Search

We investigate the effect of polydispersity on the properties of curved linear brushes in good solvent and for molten brushes. To this end, we extend the strong stretching theory for polydisperse brushes to curved geometries and investigate the polymer chain end profiles, bending moduli and other properties for experimentally relevant polymer chain length distributions of the Schulz–Zimm type. We also investigate the properties of end exclusion zones that may appear in convex geometries under certain conditions and show that their position in the brush can be engineered by careful selection of the polymer length distribution. Finally, we propose a method to engineer chain end profiles by engineering the polymer length distribution. [ABSTRACT FROM AUTHOR]

A combination of atomistic molecular dynamics (aMD) simulations and circular dichroism (CD) analysis is used to explore supramolecular structures of amphiphilic ABA‐type triblock polymer peptide conjugates (PPC). Using the example of a recently introduced PPC with pH‐ and temperature responsive self‐assembling behavior [Otter et al., Macromolecular Rapid Communications 2018, 39, 1800459], this study shows how molecular dynamics simulations of simplified fragment molecules can add crucial information to CD data, which helps to correctly identify the self‐assembled structures and monitor the folding/unfolding pathways of the molecules. The findings offer insights into the nature of structural transitions induced by external stimuli, thus contributing to the understanding of the connection of microscopic structures with macroscopic properties. [ABSTRACT FROM AUTHOR]

Compression and interpenetration of two opposing polymer brushes formed by end-grafted adsorption-active chains are studied by the numerical self-consistent field approach and by analytical theory. For sufficiently strong polymer–surface attraction, a fraction of chains in the adsorption-active brush condenses into a near-surface layer, while the remaining ones form the outer brush with reduced effective grafting density. Analysis shows that the normal pressure in adsorption-active brushes can be understood in terms of the effective grafting density concept although the pressure at small separations is affected by the presence of the dense adsorbed phase. We propose a simple theory modification that accounts for this effect. We also formulate a procedure for extracting the value of the effective grafting density directly from the pressure vs separation curves by inverting the equation of state. In contrast to the normal pressure, the interpenetration of the two opposing adsorption-active brushes demonstrates a much more intricate behavior. At weak to moderate compressions, the effective grafting density concept works well but fails spectacularly at small interbrush separations. We identify two interpenetration regimes for adsorption-active brushes: (i) at separations larger than the ideal Gaussian coil size N1/2, the overlap of the two brushes is concentrated in the mid-plane region, in the same way as in brushes grafted onto non-attractive surfaces; (ii) at separations less than N1/2, the brush overlap is strongly enhanced in the wall regions where the attractive interaction plays an important role both in generating the dense layer for the "proper" brush and in attracting the "foreign" chains. [ABSTRACT FROM AUTHOR]

Self-consistent field (SCF) theory serves as a robust tool for unraveling the intricate behavior exhibited by soft polymeric materials. However, the accuracy and efficiency of SCF calculations are crucially dependent on the numerical methods employed for system discretization and equation-solving. Here, we introduce a simple three dimensional SCF algorithm that uses real-space methods and adaptive discretization, offering improved accuracy and efficiency for simulating polymeric systems at surfaces. Our algorithm's efficacy is demonstrated through simulations of two distinct polymeric systems, namely, block copolymer (BCP) films and polymer brushes. By enhancing spatial resolution in regions influenced by external forces and employing finer contour discretization at grafting chain ends, we achieve significantly more accurate results at very little additional cost, enabling the study of 3D polymeric systems that were previously computationally challenging. To facilitate the widespread use of the algorithm, we have made our 1D-3D SCF code publicly available. [ABSTRACT FROM AUTHOR]

