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5. Kittel Ch3-7. Zipper problem. A zipper has N links; each link has a state in which it is closed with energy 0 and a state in which it open with energy &. We require, however, that the zipper can only unzip from the left end, and that the link number s can only open if all links to the left (1,2,...,s-1) are already open. (a) Show that the partition function can be summed in the form Z = 1- exp[-(N+1)ε/T] 1- exp(-ɛ/T) (90) (b) In the limit & >>7, find the average number of open links. The model is a very simplified model of the unwinding of two-stranded DNA molecules-see C. Kittel, Amer. J. Physics 37, 917 (1969).

5. Kittel Ch3-7. Zipper problem. A zipper has N links; each link has a state in which it is closed with energy 0 and a state in which it open with energy &. We require, however, that the zipper can only unzip from the left end, and that the link number s can only open if all links to the left (1,2,...,s-1) are already open. (a) Show that the partition function can be summed in the form Z = 1- exp[-(N+1)ε/T] 1- exp(-ɛ/T) (90) (b) In the limit & >>7, find the average number of open links. The model is a very simplified model of the unwinding of two-stranded DNA molecules-see C. Kittel, Amer. J. Physics 37, 917 (1969).

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5. Kittel Ch3-7. Zipper problem. A zipper has N links; each link has a state in which it is closed with energy 0 and a state in which it open with energy &. We require, however, that the zipper can only unzip from the left end, and that the link number s can only open if all links to the left (1,2,...,s-1) are already open. (a) Show that the partition function can be summed in the form Z = 1- exp[-(N+1)ɛ / t] 1- exp(-ε/T) (90) (b) In the limit & >>7, find the average number of open links. The model is a very simplified model of the unwinding of two-stranded DNA molecules-see C. Kittel, Amer. J. Physics 37, 917 (1969).
Transcribed Image Text:5. Kittel Ch3-7. Zipper problem. A zipper has N links; each link has a state in which it is closed with energy 0 and a state in which it open with energy &. We require, however, that the zipper can only unzip from the left end, and that the link number s can only open if all links to the left (1,2,...,s-1) are already open. (a) Show that the partition function can be summed in the form Z = 1- exp[-(N+1)ɛ / t] 1- exp(-ε/T) (90) (b) In the limit & >>7, find the average number of open links. The model is a very simplified model of the unwinding of two-stranded DNA molecules-see C. Kittel, Amer. J. Physics 37, 917 (1969).
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