The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

Relaxation times and energy barriers of rubbing-induced birefringence in glass-forming polymers

The relaxations of rubbing-induced birefringence (RIB) in several glass-forming polymers, including polycarbonate and polystyrene (PS) derivatives with various modifications to the phenyl ring side group, are studied. Significant relaxations of RIB are observed at temperatures well below the glass transition temperature T _g . The relaxation times span a wide range from ∼ 10 s to probably geological time scale. Physical aging effects are absent in the RIB relaxations. The model proposed for the interpretation of RIB in PS describes well the RIB relaxations in all the polymers investigated here. The energy barriers are of the order of a few hundred kJ/mol and decrease with decreasing temperature, in opposition to the trend of Vogel-Fulcher form for polymer segmental relaxations above T _g . The relaxation behaviors of different polymers are qualitatively similar but somewhat different in quantitative details, such as in the values of the saturated birefringence, the shape of the initial barrier density distribution functions, the rates of barrier decrease with decreasing temperature, and the dependence of relaxation times on temperature and parameter , etc. The RIB relaxations are different from any of the other relaxations below T _g that have been reported in the literature, such as dielectric relaxations or optical probe relaxations. A microscopic model for the relaxations of RIB is much desired.     

Effect of counterions on the swelling of spherical polyelectrolyte brushes

We investigate the swelling of colloidal spherical polyelectrolyte brushes in the presence of different counterions. The colloidal particles consist of a solid poly(styrene) core of ca. 100 nm diameter onto which linear polyelectrolyte chains are chemically grafted. Two types of polyelectrolyte chains have been used here: The cationic polyelectrolyte poly(2-(acryloyl)ethyltrimethylammonium chloride)) (PATAC) and the anionic poly(styrenesulfonate) (PSS). Both systems are dispersed in water and the degree of swelling of the surface layer is studied by dynamic light scattering. Adding more and more salt leads to a strong shrinking of the surface layer as expected for polyelectrolyte brushes. It is shown that data obtained at low ionic strength can be collapsed on suitable master curves for monovalent and divalent counterions, respectively. For some ions, however, high salt concentrations may lead to a re-swelling of the brush layer in case of the cationic systems. This points to specific interactions of the counterions with the PATAC chains. This strong specific interaction between the counterions and the attached polyelectrolyte may even lead to flocculation of the particles at intermediate salt concentration. Surprisingly, for iodide and magnesium counterions the solubility increases again if the salt concentration is raised to 1 mol/l. Hence, specific interaction leads to salting-out effects as well as to salting-in effects for these colloidal particles. All specific effects seen at high concentrations of added salt can be explained by the increase of the reduced excluded-volume parameter which is due to the adsorption of salt ions.     

Molecular Dynamics simulation of a polymer chain translocating through a nanoscopic pore

The detection of linear polymers translocating through a nanoscopic pore is a promising idea for the development of new DNA analysis techniques. However, the physics of constrained macromolecules and the fluid that surrounds them at the nanoscopic scale is still not well understood. In fact, many theoretical models of polymer translocation neglect both excluded-volume and hydrodynamic effects. We use Molecular Dynamics simulations with explicit solvent to study the impact of hydrodynamic interactions on the translocation time of a polymer. The translocation time τ that we examine is the unbiased (no charge on the chain and no driving force) escape time of a polymer that is initially placed halfway through a pore perforated in a monolayer wall. In particular, we look at the effect of increasing the pore radius when only a small number of fluid particles can be located in the pore as the polymer undergoes translocation, and we compare our results to the theoretical predictions of Chuang et al. (Phys. Rev. E 65, 011802 (2001)). We observe that the scaling of the translocation time varies from τ ∼ N ^11/5 to τ ∼ N ^9/5 as the pore size increases (N is the number of monomers that goes up to 31 monomers). However, the scaling of the polymer relaxation time remains consistent with the 9/5 power law for all pore radii.     

