Dextrans in Aqueous Solution. Experimental Review on Intrinsic Viscosity Measurements and Temperatur...

Martin Alberto Masuelli

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Dextrans in Aqueous Solution. Experimental Review on Intrinsic Viscosity Measurements and Temperature Effect

Martin Alberto Masuelli

Instituto de Física Aplicada, CONICET. Cátedra de Química Física II, Área de Química Física


The study of biopolymers as dextran in aqueous solution, is effectively determined by intrinsic viscosity [η] measurements at different temperatures. Molecular weight (Mv) and hydrodynamic properties can be calculated from there. The Mark-Houwink parameters indicate the dependence with temperature (T) in the range from 20 to 50ºC, ie with increasing T a increases and kM-H decreases. These hydrodynamic parameters show that these polysaccharides behave as a compact rigid sphere and contract by the increase of temperature (RH decreases) for the Mw range from 8.8 to 200kDa.

At a glance: Figures

Cite this article:

  • Masuelli, Martin Alberto. "Dextrans in Aqueous Solution. Experimental Review on Intrinsic Viscosity Measurements and Temperature Effect." Journal of Polymer and Biopolymer Physics Chemistry 1.1 (2013): 13-21.
  • Masuelli, M. A. (2013). Dextrans in Aqueous Solution. Experimental Review on Intrinsic Viscosity Measurements and Temperature Effect. Journal of Polymer and Biopolymer Physics Chemistry, 1(1), 13-21.
  • Masuelli, Martin Alberto. "Dextrans in Aqueous Solution. Experimental Review on Intrinsic Viscosity Measurements and Temperature Effect." Journal of Polymer and Biopolymer Physics Chemistry 1, no. 1 (2013): 13-21.

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1. Introduction

Dextran consists of α-D glucose units with a majority of α (1→6) glucosidic linkages between them. A few percent of R (1→3) glucosidic linkages provides side chains which appear to be short. Dextran is a branched polysaccharide, composed of α-D-glucopyranosyl residues. The mostly used commercial product/ polysaccharide is dextran, and it is produced from bacterium Leuconostoc mesenteroides, with an overall degree of branching of about 5% [1-3][1]. Dextran is soluble in water, methyl sulphoxide, formamide, ethylene glycol, glycerol, 4-methylmorpholine-4-oxide, and hexamethyl phosphamide [4]. Dextrans and their derivatives find an interest in clinical applications, as well as excipients in tablets in the pharmaceutical industry [5].

The fast increasing of these polyglucosans for medical, industrial and research purposes motivated a survey of the types obtainable. The particular dextrans which were used initially for conversion into synthetic blood-volume expanders [6, 7], human red blood cells aggregation for increasing the degree of polymerization and hence the molecular weight [8, 9, 10], hydrogels and microspheres [11], in drug transport system and its modifications as nanoparticles [12], in the removal through absorption of contaminant effluents such as heavy metals, organic molecules and inks [13], in the formation of biodegradable films [14, 15].

A lot of research has been devoted to dextrans modification in order to describe special characteristics relevant to specific applications such as surfactants [16], as visible marker [17], polysaccharides-based nanoparticles, covalent crosslinking [18], ionic crosslinking, polyelectrolyte complex, and the self-assembly of hydrophobically modified polysaccharides, and hydrophilic modified polysaccharides [19].

Molecular weight, particle size and diffusion coefficient can be determined in many studies by Dynamic Light Scattering [20, 21, 22], Gel Permeation Chromatography [23], Analytical Ultracentrifuge [24, intrinsic viscosity [1, 7, 14], size exclusion chromatography / multiangle laser light scattering / differential viscometry, Flow Field-Flow Fractionation [25], and so on.

Determination of the intrinsic viscosity has been the most used measurement in the last 60 years. Viscosity of in water solution polysaccharides depends on intrinsic characteristics of the biopolymer (such as molecular weight, volume, size, shape, surface charge, deformation facility, esterification degree, and galacturonic content) and on ambient factors (such as pH, temperature, ionic strength, solvent, etc.). The most widely used method for the characterization of macromolecules is the capillary viscometry, as it is a simple and economic method. Although, in literature there is much information on hydrodynamic measurements from determinations viscosity; very few of them evaluate the situation at different temperatures. The importance of this type of study lies in the analysis of the polysaccharide behavior at industrial processes, the requirements to reduce energy, avoid flow problems and product quality control. Many works are aimed at determining molecular weights [1, 7, 26], hydrodynamic radius, among other parameters for characterizing the physics and chemistry properties of dextran in solution.

