max peaks have been reported. The two peaks were attributed to the corresponding relaxation of the branches at the higher frequencies and the backbone at the lower frequencies. Fig. 4 shows the Q 0 data versus frequency for the PLA samples. The typical terminal scale at low frequencies Q 0 ~ ω 2 was only observed for neat PLA. For the extended-chain PLA samples containing branched species (see section 3.1), PLA1.0 and PLA1.5, the terminal region is not observed, and PLA0.5, unexpectedly, showed similar Q 0 data to PLA1.0 and PLA1.5. Before continuing with the discussion, it should be noted that these results should be taken with some caution since, on the one hand, the treated PLA samples are a heterogeneous mixture of linear and branched species of different topologies, which undoubtedly makes interpretation difficult. On the other hand, the experimental results were only obtained at one temperature, which considerably reduced the accessible frequency range so that only a part of the Q 0 ( ω ) response is observed. However, the remarkable differences between neat PLA and chain-extended PLA samples show that the effect of the branching content plays an important role. The PLA0.5, PLA1.0, and PLA1.5 showed two plateaus, which could indicate the relaxation processes related to the presence of branched and linear species. The result is similar to that found for 3-arm star-branched polyisoprene [52], where the two plateaus of Q 0 were attributed to the relaxation of the branches and the main chain. 3.1.2.2. Elastic and viscous intra-cycle non-linear responses. The third harmonic’s normalized intensity is a sensitive indicator of non-linearity, capable of identifying different molecular structures, as discussed in the previous section. A combination of FT methodology and Chebyshev decomposition can also be applied to reveal even more information contained in the non-linear response. The methodology allows the analysis of intracycle non-linear viscoelasticity in terms of the dimensionless index of non-linearity, S (strain stiffening ratio), and T (shear thickening ratio) at large amplitudes [54,55]. In general, the evolution of the non-linearity parameters in the high strain amplitudes region in the LAOS regime is quite complex. Still, some common features have been reported for the presence of LCB effects. Hyun et al. [46] studied the evolution of the normalized parameter Q/Q 0 vs. strain amplitude, γ 0 , at different frequencies for linear and comb-type branched polystyrene melts with different long branch sizes. They reported the presence of an overshoot in the Q/Q 0 (γ 0 ) curves of the branched polymers with long and entangled branches, such that the intensity of this overshoot was frequency-dependent, a behavior attributed to the presence of LCB. The overshoot was not observed in linear or branched samples with branches of lower molecular weight than entanglement. Similarly, the PLA and chain-extended PLA samples show different responses in the LAOS region. Fig. 5 shows the evolution of the viscous non-linear index (T) at a frequency of 3 Hz. Further results related to the frequency dependence of elastic and viscous non-linear indexes (S, T) for linear and chain-extended PLA are presented in Supporting Information (see Fig. S9). PLA1.5 sample shows a very noticeable frequency-dependent thickening (T >0). Similarly, although a much more modest behavior, the thickening was also observed at the Fig. 4. Frequency dependence of the zero-strain non-linearity Q 0 for linear PLA and chain extended PLA samples PLA0.5, PLA1.0, PLA1.5. Fig. 5. Non-linear viscous parameter T (Shear-Thickening Ratio) for linear PLA and chain extended PLA samples PLA0.5, PLA1.0, PLA1.5 a frequency of 3 Hz. A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 8 highest frequencies for the PLA0.5 and PLA1.0 samples. Since it is known that the presence of LCB gives rise to a very significant strain hardening behavior, it seems that the overshoot in Q/Q 0 data for branched structures reported by Hyun et al. [46] and the thickening behavior observed in chain-extended PLA samples might also be able to distinguish the topology of the branches. However, the non-linear physics capable of predicting this behavior is not known. Topological polydispersity, especially the effects of different molecular architectures of the chain-extended branched PLA, brings us this complex non-linear flow response. 