Theta Solvent Research Articles

Influence of solvent size on the mechanical properties and rheology of polydimethylsiloxane-based polymeric gels

Abstract Soft polymeric gels have utility in a broad range of medical, industrial, and military applications, which has led to an extensive research investment over the past several decades. While most gel research exploits a cross-linked polymer network swollen with small molecule solvents, this article systematically investigates the impact of the solvent molecular weight on the resulting gel mechanical properties. The model polymer gel was composed of a chemically cross-linked polydimethylsiloxane (PDMS) network loaded with a non-reactive PDMS solvent. In addition to investigating the impact of solvent loading, the solvent molecular weight was varied from 423,000 g/mol to 1250 g/mol, broadly spanning the molecular weight of entanglement for PDMS (MW ENT ∼29,000 g/mol). The gels exhibited a strong frequency dependent mechanical response when the solvent molecular weight >MW ENT . In addition, scaling factors of shear storage modulus versus solvent loading displayed a distinct decrease from the theoretical value for networks formed in a theta solvent of 2.3 with increasing measurement frequency and solvent molecular weight. The frequency dependent shear storage modulus could be shifted by the ratio of solvent molecular weights to the 3.4 power to form a master curve at a particular solvent loading indicating that mobility of entangled solvent plays a critical role for the mechanical response. In addition, the incorporation of entangled solvent can increase the toughness of the PDMS gels.

Compression of polyelectrolyte brushes in a salt-free theta solvent

This paper examines the normal force between two opposing polyelectrolyte brushes and the interpenetration of their chains that is responsible for sliding friction. It focuses on the special case of semi-dilute brushes in a salt-free theta solvent, for which Zhulina and Borisov (J. Chem. Phys. 107, 5952 (1997)) have derived analytical predictions using the classical strong-stretching theory (SST). Interestingly, SST predicts that the brushes contract as they are compressed together maintaining a polymer-free gap, which provides an explanation for the ultra-low frictional forces observed in experiment. We examine the degree to which the SST predictions are affected by chain fluctuations by employing self-consistent field theory (SCFT). While the normal force is relatively unaffected, fluctuations are found to have a strong impact on brush interpenetration. Even still, the contraction of the brushes does significantly prolong the onset of interpenetration, implying that a sizeable normal force can be achieved before the sliding friction becomes significant.

A systematic coarse-graining strategy for semi-dilute copolymer solutions: from monomersto micelles

A systematic coarse-graining procedure is proposed for the description and simulation ofAB diblock copolymers in selective solvents. Each block is represented by a small number,nA ornB, of effective segments or blobs, containing a large number of microscopic monomers.nA andnB are unequivocally determined by imposing that blobs do not, on average, overlap,even if complete copolymer coils interpenetrate (semi-dilute regime). Ultra-softeffective interactions between blobs are determined by a rigorous inversionprocedure in the low concentration limit. The methodology is applied to anathermal copolymer model where A blocks are ideal (theta solvent), B blocksself-avoiding (good solvent), while A and B blocks are mutually avoiding. Themodel leads to aggregation into polydisperse spherical micelles beyond a criticalmicellar concentration determined by Monte Carlo simulations for several size ratiosf of the two blocks. The simulations also provide accurate estimates of the osmotic pressureand of the free energy of the copolymer solutions over a wide range of concentrations. Themean micellar aggregation numbers are found to be significantly lower than those predictedby an earlier, minimal two-blob representation (Capone et al 2009 J. Phys. Chem. B 113 3629).

The Behavior of Poly(dimethylsiloxane-co-diphenylsiloxane)s in Good and Theta Solvents

In this work, we investigated the behavior of poly(dimethylsiloxane-co-diphenylsiloxane)s under good and theta solvent conditions by using turbidimetry and viscosimetry. The evolution of the optical properties as a function of the solvent quality allowed the composition of the methylbenzene/methanol mixtures at the theta point to be determined. The intrinsic viscosity was determined in good (methylbenzene) and theta (methylbenzene/methanol) solvents at T = 298 K using different approaches. The unperturbed dimension parameters were calculated and are discussed as a function of copolymer composition. The introduction of the diphenylsiloxane units into a poly(dimethylsiloxane) chain results in an increase in the unperturbed dimensions as a consequence of the decrease in chain flexibility.

