Scaling of mesoscale simulations of polymer melts with the bare friction coefficient

Both the Rouse and reptation model predict that the dynamics of a polymer melt scale inversely proportional with the Langevin friction coefficient xi. Mesoscale Brownian dynamics simulations of polyethylene validate these scaling predictions, providing the reptational friction xi(R)=xi+xi(C) is used, where xi(C) reflects the fundamental difference between a deterministic and a stochastic propagator even in the limit of xi to zero. The simulations have been performed with Langevin background friction and with pairwise friction, as in dissipative particle dynamics. Both simulation methods lead to equal scaling behavior with xi(C) having almost the same value in both cases. The scaling is tested for the diffusion g(t), the shear relaxation modulus G(t), and the Rouse mode autocorrelations of melts of C(120)H(242), C(400)H(802), and C(1000)H(2002). The derived dynamical scaling procedure is very useful to reduce run-time in mesoscale computer simulations, especially if pairwise friction is applied.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Liquid-vapor transition of systems with mean field universality class

We have considered a system where the interaction, v(r)=v(IS)(r)+xi(2)v(MF)(r), is given as a linear combination of two potentials, each of which being characterized with a well-defined critical behavior: for v(IS)(r) we have chosen the potential of the restricted primitive model which is known to belong to the three-dimensional Ising universality class, while for v(MF)(r) we have considered a long-range interaction in the Kac [J. Math. Phys. 4, 216 (1963)] limit, displaying mean field (MF) behavior. We study the performance of two theoretical approaches and of computer simulations in the critical region for this particular system and give a detailed comparison between theories and simulation of the critical region and the location of the critical point. Having shown by theoretical arguments that the system belongs to the MF universality class for any positive value of xi and shows nonclassical behavior only for xi=0, we examine to which extent theoretical approximations and simulation can reproduce this behavior. While in this limiting case theoretical approaches are known to fail, we find good agreement for the critical properties between the theoretical approaches and the simulations for xi(2) larger than 0.05.     

Scaling behavior of nonisothermal phase separation

The phase separation process in a critical mixture of polydimethylsiloxane and polyethylmethylsiloxane (PDMS/PEMS, a system with an upper critical solution temperature) was investigated by time-resolved light scattering during continuous quenches from the one-phase into the two-phase region. Continuous quenches were realized by cooling ramps with different cooling rates kappa. Phase separation kinetics is studied by means of the temporal evolution of the scattering vector qm and the intensity Im at the scattering peak. The curves qm(t) for different cooling rates can be shifted onto a single mastercurve. The curves Im(t) show similar behavior. As shift factors, a characteristic length Lc and a characteristic time tc are introduced. Both characteristic quantities depend on the cooling rate through power laws: Lc approximately kappa(-delta) and tc approximately kappa(-rho). Scaling behavior in isothermal critical demixing is well known. There the temporal evolutions of qm and Im for different quench depths DeltaT can be scaled with the correlation length xi and the interdiffusion coefficient D, both depending on DeltaT through critical power laws. We show in this paper that the cooling rate scaling in nonisothermal demixing is a consequence of the quench depth scaling in the isothermal case. The exponents delta and rho are related to the critical exponents nu and nu* of xi and D, respectively. The structure growth during nonisothermal demixing can be described with a semiempirical model based on the hydrodynamic coarsening mechanism well known in the isothermal case. In very late stages of nonisothermal phase separation a secondary scattering maximum appears. This is due to secondary demixing. We explain the onset of secondary demixing by a competition between interdiffusion and coarsening.     

Collective and self-diffusion coefficients in an ionic critical mixture: 3-methylpyridine+water+NaBr

The dynamics of concentration fluctuations of three critical samples of the 3-methylpyridine (3MP)+water+NaBr system have been measured by photon correlation spectroscopy. The collective-diffusion coefficient D shows the usual Ising behavior near the critical temperature T(c). However, as |T-T(c)| increases, the dynamic correlation length calculated from D, xi, takes values higher than the correlation length of the critical fluctuations calculated from static light scattering, xi(s). At the largest |T-T(c)| measured, xi approaches the value, xi(0,d) approximately equal to 1.13 nm, while the amplitude of xi(s) is xi(0,s)=0.38 nm. Pulsed-gradient NMR spectroscopy points out the existence of two dynamic contributions. One of them is consistent with the existence of molecular entities of hydrodynamic radius 0.31 nm, while the other one indicates the existence of aggregates rich in 3MP of radius 1.16 nm. The existence of the aggregates may explain the apparent anomalous behavior of the dynamic light scattering experiments for this system far from the critical point.     

