Interactions between polymer brush-coated spherical nanoparticles: the good solvent case

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of the grafted chains, etc.). When the nanoparticles approach very closely, some chains need to be squeezed out into the tangent plane in between the particles, causing a very steep rise of the repulsive interaction energy between the particles. We consider as a complementary method the density functional theory approach. We find that the quantitative accuracy of the density functional theory is limited to large nanoparticle separation and short chain length. A brief comparison to Flory theory and related work on other models also is presented.     

Effect of solvent on depolarized light scattering in dilute polymer solutions

An optical model of a system in which both polymer segments and solvent molecules are described as point dipoles has been used to calculate the intensity of light depolarized in scattering. The final expression consists of six terms, the physical meaning of which is briefly discussed. An approximation procedure has been worked out for the calculation of two interaction terms due to deviations of the local field in solution from the Lorentz–Lorenz field; the terms have been calculated for simple models of flexible and rigid molecules. Their dependence on molecular weight appears to be approximately the same as the intrinsic anisotropy of the polymer molecule; their contribution is nonzero even for a solvent isorefractive with the polymer.     

Impact of solvent quality on nanoparticle dispersion in semidilute and concentrated polymer solutions

We investigated how solvent quality affects the stability of polymer-grafted nanoparticles in semidilute and concentrated polymer solutions, which extends our previous studies on these types of dispersions in good solvents [Langmuir 2008, 24, 5260-5269]. As discussed in the current article, dynamic light scattering (DLS) was used to quantify the diffusion of polydimethylsiloxane-grafted silica nanoparticles, or PDMS-g-silica, in bromocyclohexane as well as in PDMS/bromocyclohexane solutions. We established that bromocyclohexane is a theta solvent for PDMS by varying the temperature of the solutions with PDMS-g-silica nanoparticles and detecting their aggregation at a theta temperature of T(Θ) = 19.6 °C. Using this temperature as a benchmark for the transition between good and bad solvent conditions, further stability tests were carried out in semidilute and concentrated polymer solutions of PDMS in bromocyclohexane at T = 10-60 °C. Irrespective of temperature, i.e., solvent quality, we found that the nanoparticles dispersed uniformly when molecular weight of the graft polymer was greater than that of the free polymer. However, when the free polymer molecular weight was greater than that of the graft polymer, the nanoparticles aggregated. Visual studies were also used to confirm the correspondence between nanoparticle stability and graft and free polymer molecular weights in a wide range of marginally poor solvents with PDMS. Further, the correspondence between nanoparticle stability and instability with graft and free polymer molecular weight and solvent quality was also supported with self-consistent mean-field calculations. Thus, by relating experiment and theory, our results indicate that nanoparticle stability in semidilute and concentrated polymer solutions is governed by interactions between the graft and free polymers under conditions of variable solvency.     

Curvature effects upon interactions of polymer-grafted nanoparticles in chemically identical polymer matrices

We study the interactions between polymer-grafted nanoparticles immersed in a chemically identical polymer melt using a numerical implementation of polymer mean-field theory. We focus on the interpenetration width between the grafted and free chains and its relationship to the polymer-mediated interparticle interactions. To this end, we quantify the interpenetration width as a function of particle curvature, grafting density, and the relative molecular weights of the grafted and free chains. We show the onset of wetting and dewetting as a function of these quantities and explain our results through simple scaling arguments to include the effects of curvature. Subsequently, we show that the interparticle potentials correlate quantitatively with the trends displayed by the interpenetration widths.     

Effect of matrix bidispersity on the morphology of polymer-grafted nanoparticle-filled polymer nanocomposites

We present a simulation study showing the effect of bidispersity in matrix homopolymer length on the wetting/dewetting of homopolymer-grafted nanoparticles and the morphology of polymer nanocomposites where the graft and matrix polymer chemistries are identical. In a bidisperse matrix with equal number of short and long chains and average matrix length greater than the monodisperse graft length, the densely grafted polymer layer is preferentially wet by the short chains and relatively dewet by the long chains. This is driven by a larger gain in entropy of mixing between graft and matrix for short matrix chains than long matrix chains. Despite the preferential wetting of the short and dewetting of long chains, matrix length bidispersity does not significantly change the overall wetting of the grafted layer. Unlike graft length bidispersity that significantly improves particle dispersion, matrix length bidispersity slightly increases particle aggregation in the polymer matrix. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1661–1668     

