Application of free‐volume theory to self diffusion of solvents in polymers below the glass transition temperature: A review

Theories based on free‐volume concepts have been developed to characterize the self and mutual‐diffusion coefficients of low molecular weight penetrants in rubbery and glassy polymer‐solvent systems. These theories are applicable over wide ranges of temperature and concentration. The capability of free‐volume theory to describe solvent diffusion in glassy polymers is reviewed in this article. Two alternative free‐volume based approaches used to evaluate solvent self‐diffusion coefficients in glassy polymer‐solvent systems are compared in terms of their differences and applicability. The models can correlate/predict temperature and concentration dependencies of the solvent diffusion coefficient. With the appropriate accompanying thermodynamic factors they can be used to model concentration profiles in mutual diffusion processes that are Fickian such as drying of coatings. The free‐volume methodology has been found to be consistent with molecular dynamics simulations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Synthesis of a novel one‐pot approach of hyperbranched polyurethanes and their properties

A new method for the synthesis of hyperbranched polymers involving the use of AB_x macromonomers containing linear units have been investigated. Two types of novel hyperbranched polyurethanes have been synthesized by a one‐pot approach. The structures of monomers and polymers were characterized by elemental analysis, ¹H NMR, ¹³C NMR, Fourier transform infrared spectroscopy, gel permeation chromatography, and thermogravimetric analysis. The hyperbranched polymers have been proven to be extremely soluble in a wide range of solvents. Polymer electrolytes were prepared with hyperbranched polymer, linear polymer as the host, and lithium perchlorate (LiClO₄) as the ion source. Analysis of the isotherm conductivity dependence of the ion concentration indicated that these hyperbranched polymers could function as a “solvent” for the lithium salt. The conductivity increased with the increasing concentration of hyperbranched polymers in the host polymer. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 40: 344–350, 2002     

Acid chloride‐functionalized hyperbranched polyester for facile and quantitative chain‐end modification: One‐pot synthesis and structure characterization

Carboxylic acid chloride end‐functionalized all‐aromatic hyperbranched polyesters were prepared from the bulk polycondensation of the AB₂ monomer 5‐(trimethylsiloxy)isophthaloyl dichloride. The acid chloride end functionality of the hyperbranched polyester was modified in situ with methanol and yielded methyl ester ends in a one‐pot process. Chain‐end functionalization and esterification were quantitative according to both potentiometric titration and ¹H NMR analysis. The signals of ¹H and ¹³C NMR spectra of the esterified hyperbranched polyester were fully assigned from model compounds of the focal, linear, dendritic, and terminal units. The degree of branching and molecular weight averages measured by ¹H and ¹³C NMR spectroscopy and multidetector size exclusion chromatography increased systematically with increasing polymerization temperatures between 80 and 200 °C. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2855–2867, 2002     

A predictive approach based on the Simha–Somcynsky free‐volume theory for the effect of dissolved gas on viscosity and glass transition temperature of polymeric mixtures

The gas concentration and pressure effects on the shear viscosity of molten polymers were modeled by using a unified approach based on a free volume theory. A concentration and pressure dependent “shift factor,” which accounts for free volume changes associated with polymer‐gas mixing and with variation of absolute pressure as well as for dilution effects, has been herein used to scale the pure polymer viscosity, as evaluated at the same temperature and atmospheric pressure. The expression of the free volume of the polymer/gas mixture was obtained by using the Simha and Somcynsky equation of state for multicomponent fluids. Experimental shear viscosity data, obtained for poly(ε‐caprolactone) with nitrogen and carbon dioxide were successfully predicted by using this approach. Good agreement with predictions was also found in the case of viscosity data reported in the literature for polystyrene and poly(dimethylsiloxane) with carbon dioxide. Free volume arguments have also been used to predict the T_g depression for polystyrene/carbon dioxide and for poly(methyl methacrylate)/carbon dioxide mixtures, based on calculations performed, again, with the Simha and Somcynsky theory. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1863–1873, 2006     

Elevation of the glass transition temperature in flexible‐chain semicrystalline polymers

In the idealized two‐phase model of a semicrystalline polymer, the amorphous intercrystalline layers are considered to have the same properties as the fully‐amorphous polymer. In reality, these thin intercrystalline layers can be substantially influenced by the presence of the crystals, as individual polymer molecules traverse both crystalline and amorphous phases. In polymers with rigid backbone units, such as poly(etheretherketone), PEEK, previous work has shown this coupling to be particularly severe; the glass transition temperature (T_g) can be elevated by tens of degrees celsius, with the magnitude of the elevation correlating directly with the thinness of the amorphous layer. However, this connection has not been explored for flexible‐chain polymers, such as those formed from vinyl‐type monomers. Here, we examine T_g in both isotactic polystyrene (iPS) and syndiotactic polystyrene (sPS), crystallized under conditions that produce a range of amorphous layer thicknesses. T_g is indeed shown to be elevated relative to fully‐amorphous iPS and sPS, by an amount that correlates with the thinness of the amorphous layer; the magnitude of the effect is severalfold less than that in PEEK, consistent with the minimum lengths of polymer chain required to make a fold in the different cases. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1198–1204, 2007     

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.     

