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Thermally induced structural transitions in cotton fiber revealed by a finite mixture model of tenacity distribution Sunghyun Nam, Daniel Ahmed Alhassan, Brian Condon, Alfred D. French, and Zhe Ling ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.7b04919 • Publication Date (Web): 09 Apr 2018 Downloaded from http://pubs.acs.org on April 9, 2018

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ACS Sustainable Chemistry & Engineering

1

Thermally induced structural transitions in cotton fiber revealed by a finite

2

mixture model of tenacity distribution

3 Sunghyun Nam,*,† Daniel Ahmed Alhassan,‡ Brian D. Condon,† Alfred D. French,† and Zhe Ling†,§

4 5 †

6 7

‡

8 9 10 11 12

United States Department of Agriculture, Agricultural Research Service, Southern Regional Research Center, 1100 Robert E. Lee Boulevard, New Orleans, LA 70124, USA.

§

Department of Mathematics, University of New Orleans, 2000 Lakeshore Drive, New Orleans, LA 70148, USA.

Beijing Key Laboratory of Lignocellulosic Chemistry, Beijing Forestry University, Tsinghua East Road, Beijing, China.

13

ABSTRACT

14

Much processing of cotton fibrous materials involves heat treatments. Despite their critical influence

15

on the properties, the structural responses of cotton fiber to elevated temperatures remain uncertain. This

16

study demonstrated that modeling the temperature dependence of the fiber tenacity distribution was a new

17

approach to uncovering the details of the thermally induced structural transitions of cotton fiber at low

18

and intermediate temperatures. As the temperature increased, the tenacity probability density developed a

19

unique pattern—periodic evolution/degeneration of bimodality—which was successfully parameterized

20

by the mixed Weibull model. Interpretation of the variation of the model’s five parameters indicates that

21

cotton fiber underwent the following sequence of transitions: glass transition at 160-220 °C, dehydration

22

at 240-260 °C, and chain scission at 280-300 °C. The crystallographic and thermogravimetric analyses

23

showed the coexistence of thermal crystallization at 180-360 °C. The decomposition of the crystalline

24

cellulose was predominant along the fiber axis, preserving the lateral crystalline structure in the remains

25

even after a 90% weight loss.

26 27 28 29 30 31

KEYWORDS: cotton cellulose; tenacity; glass transition; mixed Weibull model; crystallinity; X-ray diffraction; Rietveld refinement Corresponding Author * Sunghyun Nam. E-mail: [email protected]. Tel.: +15042864229. Fax: +15042864390 1

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INTRODUCTION

33

Under heat, cotton fiber undergoes a series of physical and chemical reactions that alter the structure

34

and ultimately the properties of the fiber.1 The structure of cotton fiber is complex. The cellulose, a linear

35

polymer of β-D-glucopyranose containing about 20,000 glucose units, is imperfectly aligned and forms

36

very small crystallites.2 Considering that the length of a crystallite (∼300 Å) is much smaller than that of

37

cellulose (∼10 µ), a cellulose chain is considered to pass through several crystallites and periodically form

38

a noncrystalline (or amorphous) phases between crystallites (i.e., the “fringed micelle” model);2 however,

39

there is considerable uncertainty regarding a complete picture of the cellulose configuration. The

40

complexity along with the inherent imperfections of the cotton structure hampers the unraveling of the

41

concurrent and consecutive thermal responses of the constituent phases. In particular, the response of the

42

amorphous phase to low or intermediate temperatures is little known. With respect to high degrees of

43

crystallinity and intra- and inter-molecular hydrogen bonds, the question remains whether cotton fiber has

44

a distinctive glass transition, at which glass-like amorphous cellulose becomes rubbery.

45

While numerous studies have examined the glass transition of synthetic polymers, there have been

46

relatively few reports regarding that of cellulose. Various wood and regenerated cellulose samples were

47

reported to have undergone glass transitions in the range of 220-250 °C by various methods.3-10 On the

48

other hand, the glass transition temperature of ramie was 160 °C in a torsion pendulum test.11 The

49

molecular dynamics modeling of the temperature effect on the specific volume of amorphous cellulose

50

estimated its glass transition temperature to be 377 °C.12 These varied results show the difficulty of

51

determining the glass transition of cellulose. Differential scanning calorimetry, which is the most widely

52

accepted technique for synthetic polymers, is not suitable for cellulose because of its small changes in

53

heat capacity.13 As an alternative, indirect methods using plasticizer or varying degrees of polymerization

54

have also been employed.3, 7

55

Regarding heat-induced structural changes in cotton, a limited number of studies14-16 have been

56

conducted. Those studies measured the glass transition temperature of cotton in a way that is similar to

2


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examining its mechanical deformation in tensile tests. However, their results were not consistent: > 240

58

°C,14 no evidence of thermal softening,15 and ca. 200 °C.16 This discrepancy was partly due to less

59

distinctive changes in tensile properties at low temperatures. A simple summary statistic, namely an

60

average, on which those studies relied, seemed to be insufficient for elucidating the thermal effects on the

61

cotton structure. Wide variations of the properties intrinsic to natural fibers are likely to mask the subtle

62

changes associated with the chain segmental motion. A complete description of the properties, therefore,

63

is necessary based on the entire distribution. Another concern is that all of the above mentioned studies

64

used cotton yarns. One of their authors11 pointed out that “it will be difficult to use such measurements to

65

obtain an accurate determination of Tg (glass transition temperature) since the mechanical properties of

66

cotton yarn are influenced by inter-fiber as well as intra-fiber forces.”

