Number-average Degree Of Polymerization Research Articles

ROMP-based Glycopolymers with High Affinity for Mannose-Binding Lectins.

Well-defined, highly reactive poly(norbornenyl azlactone)s of controlled length (number-average degree of polymerization = 10 to 1,000) were made by ring-opening metathesis polymerization (ROMP) of pure exo-norbornenyl azlactone. These were converted into glycopolymers using a facile postpolymerization modification (PPM) strategy based on click aminolysis of azlactone side groups by amino-functionalized glycosides. Pegylated mannoside, heptyl-mannoside, and pegylated glucoside were used in the PPM. Binding inhibition of the resulting glycopolymers was evaluated against a lectin panel (Bc2L-A, FimH, langerin, DC-SIGN, ConA). Inhibition profiles depended on the sugars and the degrees of polymerization. Glycopolymers from pegylated-mannoside-functionalized polynorbornene, with = 100, showed strong binding inhibition, with subnanomolar range inhibitory concentrations (IC50s). Polymers surpassed the inhibitory potential of their monovalent analogues by four to five orders of magnitude thanks to a multivalent (synergistic) effect. Sugar-functionalized poly(norbornenyl azlactone)s are therefore promising tools to study multivalent carbohydrate-lectin interactions and for applications against lectin-promoted bacterial/viral binding to host cells.

The occurrence and structural heterogeneity of arabinoxylan in commercial pilsner beers and their non-alcoholic counterparts

The impact of arabinoxylan (AX) on the brewing process and beer characteristics depends on its content and structure and is often overlooked in research and industry. This paper reports on the occurrence and structural heterogeneity of AX in a set of commercial pilsner beers and their non-alcoholic counterparts. Fractionation by graded ethanol precipitation allowed us to isolate AX-rich fractions from beer with a number-average degree of polymerisation of 4 to 308 and an average degree of substitution in the range of 0.43 to 0.88. Pilsner beers had a higher content of high-molecular-weight AX than their non-alcoholic counterparts. The structural heterogeneity among the various commercial beers differed. By comparing the chemical composition of the beers, differences in beer production methods and ingredient selection were deduced and used to tentatively explain the differences in AX content and structural heterogeneity.

Molecular weight distribution of fructans extracted from Agave salmiana leaves

Background: In mezcal industry, Agave salmiana leaves are a crop residue and a potential source of fructans. Agave fructans are a soluble fiber that can act as prebiotic in gut microbiota.
 Questions and Hypotheses: The molecular weight distribution of agave fructans extracted from leaves of Agave salmiana depends on the region where agaves growth and on the subspecies.
 Studied species: Agave salmiana Otto ex Salm Dyck, spp. salmiana and Agave salmiana spp. crassispina. 
 Study site: Twelve municipalities from Guanajuato México were sampled: Ocampo, San Felipe, San Diego de la Unión, Victoria, Xichú, Atarjea, Dolores Hidalgo, Doctor Mora, Santa Catarina, Tierra Blanca, San Miguel Allende and Comonfort.
 Methods: The base of the leaf close to the stem of Agave salmiana ssp. salmiana and A. salmiana ssp. crassispina plants, six years old, were harvested. Water s oluble carbohydrates were extracted, the content molecular weight distribution of fructans was determined by HPLC-SEC.
 Results: An average of 0.7 % of soluble carbohydrates was recovered from the leaves. The molecular weight distribution of Agave salmiana fructans was: number average molecular weight: 3,209 g/mol; average molecular weight: 5,046 g/mol; number average degree of polymerization: 19; weight average degree of polymerization: 30. High polymerization degree fructans content was greater in Agave salmiana spp. salmiana (55 %) than in Agave salmiana spp. crassispina (47 %).
 Conclusions: The leaves of Agave salmiana contain a low proportion of high-molecular-weight fructans, compared to commercial agave fructans. The results demonstrated the technical feasibility to obtain fructans from Agave salmiana leaves.