Synthesis of alkaline‐developable,photosensitive hyperbranched polyimides through the reaction of carboxylic acid dianhydrides and trisamines

Hyperbranched polyimides (HBPI)s with high glass‐transition temperatures and excellent thermal stability were synthesized through the reaction of commercially available carboxylic acid dianhydrides with tris[4‐(4‐aminophenoxy)phenyl]ethane (TAPE). In particular, hyperbranched polyimide HBPI(TAPE‐DSDA), prepared through the reaction of TAPE with 3,3′,4,4′‐diphenylsulfonetetracarboxylic dianhydride (DSDA), showed higher thermal stability and good solubility. Furthermore, alkaline‐developable, photosensitive HBPI(TAPE‐DSDA)‐MA‐CA was prepared through the reaction of HBPI(TAPE‐DSDA) with glycidyl methacrylate with tetrabutylammonium bromide as a catalyst in N‐methyl‐2‐pyrrolidinone (NMP) followed by the addition reaction of cis‐1,2,3,6‐tetrahydrophthalic anhydride with triphenylphosphine as a catalyst in NMP. The glass‐transition temperatures of HBPI(TAPE‐DSDA)‐MA‐CA were greater than 300 °C. A resist composed of 74 wt % HBPI(TAPE‐DSDA)‐MA‐CA, 22.2 wt % trimethylpropane triacrylate, and 3.8 wt % Irgacure 907 as a photoinitiator achieved a resolution of a 55‐μm line pattern and a 275‐μm space pattern by UV irradiation (1000 mJ/cm²). © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3697–3707, 2004     

On the glass transition temperature of styrene-n-butyl methacrylate copolymers in dependence on chemical composition,molecular weight,and mixtures

For statistic copolymers of styrene and n-butyl methacrylate, the relation between the glass transition temperature and the chemical composition or molecular weight of the copolymers has been determined. Further, the dependence of the glass transition temperature on the composition of binary and ternary blends from statistical poly (styrene-co-n-butyl methacrylates) of a nearly equal chemical composition but a very different molecular weight has been studied. Among several equations considered for the correlation between glass transition temperature and composition of the mentioned copolymers with relatively low molecular weights, the Gordon/Taylor and Couchman equations gave the best agreement with the experimental results. For the glass transition temperature of poly(styrene-co-n-butyl methacrylate) with an n-butyl methacrylate content of about 30 wt % in dependence on the molecular weight, the Kanig-Ueberreiter and Fox-Flory equations proved to be useful for the examined molecular weight range. The glass transition temperatures of the polymer blends have been studied for a low/high-molecular component system, a system of two low-molecular components, as well as for systems with a third component. The glass transition temperatures of the mixtures frequently exceeded those of their individual components. © 1994 John Wiley & Sons, Inc.     

Screening effects in blends of a hyperbranched,dendrimer‐like polyester with poly(4‐vinyl phenol)

We previously reported self‐association and interassociation equilibrium constant values describing hydrogen bonding in solutions of a hyperbranched polyester. These allow us to estimate the extent of intramolecular screening and the fraction of same‐chain contacts in this system as a function of generation number. In this article, we use a similar method to evaluate the degree of intramolecular screening in polymer blends. The calculated values reported here are consistent with those previously reported in our solution study, confirming the validity of the calculation procedures we used to evaluate the accessibility of functional groups in these highly branched systems. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1651–1658, 2001     

Hyperbranched polymers as scaffolds for multifunctional reversible addition–fragmentation chain‐transfer agents: A route to polystyrene‐core‐polyesters and polystyrene‐block‐poly(butyl acrylate)‐core‐polyesters

