Radiation-Induced Degradation of Guaran in Dilute Solution: Kinetics and Conformational Transition under Ultra-Low-Dose X-Rays

1. Introduction

Guaran, a natural galactomannan from the endosperm of the guar bean (Cyamopsis tetragonoloba), is a high-molecular-weight polysaccharide widely utilised in the food, pharmaceutical, and cosmetic industries [1]. Its unique structure—a linear backbone of β (1→4)-D-mannose units with α (1--6)-linked D-galactose side chains—enables it to form highly viscous aqueous solutions at low concentrations [2]. In the food industry, Guaran is indispensable as a thickener and stabiliser in dairy products, sauces, and baked goods. However, the extremely high viscosity and massive hydrodynamic volume of native Guaran often limit its application in specialised fields, such as clinical nutrition, materials science, and targeted drug delivery [3].

Recent studies have pointed out the greatest biological and functional benefits of low-molecular-weight (LMW) Guaran and its oligosaccharides [4]. In the pharmaceutical sector, LMW Guaran is increasingly used as a bioactive excipient for colon-specific drug delivery, as it remains intact within the upper gastrointestinal tract but is readily degraded by specialised colonic microflora [5]. Therapeutically, hydrolysed Guaran has demonstrated significant hypoglycaemic and hypolipidemic effects, assisting in the metabolic management of type 2 diabetes and hypercholesterolemia [6]. Furthermore, LMW Guaran serves as an excellent prebiotic fibre, stimulating the growth of beneficial gut bacteria, stabilising the gut barrier, and significantly promoting the production of short-chain fatty acids (SCFAs) [7].

Although these outstanding physiological benefits exist, traditional techniques for producing LMW Guaran—such as acid hydrolysis, enzymatic treatment, or high-temperature chemical oxidation—usually suffer from low selectivity, long processing times, or the need to use harsh chemicals that require complicated downstream purification [8,9]. Radiation-induced degradation has now appeared as a promising 'green chemistry' alternative, providing a sterile, chemical-free, and room-temperature method for accurately adjusting the polymer chain length [10]. Although high-dose gamma or electron-beam irradiation is well known for use with industrial polymers, these methods can cause severe local overheating or lead to unwanted side reactions such as radical cross-linking [11]. As a result, the application of ultra-low-dose (ULD) X-rays offers a highly novel and energy-efficient route for controlled depolymerisation. Since it operates at very low doses, it mainly acts via the indirect effects of water radiolysis, in which the secondary electrons produced result in a uniform spread of hydroxyl radicals (•OH) [12].

The objective of the study is to apply a physics-based method to investigate the kinetic properties, scaling laws, and conformational behaviour of Guaran when it is exposed to ULD X-ray irradiation in a dilute aqueous solution. This can be obtained by examining the basic first-order scission laws, the thermodynamic activation parameters obtained from the Eyring viscosity model, and the scaling coefficient (for example, the Flory and Mark-Hwang exponents); see, for example, Ref. 13. As a result, an understanding is obtained of how X-ray irradiation intensity affects the conformation of Guaran chains. Such insights are essential for developing standardised, scalable, and environmentally friendly procedures for producing functional LMW Guaran that is suitable for use in high-value industrial and medical applications.

2. Materials and Methods

1.1. Materials and Solution Preparation

The commercial-grade guar gum (Guaran) powder was obtained from Sigma Chemical Co., in St. Louis, MO, USA. Stock solutions (0.01 g. cm⁻³) were prepared by measuring a known amount of Guaran and dissolving it in double-distilled water; the mixture was then carefully stirred with a magnetic stirrer at room temperature until the gum was completely dissolved and a uniform solution was obtained.

1.2. Flow Time Measurements

The flow time (t) of native and irradiated solution samples relative to the solvent (t₀) was measured using a capillary viscometer. Specifically, an Ostwald viscometer with a 0.5 mm capillary diameter (type YUCHENGTECH, China) was immersed in a high-precision, temperature-controlled bath (TCB-7, PSL-Rheotek, USA) maintained at 24.99. Flow times (${\displaystyle \frac{t}{t_0}}$) were recorded in triplicate, and the filtered polymer solutions typically exhibited efflux times of 100 to 150 s. Flow times for both the solvent and the solution were measured in triplicate for each independent replicate. Replicate data are expressed as mean ± standard deviation (SD). The relative viscosity (η_r) and specific viscosity (η_sp) were determined as follows [14,15]:

$${\eta }_r={\displaystyle \frac{t}{t_0}}, {\eta }_{\mathit{sp}}={\eta }_r-1$$

(1)

