The effect of temperature on the colligative properties of food-grade konjac gum in water solutions

Carbohydrate Polymers 174 (2017) 456–463

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The effect of temperature on the colligative properties of food-grade konjac gum in water solutions Joanna Kruk, Kacper Kaczmarczyk, Anna Ptaszek ∗ , Urszula Goik, Paweł Ptaszek Faculty of Food Technology, ul. Balicka 122, 30-149 Kraków, Poland

a r t i c l e

i n f o

Article history: Received 17 March 2017 Received in revised form 27 June 2017 Accepted 29 June 2017 Available online 30 June 2017 Keywords: Konjac gum Colligative properties Osmotic pressure Light scattering Relaxation time Intrinsic viscosity

a b s t r a c t This research paper presents the results of tests on the colligative properties of konjac gum chains in water solutions. For this purpose, the measurements of osmotic pressure and intrinsic viscosity of aqueous solutions, in the function of konjac gum concentration and temperature were carried out. The applied methods allowed for the determination of the second osmotic virial coefficients B2 , which raised with the increase of temperature. It indicate that increase of temperature causes higher affinity of polysaccharide’s chains to water. It was determined, that the osmotic average molecular mass of the konjac gum in nonpurified solutions increases with temperature (1.07 × 105 –3.80 × 105 g × mol−1 ). Values of the reduced viscosity linearly increased in range 18–29 dL × g for all temperatures. Received values of the Huggins constant (0.81–1.72) lead that water is poor solvent for konjac gum. The theta () conditions were extrapolated for non-purified solutions − 325 K (52 ◦ C), and interpolated for purified solutions − 307 K (34 ◦ C). Based on the results of tests using the dynamic light scattering, the values of two main relaxation times (fast − 0.4–1.8 ms and slow components − 4300–5500 ms) were determined (the Kohlrausch-WilliamsWatts). The obtained autocorrelation functions were characteristic for sol type systems or these which indicate a gel-like structure. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction Konjac, a plant from the genus Amorphophallus, is a perennial plant native to subtropical highlands, mainly of Southeast Asia (Zhang, Xie, & Gan, 2005; Li & Xie, 2006). The main components of the konjac corm are carbohydrates, most notably konjac glucomannan. The concentration levels of this polysaccharide differ depending on the variety (Chua, Baldwin, Hocking, & Chan, 2010). The konjac glucomannan (KGM) is a neutral heteropolysaccharide, with the main chain composed of d-mannose and d-glucose units, linked by a ␤-(1 → 4)-glycosidic bond (Katsuraya, 2003). These units occur in the molar ratio of 1.6:1.0, respectively. In the main chain the acetyl groups, 1 for 19 glucose units, are located at carbon C-6, and the substitution level is at 5–10% (Tatirat, Charoenrein, & Kerr, 2012; Ratcliffe, Williams, English, & Meadows, 2013). The presence of branching and acetyl groups affects the solubility of KGM (Ratcliffe et al., 2013). An increased deacetylation of the KGM chain causes a decreased solubility of the KGM, which is a result of reduced formation of intra- and inter-molecular hydrogen bonds between KGM’s chains (Chen, Li, & Li, 2011). This polysaccharide

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (A. Ptaszek). http://dx.doi.org/10.1016/j.carbpol.2017.06.116 0144-8617/© 2017 Elsevier Ltd. All rights reserved.

exhibits very high ability to absorb water, around 100 g of water/1 g KGM. The polymerisation of KGM, using acrylic acid and acrylamide or kaolin, leads to the creation of superabsorbents, with absorption capabilities significantly increased compared to the originating polysaccharide (Li, Ji, Xia, & Li, 2012). Konjac glucomannan is allowed for use in the food industry in Europe and USA (Tester & Al-Ghazzewi, 2013). It is used as a food additive, where it acts as a thickening and stabilising agent, and is also used as dietary fibre. It is also utilised in the production of low- calorie foods, such as solid beverages, noodles, tofu, jellies and snacks, as well as dietary supplements (Zhao et al., 2015). The physico-chemical characteristics of the KGM solutions haven’t been fully described, mainly due to the difficulty in obtaining easily soluble and well-purified samples (Yoshimura & Nishinari, 1999). The research on this subject covered the production of KGM samples, by means of extraction from konjac flour (Tatirat & Charoenrein, 2011; Chua et al., 2012). The studies of the physico-chemical characteristics of native KGM solutions include the determining of the weight average molecular masses using methods such as gel permeation chromatography (GPC), dynamic light scattering (DLS), as well as intrinsic viscosity (Kishida, Okimasu, & Kamata, 1978; Nishinari, Williams, & Phillips, 1992; Qi, Li, & Zong, 2003; Ratcliffe, Williams, Viebke, & Meadows, 2005). Additionally, the values of critical overlap concentration c* for KGM solutions have also been described. For the extracts