Internal motions of linear chains and spherical microgels in dilute solution

It is well known that for a flexible polymer chain in dilute solution, two different types of motions mainly contribute: the translation motion of the centres of mass of individual polymer chains; and the internal modes generated from the motions of segments with respect to the centre of mass of the chain. During the past two decades, with the advances in light scattering instrumentation and sophisticated methods of data analysis, both types of motions can be distinguished in experiments and utilized for testing molecular theories of polymer chain dynamics in dilute solution. In this article, we first review some previous experiments, in particular the dynamical properties of polystyrene (PS) and polyisoprene (PIP) chains in good and theta (Θ) solvents, and then our own results, including a comparative study of the internal motions of poly(N-isopropylacryl-amide) (PNIPAM) linear chains and spherical microgels under good solvent conditions. The final part of this article deals with how the solvent quality (the solution temperature) affects the internal mobility of PNIPAM linear chains and microgels.

Adaptive Multiscale Molecular Dynamics of Macromolecular Fluids

Until now, adaptive atomistic-coarse-grain (A/CG) molecular dynamics simulations have had very limited applicability because the on-the-fly CG → A transformation is problematic for all but those molecules whose CG representation consists of a single particle. Here, we solve this problem by combining a transitional healing region with a rotational dynamics of rigid atomistic fragments in the CG region. Error control is obtained by analysis of the A ↔ CG energy flow. We illustrate the method with adaptive multiscale simulations of liquid hexane and of a dilute polymer solution in a theta solvent.

Influence of the Solvent Quality on the Thermodynamic Behavior of Polymethylphenylsiloxane Solutions

In this work we investigate the effect of the solvent quality on the thermodynamic behavior of the polydimethyldiphenylsiloxane copolymer by using turbidimetry and viscosimetry. The turbidimetric method was used for the determination of the composition of the solvent mixture at the theta point. The experimental data obtained by using the capillary viscometry both in good and theta solvent conditions have been processed by using classical Huggins equation and new Wolf model (2007), which allows the calculation of intrinsic viscosities and other hydrodynamic parameters. The results obtained by using the two approaches were discussed comparatively. The conformational properties of copolymer in solution depend on their molecular structure, which is essentially dominated by the solvent quality, reflecting the balance of the interactions between the polymer chains and each solvent and that between solvent molecules.

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.

Brownian dynamics simulations of single polymer chains with and without self-entanglements in theta and good solvents under imposed flow fields

The effects of self-entanglements (spring-spring uncrossability) and solvent quality on the static and dynamic properties of a polymer chain in shear and extensional flows are investigated using Brownian dynamics simulations. We model the polymer chain by a sequence of beads connected by finitely extensible non-linear elastic springs, and spring-spring uncrossability is enforced by applying a spring-spring repulsive potential together with an adaptive time-stepping. Our findings suggest that chain uncrossability has an insignificant effect on the dynamics of a polymer chain. Furthermore, we considered four different combinations of intramolecular interactions: (i) no interactions, (ii) repulsive spring-spring and attractive bead-bead interactions, (iii) only repulsive bead-bead interactions, and (iv) only repulsive spring-spring interactions. The first two cases model “theta” solvents, where the radius-of-gyration of a polymer chain, Rg∼N0.5, where N is the number of beads. For appropriately chosen parameters of interaction potentials, the last two cases model good solvents, where Rg∼N0.59. In the presence of a simple shear flow, the stretching behavior is alike in all the cases except case (ii). In case (ii), the polymer chain forms “pearl-necklace-like” structures at zero Weissenberg number, Wi. With an increase in Wi, Rg first increases due to stretching of bonds between neighboring “pearls,” and then decreases when the decrease in the number of pearls becomes limiting. In the presence of an extensional flow, normal stretching behavior is observed even in case (ii); the number of pearls increases with increasing extension rate because larger pearls break into smaller “pearls.” The results show that even for fixed overall solvent quality for a chain at rest (e.g., a theta solvent), the ability of the chain to stretch in a shear flow is sensitive to the nature of intramolecular interactions. A chain with short-range attraction (between beads) and a long-range repulsion (between springs) tuned to balance each other and so create a theta condition at rest does not stretch much in a shear flow, while a chain for which the theta condition is achieved by applying no interactions at all does stretch in a shear flow.

