Linear viscoelastic relaxation modulus of polydisperse poly(dimethylsiloxane) melts containing unentangled chains

This work analyzes the relationship between the shear relaxation modulus of entangled, linear and flexible homopolymer blends and its molecular weight distribution (MWD) when a fraction of the sample contains chains with molecular weight M lower than the effective critical molecular weight between entanglements Mc_eff. This effective critical parameter is defined in terms of the critical molecular weight between entanglements M_c of the bulk polymer that forms the physical network and the effective mass fraction Wc_eff of the unentangled chains. In the terminal zone of the linear viscoelastic response, the double reptation mixing rule for blended entangled chains and a modified law for the relaxation time of chains in a polydisperse matrix are considered, where the effect of chains with M<Mc_eff is included. Although chain reptation with contour length fluctuations and tube constraint release are still the relevant mechanisms of chain relaxation in the terminal zone when the polydispersity is high, it is found that the presence of a fraction of molecules with M<Mc_eff modifies substantially the tube constrain release mode of chain relaxation. In this sense, a modified relaxation law for polymer chains in a polydisperse entangled melt that includes the effect of the MWD of unentangled chains is proposed. This law is validated with rheometric data of linear viscoelasticity for well-characterized polydimethylsiloxane (PDMS) blends and their MWD obtained from size exclusion chromatography. The short time response of PDMS, which involves the glassy modes of relaxation, is modeled by considering Rouse diffusion between entanglement points of chains with M>Mc_eff. This mechanism is independent from the MWD. The unentangled chains with M<Mc_eff occluded in the polymer network also follow Rouse modes of relaxation although they exhibit dependence on the MWD.     

Surface fluctuations of polymer brushes probed by diffuse X-ray scattering

The diffuse scattering from the surfaces of melt and glassy polymer brushes has been studied systematically for the first time using polystyrene (PS) and poly(n-butylacrylate) (PnBA) brushes synthesized by free radical polymerization. The data show unambiguously that the diffuse scattering behavior varies systematically with brush thickness for both types of brushes. We attribute a cross-over in scattering with q_x, the in-plane scattering vector, to the presence of surface thermal fluctuations and their suppression for longer wavelengths, a phenomenon already reported for films of untethered chains. Long wavelength fluctuations are suppressed more strongly on the surface of a PS brush than on the surface of a film of untethered (‘free’) PS chains of comparable thickness, so that even in films of thickness, d, such that d/R_g>5 clear evidence of the suppression of fluctuations can still be seen in the experimentally available range of q_x. Fluctuations are suppressed for q_x less than a lower wavevector cut-off, q_l,c, which changes with film thickness, though much more weakly than for films of free chains. For values of d/R_g<4, where R_g is the unperturbed radius of gyration of a comparable free chain, q_l,c drops as d increases. For d/R_g>4 q_l,c begins to increase with brush thickness, in qualitative agreement with theory, indicative of a transition to a true ‘brush’ state in which stretching of the chains makes longer wavelength fluctuations at the surface unfavorable. Measurements with PnBA brushes having T_g substantially below room temperature confirm the trends mentioned above. Further, they give evidence that the value of q_l,c is temperature insensitive above T_g.     

Modelling tie chains and trapped entanglements in polyethylene

A Monte Carlo random walk model was developed to simulate the chain structure of amorphous layers in polyethylene. The chains emerging from the orthorhombic crystal lamellae were either folding back tightly (adjacent re-entry) or performing a random walk (obeying phantom chain statistics) forming statistical loops or tie chains. A correct amorphous density (ca. 85% of the crystalline density) was obtained by controlling the probability of tight folding. Important properties like fracture toughness depend on the number of chains covalently linking together the crystalline regions. The model structure was analysed with a novel numerical topology algorithm for calculating the concentration of tie chains and trapped entanglements. The numerical efficiency of the algorithm allowed molecular cubic systems with a side length of 100 nm to be readily analysed on a modern personal computer. Simulations showed that the concentration of trapped entanglements was larger than the concentration of tie chains and that the thickness of the amorphous layer (L_a) had a greater impact than the crystal thickness (L_c) on the tie-chain concentration. In several other commonly used models, such as the Huang–Brown model, the influence of trapped entanglements and the effect of the L_a/L_c ratio are neglected. Simulations using as input the morphology data from Patel generated results in agreement with experimental rubber modulus data.     

