THE OBSERVATION OF INTERNAL MOTION OF LINEAR POLYSTYRENE CHAINS IN CYCLOHEXANE AROUNDθTEMPERATURE

A high molecular weight (M_w=1.85×10~7) polystyrene (PS) with narrow distribution was prepared by high vacuum anionic polymerization in tetrahydrofuran.By use of dynamic light scattering,the dynamics of PS chains in cyclohexane was studied around theθtemperature.For the first time,we have observed the internal motion of polymer chains in solutions below theθtemperature by using dynamic light scattering at smaller angles (even qR_g<1).

Internal motion of the complex oscillators near main resonance

An analytical study of the two degrees of freedom nonlinear dynamical system is presented. The internal motion of the system is separated and described by one fourth order differential equation. An approximate approach allows reducing the problem to the Duffing equation with adequate initial conditions. A novel idea for an effective study of nonlinear dynamical systems consisting in a concept of the socalled limiting phase trajectories is applied. Both qualitative and quantitative complex analyses have been performed. Important nonlinear dynamical transition type phenomena are detected are investigated analytically.

Structural Feature and Internal Motion of Hyperbranching Cluster System with Low Polydispersity and Featured Pattern in Dilute Solutions

This work reports the structural feature and internal motion of one novel hyperbranching cluster system in dilution solution.The cluster system is composed of HB-PS_(300)-g-Pt BA_(45) hypergraft copolymer chains with uniform subchain,high molar mass and low polydispersity(M_(w)=1.73×106 g/mol and<M_(w)/M_(n)>≈1.07),where HB-PS and Pt BA represent hyperbranched polystyrene core and poly(tert-butyl polyacrylate)graft,respectively.In the selective solvent of PS blocks(cyclohexane,T_(θ)=34.5℃),the aggregation kinetics and structural feature are found to be precisely tunable for assembled clusters by the aggregation temperature(11℃<T<17℃)and time(0 h<t<24 h).An interesting structural evolution kinetics is observed,namely,the fractal dimension(d_(f))of clusters is found to first increases and then decreases with t,eventually,it reaches a plateau value of d_(f)≈3.0,corresponds to a uniform spherical structure.By using dynamic light scattering(DLS)to monitor the number and strength of relaxation modes inΓ(q)withΓbeing the decay rate and q being the scattering vector,it is quantitatively revealed that the relaxation,intensity contribution and mode origin of internal motions of clusters are neither similar with previously reported cluster systems with high polydispersity,nor with the classical linear chain systems.In particular,in the broad range of 2.0<qR_(h)<6.0,we have observed that the reduced first cumulant[Γ^(*)=Γ(q)/(q^(3)k_(B)T/η_(0))]does not display an asymptotic behavior.Whereas,a better asymptotic behavior is observed by plottingΓ(q)/q^(4) versus qRh.For the first time,our observation provides direct evidence supporting that,for hyperbranching cluster system with low polydispersity and high local chain segment density,the hydrodynamic interaction is greatly weakened due to the enhanced hydrodynamic shielding effect.

Nodal structure of the wave function for a two-dimensionalhydrogen molecular ion

Under the Born-Oppenheimer approximation, the exact solution of the Schrodinger equation for a two-dimensional hydrogen molecular ion is obtained through separation of variables. The inter-quantum numbers and the modes of internal motion are determined by analysing the nodal structure of the wavefunction. The eigenstates are classified and the classical periodic orbits corresponding to the modes of internal motion are found.