Theta Solvent Research Articles

Adsorption of Polystyrene from Theta Condition on Cellulose and Silica Studied by Quartz Crystal Microbalance.

Adsorption of hydrophobic polymers from a nonpolar solvent medium is an underutilized tool for modification of surfaces, especially of soft matter. Adsorption of polystyrene (PS) from a theta solvent (50/50 vol % toluene/heptane) on ultrathin model films of cellulose was studied with a quartz crystal microbalance with dissipation monitoring (QCM-D), using three different PS grades with monodisperse molecular weights (Mws). Comparison of cellulose to silica as an adsorbent was presented. Adsorption on both surfaces was mainly irreversible under the studied conditions. Characteristically to polymer monolayer formation, the mass of the adsorbing polymer increased with its Mw. The initial step of the layer formation was similar on both surfaces, but silica showed a stronger tendency for the formation of a loosely bound overlayer upon molecular rearrangements as the adsorption process proceeded. Despite the slightly less extended layers formed on cellulose at increasing Mw values, the overall thickness of the adsorbing wet layers on both surfaces was of the similar order of magnitude as the radius of gyration of the adsorbate molecule. Decent degree of hydrophobization of cellulose could be reached with all studied PS grades when the time allowed for adsorption was sufficient. QCM-D, a method conventionally utilized for studying aqueous systems, turned out to be a suitable tool for studying the adsorption process of hydrophobic polymers on soft polymeric matter such as cellulose taking place in a nonpolar solvent environment.

Diffusion and thermodiffusion of the ternary system polystyrene + toluene + cyclohexane.

We have studied diffusion and thermodiffusion in the ternary system polystyrene + toluene + cyclohexane over the entire composition range of the binary solvent toluene + cyclohexane and for polymer concentrations up to 0.1 mass fractions by multi-color optical beam deflection. The polystyrene molar masses were 4.88 and 17.90 kg/mol. The inversion problem of the contrast factor matrix could be avoided by reasonable a priori assumptions about the diffusion eigenvectors. The fast mode of the bimodal dynamics is attributed to the interdiffusion of the two solvents at constant polymer concentration, whereas the slow mode is due to the diffusion of the polymer with respect to the binary solvent. The amplitude of the fast mode vanishes in the pure toluene and the pure cyclohexane limits of the mixed solvent. The amplitude of the slow mode increases with polymer concentration. The composition and temperature dependence of the slow diffusion eigenvalue, the hydrodynamic correlation length, and the Soret coefficient of the polymer reflect the transition from a good to a theta solvent with increasing cyclohexane content and with decreasing temperature. Due to cross diffusion, cyclohexane reverses its migration direction between the fast and the slow mode, leading to a positive thermodiffusion but a negative Soret coefficient. The polymer thermodiffusion coefficients during the slow mode vary by approximately a factor of two, depending on the solvent composition. Rescaling with the solvent viscosity collapses all data onto a single master curve with an extrapolated value of ηDT ≈ 6 × 10-15Pam2K-1 in the dilute limit. This value is well known from various other binary polymer/solvent mixtures.

Intrinsic viscosity and dielectric relaxation of ring polymers in dilute solutions.

The absence of chain ends makes ring polymers distinctly different from their linear analogues. The intrinsic viscosity, complex viscosity and the dielectric relaxation of ring polymers are investigated within the tenets of the optimized Rouse-Zimm theory. The distance dependent excluded volume interactions (EVIs) are obtained from Flory's mean field theory. The hydrodynamic interactions (HIs) between the pairs of monomers are estimated using the preaveraged Oseen tensor. The intrinsic viscosity of linear and ring polymers both with and without EVI are compared as a function of ring size. A monotonically increasing trend of the intrinsic viscosity is observed in both cases. The intrinsic viscosity of both linear and ring polymers both with and without EVI show a very good agreement with the experimental results of polystyrene over a wide range of molecular weights in both good and theta solvents, respectively. The fractal dimensions of the ring polymers with EVI lie between that of a random walk and a self-avoiding walk model of linear polymers in three dimensions. The ring size increases with EVI and the effect of EVI is stronger on larger rings than that on smaller rings. The dielectric relaxation follow a connectivity independent universal scaling behavior at low and high frequency regions. The imaginary part of the complex dielectric susceptibility displays a local maxima in the intermediate frequency region, which reveals a structure dependent behavior of the rings. The theoretically calculated dielectric loss of ring polymers with HI matches well with those obtained from experiments.

