Rheological behavior of ultrahigh molecular weight polyethylene semidilute solutions. II. Effect of aluminium stearate

The effect of aluminium stearate on the rheological behavior of ultra-high molecular weight polyethylene (UHMWPE) semidilute solutions with paraffin oil as the solvent has been investigated. Adding aluminium stearate to paraffin oil can prevent the spinning solution from adhering to the pipe or screw, greatly improving the flow behavior of UHMWPE solutions. The geometric sizes of spinnerette hole, such as length–diameter ratio L/D and entrance angle of a capillary, also affect the flow behavior of the spinning solution. The calculated first normal stress difference σ₁₁ ? σ₂₂ and the Bagley-end correction e from experimental data show that the elastic effect on spinning solutions in flow is quite large, although the shear rate is below 20 s^?1.     

Anomalous Viscosity Behavior in Aqueous Solutions of Hyaluronic Acid

Summary Effects of steady shear flows on intermolecular interactions in dilute and semidilute aqueous solutions of hyaluronic acid (HA) are reported. Pronounced shear thinning behavior is observed for solutions of HA at high shear rates, and no hysteresis effects are detected upon the subsequent return to low shear rates. With the aid of the asymmetric flow field-flow fractionation (AFFFF) technique, it is shown that mechanical degradation of the polymer does not take place in these shear viscosity experiments, even at high shear rates. The low shear rate viscosity of a semidilute HA solution decreases by approximately 40% when the temperature is increased from 10 °C to 45 °C. It is shown that when a dilute HA solution is exposed to a low fixed shear rate (0.001 s^-1), a marked viscosification occurs in the course of time and prominent intermolecular complexes are formed. It is argued that shear-induced alignment and stretching of polymer chains promote the evolution of hydrogen-bonded structures, where cooperative zipping of stretched chains generates a network. At a higher constant shear rate (0.1 s^-1), the viscosity decreases as time goes because of the alignment of the polymer chains, but the higher shear flow perturbation prevents the chains in dilute solutions from building up association complexes. The viscosity of an entangled HA solution is not changed in the considered time window at this shear rate, but the network structures breakdown at the highest shear rate (1000 s^-1), and then they are restored upon return to a low shear rate.     

Melt flow behavior in capillary extrusion of nanosized calcium carbonate‐filled poly(L‐lactic acid) biocomposites

Nanosized calcium carbonate (nano‐CaCO₃)‐filled poly‐L ‐lactide (PLLA) biocomposites were compounded by using a twin‐screw extruder. The melt flow behavior of the composites, including their entry pressure drop, melt shear flow curves, and melt shear viscosity were measured through a capillary rheometer operated at a temperature range of 170–200°C and shear rates of 50–10³ s^?1. The entry pressure drop showed a nonlinear increase with increasing shear stress and reached a minimum for the filler weight fraction of 2% owing to the “bearing effect” of the nanometer particles in the polymer matrix melt. The melt shear flow roughly followed the power law, while the effect of temperature on the melt shear viscosity was estimated by using the Arrhenius equation. Hence, adding a small amount of nano‐CaCO₃ into the PLLA could improve the melt flow behavior of the composite. POLYM. ENG. SCI., 52:1839–1844, 2012. © 2012 Society of Plastics Engineers     

Capillary and slit flow behavior of concentrated solutions of a rod-like polymer

This paper is concerned with the flow behavior of isotropic solutions of the rod-like polymer, poly(p-phenyleneterephthalamide) (PPT), in 100 percent sulfuric acid. Studies include entry flow visualization in a slit die and solution fracture, and die swell in capillaries and a slit die. It was observed that solutions of PPT exhibit nearly negligible die swell, a slip-stick type of fracture that disappears at high shear rates, and radial entry flow patterns similar to Newtonian fluids. Fracture was associated with the plateau in the shear stress vs shear rate curve. Because values of the wall shear stress (τ_w.) obtained from capillary measurements were in good agreement with those obtained from a cone-and-plate rheometer and values of the loss modulus (G″) obtained from small-strain dynamic oscillatory measurements, it is believed that the rheological properties lead to the flow instability. These results are in agreement with the predictions of a recent theory by Doi and Edwards for concentrated solutions of rod-like molecules. Data are also presented for a flexible chain polyamide, nylon 6,6, in 100 percent H₂SO₄ for the purpose of comparing the flow characteristics of rigid and flexible chain polymers.     

