Viscoelastic properties of star-shaped polymers

Abstract

fruitful discussions with S. M. Lindsay. References and Notesproperties of PDMS in the temperature range 223-323 K.' As shown in ref 11, this is barely into the temperature interval where any deviation from a simple Arrhenius behavior is detected and surely cannot be used to estimateTo. More recent attempts13 to determine To from viscosities produced even more outrageous results (To = 67 K).The very rapid change in relaxation frequency with temperature near 150 K demands that To be well above 81 K.The empirical parameters in eq 10 can also be interpreted in terms of the free volume of the liquid according to the WLF12 equation. PDMS was thought to have an unusually high fractional free volume at the glass transition.12 The WLF parameters calculated from our results are clg = 14.6 and c2g = 20 K. This leads to a calculated fractional free volume at the glass transition of f g / B = 0.030. This is higher than some polymers, but well within the normal range. The value of Tg listed in ref 12 is 150 K. It now appears that this value was obtained with semicrystalline PDMS. The value reported by Yim and St. Pierre' was obtained with shock-quenched amorphous PDMS. The difference can be rationalized by the results of Adachi et obtained by dielectric relaxation on both amorphous and crystalline PDMS. The dielectric loss maximum shifts by approximately 2 orders of magnitude when the sample crystallizes. This corresponds to approximately 4 K in the region of Tr The elevation of the glass transition temperature of the amorphous part in a semicrystalline polymer is a Yim, A.; St. Pierre, L. E.

Rheology of Star-Branched Polyisobutylene

“…The viscosity of polymers having sufficiently long branches will have a stronger dependence on molecular weight than the power law found for linear chains (eqs 2 and 3). An exponential relationship has been proposed [15][16][17] 37 vertically scaled to superpose on the data for L176.…”

“…The general consensus is that stress relaxation and diffusion entail arm retraction, which causes an exponential increase with branch length of both the zero-shear viscosity and the diffusion constant. [10][11][12][13][14][15][16][17][18] This arm retraction is believed 19 to be the cause of two other phenomena associated with branched polymers: more temperature-dependent rheological properties and thermorheological complexity in the terminal zone. [20][21][22][23][24][25][26][27] The transient, compact structure would alter the distribution of rotational states, in turn giving rise to a thermal barrier to terminal relaxation, which is absent for linear polymers.…”

Stress relaxation in diblock copolymers

“…The calculation of the probability P v (t) proceeds similarly to that of Pearson and Helfand [16] in their study of relaxation of star polymers. In the tube model, the primitive chain consists of L/a segments with L = V /bR e the length of the primitive tube and a = R e its step length (R e is the typical distance between entanglements).…”

“…It can be obtained by solving a first-passage problem [16]. This probability density is the same as that of a diffusing particle (the free chain end) in the harmonic potential U = (3αk B T /2L…”

“…Then, the survival probability at time t of a tail of volume v is given by P v (t) = y −∞ dx p(x, t; x 0 ; y), since, as long as x ≤ y, the primitive chain has never contracted by an amount larger than y. In the limiting case of t ≫ t R and of x ≫ ∆L the probability P v (t) is obtained as [16] …”