Chain length and amino acid composition dependence of coil-globule transition in intrinsically disordered proteins.

A fundamental question related to intrinsically disordered proteins (IDPs) is whether they undergo a coil-to-globule transition with changes in cosolvent conditions. IDPs are hetero-polymers and finite in size. The chain length and amino acid composition could lead to the varying extent of compaction in IDPs and the coil-to-globule transition (theta condition). To probe the theta condition in polypeptides, we studied the behavior of polyleucine and polyglutamine with six different chain lengths (N = 16 to 512) in various concentrations (0 to 8 M) of Urea (denaturant) and TMAO (osmolyte) using coarse-grained models and computer simulations. The Flory scaling exponent of polyleucine (polyglutamine) undergoes a transition from approximately 0.6 (0.6) to 0.3 (0.5) with increasing N in water. We observed that the theta condition for both the IDPs strongly depends on N and varies as N−0.5. Depending on N, polyglutamine (polyleucine) chains reach the theta condition at different [TMAO] ([TMAO] or [Urea]), confirming that in addition to chain length, the amino acid composition also influences the theta solvent condition for the IDPs. Moreover, the theta point for smaller chain lengths (N = 16 to 64) calculated using the structure factor mimicking the small-angle X-ray scattering (SAXS) experiments and using pair distances mimicking fluorescence resonance energy transfer (FRET) experiments are in disagreement. The theta condition computed using the structure factor and pair distances converge to the same point only at large N. As the theta condition is correlated with the critical condition of liquid-liquid phase separation (LLPS) for IDPs, we predict that LLPS propensity of IDPs will increase with N.

Structure and Intermolecular Interactions in Aqueous Solutions of Polyethylene Glycol.

Aqueous solutions of polyethylene glycol are studied by small-angle neutron scattering over a broad range of polymer molecular masses and concentrations. The scattering data were modeled by a Gaussian chain form factor combined with random phase approximation, which provided good fits over the whole studied concentration range. The results showed that polyethylene glycol in the molecular mass range –20 kDa in water at physiological temperature T = 37 C behaves like a random coil in nearly theta solvent conditions. The obtained results serve as a reference for the description of complex mixtures with PEG used in various applications.

Inorganic Reinforced Poly(ionic liquid) Microcapsules: Confined Cooling-Assisted Phase Separation Self-Assembly and Enhanced Electroresponsive Properties.

A simple preparation of inorganic reinforced poly(ionic liquid) (PIL) microcapsules by combining dispersion polymerization and confined cooling-assisted phase separation self-assembly is reported. Silane coupling agent-modified PIL microbeads are first prepared by dispersion polymerization. Then, the microbeads are dissolved in a theta solvent composed of good solvent and non-solvent to form hollow SiOx microcapsules at a relatively high temperature. Finally, the solution is cooled to induce the nucleation and growth of dissolved PIL chains on the inner and outer surface of hollow SiOx microcapsules to form inorganic reinforced microcapsules with asymmetric PIL/SiOx /PIL sandwich-like shell. The morphology of microcapsules can be controlled by adjusting PIL concentration and cooling rate. The inorganic reinforced microcapsules show enhanced suspended stability and electroresponsive characteristic when used as the dispersed phase of smart suspensions.

