聚合物的玻璃化转变和孤立链的内旋转异构化能

玻璃化转变时的自由体积,对不同结构的聚合物不是常数,已由实验得到了说明。其原因是玻璃化转变时的体积膨胀系数部分地来自分子链构象变化的贡献。本文在文献[2]和[5]的基础上将Dimarzio定义的链倔硬能(?)与Lipotov关于玻璃化自由体积表达式联系起来,得到了T_g时的自由体积和孤立链的内旋转异构化能的关系式 上式的计算值和文献值较为一致,因此可以作为估算孤立链柔顺性参数的方法。     

Analysis of the melt viscosity and glass transition of polystyrene

The melt viscosity, the glass transition, and the effect of pressure on these are analyzed for polystyrene on the basis of the Tammann-Hesse viscosity equation: log η = log A + B/(T ? T₀). Evidence that the glass transition is an isoviscosity state (log η_g ? 13) for lower molecular weight fractions (M < M_c) is reviewed. For a polystyrene fraction of intermediate molecular weight (M ? 19,000; t_g = 89°C.), it is shown that B is independent of the p–v–T state of the polymer liquid and that dT₀/dP = dT_g/dP. This is consistent with the postulate that B is determined by the internal barriers to rotation in the isolated polymer chain. Relationships are derived for flow “activation energies” at constant pressure and at constant volume, and for the “activation volume.” Values for polystyrene along the zero-pressure isobar and along the constant viscosity, glasstransition line are reported. For the latter, ΔV_g* is constant and corresponds to about 10 styrene units. The “free volume” viscosity equation: log η = log A + b/2.3?, is reexamined. For polystyrene and polyisobutylene, ?_g/b = 0.03, but ?_g and b themselves differ appreciably in these polymers. The parameter b is the product of an equilibrium term Δα and the kinetic term B, and none of these is a “universal” constant for different polymers. The physical significance of the free volume parameter ?, particularly with regard to the “excess” liquid volume, remains undefined. Two new relationships for dT_g/dP, one an exact derivation and the other an empirical correlation, are presented.     

Effect of alkyl side chain length on the properties of polyetherimides from molecular simulation combined with experimental results

Three polyetherimides (PEIs) with the same backbone of Ultem 100 but different lengths of the alkyl side chains were simulated by using molecular dynamics and molecular mechanics techniques to investigate the effect of side chain length on their properties and physical mechanism behind. Simulation results, which are consistent to the experimental data, show that PEI‐5 with four methylene units in each alkyl side chain has higher T_g (glass transition temperature) and higher tensile strength, but lower tensile elongation at break than those of PEI‐6 with five and PEI‐8 with seven methylene units in each alkyl side chain. However, unlike the traditional phenomena, conformational analysis provides that PEI‐5 with the highest T_g gives the highest flexibility to the polymer chain, whereas PEI‐8 with the lowest T_g imparts the lowest flexibility resulting from attachment of longer alkyl side chain increase the rigidity of backbone. From the calculated ratio of the accessible volume to the total volume for each system, the highest ratio of PEI‐8 indicates that long alkyl side chains generate more free volume than short side chains, acting as an internal plasticizer in bulk structure. It is the internal plasticizing effect that is predominantly responsible for the abnormal properties, instead of the rigidity from side chains. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 595–599, 2010     

Extension of the chain‐end,free‐volume theory for predicting glass temperature as a function of conversion in hyperbranched polymers obtained through one‐pot approaches

Compared with linear polymers, more factors may affect the glass‐transition temperature (T_g) of a hyperbranched structure, for instance, the contents of end groups, the chemical properties of end groups, branching junctions, and the compactness of a hyperbranched structure. T_g's decrease with increasing content of end‐group free volumes, whereas they increase with increasing polarity of end groups, junction density, or compactness of a hyperbranched structure. However, end‐group free volumes are often a prevailing factor according to the literature. In this work, chain‐end, free‐volume theory was extended for predicting the relations of T_g to conversion (X) and molecular weight (M) in hyperbranched polymers obtained through one‐pot approaches of either polycondensation or self‐condensing vinyl polymerization. The theoretical relations of polymerization degrees to monomer conversions in developing processes of hyperbranched structures reported in the literature were applied in the extended model, and some interesting results were obtained. T_g's of hyperbranched polymers showed a nonlinear relation to reciprocal molecular weight, which differed from the linear relation observed in linear polymers. T_g values decreased with increasing molecular weight in the low‐molecular‐weight range; however, they increased with increasing molecular weight in the high‐molecular‐weight range. T_g values decreased with increasing log M and then turned to a constant value in the high‐molecular‐weight range. The plot of T_g versus 1/M or log M for hyperbranched polymers may exhibit intersecting straight‐line behaviors. The intersection or transition does not result from entanglements that account for such intersections in linear polymers but from a nonlinear feature in hyperbranched polymers according to chain‐end, free‐volume theory. However, the conclusions obtained in this work cannot be extended to dendrimers because after the third generation, the end‐group extents of a dendrimer decrease with molecular weight. Thus, it is very possible for a dendrimer that T_g increases with 1/M before the third generation; however, it decreases with 1/M after the third generation. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1235–1242, 2004     

