Monte Carlo study of the coil-to-globule transition of a model polymeric system

Monte Carlo computer simulations of single, flexible, self-avoiding chains on a cubic lattice have been performed upon conditions of increasing segment–segment cohesive energy (deteriorating solvent quality). The simulations spanned a wide range of chain lengths (20–10,000, i.e., up to molecular weights of a few millions) and cohesive energies (0.0–0.45k_BT, i.e., from athermal to very poor solvents). The chain length dependence of the chain size in poor solvents was characterized by a wide plateau of almost null growth for intermediate chain lengths. This plateau was linked to the development of the incipient constant density core, while genuine power law dependence (1/3) was not reached even for the longest chains and poorest solvents simulated here. The mere appearance of a core required substantial chain lengths (higher than 1000; molecular weights of a few hundred thousands), while short chains underwent a gradual densification devoid of any qualitative changes in the density distribution. Sufficiently long chains became more but not quite spherical and underwent a reasonably sharp second order phase transition. The findings were generally in agreement with predictions of mean-field theory and with the use of the standard scaling variables, despite slight inconsistencies. Nevertheless, the results stress the fact that short chains never form a constant density core and that core-dominance on the globule's properties (“volume approximation”) is only valid for extraordinarily long chains [molecular weight of O(10⁹)], an effect linked to the relatively diffuse nature of the surface layer and originating from chain connectivity in conjunction with spherical geometry. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3651–3666, 2006     

New copolymers of a tautomerizable β‐ketonitrile monomer: Synthesis,characterization and solution tautomerism

The monomer 2‐methyl‐3‐oxo‐5‐phenyl‐4‐pentenonitrile (MOP) was prepared by reaction of ethyl cinnamate and propionitrile in alkaline mixture. This monomer exhibits three possible tautomeric forms. The tautomeric equilibria of MOP and its copolymers with styrene in different solvents were analyzed by ¹H NMR spectroscopy. The bulk and solution radical copolymerization initiated with azobisisobutyronitrile was carried out at 60 °C. The products were characterized by ¹H NMR, ¹³C NMR, HSQC NMR, HMBC NMR, and FTIR spectroscopies. The weight‐average molecular weight and polydispersity index were analyzed with size exclusion chromatography. The monomer reactivity ratios were obtained with the Fineman‐Ross method, obtaining a value of r₁r₂ = 0.286. MOP copolymer composition as well as the nature of the solvent significantly affected the tautomeric equilibrium. Regression analysis of the copolymer composition with solvatochromic parameters showed a good linear correlation, as quantitatively expressed by means of the linear solvation energy relationship using the empirical set of Kamlet‐Taft solvent parameters. This behavior could be attributed to polymer–polymer or polymer‐solvent interactions prevalent in solvents of different polarity, which are responsible for changes in macromolecular chain conformations, as confirmed by FTIR and viscometric studies. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Grafted polymers under strong shear: Scaling and non-equilibrium Monte Carlo studies

End-grafted polymer chains exposed to strong shear solvent flow in the x-direction are investigated by a non-equilibrium Monte Carlo method using the bond-fluctuating model. The solvent flow is modelled by an enhanced jump rate of monomers in the flow direction. Under strong enough shear flow, the shear force is non-linear with the blob size ζ depending on the shear force and not on the monomer volume fraction ϕ. For the case of a grafted single chain, our data on the end-to-end distance of the polymer for a wide range of shear rate γ agree well with the proposed scaling form and compare reasonably well with the Langevin force law in the extreme strong shear case. Also the scaling for the blob size is derived with ζ = aN^vK(γN^2+v) for some scaling function K, and verified by our simulation data. For the case of a polymer brush, we derive the crossover force scale F^* separating the weak and strong shear regime with F^*a/(kT) = ϕ^v/(3v−1) where v is the usual self-avoiding walk exponent. For the case of a polymer brush under strong shear, the velocity profile, v(z), inside and above the brush is calculated analytically by treating the flow as in a porous medium and solving the Brinkman equation. The solution of the velocity profile is then combined with non-equilibrium Monte Carlo simulation data which allow a self-consistent determination of the chain end-to-end length and the incline angle of the chain. Also we derive the scaling form for the positions x(n) of the nth monomer and verify it by our simulation data. We further obtain an analytical expression for x(n) in terms of the effective viscosity η of the model, given by F = ηav(z). The effective viscosity is also found from our simulation to be ηa²/(kT) ≃ 0.02 ± 0.005.     