Table 1 shows some values of dextrans Mark-Houwink parameters, from literature consulted, where all data are based on the logarithmic plot of intrinsic viscosity [η] and molecular weight Mw.

Table 1. Intrinsic viscosity, molecular weight, Mark-Houwink parameters dates of various studies released with dextrans at different temperatures

From Table 1, It is worth noting that the value of σ2 is above 0.95, being an acceptable value for viscosimetric measurement. The same way, many of these authors emphasize the non-linear or hyperbranched of dextran molecular weight range from 9 to 2000kDa [3,5,8,16, 37,38]. In the case of the work performed in references [34, 35, 36] they studied using the number average molecular weight, which rearranges the value of a and forces it to enter into unbranched or linear molecules, on the other hand, if molecular weights are used the value would be less than 0.5.

If plotted for all molecular weights, the double logarithm of [η] and Mw, the value of “a” obtained in all cases shows a value smaller than 0.5, which reports that dextran macromolecule has a degree of hyperbranched with increasing molecular weight and increases much for higher Mw (< 200kDa) which making the application of M-H method more difficult.

Although, intrinsic viscosity is a molecular parameter that can be interpreted in terms of molecular conformation, it does not offer as high resolution on molecular structure as other methods such as Light Scattering, Circular Dichroism, Sedimentation Velocity, Sedimentation Equilibrium, Size Exclusion Chromatography Coupled to Multi-Angle Laser Light Scattering (SEC-MALLS), High-performance Size Exclusion Chromatography (HPSEC), Gel Permeation Chromatography (GPC), NMR, X-rays, etc. Intrinsic viscosity determination offers a simple and useful method that requires low cost equipment and yields useful information on soluble macromolecules.

In this work, hydrodynamic properties are investigated in different dextran aqueous solutions with different molecular weights (8.8-2000kDa), in a temperature range from 20ºC to 50ºC. The Mark-Houwink parameters and the effect of temperature on them are specifically studied. In order to understand the behavior of this biopolymer in water and to support changes at the M-H parameters with temperature, the hydrodynamic parameters are analyzed (hydrodynamic radius, (RH); Simha number, (ν(a/b)); Perrin parameter (P); Flory parameter (0); and stiffness chain (dln[η]/dT)).

2. Theory

The solution viscosity (η) is related to the solvent viscosity (ηo), resulting in the relative viscosity,


where η (poise) is the viscosity, the ρ (g/cm3) fluid density, and t the liquid draining time (s) subscript zero is referred to solvent, and without subscript is referred to the solution [40], and inherent viscosity is ηi = ηr -1.

Huggins equation [41] gives the relation to the relative viscosity increase (ηi),


where c is the solute concentration (g/cm3), [η] is the intrinsic viscosity (cm3/g), and kH represents Huggins’ constants (cm3/g). The [η] is connected to the dimensions of the biopolymer molecule isolated in a certain solvent.

The first term on the left-hand side of equation 2 (ηi/c) has a linear relation as a function of the concentration (c in g/cm3), where is the intrinsic viscosity [η] is given by (c→0) [42, 43]. The intrinsic viscosity calculation requires several concentrations, and because of this inconvenient will not use the Huggins method in this paper. The intrinsic viscosity can be easily calculated by the Solomon-Ciuta single-point equation [44, 45],


By studying the molecular weights of various solutions of polymer, Solomon-Ciuta arrived at the formula which allowed the calculation of the intrinsic viscosity of polymer solutions by a single viscosity determination. The formula is verified for different systems of polymer-solvent and the values are in accord with those obtained by extrapolation.