Preparation of Poly(Ionic Liquid) Microbeads by Evaporation‐Assisted Phase Separation

AbstractThe authors reported a simple and high‐yield evaporation‐assisted phase separation (EAPS) method to prepare poly(ionic liquid) (PIL) microbeads, in particular submicron microbeads. Irregular PIL powder or bulk is dissolved in a theta solvent composed of volatile good solvent and less volatile non‐solvent at room temperature, and then PIL microbeads are formed by evaporation of the solution at a temperature lower than the boiling point of volatile good solvent. The yield of microbeads, in particular, submicron microbeads, prepared by the EAPS method can reach 99%. The mechanism of microbead formation is studied by tracing the nucleation and growth process by the light transmittance. The key parameters to control the size and morphology of microbeads are investigated and discussed.

Polycation radius of gyration in a polymeric ionic liquid (PIL): the PIL melt is not a theta solvent.

The conformation of the polycation in the prototypical polymeric ionic liquid (PIL) poly(3-methyl-1-aminopropylimidazolylacrylamide) bis(trifluoromethylsulfonyl)imide (poly(3MAPIm)TFSI) was probed using small-angle neutron scattering (SANS) and ultra-small-angle neutron scattering (USANS) at 25 °C and 80 °C. Poly(3MAPIm)TFSI contains microvoids which lead to intense low q scattering that can be mitigated using mixtures of hydrogen- and deuterium-rich materials, allowing determination of the polycation conformation and radius of gyration (Rg). In the pure PIL, the polycation adopts a random coil conformation with Rg = 52 ± 0.5 Å. In contrast to conventional polymer melts, the pure PIL is not a theta solvent for the polycation. The TFSI- anions, which comprise 48% v/v of the PIL, are strongly attracted to the polycation and act like small solvent molecules which leads to chain swelling analogous to an entangled, semi-dilute, or concentrated polymer solution in a good solvent.

Influence of solvent quality on depletion potentials in colloid-polymer mixtures.

As first explained by the classic Asakura-Oosawa (AO) model, effective attractive forces between colloidal particles induced by depletion of nonadsorbing polymers can drive demixing of colloid-polymer mixtures into colloid-rich and colloid-poor phases, with practical relevance for purification of water, stability of foods and pharmaceuticals, and macromolecular crowding in biological cells. By idealizing polymer coils as effective penetrable spheres, the AO model qualitatively captures the influence of polymer depletion on thermodynamic phase behavior of colloidal suspensions. In previous work, we extended the AO model to incorporate aspherical polymer conformations and showed that fluctuating shapes of random-walk coils can significantly modify depletion potentials [W. K. Lim and A. R. Denton, Soft Matter 12, 2247 (2016); J. Chem. Phys. 144, 024904 (2016)]. We further demonstrated that the shapes of polymers in crowded environments sensitively depend on solvent quality [W. J. Davis and A. R. Denton, J. Chem. Phys. 149, 124901 (2018)]. Here, we apply Monte Carlo simulation to analyze the influence of solvent quality on depletion potentials in mixtures of hard-sphere colloids and nonadsorbing polymer coils, modeled as ellipsoids whose principal radii fluctuate according to random-walk statistics. We consider both self-avoiding and non-self-avoiding random walks, corresponding to polymers in good and theta solvents, respectively. Our simulation results demonstrate that depletion of polymers of equal molecular weight induces much stronger attraction between colloids in good solvents than in theta solvents and confirm that depletion interactions are significantly influenced by aspherical polymer conformations.

Conformation of poly(ethylene glycol) in aqueous cholinium amino acid hybrid solvents

