Yu.Ya. Gotlib

The influence of the chemical crosslinking network on the spin-spin relaxation of crosslinked and swelling polymer systems

Abstract Crosslinked and swollen polymer systems have been found to give rise to a ridge on the plots of spin-spin relaxation times T 2 against temperature; this is explained by an incomplete averaging of the nuclear magnetic dipole-dipole interactions during an isotropic movement of chain segments between network joints. A simple sectional model of a chain with both ends fixed is used to get a theoretical dependence of the T 2 in the range of the ridge on the length and equilibrial rigidity of the chain section. The theoretical results are in good agreement with the experimental as far as it concerns the T 2 dependence on the number of crosslinkages and the absolute value of T 2 in the region of the ridge.

Study of intramolecular crosslinking of polymer chains using the Monte Carlo method

Abstract The Monte Carlo method was used for simulating polymer chain conformation on a computer in order to examine intramolecular crosslinking of macromolecules with reactive groups arranged at equal distances, without considering volumetric effects. Calculations were made chains using a volumetric centered lattice 30–150 units in length. It was shown that crosslinking takes place with auto-acceleration, the rate and acceleration increasing with an increase of chain length. Reaction kinetics in the initial stages are described by a simple equation. Average dimensions, the form and distribution of units of the polymer sphere were evaluated according to the extent of crosslinking. It was also shown that the distribution of reaction products according to the number of crosslinks is much wider than the Poisson distribution.

Local chain unit densities and the intramolecular movements in solutions of macromolecules

The correlations between intramolecular movements (IMM) and average local chain unit densities are examined in a solution of macromolecules. The local density, in contrast with the average, was found to be almost independent of chain length in good solvents; it depended only on the thermodynamic rigidity of the chain and the radius of the individual, selected averaging region. There is a strong dependence of average and local densities of chain unit in poor solvents (precipitants) on the degree of polymerization. The IMM periods τ associated with small scale chain unit movements in the chain are assumed to be controlled by local changes and not by the average chain unit density. The experimental τ functions of solvent quality are evaluated with respect to polarized luminescence and dielectric relaxation of the polymers. Assessments of local chain unit density have been obtained for poly-p-chlorostyrene in various solvents from the dielectric relaxation periods as a function of concentration.

Polarized luminescence in the investigation of the molecular-weight dependence of the rotational motion of macromolecules in solution☆

Abstract A study was made of the effect of molecular weight on the intramolecular mobility of macromolecules in solution for acrylic polymers containing luminescent markers (LM) situated in the main chain or the side groups of the macromolecules. The relations between relaxation times and mol. wt. τ ω ( M ) were investigated for non-ionized polymethacrylic acid in water with LM of different structures in the range M 2700–330,000. The τ ω ( M ) curve revealed the transition from the region of large M values ( M > 10 4 ), where τ ω is not a function of M to the region of low M ( M 4 ) where τ ω is reduced with decreasing M . In the range of low M the τ ω (M) relationship was elucidated in terms of the theory of Gaussian sub-chains for a finite number of segments. It is shown that with low M the equation 1/ τ ω whole +1/ τ intra is satisfied, i.e. the mobility of the macromolecules may be represented in a first approximation as the sum of the contributions of the rotation of the macromolecule as a whole 1/ τ whole and of the intramolecular mobility 1/ τ intra .

Polarized luminescence for longitudinal components of radiation oscillators in the main chain of “labelled” macromolecules (polymethyl methacrylate)

A polarized luminescence (PL) theory is proposed for macromolecules with a luminescence group label incorporated in the main chain for the longitudinal component of the radiation oscillator. The theory is based on a dynamic visco-elastic macromolecular model considering the flexural rigidity of the chain (Onishi-Hirst-Harris-Simon model). A theoretical relationship was derived between depolarization of luminescence 1/P and the ratio (τf/τ∗) (where τf is the duration of luminescence, τ∗—value proportional to the time of rotary diffusion of a kinetic unit not included in the chain) or parameter T/η (T being the absolute temperature and η, the solvent viscosity). Values of 1/P and the form of curves 1/P (τf/τ∗) (or 1/P (T/η)) appear to depend (with given dimensions and coefficient of friction of the kinetic unit) on the number of kinetic units ν=A/l, contained in the statistical chain segment (on the relative thermodynamic chain rigidity). It follows from a comparison of theory with experimental results of PL of polymethyl methacrylate with LM in the main chain in a mixed methylacetate-triacetin solvent that the most satisfactory agreement between theory and experiment is obtained if we assume that the dimensions and hydrodynamic diameter of a kinetic unit for the motion of the main PMMA chain are similar in practice or even greater than the dimensions of a statistical segment (∼six mono-units).

