G Conzatti

D Faucon

M Castel

F Ayadi

S Cavalie

A Tourrette
email: audrey.tourrette@univ-tlse3.fr

Alginate/chitosan polyelectrolyte complexes: A comparative study of the influence of the drying step on physicochemical properties

Keywords:

CO 2 drying Hot air drying Physical-chemistry

Polyelectrolyte complexes (PE Cs) based on Alginate and Chitosan were prepared for biomedical appli cation. These two biopolymers are valuable resources for biomedical applications. ln the present work, three PE Cs materials were produced using three different drying techniques: hot air drying, lyophiliza tion and supercritical C0 2 drying. The choice of the d ry ing technique allowed producing different type of structures, with different porosity scale. ln order to evaluate their potential as intra-abdominal wound dressings, swelling ability in various media, enzymatic resistance and drug release behavior of the result ing materials was studied. lt was shown that the increase of the porosity improved the swelling ability, without altering the resistance of the materials, whereas drug release studies revealed that the majority of the drug was released within the first 24 h whatever the drying process.

Introduction

Polysaccharides have been widely used in recent decades as potential biomaterials. They have received particular attention in various fields such as wound dressing or scaffolds. ln particular, alginate and chitosan are interesting biopolymers as they are cheap and well tolerated by the immune system [START_REF] Lee | Alginate: properties and biomedical applications[END_REF][START_REF] Sahoo | Chitosan: The most valuable derivative of chitin[END_REF]. Although their use in polyelectrolyte com plex (PEC) is widely reported [START_REF] Lawrie | Interactions between alginate and chitosan biopolymers characterized using FTIR and XPS[END_REF][START_REF] Li | Characterization and biodegradation of chitosan-alginate polyelectrolyte complexes[END_REF][START_REF] Yan | PEC films prepared from chitosan-alginate coacervates[END_REF], the drying step is critical to ensure the desired structure.

Alginate, extracted from brown algae and bacteria, is a bio compatible and biodegradable polymer. Alginate has a linear structure and is composed of two blacks of n-L-guluronic (G) and �-o-mannuronic (M) acid residues (Aarstad, T0ndervik, Sletta, & Skjâk-Br.ek, 2012;[START_REF] Augst | Alginate hydrogels as biomaterials[END_REF][START_REF] Lee | Alginate: properties and biomedical applications[END_REF]. The G/M ratio and the structural repartition of these two blacks have a real impact on the alginate characteristics, and as with most of the biopolymers, it is not obvious to speak about one kind of alginate [START_REF] Aarstad | Alginate sequencing: an analysis of block distribution in alginates using specific alginate degrading enzymes[END_REF][START_REF] Lee | Alginate: properties and biomedical applications[END_REF][START_REF] Meng | Alginate block fractions and their effects on membrane fouling[END_REF][START_REF] Pongjanyakul | Quaternary polymethacrylate-sodium alginate films: effect of alginate block structures and use for sustained release tablets[END_REF]. However, it is accepted that alginate presents good swelling abilities and it is already used as wound dressing [START_REF] Momoh | Development functional characterization of alginate dressing as potential protein delivery system for wound healing[END_REF][START_REF] Rezvanian | Development and physicochemical characterization of alginate composite film loaded with simvastatin as a potential wound dressing[END_REF] or support for cell culture (Andersen, Auk-Emblem, & Domish, 2015;[START_REF] Cuadros | Porous matrix of calcium alginate/gelatin with enhanced properties as scaffold for cell culture[END_REF]. Alginate is a polyanion that can be easily cross-linked with calcium alginate. or can interact with polycations to form PECs (REF).

Chitosan is a biocompatible polycation [START_REF] Sahoo | Chitosan: The most valuable derivative of chitin[END_REF]. Chitosan is derived from the chitin and, as for alginate, several types of chitosans exist, with various physico-chemical proper ties depending on their acetylation degree (DA) and chain length [START_REF] Bellich | The Good, the Bad and the Ugly * of Chitosans[END_REF]. Nonethe less, chitosan is known to have interesting mechanical properties compared to alginate and can be used then to strengthen alginate structures. Chitosan is already used in many applications such as drug carrier (Garg, Rath, & Gayal, 2015;[START_REF] Li | Chitosan modified halloysite nanotubes as emerging porous microspheres for drug carrier[END_REF] but also wound dressing [START_REF] Anjum | Development of antimicrobial and scar preventive chitosan hydrogel wound dressings[END_REF][START_REF] Levi-Polyachenko | Chitosan wound dressing with hexagonal silver nanoparticles for hyperthermia and enhanced delivery of small molecules[END_REF].

These two biopolymers were already used together in PECs [START_REF] Lawrie | Interactions between alginate and chitosan biopolymers characterized using FTIR and XPS[END_REF][START_REF] Li | Characterization and biodegradation of chitosan-alginate polyelectrolyte complexes[END_REF][START_REF] Yan | PEC films prepared from chitosan-alginate coacervates[END_REF] elaboration and we have already reported the effect of alginate/chitosan as the mixing technique on physico-chemical properties [START_REF] Castel | Influence of homogenization technique and blend ratio on chitosan/alginate polyelectrolyte complex properties[END_REF]. However, the drying method remains a sensitive step that can strongly involve changes in their structure and then their prop erties [START_REF] Annabi | Controlling the porosity and microarchitecture of hydrogels for tissue engineering[END_REF]. Three classic techniques are generally used to dry polymers: hot air drying, lyophilization (also called freeze drying) and supercritical CO 2 drying (SCC). The porosity but also the network shaping are parameters that can be controlled over the drying stage. It is known that in the case of tissue engi-neering, the 3D structure can be a key factor to control in order to obtain sufficient cell colonization and biological activity [START_REF] Annabi | Controlling the porosity and microarchitecture of hydrogels for tissue engineering[END_REF]. At the same time, the rigidity of the structure is determinant for an efficient cell culture [START_REF] Haugh | Crosslinking and mechanical properties significantly influence cell attachment, proliferation, and migration within collagen glycosaminoglycan scaffolds[END_REF]. Too soft structure can avoid any cell adhesion whereas too hard structure can lead to strongly attached cells with reduced motility [START_REF] Kidoaki | Microelastic gradient gelatinous gels to induce cellular mechanotaxis[END_REF]. For this purpose, the design of the developed matrix is a crucial step, and drying elaboration can afford desired properties.

In the literature, a lot of research's focus on the influence of the polymer ratio, the DA of chitosan, the M/G repartition of alginate or the technique of homogenization on alginate/chitosan PECs properties. To the best of our knowledge, only few studies report the effect of the drying process on alginate/chitosan blends and are centered on the supercritical drying [START_REF] Bueno | Effects of supercritical carbon dioxide processing on the properties of chitosan-alginate membranes[END_REF]Raman, Gurikov, & Smirnova, 2015). The comparison of the drying process on the PECs is thus not well reported. However, in the case of alginate [START_REF] Ho | Preparation of porous scaffolds by using freeze-extraction and freeze-gelation methods[END_REF][START_REF] Quraishi | Novel non-cytotoxic alginate -lignin hybrid aerogels as scaffolds for tissue engineering[END_REF] or chitosan [START_REF] Kassem | Lyophilized sustained release mucoadhesive chitosan sponges for buccal buspirone hydrochloride delivery: Formulation and In vitro evaluation[END_REF][START_REF] Kim | Chitosan fibrous 3D networks prepared by freeze drying[END_REF] pure films, the drying influence the structure of the resulting material. Hence, we think the drying process is a key point and propose a comparative study of simple processed PECs dried with either hot air, lyophilization or SCC drying. With the same early stages elaboration process, we expect variations of the biomaterial structure and properties by varying only the last step of manufacturing. In addition, alginate/chitosan PECs are generally evaluated as potential external wound dressing. One could however expect that the resulting PECs should offer interesting properties for intra-abdominal applications. In particular, pancreatic surgery may require dressings to avoid pancreatic juice excretion after partial pancreatectomies. In this purpose, the materials' obtained structures were observed by scanning electron microscopy and their physico-chemical properties were determined. Porosity, mechanical behavior and swelling properties as well as degradation were investigated and are reported here in order to evaluate their potential as gastro-intestinal wound dressings.