67

Motivated by the incomplete and contradictory data in the literature, we have measured the tensile

68

property of cotton single fiber after heat treatments and parameterized the distribution of tenacity using

69

the Weibull model.17 Based on the weakest-link theory, the Weibull model describes the probability

70

distribution of the strength by assuming that inhomogeneous flaws are randomly dispersed in the volume

71

of fiber, and its fracture is triggered by the largest flaw present. The utility of the Weibull model has been

72

demonstrated by its good fits for a variety of brittle fibers including natural lignocellulosic fibers.18-19 The

73

Weibull distribution function also well described the fracture data of nano-sized materials, i.e., carbon-

74

nanotubes,20-22 and their statistical behavior, when being incorporated into a Monte Carlo model that

75

effectively simulates the shear load transfer in different contact modes of two adjacent fibers, provided

76

good predictions of the strength of carbon-nanotube yarns.23-24

77 78

The two-parameter Weibull cumulative distribution function (CDF) can be expressed as: x   x m  F ( x; λ , m ) = ∫ f ( x; λ , m )dt =1 − exp−   , x > 0, λ > 0, m > 0 0   λ  

(1)

79

where F(x) is the probability of failure of a fiber subjected to a stress of x, λ is the scale parameter, which

80

represents the 63.2 percentile of the distribution, and m is the shape parameter (Weibull modulus), which

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81

indirectly measures the distribution of flaws within the fiber. The corresponding probability density

82

function (PDF) is given by:

83

f ( x; λ , m ) =

m x   λ λ

m−1

  x m  exp−      λ  

(2)

84

The two parameters can be determined using the maximum likelihood estimation (MLE) method, which

85

has enabled precise estimation of the Weibull parameters.25 For this method, the likelihood function (L) of

86

n random sample data is first obtained as:

87

m−1 n    x  m   m  n  1  m  x  L( x1 ,..., xn ; λ , m ) = ∏   i  exp −  i    =  m  exp − m   i =1  λ  λ   λ   λ     λ  

n m m−1 x ∑ i  ∏ xi i =1  i =1 n

(3)

88

Here λ and m are determined when the value of the measurement is most likely to occur, that is, where L

89

is maximized. This optimization can be obtained easily using the log-likelihood function.

90

91

ln L( x1 ,..., xn ; λ , m ) = n ln (m ) − nm ln (λ ) −

λm

n

n

i =1

i =1

∑ xim + (m − 1)∑ ln (xi )

(4)

The partial derivatives of ln L with respect to λ and m, respectively, are set at zero.

92

∂ ln L nm m n =− + m+1 ∑ xim = 0 ∂λ λ λ i =1

93

∂ ln L n ln λ n 1 = − n ln (λ ) + m ∑ xim − m ∂m m λ i =1 λ

94

1

(5) n

n

i =1

i =1

∑ xim ln (xi ) + ∑ ln ( xi ) = 0

(6)

Equations (5) and (6) yield the following simplified equations, respectively, for m and λ:

95

 n m   ∑ xi ln ( xi ) 1 n  m =  i =1 n − ∑ ln ( xi ) n i =1   xim  ∑  i =1

96

1 n m λ =  ∑ xim   n i =1 

−1

(7)

1

(8)

97

From the determined parameters, the mean and variance of a Weibull distribution can be calculated by the

98

following equations:

4


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99

100


 

µ = λΓ 1 +    

1  m

σ 2 = λ2 Γ1 +

(9)

2 1  2  − Γ 1 +   m m  

(10)

101

In this study, we have demonstrated that the tenacity of cotton fiber was well described by the

102

Weibull model; however, when heating the fiber, its statistical behavior changed, departing from the

103

single Weibull distribution. The distributions of fibers heated over a temperature range of 160-280 °C was

104

successfully described by a finite mixture model—a mixture of two Weibull distributions. The determined

105

five parameters, which characterized a complex pattern of the distribution, were interpreted in terms of

106

the thermal reactions of cotton fiber. To assist and support the interpretation, the results of

107

crystallographic and thermogravimetric analyses were consulted. These analyses also aided in revealing

108

changes in the crystalline phase at higher temperatures (300-500 °C).

109 110

EXPERIMENTAL SECTION

111

Materials and sample preparation. American Upland raw cotton fiber was acquired from the

112

national registry. To remove noncellulosic components, which were found to alter the thermal reactions of

113

cellulose,26-27 the scouring of cotton fiber was carried out. Using an overflow-jet dyeing apparatus

114

(Werner Mathis USA Inc., Concord, NC), cotton fiber was circulated in an aqueous solution containing

115

NaOH (1.8 g/L) and Triton X-100 (0.2 g/L) with a liquid-to-fiber ratio of 22:1 at 100 °C for 60 min. The

116

fiber was then washed in circulating water at 100 °C for 20 min, followed by cold-water washing for 20

117

min. The scoured fiber was neutralized in an aqueous solution of acetic acid (0.25 g/L) for 10 min, rinsed

118

with cold water, and air dried.

119

The scoured cotton fiber was heated using a TGA Q500 thermal gravimetric analyzer (TA

120

Instruments, New Castle, DE) under a nitrogen atmosphere. The nitrogen flow into the furnace was

121

maintained at a rate of 90 mL/min. When the furnace reached the desired temperature with a heating rate

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122

of 10 °C/min, the sample was cooled to room temperature. The control sample (no heat treatment) was

123

denoted as fiber at a temperature of 25 °C.

124

Characterization. The linear density (LD) and tensile properties of heated cotton fiber—elongation,

125

force to break, tenacity, modulus, time to break, and work to rupture—were measured using a Favimat

126

tester (Textechno H. Stein GmbH). A single fiber was clamped with a gauge length (l) of 12 mm and pre-

127

tensioned with a force (T) of 0.5 cN. According to the vibroscopic technique (ASTM D 1577), the LD

128

(g/cm = 1/9×10-5 denier) was determined from the resonant frequency of the transverse vibration of the

129

fiber using the following equation:

130

LD = ρA =

T

(11)

4l 2 f 2

131

where ρ, A, and f are the density of fiber (g/cm3), the cross-sectional area of fiber (cm2), and the resonant

132

frequency (Hz), respectively. The same fiber section was extended with a load cell of 210 cN and a cross-

133

head speed of 2 mm/min until the fiber broke. The precision for measuring tensile force was within 1 mN.