J. Kruk et al. / Carbohydrate Polymers 174 (2017) 456–463

of konjac flour the concentration was 0.29 g × dL−1 (Murakami & Motozato, 1992), while for commercial KGM samples it was 0.08 g × dL−1 (Ratcliffe et al., 2005). The use of light scattering methods in the study of molecular parameters is based on the interpretation of results of measurements carried out in a wide range of biopolymer concentrations, and the angles in which the intensity of light scattered by the biopolymer coils is defined. The test results allow for the determination of the weight average Mw , number average Mn molecular mass, virial coefficients (B2 ), and the gyration radius Rg , and hydrodynamic radius Rh . The literature data indicates that the majority of results obtained for the konjac gum solutions fall outside the scope of the linear correlation between the intensity of light scattered and the value of the scattering vector. This is due to the nature of interactions between the chains and the water solvent. The study by Ratcliffe et al. (2005) presented a comparison of the values of Mw , Mn , and Rg , estimated with the use of non-linear models. Li & Xie (2006) researched the geometry of the konjac gum chains in a water solution with an initial concentration of 1% (w/w), with the addition of 0.2 mol × L−1 NaCl. Their studies also covered the influence of average molecular mass on the conformational properties, and to that effect the konjac gum sample was subjected to controlled hydrolysis. The authors interpreted the results using linear extrapolation in the Zimm plot. They estimated the values of mass average molecular mass (native KGM 1.036 × 105 g × mol−1 ), the second virial coefficient, and the radius of gyration Rg (105 nm) from the linear regression. The determined value A2 = −1.587 × 10−3 mol × mL × g−2 is negative, and, as the authors suggested, requires further studies. The authors observed, that the molecular chains were extending, semi-flexible and a little rigid (Li & Xie, 2006). The biopolymer concentration used in the study was close to overlap c*, which explains the complex behaviour of chains in the solution. Jian, Siu, and Wu (2015), in turn, focused on the influence of pH on the conformational properties of the konjac gum chains. The solution’s pH was controlled using an addition of NaOH or HCl (pH = 4, 7, 9, 10), and the authors presented test results for two concentrations of KGM (0.02 g × dL−1 and 0.05 g × dL−1 , c* = 0.08 g × dL−1 ). In the case of the g × dL−1 solution, the pH increase resulted in a rise of the average molecular mass from 1.318 × 106 g × mol−1 to 2.035 × 106 g × mol−1 and a slight increase of Rg (123.6–129.9 nm). For the solution of 0.05 g × dL−1 the values of B2 have been determined to be positive, apart from the value of B2 for the pH = 10. The authors concluded that KGM remained in random coil conformation in all pH conditions. It follows from the above analysis, that the interpretation of measurement results obtained with the use of DLS/SLS remains open, and could be supplemented by the analysis of classic colligative properties, represented by the osmotic pressure. In research literature, there is an apparent lack of studies concerning osmotic characteristics of the KGM solutions. Moreover, there aren’t many reports on the use of DLS in the studies of hydrodynamic properties of these solutions in the wide range of temperatures and concentrations. The results of osmotic, as well as hydrodynamic studies, can provide valuable data on the properties of KGM chains in water solutions. The aim of this work was to evaluate the impact of temperature on interactions between konjac gum chains and solvent in dilute aqueous solutions using colligative and hydrodynamic methods.

2. Materials and methods 2.1. Materials In this study, a commercial sample of konjac gum was used as ˛ Kolonia, Poland). research material (AGRO-SMAK, Debe