Effect of solvent quality on the conformations of a model comb polymer

The effect of solvent quality on the equilibrium structure of a densely branched comb polymer is investigated based on the structure factor analyses by off-lattice Monte Carlo simulations. First, theta temperature (theta(infinity)) must be determined to identify the solvent condition. We locate the characteristic temperature theta(A)(N) at which the second virial coefficient vanishes and the transition temperature theta(R)(N) at which radius of gyration R(g) of the chain varies most rapidly with temperature, i.e., d(2)R(g)/dT(2)|(theta(R)) = 0. N represents the total number of monomers of a comb. As N --> infinity, theta(A) and theta(R) coincide to a point that is identified as the true theta temperature (theta(infinity)). The structure factors of the main chain, the side chain, and the whole polymer are calculated, respectively. It is found that at T = theta(infinity), the structural factors S(qR(g)) for the overall comb polymers match quite well with those of their Gaussian counterparts. When T< theta(infinity), the overall comb polymer assumes collapsed conformations, similar to a homogeneous sphere. However, the structure factor of the side chain indicates that it always remains in an expanded state regardless of the solvent condition. It is attributed to the strong interactions between side chains. The same effect leads to enhanced rigidity of the main chain in comparison to the linear chain, as clearly observed from the rescaled Kratky plot.     

Chain conformations and phase separation in polymer solutions with varying solvent quality

Molecular dynamics simulations are used to investigate the conformations of a single polymer chain, represented by the Kremer-Grest bead-spring model, in a solution with a Lennard-Jones liquid as the solvent when the interaction strength between the polymer and solvent is varied. Results show that when the polymer-solvent interaction is unfavorable, the chain collapses as one would expect in a poor solvent. For more attractive polymer-solvent interactions, the solvent quality improves and the chain is increasingly solvated and exhibits ideal and then swollen conformations. However, as the polymer-solvent interaction strength is increased further to be more than about twice the strength of the polymer-polymer and solvent-solvent interactions, the chain exhibits an unexpected collapsing behavior. Correspondingly, for strong polymer-solvent attractions, phase separation is observed in the solutions of multiple chains. These results indicate that the solvent becomes effectively poor again at very attractive polymer-solvent interactions. Nonetheless, the mechanism of chain collapsing and phase separation in this limit differs from the case with a poor solvent rendered by unfavorable polymer-solvent interactions. In the latter, the solvent is excluded from the domain of the collapsed chains while in the former, the solvent is still present in the pervaded volume of a collapsed chain or in the polymer-rich domain that phase separates from the pure solvent. In the limit of strong polymer-solvent attractions, the solvent behaves as a glue to stick monomers together, causing a single chain to collapse and multiple chains to aggregate and phase separate.     

Silane grafting of TiO2 nanoparticles: dispersibility and photoactivity in aqueous solutions

Titania nano‐sized particles were treated by various amounts of tetraethyl orthosilicate precursor. The extent of grafting was characterized using Fourier transform infrared (FTIR) and ultraviolet‐visible (UV‐Vis) spectroscopy techniques, thermal gravimetric analysis, X‐ray fluorescence and zeta potential measurements. Sedimentation behaviour of titanium dioxide (TiO₂) nanoparticles in aqueous solutions was evaluated visually and using a separation analyser. Photocatalytic activity of nanoparticles was studied by photo‐activated degradation reaction of Rhodamine B dyestuff in aqueous solutions. The results showed that grafted particles had acquired enhanced dispersion stability and lower photocatalytic activity in aqueous solutions. Untreated TiO₂ dispersions settled rapidly and sedimentation completed within 24 h through the coagulation mechanism, whereas that of the silica‐treated nanoparticles, depending on the silica content, showed different degrees of stability by flocculation mechanism. Photodebleaching of Rhodamine B in the presence of treated nanoparticles is evident by weaker intensity of UV absorption peak of 554 nm due to lowering concentration of Rhodamine B accompanied with the blue shift in UV absorption peaks. However, untreated TiO₂ nanoparticles showed only weaker intensity of UV absorption peak. Copyright © 2011 John Wiley & Sons, Ltd.     

Phase separation of polymer solutions on a solvent surface

Study of the dynamics of liquid droplets of dilute and semidilute polymer solutions on the surfaces of liquid subphases representing solvents for corresponding polymers has shown that a spot of a rather stable layer is formed on an air–liquid interface. The spot spreads over a liquid subphase surface to yield a monomolecular polymer layer. At the same time, the solvent passes into the solution, so that the polymer or its concentrated solution remains on the subphase surface. The polymer does not dissolve in the bulk subphase for several hours. The stability of the polymer spot has been explained under the assumption that the interfacial surface possesses elastic properties and hinders the penetration of macromolecules into the bulk subphase. Desolvation of macromolecules followed by phase separation occurs on the surface. The initial rate of the phase separation of the solution is rather high, while the time dependence of the diameter of the spreading spot is described by a scaling law with an exponent almost equal to 2/3.     

