Molecular Transport in Liquids and Glasses

Journal of Chemical Physics - Tập 31 Số 5 - Trang 1164-1169 - 1959
Morrel H. Cohen1, David Turnbull2
1University of Chicago, Chicago, Illinois
2General Electric Research Laboratory, Schenectady, New York

Tóm tắt

We have derived, by using simple considerations, a relation between the diffusion constant D in a liquid of hard spheres and the ``free volume'' vf. This derivation is based on the concept that statistical redistribution of the free volume occasionally opens up voids large enough for diffusive displacement. The relation is D=A exp[−γv*/vf], where v* is the minimum required volume of the void and A and γ are constants. This equation is of the same form as Doolittle's [J. Appl. Phys. 22, 1471 (1951)] empirical relation between the fluidity φ of simple hydrocarbons and their free volume. It has been shown [Williams, Landel, and Ferry, J. Am. Chem. Soc. 77, 3701 (1955)] that the Doolittle equation also can be adapted to describe the abrupt decrease in molecular kinetic constants with decreasing temperature that accompanies the glass transition in certain liquids. Our result predicts that even the simplest liquids would go through this glass transition if sufficiently undercooled and crystallization did not occur. The problem of transport in actual simple and network liquids also is discussed. It is shown that data on self-diffusion in some simple van der Waals liquids and liquid metals are described satisfactorily by our relation with v* near the molecular volume for the van der Waals liquids and near the volume of the ion, corresponding to the highest valence state, for the metals.

Từ khóa


Tài liệu tham khảo

1948, Chem. Revs., 43, 219, 10.1021/cr60135a002

1958, J. Chem. Phys., 29, 1049, 10.1063/1.1744654

1952, J. Chem. Phys., 20, 1567, 10.1063/1.1700217

1956, J. Chem. Phys., 24, 746, 10.1063/1.1742602

1913, Z. Physik. Chem., 84, 644

1958, J. Chem. Phys., 28, 1037, 10.1063/1.1744341

1936, J. Chem. Phys., 4, 283, 10.1063/1.1749836

1937, J. Chem. Phys., 5, 896, 10.1063/1.1749960

1950, J. Appl. Phys., 21, 581, 10.1063/1.1699711

1951, J. Phys. Chem., 55, 221, 10.1021/j150485a010

1954, J. Polymer Sci., 14, 315, 10.1002/pol.1954.120147514

1951, J. Appl. Phys., 22, 1471, 10.1063/1.1699894

1955, J. Am. Chem. Soc., 77, 3701, 10.1021/ja01619a008

1953, J. Chem. Phys., 21, 1850, 10.1063/1.1698677

1956, J. Chem. Phys., 24, 418, 10.1063/1.1742490

1959, J. Chem. Phys., 30, 748, 10.1063/1.1730037

1942, Trans. Faraday Soc., 38, 322, 10.1039/tf9423800322

1943, Trans. Faraday Soc., 39, 48, 10.1039/tf9433900048

1959, Bull. Am. Phys. Soc., 4, 157

1958, Phys. Rev., 112, 804, 10.1103/PhysRev.112.804

1955, J. Chem. Phys., 23, 659, 10.1063/1.1742072

1959, Phys. Fluids, 2, 87, 10.1063/1.1724398

1959, J. Chem. Phys., 30, 159, 10.1063/1.1729868

1957, J. Chem. Phys., 27, 259, 10.1063/1.1743682

1955, J. Chem. Phys., 23, 1851, 10.1063/1.1740591

1949, J. Chem. Phys., 17, 668

Thông tin
Thông tin xuất bản

Journal of Chemical Physics

Tập 31 Số 5

1164-1169

Thông tin tác giả