Universal behaviour of glass transition exponents in various polymeric systems

The fast transient fluorescence (FTRF) technique was used to study the critical exponents during glass transition in free-radical cross-linking copolymerization (FCC). Methyl methacrylate (MMA), ethyl methacrylate (EMA) and various combinations of MMA with EMA were used during FCC experiments. Pyrene (Py) was used as a fluorescence probe and its fluorescence lifetimes from its decay traces were measured during glass transition. Changes in the viscosity of the pre-gel solutions due to glass formation dramatically increased the Py fluorescent lifetimes, which were used to study the glass transition of MMA, EMA and their mixtures as a function of time, at various temperatures and monomer concentrations. The results were interpreted in the view of percolation theory. The critical exponents, β and γ, were measured near the glass transition point and found to be around 0.37 ± 0.015 and 1.69 ± 0.05, respectively, in all systems studied, which are in good agreement with the static percolation results.     

A fluorescence study on the critical exponents for the linear polymerization of butyl-methacrylate

The steady-state fluorescence (SSF) technique was used to study the sol-gel transition for the linear bulk polymerization of butyl methacrylate (BMA), carried out above the glass transition temperature of polybutylmethacrylate (PBMA) (T _g?=?20°C). Pyrene (P_y) was used as the fluorescence probe. The increase in P_y intensity was monitored during free radical polymerization of BMA by using SSF technique. Changes in the viscosity of the pregel solutions due to gel formation dramatically enhance the fluorescent yield of aromatic molecules. This effect is used to monitor the sol-gel transition of BMA, as a function of time, at various temperatures. The results are interpreted in the view of percolation theory. The gel fraction exponent β?=?0.39?±?0.02 agreed the best with the static percolation values for the linear bulk BMA polymerization carried out above T _g but weight average degree of polymerization exponent,?γ?deviated from the percolation results.     

Studying of the critical exponents around the glass transition in bulk polymerization of ethyl methacrylate by using fluorescence techniques

The glass transition during bulk polymerization was studied in free-radical crosslinking copolymerization (FCC) of ethyl methacrylate (EMA), using both the steady-state fluorescence (SSF) and the fast transient fluorescence (FTRF) techniques. Pyrene (Py) was used as a fluorescence probe. Changes in the viscosity of the pregel solutions due to gel formation dramatically enhance the fluorescent yield of Py molecules. The reaction time at which the Py intensity and lifetime exhibit a sudden increase corresponds to the reaction time at which the rate of polymerization becomes maximum resulting from the gel effect. This effect is used to study the gelation of EMA, as a function of time, at various crosslinker concentrations and different temperatures. The results were interpreted in the view of percolation theory. The gel fraction, β and weight average degree of polymerization, γ exponents β?=?0.37?±?0.01, γ?=?1.71?±?0.04 and β?=?0.36?±?0.002, γ?=?1.687?±?0.01 are found in agreement with percolation results for SSF and FTRF measurements, respectively.     

A fluorescence study for the critical behavior of polymethylmethacrylate doped by multiwalled carbon nanotube (PMMA–MWNT) composite bulk gel systems

Polymethylmethacrylate (PMMA) doped by multiwalled carbon nanotube (MWNT) bulk gels were prepared with different amounts of MWNTs varying in the range between 1 and 20 wt%. Free-radical cross-linking copolymerization of PMMA–MWNT composite bulk gels was characterized by the steady-state fluorescence technique. Ethylene glycol dimethacrylate (EGDM) and pyrene (P _y ) were introduced as cross linker and fluorescence probe, respectively. Changes in the viscosity of the pregel solutions due to glass formation dramatically increased the P _y fluorescent intensities, which were used to study the glass transition of PMMA–MWNT composite gels for various MWNT contents. The fluorescence intensity of P _y is proportional to the average size of the glassy regions below and to the strength of the infinite network above the glass transition point. Observations around the glass transition point show that there are three regimes for MWNT concentration in which the gel fraction exponent, β, and the weight average degree of polymerization exponent, γ, differ drastically from percolation results, given in three dimensions as β=0.41 and γ=1.80.     

Molecular alignment during gel formation from methyl methacrylate: An excimer fluorescence study

Glass transition during bulk polymerization was studied in free-radical cross-linking copolymerization (FCC) of methyl methacrylate (MMA) using the steady-state fluorescence (SSF) technique. Naphthalene (N) was used as a monomer and excimer forming probe. Changes in the viscosity of the pregel solutions due to gel formation dramatically enhance both monomer and excimer fluorescent yield of N molecules. The reaction time at which the monomer and excimer intensities exhibit a sudden increase corresponds to the reaction time at which the rate of polymerization becomes maximum resulting from the gel effect. This effect was used to study the gelation of MMA, as a function of time, in various N concentrations. The results were interpreted in the view of percolation theory. The gel fraction, β, and weight average degree of polymerization, γ, exponents β?=?0.40?±?0.02 and γ?=?1.70?±?0.07 were found in agreement with percolation results for both monomer and excimer measurements, respectively.     

