Theta Conditions Research Articles

Solution properties of ultrahigh molecular weight polymers—20. Polymer chain dimensions of poly(methyl methacrylate)

The paper is concerned with the evaluation of ultrahigh molecular weight poly(methyl methacrylate) dimensions over a wide concentration range in different solvents, by use of a model proposed by Qian and Rudin. The model allows the estimation of the unperturbed dimensions, and the obtained values are close to previous experimental data obtained in theta conditions and with those listed in the literature.

Neutron reflection from polystyrene adsorbed on silica from cyclohexane at temperatures at and below the theta temperature

Using neutron reflection, we have studied the adsorption of polystyrene onto amorphous silica from a cyclohexane solution with changing temperature, thus varying the solvent conditions, from better than theta conditions to below the cloud point, T cloud, where phase separation occurs. For this system, T cloud was determined by light scattering to be 21.9°C. We observe a dramatic increase in adsorption near the cloud point. The adsorption is reversible and the rate of establishment of equilibrium is fast. At 22°C, equilibrium is established in 25 min. Our measurements are very sensitive to adsorption at temperatures below 22.5°C where the layer is sufficiently thick and dense to give total reflection. Our reflectivity profiles are not sensitive to the shape of the tail of the decay into solution, but the thickness of the main part of the adsorbed layer is much larger than R g, of the order of 1000 Å in comparison with an R g of 160 Å. The surface excess at 22.5°C is 2.2 ± 0.8 mg m −2. As the temperature is reduced, further adsorption occurs and at 15°C the surface excess is 6.5 ± 0.8 mg m −2.

Polymer adsorption at liquid/air interfaces under lateral pressure

We present calculations of surface tension of absorbed polymer solutions at the liquid/air interface. Lateral changes in the area per monomer on the surface are induced by changing the surface pressure (lateral compression), while keeping the total surface excess fixed. Lateral compression of the adsorbed layer immersed in a good solvent results in an increase in the surface monomer concentration and surface pressure up to a critical area per monomer value where the compressibility of the system vanishes. Our mean-field model is not appropriate to describe more compressed states. Calculations are repeated in theta and bad solvent conditions, and yield similar behavior of the isotherms.

Elastic scattering and relaxation modes of cyclic diblock copolymer chains in solution: Rouse model

In this work the static and dynamic scattering properties of (A-B) r ring diblock copolymer satisfying the optical theta condition is considered in detail. The results show substantial differences with respect to linear diblock copolymers. This is mainly due to the effect of connectivity of the chain extremities A and B, leading to different conformations for both types of diblock copolymer chains. The additional entropic interaction in cyclic chains induces a decrease of the scattering intensity and a shift of the location of its maximum to a higher q value. As for the dynamic (in the Rouse model), the fact that the two extremities are connected speeds up the frequency of the interdiffusion mode and shift its minimum to higher q value.

Off-lattice Monte Carlo simulation of dilute and concentrated polymer solutions under theta conditions

A recently introduced bead-spring type model of polymer chains with purely repulsive interactions between the beads is modified to allow for attractive forces at intermediate distances. This new model is suitable for the study of thermal properties of three-dimensional polymer solutions and melts and can be efficiently simulated with Link–Cell Monte Carlo methods. As a first step, the single chain lengths up to N=128 beads are studied and the theta temperature θ is located. It is shown that the data are compatible with the theoretically predicted crossover scaling behavior, and that the properties of collapsed chains can be studied for reasonably low temperatures T<θ. In addition to static properties (chain radii, polymer density inside the coil, internal energy, specific heat) also dynamic properties are obtained, namely various mean square displacements and relaxation times and the self diffusion constant. While for T=θ (and long enough chains), there is reasonable agreement with the Rouse model, a different behavior occurs for collapsed chains. As a second step, the behavior of the polymer solution at T=θ is studied as function of concentration. There is a clear increase of the chain gyration radii with concentration φ, although the values of 〈Rg2〉T=Θ in the highly concentrated regime (melts) are still smaller than their counterparts for the corresponding ‘‘athermal’’ model (with purely repulsive interactions) at melt densities. Thus one cannot identify the chain linear dimensions at the θ point with the chain dimensions in melts quantitatively. For the chain lengths studied (N≤64) the dynamic properties are compatible with Rouse behavior at all concentrations.

