Monte Carlo simulation of the response of ferromagnetic polymer chain to external magnetic field

The response of ferromagnetic Ising polymer chain in dilute solution to external magnetic field is investigated using Monte Carlo technique. It is found that both magnetic and spatial conformational properties are dependent on the external field, chain length, and temperature. They behave differently at temperatures below and above the zero-field critical temperature T_c⁰. Simulation results indicate that the model chain is a possible candidate for recording material and molecular mechanism.     

Study of three different families of water-soluble copolymers: synthesis, characterization and viscoelastic behavior of semidilute solutions of polymers prepared by solution polymerization

Polymer chains consisting of water-soluble polyacrylamides, hydrophobically modified with low amounts of N,N-dialkylacrylamides (N,N-dihexylacrylamide (DHAM) and N,N-dioctylacrylamide (DOAM)) have been prepared via free radical solution polymerization, using two hydrophobic initiators derived from 4,4′-azobis(4-cyanopentanoic acid) (ACVA) containing long linear chains of 12 (C12) and 16 (C16) carbon atoms. This procedure resulted in polyacrylamides containing hydrophobic groups along the chain as well as at the chain ends. This class of polymers, termed ‘combined associative polymers’, has been studied and compared with the multisticker (with hydrophobic groups along the polymer chain) and telechelic (with hydrophobic groups at the chain ends) associative polymers, which were prepared with DHAM or DOAM and with the hydrophobic initiator (ACVA) modified with alkyl chains of two different lengths. The viscoelastic properties of these different families of associative polymers were investigated using steady-flow and oscillatory experiments. The effect of type, localization and concentration of the hydrophobic groups on the viscosity of the associative polymer solution was investigated. All viscosity curves clearly show two different regimes within the semidilute range: a first unentangled regime where the viscosity increases moderately; and a second entangled regime where the viscosity varies according to a power law, proportional to C⁴. The relaxation time, T_R, and the plateau modulus, G₀, showed relatively high values which increased with the number of carbon atoms in the hydrophobic groups. The combined associative polymer (PAM-co-DHAM/ACVA12) showed relaxation times that remained relatively constant along the concentrations studied, but very high values of G₀.     

Chain walking copolymerization of ethylene with cyclopentene - Effect of ring incorporation on polymer chain topology

Chain walking ethylene copolymerizations with cyclopentene (CPE) as the ring-forming comonomer were carried out in this study to investigate the tuning of polyethylene chain topology via the unique strategy of ring incorporation. Four sets of polymers containing five-membered rings on the polymer backbone at various low contents (in the range of 0-7.5 mol%) were synthesized by controlling CPE feed concentration at four different ethylene pressure/temperature combinations (1 atm/15 °C, 1 atm/25 °C, 1 atm/35 °C, and 6 atm/25 °C, respectively) using a Pd-diimine catalyst, [(ArNC(Me)-(Me)CNAr)Pd(CH₃)(NCMe)]⁺SbF₆⁻ (Ar = 2,6-(iPr)₂C₆H₃). The polymers were characterized extensively using ¹³C nuclear magnetic resonance (NMR) spectroscopy, triple-detection gel permeation chromatography (GPC), and rheometry to elucidate the chain microstructures and study the effect of ring incorporation on polymer chain topology. It was found that CPE was incorporated in the copolymers primarily in the form of isolated cis-1,3 ring units, along with a small fraction in the form of isolated cis-1,2 ring units. Significant linearization of polymer chain topology was achieved with ring incorporation in each of the three sets of polymers synthesized at 1 atm on the basis of the incrementally raised intrinsic viscosity curves in the Mark-Houwink plot and the significantly enhanced zero-shear viscosity of the polymer melts with the increase of ring content despite the decreasing polymer molecular weight. For the set of polymers synthesized at 6 atm/25 °C, the effect of ring incorporation on polymer chain topology was negligible or weaker due to their linear chain topology resulting at this polymerization condition. The results obtained in this study support the proposed blocking effect of backbone-incorporated rings on catalyst chain walking, and demonstrate that effective tuning of polyethylene chain topology from hyperbranched to linear can be conveniently achieved via CPE incorporation while without changing ethylene pressure or polymerization temperature.     