Materials and methods

Materials

Sodium alginate medium viscosity, chitosan, calcium chloride, phosphate buffer saline (PBS) and acetic acid were purchased from Sigma-Aldrich and used as received. Eosine disodique was furnished by DistriBS, sodium dihydrogenophosphate by RectaPur, disodium hydrogenophosphate, sodium hydroxide, Tris(hydroxymethyl)aminomethane (TRIS) and Tris(hydroxymethyl)aminomethane hydrochloric salt (TRIS, HCl) by Fischer and pancreatin from porcine pancreas (PPP) by Acros organics. All experiments were performed in distilled water.

Polysaccharides were characterized as previously reported [START_REF] Castel | Influence of homogenization technique and blend ratio on chitosan/alginate polyelectrolyte complex properties[END_REF]. The G/M units ratio of alginate was estimated by NMR [START_REF] Vilén | Application of diffusion-edited NMR spectroscopy for selective suppression of water signal in the determination of monomer composition in alginates[END_REF] to M/G = 2,93. Its Mw was determined by viscosimetry with ␣ and parameters known as 1.13 and 6.9 × 10 -4 ml g -1 [START_REF] Martinsen | Comparison of different methods for determination of molecular weight and molecular weight distribution of alginates[END_REF], respectively, to be 96 kDa. The deacetylation degree (DD) of chitosan was estimated to be 81% by the Shigemasa method [START_REF] Shigemasa | Evaluation of different absorbance ratios from infrared spectroscopy for analyzing the degree of deacetylation in chitin[END_REF] and its Mw (␣ = 0.93, = 1.81 × 10 -1 ml g -1 [START_REF] Kasaai | Calculation of Mark-Houwink-Sakurada (MHS) equation viscometric constants for chitosan in any solvent-temperature system using experimental reported viscometric constants data[END_REF]) equal to 1 200 kDa.

Elaboration of the polyelectrolyte complex

A solution containing 0.34% v/v acetic acid and 1.5% w/w of chitosan, and a solution of 1.5% w/w of sodium alginate were prepared overnight using a mechanical stirrer, 500 rpm. The two solutions were then poured into a glass petri dish with a mass ratio of 63/37 alginate/chitosan and mixed using an Ultra-Turax mixer (11,000 rpm) for 10 min. The resulting PEC was then partially dried in an oven at 50 • C overnight. A treatment with a 1% w/v CaCl 2 was then performed for 3 h. Afterwards, the gelified PECs were washed thoroughly with distilled water 3 times. Three drying methods were then used.

Hot air dryingxero

The freshly partially dried PECs were placed in an oven at 50 • C overnight, until the mass was constant. Plate semi-transparent films were obtained and are referenced as Xero.

Lyophilizationlyoph

Partially dried PECs were frozen in liquid nitrogen and left 2 days under reduced pressure (4.10 -4 mbar) in a Heto CT 60e lyophilizer. White, expanded foams were obtained and are referenced as Lyoph.

Super critical CO 2 drying -SCC

In order to avoid gel shrinkage, water was gently replaced by ethanol by 10 min successive baths of 1 0%, 30%, 50%, 70% and 100% (v/v) EtOH/water mixtures and then two times in 100% absolute EtOH [START_REF] Robitzer | Nitrogen sorption as a tool for the characterisation of polysaccharide aerogels[END_REF]. The resulting alcogels were then placed in a CO 2 super critical dryer (Polarion 3100). The vat was filled with CO 2 , the system purged 3 times and re-filled. When no EtOH was detected any more, the temperature was set to 45 • C and the pressure to 100 bar in order to reach supercritical conditions. The samples were left 20 min before depressurization. The resulting samples were white and quite soft and are referenced as SCC.

2.6. Characterizations 2.6.1. SEM Scanning electron microscopy (SEM) imaging was performed using a FEG-FEI Quanta 250, operating at 5 kV. Before observation, samples were recovered by 10 nm of platinum.

Volumetric experiments

In order to determine the surface area, the Brunauer, Emmett et Teller (BET) method was performed using a Micrometrics Tristar II analyzer. Samples were degassed in situ at 353 K for one night prior to analysis. Adsorption-desorption isotherms of nitrogen were plotted at 77 K.

Swelling

Swelling studies were done at RT in different solvents: H2O, PBS buffer (pH 7.4, [Na] = 137 mM) andTRIS buffers. TRIS buffers were prepared either by adjusting pH of a TRIS, HCl salt solution with NaOH, referred as "TRIS/NaOH buffer" (pH 7.4, [Na] = 7 mM) or by the TRIS base coumpound, referred as "TRIS" (pH 7.4). The percentage of swelling of mass (or volume) was calculated through the equation:

S w = m f -m i m i × 100 (%)
Where S w is the swelling in terms of percentage, m f is the final mass (or volume) of the sample and m i its initial mass (or volume).

Enzymatic environment evaluation

In order to study the behavior in an enzymatic medium, swelling and degradation studies were performed at 37 • C in a pancreatic simulated media containing 3,5 g L -1 of pancreatin from porcine pancreas (PPP) in phosphate buffer (Na 2 HPO 4 and NaH 2 PO 4 ) pH 8. Swelling measures were performed using the same protocol as described above. The enzymatic activity of PPP was evaluated following the Phadebas Amylase Kit test protocol. Briefly, PPP solutions were treated with Phadebas Amylase tablets at 37 • C for 15 min and subsequently with a 0.5 M NaOH solution. The mixtures were then centrifuged (1500g). The supernatant was taken and centrifuged another time. The supernatant was then analysed through UV-vis spectroscopy using a SHIMADZU UV-1800 spectrometer (620 nm). At t = 0, the enzymatic activity of an 8 mg/L solution was determined as 953 Units per litre (U/l). The activity was then calculated as 80% ± 10 after two days, compared to t=0, using the formula:

Activity U/l = 60 × e -5,8908+ √ 70,8436+13,9082×ln(Absorbance)
For the degradation studies, the media was thus replaced every two days in order to keep an efficient enzymatic activity and the experiment was continued for 14 days. A control sample was made with a xerogel placed in a buffer pH 8, without enzymes. The degradation was evaluated with the following formula:

D = m f V f -m i (V i ) m f V f × 100 (%)
Where D is the degradation in term of percentage, m f (V f ) is the final mass (volume) of the sample and m i (V i ) its initial mass (volume).

Drug release studies

Release kinetics studies were done in phosphate buffered saline (PBS) solution (pH 7.4). Samples (10 × 10 mm) were first placed in buffers containing 0.5 g/L of eosin for 12 h. After impregnation, the mass of each eosin/PBS solution was measured in order to determine the remaining volume (density was considered as equal to 1); the eosin concentration was evaluated by UV-vis spectroscopy using a SHIMADZU UV-1800 spectrometer (517 nm). The remaining eosin quantity was then compared to the initial eosin amount to get the mass of eosin incorporated in the PECs samples m incorporated . After impregnation, samples were then placed directly in an eosin free PBS solution under gentle agitation and aliquots were taken at the desired time for 3 days. Volume was maintained constant by replacing aliquots by eosin free PBS solution. Each aliquot was analyzed through UV-vis spectroscopy (517 nm), and the cumulative released eosin mass was calculated via the formula m released = m aliquot , were m aliquot correspond to the mass of eosin removed within the aliquot. Percentages of release were determined as the ratio of m released x 100/m incorporated .

