#### 2.1. Chain Scission Kinetics of Acid Hydrolysis and Dispersity Analysis

The chain scission kinetics of the partial hydrolysis process for all polysaccharides was investigated by the following equation:

Whereas m

_{0} is the average repeating unit molar mass, and

M_{n(t)} and

M_{n}_{(0)} are the number-average molecular weights [g/mol] at time

t and time 0, respectively. The term on the left-hand side of the equation indicates the number of broken bonds per anhydro monosaccharide unit. By plotting the inverse of the degree of polymerization (1/

DP_{n} = m

_{0}/

M_{n}) over the time course of the degradation, the rate at which a polysaccharide chain breaks during a partial acid hydrolysis was obtained. This plot with m

_{0}/

M_{n} = 1/

DP_{n} representing the increase in relative amount of reducing ends was done for guar galactomannan (samples GM38 and GM21 with different degrees of galactose substitution), arabinoxylan (AX), and xyloglucan (XG) (see

Figure 2a). A linear relationship between m

_{0}/

M_{n} and hydrolysis time was established for GM38 (R

^{2} = 0.99), which is in agreement with Equation (1), confirming that glycosidic linkages within the polysaccharide backbone were equally susceptible to cleavage, and hence random chain scission occurred with a rate constant (

k) of 1.67·10

^{−4} h

^{−1}. An almost perfect positive linear relationship between m

_{0}/

M_{n} and time of hydrolysis was found (Pearson’s correlation coefficient (r) = 0.99), indicating that the number of broken bonds per anhydro-monosaccharide unit was strictly related to the hydrolysis time. A similar trend was observed for the hydrolysis of GM21. The coefficient of determination (R

^{2}) was 0.95, Pearson’s correlation coefficient (r) was 0.97, and the rate constant (

k) was 2.24·10

^{−4} h

^{−1} indicating that the reaction was faster for GM21 than GM38 as obvious from the steeper slope (

Figure 2a). A lower degree of galactose substitution on the mannose backbone in GM21 seems to positively influences the rate of cleavage. XG followed a similar trend as GM38 denoting that the chain scission followed a random cleavage. The rate constant (

k) was 9.71·10

^{−5} h

^{−1}, the coefficient of determination (R

^{2}) was 0.99 and, Pearson’s correlation coefficient (r) was 0.99. Arabinoxylan had the highest kinetic rate constant (

k) of 3.4·10

^{−4} h

^{−1} confirming that glycosidic linkages between aldopentopyranoside rings are hydrolyzed faster than linkages between aldohexopyranoside rings.

Although most of the studies related to the mechanism of action involved in the hydrolysis of polysaccharides are yet to be understood, some hypotheses can be formulated by comparing the different kinetic rate constants (k) obtained for the hydrolysis of galactomannan (GM38, GM21), arabinoxylan (AX), and xyloglucan (XG).

Up to now, the most accepted mechanism that explains the process by which a polysaccharide is hydrolyzed is the “cyclic” type. Briefly, the glycosidic oxygen atom is protonated by the acid, rendering it a good leaving group under the formation of an oxocarbenium ion, which exists in the half-chair conformation and which in turn reacts with a water molecule to form the reduced sugar [

26]. It is also known that the glycosidic bond at the non-reducing end is hydrolyzed faster than an internal bond. The formation of oxocarbenium ion is accompanied by a change of the sugar unit conformation, for which C-2, C-1, O, and C-5 are in a planar conformation. Therefore, the hydrolysis of an internal bond would involve a reorientation of the bulky group

Timell reported the rate constants and kinetic parameters for eight disaccharides undergoing acidic hydrolysis with 0.5 M sulphuric acid [

27]. Of interest for our study are the values found for cellobiose, mannobiose, xylobiose that can be compared with our chain scission rate constant obtained for xyloglucan, galactomannan, and arabinoxylan. Considering the β-(1→4)-linked disaccharides, it was found that the relative rates of hydrolysis were in the order of xylose > galactose > mannose > glucose. This is in agreement with the trend shown in the

Figure 2, where the rate of chain scission was in the order of arabinoxylan > galactomannan > xyloglucan. It was demonstrated by BeMiller that a restriction in the flexibility of the molecules in the ground state and in the transition state, measure by the entropy of activation (ΔS

^{‡}), decreases the rate of the hydrolysis [

28]. For linearly-branched polysaccharides the degree of substitution in the backbone chain can influence the freedom of motion of the molecules in the ground state and in the transition state. This could explain why galactomannan with higher degree of substitution (GM38) hydrolyzed slower than the one with less degree of substitution (GM21).