Universality in gelation of epoxy acrylate with various photoinitiators: a photo differential scanning calorimetric study

Photo-differential scanning calorimetric (Photo-DSC) technique was used to study the gelation of P-3038 (epoxy acrylate (EA) 75% and tripropyleneglycoldiacrylate (TPGDA) 25%) in the presence of various thioxanthone-based initiators, namely, thioxanthone (TX), 5-thia-naphtacene-12-one (TX-NP), 2-(carboxymethoxy) thioxanthone (TX-OCH₂COOH), 2-thioxanthone-thioacetic acid (TX-SCH₂COOH), and 2-mercaptothioxanthone (TX-SH). Photopolymerization reactions were performed under identical conditions of temperature, initiator concentration, and UV light intensity. Photo-DSC technique allowed us to monitor the gelation, without disturbing the system mechanically, and to test the universality of the gelation as a function of some kinetic parameters like initiator concentration. During gelation, it was observed that all conversion curves present a good sigmoidal behavior by predicting to employ percolation model. Observations around the glass transition point, t _g shows that the gel fraction exponents β obeyed the percolation picture. On the other hand, t _g was found to be much higher for the crosslinked networks obtained with TX-OCH₂COOH and TX-SCH₂COOH initiators than those with the other initiators.     

Critical Exponents of Photoinitiated Gelation at Different Light Intensities

A photo-differential scanning calorimetric (Photo-DSC) technique was used to study the photoinitiated radical polymerization of a 75% epoxy diacrylate (EA) and 25% tripropyleneglycoldiacrylate (TPGDA) mixture with 2-mercaptothioxanthone (TX-SH) as photoinitiator by using different light intensities. Photopolymerization reactions were carried out under identical conditions of temperature and initiator concentration. It was observed that all conversion curves during gelation at various UV light intensities present good sigmoidal behavior as predicted by the percolation model. Observations around the critical time, called the glass transition point (t_g), taken for polymerization to reach the maximum rate (Rp _max) show that the gel fraction exponents β obeyed the universal percolation picture. On the other hand, Rp _max, t _g, and final conversion values were found to be dependent on the UV light intensity.     

Drying of heterogels swollen in organic vapor

Fast transient fluorescence technique (FTRF), which uses a Strobe Master System (SMS), is used to study swelling and drying of disc shape heterogels. Disc shape heterogels are prepared by free radical copolymerization (FCC) of methyl (methacrylate) (MMA) and styrene (S) with ethylene glycol dimethacrylate (EGDM). Pyrene (P_y) is introduced as a fluorescence probe during polymerization and lifetimes, τ, of P_y are measured during the in-situ swelling process. Chloroform was used as an organic vapor agent to induce gel swelling. It is observed that τ values decrease as swelling proceeds. The Li-Tanaka equation is used to determine the time constant, τ_c, and cooperative diffusion coefficients, D _c, for the swelling processes. Lifetimes of pyrene increase during drying. An empirical equation is introduced to determine the desorption coefficient, D, for drying. Heterogels with high S content swell and dry much more slowly than heterogels with low S content.     

Percolation approach to film formation from surfactant-free polystyrene particles

In this study, a film formation process from surfactant-free polystyrene (PS) latex particles is reported. Steady state fluorescence (SSF) and photon transmission (UVV) techniques were used to study the evolution of film formation. The latex films were prepared from pyrene (P)-labeled PS particles at room temperature and annealed at time intervals of 2.5?min above the glass transition temperature (T _g) of PS. During the annealing processes, the transparency of the film changed considerably. Fluorescence intensity (I _0P) from P was measured after each annealing step to monitor the stages of film formation. Evolution of transparency of latex films were monitored by using photon transmission intensity, I _tr. A drastic increase in I _tr and I _0P above the critical annealing times, t _r and t _c were attributed, respectively to percolation behavior of PS material from one side to the other side of the latex film. Critical exponents, β of percolation clusters were measured and found to be around 0.35 and 0.25 for I _tr and I _0P measurements, respectively.     

Can the glass transition in bulk polymers be modeled by percolation picture?

