NMR determination of topological structure and self-diffusion of linear polymers

Influence of Three-Spin Groups on the Primary Echo in Linear Polymers with Free Ends

“…This paper develops the theory of DFI and SE signals in linear polymers containing isolated three-spin groups with arbitrary DDI constants. Based on the previously proposed theory [6,7], a formula for the primary echo signal in linear polymers containing isolated three-spin groups was obtained. The DFI and SE signals in linear polymers with a group of three spins of 1/2 with equivalent and arbitrary DDI constants were calculated using the exact analytical formula [9,10].…”

“…In the case of equivalent kernels with a constant DDI b, the DFI formula takes the form (2) To calculate the DFI in linear polymers without linkages, we used the dynamic model of the polymer ( ) [6,7], in which the polymer chain consists of N 0 statistically independent segments. The movement of the polymer chain in a wide temperature range at a temperature above the glass transition temperature T gt is represented in the form of several types of movements: in the low-temperature region, only a small-scale molecular movement within the segments appears, and in the medium-temperature region, a large-scale (segmental) movement of the segments appears.…”

“…The decay of free induction in a linear polymer containing isolated three-spin groups is expressed by the following formula: (5) where is the DFI in the system of three spins (1). The SE expression for the entire spin system looks similar: (6) where is the primary echo signal in polymers [7]. The formula for calculating the primary echo signal in polymers was obtained based on the general theoretical approach proposed in [6] and is related to the mean square of the random phase change due to the change in the local magnetic field at the spin of the nucleus by the relation (7) To define the bond with the mean square of the displacement of the nuclei, formulas are obtained that are valid for any random processes.…”

“…The SE expression for the entire spin system looks similar: (6) where is the primary echo signal in polymers [7]. The formula for calculating the primary echo signal in polymers was obtained based on the general theoretical approach proposed in [6] and is related to the mean square of the random phase change due to the change in the local magnetic field at the spin of the nucleus by the relation (7) To define the bond with the mean square of the displacement of the nuclei, formulas are obtained that are valid for any random processes. By the condition of additivity of displacements r(t i , t j ) on the time interval [t i , t j ] for each realization of a random process, the equality (8) For the correlation of displacements of stationary processes, an equivalent formula is obtained: (9) Using formula (9), the expression for the mean square of the displacements for the echo under stationary conditions is obtained: (10) The quantity is given by the equation (11) From formulas ( 9), (10), and (4), the relation between the SE signal and the DFI follows:…”

“…To carry out a controlled synthesis and use of linear and cross-linked polymers, data on their structure and molecular mobility are required, which are determined by various NMR methods. The pulsed NMR relaxation method is a noninvasive and informative method for studying the structure at various levels, molecular mobility, and in particular diffusion, in a condensed medium [1][2][3][4][5][6][7]. In the presence of isolated three-spin groups in the polymer, broadening of the spectra is observed under the influence of the surrounding spins and partial averaging of their dipole interaction [8,9].…”