Photon correlation spectroscopy of polymer solutions

A polynomial subdistribution method for analyzing the correlation profile in photon correlation spectroscopy of polymer solutions is described. This method generates a continuous distribution function from the measured photoelectron time-correlation function, which can be related to particle size or molecular weight distribution of solute. The method is tested using simulated data for unimodal and bimodal distributions and compared with cumulant and histogram methods, respectively. The polynomial subdistribution method has an advantage in that it not only generates a continuous distribution curve but also works well for bimodal distributions whose peaks are close together.     

Photon correlation spectroscopy of crosslinked polystyrene networks in the swollen state: Influence of macromolecular polydispersity

We report measurements of the correlation function of light scattered from thermally excited longitudinal fluctuations in crosslinked polystyrene networks at equilibrium. In order to investigate the influence of the polydispersity of linear chain elements between successive branch points, we synthesized a network by means of anionic block copolymerization, using a mixture of two “precursor” polystyrenes of different molecular weights to initiate polymerization of a small amount of divinyl-benzene (DVB). The correlation function for fluctuations having a wave vector K, has the form of an exponential decay, exp (?Γ). The decay rate is given by Γ = D′K², where D′ represents the diffusion constant of longitudinal modes of the network. We also present measurements of the correlation function of light scattered from gels prepared by anionic block copolymerization of styrene and DVB with only one “precursor” polystyrene and by a free-radical process. In the latter case, the gels should have a wide distribution of linear chain lengths between branch points.     

Photon correlation spectroscopy of compatible polymer blends

The dynamics of concentration fluctuations in compatible polymer mixtures can be investigated by dynamic light scattering. The experiment yields both the dynamic and static structure factors from which the mutual diffusion coefficient and the segment-segment interaction parameter can be obtained. Examples of applications are the unentangled blends poly(ethylene oxide/poly(propylene oxide) and polystyrene/poly(phenylmethylsiloxane) in the one phase region.     

Theory of the local mode relaxation in the glassy state of polymers

The local modes refer to vibrational motions of the main chain in the glassy state which are thermally excited with a relatively large amplitude and are consequently strongly damped into relaxational motions by the intermolecular viscous force. This paper describes a theory of strengths of the dynamic mechanical and dielectric local mode relaxations, in the latter of which the correlation of dipole arrangement along the main chain is considered. The results are compared with the observed strength and its dependence on temperature and pressure, in particular for the dielectric β relaxation of poly(vinyl chloride). Satisfactory agreement is obtained between theory and experiment.     

The effects of cyclic loading on polymers in a glassy state

The effects of cyclic loading on several physical properties of some polymers have been investigated. The results indicate that internal damping, shear modulus, heat capacity, and density of poly(methyl methacrylate) and alkali-polymerized polyamide 6 in the glassy state undergo changes during cyclic loading well before the appearance of crazes. It is suggested that cyclic loading induces a nonuniform volume contraction in the structure of the material.     

Photon correlation spectroscopy of polystyrene near the glass–rubber relaxation

Polarized Rayleigh scattering is studied near the glass-rubber relaxation in atactic polystyrene using photon correlation spectroscopy. Average relaxation times determined from the data agree well with previous results obtained using depolarized Rayleigh scattering. The light scattering results follow the same trend observed by dielectric and mechanical relaxation studies, but the times for orientational relaxation are longer by approximately two orders of magnitude. Also, an extensive discussion of the experimental techniques necessary to use photon correlation spectroscopy of polymers near the glass-rubber relaxation is presented.     

