It is known that relative elongation ~. can be used as one measure of the uniaxial deformation of polymeric structures, especially in regard to cross-linked polymers [ 1 ]. However, it can be concluded from the available empirical data that this measure satisfactorily describes the behavior of a polymer only if ~. < 2-3. For several reasons, relative elongation cannot be used if the deformation of the polymer is substantial [2]. One of these reasons, in our opinion (particularly for polymers having globular structures) is the formation of knots in the molecular filaments that comprise a molecular unit (globule).In connection with this, it is interesting to attempt to determine the dependence of the deformation measure on the presence of knots in a globule in the form of a function of ~..We make the following assumptions: 9 for the duration of the stretching process, the globule is a sphere with the initial radius R 0 and the running radius R;9 the process of deformation of the globule entails pulling from it a perfectly inextensible filament having the radius r;9 as a first approximation, we ignore the theological properties of the material undergoing deformation; 9 we assume that the coefficient of friction f between the molecular filaments of the globule is constant and is independent of the forces and the speeds at which the filaments slide relative to one another; 9 we assume that the knots are uniformly distributed in the globule and are separated the distance l 0 from one another along a molecular filament; also, during uniaxial deformation, the knots are gathered together into the form of a loop at the exit from the globule.Knowing that the force P0 with which the first knot (loop) is stretched into a filament exiting the globule depends on the theological and other parameters (which are not examined in this article), we use Euler's formula [3] to calculate the tensile force on the nth knot:where ~p = 2~zn is the inclusion angle of the filament being stretched; n is the number of knots (loops).The total pulling force F will obviously be represented by the sum of the frictional forces from each of these knots: n
F=fPnfdn. 0We find the relationship between the number of knots n and the measure of deformation ~, in accordance with the scheme depicted in Fig. 1. The difference between the initial and current volumes of the globule can be considered to be roughly equal to the volume of a molecular filament pulled from the globule:1 Russian College of Chemical Engineering. 2 MGUII~.
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