457

2.2. Protein content analysis The protein content in the food-grade konjac gum was determined by the Kjeldahl method, was (1.02 ± 0.01)% (ISO 1871:2009). 2.3. Solutions preparation Aqueous solutions of the konjac gum were prepared in concentrations of 0.0025–0.0200 g × dL−1 . Such range of concentration was chosen because authors want to analyse interactions in dilute solutions (below overlap concentration c*). The samples were prepared in distilled and degassed water, and then shaken at 40 ◦ C for 4 h. After this time, to prevent the development of microorganisms, a solution of 0.01% (w/w) sodium azide was added to the samples. The prepared solutions were left for 24 h. After that time, the solutions were centrifuged (5000 rpm (2683 × g), time 10 min, temp. 23 ◦ C), in order to separate the non-soluble fractions of the research material. The prepared solutions were then used to study the colligative properties, intrinsic viscosity, and DLS measurements (day-1). Additionally, after subsequent 24 (day-2) and 48 h (day-4) storage of the solutions in 23 ◦ C temperature, they were again used in DLS and osmotic measurements. 2.4. Purification of konjac gum solutions (deproteinization) The konjac gum solutions were deproteinised with the use of the Carrez I and Carrez II solutions (Goycoolea & Chronakis, 1998; Borromei et al., 2009; Culhaoglu, Zheng, Méchin, & Baumberger, 2011). For this purpose, samples with concentration levels 10 times higher than unpurified solutions were prepared, according to the procedure described above. After 24 h, and centrifuging of the undissolved fractions, the following methodology was applied: 25 mL of the solution and 25 mL of distilled water were measured into a 250 mL volumetric flask, then 2.5 mL of the Carrez I solution was added, the flask contents were mixed and set aside for 5 min. After that time 2 mL of the Carrez II solution were mixed in, and filled up with distilled water to the volume of 250 mL. After 15 min, the solution was filtered through a fluted filter into a dry container. 2.5. Molecular characteristic of the konjac gum − determination of the molecular mass distribution The measurements of the distribution of molecular masses were performed by means of gel permeation chromatography (GPC), using a system of two columns: Ultrahydrogel-2000 and Ultrahydrogel-500 (Waters, USA), connected in a series with an RI detector (Knauer, Germany). A solution of 0.1 mol × L−1 NaNO3 and 0.02% NaN3 in water was applied as an eluent. Flow rate was set to 0.6 mL × min−1 and a sample volume of 100 mL was injected. The sample concentration was ca. 5 mg × mL−1 . Calibration was performed using pullulan standards (Shodex, Japan) (Lukasiewicz, Bednarz, & Ptaszek, 2011). The following values were obtained for the konjac gum chains: weighted molecular mass Mw = 9.9 × 105 g × mol−1 , number molecular mass Mn = 6.2 × 105 g × mol−1 , polydispersity 1.6. 2.6. Measurements of osmotic pressure () All the prepared solutions were subjected to the measurements of osmotic pressure at temperatures ranging from 303 K (30 ◦ C) to 313 K (40 ◦ C), at temperature increase intervals of 2 K. The temperature control accuracy for the osmotic pressure was 0.1 K. The measurements were carried out using a membrane osmometer OSMOMAT 090 (Gonotec, Berlin, Germany) utilising a membrane with cut-off value of 10 000 g × mol−1 . For all tested samples the measurements were done in four repetitions. The obtained results

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were subject to analysis involving the estimation of parameters of the osmotic equation of state:  RT · [1 + B2 (T ) · c + B3 (T ) · c 2 + B4 (T ) · c 3 ] = c MW

(1)

In this equation, c is the concentration of the dissolved substance, MW is the average osmotic molecular mass and B2 (T ), B3 (T ) and B4 (T ) are the osmotic virial coefficients. All calculations were carried out using the nonlinear algorithm of Marquardt-Levenberg. The target function was formulated as:

 N

2M−L |osm =

jı cj



−

ˆj 

cj



→

2

min

(2)

MW >0,B2 (T ),B3 (T ),B4 (T )

j=1

where

ı j

cj

are values of experimental osmotic pressure and

ˆj  cj were

calculated from Eq. (1). 2.7. Measurements of viscosity and determination of intrinsic viscosity [] Solutions of konjac gum of similar concentrations as in the above-mentioned osmometric tests, were subject to viscosity measurements using a system consisting of Ubbelohde viscometer (SI Analytics, Germany) with a capillary constant (K) of 0.005 mm2 × s−2 , electronic clock ViscoClock, (SI Analytics, Mainz, Germany) and a water bath (CT52, SI Analytics, Mainz, Germany) with temperature control accuracy 0.01 K. The measurements were carried out in the range of temperatures from 30 ◦ C to 50 ◦ C, with the interval temperature increase of 2 K. The viscosity␩ of the solutions was calculated using the capillary constant (K). As the first step (Macosko, 1994), the specific viscosity ␩sp was calculated according to the Eq. (3a): sp =

 − sol  = −1 sol sol

(3a)

where sol is the viscosity of water. The second step was to introduce the reduced viscosity, red , independent of the polysaccharides’ concentration, c: red =

sp c

(3b)