HypothesisHybrid solvents based on cholinium amino acid ionic liquids ([Ch][AA] ILs) mixed with water are environmentally benign solvents with low toxicity. [Ch][AA] ILs are used in biomass pretreatment processes to dissolve targeted (macro)molecules such as lignin from lingnocellulose. Understanding how [Ch][AA] ILs dissolve polymers is therefore of great interest for the rational design of ILs towards industrial application. Variation of the IL anion and the water concentration are hypothesised to change the solvent properties of [Ch][AA] hybrid solvents. Therefore, we probe the solvent quality of [Ch][AA] aqueous solutions with different anions (glycinate, prolinate and argininate) and water concentration for the simple model solute poly(ethylene glycol) (PEG). ExperimentsPartial phase diagrams were produced to probe the salting-out effect of [Ch][AA] ILs towards PEG (Mw = 38 kDa). Small-angle neutron scattering experiments of deuterated PEG in hydrogenous [Ch][AA] aqueous solutions were performed to determine the polymer radius of gyration at infinite dilution (Rg,0) via Zimm-plots. Polymer concentration dependent apparent Rg values were obtained fitting an excluded volume polymer model onto the scattering data. Blends of hydrogenous and deuterated PEG under zero average contrast conditions were analysed to probe Rg at high polymer concentrations. FindingsHydrogen bond capacity of the anion is key to the salting-out effect of [Ch][AA] ILs on PEG. Rg,0 depends on anion species and water concentration. At IL:water = 1:30 (mole:mole) and 37 °C, cholinium argininate and cholinium glycinate are close to theta solvents while cholinium prolinate and dilute cholinium argininate (IL:water = 1:100) are between theta and good solvents.

Variable temperature asymmetric flow field-flow fractionation for the topology separation of poly(methyl methacrylate)

Size exclusion chromatography is the method of choice for the molar mass analysis of polymers, however, it is not selective towards polymer microstructure. Counterintuitively, asymmetric flow field-flow fractionation (AF4), a channel-based molar mass analysis technique, has been shown to be able to fractionate poly(methyl methacrylate (PMMA) according to tacticity. This was revealed by investigating the solution behaviour of syndiotactic- (s-PMMA), atactic- (a-PMMA) and isotactic (i-PMMA) poly(methyl methacrylate) of similar molecular masses in solvents with different thermodynamic properties. In addition to developing a selective fractionation method, the effects of solvent quality and channel temperature on the fractionation were investigated. It was concluded that the thermodynamic quality of the carrier liquid has a significant influence on the retention behaviour of polymers in AF4. It was shown that the separation of s-PMMA and i-PMMA can be improved by using a theta solvent (acetonitrile) as the carrier liquid instead of thermodynamically good solvents such as tetrahydrofuran and chloroform. In addition, it was found that by using a non-stereocomplexing solvent for PMMA, such as chloroform, blends of s-PMMA and i-PMMA can be separated. Lastly, it was established that the AF4 channel temperature has an influence on the retention behaviour of the PMMA samples. For THF as carrier liquid it was found that the maximum difference in retention between s-PMMA and i-PMMA can be achieved at a channel temperature of 35 °C. In the case of ACN being the carrier liquid, it was observed that the retention behaviour of i-PMMA was significantly more influenced by a change in temperature as compared to s-PMMA and a-PMMA.

Universal size ratios of Gaussian polymers with complex architecture: radius of gyration vs hydrodynamic radius

We study the impact of arm architecture of polymers with a single branch point on their structure in solvents. Many physical properties of polymer liquids strongly dependent on the size and shape measures of individual macromolecules, which in turn are determined by their topology. Here, we use combination of analytical theory, based on path integration method, and molecular dynamics simulations to study structural properties of complex Gaussian polymers containing f^c linear branches and f^r closed loops grafted to the central core. We determine size measures such as the gyration radius R_g and the hydrodynamic radii R_H, and obtain the estimates for the size ratio R_g /R_H with its dependence on the functionality f=f^c+f^r of grafted polymers. In particular, we obtain the quantitative estimate of the degree of compactification of these polymers with increasing number of closed loops f^r as compared to linear or star-shape molecules of the same total molecular weight. Numerical simulations corroborate theoretical prediction that R_g /R_H decreases towards unity with increasing f. These findings provide qualitative description of polymers with complex architecture in theta solvents.