Release curves were fitted with the Korsmeyer-Peppas model, owing to the equation m released /m incorporated = Kt n , where K is a general descriptive constant, called release rate constant and n is the release exponent [START_REF] Dash | Kinetic modeling on drug release from controlled drug delivery systems[END_REF][START_REF] Korsmeyer | Mechanisms of solute release from porous hydrophilic polymers[END_REF]. The fitting was performed using a power type equation with a confident interval of 95%.

Results and discussion

Structural characterization

The three obtained materials were all made of alginate/chitosan blends. However, they presented various aspects (Fig. 1). Hot air samples (Xero) were semi-transparent whereas freeze drying (Lyoph) resulted in relatively thick foams. Supercritical dried samples (SCC) were macroscopically between Xero and Lyoph, that is to say thin and opaque. These observations let to expect different internal structures. Fig. 2 shows the SEM pictures of Xero, Lyoph and SCC. Xero samples showed compact structure, with no external macroporosity. The liquid/air surface energy tends to collapse PECs polymer chains during the drying process and explains the formation of a compact xerogel. Nonetheless, collapsed planar sheets are present and led to the presumed oriented collapse of PEC network. This orientation can reasonably be explained by the "plane by plane" superficial water evaporation during the process. The use of other drying methods prevented the collapse of the polymer chains and the resulting materials showed macroporosities.

The lyophilization process implies the freezing of the water contained in the PEC. Despite the elimination of water, the freezing step is a key point during the lyophilization process. Various techniques are possible, but herein, the freezing step was performed by quench freezing type process, using liquid nitrogen [START_REF] Kasper | The freezing step in lyophilization: Physico-chemical fundamentals, freezing methods and consequences on process performance and quality attributes of biopharmaceuticals[END_REF]. In solution, this type of freezing induces a fast freezing rate, with the formation of small ice crystals followed by directional solidification. In our case, water is trapped within the PECs. The water crystals grow quickly while freezing, limiting polymer reorganization. Large water crystals are thus formed within the material and the following sublimation extracts the water which leaves place for relatively large cavities. The frozen state of the PECs prevents any structure collapsing as it rigidifies the structure and avoids any polymer solvation. As a result, networked sheets with interconnected pores were obtained, as already observed in the literature for alginate [START_REF] Annabi | Controlling the porosity and microarchitecture of hydrogels for tissue engineering[END_REF][START_REF] Cuadros | Porous matrix of calcium alginate/gelatin with enhanced properties as scaffold for cell culture[END_REF] or chitosan [START_REF] Annabi | Controlling the porosity and microarchitecture of hydrogels for tissue engineering[END_REF][START_REF] Kassem | Lyophilized sustained release mucoadhesive chitosan sponges for buccal buspirone hydrochloride delivery: Formulation and In vitro evaluation[END_REF] hydrogels. Additionally, a "surface skin" was formed at the bulk/air interface, due to water evaporation induced surface tension, as generally observed for this type of drying [START_REF] Ho | Preparation of porous scaffolds by using freeze-extraction and freeze-gelation methods[END_REF]. Supercritical CO 2 (SCC) drying is an alternative method to lyophilization and avoids the freezing of the samples. In counterpart, water has to be first replaced by ethanol to obtain an alcogel. As PECs/ethanol interactions are not favorable, a slight shrinkage was observed, and it may be that a slight morphology change occurred [START_REF] Robitzer | Nitrogen sorption as a tool for the characterisation of polysaccharide aerogels[END_REF]. Ethanol is miscible with CO 2 and can then be replaced by successive CO 2 baths in the supercritical chamber. After being brought below its critical point, CO 2 was evacuated from the chamber. The advantage is that the supercritical state of CO 2 eliminates liquid/air interface and thus no surface tension exists while drying [START_REF] Cardea | Supercritical gel drying of polymeric hydrogels for tissue engineering applications[END_REF][START_REF] Robitzer | Supercritically-dried alginate aerogels retain the fibrillar structure of the hydrogels[END_REF]. No denaturation, e.g. collapsing, occurs during the process. The obtained structure was a 3D nanofibrillated structure, which should be close to hydrogel structure. These observations correlate bulk densities: 860, 40 and 220 mg cm -3 were obtained for Xero, Lyoph and SCC samples, respectively (Table 1). These densities can be linked to the collapsed or expanded states during the drying, and the lower densities obtained for Lyoph samples are explained by the fact that no bulk collapsing occurs during the whole process in addition to the hole formation during water freezing expansion.

The BET methods results are presented in Fig. 3. Due to its collapsed state, Xero showed no adsorption, which is consistent with a low surface area and thus no or poor porosity. This type of isotherm was already reported for polysaccharides [START_REF] Robitzer | Nitrogen sorption as a tool for the characterisation of polysaccharide aerogels[END_REF]. N2 sorption studies are not suitable for large pores, e.g. macroporosity. By the way, Lyoph and SCC were shown to have a type IV isotherm, characteristic of mesoporous materials (Fig. 3a andb). This kind of isotherm is explained by the formation of an adsorbed monolayer at low pressure, meaning that a slight adsorbed amount was detected, followed by multilayer formation so a strong increase in adsorption was observed. Also an H3 type hysteresis can be observed, describing slit-shaped pores [START_REF] Leofanti | Surface area and pore texture of catalysts[END_REF][START_REF] Rio | Synthesis and Characterization of Mesoporous Aluminosilicates for Copper Removal from Aqueous Medium[END_REF]. Higher adsorbed quantities were observed for SCC samples, and surface areas of 160 and 220 m 2 g -1 for Lyoph and SCC samples, respectively, were then calculated (Table 1). Cumulative pore volume indicated a large pore volume for SCC, around two times higher than Lyoph (Fig. 3c). This result can be surprising owing to the higher bulk density obtained for SCC, but the cumulative pore volume measured by the adsorption/desorption method does not take into account the large macroporosity of the material, leading to a wide undervaluation of this value. In this case, the measured value for Lyoph, which has a microsized structure, has to be carefully considered. However, the cumulative pore volume plot is revelatory of the higher mesoporosity of SCC. Pore size distribution confirmed that in addition to macropores observed through SEM, Lyoph and SCC samples presented mesoporosity (Fig. 3d). Indeed, both present pores starting from 10 nm width up to 100 nm. The more numerous pores had width around 25 nm for both dried samples, but the mean pore sizes were about 28 and 35 nm for Lyoph and SCC, respectively. A narrower pore size distribution was thus observed for Lyoph compared to SCC. This can be consistent with the freeze drying process: the ice formation is a homogeneous process and leads to similar pores throughout the material.

