Analysis of rheological properties of food macromolecules at infinitely diluted and fixed high concentrations in aqueous NaCl solutions

Abstract

The viscometric parameters intrinsic viscosity [η] and apparent viscosity η^a_H, and several derived parameters, were compared for food macromolecules in water and aqueous NaCl solutions. On dilution of the macromolecules, the [η] values of polyelectrolytes were more strongly dependent on the NaCl concentration than were those of non-polyelectrolytes. At a fixed high concentration of macromolecules, the η^a_H of almost all macromolecules was barely affected by NaCl. However, the η^a_Hvalue of xanthan increased with the NaCl concentration. The activation energy of η^a_Hwas lower in xanthan solutions containing various NaCl concentrations, implying that xanthan is thermally stable. Considering other various viscometric parameters, the rheological properties of food macromolecules were classified into four groups, which were partly based on their approximate molecular weights.

Introduction

Interactions between hydrocolloids and solvent/co-solutes are the predominant factors determining their functional properties in food systems (Amini and Razavi, 2012; Yousefi et al., 2014). Intermacromolecular interactions are affected by the coexistence of low-molecular-weight (M_w) substances (Sato et al., 2004; Sato and Miyawaki, 2008). The viscosity of a macromolecule solution containing a co-solute is influenced by various types of intermolecular interactions, but mainly by intermacromolecular interactions (Sato and Miyawaki, 2008), which are in turn affected by electrostatic effects, hydrogen bonding, and hydrophobic interactions. Electrostatic effects are exerted through changes in ionic strength (Sato et al., 2004), whereas changes in viscosity in the presence of NaCl are caused by changes in macromolecule conformation (Wyatt et al., 2011).

The effects of NaCl concentration on intrinsic viscosity [η] have been investigated in various polysaccharides; for example, a study of the molecular properties of cress seed gum macromolecules in various aqueous solutions compared the [η] values in 0–0.1 mol/L NaCl solutions, and found reductions in [η], even in sucrose solutions (Behrouzian et al., 2014). Pectin gels were also influenced by non-covalent forces, as they dissociated into macromolecular subunits in a 0.05 mol/L NaCl solvent (Fishman et al., 1993). Another study reported no systematic changes in [η] for mesquite gum in solutions containing 0.05–2.0 mol/L NaCl (Goycoolea et al., 1995). A study also compared the [η] values of several synthesized polyelectrolytes in solutions containing 0–5.0 mol/L NaCl (Pavlov et al., 2013). The [η] values of sage seed gum in 0–0.2 mol/L NaCl at 25 °C were reduced by 20–30% at this temperature, according to the Huggins and Kraemer equations (Yousef et al., 2014), and the [η] of balangu seed gum decreased in solutions with increasing NaCl concentration (Amini and Razavi, 2012). The [η] of xanthan gum in a 0.3 mol/L NaCl solution decreased compared to that in water (Southwick et al., 1982). The [η] values of chitosan, pectin, and alginate in < 0.8 mol/L NaCl solutions have also been compared (Abododinar et al., 2014).

It has been suggested that the [η] value is a suitable parameter for comparing polymeric materials with similar M_w. Otherwise, its use has been restricted to comparing series of macromolecules with similar repeating chains, such as comparing [η] among xanthan gums (Sato et al., 1984a; Sho et al., 1986). In this study, [η] values were used to compare the viscosity behaviors of various macromolecules, electrolytes, and non-electrolytes in aqueous NaCl solutions.

A previous study used viscometric techniques to compare the physical properties of various macromolecules in water and in aqueous sucrose solutions (Sato and Miyawaki, 2012). The effects of salts on molecular conformation and solution rheology have been explored mainly in ionic hydrocolloids such as xanthan, whereas those of non-ionic hydrocolloids such as guar gum remain poorly understood (Samutsri and Suphanthrika, 2012). Most studies that examined the differences in properties between polyelectrolytes and neutral polymers have focused on polymers in dilute or semi-dilute solutions (Wyatt et al., 2011).

In this study, we investigated the effects of NaCl concentration on the viscosity of solutions of macromolecules with different M_w and different active charge groups. We compared the intermacromolecular interactions among different macromolecules, electrolytes, and non-electrolytes in various NaCl solutions at both infinite dilutions and at fixed high concentrations.Text, Body

Materials and Methods

Materials    Polyethylene glycol 35000 (PEG35000; M_w = 37 407) (Bertoluzzo et al., 2007) was purchased from Merck (Tokyo, Japan) and dextran T40 (DexT40; M_w = 36 163) (Sidebotham, 1974; Aquino and Franco, 2009) was purchased from GE Healthcare (Tokyo, Japan). Xanthan gum (Bradshaw et al., 1983; Jansson et al., 1975; Tomofuji et al., 2022), apple and citrus pectins (Kar and Arslan, 1999a; Kjøniksen et al., 2005), low-viscosity sodium alginate (Gomez et al., 2009), guar gum (Barth and Smith, 1981; Vijayendran and Bone, 1984), and locust bean gum (Barak and Mudgil, 2014) were purchased from Sigma-Aldrich (St. Louis, MO, USA). The galacturonic acid and methoxyl contents of the citrus pectin were 79.5% and 8.1%, respectively, with a degree of esterification (DE) of 57.9%, according to technical data provided with the product; those for apple pectin were 79.0% and 8.7%, respectively (DE = 62.1%) (Sato et al., 2004). These pectins are classified as high-methoxyl pectins (Glenn, 1953). We calculated the mannuronic acid to galacturonic acid ratio of sodium alginate as 1.3 using a simple chemical method involving partial hydrolysis with an acid (Haung et al., 1974). The non-electrolytes used in this study, except PEG35000 and DexT40, were guar gum and locust bean gum, which were selected based on the dimensions of the macromolecules and were obtained from Sigma. All reagents used in this study were of reagent grade and were used without further purification. Water content was analyzed by oven drying at 110–120 °C for accurate concentration calculations that were performed in duplicate.