Chain flexibility and dynamics of alginate solutions in different solvents

Mechanical rheometry, specifically rotational rheometry, squeeze flow, and capillary rheometry, and two microrheology methods, namely multiple-particle tracking (MPT) and diffusing wave spectroscopy (DWS) have been used to get new insight into structural and dynamical properties of alginate dissolved in solvents widely used for bioprinting, namely deionized water, phosphate-buffered saline (PBS), and Dulbecco Modified Eagle Medium (DMEM) cell media. Results demonstrate that alginate rheological properties depend on the solvent quality at concentrations higher than 1 wt.%. In this high concentration regime, in aqueous salt-free and PBS solutions, experimental scaling exponents for the concentration dependence of the specific viscosity ηsp and the plateau modulus G0 agree well with theoretical predictions for neutral polymers in good solvent whereas for the terminal relaxation time TR, the exponent is slightly higher than theoretically predicted, presumably due to the formation of aggregates. For alginate dissolved in DMEM, all exponents for ηsp, G0, and TR agree with predictions for polymers in theta solvents, which might be related to the formation of polyelectrolyte complex as a result of interactions between alginate and amino acids. Chain persistence length lp values, as determined directly from high frequency rheometry for the first time, are independent of alginate concentration and temperature. Lower absolute lp values were found for DMEM solutions compared with the other solvents. Moreover, scaling exponents for ηsp, G0, and TR do not change with temperature, within 20 and 60 °C. These findings suggest no change in the conformation of alginate chains with temperature.Graphical abstractAlginate rheological properties depend on the solvent quality

Non-monotonic phase behaviour of a mixture containing non-adsorbing particles and polymerising rod-like molecules

Hypothesis: Previous works have shown that many-body interactions induced by dispersants with increasing correlation length will generate a diminishing two-phase region [Soft Matter 14, 6921 (2018)]. We conjecture that the attenuation of the depletion attraction due to many-body interactions is a ubiquitous phenomenon in medium-induced interactions. We propose mixtures of colloidal particles and rod-like polymers as a feasible experimental system for verifying these predictions, since the intra-molecular correlations are not screened in a good solvent for rod-like polymers as they are in flexible polymers. The length of the rods can grow and become the dominant length scale that determines the range of the depletion interactions for the imbedded non-adsorbing particles.Simulations: We study many-body depletion forces induced by polymerizing rod-like polymers on spherical non-adsorbing colloids, using Metropolis Monte Carlo simulations. We also employ a simple mean-field theory to further justify our numerical predictions.Findings: We demonstrate that the phase diagram displays the same qualitative features that have previously been predicted by many-body theory, for mixtures containing flexible polymers under theta solvent conditions. The contraction of the particle two-phase region that we observe, as the correlation length increases beyond some specific value, could be a signature of the weakening of the depletion caused by many-body effects.

Symmetry Transitions of Polymer-Grafted Nanoparticles: Grafting Density Effect

We examined the packing structure of polystyrene-coated gold nanoparticles (Au@PS) as a function of grafting density. A series of Au@PS nanoparticles with grafting densities in the range of 0.51–1.94 chains nm–2 were prepared by a ligand exchange process using thiol-terminated PS and then self-assembled at a liquid–air interface. We observed a transition from disordered to body-centered cubic (bcc) to face-centered cubic (fcc) arrangements with increasing grafting density, even though the ligand length-to-core radius ratio (λ) was as high as 3.0, a condition that typically favors nonclose-packed bcc symmetry in the self-assembly of hard nanoparticles. To explain this phenomenon, we define λeff to include the concentrated polymer brush regime as part of the “hard core”, which predicts that the softness of Au@PS nanoparticles is reduced from 1.53 to 0.14 in a theta solvent as the grafting density increases from 0.51 to 1.94 chains nm–2. This new definition of λ can also predict the effective radii of nanopa...

A deep insight into the polystyrene chain in cyclohexane at theta temperature: molecular dynamics simulation and quantum chemical calculations.

