## 3 Results and Discussion
### Degradation Kinetics and Chain Scission Mechanisms  
The intrinsic viscosity and MW of KGM fractions decreased rapidly in the initial period of US treatment (\(\leq\)20 min) and then slowly in the remaining period (Figure 2a,b). In Figure 2b, the initial value of [\(\eta\)] for KGM was 1803.5 mL\(\cdot\)g\({}^{-1}\), which was close to values reported by [PERSON] et al. [37] (18.6-19.9 dL\(\cdot\)g\({}^{-1}\)), [PERSON] et al. [3] (12.7-23.6 dL\(\cdot\)g\({}^{-1}\)), and [PERSON] et al. [38] (16.0-20.0 dL\(\cdot\)g\({}^{-1}\)), but higher than values determined by [PERSON] et al. [39] (7.65-13.0 dL\(\cdot\)g\({}^{-1}\)). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
\begin{tabular}{c} **Sonication** \\ **Time (min)** \\ \end{tabular} & \(M_{\mathrm{w}}/M_{\mathrm{n}}\) & \(R_{\mathrm{h}}\) **(nm)** & \(<\)\(R_{\mathrm{g}}\)\(>\)\({}_{2}\) **(nm)** & \multicolumn{2}{c}{**Higher-MW Region a**} \\ \cline{3-6}  & & & & \(\alpha\) & \(L_{\mathrm{p}}\) **(nm)** \\ \hline
0 & 1.5 & 60.0 & 104.5 & 0.79 & 10.3 \\
2 & 1.3 & 33.6 & 55.9 & 0.51 & 7.1 \\
4 & 1.3 & 22.7 & 39.6 & 0.62 & 7.2 \\
6 & 1.3 & 19.7 & 33.3 & 0.65 & 7.4 \\
10 & 1.2 & 16.5 & 28.7 & 0.69 & 7.4 \\
20 & 1.2 & 13.8 & 25.4 & 0.73 & 7.3 \\
30 & 1.2 & 12.9 & 24.9 & 0.77 & 7.5 \\
60 & 1.2 & 11.1 & 26.9 & 0.95 & 9.1 \\ \hline \hline \end{tabular}  
* MW distributions selected for \(\alpha\) values and \(L_{\mathrm{p}}\) calculation were based on Mark–Houwink plots shown in Figures S2 and S3 (Supplementary Materials); \(\alpha\) was calculated from the Mark–Houwink equation; \(L_{\mathrm{p}}\) was the persistence length.  
\end{table} 
Table 1: Effects of ultrasonication (US) on molecular properties and conformation of konjac glucomannan (KGM) fractions derived from analysis with high-performance size-exclusion chromatography (HPSEC) equipped with multi-angle laser light scattering (MALLS) detector, viscometer (Vis), and refractive index RI detector. MW—molecular weight. Figure 1: High-performance size-exclusion chromatography (HPSEC) chromatograms of konjac glucomannan (KGM) fractions (US-0, US-4, US-10, and US-60: ultrasonication (US) treatment for 0, 4, 10, and 60 min at a fixed amplitude of 60%). Ultrasonic degradation of polymers follows two primary chain scission mechanisms: random chain scission and midpoint chain scission [40]. The degradation kinetics for random chain scission can be represented by the classical Schmid model relating the rate of degradation to MW [41]. \[\frac{M_{e}}{M_{t}}+\ln\biggl{(}1-\frac{M_{e}}{M_{t}}\biggr{)}=\frac{M_{e}}{M_{ i}}+\ln\biggl{(}1-\frac{M_{e}}{M_{i}}\biggr{)}-\frac{k_{1}}{c}\biggl{(}\frac{M_{e}}{m} \biggr{)}^{2}t, \tag{1}\]  
where \(M_{\rm i}\) and \(M_{t}\) represent the initial average MW and the MW at time \(t\) of the US treatment, respectively, \(M_{\rm e}\) is the final limiting average MW, \(m\) represents the MW of the monomer, \(c\) is the initial molar concentration of the polymer, and \(k_{1}\) is the degradation rate constant. With this model equation, the plot of \(-(M_{\rm e}/Mt)\) - \(\ln((1-(M_{\rm e}/Mt)\) versus time \(t\) is linear. For midpoint chain scission, the degradation kinetics can be represented by the following first-order kinetic model [42]:  
\[\ln((M_{\rm i}-M_{\rm e})/(M_{t}-M_{\rm e}))=kM_{\rm e}t. \tag{2}\]  
The final limiting MW \(M_{\rm e}\) value for the KGM fractions was attained upon US treatment of KGM for 2 h as 20.7. Figure 2c,d show the plots and linear regression results of experimental data according to the model equations, \(-(M_{\rm e}/M_{\rm i})-\ln((1-(M_{\rm e}/M_{t})\) versus \(t\) for the random scission (Equation (1)) and \(\ln((M_{\rm e}-M_{\rm i})/(Mt-M_{\rm i}))\) versus \(t\) for the midpoint scission (Equation (2)), respectively. Obviously, the experimental data fitted closely to the random chain session model (Figure 2c) but not to the midpoint scission model (Figure 2d), suggesting that the US degradation of KGM was mainly achieved through the random chain scission mechanism.