134

For each sample, 100 fibers were tested.

135

X-ray diffraction (XRD) measurements were conducted using an XDS 2000 diffractometer (Scintag

136

Inc.). Cotton fiber was ground to a powder using a Mini Wiley Mill (Thomas Scientific, Swedesboro, NJ)

137

with a 40 mesh screen (0.42 mm). Approximately 0.15 g of the ground sample was pressed with 127 MPa

138

of pressure in a hydraulic press, cut into a 2.5 cm diameter circular disc, and mounted on the sample

139

holder. The diffraction pattern of the sample was recorded using Cu-Ka radiation generated with 43 kV

140

and 38 mA (1.54056 Å). Angular scanning was conducted from 8° to 38° with a scanning rate of 0.6°/min.

141

No background correction was made. The obtained X-ray diffractograms, after 9-point smoothing and

142

normalization of intensity, were analyzed using the Rietveld powder diffraction method in the MAUD

143

program (Materials Analysis Using Diffraction, version 2.7). For crystalline phase, the cellulose Iβ crystal

144

information file28-29 was employed. The cellulose II information was to generate an amorphous pattern by

145

using a very small crystallite size (12 Å).30 Eleven parameters—scale factor, three parameters of a 2nd

6


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146

order polynomial function for the background, crystallite size, three parameters for the dimensions of the

147

Iβ unit cell (a, b, and γ), two parameters for the March-Dollase preferred orientation along the (001) plane

148

of cellulose Iβ (coefficient and weight), and the volume fraction of the amorphous phase—were included

149

in the Rietveld refinement. For the 400 °C sample, which underwent a significant loss of crystallinity,

150

additional parameters for the preferred orientation of the amorphous phase and the anisotropy of the

151

crystallites (i.e., Popa’s Rules31) had to be included to achieve a good fit. The amount of amorphous

152

cellulose was calculated from the area of the calculated pattern for amorphous cellulose divided by the

153

sum of the areas for crystalline cellulose and amorphous cellulose. The d-spacing was calculated using

154

Bragg’s Equation:

155

nλ = 2d sin θ

(12)

156

where n is an integer, λ is the wavelength of the X-ray radiation, d is the spacing between the planes, and

157

θ is the diffraction angle of the peak.

158 159

For thermogravimetric (TG) analysis, the TG and differential TG thermograms collected from the TGA Q500 analyzer were analyzed using Universal Analysis 2000 software (TA Instruments).

160

Data analysis. Analyses of the tenacity data were carried out using R software.32 The parameter

161

estimates of the mixed Weibull distribution were obtained by performing non-linear least squares

162

optimization using the Levenberg-Marquardt algorithm. To visualize the classification of the temperature

163

effect, principal component analysis (PCA) was applied to the data. The PCA provided a general

164

overview plot by converting 14 experimental variables from tensile, crystallographic, and

165

thermogravimetric analyses—which might be correlated—into two linearly uncorrelated variables

166

(principal components: PC1 and PC2) that maintain about 85% variability. The determination of the

167

number of principal components was verified using the leave-one-out cross-validation method.

168 169

7



170

RESULTS AND DISCUSSION

171

Tensile properties. Favimat, which can differentiate single fibers based on tensile properties and

172

fineness, has been usefully used in cotton testing.33 Figure 1a shows force-elongation curves for control

173

cotton fiber. As expected for natural fibers, cotton exhibited wide variations in the response to external

174

force. The force-elongation curve of cotton fiber has, however, been known to be distinct from those of

175

other natural fibers—wool and silk—due to its lower extensibility (determined as the elongation at break

176

in the curve).34 The stiffness of cotton fiber is attributed to its high crystallinity;35 that is, it contains a

177

small amount of flexible amorphous cellulose, which is characterized by disorder in the orientation of

178

cellulose chains.36-37 Therefore, the amorphous content is one of important factors to influence the tensile

179

behavior of fibers.

180

In this study, the heat treatment was conducted in the range of 160-500 °C, but only the fibers that

181

were heated to 300 °C were strong enough for tensile tests. The heat treatment did not change greatly the

182

force-elongation curve shape of cotton fiber, i.e., a short, linear regime followed by a long, slightly

183

nonlinear regime extending until break, but the treatments above 220 °C greatly shrunken the curve

184

toward origin (Figures 1b and S1). A considerable drop in the number of successful tests was observed at

185

260 °C. The heat effect was also manifest in the fracture morphology. The micrograph of fractured

186

control fiber showed the frayed separation of microfibrils along the fiber axis (inset of Figure 1a). As the

187

temperature increased, this irregular axial splitting was less observable (inset of Figure 1b). At 300 °C,

188

clean fractures across the fiber diameter were dominant (Figure S1g).

189

The average values of linear density and tensile properties—elongation, force to break, tenacity,

190

modulus, time to break, and work to rupture—at increments of 20 °C are presented in Table 1. Since the

191

variances across the samples were inhomogeneous, a nonparametric multiple comparison test (Mann-

192

Whitney U test with Holm’s correction) was conducted. No significant change in linear density was

193

observed until 300 °C. On the other hand, tensile properties coherently exhibited significant reductions at

194

220, 240, and 260 °C. 8


Page 8 of 29

Page 9 of 29

9.0

9.0

b

a 7.2

Force (g)

7.2

Force (g)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5.4

3.6

5.4

3.6

1.8

1.8

0

0 0

4

8

12

16

0

20

4

12

16

20

Elongation (%)

Elongation (%)

195

8

196

Figure 1. Selected force–elongation curves obtained by Favimat testing and fiber fracture morphology:

197

(a) control cotton fiber and (b) cotton fiber heated at 260 °C. Scale bars are 5 µm.