Molecular characteristics of an atactic polystyrene (aPS) chain with different lengths in a theta solvent, cyclohexane at 307.65K, were studied via molecular dynamics (MD) simulation. The interaction energy of the aPS dilute solution models and Flory-Huggins (FH) interaction parameter were calculated to investigate the effect of the chain molecular weight on its compatibility with the solvent molecules. The simulation results illustrated that increasing the chain length increased the interactions between the chain and the solvent molecules. The chain dimensions via calculating the radius of gyration (Rg) and end-to-end distance, <r0>, were measured. Mean square displacement (MSD) and diffusivity coefficient of the chains were calculated to determine their dynamic behavior. The results exhibited that two factors of the chain movability and size were important for the diffusion in oligomeric state. Additionally, viscosity of the resultant dilute solutions was calculated via nonequilibrium molecular dynamics simulation (NEMD). Moreover, the steric hindrance of the chains was determined by radial distribution function (RDF) analysis. The calculated characteristics of the chain and solution viscosity results showed a good agreement with experimental published works. Measurement of the potential field of cyclohexane-cyclohexane and aPS-cyclohexane pairs was also based on their potential field via quantum chemical calculations to determine the special orientation of the solvent molecules to each other and to the polymer segments, respectively. Graphical abstract (a) The equilibrated dilute solution model of polystyrene in cyclohexane at theta temperature (the red and yellow balls represent carbon and hydrogen atoms, respectively. The cyclohexane molecules are illustrated in line style in the box), (b) the electrostatic potential field around an optimized structure containing two cyclohexane molecules, and (c) around the sole cyclohexane molecule and polystyrene with two repeating units (carbon and hydrogen atoms are represented in green and yellow, respectively).

Influence of solvent quality on conformations of crowded polymers.

The structure and function of polymers in confined environments, e.g., biopolymers in the cytoplasm of a cell, are strongly affected by macromolecular crowding. To explore the influence of solvent quality on conformations of crowded polymers, we model polymers as penetrable ellipsoids, whose shape fluctuations are governed by the statistics of self-avoiding walks, appropriate for a polymer in a good solvent. Within this coarse-grained model, we perform Monte Carlo simulations of mixtures of polymers and hard-nanosphere crowders, including trial changes in polymer size and shape. Penetration of polymers by crowders is incorporated via a free energy cost predicted by polymer field theory. To analyze the impact of crowding on polymer conformations in different solvents, we compute the average polymer shape distributions, radius of gyration, volume, and asphericity over ranges of the polymer-to-crowder size ratio and crowder volume fraction. The simulation results are accurately predicted by a free-volume theory of polymer crowding. Comparison of results for polymers in good and theta solvents indicates that excluded-volume interactions between polymer segments significantly affect crowding, especially in the limit of crowders much smaller than polymers. Our approach may help to motivate future experimental studies of polymers in crowded environments, with possible relevance for drug delivery and gene therapy.

Structural, macro- and micro-mechanical properties of supramolecular bi-component l-Lysine-sodium tetraphenyl borate based hydrogels