2.3. Determination of Intrinsic Viscosity and Molar Mass

The intrinsic viscosity ([η]) of native and irradiated samples was determined using the single-concentration Solomon-Ciută approximation (Eq. 2) [16]. Subsequently, the intrinsic viscosity [η] was converted to viscosity-average molecular weight (M) utilising the Mark-Houwink-Sakurada relationship (Eq 3) [17,18].

$$\left[\eta \right]={\displaystyle \frac{(2 {\eta }_{\mathit{sp}}-{2 \mathit{ln} \eta }_r{)}^{0.5}}{C}}$$

(2)

$$M_r={(\left[\eta \right] / k_{\left[\eta \right]} )}^{1/\alpha }$$

(3)

where M_r = M/1 g.mol⁻¹ , k_[η] = 666 mol.g⁻¹and α = 0.72 [19]

2.4. Irradiation Procedure

Dilute Guaran solutions were irradiated with a digital linear accelerator (Elekta Infinity™, Elekta AB, Stockholm, Sweden) at the National Oncology Centre in Benghazi, Libya. The accelerator was operated using a 6 MV photon beam under ambient conditions. The use of 6 MV photon beams with Elekta Infinity linear accelerators has been previously reported in the literature, including studies describing the dosimetric and commissioning characteristics of this accelerator system [20,21].

The Guaran solutions were exposed to absorbed X-ray doses varying from 0.2 to 2 Gy at a constant dose rate of 1 Gy.s⁻¹ . The irradiation conditions were kept consistent across all samples to ensure reproducibility of the degradation experiments. After irradiation, the samples were tested for viscosity at predetermined time intervals to monitor changes in their molecular characteristics and evaluate any post-irradiation degradation. All radiation degradation experiments were carried out three times (n = 3) using independent, fresh batches of Guaran solutions to ensure reproducibility.

The irradiation parameters, including the accelerator model, photon energy, absorbed dose range, and dose rate, were recorded for each experimental run. These parameters were used to evaluate radiation-induced changes in dilute Guaran solutions and their subsequent conformational behaviour.

2.5. Kinetics Analysis

2.5.1. Rate and Half-Life Dose

Assuming a random scission process following first-order kinetics, the degradation rate constant (k) was determined by linear regression of the reciprocal molar mass against the absorbed dose (D) [22,23]:

$${\displaystyle \frac{1}{M_D}}={\displaystyle \frac{1}{M_o}}+{\displaystyle \frac{\mathit{kD}}{M_u}}$$

(4)

where M_D and M_o represent the molar masses at dose D and dose zero, respectively. The initial degradation followed pseudo-first-order exponential decay kinetics. The half-life dose (D_1/2), defined as the absorbed X-ray dose required to reduce the initial macromolecular parameters by 50%, was calculated using Equation 5 as [23]:

D_1/2 = ln2/k

(5)

2.5.2. Radiation Yield Relations

Based on the changes in M as a function of delivered dose, the fundamental SI radiation chemical yield of chain scission (G(s), mol.J⁻¹) was determined via Equation 6 [24]:

$$\mathrm{G}(\mathrm{s})={\displaystyle \frac{C.k}{\rho .M_o}}$$

(6)

where C is the polymer concentration (0.01 g.cm⁻³), ρ is the solution density (≈1.0 g.cm⁻³), and M₀ is the initial viscosity-average molar mass (M₀). To allow direct comparison with historical literature, G(s)was converted to traditional units of scissions per 100 eV using Equation 7 [25]:

$${G\left(s\right)}_{[\frac{\mathit{Scission}}{100\mathit{eV}}]}={G\left(s\right)}_{[\frac{\mathit{mol}}{J}]}\mathrm{X} 9.648 \mathrm{X} {10}^6$$

(7)

2.5.3. Thermodynamic Activation Parameters

The activation energy (E_[η]) and pre-exponential factor (A_[η]) across varying molar mass ranges were determined using the Arrhenius-type relation (Eq. 8). The entropy of activation (ΔS^‡) was subsequently derived from the Eyring equation (Eq. 9) [14,26]:

ln[η] = ln ln A_[η] + E_[η] /RT

(8)

$$\mathit{ln} \mathit{ln} A_{\left[\eta \right]}={\displaystyle \frac{{e.k}_B.T}{h}}+{\displaystyle \frac{{\mathit{\Delta S}}^{‡}}{R}}$$

(9)

2.5.4. Statistical Treatment

Linear regression analysis was performed using Statistic a (version 13.5.0.17, TIBCO Software Inc., Palo Alto, CA, USA). The goodness-of-fit for kinetic models was evaluated using the coefficient of determination R2), and the derived rate constants (ks) and thermodynamic parameters are reported alongside their (95%) confidence intervals (Cl).