The relation between Mw and the intrinsic viscosity is given by Mark-Houwink equation,


The calculation of Mark-Houwink parameters is carried out by the graphic representation of the following equation:


where kMH (cm3/g) and a are Mark-Houwink constants, depending on the type of polymer, solvent, and temperature of intrinsic viscosity determinations [46]. The exponent a is a function of polymer geometry, and varies from 0.5 to 2 and exponent is dimensionless. These constants can be determined experimentally by measuring the intrinsic viscosity of several polymer samples for which the molecular weight has been determined by an independent method (i.e. osmotic pressure or light scattering). Using the polymer standards, a plot of the ln [η] vs ln Mw usually gives a straight line. The slope is a value and intercept is equal to the ln kMH value [47]. The Mark-Houwink exponent bears the signature of a three-dimensional configuration of a polymer chain in the solvent environment. For a values from 0-0.5 a rigid sphere is predicted in a ideal solvent, from 0.5-0.8 a random coil in good solvent, and from 0.8-2 a rigid or rod like shape is expected (stiff chain). The fact that the intrinsic viscosity of a given polymer sample is different according to the solvent used gives and insight about the general shape of polymer molecules in solution. A long-chain polymer molecule in solution takes on a somewhat kinked or curled shape, intermediate between a tightly curled mass (coil) and a rigid linear configuration. All possible degrees of curling can be displayed by any molecule, but there will be an average configuration which will depend on the solvent. In a good solvent, which shows a zero or negative heat of mixing with the polymer, the molecule is less-extended, and the intrinsic viscosity is high. The Mark-Houwink “a” constant is close to 0.75 (or higher) for these “good” solvents. In a “poor” solvent which shows a positive heat of mixing, segments of a polymer molecule attract each other in solution more strongly than attract the surrounding solvent molecules. The polymer molecule assumes a tighter configuration, and the solution has a lower intrinsic viscosity. The Mark-Houwink “a” constant is close to 0.5 in “poor” solvents. For a rigid or rod like polymer molecule that is greatly extended in solution, the Mark-Houwink “a” constant approaches to a value of 2.0 [48].The hydrodynamic radius (RH), for a sphere (ν(a/b) = 2.5) is given by the Einstein relation [49],


For simplicity, macromolecules are treated as rigid molecules for a hydrodynamic study. It is worth noting that the size of macromolecules is much bigger than that of solvent (water) molecules [50].

Hydrodynamic properties, such as the intrinsic viscosity, [η], and equilibrium solution properties such as the hydrodynamic radius RH can be combined to construct dimensionless quantities that are universal since they are of being independent of the macromolecular particle size, while they depend more or less sensitively on its shape [51].

Typical examples are the classical size-independent combinations like the Flory parameter, which that combine the intrinsic viscosity, [η], and the gyration radius, Rg:


These quantities have been proposed along the years, by different eminent scientists, after whom they are named. As a consequence of the diversity in their origin, the set of classical universal size independent quantities suffers from shortcomings. For a sphere and a random coil 0 the values are 9.23x1023 mol-1 and 2.60x 1023mol-1, respectively. Thus, it is accepted that, for every flexible-chain polymer in a Θ (ideal) solvent, there is a universal value of 0 = 2.1-2.5x1023mol-1 [52]. The intrinsic viscosity classical theory of random coils at Θ conditions [η]0 predicts the quotient a0 = d ln[η]0/d ln M to decrease from unity to 0.5 as the chain length increases. The proportionality between [η]0 and M0.5 is obtained as a limiting law for the no draining regime. For a given polymer-solvent pair, the theta condition is satisfied at a certain temperature, called the theta (Θ) temperature or theta point. A solvent at this temperature is called a theta solvent [53].

For rigid macromolecules, it is also conventional to combine a solution property with the volume of the particle itself, or with a quantity directly derived from it [54, 55, 56]. Thus, it is a common practice to express the frictional coefficient of rigid structures as


Where f0 is the frictional coefficient of a sphere having the same hydrodynamic (hydrated or solvated) volume V as the particle. The term f/f0 is sometimes denoted as P, Perrin constant. A similar combination involves the intrinsic viscosity and specific volume:


ν(a/b) is called Einstein viscosity increment, and Vs is specific volume (cm3/g). For ellipsoids, as studied by Simha, ν(a/b) is a function of axial ratio.

3. Experimental Section

3.1. Samples

Seven dextrans, provided by Sigma, with molecular weight of 8.8, 40, 71.9, 110, 200, 580 and 2000 kDa. The solutions were prepared in bidestilated water at 1, 0.75, 0.5, 0.25 % wt.