3.2. Crystallization behavior Table 3 summarizes the peak temperatures of each transition and the X c values determined by non-isothermal DSC measurements for each sample. The DSC traces are reported in the Supporting Information, Fig. S10. As observed, linear PLA displays T g , T cc and T m values of 58.8 ◦C, 129.8 ◦C and 170.7 ◦C, respectively. The very tiny exotherm from 115 to 90 ◦C of the black DSC plot of Fig. S10a indicates that the linear polymer only barely crystallizes during cooling from the melt at 20 ◦C/min, as expected for linear PLA with 1 % D-isomer content [56,57]. The latter is backed by the nearly identical cold crystallization and melting enthalpies determined from the second heating scan. The use of a chain extender significantly changed the crystallization behavior of the PLA: modified PLAs show a crystallization peak between 93.1 ◦C and 95.6 ◦C when cooling from the melt at 20 ◦C/min, and the T c shows a decreasing trend as the number of branches increases. In addition, the T cc suffers a dramatic decrease from 129.8 ◦C for linear PLA to around 106.2–107.4 ◦C corresponding to branched PLAs. This improvement in the crystallization ability of PLA, i.e., the appearance of a crystallization peak and decreases in the T cc , promoted by the presence of LCB, has been previously reported in the literature, and it has been ascribed to a higher nucleation ability of branched structures [58–60]. There is also a significant influence of the pre-existing crystals grown upon cooling, which facilitates the crystallization during the subsequent heating scan. The presence of crystals before heating explains why all the branched samples could crystallize in the same temperature range. The presence of LCB does not produce significant changes in the T g and T m of PLA (differences are within 1 ◦C). Regarding the X c , it is observed that the sample with the smallest amount of Joncryl has the highest X c . As the higher amount of Joncryl can be associated with a higher amount of LCB (according to our rheological results shown above), the results in Table 3 suggest that there is an optimum branching degree to achieve the maximum X c value. Mihai et al. [61] reported an acceleration of the crystallization of branched PLA samples at increasing chain extender contents based on the shifts observed in the T c and T cc . However, they observed a reduction in the number of PLA chains that could crystallize due to the interruption that branches caused in the linear PLA chains. Similarly, in the current work, for branched samples, a crystallization peak is observed during cooling from the melt, the T cc shifts towards lower temperatures, and higher X c values compared to that of linear PLA are obtained. However, the T c and X c values decrease as the amount of branches increases. These results suggest that, although the presence of branches accelerates the crystallization process of PLA beyond a critical branch content, branches disrupt the linearity of the PLA chain, hindering their non-isothermal crystallization ability. Thus, the X c values of PLA samples with higher branch contents are lower than those with low branch contents. In a previous work [62], we observed that the X c of PCL reaches a maximum value at a particular M n , which decreases with increasing molecular weight due to a reduction in chain diffusion. As shown in Table 1, the molecular weight of PLA increases with the amount of chain extender. Then, both the increase of the molecular weight and the presence of LCB in chain-extended PLA samples affect X c values. Thus, a reduction in chain diffusion and, hence, in X c might be expected with increasing the amount of Joncryl. This phenomenon will be discussed in more detail below. Fig. 6 shows the PLOM micrographs for all the studied samples collected at 25 ◦C after melting at 200 ◦C for 3 min and cooling at 20 ◦C/ min. In all the cases, crystallization occurs through the formation of spherulites. For the linear PLA (see Fig. 6a), only very small and few spherulites are observed, which explains why no signal of crystallization was detected in non-isothermal DSC measurements. These results highlight the low capacity of this sample to crystallize under nonisothermal conditions. As reported in the literature [58,59], larger quantities of spherulites are observed as the amount of LCB increases. Since similar conditions are used for the non-isothermal crystallization process, this result indicates