Properties of Poly(3-hydroxybutyrate-co-3-hydroxyvalerate)/Polycaprolactone Polymer Mixtures Reinforced by Cellulose Nanocrystals: Experimental and Simulation Studies

Poly(3-hydroxybutyrate-co-3-hydroxyvalerate)/polycaprolactone (PHBV/PCL) polymer mixtures reinforced by cellulose nanocrystals (CNCs) have been obtained. To improve the CNC compatibility with the hydrophobic PHBV/PCL matrix, the CNC surface was modified by amphiphilic polymers, i.e., polyvinylpyrrolidone (PVP) and polyacrylamide (PAM). The polymer composites were characterized by FTIR, DSC, TG, XRD, microscopy, BET surface area, and tensile testing. The morphological, sorption, thermal, and mechanical properties of the obtained composites have been studied. It was found out that with an increase in the CNC content in the composites, the porosity of the films increased, which was reflected in an increase in their specific surface areas and water sorption. An analysis of the IR spectra confirms that hydrogen bonds can be formed between the CNC hydroxyl- and the –CO– groups of PCL and PHBV. The thermal decomposition of CNC in the PHBV/PCL/CNC composites starts at a much higher temperature than the decomposition of pure CNC. It was revealed that CNCs can either induce crystallization and the polymer crystallite growth or act as a compatibilizer of a mixture of the polymers causing their amorphization. The CNC addition significantly reduces the elongation and strength of the composites, but changes Young’s modulus insignificantly, i.e., the mechanical properties of the composites are retained under conditions of small linear deformations. A molecular-dynamics simulation of several systems, starting from simplest binary (solvent-polymer) and finishing with multi-component (CNC—polymer mixture—solvent) systems, has been made. It is concluded that the surface modification of CNCs with amphiphilic polymers makes it possible to obtain the CNC composites with hydrophobic polymer matrices.


Introduction
Cellulose is one of most available renewable natural resources with an annual production rate of about 1000 billion tons. As a cheap biopolymer, cellulose plays an important role in production of ecologically pure biocompatible and biodegradable functional materials. Rod-like particles of cellulose nanocrystals (CNCs) can be isolated from cellulose fibers under acid or enzymatic hydrolysis conditions. The dimensions of these particles ranges from 100 to 1000 nm in length and from 5 to 50 nm in diameter depending on hydrolysis conditions and raw material used [1,2].
At present, CNCs attract attention by material scientists not only due to their availability and ecological compatibility but also because of their unique combination of physical and chemical properties: biocompatibility, biodegradability, large specific surface area and high modulus of elasticity [3,4]. The application of CNCs as fillers in polymers allows materials to gain new quality, improving their mechanical, optical and sorption properties, electrical performance, and control humidity [5].
The modified CNCs were prepared by mixing 0.5 g of PAM (or PVP), 10 mL of distilled water and the required amount of an aqueous CNC suspension to achieve the PAM (or PVP) content of 10 wt.%. Then the modified CNC samples were lyophilized. Before the lyophobization, the samples were stored frozen at −40 • C for 2 days. Then they were placed in a freeze drying chamber. The drying took place for 48 h at a pressure of 6 Pa, and a temperature of −54 • C. The lyophilized modified CNC samples were dispersed in DCM for 2 h with vigorous stirring followed by 30 min of ultrasonic treatment, and used for production of PHBV/PCL/CNC composite films.

Preparation of PHBV/PCL/CNC Composite Films
Two series of composites with different ratios of polymers PHBV and PCL (1:1 and 1:2) were obtained. To obtain composites with 1:1 polymer ratio, 0.5 g of PHBV and 0.5 g of PCL were stirred in 10 mL of a CNC suspension in DCM for 2 h at room temperature to dissolve the components. To obtain composites with 1:2 polymer ratio, 0.25 g of PHBV and 0.5 g of PCL were used, respectively. The prepared mixtures were cast into glass Petri dishes and dried at room temperature. The samples obtained were designated as PHBV/PCL(1:1), PHBV/PCL(1:1)/CNC(PVP)-5, PHBV/PCL(1:2)/CNC(PAM)-10, etc., where 5, 10 is the content of CNCs in the composite, wt.%; 1:1 or 1:2 is the ratio of PHBV and PCL in their mixture; PVP or PAM is an amphiphilic polymer for the surface modification of the CNC particles.

Characterization
To investigate the morphology of the samples, a VEGA3 TESCAN scanning electron microscope (SEM) (Brno, Czech Republic) and a Soptop CX40P polarization optical microscope (POM) (Sunny Instruments, Ningbo, China) were employed.
To determine the specific surface area of the samples, a NOVAtouch NT LX Quantachrome (Boynton Beach, FL, USA) automatic analyzer was applied. Before measurements, the samples were kept for 3 h in a vacuum at 50 • C. The low-temperature (-196 • C) isotherms of nitrogen adsorption and desorption were measured at relative pressure of 0.01-0.95. The specific surface areas of the samples under study were calculated by the Brunauer-Emmett-Teller (BET) method.
The isotherms of water adsorption and desorption were registered under controlled humidity at 25 • C. The values of water uptake were determined gravimetrically.
The FTIR spectra were recorded in the range of 4000-400 cm −1 using a VERTEX 80v spectrophotometer (Bruker, Ettlingen, Germany). The samples with 1 mg of the compound to be analyzed, together with 100 mg of potassium bromide, were pressed into tablets.
The DSC measurements were performed on a DSC 204 F1 (Netzsch, Selb, Germany) in an atmosphere of ultrapure grade dry argon at a flow rate of 15 mL min −1 and a heating rate of 10 K min −1 using standard aluminum crucibles. The degree of crystallinity (χ c ) of the samples was calculated by the following equation: where ∆H m is the heat of fusion measured from DSC thermograms, w is the weight fraction of a semicrystalline polymer in a polymer binary blend or in a CNC-based composite, ∆H m 0 is the heat of fusion of the 100% crystalline polymer. ∆H m 0 values reported in previous works are 157 and 146.6 J g −1 for PCL and PHBV, respectively [34,35].
The TG analysis was performed using a TG 209 F1 Iris thermomicrobalance (Netzsch, Selb, Germany) with platinum crucibles in a dry argon atmosphere at a flow rate of 30 mL min −1 , and a heating rate of 10 K min −1 .
The X-ray diffraction analysis was performed using a Bruker D8 Advance powder diffractometer (Bruker, Rheistetten, Germany) according to the Bragg-Brentano scheme with Cu-Kα radiation (λ = 0.1542 nm). The crystallinity index was determined by the Segal method. The crystallinity of PHBV and PCL was calculated in Diffrac.Suite program package.
The tensile properties of the sample films were evaluated using an I 1158 M-2.5-01-1 tensiletesting machine (Ivanovo, Russia) at a loading rate of 1 mm per min −1 in the tension mode.