The variation of the dispersity index (

Đ) as a function of degree of scission (

N) was investigated for all the studied polysaccharides. The degree of scission

indicates the fraction of broken bonds per polymer chain during acid hydrolysis (see

Figure 2b). GM38 increased its dispersity value from 1.15 ± 0.01 to 1.70 ± 0.06. A similar result was found for GM21, its dispersity increased significantly from 1.58 ± 0.03 to 1.83 ± 0.12 (

p = 0.0109). For XG, the dispersity remained constant as degradation proceeded with an approximate value of 1.6, indicating that large chains were degraded with the same probability as smaller chains. All these results are largely consistent with the theoretical prediction for a random-chain scission model according to the following function [

29]

where

N is the degree of scission and

Đ is the dispersity (

M_{w}/

M_{n}). As reported by Yoon et al. [

29], three conditions may occur when a random chain scission happens. When

Đ of the native polymer is less than 2, it will increase up to 2 during the degradation. If it is greater than 2, it will decrease to 2, and if the initial value is close to 2, the dispersity will remain constant during the hydrolysis process.

Concerning AX, it was not possible to determine the appropriate values of m

_{0}/

M_{n} and

Đ by integrating the polymer peak in the chromatogram, due to the formation of aggregates after 3 h of hydrolysis (see

Figure 3).

As expected, partial hydrolysis followed the random chain scission model, and the time of hydrolysis seems to be the main factor influencing the relative amount of reducing end per polymer chain produced during the process. Moreover, the degree of substitution on the backbone polymer chain has an inverse linear correlation with the reaction rate constant, as shown by comparing k of GM21, GM38, and XG.

#### 2.1.1. Conformational Analysis

All the samples were also analyzed for their conformational properties in solution using the Mark-Houwink-Sakurada equation, which describes the relationship between the intrinsic viscosity ([

η]) and

M_{w}:

Using a double log plot of the intrinsic viscosity [

η] versus

M_{w} (Equation (4)), it was possible to determine the average conformation of the polymer in solution for each polymer sample (

α) [

30]. From the Mark-Houwink plot analysis, it was shown that the curves of all the native and hydrolyzed polysaccharide samples had two or more deflections along the molecular weight distribution, and therefore, more than one α value was determined (see

Figure 4a–d). For example, guar galactomannan (Gal:Man = 21:79) treated with HCl for 24 h (GM21 (24 h)) consist of compact polymer chains up to a

M_{w} ~ 60 kDa (

α = 0.232 ± 0.069), and more stiff-rod like chains (

α = 1.310 ± 0.140) when the molecular weight is higher than 60 kDa. Considering arabinoxylan hydrolyzed for 3 h with HCl (AX (3 h)), it was possible to define even three regions in the curve with different

α values. A stiff conformation was observed for

M_{w} < 30 kDa, a more extended for 30 kDa <

M_{w} < 200 kDa and, a contracted conformation for

M_{w} > 200 kDa. Except for native XG at lower molecular weight (

M_{w} < 500 kDa) and native GM21 at higher molecular weight (

M_{w} > 630 kDa), for all other native polysaccharides,

α values ranged between 0.5 and 0.7, with Mark-Houwink plot not deviating much from a linear pattern throughout the whole molecular weight distribution. This

α-range suggests that native AX (at

M_{w} < 160 kDa), GM38 (at

M_{w} < 1000 kDa), GM21 (at

M_{w} < 630 kDa), and, XG (at

M_{w} > 500 kDa) adopted the same overall random coil conformation in solution. However, from the native to the hydrolyzed samples, the

α value changed, meaning that the hydrolysis was, to some extent, influencing the hydrodynamic property of the polysaccharides. In particular, newly produced low molecular weight fractions adopted a stiff rod-like chain conformation.

#### 2.1.2. Relationship Between Hydrodynamic Radius and Intrinsic Viscosity

The correlation between intrinsic viscosity [

η] and hydrodynamic radius (

R_{h}) of native and hydrolyzed polysaccharides, at a given concentration and solvent, was investigated (see

Table 1). Intrinsic viscosity and hydrodynamic radius are sensitive to the extension of a polymer chain and their interrelation can be used to hypothesize the supramolecular organization of a macromolecule in solution. For all the polysaccharides, [

η] and

R_{h} decrease with increasing hydrolysis time in accordance with their decreasing

M_{w} (see

Table 2,

Table 3,

Table 4 and

Table 5). Lower values of [

η] and

R_{h} indicate a more condensed structure and higher molecular density. The resulting compact structure is in agreement with the α values reported in

Figure 3a (e.g., α

_{(GM21 Native)}) = 0.592 ± 0.035 (

M_{w} < 630 kDa); 1.011 ± 0.017 (

M_{w} > 630 kDa) and α

_{(GM21 (24h)} = 1.305 ± 0.1040 (

M_{w} < 60 kDa); 0.232 ± 0.009 (

M_{w} > 60 kDa)) which indicated that acid treatment led to a stiffer conformation.

