I. A. Torchinskii

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).

Theory of the Relaxation spectra of polymer networks with included hard rodlike particles manifested in NMR

A theory of nuclear magnetic resonance relaxation of13C nuclei and nuclear Overhauser effect (NOE) of polymer networks with included rodlike particles is developed for the case when the length of each rod is comparable or greater than the average distance between neighboring crosslinks. The long-scale dynamics of the network is described by means of a regular cubic “coarse-grained” model. The effects of entanglements of long rods in the network are described by a quasi-elastic potential acting between rods and network fragments. The frequency dependences of 1/T1C and NOE are calculated for the case when the internuclear vector is directed along each rodlike particle. The frequency dependences of 1/T1C and NOE for rods included into a polymer network are shifted to high frequencies as compared with these dependences for free rods due to quasi-elastic interactions between rods and network fragments. At strongly different viscoelastic parameters of rods and network fragments, the frequency dependences of 1/T1C and NOE may have two maxima. The high-frequency maximum corresponds to localized motions of rods at immobile network domains. The low-frequency maximum is caused by involving rods in long-scale network motions. The intensity of the low-frequency maximum increases when the degree of interactions between rods and the network increases.

Rotational and translational relaxation times of quasi-elastic and rigid dumbbells elastically bound to polymer network junctions

The dynamics of a rigid rod located between fixed junctions of a polymer network is studied. Three approaches are used in the solution of this problem. The first is based on the viscoelastic model, where a rigid rod is simulated by an elastic dumbbell with a fixed average length; the second includes solution of equations of motion for projections of the rigid rod using the Lagrangian multipliers under the constraint condition; and the third involves solution of the diffusion equation in the presence of an elastic potential. The second and third approaches allow calculation of orientational relaxation times for rod projections under the action of a strong orienting field. The dependences of the relaxation times of orientational and translational motions of the rod projections on the coordinate axes and the orientational relaxation times of mean-square rod projections on the model parameters (the distances between fixed polymer network junctions, the length of the rigid rod, and the elastic coefficient characterizing the binding between the rod and the network) are found.

Relaxation time spectra and relations of polarization luminescence of macromolecules with luminescent tracers

Abstract A theoretical study was made of the effect of the form and with of various relaxation time spectra — Cole-Cole, Cole-Davidson, Frohlich “semi-empirical” distributions on the dependence of relative depolarization of luminescence Y ( T / ν ) (where T is the absolute temperature, and ν — solvent viscosity). Relations were derived of Y / T / ν for all spectrum types studied with different spectrum width parameters. It was shown that the relations of polarization luminescence (PL) depend largely on the form of the relaxation time spectrum. For the broad symmetrical Cole-Cole distribution ( Y / T / ν ) has no linear sections over the entire range of variation of T / ν , while for the asymmetrical Cole - Davidson distribution and finite “box” type Frohlich distribution values of Y ( T / ν ) go outside the linear asymptote with high values of T / ν . For all types of distribution a widening of the spectrum increases the curvature of T / T / ν . From a comparison of theory and experiment on PL of macromolecules with luminescent tracers parameters of spectrum width were evaluated, which may be used to describe experimental results. These parameters appeared to be close to parameters obtained from investigations of dielectric relaxation of polymer solutions of the same class.