Polydisperse hyperbranched polyesters were modified for use as novel multifunctional reversible addition–fragmentation chain‐transfer (RAFT) agents. The polyester‐core‐based RAFT agents were subsequently employed to synthesize star polymers of n‐butyl acrylate and styrene with low polydispersity (polydispersity index < 1.3) in a living free‐radical process. Although the polyester‐core‐based RAFT agent mediated polymerization of n‐butyl acrylate displayed a linear evolution of the number‐average molecular weight (M_n) up to high monomer conversions (>70%) and molecular weights [M_n > 140,000 g mol^?1, linear poly(methyl methacrylate) equivalents)], the corresponding styrene‐based system reached a maximum molecular weight at low conversions (≈30%, M_n = 45,500 g mol^?1, linear polystyrene equivalents). The resulting star polymers were subsequently used as platforms for the preparation of star block copolymers of styrene and n‐butyl acrylate with a polyester core with low polydispersities (polydispersity index < 1.25). The generated polystyrene‐based star polymers were successfully cast into highly regular honeycomb‐structured microarrays. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3847–3861, 2003     

Temperature and pressure dependence of the free volume in the perfluorinated polymer glass CYTOP: A positron lifetime and pressure‐volume‐temperature study

The microstructure of the free volume was studied for an amorphous perfluorinated polymer (T_g = 378 K). To this aim we employed pressure–volume–temperature experiments (PVT) and positron annihilation lifetime spectroscopy (PALS). Using the Simha‐Somcynsky equation of state the hole free volume fraction h and the specific free and occupied volumes, V_f = hV and V_occ = (1 ? h)V, were determined. Their expansivities and compressibilities were calculated from fits of the Tait equation to the volume data. It was found that in the glass V_occ has a particular high compressibility, while the compressibility of V_f is rather low, although h (300 K) = 0.108 is large. In the rubbery state the free volume dominates the total compressibility. From the PALS spectra the hole size distribution, its mean, 〈v_h〉, and mean dispersion, σ_h, were calculated. From a comparison of 〈v_h〉 with V_f a constant hole density of N_h′ = 0.25 × 10²¹ g^?1 was estimated. The volume of the smallest representative freely fluctuating subsystem, 〈V_SV〉 ∝ 1/σ_h², is unusually small. This was explained by an inherent topologic disorder of this polymer. 〈v_h〉 and σ_h show an exponential‐like decrease with increasing pressure P at 298 K. The hole density, calculated from N_h′ = V_f/〈v_h〉, seems to show an increase with P which is unexpected. This was explained by the compression of holes in the glass in two, rather than three, dimensions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2519–2534, 2007     

Effect of chain structure on the glass transition temperature and viscoelastic property of cis‐1,4‐polybutadiene via molecular simulation

In this work, by adopting the united atom model of cis‐1,4‐poly(butadiene) (PB), we systemically investigate the effect of the chain structure on the glass transition temperature (T_g) and the viscoelastic property of PB system. First, we analyze the atom translational mobility, bond reorientation dynamics, torsional dynamics, conformational transition rate, and dynamic heterogeneity of the PB chains with different chain structures in detail by determining the corresponding T_g. In addition, our results clearly indicate that with the decrease of the amount of the free end atoms of PB via the end‐linking method, the mobility of the PB chains quickly decreases. As a result, the T_g of the PB chains gradually increases. Depending on the chain structure and the calculation method, the T_g of the PB chains varies from 154 to 240 K. In addition, the temperature dependence of the dynamic properties has different Arrhenius behaviors above and below T_g. The calculated activation energy varies from 7.37 to 16.37 KJ/mol for different chain structures above T_g, which can be compared with those for other polymers. In addition, through the end‐linking approach the strong interaction between the PB chains improves the storage modulus G′ and the loss modulus . Meanwhile, the immobility of the free end atoms effectively reduces the friction loss of the chains under the shear field, which is reflected by the low loss factor . In summary, this work can further help to understand the effect of the chain structure on the dynamic properties of the PB chains. Meanwhile, it provides an effective approach to reduce the energy loss during the dynamic periodic deformation, which can cut the fuel consumption via the end‐linking method. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1005–1016     

Synthesis of fluorene‐based hyperbranched polymers for solution‐processable blue,green, red,and white light‐emitting devices