1.6. Conformational Modelling

2.6.1. Evaluation of the Chain Conformations

Chain conformations were evaluated using the self-avoiding walk model (SA-WM) and the random walk model (RWM) equations, as listed in Table 1 [14,15,27,28]. The SA-WM equations are used to determine scaling laws, and the RWM equations are used to determine dimensions at theta (Ѳ) conditions. The transition to theta (Ѳ) conditions was determined theoretically using Equation 19, enabling characterisation of unperturbed dimensions without additional solvent tuning [28].

2.6.2. Experimental Variability

To address experimental variability, all conformational parameters derived from self-avoiding walk models (SAWMs) and random walk models (RWMs) were calculated using mean intrinsic viscosity values. The results were validated against literature-established thresholds to confirm the mathematical stability of the model outputs.

3. Results and Discussion

3.1. Rate and Scission Efficiencies

The ultra-low-dose ULD X-ray irradiation of guaran in a dilute aqueous solution (0.01 g. cm⁻³) was studied at 25 °C. Figure 1 shows the viscosity-average molar mass (M display a clear exponential decrease as radiation dose (D) increase. This initial, rapid decrease in molar mass (M) is typical of the radiolytic degradation of hydrophilic polysaccharides in aqueous systems [29,30]. In dilute solutions, the degradation mechanism is predominantly driven by indirect effects arising from water radiolysis, in which highly reactive hydroxyl radicals (•OH) abstract hydrogen atoms from the carbohydrate backbone, leading to glycosidic bond cleavage [31,32].

To establish the kinetic mechanism involved in this process, a linear first-order scission plot was prepared by plotting (1/M) against the effective irradiation dose (D). As shown in Figure 2, a clear linear relationship is evident, yielding the equation Y = 0.0012 + 0.0015 X and a high correlation coefficient (R² = 0.9932). The strong linearity indicates that the X-ray-induced degradation of guaran obeys classic first-order random-chain scission kinetics, which is in good agreement with the Charlesby-Rosiak model for polymer degradation in solution [33,34].

The quantitative kinetic and efficiency parameters extracted from the experimental data are summarised in Table 2. The first-order degradation rate constant (k) was determined to be 0.243 kGy⁻¹, highlighting the high susceptibility of the guaran macromolecular chain to ultra-low-dose X-ray exposure [29,30]. Correspondingly, the D_1/2 value via Equation 5 (ln2/k) was 2.85. This low half-life dose requirement emphasises the extreme efficiency of the ULD X-ray process in altering the macrostructural dimensions of the polysaccharide without requiring massive energy thresholds.

The quantitative kinetic and efficiency parameters extracted from the experimental data are summarised in Table 2. The first-order degradation rate constant (k) was determined to be 0.243 kGy⁻¹, highlighting the high susceptibility of the guaran macromolecular chain to ultra-low-dose X-ray exposure [29,30]. Correspondingly, the D_1/2 value via Equation 5 (ln2/k) was 2.85 . This low half-life dose requirement emphasises the extreme efficiency of the ULD X-ray process in altering the macrostructural dimensions of the polysaccharide without requiring massive energy thresholds.

3.2. Transition State Model

Figure 3 shows the structural behaviour of Guaran fractions and their conformational stability as temperature increases, using an Arrhenius-type plot of the natural logarithm against the inverse of the temperature (Eq. 8). The thermodynamic activation parameters obtained from the Eyring relationship provide important structural insights (Table 3) [14,26]. The flow activation energy (E_[η]) decreases from 4.20 kJ.mol⁻¹in the case of the high molar mass (HM) fractions to 2.13 kJ.mol⁻¹ for the small molar mass (SM) fractions. This stepwise reduction shows that the long polymer chains have greater structural resistance to thermal flow because of their larger initial coil size and greater degree of intermolecular entanglement; in fact, when X-ray scission cuts the backbone into smaller pieces, these topological constraints are lost, which in turn lowers the energy barrier required for the polymer segments to align and flow [14,26,36].

Furthermore, in Table 3, the pre-exponential factor ( A_[η]) drops from 19.67 to 13.5, which shows that the shorter cleaved chains carry out conformational rearrangements less often when undergoing shear deformation [14,36]. Most significantly, the activation entropy (ΔS^‡ ) values for all the fractions are strongly negative and lie within a small range, from - 250.24 to - 250.65 J.K⁻¹mol⁻¹ . These large negative values show that the transition state observed during liquid shear flow is highly ordered, causing the galactomannan chains to adopt a rigid orientation and leading to a substantial loss of conformational degrees of freedom [14,36,37]. The fact that ΔS^‡ is identical across all molecular weights, indicating that ULD X-ray exposure merely reduces chain length without altering the underlying chemical structure or the basic thermodynamic mechanism involved in the movement of polymer segments.