Neodymium-based one-precatalyst/dual-cocatalyst system for chain shuttling polymerization to access cis-1,4/trans-1,4 multiblock polybutadienes

A new chain shuttling polymerization system was developed that utilizes only one neodymium precatalyst and two different types of cocatalysts to prepare cis-1,4/trans-1,4 stereo multiblock polybutadienes. This study provides a new alternative to achieve conjugated diene chain shuttling polymerization. For the butadiene polymerization with Nd(Oi-Pr)3/MMAO/Mg(n-Bu)2 system, a gradual reduction of the Mn of the resultant polymer with Mg(n-Bu)2 content increased while retaining narrow molecular weight distributions and unimodal GPC profiles, which indicated the occurrence of fast and reversible chain transfer. The trans-1,4 content increased from 7.7 % to 50.6 % with Mg(n-Bu)2 content increased, Mg(n-Bu)2 both served as cocatalyst to generate trans-1,4 regulating species and as chain transfer agent capable of shuttling the formed polymer chains between the two active species. Furthermore, the number-average degree of polymerization of the trans and cis blocks can be calculated from 13C NMR analysis. Differential scanning calorimetry and dynamic mechanical analysis was also performed to further validate the cis-1,4/trans-1,4 multiblock structure.

Anisotropic pyrochemical dry etching of fluorinated ethylene propylene induced by pre-irradiation with synchrotron radiation

Anisotropic pyrochemical micro-etching induced by synchrotron x-ray irradiation is developed as a microfabrication process for fluorinated ethylene propylene (FEP). X-ray irradiation is performed at room temperature, and the irradiation area is etched by heating in an oven. By measuring the irradiation area using Raman spectroscopy, the peak of the Raman spectrum is shown to decrease with an increasing irradiation dose. It is also observed that the etching can be performed at a heating temperature of around 200 °C while maintaining the chemical composition of the surface. The etching mechanism is speculated to be as follows: x-ray irradiation causes chain scission, which decreases the number-average degree of polymerization. The melting temperature of irradiated FEP decreases as the polymer chain length is decreased so that the irradiated area can be evaporated at low temperatures of post-heating. In this way, we demonstrate that anisotropic pyrochemical micro-etching of FEP proceeds only in the depth direction where x rays are absorbed. It is possible to avoid deterioration of the shape accuracy arising from thermal expansion during the transfer process of the mask pattern by separating pre-irradiation from post-heating. Through this method, it becomes possible to realize a high precision microstructure of FEP in a large area.

Probing Thermoresponsive Polymerization-Induced Self-Assembly with Variable-Temperature Liquid-Cell Transmission Electron Microscopy

Summary We directly initiate and visualize the formation of polymeric nanomaterials via variable-temperature liquid-cell transmission electron microscopy (VT-LCTEM). With temperature control in the liquid cell, reversible addition-fragmentation chain transfer polymerization was thermally initiated, leading to the formation of amphiphilic block copolymers that assemble upon dispersion polymerization-induced self-assembly (PISA). In combination with traditional ex situ analyses, VT-LCTEM enabled not only the characterization of the nanoparticles in situ but also the observation of a thermal phase transition. Critically, because these assemblies form from thermoresponsive components, any temperature changes during sample preparation and analysis can alter morphologies, necessitating direct in situ characterization of reaction progression. We believe that the findings and the technique described herein will lead to unprecedented possibilities for the development and characterization of self-organizing soft matter.

Theory of chain growth in chemical oxidative polymerization of aniline derivatives

A theoretical approach has been proposed for the establishment of quantitative relationship between the number-average molecular weight of products of the oxidative polymerization of aromatic amines and both reagent concentrations and temperature. The derived equation to estimate the number-average degree of polymerization was evaluated using the corresponding experimental data reported in the literature. It was demonstrated that the developed theory can adequately describe an increase in the molecular weight of aromatic amine polymers upon an increasing monomer conversion and decreasing temperature and oxidizer/monomer molar ratio. Proposed assumptions about the mechanism of chain growth in the oxidative polymerization of aromatic amines reflect the key features of influence of the ratio of reactants and acidity of the medium, as well as the structure of oxidizing agent on the number-average degree of polymerization of the resulting polymers. Predictions about the influence of various factors on the molecular weight of products of the oxidative polymerization of aromatic amines have been made.

Simulation and Analysis of Propylene Coordination Polymerization Process Based on Aspen (polymer) plus

Based on the industrial conditions of coordination polymerization of polypropylene, Polymer plus was used to simulate and analyze the coordination process of propylene. The effects of the amount of propane, main catalyst (TiCl4), chain transfer agent (hydrogen), shielding gas (nitrogen), and monomer (propylene) on the number average degree of polymerization (DPN), the weight average degree of polymerization (DPW), the number average molecular weight (MWN), the weight average molecular weight (MWW), the polydispersity index (PDI), and the throughput of polypropylene were explored to guide actual production in this paper. Through analysis, the polymerization degree and molecular weight of polypropylene could be adjusted by hydrogen in actual production. The monomer (propylene) should be purified as much as possible to reduce the feed amount of propane. The increase of the propylene contributed to the molecular weight and polymerization degree of the product. The increase in the nitrogen feed amount had no effect on the product performance index. The feed amount of nitrogen could be adjusted as needed according to the actual equipment specifications. The catalyst has the greatest influence on the comprehensive performance index of the product, thus the amount of main catalyst TiCl4 must be strictly controlled.