For the purpose of making hyperbranched polymer (Hb‐Ps)‐based red, green, blue, and white polymer light‐emitting diodes (PLEDs), three Hb‐Ps Hb‐ terfluorene ( Hb‐TF ), Hb ‐4,7‐bis(9,9′‐dioctylfluoren‐2‐yl)‐2,1,3‐benzothiodiazole ( Hb‐BFBT ), and Hb‐ 4,7‐bis[(9,9′‐dioctylfluoren‐2‐yl)‐thien‐2‐yl]‐2,1,3‐benzothiodiazole ( Hb‐BFTBT ) were synthesized via [2+2+2] polycyclotrimerization of the corresponding diacetylene‐functionalized monomers. All the synthesized polymers showed excellent thermal stability with degradation temperature higher than 355 °C and glass transition temperatures higher than 50 °C. Photoluminance (PL) and electroluminance (EL) spectra of the polymers indicate that Hb‐TF , Hb‐BFBT , and Hb‐BFTBT are blue‐green, green, and red emitting materials. Maximum brightness of the double‐layer devices of Hb‐TF , Hb‐BFBT , and Hb‐BFTBT with the device configuration of indium tin oxide/poly(3,4‐ethylene dioxythiophene):poly(styrene sulfonate)/light‐emitting polymer/CsF/Al are 48, 42, and 29 cd/m²; the maximum luminance efficiency of the devices are 0.01, 0.02, and 0.01 cd/A. By using host–guest doped system, saturated red electrophosphorescent devices with a maximum luminance efficiency of 1.61 cd/A were obtained when Hb‐TF was used as a host material doped with Os(fptz)₂(PPh₂Me₂)₂ as a guest material. A maximum luminance efficiency of 3.39 cd/A of a red polymer light‐emitting device was also reached when Hb‐BFTBT was used as the guest in the PFO (Poly(9,9‐dioctylfluorene)) host layer. In addition, a series of efficient white devices were, which show low turn‐on voltage (3.5 V) with highest luminance efficiency of 4.98 cd/A, maximum brightness of 1185 cd/m², and the Commission Internationale de l'Eclairage (CIE) coordinates close to ideal white emission (0.33, 0.33), were prepared by using BFBT as auxiliary dopant. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

ToF‐SIMS for the characterization of hyperbranched aliphatic polyesters: probing their molecular weight on surfaces based on principal component analysis (PCA)

A series of 2,2‐bis(hydroxymethyl)propionic acid (Bis‐MPA) hyperbranched aliphatic polyesters with different molecular weights (generations) is analysed for the first time by time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS). The main negative and positive low‐mass fragments are identified in the fingerprint part of the spectra (m/z < 400) and are principally assigned to fragmentation of the Bis‐MPA repeating units. In addition, it is shown that the fragmentation pattern is highly affected by the functional end‐groups. This is illustrated for a phthalic acid end‐capped hyperbranched polymer and for an acetonide‐terminated dendrimer analog. Also, typical fragments assigned to the ethoxylated pentaerythritol core molecule are detected. These ions show decreasing intensities with increasing molecular weight. This intensity dependency on the generation is used to calibrate the molecular weight of hyperbranched polyesters on the surface. To obtain quantitative information, a principal component analysis (PCA) multivariate statistical method is applied to the ToF‐SIMS data. The influence of different normalization procedures prior to PCA calculation is tested, e.g. normalization to the total intensity, to the intensities of ions assigned to the Bis‐MPA repeating unit or to intensities of fragments due to the core molecule. It is shown that only one principal component (PC1) is needed to describe most of the variance between the samples. In addition, PC1 takes into account the generation effect. However, different relationships between the PC1 scores and the hyperbranched mass average molecular weights are observed depending on the normalization procedure used. Normalization of data set ion intensities by ion intensities from the core molecule allows linearization of the SIMS intensities versus the molecular weight and allows the hyperbranched polymers to be discriminated up to the highest generations. In addition, PCA applied to ToF‐SIMS data provides an extended interpretation of the spectra leading to further identification of the correlated mass peaks, such as those of the Bis‐MPA repeating unit (terminal, dendritic and linear) and those of the core molecule. Finally, the work presented demonstrates the extreme potential of the static ToF‐SIMS and PCA techniques in the analysis of dendritic molecules on solid surfaces. Copyright © 2003 John Wiley & Sons, Ltd.     

Above,below, and in‐between the two glass transitions of ultrathin free‐standing polystyrene films: Thermal expansion coefficient and physical aging

In previous work we observed two simultaneous transitions in high molecular weight (MW) free‐standing polystyrene films that were interpreted as two thickness‐dependent reduced glass transition temperatures (T_gs). The weaker lower transition agreed well with the MW‐dependent T_g(h) previously reported, while the much stronger upper transition matched the MW‐independent T_g(h) previously observed in low‐MW free‐standing films. Here, we investigate the nature of these two transitions by inspecting the temperature dependence of the films' thermal coefficient of expansion (TCE) and present physical aging measurements using ellipsometry both below and in‐between the two transitions. TCE values indicate approximately 80 to 90% of the film solidifies at the upper transition, while only 10 to 20% remains mobile to lower temperatures, freezing out at the lower transition. Physical aging is observed at a temperature below the upper transition, but above the lower transition, indicative of the upper transition being an actual glass transition associated with the α‐relaxation. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 64–75     