Adsorption of random copolymers by a selective layer: Monte Carlo studies

We use scaling arguments and computer simulations to investigate the adsorption of symmetric AB-random copolymers (RC) from a diluted solution onto a selective ABA layer. Depending on the ratio between the layer thickness and the size of excess blobs, d/xi, three regimes of RC adsorption are predicted. For large values of the layer thickness RC adsorption can be understood as adsorption on two selective interfaces where sequences of RC chains form bridges. When the layer thickness is of the order of xi, excess blobs are trapped in the layer and localize the copolymer chain strongly. If the layer thickness is very small a weak adsorption scenario is predicted where large loops are formed outside the layer. Our simulations using the bond fluctuation model are in good agreement with the scaling predictions. We show that chain properties display non-monotonous behavior with respect to the layer thickness with optimal values for d approximately xi. In particular, we discuss simulation results for density profiles, statistics of bridges, loops and tails formed by the adsorbed chains, as well as for the adsorption order parameter and free energy.     

Translational diffusion in sucrose benzoate near the glass transition: probe size dependence in the breakdown of the Stokes-Einstein equation

The translational diffusion coefficient D(trans) for rubrene, 9,10-bis(phenylethynyl)anthracene (BPEA), and tetracene in the fragile molecular glass-former sucrose benzoate (SB) (Tg=337 K) was studied as a function of temperature from Tg+3 K to Tg+71 K by use of the holographic fluorescence recovery after photobleaching technique. The values of D(trans) vary by five to six orders of magnitude in this temperature range. Contrary to the predictions of the Stokes-Einstein equation, the temperature dependence of probe diffusion in SB over the temperature range of the measurements is weaker than that of T/eta, where eta is the shear viscosity. In going from the crossover temperature Tx approximately 1.2Tg to Tg, D(trans)eta/T increases by factors of 2.4+/-0.2 decades for rubrene, 3.4+/-0.2 decades for BPEA, and 3.8+/-0.4 decades for tetracene. The decoupling between probe diffusion in SB and viscosity is characterized by the scaling law D(trans) approximately T/eta(xi), with xi=0.621 for tetracene, 0.654 for BPEA, and 0.722 for rubrene. Data for probe diffusion in SB are combined with data from the literature for probe diffusion in ortho-terphenyl and alphaalphabeta-tris(naphthyl)benzene in a plot of enhancement versus the relative probe size parameter rho(m)=(m(p)m(h))(1/3), where m(p) and m(h) are, respectively, the molecular weights of the probe and host solvent. The plot clearly shows a sharp increase in enhancement of translational diffusion at rho(m) approximately 1. By applying temperature shifts, D(trans) for probe diffusion in SB and the dielectric relaxation time tau(D) can be superimposed on a single master curve based on the Williams-Landel-Ferry equation. This suggests that the dynamics of probe diffusion in SB is described by the scaling relationship D(trans) approximately 1/tau(D)(T+DeltaT), where tau(D)(T+DeltaT) is the temperature-shifted dielectric relaxation time. The results from this study are discussed within the context of dynamic heterogeneity in glass-forming liquids.     

Analytical phase diagrams for colloids and non-adsorbing polymer

We review the free-volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20 (1992) 559] for the phase behavior of colloids in the presence of non-adsorbing polymer and we extend this theory in several aspects: (i) We take the solvent into account as a separate component and show that the natural thermodynamic parameter for the polymer properties is the insertion work Pi(v), where Pi is the osmotic pressure of the (external) polymer solution and v the volume of a colloid particle. (ii) Curvature effects are included along the lines of Aarts et al. [J. Phys.: Condens. Matt. 14 (2002) 7551] but we find accurate simple power laws which simplify the mathematical procedure considerably. (iii) We find analytical forms for the first, second, and third derivatives of the grand potential, needed for the calculation of the colloid chemical potential, the pressure, gas-liquid critical points and the critical endpoint (cep), where the (stable) critical line ends and then coincides with the triple point. This cep determines the boundary condition for a stable liquid. We first apply these modifications to the so-called colloid limit, where the size ratio q(R)=R/a between the radius of gyration R of the polymer and the particle radius a is small. In this limit the binodal polymer concentrations are below overlap: the depletion thickness delta is nearly equal to R, and Pi can be approximated by the ideal (van't Hoff) law Pi=Pi(0)=phi/N, where phi is the polymer volume fraction and N the number of segments per chain. The results are close to those of the original Lekkerkerker theory. However, our analysis enables very simple analytical expressions for the polymer and colloid concentrations in the critical and triple points and along the binodals as a function of q(R). Also the position of the cep is found analytically. In order to make the model applicable to higher size ratio's q(R) (including the so-called protein limit where q(R)>1) further extensions are needed. We introduce the size ratio q=delta/a, where the depletion thickness delta is no longer of order R. In the protein limit the binodal concentrations are above overlap. In such semidilute solutions delta approximately xi, where the De Gennes blob size (correlation length) xi scales as xi approximately phi(-gamma), with gamma=0.77 for good solvents and gamma=1 for a theta solvent. In this limit Pi=Pi(sd) approximately phi(3gamma). We now apply the following additional modifications: With these latter two modifications we obtain again a fully analytical model with simple equations for critical and triple points as a function of q(R). In the protein limit the binodal polymer concentrations scale as q(R)(1/gamma), and phase diagrams phiq(R)(-1/gamma) versus the colloid concentration eta become universal (i.e., independent of the size ratio q(R)). The predictions of this generalized free-volume theory (GFVT) are in excellent agreement with experiment and with computer simulations, not only for the colloid limit but also for the protein limit (and the crossover between these limits). The q(R)(1/gamma) scaling is accurately reproduced by both simulations and other theoretical models. The liquid window is the region between phi(c) (critical point) and phi(t) (triple point). In terms of the ratio phi(t)/phi(c) the liquid window extends from 1 in the cep (here phi(t)-phi(c)=0) to 2.2 in the protein limit. Hence, the liquid window is narrow: it covers at most a factor 2.2 in (external) polymer concentration.     