Computational Details
The classical molecular dynamics (MD) simulation was carried out using the GPU version of GROMACS 5.0.7 [36]. For the PVP macromolecule (Figure 1a), we applied the united atoms model based on GROMOSG53a6 parameters, which had been earlier employed to study the PVP-cellulose-water system [37]. For the PCL macromolecule (Figure 1b), we used the united atoms model provided in [38]. The PCL and PVP macromolecules have a comparable chain length, although their degree of polymerization is different. We used Avogadro to construct the initial structure of the PCL and PVP macromolecules containing 10 and 60 monomer units (with the molecular weights of 1162.6 and 6668.6 g/mol, respectively) [39]. Due to the fact that commercially available PHBV grades only have up to 20 mol% hydroxyvalerate content [40], we have constructed the polymer chain containing from 18 hydroxybutyrate units and 2 hydroxyvalerate units (with the molecular weight of 1838 g/mol) by means of Avogadro as well (Figure 1c). In order to generate united atom topology of PHBV macromolecule based on Gromos 54A7 parameters we used Automated Topology Builder [41]. The initial structure of a DCM molecule and potential parameters were taken from the Automatic Topology Builder [41] as well. For water molecules, we applied the SPC/E (Extended Simple Point Charge) model [42]. For cellulose, GRO-MOS54a7 force field parameters were used [41]. The initial structure of a CNC particle (as a model of Iβ cellulose) was built with the Cellulose Builder toolkit [43] based on the experimental crystallographic data [44], and consisted of 9 glucan chains with the degree of polymerization of 10. The NpT simulations were performed at 0.1 MPa (Parrinello-Rahman barostat) and 298 K (Nose-Hoover thermostat [45,46]. For long-range interactions with a cutoff distance of 1.5 nm (both the van der Waals and the electrostatic interactions), the particle-mesh Ewald (PME) method was used [47,48]. The data for analysis were collected every 0.1 ps with the time step of 1 fs.

Morphological and Adsorption Properties of PHBV/PCL/CNC Composites
Structural features of polymeric materials largely determine their consumer properties and prospects for use in a particular area. The use of pure PCL and PHBV as materials is limited by their high hydrophobicity, low melting points, and low mechanical strength. An effective way to regulate the supramolecular, morphological and porous structure of materials based on PCL and PHBV may be the formation of composite films from their mixed solutions, as well as the use of fillers and reinforcing additives. Establishing the relationship between the composition, morphology and properties of films is an important task and the basis for obtaining composites with the required consumer properties. The properties of PHBV/PCL mixtures have been studied in several works [49][50][51]. In our work, we investigated the features of PHBV/PCL/CNC composite films. The use of PVP-or PAM-modified CNC allows PHBV/PCL/CNC composite films to be prepared by casting from a solution in DCM. It can be seen that the surfaces of the PHBV/PCL/CNC composite films are inhomogeneous, with a pronounced porosity. As shown by cross section images, a porous structure is characteristic of the entire volume of the films. With an increase in the CNC content in the composites, the porosity of the films increases, which is reflected in an increase in their specific surface areas and water sorption (Table 1). In polarized light, it can be seen that pure PCL crystallizes in the form of large spherulites. The formation of a mixture with PHBV, as well as the addition of CNCs, leads to a considerable decrease in the PCL spherulite size and then to their complete disappearance (Figures 4, S4 and S5).