Continuity of solvent quality in polymer solutions. Poor-solvent to Θ-solvent continuity in some polystyrene solutions

Critical temperatures for polystyrene/methyl acetate (PS/MA) and polystyrene/ethyl formate (PS/EF) solutions were measured at positive (PS/MA, PS/EF) and negative (PS/MA) pressure. The results confirm that solvent quality is sensitive to pressure; some solvents, designated Θ, at P_nominal ∼ 0, undergo a Θ-to-poor transition at negative pressure, and others, nominally designated “poor,” show a poor-to-Θ transition at positive pressure. Thus, any dichotomous division into sets of “poor” and “Θ” solvents is inaccurate, unless it accounts for the effects of pressure and other variables on solvent quality. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 1251–1259, 1997     

Noncontinuum effects on the mobility of nanoparticles in unentangled polymer solutions

The results for the diffusivity of nanoparticles in unentangled semidilute polymer solutions obtained using coarse‐grained simulations are presented. The results indicate that for particle sizes smaller than the polymer radius of gyration, the nanoparticle diffusivities deviate from Stokes–Einstein predictions and depend explicitly on the polymer radius of gyration and the polymer solution correlation lengths. Scaling ideas proposed are invoked for rationalizing such noncontinuum effects and demonstrate that the simulation results could be collapsed onto a single universal function of the depletion thickness, the polymer radius of gyration, and the particle radius. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2145–2150.     

Spontaneous formation of gold nanoparticles in poly(ethylene oxide)-poly(propylene oxide) solutions: solvent quality and polymer structure effects

We report here on the effects that the solution properties of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) block copolymers have on the reduction of hydrogen tetrachloroaurate(III) hydrate (HAuCl4.3H2O) and the size of gold nanoparticles produced. The amphiphilic block copolymer solution properties were modulated by varying the temperature and solvent quality (water, formamide, and their mixtures). We identified two main factors, (i) block copolymer conformation or structure (e.g., loops vs entanglements, nonassociated polymers vs micelles) and (ii) interactions between AuCl4- ions and block copolymers (attractive ion-dipole interactions vs repulsive interactions due to hydrophobicity), to be important for controlling the competition between the reactivities of AuCl4- reduction in the bulk solution to form gold seeds and on the surface of gold seeds (particles) and the particle size determination. The particle size increase observed with increased temperature in aqueous solutions is attributed to enhanced hydrophobicity of the block copolymer, which favors AuCl4- reduction on the surface of seeds. The lower reactivity and higher particle sizes observed in formamide solutions are attributed to the shielding of ion-dipole interaction between AuCl4- ions and block copolymers by formamide, which overcomes the beneficial effects of formamide on the block copolymer conformation (lower micelle concentration).     

Effect of metal nanoparticles on the optical properties of the solutions of porphyrinates and MEH-PPV polymer

The interactions of metal nanoparticles, which were synthesized in inverse micelles, with a number of porphyrinate molecules and a poly[2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene] (MEH-PPV) polymer in solutions were examined by spectrophotometry in order to study the effects of various additives on the efficiency of sun energy absorption and conversion by photosensitive polymer layers. The optical absorption and luminescence spectra of the solutions of Ag, Pd, and Pt nanoparticles and the solutions of Pd(II) and Pt(II) meso-tetra(benzo-15-crown-5)porphyrinates and the MEH-PPV polymer were measured previously.     

Influence of solvent quality on polymer solutions: a Monte Carlo study of bulk and interfacial properties

The effect of solvent quality on dilute and semidilute regimes of polymers in solution is studied by means of Monte Carlo simulations. The equation of state, adsorption near a hard wall, wall-polymer surface tension, and effective depletion potential are all calculated as a function of concentration and solvent quality. We find important differences between polymers in good and theta solvents. In the dilute regime, the physical properties for polymers in a theta solvent closely resemble those of ideal polymers. In the semidilute regime, however, significant differences are found.     

Vitrification of polymer solutions as a function of solvent quality, analyzed via vapor pressures

Vapor pressures (headspace sampling in combination with gas chromatography) and glass transition temperatures [differential scanning calorimetry (DSC)] have been measured for solutions of polystyrene (PS) in either toluene (TL) (10-70 degrees C) or cyclohexane (CH) (32-60 degrees C) from moderately concentrated solutions up to the pure polymer. As long as the mixtures are liquid, the vapor pressure of TL (good solvent) is considerably lower than that of CH (theta solvent) under other identical conditions. These differences vanish upon the vitrification of the solutions. For TL the isothermal liquid-solid transition induced by an increase of polymer concentration takes place within a finite composition interval at constant vapor pressure; with CH this phenomenon is either absent or too insignificant to be detected. For PS solutions in TL the DSC traces look as usual, whereas these curves may become bimodal for solutions in CH. The implications of the vitrification of the polymer solutions for the determination of Flory-Huggins interaction parameters from vapor pressure data are discussed. A comparison of the results for TL/PS with recently published data on the same system demonstrates that the experimental method employed for the determination of vapor pressures plays an important role at high polymer concentrations and low temperatures.     