Recently, a novel class of responsive uncharged polymer brushes has been proposed [Klushin et al., J. Chem. Phys. 154(7), 074904 (2021)] where the brush-forming chains have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush with a reduced grafting density. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly as a response to changes in environmental parameters. In this paper, we use numerical self-consistent field calculations to study this phenomenon in polydisperse brushes. Our results reveal an unexpected effect: Although all chains are chemically identical, shorter chains are adsorbed preferentially. Hence, with the increase in the surface affinity parameter, a reduction in the surface grafting density of the residual brush is accompanied by a change in the shape of its molecular mass distribution (MMD). In particular, an originally bidisperse brush can be effectively transformed into a nearly monodisperse one containing only the longer chain fraction. We introduce a method of assigning different chain conformations to one or the other microphase, based on analyzing tail length distributions. In a polydisperse brush with a uniform MMD, short chains are relegated to the adsorbed phase, leading to a narrower effective MMD in the residual brush. Preferential adsorption is not absolute, and longer chains are also partially involved in adsorption. As a result, not only the width of the distribution decreases but also its shape evolves away from the initial uniform distribution. We believe that the effect of preferential adsorption stems from a fundamental property of a polydisperse brush, which is characterized by a spectrum of chemical potential values for monomers belonging to chains of different lengths. Hence, preferential adsorption is also expected in polyelectrolyte brushes; moreover, brush polydispersity would affect coexistence with any other condensed phase, not necessarily related to adsorption. [ABSTRACT FROM AUTHOR]

We propose a novel class of responsive polymer brushes, where the effective grafting density can be controlled by external stimuli. This is achieved by using end-grafted polymer chains that have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly and in a controlled way as a response to changes in environmental parameters. The effect is demonstrated by numerical self-consistent field calculations and analyzed by scaling arguments. Since the thickness of the denser layer is about a few monomer sizes, its capacity to form a microphase is limited by the product of the brush chain length and the grafting density. We explore the range of chain lengths and grafting densities where the effect is most pronounced. In this range, the SCF studies suggest that individual chains inside the brush show large rapid fluctuations between two states that are separated by only a small free energy barrier. The behavior of the brush as a whole, however, does not reflect these large fluctuations, and the effective grafting density varies smoothly as a function of the control parameters. [ABSTRACT FROM AUTHOR]

Intrinsically disordered regions (IDRs) in protein sequences are emerging as functionally important elements for interaction and regulation. While being generally flexible, we previously showed, by observation of experimentally obtained structures, that they contain regions of reduced sequence complexity that have an increased propensity to form structure. Here we expand the universe of cases taking advantage of structural predictions by AlphaFold. Our studies focus on low complexity regions (LCRs) found within IDRs, where these LCRs have only one or two residue types (polyX and polyXY, respectively). In addition to confirming previous observations that polyE and polyEK have a tendency towards helical structure, we find a similar tendency for other LCRs such as polyQ and polyER, most of them including charged residues. We analyzed the position of polyXY containing IDRs within proteins, which allowed us to show that polyAG and polyAK accumulate at the N-terminal, with the latter showing increased helical propensity at that location. Functional enrichment analysis of polyXY with helical propensity indicated functions requiring interaction with RNA and DNA. Our work adds evidence of the function of LCRs in interaction-dependent structuring of disordered regions, encouraging the development of tools for the prediction of their dynamic structural properties. [ABSTRACT FROM AUTHOR]

There is increasing evidence that many intrinsically disordered regions (IDRs) in proteins play key functional roles through interactions with other proteins or nucleic acids. These interactions often exhibit a context-dependent structural behavior. We hypothesize that low complexity regions (LCRs), often found within IDRs, could have a role in inducing local structure in IDRs. To test this, we predicted IDRs in the human proteome and analyzed their structures or those of homologous sequences in the Protein Data Bank (PDB). We then identified two types of simple LCRs within IDRs: regions with only one (polyX or homorepeats) or with only two types of amino acids (polyXY). We were able to assign structural information from the PDB more often to these LCRs than to the surrounding IDRs (polyX 61.8% > polyXY 50.5% > IDRs 39.7%). The most frequently observed polyX and polyXY within IDRs contained E (Glu) or G (Gly). Structural analyses of these sequences and of homologs indicate that polyEK regions induce helical conformations, while the other most frequent LCRs induce coil structures. Our work proposes bioinformatics methods to help in the study of the structural behavior of IDRs and provides a solid basis suggesting a structuring role of LCRs within them. [ABSTRACT FROM AUTHOR]

