Low Monomer Concentration Research Articles

Improvement of Adhesive Strength of Poly(tetrafluoroethylene) Plates through Oxygen Plasma Treatment and Subsequent Photografting of Methacrylic Acid

Methacrylic acid (MAA) was grafted onto the surface of a poly(tetrafluoroethylene) (PTFE) plate by the combined use of the plasma treatment and photografting, and the adhesive strength between the MAA-grafted PTFE (PTFE-g-PMAA) plates with the same grafted amounts was investigated in relation to the location of grafting as well as the wettability and water absorptivity. The grafted amount at which the substrate breaking occurred at lower grafted amounts for the PTFE-g-PMAA plates prepared by the plasma treatment for shorter times before the photografting and by the photografting at higher monomer concentrations and/or at lower monomer concentrations after the plasma treatment. These grafting conditions are found to be factors affecting the location of photografting, the thickness and water absorptivity of the grafted layer, and wettability of the surface of the grafted layer. The substrate breaking was observed at the minimum grafted amount (about 2.2 µmol/cm2) for the PTFE-g-PMAA plates prepared at 2.0 M and 60°C after the plasma treatment for 10 s and at 2.0 M and 40°C after the plasma treatment for 120 s. The obtained results support that the combination of the oxygen plasma treatment with photografting of MAA is an effective procedure to enhance the adhesivity of the PTFE surface.

Effect of the charge interactions on the composition behavior of acrylamide/acrylic acid copolymerization in aqueous medium

Acrylamide and sodium acrylate are copolymerized in aqueous solution to study the influence of monomer concentration and ionic strength onto the reactivity ratios using in-situ 1H NMR. Increasing the monomer content leads to larger reactivity of the ionized monomer. At low monomer concentration, this effect was reproduced by adding NaCl to increase the ionic strength, indicating that the reaction kinetics is largely governed by charge interactions. On the contrary, this was not observed at higher monomer content, suggesting that non-electrostatic effects are mainly responsible of the monomer concentration dependence at these conditions. A comprehensive mathematical model was developed to predict copolymer composition as a function of monomer concentration and ionic strength. It is based on a previously-proposed rate law of propagation for ionized monomers, which has been expanded to cover any ionization degree of acrylic acid. The model is capable to reproduce composition data from different sources obtained in a wide range of reaction conditions.

Supercritical continuous precipitation polymerization of acrylic acid in a droplet-based millifluidic device

In this work, a high pressure droplet-based millifluidic device was developed to achieve the continuous precipitation polymerization of acrylic acid in a green reaction medium: a supercritical mixture of 10 wt% ethanol in CO2 (15/19.5 MPa and 75 °C). To avoid clogging the tubular reactor of 762 µm ID, a segmented flow of an aqueous solution of monomer dispersed in the supercritical mixture (containing the initiator) was generated. During the reaction, the droplets were used as reservoirs which enable the continuous transfer of the monomer to the CO2-rich phase. This work shows that a large range of molar masses of poly(acrylic acid) (from 20,000 to 120,000 g.mol−1) with low polydispersity index (from 1.35 to 1.70) can be obtained. Due to the rapid transfer of the monomer compared to its conversion and the resulting low monomer concentration in the reactive medium, the molar mass distributions are not dependent on the residence time but rather on the initial monomer and initiator concentrations only. Hence in the investigated experimental conditions, the continuous reactive extraction process helps to achieve the precipitation polymerization without clogging the tubular reactor and in mastering the molar mass distribution. The effect of pressure influencing the molar mass distribution of poly(acrylic acid) as well as the competition between two possible loci of polymerization are also discussed.

Mechanisms and rates of nucleation of amyloid fibrils.

The classical nucleation theory finds the rate of nucleation proportional to the monomer concentration raised to the power, which is the "critical nucleus size," nc. The implicit assumption, that amyloids nucleate in the same way, has been recently challenged by an alternative two-step mechanism, when the soluble monomers first form a metastable aggregate (micelle) and then undergo conversion into the conformation rich in β-strands that are able to form a stable growing nucleus for the protofilament. Here we put together the elements of extensive knowledge about aggregation and nucleation kinetics, using a specific case of Aβ1-42 amyloidogenic peptide for illustration, to find theoretical expressions for the effective rate of amyloid nucleation. We find that at low monomer concentrations in solution and also at low interaction energy between two peptide conformations in the micelle, the nucleation occurs via the classical route. At higher monomer concentrations, and a range of other interaction parameters between peptides, the two-step "aggregation-conversion" mechanism of nucleation takes over. In this regime, the effective rate of the process can be interpreted as a power of monomer concentration in a certain range of parameters; however, the exponent is determined by a complicated interplay of interaction parameters and is not related to the minimum size of the growing nucleus (which we find to be ∼7-8 for Aβ1-42).

