Silver-cotton nanocomposites: Nano-design of microfibrillar structure causes morphological changes and increased tenacity

The interactions of nanoparticles with polymer hosts have important implications for directing the macroscopic properties of composite fibers, yet little is known about such interactions with hierarchically ordered natural polymers due to the difficulty of achieving uniform dispersion of nanoparticles within semi-crystalline natural fiber. In this study we have homogeneously dispersed silver nanoparticles throughout an entire volume of cotton fiber. The resulting electrostatic interaction and distinct supramolecular structure of the cotton fiber provided a favorable environment for the controlled formation of nanoparticles (12 ± 3 nm in diameter). With a high surface-to-volume ratio, the extensive interfacial contacts of the nanoparticles efficiently “glued” the structural elements of microfibrils together, producing a unique inorganic-organic hybrid substructure that reinforced the multilayered architecture of the cotton fiber.


Supplementary Methods
Scouring. Scouring was carried out by agitating cotton fiber in an aqueous solution containing NaOH (1.8 g/L) and Triton X-100 (0.2 g/L) with a liquid-to-fiber ratio of 22.4:1 at 100 C for 60 min. After the treatment, the fiber was washed in circulating water at 100 C for 20 min, followed by cold water for 20 min. The scoured fiber was then neutralized with a solution of acetic acid (0.25 g/L) for 10 min, rinsed multiple times, and air-dried.
Density. The density of the nanocomposite fiber was calculated based on the weight fractions of fiber and nanoparticles using a binary mixing equation: where  NC ,  f ,  NP are the densities of the nanocomposite fiber, the fiber matrix, and the nanoparticles, respectively, and w f and w NP are the weight fractions of the fiber and nanoparticles, respectively.
Percentages of cellulose Iβ, cellulose II, and amorphous cellulose. The crystallinity and the extent of conversion to cellulose II were determined by the simulation of XRD patterns with the calculated patterns of cellulose I, cellulose II, and amorphous cellulose for cotton fiber. The diffraction pattern of control cotton was calculated by the following equation: where w c is the fraction of crystalline cellulose and I c and I a are the intensities of crystalline and amorphous celluloses, respectively. For partially mercerized cotton (i.e., alkali-treated cotton and Agcotton NC fiber), a ternary mixing equation was used: where w c,Iβ , w c,II , and w a are the fractions of the cellulose Iβ, cellulose II, and amorphous cellulose, respectively, and I c,Iβ , I c,II , and I a are the intensities of the crystalline cellulose Iβ, crystalline cellulose II, and amorphous cellulose, respectively.
where  is the scale parameter and m is the shape parameter (Weibull modulus). These two unknowns can be estimated from the empirical distribution function (F n ) for n independent and identically distributed tenacity values.
where I is the indicator function, equal to 1 for  i ≤  and 0 otherwise. This empirical distribution can be commonly obtained by the following equation: where n is the total sample size, and i is the index of the tenacity value when the tenacity data are arranged in ascending order. From the determined parameters, the theoretical average ( ) and coefficient variation of tenacity (CV) can be calculated by the following equations, respectively: For the LLS method, the following linear form is obtained by taking double natural logarithms of both sides of equation (S5): where the m is directly obtained from the slope, and the  is deduced from the intercept in the liner fit.
The  and m can be determined when the value of the measurement is most likely to occur, that is, the L is maximized. This optimization can be obtained by using the log-likelihood function for easier computation.
Subsequently, the partial derivatives of ln L with respect to m and  are set to zero.
Equations (S14) and (S15) yield simplified likelihood equations, respectively, for m and : which can be numerically solved.

Goodness-of-fit test.
The Kolmogorov-Smirnov goodness-of-fit test was performed to examine whether the obtained tenacity data can be described by the Weibull distribution. Under the hypothesis that the data follow the Weibull distribution, the test statistic (D KS ), which is the greatest vertical distance between the empirical and Weibull distributions, can be measured: where F n () is the empirical distribution and F m, () is the Weibull distribution with the parameters determined from the MLE method. When the hypothesis is true for a large sample size, D KS is distributed with its own distribution function. Therefore, if the hypothesis is true, D KS is smaller than the critical value (D C ) determined from a significance level ().  = 0.05 was used in this study.  Figure S5. Empirical cumulative distributions of tenacity for control cotton fiber, alkali-treated cotton fiber, and Ag-cotton NC fiber plotted with two-parameter Weibull fits.