Intrinsic viscosity measurements in macromolecule solutions with various NaCl concentrations    The concentrations of diluted macromolecule solutions were adjusted to 0.1–0.3 g/L with 10⁻⁵ to 10⁻¹ mol/L NaCl solutions. The viscosity η_H was measured at 25 °C using a Cannon-Fenske capillary viscometer (Sibata Scientific Technology, Souka, Japan) and a density meter (DMA4500; Anton Paar, Graz, Austria). The efflux times of solvents and macromolecular solutions were measured in triplicate and averaged (Samutsri and Suphanthrika, 2012) using the arithmetic mean.

To obtain [η], several equations have been proposed (Abododinar et al., 2014; Huggins, 1942; Kontogiorgos et al., 2012; Khouryieh et al., 2006; Kraemer, 1938; Launay et al., 1997; Lin and Lai, 2009; Migliori et al., 2010; Samutsri and Suphatharika, 2012; Sato and Miyawaki, 2012; Tanglertpaibul and Rao, 1987; Vahid et al., 2011; Yousefi et al., 2014). First, [η] was determined according to the Huggins equation (Huggins, 1942), as follows:   

  

Next, the Kraemer equation (Kraemer, 1938) was used to compare [η] between water and various NaCl solutions, as follows:   

  

where, η_w is the viscosity of water, C is the macromolecule concentration, k is the Huggins constant (Abododinar et al., 2014; Huggins, 1942; Khouryieh et al., 2006; Kontogiorgos et al., 2012; Launay et al., 1997; Lin and Lai, 2009; Migliori et al., 2010; Samutsri and Suphatharika, 2012; Sato and Miyawaki, 2012; Tanglertpaibul and Rao, 1987; Vahid et al., 2011; Yousefi et al., 2014), and k′ is the Kraemer constant (Abododinar et al., 2014; Khouryieh et al., 2006; Kraemer, 1938; Migliori et al., 2010; Sato and Miyawaki, 2012; Tanglertpaibul and Rao, 1987; Vahid et al., 2011; Yousefi et al., 2014).

Intrinsic viscosity [η] is a measure of the hydrodynamic volume occupied by a macromolecule (Khouryieh et al., 2006; Lin and Lai, 2009), and it varies with the M_w of the macromolecule (Sato and Miyawaki, 2012; Tanglertpaibul and Rao, 1987). In the case of xanthan, although [η] does not reflect the size and conformation of a single molecule due to the fraction of insoluble polymer or microgel in aqueous solutions (Merino-González and Kozina, 2017), it provides an indication of the average characteristic volume of a substance.

The [η] in aqueous NaCl solutions of various concentrations, [η]_i, was measured, and the relation between [η]_i and the reciprocal square root of ion strength, I^−1/2, was investigated. The original definition of ion strength, I, is 1/2Σm_i z_i², where m_i is the concentration (molality) and z_i is the number of charges on the ion (Chang, 2000). However, the concentration can also be expressed as molarity, which results in approximately equal values of I in dilute solutions (Zhou, 2016). Therefore, we used molarity units in this study. For NaCl in water, I = m_i, because z_i² = 1.

The parameters Slope^L and SD^L were estimated using the viscosities at 0.05 wt % of the macromolecule in aqueous NaCl solutions. Slope^L is the slope of the linear regression line between η_Li, i = 0, 0.01, and 0.1, and the NaCl concentration (mol/L). SD^L was determined using the following equation of standard deviation:   

where, η_Li is the viscosity of 0.05 wt % macromolecule in aqueous NaCl solutions at 25 °C, and η_Lmean is the arithmetic mean of η_Li.