The concentration c is given in g × dL−1 . The method of analysis was based on determining the intrinsic viscosity [] and Huggins constant KH from the equation (Macosko, 1994): red =

sp = [] + KH · []2 · c c

(3c)

All calculations were carried out using the nonlinear minimization algorithm of Marquardt-Levenberg: 2M−L |vis =

N  

ıj,red −  ˆj

j=1

2

→

KH ,[]>0

min

(4)

where ıj,red are values of experimental reduced viscosity and  ˆj were calculated from Eq. (3c). 2.8. Dynamic light scattering measurements (DLS) Dynamic light scattering measurements were carried out at 30 ◦ C and 40 ◦ C on a Brookhaven DLS/SLS BI-160 goniometer with digital autocorrelator BI-9000AT (Brookhaven, New York, USA). A solid-state laser (JDSU, CDPS532M-050) with output power of 50 mW at ␭ = 532 nm was used as the source of light. The studies of the solutions’ properties were performed at the scattering angle of 90◦ . The time–average intensity correlation functions g 2 () − 1 were obtained with an acquisition time of 300 s for each run, with

the help of 9KDLSW − Brookhaven Instruments Dynamic Light Scattering Software version 2.15. The obtained time dependence can be described by a following Kohlrausch-Williams-Watts (KWW) stretched exponential function (Shibayama, Tsujimoto, & Ikkai, 2000):

 g 2 () − 1 ≈

 A · exp

−

 f



 ˇ  2 

+ (1 − A) · exp −

s

(5)

where  f and  s are relaxation times of the fast and slow components (s), ˇ is the exponent of the stretched exponential, and ␶ is the delay time. A and (1-A) represent the fractional contribution of the two processes. The Marquardt-Levenberg method was applied as the minimization algorithm to estimate Eq. (5) parameters using the least squares method. Hydrodynamic radius Rh represents the radius of a sphere delineating the macromolecule’s chain, whose capability of movement in the solution is described by the value of diffusion coefficient D. The values of translational diffusion coefficient Df of fast components, and Ds of slow components, can be obtained from equation: Df =

1 f · q2

(6a)

Ds =

1 s · q2

(6b)

where q =

4·n 

· sin

 2

is the value of magnitude of the

scattering wave vector. The hydrodynamic radius for fast components can be calculated according to the Stokes-Einstein equation: Rh =

kB · T 6 · sol · Df

(7)

where kB is the Boltzmann constant, T is the absolute temperature in Kelvin, ␩sol is the water viscosity at temperature T. 3. Results The value of the reduced osmotic pressure for non-purified solutions decreased in the function of the polysaccharide’s concentration; moreover, the correlation is strongly non-linear (Fig. 1a). In the case of measurements done in lower temperatures of 30–34 ◦ C, the values of reduced pressure are the highest, in the range of 125–250 mmH2 O/(g × dL−1 ) for the lowest sample concentration (Fig. 1a). These values indicate good water-absorption capabilities of these solutions. The temperature increase causes a visible decrease of the c value. This behaviour indicates that the rise of temperature does not increase the konjac gum chains’ affinity to water and is not conductive to the water retention by the solution. This observation is also reflected in the correlation of the second osmotic virial coefficient to temperature (Table 1, non-purified). The values of B2 are negative. This could indicate the presence of two phenomena: a small affinity of konjac gum chains to the water solvent, or aggregation of polysaccharide’s chains. The extrapolation of the reduced osmotic pressure to zero konjac gum concentration allowed for the determination of the osmotic average molecular mass MW (Table 1, non-purified). The lowest osmotic average molecular masses were obtained at lower temperatures (30–34 ◦ C). In-depth analysis of the osmotic tests results (30 ◦ C–40 ◦ C) indicates an increase of MW in the function of temperature, but this correlation is highly non-linear. A visible increase of the osmotic average molecular mass could be a result of the chain aggregation, which is caused by the limited solubility in water. Contrary behaviour was observed in the case of solutions subjected previously to the purification (deproteinization) (Fig. 1b). The analysis of the changes of reduced osmotic pressure in the

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459

Fig. 1. a) Reduced osmotic pressure as a function of non-purified konjac gum solutions’ concentration at temperature range 30–40 ◦ C with increase intervals of 2 K, b) Reduced osmotic pressure as a function of purified konjac gum solutions’ concentration at temperature range 30–40 ◦ C with increase intervals of 2 K.