Simulation and Analysis of Propylene Coordination Polymerization Process Based on Aspen (polymer) plus

Based on the industrial conditions of coordination polymerization of polypropylene, Polymer plus was used to simulate and analyze the coordination process of propylene. The effects of the amount of propane, main catalyst (TiCl4), chain transfer agent (hydrogen), shielding gas (nitrogen), and monomer (propylene) on the number average degree of polymerization (DPN), the weight average degree of polymerization (DPW), the number average molecular weight (MWN), the weight average molecular weight (MWW), the polydispersity index (PDI), and the throughput of polypropylene were explored to guide actual production in this paper. Through analysis, the polymerization degree and molecular weight of polypropylene could be adjusted by hydrogen in actual production. The monomer (propylene) should be purified as much as possible to reduce the feed amount of propane. The increase of the propylene contributed to the molecular weight and polymerization degree of the product. The increase in the nitrogen feed amount had no effect on the product performance index. The feed amount of nitrogen could be adjusted as needed according to the actual equipment specifications. The catalyst has the greatest influence on the comprehensive performance index of the product, thus the amount of main catalyst TiCl4 must be strictly controlled.

Swelling of multi-responsive spherical polyelectrolyte brushes across a wide range of grafting densities

Multi-stimulus responsive weak polyelectrolyte brushes were grafted by surface-initiated atom transfer radical polymerization from spherical silica nanoparticles across a wide range of grafting densities approaching the limit of close packing of grafting sites: a regime not previously explored in the brush swelling literature. Brushes consisted of poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) homopolymers or poly(2-(dimethylamino)ethyl methacrylate)-r-poly(4-metharyloyloxyazobenzene) random copolymers P (DMAEMA-r-MOAB) and were subjected to pH-, temperature-, and photoisomerization-induced swelling and deswelling. Homopolymer brushes were prepared at grafting densities ranging from 0.12 to 1.4 nm−2 and number average degrees of polymerization ranging from 300 to 1200. Two copolymer brushes with 8 mol% and 13 mol% of the nonionizable, photoresponsive MOAB units were compared with homopolymer brushes prepared at similar grafting densities and degrees of polymerization. Dynamic light scattering was used to measure the hydrodynamic radius of grafted nanoparticles, and thus brush thickness, in water. Brush swelling in response to increased DMAEMA protonation followed a single scaling behavior across the full range of degrees of polymerization and grafting densities. Incorporating azobenzene-containing MOAB comonomers introduced a modest photoresponsive control of brush swelling and decreased the brush thickness relative to the comparable PDMAEMA homopolymer brush, without affecting the scaling with respect to protonation. PDMAEMA brushes exhibited a pH-dependent lower critical solution temperature behavior, resulting in a thermal collapse of up to 50% upon heating. This work demonstrates that scaling behaviors previously tested at low grafting densities hold for extremely high grafting densities and that they are unaffected by moderate nonionizable comonomer content.

Simulation and Optimization of Polystyrene Free Radical Polymerization Process

A model for bulk polymerization of styrene was established by using the POLYMER module of ASPEN PLUS. The effects of the chain initiator (TBP), solvent (ethylbenzene) and the chain transfer agent (DDM) on the yield, number average degree of polymerization(DPN), weight average degree of polymerization(DPW), number average molecular weight(Mn), weight average molecular weight(Mw) and the polydispersity index(PDI) of polystyrene were investigated. Through the analysis, we can first consider the amount of styrene to obtain roughly the parameters of the polystyrene process. As the use of initiator in polymerization has the optimal value, we must strictly control the amount of TBP according to the amount of monomer styrene, and adjust the amount of chain transfer agent to control the product quality accurately.