Glass‐Transition Temperature as a Function of Conversion in Hyperbranched Polymers Obtained by Self‐Condensing Vinyl Polymerization

Chain‐end free volume theory is extended for studying the glass‐transition temperature (T_g) as a function of conversion in hyperbranched polymers. T_g is found to have a non‐linear inverse relationship to the molecular weight for polymers obtained by self‐condensing vinyl polymerization (SCVP). During the monomer conversion process, T_g decreases with the increase in molecular weight (P) in the low conversion range, then levels off in the high conversion range.     

Miscibility and orientation behavior of poly(vinyl alcohol) / poly(vinyl pyrrolidone) blends

The miscibility of poly(viny1 alcohol)/poly(vinyl pyrrolidone) (PVA/PVP) blends is investigated by differential scanning calorimetry (DSC) and wide-angle x-ray diffraction (WAXD). The molecular orientation induced by uniaxial stretching of the blends is also examined by WAXD and birefringence measurements. It is shown by the DSC thermal analysis that the polymer pair is miscible, since a single glass transition temperature (T_g) is situated between the T_gs of the two homopolymers at every composition. The T_g versus composition curve does not follow a monotonic function but exhibits a cusp point at a PVP volume fraction of a little under 0.7, as in a case predicted by Kovacs' theory. The presence of a specific intermolecular interaction between the two polymers is suggested by an observed systematic depression in the melting point of the PVA component. A negative value of the polymer-polymer interaction parameter, χ₁₂ = 0.35 (at 513 K), is estimated from a thermodynamic approach via a control experiment using samples crystallized isothermally at various temperatures. The extent of optical birefringence (Δn) of the drawn blends decreases drastically with increasing PVP content up to 80 wt %, when compared at a given draw ratio, and ultimately Δn is found to change from positive to negative at a critical PVP concentration of a little over 80 wt %. Discussion of the molecular orientation behavior takes into consideration a birefringence compensation effect in the miscible amorphous phase due to positive and negative contributions of oriented PVA and PVP, respectively.     

Effect of conformational parameters on physical properties of polymers containing pendant phenoxyphthalonitrile substituents

Heteroaromatic polymers are considered to be high performance organic materials due to their unique and highly attractive properties, including outstanding thermal and mechanical resistance, that arise from their aromatic structure and strong interactions between macromolecular chains. Modification or designing new molecular architectures with tailored physico-chemical characteristics allows expanding the applications of these materials in various advanced technologies. Herein, a series of polymers containing bulky phenoxyphthalonitrile pendant units was synthesized and their physical properties were studied and correlated with their conformational parameters, as well as free and van der Waals volumes. For comparison, the related polymers without lateral moieties were also investigated to highlight the effect of bulky substituent on the polymer rigidity. Thus, it is shown that conformational rigidity determines the packing of macromolecules in solid state, and, therefore, the free volume, glass transition, and decomposition temperatures. The values found experimentally for T _g correlate well with those obtained using the conformational rigidity parameters. The dependence of T _g of these polymers on Kuhn segment is described by linear equations, with very good factors of convergence. The correlations established by Monte Carlo method allow obtaining the T _g values for related polymers where the experimental measurement of this parameter is difficult.     

高聚物玻璃化转变温度和分子参数的关系 Ⅰ.高聚物链柔性与Tg的关系

 本文采用晶格模型,以动力学链段长度作为统计单元大小,推导了高聚物玻璃化温度T_8和链静态刚性因子σ²(T₈),链动态刚性因子β(T₈)以及聚合度DP等分子参数之间的关系。具体讨论了链柔性对T₈的影响。理论预测和几十种聚合物的实验数据能较好吻合,分析结果表明T₈值基本上取决于高聚物链σ(T₈)大小。     

Free volume microstructure of amorphous polymers at glass transition temperatures from positron annihilation spectroscopy data

The analysis of annihilation characteristics of ortho-positronium at conventional calorimetric glass transition temperatures for a series of amorphous polymers reveals empirical correlations of average lifetime of o-Ps , and of its product with a relative intensityI _3g with appropriateT _g ^DSC values. These trends in terms of free volume mean that both the average size of free volume hole entityv _hg and the fractional free volume grow with increasingT _g ^DSC . The results are discussed considering the chemical microstructure as well as possible mechanisms acting in glass transition. A relation is indicated between geometric and flexibility characteristics of chains and thev _hg andf _g parameters of free volume microstructure on the one side and potential motional processes responsible for solidification of the amorphous system on the other side.     