A technique to infer structural information for low level long chain branched polyethylenes

A technique is proposed to relate the weight average molecular weight of linear chains, M_wBL, in low level long chain branched polyethylenes to their linear viscoelastic data. The new method is based on a previously reported empirical technique [Macromolecules 33 (2000) 7481] and was developed through the use of basic molecular theories. The new technique was applied to model systems whose linear viscoelastic properties were simulated using the molecular model of Milner et al. [Macromolecules 31 (1998) 9345] and to long chain branched metallocene polyethylenes. It is applicable to branched polyethylenes with low levels of long chain branching. In the case of a branched metallocene polyethylene, the structural parameter, M_wBL, inferred from the rheological data together with the GPC data such as M_w or M_n of the sample describes all aspects of the structure of the polymer. In the case of highly branched polymers, a possible modification of the technique is also proposed.     

Dilute solution properties of hydrophobically associating polyacrylamide: fitted by different equations

In this paper six different equations were used to fit the data of dilute solution of both nonionic (PBAM3) and ionic (PBAMS) hydrophobically associating polyacrylamide with and without the addition of NaCl. The results showed that Fedors equation was the most accurate equation to describe the dilute solution properties of these kinds of polymers. The lower value of the polymer concentration parameter (C_m) in Fedors equation was corresponded to the higher value of the constant k in Schulz-Blaschke equation for PBAM3 system. Two types of polymers had anti-polyelectrolyte effect. In dilute solution the PBAMS polymer chains had a more extended conformation than those of PBAM3 due to the existence of ionic groups.     

The effects of charge densities on the associative properties of a pH-responsive hydrophobically modified sulfobetaine/sulfur dioxide terpolymer

Sulfur dioxide, zwitterionic monomer, 3-(N,N-diallylammonio)propanesulfonate and a hydrophobic monomer N,N-diallyl-N-octadecylammonium chloride were cycloterpolymerized in dimethyl sulfoxide using azobisisobutyronitrile (AIBN) as the initiator to afford water-insoluble polysulfobetaines (PSB) in excellent yields. The PSBs were converted into the corresponding anionic polyelectrolyte (APE) by treatment with 1 equiv. of sodium hydroxide. Treating the pH-responsive PSB polymers with different equivalents of NaOH varied the zwitterionic and anionic charge densities in the polymer chain. The polymer chains with zwitterionic fraction greater than 0.5 were found to be insoluble in water. The solution properties of the APE and PSB/APE systems containing varying amount of the hydrophobic monomers in the range 0-10 mol% were investigated by viscometric techniques. It was found that PSB/APE polymer with a ratio of 33:67 for the zwitterionic and anionic fractions in the polymer chains, respectively, gave the highest viscosity value. The polymer concentration (C*_HA) of around 1 g/dl was required for the manifestation of significant hydrophobic associations. The polymer solutions exhibited sharp increase in viscosity with increasing polymer concentrations in salt (NaCl)-free as well as salt-added solutions. The presence of sodium chloride is shown to enhance intermolecular associations in polymers having hydrophobes in the lower mol% range, whereas, intramolecular associations were manifested in polymers containing higher proportions of the hydrophobes.     

Observation of single chain motion in a polymer melt

Molecular motion of single polymer chains has been investigated in a melt sample of polytetrahydrofuran and compared with results for the same polymer in dilute solution. Using a high resolution neutron scattering technique motion over distances up to 30 Å has been observed with an energy resolution of 0.01 μeV (～10⁷s^?1). The motion of the chains in the melt is described by the Rouse model and a friction factor per segment has been extracted from the data. This compares well with values obtained from viscosity and bulk relaxation measurements on similar polymers.     

Dynamics of polymer molecules using neutron spin—echo

The dynamics of single polymer chains have been investigated in dilute solution and in the melt using the neutron spin—echo technique. In dilute solution the intramolecular motion is described to a first approximation by that for a Rouse chain incorporating hydrodynamic interactions (Zimm). It is characterised by an inverse correlation time which may be normalised by temperature, solvent viscosity and segment size, and which for long chains varies as Q³ at small scattering angles (Q is the change in wavevector on scattering). At very low Q vectors the predicted ‘universal’ regime is observed, but over most of the accessible range chemical structure also becomes important. For short chains, deviations from this Q³ behaviour are associated with overall molecular diffusion. In the melt, chain entanglements come into play and modify the simple Rouse-type motion. The correlation functions are described by a combination of Rouse motion over short distances and times and a long-time slow-motion predicted by the reptation model of melt dynamics.     