3.2. Viscosity

Measurements were made with a Ubbelohde C type “suspended level” viscometer [57] (IVA, Argentina); with a diameter capillary of 0.81mm and water draining time of 35.89s at 20°C, with viscometer constant of 0.027883 mm2/s [58]. The range of temperatures used was 25-50 (±0.1) ºC and it was regulated by thermostatic bath Haake C. The viscosity measurements required Hagenbach-Couette correction time (tg 37.31s).

3.3. Density

The solution was measured using an Anton Paar DMA35N densitometer.

3.4. Gel Permeation Chromatography

The measurements of dextrans molecular weight were determined by size exclusion HPLC (Gilson, France) with Refraction Index detector using a Polysep-GFC-P5000 column (7.80×30 mm). The column was eluted with bidestilled water a flow rate of 0.8 ml/min, injection 5μL, back pressure 200psi. Dextran standards with sequence molecular weight from 8.8, 40, 71.9, 110, 200, 580 and 2000 kDa were utilized for the plot of calibration curve.

4. Results and Discussion

Table 2 shows that comparing the intrinsic viscosity data obtained from the Huggins method and the Solomon-Ciuta single-point method, a similar values are obtained and the %RE is lower for low Mw and it increases for higher Mw. Use of the single point method is correct because it is based in the Huggins method (HM); owing the HM requiring many viscosity and density measurements (at least four) for each Mw, but Solomon Ciuta method with a single measure is sufficient. The analysis of errors using the Solomon-Ciuta method is compared with HM [59].

In order to confirm the molecular weight the gel permeation chromatography (GPC) for standard dextrans is used in a range of molecular weights from 8.8 to 2000kDa and these correspond to the following equation,


where tr is the column retention time in minutes (σ2 of 0.9792).

Table 2. Comparison of intrinsic viscosity released by Huggins and Salomon-Ciuta methods for 8.8 and 2000kDa Mw at different temperatures

The Solomon-Ciuta single-point method is used for calculating dextran intrinsic viscosity and the error relative is calculated, and %RE respect to Huggins method is >4.18% for 2000kDa, and >2.06% for 8.8kDa (Table 2). These values indicate for dextrans in dilute aqueous solution, both methods give very similar results of the intrinsic viscosity and the respective Mw. Table 3 shows the intrinsic viscosity for the rest of the dextrans obtained by using the single-point method, measured at different temperatures.

Table 3. Intrinsic viscosity for dextrans released at different temperatures

The M-H equation is empirical and valid for monodisperse polymers, and it is applied to biomacromolecules (complex, hyperbranched, crosslink), taking the precaution of comparing the value of Mv with the polydispersity index (qM-H). The molecular weight of dextran samples can be obtained by a variety of methods including light scattering, HPLC/SEC, sedimentation, osmometry and end-group analysis. Various average molecular weights (Mv, Mn, Mw, and Mz) instead of Mv were substituted in M-H equation. The value of Mv is different from Mn, Mw, and Mz in a polydisperse polymer sample [38, 60, 61, 62]. Determination of constants, kM-H and a, from the intrinsic viscosity data, requires a series of monodisperse polymer samples with known molecular weight or a series of polydisperse polymer samples with known viscosity average molecular weights, Mv. In general, Mv is not experimentally accessible, whereas other average molecular weights are accessible. The equation 4 can be rearranged and resulted in a modified M-H equation as follows:




where the value qM-H is the polydispersity correction factor, and it is a statistical function of the molecular weight distribution. It is a measure of the width of molecular weight distributions (MWD) as well as probability of molecular weight distribution curve (GPC). The value of qM-H varies from one sample to another one, because it is a function of a and the average molecular weights (Mv, Mw). Alternatively, the value of qM-H can be calculated using numerical methods and other-average molecular weights (Mn, Mw, Mz) according to where c and d are empirical polynomial functions of the exponent a.


The qM-H values given by equation 13, these vary from 0.9993 to 0.9841 for the range between 8.8 to 200kDa in a temperature range of 20 to 40°C. This low polydispersity realizes that the Mark-Houwink equation is forced at a given Mw regardless of the hyperbranched nature of the dextran molecule. In this sense, the largest deviations were obtained for the highest molecular weight (580-2000kDa with values from 0.8467 to 0.7346).