We present a new system of bi-component hydrogels formed of l-lysine hydrochloride mixed with sodium tetraphenyl borate with unusual viscoelastic properties which might be useful in tissue engineering, nano-particles synthesis or bioseparation. Beside cationic-anionic molecular interactions, 1H-NMR experiments have also shown the presence of π-electrons cloud interactions as well as hydrogen bonds stabilizing the supramolecular structure. Bulk rheological and mechanical properties have been characterized using steady and oscillatory shear rheometry as well as uniaxial compression tests. Microstructural information has been deduced from multi particle tracking (MPT) optical microrheology and cryo-preparation scanning electron microscopy (SEM). These gels are shear thickening at low concentrations and shear thinning at higher gelator concentration. Shear and Young’s modulus data obtained from different techniques agree fairly well. Zero shear viscosity as well as modulus data obtained for gels with equimolar lysine and borate concentration exhibit concentration dependence η0∼c5±0.5and G0∼c3.4±0.35, respectively. The scaling exponent for η0agrees well with predictions for neutral polymer in theta solvent or wormlike micelles in the slow breaking regime whereas the variation in G0 is unexpectedly high. We attribute this to the unique microstructure consisting of a cellular structure composed of thin sheets connected by tiny fibers. At low concentrations the mesh size of this structure is about 10 μm and fiber diameter increases from ∼200 nm to ∼2 μm, only at the highest gelator concentration of 7 wt.% the mesh size shrinks to ∼5 μm and the fiber diameter to ∼400 nm. Consistently, tracer particles in low concentrated gels diffuse freely in an aqueous environment. At higher gelator concentration, however, gelation takes place so fast that tracers are trapped in the elastic sheets / fibrous regions and the modulus GMPT´ agrees fairly well with bulk data. Varying the molar ratio of both gel-forming components results in a pronounced viscosity maximum at fixed total gelator concentration. Corresponding microstructural changes could again be visualized using cryo-SEM consistent with MPT data. At high lysine fraction, a coarse coral reef type sheet structure is found while at low lysine to borate ratio a network of thick struts is formed. Finally, diffusing wave spectroscopy experiments performed on samples with different lysine to borate ratio revealed that the plateau modulus G0 is almost independent of temperature whereas the relaxation time TR becomes faster as temperature increases.

Scaling Laws for Polymer Chains Grafted onto Nanoparticles

AbstractAn experimental approach is presented for identifying the scaling laws for polymer chains grafted onto gold nanoparticles. Poly(ethylene oxide) of various molecular weights are grafted onto gold nanoparticles via thiol end‐functional groups. The polymer‐grafted nanoparticles are self‐assembled into monolayers from solvents of different quality. Over a significant range of graft densities, nanoparticle monolayers deposited from good (athermal) solvent exhibit particle spacing that scales according to theoretical predictions for chains in dilute solution. This unexpected result for ordered nanoparticle monolayers is discussed in the context of the deposition process. In monolayers deposited from theta solvent, molecular weight scaling of particle spacing breaks down, possibly due to chain length dependence of solvent quality. In poor solvent, the structure of nanoparticle assemblies is not sufficiently ordered to obtain reliable measurements, possibly due to loss of nanoparticle dispersion. This approach opens up the possibility for accurate measurement of the effect of solvent on grafted chain scaling in nanoparticle assemblies.

Size of Elastic Single-Chain Nanoparticles in Solution and on Surfaces

We introduce herein a simple model of covalent-bonded single-chain nanoparticles (SCNPs) by considering these intrachain cross-linked nano-objects as elastic unimolecular networks. According to this model, each SCNP is regarded as a network of elastic strands connected by cross-links. The free energy of the SCNP is decomposed in two contributions: (i) an elastic free energy due to the presence of these strands and (ii) an excluded volume contribution arising from the balance of monomer–monomer and monomer–solvent interactions. We provide scaling law expressions for the size (R), diffusion coefficient (D), apparent molar mass (Mapp), and shrinking factor (⟨G⟩) of elastic SCNPs in good, theta, and bad solvents. Also, we derive scaling laws for the height (H) of elastic SCNPs deposited on both low- and high-surface free energy substrates. A comparison of experimental results to model predictions for covalent-bonded polystyrene SCNPs in solution of narrow molecular weight distribution (1.09 ≤ Đ ≤ 1.26), different amount of reactive groups (0.025 ≤ x ≤ 0.3), and varying precursor molar mass (44 ≤ M ≤ 235 kDa) is performed based on literature data. For the same system, a similar comparison of experimental and theoretical H data corresponding to the case of SCNPs deposited on low- and high-energy substrates is also carried out. This simple elastic model provides a useful framework for connecting the amount of reactive groups and precursor molar mass with the size upon intrachain cross-linking for a variety of covalent-bonded SCNPs both in solvents of different quality and on substrates of different surface free energy.