Kinetic theory of A2+B3+B2 type hyperbranched polymerization

The kinetics of the hyperbranched polymerization with A2, B3 and B2 monomer has been developed in this work. The analytical expressions of the size distribution function and the various molecular parameters of the resulting hyperbranched polymers were derived. Compared with A2+B3 type hyperbranched polymerization, with the addition of B2 type monomer in the reaction system, the gel range moves in smaller value and a narrower interval of the initial functional ratio (α), i.e. initial ratio of B to A group in respective B3 and A2 monomer. At a specified feed ratio α, the addition of B2 monomer can enhance the critical conversion of A groups and reduce that of B groups as well. The addition of linear B2 monomer in reaction system can significantly reduce the degree of branching and improve the number-average degree of polymerization for the products obtained. In this way, according to the theoretical research in this work, molecular structure and parameters can be effectively designed by choosing the appropriate feed ratio of monomers for the hyperbranched polymerization of A2+B3+B2 type.

Poly(amino acid)-grafted polymacrolactones. Synthesis, self-assembling and ionic coupling properties

Polyglobalide (PGl) with number average polymerization degree of ~20 was prepared by enzymatic ROP and then polyfunctionalized at 60% with aminothioethylene groups. The PGl20-(NH2)12 copolymer was used as macroinitiator for the ROP of NCAs of BLG (γ-benzyl L-glutamate) and ZLL (εN-carbobenzoxy-l-lysine) protected amino acids to produce neutral polypeptide-grafted polyglobalides poly[Gl20-graft-(AA)z] with z = 5 and 12, which upon deprotection, afforded anionic and cationic copolymers, respectively. Both protected and deprotected graft copolymers were characterized in full detail by NMR, and their thermal properties were evaluated by TGA and DSC. The structure of these copolymers in the solid-state was examined by FTIR and XRD using synchrotron radiation. All grafted polyglobalides were amorphous but the polypeptide side chains were arranged in either alpha-helix or beta-sheet conformation, and reliable indications on the occurrence of supramolecular structures were frequently found. The capacity of poly[Gl20-graft-(AA)z] copolymers to self-assemble in aqueous medium was evidenced by the preparation of well-shaped spheroidal nanoparticles with a diversity of sizes depending on copolymer composition and charge. Loading and release of doxorubicin (DOX) from nanoparticles made of negatively charged poly[Gl20-graft-(LGA)12] as well as DNA complexation with cationic poly[Gl20-graft-(LL)5] were explored to appraise the potential of these copolymers for building drug delivery systems.

Simulation of Radical Polymerization Using Fixed Coefficients

The calculation of the number-average degree of polymerization is considered exemplified by the radical polymerization of styrene, which is carried out at 343, 348, and 353 K. The system of differential equations on the graph using corrections specified as formulas has been applied for the calculation. When using the minimum set of initial data, the error of the calculated and experimental values is 40, 33.3, and 37.5% at 343, 348, and 353 K, respectively. The inverse kinetic problem has been solved.

Bisurea-Functionalized RAFT Agent: A Straightforward and Versatile Tool toward the Preparation of Supramolecular Cylindrical Nanostructures in Water

We report a versatile and simple approach to produce cylindrical micelles by the direct dissolution of polymers in water. The developed strategy relies on a RAFT agent functionalized by a bisurea sticker that allowed to synthesize a series of α-bisurea-functionalized poly(N,N-dimethylacrylamide) (PDMAc), poly(acrylic acid) (PAA), polyacrylamide (PAM), and poly(2-(N,N-dimethylamino)ethyl acrylate) (PDMAEA) with number-average degrees of polymerization (DPn) varying from about 10 to 50. Their spontaneous self-assembly in water was studied by electron microscopy (cryo-TEM), neutron scattering (SANS), and calorimetry (ITC) analyses which showed that long cylindrical micelles are spontaneously formed in water. The crucial role of the bisurea sticker end-groups was established by comparison with the corresponding bisurea-free model polymers that only formed spherical micelles. Finally, we have shown that it is possible to trigger reversibly the assembly/disassembly of the nanofibers by pH changes.

The Chain Length Distribution of an Ideal Reversible Deactivation Radical Polymerization.

The chain length distribution (CLD) of a reversible deactivation radical polymerization at full conversion is shown to be a negative binomial distribution with parameters that are simple functions of the number-average degree of polymerization and either the chain transfer constant (in the case of polymerizations that incorporate a reversible chain transfer step) or the concentrations of dormant polymer chains and deactivating agent and the rate constants of propagation and deactivation (other types of RDRP). Expressions for the CLD at intermediate conversions are also derived, and shown to be consistent with known expressions for the number-average degree of polymerization and dispersity. It is further demonstrated that these CLDs are well-approximated by negative binomial distributions with appropriate choice of parameters. The negative binomial distribution is thus a useful model for CLDs of reversible deactivation radical polymerizations.