198 199

Table 1. Linear density and tensile properties of cotton fiber heated at incremental temperatures. Temperature (°C)

No. of successful tests out of 100

Linear density (denier)

25 (control)

88

160

Elongation (%)

Force to break (cN)

Tenacity (cN/denier)

Modulus (cN/denier)

Time to break (s)

Work to rupture (µJ)

1.70A b (0.38)

a

9.30A (2.78)

4.17A (1.79)

2.43AB (0.97)

23.65A (8.06) c (45)

5.84A (1.66)

24.0A (12.8)

95

1.66A (0.41)

9.37A (3.20)

4.37A (1.88)

2.66A (1.04)

23.09A (6.48) (47)

5.89A (1.91)

25.3A (13.8)

94

1.55A (0.29)

9.40A (2.74)

4.00AB (1.83)

2.55A (1.00)

23.39A (8.54) (46)

5.90A (1.63)

23.7A (13.1)

94

1.62A (0.31)

8.31AB (2.67)

4.02AB (1.76)

2.49A (0.96)

22.34A (9.44) (31)

5.25AB (1.62)

21.7AB (11.5)

220

91

1.61A (0.29)

8.13B (2.65)

3.36B (1.58)

2.07B (0.83)

18.31B (9.38) (25)

5.13B (1.58)

18.2B (10.5)

240

91

1.65A (0.35)

5.43C (2.16)

2.68C (1.15)

1.64C (0.66)

13.34B (11.44) (4)

3.52C (1.29)

10.7C (6.9)

180

200

9



200 201 202 203 204

Page 10 of 29

2.84C (1.07)

6.9D (4.0)

-

2.73C (1.25)

0.06D (0.05)

-

1.77C (0.76)

0.03D (0.02)

260

57

1.62A (0.32)

4.27C (1.84)

2.16CD (0.77)

1.35CD (0.46)

-

280

37

1.67A (0.26)

4.12C (2.08)

1.70D (0.79)

1.01D (0.40)

300

6

1.69A (0.14)

2.52C (1.23)

1.27D (0.50)

0.74D (0.27)

d

a

Averages followed by different letters are significantly different (p < 0.05) based on Mann-Whitney U multiple b c d comparison tests with Holm’s correction; standard deviation; number of successful measurements; could not be determined.

205

Single Weibull model. Summary statistics (averages and standard deviations) do not give any

206

information about the shape of the distribution. Examination of alteration patterns in the distribution with

207

a proper parametric model is expected to help in understanding the underlying thermal process of cotton

208

fiber. We first applied the single Weibull model to the tenacity data for all samples except the one that

209

was heated to 300 °C, whose sample size was too small to be modeled. Two parameters estimated by the

210

MLE (Equations 3-8) and the calculated means (Equation 9) and coefficients of variation (Equation 10)

211

are presented in Table 2. In the variation of λ, there were two slope changes at 160 and 200 °C: a slight

212

increase upon heating to 160 °C and a rapid linear drop above 200 °C. The effect of temperature on m was

213

relatively less notable except for a large increase at 260 °C. The theoretical means agreed well with the

214

experimental average values of tenacity. To visualize the fit of the single Weibull model, the empirical

215

density is plotted with the respective Weibull density, as seen in Figure 2. It was found that the empirical

216

densities formed a complex shape—multimodality. The modality of the tenacity distribution depended on

217

the heating temperature; for example, bimodality was apparent at 240 °C but was dramatically dissipated

218

at 260 °C.

219

Concerned with the observed departure of the empirical density from unimodality, the goodness of fit

220

of the single Weibull model was quantitatively evaluated using the Kolmogorov-Smirnov (K-S) test.

10


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221

Under the hypothesis that the data follow the Weibull distribution, the test statistic (D), which is the

222

largest vertical distance between the empirical CDF and the Weibull CDF, can be measured as

223

D = sup Fe ( xi ) − F ( xi )

(13)

1≤i ≤ n

224

where n is the number of data points, Fe(xi) is the empirical CDF at the ith x value (tenacity)—a step

225

function that increases by 1/n at the value of each increasingly ordered data—and F (xi) is the determined

226

Weibull CDF. In the hypothesis test, a new data set was resampled from the original data with

227

replacement, and the corresponding empirical CDF was obtained. If the test statistic (D) calculated by

228

Equation (13) is smaller than the critical value ( = 1.358 / n ) at a significance level of 0.05, the

229

hypothesis was accepted. The percentage acceptance (A) and the average value of D obtained from 100

230

resampling procedures are presented in Table 2. The A for the control cotton was approximately 85%,

231

showing a relatively good fit of the single Weibull model. Its goodness of fit, however, gradually

232

deteriorated for the fibers heated until reaching 220 °C, and further heating at higher temperatures

233

substantially reduced the A.

234 235

Table 2. Single Weibull parameters, means, and coefficients of variation for the tenacity of cotton fiber

236

heated at incremental temperatures and the Kolmogorov-Smirnov goodness-of-fit test results. Temperature (°C)

Single Weibull Parameters

µ (cN/denier)

CV

K-S test

a

λ (cN/denier)

m

25

2.72 b (0.11)

2.71 b (0.24)

2.42

39.8

0.113 d (0.6391)

84.8

160

2.99 (0.11)

2.84 (0.23)

2.66

38.2

0.116 (0.5740)

80.4

180

2.87 (0.11)

2.77 (0.22)

2.55

39.1

0.1203 (0.5437)

79.4

200

2.80 (0.11)

2.84 (0.23)

2.49

38.1

0.1163 (0.5821)

81.0

220

2.33 (0.10)

2.68 (0.21)

2.07

40.3

0.1098 (0.6467)

81.8

A (%)

D c

11



237 238 239

240

1.85 (0.07)

2.75 (0.23)

1.64

39.3

0.136 (0.4362)

56.4

260

1.51 (0.07)

3.17 (0.32)