Moreover, the intrinsic viscosity is independent from the molecular weight of a polysaccharide species, in the sense that two polysaccharide structures with comparable M_{w} may have different [η]. For example, the intrinsic viscosity of GM21_{(Native)} (M_{w} = 380 kDa, [η] = 6.61 ± 0.04 g/L) was almost twice the number of AX_{(Native)} (M_{w} = 320 kDa, [η] = 3.57 ± 0.04 g/L). Therefore, the highest intrinsic viscosity for GM21_{(Native)} implies a more open structure (higher R_{h}) and lower density. Another parameter that increases the density in solution is the degree of branching. This is in agreement with the intrinsic viscosity values of GM21 and GM38. The lower degree of galactose substitution on GM21 backbone made its intrinsic viscosity in solution lower than that of GM38. The effect of partial acid hydrolysis on the viscoelastic properties of galactomannan, arabinoxylan and xyloglucan under dynamic shear condition, as a measure of the elastic and viscous material response, could be a valuable future study for exploring structure and performance of the newly produced hydrolyzed fractions.

#### 2.1.3. Molecular Weight and Dispersity Analysis of Hydrolyzed and Fractionated Polysaccharides

M_{w} and

Đ of all native, hydrolyzed, and precipitated polysaccharide fractions were analyzed using HPSEC. Guar polymer chains GM21 and GM38 (see

Table 2 and

Table 3) were significantly degraded to a lower

M_{w} after 3 and 24 h of hydrolysis, while

Đ increased over time.

Changes observed in molecular properties of XG during 6 and 48 h of hydrolysis (see

Table 4) were comparable to those observed with GM21 and GM38 (see

Table 2 and

Table 3).

A comparable

M_{w} reduction was found for arabinoxylan after 3 and 12 h of hydrolysis; however, Đ decreased during depolymerization (see

Table 5).

Comparing the two galactomannans after 3 and 24 h of hydrolysis, we found that the quantity of isopropanol necessary to start the precipitation was higher for GM38 (16 and 19% after 3 and 24 h hydrolysis, respectively) than for GM21 (14 and 15% after 3 and 24 h hydrolysis, respectively). Most likely, the higher degree of galactose substitution on the mannose backbone discourages the formation of intermolecular interaction, requiring more alcohol to initialize the precipitation for GM38. In addition, considering GM21 after 24 h hydrolysis, its stiffness (

α = 1.305,

M_{w} < 60 kDa), might help the aggregation process. Intermolecular interaction between polymer segments are privileged for a stiff rod conformation since polymer chains can simply assemble together, leading a precipitate formation. Instead, for a random coil conformation (0.5 <

α < 0.8), polymer chains need first to rearrange nicely to optimized the intermolecular interaction [

31].

Gradient precipitation is based on the solubility of the polymer, which in turn depends on its M_{w}. The more soluble a polysaccharide is, the higher alcohol concentration is needed to initiate the precipitation. Polysaccharide fractions usually precipitate in a descending order of molecular weight with increasing isopropanol concentration.

Four and three fractions of arabinoxylan were obtained with

i-prOH precipitation after 3 and 12 h of hydrolysis, respectively (see

Table 5). For both AX (3 h) and AX (12 h), the substitution degree positively correlates with isopropanol concentration, which is in agreement with Dervilly, Saulnier [

32]. With the increase of Ara residues as side chains, the polysaccharides become more water soluble, demanding more isopropanol to accomplish the precipitation. However, considering AX (3 h), its consecutive fractions were collected in an ascending order of molecular weight, not following the rule that the highest molecular weight molecules would precipitate first (see

Table 5). The backbone weight average molecular weight (

${M}_{w}^{AX\left(\mathrm{pi},backbone\right)}$ =

${M}_{w}^{AX\left(pi\right)}$ (% Xyl)) of AX (3 h) fractions, such as p1 with p3, were very comparable (

${M}_{w}^{AX\left(p1\right)}$ = 84 kDa,

${M}_{w}^{AX\left(p1,backbone\right)}$ = 61 kDa;

${M}_{w}^{AX\left(p3\right)}$ = 114 kDa,

${M}_{w}^{AX\left(p3,backbone\right)}$ = 80 kDa). Therefore, for AX (3 h) the gradient precipitation depends mainly on the solubility of the polysaccharide fractions controlled by the substitution pattern than their