Architecture of prototype copolymer brushes composed of alternating structure and intramolecular phase separation of side chains in solution

Atom transfer radical polymerization (ATRP) was applied to the synthesis of prototype copolymer brushes composed polystyrene/poly(t‐butyl methacrylate) (PS/PBMA) alternating structure. Dilute solution properties of prototype copolymer brush were investigated by static and dynamic light scattering (SLS and DLS) in tetrahydrofuran (THF). As a result, such prototype copolymer brush composed of short aspect ratio formed a star‐like single molecule in THF. To discuss the intramolecular phase separation of PS/PBMA brushes in solution, we determined the radius of gyration (R_g) and cross‐sectional radius of gyration (R_g,c) of prototype copolymer brush by small‐angle X‐ray scattering (SAXS) using Guinier's plots in THF and styrene. We used styrene as solvent to cancel each other out with the electron density of PS side chains. Both R_g and R_g,c obtained in styrene decreased drastically compared with those obtained in THF. These results indicated strongly that PS and PBMA side chains of prototype brushes formed intramolecular phase separation even in good solvent. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Structure and physical properties of dried Tetra-PEG gel

We investigated crystal structure, and thermal, swelling, and deformation behaviors of dried tetrafunctional (polyethylene glycol) gel, Tetra-PEG gel, with narrow molecular distribution. Tetra-PEG gel consists of two kinds of symmetrical tetrahedron-like PEG macromonomers with a fixed molecular weight. In spite of network structure with rather small molecular weight between cross-links (M_c) (≈5000), the dried Tetra-PEG gels were found to be capable of crystallization. The crystalline melting temperature (T_m) and the degree of crystallinity (X_c) of dried Tetra-PEG gels obtained by differential scanning calorimetry (DSC) were substantially constant against the polymer volume fraction at preparation (?₀). Furthermore, the corrected elastic modulus (G) of dried Tetra-PEG gels did not depend on ?₀. These experimental results indicate that the there exist negligible entanglements in the dried Tetra-PEG network irrespective of ?₀. In other words, Tetra-PEG gels do not have significant topological inhomogeneities.     

Role of chain entanglements on fiber formation during electrospinning of polymer solutions: good solvent, non-specific polymer-polymer interaction limit

Chain entanglements are one of many parameters that can significantly influence fiber formation during polymer electrospinning. While the importance of chain entanglements has been acknowledged, there is no clear understanding of how many entanglements are required to affect/stabilize fiber formation. In this paper, polymer solution rheology arguments have been extrapolated to formulate a semi-empirical analysis to explain the transition from electrospraying to electrospinning in the good solvent, non-specific polymer-polymer interaction limit. Utilizing entanglement and weight average molecular weights (M_e, M_w), the requisite polymer concentration for fiber formation may be determined a priori, eliminating the laborious trial-and-error methodology typically employed to produce electrospun fibers. Incipient, incomplete fiber formation is correctly predicted for a variety of polymer/solvent systems at one entanglement per chain. Complete, stable fiber formation occurs at ≥2.5 entanglements per chain.     