Polarized luminescence as used for analyses of high frequency twisting vibrations in macromolecules

Abstract Theoretical correlations for degrees of luminescence polarization have been analysed for different models of inhibited internal rotation and twisting vibrations. It was found that average amplitudes can be determined for high-frequency twisting vibrations (HTV) in the main chain and in side radicals by means of the polarized luminescence of “labelled” macromolecules with luminescing groups (LG). The HTV amplitudes were found by comparing theoretical considerations with experimental findings. The HTV amplitudes depend on interactions between the anthracene nucleus and the macromolecular units nearest to the LG, and likewise on the length and flexibility of the side radical containing the LG. Matters relating to these correlations are discussed.

The dynamics of semi-rigid polymer chains☆

Dynamic equations have been formulated for a minute pseudo-elastic chain consisting of a finite number of elements; these equations correctly describe the statistical properties of a semi-rigid chain. Dynamic equations for a helical polymer chain model (the Kratky-Porod model) have been arrived at by a limited transition; these are correct for the statistical properties of only a chain of persistant length. The relaxation times got from the equations and extreme conditions depend on the typical time τ and the La ratio. The movement equation and the extreme conditions differ from the corresponding Hearst and Harris equations.

Simulating the dynamic behaviour of polymer chains using the Monte Carlo method

The Monte Carlo method and a computer were used to simulate the dynamic behaviour of an individual macromolecule in a dilute solution with a good solvent and without hydrodynamic interaction. The rotary-isomer motion of a macromolecular model on a cubic lattice was presented by the transition of groups of two or three units, selected at random. Calculations were carried out using degrees of polymerization N = 16, 32 and 64. It was shown that for a chain model with two types of mobile unit, in contrast with the chain with one type of mobile unit, correlation times of large scale fluctuations increase with an increase of the degree of polymerization N and N2 and are close to correlation times for a freely linked chain. Studies were made of correlation times of characteristics of individual units.

Proton magnetic relaxation in concentrated polymethylmethacrylate solutions

Studies were made of the temperature relations of proton magnetic relaxation times T1 and T2 at a resonant frequency of 18·6 Mc/s for solutions of PMMA fractions (M = 3×104−1·7×106) in proton free solvents with polymer concentration of 5–80 mole%. It was shown that the minimum on the curve of the temperature dependence T1 observed in PMMA solutions with polymer concentrations of 5–30% is due to superposition of two coexisting ranges of relaxation caused by the motion of the main chain and the natural rotation of α-methyl groups. The effective activation energy of the relaxation process, of which the correlation times determine T2, increases with a reduction of temperature from 4–5 to 8–10 kcal/mole. Time T1 is independent of M in the range of M values studied. Starting from a polymer concentration of 10% time T2 depends on M at high temperatures; the higher the concentration, the more marked is this dependence and on lowering temperature, dependence on M ceases. An assumption is proposed, according to which an increase in the effective activation energy for T2 and a weakening of the dependence of T2 on M are due to intensification of interaction between the chains as temperature decreases. The nuclear intermolecular effect for high polymer concentrations is ∼20% of the total effect, i.e. relaxation is basically due to intramolecular nuclear interactions. Molecular mobility decreases with an increase of viscosity and a deterioration of the thermodynamic quality of the solvent. The effect of solvent properties on T2 is stronger than on T1.

Molecular dynamics of a polymer chain with a crosslink

The method of molecular dynamics has been used to study the behaviour of a polymer chain made up of rigid interacting links with practically free internal rotation. A single slightly deformed crosslink, whose length is equal to the length of a link, is introduced into the chain. A condensed polymeric system at high temperature is discussed. It is shown that the translational and rotational mobility of the crosslink are appreciably impeded. The impeding effect of the crosslink spreads to a small number of adjacent chain elements (one link for the orientational mobility and 4–8 links for the translational mobility). The results of a numerical experimental are compared with an analytical calculation for a viscoelastic model of sub-chains with a crosslink and with experimental data obtained using polarization luminescence, the crosslink being labelled. The ways in which certain dynamic properties of crosslinked systems depend on the mole fraction of crosslinks have been calculated.