Synthesis of surface molecular imprinted polymers based on carboxyl-modified silica nanoparticles with the selective detection of dibutyl phthalate from tap water samples

In this work, the molecular imprinted polymers were synthesized with the low monomer concentrations for dibutyl phthalate (DBP). The polymers were prepared over carboxyl-modified silica nanoparticle, which used methacrylic acid as the functional monomer, ethylene glycol dimethacrylate as the cross-linker agent and azoisobutyronitrile as the initiator in the process of preparation. Various measures were used to characterize the structure and morphology in order to get the optimal polymer. The characterization results show that the optimal polymer has suitable features for further adsorption process. And adsorption capacity experiments were evaluated to analyze its adsorption performance, through adsorption isotherms/kinetics, selectivity adsorption and desorption and regeneration experiments. These results showed that the molecular imprinted polymers had a short equilibrium time about 60min and high stability with 88% after six cycles. Furthermore, the molecular imprinted polymers were successfully applied to remove dibutyl phthalate. The concentration range was 5.0–30.0μmolL−1, and the limit of detection was 0.06μmolL−1 in tap water samples.

Charge tunable thin-film composite membranes by gamma-ray triggered surface polymerization

Thin-film composite poly(amide) (PA) membranes have greatly diversified water supplies and food products. However, users would benefit from a control of the electrostatic interactions between the liquid and the net surface charge interface in order to benefit wider application. The ionic selectivity of the 100 nm PA semi-permeable layer is significantly affected by the pH of the solution. In this work, for the first time, a convenient route is presented to configure the surface charge of PA membranes by gamma ray induced surface grafting. This rapid and up-scalable method offers a versatile route for surface grafting by adjusting the irradiation total dose and the monomer concentration. Specifically, thin coatings obtained at low irradiation doses between 1 and 10 kGy and at low monomer concentration of 1 v/v% in methanol/water (1:1) solutions, dramatically altered the net surface charge of the pristine membranes from −25 mV to +45 mV, whilst the isoelectric point of the materials shifted from pH 3 to pH 7. This modification resulted in an improved water flux by over 55%, from 45.9 to up 70 L.m−2.h−1, whilst NaCl rejection was found to drop by only 1% compared to pristine membranes.

A Model Prediction for Chenodeoxycholate Aggregate Formation

A relationship between the chenodeoxycholate (CDC) monomer concentration and the total concentration of CDC was established using a kinetic dialysis technique. Meanwhile, the sizes of the formed simple CDC micelles were measured by a quasielastic light-scattering (QLS) technique to be nearly constant. The QLS results led to a suggestion for equilibrium models of CDC aggregate formation. According to the established relationship and the suggested models, the best curve-fitting model was selected by a least-squares technique. Furthermore, the model parameters were quantified. Based on the quantified parameters, at a minimum detectable concentration of simple CDC micelles to be ∼0.2 mM, an appropriate model corresponding concentration of CDC monomers was estimated to be ∼3.08 mM. This value is consistent with a minimum monomer CDC concentration of ∼3.13 mM for simple CDC micelle formation estimated according to the present QLS detection and the model prediction. The consistency confirms the model prediction that at a low CDC monomer concentration (<3 mM), the concentration of stable CDC dimers is much higher than that of simple CDC micelles but the contribution of simple CDC micelles to the total CDC concentration cannot be negligible.

Effect of thickness on the capacitive behavior and stability of ultrathin polyaniline for high speed super capacitors

In this work four polyaniline (PANI) film electrode with different thickness were synthesized by electrochemical method on the surface of glassy carbon (GC) electrode. Four polymer films with various thicknesses from 0.5 to 11 μm were synthesized. Electropolymerization occurs in low monomer concentration. Morphology study of electrode shows that surface structure of polymers depends on film thickness. Capacitance of electrode was studied by CV and charge-discharge (CD) methods. Specific capacitance (SC) of electrodes using cyclic voltammetry were calculated 620, 247 F g–1 for thinnest and thickest polymer film, respectively. Stability of electrodes was studied during 1000 voltammogram cycles. Results show that with the increase of thickness the stability of electrodes enhanced and reach to a maximum and then decreased.