Furthermore, the influence of temperature on the intrinsic viscosity is given by the chain flexibility parameter (dln[η]/dT), which gives information about the conformation of the macromolecule chain in solution [62]. As intrinsic viscosity of dextrans decreases with an increase in solution temperature; chain flexibility enhances with an increase in temperature (see Table 4) showing that the intrinsic viscosity of dextran (with different molecular weights Mw from 8.8 to 200kDa) decreases linearly with an temperature increase in solution, but change to high molecular weight to hyperbranched macromolecule.

For a limited temperature range, the viscosity of a polymer solution varies generally following a relation similar to that of usual liquids (Årrhenius plot), where the polymer concentration is not very high and that temperature remains far enough from glass transition [38], and for system PEA–organic solvents see reference [63].

Figure 1. RH vs. T. a)- Mw from 8.8 – 110 kDa ; b)- Mw form 200 – 2000 kDa

Table 4. Stiffeness chain parameter obtained for dextrans

At the same temperature, the hydrodynamic radius and the intrinsic viscosity are higher for different molecular weights, while these properties decrease with an increase of temperature at the same molecular weight (Figure 1). Studies carried out at different ionic strength you can see them in the references [64, 65] and works with different solvents in the references [66, 67].

Figure 3. Effect of temperature on Marck-Houwink parameters

Figure 2 shows the classical method for calculating Mark-Houwink parameters, where a linear relation between the intrinsic viscosity and the molecular weight is established for each temperature. Figure 3 shows that the parameters vary with temperature, evidencing a clear functionality of them. These studies on Mark-Houwink parameters are usually carried out at a given temperature, obtaining a consistent result but in a very limited temperature range [68].

Table 5 shows the data of Mark-Houwink parameters determined in figure 4 from linear regressions with σ2 values higher than 0.9797. The calculated dextran molecular weights are corroborated by those tabulated data by the manufacturer with a relative error lower than 10%, being the exception dextrans 580 and 2000kDa with the highest relative error. There is a deviation from linearity after 580kDa [69, 70]. The Dextrans intrinsic viscosity is determined as a function of the molecular weight in water and NaOH 0.5 M see reference [1]. They concluded that a power law behavior seems to be approached only in the small molecular weight region. The reason for a nonlinear Mark-Houwink relationship is confirmed by the intrinsic viscosity which in contrast with scaling prediction shows no power law behavior. The flattening of the curves at higher molecular weight is in agreement with an increased branching density. The dextran was chosen as another branched polysaccharide which, like the others was suspected to show hyperbranched behavior. This conjecture found to be correct. All branched polysaccharide types could be described approximately by the hyperbranching theory. In contrast to linear chains, power law behavior is observed only asymptotically at large Mv. In fact, short chains do contain minor branching points. The effect of branching is best recognized from the molecular weight dependencies of [η].

Table 5. The a and kM-H parameters and their standard deviation (σ2) calculated from plot 4

Dextran theta temperature between 43.14 and 44.44ºC for all the range of molecular weights explains the deviation at 45 and 50ºC [36, 37].

A simple way of universalizing the measurements is shown in figure 4 where there is a curve at each temperature for every molecular weight. This universalization of the parameter´s leads to a higher error ratio in the calculation of the respective molecular weights. The values of Mark-Houwink parameters universalized for the range of working temperatures are the following: 0.4267 for a*, and 0.1455 cm3/g for k*M-H, with σ2 of 0.9399. Conducting a comparative analysis of the data shown in Table 1 can observer that parameter data Mark-Houwink “a”, obtained by these authors are very similar to that obtained in this work, which affirms its validity.

In the range of working temperatures and molecular weights of dextrans, similar intrinsic viscosity results obtained by other researchers and published here are slight, as shown in tables 1 and 3. At 20°C data "a" value obtained in this work is intermediate to those given by references [1, 37] while the value of kM-H is lower. At 25°C both values of a and kM-H are within the range reported by [3, 8, 16]. The above data are not useful because it can not be compared with those obtained in this work. This situation is mainly the result of using dextans, solvent, additives, etc. of different origins. Similar results are obtained in references [35, 36, 37], using a system of dextran / ethylene glycol, and dextran/dimethylsulfoxide, respectively. Therefore, the trend of "a" and kM-H decreases with T, where the presence of ethylene glycol or dimethylsulfoxide strongly changes the interactions of this solvent with the macromolecule. Ultimately they concluded that the temperature increment found to be an effective force in disturbing these interactions, mainly between polymer-polymer and polymer-solvent molecules for the used system.