Using Brownian dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order (in the infinite chain length limit, the stretching degree of the chain jumps discontinuously), the characteristic relaxation time is found to grow according to a power law as the transition point is approached. We present a dynamic effective interface model which reproduces these observations and provides an excellent quantitative description of the simulation data. The generic nature of the theoretical model suggests that the unconventional mixing of features that are characteristic for first-order transitions (a jump in an order parameter) and features that are characteristic of critical points (an anomalous slowdown) may be a common phenomenon in force-driven phase transitions of macromolecules. [ABSTRACT FROM AUTHOR]

Lipid‐based nanoparticles and lipoplexes containing ionizable lipids are among the most successful nanocarriers for mRNA‐based therapies. The molecular structure of these assemblies is still not fully understood, as well as the role played by the ionizable lipids. SAXS experiments have shown that lipoplexes including the ionizable lipid 2‐dioleyloxy‐N,N‐dimethyl‐3‐aminopropane (DODMA), under specific conditions, have a lamellar structure, where lipid bilayers are separated by mRNA‐rich layers, with an overall spacing between 6.5 and 8.0 nm and a complex pH‐dependence. Here, the structure and dynamics of these lipoplexes are investigated at varying pH and mRNA concentration using multiscale molecular dynamics simulations. It is observed that the interaction between DODMA and RNA is slightly attractive only at low pH levels, while it becomes effectively repulsive at high and intermediate pH. This results into a pH‐dependent relocation of the RNA inside the multilayers, from the lipid head groups at low pH to a more uniform distribution inside the hydrophilic slabs of the multilayers at high pH. It is also observed that at high pH, DODMA lipids shift toward the hydrophobic part of the bilayer, consequently increasing their leaflet‐flipping rate, a phenomenon which may ultimately affect the fusion process of the lipoplex with the endosomal membrane. [ABSTRACT FROM AUTHOR]

Exact values for bulk and shear viscosity are important to characterize a fluid, and they are a necessary input for a continuum description. Here we present two novel methods to compute bulk viscosities by non-equilibrium molecular dynamics simulations of steady-state systems with periodic boundary conditions -- one based on frequent particle displacements and one based on the application of external bulk forces with an inhomogeneous force profile. In equilibrium simulations, viscosities can be determined from the stress tensor fluctuations via Green-Kubo relations; however, the correct incorporation of random and dissipative forces is not obvious. We discuss different expressions proposed in the literature and test them at the example of a dissipative particle dynamics fluid. [ABSTRACT FROM AUTHOR]

We study the complex formation between one long polyanion chain and many short oligocation chains by computer simulations. We employ a coarse-grained bead-spring model for the polyelectrolyte chains and model explicitly the small salt ions. We systematically vary the concentration and the length of the oligocation and examine how the oligocations affects the chain conformation, the static structure factor, the radial and axial distribution of various charged species, and the number of bound ions in the complex. At low oligocation concentration, the polyanion has an extended structure. Upon increasing the oligocation concentration, the polyanion chain collapses and forms a compact globule, but the complex still carries a net negative charge. Once the total charge of the oligocations is equal to that of the polyanion, the collapse stops and is replaced by a slow expansion. In this regime, the net charge on the complexes is positive or neutral, depending on the microion concentration in solution. The expansion can be explained by the reduction of the oligocation bridging. We find that the behavior and the structure of the complex are largely independent of the length of oligocations, and very similar to that observed when replacing the oligocations by multivalent salt cations, and conclude that the main driving force keeping the complex together is the release of monovalent counterions and coions. We speculate on the implications of this finding for the problem of controlled oligolyte release and oligolyte substitution. [ABSTRACT FROM AUTHOR]

