The Statistical Length of Long-Chain Molecules

1946 ◽  
Vol 19 (4) ◽  
pp. 1002-1008 ◽  
Author(s):  
L. R. G. Treloar
Keyword(s):  
Independent Method ◽  
Distribution Functions ◽  
Research Association ◽  
Chain Molecules ◽  
Isoprene Unit ◽  
Fundamental Research ◽  
A Chain ◽  
Long Chain

Abstract A formula is derived for the complete function representing the probability of a given distance between the ends of a chain of universally jointed equal links. The formula is computed for chains of 25 and 100 links. The distribution functions derived from this formula are compared with those previously worked out by an independent method for polyisoprene and paraffin chains. It is shown that the polyisoprene chain is statistically equivalent to a randomly-jointed chain of length corresponding to 1.42 links per isoprene unit. This work forms part of a program of fundamental research on rubber undertaken by the Board of the British Rubber Producers' Research Association.

scholarly journals The torsional flexibility of aliphatic chain molecules

1940 ◽  
Vol 174 (956) ◽  
pp. 137-144 ◽  
Keyword(s):  
Room Temperature ◽  
Threshold Energy ◽  
Chain Molecule ◽  
Aliphatic Chain ◽  
Chain Molecules ◽  
Distortion Effect ◽  
A Chain ◽  
Single Bonds ◽  
Long Chain ◽  
Made In

The rotation of the CH 3 groups round the single C—C bond in ethane is associated with a threshold energy of about 3000 gcal./gmol. or 2 x 10 -13 erg/mol. (Schäfer 1938; Kistiakowsky, Lacher and Strutt 1939). In an aliphatic CH 2 chain where the carbon atoms are linked together by single bonds the corresponding energy must be of the same order and is most likely rather smaller. Supposing we consider any particular C—C bond in the chain and treat the two parts at each side of this bond as rigid rotators, then their kinetic energy would be 2 x 1/2 kT which at room temperature amounts to about one-fifth of the threshold energy. It seems very likely under these circumstances that a chain molecule of say ten to twenty carbon atoms should already at room temperature show signs of distortion due to internal rotation. If this is true, then the previously observed increase of the crystal symmetry at the melting-point of paraffins (Müller 1930, 1932) and the corresponding changes of the polarization of long-chain ketones (Müller 1937, 1938) can no longer be ascribed entirely to a rotation of the molecule in the field of the surrounding molecules but must at least partly be due to this internal distortion. It is clear that a distortion of this type tends to destroy the anisotropy of the molecule and to give an apparent isotropy to the crystal. The present experiments were made in order to obtain an estimate of the magnitude of the distortion effect. It is found to be surprisingly large.

On random walks with restricted reversals

1958 ◽  
Vol 54 (1) ◽  
pp. 48-59 ◽  
Author(s):  
C. Domb ◽  
M. E. Fisher
Keyword(s):  
Random Walks ◽  
Distribution Functions ◽  
Asymptotic Estimates ◽  
Exact Enumeration ◽  
Chain Molecules ◽  
Physical Interest ◽  
Cooperative Phenomena ◽  
Starting Point ◽  
Correlated Random Walks ◽  
Long Chain

1. Introduction. Problems of unrestricted random walks on lattices have been considered by many authors and methods have been discovered for the exact enumeration of the number of walks between two points, for obtaining asymptotic estimates of the distribution functions and for evaluating special parameters such as the probability of ultimate retum to the starting point. By an unrestricted walk we mean one in which the probability of the next step at any stage is not influenced by the previous choice of steps. The corresponding problems for restricted (or correlated) random walks are more difficult and fewer results have been obtained. Restricted walks are, however, of considerable physical interest in connexion with the statistical behaviour of long chain molecules, the theory of cooperative phenomena in crystals and in other applications.

The number of configurations of a cooperative assembly

1942 ◽  
Vol 38 (1) ◽  
pp. 109-124 ◽  
Author(s):  
A. R. Miller
Keyword(s):  
Three Dimensional ◽  
Square Lattice ◽  
Research Association ◽  
Equilibrium Conditions ◽  
Chain Molecules ◽  
Cubic Lattice ◽  
Research Scholarship ◽  
Fundamental Research ◽  
Cooperative Assembly