3.3. Scaling Characteristics

The scaling behaviour of Guaran under ULD X-ray irradiation was evaluated. This evaluation examined the relationship between molar mass (M) and its hydrodynamic dimensions. The corresponding data are shown in Figure 4 and Table 4. Radiation scission causes the molar mass to decrease from 741.3 to 265.8 kg. mol⁻¹ . As a result, a matching contraction of the polymer coil is observed. The intrinsic viscosity( [η]) drops from 862.38 to 412 cm³.g⁻¹ [19]. Furthermore, the radius of gyration (R_g) shrinks from 55.73 to 30.12 nm.As M decreases, the overlap concentration (C^*) systematically increases from 0.891 to 1.93 mg cm⁻³. This Shift indicates that shorter fragments require higher concentrations to touch. Therefore, more molecules are needed to transition from dilute to entangled semi-dilute states [27].

The solvent quality and chain expansion were characterised by the exponent coefficients shown in Table 5. These coefficients were derived from equations 12-14, using the slopes in Figure 4. The double-logarithmic scaling plots yield a Mark-Houwink exponent (α) of 0.83. According to the standard polymer scaling relation α = 3ν − 1, this indicates a Flory exponent (ν) of 0.61 [15,19]. A Flory exponent of ν ≈0.60 is the classic hallmark of a self-avoiding random walk in a thermodynamically "good solvent"[15,27,38]. This indicates that despite the extensive backbone cleavage caused by X-rays, water remains an excellent solvent for the fragmented Guaran, with no signs of radiation-induced hydrophobic aggregation or coil collapse. The fact that the negative scaling exponent of the critical overlap concentration${\nu }_{C^{*}}=-0.64$ agrees with the theoretical prediction of C^*~M^{1 − 3ν} confirms this behaviour [39,40].

Moreover, the structure ratio (${\rho }_S={\displaystyle \frac{R_g}{R_h}}$), in Eq.15, lying between 0.63 and 0.65, clearly supports a random-coil conformation and thus confirms that the polymer retains its flexible-to-semi-rigid structural character throughout the low-dose treatment [15,27].

3.3. Stiffness and Unperturbed Dimensions

To predict the difference between the inherent flexibility of the galactomannan backbone and that resulting from solvent swelling, the chain parameters under undisturbed conditions were obtained using the idealised model (Figure 5, Table 6).

Both the unperturbed end-to-end distance (R_Ѳ) and the characteristic ratio (C_N) decrease as the molar mass decreases; this is because shorter chains require less space [27]. Most importantly, the persistence length (l_p ) remains constant, varying only slightly from 29.6 nm to 25.4 nm during the radiation process [41]. The small decrease in l_p indicates that although random chain scission is the main degradation event, exposure to ULD X-rays might also lead to minor structural changes, for example via partial loss or rearrangement of the galactose side chains [42]. Debranching generally reduces local steric hindrance and therefore slightly increases the flexibility of the backbone. Nevertheless, the fact that it remains above 25 nm shows that Guaran still keeps its typical semi-flexible random-coil structure [41]. The ULD radiation process reduces the polymer's hydrodynamic size without causing it to collapse into a compact globule, so that its key physical properties are preserved; it can be used in applications that depend on specific viscosity thresholds in solution [13,42].

4. Conclusions

The research examined the kinetics of radiation-induced degradation and the conformational changes in Guaran upon exposure to ultra-low-dose (ULD) X-ray irradiation in a dilute aqueous solution. The degradation process obeys clean first-order scission kinetics and has an apparent rate constant k of 0.243 kGy⁻¹, indicating that the polysaccharide backbone is highly susceptible to attack by radicals formed via the radiolysis of water. The analysis based on the Eyring model showed that the intrinsic activation energy for flow decreases with decreasing chain length, whereas the strongly negative activation entropy indicates a highly ordered transition state during shear flow. Assessments of the conformation and scaling properties showed that the irradiated Guaran still has a flexible, self-avoiding random-coil structure in water, with the persistence length remaining constant at 25-30 nm. This indicates that exposure to ULD X-rays systematically cuts the polymer chains without damaging the native semi-flexible backbone structure. Ultimately, the study proved that clinical-grade, low-dose X-ray sources can be used to precisely control the molecular weight and hydrodynamic properties of galactomannans for specific industrial and biomedical applications.