Glass transition of the two distinct single-chain particles of poly(N-isopropylacrylamide)

Two distinct single-chain particles of poly(N-isopropylacrylamide) (PNIPAM) in the state of loose coil and compact globule, have been prepared successfully below and above the lower critical solution temperature (LCST) in extreme dilute aqueous solution by the freeze-drying method, respectively. During the preparation of the compact globular single-chain sample, the surfactant of sodium n-dodecyl sulfate (SDS) was added into the system to prevent aggregation of globular single chains formed at a temperature above the LCST. After all the coil has been transformed into the compact globular particle, the SDS molecules were removed by dialysis. The glass transition temperature (T_g) of the two single-chain samples has been measured by differential scanning calorimetery (DSC) in comparison with that of bulk polymer. It was found that the T_g of the single-chain sample in compact-globule state was very near to that of the bulk polymer, whereas the T_g of the single-chain sample in loose-coil state was approximately 6 K lower than that of the bulk polymer. After treating the sample with repeated DSC cycles, the T_g of the single-chain sample in loose-coil state rose up successively near to that of the bulk polymer. These results have been explained in terms of the effect of entanglement on the mobility of the polymer segments in the two distinct single-chain samples.     

Correlation in a Gaussian chain with the ends fixed

We consider an ideal chain whose ends are fixed without fluctuation at different points, possibly by optical tweezers. We derive a two-point probability distribution of a corresponding random walk and explicitly calculate the scattering function. We find that the contour plot of the resulting function shows a kind of normal butterfly pattern, contaminated by wavy texture. These results are compared with some representative previous models.     

A non-Gaussian model in polymeric network

We investigate a finite chain approximation, the non-Gaussian Tsallis distribution, to the polymeric network, which gives an improvement to the Gaussian model. This distribution presents some necessary characteristics, like a cutoff to the maximum chain length and a continuous limit to the Gaussian one for a large number of monomers. It also presents a simple quadratic structure that allows to generalize the Gaussian properties such as exact-moments calculation and Wick theorem. We obtain the free-energy density in its full tensorial structure.     

Polymer brushes near the crystallization density

In this paper, polymer brushes are studied via molecular-dynamics simulations at very high grafting densities, where the crossover between the brush regime and the polymer-crystal regime is taking place. This crossover is directly observed with the structure factor and pair-correlation function. With increasing grafting density, this crystallization is progressing from the core layer of the brush towards the surface layer. The same process is analyzed using the lateral fluctuations of the monomers as a signature of their diminishing mobility. Additionally, bond forces and the chain excess free energy indicate a transition from the brush regime to the overstretched regime, which is in agreement with predictions of a modified self-consistent field theory.     

Analysis of polymer adsorption onto colloidal particles

The structure of the layer formed after polymer adsorption onto a spherical particle is numerically studied by means of the application of the Single-Chain Mean-Field theory. We have determined several overall layer properties including the monomer volume fraction profiles, the layer thickness, adsorbances related to loops and to tails, as well as the variation of the crossover distance between loops and tails for different particle radii and fixed polymer length. When the radius of the sphere is small enough to affect the loop layer, one enters a single-adsorbed-chain regime, characterized by a critical sphere radius. In this regime, structural changes in the adsorbed layer arise. For such small sphere, the loop layer is confined to a region whose thickness is of the order of the radius of the adsorbing sphere, and two long tails dominate the outer layer and the adsorbance due to tails dominates that due to loops. An analysis of the structure of the outer tail layer for this small sphere case is also presented.     