In addition to the microscale shape observed by SEM, the BET measurements then showed that the overall mesopore volume and the pore size distribution can be directly tailored by the choice of the drying process. Additionally, the neat molar energy of adsorption, defined as E=E ads -E L , where E ads is the adsorption energy and E L the liquefaction energy (5.6 kJ mol -1 pour N 2 ), can be calculated through the equation E = RTln(C-BET), where C-BET is a BET constant reliable to the strength of the interaction between adsorbate (N 2 ) and the surface [START_REF] Robitzer | Nitrogen sorption as a tool for the characterisation of polysaccharide aerogels[END_REF][START_REF] Trisunaryanti | Calculation of nitrogen adsorption enthalpy on various catalysts[END_REF]. E represents the difference of energy between surface/N 2 interactions involved in the first adsorption layer formation, and the liquefaction energy involved in following layer adsorption, and is characteristic of the surface. It was found to be 3.3 kJ mol -1 for Lyoph (C-BET = 160.8) and 3.4 kJ mol -1 for SCC (C-BET = 206.6) (Table 1). It gives an estimation of the affinity between the gas and the solid, but has to be carefully considered while looking for mesoporous materials, as small pores tend to artificially increase this value. By the way, these values are in the range of polysaccharide values [START_REF] Robitzer | Nitrogen sorption as a tool for the characterisation of polysaccharide aerogels[END_REF]. These are relatively high, which is consistent with PECs surfaces. Indeed, as a PEC results from electrostatic interactions, it is a highly polar material. This high polarity favors a specific organization of quadripolar N 2 molecules as it adsorbs on the surface, and allows dense layers to form.

Finally, the similar net molar energy obtained for Lyoph and SCC indicates that interactions between alginate and chitosan within the PECs are not influenced by the drying process. Nonetheless, modification of the internal structures (not only meso-but especially macroporosities) are characteristics that are directly driven by the drying step. In the following section, the influence of these variations will be discussed.

Swelling properties

The swelling properties were investigated in terms of mass and volume (Fig. 4). A previous study reported that swelling ability of alginate/chitosan PECs is related to the hydrophilic character of alginate [START_REF] Castel | Influence of homogenization technique and blend ratio on chitosan/alginate polyelectrolyte complex properties[END_REF]. Herein, we clearly determined that an increase in the surface area leads to higher swelling abilities of the matrices. After 24 h, samples were considered full and by introducing porosity, swelling can be multiplied by more than 2 times in the case of the SCC, compared to the Xero. Lower swelling degree (1600%, in TRIS pH7.4) for dried alginate under supercritical CO 2 [START_REF] Quraishi | Novel non-cytotoxic alginate -lignin hybrid aerogels as scaffolds for tissue engineering[END_REF] was reported. The Lyoph matrices showed intermediate absorption around 4 000%. Similar results were obtained with lyophilized cross-linked carboxymethyl chitin [START_REF] Zhao | Preparation and characterization of cross-linked carboxymethyl chitin porous membrane scaffold for biomedical applications[END_REF] (in phosphate buffer, pH 7.4). We can also mention that freeze dried chitosan sponge showed only 2 000% of absorption (in 2% agar water) [START_REF] Kassem | Lyophilized sustained release mucoadhesive chitosan sponges for buccal buspirone hydrochloride delivery: Formulation and In vitro evaluation[END_REF]. All these results indicate an interesting water uptake ability of the present matrices, especially for the supercritical drying.

Additionally, volume variations showed that xerogels tend to widely increase their size while swelling (up to 2 300%). Indeed, the collapsed chains permit an extension of the structure. On the other hand, aerogels, and especially Lyoph, were not able to grow as their structures were already expanded.

However, owing to the electrostatic character of PECs, the surrounding media can be of critical importance in term of swelling abilities. The influences of three buffers were evaluated: PBS (pH 7.4), TRIS/NaOH (pH 7.4) and TRIS (pH 7.4). The presence of PBS (buffer pH 7.4) in the media tends to strongly reduce the absorption abilities of Xero and SCC materials whereas it has no significant effect on Lyoph samples (Fig. 5). A diminution was also observed for the TRIS/NaOH and TRIS buffer (same pH, 7.4). In opposition, distilled water is slightly acidic. One could assume this effect is pH driven: at pH 7.4 the amines of chitosan are partially deprotonated (pKa of 6.3 [START_REF] Pillai | Chitin and chitosan polymers: Chemistry, solubility and fiber formation[END_REF]). This deprotonation is supported by ATR-FTIR measurements (Supporting information, Fig. S1).

Two hypothesis can then be drawn: i) the reduction of charge of the chitosan moieties results in less favorable hydrophilic interactions with water and ii) the deprotonation leads to the decomplexation of the PEC which can result in a partial solubilisation of alginate. In both cases, the resulting effect on the swelling percentages is a diminution. Nonetheless, the lower swelling diminution in the case of TRIS/NaOH and, more importantly, TRIS buffer, in the case of SCC, leads to assumption of the influence of the nature of the buffer salt on the PEC. Especially, we assume the formation alginate excess cross-linking is destroyed while Na + replaced Ca 2+ ions, and the PECs structure tends to collapse and/or solubilize, as observed by ATR-FTIR (Supporting information, Fig. S1) and energy dispersive X-ray spectroscopy (EDS, Supporting information Table S2). The presence of Na in the media could also facilitate the xerogels expansion while forming Na-alginate interactions and thus partially counterbalance the negative effect of the increase of the pH on the absorption ability of the material. Hence, for Xero, TRIS treatment exhibited the lower swelling percentage, as this solution contain only possible trace sodium content. The independence of Lyoph to its surrounding medium could be attributed to the relative large pores of Lyoph, responsible for the major part of the absorption of water. The water included in these large cavities is less affected by the state of the polymer. Even if the material is affected by the pH and/or the presence of phosphates, its overall macrostructure is kept intact.

Behavior in enzymatic media

Materials behavior was evaluated in pancreatin from porcine pancreas (PPP) in order to evaluate their potential interest as pancreas wound dressings. Indeed, it can arise that, after partial pancreatic resection; some pancreatic juice can leak through sur-gical sutures. Absorption and resistance against these leakages are properties that a material should have in order to help pancreatic surgery. The solution was buffered with a sodium phosphate salt. PPP is an enzymes digestive cocktail produced by the exocrine cells of pancreas. It contains, among others, amylase, trypsin, lipase, ribonuclease and protease and is supposed to join the duodenum to help digestive functions. The enzymes activity depends on the temperature and the pH. Each enzyme has a pH dependent optimal pH, but an overall pH set to 8 allows efficient activity while reproducing the biological environment of this juice [START_REF] Biochemical Corporation | Manual of clinical enzyme measurements[END_REF]. The swelling over 24 h was measured (Fig. 6, right). The uptakes of the three materials significantly decreased compared to those obtained above in media without enzymes. The higher uptake was obtained for Lyoph samples (1300%), while SCC (1000%) and Xero (790%) remained low. The sodium contained in the buffer salt would explain this decrease, as the possible degradation due to enzymatic activity.

However, as potential wound dressings, materials have also to exhibit resistance to possible harsh conditions. Degradation studies were performed in the same enzymatic media for 14 days (Fig. 6, left). Despite the harsh conditions, the mass loss is not due to the enzymatic activity, as was shown by comparing samples with a control in water. It should be more related to partial solubilization of polysaccharides, especially alginate which is water soluble and affected by the presence of sodium in the buffer salt. Indeed, it was already shown that chitosan has a better resistance to this pancreatic medium than alginate which degraded by 6 days [START_REF] Castel | Influence of homogenization technique and blend ratio on chitosan/alginate polyelectrolyte complex properties[END_REF]. By the way, the presence of enzymes seems to stabilize all of the three materials. In all cases, the degradation rates stayed under 35% after two weeks. Two weeks is generally the minimum time needed to achieve good healing. These degradation rates are low enough to ensure a good conservation of the wound dressing properties during the healing, but at the same time are not so low that a second operation would be needed to remove the wound dressing. However, we see that the SCC exhibits a lower degradation, indicating a higher resistance, probably due to its more highly interconnected nanometric structure which maintains a cohesive state.