Measurement of apparent viscosity at a fixed high macromolecule concentration    Powders containing each macromolecule were suspended and dissolved in aqueous NaCl solutions at 50 °C. The macromolecule concentrations were fixed at 10 wt % for PEG35000 and DexT40 due to their low apparent viscosity, and at 0.5 wt % for guar gum, locust bean gum, and xanthan due to their high apparent viscosity. To compare the viscosities of these solutions at the same macromolecule concentration, we also prepared 2 wt % macromolecular aqueous solutions of both PEG35000 and DexT40 for viscosity measurements using a Cannon-Fenske capillary viscometer. The concentrations of citrus pectin, apple pectin, and sodium alginate were fixed at 2 wt %. The prepared sample solutions were stored overnight at 50 °C until use. For all macromolecules, the temperature and incubation time were fixed to avoid degradation; for example, citrus pectin degrades upon heating, resulting in decreased M_w (Diaz et al., 2007). We poured 7 mL of each sample solution into the cell of a rotational viscometer (B8L; Tokimec, Tokyo, Japan) with rotational speeds of 0.5–100 rpm at 25 °C. The apparent viscosity (η^a_H) was measured at a shear rate of 16.8 s⁻¹. When η^a_Hcould not be measured at a shear rate of 16.8 s⁻¹ (Sato and Miyawaki, 2012), it was estimated using a power law model, as follows:   

where, m is the consistency coefficient and n is the flow behavior index. Eq. 6 was adapted for non-Newtonian fluids.

Macromolecule solutions at fixed high concentrations contained 0.5–2 g of the macromolecule, 0–0.6 g of NaCl, and 100 g of water, for a final concentration of 2 wt % wherever possible. Macromolecules with M_w > 10⁶ were conventionally fixed at 0.5 wt % due to their water solubility.

The parameters Slope^H and SD^H were also estimated using the same measurement as for the parameters Slope^L and SD^L, but using the apparent viscosities η^a_Hin aqueous NaCl solutions at a shear rate of 18.6 s⁻¹ instead of η_Li.

Determination of the activation energy of apparent viscosity for macromolecules in NaCl solutions    The activation energy E_a of η^a_H in NaCl solutions at 5–40 °C was determined using the Arrhenius equation (Busch et al., 2018; Karataş and Arslan, 2016) or an Arrhenius-type equation (Kar and Arslan, 1999b; Sato and Miyawaki, 2012), as follows:   

where, η₀ is a pre-exponential factor (mPa·s), R is a gas constant (= 8.3145 J/mol/K), and T is the absolute temperature (K). The effect of temperature on viscosity is generally expressed by the Arrhenius (Arrhenius, 1889) and Andrade (Andrade, 1930) equations (Karataş and Arslan, 2016).

The viscosities of PEG35000 and DexT40 at 2 wt % of the macromolecule were calculated from the dynamic viscosity measured using the capillary viscometer and density meter, rather than by η^a_H.

Results and Discussion

Intrinsic viscosity of macromolecules in aqueous NaCl solutions    The reduced viscosity of a solution in an infinitely diluted state is represented by [η], at which macromolecules in solution are isolated from one another with negligible intermolecular interaction (Sato and Miyawaki, 2012). Although several equations have been used to obtain [η] (Abododinar et al., 2014; Huggins, 1942; Kontogiorgos et al., 2012; Khouryieh et al., 2006; Kraemer, 1938; Launay et al., 1997; Lin and Lai, 2009; Migliori et al., 2010; Samutsri and Suphatharika, 2012; Sato and Miyawaki, 2012; Tanglertpaibul and Rao, 1987; Vahid et al., 2011; Yousefi et al., 2014), we adopted the Huggins (Huggins, 1942) and Kraemer equations (Kraemer, 1938) to calculate [η] values for xanthan gum (a polyelectrolyte) and guar gum (a non-polyelectrolyte). Both macromolecules had [η] values of similar orders with high determination coefficients (R²) regardless of the equation used, although the Kraemer equation produced slightly lower [η] values than the Huggins equation (Fig. 1). For xanthan in water, these equations produced slightly different [η] estimates, with the same y-intercept, although they were very similar to those of other macromolecules in NaCl solution. A previous study reported slightly higher [η] values for both macromolecules derived from different sample lots. Despite slight differences in [η] in water, we calculated [η] for xanthan and guar gum in the range of 0.1–0.3 g/L NaCl due to the linearity of the Huggins equation and its general consistency with the Kraemer equation estimates.

Fig. 1.

Comparison of regression lines for the intrinsic viscosity of xanthan and guar gum in water and 0.1 mol/L aqueous NaCl solution, determined using the Huggins and Kraemer equations.

The [η] values of the tested polyelectrolytes and non-polyelectrolytes, in water and in 0.1 mol/L NaCl ([η]_0.1), are listed in Table 1. Polyelectrolytes showed greater differences between [η] and [η]_0.1 than non-polyelectrolytes. This is discussed further in the last section, Classification of apparent viscosity of macromolecules in aqueous NaCl solutions. In addition, [η]_∞ was estimated to be almost the same as [η]_0.1.

Table 1. Stiffness parameter and its related parameters, along with reduced viscosity at 25 °C.

Macromolecule	Mw	[η]0.1	[η]∞	[η]	[η]*	Parameter	Parameter	ηared
	(× 103)	(dL/g)	(dL/g)	(dL/g)	(dL/g)	S	B	(dL/g)
Non-polyelectrolytes
PEG35000	37	0.2	0.3	1.1	3.2	0.012	0.097	0.8**
DexT40	36	0.4	0.5	1.4	4.0	−0.001	−0.003	0.2**
Guar gum	2 200*1	8.2	7.9	11.3	-	0.082	0.005	345.8***
Locust bean gum	300-2 000*2	8.5	8.3	11.5	-	0.034	0.002	146.0***
Polyelectrolytes
Apple pectin	∼100	0.9	0.9	11.9	16.3	0.149	0.171	35.0**
Citrus pectin	∼100	0.9	1.3	21.7	24.5	0.151	0.173	30.5**
Alginate	∼100	1.3	0.9	33.0	44.0	0.276	0.196	37.6**
Xanthan	∼1 000<*3, 4	14.7	12.8	77.6	64.4	0.877	0.027	626.5***

M_w, Molecular weight

*1, Vijayendran and Bone (1984).