Recent observations (Eur. Phys. J. E 9, 135 (2002)) showed that the vitrification process, which sets in during the linear bulk methyl methacrylate (MMA) polymerization carried out below glass transition temperatures, can be modelled by static percolation picture. To generalize this observation for different kind of bulk linear or crosslinked polymers not enough data are present in the literature. To cover partly this deficit we studied the glass transition of MMA and styrene (Sty) crosslinking copolymerization in varying ratios of MMA and Sty. Both the fluorescence intensity I and the lifetime of pyrene (Py) used as a nanosecond in situ fluoroprobe were monitored during the gelation time. Both I and increase dramatically as a result of the reduced mobility of the probes trapped in the glassy regions, appearing near the glass transition point. The average size of the glassy regions just below, and the strength of the infinite network formed upon the connection of the glassy regions above the glass transition point obey power law relations. The data around were interpreted on the basis of the percolation theory and we observed that the corresponding exponents and give static percolation values independent of the polymer composition.Received: 9 July 2004, Published online: 1 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 64.70.Pf Glass transitions - 82.35.Jk Copolymers, phase transitions, structure     

Slow regions percolate near glass transition

A nanosecond scale in situ probe reveals that a bulk linear polymer undergoes a sharp phase transition as a function of the degree of conversion, as it nears the glass transition. The scaling behaviour is in the same universality class as percolation. The exponents γ and β are found to be 1.7±0.1 and 0.41±0.01 in agreement with the best percolation results in three dimensions. Received 29 August 2002 RID="a" ID="a"e-mail: erzan@gursey.gov.tr e-mail: erzan@itu.edu.tr     

Frustrated percolation,spin glasses and glasses

Summary The static and dynamic properties of the frustrated percolation model are investigated. This model, which contains frustration as an essential ingredient, exhibits two transitions: a percolation transition at a temperatureT _p with critical exponents of the ferromagnetic (s=1/2)-state Potts model, and a second transition at a lower temperatureT _g in the same universality class of the Ising spin glass model. AboveT _p the time-dependent autocorrelation function is characterized by a single exponential, while forT _p>T>T _g preliminary numerical results show a broad shoulder or plateau typical of a structural glass transition. BelowT _g the system is in glassy state with an infinitely long relaxation time. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

Dynamic and static light scattering study of the formation of cross-linked PMMA gels

Free radical co-polymerization of methyl methacrylate (MMA) and ethyl glycol dimethyl metacrylate (EGDMA) was investigated in solution at different molar ratios R = [EGDMA]/[MMA] between 0 and 0.05. Initially mainly linear PMMA was formed with weight average molar mass 7.5 g/mol independent of R. At larger reaction extents branched polymers were formed and the systems gelled. The scattering intensity rose initially with the reaction extent, but reached a plateau value at larger reaction extents. The plateau value increased strongly with R. Dynamic light scattering showed the appearance of a slow relaxation not observed in linear PMMA solutions. The data can be interpreted by assuming that the excess scattering originates from the branching points and relaxes through self diffusion of the branched particles. The results agree with predictions of the percolation model for gelation and Rouse dynamics. Viscosity measurements corroborate this interpretation. Measurements on a progressively diluted sample quenched close to the gel point again showed quantitative agreement with the percolation model for gelation. Received 11 May 1998 and Received in final form 22 October 1998     

Depletion effects and gelation in a binary hard-sphere fluid

A study of the binary hard-sphere fluid with size ratio [sgrave]_B/[sgrave]_A = 0.1 is reported. Molecular dynamics and Monte Carlo simulations have been carried out over the mole fraction (x _A) range 0.002-0.1 and over the high density range where several recent authors have predicted a thermodynamic demising transition on the basis of integral equations. In this region, there is no evidence of such first-order thermodynamic phase separation, or two fluid phases. The effect of the depletion force, arising from the entropic exclusion of B spheres from between two A spheres, as x _B is increased at constant packing fraction y _A, is to cause a large increase in the partial pressure of A and the radial distribution function of A at contact, a reduction on the mobility of A, and eventually, at a sufficient x _B, the gelation of component A to an open, low coordination, amorphous structure. This gelation transition of A shows discontinuities similar to a glass transition; it can be traced back to the hard sphere glass formation as x _B approaches zero. Thermodynamic properties are reported over the range studied, and used to evaluate the predictions of current theories and the accuracy of equations of state. The Boublik—Mansoori—Carnahan—Starling—Leland equation is found to be remarkably accurate in this region, over the whole fluid range, but shows systematic deviations at high packing densities.     