1.35

34.6

0.162 (0.4964)

73.2

280

1.14 (0.07)

2.66 (0.32)

1.01

40.5

0.222 (0.4011)

55.2

CV (coefficient of variation) = σ/µ; standard error; average value of D from 100 resampling procedures; average p-value from 100 resampling procedures.

a

b

c

d

Probability density

1.2

a

b

c

d

e

f

g

h

Empirical Single Weibull

1.0 0.8 0.6 0.4 0.2

Probability density

1.2 0.0 1.0 0.8 0.6 0.4 0.2 1.2 0.0 1.0

0

0.8 0.6 0.4 0.2

0

1

2

3

4

5

0 6

1

2

3

4

5



2

3

4

5

6


0.0

240

1

Probability density

Probability density

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 29

6

2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

i

0

1

2

3

4

5

6


241

Figure 2. Empirical density and predicted single Weibull probability density of the tenacity of cotton

242

fiber heated at incremental temperatures: (a) control, (b) 160 °C, (c) 180 °C, (d) 200 °C, (e) 220 °C, (f)

243

240 °C, (g) 260 °C, (h) 280 °C, and (i) 300 °C.

244

12


Page 13 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

245 246 247


Mixed Weibull model. Improved expression of the tenacity distribution of heated cotton fibers was attempted using a mixture of two Weibull functions. The PDF of a mixed Weibull distribution is: f ( x; α , λ1 , m1 , λ2 , m2 ) = αf1 ( x; λ1 , m1 ) + (1 − α ) f 2 ( x; λ2 , m2 )

(14)

248

where fj(x; λj, mj) is the PDF of a Weibull distribution with j = 1, 2, and α is the relative abundance of the

249

jth component with a constraint of 0 ≤ α ≤ 1. The corresponding CDF of the mixed distribution is:

250

F ( x; α , λ1 , m1 , λ2 , m2 ) = αF1 ( x; λ1 , m1 ) + (1 − α )F2 (σ ; λ2 , m2 )

(15)

251

The five parameters, α, λ1, m1, λ2, and m2, defining the functions in Equations (14) and (15), were

252

determined by the non-linear least squares optimization. The mean and variance for the mixed Weibull

253

distribution can, respectively, be calculated by:

254

µ m = αµ1 + (1 − α )µ 2

(16)

255

σ m2 = α (σ 12 + µ12 ) + (1 − α )(σ 22 + µ 22 ) − [αµ1 + (1 − α )µ 2 ]2

(17)

256

where the µi and σ i2 are, respectively, the mean and variance of a Weibull distribution defined by λi and

257

mi with i = 1, 2. The determined parameters of the mixed Weibull model and its goodness of fit test

258

results are presented in Table 3. The A for heated fibers greatly increased, particularly for those treated at

259

high temperatures. Figure 3 shows the mixed Weibull densities plotted with the corresponding two

260

component densities (designated as Weibull 1 and Weibull 2). Clearly, almost all experimental data points

261

fell right on the mixed Weibull prediction. It is interesting to see how the shape and location of the

262

component densities systematically varied with temperature. This variation pattern was examined by

263

plotting the five parameters as well as the distance between the two modes as a function of temperature,

264

as seen in Figure 4.

265

The control cotton itself showed bimodality, i.e., appearance of the second component (5% Weibull

266

1) at lower tenacity, signifying intrinsic inhomogeneity of the population. The source of the Weibull 1 is

267

likely to be a small group of immature (weak) cotton fibers and/or damaged fibers during the mechanical

268

cleaning process. Therefore, an increase in α (abundance of the Weibull 1) is associated with the extent of

13



Page 14 of 29

269

fiber damage by the heat treatment. The α considerably increased above 220 °C. Below 220 °C, the

270

parameters of the Weibull 1 (λ1 and m1) increased whereas those of the Weibull 2 (λ2 and m2) remained

271

relatively steady. These results indicate that the Weibull 1 responded more sensitively to low

272

temperatures than the Weibull 2. Also, the weaker dependence of the Weibull 2 on the temperature, i.e.,

273

maintaining the initial density, suggests that the low-temperature thermal reaction occurred randomly

274

throughout the population. At 220 °C, the Weibull 2 shifted to lower tenacities (drop in λ2) to merge with

275

the Weibull 1 (as indicated by a decrease in the distance between the two modes). This degeneration of

276

bimodality toward unimodality suggests that the corresponding thermal reaction propagated beyond

277

complete consumption of the initial component density.

278 279

Table 3. Mixed Weibull parameters, means, and coefficients of variation for the tenacity of cotton fiber

280

heated at incremental temperatures and the Kolmogorov-Smirnov goodness-of-fit test results. Mixed Weibull Parameters Temperature (°C)

281 282

a

α

λ1 (cN/denier)

λ2

m1

(cN/denier)

K-S test m2

µ (cN/denier)

CV

a

A (%)

D c

25 (control)

0.05 b (0.01)

1.10 (0.03)

3.03 (0.30)

3.00 (0.01)

2.82 (0.03)

2.58

41.2

0.124 d (0.5454)

72.8

160

0.04 (0.01)

0.95 (0.08)

2.79 (0.64)

3.17 (0.01)

2.86 (0.04)

2.75

40.7

0.117 (0.5679)

81.5

180

0.06 (0.01)

1.34 (0.04)

3.39 (0.36)

3.03 (0.01)

2.90 (0.05)

2.61

40.3

0.117 (0.5670)

82.2

200

0.08 (0.01)

1.67 (0.01)

4.55 (0.20)

2.98 (0.01)

2.80 (0.03)

2.56

40.4

0.111 (0.6206)

86.0

220

0.02 (0.00)

1.81 (0.02)

11.44 (1.75)

2.39 (0.01)

2.78 (0.01)

2.12

38.9

0.105 (0.6933)

87.6

240

0.40 (0.01)

1.18 (0.01)