Universal aspects of hydrogel gelation kinetics, percolation and viscoelasticity from PA-hydrogel rheology

Polyacrylamide (PA) hydrogels have been studied extensively, but fundamental aspects of their gelation kinetics, percolation dynamics, and viscoelasticity are still not well understood. This paper focuses on the rheology of PA hydrogels having unusually low monomer concentrations (ca ≈ 3 w% equivalent to 0.42 mol l−1). These furnish loss tangents that span 4 orders of magnitude when varying the crosslinker concentration. An optimum crosslinker concentration (cbis/ca ≈ 2.5 mol. % equivalent to 5.3 w%) is identified, below which the storage modulus G′ increases almost linearly, and the loss modulus G″ acquires a local maximum. Above the optimum crosslinker concentration, G′ and G″ both plateau, accompanied by a notable decrease in the maximum strain (increase in brittleness) before breaking. The dynamic shear moduli reveal universal dynamics at the gel point, as indicated by (i) scaling exponents (y = 3.1 ± 0.1, z = 2.1 ± 0.1 and Δ = 0.70 ± 0.02) that are consistent with the de Gennes [“On a relation between percolation theory and the elasticity of gels,” J. Phys. Lett. 37, L1–L2 (1976)] electrical network analogy, and (ii) a critical relaxation exponent that is close to the Rouse limit Δ = 2/3 from the scaling theory of Martin. A close correspondence of the exponents with that of Adam and Delsanti [Macromolecules 18, 2285–2290 (1985)] for the radical copolymerization of a different material supports the long-standing hypothesis that dynamics at the gel point are universal for a prescribed gelation mechanism.

Helical pitch dependence of the electro-optic characteristics in polymer/cholesteric liquid crystal nanocomposites

The helical pitch (p) dependence of the electro-optic characteristics in low monomer concentration polymer/cholesteric liquid crystal (PChLC) nanocomposites is reported. Four mixtures with different helical pitches were prepared by mixing a ChLC and a mesogenic monomer with a photoinitiator, and polymerized at room (20 °C) or low (−20 °C) temperatures to fabricate samples exhibiting the 'polymer-stabilized' and 'deformation-free' responses, respectively. Reflecting the difference in the electro-optic response modes, the threshold electric field showed different dependencies on the helical pitch. The 'polymer-stabilized' PChLCs showed a p-0.57 dependence on the pitch, which is a consequence of the response being dominated by the Helfrich deformation. The 'deformation-free' samples, on the other hand, showed a smaller dependence on pitch of approximately p-0.33. The decrease in the pitch dependence is described as a consequence of the nano-confined LC molecules undergoing a Fredericks-type reorientation instead of a helix deformation.

Photopolymerization of acrylamide in the very low monomer concentration range

The polymerization kinetics of acrylamide (AAm) initiated by the photoinitiator DAROCUR2959 (DAR2959) under UV light irradiation were investigated. Variations of polymerization rate with AAm concentration and conversion were studied. Under the present low monomer concentrations the gel effect as well the difusion-controlled termination reactions are expected to be postponed or suppressed. The polymerization rate vs. conversion curve of the photoinduced polymerization of AAm was described by two non-stationary rate intervals and the initial rate maximum. In both intervals the polymerization rate decreased with conversion and the decrease was much more pronounced in the low conversion region. Furthermore, the polymerization rate was observed to decrease with increasing monomer concentration. The polymerization behavior was discussed in terms of the intra and intermolecular chain transfer processes (mainly to backbiting) and the decrease of propagation rate coefficient with the monomer concentration. Furthermore, the chain transfer reactions including backbiting step initiate the formation of less reactive radicals and/or the retardation of the polymerizaton.

Polyaniline@SnO2 heterojunction loading on flexible PET thin film for detection of NH3 at room temperature

We prepared a heterostructure hybrid of PANI and SnO2 by a rapid and facile in situ chemical oxidation polymerization under very low monomer concentration, and the hybrid was loaded on a flexible PET thin film to structure a smart NH3 sensor. The structure, morphology and thermal stability of the hybrid were characterized by various analysis methods. Compared with those reported in literatures, the hybrid-based sensor not only has high sensitivity, good selectivity and wide linear response to NH3 at room temperature of 21°C but also has flexible, structure simple and wearable performance. The room temperature operating of the sensor is particularly interesting, which leads to low-power consumption, environmental safety and long life times of the sensing materials. The improvement of sensing properties is attributed to the complementary and synergistic effect between SnO2 and PANI, and formation of p−n heterojunction at the interface in hybrid.