that the number of primary nuclei increases with LCB content. Isothermal PLOM measurements were carried out to understand better the effect of branches on PLA’s nucleation and growth kinetics. Fig. 7 shows the nucleation density ( ρ nuclei ) data as a function of time obtained at different isothermal crystallization temperatures for PLA, PLA0.5, and PLA1.0 (PLOM micrographs illustrating PLA crystallization at different times and temperatures have been included in the SI, Fig. S11). Note that data corresponding to the PLA1.5 are missing due to degradation problems during the measurements. For any given temperature, the nucleation density increases almost linearly at short times and tends to saturation as time increases. As is typical in polymers, heterogeneous nuclei need more time to be activated as crystallization temperature increases. Moreover, nucleation density decreases with increasing crystallization temperature since the driving force for primary nucleation (or nucleation) increases with supercooling (ΔT =T m 0 −T c ) [63] in the high-temperature range. Fig. 8 represents the nucleation density after 2 min of isothermal crystallization and the nucleation rate (I) values (calculated from the initial slopes of the straight lines at low nucleation times in Fig. 7) as a function of the T c for PLA, PLA0.5, and PLA1.0. If the three samples are compared, it is observed that, for a given T c , the samples with LCB display higher nucleation density (Fig. 8a) and nucleation rate (Fig. 8b) values. While linear PLA can hardly nucleate at T c s larger than 110 ◦C, branched PLAs can generate active nuclei at higher T c values. Moreover, both parameters ( ρ nuclei and I) increase with the amount of LCB. Although the ρ nuclei and I of PLA1.5 could not be measured, based on non-isothermal PLOM observations, a further increase of the mentioned parameters was expected. Bai et al. [64] also observed an enhancement in the nucleation density of PLA with increasing long-chain branching degree, and PLOM observations available in the literature agree with the higher nucleation ability of branched PLA samples compared to their linear homologs [13,58,65,66]. These results indicate that branched PLAs possess lower free energy barriers for primary nucleation than linear PLA and that primary nucleation decreases as the amount of LCB increases. This phenomenon has been ascribed to the grafting points acting as nucleating sites [64]. The branch point itself is a defect that interrupts the crystallizable PLA linear sequence; thus, it has to be located in the intervening amorphous layer of the sample between the crystalline lamellae. We speculate that such branch points at the lamellae surface may induce chain conformations that are favorable to Table 3 T c , T g , T cc , T m and X c data obtained from non-isothermal DSC scans. Sample T c,onset (◦C) a T c,peak (◦C) a T g (◦C) b T cc (◦C) b T m (◦C) b X c (%) a PLA – – 58.8 129.8 170.7 0 PLA/Joncryl 0.5 % 109.0 95.6 59.8 106.4 172.0 5 PLA/Joncryl 1.0 % 105.4 94.6 59.7 107.4 172.0 3 PLA/Joncryl 1.5 % 107.5 93.1 60.3 106.2 171.9 2 a Determined from the cooling DSC scan. b Determined from the second heating DSC scan. A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 9 [73] J. Maiz, G. Liu, F. Ruip´ erez, N. Delbosc, O. Coulembier, D. Wang, A.J. Müller, How cyclic chain toplogy can reduce the crystallization rate of poly(3-hexylthiophene) and promote the formation of liquid crystalline phases in comparison with linear analogue chains, J. Mater. Chem. 7 (2019) 6548–6558, https://doi.org/10.1039/ x0xx00000x. [74] R.A. P´ erez-Camargo, L. Meabe, G. Liu, H. Sardon, Y. Zhao, D. Wang, A.J. Müller, Even-odd effect in aliphatic polycarbonates with different chain lengths: from poly (hexamethylene carbonate) to poly (dodecamethylene carbonate), Macromolecules 54 (2021) 259–271, https://doi.org/10.1021/acs.macromol.0c02374. [75] A.T. Lorenzo, M.L. Arnal, J. Albuerne, A.J. Müller, DSC isothermal polymer crystallization kinetics measurements and the use of the Avrami equation to fit the data: guidelines to avoid common problems, Polym Test 26 (2007) 222–231, https://doi.org/10.1016/j.polymertesting.2006.10.005. [76] M.L. Di Lorenzo, The crystallization and melting processes of poly(L-lactic acid), Macromol. Symp. 234 (2006) 176–183, https://doi.org/10.1002/ masy.200650223. A. Fern´ andez-Tena et al. International Journal of Biological Macromolecules 282 (2024) 136783 16