3.13 (0.02)

2.29 (0.01)

4.28 (0.05)

1.67

41.9

0.110 (0.6410)

85.2

260

0.76 (0.19)

1.48 (0.02)

3.48 (0.14)

1.79 (0.24)

2.72 (0.22)

1.39

35.4

0.169 (0.4966)

72.6

280

0.87 (0.02)

0.97 (0.01)

3.37 (0.06)

1.84 (0.05)

7.15 (1.69)

0.98

41.3

0.169 (0.6675)

87.8

b

c

d

CV: coefficient of variation; standard error; average value of D from 100 resampling procedures; average pvalue from 100 resampling procedures. 14


Page 15 of 29

Probability density

1.50

a

b

c

d

e

f

g

h

1.25 1.00 0.75 0.50 0.25

Probability density

1.50 0.00 1.25 1.00 0.75 0.50 0.25

1.50 0.00

Probability density

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.25

0

1

2

3

4

5

6


1.00

Empirical Mixed Weibull Weibull 1 Weibull 2

0.75 0.50 0.25 0.00 0

283

1

2

3

4


5

6 0

1

2

3

4

5

6


284

Figure 3. Empirical density and estimated mixed Weibull probability density of the tenacity of cotton

285

fiber heated at incremental temperatures: (a) control, (b) 160 °C, (c) 180 °C, (d) 200 °C, (e) 220 °C, (f)

286

240 °C, (g) 260 °C, and (h) 280 °C.

287 288

Higher temperatures induced a similar pattern—bimodality was developed at 240 °C, dissipated at

289

260 °C, and redeveloped at 280 °C. The development of new bimodality indicates the initiation of another

290

type of thermal reaction. The aggressive thermal effects on the fiber strength in these regimes were

291

reflected by the larger variations of the parameters. Compared with the low-temperature stage (below 220

292

°C), the weight of the Weibull 1 (α) increased, and the life span of the bimodality shortened. For example,

293

the first bimodality survived for 60 °C increments; the second one for 20 °C increments; and the third one, 15



294

upon development, had already degenerated to show unimodal-like appearance. Another feature is that

295

not only λ1 and m1 but also λ2 and m2 were functions of temperature. Such a complex pattern, whereby

296

both of the component densities varied, implies that the thermal reactions at 220-280 °C depended on the

297

original strength of the fiber. The variation of m suggests that the more uniform distribution of less

298

variable flaw size was induced in the Weibull 1 at 220 °C and in the Weibull 2 at 280 °C.

299 1.0

a

0.8

α

0.6 0.4 0.2 0.0

12

b

Weibull 1 Weibull 2

10

m

8 6

5

4 2

c 3

4

2 3 1 2 0 1

-1 -2 0

50

100

150

200

250

0 300

Distance between modes (cN/denier)

4

λ (cN/denier)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 29

300

Temperature (°C)

301

Figure 4. Variation of the mixed Weibull parameters as a function of temperature.

302 303

Thermally induced structural transitions. The structure of cotton fiber is generally described by the

304

fringed micelle model,2 in which the cellulose chains pass through both crystalline and amorphous 16


Page 17 of 29

305

regions. When an external force is applied to the fiber, it is concentrated mostly on weak elements in the

306

structure, i.e., amorphous segment. Therefore, the fiber strength and elongation are sensitive to changes in

307

the amorphous structure, showing their coherent dependence on the temperature in the isodensity contours

308

of the tenacity-elongation bivariate distribution (Figure 5).

0.0752

0.0658

0.0564

0.0470

0.0376

0.0282

0.0188

0.00940

0.00

309

Elongation (%)

20

a

b

c

d

e

f

g

h

15 10 5

200

Elongation (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


15 10 5 0 0

310

1

2

3

4

5


6 0

1

2

3

4

5


6 0

1

2

3

4

5


6 0

1

2

3

4

5

6


311

Figure 5. Isodensity contour plots of the tenacity-elongation joint empirical density for cotton fibers

312

heated at incremental temperatures: (a) control, (b) 160 °C, (c) 180 °C, (d) 200 °C, (e) 220 °C, (f) 240 °C,

313

(g) 260 °C, and (h) 280 °C.

314 315

For the examination of the crystalline region, crystallographic and thermogravimetric (TG) analyses

316

were conducted. Figure 6 shows the X-ray diffraction patterns of cotton fibers heated from 160 to 500 °C.

317

As shown by the selected calculations (Figures 6b and 6c), the Rietveld refinement produced an excellent

318

fit with the experimental pattern; the correlation coefficients between calculated and experimental

319

diffraction peak intensities were higher than 0.99 for all samples studied. The calculated crystallite size,

320

d-spacing, and amorphous content as a function of temperature as well as the selected crystallite models 17



are presented in Figure 7. Figure 8 shows the weight loss and weight loss rate of the fiber heated at a rate

322

of 10 °C/min.

a

500 °C

Experimental Calculated Cellulose Iβ Amorphous Background

b

400 °C (200)

10000

380 °C

Intensity

8000

360 °C 340 °C

Calculated intensity

321

10000

R2 = 0.9980

8000 6000 4000 2000 0 0

2000 4000 6000 8000 10000

Measured intensity

6000 4000

320 °C

(1-10) (110)

2000

300 °C

0 12

280 °C

16

20

24

28

32

36

2θ (°)

260 °C

Calculated intensity

c

240 °C

10000

220 °C

8000

200 °C

Intensity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 29

180 °C 160 °C

10000

R2 = 0.9986

8000 6000 4000 2000

6000

0 0

2000 4000 6000 8000 10000

Measured intensity

4000 2000

25 °C

0

10

323

15

20

25

30

12

35

16

20

24

28

32

36

2θ (°)

2θ (°)

324

Figure 6. (a) X-ray diffraction patterns of control cotton fiber (25 °C) and cotton fibers heated to from

325

160 to 500 °C. Selected calculated diffraction patterns with the Rietveld powder diffraction method for

326

cotton fibers heated to (b) 260 °C and (c) 400 °C. The inset shows the correlation between measured

327

and calculated diffraction peak intensities.