Positron annihilation lifetime studies of changes in free volume on cross-linking cis-polyisoprene,high-vinyl polybutadiene,and their miscible blends

Measurements of average free volume hole sizes, 〈v_f〉, and the fractional free volumes, f_ps, in vulcanized cis-polyisoprene (CPI), high-vinyl polybutadiene (HVBD), and their 50 : 50 blend were made via determination of orthopositronium annihilation lifetimes. The results are compared to corresponding data on the uncured materials. On crosslinking, 〈v_f〉 decreases in the rubbery state but remains essentially unchanged in the glass. This is consistent with the expectation that the crosslinks greatly restrict the thermal expansion of the chains above the glass transition temperature (T_g) but have less influence on the packing density in the glass. Scaling relationships between 〈v_f〉, f_ps, the thermal expansion coefficient α_f = df_ps/dt, and T_g are examined. We find that 〈v_f〉_g, the hole volume at T_g, and f_ps,g, the fractional free volume at T_g, each increase significantly with increasing T_g. This behavior is consistent with previous observations reported in the literature and has been interpreted as a manifestation of the kinetic character of the glass transition. High-T_g polymers need a larger free volume to pass into the liquid state. The change in expansion coefficient on passing from the glass to the liquid, Δα_f = α_f,l − α_f,g, increases slowly with T_g, as predicted by free volume theory. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2754–2770, 1999     

Theoretical and Predictive Modelling of Physical Properties of Polymers

The application of Boltzmann statistics to a complete distribution of molecular conformation energies of simplified homo‐ and copolymer models gives meaningful information about temperatures at which phase transitions take place in the bulk. We have calculated in the conformation statistical distribution (CSD) approximation Helmholtz free energy variation versus temperature δF = δU–TδS, where U and S are, respectively, the internal molecular energy and the Gibbs statistical entropy of the considered polymeric model. The deepest minima correspond to glass‐transition temperature (T_g) and melting temperature (T_m) of modelled polymers, while the remaining peaks are related to some other transitions, the existence of which is also experimentally proven. The adopted method is able to give T_g and T_m as a function of the molecular weight of polymers. Some indications can also be achieved about the instability of polymers. The same procedure has been applied to copolymers and blends and has given acceptable results for T_g and T_m as functions of the material microstructure and composition. Other thermal and mechanical properties, such as moduli, mobilities, chemical resistance to oxidation, physical tendency to miscibility, have been directly or indirectly estimated.     

Correlation between glass transition temperature and chain structure for randomly crosslinked high polymers

The empirical form for the dependence, T_g(n) ≅ T_g(∞)·(1 + α/n), of the glass transition temperature T_g on the average number n of repeat units between crosslinks, is generalized for randomly crosslinked high polymers. The new form, T_g(n) ≅ T_g(∞) · [1 + c/(n·N_rot)], is based on a correlation study of data for 77 samples of 10 different sets of resins. The fitting parameter α is resolved into composition-dependent N_rot and composition-independent c terms. N_rot summarizes the average number of rotational degrees of freedom per repeat unit, and is estimated in a straightforward manner from the structure and mol fraction of each repeat unit. The value of c is found from data analysis to be 5 ± 2. The results of this work are consistent with expectations based on the entropy theory of glasses, and provide improved understanding and predictive ability for the properties of crosslinked polymers. © 1996 John Wiley & Sons, Inc.     

Polycondensations of dicarboxylic acids and diols derived from optically active amino alcohols

Polycondensations of dicarboxylic acids with diols having amide moieties derived from optically active amino alcohols were carried out. Polymers with M _ns 8,700–17,400 were obtained by the polycondensations using 1.2 eq. of 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide hydrochloride (EDC·HCl) in DMF at room temperature for 8 h in satisfactory yields. The T_g of the polymer rose with decrease of the methylene chain length of the dicarboxylic acid. In the T_gs of the polymers from L-leucinol, even-odd effect was observed with increase of the methylene chain length of the dicarboxylic acid. The molecular rotation values of the polymers were constant except for the polymer from succinic acid, which showed the negatively largest one. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2925–2934, 1997     

Isotope effect in gas transport. II. Effect of the glass transition on the size of the free volume element

A diffusive gas-transport isotope effect is used to estimate the size of the free volume element above and below the glass transition for poly(ethyl methacrylate) and poly(vinyl fluoride). The cavity size, as measured by the hydrogen probe molecule, is apparently larger in the glassy region for both polymers than it is above T_g. It is postulated that the number of free volume elements essentially decreases below T_g, so that the total free volume, which is the sum of all such elements, is smaller below the glass transition, in accord with density measurements on bulk polymers.     