Impact of molecular mass on the elastic modulus of thin polystyrene films

Surface wrinkling was used to determine the elastic modulus at ambient temperature of polystyrene (PS) films of varying thickness and relative molecular mass (M_n). A range of M_n from 1.2 kg/mol to 990 kg/mol was examined to determine if the molecular size impacts the mechanical properties at the nanoscale. Ultrathin films exhibited a decrease in modulus for all molecular masses studied here compared to the bulk value. For M_n > 3.2 kg/mol, the fractional change in modulus was statistically independent of molecular mass and the modulus began to deviate from the bulk as the thickness is decreased below ≈50 nm. An order of magnitude decrease in the elastic modulus was found when the film thickness was ≈15 nm, irrespective of M_n. However, an increase in the length scale for nanoconfinement was observed as the molecular mass was decreased below this threshold. The modulus of thin PS films with a molecular mass of 1.2 kg/mol deviated from bulk behavior when the film thickness was decreased below ≈100 nm. This result illustrates that the modulus of thin PS films does not scale with molecular size. Rather, the quench depth into the glass appears to correlate well with the length scale at which the modulus of the films deviates from the bulk, in agreement with molecular simulations from de Pablo and coworkers [31] and recent experimental work [35].     

Craze microstructure and molecular entanglements in polystyrene-poly(phenylene oxide) blends

Polystyrene and poly(phenylene oxide) are miscible over the entire range of compositions. Thin films of five blends of high molecular weight polystyrene (PS) with high molecular weight poly(phenylene oxide) (PPO), and four blends of low molecular weight PS (whose molecular weight lies below its entanglement molecular weight M_e) with the same PPO have been prepared. Following bonding of these films to copper grids, crazes were grown by uniaxial straining in air. Suitable crazes were then observed by transmission electron microscopy. From microdensitometry of the image plates it is possible to measure the extension ratio λ_craze within crazes in the nine blends. These measured values are compared with predicted values of λ_max, computed from λ_max = I_ed, where I_e is the chain contour length between entanglements and d is the root mean square end-to-end distance for a chain of molecular weight M_e. For the high molecular weight PS blends λ_max depends on the entanglement properties of both PS and PPO chains. For the low molecular weight PS blends, the PS chains cannot form part of the entanglement network and the correct value of λ_max is obtained from appropriate scaling of the pure PPO value. Comparison of λ_craze and λ_max for both types of blends shows excellent agreement, demonstrating the importance of the entanglement network in determining craze parameters and hence the toughness of a given polymer.     

Radiation induced embrittlement of PTFE

The radiochemical degradation of polytetrafluoroethylene (PTFE) samples has been studied in air at dose rate 100 Gy/h for doses up to 5000 Gy, at ambient temperature. The polymer degradation has been monitored by DSC, tensile testing and Essential Work of Fracture (EWF) testing. Some fractured samples have been observed by scanning electron microscopy. The polymer undergoes a fast chain scission, its number average molar mass is divided by about 20 for a dose of 1000 Gy and tends towards a pseudo asymptotic value of ∼20 kg mol⁻¹ (against 6200 kg mol⁻¹ initial value). The modulus and yield characteristics seem to be almost unaffected whereas ultimate properties undergo strong variations. The ultimate elongation ε_R and the EWF plastic work characteristic βw_p first increase and then decrease. The ultimate stress decreases and tends towards a pseudo asymptotic value. The mechanisms of radiation induced ultimate property changes are discussed. The first stage could be due to the destruction of non-extended tie molecules (due to the presence of very long chains) responsible for interfibrillar bridging during fracture. The (more classical) second stage is a progressive embrittlement due to the destruction of the entanglement network. The critical molar mass M′_c for embrittlement is such as M′_c∼50M_e, M_e being the molar mass between entanglements in the melt. This relationship could be a general characteristic of high crystallinity non-polar polymers.     

Rheological properties of concentrated solutions of agarose in ionic liquid

The rheological properties of agarose solutions were examined under the effect of entanglement coupling between agarose chains. Agarose solutions were prepared by using an ionic liquid 1‐butyl‐3‐methylimidazolium chloride as a solvent. The concentration of agarose was varied from 1.1 × 10¹–2.1 × 10² kg m^?3. The master curves of the angular frequency (ω) dependence of the storage modulus (G′) and the loss modulus (G″) showed a rubbery region in the middle ω region and a flow region at low ω region, respectively. The molecular weight between entanglements (M_e) for agarose was calculated from the plateau modulus. Moreover, M_e for agarose melt was determined to be 2.3 × 10³ from the concentration dependence curve of M_e. By using well‐known empirical relations in polymer rheology, information on molecular characteristics of sample agarose was derived. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Fabrication of oriented electrospun cellulose nanocrystals–polystyrene composite fibers on a rotating drum