Scattering properties of gradient heteropolymers obtained by “living” free-radical copolymerization

An original, quantitative, theory of “living” radical copolymerization has been developed proceeding from the current concepts of its kinetics and mechanism. This theory enables one to calculate both the dependence of monomers' conversion on time and any statistical characteristics of the chemical structures of the copolymers formed. Expressions have been derived describing the angular dependence of the scattering amplitude of the copolymerization products. The results of quantitative calculations of these characteristics have been also presented to exemplify the potentialities of the theory. Received 13 February 2001 and Received in final form 4 February 2002     

The use of fractional orders in the determination of birefringence of highly dispersive materials by the channelled spectrum method

The channelled spectrum employing polarized light interference is a very convenient method for the study of dispersion of birefringence. However, while using this method, the absolute order of the polarized light interference fringes cannot be determined easily. Approximate methods are therefore used to estimate the order. One of the approximations is that the dispersion of birefringence across neighbouring integer order fringes is negligible. In this paper, we show how this approximation can cause errors. A modification is reported whereby the error in the determination of absolute fringe order can be reduced using fractional orders instead of integer orders. The theoretical background for this method supported with computer simulation is presented. An experimental arrangement implementing these modifications is described. This method uses a Constant Deviation Spectrometer (CDS) and a Soleil Babinet Compensator (SBC).     

Spherical polyelectrolyte block copolymer micelles: Structural change in presence of monovalent salt

Spherical polyelectrolyte block copolymer micelles were investigated as a function of added NaCl salt concentration using Small-Angle Neutron Scattering (SANS) and Light Scattering (LS). The micelles are formed by the self-association of charged-neutral copolymers made of a long deuterated polyelectrolyte moiety (NaPSS_d)₂₅₁ and a short hydrophobic moiety (PEP)₅₂. In presence of salt, the core shape and the aggregation number of the micelles are not affected. The hydrodynamic radius of the micelle is found to be identical to the radius of the whole micelle deduced from neutron scattering and thus the hydrodynamic radius is a valid measure of the corona thickness. At the lowest salt concentrations investigated the thickness of the corona, R_s, remains essentially constant and a contraction is observed above an added-salt concentration c_s of 2×10^-2 M where this crossover concentration corresponds to the average ionic strength of the free counterions in the corona. The contraction takes place while maintaining a rod-like behavior of the chains at short scale and obeys to: R_s c_s^-0.18. The exponent 0.18 suggests an electrostatic persistence length proportional to the Debye screening length.     

Flow birefringence,stress optical rule and rheology of four micellar solutions with the same low shear viscosity

The flow birefringence and the rheological properties of four viscoelastic solutions having nearly the same zero shear viscosity and subjected to shear flows are investigated in the linear and non-linear domains. The surfactant used for the samples is the cetyltrimethylammonium chloride in water at the concentration of 100 mmol/l with an organic salt, the sodium salicylate. The low shear viscosity curve versus the salt concentration is non-monotonic and has two maxima separated by a minimum forming four domains in which the salt concentration is chosen. For the two solutions belonging to the inner branch, i.e. between the two maxima, a simple Maxwellian behaviour is observed and shear banding occurs as confirmed by the flow birefringence pictures. Contrary to the results of P. Fisher (1996) where the unstable flow regime is restricted to the first decreasing part of the low shear viscosity curve of a cetylpyridinium chloride solution, we show that shear banding exits in a wider domain of the salt concentration. Received 18 November 2002 / Published online: 1 April 2003 RID="a" ID="a"e-mail: Decruppe@lpli.sciences.univ-metz.fr     

Electric birefringence study of an amyloid fibril system: The short end of the length distribution

In this article, a system of amyloid fibrils, based on the protein β-lactoglobulin, is studied by transient electric birefringence. Single pulses of an electric field were applied to the solution, and the initial rise and subsequent decay of birefringence analysed. The decay takes place on a range of relaxation times, and therefore contains information about the length distribution of fibrils in the system. The information can be extracted using theories of the electric polarisability of polyelectrolyte rods, since the fibrils are an example of these. Despite the long-standing complications of such theories, useful quantitative information about the system can still be obtained. Using the Fixman model of polyelectrolyte polarisability, we obtain a measurement of the short end of the length distribution which shows the fibril concentration as a function of length rising linearly from 0.02-2 μm. The short end of the length distribution was unobtainable in our previous study using rheo-optics (S.S. Rogers et al., Macromolecules 38, 2948 (2005)), but reasonable agreement between the two techniques shows they are complementary.     