The effect of concentration,temperature, and molecular weight on the dynamics of rigid-rod molecules in semi-dilute solutions

The dynamics of rigid-rod-like molecules are studied using rheo-optical techniques. Measurements of flow birefringence as a function of shear rate are utilized to understand the scaling behavior of rotational diffusivity with respect to concentration and temperature. The concentration scaling exponent increases with increasing concentration and the scaling laws are valid in narrow concentration windows. The Doi-Edwards (DE) scaling law D_r ∼ c⁻², holds at very high concentrations (cL³ > 150). The concentration scaling exponent decreases dramatically with increasing temperature at concentrations, cL²d > 1. Scaling of rotational diffusivity, with respect to temperature and solvent viscosity in the semidilute regime, does not follow the predictions of DE theory (and related caging ideas). On the contrary, a model proposed by Fixman was found to explain both the temperature and concentration dependence of the rotational diffusivity. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36 : 181–190, 1998     

Chain length‐dependent termination in pulsed‐laser polymerization. VIII. The temperature dependence of the rate coefficient of bimolecular termination in the bulk polymerization of styrene

The photosensitized polymerization of styrene in bulk was investigated in the temperature range of 25–70°C with respect to the average rate coefficient of bimolecular chain termination k̄_t, especially its chain length dependence at low conversions, by means of pulsed laser polymerization (PLP). Three methods were applied: two of them were based on equations originally derived for chain length independent termination taking the quantity k_t contained therein as an average k̄_t, while the third one consisted in a nonlinear fit of the experimental chain length distribution (CLD) obtained at very low pulse frequencies (LF‐PLP) to a theoretical equation. The exponent b characterizing the extent of chain length dependence was unanimously found to decrease from about 0.17–0.20 at 25°C to 0.08–0.11 at 70°C, slightly depending on which of the three methods was chosen. This trend toward more “ideal” polymerization kinetics with rise of polymerization temperature is tentatively ascribed to a quite general type of polymer solution behavior that consists in a (slow) approach to a lower critical solution temperature (LCST), which is associated with a decrease of the solvent quality of the monomer toward the polymer, an effect that should be accompanied with a decrease of the parameter b. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 697–705, 2000     

Novel solvent effects in the photopolymerization of methyl methacrylate by use of quinoline–bromine charge-transfer complex as photoinitiator

Photopolymerization of MMA was carried out at 40°C in diluted systems by use of quinolinebromine (Q–Br₂) charge-transfer complex as the initiator and chloroform, carbon tetrachloride, chlorobenzene, dioxane, THF, acetone, benzene, toluene, quinoline, and pyridine as solvents. The results showed variable monomer exponents ranging from 1 to 3. For chloroform, carbon tetrachloride, and chlorobenzene, the monomer exponent observed was unity; for other solvents used, the value of the same exponent was much higher (between 2 and 3). Initiation of polymerization is considered to take place through radicals generated in the polymerization systems by the photodecomposition of (Q–Br₂)–monomer complex (C) formed instantaneously in situ on addition of the Q–Br₂ complex in monomer. The kinetic feature of high monomer exponent is considered to be due to higher order of stabilization of the initiating complex (C) in presence of the respective solvents. In the presence of the retarding solvents, very low or zero initiator exponents were also observed, depending on the nature and concentration of the solvents used. The deviation from the square-root dependence of rate on initiator concentration becomes higher at high solvent and initiator concentrations in general. This novel deviation is explained on the basis of initiator termination, probably via degradative chain transfer involving the solvent-modified initiating complexes and the propagating radicals.     

Scaling analysis of the temperature dependence of intrinsic viscosity

The scaling predictions for the temperature dependence of the intrinsic viscosity of flexible polymers are briefly reviewed. When the predictions are fit to a power law over a fixed range of chain length, a relation between the exponent and prefactor of the Mark–Houwink–Sakurada equation emerges. In comparing with the experimental data compilation of Rai and Rosen, we conclude that real polymer systems are nowhere near the true good solvent limit, even when the exponent matches the good solvent prediction. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1989–1991, 1997     

Reaction between ethanol and silicon–hydrogen of poly(p-vinylphenyldimethylsilane)