The reaction of ABm monomers (m = 2, 3) with a multifunctional Bf -type polymer chain ("hypergrafting") is studied by coarse-grained molecular dynamics simulations. The ABm monomers are hypergrafted using the slow monomer addition strategy. Fully dendronized, i.e., perfectly branched polymers are also simulated for comparison. The degree of branching of the molecules obtained with the "hypergrafting" process critically depends on the rate with which monomers attach to inner monomers compared to terminal monomers. This ratio is more favorable if the ABm monomers have lower reactivity, since the free monomers then have time to diffuse inside the chain. Configurational chain properties are also determined, showing that the stretching of the polymer backbone as a consequence of the "hypergrafting" procedure is much less pronounced than for perfectly dendronized chains. Furthermore, we analyze the scaling of various quantities with molecular weight M for large M (M > 100). The Wiener index scales as M2.3, which is intermediate between linear chains (M³) and perfectly branched polymers (M² ln(M)). The polymer size, characterized by the radius of gyration Rg or the hydrodynamic radius Rh, is found to scale as Rg,h ∝ Mν with ν ≈ 0.38, which lies between the exponent of diffusion limited aggregation (ν = 0.4) and the mean-field exponent predicted by Konkolewicz and co-workers [Phys. Rev. Lett. 98, 238301 (2007)] (ν = 0.33). [ABSTRACT FROM AUTHOR]

We propose an efficient simulation algorithm based on the dissipative particle dynamics (DPD) method for studying electrohydrodynamic phenomena in electrolyte fluids. The fluid flow is mimicked with DPD particles while the evolution of the concentration of the ionic species is described using Brownian pseudo particles. The method is designed especially for systems with high salt concentrations, as explicit treatment of the salt ions becomes computationally expensive. For illustration, we apply the method to electro-osmotic flow over patterned, superhydrophobic surfaces. The results are in good agreement with recent theoretical predictions [ABSTRACT FROM AUTHOR]

We report results of dissipative particle dynamics simulations and develop a semi-analytical theory of an anisotropic flow in a parallel-plate channel with two superhydrophobic striped walls. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. It allows us to optimize area fractions, slip lengths, channel thickness, and texture orientation to maximize a transverse flow. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations, and may also find applications in passive microfluidic mixing. [ABSTRACT FROM AUTHOR]

We investigate the properties of membranes under tension by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers. We give a comprising overview of the behavior of several membrane characteristics, such as the area per lipid, the monolayer overlap, the nematic order, and pressure profiles. Both the low-temperature regime, where the membranes are in a gel Lβ′ phase, and the high-temperature regime, where they are in the fluid Lα phase, are considered. In the Lβ′ state, the membrane is hardly influenced by tension. In the fluid state, high tensions lead to structural changes in the membrane, which result in different compressibility regimes. The ripple state Pβ′, which is found at tension zero in the transition regime between Lα and Lβ′, disappears under tension and gives way to an interdigitated phase. We also study the membrane fluctuations in the fluid phase. In the low-tension regime the data can be fitted nicely to a suitably extended elastic theory. At higher tensions the elastic fit consistently underestimates the strength of long-wavelength fluctuations. Finally, we investigate the influence of tension on the effective interaction between simple transmembrane inclusions and show that tension can be used to tune the hydrophobic mismatch interaction between membrane proteins. [ABSTRACT FROM AUTHOR]

We study the adsorption of ideal random lattice copolymers with correlations in the sequences on homogeneous substrates with two different methods: An analytical solution of the problem based on the constrained annealed approximation introduced by Morita in 1964 and the generating function technique, and direct numerical simulations of lattice chains averaged over many realizations of random sequences. Both methods allow to calculate the free energy and different conformational characteristics of the adsorbed chain. The comparison of the results for random copolymers with different degree of correlations and different types of nonadsorbing monomers (neutral or repelling from the surface) shows not only qualitative but a very good quantitative agreement, especially in the cases of Bernoullian and quasialternating random sequences. [ABSTRACT FROM AUTHOR]

We present mesoscopic simulations of the counterion-induced electro-osmotic flow in different electrostatic coupling regimes. Two simulation methods are compared, dissipative particle dynamics (DPD) and coupled lattice-Boltzmann/molecular dynamics (LB/MD). A general mapping scheme to match DPD to LB/MD is developed. For the weak coupling regime, analytic expressions for the flow profiles in the presence of partial-slip as well as no-slip boundary conditions are derived from the Poisson–Boltzmann and Stokes equations, which are in good agreement with the numerical results. The influence of electrofriction and partial slip on the flow profiles is discussed. [ABSTRACT FROM AUTHOR]