Ring-Opening Metathesis Polymerization of a Diolefinic [2]-Catenane–Copper(I) Complex: An Easy Route to Polycatenanes

A dilute (30 mM) dichloromethane solution of the copper(I) complex 1·Cu+ of a [2]-catenane composed of two identical 28-membered macrocyclic alkenes featuring a phenanthroline moiety in the backbone was subjected to ring-opening metathesis polymerization (ROMP) with second-generation Grubbs catalyst. Shortly after mixing of reactants, the dark red solution transformed into a gel. The bis(phenanthroline)copper(I) units were effectively preserved during ROMP, as evinced by spectroscopic analysis. This implies that the putative metal alkylidene pseudorotaxane intermediates did not undergo dethreading processes but were involved in ring–chain equilibria strongly biased toward the ring products at the low monomer concentration employed in the ROMP reactions. MALDI-TOF mass spectra of the reaction mixtures obtained at an early stage of the reaction revealed a distribution of interlocked oligomers (1·Cu+)n(PF6–)n−1 with n up to 7, with no traces of peaks ascribable to open chain species. Rheological and mechanic...

Facile synthesis of high density polypyrrole nanofiber network with controllable diameters by one step template free electropolymerization for biosensing applications

In this paper, we report fabrication of enzymatic glucose biosensor based on growth of high density polypyrrole (PPy) nanofiber network using one step template free electropolymerization method. PPy was grown potentiostatically on gold coated glass substrates. Significant changes in the sensing response were observed for biosensors fabricated with different concentrations of pyrrole (Py) monomer and polymerization potentials. Among the fabricated biosensors, the highest sensitivity of 1.9mAcm−2M−1, with a wide range of linear operation (125μM–11.25mM) was observed for 0.15M Py concentration and 0.8V polymerization potential. The observed results indicate that low monomer concentration and moderately low polymerization potential is highly suitable for growth of PPy nanofiber network with controllable fiber diameters having high aspect ratio, resulting in high sensitivity for biosensor application.

Preparation, Structure, and Orientation of Pyrite FeS2{100} Surfaces: Anisotropy, Sulfur Monomers, Dimer Vacancies, and a Possible FeS Surface Phase

Sulfur dimer (S22–) terminated pyrite FeS2{100} surfaces with a low energy electron diffraction (LEED) pattern of 2 × 1 symmetry are reported. The 2 × 1 symmetry correlates with the orientation of the anisotropic surface structure and external symmetry of macroscopic striations on the pyrite cube face. The basic condition to form these surfaces is a mild 200 V Ne+ sputter-cleaning procedure followed by a 570 K anneal of the sample in a 10–7 Torr S2(g) atmosphere. Controlled amounts of surface sulfur monomers (S2–) can be introduced by mild sputtering of the sulfur dimer terminated surfaces. At low monomer concentrations the surface displays the same characteristic 1 × 1 LEED pattern as that for fracture-generated surfaces. With increasing sulfur depletion, a (1/√2 × 1/√2)R45° LEED pattern emerges, and soft X-ray photoelectron spectroscopy (XPS) results show a sulfur dimer deficient near-surface region and a new high binding energy sulfur spectral component suggesting the presence of local coordination env...

Control of Thickness, Morphology and Band Gap of Poly-(3.4-ethylenedioxythiophene) Electrochemically Growth (e-PEDOT) to Use It as Anodic Buffer Layer in Organic Photovoltaic Cells