Table 1 Osmotic average molecular masses MW , second osmotic virial coefficients B2 (Eq. (1)) compared with Huggins coefficient KH and intrinsic viscosity [␩] from (Eq. (3c)). The goodness of nonlinear model (Eq. (1)) fitting to experimental data was presented as 2M−L |osm . purified ◦

non-purified

T, K ( C)

MW × 10 g mol

303 (30) 305 (32) 307 (34) 309 (36) 311 (38) 313 (40) 323 (50)

15.57 ± 1.78 0.68 ± 0.07 0.60 ± 0.03 0.61 ± 0.03 1.32 ± 0.07 0.66 ± 0.03 –

a

5

−1

−4

B2 × 10

3

cm mol

−2.13 ± 0.91 −1.71 ± 0.63 0.52 ± 0.06 1.31 ± 0.30 2.45 ± 0.66 3.39 ± 0.38 –

−1

−2

g

2M−L |osm

MW × 105 g mol−1

B2 × 10−4 cm3 mol−1 g−2

2M−L |osm

KH –

[␩]a g dL−1

668.84 441.95 152.94 58.59 178.74 18.70 –

1.07 ± 0.05 1.04 ± 0.05 1.63 ± 0.12 2.62 ± 0.08 3.31 ± 0.06 3.80 ± 0.07 –

−6.10 ± 0.09 −5.40 ± 0.38 −4.33 ± 0.42 −4.03 ± 0.39 −4.28 ± 0.31 −3.08 ± 0.43 –

27.59 553.76 142.11 18.16 14.46 25.31 –

1.72 ± 0.22 – – 1.34 ± 0.13 – 1.08 ± 0.15 0.81 ± 0.06

17.88 ± 0.54 – – 18.23 ± 0.36 – 19.47 ± 0.97 20.83 ± 0.42

1.1 < sp < 2.0.

function of concentration indicates that the increase of the polysaccharides’ concentration implies an increase of c . It is also worth noteworthy, that in comparison to non-deproteinized solutions, the reduced osmotic pressure assumes decidedly higher values: in the range 200–600 mmH2 O/(g × dL−1 ). Data obtained for 30 ◦ C is an exception − the reduced osmotic pressure increases from 20 to 160 mmH2 O/(g × dL−1 ). The analysis of the change of B2 in the function of temperature (Table 1, purified) clearly indicates an increase of this parameter’s value with the rise of temperature. In the first two temperatures, B2 assumes negative values, at 34 ◦ C the second virial coefficient becomes positive and its value increases until it reaches 3.39 × 10−4 cm3 × mol × g−2 at 40 ◦ C. The measurements of the reduced viscosity ␩red of the nonpurified (Fig. 2) aqueous solutions of konjac gum indicate a visible linear increase of reduced viscosity corresponding to the increase of polysaccharide concentration. At the concentration of 0.0025 g × dL−1 the highest value of ␩red was observed in relation to the 50 ◦ C temperature, and the lowest for 30 ◦ C. For the 0.0075 g × dL−1 concentration, the smallest differences in values for this parameter were noted for the 30, 40, and 50 ◦ C temperatures. In the range of concentrations from 0.01 to 0.02 g × dL−1 the reduced viscosity assumes the highest values for 30 ◦ C temperature, and the lowest at 50 ◦ C. The concentrations of the solutions did not exceed 0.03 g × dL−1 < c*, and therefore the tests described in this study were done in dilute solution conditions (Ratcliffe et al., 2005). The fitting of the Huggins model to the test data, allowed for the estimation of the value of intrinsic viscosity (Table 1). It is at the 17–20 dL × g−1 level, and its values are consistent with the test results of other researchers (Cheng, AbdKarim, & Seow, 2007; Gao & Nishinari, 2004; Kishida et al., 1978; Kök, Abdelhameed, Ang, Morris, & Harding, 2009; Li & Xie, 2006; Liu et al., 2015; Lu, Zhang, Zhang, & Zhou, 2003; Luo, He, & Lin, 2013; Prawitwong, Takigami,