*2, Barak and Mudgil (2014).

*3, Merino-Gonzalez. and Kozina (2017).

*4, Erten et al. (2014).

[η]_0.1, Intrinsic viscosity in 0.1 mol/L aqueous NaCl solution.

The parameter [η]_∞ was calculated from [η]_i intercept in the [η]_i and I^−1/2 linear relationship.

[η]*, Intrinsic viscosity in water in the reference; Sato and Miyawaki (2012).

Parameters S and B were calculated using ν = 1.3 according to the references (Abdododinar et al. 2014; Brunchi et al., 2014; Smidsrod and Haung 1971).

** 2 wt % of the macromolecule in water

***0.5 wt % of the macromolecule in water

Appendix η^a_red data; 2.2 for PEG35000 and 0.3 for DexT40 at 10 wt % of the macromolecule in water, respectively.

Although [η] is related to M_w by Staudinger's rule, the Mark-Houwink exponential equation of M_w conforms to several unbranched polymers (Brunchi et al., 2014; Kato et al., 1960; Sookne and Harris, 1945):   

where, K is a constant. At a fixed ion strength of 0.1, the exponent α in Eq. 8 is 1.0 (Smidsrød, 1970; Smidsrød and Haung, 1971).

The physical meaning of [η] is also explained by the Flory-Fox equation (Savi-Junior. et al., 2015) for linear macromolecules, as follows:   

where, φ is the Fox-Flory constant and R_g is the viscometric radius of gyration.

According to both Eq. 8 and Eq. 9, [η] is influenced by the M_w of the macromolecule. Although it is better to compare [η] for polymeric materials of similar M_w to conduct a comparative study of macromolecules with different structures, [η] provides an estimate of the size and structure of the polymer chains in a given solvent (Hellebois et al., 2021).

The relationship between [η]_i and I^−1/2 is shown in Fig. 2 to illustrate the effect of NaCl concentration on [η] (Smidsrød and Haung, 1971). According to Fixman's theory, we measured the slope of the linear regression line between [η]_i and I^−1/2. The data do not show exact linearity between [η]_i and I^−1/2 throughout the entire ionic strength range; therefore, the adaptable range of I^−1/2 to compare [η]_i of the food macromolecules tested here remains unclear, whereas that around I = 0.1 (I^−1/2 ≈ 3.16) shows consistently good linearity and is included in most relevant studies (Smidsrød and Haung, 1971). Therefore, we attempted to clarify the adaptable range of I^−1/2, as follows. Our data for various macromolecules, including four polyelectrolytes and four non-polyelectrolytes, showed that [η]_i and I^−1/2 have a linear relationship below I^−1/2 = 30 by comparison of the differences in [η]_i among these macromolecules, although the range of I^−1/2 was set below 10 or 15 for alginate (Smidsrød and Haung, 1971), below ∼15 for balangu seed gum (Amini and Razavi, 2012), and below 20 for xanthan (Brunchi et al., 2014). To clarify the stiffness of the molecular chain in polyelectrolytes, we determined S, which represents the slope of the relationship between I^−1/2 and [η]_i. According to Fixman's theory, for polyelectrolytes, S is proportional to M_w and is applicable only to a certain range of M_w. To evaluate the effects of salt concentration in a manner that is independent of M_w, we also estimated the empirical parameter B using both the [η] value at I^−1/2 = 0.1 ([η]_0.1) and S (Brunchi et al., 2014; Smidsrød and Haung, 1971). The values of these parameters are shown in Table 1, using ν = 1.3 in Eq. 10 (Smidsrød and Haung, 1971).

Fig. 2.

Dependence of the intrinsic viscosity of various macromolecules in aqueous NaCl solutions on the inverse square root of ionic strength (I^−1/2).

  

As S encompasses the contribution of macromolecular M_w, B values should be compared to obtain a preliminary measure of the relative stiffness of different polymer chains (Smidsrød and Haung, 1971). Lower values of B indicate stiffer molecular chains. Generally, B < 0.097 for non-polyelectrolytes; these macromolecules are stiff due to the lack of active sites, such as anionic groups. The S values of guar gum and locust bean gum were slightly higher than those of other non-electrolytes, where higher S values indicate a greater contribution of M_w.

Polyelectrolytes had higher B values than non-electrolytes, indicating the greater flexibility of polyelectrolytes. Xanthan gum had the highest S value among electrolytes due to its high M_w, and although its B value (0.027) was extremely low in water, it was 5-fold higher than the reference (0.005) (Brunchi et al., 2014) and slightly higher than, or equal to, those of non-polyelectrolytes. Thus, xanthan gum showed the highest molecular chain stiffness among the polyelectrolytes tested in this study.