Drug release

Drug release studies were performed in order to determine the ability of the 3 types of sample to incorporate and release eosin over time and to relate them to their structure. Results are shown in Fig. 7. In order not to modify the structure of PECs, the loaded eosine matrices were directly put in the release media without being dried. After being immerged in an 0.5 g L -1 eosin bath for 12 h, the dropped eosin per gram of PEC was estimated by indirect assays to be of 92 ± 4 mg/g, 102 ± 10 mg/g and 80 ± 11 mg/g for Xero, Lyoph and SCC samples, respectively. One could expect that by increasing the surface area, the quantity of adsorbed hydrophilic eosin would increase. This phenomenon was observed between Xero and Lyoph but SCC, which had a larger surface area, showed lower adsorption. The water uptake of SCC is decreased by the presence of PBS which explains this phenomenon, as already discussed. This effect could however be amplified by the modification of the material due to the process. Indeed, the passage via an alcogel needed to process SCC could lead, as EtOH is less polar than water and is a non-solvent for PECs, to the modification of the superficial conformation of the polymer chain and then to the reduction of its hydrophilicity. At the same time, Lyoph samples are quickly frozen so no conformation modification is possible and then hydrophilic moieties are still externally oriented. This would increase its affinity to eosin. This explanation is relativized by the similar neat molar energy of adsorption obtained for SCC and Lyoph samples. If this energy has to be carefully considered, the contribution of the macrostructure of Lyoph has to be added to the equation.

In all cases, the three samples seem to reach the maximum of cumulative release after one day (Fig. 7). The relative eosine liberation showed Lyoph exhibited low percentages of release compared to Xero and SCC. This observation is in agreement with the fact that Lyoph samples have much more affinity with eosin than SCC samples. However, not a huge difference was observed between Xero and SCC in terms of percentage of excretion. We would explain this by the fact that Xero has a much more compact structure and that eosin would be located at the outer region of xerogels. The following release would be faster than Lyoph, but still seem to be slightly lower than for SCC.

The diffusion through the sample volume should also be considered. All samples were taken with the same surface, but the Lyoph samples were much thicker. As a result, the distance from the sample core to the external medium is much more important for these samples. A reduction of the release quantity can then be obtained.

The release kinetic was fitted by the Korsmeyer-Peppas model for percentages of release inferior to 45% (30% for Lyoph), which correspond to the linear part of the log/log curves (Fig. 8, dashed lines) [START_REF] Dash | Kinetic modeling on drug release from controlled drug delivery systems[END_REF][START_REF] Korsmeyer | Mechanisms of solute release from porous hydrophilic polymers[END_REF]. This model is indicated for polymeric materials and gives the descriptive parameters K, the release rate constant, and n, the release exponent. The low deviation between the linear fit and experimental curves indicated that the release is mainly driven, at these low release percentages, by diffusion process. In polymeric porous materials, two diffusion processes can basically be kept in mind: diffusion of the drug through the water-filled pores and, as the polymers swell, diffusion through the swollen polymer is to be considered [START_REF] Korsmeyer | Mechanisms of solute release from porous hydrophilic polymers[END_REF]. K incorporates the overall solute diffusion and geometric characteristics of the system. In our case, matrices were already swollen when the release started. K parameter showed to be higher for Lyoph and SCC samples, which is consistent with the higher surface area of these samples: the higher interfacial contact area between the polymers and the water led to a faster swollen polymers/pore filled water drug exchange, then a straightforward diffusion could be achieved and diffusion resistance was lowered. The higher K calculated for Lyoph samples can be attributed to the larger macropores of these structures which facilitate water diffusion. Parameter n gives information about the release mechanism. All types of samples gave n exponents between 0.60 and 0.70. These values are characteristic of a non-Fickian (also called anomalous) diffusion behavior [START_REF] Costa | Modeling and comparison of dissolution profiles[END_REF][START_REF] Dash | Kinetic modeling on drug release from controlled drug delivery systems[END_REF]. This type of diffusion is relevant to a polymer-solvent-solute system, indicating that the already swollen polymer obstructs the eosine diffusion. Despite the steric barrier, this is also due to the carboxylate function of eosine, able to interact with chitosan's amines, thus the PECs materials do not act as inert support matrices: these PECs/eosines interactions limit the release and around 40% of the amount of antiseptic remains in the matrices after two days. After this period, a very low release rate seems to occur.

Conclusion

In this work, we proposed the comparative study of three different drying techniques and their structural and physicochemical impact on alginate/chitosan PEC's as potential gastro-intestinal wound dressings.

The choice of drying process can highly affect the structure of a given polysaccharide material, and allow the tuning of its porosity and also its internal organization. More precisely, classic hot air drying led to a compact xerogel, whereas lyophilization and SCC drying gave rise to 3D architectures, with either a sheets network or a nanofibrillar structure, respectively.

If the structure varies strongly, its impact on the physicochemical was mainly observed on the swelling ability of the designed materials. Especially, by introducing a macro and micro porosity the swelling ability is strongly increased. However, the swelling is directly related to the external medium, and the higher porosity does not systematically imply the higher uptake. Indeed, the optimal material is dependent of the surrounding media. Additionally, we showed that evaluation in pancreatic juice simulated media significantly reduced the swelling ability. Evaluations of these materials should then be performed owing to the desired application in order to drive the choice of the drying process. In all cases, the increase of porosity does not involve a decrease in the enzymatic resistance. In addition, the drying process could produce a change in the interactions between the matrix and the eventual drug molecule, which can modify its release ability. Incorporation of the eosin before the drying process would be an interesting perspective in order to obtain a swelling-controlled release system, possibly able to increase the release time, as the swelling of the polymer during the release is a factor that slows down the diffusion. All these observations showed an interesting potential for the three kind of materials as gastro-intestinal wound dressings and the choice of the drying process would not have to be neglected.

Fig. 1 .

 1 Fig. 1. The three different materials: (left) a hot air dried Xero, (middle) a freeze dried Lyoph, and (right) a supercritical dried sample SCC.

Fig. 2 .

 2 Fig. 2. SEM images of a) and b) xerogels, c) and d) lyophilized, and e) and f) SCC samples. Image magnifications are adapted to the different kind of structures and architecture scales obtained.

Fig. 3 .

 3 Fig. 3. Isotherms of adsorption and desorption of (a) Lyoph, and (b) SCC samples. (b) cumulative curves of pores volumes and (d) dV/dlog(w) curves.

Fig. 4 .

 4 Fig. 4. Massic (left) and volumic (right) swelling percentages of Xero, Lyoph, and SCC in water, 24 h.

Fig. 5 .

 5 Fig. 5. Influence of the media on the swelling rate.

Fig. 6 .

 6 Fig. 6. (Right) swelling and (left)degradation percentages in pancreatic medium after 14 days in 3,5 g L-1 PPP in phosphate buffer (Na2HPO4 and NaH2PO4) pH 8 at 37 • C. Reference sample was a xerogel placed in a buffer pH 8, without enzymes.

Fig. 7 .

 7 Fig. 7. Drug release kinetics of eosin in term of percentages of incorporated eosin.

Fig. 8 .

 8 Fig. 8. Logarithm plots of release curves (solid lines) and linear fitting plots (dashed lines).

Table 1

 1 Structural properties of samples.

	Sample type	Bulk density (mg/cm 3 )	Surface area (m 2 /g)	C-BET	Net molar energy of adsorption (kj/mol)
	Xero	821 ± 80	-	-	-
	Lyoph	37 ± 2	160	160.8	3.3
	SCC	175 ± 31	220	206.6	3.4

Acknowledgement

Authors would like to thank the French National Research Agency for its financial support (ANR-14-CE17-0002-01, FP-BioPrev project).