Forced translocation of polymer chains through a nanotube: A case of ultrafiltration

Translocation of polymer chains under the application of an external force has been studied through coarse-grained Monte Carlo simulations. The chains are pulled through a nanotube of finite length and diameter and their translocation times measured. The average translocation time, τ follows a scaling relation involving the chain length, N and applied force, F as, τ ∼ N^ν′F^−μ, where ν′ and μ are two different exponents (ν′ = 0.674, and μ = 0.95 ± 0.05). The scaling law is closely similar to the nanopore translocation scaling law reported by Milchev et al. [Ann N Y Acad Sci 2009;1161:95]. Characteristic signatures of the chain escape time have been exhibited by the square of end-to-end distance R², axial radius of gyration R_g−x and other constituent properties. The behavior of the linear polymers under the application of a pulling force has been exploited to gain insights into the ultrafiltration process of unentangled polymers in dilute solution. The generic pulling force-translocation time (F, τ) data obtained through simulation can be matched reasonably well with the hydrodynamic force-critical macroscopic flow time (f_h, Q_c⁻¹) data and also with the hydrodynamic force-reduced critical microscopic flow time (f_h, q_c⁻¹) data obtained in the ultrafiltration experiment on long linear polystyrene chains in cyclohexane, as recently reported by Ge et al. [Macromolecules 2009;42:4400] The simulation technique reported here may be extended to study biomolecular transports occurring in long protein channels, as studied experimentally through current-time or voltage-time traces.     

Effect of block compositions of amphiphilic block copolymers on the physicochemical properties of polymeric micelles

Amphiphilic block copolymers with various chain lengths of poly(n-butyl methacrylate) blocks (PBMA) and poly(N-acryloylmorpholine) blocks (PAM) were prepared by RAFT polymerization. Packing parameter of block polymers in water (β < 0.2) indicated the formation of core-corona structures, which was further confirmed from a difference between core- and corona-forming chain surface areas. Hydrodynamic micellar size was related with the numbers of BMA (N_BMA) and AM (N_AM), and their ratios (N_BMA/N_AM). With increasing N_BMA/N_AM value, the polymer aggregation numbers and inner core sizes increased, while the critical micelle concentrations, the corona thickness, and the second virial coefficient of block copolymer micelles decreased. These properties changed with increasing N_BMA/N_AM value resulted in a linear increase in corona chain unit density (ρ_AM) that limited chain mobility. Thus, the interaction between the micelles and serum protein at low ρ_AM disappeared at a higher value. Consequently, both micellar properties and biocompatible effect can be regulated by tailoring the block compositions of amphiphilic polymers.     

Dynamics of ESIPT fluorescent methylmethacrylate-benzazole dye copolymers

The dynamics of fluorescent methylmethacrylate-benzazole dye copolymers were investigated in different concentration regimes by dynamic light scattering. In the dilute regime the polymer behaves as typical polydisperse linear chains in good solvent with a dynamics dominated by a single fast mode. In the semidilute regime, the cooperative diffusion coefficient, D_coop and the correlation length, ξ could be obtained. Above the semidilute regime the intensity autocorrelation functions show two-step decays, indicating the existence of low range correlations. The dye incorporation, even though small, affects the copolymer dynamics behavior in concentrated solutions if compared to PMMA, which is probably ascribed to a polymer-solvent interaction.     

Influence of initial chain conformation on the formation of mesoglobule phase in a dilute heteropolymer solution

We have observed, for the first time, that when the initial chain conformation changed from coil to globule, the association of linear poly(N-vinylcaprolactam-co-sodium acrylate) chains could gradually change from a reaction limited to diffusion limited process, reflected in a change of the fractal dimension of the resultant aggregates from ∼2.5 to ∼1.6. Such an influence of the initial chain conformation has been overlooked in past studies of the formation of the mesoglobule phase in a dilute heteropolymer solution.     