Parameter B was proposed by Smidsrød and Haung (1971) to overcome the restriction of comparing [η]_i at a fixed ionic strength (typically 0.1 mol/L) (Abododinar et al., 2014); values of parameters S and B were reported for several polyelectrolytes, ranging from 0.18 to 1.04 and 0.044 to 0.24 (Smidsrød and Haung, 1971), respectively. In the present study, the B value for alginate (0.196) was 5-fold higher than that (0.04) reported by Smidsrød and Haung (1971), indicating that the alginate used in this study was more flexible than that used in their study.

Brunchi et al. (2014) also compared the B values of several electrolytes, and reported that they ranged from 10⁻¹ to 10⁻³. A B value of the order of 10−1 implies a highly flexible polymer chain. For this reason, pectins and alginate are considered to be flexible polymers, whereas xanthan, guar gum, and locust bean gum are stiff polymers due to their low B values. These differences may indicate molecular variation; however, our results indicate that the polymer chains of xanthan are stiffer than those of other polyelectrolytes. Although fitting S and B to non-electrolytes is inappropriate, they could have low values below the order of 10⁻².

Table 2 shows the capillary viscosity values of macromolecules (0.05 wt %) in NaCl solution. Most macromolecules had a capillary viscosity of ∼1 mPa·s; however, xanthan solutions showed a range of 2–7 mPa·s. Thus, xanthan may be a potent supplier of viscosity, even at macromolecular concentrations as low as 0.05 wt %. The capillary viscosity values of most macromolecule aqueous solutions fluctuated around 1 mPa·s, with those of alginate and xanthan tending to decrease as the NaCl concentration increased to 0.1 mol/L, implying an influence of NaCl concentration.

Table 2. Viscosity of 0.05 wt % macromolecule in aqueous NaCl solutions using Cannon-Fenske capillary viscometer at 25 °C.

mPa · s
Macromolecule	NaCl concentration (mol/L)
	0	0.01	0.1
Non-polyelectrolytes
PEG35000	0.92	0.92	0.93
DexT40	0.91	0.91	0.91
Guar gum	1.66	1.65	1.63
Locust bean gum	1.39	1.33	1.30
Polyelectrolytes
Apple pectin	1.19	1.06	1.05
Citrus pectin	1.33	1.08	1.06
Alginate	1.85	1.16	1.08
Xanthan	6.97	2.69	2.36
Only solvent	0.89	0.90	0.91

The unit of viscosity can be seen in the upper right corner.

Effects of NaCl concentration on apparent viscosity at a fixed high macromolecular concentration    The effect of shear rate on η^a_H in 0–0.1 mol/L NaCl solutions at 25 °C is shown in Fig. 3. The flow properties of the macromolecule solutions can be used to determine whether solutions are Newtonian or non-Newtonian (Marcotte et al., 2001). In this study, aqueous solutions of PEG35000, DexT40, apple pectin, citrus pectin, and alginate showed Newtonian properties, whereas xanthan and guar gum showed shear thinning properties at the tested shear rate range. However, previous studies have suggested that pectin solutions show shear thinning at low shear rates (Sato et al., 2004); these differences may be due to differences in scale. The shear rate–viscosity relationships of all macromolecules in water yielded curves with almost identical shapes for 0.01 and 0.1 mol/L NaCl solutions, implying small electrostatic effects of the solvent on η^a_H. We also compared the apparent viscosity values of the non-Newtonian macromolecules, xanthan and guar gum, at a shear rate of 16.8 s⁻¹, among solvents including water and 0.01 and 0.1 mol/L NaCl aqueous solutions. We adopted the power law shown in Eq. 6 to represent the relationship between η^a_H and shear rate for xanthan and guar gum, because it is the model that is most widely used to describe the flow properties of non-Newtonian fluids with high R² values (Marcotte et al., 2001). The parameter n is useful for estimating Newtonian flow, with non-Newtonian flow seen for both xanthan gum and guar gum. The estimated parameters, including the consistency coefficient m and flow behavior index n, are listed in Table 3. The xanthan solution was shown to be a non-Newtonian fluid by its low n value. Using m and n, we determined the viscosity characteristics of xanthan and guar gum solutions at various shear rates. The apparent viscosity values of various macromolecule solutions at a shear rate of 16.8 s⁻¹ and different NaCl concentrations are listed in Table 4. We compared these values to analyze intermolecular interactions at fixed high concentrations (Sato and Miyawaki, 2012). All solutions except xanthan had almost identical η^a_H values, varying within a range of 10 mPa·s, implying that these macromolecules are stable at 25 °C, regardless of the NaCl concentration, at least below 0.1 mol/L. The η^a_H value of xanthan in 0.1 and 0.01 mol/L NaCl solution was expected to be larger than that in water, even though it has been reported to be incompletely solvated, retaining a weak, gel-like structure in water (Morris et al., 1983).

Fig. 3.

Effect of shear rate on the apparent viscosity of macromolecules in aqueous NaCl solutions at 25 °C. Open circles and triangles indicate xanthan and guar gum, respectively. Closed circles indicate polyethylene glycol 35000 (PEG 35000). ▼, ◢, and ▲ indicate citrus pectin, locust bean gum, and dextran T40 (DexT40), respectively. Diamonds and squares indicate apple pectin and alginate, respectively.