Brownian dynamics simulations of bead-rod-chain in simple shear flow and elongational flow

We have simulated a dilute polymer solution under simple shear and elongational flows using the bead-rod-chain model, by incorporating intra-chain hydrodynamic interaction and excluded volume effects. Configurational properties and rheological quantities were calculated. For the simple shear flow, shear rate dependencies of chain's size, shape, and rotation were monitored. Shear-thinning was observed at all shear rates. In addition, the critical strain rate, ε_c, at which the polymer undergoes a coil-stretch transition under elongational flow, was investigated. The slope at the inflection point of the log(R_g²) vs log(ε) curve increased as the chain length increased, indicating a possible first order transition, in agreement with theories and experiments.     

Mechanical degradation of semi-dilute polymer solutions in laminar flows

Mechanical degradation of a semi-dilute solution of non-hydrolyzed polyacrylamide was studied under laminar flow conditions through fine capillary systems. Using a multi-pass device and capillary tubes of the same diameter and of various lengths we have shown that mechanical degradation (i) occurs at a critical value of the wall shear rate, chosen as a reference deformation rate, which is slightly higher than that of the appearance of high pressure losses in the entrance region of the capillary tube; (ii) is independent of the capillary tube length; (iii) increases with the number of passes N up to a maximum value for a limiting number of passes N_lim which is a decreasing function of deformation rates but does not depend on capillary length. The amount of degradation is expressed in terms of loss of viscous dissipation in shear and transient elongational flow. This last point is determined by studying the total end pressure loss through the capillary tube as a function of the pass number. The high pressure loss is related to viscous dissipation on macromolecules stretched by rapid converging flow. A comparison between a fresh and a fully degraded solution indicates that the degradation affects shear viscosity much less than viscous dissipation in rapid converging flow which is related to the properties of extended macromolecules. Both experimental results and theoretical interpretation suggest that, in our capillary system, the mechanical degradation occurs in the entrance region of the capillary where macromolecules are stretched and consequently submitted to extensional forces which can overcome the C–C bonds strength.     

Thermal response of low molecular weight poly-(<Emphasis Type="Italic">N</Emphasis>-isopropylacrylamide) polymers in aqueous solution

Temperature-induced phase transition of three low-molecular-weight samples (M _w  < 1.2 × 10⁴) of poly(N-isopropylacrylamide) was studied with the aid of turbidimetry, dynamic light scattering, and rheology. We have demonstrated that the lower critical solution temperature depends on the length of the chain and the concentration of the polymer in the low molecular weight range. The turbidity results show a transition peak in the turbidity curve at intermediate temperatures. This peak, as well as the cloud point, is shifted toward lower temperatures when the molecular weight and the concentration of the polymer increase. The DLS measurements disclose a fast and a slow relaxation mode, which in both cases are found to be diffusive. The fast mode is linked to the diffusion of small species in the solution, and the slow mode is associated with the formation of large aggregates. The formation of these aggregates is less pronounced in solutions of polymers with low molecular weight and the incipient aggregation is shifted to higher temperatures. The shear viscosity measurements show the formation of weak aggregates, which are easily broken in solutions of short polymers. This effect is less pronounced when the molecular weight of the sample is increased. At certain shear rates, temperature-induced transition peaks of the viscosity are observed.     

Measurement of the viscosity of guar gum solutions to 50,000 s−1 using a parallel plate rheometer

It is frequently necessary to measure the viscosity of polymer solutions at high shear rates to obtain data under the conditions encountered in industrial processes. Such measurements are most often made on a capillary viscometer. This paper presents a method of determining solution viscosities at shear rates up to 50,000 s^?1 in a rotational rheometer using a parallel plate geometry. The two keys to performing these measurements are very small gaps between the parallel plates (on the order of 50 microns) to eliminate inertial secondary flows, and the ability to increase and decrease the shear rate quickly to minimize viscous heating. A technique for setting and measuring small gaps is presented. Possible sources of error including inertia, axial compliance, and viscous heating are analyzed. A comparison Is made between the viscosity of a 0.7 percent hydroxypropyl guar (HPG) solution measured on the parallel plate rheometer and the viscosity measured in a capillary viscometer. Viscosities of HPG solutions having concentrations of 0.25, 0.50, 1.00, and 1.45 percent are presented over the shear rate range 100 to 50,000 s^?1.     