Nitrobenzene (CNC-1), trifluoromethyl benzene (CNC-2) modified and polystyrene-grafted (CNC-g) cellulose nanocrystals in polystyrene (PS)-N,N dimethylformamide (DMF) solutions were electrospun and collected as stretched and aligned fibers on a rotating drum. Scanning electron microscope pictures showed significant alignment in the case of unmodified and nitrobenzene-modified CNC-1/PS nanocomposite fibers once the linear speed of rotor reached to 15 m s⁻¹. Fiber diameter decrease was more strong with rotor speed increase in the case of trifluoromethyl benzene modified (CNC-2) and polystyrene-grafted (CNC-g) cellulose nanocrystals/PS systems. Dynamic mechanical analysis including storage and elastic modulus of electrospun-oriented fibers were performed on surface-modified and polymer-grafted CNC/PS samples. According to α transition peak, the increase in the glass-transition temperature with filler concentration was the highest in polymer-grafted CNC-g/PS composite fibers. It was due to the interpenetration of grafted polymer brushes and free polymer chains in continuous phase and resulted in restrictions of motions of polymer chains in the PS matrix. The elastic moduli of nitrobenzene (CNC-1) and trifluoromethyl benzene (CNC-2)-modified CNC-filled PS composite fibers agreed well with percolation model, which indicates the CNC–CNC interactions and network formation with an increase in concentration. Magnitude of the elastic modulus of polymer grafted CNC-g at 0.33 vol % in PS was significantly higher than the prediction from percolation theory. It was due the immobilized polymer chains around CNC-g particles. However, grafted polymer chains, at higher CNC concentrations acted like stickers among CNC particles and caused CNC agglomerates with entrapped free polystyrene from the matrix, thus caused a decrease in the elastic modulus. © 2020 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020 , 137, 48942.     

Variation of periodic crazing based on polymer blends of an ultra‐high and a low molecular weight poly(methyl methacrylate)

Periodic crazes are caused in a polymer film by the unique mechanical method using bending. Generation of a craze depends on entanglements of the molecular chains of a polymer. Therefore, control of composite morphology of periodic crazes was attempted by varying the entanglements of molecular chains. An effective entanglement network became sparse by polymer blends of an ultra‐high molecular weight polymethylmethacrylate (PMMA) and a low molecular weight PMMA. Consequently, the composite morphology of periodic crazes caused in the blend film varied. In other words, the periodic craze can be used for the evaluation of the effective entanglements. In addition, it was figured out that PMMA of which the number‐average molecular weight (M_n) is less than twice of the effective entanglement molecular weight (M_e^*) works as a plasticizer in the blend film. And also, it was revealed that the mechanical properties of the blend film decreased dramatically at M_n ≒ 6M_e^*. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 44332.     

Effects of molecular weight and molecular weight distribution on creep properties of polypropylene homopolymer

The molecular weights of the industrial-grade isotactic polypropylene (i-PP) homopolymers samples were determined by the melt-state rheological method and effects of molecular weight and molecular weight distribution on solid and melt state creep properties were investigated in detail. The melt-state creep test results showed that the creep resistance of the samples increased by M_w due to the increased chain entanglements, while variations in the polydispersity index (PDI) values did not cause a considerable change in the creep strain values. Moreover, the solid-state creep test results showed that creep strain values increased by M_w and PDI due to the decreasing amount of crystalline structure in the polymer. The results also showed that the amount of crystalline segment was more effective than chain entanglements that were caused by long polymer chains on the creep resistance of the polymers. Modeling the solid-state viscoelastic structure of the samples by the Burger model revealed that the weight of the viscous strain in the total creep strain increased with M_w and PDI, which meant that the differences in the creep strain values of the samples would be more pronounced at extended periods of time.     