Diffusion in glassy polymers

Two versions of the free‐volume theory of diffusion are compared by considering differences in the predictions for the activation energy for the diffusion process. A number of data‐theory comparisons for free‐volume theory are discussed and evaluated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 785–788, 2003     

Photoviscoelastic behavior of amorphous polymers during transition from the glassy to rubbery state

Tensile stress‐relaxation experiments with simultaneous measurements of Young's relaxation modulus, E, and the strain‐optical coefficient, C_?, were performed on two amorphous polymers—polystyrene (PS) and polycarbonate (PC)—over a wide range of temperatures and times. Master curves of these material functions were obtained via the time‐temperature superposition principle. The value of C_? of PS is positive in the glassy state at low temperature and time; then it relaxes and becomes negative and passes through a minimum in the transition zone from the glassy to rubbery state at an intermediate temperature and time and then monotonically increases with time, approaching zero at a large time. The stress‐optical coefficient of PS is calculated from the value of C_?. It is positive at low temperature and time, decreases, passes through zero, becomes negative with increasing temperature and time in the transition zone from the glassy to rubbery state, and finally reaches a constant large negative value in the rubbery state. In contrast, the value of C_? of PC is always positive being a constant in the glassy state and continuously relaxes to zero at high temperature and time. The value of C_σ of PC is also positive being a constant in the glassy state and increases to a constant value in the rubbery state. The obtained information on the photoelastic behavior of PS and PC is useful for calculating the residual birefringence and stresses in plastic products. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2252–2262, 2001     

Fundamental relationship between the nonequilibrium glassy state and yield stress of amorphous polymers

This paper reports the theoretical prediction and experimental verification of the connection between the yield stress of amorphous polymers and the physical aging phenomenon. The analysis reveals the existence of a fundamental relationship between the nonequilibrium glassy state and the thermally activated process controlling viscoelastic and plastic deformation. The results show that the volume relaxation and deformation kinetics share the same relaxation times, and that the activation energy for deformation below T_g is much smaller than previously mentioned in the literature. This indicates that the phenomenon of physical aging plays a very important role in the deformation and processing of polymers at low temperatures. The effect of quenching and annealing on the yield stress is described in terms of the mean energy of hole formation, the departure of volume from its equilibrium state, the distribution of hole energies, and lattice volume. The same set of molecular parameters obtained from the molecular kinetic theory of the glass transition and volume relaxation predicts the yield stress as a function of cooling rate, annealing time, temperature, and strain rate.     

Photon correlation spectroscopy of poly(methyl methacrylate) near the glass transition

Poly(methyl methacrylate) (PMMA) has been studied by photon correlation spectroscopy in the temperature range 120–150°C. The relaxation functions for longitudinal density fluctuations were determined and analyzed using the empirical function ?(t) = exp[?(t/τ)^β]. The average relaxation times were calculated for each temperature and compared to mechanical and dielectric relaxation data. The agreement between the various techniques for the primary glass–rubber relaxation was good. The relaxation function observed by light scattering became increasingly broad as the temperature was lowered. This is similar to the results reported previously for poly(ethyl methacrylate) (PEMA). In fact, the light-scattering relaxation function is dominated by the secondary relaxations in these two polymers. Nevertheless, the average relaxation time 〈τ〉 is dominated by the longest relaxation times associated with the primary glass–rubber relaxation.     

Photon correlation spectroscopy of polystyrene as a function of temperature and pressure

Photon correlation spectroscopy is employed to study the slowly relaxing density and anisotropy fluctuations in bulk atactic polystyrene as a function of temperature from 100 to 160°C and pressure from 1 to 1330 bar. The light-scattering relaxation function is well described by the empirical function ?(t) = exp[?(t/τ)^β], where for polystyrene β = 0.34. The average relaxation time is determined at each temperature and pressure according to 〈τ〉 = (τ/β)Γ(1/β) where Γ(x) is the gamma function. The data can be described by the empirical relation 〈τ〉 = 〈τ〉₀ exp[(A + BP)/R(T ? T₀)] where R is the gas constant and T₀ is the ideal glass transition temperature. The empirical constant A/R is in good agreement with that determined from the viscosity or the dielectric relaxation data (1934 K). The empirical constant B can be interpreted as the activation volume for the fundamental unit involved in the relaxation and is found to be comparable to one styrene subunit (100 mL/mol). The quantity B appears to be a weak function of temperature. The use of pressure as a tool in the study of light scattering near the glass transition now has been established.     