This contribution presents the electrochemical control of thickness, morphology and band gap of the polymer film poly[3,4-ethylenedioxythiophene] (PEDOT), which was obtained by electropolymerization of monomer 3,4-ethylenedioxythiophene (EDOT) in the transparent conductive indium-tin oxide (ITO). This study was carried out using mixtures of dry organic solvents such as acetonitrile, toluene and dichloromethane to determine the effect of the polarity solvent in the polymerization kinetics of the monomer EDOT. For this, cyclic voltammetry was used. It was observed that pure acetonitrile and the acetonitrile-dichloromethane mixture (2:1, v/v), the polymerization kinetics is very fast and the obtained films showed similar responses in both cases, however, the kinetics obtained for the mixture of toluene-acetonitrile (4:1, v/v) was slower, indicating that in a medium of higher polarity, the polymerization kinetics is much faster than in a medium of lower polarity. This fact coupled with low concentrations of monomer EDOT, let us to control the thickness and morphology of the electropolymerized PEDOT films (e-PEDOT). An optimization of the desired film properties was achieved through the implementation of the chronoamperometric technique (CA) for the electropolymerization. Here, the time of deposit and a low concentration of the EDOT monomer gave the desired thickness of the polymer film with a uniformly rough morphology. Furthermore, the study of the response UV -Vis of the films e-PEDOT was performed and found that optical band gap depends on the experimental conditions used to obtain the e-PEDOT films. Finally, these e-PEDOT films were used as buffer layers in organic photovoltaic cells (OPVs) with bulk heterojunction architecture and their performance was compared with those constructed with the classical spin cast deposited PEDOT-PSS buffer layer. Acknowledgments: Funding for this research was obtained by CONACYT-CB project number 179356. The technical AFM support of Ing. Mario Monroy (Instituto de Física UNAM)

Preparation of aliphatic–aromatic polyimide particles by polycondensation of diethyl hexafluoroisopropylidenediphthalate and diaminooctane in ethylene glycol

Polycondensation of nylon salt-type monomer composed of diethyl hexafluoroisopropylidenediphthalate and diaminooctane was performed at 130°C in ethylene glycol to form confetti-shaped particles. Before the polycondensation, the salt monomer solution was homogeneous. As the polycondensation proceeded, the solution became turbid and polyimide particles grew to around 7 μm for 8 h. After the polycondensation, small particles precipitated and got deposited onto large particles to form confetti-shaped particles. Rod-shaped particles were also formed by the polycondensation at low monomer concentration in a long reaction time. They were found to be crystalline in form.

A New Technique of Electro-Synthesis of Polypyrrole Nanoparticles

We report here a novel two phase electro-oxidation technique of synthesis of submicron size polypyrrole (ppy) from pyrrole (py) onto a steel electrode. Pyrrole forms a hydrogen bonded red colour complex with picric acid which is almost insoluble in water but soluble in di-chloromethane (DCM). Again, water and DCM forms an immiscible solvent pair. We demonstrated that nano sized polypyrrole is deposited on to a steel anode coupled with a Pt cathode by passing a small current of 0.25 mAcm-2 for a period of 600 seconds when electro-oxidation is carried out in aqueous saturated picric acid phase placed over DCM phase containing a solution of pyrrole-picrate complex. TEM picture shows formation of nano sized polymers. This is probably due to slow diffusion of pyrrole- picrate complex from organic phase to aqueous phase and its extremely low concentration at the electrode surface probably control the chain growth kinetics.Key words: Electro-oxidation, Nanosized polypyrrole, Pyrrole-picric acid complex .Introduction Polypyrrole is a promising conducting polymer for wide variety of electronic, opto-electronic and electro-chemical devices including electrode materials of aqueous and non-aqueous batteries. It is easily deposited on to metallic and carbon substrates by electro- polymerization of pyrrole in a suitable organic solvent. Major problems of electro-oxidation of pyrrole in aqueous medium are its poor solubility in water and corrosions of non-noble metal anode in acidic solution. Previously, we had reported electro-polymerization of pyrrole on to steel substrate using aqueous picric acid as dopant. We found polypyrrole films so deposited were brittle. Polymer chain growth kinetics depends on concentration of monomer as well as radical, this can be controlled taking advantage of the fact that both pyrrole and pyrrole-picrate complex are more soluble in DCM but less soluble in water, hence a two phase electro-oxidation as reported here is expected to produce submicron size polymer. To the best of our knowledge, this technique of two phase electro-oxidation of preparation of nanosized polymer has not been reported earlier.Material and MethodChemicalsPyrrole (Fluka), Picric acid (Merck) and Dichloromethane (Merck) were used as obtained. Triple distilled water was prepared using a all glass setup.Pyrrole (1ml) was taken in a 50ml cylindrical beaker to which 1ml saturated aqueous picric acid (picric acid is only slightly soluble in water) was added when reddish globules of Pyrrole-picric acid (py-pic)complex was formed. To this solution 8ml of DCM was added when py-pic complex dissolved forming a yellow solution. Ten ml of saturated picric acid was then poured over this DCM solution of py-pic complex to form a two phase system. A working electrode of thin steel sheet (4cm-2) and a counter Pt electrode of same dimensions were placed in the aqueous phase just over the phase boundary , a current of 0.25 mA cm-2 under galvanostatic condition was passed for 600 seconds when a blue-black deposition of poly-pyrrole was formed on to working electrode .The deposition was taken out with a sharp knife for TEM analysis. For CV of pyrrole-picrate complex in DCM the solution was prepared as stated above using 0.01M KClO3 as electrolyte. All electro-chemical measurements were taken by PAR VarsaStat (II )Potentiostat/Galvanostat. Results and Discussions A simple experimental arrangement was used in this study. It may be mentioned that the electrodes were kept just above the phase boundary in order to avoid large migration distant of the py-pic complex. Pyrrole forms a complex via hydrogen bonding with trinitro-benzene derivatives including picric acid which is soluble in DCM. From CV of py-pic it is known pyrrole oxidation potential is lowered due its hydrogen bonding with –NO2 group of picric acid. We propose py-pic complex will easily deprotonated to form pyrrole anion which will form pyrrole radical upon anodic-oxidation which is prerequisite for polymerization It is reported polypyrrole film depositions on to different substrate material are best obtained under galvanostatic condition at a current density of 25mA cm-2, we have therefore used this optimised condition in our study. With deposition of ppy film, the resistance of steel electrode surface increases as indicated in potential –time deposition curve.Now the major advantage of two phase electro-oxidation in this case is that the ppy-pic complex is soluble in DCM and it slowly diffuse to aqueous phase resulting a low concentration of monomer in the vicinity of the electrode surface which retards the chain growth kinetics of polypyrrole formation. TEM picture shows these polymers are of almost spherical in shape with diameters of 250-300 nm.We concluded that nano size polypyrrole are easily synthesized by a two phase electro-deposition technique using DCM and water as two immiscible solvent pair and picric acid as complexing agent.