A model for predicting solvent self-diffusion coefficients in nonglassy polymer/solvent solutions

Cohen-Turnbull diffusion theory is used to develop a model for predicting solvent self-diffusion coefficients D₁ in nonglassy polymer/solvent solutions. Polymer molecules are envisioned as hindering solvent mobility by reducing the average free volume per unit mass in the system and through the lower mobility of polymer segments relative to solvent molecules. The concentration dependence of D₁ predicted by the model is in reasonable agreement with data for the solvents heptane, hexadecane, benzene, cyclohexane, and decalin in polyisobutylene (PIB), and for toluene in polystyrene, poly(methyl mothacrylate), and PIB. Although none of the data is for high concentrations of polymer (volume fractions ?≥0.9) it is anticipated the model will be less representative in this regime where the assumptions in its development are unsure. The model also demonstrates the correct temperature and concentration dependence of the apparent activation energy for diffusion. The only experimental data needed to use the model are the viscosity and critical volume of the pure solvent, and the specific volume of both the solvent and mixture. No binary transport data are required.     

Formation of the bimodal ensemble of silver nanoparticles in polymer solutions

Silver nanoparticles synthesized in polymer solutions are studied by spectroscopy (in near ultraviolet, visible, and infrared spectral regions) and high-resolution transmission electron microscopy. It is established that the ensemble with bimodal particle size distribution is formed from initially polydisperse nanoparticle ensemble in methylhydroxy ethyl cellulose solution. In contrast to the classical scheme of the ripening of colloidal dispersions, the number of small particles increases with time in the studied system; moreover, particles with a size of about 2 nm turned out to be stable. The large particles grow with time and their concentration drops.Translated from Kolloidnyi Zhurnal, Vol. 67, No. 1, 2005, pp. 87–93. Original Russian Text Copyright © 2005 by Serebryakova, Uryupina, Roldughin.     

Thermal diffusion of dilute polymer solutions: the role of solvent viscosity

We have performed measurements of the thermal diffusion coefficient D(T) in the dilute limit on polystyrene in cyclo-octane, cyclohexane, benzene, toluene, tetrahydrofuran, ethyl acetate, and methyl ethyl ketone and of poly(dimethyl-siloxane) in toluene. These data have been combined with literature data to test various theoretical predictions. The viscosity is identified as the dominating and only relevant solvent parameter. On the polymer side, the size or mass of an effective correlated segment determines the strength of the Soret effect. Large and heavy effective segments, as found in stiffer chains, lead to higher D(T).     

Effect of solvent surface tension on the radius of hematite nanoparticles

In this work, the hematite (Fe₂O₃) nanoparticles were synthesized by homogeneous precipitation in alcohol (tert-butanol)/water mixed solvents with varied surface tension. The surface tension of the solvent was decreased from 55.8 to 15.9 mN m^?1 by the increasing of the alcohol content from 20 to 80 vol %. The size of the particles was determined by BET, XRD and TEM techniques. Based on XRD results, the crystalline phase of Fe₂O₃ in all samples was attributed to the cubic hematite structure. The results show that the average particle size of the prepared hematite samples is decreased from 38 to 14 nm upon decreasing surface tension from 55.8 to 15.9 mN m^?1.     

Phase diagram for microphase separation transition in poor solvent polymer solutions

In the present paper, we consider the possibility of microphase separation transition in poor solvent polymer solutions. It is shown that this phenomenon can take place if the following two conditions are fulfilled: i) there is a large entropic contribution to the entropy of polymer/solvent mixing, i.e., solvent acts like a plastisizer; ii) this entropic contribution is nonlocal. Both conditions are met below the glass transition temperature for the pure polymer near the so-called Berghmans point when the glass transition curve intersects the liquid-liquid phase separation curve for polymer solutions. The phase diagram for the microphase separation transition is calculated within the framework of weak segregation approximation first proposed by Leibler for block-copolymer systems. The regions of stability of different microdomain structures (lamellar, triangular, body-centered-cubic) are obtained. It is shown that under certain conditions the phase diagram can have two critical points related to the macro- and microphase separation respectively.This paper is dedicated to Prof. E. W. Fischer on the occasion of his 65th Birthday.This work was done in the course of the Humboldt Research Award stay of A.R. Khokhlov at the Max-Planck-Institute for Polymer Research in Mainz. During this stay A.R.K. greatly benefited from numerous discussions with Professor E.W. Fischer who introduced him to the fascinating field of glass transition in polymer systems and formulated several new directions for future research.