Origin of High Segmental Mobility at Chain Ends of Polystyrene

Effects of solvents on segmental dynamics of polystyrene (PS) at the chain end have been studied by the site-specific spin-label method of electron spin resonance (ESR). PS’s having similar number-average molecular weight (ca. 25 kDa) but labeled with a nitroxde at the chain end (E-PS) or midchain segments (M-PS) individually were used for the measurements. Toluene and dioctyl phthalate (DOP) which are good and theta solvents, respectively, for PS were selected as solvents. The temperature variation of ESR spectra was simulated based on the “macroscopic order with microscopic disorder” model to determine the segmental mobility of the labeled segment. The E-PS showed obviously and slightly higher mobility compared to the M-PS in the bulk PS and in the concentrated PS/DOP (50/50) solution, respectively. On the other hand, the E-PS showed the same mobility with the M-PS within experimental uncertainties in the dilute PS/toluene (1/99), concentrated PS/toluene (60/40), and dilute PS/DOP (3/97) solutions. Name...

Synchrotron X-ray Scattering Characterization of the Molecular Structures of Star Polystyrenes with Varying Numbers of Arms

We have synthesized well-defined multiarmed star polystyrenes, with 6, 9, 17, 33, and 57 arms, and studied their molecular shapes and structural characteristics in a good solvent (tetrahydrofuran at 25 degrees C) and in a theta (Theta) solvent (cyclohexane at 35 degrees C) by small-angle X-ray scattering (SAXS) using a synchrotron radiation source. Analysis of the SAXS data provided a detailed characterization of the molecular shapes, including the contributions of the blob morphology of the arms, the radius of gyration, the paired distance distribution, the radial electron density distribution, and the Zimm-Stockmayer and Roovers g-factor, for the multiarmed star polystyrenes. In particular, the molecular shapes of the star polystyrenes were found to change from a fuzzy ellipsoid, for the 6-armed polystyrene, to a fuzzy sphere, for the 57-armed polystyrene, with an increasing number of arms. The ellipsoidal character of the star polystyrenes with fewer arms may originate from the extended anisotropically branched architecture at the center of the molecule. The arms of the star polystyrenes were found to be more extended than those of the linear polystyrenes. Furthermore, the degree of chain extension in the arms increased with the number of arms.

Viscometric Study of Poly(2-cinnamoyloxyethyl methacrylate)

Six poly(2-cinnamoyloxyethyl methacrylate) (PCEMA) samples with low polydispersity indices were derived from precursors prepared by anionic polymerization. Their intrinsic viscosities were determined in tetrahydrofuran (THF) and chloroform at 25 °C and in p-xylene between 55 and 82 °C. The data were treated to yield the Mark−Houwink−Sakurada parameters K and a. The a values suggested that THF and chloroform were good solvents for PCEMA at room temperature. The intrinsic viscosity data obtained in p-xylene were also analyzed by the Burchard−Stockmayer−Fixman method. Both the a values and the results of data treatment by the Burchard−Stockmayer−Fixman method suggest that p-xylene was a theta solvent for PCEMA at 60 °C. Using the K value at the theta temperature, we determined for PCEMA a characteristic ratio of 12.6, which is the ratio between its mean-square end-to-end distance in a theta solvent and that of a random flight chain.

Nonideal behavior of the intramolecular structure factor of dilute polymers in a theta solvent

We study the configurational properties of single polymers in a theta solvent by Monte Carlo simulation of the bond fluctuation model. The intramolecular structure factor at the theta point is found to be distinctively different from that of the ideal chain. The structure factor shows a hump around q approximately 5/Rg and a dip around q approximately 10/Rg in the Kratky plot with Rg being the radius of gyration. This feature is apparently similar to that in a melt. The theoretical expression by the simple perturbation expansion to the first order in terms of the Mayer function can be fitted to the obtained structure factor quite well, but the second virial coefficient cannot be set to zero.