Table 3. Power-law parameters for apparent viscosity of 0.5 wt % macromolecule in aqueous NaCl solutions at 25 °C.

Macromolecule	NaCl concentration (mol/L)
	0			0.01			0.1
	m	n	R2	m	n	R2	m	n	R2
Non-polyelectrolytes
Guar gum	293.7	0.765	0.972	266.9	0.782	0.970	282.7	0.772	0.973
Polyelectrolytes
Xanthan	2329.6	0.239	1.000	2943.8	0.225	1.000	3073.2	0.231	1.000

Table 4. Apparent viscosity at a shear rate of 16.8 s⁻¹ for macromolecule in aqueous NaCl solutions at 25 °C.

mPa · s
Macromolecule	NaCl concentration (mol/L)
	0	0.01	0.1
Non-polyelectrolytes
PEG35000	20.3	20.4	20.7
DexT40	3.7	3.6	4.4
PEG35000*	2.3	2.3	2.3
DexT40*	1.3	1.3	1.3
Guar gum	151.3	144.2	148.4
Locust bean gum	64.4	66.7	57.7
Polyelectrolytes
Apple pectin	61.8	65.3	67.9
Citrus pectin	54.0	54.9	59.9
Alginate	66.3	61.6	59.6
Xanthan	273.4	331.0	351.1

The macromolecular concentration was 10 wt % for PEG35000 and DexT40, 2 wt % for apple pectin, citrus pectin, and alginate, and 0.5 wt % for xanthan, guar gum, and locust bean gum, respectively.

*  The macromolecular concentration was 2 wt % and the viscosity of macromolecule was measured using Canon-Fenske capillary viscometer.

The unit of apparent viscosity can be seen in the upper right corner.

Intermolecular interactions at infinite dilution and fixed high concentration    At a fixed high concentration, the apparent reduced viscosity, η^a_red, can be determined as follows (Sato and Miyawaki, 2012):   

where, η_w is the viscosity of pure water.

A comparison of η^a_red and [η] for various macromolecule solutions is shown in Table 1. The η^a_red values were nearly equal to [η] for PEG35000, DexT40, apple pectin, citrus pectin, and alginate, whereas η^a_red was substantially higher than [η] for guar gum, locust bean gum, and xanthan in water. Differences between [η] and η^a_red appear to reflect those between intermolecular interactions among macromolecules at infinite dilution and the fixed high concentration, respectively. This is discussed further in the section Classification of apparent viscosity of macromolecules in aqueous NaCl solutions.

Effects of temperature on the apparent viscosity of macromolecules at fixed high concentrations in NaCl solution    The effects of temperature on the η^a_H values of macromolecules in solutions containing various concentrations of NaCl are shown in Fig. 4. A plot of ln (η^a_H) at a shear rate of 16.8 s⁻¹ against the reciprocal of temperature yielded a straight line. The regression lines for 0.5 wt % xanthan in 0.01 and 0.1 mol/L NaCl solutions were nearly identical, and only slightly different from that of xanthan in water. On the other hand, the regression lines for apple pectin, guar gum, and PEG3500 were similar in water and solutions containing various NaCl concentrations. All of the macromolecules, except xanthan, had similar slopes, regardless of the NaCl concentration (data not shown). The citrus pectin curve showed high ln (η^a_H) values at low temperatures (5 °C and 10 °C; 1000/K = 3.5–3.6), similar to our results for apple pectin; this might have been due to gel transition at low pectin temperatures, which can result in slightly steeper slopes.

Fig. 4.

Arrhenius plots of the apparent viscosity of aqueous macromolecule solutions with water (circles), 0.01 mol/L aqueous NaCl solution (triangles), or 0.1 mol/L aqueous NaCl solution (squares) as the solvent.

Based on the Arrhenius equation [Eq. 7] used in this study, the E_a values of various macromolecules were determined from the slopes of these plots at different NaCl concentrations (Table 5). Thermodynamic flow stability, represented by E_a, approached zero for xanthan in water, but ranged from 19 to 26 kJ/mol for guar gum, locust bean gum, and alginate in water; these values are equal to, or slightly greater than, that of water alone (17 kJ/mol) (Sato and Miyawaki, 2008). Thus, the effect of temperature on viscosity markedly affects solvent–solvent interactions. Among the tested macromolecules, pectins had the highest E_a (28.3–33.8 kJ/mol), with slightly steeper slopes of the Arrhenius equation. At a fixed high-macromolecule concentration, all non-polyelectrolytes and polyelectrolytes, except xanthan, had similar E_a values at various NaCl solution concentrations, which were also similar to those in water. For xanthan, E_a increased when NaCl was added to the solution, but remained substantially lower (0.6–4.0 kJ/mol) than those of all other macromolecules at all NaCl concentrations. An E_a value of 5.74 kJ/mol was reported previously for 1% xanthan (Marcotte et al., 2001), which was higher than that obtained for 0.5 wt % xanthan in water in this study (0.6 kJ/mol). Our lower E_a values (∼4.0 kJ/mol) may have promoted xanthan molecule entanglement in solutions, despite the electroviscous-like effects on this polyelectrolyte induced by NaCl.