A kinetic approach to the polymer reaction, with KOH as catalyst, between ethanol and poly(p-vinylphenyldimethylsilane) containing silicon–hydrogen as a functional group on the side chain was carried out. The rate equation was obtained by measuring the initial rate of the model reaction as v = k[KOH] [SiH] [EtOH] in benzene and v = k[KOH] [SiH] in methyl ethyl ketone. It was observed that the rate of reaction was affected by the polarity of the solvents. In the polymer reaction the rate constant decreased markedly with increasing ethanol concentration. A change of viscosity of the polymer in various solvents was observed to have a good correlation with the decrease in reaction rate in corresponding solvents. In mixed solvents, consisting of both good and poor solvents for the polymers, the reaction rate depended upon two factors, the entanglement of the polymer chain and the polarity of the solvents. The equivalent globular model of the polymer chain is suggested for study of the polymer reaction. A schematic local-distribution curve of the reaction species is proposed.     

Gamma radiation-initiated polymerization of styrene at high pressure. II. Chain termination

The pressure dependence of the termination rate constant k_t for the free radical polymerization of monomers such as styrene is a function of polymer chain length, chain stiffness, and monomer viscosity, all of which influence the rate of segmental diffusion of an active radical chain end out of the coiled polymer chain to a position in which it can react with a proximate radical. Although k_t is not sensitive to changes in chain length, the large increase in molecular weight is responsible for a significant reduction in k_t at high pressures. For most of the common vinyl polymers, which exhibit some degree of chain stiffness, k_t is inversely proportional to a fractional power of the monomer viscosity because it depends in part on the resistance of chain segments to movement and in part on the influence of viscosity in controlling diffusion of the chain ends. The fractional exponent appears to increase with pressure and this is interpreted as evidence that the polymer chains become more flexible in a more viscous solvent. Because the fractional exponent is higher for more flexible chains, the value of the activation volume for chain termination is an indication of the degree of flexibility of the polymer chains, provided that the monomer is a good solvent for the polymer and that chain transfer is negligible.     

Monte carlo simulations of polydisperse polymers grafted on spherical surfaces

This article presents effects of polydispersity in polymers grafted on spherical surfaces on grafted polymer chain conformations, grafted layer thickness, and free‐end monomer distribution within the grafted layer. At brush‐like grafting densities, as polydispersity index (PDI) increases, the scaling exponent of radius of gyration of grafted chains approaches that of a single chain grafted on the same nanoparticle, because polydispersity alleviates monomer crowding within the brush. At high PDI, the chains shorter than the number average chain length, N_n, have more compressed conformations, and the chains longer than N_n overall stretch less than in the monodisperse case. As seen in polydisperse flat brushes at high grafting densities, the grafted layer thickness on spherical nanoparticle increases with PDI. Polydispersity eliminates the region near the surface devoid of free‐end monomers seen in monodisperse cases, and it reduces the width of free‐end monomer distribution and shifts the free‐end monomer distribution close to the surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Lattice Monte Carlo investigations on copolymer systems, 1. Diblock copolymers

Symmetric diblock copolymers in dilute solution were examined by means of Monte Carlo simulations on a cubic lattice with respect to chain- and block dimensions, shape, local structure and number of contacts. The solvent was either a common good one, a common θ-solvent or a selective one for the two blocks. In all cases, repulsive interactions are operative between the blocks. In addition, the underlying homopolymers (athermal and θ) were divided into two parts (and treated as a block copolymer) for comparison. Chain-length was varied from 40 to 1280 segments leading to the expected values for the critical exponent 2v ≈ 1.2 for good solvent quality and 2v ≈ 1.0 for θ-solvent. Copolymers in a selective solvent scale with an intermediate exponent, 2v ≈ 1.13. The deviation of the mean squared dimensions of the copolymers from the sum of those of two homopolymers of the same length and for the same solvent quality as the blocks is largest for block copolymers in a common θ-solvent (where it exceeds 20%), while the blocks themselves have mostly the same dimensions as their underlying homopolymers of equal length. The shape of the copolymers, expressed by the parameter δ (asphericity) becomes more rod-like with increasing chain-length if there are (compact) θ-blocks in the molecule which are subject to mutual repulsive interaction. In these cases, θ exceeds the value of the homopolymers in the limit of infinite chain-length. The number of contacts per segment approaches a limiting value with increasing chain-length which is ≈0.20 for athermal chains and athermal blocks. For θ-chains and θ-blocks, a limiting value is not yet reached within the range of chainlengths investigated. The number of contacts per segment between two different blocks quickly tends to zero with increasing chain-length.     