Oxyalkylene polymers with alkylsulfonylmethyl side chains: Gas barrier properties

Gas barrier properties of alkylsulfonylmethyl-substituted poly(oxyalkylene)s are discussed. Oxygen permeability coefficients of three methylsulfonylmethyl-substituted poly(oxyalkylene)s, poly[oxy(methylsulfonylmethyl)ethylene] (MSE), poly[oxy(methylsulfonylmethyl)ethylene-co-oxyethylene] (MSEE), and poly[oxy-2,2-bis (methylsulfonylmethyl)trimethylene oxide] (MST) were measured. MSEE, which has the most flexible backbone of the three polymers, had an oxygen permeability coefficient at 30°C of 0.0036 × 10⁻¹³ cm³(STP)·cm/cm²·s·Pa higher than that of MSE, 0.0014 × 10⁻¹³ cm³(STP)·cm/cm²·s·Pa, because the former polymer's T_g was near room temperature. MST with two polar groups per repeat unit and the highest T_g showed the highest oxygen permeability, 0.013 × 10⁻¹³ cm³(STP) · cm/cm²·s·Pa, among the three polymers, probably because steric hindrance between the side chains made the chain packing inefficient. As the side chain length of poly[oxy(alkylsulfonylmethyl)ethylene] increased, T_g and density decreased and the oxygen permeability coefficients increased. The oxygen permeability coefficient of MSE at high humidity (84% relative humidity) was seven times higher than when it was dry because absorbed water lowered its T_g. At 100% relative humidity MSE equilibrated to a T_g of 15°C after 2 weeks. A 50/50 blend of MSE/MST had oxygen barrier properties better than the individual polymers (O₂ permeability coefficient is 0.0007 × 10⁻¹³ cm³(STP)·cm/cm² ·s·Pa), lower than most commercial high barrier polymers. At 100% relative humidity, it equilibrated to a T_g of 42°C, well above room temperature. These are polymer systems with high gas barrier properties under both dry and wet conditions. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 75–83, 1998     

Physical aging and glass transition of hairy nanoparticle assemblies

Matrix free assemblies of polymer-grafted, “hairy” nanoparticles (aHNP) exhibit novel morphology, dielectric, and mechanical properties, as well as providing means to overcome dispersion challenges ubiquitous to conventional polymer-inorganic nanocomposite blends. Physical aging of the amorphous polymer glass between the close-packed nanoparticles (NPs) will dominate long-term stability; however, the energetics of volume recovery within the aHNPs is unknown. Herein, we compare glass transition temperature (T_g) and enthalpy recovery of aHNPs to NP-polymer blends, across different nano-silica loadings (0–50 v/v%) and canopy architecture of polystyrene (PS) grafted silica. For aHNPs, the grafting of PS to silica imposes an additional design constraint between silica volume fraction, graft density, and graft molecular weight. At low and intermediate silica volume fraction, the T_g of blended nanocomposites is independent of silica content, reflecting a neutral polymer-NP interface. For aHNPs, the T_g decreases with silica content, implying that chain tethering decreases local segment density more than the effect of molecular weight or polymer-NP interactions. Additionally, the T_g of the aHNPs is higher than a linear matrix of comparable molecular weight, implying a complementary effect to local segment density that constrains cooperativity. In contrast, enthalpy recovery rate in the blend or aHNP glass is retarded comparably. In addition, a cross-over temperature, T_x, emerges deep within the glass where the enthalpy recovery process of all nanocomposites becomes similar to linear unfilled matrices. Differences between structural recovery in aHNP and blended nanocomposites occur only at the highest silica loadings (∼ 50 v/v%), where enthalpy recovery for aHNPs is substantially suppressed relative to the blended counterparts. The absence of physical aging at these loadings is independent of brush architecture (graft density or molecular weight of tethered chains) and indicates that the impact of chain tethering on effective bulk structural relaxation starts to appear at particle-particle surface separations on the order of the Kuhn length. Overall, these observations can be understood within the context of how three separate structural characteristics impact local segment density and relaxation processes: the dimension and architecture of the tethered polymer chains, the separation between NP surfaces, and the confinement imposed by chain tethering and space filling within the aHNP. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 319–330     