Entanglement interactions in polymers and the chain contour concentration

The plateau region in viscoelastic response is one of several characteristics of concentrated polymer liquids which have been attributed to chain entanglement interactions. The plateau modulus G⁰_N is insensitive to temperature and independent of chain length for long chains. It varies with polymer species in the undiluted state: it also varies with polymer concentration in a manner which is essentially independent of species. We propose here that the species dependence and the concentration dependence are related, and that to a first approximation both are manifestations of a universal law relating a mechanical interaction density, measured by $\text{G}{}^0{}_{\mathrm{N}}\text{kT}$ to the length of uncrossable chain contour per unit volume. Data on many species and concentrations support this proposition and conform reasonably well to a universal power law: G in which v is the number of chains per unit volume, L is the chain contour length, and/is the Kuhn step length of the species.     

Synthesis and polymerization of maleimide-type new macromonomer with polystyrene having controlled chain length

A new reactive and functionalized polystyrene with a maleimide moiety at the one polymer end was synthesized with N-(4-(1-chloroethyl)pheyl)maleimide (CEPMI)/SnCl₄/tetra-butylammonium chloride (TBAC) initiating system. The polymer obtained with the CEPMI/SnCl₄/TBAC initiating system under the condition of [TBAC]/[SnCl₄] = 1 was to be maleimide-type macromonomer with polystyrene having controlled molecular weight of polystyrene (VI). VI could be polymerized with anionic and radical initiators to give new type graft polymer (poly[N-(4-ethylphenyl)maleimide]-graft-polystyrene) with controlled chain length with respect to side chains.     

Study of solution properties of poly(deamino‐tyr‐tyr carbonate hexyl ester) by light scattering and viscometry in dilute and semidilute regime

The structure and properties of poly(deamino‐tyr‐tyr carbonate hexyl ester), in dilute and semidilute solutions, were studied using static, dynamic light scattering, and viscometry. The overlap concentration, c^* is determined by viscosity. The angular dependence of Zimm plots shows no downturn at low angles. In addition, bimodal distribution curves were computed from the quasielastic measurements. The radius of gyration and the second virial coefficient A₂ are found to be respectively 45.8 nm and 9.4 mol cm³ g^?2. The correlation and persistence lengths are discussed. The poly (deamino‐tyr‐tyr carbonate hexyl ester) or poly(DTH‐carbonate) chain in THF, at T = 20°C, behaves as a wormlike chain with persistence length. The persistence length obtained using light scattering is compared with that obtained using viscosity with good agreement. These values obtained from these measurements reflect a high degree of local chain persistence. The reduced viscosity in dilute regime provides a value of apparent viscosity hydrodynamic radius three times lower than obtained by static light scattering. POLYM. ENG. SCI., 50:1605–1612, 2010. © 2010 Society of Plastics Engineers     

Cyclization dynamics of polymers: 7. Applications of the pyrene excimer technique to the internal dynamics of poly(dimethylsiloxane) chains

Poly(dimethylsiloxane) (PDMS) polymers end-capped on both ends with pyrene chromophores have been synthesized. Rate constants for end-to-end cyclization 〈 k₁ 〉 have been determined for dilute solutions of these polymers in toluene solution using a combination of fluorescence decay and steady-state fluorescence measurements. While precise values of the critical exponent for the chain length (N¯) dependence of 〈 k₁ 〉 are not yet available, these results are consistent with the N¯^{? 3/2} dependence predicted by Wilemski-Fixman theory. PDMS chains cyclize somewhat more than two times faster than polystyrene chains of the same length in solvents of similar solvating power and viscosity. These results provide strong support for similar predictions made several years ago by Perico and Cuniberti, who used intrinsic viscosity data to parametrize the Rouse-Zimm model for analysis of polymer cyclization dynamics.     