“SPURT FRACTURE” IN CAPILLARY FLOW

The critical conditions under which flow curves in capillary flow abruptly change their slope to zero (spurt) and the influence of solvent additive and solvent power on this phenomenon have been investigated. Based on a forced high elastic state concept an expression for the so-called spurt phenomenon, i.e. fracture-induced slip at the wall in a capillary of a capillary rheometer, is deduced. It is found that the spurt fracture stress, τ^s _cr, and the spurt fracture shear rate, γ^s _cr, can be represented by the master curve log (τ ^s _crr ((p/M_c)PE(M_c/p))^2/3 against log (a_T γ^s _cr), where a_T is the WLF shift factor, M_c the molecular weight between entanglements and p the density.

Estimation of slip rates at the wall and measurements on slightly crosslinked high density polyethylene supports the assumption that spurt results from melt fracture at the capillary wall.

Only addition of the non-solvent calcium stearate (with high density polyethylene) results in flow behavior which significantly deviates from that found for samples containing good solvents. Gel permeation chromato-graphy indicates that if chain scission resulting in lower molecular weight takes place, it will be limited to thin layers near the capillary wall.

melt fracture in the capillary cannot be reached. The flow behavior is influenced by addition of the non-solvent calcium stearate. The slopes of the flow curves is changed at relatively low shear rates but the high molecular weight polymer DMDS 5140 never the less shows spurt behavior at the same stress as for the pure sample.

This behavior may tentatively be interpreted as being caused by the formation of a boundary layer of non-solvent at low shear rate the thickness of which depends on the polymer and flow field. At stresses corresponding to the critical conditions, fracture in the polymer takes place. The interface between the non-solvent layer and the polymer matrix must according to Han61 be expected to be unstable     

Rheological properties of liquid crystalline solutions of ethyl celluloses with different molecular weight in m-cresol

Steady-state shear rheological properties of liquid crystalline solutions of four ethyl celluloses (ECs) were determined at a low shear rate (1 s^?1) and at relatively high shear rates by using two rheometers (cone-plate and capillary types), and were compared with those of liquid crystalline hydroxypropyl cellulose (HPC). The effect of molecular weight (MW) on the viscoelastic behavior was also determined. The viscoelastic behavior was also determined. The viscometric behavior of EC solutions was similar to that of HPC solutions: (1) with respect to temperature, the shear viscosity (η) at shear rate of 1 s^?1 exhibited a minimum (η_min) and a maximum (η_max), and the concentration–temperature superposition for η could be applied; (2) the behavior of η at relatively high shear rates as a function of shear rate or polymer concentration was typical of lyotropic liquid crystals. The MW dependence of η_min was greater than that of η_max for EC solutions. The behavior of the elastic parameters such as Bagley correction factor (v), entrance pressure drop (ΔP_ent), and die swell (B) at relatively high shear rates for EC solutions was essentially similar to that for HPC solutions: (1) the shear rate or stress dependence of the elastic parameters was greatly dependent on whether the polymer solution was in a single phase or biphase; (2) with respect to concentration the elastic parameters showed a maximum and a minimum and the maximum or minimum point for each parameter was not always identical to each other. η for the isotropic or fully anisotropic solutions at a given concentration (C) increased, whereas η for the solutions in the vicinity of the biphasic region showed a minimum, with respect to MW. The slope of η at a given shear rate vs. CM _w depended on shear rate, and this slope for the isotropic solutions appeared to be greater than that for fully anisotropic solutions. ΔP_ent and v at a given concentration showed either a monotonical increase or a maximum or minimum with MW, and this behavior was not fully consistent with that of η. B for the isotropic solutions increased and B's for both biphasic and fully anisotropic solutions were almost constant, with MW.     