Table 5. Activation energy of flow for macromolecule in aqueous NaCl solutions.

kJ/mol
Macromolecule	NaCl concentration (mol/L)
	0	0.01	0.1
Non-polyelectrolytes
PEG35000	23.3	23.4	23.1
DexT40	23.4	19.4	16.5
PEG35000*	20.9	20.9	20.8
DexT40*	18.2	18.0	17.9
Guar gum	19.1	19.7	19.1
Locust bean gum	26.0	25.9	26.5
Polyelectrolytes
Apple pectin	31.4	32.3	33.8
Citrus pectin	28.3	29.0	31.4
Alginate	23.1	22.8	24.2
Xanthan	0.6	3.9	4.0
Only solvent **	17.1	17.2	17.2

The macromolecular concentration was 10 wt % for PEG35000 and DexT40, 2 wt % for apple pectin, citrus pectin, and alginate, and 0.5 wt % for xanthan, guar gum, and locust bean gum, respectively.

*  The macromolecular concentration was 2 wt % and the viscosity of macromolecule was measured using Canon-Fenske capillary viscometer.

**  Activation energy of flow for only solvent, and the viscosities of only solvent were calculated from the dynamic viscosity measured using the capillary viscometer and density meter, rather than by η^a_H. The unit of activation energy of flow can be seen in the upper right corner.

Classification of apparent viscosity of macromolecules in aqueous NaCl solutions   Table 6 summarizes the apparent-viscosity measurements of aqueous macromolecule solutions containing NaCl in this study. Previously, the apparent viscosity and its derived parameters were analyzed for macromolecules in sucrose solutions, and yielded three groups – Groups A, B, and C (Sato and Miyawaki, 2012). In Group A, which included PEG35000 and DexT40, intermolecular interactions among macromolecules were very weak. Group B included pectins and alginate, and had an intermediate extent of intermacromolecular interactions. Xanthan belonged to Group C, in which intermacromolecular interactions were strong. A new group, Group A₂, was added to the previous macromolecular groups classified according to their apparent viscosity (Sato and Miyawaki, 2012) and Group A was renamed Group A₁.

Table 6. Classification of apparent viscosity of macromolecules in aqueous NaCl solutions using novel viscometric parameters at the tested condition.

Group	Type	Name			A high dilution		A fixed high concentration		Ea in aqueous NaCl solutions
			ηared / [η]	[η]/ [η]0.1	SlopeL	SDL	SlopeH	SDH	(kJ/mol)
A1	Non-P	PEG35000	0.7	5.5	0.1	0.006	3.74	0.21	23.3±0.2
							0*	0*	20.9±0.1
		DexT40	0.1	3.5	0	0	7.74	0.44	19.8±3.5
							0*	0*	18.0±0.2
A2	Non-P	Guar gum	30.6	1.4	−0.27	0.015	0.93	3.57	19.3±0.3
		Locust bean	12.7	1.4	−0.68	0.046	−80.16	4.68	26.1±0.3
		Gum
B	P	Apple pectin	2.9	13.2	−0.89	0.078	48.30	3.06	32.5±1.2
		Citrus pectin	1.4	24.1	−1.72	0.673	57.64	3.18	29.6±1.6
		Alginate	1.1	25.4	−5.01	0.433	−49.29	3.44	23.4±0.7
C	P	Xanthan	8.1	5.3	−29.31	2.572	557.97	40.33	2.8±1.9

At a high dilution, the macromolecular concentration was adjusted to 0.05 wt % for all macromolecules.

At a fixed high concentration, the macromolecular concentration was 10 wt % for PEG35000 and DexT40, 2 wt % for apple pectin, citrus pectin, and alginate, and 0.5 wt % for xanthan, guar gum, and locust bean gum, respectively.

*  The macromolecular concentration was 2 wt % and the viscosity of macromolecule was measured using Cannon-Fenske capillary viscometer.

Non-P is a non-polyelectrolyte, and P is a polyelectrolyte.

E_a is the activation energy of flow for the macromolecule in aqueous NaCl solutions (0, 0.01, 0.1 mol/L) and expressed the arithmetic mean ± standard deviation (n = 3).

In this study, several novel parameters were proposed and the rheological properties of eight representative macromolecules were compared. First, molecular entanglement was analyzed using the parameter η^a_red/[η], which represents the difference in intermolecular interactions among the macromolecules in water at 25°C. Higher values of this parameter indicate more entanglement of the macromolecule at a fixed high concentration compared to those at an infinite dilution. The η^a_red/[η] values of guar gum and locust bean gum were highest, followed by xanthan. These macromolecules have a M_w of at least > 300 × 10³, which is at least three-fold higher than the maximum M_w of pectins and alginate and eight-fold higher than both PEG35000 and DexT40.