Hexadecyl-functionalized lamellar mesostructured silicates and aluminosilicates designed for polymer-clay nanocomposites. Part II: Dispersion in organic solvents and in polystyrene

Layered mesostructured silicates and aluminosilicates with covalently attached hexadecyl groups (denoted as C₁₆-LMS, C₁₆-LMAS, and a sample with layers whose thickness was increased by additional silicate, C₁₆-SiO₂-LMAS) were investigated as synthetic clays for dispersion and exfoliation in polymer melts. The dispersion of these clays in 13 organic solvents and their performance in polystyrene (PS) nanocomposites were examined. The three synthetic clays dispersed and formed gels in aromatic solvents and in a branched alkyl solvent (2,6,10,14-tetramethylpentadecane, TMPD) based on visual observations and rheology. The elastic moduli (G′) of the toluene/clay dispersions for all three clays were similar when compared at equal inorganic content. The synthetic clays were blended with PS samples of various molecular weights. Melt rheology of the PS/clay nanocomposites showed a dramatic increase in elastic modulus compared with neat PS and formation of a G′ plateau at low frequencies. The plateau occurred at higher G′ values for C₁₆-LMAS than for C₁₆-SiO₂-LMAS or C₁₆-LMS, indicating that C₁₆-LMAS has higher strength and/or higher aspect ratio and can thus withstand the stresses of melt mixing. Increasing the molecular weight of PS increased G′ of the PS/C₁₆-LMAS nanocomposites. By small angle X-ray (SAXS) and transmission electron microscopy C₁₆-LMAS showed better dispersion and a higher aspect ratio in the PS-nanocomposite than C₁₆-SiO₂-LMAS.     

Effect of molecular weight on the dissolution properties of polystyrene latex films

An in situ steady-state fluorescence (SSF) technique was applied in order to study the dissolution process of polystyrene (PS) latex films. The effect of the molecular weight M _w of the PS on the dissolution rate was investigated. The PS chains were copolymerized with (1-pyrene)methyl methacrylate in order to make use of pyrene (P) as a fluorescent probe to monitor the dissolution process. Seven different films were prepared from P-labeled PS latex dispersions with different molecular weights at room temperature. These films were then annealed at 200 °C for 15 min to complete the film formation process before dissolution. The dissolution of PS films in a toluene (70 %)–cyclohexane (30 %) mixture was monitored in real time by watching the change in the fluorescence intensity of P, I _P. We used a model that included both case I and case II diffusion kinetics to interpret the results of the dissolution experiments. The relaxation constants k ₀ and the dissolution coefficients D _d of the polymer chains were measured. Two different dissolution coefficients were obtained, which were attributed to the small and long polymer chains in the film, considering the high polydispersity of the polymer. It was also found that both of the D _d values scaled with M _w according to the law D _d ≈ M ^?n .     

Adhesion and friction behaviours of polydimethylsiloxane - A fresh perspective on JKR measurements

The self-adhesion of a variety of polydimethylsiloxanes (PDMS) has been investigated using a newly developed JKR apparatus that can also determine the associated friction behaviour of the same sample. The results have been interpreted using the complete JKR model by incorporating the indentation data also in the analysis. By varying the molecular mass M_c of PDMS from 6 to 28 kg/mol the elastic modulus E decreases from 1.16 to 0.71 MPa while the work of adhesion remains about constant. In contrast measurements of the friction of the same systems indicate an increase of the friction force. Introduction of dangling chains leads to a strong decrease of E from 1.16 to 0.56 MPa for low M_c and from 0.71 to 0.09 MPa for high M_c and again only to minor changes in W. The latter results can be understood from an inward distribution of the dangling ends.     