Nonstoichiometric Stille Coupling Polycondensation Via Intramolecular Pd(0) Catalyst Transfer Using Excess Imide-Based Dibromo Monomers

π-Conjugated polymers are widely used for the organic electronic devices, such as Organic Light Emitting Diodes (OLED), Organic Photovoltaics (OPV) and Organic Thin-film Transistors (OTFT). These polymers are typically synthesized by AA+BB type polycondensations based on a transition-metal-catalyzed cross-coupling reaction. Generally, the number-average degree of polymerization of polymers (X n) synthesized by AA+BB-type polycondensations is generally determined by Carothers equation as X n=(1+r)/(1+r-2rp), where r is the stoichiometric molar ratio between AA and BB monomers and p is the extent of the reaction. Thus, the molecular weight of the polymers relies significantly on the stoichiometry of the monomers. In our previous report, high-molecular-weight n-type polymers were exceptionally obtained from 2,5-bis(trimethylstannyl)thiophene (1) and 1~10 fold excesses of 4,9-dibromo-2,7-bis(2-decyltetradecyl)benzo[lmn][3,8]-phenanthroline-1,3,6,8-tetraone by the Stille coupling polycondensation. The reason for the successful nonstoichiometric Stille coupling polycondensation can be explained by the intramolecular Pd(0) catalyst transfer after the substitution reaction of a bromo moiety of the dibromo-monomer with one distannyl-monomer, resulting in the C-Pd(II)-Br terminal via Pd(0)-π association, which can be readily substituted with other distannyl-monomers to afford all-stannylated oligomeric/polymeric terminals. Therefore, the excess dibromo monomers are not consumed for capping the oligomeric/polymeric during polymerization. In addition, it was suggested that the intramolecular Pd(0) catalyst transfer was promoted by the electron-deficient NDI structure in the model reactions. On the other hand, Yokozawa group also reported nonstoichiometric Suzuki-Miyaura coupling polycondensation via intramolecular Pd(0) catalyst transfer almost at the same time. In this report, they concluded that the electron-rich monomers are suitable for the intramolecular Pd(0) catalyst transfer because of the strong Pd(0)-π interaction between Pd(0) and dibromo monomers. Therefore, determining the criteria for the Pd(0) catalyst-transfer systems using electron-deficient monomers is necessary to extend the applicable monomers for stoichiometry-independent polycondensations. Here, we report the effect of monomer structures and ligand types suitable for the nonstoichiometric Stille coupling polycondensation. First, the model reactions were examined between 2-tributylstannylthiophene (2) and 1 molar equiv. 1,3-dibromo-5-octylthieno[3,4-c]pyrrole-4,6-dione (3), or N-octyl-3,6-dibromophthalimide (4) which have the imide-substituent and the compact thiophene/phenylene skeletons. The results implied that the intramolecular Pd(0) catalyst transfer occurred using 3 with tri(o-tolyl)phosphine (P(o-tolyl)3) as the ligand; however, no catalyst transfer occurred using 4 with P(o-tolyl)3, judged from the presence/absence of the monoadduct product. On the other hand, the employment of a more electron-rich ligand, tri(t-butyl)phosphine (P(t-Bu)3), led to the intramolecular Pd(0) catalyst transfer on 4. It was suggested that the strong electron-donating ligand promoted the intramolecular Pd(0) catalyst transfer. Based on the model reactions, we examined the polymerization between 1 and 1,3-dibromo-5-(2-hexyldecyl)thieno[3,4-c]pyrrole-4,6-dione (5) or N-(2-hexyldecyl)-3,6-dibromophthalimide (6) under the nonstoichiometric conditions. Unfortunately, only oligomers were obtained in stoichiometric and nonstoichiometric condition between 1 and 5. In contrast, the high-molecular-weight polymers could be synthesized using 6 with P(t-Bu)3 under the nonstoichiometric conditions ([6]0/[1]0 =2~10). All polymers were confirmed to have almost the same structure by 1H NMR spectroscopy. The model reaction was further investigated using another electron-deficient benzothiadiazole (BTz)-based monomer instead of 4. However, the catalyst transfer does not appear to happen on the BTz monomer with any of the tested Pd catalysts including Pd2(dba)3/P(o-tolyl)3, Pd/P(t-Bu)3 and PEPPSI- i Pr based on the fact that mono-substituted products were obtained from the reaction between 2 and an equimolar amount of 4,7-dibromo-2,1,3-benzothiadiazole under all conditions. This result indicate that the specific feature of the imide substituents is necessary for the successful nonstoichiometric Stille coupling polycondensation. In conclusion, the high-molecular-weight polymers could be obtained under the nonstoichiometric conditions between 1 and 6 ([6]0/[1]0 =2~10) via the intramolecular Pd(0) catalyst transfer. The strong-electron donating phosphine ligand and the imide-substituent is crucial for the success of the intramolecular Pd(0) catalyst transfer in nonstoichiometric Stille coupling polycondensation. Figure 1