Table 6. Comparative analysis (%RE = 100 {Mw – Mv}/ Mw) between molecular weights provided by manufacturer (Mw), and Mv calculated with Mark-Houwink parameters in this work

A similar article of dextran/water [35] clearly demonstrating the dependence of Mark-Houwink parameters with temperature. The correct way to interpret what Mark-Houwink parameters is determined graphically ln [η] versus ln Mw, where Mw is the molecular weight provided by manufacturer, and calculate the percentage relative error (%RE) respect to Mw. The a value is higher than calculated in this work, because these calculations were performed with number average molecular weight (Mn) which rearranges the value of a and forces him to enter into unbranched or linear molecules (a > 0.5), on the other hand, if molecular weights (Mw) ware used to value would be less than 0.5.

The value of kM-H in this work decreases with increasing temperature in contrast to published by reference [34] where kM-H increases. The explanation for the anomalous values of a and kM-H is because the mixture solute-solvent is highly compatible due a great compaction of biopolymer, from undisturbed state in the absence of interactions, where free energy of mixing less than zero, and emphasize the nature non-linear or hyperbranched of dextran for Mw high to 200kDa.

Working with the molecular weights given by the manufacturer and compare them with the molecular weights, calculated from the Mark-Houwink parameters in this work; can be seen that the %RE obtained, see Table 6.

The parameters of Mark-Houwink for polymers can vary with the polymer solution and temperature. This is because the macromolecule hydrodynamic radius changes the solution type and temperature via change in their chain flexibility. In a good solvent, a temperature increase results in an intrinsic viscosity decrease and in a less-extended conformation (RH<), because the entropy value increases with an increase in temperature and it is unfavorable for an extended conformation. In the case of a poor solvent, a temperature increase causes an increase in entropy and intrinsic viscosity and is favorable for the extended conformation. Mark-Houwink values confirm that for these conditions dextrans behave as rigid spheres with a tendency at compaction as temperature increases.

Analyzing the values of the hydrodynamic properties of dextran in aqueous solution, it can be seen in Table 7, that all vary with the temperature. The values of 0 decreases from 2.5429 to 2.3326 x 1023mol-1 demonstrating a relative flexibility of particles. The value of P increases from 1.0272 to 1.2694 (spherical shape with tendency to spheroid for high Mw). The ν(a/b) value is 2.5 which confirms that dextran in aqueous solution is a biopolymer with a spherical conformation for an Mw range from 8.8 to 200kDa, and with tendency to compaction with increasing temperature (RH decreases).

Table 7. Hydrodynamic parameters of dextrans at different temperatures

5. Conclusions

The Mark-Houwink parameters is calculated molecular weights range from 8.8 to 200kDa. The numerical value of a indicates that dextrans acquire the shape of a rigid sphere in aqueous solution; and kM-H demonstrates that under water the value decreases with temperature [71, 72]. The great deviation at 2000kDa occurs due to the large hyperbranched structure of the macromolecule, generating a change in its conformation and, therefore, a change in the way it flows [73]. The values of Mark-Houwink parameters could be universalized with certain precautions, being an indication for the calculation of molecular weight in the temperature range of 20-40ºC.

The lack of data on the uniformity of intrinsic viscosity measurements in the system water/dextran, highlights the significant influence of the solvent and temperature [74]. The molecular weight and Simha number do not change in this temperature range (Mw from 8.8-200kDa), P slightly change, showing modifications in the hydrodynamic properties of the biopolymer in aqueous solution as [η] and RH.

The temperature increment can induce a macromolecule compaction (decreases in RH and [η]), generating by this way, a greater difficult to flowing due at requires an increase of energy consumption (Eavf<). This phenomenon is observed in the case of hyperbranched biopolymers evidencing an increase of a with temperature.


The author thanks Universidad Nacional de San Luis (Project 2-81/11), FONCyT (PICT 2004-N°23-2548 and PICT 2008-N°21-84), and CONICET (PIP 6324 Res. 1905/05) for their financial support.


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