328 329

Collecting all 14 variables from tensile, crystallographic, and thermographic data, PCA was

330

conducted. Figure 9 shows the loading of the variables in the bidimensional space defined by PC1 and

18


Page 19 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


331

PC2, which explained 61.8% and 22.8% of the total variance of the original data set, respectively. For

332

PC1, tenacity, elongation, work to rupture, number of successful tensile tests, amorphous content, and λ2

333

showed negative loadings, whereas weight loss, α, and crystallite size showed positive loadings,

334

indicating their close association with the extent of the thermal impact—the higher the score, the greater

335

the thermal damage. On the other hand, PC2, which has positive loadings of λ1, m1, and crystallite size,

336

but negative loadings of m2, d-spacing, and distance between the modes, was related to the progress of

337

thermal reactions—the higher the score, the closer to the fullest extent the corresponding thermal reaction.

338

Taking all analyses into account, five thermal responses of cotton fiber can be proposed, whose

339

schematics are included in Figure 9.

340

1) Glass transition at 160-220 °C: At 160 °C, slight decreases in α and λ1 as well as a slight increase

341

in λ2 indicate that there was a release of the internal stresses that were locked within the fiber during fiber

342

development or storage. The tenacity of the minor group of inferior fibers with less crystallinity (denoted

343

as a smaller size of the fiber schematic in Figure 9) was more sensitive to this chain relaxation. The

344

resulting moderate improvement in the tenacity of the immature, weak fibers diluted the intrinsic

345

inhomogeneous characteristic of the population. In the schematic in Figure 9, such thermal softening is

346

denoted by coloring the amorphous segments with a lighter shade of yellow. At 180-200 °C, increases in

347

α as well as noticeable increases in λ1 and m1 but relative steadiness in λ1 and m1 suggest that the thermal

348

softening randomly propagated throughout the population. At 220 °C, the degeneration of bimodality

349

indicates that the glass transition proceeded to the fullest possible extent. This broad range of glass

350

transition temperatures was characterized by negative values on the PC1 axis. The PC1 score of 220 °C is

351

close to zero. Its location between the temperatures with negative PC1 values (25-200 °C) and those with

352

positive PC1 values (240-280 °C) indicates a transitional temperature between thermal softening and

353

thermal decomposition.

354

2) Dehydration at 240–260 °C: Development of a new bimodality at 240 °C and its dissipation at 260

355

°C indicate the occurrence of the second thermal response: the dehydration of cellulose including 19



356

intramolecular reactions, which involves the loss of water and causes the thermochemical transformation

357

of cellulose.1 This dehydration temperature was in excellent agreement with that determined by FT-IR.38

358

The resulting dehydrocellulose was denoted in red in the schematic (Figure 9). The variations of the

359

parameters of both the component densities in this temperature regime indicate that the dehydration

360

reaction was not random but rather depended on the strength of the fiber. In the PCA plot, 240 and 260 °C

361

were located on different quadrants, signifying the level of the dehydration.

362

3) Chain scission at 280-300 °C: Development of a new bimodality but with severe transformation

363

toward the unimodality at 280 °C suggests the occurrence of an aggressive thermal event—chain scission

364

by decomposition of dehydrocellulose or depolymerization. The chain scission was also supported by

365

steep drops in the number of successful tensile tests out of 100 as well as the clean fracture morphology

366

(Figure S1). At 300 °C, only six samples were successfully tested (Table 1), indicating that those fibers

367

were too weak to withstand the pretension of the tensile test.

368

4) Thermal crystallizations at 180-360 °C: The analyses of the X-ray diffraction patterns revealed that

369

thermal crystallization occurred concurrently with thermal softening and decomposition. Figure 7b shows

370

that the amorphous content decreased periodically, reaching the local minima at 200, 260, and 320 °C. It

371

is also apparent from the d-spacing calculation (Figure 7a) that the crystallites expanded and shrunk with

372

a similar pattern observed in the amorphous content. Approximately 20% reductions in amorphous

373

content were observed at 200 and 260 °C as compared with the content of control cotton. One may

374

question whether such reductions would have resulted from the loss of the amorphous cellulose. The

375

weight-loss profile (Figure 8) shows that after a 3.6% reduction due to the loss of moisture, there were no

376

obvious weight reductions until 220 °C and a negligible reduction (0.1%) at 260 °C. Further evidence of

377

crystallization is that crystallite size gradually increased (Figure 7a). When reaching 360 °C, one more

378

chain layer was incorporated into the original 22 layers in the (200) lattice plane (Figure 7c). One source

379

of the additional layer could be paracrystalline cellulose (an intermediate phase between crystalline and

380

amorphous regions). Another source could be amorphous cellulose decomposing in the previous stage.

20


Page 20 of 29

Page 21 of 29

381

With free chain ends, amorphous cellulose could be more easily crystallized than when it was bound

382

between crystallites.

b

3.92

400

3.88

380 360 24 22 20 18 16 14

Number of (200) plane Crystallite size

40

12 10

35 50

320 300 280 260 240 220 200 180

100 150 200 250 300 350 400

160

Temperature (°C)

b

340

Temperature (°C)

3.84 94 92 90 88 86 84 82 80

Number of (200) plane

a

d-spacing (Å)

383

Crystallite size (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25

o

10

c

15

20

25

30

60

65

Amorphous cellulose (%)

a

400 °C 25 °C

360 °C

384 385

Figure 7. (a) The variations of d-spacing, crystallite size, and number of the (200) lattice plane as a

386

function of temperature. (b) percentage amorphous content calculated using the Rietveld powder

387

diffraction method. (c) crystallite models for control and heated cotton fibers by diagonal truncation,

388

which terminates along the (1-10) and (110) planes using the Mercury program39 with the published

389

coordinates.28-29 The numbers of glucose units in width for control, 360 °C, and 400 °C were 198, 213,

390

and 60, respectively.

