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ORGANIC AND PHYSICAL CHEMISTRY OF POLYMERS phần 8

Không đóng trình duyệt đến khi xuất hiện nút TẢI XUỐNG Tải xuống

Phương trình này rất hữu ích vì nó cho phép một để xác định sự biến đổi năng lượng entropy và nội bộ do định hướng chuỗi khối lượng liên tục từ đo lường của F là một hàm của nhiệt độ (L0 nên được đo ở nhiệt độ mỗi) ở áp suất không đổi và kéo dài. | 434 MECHANICAL PROPERTIES OF POLYMERS pressure to compensate. Such an experiment is thus not practical. Because Flory showed that dS dL T V corresponds to dF dT p X where X denotes the relative elongation L L0 F can accordingly be expressed as follows 9 E dF F dLjTV T dT 12.15 p x The latter equation is useful because it allows one to determine the variation of entropy and internal energy due to the chain orientation at constant volume from the measurement of F as a function of the temperature L0 should be measured at each temperature at constant pressure and elongation. The experimenter then observes that the contribution of internal energy is negligible compared to that of entropy. 12.2.2. Statistical Theory of Rubber Elasticity As indicated previously an elastomer can be identified with an assembly of Nv chains connected through Nự randomly distributed cross-links that are separated from one another by a quadratic average end-to-end distance r2 0 satisfying a Gaussian distribution function P n r see Chapter 5 . In the following treatment the network is considered ideal without dangling chains and entanglements. P n r 3 2n r2 0 3 2 exp -3 r2 2 r2 0 12.16 On the one hand this function can be used to calculate the probability of finding a given chain end of the network in the spherical envelope of radius r and thickness dr with the other end corresponding to the origin on the other hand the function can be used to calculate the entropy of the same chain s k ln P n r where k is Boltzmann s constant. Thus the free energy Gi r of this chain is written as Gi r H - kT ln 3 2n r2 0 3 2 kT 3 r2 2 r2 0 12.17 After regrouping the first two terms in the constant C T depending on temperature one obtains for an assembly of Nv elastic chains G r C T NukT 3 r 2 2 r 2 0 The stretching of an elastomeric network changes its Gibbs free energy AGelas in two ways on the one hand by inducing conformational changes within each elastic chain of the network G r - G r0 and on the other .