Morphological and Adsorption Properties of PHBV/PCL/CNC Composites
Structural features of polymeric materials largely determine their consumer properties and prospects for use in a particular area. The use of pure PCL and PHBV as materials is limited by their high hydrophobicity, low melting points, and low mechanical strength. An effective way to regulate the supramolecular, morphological and porous structure of materials based on PCL and PHBV may be the formation of composite films from their mixed solutions, as well as the use of fillers and reinforcing additives. Establishing the relationship between the composition, morphology and properties of films is an important task and the basis for obtaining composites with the required consumer properties. The properties of PHBV/PCL mixtures have been studied in several works [49][50][51]. In our work, we investigated the features of PHBV/PCL/CNC composite films. The use of PVPor PAM-modified CNC allows PHBV/PCL/CNC composite films to be prepared by casting from a solution in DCM. It can be seen that the surfaces of the PHBV/PCL/CNC composite films are inhomogeneous, with a pronounced porosity. As shown by cross section images, a porous structure is characteristic of the entire volume of the films. With an increase in the CNC content in the composites, the porosity of the films increases, which is reflected in an increase in their specific surface areas and water sorption (Table 1). In polarized light, it can be seen that pure PCL crystallizes in the form of large spherulites. The formation of a mixture with PHBV, as well as the addition of CNCs, leads to a considerable decrease in the PCL spherulite size and then to their complete disappearance (Figure 4, Figures S4 and S5).                An increase in CNC content in the composites leads to a significant increase in water sorption (Figures 7 and 8). As stated by their shape, the water adsorption isotherms may be assigned to type II isotherms according to Brunauer's classification [52]. The isotherms under study are characterized by a significant increase in water vapor adsorption in the     An increase in CNC content in the composites leads to a significant increase in water sorption (Figures 7 and 8). As stated by their shape, the water adsorption isotherms may be assigned to type II isotherms according to Brunauer's classification [52]. The isotherms under study are characterized by a significant increase in water vapor adsorption in the An increase in CNC content in the composites leads to a significant increase in water sorption (Figures 7 and 8). As stated by their shape, the water adsorption isotherms may be assigned to type II isotherms according to Brunauer's classification [52]. The isotherms under study are characterized by a significant increase in water vapor adsorption in the region of increased relative pressures and practically no hysteresis. This behavior is inherent in polymolecular adsorption on macroporous hydrophobic adsorbents [53].
Polymers 2022, 14,340 10 of 32 region of increased relative pressures and practically no hysteresis. This behavior is inherent in polymolecular adsorption on macroporous hydrophobic adsorbents [53].

FTIR Analysis
For neat PCL, main characteristic bands are observed in the FTIR spectra: 2945 and 2864 cm -1 (asymmetric and symmetric vibrational vibrations of CH2), 1729 cm -1 (C=O vibrations), 1240 and 1166 cm -1 (asymmetric and symmetric C-O-C vibrations). For neat PHBV, the absorption bands at 1280, 1456, 1723, 2930, and 2979 cm −1 refer to stretching vibrations -COC-, bending vibrations -CH2-, stretching vibrations -CO-in ester, and symmetric and asymmetric stretching vibrations -CH3, respectively [54] ( Figure S6). In the FTIR spectra of PHBV/PCL mixtures, an overlap of spectral bands characteristic for pure PHBV and PCL is observed [49][50][51]. FTIR spectra of CNC are characterized by intense absorption bands in the range of wavenumbers 3300-3500 cm −1 and 2800-3000 cm −1 , which correspond to stretching vibrations of OH-groups and CH-bonds of cellulose. The absorption region 950-1200 cm −1 is assigned to valence vibrations of C-O, C-C of a pyranose ring structure [29]. In the PHBV/PCL/CNC composites, the spectral bands mostly overlap, and that fact complicates their interpretation. In addition, cellulose characteristic

FTIR Analysis
For neat PCL, main characteristic bands are observed in the FTIR spectra: 2945 and 2864 cm -1 (asymmetric and symmetric vibrational vibrations of CH2), 1729 cm -1 (C=O vibrations), 1240 and 1166 cm -1 (asymmetric and symmetric C-O-C vibrations). For neat PHBV, the absorption bands at 1280, 1456, 1723, 2930, and 2979 cm −1 refer to stretching vibrations -COC-, bending vibrations -CH2-, stretching vibrations -CO-in ester, and symmetric and asymmetric stretching vibrations -CH3, respectively [54] ( Figure S6). In the FTIR spectra of PHBV/PCL mixtures, an overlap of spectral bands characteristic for pure PHBV and PCL is observed [49][50][51]. FTIR spectra of CNC are characterized by intense absorption bands in the range of wavenumbers 3300-3500 cm −1 and 2800-3000 cm −1 , which correspond to stretching vibrations of OH-groups and CH-bonds of cellulose. The absorption region 950-1200 cm −1 is assigned to valence vibrations of C-O, C-C of a pyranose ring structure [29]. In the PHBV/PCL/CNC composites, the spectral bands mostly overlap, and that fact complicates their interpretation. In addition, cellulose characteristic

FTIR Analysis
For neat PCL, main characteristic bands are observed in the FTIR spectra: 2945 and 2864 cm −1 (asymmetric and symmetric vibrational vibrations of CH 2 ), 1729 cm −1 (C=O vibrations), 1240 and 1166 cm −1 (asymmetric and symmetric C-O-C vibrations). For neat PHBV, the absorption bands at 1280, 1456, 1723, 2930, and 2979 cm −1 refer to stretching vibrations -COC-, bending vibrations -CH 2 -, stretching vibrations -CO-in ester, and symmetric and asymmetric stretching vibrations -CH 3 , respectively [54] ( Figure S6). In the FTIR spectra of PHBV/PCL mixtures, an overlap of spectral bands characteristic for pure PHBV and PCL is observed [49][50][51]. FTIR spectra of CNC are characterized by intense absorption bands in the range of wavenumbers 3300-3500 cm −1 and 2800-3000 cm −1 , which correspond to stretching vibrations of OH-groups and CH-bonds of cellulose. The absorp-tion region 950-1200 cm −1 is assigned to valence vibrations of C-O, C-C of a pyranose ring structure [29]. In the PHBV/PCL/CNC composites, the spectral bands mostly overlap, and that fact complicates their interpretation. In addition, cellulose characteristic bands do not appear due to CNC low content in the composite. However, CNC incorporation into PHBV/PCL polymer matrix leads to broadening of the stretching vibration bands at 3300 cm −1 and 1730 cm −1 , responsible respectively for -OH and C=O stretching vibrations, and may be associated with the hydrogen bond formation (Figure 9a and Figures S7a-S9a). In addition, it should be noted that with an increase in the CNC content, the 1728 cm −1 band characterizing vibrations of the -CO-group involved in hydrogen bonds, shifts towards lower wavenumbers, while the 1746 cm −1 band (characterizes the vibrations of free unbound groups -CO-) shifts towards higher ones. This may serve as an evidence for the hydrogen bond formation between the CNC hydroxyls and the -CO-groups of PCL and PHBV (Figure 9b and Figures S7b-S9b).