M_{w}. For GM21, no significant difference was found on the average molecular weight of the polysaccharide fractions, and for AX, only the

M_{w} of first fraction p1 was significantly different from the hydrolyzed sample. Therefore, their

M_{w} are not apparently related to isopropanol concentration. In addition to the dispersity parameter, the asymmetry factor (A

_{s}) (see

Figure 5) and the molecular-weight distribution functions (MWDs) of native, hydrolyzed, and precipitated polysaccharide fractions were investigated (see

Figure 6). Particular attention was given to the symmetry of the function with respect to the maximum point of the Gaussian distribution (number-average molecular weight), which is related to the absolute composition of the polymer chain lengths [

33]. From almost all of the distribution functions shown in

Figure 6, we observed that the curves did not deviate significantly from a normal distribution function, meaning that the samples consist of the same statistical segment length. However, GM21

_{(24h)}, GM38

_{(24h)}, GM38

_{(24h,p3)}, and XG

_{(24h,p3)} deviated from the symmetrical shape. The asymmetry factor (A

_{s}) is a measure of the polysaccharide’s skewness and it is defined as:

When a distribution is negative skew (As < 1), the polymer population contains a larger fraction of low molecular-weight polymer chains, contrariwise when the shape is positively skew (As > 1) a larger fraction of high molecular-weight chains is present.

For GM21_{(24h)}, the distribution shifted to the higher region of molecular weight (As = 0.9), while for GM38_{(24h)} was the opposite (As = 1.4). GM38_{(24h,p3)} and XG_{(24hp3)} both showed a negative skew trace.

In conclusion, with the exception of AX (3 h), for all the other precipitated samples, we obtained fractions with dispersity lower than the original hydrolyzed samples before fractionation. The best results with regard to low dispersity were achieved for the second precipitate of GM21 and GM38 hydrolyzed for 24 h and 3 h, respectively (${\u0110}_{GM21}^{24h,p2}$ = 1.004 ± 0.002, ${\u0110}_{GM38}^{3h,p2}$ = 1.193 ± 0.003). Partial acid hydrolysis significantly degraded the M_{w} of the native polysaccharides, and isopropanol precipitation was a valid method for obtaining polymer fractions with lower dispersity than the hydrolyzed polysaccharide fractions. Finally, with few exceptions, acid hydrolysis coupled with i-PrOH precipitation can control the MWD shape, leading to samples with similar chain length.

#### 2.2. Monosaccharide Ratios

The monosaccharide ratio of native and HCl-treated and fractionated polysaccharide was determined using high-performance anion-exchange chromatography-pulsed amperometric detection (HPAEC-PAD) after complete hydrolysis to understand whether the partial acidic hydrolysis could affect the uniformity of the polysaccharide samples. For GM21 (3 h) and GM21 (24 h), a statistically significant difference was found between the monosaccharide ratio of the first precipitate and that of the other two precipitated fractions (see

Table 2). However, two out of three fractions did not differ statistically from the native compound, emphasizing that the acid hydrolysis did not significantly affect the uniformity of the final products. No variation on the monosaccharide ratio was found when comparing the GM38 fractions within each time point with each other (see

Table 3). Nevertheless, the monosaccharide ratio of the hydrolyzed fractions differed from the native polysaccharide’s ratio, indicating that the homogeneity of the polysaccharide population remains constant regardless of hydrolysis time. A strong difference in the monosaccharide ratio was observed for AX, both within a group of fractionated samples and between the fractions and the starting polysaccharide (see

Table 5). Therefore, the acid hydrolysis had a significant impact in increasing the heterogeneity of the final product, or at least revealed it. The same was observed for XG (see

Table 4). After 6 h of hydrolysis, the monosaccharide ratio of the collected fractions did not differ from the native xyloglucan. However, after 48 h, the percentage of galactose and xylose sidechains changed. Specifically, galactose reduced its relative content by roughly a quarter and xylose increased it by around a quarter (XG Native: Xyl:Gal = 23:15; XG

_{(p1)}: Xyl:Gal = 29:11; XG

_{(p2)}: Xyl:Gal = 27:12; XG

_{(p3)}: Xyl:Gal = 31:13).

Lastly, partial acid hydrolysis in combination with precipitated fractionation seems to modify the uniformity of the studied polysaccharides, or at least reveal their heterogeneity. In particular, the highly substituted galactomannan (GM38), arabinoxylan, and the longest hydrolyzed xyloglucan (XG 48 h) seem to increase their heterogeneity after partial hydrolysis.