Appendix A. Supplementary data

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.carbpol.2017.05. 023. ). These data support the hypothesis that Na replaces the Ca ions, especially in the case of PBS treatments, with a shift from Ca-COO -(1596 cm -1 ) to Na-COO -(1603 cm -1 ). In addition, the pH 7.4 lead to a decrease of the NH3 + chitosan band (1530 cm -1 ), thus PEC decomplexation could occur. The increase of cationic amines NH3 + in the case of TRIS/NaOH and TRIS buffers is attributed to the tris(hydroxymethyl)aminomethane amines linked to the alginate COO -[1].

Alginate/chitosan polyelectrolyte complexes

Associated literature:

[1] G. Lawrie, I. Keen, B. Drew, A. Chandler-Temple, L. Rintoul, P. Fredericks, et al., Interactions between alginate and chitosan biopolymers characterized using FTIR and XPS, Biomacromolecules. 8 (2007) Presented values correspond to the mean of three measurements.

[Na] refers to the concentration of sodium in the designated solution.


Геоінформаційного Простору Національної Академії Наук України

Україна Київ

Виробниче Підприємство «tzhk»

Україна Одеса

Timkov

Valery ; Timkov

Serg ; Zhukov

Vladimir ; Afanasiev

THE METHOD FOR INCREASING THE ACCURACY OF SOME FUNDAMENTAL PHYSICAL CONSTANTS

Keywords: електричного заряду, температури Планка, прискорення Планка, сили Планка, енергії Planck's constants, fundamental physical constants, fractals, the accuracy units of measure

Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції МЕТОДИКА ПІДВИЩЕННЯ ТОЧНОСТІ ДЕЯКИХ ФУНДАМЕНТАЛЬНИХ ФІЗИЧНИХ КОНСТАНТ Тімков В.Ф. 1 ; Тімков С.В. 2 ; Жуков В.О. 2 ; Афанасьєв К.Є. 2 1 -кандидат технічних наук, доцент, старший науковий співробітник, Інститут телекомунікацій та глобального

        (1)
From [START_REF]Fundamental Physical Constants[END_REF] it follows that the accuracy of the numerical values ,

The speed of light in a vacuum according to CODATA-2014 [START_REF]Fundamental Physical Constants[END_REF]:

11 299 792 458 m . сs   (3)
The Planck charge p q :

where: ethe elementary electric charge according to CODATA-2014 [1]:   the fine structure constant according to CODATA-2014 [1]: 33 .

7.297 352 5664 10 (0.000 000 0017 10 )

     (6)
It is known [START_REF] Timkov | Electric charge as a function of the moment of mass. The gravitational form of Coulomb`s law[END_REF] that:

Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції

       (8)
The Planck constant over 2pi h : The Planck constant over 2pi h according to CODATA-2014 [1]:

34 .

1.054 571 800 [START_REF] Palmer | Hydrogen in the Universe[END_REF] 10

Js    h ( 10
)
The gravitational constant G :

3 11 3 1 2 2 [START_REF]Planck Publications: Planck 2015 Results[END_REF].674 082 298 [START_REF] Grieb | The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological Од есь ка д ер жа с Міжнародної науково-практичної конференції implications of the Fourier space wedges of the final sample[END_REF] ,

p pp l G m kg s mt       (11)
The Gravitational constant according to CODATA-2014 [START_REF]Fundamental Physical Constants[END_REF]:

where p E  the Planck energy, k  the Boltzmann constant, according to CODATA- 2014 [START_REF]Fundamental Physical Constants[END_REF]:

23 1 1.380 648 52(79) 10 , K k J    (18)
The Planck temperature according to CODATA-2014 [START_REF]Fundamental Physical Constants[END_REF]:

Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції 32 .

1.416 808(33) 10 ( 33)

p E p TK k    (19)
Analysis of the formulas [START_REF]Fundamental Physical Constants[END_REF][START_REF] Timkov | Electric charge as a function of the moment of mass. The gravitational form of Coulomb`s law[END_REF][START_REF] Timkov | Fractal structure of the fundamental constants. Numerical evaluation of the values of some of the fundamental constants with the use of the major characteristics of the muon[END_REF][START_REF] Timkov | Fractal genesis of the angles of the neutrino mixing matrix[END_REF][START_REF] Aghanim | Planck 2018 results. VI. Cosmological parameters[END_REF][START_REF]Planck Publications: Planck 2015 Results[END_REF][START_REF] Cowen | European probe shoots down dark-matter claims[END_REF][START_REF] Bucher | Planck 2013 results. I. Overview of products and scientific Results[END_REF][START_REF] Bennett | Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Final maps and results[END_REF][START_REF] Grieb | The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological Од есь ка д ер жа с Міжнародної науково-практичної конференції implications of the Fourier space wedges of the final sample[END_REF][START_REF] Macaulay | First Cosmological Results using Type Ia Supernovae from the Dark Energy Survey: Measurement of the Hubble Constant[END_REF][START_REF] Timkov | Planck universal proportions. Gravitationalelectromagnetic resonance[END_REF][START_REF] Palmer | Hydrogen in the Universe[END_REF](14)(15)(16)(17)(18)(19) shows that the numerical estimates of the values of the fundamental constants that can be obtained on the basis of the Planck constants:

, , , p p p l m t differ significantly from their standard values, which are presented in CODATA [START_REF]Fundamental Physical Constants[END_REF]. To improve the accuracy of these fundamental constants, it is necessary to increase the accuracy of the Planck constants:

. ,,

p p p l m t

The choice of standards of fundamental constants

To select standards of fundamental constants, we use the following criteria:

1. The accuracy of the numerical value of the fundamental constant should have the maximum possible value. That is, the number of decimal places after the decimal separator should be the largest.

2. The standard uncertainty of the fundamental constant should have the minimum possible value.

3. The numerical value of the fundamental constant is determined (confirmed) experimentally.

The following fundamental constants correspond to such criteria [START_REF]Fundamental Physical Constants[END_REF]: the speed of light in vacuum:

The second equation is defined on the basis of patterns: an electric charge -a function of the mass moment [START_REF] Timkov | Electric charge as a function of the moment of mass. The gravitational form of Coulomb`s law[END_REF]. Then:

     (23)
The third independent source for estimating the values of Planck's constants: ,, p p p l m t is determined on the basis of a pattern [3,4]: Planck's constants: masses p m and lengths p l are golden algebraic fractals of the main characteristics of a muon: its mass m   and its Compton wavelength over 2pi , С   D then:

p m l      (28) 44 .
5.390 739 861 10

p t s      (29)
Let the value of the moment of the Planck mass pp ml , which is given in formula ( 23) is a standard, then we make a comparison of the Planck constants -the length and the mass according to formulas ( 1

The analysis of formulas ( 23), ( 31) and (33) shows that the concept of the fractal connection of the hypothetical Planck particle and muon can be used as a third independent source to increase the accuracy of the values Planck's constants:

of the mass, of the length, of the time. In [START_REF] Timkov | Electric charge as a function of the moment of mass. The gravitational form of Coulomb`s law[END_REF] it was shown that the moment of the Planck mass is equal to the moment of the mass of the electron, which is defined through the Bohr radius, then the equality is true:

0 , p p e m l m a   (34)
where: 0 ,, e am   it is, respectively: the Bohr radius, the fine-structure constant, the electron mass. According to [START_REF]Fundamental Physical Constants[END_REF] the mass of electron equals: .

С mc  h D ( 36
)
Whence the moment of particle mass:

. С m c  h D ( 37
)
From formulas (34) and (37) it follows that:

. From formulas (37) and (38) it also follows that:

0 0 ... . p e n n p p e C C C C C p n m l m m m m m c             h D D D D D (41)
The mass moments of all elementary particles, which are determined through their Compton wavelength over 2pi, are equal to each other and equal to the Planck mass moment.