Thermal Properties
Thermal characteristics of the PHBV/PCL/CNC composites were obtained based on the analysis of differential scanning calorimetry (DSC) and thermogravimetry (TG) data. DSC curves were obtained at heating and cooling (Figures 10, 11 and S10-S12). The values of the melting temperature Tm, the crystallization temperature Tcryst, the heat of fusion (ΔHm) and the degree of crystallinity (χc) of the polymers in the composites with CNCs are given in Table 2. The pure PCL melts at 55.6 °C and crystallizes at 24.1 °C. In the composites under study, the PCL melting point practically does not change, and the crystallization temperature varies within 30 °C. DSC curves for the pure PHBV show two melting endothermic peaks: low-temperature (Tm1 = 145.7 °C) and high-temperature (Tm2 = 156.5 °C). The appearance of the high-temperature peak is attributed to the melting of more perfect polymer crystals formed as a result of primary crystallization, while the low-temperature peak is attributed to the melting of less structured crystals formed by secondary crystallization [18]. The PHBV/PCL/CNC composites are also characterized by double melting peaks, but their position and intensity differ from the pure PHBV. The intensity of the low-temperature peak slightly decreases, the temperature Tm1 tends to decrease. The intensity of the high-temperature peak remains almost unchanged, as the melting point Tm2 does, while the crystallization temperature tends to decrease.

Thermal Properties
Thermal characteristics of the PHBV/PCL/CNC composites were obtained based on the analysis of differential scanning calorimetry (DSC) and thermogravimetry (TG) data. DSC curves were obtained at heating and cooling ( Figures 10, 11 and Figures S10-S12). The values of the melting temperature T m , the crystallization temperature T cryst , the heat of fusion (∆H m ) and the degree of crystallinity (χ c ) of the polymers in the composites with CNCs are given in Table 2. The pure PCL melts at 55.6 • C and crystallizes at 24.1 • C. In the composites under study, the PCL melting point practically does not change, and the crystallization temperature varies within 30 • C. DSC curves for the pure PHBV show two melting endothermic peaks: lowtemperature (T m1 = 145.7 • C) and high-temperature (T m2 = 156.5 • C). The appearance of the high-temperature peak is attributed to the melting of more perfect polymer crystals formed as a result of primary crystallization, while the low-temperature peak is attributed to the melting of less structured crystals formed by secondary crystallization [18]. The PHBV/PCL/CNC composites are also characterized by double melting peaks, but their position and intensity differ from the pure PHBV. The intensity of the low-temperature peak slightly decreases, the temperature T m1 tends to decrease. The intensity of the high-temperature peak remains almost unchanged, as the melting point T m2 does, while the crystallization temperature tends to decrease.          Changes in the degree of crystallinity of the polymers are complicated: in the PHBV/ PCL(1:1) mixture, an increase in the CNC content in the composites increases the degree of crystallinity of the polymers, while in the PHBV/PCL(1:2) mixture the opposite trend is observed. Thus, under different conditions, CNCs can act both as an initiator of crystallization and growth of polymer crystallites and as a compatibilizer of polymer mixtures, causing their amorphization and improving miscibility [55].
The thermogravimetric (TG) curves and corresponding derivative thermogravimetry (DTG) curves of the PHBV/PCL mixtures and PHBV/PLC/CNC composites are shown in Figure 12 and Figures S13-S16, and the appropriate characteristic data are listed in Table 3. The TG curves of the PHBV/PCL mixtures contain two regions of weight loss corresponding to the decomposition of the individual polymers ( Figure S13). The TG analysis data show a slight increase in the decomposition temperature of PHBV in a mixture with PCL as compared to pure PHBV, while the decomposition temperature of PCL remains practically unchanged. It should be noted that the thermal decomposition of CNCs in the composites occurs at a significantly higher temperature than the decomposition of pure CNCs, for which T on = 200 • C and T max = 240 • C [56] (Figures S15 and S16). Only in the case of the PVP-modified CNCs on the TG curves can one observe the appearance of a low-temperature shoulder, responsible for the CNC decomposition ( Figure 12 and Figure S14). the case of the PVP-modified CNCs on the TG curves can one observe the appearance of a low-temperature shoulder, responsible for the CNC decomposition (Figures 12 and S14).   [59], are practically invisible due to the low CNC content and the complexity of the multicomponent system (Figures 13 and S18).

X-ray Diffraction Analysis
The total crystallinity of PHBV and PCL polymers in the composites with CNCs is shown in Table 4. The data of X-ray diffraction analysis mainly confirm the DSC data about complicated dependence of crystallinity of the polymers on the CNC content in the composites.    [59], are practically invisible due to the low CNC content and the complexity of the multicomponent system ( Figure 13 and Figure S18). the case of the PVP-modified CNCs on the TG curves can one observe the appearance of a low-temperature shoulder, responsible for the CNC decomposition (Figures 12 and S14).   [59], are practically invisible due to the low CNC content and the complexity of the multicomponent system (Figures 13 and S18).