Solution characterization of the novel organometallic polymer poly(ferrocenyldimethylsilane)

A series of four well‐defined poly(ferrocenyldimethylsilane) (PFS) samples spanning a molecular weight range of approximately 10,000–100,000 g mol⁻¹ was synthesized by the living anionic polymerization of dimethyl[1]silaferrocenophane initiated with n‐BuLi. The polymers possessed narrow polydispersities and were used to characterize the solution behavior of PFS in tetrahydrofuran (THF). The weight‐average molecular weights (M_w ) of the polymers were determined by low‐angle laser light scattering (LALLS), conventional gel permeation chromatography (GPC), and GPC equipped with a triple detector (refractive index, light scattering, and viscosity). The molecular weight calculated by conventional GPC, with polystyrene standards, underestimated the true value in comparison with LALLS and GPC with the triple detection system. The Mark–Houwink parameter a for PFS in THF was 0.62 (k = 2.5 × 10⁻⁴), which is indicative of fairly marginal polymer–solvent interactions. The scaling exponent between the radius of gyration and M_w was 0.54, also consistent with marginal polymer–solvent interactions for PFS in THF. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3032–3041, 2000     

Test of the des Cloiseaux Law by Membrane Osmometry on Pullulan

The des Cloiseaux law Π ∼︁ C^9/4 describing the scaling relation between osmotic pressure and concentration in semi‐dilute solutions of neutral polymers in athermal solvent (good solvent) was tested on pullulan, which is a linear polysaccharide, using membrane osmometry. The experimentally determined exponent is 2.2865 ± 0.026, which agrees well with this power law and disagrees with the theoretical value of 2 based on the mean field approximation.     

Monte Carlo simulation of dendrimers in variable solvent quality

We study via lattice Monte Carlo simulation and Flory theory the properties of g=1-6 dendrimers in variable solvent quality. For all the generations studied, we find that the radius of gyration R(g) collapses significantly (factor of 2) going from athermal to extreme poor solvent conditions, indicating that varying solvent quality is an effective means of controlling dendrimer size. We also find that in athermal, theta, and extreme poor solvent conditions, the radius of gyration of dendrimers scales with the total number of monomers roughly as R(g) approximately N(1/3). However, a more careful analysis shows that in athermal and theta solvents, there is, in fact, a small but systematic deviation of R(g) from R(g) approximately N(1/3) scaling and the simulation data is described better by the Flory theory prediction of R(g) approximately N(1/5)[(g+1)m](2/5) in athermal solvents and R(g) approximately N(1/4)[(g+1)m](1/4) in theta solvents. We also find for our simulation data that stronger deviations from constant density scaling are possible, with scaling behavior as shallow as R(g) approximately N(0.26) possible for solvent conditions in between theta and the completely collapsed state. It is evident therefore that dendrimers do not obey (or even approximately obey) R(g) approximately N(1/3) scaling under all solvent conditions. Under all solvent conditions, we find that the intramolecular density is dense corelike (i.e., the density maximum is in the interior of the dendrimer) and terminal groups are delocalized throughout the dendrimer.     

Solution properties,unperturbed dimensions,and chain flexibility of poly(1‐adamantyl acrylate)

Poly(1‐adamantyl acrylate) (PAdA) exhibits much higher glass transition and degradation temperatures than other polyacrylates. However, the quantitative evaluation of the stiffness of this polymer chain has not been reported previously. In this study, the dilute solution properties and conformational characteristics of PAdA were evaluated using viscometry and scattering techniques. The unperturbed dimensions of this polymer were evaluated using the Burchard–Stockmayer–Fixman extrapolation and the touched‐bead wormlike chain model. The PAdA chain has a comparable persistence length, diameter per bead and characteristic ratio to poly(methyl methacrylate) and polystyrene. All these results indicate that PAdA is less flexible than common polyacrylates. In addition, the second virial coefficients (A₂) of PAdA in different solvents obtained by static light scattering were compared. Among the solvents investigated, tetrahydrofuran is a moderate solvent. Radius of gyration of a polymer sample in the various solvents ranged from 16.8 to 30.3 nm. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1526–1531     