Molecular weight-dependent physisorption of non-charged poly(9,9-dioctylfluorene) onto the neutral surface of cuboidal γ-alumina in toluene

To understand how polymers physisorb onto solid surfaces, we investigated the physisorption behavior of non-charged, semiflexible poly(9,9-dioctylfluorene) (PF8) with three different number-average degrees of polymerization (DPn) as photoluminescent and chromophoric probes onto cuboidal γ-alumina in toluene at 5, 25, and 50 °C. PF8 revealed noticeable DPn and temperature dependencies in its physisorption behaviors. Molecular mechanics (MM)/molecular dynamics (MD) simulations [consistent valence force field (CVFF)] and Moller–Plesset second-order perturbation theory (MP2) with 6-31 G(d,p) calculations suggested that the PF8 in toluene has multiple interactions from CH/π to C–H/O interactions on the (110) surface of γ-alumina. The competition between multiple intermolecular CH/π and C–H/O interactions was crucial for the spontaneous physisorption of PF8 to occur in the presence of a solvent quantity of toluene. Calculations by time-dependent density functional theory (TD-DFT) with Becke three parameter Lee-Yang-Par (B3LYP) method and 6–31 G(d,p) basis set of a model fluorene 9-mer indicated that the π–π* absorption wavelength largely depends on the regularity of the dihedral angles between fluorene rings, while the intensity and spectral width of the π–π* absorption band are largely influenced by the regularity of the dihedral angles. Solution-phase physisorption systems are a result of the inherent nature of several competitive weak intermolecular interactions coexisting among the polymers, surface, and solvents. Noticeable molecular weight and temperature dependency for physisorption behavior of semiflexible, non-charged poly(9,9-n-dioctylfluorene) (PF8) onto cuboidal γ-alumina in toluene were found. MM/MD simulations (CVFF) and quantum mechanical (MP2/6-31G(d,p)) calculations suggested that PF8 swaps interacting toluene for (110) surface of γ-alumina by changing the interaction from CH/π interactions to C-H/O interactions of γ-alumina in toluene. The competition between multiple intermolecular CH/π and C-H/O interactions was crucial whether the spontaneous physisorption of PF8 occurs in place of solvent quantity of toluene. The solution-phase physisorption systems should be the consequence of several weak attractive intermolecular interactions coexisting between polymers, surface, and solvents

Statistic thermodynamic analysis of fructans – Part 4: Modeling inulin biosynthesis as a non-equilibium thermodynamic process

A model for the mathematical description of inulin biosynthesis with particular focus on the dynamics of the sucrose and 1-kestose concentration has been developed. The model takes into account the specific action of the two involved enzymes SST and FFT. In principle, inulin biosynthesis can thus be described as a thermodynamically stabilizing process leading into a stable nodal sink over time. In the initial phases of the reaction, oscillation of sucrose and 1-kestose concentration is observed, dampening rapidly for both products into a stable steady state condition. Applying the same boundary conditions, a higher number average degree of polymerization will lead to a higher frequency and amplitude in oscillation.

Statistic thermodynamic analysis of fructans – Part 3: Relationship between polymer structure and mixing entropy at equilibrium conditions

The reduced mixing entropy, which is a concentration and unimer independent equivalent to the polymer mixing entropy defined by Flory, for various probabilistic distributed polymer distributions is calculated. The unbranched most probable distribution proves to reach an extremum value at any given number average degree of polymerization, clearly differentiating it from both broader and narrower polymer distributions with branching structures. Entropy driven polymerization reactions thus inevitably produce unbranched polymer structures as discussed for the case of inulin biosynthesis.