X-ray Diffraction Analysis
The total crystallinity of PHBV and PCL polymers in the composites with CNCs is shown in Table 4. The data of X-ray diffraction analysis mainly confirm the DSC data about complicated dependence of crystallinity of the polymers on the CNC content in the composites.  The total crystallinity of PHBV and PCL polymers in the composites with CNCs is shown in Table 4. The data of X-ray diffraction analysis mainly confirm the DSC data about complicated dependence of crystallinity of the polymers on the CNC content in the composites. Table 4. The total crystallinity of PHBV and PCL polymers in the composites with CNCs.

Sample
The

Tensile Properties
Neat PCL is an elastic polymer characterized by a very high relative deformation at break (over 700%). On the contrary, neat PHBV is a very brittle polymer, the relative elongation at break of which does not exceed 1.5% ( Figure S19). The mixtures of the polymers are characterized by a significant decrease in the elongation at break with the retention of strength characteristics ( Table 5). The CNC addition significantly reduces the elongation and strength, i.e., the composite material becomes less elastic and more brittle (Figures S20 and S21). At the same time, with an increase in the CNC content, Young's modulus changes insignificantly, which indicates that the mechanical properties of the composites are retained under conditions of small linear deformations (Table 5).  The simulation details of the systems consisting of CNC, PVP, PHBV, and a solvent are presented in Table 6.  Figure 14 shows the initial configuration of the PHBV macromolecule and its conformation after 1 ns simulation in vacuum.
Despite its hydrophobic nature, the PHBV macromolecule is capable of forming hydrogen bonds (HBs) with water molecules. The average amount of HB per one monomer unit of the polymer is 0.50.
A cellulose nanoparticle with adsorbed PHBV macromolecule was placed in a cubic box filled with DCM molecules. Since DCM is a good solvent for PHBV, it is supposed that the polymer can be desorbed from the CNC surface. To verify this suggestion, the number of close contacts of any CNC atoms with PHBV within a distance of 0.5 nm as well as the number of HBs formed by the polymer and CNC was calculated as a function of time ( Figure 16). It is seen that, during the first 4-5 ns, the PHBV is completely desorbed from the CNC surface and goes into the solution bulk. Despite its hydrophobic nature, the PHBV macromolecule is capable of forming hydrogen bonds (HBs) with water molecules. The average amount of HB per one monomer unit of the polymer is 0.50.
A cellulose nanoparticle with adsorbed PHBV macromolecule was placed in a cubic box filled with DCM molecules. Since DCM is a good solvent for PHBV, it is supposed that the polymer can be desorbed from the CNC surface. To verify this suggestion, the number of close contacts of any CNC atoms with PHBV within a distance of 0.5 nm as well as the number of HBs formed by the polymer and CNC was calculated as a function of time ( Figure 16). It is seen that, during the first 4-5 ns, the PHBV is completely desorbed from the CNC surface and goes into the solution bulk.  (Table 6, System 8) triggered the desorption process similar to the process for PCL/PVP/CNC [33]. Figure 17 shows a rapid increase in the radius of gyration and end-to-end distance of PVP and PHBV in the first nanosecond of the simulation process, with further fluctuation near constant values: <R e-t-e > = 4.54 ± 0.15, <R g > = 1.71 ± 0.03 and <R e-t-e > = 3.43 ± 0.24, <R g > = 1.30 ± 0.05 nm for PVP and PHBV, respectively. Despite its hydrophobic nature, the PHBV macromolecule is capable of forming hydrogen bonds (HBs) with water molecules. The average amount of HB per one monomer unit of the polymer is 0.50.
A cellulose nanoparticle with adsorbed PHBV macromolecule was placed in a cubic box filled with DCM molecules. Since DCM is a good solvent for PHBV, it is supposed that the polymer can be desorbed from the CNC surface. To verify this suggestion, the number of close contacts of any CNC atoms with PHBV within a distance of 0.5 nm as well as the number of HBs formed by the polymer and CNC was calculated as a function of time ( Figure 16). It is seen that, during the first 4-5 ns, the PHBV is completely desorbed from the CNC surface and goes into the solution bulk.   (Table 6, System 8) triggered the desorption process similar to the process for PCL/PVP/CNC [33]. Figure 17 shows a rapid increase in the radius of gyration and end-to-end distance of PVP and PHBV in the first nanosecond of the simulation process, with further fluctuation near constant values: <Re-t-e> = 4.54 ± 0.15, <Rg> = 1.71 ± 0.03 and <Re-t-e> = 3.43 ± 0.24, <Rg> = 1.30 ± 0.05 nm for PVP and PHBV, respectively.    (Table 6, System 8) triggered the desorption process similar to the process for PCL/PVP/CNC [33]. Figure 17 shows a rapid increase in the radius of gyration and end-to-end distance of PVP and PHBV in the first nanosecond of the simulation process, with further fluctuation near constant values: <Re-t-e> = 4.54 ± 0.15, <Rg> = 1.71 ± 0.03 and <Re-t-e> = 3.43 ± 0.24, <Rg> = 1.30 ± 0.05 nm for PVP and PHBV, respectively.  The PVP and PHBV macromolecules, which were at a greater distance from the CNC and did not have direct contacts with it, were desorbed first and passed into the solution. The PVP molecules that were in direct contact with the CNC were not completely desorbed, although the number of PVP-CNC contacts decreased significantly by the end of the simulation (Figure 18). The number of PVP-PHBV contacts during the composite dissolution in DCM also decreased sharply and reached an average value of 114 (Figure 18e). The number of contacts between the polymers of the same type also rapidly decreased in the first 5 ns, and then N C fluctuated near a constant value. It should be noted that the number of PVP-PVP and PHBV-PHBV contacts (Figure 18c,d) includes not only the contacts between different macromolecules, but also those between the atoms of one (the same) macromolecule; therefore, these values of N C are quite large compared to those for pairs polymer-CNC or PVP-PHBV (Figure 18a,b,e). The PVP and PHBV macromolecules, which were at a greater distance from the CNC and did not have direct contacts with it, were desorbed first and passed into the solution. The PVP molecules that were in direct contact with the CNC were not completely desorbed, although the number of PVP-CNC contacts decreased significantly by the end of the simulation (Figure 18). The number of PVP-PHBV contacts during the composite dissolution in DCM also decreased sharply and reached an average value of 114 (Figure 18e). The number of contacts between the polymers of the same type also rapidly decreased in the first 5 ns, and then NC fluctuated near a constant value. It should be noted that the number of PVP-PVP and PHBV-PHBV contacts (Figure 18c,d) includes not only the contacts between different macromolecules, but also those between the atoms of one (the same) macromolecule; therefore, these values of NC are quite large compared to those for pairs polymer-CNC or PVP-PHBV (Figure 18a,b,e). Figure 19, which shows the time dependence of the polymer-cellulose HB number, also indicates that the PVP molecules were not completely desorbed from the CNC sur-  Figure 19, which shows the time dependence of the polymer-cellulose HB number, also indicates that the PVP molecules were not completely desorbed from the CNC surface, and by the end of the simulation, the polymer formed about 17.8 HBs with the hydroxyl groups of the cellulose nanoparticles. At the same time, the number of HBs formed by the PHBV with the cellulose is much lower than that of the PVP-CNC HBs, which once again confirms the fact of the low affinity of the hydrophobic polymer (PHBV) and hydrophilic cellulose nanoparticles (CNCs). face, and by the end of the simulation, the polymer formed about 17.8 HBs with the hydroxyl groups of the cellulose nanoparticles. At the same time, the number of HBs formed by the PHBV with the cellulose is much lower than that of the PVP-CNC HBs, which once again confirms the fact of the low affinity of the hydrophobic polymer (PHBV) and hydrophilic cellulose nanoparticles (CNCs).