Monte Carlo simulation of tetrahedral chains, 6. Linear and star‐branched polymers near to theta conditions

AbstractBy use of the pivot algorithm, star‐branched chains with F = 4, 8 and 12 arms of length n and linear chains (F = 2) are generated on a tetrahedral lattice (120 ⩽ nF ⩽ 3 840). By taking into account non‐bonded nearest‐neighbour interactions (each contact contributes an energy ϕ · kT to the total energy of the configuration) a variation of the thermodynamic quality of the solvent is simulated by a variation of the energy parameter ϕ in the range −0,425 to −0,525. The energy parameter ϕ⊙ = −0,475, characteristic of theta conditions, was evaluated by use of an intramolecular criterion (proportionality between mean‐square dimensions and total chain‐length) and confirmed by a crossover scaling analysis. Theta dimensions are found to be larger than those of nonreversal random walks, the deviation growing with increasing number of arms.

Cold denaturation-induced conformational changes in phosphoglycerate kinase from yeast

The temperature-dependent conformational equilibrium of 3-phosphoglycerate kinase has been studied in the temperature range from 1 to 30 degrees C by means of dynamic light scattering, small-angle X-ray scattering, differential scanning calorimetry, circular dichroism spectroscopy, and fluorescence spectroscopy. At 28 degrees C and in the presence of 0.7 M guanidine hydrochloride (GuHCl), the radius of gyration (RG) and the Stokes radius (RS) are 2.44 and 3.09 nm, respectively. Decreasing the temperature effects unfolding of the molecule, a process that involves two stages. The two stages correspond to the successive unfolding of the N-terminal and C-terminal domains. The peak maxima of the excess heat capacity, determined from differential calorimetric scans, extrapolated to 0 scan rate, are positioned at 16.5 degrees C for the N-terminal domain and at 6.3 degrees C for the C-terminal domain. At 4.5 degrees C, the radius of gyration and the Stokes radius increase to 7.8 and 4.8 nm, respectively. The persistence length and the length of the statistical chain segment of the unfolded polypeptide chain are 1.74 and 3.48 nm, corresponding to five and ten amino acids, respectively. At 1 degrees C, the dimensions of the unfolded chain nearly agree with the predicted dimensions under theta conditions. Thus, the conformational changes upon cold denaturation can be described by a transition from a compactly folded molecule to a random coil. The conformation-dependent ratio rho = RGRS-1 increases from rho = 0.79 to rho = 1.63. The volume of the unfolded chain is 30 times larger than that of the folded chain in the native state.(ABSTRACT TRUNCATED AT 250 WORDS)

Static scattering from cyclic copolymers in solution

The static scattering properties of cyclic diblock copolymers in solution are studied. The case of a symmetric diblock in a solvent satisfying the optical theta condition is considered in details. The results show substantial differences with respect to linear diblock copolymers. The additional entropic interaction in cyclic chains induces a decrease of the scattering intensity and a shift of the location of its maximum to a higher q value. This results in a substantial compatibility enhancement as compared to linear copolymers.

Kinetics of critical fluctuations in ternary polymer solutions

AbstractThe time evolution of the static structure factor following a sudden temperature jump ΔT is investigated in the case of a symmetric mixture of two polymers and a solvent in the optical theta conditions. The two reverse processes corresponding to ΔT > 0 and ΔT < 0 are considered, and the kinetics of approach towards the final states are investigated both in the Rouse limit and in the presence of hydrodynamic interactions.

Copolymer‐monomer miscibility during copolymerization

AbstractSignificant drift in the compositions of copolymer and of unreacted monomer mixture is predicted to occur during the bulk copolymerization of N‐vinyl‐2‐pyrrolidone (VP) with butyl acrylate (BA), when the inital feed mixture contains 75 wt.‐% VP. The drift in copolymer composition has been confirmed by 1 the optical appearance and glass transition (Tg) behaviour of the products of the γ‐ray initiated copolymerization at various fractional conversions (C) and 2 the Tg behaviour of low‐conversion samples of poly(VP‐co‐BA) blended in propertions so as to simulate the overall composition of material that would be present cumulatively at selected values of C during an actual copolymerization. The compositions of unreacted monomer mixtures co‐existing with copolymer at selected conversions have been calculated and intrinsic viscosities [η] of blends dissolved in these VP/BA mixtures have been measured. Theta conditions for the blends have been established turbidimetrically in chloroform/heptane and the corresponding values of [η]Θ measured. The chain expansion factors thereby derived from [η] and [η]Θ show a decreasing affinity of copolymer for residual monomer during the course of copolymerization.