Control on the topological structure of polyolefin elastomer by reactive processing

The feasibility of preliminary tailoring of the long chain branched (LCB) polymer through complex flow field was evaluated in the torque rheometer, for the reaction of melt polyolefin elastomer (POE) with peroxides at elevated temperatures. With the compensation of temperature, the strength of complex shear flow could be the only factor affecting the reaction kinetics and mechanism. The results of sample characterization by the rheological and dilute polymer solution methods indicated that the degradation mainly made the length of LCB arm shorter and shorter as the rotational speed increases. Extremely, a certain amount of LCB degraded to be linear chains again due to the scission approaching the branching point at intense mixing condition. One new LCB index (D_LCB) was defined from nonlinear oscillatory shear, and a nearly linear relationship between it and long chain branching index (LCBI) was found, which can be a map to quantify LCB level by Fourier Transform Rheology (FTR).     

Factors effecting a loss of flocculation activity of polyacrylamide solutions: Shear degradation,cation complexation,and solution aging

Polyacrylamide and poly(acrylamide-co-acrylic acid) flocculant solutions were subjected to shear degradation in a rotating cone instrument. At constant shear rate, shear degradation was minimized (highest limiting intrinsic viscosity) by the use of a lower solution concentration and high ionic strength of the polymer solution. Resistance to shear degradation also increased with increasing anionic character of the polyacrylamide. Sheared polymers showed reduced performance as flocculants of coal preparation plant tailings, their major commerical application in the U.K. Partially anionic polyacrylamide solutions were completely inactivated in the presence of certain multivalent cations. Aluminium, iron_III, lead, copper, and zinc ions formed complexes with the carboxyl groups on the polymer, resulting in zero flocculation activity. Nonionic polyacrylamides were unaffected. Viscosity–aging of polyacrylamide solutions was observed over a period of several months, but was insufficient to affect the flocculation activity. In the presence of 3% ethanol or methanol, no aging was observed in solutions stored for over a year.     

Functionalizing polymer surfaces by field‐induced migration of copolymer additives—role of shear fields

Flow‐induced migration polyethylene‐co‐methacrylic acid (PE‐co‐MA) and polystyrene‐b‐polydimethylsiloxane (PS‐b‐PD MS) copolymer additives in commercial long‐chain branch polyethylene (PE) and narrow‐molecular distribution polystyrene (PS) hosts was investigated in a capillary flow device. Attenuated Total Reflection Fourier Transform Infrared (ATR‐FTIR) spectroscopy and Dynamic Contact Angle (DCA) measurements were used to characterize surface composition of polymer specimen following extrusion through metallic dies with various length‐to‐diameter (L/D) ratios, (1100 ? L/D ? 3000). Results from experiments covering a broad range of shear rates and polymer residence times in the dies are reported. Provided that the polymer residence time in the die is sufficiently long, shear is found to increase the concentrations of low molecular weight copolymer additives on the host polymer's surface. The surface composition of copolymer additive is found to vary strongly with the wall shear rate and die L/D ratio. Decreasing the die diameter at fixed flow rate is found, for example, to be a more effective method for enhancing transport of additive to a polymer's surface than increasing shear rate at fixed diameter. A mechanism based on shear‐induced diffusion is proposed to explain the observed migration.     

Mechanical stability of high‐molecular‐weight polyacrylamides and an (acrylamido tert‐butyl sulfonic acid)–acrylamide copolymer used in enhanced oil recovery

High‐molecular‐weight partially hydrolyzed and sulfonated polyacrylamides are widely used in enhanced oil recovery (EOR). Nonionic polyacrylamide and polyacrylamide‐based microgels are also used in water shut‐off treatments for gas and oil wells. A comparative study of the mechanical degradation for three linear polyacrylamides and a microgel is presented. Mechanical degradation is quantified from the loss of the viscosity of the polymer solution as it passes through a stainless steel capillary with a length of 10 cm and an internal diameter of 125 µm. The critical shear rate above which degradation increases exponentially was found to depend on the chemical structure of the polymer, molecular weight, and electrolyte strength. The nonionic polyacrylamide shows higher degradation and lower critical shear rate compared with a sulfonated polyacrylamide with similar molecular weight. Moreover, the nonionic polyacrylamide with a higher molecular weight results in lower mechanical degradation. The higher mechanical stability of the sulfonated polymer is attributed to the higher rigidity of its molecules in solution. On the other hand, the ability of the high‐molecular‐weight polymers to form transient, flow‐induced microgels boost their mechanical stability. This ability increases with the increase in the molecular weight of the polymer. Indeed, the microgel solution used in this study demonstrates exceptional mechanical stability. In general, mechanical stability of linear polymers used in chemical enhanced oil recovery can be enhanced by tailoring a polymer that has large side groups similar to the sulfonated polyacrylamide. Also, polyacrylamide‐based microgels can be applied if high mechanical stability is required. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40921.     