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, ε(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of ε(AB)*, suggesting that the ratio of the energy scales--and the corresponding empty fluid regime--is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime.     

Critical dynamics of the binary system nitroethane/3-methylpentane: relaxation rate and scaling function

Shear viscosity and dynamic light scattering measurements as well as ultrasonic spectrometry studies of the nitroethane/3-methylpentane mixture of critical composition have been performed at various temperatures near the critical temperature, T(c). A combined evaluation of the shear viscosity and mutual diffusion coefficient data yielded the amplitude, xi(0), of the fluctuation correlation length, xi, assumed to follow power law, and the relaxation rate, Gamma, or order parameter fluctuations. The latter was found to follow power law with the theoretical universal exponent. The amplitudes xi(0) = 0.23 +/- 0.02 nm and Gamma(0) = (125 +/- 5) x 10(9) s(-1) nicely agree with literature values. Using the relaxation rates resulting from the viscosity and diffusion coefficient data, the scaling function has been calculated assuming the ultrasonic spectra to be composed of a critical part and a noncritical background contribution. The experimental scaling function fits well to the predictions of the Bhattacharjee-Ferrell dynamic scaling model with scaled half-attenuation frequency, Omega(BF)1/2= 2.1. The amplitude of the sonic spectra yields the amount |g| = 0.26 of the adiabatic coupling constant, g, in fair agreement with -0.29 from another thermodynamic relation.     

The effect of matrix structure on the diffusion of fluids in porous media

The effect of matrix structure on the transport properties of adsorbed fluids is studied using computer simulations and percolation theory. The model system consists of a fluid of hard spheres diffusing in a matrix of hard spheres fixed in space. Three different arrangements of the fixed spheres, random, templated, and polymeric, are investigated. For a given matrix volume fraction the diffusion coefficient of the fluid, D, is sensitive to the manner in which the matrix is constructed, with large differences between the three types of matrices. The matrix is mapped onto an effective lattice composed of vertices and bonds using a Voronoi tessellation method where the connectivity of bonds is determined using a geometric criterion, i.e., a bond is connected if a fluid particle can pass directly between the two pores the bond connects, and disconnected otherwise. The percolation threshold is then determined from the connectivity of the bonds. D displays universal scaling behavior in the reduced volume fraction, i.e., D approximately (1-phi(m)phi(c))(gamma), where phi(m) is the matrix volume fraction and phi(c) is the matrix volume fraction at the percolation threshold. We find that gamma approximately 2.2, independent of matrix type, which is different from the result gamma approximately 1.53 for diffusion in lattice models, but similar to that for conduction in Swiss cheese models. Lattice simulations with biased hopping probabilities are consistent with the continuous-space simulations, and this shows that the universal behavior of diffusion is sensitive to details of local dynamics.     