Free energy barrier for compact chains escaping from a small sphere

In this paper, the process of compact polymer chains escaping from a small sphere to a large one in the view of thermodynamics is investigated in detail based on the pruned-enriched-Rosenbluth method (PERM), which is quite efficient for the three-dimensional polymers on the simple-cubic lattice. In our simulation, three representative states of a polymer chain during the escaping process are studied, and some statistical properties of the chain size and the chain shape, such as mean-square radius of gyration per bond 〈S²〉/N and the shape factor 〈δ^∗〉 are investigated. Our aim is to illuminate how the size and shape of the compact chains change during the escaping process. The changes of 〈S²〉/N and 〈δ^∗〉 are not monotone and it is due to the fact that the chain should stretch itself in the escaping process. In the meantime, some thermodynamic properties are also calculated here. The hole is designed to be small enough to allow only one monomer at a time and it thus reduces the number of allowed chain conformations and breaks contacts between monomers at the beginning of the process. Additionally, we discuss the free energy barrier per bond H₂ − H₁ = ΔH of a compact chain, and here H₂ is the maximum free energy per bond during the process and H₁ is the minimum one when the compact chain is within the small sphere. Averaging free energy barrier over chain length N is convenient for the comparison with different chain lengths. ΔH as a function of chain length N and radius r₁ of the small sphere is also studied and our result shows that ΔH for longer chains is lower means that it is relatively easier for each bond in longer chains to surmount the free energy barrier to escape. Some discussions about the self-avoiding walk (SAW) and swollen chains are also made for the comparison, and our results also show that the restriction of the small sphere on the SAW and the swollen chains is more effective because of their relatively looser intrinsic structure.     

Determination of the conformation of polymers in the amorphous solid state and in concentrated solution by neutron diffraction

From the coherent neutron scattering on dilute solid solutions of the ordinary polymer within the deuterated polymer, conformation parameters of polymer chains in amorphous solid states can be determined. In this way vitreous poly(methyl methacrylate) (PMMA) has been investigated. The chains form unperturbed coils and the radius of gyration is very near to the corresponding value in dilute solutions of the same polymer in the low molecular θ-solvent butyl chloride. The same principle of measurement has been applied to concentrated solutions of PMMA in D-acetone. The solutions contained 50% polymer, the main part of which (98% and more) was deuterated so that the system was optically dilute for neutron scattering on H-PMMA. A monotonic dependence of the radius of gyration and of thermodynamic parameters on the concentration has been found. A first result is presented for a mixture of two polymers. A dilute solid dispersion of poly(α-methylstyrene) (PMS) within D-PMMA has been investigated at M_w = 250 000. The samples are limpid. The PMS forms micelles of 16 molecules (weight average). The radius of gyration of the micelles, r_z is 170 Å.     

Wall slip of molten polymers

There is considerable experimental evidence that the classical no-slip boundary condition of fluid mechanics is not always a valid assumption for the flow of high molecular weight molten polymers. In fact, molten polymers slip macroscopically at solid surfaces when the wall shear stress exceeds a critical value. Moreover, for linear polymers there exists a second critical wall shear stress value at which a transition from a weak to a strong slip occurs. These two modes of slip (weak and strong) are due to flow-induced chain detachment/desorption at the polymer/wall interface and to chain disentanglement of the polymer chains in the bulk from a monolayer of polymer chains adsorbed at the interface. In this review, the two physical mechanisms of slip are discussed and validated on the basis of published experimental data. The slip velocity of molten polymers is a complex function and has been reported to depend on wall shear and normal stresses, temperature, and molecular characteristics of polymers (molecular weight and its distribution). Proposed slip models, static and dynamic, are also reviewed and their significance on the rheology and flow simulations of molten polymers is discussed.     

On the chain cross-sectional area and motion of macromolecular chains

This paper attempts to relate the chain cross-sectional area to the glass transition temperature of a polymer and to discuss the effect of the chain cross-sectional area in view of the motion of molecular chains. It has been found that the definite relationship between glass transition temperature and cross-sectionalarea can be obtained only when taking account of intermolecular interaction of polymer chains. It is considered that the chain cross-sectional area will characterize the chain flexibility of a polymer since the glass transition temperature is related both to intermolecular interaction and chain flexibility of a polymer. The concept of the structural parameter cross-sectional area per chain, first introduced by Vincent¹ and used by Boyer and Miller,^2–5 is useful in empirically correlating properties and structures of polymers. The glass transition temperature is a basic parameter of bulk polymers and is characteristic of their intermolecular interactions and chain flexibility. This paper attempts to relate chain cross-sectional areas to glass transition temperatures of polymers and to discuss the effect of the chain cross-sectional area in view of the motion of molecular chains.