391 392

5) Decomposition of crystalline cellulose at 340-500 °C: Above 340 °C, the weight loss exceeded the

393

initial amount of amorphous cellulose, indicating the deconstruction of crystalline cellulose, which

21



394

yielded amorphous residues. At 380 °C causing about 90% weight loss, the production of amorphous

395

cellulose overtook its consumption to increase the amorphous content (Figure 7b). One may assume that

396

such drastic destruction would result in no crystalline structure subsisting in the remains. Surprisingly,

397

however, the X-ray diffraction pattern of the fiber heated to 380 °C was as detailed as that of control

398

cotton (Figure 6a); moreover, its crystallite size and the number of the (200) planes were comparable to

399

those of control fiber. This manifests the unzipping depolymerization reaction along the c-axis (fiber axis).

400

Even at 400 °C, where the major decomposition ended, the characteristic diffraction peaks of cotton were

401

still detectable. At 400 °C, the amorphous content increased to 61% (Figure 7b), and the width of

402

crystallites decreased by more than half (Figure 7c). Finally, no distinctive X-ray diffraction could be

403

collected for the sample heated to 500 °C (Figure 6a).

404

5.3

100

9

a

b

320 °C

8

5.1

5 4

5.0

3 2

4.9

354 °C

Weight (%)

Weight (mg)

3.0 80

7 6

50

100

150

200

250

300

2.5

60

2.0

40

1.5 1.0

20

380 °C

1 4.8

3.5

0 100

0 350

200

300

400

500

0.5

900

Temperature (°C)

Temperature (°C)

405 406

Figure 8. (a) Weight and percentage weight loss of cotton fiber at 30-320 °C. (b) Profiles of percentage

407

weight loss and weight-loss rate in the range of 100-980 °C, showing a rapid, major weight loss of

408

cotton cellulose occurring between 320 and 380 °C.

409 410

22


0.0 1000

Weight loss rate (%/°C)

5.2

Weight loss (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 29

Page 23 of 29

240 °C

260 °C

PC2 (22.8) 4 220 3

220 °C

280-300 °C

2 200 260

1 180 -6

180-200 °C

-5

-4

-3

-2

-1

1

2

3

4

5

6

240

-1

PC1 (61.8)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


320-340 °C

25 160

-2 280 -3

160 °C

360-380 °C

-4

400 °C

25 °C

411 412

Figure 9. PCA scores of the heated cotton fibers at different temperatures presented in the space

413

defined by the first two principal components and the schematic of the structural transformation of

414

cotton fiber as increasing the temperature.

415 416

CONCLUSIONS

417

Due to the complexity of cotton structure, identifying structural transformation under heat treatments

418

is not a trivial task. In particular, the glass transition of cotton fiber has been a controversial topic. In this

419

study, the stepwise thermal response of cotton fiber to elevated temperatures was revealed by

420

parameterizing the periodic pattern of bimodality in the tenacity distribution using the mixed Weibull

421

model. Analyzing variations of the five parameters identified the glass transition at 160-220 °C. This

422

broad glass transition temperature could not be detected by the simple summary statistics reported in the

23



423

literature. Two subsequent thermal responses—dehydration at 240-260 °C and chain scission at 280-300

424

°C—were also identified. Unlike the glass transition, which was randomly propagated throughout the

425

population, the latter reactions depended on fiber strength. The analyses of the X-ray diffraction patterns

426

using the Rietveld refinement method provided information on thermal crystallization and the destruction

427

of the crystalline structure. The results of this study demonstrate that a finite mixture model not only fully

428

described the complex statistical behavior of the tenacity of heated cotton fibers but also provided clues

429

regarding the thermal responses of cotton fiber and their characteristics. Identification of such structural

430

alterations induced by heat would contribute to enhancing the thermal processing sustainability and

431

efficiency of cotton fibrous materials.

432 433

ASSOCIATION CONTENT

434

Supporting Information

435

The supporting Information: the force–elongation curves and fiber fracture images of cotton fibers heated

436

at incremental temperatures is available.

437

AUTHOR INFORMATION

438

Corresponding Author

439

*

440

Present Address

441

Daniel Ahmed Alhassan: Department of Mathematics, Missouri University of Science and Technology,

442

Rolla, MO 65409, USA.

443

Notes

444

This research received no specific grant from any funding agency in the public, commercial, or not-for-

445

profit sectors. The USDA is an equal opportunity provider and employer. The authors declare no

446

competing financial interest.

Sunghyun Nam: Tel.: +15042864229. Fax: +15042864390. E-mail: [email protected].

24


Page 24 of 29

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447


ACKNOWLEDGEMENTS We thank Teresa Morgan for her tensile testing and thank Tanya Goehring and Mohammad

448 449

Saghayezhian for their XRD measurements.

450 451

REFERENCES

452

(1)

Wiley: New York, 1985.

453 454

Nevell, T. P.; Zeronian, S. H., Cellulose Chemistry and its Applications. Halsted Press, John

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For Table of Contents Use Only

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TOC graphic

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f ( x; α , λ1 , m1 , λ2 , m2 ) = αf1 ( x; λ1 , m1 ) + (1 − α ) f 2 ( x; λ2 , m2 )

1.0

1.0

0.8

0.8

Probability density

Probability density

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.6 0.4 0.2 0.0

0.6 0.4 0.2 0.0

0

1

2

3

4

5

6

0

2

3

4

5

6



555

1

556 557

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A finite mixture model described the fracture behavior of heated cotton fibers and revealed their thermal

559

responses for the improved sustainability of heat processing.

Synopsis

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Thermally induced structural transitions in cotton ... - ACS Publications

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