Isomolar semigrand ensemble molecular dynamics: development and application to liquid-liquid equilibria

An extended system molecular dynamics method for the isomolar semigrand ensemble (fixed number of particles, pressure, temperature, and fugacity fraction) is developed and applied to the calculation of liquid-liquid equilibria (LLE) for two Lennard-Jones mixtures. The method utilizes an extended system variable to dynamically control the fugacity fraction xi of the mixture by gradually transforming the identity of particles in the system. Two approaches are used to compute coexistence points. The first approach uses multiple-histogram reweighting techniques to determine the coexistence xi and compositions of each phase at temperatures near the upper critical solution temperature. The second approach, useful for cases in which there is no critical solution temperature, is based on principles of small system thermodynamics. In this case a coexistence point is found by running N-P-T-xi simulations at a common temperature and pressure and varying the fugacity fraction to map out the difference in chemical potential between the two species A and B (mu(A)-mu(B)) as a function of composition. Once this curve is known the equal-distance/equal-area criterion is used to determine the coexistence point. Both approaches give results that are comparable to those of previous Monte Carlo (MC) simulations. By formulating this approach in a molecular dynamics framework, it should be easier to compute the LLE of complex molecules whose intramolecular degrees of freedom are often difficult to properly sample with MC techniques.     

Simulations of concentrated suspensions of rigid fibers: relationship between short-time diffusivities and the long-time rotational diffusion

Brownian dynamics simulations of the behavior of suspensions of fibers demonstrate that the scaling of the rotational diffusivity with respect to the number density (nL3) is a sensitive function of the thickness and the parameter L2D(R0)/D(T0), where D(R0) is the rotational diffusivity at infinite dilution, D(T0) is the average center-of-mass diffusivity at infinite dilution, and L is the fiber length. Existing theories for the long-time rotational diffusivities of rigid fibers in the semidilute and concentrated regimes fail to accurately account for the relationship with the dilute values of the rotational and translational diffusivities of the various physical models used to simulate the fibers. The concentration regime studied in this work ranges from a number density of nL3 approximately 0-150, which is below the transition from an isotropic to nematic state. The effect of the fiber thickness was studied by performing simulations of rods with aspect ratios (fiber length over diameter) of 25, 50, and 500, as well as performing projections for infinitely thin fibers. The excluded volume of the rods was enforced through the use of short-range potentials. For a rod with an aspect ratio of 50 with a parameter of L2D(R0)/D(T0)=9, which corresponds to a slender-body model of the individual fibers, the rotational diffusivity (D(R)) scales as D(R)/D(R0) approximately (nL3)(-1.9) in the concentration regime of 70 < or = nL3 < or = 150. Similarly with a parameter of L2D(R0)/D(T0)=4, corresponding to a rigid-dumbbell model, the rotational diffusivity scales as D(R)/D(R0) approximately (nL3)(-1.1) over the same range of concentrations. For rods with aspect ratios of 25, it is observed that a difference in the scaling is seen for L2D(R0)/D(T0) approximately < 8, with higher values of this ratio exhibiting essentially the same scaling. Additional values of the ratio L2D(R0)/D(T0) were investigated to determine the overall behavior of the suspension dynamics with respect to this parameter. These findings resolve discrepancies between simulation results for rotational diffusivities reported by previous investigators and provide new insights for the development of an accurate theory for the diffusivity of rigid rods suspended in solution.     

Sound attenuation, shear viscosity, and mutual diffusivity behavior in the nitroethane-cyclohexane critical mixture

The shear viscosity eta(s), mutual diffusion coefficient D, and ultrasonic attenuation spectra of the nitroethane-cyclohexane mixture of critical composition have been measured at various temperatures near the critical temperature T(c). The relaxation rate of order parameter fluctuations resulting from a combined evaluation of the eta(s) and D data follows power law behavior with the theoretical exponent and with the large amplitude Gamma(o)=(156+/-2)x10(9) s(-1). The ultrasonic spectra have been evaluated in terms of a critical contribution and a noncritical background contribution. The amplitude of the former exhibits a temperature dependence, in conformity with a temperature dependence in the adiabatic coupling constant (|g| = 0.064 near T(c) and 0.1 at T-T(c)=3 K). If the variation of the critical amplitude with T is taken into account the experimental attenuation coefficient data display a scaling function which nicely fits to the theoretical prediction from the Bhattacharjee-Ferrell dynamic scaling model [R. A. Ferrell and J. K. Bhattacharjee, Phys. Rev. A 31, 1788 (1985)].     