Examining Polyglutamine Peptide Length: A Connection between Collapsed Conformations and Increased Aggregation

Abnormally expanded polyglutamine domains in proteins are associated with several neurodegenerative diseases, of which the best known is Huntington's. Expansion of the polyglutamine domain facilitates aggregation of the affected protein, and several studies directly link aggregation to neurotoxicity. The age of onset of disease is inversely correlated with the length of the polyglutamine domain; this correlation motivates an examination of the role of the length of the domain on aggregation. In this investigation, peptides containing 8 to 24 glutamines were synthesized, and their conformational and aggregation properties were examined. All peptides lacked secondary structure. Fluorescence resonance energy transfer studies revealed that the peptides became increasingly collapsed as the number of glutamine residues increased. The effective persistence length was estimated to decrease from ∼11 to ∼7 Å as the number of glutamines increased from 8 to 24. A comparison of our data with theoretical results suggests that phosphate-buffered saline is a good solvent for Q8 and Q12, a theta solvent for Q16, and a poor solvent for Q20 and Q24. By dynamic light scattering, we observed that Q16, Q20, and Q24, but not Q8 or Q12, immediately formed soluble aggregates upon dilution into phosphate-buffered saline at 37 °C. Thus, Q16 stands at the transition point between good and poor solvent and between stable and aggregation-prone peptide. Examination of aggregates by transmission electron microscopy, along with kinetic assays for sedimentation, provided evidence indicating that soluble aggregates mature into sedimentable aggregates. Together, the data support a mechanism of aggregation in which monomer collapse is accompanied by formation of soluble oligomers; these soluble species lack regular secondary structure but appear morphologically similar to the sedimentable aggregates into which they eventually mature.

Tension amplification in molecular brushes in solutions and on substrates.

Molecular bottle-brushes are highly branched macromolecules with side chains densely grafted to a long polymer backbone. The brush-like architecture allows focusing of the side-chain tension to the backbone and its amplification from the pico-Newton to nano-Newton range. The backbone tension depends on the overall molecular conformation and the surrounding environment. Here we study the relation between the tension and conformation of the molecular brushes in solutions, melts, and on substrates. In solutions, we find that the backbone tension in dense brushes with side chains attached to every backbone monomer is on the order of f(0)N(3/8) in athermal solvents, f(0)N(1/3) in theta solvents, and f(0) in poor solvents and melts, where N is the degree of polymerization of side chains, f(0) approximately equal k(B)T/b is the maximum tension in side chains, b is the Kuhn length, k(B) is Boltzmann's constant, and T is the absolute temperature. Depending on the side chain length and solvent quality, molecular brushes develop tension on the order of 10-100 pN, which is sufficient to break hydrogen bonds. Significant amplification of tension occurs upon adsorption of brushes onto a substrate. On a strongly attractive substrate, maximum tension in the brush backbone is approximately f(0)N, reaching values on the order of several nano-Newtons, which exceeds the strength of a typical covalent bond. At low grafting density and high spreading parameter, the cross-sectional profile of an adsorbed molecular brush is approximately rectangular with a thickness approximately b (A/S)1/2, where A is the Hamaker constant, and S is the spreading parameter. At a very high spreading parameter (S > A), the brush thickness saturates at monolayer approximately b. At a low spreading parameter, the cross-sectional profile of adsorbed molecular brush has a triangular tent-like shape. In the cross-over between these two opposite cases, covering a wide range of parameter space, the adsorbed molecular brush consists of two layers. Side chains in the lower layer gain surface energy due to the direct interaction with the substrate, while the second layer spreads on the top of the first layer. Scaling theory predicts that this second layer has a triangular cross-section with width R approximately N(3/5) and height h approximately N(2/5). Using self-consistent field theory we calculate the cap profile y(x) = h(1 - x2/R2)2, where x is the transverse distance from the backbone. The predicted cap shape is in excellent agreement with both computer simulation and experiment.

Thermal blob size as determined by the intrinsic viscosity

It is shown that the mass of the thermal blob, normalized by the mass of its effective monomer, is a unique function of the solvent quality represented by the Mark–Houwink–Sakurada exponent. This function specifies the relation between intrinsic viscosity and that measured in a theta solvent. As a result, the Mark–Houwink–Sakurada exponent can be determined from intrinsic viscosities measured for a single molecular mass. The form of the derived function is also confirmed by the constancy of calculated thermal blob mass for a given polymer of different molecular masses, dissolved in a solvent of a given quality.