Proton NMR investigation of the local dynamics of PEO in PEO/PMMA blends

Longitudinal relaxation of proton magnetisation was used to characterize the molecular motions of PEO chains in compatible PEO (hydrogenated)/PMMA (deuterated) blends. Both the temperature and the PEO concentration, Φ, were varied. A maximum in the spin–lattice relaxation rate was observed and its properties were analyzed as a function of Φ. For Φ ≤ 0.50, the maximum is observed below the glass transition temperature of the blend; this shows that PEO chains dispersed in a matrix of PMMA remain highly mobile on a local scale even below T_g(Φ). A frequency–temperature correspondence procedure, applied to the measurements performed at two Larmor frequencies, 32 and 60 MHz, leads to a characteristic correlation time for PEO molecular motions. Its temperature dependence obeys a WLF free volume relation above the glass transition of the blends. The PEO free volume fraction and its thermal expansion are strongly reduced by the presence of the PMMA chains. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1095–1105, 1997     

The linear rheological responses of wedge‐type polymers

The linear rheological responses of a series of specially designed wedge‐type polymers synthesized by the polymerization of large molecular weight monomers have been measured. These wedge polymers contained large side groups which contained three flexible branch chains per polymer chain unit. The master curves for these polymers were obtained by time temperature superposition of dynamic data at different temperatures from the terminal flow regime to well below the glass transition temperature, T_g. While these polymers maintained a behavior similar to that of linear polymers, the influence of the large side group structure lead to low entanglement densities and extremely low rubbery plateau modulus values, being near to 13 kPa. The viscosity molecular weight dependence was also somewhat higher than that normally observed for linear polymers, tending toward a power law near to 4.2 rather than the typical 3.4 found in entangled linear chains. The glassy modulus of these branched polymers is also found to be extremely low, being less than 100 MPa at T_g ?60 °C. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 899–906     

Isothermal crosslinking studies on polyquinoxalines by dynamic mechanical methods

Torsional braid analysis was used to investigate the crosslinking behavior of linear quinoxaline polymers with and without reactive side groups. The kinetic parameter followed was the glass transition temperature during isothermal exposure in an inert atmosphere. With high molecular weight polyamide-quinoxaline copolymers (PPAQ), an initial decrease in T_g was observed during heat exposure which was followed by a subsequent increase in T_g. This was attributed to simultaneous chain scission and crosslinking reactions. Since the effect of random chain scission on the initial change in T_g of the highest molecular weight polymer samples is much stronger than on low molecular weight analogues, a T_g minimum was observed only on the highest molecular weight polymers. Because of the complexity of the reactions occurring one must consider the activation energies obtained from the Arrhenius plots as “apparent” activation energies. No attempt was made to elucidate the mechanisms of these reactions. It has been shown that isothermal heat exposure of high-temperature aromatic polymers in an inert atmosphere leads to crosslinking. In general, however, linear polymers that have reactive side groups such as methyl or carboxyphenyl groups along the polymer chain crosslink more rapidly than the analogs without these groups.     

The Spin Probe Dynamics and the Free Volume in a Series of Amorphous Polymer Glass-Formers

We report the results of a combined study of the local structure and the reorientation dynamics in a series of five amorphous polymers of different fragility: cis-trans-1,4-poly(butadiene) (c-t-1,4-PBD), cis-1,4-poly(isoprene) (cis-1,4-PIP), poly(isobutylene) (PIB), poly(vinyl methylether)(PVME) and poly (propylene glycol) (PPG) by using two different probe methods. The reorientation dynamics of the molecular spin probe 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) from electron spin resonance (ESR) is related to the annihilation behaviour of the atomic ortho-positronium (o-Ps) one as obtained by positron annihilation lifetime spectroscopy (PALS). It was found that a slow to fast transition in the spin probe rotation mobility at the operationally defined spectral temperature parameter, T_50G, is connected with the mean o-Ps lifetime, τ₃ (T_50G) = (2.04 ± 0.26) ns. Consequently, using the free-volume concept of the o-Ps annihilation in terms of a quantum-mechanical model of o-Ps lifetime this transition can be connected with the occurrence of the mean free volume hole, V_h (T_50G) = (102 ± 17) ų, nearly independent of the chemical composition and the basic structural relaxation parameters of the amorphous polymers investigated. Finally, the free volume hole distribution aspect of the slow to fast transition indicates the presence of a sufficient free volume fluctuation at T_50G for both typical fragile PVME and strong PIB polymer and emphasizes the essential role of free volume in the spin probe dynamics.