& Phillips, 2007; Ratcliffe et al., 2005; Tatirat et al., 2012; Yang et al., 1998; Yoshimura & Nishinari, 1999; Yang, Wang, Nakajima, Nishinari, & Brenner, 2013). Kishida et al. (1978) studied the properties of konjac flour solutions, as well as its hydrolysates and, depending on the weight average molecular weight, obtained data in the range of 4.6–18.8 dL × g−1 . The Ratcliffe et al. (2005) study collated the values of intrinsic viscosity estimated for commercial grade KGM, which, depending on the tested sample, varied in the range of 17.2–20.0 dL × g−1 . The values of the intrinsic viscosity described in our study are consistent with the range described in study literature (Table 1). The changes in the intrinsic viscosity caused by the temperature increase are non-linear. An increase of the intrinsic viscosity corresponding to the rise of temperature can be clearly observed. These values are determined by the interactions in the polymer-solvent system and define the conformation and size of the polysaccharide chains in the solution. The Huggins constant assumes values of 1.72 at 30 ◦ C and 0.81 at 50 ◦ C. The values of KH > 1 indicate, that water is a poor solvent for konjac gum. The reversed correlation between the Huggins coefficient and temperature (Table 1) indicates, that the temperature increase changes the biopolymer-solvent interactions. These observations were confirmed by the results of the DLS tests (Fig. 3a-b). The course of the g 2 () − 1 dependency on relaxation time ␶ indicates the presence of macromolecular compounds in the solution. In the range of long relaxation times (105 –107 ␮s), the autocorrelation function does not disappear (Fig. 3a-b). Moreover the autocorrelation functions show a bimodal character. Due to specific character of autocorrelation functions, it was impossible in this case, to apply CONTIN to determine the distribution of chain sizes and values of the diffusion coefficient, similarly to the studies on xanthan gum (Rodd, Dunstan, & Boger, 2000). This behaviour is

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Fig. 2. Dependence of reduced viscosity of non-purified konjac gum solutions’ concentration.

Fig. 3. Time-intensity correlation function for konjac gum water solutions after 24 h at a) 30 ◦ C and b) 40 ◦ C.

specific for solutions of synthetic polymers (Fang, Brown, & Konak, 1991; Ngai, Wu, & Chen, 2004; Liu, Gao, & Oppermann, 2006). The autocorrelation function is characteristic of ‘sol’ type systems (Shibayama et al., 2000), as well as solutions of xanthan gum (Rodd et al., 2000) − which forms a gel-like structure (Viebke, 2005). In both these cases, in the long relaxation time range (>100 s), a nondiminishing autocorrelation function can be observed. The course of the autocorrelation function allows however for the estimation of these solutions’ properties. Mathematical analysis requires the use of KWW equation to the test data. Based on two main relaxation times:  f for fast components and  s for slow components, the diffusion coefficients D and hydrodynamic radii Rh were calculated (Table 2). In the case of test data obtained at 30 ◦ C, the relaxation times of the fast components are around 0.4–1.8 ms, while relaxation times of the slow components are much longer, around few seconds. The values of the diffusion coefficient Df , determined for all solutions tested 24 h after preparation, in 30 ◦ C and 40 ◦ C, fall within the range from 0.5 × 10−12 m2 /s to 2 × 10−12 m2 /s, and are similar to the ones presented in the study by Ratcliffe et al. (2005). Their dependency on the biopolymers’ concentration can be considered as linear, and it is possible to extrapolate the value of

Df to the null concentration of konjac gum in the solution. The values of Df corresponding to the infinite dilution of the tested solutions are presented in Table 2. For the temperature of 30 ◦ C the obtained value was 1.91 × 10−12 m2 /s, while at 40 ◦ C it was 1.67 × 10−12 m2 /s. The storage of the solutions in ambient temperature conditions affected the relaxation behaviours (Table 2). The values of the diffusion coefficients for fast modes increased significantly, as did the share of the fast relaxation behaviours (90%). The analysis of the autocorrelation function, and the values of the KKW equation coefficients as a result, indicates a presence of slow relaxation phenomena, represented by slow relaxation times. The values of the diffusion coefficient for the slow modes are practically independent from the biopolimer’s concentration, and their average values are presented in Table 2. The share of behaviours of the ‘slow’ type is visible for samples tested on the first day (40–50%) and decreases to 10% during the storage of the solutions. It can therefore be concluded, that the relaxation phenomena in the konjac gum solutions are primarily shaped by the fast relaxation processes and can be represented with the use of fast mode relaxation times. Determination of the values of fast mode diffusion coefficients enables the calculation of the average hydrodynamic radius value for each of the studied solutions (Fig. 4). As demonstrated, an

J. Kruk et al. / Carbohydrate Polymers 174 (2017) 456–463

461

Table 2 Diffusion coefficients for fast (Eq. (6a)) and slow (Eq. (6b)) components and hydrodynamic radii (Eq. (7)). These values were obtained on the basis of relaxation times ␶f and ␶s estimated from KWW model (Eq. (5)). T, K (◦ C)