The parameter [η]/[η]_0.1 represents the effects of ion strength induced by NaCl in aqueous solution on [η], which clarifies the conformational properties in solution, resulting in the difference in apparent hydrodynamic volume occupied by the macromolecule (Amini and Razavi, 2012; Lai and Chiang, 2002) between water and 0.1 mol/L aqueous NaCl solutions. Where its value exceeds 1, the macromolecular conformation may be wider in shape in water than in NaCl solution. The values of this parameter for pectins and alginate are 13–25, implying a greater change in shape of each macromolecule. Other macromolecules changed shape very little when compared with the values of the [η]/[η]_0.1 parameter in Group B. The parameter for xanthan was relatively small, and was of the same order as PEG35000. This may have been due to the absolute values of intrinsic viscosity in water and in 0.1 mol/L NaCl solution, as shown in Table 1. Xanthan was considered to adopt a double-helix structure and be rigid in aqueous NaCl at 0.01 mol/L (Nakasuga and Norisuye, 1988; Tomofuji et al., 2022) and 0.1 mol/L (Sato et al., 1984a; Sato et al., 1984b). Although a fraction of insoluble polymer or microgel may be involved in the calculation of [η] for macromolecules with M_w > 10⁶ (Merino-González and Kozina, 2017), [η]/[η]_0.1 values were low for these high-M_w macromolecules which belonged to Groups A₂ and C.

At high macromolecule dilutions, the parameter Slope^L represents the slope of the linear regression line between η_Li and the concentration of NaCl in a macromolecular solution. Therefore, lower absolute values of SlopeL represent the stiffness of macromolecules at infinite dilution. A negative value of Slope^L indicates that η_Li decreases as the NaCl concentration increases for a given macromolecule. SD^L represents the variation in η_Li when i = 0, 0.01, or 0.1. Non-polyelectrolytes appeared to have very low values of Slope^L and SD^L. Pectins and alginate had intermediate values of Slope^L and SD^L. In contrast, xanthan had higher absolute Slope^L and SD^L values, indicating the high sensitivity of η_Li to NaCl concentration, with η_Li decreasing as the NaCl concentration increased up to at least 0.1 mol/L NaCl. Therefore, while a tendency of η_Li to decrease due to ionic effects induced by NaCl was observed for many macromolecular solutions, it was remarkable for aqueous xanthan solution. In addition, the [η]/[η]_0.1 parameter was very low for non-polyelectrolytes, indicating that the conformation was stable at infinite macromolecule dilutions in NaCl solution. Basically, the parameter Slope^L is widely considered to have the almost same scientific meaning as the parameter S. In fact, the relationship between SlopeL and the parameter S can be depicted by a quadratic equation with R² = 0.998 (data not shown).

At a fixed high macromolecule concentration, using only the apparent viscosity η^a_Hi at a shear rate of 16.8 s⁻¹ (Sato and Miyawaki, 2012) with several NaCl concentrations (0–0.1 mol/L), the effects of NaCl on the macromolecule conformation in aqueous solutions was investigated with both Slope^H and SD^H to compare and classify the viscometric patterns of food macromolecules. Instead of η^Li at a high macromolecule dilution, the relationship between η^a_Hi and NaCl concentration was compared with both Slope^H and SD^H at a fixed high macromolecule concentration. At these macromolecule concentrations, the absolute parameters were small for both PEG35000 and DexT40 (Group A₁). The values of Slope^H and SD^H were markedly lower for non-polyelectrolytes (i.e., guar gum and locust beam gum; Group A₂) and polyelectrolytes (i.e., pectins and alginate; Group B) than for xanthan (Group C). Regardless of the sign of Slope^H, marked stability of η^a_Hi was observed for all macromolecules examined, except xanthan, due to the lower absolute values of both Slope^H and SD^H compared to that of xanthan in NaCl solutions, respectively.

However, the temperature dependency of apparent viscosity in NaCl solutions was low for xanthan, such that E_a was almost zero despite the increase in E_a observed at higher concentrations of NaCl in solution when compared with xanthan in water samples (Table 5). The low temperature sensitivity of the viscosity of xanthan solution has been demonstrated to be favorable for use as a stable food thickener, not only in water (Sato and Miyawaki, 2012), but also in the presence of NaCl. In addition, the temperature dependency of flow at a fixed high macromolecule concentration appeared to have a dominant effect on water–water interactions due to the similar order of E_a (19–20 kJ/mol for guar gum; 25–27 kJ/mol for locust bean gum) compared to 17 kJ/mol for water alone (Sato and Miyawaki, 2012), and NaCl at concentrations < 0.1 mol/L had little effect on E_a (Table 5).

In summary, these observations of viscometric behavior at infinite dilution and fixed high concentrations indicate that a novel group, Group A₂, should be added for non-electrolytes with high M_w that includes both guar gum and locust beam gum, the conformations of which show weak effects of NaCl at both infinite dilution and fixed high concentrations. Thus, while the classification proposed here is based partly on the approximate M_w of non-polyelectrolytes and polyelectrolytes, the characteristics of their chemical structures should be investigated, especially the unique rheological properties observed in Group C.

Acknowledgements    We thank Dr. Tai-Ying Chiou, Ms. Erina Ono, Ms. Ayako Iwamoto, and Ms. Yuma Nanamori for their assistance. This research received no grants from funding agencies in the public, commercial, or not-for-profit sectors.

Conflict of interest    There are no conflicts of interest to declare.

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