Computational synthesis,structure, and glass transition of (1,4) Cis‐polyisoprene‐based nanocomposite by multiscale modeling

The main goal of the present study was to produce insights from the atomistic modeling into the structural changes in elastomer‐based polymer nanocomposites caused by the surface modifications of the filler particles, and by the crosslinking of the participating polymer matrix. The fully atomistic molecular‐dynamics computer simulations of crosslinked (1,4) cis‐polyisoprene (PI) films capped by amorphous silica substrates was set‐up, in the presence of realistic coupling and covering agents. The PI film stratified structure has been studied in the proximity of the corresponding glass transition, by varying the degree of crosslinking and the PI film thickness. Some monomer ordering induced by the pristine (bare) silica disappeared almost completely in films with modified surfaces. The average monomer density increased with degree of crosslinking. As compared with PI bulk, the glass‐transition temperature was slightly larger for highly crosslinked PI films with bare silica and surfaces with coupling agents, and increased with increasing confinement. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 473–485     

Synthesis,characterization and polymerization characteristics of new dimethacrylates,derived from 3,3,5‐trimethylcyclohexan‐1‐one–phenol adducts,as monomers for dental composites

The object of this study was to synthesize, characterize and evaluate several new dimethacrylate monomers, in order to discover new compositions for possible formulation of improved dental restoratives. Dimethacrylates derived from the 3,3,5‐trimethylcyclohexan‐1‐one–phenol reaction products were prepared and characterized by Fourier transform infrared and nuclear magnetic resonance. Thermal‐ and photopolymerization characteristics of these experimental monomers, in blends with triethyleneglycol dimethacrylate (TEGDMA), were evaluated by differential scanning calorimetry and differential photocalorimetry. An additional dimethacrylate derived from the 3,3,5‐trimethylcyclohexanone–phenol adduct, supplied by Bayer AG, was also evaluated during the study. A control for comparison consisted of a 2,2‐bis[4‐(2‐hydroxy‐3‐methacryloyloxy‐propyl) phenyl]propane (BisGMA) blend with TEGDMA. It was found that the polymerization behavior and properties of the visible light‐cured neat resins were dependent on their chemical structures. The experimental resins exhibited comparable curing characteristics, lower water sorption, higher wet glass transition temperature, and other improved properties, compared with the polymerized BisGMA/TEGDMA control. The more rigid and hydrophobic nature of the experimental resins, accomplished by incorporation of the bulky trimethyl‐substituted cyclohexyl moiety in the novel dimethacrylates, was considered to be the major factor contributing to the improved properties. These new dimethacrylates, for formulating thermosets with lower water sorption and higher glass transition temperature, may offer a path to improving composites for a variety of applications, including such things as dental restoratives and bone cements. Copyright © 1999 John Wiley & Sons, Ltd.     

Free volume,glass transition,and degree of branching in metallocene‐based propylene/α‐olefin copolymers: Positron lifetime,density, and differential scanning calorimetric studies

Positron annihilation lifetime spectroscopy (PALS), density, and differential scanning calorimetric (DSC) measurements were used to study systematically the variation of the glass‐transition temperature (T_g) and the size v and number density N_h of local free volumes in n‐alkyl‐branched polypropylenes. The samples were metallocene‐catalyzed propylene copolymers with different α‐olefins (from C₄ to C₁₆) and a different α‐olefin content (between 0 and 20 mol %). From the total specific volume and crystallinity the specific volume of the amorphous phase V_a was estimated and used to calculate the fractional free (hole) volume h and value of N_h. The variations of T_g, v, V_a, h, and N_h were related to the degree (number and length) of branching. T_g decreases and v increases linearly with the number and length of n‐alkyl branches. This behavior was attributed to an increased segmental mobility caused by branching. Both values, T_g and v, follow linear master curves as a function of the degree of branching (DB) if this is defined as the number of all side‐chain carbons with respect to a total of 1000 (main‐chain and side‐chain) carbons. Only propylene/1‐butene copolymers deviated from these relations. A linear relation between v and T_g was also found. The number density of holes was estimated to be N_h = 0.49(±0.07) nm^?3 and N_h′ = 0.58(±0.11) × 10²¹ g^?1, respectively. It shows a slight variation with the DB, which is also seen in the behavior of the specific volume V_a. This variation was explained by the appearance of sterical hindrances resulting from short‐chain branches that may prevent an efficient packing of the chains. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 434–453, 2002; DOI 10.1002/polb.10108