Dynamic heterogeneities in glassy polymers

The photoinduced isomerization of molecules incorporated in a glassy polymer matrix exhibits a wide spectrum of quantum yields. The source of the spectrum is matrix heterogeneities. The kinetics of the photoisomerization of 1-naphthyl-p-azomethoxybenzene in poly(ethyl methacrylate) and poly(n-butyl methacrylate) films is first used to study the rearrangement of the environments of photochromic molecules. The nonequilibrium distribution of cis molecules over the spectrum is obtained via conversion of trans molecules with the highest quantum yield into the cis form with the use of 405-nm light. The kinetics of attainment of the photostationary ratio for concentrations of cis and trans isomers under the action of light with a wavelength of 546 nm is studied through variation in the pause between the conversion of molecules into the cis form and the beginning of the studied process. It is shown that reversible changes in the structure of polymer matrices occur at a high rate at temperatures much lower than the glasstransition temperature.     

Molecular motion in solid polymers detected by photon correlation spectroscopy

Molecular relaxation in the 10–10⁶ Hz region in a solid amorphous polymer PMMA has been detected by photon correlation spectroscopy. Relaxation times are found to depend strongly on sample annealing and sample temperature equilibration. The main relaxation frequencies, determined around the glass-rubber transition. T_g, are in good correspondence with values obtained by other methods.     

Photon time-of-flight spectroscopy

The feasibility of photon time-of-flight spectroscopy using optical waveguides is demonstrated     

Photon correlation spectroscopy of syndiotactic poly (n-butyl methacrylate) near the glass transition

Slow relaxing longitudinal density fluctuations in bulk syndiotactic poly (n-butyl methacrylate) [PBMA] were studied by photon correlation spectroscopy as a function of temperature from 70 to 90°C. The shape of the light-scattering relaxation function broadened as the temperature approached the glass transition (T_g = 55°C). The average relaxation time shifted with temperature, consistent with previous studies of PBMA. The relaxation functions were analyzed in terms of a distribution of relaxation rates. The calculated distribution was clearly bimodal and the shape altered with temperature. The higher frequency peak in the distribution corresponds well with previous mechanical and dielectric relaxation studies of the intramolecular relaxation of the acrylate ester side chain. The resolution of the distribution into two modes is due to a well-defined side-chain motion with relaxation strength comparable to the primary glass-rubber relaxation. © 1994 John Wiley & Sons, Inc.     

Photon correlation spectroscopy of bulk poly(n-hexyl methacrylate) near the glass transition

Slowly relaxing longitudinal density fluctuations in an optically perfect sample of bulk poly(n-hexyl methacrylate) (PHMA) have been studied by photon correlation spectroscopy in the temperature range 10–36°C. The glass transition temperature for this sample was measured to be T_g = −3°C by differential scanning calorimetry. The optical purity of the sample was verified by Rayleigh-Brillouin spectroscopy and the Landau-Placzek ratio was observed to be 2.3 at 25°C. Light-scattering relaxation functions were obtained over the time range 10⁻⁶-1 s. The shape of the relaxation functions broadened as the temperature was lowered towards the glass transition. Quantitative analysis of the results was carried out using the Kohlrausch-Williams-Watts (KWW) function to obtain average relaxation times, 〈τ〉, and width parameters, β. The width parameter decreased from 0.43 to 0.21 over the temperature interval, as suggested by visual inspection. Average relaxation times shifted with temperature in a manner consistent with previous mechanical studies of the primary glass-rubber relaxation in PHMA. The relaxation functions were also analyzed in terms of a distribution of relaxation rates, G(Γ). The calculated distributions were unimodal at all temperatures. The average relaxation times obtained from G(Γ) were in agreement with the KWW analysis, and the shape of the distribution broadened as the sample was cooled. The rate at which G(Γ) displayed a maximum correlated well with the corresponding frequency of maximum dielectric loss for PHMA. The temperature dependence of these two quantities could be reproduced with an Arrhenius activation energy of 21 Kcal/mol. A consistent picture of the molecular dynamics of PHMA near the glass transition requires a strong secondary relaxation process with a different temperature dependence from the primary glass-rubber relaxation. The present results suggest that the behavior of PHMA is similar to the other poly(alkyl methacrylates). © 1996 John Wiley & Sons, Inc.