GATE (TF) Textile 2007 Question Paper Solution | GATE/2007/TF/77

Given the length of crystalline region as 90\mathring{A}, crystalline density of polyester as 1.445 g/cc and amorphous density as 1.335 g/cc.

Question 77 (Textile Engineering & Fibre Science)

Assuming a linear two phase model of crystalline and amorphous regions for these fibres, the amorphous length would be

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Length of crystalline region(Lc)=90 A^o

Crystalline density(\rho_c)=1.445 g/cc

Amorphous density(\rho_a)=1.335 g/cc

Density of fibre(\rho)=1.399 g/cc

Fractional crystallinity=?


Fractional crystallinity=\frac{\rho_c}{\rho} \times \frac{\rho-\rho_a}{\rho_c-\rho_a}

Fractional crystallinity=\frac{1.445}{1.399} \times \frac{1.399-1.335}{1.445-1.335}

Fractional crystallinity=1.033 \times \frac{0.064}{0.11}

Fractional crystallinity=1.033 \times 0.58

Fractional crystallinity=0.60

Percentage crystallinity=60%

Crystallinity =\frac{M_c}{M}

Where, Mc=crystalline mass and M is the total mass

Mass(M)=Volume(V) x Density(d)

M=A \times L \times \rho


M_c=A \times L_c \times \rho_c

Crystallinity =\frac{M_c}{M}

Crystallinity =\frac{A \times L_c \times \rho_c}{A \times L \times \rho}

Crystallinity =\frac{L_c \times \rho_c}{ L \times \rho}


Crystallinity =\frac{L_c \times \rho_c}{ (L_c+L_a)  \times \rho}

Crystallinity =\frac{90 \times 1.445}{ (90+L_a)  \times 1.399}

0.60 =\frac{130.05}{ (90+L_a)  \times 1.399}

0.60 \times 1.399 \times (90+L_a)=130.05

0.84 \times (90+L_a)=130.05





Amorphous length La=60 A^o (Ans)

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