We present a large-scale molecular-dynamics study of nematic-paranematic interfaces under shear. We use a model of soft repulsive ellipsoidal particles with well-known equilibrium properties, and consider interfaces which are oriented normal to the direction of the shear gradient (common stress case). The director at the interface is oriented parallel to the interface (planar). A fixed average shear rate is imposed with moving periodic boundary conditions, and the heat is dissipated with a profile-unbiased thermostat. First, we study the properties of the interface at one particular shear rate in detail. The local interfacial profiles and the capillary wave fluctuations of the interfaces are calculated and compared with those of the corresponding equilibrium interface. Under shear, the interfacial width broadens and the capillary wave amplitudes at large wavelengths increase. The strain is distributed inhomogeneously in the system (shear banding), the local shear rate in the nematic region being distinctly higher than in the paranematic region. Surprisingly, we also observe (symmetry-breaking) flow in the vorticity direction, with opposite direction in the nematic and the paranematic state. Finally, we investigate the stability of the interface for other shear rates and construct a nonequilibrium phase diagram. [ABSTRACT FROM AUTHOR]

The effect of surface roughness on the structure of liquid crystalline fluids near solid substrates is studied by Monte Carlo simulations. The liquid crystal is modeled as a fluid of soft ellipsoidal molecules and the substrate is modeled as a hard wall that excludes the centers of mass of the fluid molecules. Surface roughness is introduced by embedding a number of molecules with random positions and orientations within the wall. It is found that the density and order near the wall are reduced as the wall becomes rougher, i.e., the number of embedded molecules is increased). Anchoring coefficients are determined from fluctuations in the reciprocal space order tensor. It is found that the anchoring strength decreases with increasing surface roughness. [ABSTRACT FROM AUTHOR]

We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple equations for the adsorption-desorption transition line. We show that it is preferable to have a small amount of strongly adsorbing sites or monomers rather than a greater amount of weakly adsorbing ones. The results are discussed with respect to their implications for the physics of molecular recognition. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present an analysis of the structure of the fluctuation-induced microemulsion phase in a ternary blend of balanced AB diblock copolymers with equal amounts of A and B homopolymers. To this end, graphical analysis methods are employed to characterize two-dimensional configuration snapshots obtained with the recently introduced field-theoretic Monte Carlo method. We find that a microemulsion forms when the mean curvature diameter of the lamellar phase coincides roughly with the periodicity of the lamellar phase. Further, we provide evidence to the effect of a subclassification of the microemulsion into a genuine and a defect-driven region. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A system of soil ellipsoid molecules confined between two planar walls is studied using classical density-functional theory. Both the isotropic and nematic phases are considered. The excess free energy is evaluated using two different Ansätze and the intermolecular interaction is incorporated using two different direct correlation functions (DCF's). The first is a numerical DCF obtained from simulations of hulk soft ellipsoid fluids and the second is taken from the Parsons-Lee theory. In both the isotropic and nematic phases the numerical DCF gives density and order parameter profiles in reasonable agreement with simulation. The Parsons-Lee DCF also gives reasonable agreement in the isotropic phase but poor agreement in the nematic phase. [ABSTRACT FROM AUTHOR]

Using a reference system approach, we develop an analytical theory for the adsorption of random heteropolymers with exponentially decaying and/or oscillating sequence correlations on planar homogeneous surfaces. We obtain a simple equation for the adsorption-desorption transition line. This result as well as the validity of the reference system approach is tested by a comparison with numerical lattice calculations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