Temperature-triggered fast-disintegrating polyNIPAM particles via semicontinuous heterophase polymerisation

Crosslinker-free poly(n-isopropylacrylamide) (polyNIPAM) particles produced by conventional emulsifier-free heterophase polymerisations contain gels and do not easily and completely disintegrate in water, if at all. These particles, when cooled below lower critical solution temperature (LCST) swell first and then gradually shrink, due to their slow rate of disintegration. We first show that only particles formed using very low monomer concentration, which have a low molecular weight, are fully soluble in water. Then, we describe a seeded semicontinuous route which was designed in order to be able to maintain a low monomer concentration in water in the course of reaction and control the length and location of growing chains. Nanoparticles produced via semicontinuous approach not only disintegrated in water very quickly but also dissolved in water completely as soon as LCST was reached. This finding may also find applications in technologically important processes for dissolution of macromolecules in solvents.

How to Determine the Size of Folding Nuclei of Protofibrils from the Concentration Dependence of the Rate and Lag-Time of Aggregation. II. Experimental Application for Insulin and LysPro Insulin: Aggregation Morphology, Kinetics, and Sizes of Nuclei

Insulin is a commonly used protein for studies of amyloidogenesis. There are a few insulin analogues with different pharmacokinetic characteristics, in particular the onset and duration of action. One of them is LysPro insulin. The behavior of LysPro insulin in the process of amyloid formation has not been studied in detail yet. To quantitatively investigate the differences between insulin and LysPro insulin in the aggregation reaction, we used thioflavin T fluorescence assay, electron microscopy, X-ray diffraction methods, and theoretical modeling. Kinetic experimental data for both insulin samples demonstrated the increase of the lag-time for LysPro insulin at low concentrations of monomers, particularly at 2 and 4 mg/mL, which corresponds to the pharmaceutical concentration. However, the morphology of insulin and LysPro insulin fibrils and their X-ray diffraction patterns is identical. Mature fibrils reach 10-12 μm in length and about 3-4 nm in diameter. The obtained analytical solution allow us to determine the sizes of the primary and secondary nuclei from the experimentally obtained concentration dependences of the time of growth and the ratio of the lag-time duration to the time of growth of amyloid protofibrils. In the case of insulin and LysPro insulin, we have exponential growth of amyloid protofibrils following the "bifurcation + lateral growth" scenario. In accord with the developed theory and the experimental data, we obtained that the size of the primary nucleus is equal to one monomer and the size of the secondary nucleus is zero in both insulin and LysPro insulin.