Intrinsic viscosity–molecular weight relationship for chitosan

The intrinsic viscosity–molecular weight relationship for chitosan was determined in 0.25 M acetic acid/0.25M sodium acetate. Chitosan samples with a degree of acetylation (DA) between 20 and 26% were prepared from shrimp‐shell chitosan by acid hydrolysis (HCl) and oxidative fragmentation (NaNO₂). Absolute molecular weights were measured by light scattering and membrane osmometry. Size exclusion chromatography (SEC) was used to determine average molecular weights (M_n, M_v, and M_w) and polydispersity. The following Mark–Houwink–Sakurada equation (MHS) is proposed for chitosan of M_w in the range of 35–2220 kDa: The value of the MHS exponent a suggests that chitosan behaves as a flexible chain in this solvent. Examination of MHS constants obtained in this work and those available in the literature with other solvents indicates that a and K are inversely related and that they are influenced by DA, and pH and ionic strength of the solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2591–2598, 2000     

Conformational changes of a polyelectrolyte in mixtures of water and acetone

Samples of a polyelectrolyte poly(methacryloylethyl trimethylammonium methylsulfate), PMETMMS, with molar masses M_w = 22−25 × 10⁶ were examined with viscosity, static light scattering, and conductivity measurements in a water–acetone solvent. Because acetone is a nonsolvent for this polymer the measurements were performed to determine the influence of the solvent composition, the polymer concentration, and the presence of added ions on the conformation of the polyelectrolyte in mixed solvents. The possible influence of a hydrodynamic field on the polymer conformation was also studied. The viscosity of the polymer solutions as a function of polymer concentration, as well as of the solvent composition, was studied using a broad range of shear rates. When the mass fraction of acetone in the solvent, γ, is below 0.5, the solutions show a usual polyelectrolyte behavior. When γ ≥ 0.80, the polymer adopts a compact conformation. This is observed as a decrease of the radius of gyration, R_g, second virial coefficient, A₂, the viscosity, and also as a change in the conductivity of the solution. The change in the polymer conformation may be induced also by dilution. When 0.60 ≤ γ < 0.80, a gradual decrease in the polymer concentration leads to a sudden decrease of the reduced viscosity, which indicates a decrease in the particle size. The values of M_w measured by static light scattering were constant in all experiments. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1107–1114, 1998     

Synthesis of methyl‐substituted azobenzene–carbazole conjugated copolymers with photoinduced structural changes

Azobenzene switches its structure instantaneously by reversible trans‐to‐cis and cis‐to‐trans photoisomerization with light irradiations. Dynamic change in polymer structure is expected via introducing an azobenzene unit into the main chain. In this study, a set of methyl‐substituted azobenzene–carbazole conjugated copolymers is synthesized by the Suzuki–Miyaura coupling method. Introduction of methyl substituents to the azobenzene unit of the monomer, and polymerization in a high‐boiling solvent improve the molecular weight of the polymer. Decrease of effective conjugation length due to the twisted structure of the main chain allows progress of photoisomerization. The microstructure of the polymer was determined with grazing incidence X‐ray diffraction (GIXD) measurements using synchrotron radiation. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1756–1764     

Photopolymerization of methyl methacrylate using a morpholine–sulfur dioxide charge-transfer complex as the photoinitiator

Photopolymerization of the vinyl monomer (M) of methyl methacrylate (MMA) was kinetically studied by using near-UV/visible light at 40°C and employing a morpholine (MOR)–sulfur dioxide (SO₂) charge-transfer (C-T) complex as the photoinitiator. The rate of polymerization (R_P) was found to be dependent on the morpholine: sulfur dioxide mole ratio; the 1 : 2 (MOR–SO₂) complex acted as the latent initiator complex C which underwent further complexation with the monomer molecules to give the actual initiating complex I. Using the 1 : 2 (MOR–SO₂) C-T complex as the latent initiator, the observed kinetics may be expressed as R_P [MOR–SO₂]^0.27[M]^1.10. Benzoquinone behaved as a strong inhibitor. Polymers obtained tested positive for the incorporation of a sulphonate-type end group. Polymerization followed a radical mechanism. Kinetic nonideality as revealed by a low initiator exponent and monomer exponent of greater than unity was explained on the basis of a prominent primary radical termination effect. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 1973–1979, 1998