Degree of swelling and extent of crowding of flexible polymer coils in low concentration region

Abstract At infinite dilution, a flexible polymer chain is an isolated coil swollen with solvent. The situation may be treated in a manner analogous to the swelling equilibrium of a lightly crosslinked network. From the thermodynamic relation, the degree of swelling of the polymer coil may be estimated (1, 2). This value, the degree of chain extension, was found to be somewhat larger than that estimated from intrinsic viscosity. This finding was interpreted to mean that the chain segments in the periphery of the coil are more extended than the average coil extension (1). In the present work the dilute but finite concentration range was examined. In this case a polymer coil is in equilibrium with solvent containing polymer chains of the same kind. As the concentration is increased, the excess extension of the chain segments in the periphery of the coil diminishes. With further concentration increase, the polymer coil continues to decrease in size to the size defined by the theta condition, when the free so...

Mode selection in the dynamics of sheared polymer solutions.

We report transient light scattering measurements upon the cessation of shear for a semidilute polymer solution under theta conditions. The polymer solution demonstrates two modes of relaxation for concentration fluctuations in equilibrium. The transient mensurements show that the mechanism that couples the concentration fluctuafions to the shear flow, and thereby enhances concentration fluctuations, selectively enhances only the slower of the two equilibrium modes

Intrinsic viscosity of flexible polymers in unbounded and bounded Newtonian shear flow

The zero-shear-rate intrinsic viscosity of a polymer in an athermal and THETA solvent in free space and confined in a slit is investigated by Monte Carlo simulations of self-avoiding random walks on a simple cubic lattice. The intrinsic viscosity in a Newtonian shear flow is calculated by Zimm's algorithm. The results for an unbounded system are in excellent agreement with several scaling predictions. The intrinsic viscosity is below its unbounded value when the coil is squeezed. The effect of hydrodynamic interactions between walls and chain segments on the intrinsic viscosity is negligible. The differences between THETA and athermal solvent conditions gradually diminish with a decrease in the width of the slit as witnessed by the intrinsic viscosity and the scaling exponent for the radius of gyration. This is due to the fact that the solvent quality improves for a decreasing slit width; i.e., a THETA-solvent in three dimensions becomes a good solvent in two dimensions. The increase in excluded volume implies that there is a distinct difference between THETA-chains (i.e., chains that behave as random walks in free space) and real random walks. In the latter case the value of the component of the radius of gyration parallel to the walls is independent of the slit width. For real THETA-chains it increases.

Static and dynamic wetting behavior of poly(ethylene oxide) layer formed on mica substrate

Dynamic wetting of poly(ethylene oxide)-, PEO, grafted mica surface has been investigated by a tensiometric method based on the Wilhelmy balance. Advancing and receding contact angles were determined under static conditions as well as at different contact line velocities in the range 0.1–5.0 mm s −1. The wetting medium and conditions were chosen according to the phase behaviour of PEO determined in solution. Wetting parameters characterizing the surface/liquid interaction measured on a system below and above the theta conditions differ considerably. Contact angles of water or aqueous electrolyte solution were found to be increased while heterogeneity of the surface was reduced with increasing temperature and salt concentration stressing the role of chain mobility in the special properties of PEO surface.

Design of diffractive singlets for monochromatic imaging

The Seidel aberrations of a rotationally-symmetric diffractive lens with an arbitrary phase profile are presented. It is shown that by a proper choice of phase function and aperture stop position, third-order coma and astigmatism can be eliminated for any chosen conjugate ratio. Since a diffractive lens has an inherent zero value for the Petzval sum, the image plane is flat in both tangential and sagittal meridians. The substrate curvature of the lens may be chosen to introduce a prescribed amount of distortion to allow for use as a Fourier transform lens or a laser scan lens. Examples are given of lens performance in finite conjugate imaging and laser scanning, where the f - theta condition is satisfied.