Intermolecular Interactions in Binary PHBV/PCL System in DCM and Vacuum
Modeling of three systems was carried out, with low and high polymer concentration in DCM (Systems 1 and 2, respectively), as well as modeling of a composite consisting of PCL and PHBV (in vacuum) (System 3). The simulation details of the systems consisting of PCL, PHBV, and DCM are presented in Table 7. Figure 21 shows the snapshots of the Systems 1-3 at the end of the simulation.  face, and by the end of the simulation, the polymer formed about 17.8 HBs with the hydroxyl groups of the cellulose nanoparticles. At the same time, the number of HBs formed by the PHBV with the cellulose is much lower than that of the PVP-CNC HBs, which once again confirms the fact of the low affinity of the hydrophobic polymer (PHBV) and hydrophilic cellulose nanoparticles (CNCs).

Intermolecular Interactions in Binary PHBV/PCL System in DCM and Vacuum
Modeling of three systems was carried out, with low and high polymer concentration in DCM (Systems 1 and 2, respectively), as well as modeling of a composite consisting of PCL and PHBV (in vacuum) (System 3). The simulation details of the systems consisting of PCL, PHBV, and DCM are presented in Table 7. Figure 21 shows the snapshots of the Systems 1-3 at the end of the simulation.

Intermolecular Interactions in Binary PHBV/PCL System in DCM and Vacuum
Modeling of three systems was carried out, with low and high polymer concentration in DCM (Systems 1 and 2, respectively), as well as modeling of a composite consisting of PCL and PHBV (in vacuum) (System 3). The simulation details of the systems consisting of PCL, PHBV, and DCM are presented in Table 7. Figure 21 shows the snapshots of the Systems 1-3 at the end of the simulation. Table 7. Simulation details of the systems: number of molecules, macromolecules or particles (N), simulation time (t), and edge length of the simulation boxes (L).   Based on the simulation results, average values of the radius of gyration and end-to-end distance of the polymer macromolecules were calculated (Table 8), as well as the number of close contacts of the polymer atoms within 0.5 nm (Table 9) (averaging was carried out over the last 5 ns of the simulation).  Based on the simulation results, average values of the radius of gyration and endto-end distance of the polymer macromolecules were calculated (Table 8), as well as the number of close contacts of the polymer atoms within 0.5 nm (Table 9) (averaging was carried out over the last 5 ns of the simulation). Table 8. The values of the end-to-end distance R e-t-e and radius of gyration R g for PCR and PHBV, averaged over the last 5 ns of the simulation.

System
PCL PHBV R e-t-e , nm R g , nm R e-t-e , nm R g , nm  Table 9. The number of close contacts between any pair of the polymer atoms within 0.5 nm averaged over the last 5 ns of the simulation. DCM is a good solvent for PCL and PHBV, as evidenced by the R g and R e-t-e values. In a dilute solution, the R g and R e-t-e values are slightly higher than in a concentrated solution of the polymer mixture (Table 8). At low concentrations, PCL and PHBV macromolecules in DCM practically do not interact with each other: the number of close contacts over the last 5 ns of the simulation is 0 ( Table 9, System 1).