Rheological behaviour of some amphiphilic β‐cyclodextrin‐based azo aromatic polyurethanes in N,N‐dimethylformamide solutions

Amphiphilic β‐cyclodextrin‐based azo aromatic poly(ether urethane)s with different soft segment lengths have been synthesized and characterized. Hydrogen bonding in these systems was demonstrated by Fourier transform infrared spectroscopy analysis (carbonyl stretching region). A rheological study was performed on solutions of the synthesized poly(ether urethane)s in N,N‐dimethylformamide at various concentrations and temperatures by employing parallel plate geometry, and a comparative evaluation of the influence of the structural components on the viscometric responses was performed. The rheological behaviour was found to be strongly dependent on the chemical composition of the synthesized polyurethanes which promotes self‐assembly and structuring in solution. Hard segment content and polymer concentration influence pseudoplastic shear‐thinning flow behaviour. The rheology can be interpreted in terms of hydrophobic associations and chain entanglements and a hydrogen bonding network occurring in solution. The start‐up flow of the polymer solutions is determined by the lifetime of the associative polymer segments. Shear stress plateaux indicative of ‘shear banding’ behaviour explained by the structuring of the polymer solutions at increased temperatures were obtained. The studied amphiphilic polyurethane solutions are thermoresponsive systems exhibiting viscosity increase with increasing temperature contrary to the usual Arrhenius thermo‐thinning behaviour. At constant shear rate viscosity was found to increase with increasing temperature due to thermo‐association. © 2014 Society of Chemical Industry     

Water soluble acrylamide polymers, 2. Aging and viscous flow of aqueous solutions of polyacrylamide and hydrolyzed polyacrylamide

The aging of aqueous solutions of polyacrylamide which appears experimentally as a decrease of solution viscosity and which is probably caused by microorganisms may be prevented by the addition of a small amount (0.02 wt.-%) of an antimicrobial agent such as sodium azide. Aluminium chloride causes a very strong decrease of the viscosity during a prolongated storing time. The addition of aluminium ions to the polymer solution leads to a complexing of amidic groups with aluminium cations and probably also to decrease of the dimensions of individual polymer coils. The viscous flow of aqueous solutions of polyacrylamide and hydrolyzed polyacrylamides was studied as a dependence of the shear gradient D on the shear stress τ and was described by the relation D = k · τⁿ, where k and n denote constants. Both constants depend on the polymer concentration, the degree of polymerization and the content of carboxylic groups in the polymer. The greatest deviations from the Newtonian behaviour were found in the range of molecular weights over 2 · 10⁶ g/mol and practically no deviations were observed for polyacrylamide with molecular weights below 1 · 10⁶ g/mol. The dependence of the viscosity on the shearing time at different shear rates (300, 600 and 1200 s^?1) which was observed in solutions of polyacrylamide, hydrolyzed polyacrylamide and poly-(N,N-dimethyl)-acrylamide was explained by an entanglement model.     

Viscoelastic properties of polyamic acid solutions—precursors of polyimides

The rheology of polyamic acid (PAA) solutions, precursors of polyimides used in microelectronic device applications, has been investigated by dynamic (oscillatory) shear flow measurements. Frequency dependent storage and loss moduli and dynamic viscosity were measured in the frequency range 10^?1 to 10³ rad/s at 23°C. The storage modulus G′ (ω) and loss modulus G″ (ω) exhibited quadratic and linear dependence in frequency at low frequencies respectively, the viscoelastic fluid behavior commonly predicted for polymer solutions from many molecular theories. At high frequencies both dynamic moduli become proportional to ω^2/3. The results show that PAA solutions are very high loss viscoelastic fluids, judging from the loss tangent values which far exceed unity. It is suggested that dynamic viscoelastic properties could be used to monitor the degree of imidization since there is a gradual change from viscoelastic fluids to soft viscoelastic solids to hard viscoelastic solids as PAA is converted to polyimides. Onset of non-Newtonian flow as shown on the frequency dependent dynamic viscosity was in the range 30 to 200 rad/s. The viscoelastic constants, zero-shear rate viscosity η_o and steady-state compliance J_e⁰, where also determined from the dynamic data and compared to previous steady shear flow results.     