Synthesis of binary mixed homopolymer brushes by combining atom transfer radical polymerization and nitroxide-mediated radical polymerization

This communication describes a novel strategy to synthesize binary mixed homopolymer brushes from mixed self-assembled monolayers (SAMs) on silica substrates by combining atom transfer radical polymerization (ATRP) and nitroxide-mediated radical polymerization (NMRP). Mixed SAMs terminated by ATRP and NMRP initiators were prepared by coadsorption of two corresponding organotrichlorosilanes from toluene solutions. Mixed poly(methyl methacrylate) (PMMA)/polystyrene (PS) brushes were synthesized by ATRP of MMA at 80 °C followed by NMRP of styrene at 115 °C. Corresponding ‘free’ initiators were added into the solutions to control the polymerizations. We have found that the brush thickness increases with molecular weight in a nearly linear fashion. For a series of binary brushes consisting of PMMA of molecular weight of 26,200 and PS of various molecular weights, we have observed a transition in water contact angles with increasing PS molecular weight after CH₂Cl₂ treatment. Moreover, binary mixed polymer brushes with comparable molecular weights for two grafted polymers undergo reorganization in response to environmental changes, exhibiting different wettabilities.     

Planar Brush of End-Tethered Molecular Bottle-Brushes. Scaling Mode

We present a scaling theory describing structural properties of brushes formed by molecular bottle-brushes tethered by the ends of the main chains to inert planar surface. We consider bottle-brushes where q ≥ lateral side chains (grafts) emanate from each of the branching points regularly distributed along the main chain (backbone). Such macromolecule can be envisioned as an array of polymer stars whose centres are connected by flexible spacers into a necklace. We demonstrate that such starlike mode of branching leads to novel features both in conformations of individual bottle-brushes in solution and in appearance of additional scaling regime for brushes formed by bottle-brushes tethered to the surface.     

Effect of chain length distribution on thermal characteristics of model polytetrahydrofuran (PTHF) networks

A series of model polytetrahydrofuran (PTHF) networks were synthesized via end-linking reactions of α, ω-allyl PTHF oligomers with a stoichiometric tetrafunctional crosslinker. The telechelic PTHF oligomers were synthesized by living cationic ring-opening polymerization of tetrahydrofuran followed by a termination reaction with allyl alcohol. Networks thus prepared have well-controlled architecture in terms of the inter-crosslink chain length (M_c) and chain length distribution: resulting in unimodal, bimodal and clustered structures. Unimodal network was prepared by using polymer chains of same molecular weight, bimodal networks were synthesized by using two groups of polymer chains with different average molecular weights, and the clusters are prepared by incorporating clusters of networks with small molecular weight chains in a network matrix made of longer chains. Thermal characteristics of these model networks were investigated as a function of crosslink density, as well as inhomogeneities of crosslink distribution using DSC. We demonstrate that glass transition temperature (T_g) and crystallization behavior (melting temperature and crystallinity) of the networks are both strongly influenced by crosslink density (M_c). By comparing the unimodal, bimodal and clustered networks with similar average M_c, the effects of inhomogeneities in the crosslink distribution on the thermal properties were also investigated. Results show that inhomogeneities have trivial influence on T_g, but strongly affects the crystallization behavior. Moreover, the effects of the content ratio and length ratio between long and short chains, and the effects of cluster size and size distribution on the thermal characteristics were also studied.     

Influence of cross-link density on the properties of ROMP thermosets

A norbornene-based cross-linker was synthesized and mixed at different loadings with two separate monomers for self-healing polymer applications: 5-ethylidene-2-norbornene (ENB) and endo-dicyclopentadiene (endo-DCPD). The monomer/cross-linker systems were polymerized by ring-opening metathesis polymerization (ROMP) with Grubbs' catalyst. The thermal-mechanical properties of the polymerized networks were evaluated by dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC) and the curing process was monitored by parallel plate oscillatory rheometry. The viscosities of the pre-polymer blends are shown to be adequately low for self-healing, and exhibit a high ROMP reactivity to form cross-linked networks with enhanced thermal-mechanical properties. The addition of cross-linker increases the glass transition temperature (T_g) and the storage modulus both above and below T_g. The storage modulus increase above T_g is used to estimate the molecular weight (M_c) between entanglements or cross-link sites for both ENB and endo-DCPD-based networks. The cross-linker also greatly accelerates network formation as defined by the gelation time.