Solution Properties of Poly(Methyl Methacrylate) in Dimethylsulfoxide

The solution properties of polymethylmethacrylate in dimethylsulfoxide were studied using multi-angle light scattering and an online viscometer coupled to size exclusion chromatography. The data demonstrate that DMSO is a suitable eluent for the determination of the molecular weight of PMMA by SEC. The Mark-Houwink coefficients K and α were determined as a function of temperature. At 35°C, DMSO is a theta solvent for PMMA, and it becomes a good solvent as the temperature increases. The unperturbed dimension Kθ was calculated using three different procedures. The data do not show evidence of a conformational transition controlled by the temperature such as the one reported in benzene and confirm the existence of a general relationship between the ratio K/Kθ and α. In the case of PMMA, the comparison of the dipole moment of the side group to that of the solvent can be used to predict the existence of a conformational transition.

X-ray scattering studies on molecular structures of star and dendritic polymers

We studied the molecular shapes and structural characteristics of a 33-armed, star polystyrene (PS-33A) and two 3rd-generation, dendrimer-like, star-branched poly(methyl methacrylate)s with different architectures (PMMA-G3a and PMMA-3Gb) and 32 end-branches under good solvent and theta (Θ) solvent conditions by using synchrotron small angle X-ray scattering (SAXS). The SAXS analyses were used to determine the structural details of the star PS and dendrimer-like, star-branched PMMA polymers. PS-33A had a fuzzy-spherical shape, whereas PMMA-G3a and PMMA-G3b had fuzzy-ellipsoidal shapes of similar size, despite their different chemical architectures. The star PS polymer’s arms were more extended than those of linear polystyrene. Furthermore, the branches of the dendrimer-like, star-branched polymers were more extended than those of the star PS polymer, despite having almost the same number of branches as PS-33A. The differences between the internal chain structures of these materials was attributed to their different chemical architectures.

Structure of bottle-brush polymers in solution: A Monte Carlo test of models for the scattering function

Extensive Monte Carlo results are presented for the structure of a bottle-brush polymer under good solvent or theta solvent conditions. Varying the side chain length, backbone length, and the grafting density for a rigid straight backbone, both radial density profiles of monomers and side chain ends are obtained as well as structure factors describing the scattering from a single side chain and from the total bottle-brush polymer. To describe the structure in the interior of a very long bottle brush, a periodic boundary condition in the direction along the backbone is used, and to describe effects due to the finiteness of the backbone length, a second set of simulations with free ends of the backbone is performed. In the latter case, the inhomogeneity of the structure in the direction along the backbone is carefully investigated. We use these results to test various phenomenological models that have been proposed to interpret experimental scattering data for bottle-brush macromolecules. These models aim to extract information on the radial density profile of a bottle brush from the total scattering via suitable convolution approximations. Limitations of this approach and the optimal way to perform the analysis of the scattering data within this approach are discussed.

A molecular simulation study of the structure and tribology of polymer brushes: Comparison of behavior in theta and good solvents

Implicit solvent Brownian dynamics simulations of the structure and tribology of opposing polymer-brush covered surfaces have been carried out as a function of surface separation and solvent quality. Consistent with experiment, shear forces were found to be greater under theta solvent conditions than in a good solvent at equal relative separations (normalized by the respective height of the brushes in theta and good solvents). Much higher relative compression is required before the onset of significant shear forces in good solvent compared to theta solvent. The dependence of shear force for a given relative separation on solvent quality can be accounted for by differences in interpenetration of the brushes. When compared as a function of absolute surface separation, greater interpenetration and greater shear force are observed at large separations for the brushes in good solvent than in theta solvent, consistent with the greater brush height in good solvent. At shorter separations, corresponding to moderate to high compression, brush–brush interactions result in significant deformation of the brushes. In this regime, greater interpenetration and greater shear forces are observed in theta solvent at a given separation, in qualitative agreement with experiment.