Measurement of adhesion energies and Young's modulus in thin polymer films using a novel axi-symmetric peel test geometry

We present a novel method of probing adhesion energies of solids, particularly polymers. This method uses the axi-symmetric deformation of a thin spincast polymer membrane brought into contact with a flat substrate to probe the work of adhesion. The use of a thin membrane minimizes uncertainty in the radius of contact, while the use of spincast films provides very smooth surfaces by means of a very simple method. The experimental profile of the deformed membrane shows good agreement with the expected logarithmic profile. The experimental setup enables the measurement of Young's modulus and the solid-solid work of adhesion for thin films. The value obtained for Young's modulus of polystyrene (PS) was found to be in agreement with other conventional measurement techniques. In addition, measurement of the work of adhesion at the PS/silicon oxide interface was possible. The apparatus is well suited to studying the dependence of Young's modulus, work of adhesion and fracture energy on membrane thickness, temperature, pulling rate, and ageing of the interface, and can readily be modified to study biologically relevant samples.     

DNA ejection from bacteriophage: Towards a general behavior for osmotic-suppression experiments

We present in this work in vitro measurements of the force ejecting DNA from two distinct bacteriophages (T5 and λ using the osmotic-suppression technique. Our data are analyzed by revisiting the current theories of DNA packaging in spherical capsids. In particular we show that a simplified analytical model based on bending considerations only is able to account quantitatively for the experimental findings. Physical and biological consequences are discussed.     

Determination of the Li/Nb ratio in lithium niobate by means of birefringence and Raman measurements

Two optical methods for the determination of the Li/Nb ratio in lithium niobate (LiNbO₃) are discussed. Data for the optical birefringence method are presented, they cover the entire composition range in which LiNbO₃ can be fabricated and a wide spectral region. The line-widths of lattice modes have been measured by means of Raman scattering as a function of the Li/Nb ratio for single crystals with polished and rough surfaces.     

Temporal oscillations of the shear stress and scattered light in a shear-banding-shear-thickening micellar solution

The results of optical and rheological experiments performed on a viscoelastic solution (cetyltrimethylammonium bromide + sodium salicylate in water) are reported. The flow curve has a horizontal plateau extending between two critical shear rates characteristic of heterogeneous flows formed by two layers of fluid with different viscosities. These two bands which also have different optical anisotropy are clearly seen by direct observation in polarized light. At the end of the plateau, apparent shear thickening is observed in a narrow range of shear rates; in phase oscillations of the shear stress and of the first normal stress difference are recorded in a shearing device operating under controlled strain. The direct observation of the annular gap of a Couette cell in a direction perpendicular to a plane containing the vorticity shows that the turbidity of the whole sample also undergoes time dependent variations with the same period as the shear stress. However no banding is observed during the oscillations and the flow remains homogeneous.     

Physical aging of glassy PMMA/toluene films: Influence of drying/swelling history

Gravimetry experiments in a well-controlled environment have been performed to investigate aging for a glassy PMMA/toluene film. The temperature is constant and the control parameter is the solvent vapor pressure above the film (i.e. the activity). Several experimental protocols have been used, starting from a high activity where the film is swollen and rubbery and then aging the film at different activities below the glass transition. Desorption and resorption curves have been compared for the different protocols, in particular in terms of the softening time, i.e. the time needed by the sample to recover an equilibrium state at high activity. Non-trivial behaviors have been observed, especially at small activities (deep quench). A model is proposed, extending the Leibler-Sekimoto approach to take into account the structural relaxation in the glassy state, using the Tool formalism. This model well captures some of the observed phenomena, but fails in describing the specific kinetics observed when aging is followed by a short but deep quench.