From formulas (21) and (41) it follows that:

                 D D D h D (42)
Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції That is, formula (42) confirms the pattern [START_REF] Timkov | Electric charge as a function of the moment of mass. The gravitational form of Coulomb`s law[END_REF] that the electric charge is a function of the mass moment. It also means that there is an opportunity to improve the accuracy of Planck's constants estimates: of the mass, of the length, of the time to a value of The elementary electric charge, expressed in terms of the Rydberg constant:

e ye mc R cR m c cR J R             h (47)
The value y R of the Rydberg constant times hc in J according to CODATA-2014 [1]:

Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції 18 2.179 872 325(27) 10 .

y R J    (48)
The value c R of the Rydberg constant times c in Hz:

          D D hD (49)
where e k it is the electric force constant, or the Coulombs constant:

The Josephson constant J K , as the reciprocal of the magnetic flux quantum:

J p ee K Hz V ec eZ ec             h (56)
The value of the Josephson constant according to CODATA-2014 [START_REF]Fundamental Physical Constants[END_REF]:

9 1 1
483 597.8525(0.0030) 10 .

J K Hz V    (57)
The constant atomic unit of energy, or the constant Hartree energy h E :

          (83)
The value of the estimate of the Planck power with accuracy 9 10  is:

52 1 1
3.628 936 797 10 .

p P J s     ( 84
)
The estimate of the Planck temperature p T   , which is determined on the basis of the characteristics of the muon: 32 1.416 917 77 [START_REF] Grieb | The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological Од есь ка д ер жа с Міжнародної науково-практичної конференції implications of the Fourier space wedges of the final sample[END_REF] .

p p E TK k        (85)
Estimates of the Planck constant over 2pi h , which are determined on the basis of the characteristics of the muon:

Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції

e ee C m c m c Js R         hD (88)
Comparative analysis of formula ( 9) on the one hand and formulas (86,87,88) on the other hand with a standard using formula [START_REF] Grieb | The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological Од есь ка д ер жа с Міжнародної науково-практичної конференції implications of the Fourier space wedges of the final sample[END_REF] shows that Planck's constants: of the length, of the mass, of the time, which are determined based on the characteristics of the muon, are more preferable in the application, than their standard values.

The accuracy of the operands in formula (88) is not lower than 10 10  , then taking into account formulas (86,87), the estimate of the Planck constant over 2pi h can be represented as: 34 .

571 8001 10

Js    h (89)
Estimates of the Gravitational constant G , which are determined on the basis of the characteristics of the muon:

p pp l G m kg s mt           (90) or: 2 11 3 1 2
6.673 045 869 10 ,

p p lc G m kg s m           (91)
or:

p c G m kg s m         h (92)
or:

p tc G m kg s         h (94) or
p pp kT G m kg s mF           (97)
The average value of the estimate of the Gravitational constant by the formulas (90 -97):

Or taking into account the accuracy of the operands:

19 .

1.602 176 620 80 10 eC   (100) Estimation of the basic characteristics of the hypothetical Planck particle based on the characteristics of the muon increases the accuracy of the values of some fundamental physical constants.

Analytical estimate of the numerical value of the Hubble constant

The numerical value of the mass [START_REF]Fundamental Physical Constants[END_REF] of some elementary particles: electron, muon, proton, neutron and Planck's hypothetical particle will be presented in the form of the golden algebraic fractal (next -GAF) [START_REF] Timkov | Fractal structure of the fundamental constants. Numerical evaluation of the values of some of the fundamental constants with the use of the major characteristics of the muon[END_REF][START_REF] Timkov | Fractal genesis of the angles of the neutrino mixing matrix[END_REF], and the data will be entered in Table 1. Based on experimental data estimates of the Hubble constant, which were obtained from various sources: the Planck Mission [START_REF] Aghanim | Planck 2018 results. VI. Cosmological parameters[END_REF][START_REF]Planck Publications: Planck 2015 Results[END_REF][START_REF] Cowen | European probe shoots down dark-matter claims[END_REF][START_REF] Bucher | Planck 2013 results. I. Overview of products and scientific Results[END_REF], the Wilkinson Microwave Anisotropy Probe (WMAP 9 years, combined with other measurements) [START_REF] Bennett | Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Final maps and results[END_REF], SDSS-III Baryon Oscillation Spectroscopic Survey [START_REF] Grieb | The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological Од есь ка д ер жа с Міжнародної науково-практичної конференції implications of the Fourier space wedges of the final sample[END_REF], DES Collaboration [START_REF] Macaulay | First Cosmological Results using Type Ia Supernovae from the Dark Energy Survey: Measurement of the Hubble Constant[END_REF],

using the law "Planck's Universal Proportions" [START_REF] Timkov | Planck universal proportions. Gravitationalelectromagnetic resonance[END_REF], calculate the estimate of the mass of the observable Universe. The obtained data, including the value of the estimated mass of the observable Universe in the form of a GAF, are presented in Table 2. Where in Table 2 the value of g f is:

5 0.5 2sin(18 ) 2cos(72 ) 0.61803398874989484820...

2 g f        (101)
It is known [START_REF] Palmer | Hydrogen in the Universe[END_REF]14] that the mass of the baryonic matter of the observable Universe consists of more than 75% protons. Then, taking into account that the electron mass is much less than the proton and neutron masses, and also that the neutron and proton masses are close in value, we can conditionally assume that the mass of the observable Universe is 75% composed of protons and 25% of neutrons.

Analysis of the data in Tables 1 and2 shows that the mantissas of the masse of the observable Universe are very close to the mantissas of the masses of the proton and neutron, in all cases, except for the data from WMAP.

Let the mass of the observable universe is formed only from protons. Then, assuming that the mass of the observable Universe and the mass of the proton are one and the An analytical estimate of the Hubble constant is consistent with experimental data.

T M s H s T                    (

Results

The results of the study are presented in Table 3 (km/s)/ Mpc Conclusions. Since units of measurement of most constants and variables of gravitational and electromagnetic interactions can be expressed in units of measurement: of the length, of the mass and of the time, that is, through: meter, kilogram and second, then it is convenient to choose Planck constants: of the length, of the mass, of the time as the basis of fundamental physical constants. However, in the practical use of these constants problems arise: 1) their low accuracy; 2) indirect, not direct connection with the characteristics of real elementary particles. To eliminate these problems, it is proposed to establish a direct relationship between the characteristics of the hypothetical Planck particle and the characteristics of the muon. Since the characteristics of the muon and the hypothetical

  light in vacuum c , taking into account (

(

  ) and (27,28). The value of the moment of the mass of Planck by the formula (1the accuracy of the values of the constants in the formula (the moment of the mass of Planck by the formulas (27,28): the accuracy of the values of the constants in the formulas

  that the Compton wavelength over 2pi C D of any elementary particle with a mass mis equal to:

9 10 , 10 

 91010  and the composition of these constants -the mass moment -to a value of 10 .Improving the accuracy of the numerical values of the estimates of some fundamental physical constantsThe Rydberg constant R  is one of the most accurately measured fundamental constants. Obviously, it is convenient to use this constant to estimate the accuracy of other fundamental physical constants, for example, the fine structure constant. Let us specify the value of the fine structure constant in terms of the Rydberg constant and the Bohr radius. The Bohr radius has the same accuracy value as the fine structure constant, but its standard uncertainty value is less. Then: 0 4 0.007 297 352 5663 119 669 893 690... aR    (43) On the basis of formulas (39,43), we specify the estimate the value of the fine structure constantof the values of the fine structure constant: of the standard according to CODATA-2014 by the formula (6), as well as by formulas (43) and (44) shows that the weight of the tenth digit of the standard value of the fine structure constant (number 4) is greater than by the formulas (43,44).