By computer simulations of systems of ellipsoids, we study the influence of the isotropic/nematic phase transition on the direct correlation functions (DCF) in anisotropic fluids. The DCF is determined from the pair distribution function by solving the full Ornstein-Zernike equation, without any approximations. Using a suitable molecular-fixed reference frame, we can distinguish between two qualitatively different contributions to the DCF: One which preserves rotational invariance, and one which breaks it and vanishes in the isotropic phase. We find that the symmetry preserving contribution is barely affected by the phase transition. However, symmetry breaking contributions emerge in the nematic phase and may become quite substantial. Thus the DCF in a nematic fluid is not rotationally invariant. In the isotropic fluid, the DCF is in good agreement with the prediction of the Percus-Yevick theory. [ABSTRACT FROM AUTHOR]

By Monte Carlo simulations of a soft ellipsoid model for liquid crystals, we study whether a layer of grafted liquid-crystalline chain molecules can induce tilt in a nematic fluid. The chains are fairly short (four monomers) and made of the same particles as the solvent. They are attached to a substrate which favors parallel (planar) alignment. At low grafting densities, the substrate dominates and we observe planar alignment. On increasing the grafting density, we find a first order transition from planar to tilted alignment. Beyond the transition, the tilt angle with respect to the surface normal decreases continuously. The range of accessible anchoring angles is quite large. [ABSTRACT FROM AUTHOR]

Studies the size-dependence of interfacial profiles between coexisting phases of polymer mixtures in thin films. Results of Monte Carlo simulations; Capillary wave broadening of the intrinsic profile; Delocalized interfaces in confined geometry; Interfacial profiles; Testing of capillary wave concepts for interfacial fluctuations.

Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions between finite-sized particles in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that at high frequencies, the compressibility of the fluid has a significant impact on the frequency-dependent pair interactions. The predictions of hydrodynamic theory are compared to molecular dynamics simulations of two nanocolloids in a Lennard-Jones fluid. For this system, we reconstruct memory functions by extending the inverse Volterra technique. The simulation data agree very well with the theory, therefore, the theory can be used to implement dynamically consistent hydrodynamic interactions in the increasingly popular field of non-Markovian modeling. [ABSTRACT FROM AUTHOR]

We discuss different mechanisms for curvatureinduced domain formation in multicomponent lipid membranes and present a theoretical model that allows us to study the interplay between the domains. The model represents the membrane by two coupled monolayers, which each carry an additional order parameter field describing the local lipid composition. The spontaneous curvature of each monolayer is coupled to the local composition; moreover, the lipid compositions on opposing monolayers are coupled to each other. Using this model, we calculate the phase behavior of the bilayer in mean-field approximation. The resulting phase diagrams are surprisingly complex and reveal a variety of phases and phase transitions, including a decorated microdomain phase where nanodomains are aligned along the microdomain boundaries. Our results suggest that external membrane tension can be used to control the lateral organization of nanodomains (which might be associated with lipid "rafts") in a multicomponent lipid bilayer. [ABSTRACT FROM AUTHOR]

We review various methods to investigate the statics and the dynamics of collective composition fluctuations in dense polymer mixtures within fluctuating-field approaches. The central idea of fluctuating-field theories is to rewrite the partition function of the interacting multi-chain systems in terms of integrals over auxiliary, often complex, fields, which are introduced by means of appropriate Hubbard--Stratonovich transformations. Thermodynamic averages such as the average composition and the structure factor can be expressed exactly as averages of these fields. We discuss different analytical and numerical approaches to studying such a theory: The self-consistent field approach solves the integrals over the fluctuating fields in saddle-point approximation. Generalized random phase approximations allow one to incorporate Gaussian fluctuations around the saddle point. Field theoretical polymer simulations are used to study the statistical mechanics of the full system with Complex Langevin or Monte Carlo methods. Unfortunately, they are hampered by the presence of a sign problem. In a dense system, the latter can be avoided without losing essential physics by invoking a saddle point approximation for the complex field that couples to the total density. This leads to the external potential theory. We investigate the conditions under which this approximation is accurate. Finally, we discuss recent approaches to formulate realistic time evolution equations for such models. The methods are illustrated by two examples: A study of the fluctuation-induced formation of a polymeric microemulsion in a polymer-copolymer mixture and a study of early-stage spinodal decomposition in a binary blend. [ABSTRACT FROM AUTHOR]