Stiffness exponents for lattice spin glasses in dimensions $\mathsf{d = 3,\ldots,6}$

The stiffness exponents in the glass phase for lattice spin glasses in dimensions are determined. To this end, we consider bond-diluted lattices near the T = 0 glass transition point p^*. This transition for discrete bond distributions occurs just above the bond percolation point p_c in each dimension. Numerics suggests that both points, p_c and p^*, seem to share the same 1/d-expansion, at least for several leading orders, each starting with 1/(2d). Hence, these lattice graphs have average connectivities of near p^* and exact graph-reduction methods become very effective in eliminating recursively all spins of connectivity , allowing the treatment of lattices of lengths up to L = 30 and with up to 10⁵-10⁶ spins. Using finite-size scaling, data for the defect energy width over a range of p > p^* in each dimension can be combined to reach scaling regimes of about one decade in the scaling variable . Accordingly, unprecedented accuracy is obtained for the stiffness exponents compared to undiluted lattices (p = 1), where scaling is far more limited. Surprisingly, scaling corrections typically are more benign for diluted lattices. We find in for the stiffness exponents y₃ = 0.24(1), y₄ = 0.61(2), y₅ = 0.88(5), and y₆ = 1.1(1).Received: 29 October 2003, Published online: 20 April 2004PACS: 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.10.Nr Spin-glass and other random models - 02.60.Pn Numerical optimization     

Cluster Structure of Collapsing Polymers

In order to better understand the geometry of the polymer collapse transition, we study the distribution of geometric clusters made up of the nearest neighbor interactions of an interacting self-avoiding walk. We argue for this new correlated percolation problem that in two dimensions, and possibly also in three dimensions, a percolation transition takes place at a temperature lower than the collapse transition. Hence this novel transition should be governed by exponents unrelated to the -point exponents. This also implies that there is a temperature range in which the polymer has collapsed, but has no long-range cluster structure. We use Monte Carlo to study the distribution of clusters on the simple cubic and Manhattan lattices. On the Manhattan lattice, where the data are most convincing, we find that the percolation transition occurs at _p =1.461(3), while the collapse transition is known to occur exactly at =1.414.... We propose a finite-size scaling form for the cluster distribution and estimate several of the critical exponents. Regardless of the value of _p , this percolation problem sheds new light on polymer collapse.     

Selective sublattice dilution in ordered magnetic compounds: A new kind of percolation problem

A magnetic binary system is considered whereA-atoms andB-atoms occupy different sublattices but it is an exchangeJ _AB which is responsible for magnetic ordering. Diluting such a system with nonmagnetic atoms it is natural to treat situations where the dilution probability is different for both sublattices. In particular the extreme cases, where either only theA-sublattice or only theB-sublattice is diluted, is discussed for a variety of lattice structures atT=0. It is shown that in some cases the problem can be reduced to ordinary site- or bond percolation problems, while in other cases a new kind of percolation problem arises. Particular attention is paid to the case of spinel structures, and a discussion of recent experiments on the mixed systemyMg₂TiO₄–(1–y)MgFe₂O₄ is given. It is shown that additional frustration effects due to competing interactions are necessary to explain the breakdown of magnetic order upon dilution in that material. Critical exponents for this new kind of percolation problem are also estimated by Monte-Carlo methods and it is suggested that it belongs to the same universality class as usual percolation. As a check of the numerical procedures we redetermine the percolation concentrations of both sublattices of the spinel structure, and find that some of the earlier work on this problem is rather inaccurate.     

Li and Nb codoping in dielectric properties and phase transitions of KTaO3: Reentrant dipolar glass and long-range dipole ordering

Abstract

The highly polarizable perovskite-type oxide, KTaO₃ doped simultaneously with Li⁺ and Nb⁵⁺ (K_1?xLi_xTa_1?yNb_yO₃, KLTN), reveals unexpected properties and ordering effects. Studies of the dielectric permittivity ?'(T, f) (10—300K, 100Hz-1 MHz) for x = 0.0014 and y = 0.024 show collective dipolar ordering effects with a transition from paraelectric into a mixed phase (coexisting dipole-glass-like and long-range ordered ferroelectric phases) taking place near 39 K. At 15 K another phase transition into a reentrant dipolar glass-like state is observed. Such a sequence of transitions and the existence of a reentrant glass state are unknown for electrical dipolar systems.     

Scale-free random graphs and Potts model

We introduce a simple algorithm that constructs scale-free random graphs efficiently: each vertexi has a prescribed weight P_i ∝ i^-μ (0 < μ< 1) and an edge can connect verticesi andj with rateP _i P _j . Corresponding equilibrium ensemble is identified and the problem is solved by theq → 1 limit of the q-state Potts model with inhomogeneous interactions for all pairs of spins. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density. Various critical exponents associated with the percolation transition are also obtained together with finite-size scaling forms. The process of forming the giant cluster is qualitatively different between the cases of λ > 3 and 2 < λ < 3, whereλ = 1 +μ ^-1 is the degree distribution exponent. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finiteN shows double peaks.