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branched aggregates that can increase the viscosity of the solu- tion. However, the calcium route led to lower viscosity owing to the presence of residual calcium ions in the nal product. These calcium ions can interfere with the alginate chains, resulting in lower viscosity. These mechanisms were also con rmed by Gomez et al. , 21 as they reported that the acid route produced sodium alginates with a higher viscosity than those via the calcium route. This could be explained by the breakage of the ether bond by the acid solution used in both the calcium alginate and alginic acid routes, leading to low viscosities. Thus, USAR, UKAR, and CMAL were chosen for further experiments to produce bres because of their higher molecular weights. 3.2.2 FTIR. Fig. 7 shows the main functional groups and chemical bonds of the commercial alginate and alginates extracted from S. polycystum and L. japonica as revealed by the FTIR spectra. The commercial alginate and alginates extracted from S. polycystum , and L. japonica displayed a similar broad absorption peak at 3300 cm − 1 , which was attributed to OH- bending vibration. In addition, a weak band near 2925 cm − 1 was attributed to CH-stretching vibration. 31 – 33 The asymmetric and symmetric stretching vibrations of carboxylate (R-COO − ) groups were observed at absorption peaks at approximately 1645 and 1410 cm − 1 . 31,33 The peak at approximately 1090 cm − 1 is assigned to symmetrical C – O – C stretching. 34 Another peak attributed to alginates was located at 1290cm − 1 and was assigned to the C – O – Cgroup. 31 Other peaks at 820 and 940 cm − 1 correspond to C – H bonds from mannur- onic acid and uronic acid residues. 35 The FTIR spectra of sodium alginates obtained from S. pol- ycystum and L. japonica clarify that they have a chemical struc- ture similar to that of commercial sodium alginate. This was con rmed by successful extraction of the sodium alginates. 3.3 Single- bres characteristics 3.3.1 Statistical distribution of tensile strength. Weibull analysis, a commonly used statistical technique for analysing the physical behaviour of brittle materials in terms of strength, was predicated based on the idea that the failure due to the most signi cant fault caused the overall failure of the spec- imen. 36 The strength of the bres was found to be statistically distributed because of the di ff erent severities of faults along the volume of the bres. Therefore, the distribution of the bre strength, s f , under tension is generally described using mean values of the standard Weibull modulus.
Fig. 8 Weibull plots for di ff erent types of calcium alginate fi bre sources.
the Weibull distribution. F in eqn (5), also known as the prob- ability index, was estimated using the following approximation:
(9)
F = ( n − 0.5)/ N ,
where n is the rank of the n -th number in the ascending ordered strength data point ( n = 1 corresponds to the smallest and i = n corresponds to the largest) and N is the total number of samples. The inherent defect distribution along the bres and the bre-to- bre strength variability within a batch of bres resulting from processing variances and damage brought about by handling the bres are two major factors in uencing the strength variability. To analyse the statistical distribution of the bre strength, a plot of the tensile strength for the di ff erent sources of calcium alginates based on the Weibull modulus is shown in Fig. 8. In all cases, the R 2 coe ffi cient was relatively high ( $ 0.95), indicating a satisfactory degree of linearity. Thus, the bre strength can be e ff ectively described using the Weibull function.
(7)
F = 1 − exp(( − s f )/ s o ) m ,
where F is the failure probability of the bres and m is the Weibull modulus, that is, the variability of the distribution. s 0 denotes the characteristic strength. By rearranging and taking the natural logarithm of the variables on both sides of eqn (5), eqn (6) is obtained:
(8)
ln(ln(1/(1 − F ))) = m ln s f − m ln s o
Fig. 9 Tensile strength of calcium alginate fi bres from di ff erent sources.
Hence, a plot of X = ln s f vs. Y = ln(ln(1/(1 − F ))) should be a straight line if the material strength variability is described by
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