System N C (PCL-PHBV) N C (PCL-PCL) N C (PHBV-PHBV)
After the removal of DCM from the solution with a high content of the polymers, the number of PCL-PHBV close contacts increased more than 38 times (Table 9, System 3). Compared with the R e-t-e and R g values of individual PCL and PHBV macromolecules in vacuum (<R e-t-e > = 0.82 ± 0.23 nm, <R g > = 0.71 ± 0.05 nm, and <R e-t-e > = 1.01 ± 0.43 nm, <R g > = 0.69 ± 0.04 nm, for PCL and PHBV, respectively), the R e-t-e and R g values for PCL and PHBV (System 3) are significantly higher. That is, in the polymer mixture, the PCL and PHBV macromolecules are not in the form of a dense globule, but in the conformation of expanded chains (as in a concentrated solution). It should be noted that not only atoms of different polymer contribute to the value of N C (Table 9), but also atoms belonging to the same polymer chain are taken into account. Therefore, the number of PCL-PCL and PHBV-PHBV contacts in System 1 is not equal to 0. The calculated density of the final polymer mixture in vacuum (System 3) was equal 1081 ± 7 kg/m 3 . The experimental density of the pure polymers is 1245 kg/m 3 [60] and 1145 kg/m 3 for PCL and PHBV, respectively.
The radial distribution functions (RDFs) between the centers of mass of PCL and PHBV macromolecules in DCM and vacuum were calculated ( Figure 22). In DCM, the first RDF maxima are at 2.0, 1.5, and 0.5 nm for the interactions of PCL-PCL, PHBV-PHBV, and PCL-PHBV, respectively. In vacuum, the first maxima at the corresponding RDFs are observed at shorter distances of 0.59, 0.76, and 0.28 nm, respectively. So, both in System 2 and in System 3, the PCL-PHBV interactions are more preferable than the PCL-PCL or PHBV-PHBV interactions. Cellulose nanoparticle with adsorbed PVP was placed in the center of a cubic box with periodic boundary conditions. After that, 10 molecules of PCL and 10 molecules of PHVB were added randomly to the box with the CNC/PVP sample. This system was then put into an NpT ensemble with a pressure of 1 MPa and a temperature of 500 K for 1 ns with a simulation time step of 1 fs. This step allows the composite structure to be slowly compressed to obtain the initial amorphous matrix. Then, the temperature was set to 298 K and a pressure of 0.1 MPa for 10 ns. The density of the final matrix was 1.17 g/cm 3 . The final configuration of the composite obtained at the previous step was placed in the center of a cubic box with periodic boundary conditions containing 11,000 DCM molecules. The simulation was performed in NpT ensemble at 298 K and 0.1 MPa for 10 ns. Figure 23 shows an increase in the number of close contacts between atoms of the composite components in the initial simulation period at 500 K and 1 MPa and in the equilibrium period at 298 K and 0.1 Pa. In the first 100 ps, the initial decrease of R g and R e-t-e values for PCL and PHVB with achieving their minima is observed (inset in Figure 24). This behavior is due to the folding of PCL and PHBV macromolecules into globules in vacuum. After 100 ps, the R g and R e-t-e values begin to rise and reach a plateau. This growth is associated with the transition of PCL and PHBV macromolecules to the conformation of expanded chains as a result of interaction with PVP on the CNC surface. It should be noted that, in comparison with PCL, PHBV has a larger number of close contacts with PVP, i.e., interacts better with it. Cellulose nanoparticle with adsorbed PVP was placed in the center of a cubic box with periodic boundary conditions. After that, 10 molecules of PCL and 10 molecules of PHVB were added randomly to the box with the CNC/PVP sample. This system was then put into an NpT ensemble with a pressure of 1 MPa and a temperature of 500 K for 1 ns with a simulation time step of 1 fs. This step allows the composite structure to be slowly compressed to obtain the initial amorphous matrix. Then, the temperature was set to 298 K and a pressure of 0.1 MPa for 10 ns. The density of the final matrix was 1.17 g/cm 3 . The final configuration of the composite obtained at the previous step was placed in the center of a cubic box with periodic boundary conditions containing 11,000 DCM molecules. The simulation was performed in NpT ensemble at 298 K and 0.1 MPa for 10 ns. Figure 23 shows an increase in the number of close contacts between atoms of the composite components in the initial simulation period at 500 K and 1 MPa and in the equilibrium period at 298 K and 0.1 Pa. In the first 100 ps, the initial decrease of Rg and Re-t-e values for PCL and PHVB with achieving their minima is observed (inset in Figure  24). This behavior is due to the folding of PCL and PHBV macromolecules into globules in vacuum. After 100 ps, the Rg and Re-t-e values begin to rise and reach a plateau. This growth is associated with the transition of PCL and PHBV macromolecules to the conformation of expanded chains as a result of interaction with PVP on the CNC surface. It should be noted that, in comparison with PCL, PHBV has a larger number of close contacts with PVP, i.e., interacts better with it.    In Figure 25 the structure of final configuration of the composite PHVB/PCL/PVP/CNC is presented (the simulated cell and its periodic images). As DCM is a good solvent for the polymers, in a DCM solution they are desorbed from the surface of the composite. In Table 10 the values of the end-to-end distance and radius of gyration of the polymers in vacuum, water, and DCM are compared. In vacuum, the Re-t-e and Rg values for the polymer macromolecules in the composite are higher compared to the values for individual macromolecules. At the same time, in DCM, the Re-t-e and Rg values for the polymer macromolecules in the composite are only slightly lower than the values for the individual macromolecules in the solvent. This suggests that not all macromolecules are completely desorbed from the composite surface and pass into the solution bulk by the end of the simulation, and a small part of them form HBs with the cellulose nanoparticle. Table 11 shows that average number of HBs significantly decreases for pairs CNC-PCL and CNC-PHVB. However, for the CNC-PVP pair, the <nHB> value remains almost the same. In vacuum, the Rg values for PCL and PHBV As DCM is a good solvent for the polymers, in a DCM solution they are desorbed from the surface of the composite. In Table 10 the values of the end-to-end distance and radius of gyration of the polymers in vacuum, water, and DCM are compared. In vacuum, the R e-t-e and R g values for the polymer macromolecules in the composite are higher compared to the values for individual macromolecules. At the same time, in DCM, the R e-t-e and R g values for the polymer macromolecules in the composite are only slightly lower than the values for the individual macromolecules in the solvent. This suggests that not all macromolecules are completely desorbed from the composite surface and pass into the solution bulk by the end of the simulation, and a small part of them form HBs with the cellulose nanoparticle. Table 11 shows that average number of HBs significantly decreases for pairs CNC-PCL and CNC-PHVB. However, for the CNC-PVP pair, the <nHB> value remains almost the same. In vacuum, the R g values for PCL and PHBV as individual macromolecules are practically equal; however, in the composite, the R g value for PHBV is greater than that for PCR. This may indicate that, in comparison with PCL, PHBV interacts more intensively with PVP on the CNC surface, and its macromolecules in the composite are in more expanded conformation than PCL macromolecules.  Figure 26 shows the initial and final configurations of the PHBV/PCL/PVP/CNC composite in DCM. It can be seen that by the end of the simulation, the PCL, PHBV, and most of the PVP macromolecules passed into the solution bulk.
The time dependence of the number of close contacts between any pair of CNCpolymer, polymer-polymer, CNC-DCM, polymer-DCM atoms confirms the previously observed behavior of the composite in the solvent. The solvent molecules tend to penetrate the interior of the composite. The high affinity of PCL, PHBV, and PVP with the solvent promotes the dissolution of the composite. This is evidenced by an increase in the number of close contacts between the components of the system and the solvent (Figure 27b) and a decrease in the number of close contacts in polymer-polymer and CNC-polymer pairs (Figure 27a).