Theory of relaxation spectra for two identical interpenetrating polymer networks

Viscoelastic models for the description of the relaxation characteristics of two identical swollen interpenetrating polymer networks with different topologies moving against the background of an external viscous medium are considered. Two dynamic models that differ in the character of mutual interaction between network junctions are proposed. According to the first model, viscoelastic interaction is assumed to be constant and provided by the entanglements between a junction of one network with eight symmetrically arranged junctions of the other network. The second model involves (i) the predominant interaction between multiple-network junctions most closely located owing to entanglements and (ii) a weaker interaction with more distant junctions of neighboring cells. For the systems composed of two interpenetrating networks, relaxation-time spectra and average inverse relaxation-time spectra are compared with the corresponding spectra and characteristic times for individual noninteracting regular networks. Both models can involve two branches of the relaxation spectrum. One branch is a collective branch corresponding to the motion of the double network, whose parameters are controlled by the constants of elasticity of each of the interacting networks as well as by the effective mutual viscoelastic interactions between networks. This low-frequency branch is characterized by a broad spectrum of relaxation times. The second branch is a high-frequency branch that is primarily provided by mutual local motions of two interacting networks. This branch is characterized by a comparatively narrow relaxation spectrum and depends on quasielastic constants, which describe network entanglements, and on the characteristic elasticity of each network. The second branch does not involve any infinitely long relaxation times for infinitely continuous networks.

Effect of internal friction on the polarized luminescence of solutions of macromolecules with luminescent markers in the main chain

In the light of theoretical analysis a study is made of the extent to which internal friction may influence polarized luminescence (PL) regularities of macromolecules with luminescent markers in the main chain. Rotary-isomeric and viscoelastic models of polymer chains are considered. It is shown that internal friction leads to a narrowing of the relaxation time spectrum and to reduced curvature in plots of reduced polarization of luminescence Y vs. the T/ν ratio (where T is the absolute temperature, and ν is solvent viscosity). On comparing theoretical considerations with PL experiments for the labelled polyamido-acid one can conclude that internal friction may well be one reason for the low degree of curvature of Y (T/ν) and for a corresponding narrowing of the relaxation time spectrum appearing in experiments.

Local relaxation properties of polymer chains containing inclusions

Abstract A theory of the dynamic properties of polymeric chains containing an inclusion has been developed on the basis of a model of Gaussian subchains. Time correlation functions for the average projections of the inclusion element on to an individual direction have been found. Both linear chains containing singular elements (bridges, impurity polar groups) and also slightly crosslinked systems with crosslinking bridges have been considered. The frequency dependence has been found for the complex compliance (and for the dielectric permeability) for various values of the ratios λ 1 / λ and K 1 / K ( K and λ and K 1 and λ 1 are the coefficients of statistical elasticity and of friction for the standard chain segment and for the inclusion element respectively). The dependence of the inverse luminescence polarization on the inclusion parameters has been investigated. The motion of the end segments of finite chains containing an inclusion in the middle has been studied.

Hydrodynamic interactions and their effect on local high frequency processes in the polymer chain (Polarized luminescence, NMR)☆

A theoretical study has been made of the influence of hydrodynamic interactions on the mechanism of polarized luminescence and NMR of macromolecules in solution. The depolarization function for the luminescence Y (T/n) has been formulated (in which T - the absolute temperature; n - solvent viscosity) and equations have also been obtained for the spin-lattice relaxation time T1 (in the high frequency range) for chains with strong hydrodynamic interactions, the chain consisting of 10, 30 or 100 segments modelled by a Gaussian sub-chain. The hydrodynamic interactions due to space effects have been found not to affect the shape of the Y (T/n) function in the range 1 < Y < 3 and the mol.wt. dependence of mobility (determined by polarizing luminescence) θωN for chains with a strong hydrodynamic interaction at small N values shows the behaviour typical of freely permeated chains. The change to the region in which θωN is practically independent of N in the presence of the hydrodynamic reaction is at N ≈ 5–6.

Distribution of the correlation times and patterns of 13C nuclear magnetic relaxation and the overhauser effect

The dependences of the spin lattice relaxation time T1c and the Overhauser effect for different correlation time distributions used to describe the relaxational properties of polymers are examined. The dependence of Tc and the value of the nuclear Overhauser effect has been established (as a function of ωcτ where ωc is the resonance frequency and τ is the time characteristic of the given spectrum) on the form, width and asymptotic behaviour of the correlation time spectra for short and long times. These values are sensitive to the parameters of the relaxation spectra and may serve for their discrimination.