A

Fast modes  f ms

298 (25) 303 (30)

313 (40)

a

day-1 day-2 day-4 day-1 day-2 day-4

– 0.6 ± 0.1 0.9 ± 0.1 0.9 ± 0.1 0.5 ± 0.1 0.9 ± 0.1 0.9 ± 0.1

– 1.6(±5%) 0.6(±7%) 0.6(±7%) 1.8(±5%) 0.4(±8%) 0.4(±8%)

Slow modes Df × 10−12 m2 s−1 a

1.53 1.91 5.34 5.34 1.67 8.77 8.75

Rh nm a

144 146 52 52 176 37 38

 s ms

Ds × 10−16 m2 s−1

– 5500(±5%) 5100(±6%) 5100(±6%) 4300(±3%) 5300(±5%) 5300(±5%)

– 6.30 5.96 5.96 7.07 5.77 5.77

Ratcliffe et al. (2005).

Fig. 4. Changes in hydrodynamic radii (Rh ) with concentration of non-purified konjac gum solutions.

increase in the konjac gum concentration causes and increase of the average hydrodynamic radius. Such behaviour is typical for diluted solutions (c < c*). Extrapolation of the Rh value to null concentration enables the determination of the hydrodynamic radius value at the dilution tending to infinity (Table 2). The chains of konjac gum present in the solutions stored for 24 h are characterised by the hydrodynamic radius of 146 nm in 30 ◦ C and 176 nm in 40 ◦ C. The values of Rh obtained with the use of the KKW equation parameters are consistent with the findings presented in the study by Ratcliffe et al. (2005), which had been obtained for solutions tested at 25 ◦ C, using the CONTIN program. In the case of solutions stored for over 24 h, a reduction of the Rh radius value was observed: 52 nm for 30 ◦ C and 38 nm for 40 ◦ C. This suggests that over time the hydrodynamic radius of the chains decreases, most probably due to an occurrence of two events. The first might be related to the collapse of the chains caused by water being squeezed out, and the second could be due to the precipitation of aggregates in the solution due to “hyperentanglements”. The presence of these aggregates is confirmed by visual observations of the behaviours of stored solutions (increasing sedimentation over time), as well as long relaxation on times determined with the use of KKW model. The values of slow mode times are in the range of 4000–5000 ms. The share of the slow processes is the highest on the first day after solution preparation, and is a result of the fact that the autocorrelation function does not disappear in time. The above observations lead to a conclusion, that the solution undergoes aging. The aggregates are precipitated from the solution,

and only the chains of shorter lengths remain. The course of the autocorrelation function obtained in day-2 and day-4 confirmed the disappearance of the slow relaxation processes, which was reflected in the increasing values of the fast mode shares from 50% to 90%. Above mentioned observation might be caused by the fact that larger chains of konjac gum creates “hyperentanglements” and because water is a weak solvent (KH value above 1) for this polymer, the water is squeezed out and these larger aggregates sediment. Furthermore, Rh values indicate the thermodynamic equilibrium in solution. Based on results obtaining by Picout, Ross-Murphy, Jumel, and Harding (2002) and Chen et al. (2011) aggregation and precipitation are strongly connected with existence of long segments of unsubstituted mannans which are vulnerable to aggregation with other comparable segments in solution.

4. Discussion The two relaxation times obtained for the konjac gum solution (fast and slow components) are not an exception when it comes to the behaviours of polymer solutions. Similar observations relate to the cross-linking of synthetic polymers in sol state, where relaxation times observed for the fast and slow components were, respectively, in the range of 0.05–0.5 ms and 55–500 ms (Ngai et al., 2004), as well as 0.02–0.04 ms and 0.5–2 ms, respectively (Liu et al., 2006). In our studies the ␶s values for slow components are in the range of 400–600 ms and correspond to a behaviour typical of chain cross-linking in a solution (Ngai et al., 2004). The mix-

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Fig. 5. Changes in reduced osmotic pressure over time, dependence of konjac gum concentration. In the case of storage solutions (day-2, day-4) the range of solutions’ real concentration is differ. It is due to the observation of precipitation and sedimentation process of konjac gum chains in the event of concentrations lower than 0.005 and above 0.01 g × dL−1 , b) Second virial coefficient (B2 ) and Huggins constant (Kh ) as a function of temperature.