CNC-PHVB
2.9 ± 0.3 0.53 ± 0.67 CNC-PVP 38.9 ± 0.5 34.7 ± 3.9 Figure 26 shows the initial and final configurations of the PHBV/PCL/PVP/CNC composite in DCM. It can be seen that by the end of the simulation, the PCL, PHBV, and most of the PVP macromolecules passed into the solution bulk. The time dependence of the number of close contacts between any pair of CNC-polymer, polymer-polymer, CNC-DCM, polymer-DCM atoms confirms the previously observed behavior of the composite in the solvent. The solvent molecules tend to penetrate the interior of the composite. The high affinity of PCL, PHBV, and PVP with the solvent promotes the dissolution of the composite. This is evidenced by an increase in the number of close contacts between the components of the system and the solvent ( Figure  27b) and a decrease in the number of close contacts in polymer-polymer and CNC-polymer pairs (Figure 27a). Figure 28 shows the radial distribution functions (RDFs) between the centers of mass of the composite components in vacuum. The maxima on the RDF curves for the PCL-PCL and PVP-PCL pairs are in the range of 0 to 0.5 nm. Comparing the RDFs for the pairs PHBV-PHBV and PCL-PCL, we can say that PCL macromolecules in the composite have a denser packing. This suggests that, compared with PHBV, PCL has a closer contact with PVP. In DCM, all the peaks on the RDFs shift towards larger distances, indicating the desorption process and the movement of the polymer macromolecules into the solution bulk ( Figure 29).   Figure 28 shows the radial distribution functions (RDFs) between the centers of mass of the composite components in vacuum. The maxima on the RDF curves for the PCL-PCL and PVP-PCL pairs are in the range of 0 to 0.5 nm. Comparing the RDFs for the pairs PHBV-PHBV and PCL-PCL, we can say that PCL macromolecules in the composite have a denser packing. This suggests that, compared with PHBV, PCL has a closer contact with PVP. In DCM, all the peaks on the RDFs shift towards larger distances, indicating the desorption process and the movement of the polymer macromolecules into the solution bulk ( Figure 29).

Conclusions
CNC composites with PCL and PHBV with different PHBV/PCL ratios (1:1 and 1:2) have been obtained. In order to improve the CNC compatibility with the hydrophobic PCL/PHBV matrix, the CNC particle surface was modified by amphiphilic PVP and PAM polymers. The morphological, sorption, thermal, and mechanical properties of the ob-

Conclusions
CNC composites with PCL and PHBV with different PHBV/PCL ratios (1:1 and 1:2) have been obtained. In order to improve the CNC compatibility with the hydrophobic PCL/PHBV matrix, the CNC particle surface was modified by amphiphilic PVP and PAM polymers. The morphological, sorption, thermal, and mechanical properties of the obtained composites have been studied. An analysis of the IR spectra confirms that a hydrogen bond can be formed between the CNC hydroxyl-and the -CO-groups of PCL and PHBV. The thermal characteristics of the PHBV/PCL/CNC composites have been determined based on the DSC and TG data analysis. It is noted that the thermal decomposition of CNC in the PHBV/PCL/CNC composites starts at a much higher temperature than the decomposition of pure CNC. Based on the DSC and XRD data analysis, it is concluded that, depending on the conditions, CNCs can either induce crystallization and polymer crystallite growth or act as a compatibilizer of a mixture of polymers causing their amorphization and improving miscibility. The mixture of PHBV/PCL polymers has a much lower relative elongation at break at the same strength characteristics. At the same time, an increase in the CNC content changes Young's modulus insignificantly, which means that the composite mechanical properties remain unchanged in conditions of small linear deformations. A molecular-dynamics simulation of several systems, starting from simplest binary (solventpolymer) and finishing with multi-component (CNC-polymer mixture-solvent) ones, has been made in order to study the mechanisms of CNC interaction with the polymers in a composite and identify the specific features of the interactions between the system components. The obtained results make it possible to improve the CNC compatibility with hydrophobic polymer matrices and identify and study in more detail the mechanisms of CNC interaction with hydrophilic and hydrophobic polymers in a composite.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.