R

  s constant over 2pi, expressed in terms of the Rydberg constant: of the Rydberg constant times hc in J: 872 325 506... 10 42

  the quantum of the electrical resistance, or the von Klitzing constant K R : the quantum of the electrical resistance, or the von Klitzing K R constant according to CODATA-2014[START_REF]Fundamental Physical Constants[END_REF]

  д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції The value of the constant Hartree energy according to CODATA-2014 [estimates of the moment of the mass: of the proton, of the neutron, of the muon, of the electron through their Compton wavelength over 2pi: taking into account the accuracy of the neutron mass values and its Compton wavelength over 2pi: (60 -67) shows that the accuracy of estimates of the mass moments of the proton, of the neutron, of the muon, of the electron through their Compton wavelength over 2pi does not exceed the value 8 10  , that is: д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференціїIncrease the accuracy of estimating the mass values: of the proton, of the neutron, of the electron. For this we use physical law: equality of moments of particle mass through their Compton wavelength over 2pi, of the formulas (41,42), and the fact that the accuracy of Compton wavelength over 2pi of the elementary particles and the accuracy of the moments of their mass is higher than the accuracy of the values of the

  into account the accuracy of the operands in formulas (69,70,71), the mass estimates of the proton, of the neutron, of the electron are as follows: new estimates of the mass moments of the proton, of the neutron and of the electron, taking into account the estimates of the values of their mass in formulas (72,73,74), will be close to the value of the mass moment by formula (22). Let us specify the values of the estimates of the Rydberg constant time hc in J and constant Hartree energy taking into account the calculated value of the electron mass of the values of Planck's constants -of the mass, of the length and of the time, as fractals of the main characteristics of the muon, and which are represented by the formulas (24,25,26), we calculate the estimates of the constants: the Planck acceleration p a   : Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-

  д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-

  this is the Hubble time.The value of the evaluation of the Hubble constant in the traditional form: the analytical evaluation of the Hubble constant taking into account the percentage ratio of protons and neutrons can be represented as: д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції

Table 1 .

 1 The mantissa, the structural level of the GAF: electron, muon, proton, neutron, hypothetical Planck particle.

	Particle name	Particle mass, kg	Mantissa	level GAF
	electron	9.10938356•10 -31 1.13164233169	144
	muon	1.883531594•10 -28 1.17578810591	133
	proton	1.672621898•10 -27 1.52336288580	129
	neutron	1.674927471•10 -27 1.52546271742	129
	Planck part.	2.1766388345•10 -8 1.17578810591	37

Table 2 .

 2 The Estimation of the mass of the observable Universe based on the Hubble constant, which is obtained from the various experimental sources of the information.

	Name of the	Hubble const.,	Mass of the	GAF form of a
	data source	(km/s)/Mpc	Universe, kg	mass of the
				Universe, kg
	Planck Mission Planck Mission	67.66±0.42 67.74±0.46	1.8414357•10 53 1.52158398•f g 1.839260•10 53 1.51978700•f g	-254 -254
	Planck Mission WMAP SDSS-III BOSS	67.80±0.77 69.32±0.80 67.6(+0.7)(-0.6) 1.8430700•10 53 1.522934498•f g 1.837633•10 53 -254 1.5184420•f g -254 1.797339•10 53 1.485146740•f g -254
	DES Collaborat.	67.77±1.30	1.838447•10 53	1.51911424•f g	-254

  Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції same golden algebraic fractal, but on different structural levels of matter, we choose the proton mantissa as the standard, and on its basis, we estimate the mass of the

	observed Universe	M	p U		:
		M	p U	 	4 25 f  . g 8580. 3628 523 1. . 		53 0 1 8 3 8 5153510... 1 . 4 5 8 	kg	.	(102)
	Let the mass of the observable Universe and the mass of the neutron -is one and the
	same golden algebraic fractal, but on different structural levels of matter, then choose
	of the mantissa of the neutron as standard, and on its basis to estimate of the mass of
	the observable Universe	M	n 0 :
												U
		M	0 n		1.5 2546 27174 172...		f	2 54  g		53 0 . 1 .. . 4 12 75190 1 8 6 9 	kg	.	(103)
			U
	Let us estimate the mass of the observable Universe	M	0 pn   , provided that it
													U
	consists of 75% protons and 25% neutrons:
	M	0 p n    0.75 p M 		0.25		M	0 n		53 . 1.84422382448890... 10 kg 	(104)
		U										U	U
	To estimate the Hubble constant taking into account formula (104), we use the law
	"Planck's Universal Proportions" and calculate the proportionality coefficient 1   at
													pt
	the base this law:
														
									1 pt 		t	p 			2.4766349727317... 10 	36 1 s kg 	1 . 	(105)
												m
													p
	The Hubble constant estimate	H	0 pn  	for the observable Universe, which consists of
	protons and neutrons, is equal to:
	0 p n UU 1 p n 0 pt		17 ... 10 ; .5675 4	0 p n	1	0	2 .18939	... 0 1	18 1	,
													pn
													U

Table 3 .

 3 . Presents the final results of research to improve the accuracy of some fundamental physical constants.

	The name of the	Constant value	Constants proposed in the	The unit
	constant	CODATA-2014,	research	of
		Planck Mission		measure
				ment
	the gravitational	6.674 08•10 -11	6.673 045 870•10 -11	m -3 kg -1 s -
	constant			2
	the Planck constant 1.054 571 800 •10 -34	1.054 571 8001 •10 -34	m 2 kg 1 s -2
	the elementary	1.602 176 620 8•10 -19 1.602 176 620 80•10 -19	C
	charge
	the Planck length	1.616 229•10 -35	1.616 103 153•10 -35	m
	the Planck mass	2.176 470•10 -8	2.176 638 835•10 -8	kg
	the Planck time	5.391 16•10 -44	5.390 739 861•10 -44	s
	the Planck	1.416 808•10 32	1.416 917 77•10 32	K
	temperature
	the electron mass	9.109 383 56•10 -31	9.109 383 557 60•10 -31	kg
	the proton mass	1.672 621 898•10 -27	1.672 621 897 680•10 -27	kg
	the neutron mass	1.674 927 471•10 -27	1.674 927 471 46•10 -27	kg
	the Rydberg	2.179 872 325•10 -18	2.179 872 324 93•10 -18	J
	constant in J
	the Rydberg	3.289 841 960	3.289 841 960 355 2•10 15	Hz
	constant in Hz	355•10 15
	the von Klitzing	25 812.807 4555	25 812.807 4554 31940	Ω
	constant
	the constant	4.359 744 650•10 -18	4.359 744 649 86•10 -18	J
	Hartree ener.
	the Josephson	483 597.8525•10 9	483 597.852 474•10 9	Hz 1 V -1
	constant
	the Hubble cons.	67.66±0.42	67.55770 +0.02329

Од есь ка д ер жа вн а а ка д ем і я т е х ніч но го р е г ул ю ва н н я т а яко с ті Збірник наукових праць ІХ Міжнародної науково-практичної конференції Planck particle are golden algebraic fractals, this relationship can be established on the basis of the similarity coefficients of golden algebraic fractals. This approach improves the accuracy of the Planck length and of the Planck mass by three orders of magnitude, and of the Planck time by four orders of magnitude. Improving the accuracy of measurements of the characteristics of the muon will automatically increase the accuracy of all fundamental constants, which are determined on the basis of the Planck constants: of the length, of the mass, of the time. The analytical estimate of the Hubble constant is within the tolerances of the experimental Hubble constant values, which are obtained by Planck Mission, DES Collaboration, SDSS-III BOSS.


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