ture contains chains with a high diffusion coefficient (Df ), and their relaxation rate determines the properties of konjac gum solutions. Over time, an increase of the values of diffusion coefficients can be observed, which indicates a decrease in the chains’ hydrodynamic radius (Table 2). The analysis of osmotic properties of unpurified konjac gum samples allowed us to identify the cause of this phenomenon. It is presented here on the graph illustrating the relation of reduced osmotic pressure at 30 ◦ C and the concentration (Fig. 5a), in the function of storage time. For the stored solutions (day-2 and day4) the osmotic pressure is significantly lower, which confirms the above-mentioned collapse phenomenon, caused by the water being squeezed out from the chains. The above considerations show that initially (day-1) konjac gum chains have greater hydration capacity than in day-2, and even more day-4. These observations confirm the values of Rh , hydrodynamic radius, which over time decreases. Between 2 and 4 days there is no equality in this parameter, so a thermodynamic equilibrium has been established. The values of the second virial coefficient, obtained from Eq. (1) using data presented on Fig. 5a, are neg(−4.48 × 10−4 cm3 × mol−1 × g−2 for day-2 and ative −2.91 × 10−4 cm3 × mol−1 × g−2 for day-4). The average osmotic molecular masses, estimated based on the extrapolation to zero concentration (Eq. (1)), were: 1.23 × 105 g × mol−1 for day-2 and 2.06 × 105 g × mol−1 for day-4. In contrast, the increase of Rh value is caused by stronger interactions between chains and reduction of distances between them (Fig. 4). With an increase of the biopolymer’s concentration in the solution, the elasticity of the chains decreases and they are unable to swell (Teraoka, 2002), and results in the observed decrease of the value of ␲. In the case of samples devoid of protein (Fig. 1b) the capability for water absorption is decidedly higher (higher values of ␲). The influence of temperature on the colligative and hydrodynamic properties is complex and could be related to the presence of protein in the solution (Fig. 5b). The reduced osmotic pressure of the unpurified solutions is significantly lower, and the rise of the temperature does not positively impact on the water absorption capability of the biopolymer chains. Moreover, high values of the average osmotic molecular masses determined for the non-purified solutions suggest the creation of aggregates or complexes with proteins. The second virial coefficients’ values increases as a function of temperature (Fig. 5b). This tendency is consistent with the observations derived from the viscosity measurements −the values of KH decrease with an increase of temperature, but their value is higher than one (Fig. 5b). From the course of the KH (T) function it follows that the limit value of temperature at which the Huggins coefficient

becomes less than one is ca. 317 K (44 ◦ C). Also the temperature, extrapolated from the dependency of the second virial coefficient as a function of temperature, in which B2 > 0 (Fig. 5b), was 325 K (52 ◦ C). This temperature defines the theta () conditions, it means that polymer chain don’t interact with solvent and other chains (Teraoka, 2002). Similar situation took place for purified konjac gum solutions, but in these case value of the theta temperature was interpolated and was 307 K (34 ◦ C). This could indicate, that the rise of temperature weakens the polymer–polymer interaction, for the benefit of the interaction between konjac gum and water. This interpretation can be supported by the low substitution level of KGM chains (Davé & McCarthy, 1997; Nishinari et al., 1992; Picout et al., 2002). Above mentioned behaviours were also observed for other glucomannans (Picout et al., 2002). Our results suggest that a description of the interactions between molecules using “hyperentanglements” (Ratcliffe et al., 2005) might be appropriate.

5. Conclusions The information received using colligative and hydrodynamic methods allowed to obtainment entire notion of konjac gum’s interactions in water dilute solutions. Osmotic measurements allowed to estimate a theta conditions for purified and non-purified konjac gum solutions. Below theta condition (negative values of second virial coefficient) for purified solutions aggregation was observed. This fact manifested increasing of hydrodynamic radii (Rh ). The studies carried out indicate an occurrence of two phenomena in the konjac gum solutions. The first involves the tendency of the konjac gum chains to aggregate, confirmed by the results of osmotic measurements. Secondly, the values of the second virial coefficient are negative, and the temperature rise causes an increase of the osmotic average molecular mass. Results of osmotic measurements for non-purified konjac gum solutions showed that its colligative properties should be studied in the wider range of temperature, even more than 325 K (52 ◦ C), so it could be a starting point for the future studies.

Acknowledgments The study on osmotic properties was financed by the Polish Ministry of Science and Higher Education of the Republic of Poland as the programme BM-4766/KIAPS/2014 for Young Scientists in 2014. The DLS research properties was financed by the Polish Ministry of Science and Higher Education of the Republic of Poland as the programme BM-4786/KIAPS/2015 for Young Scientists in 2015.

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