Dynamic scaling of the critical binary mixture methanol-hexane

Acoustical attenuation spectrometry, dynamic light scattering, shear viscosity, density, and heat capacity measurements of the methanol/n-hexane mixture of critical composition have been performed. The critical part in the sonic attenuation coefficients nicely fits to the empirical scaling function of the Bhattacharjee-Ferrell [Phys. Rev. A 24, 1643 (1981)] dynamic scaling model if the theoretically predicted scaled half-attenuation frequency Omega(12) (BF)=2.1 is used. The relaxation rates of order parameter fluctuations, as resulting from the acoustical spectra, within the limits of experimental error agree with those from a combined evaluation of the light scattering and shear viscosity measurements. Both series of data display power law with amplitude Gamma(0)=44x10(9) s(-1). The amplitude of the fluctuation correlation length follows as xi(0)=0.33 nm from the light scattering data and as xi(0)=0.32 nm from the amplitude of the singular part of the heat capacity if the two-scale factor universality relation is used. The adiabatic coupling constant g=0.11 results from the amplitude of the critical contribution to the acoustical spectrum near the critical point, in conformity with g=0.12 as following from the variation of the critical temperature with pressure along the critical line and the thermal expansion coefficient.     

Phase separation of the Widom-Rowlinson mixture in confined geometry

The behavior of binary Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] mixture in confined geometry is investigated. The influence of confinement on phase separation is examined. Coexistence curves for the mixture in slitlike pores and pores of complex geometry are calculated in Monte Carlo simulations. Finite size scaling analysis is used to determine precisely the location of critical point for the bulk mixture.     

The interfacial tension and phase diagram of the Widom-Rowlinson mixture via Monte Carlo simulations

Results of Monte Carlo simulations are reported for the interfacial tension between two fluid phases in a binary mixture of penetrable spheres in which molecular pairs of like species do not interact, while those of unlike species interact as hard spheres. Semigrand canonical ensemble Monte Carlo simulations in a cubic cell with periodic boundary conditions are used to obtain histograms for various system sizes at various densities. At a given density, the interfacial tension and compositions of coexisting phases for an infinite system are evaluated via histogram analysis combined with finite-size scaling. The density dependence of the interfacial tension and phase diagram for an infinite system are thus obtained. The simulated behavior of the interfacial tension close to the critical density corroborates previous suggestions that the model belongs to the three-dimensional Ising universality class.     

Dynamical scaling of single chains on adsorbing substrates: diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.     

Phase behavior of linear heterogeneous trimers on a square lattice

Monte Carlo simulations in the grand canonical ensemble, the multiple-histogram analysis and finite-size scaling techniques have been used to study a phase behavior of trimer BAB on a square lattice. The systems with the same energies u(AA) = u(BB) and different strengths of interactions between unlike segments are considered. The AB-contacts are energetically unprofitable. There are two phase transitions: the first-order vapor-liquid transition and the second-order structural transition in the supercritical fluid. The phase diagram topology depends on the energy u(AB). The crossover between the tricritical point phase diagram topology and the critical end phase diagram topology is found. It is demonstrated that the transition to the ordered strip-like phase is non-universal.     

Small-angle neutron scattering study of temperature-induced emulsion gelation: the role of sticky microgel particles

In this work, small-angle neutron scattering (SANS) is used to probe the structural transformations that accompany temperature-induced gelation of emulsions stabilized by a temperature-responsive polymer. The latter is poly(NIPAM-co-PEGMa) (N-isopropylacrylamide and poly(ethyleneglycol) methacrylate) and contains 86 mol% NIPAM. Turbidity measurements revealed that poly(NIPAM-co-PEGMa) has a lower critical solution temperature (T(LCST)) of 36.5 degrees C in D(2)O. Aqueous polymer solutions were used to prepare perfluorodecalin-in-water emulsions (average droplet size of 6.9 mum). These emulsions formed gels at 50 degrees C. SANS measurements were performed on the poly(NIPAM-co-PEGMa) solutions and emulsions as a function of temperature. The emulsion was also prepared using a D2O/H2O mixture containing 72 vol% D2O in order to make scattering from the droplets negligible (on-contrast). The SANS data were analyzed using a combination of Porod and Ornstein-Zernike form factors. The results showed that the correlation length (xi) of the polymer scaled as xi approximately phi(p)(-0.68) at 32 degrees C, where phi(p) is the polymer volume fraction. The xi value increased for all systems as the temperature increased, which was attributed to a spinodal transition. At temperatures greater than T(LCST), the polymer solution changed to a polymer dispersion of poly(NIPAM-co-PEGMa) aggregates. The aggregates have features that are similar to microgel particles. The average size of these particles was estimated as 160-170 nm. The particles are "sticky" and are gel-forming. The on-contrast experiments performed using the emulsion indicated that the interfacial polymer chains condensed to give a relatively thick polymer layer at the perfluorodecalin-water interface at 50 degrees C. The gelled emulsions appear to consist of perfluorodecalin droplets with an encapsulating layer of collapsed polymer to which sticky microgel particles are adsorbed. The latter act as a "glue" between coated droplets in the emulsion gel.