Diluent effects on viscoelastic behavior

The effects of dilution upon the viscoelastic behavior of polymers are discussed and the related results of two investigations on solvent effects are presented. The creep behavior of a 40% polyvinylacetate (PVAc) solution where the solvent, sucrose benzoate, has a higher glass temperature than the PVAc is presented. Since the glass temperature, T g, of the solution is between that of the polymer and the solvent, it is higher than that of the neat polymer. In the second study, the viscosity and the recoverable compliance of six molecular-weight bimodal blends of a high (3.8×10 6) and a low (1.03×10 4) molecular-weight polystyrene were determined. The low molecular-weight component played the role of a Flory theta solvent at long times at all temperatures, enabling the determination of the steady-state recoverable compliance, J e o , of the high-molecular components as a function of concentration under theta conditions. Retardation spectra were determined from the reduced shear compliance curves for all the solutions and the neat components.

Unperturbed dimensions of poly(β-hydroxybutyrate) in single and binary solvents

Intrinsic viscosities [η], mean-square radii of gyration 〈 S 2〉 and weight-average molar masses M ̄ w measured in 2,2,2-trifluoroethanol (TFE) at 298 K for several samples of poly(β-hydroxybutyrate) (PHB) have been used to derive the unperturbed dimensions ( 〈r 2〉 0 M ) 1 2 via different extrapolation procedures. Theta conditions, established turbidimetrically at 298 K in two binary solvents, viz. TFE/water ( 52.6 47.4 v/ v ) and chloroform/n-heptane ( 50.2 49.8 v/v ), were confirmed by viscosity and light scattering, and enabled the unperturbed dimensions to be determined directly. The mean value of ( 〈r 2〉 0 M ) 1 2 by all procedures was 0.085 nm g −1 2 mol 1 2 , which, in conjunction with the corresponding quantity calculated on the basis of free rotation, affords a value of 1.67 for the steric factor σ. From values of [η] in chloroform over the interval 280–318 K, a value of −1.5 × 10 −4 K −1 was obtained for d ln 〈r 2〉 0 dT . Differential refractometry and light scattering on solutions of PHB in the binary theta mixtures yielded high values for the coefficient of selective adsorption of the good solvent (TFE and chloroform) in each case.

Induced flocculation in sterically stabilized ceramic powder dispersions

Stabilization of dispersions of silicon in benzene and trichloroethylene by adsorption of polystyrene [PS], poly (methyl methacrylate) [PMMA] and co-poly (styrene, methyl methacrylate) [co-PS-PMMA] was investigated. Isotherms for the adsorption of these polymers onto silicon were measured. Dispersions of silicon with adsorbed PMMA or co-PS-PMMA were found to be effectively stabilized. The degree of steric stabilization was found to depend on the polymer-medium interactions, the chemical structure of the polymers and the surface chemistry of the silicon powder. Flocculation was induced in the stabilized suspensions by the addition of n-hexane as a non-solvent. The amount of n-hexane needed to achieve theta conditions in the solvent was determined by carrying out cloud point titrations. This was compared to the critical volume of n-hexane needed to induce flocculation in the sterically stabilized silicon dispersions. The effects of polymer—medium interactions and temperature on these phenomena were observed. The present study is of direct relevance to the processing of ceramic powder dispersions used in the manufacture of ceramic monoliths and composites.

Chain conformation and viscometric behaviour of high molecular weight polystyrene in solvent/nonsolvent mixtures

Viscometric studies on high molecular weight polystyrene in solvent/nonsolvent binary mixtures are reported. Polymer behaviour is affected by the preferential adsorption phenomena determining the appearance of two theta temperatures, one intramolecular (B=0, α-1) and the other intermolecular (A2=0). For very high molecular weight polystyrene, theta intramolecular strongly approaches theta intermolecular due to a decrease in selective adsorption and in the vicinity of the theta condition the conformation transitions disappear.

Equilibrium dimensions of polymers in quenched disorder

The mean square end-to-end distance 〈R2〉Q of a good solvent solution of a single polymer in the presence of a quenched distribution of point scatterers is calculated to first order in ε=4−d by renormalization group methods. As the volume of the system becomes infinite, the quenched and annealed averages of the chain dimensions are shown to coincide, and the effect of disorder is seen essentially to generate a renormalized excluded volume interaction that, depending on its strength, leads to chain statistics characteristic of good, theta or marginal solvent conditions. At intermediate values of the volume, the chain is effectively collapsed, but there is no universal asymptotic scaling law that this behavior corresponds to. The size of the chain in this regime is predicted to vary with the square root of the volume, in contrast to the logarithmic variation predicted by Cates and Ball on the basis of mean field arguments.