Formulae are found for the number of configurations of particles on two-and three-dimensional lattices when each particle (a) occupies two closest neighbour sites, and (b) consists of three groups which occupy three sites on the lattice in such a way that adjacent groups in the molecule occupy closest neighbour sites on the lattice. Bethe's method is used to determine the equilibrium conditions of the corresponding order-disorder problem, and the number of configurations is determined from these equilibrium conditions. For the case in which the molecules occupy two closest neighbour sites on the surface the determination of the number of configurations from geometrical considerations is discussed.It is found that for molecules which occupy two closest neighbour sites the number of configurations of particles for a square lattice, a simple cubic lattice and a body-centred cubic lattice respectively are and For molecules which occupy three sites on the lattice the corresponding results are and when the molecules are perfectly flexible and and when the molecules are completely inflexible, Ns being the total number of sites in the lattice.The author wishes to thank Dr J. K. Roberts for suggesting this work; the geometrical treatment given in § 3 was developed from manuscript notes prepared by him. The problem arose during an investigation of the vapour pressure equations of solutions in which the solute molecules are chain molecules consisting of a large number of groups, undertaken as part of the programme of fundamental research of the British Rubber Producers' Research Association, whom the author wishes to thank for the grant of a Research Scholarship.

Molecular Requirements for Synthetic Rubbers

1945 ◽  
Vol 18 (3) ◽  
pp. 632-636 ◽  
Author(s):  
W. O. Baker
Keyword(s):  
Natural Rubber ◽  
Small Groups ◽  
Close Packing ◽  
Chain Molecules ◽  
Lateral Forces ◽  
Chain Compounds ◽  
Simple Chain ◽  
A Chain ◽  
Model Chain ◽  
Long Chain

Abstract Rubbery substances consist basically of long chains of atoms to which other atoms may be attached in small groups that occur repeatedly, and often regularly, like the links along a chain. There are hundreds of atoms in one of these “macro” molecules. It is the particular arrangement and the active forces between these molecules that are responsible for the elastic properties of many substances. The structure of the molecules of most synthetic rubbers as well as that of natural rubber is so complex, however, that efforts to determine, by direct study of the commercial products, what produces their rubbery characteristics have yielded results that are difficult to interpret. Progress in solving the puzzle has recently been made by starting with simple chain compounds and forming from them, by known chemical modifications, substances which have some of the properties that are found in natural rubber. Studies of these “model” chain compounds indicate that the long-chain molecules of rubbery substances must have forces between atomic groups which are small enough to permit twisting and kinking of the chains. There must also be lateral forces to hold adjacent molecules together, like a bundle of sticks, especially when the substance is stretched. Moreover, the molecules must have side groups to avoid the close packing, when unstretched, that is characteristic of crystals.

scholarly journals Integrated lipidomics and proteomics reveal cardiolipin alterations, upregulation of HADHA and long chain fatty acids in pancreatic cancer stem cells

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Claudia Di Carlo ◽  
Bebiana C. Sousa ◽  
Marcello Manfredi ◽  
Jessica Brandi ◽  
Elisa Dalla Pozza ◽  
...  
Keyword(s):  
Pancreatic Cancer ◽  
Stem Cells ◽  
Fatty Acid ◽  
Cancer Stem Cells ◽  
Acyl Chain ◽  
Fatty Acid Elongase ◽  
Acyl Chains ◽  
A Chain ◽  
Pancreatic Cancer Stem Cells ◽  
Long Chain

AbstractPancreatic cancer stem cells (PCSCs) play a key role in the aggressiveness of pancreatic ductal adenocarcinomas (PDAC); however, little is known about their signaling and metabolic pathways. Here we show that PCSCs have specific and common proteome and lipidome modulations. PCSCs displayed downregulation of lactate dehydrogenase A chain, and upregulation of trifunctional enzyme subunit alpha. The upregulated proteins of PCSCs are mainly involved in fatty acid (FA) elongation and biosynthesis of unsaturated FAs. Accordingly, lipidomics reveals an increase in long and very long-chain unsaturated FAs, which are products of fatty acid elongase-5 predicted as a key gene. Moreover, lipidomics showed the induction in PCSCs of molecular species of cardiolipin with mixed incorporation of 16:0, 18:1, and 18:2 acyl chains. Our data indicate a crucial role of FA elongation and alteration in cardiolipin acyl chain composition in PCSCs, representing attractive therapeutic targets in PDAC.

Conformational transitions of long chain molecules in frozen solutions

1989 ◽  
Vol 91 (11) ◽  
pp. 7296-7299 ◽  
Author(s):  
R. Hirschmann ◽  
J. Friedrich ◽  
E. Daltrozzo
Keyword(s):  
Conformational Transitions ◽  
Chain Molecules ◽  
Frozen Solutions ◽  
Long Chain
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