Effect of oxalic acid on the rheological properties of dope solution of poly[acrylonitrile‐co‐(methyl acrylate)‐co‐(itaconic acid)]

The very high dope viscosity of concentrated dope of poly[acrylonitrile‐co‐(methyl acrylate)‐co‐(itaconic acid)] (with M?_v = 10.67 × 10⁵g mol^?1) in DMF could be diminished significantly by the addition of oxalic acid (OXA). The change in steady shear rheological behaviour caused by OXA has been analysed for the dope using a rheometer working in the viscosity mode. The temperature dependence of η₀ conformed to the Arrhenius‐Frenkel‐Eyring equation. ΔG_v decreased marginally with OXA concentration, and the least value was observed at an OXA concentration of 0.63 % by weight. Shear thinning behaviour was observed under higher shear rates for the terpolymer solutions in the presence and absence of OXA. The pseudoplasticity index (n) showed an abrupt initial increase on addition of OXA. The OXA concentration of 0.63 % by weight was advantageous for decreasing the viscosity of the polymer dope. The reduction in viscosity is attributed to the disturbed polymer‐polymer interactions by way of H‐bonding of OXA with the polymer. OXA‐containing dope at higher shear rate could achieve very low viscosities. Copyright © 2004 Society of Chemical Industry     

Shear thickening behavior of dilute poly(diallyl dimethyl ammonium chloride) aqueous solutions

Using dynamic light scattering (DLS) and capillary dynamic viscoelasticity (DVE) analyzer, we investigated dilute (0.5 mg/ml) poly(diallyl dimethyl ammonium chloride) (PDADMAC) aqueous solution properties for three different molecular weights of PDADMACs mixed with various concentrations of NaCl. The dependence of PDADMAC molecular chain conformations in aqueous solutions on polymer molecular weight and NaCl concentration were studied. By analyzing dynamic shear viscosity η′(ω), viscoelastic relaxation times t_r, and shear rate at tube wall ?_a(ω) of PDADMAC aqueous solutions in oscillatory flows, we proposed that polymer chain conformations varied with increasing shear frequency ω via the following steps: intra-polymer associations, dissociation of intra-polymer associations, stretching of polymer chains, inter-polymer aggregations, and dissociations of inter-polymer aggregations. The intra-polymer associations lowered the n′ exponent of storage modulus G′(ω) (G′(ω) ∼ ω^n′) with n′ < 2, and the polymer chain stretching and inter-polymer aggregations caused shear thickening (i.e. upturn of η′(ω)) of PDADMAC aqueous solutions. The behaviors of the lowering of n′ exponent with n′ < 2 and the shear thickening were favored by increasing ionic strength of solutions. By comparing η′(ω) data with DLS hydrodynamic radii (R_h) data, we also confirmed the possibility of inter-polymer aggregations in dilute solutions when polymer chains were stretched in oscillatory flows.     

Evaluation on the degrading behavior of melt polyolefin elastomer with dicumyl peroxide in oscillatory shear flow by Fourier transform rheology

The degradation of melt polyolefin elastomer (POE) at the presence of dicumyl peroxides (DCP) was estimated at elevated temperature in oscillatory shear flow. Large amplitude oscillatory shear (LAOS) experiments followed by Fourier transform rheology (FTR) were carried out to detect and evaluate the branching architecture of the products. The third complex harmonic (I₃^∗) and other two parameters, small strain elastic shear modulus (M) and large strain elastic shear modulus (L), which describe the nonlinearity and elasticity of a material obtained from FTR, are mainly used to characterize the topological structure of polymer chains. The results indicate the degradation appeared just after a large amount of the long chain branches (LCB) created rather than as soon as the reaction started when the strain was applied within the linear viscoelastic regime of the original POE at high frequencies. This is different from our previous result that the dominant reaction was coupling in linear shear flow. The threshold strain for degradation decreased with the oscillatory frequency, and the frequency owned a different acting mechanism from the strain amplitude to cause the degradation reaction. Moreover, there is a kind of selectivity of shear rate on the polymer chains for degradation. Low frequency results in short linear scission segments and a long branched chain suffers from degradation more than once. At high frequency, the possibility of degradation at the sites near the branching points of LCB increases.