## 3 Results and Discussion
### Rheology  
Rheology presents information about of the behavior of polymer melts through measuring the flow (viscosity) as a function of shear rate [56]. From dynamic rheological measurements the complex viscosity (\(\eta^{*}\)) was determined for PHBV at 180 \({}^{\circ}\)C against shear rate (\(\omega\)) as frequency sweeps (also known as flow curves); results are shown in Figure 3. The PHBV flow curves show a reduction in \(\eta^{*}\) with \(\omega\) showing shear thinning behavior typical for non-Newtonian fluid [31; 57]. At high shear rates the anisotropic polymer chains with high molar mass will disentangle and aligned along the shear direction [57; 58]. Thus, less intermolecular interaction happens among the polymer chains resulting in higher free volume and a lower viscosity [31; 57; 58]. The \(\eta^{*}\) of PHBV-15 decreased more rapidly than the other PHBV samples (Figure 3 and Table 8). This might be attributed to the lower purity (80%) of the polymer and partial plasticizing effect of impurities present and high _PDI_ of 1.47 in the polymer [31; 59; 60]. Smaller chains act as a plasticizer for longer chains, increasing the free volume space between polymer chains leading to improvement in the mobility of the polymer chains. The viscosity of the polymer therefore decreases with higher slope comparing the polymers without plasticizer [60]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Sample** & **Model a** & \(F_{V}\)b & \(F_{V}\)c & \(F_{B}\)c & \(F_{VV}\)c & \(F_{V\text{W/BV}}\)c & \(F_{\text{BB}}\)c & \(F_{VVV}\)c & \(F_{BW/V\text{WB}}\)c & \(F_{BW}\)b & \(\epsilon\) \\ \hline PHBV \(-46\) & exptl & 0.23 & 0.23 & 0.77 & 0.08 & 1.01 & 0.63 & 0.03 & 0.89 & 0.09 \\  & (i) & & 0.23 & 0.77 & 0.05 & 0.17 & 0.60 & 0.01 & 0.04 & 0.14 \\  & (ii) & & 0.22 & 0.78 & 0.08 & 0.15 & 0.63 & 0.03 & 0.05 & 0.09 \\  & (iii) & & 0.22 & 0.78 & 0.09 & 0.14 & 0.64 & 0.03 & 0.05 & 0.09 \\ PHBV \(-61\) & exptl & 0.24 & 0.22 & 0.78 & 0.08 & 1.07 & 0.65 & 0.04 & 0.89 & 0.09 \\  & (i) & & 0.22 & 0.78 & 0.05 & 0.17 & 0.61 & 0.01 & 0.04 & 0.13 \\  & (ii) & & 0.21 & 0.79 & 0.07 & 0.13 & 0.66 & 0.03 & 0.05 & 0.09 \\  & (iii) & & 0.22 & 0.78 & 0.09 & 0.14 & 0.64 & 0.04 & 0.05 & 0.09 \\ PHBV \(-78\) & exptl & 0.22 & 0.23 & 0.77 & 0.08 & 0.99 & 0.62 & 0.04 & 0.88 & 0.13 \\  & (i) & & 0.23 & 0.77 & 0.05 & 0.18 & 0.59 & 0.01 & 0.04 & 0.14 \\  & (ii) & & 0.23 & 0.77 & 0.08 & 0.15 & 0.62 & 0.03 & 0.05 & 0.10 \\  & (iii) & & 0.27 & 0.73 & 0.09 & 0.18 & 0.55 & 0.04 & 0.05 & 0.13 \\ PHBV-84 & exptl & 0.21 & 0.20 & 0.80 & 0.07 & 1.09 & 0.68 & 0.04 & 0.88 & 0.08 \\  & (i) & & 0.20 & 0.80 & 0.04 & 0.16 & 0.64 & 0.01 & 0.03 & 0.13 \\  & (ii) & & 0.19 & 0.81 & 0.06 & 0.12 & 0.69 & 0.02 & 0.04 & 0.08 \\  & (iii) & & 0.20 & 0.80 & 0.07 & 0.12 & 0.68 & 0.04 & 0.04 & 0.08 \\ \hline \hline \end{tabular}  
* exptl represent experimental data; (i), (ii), and (iii) are calculated values by Bernoullian model, first-order Markovian model, and mixture of two Bernoullian random copolymers model, respectively. b 3 HV molar fraction (mol-mol\({}^{-1}\)) determined by \({}^{1}\)H-NMR spectroscopy. c \(F_{X}\), \(F_{XY}\), and \(F_{XYV}\) represent mole fractions of sequence \(X\), \(XY\), and \(XVV\), respectively, where \(X\), \(Y=V\) or \(B\).  
\end{table} 
Table 7: Experimental and calculated mole fractions of diad, and 3 HV-centered triad sequence distributions of PHBV \(-46\), \(-61\), \(-78\), and \(-84\). To quantify the shear thinning behavior, the rheological data were fitted to the Power-law (Ostwald-de Waele) model, which represents viscosity as a function of some power of the shear rate (\(\omega\)) [(31; 61)]. The Cox-Merz rule is used to establish the relationship between steady shear and dynamic shear viscosity, which is valid for PHA, PHB, and PHBV [(31; 61)]. Exchanging the steady shear terms with the dynamic viscosity terms yields a modified Power-law model, expressed as:  
\[|\eta*(\omega)|\ =\ K(\omega)^{n-1} \tag{3}\]  
The modified model has two parameters of \(K\) and \(n\) that must be fitted to experimental data.