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The structures of amphiphilic block and gradient copolymers in solution and adsorbed onto surfaces are surveyed using molecular-dynamics simulations. A bead-spring model is used to identify the general effects of the different architectures: block and gradient copolymers have equal numbers of solvophilic and solvophobic beads, and the gradient copolymer is represented by a linear concentration profile along the chain. Each type of isolated copolymer forms a structure with a globular head of solvophobic beads, and a coil-like tail of solvophilic beads. The radius of gyration of a gradient copolymer is found to be much more sensitive to temperature than that of a block copolymer due to an unravelling mechanism. At finite concentrations, both gradient and block copolymers self-assemble into micelles, with the gradient copolymers again showing a larger temperature dependence. The micelles are characterised using simulated scattering profiles, which compare favourably to existing experimental data. The adsorption of copolymers onto structureless surfaces is modelled with an attractive potential that is selective for the solvophobic beads, and the surface structures are characterised using the average height of the molecules, and the proportion of beads adsorbed. Both types of copolymer form adsorbed films with persistent micelle-like structures, but the gradient copolymers show a stronger dependence on the strength of the surface interactions and the temperature. Coarse-grained, bead-spring models allow a rapid survey and comparison of the block and gradient architectures, and the results set the scene for future work with atomistic simulations. A superficial but favourable comparison is made between the results from the bead-spring models, and atomistic simulations of a butyl prop-2-enoate/prop-2-enoic acid (butyl acrylate/acrylic acid) copolymer in n-dodecane at room temperature.

Subfractionation of asphaltenes based on their interfacial activity has begun to highlight critical differences between those asphaltenes that are strongly interfacially active (IAA) and the remaining asphaltenes (RA). Following the methods of petroleomics, representative structures of the two asphaltene fractions were determined, reflecting differences in abundant heteroatom groups, carbon number, double-bond equivalents, and single-core/multicore motifs. Using atomistic-potential-based grid-search methods, the intermolecular interactions between asphaltene–asphaltene and asphaltene–solvent (water, heptane, and toluene) were rapidly screened to identify the most favorable and therefore most likely intermolecular interactions to occur. Asphaltene–water interactions were stronger for IAA (abundance-weighted average interaction energy of −9.29 kJ/mol) than for RA (−6.32 kJ/mol), with hydrogen bonding more significant in the IAA–H2O interaction. Dimer interactions of IAA–IAA were stronger than RA–RA, and from the top 100 most favored interactions, the contribution to the total interaction energy was almost exclusively van der Waals for RA–RA (only 3% electrostatic), while for IAA–IAA, electrostatic interactions (9%) and hydrogen bonding (2%) were significant contributors in the most favored interactions. As the relative contribution of the electrostatic interaction increased, the dimer orientation less resembled that of a π–π stack. With the conception of petroleomics and large structural databases, the grid-search method is a useful atomic/molecular screening approach that provides an ideal triaging tool to rapidly assess a wide range of different molecular structures and interactions. The method is complementary to the more computationally expensive precision molecular modeling tools that are not suited to such workflows.

A workflow for tailor-made additive screening and crystallization control using a combination of molecular modeling and experimental techniques is presented. The impact of seven structurally analog...

The interplay between the solution chemistry and crystallisability of eicosane in mixed toluene : acetone solutions is examined over the full compositional range from pure toluene to pure acetone, using a combination of polythermal crystallisation experiments and molecular modelling. Enthalpies of dissolution and mixing, as well as metastable zone widths increase with increasing acetone content, up to a mol fraction of 0.85 acetone, followed by a decrease in values to pure acetone solutions. Nucleation is found to occur via an instantaneous pathway for the pure solvent systems and also when toluene is in excess, in contrast to solutions where acetone is in excess, which are found to nucleate progressively. Rationalisation through molecular modelling highlights likely changes in the solution structure, whereby eicosane can be expected to be preferentially solvated by toluene, with this solvated cluster being surrounded by a ‘cage’ of acetone molecules. This proposed structure is consistent with a model whereby solute diffusion and hence clustering is hindered when acetone is in excess, decreasing the crystallisability of the solution and effecting a change in the mechanism of nucleation. However, above a critical acetone composition, the potential for complete toluene solvation is restricted and easier crystallisation is enabled.

Asphaltenes are a complex mixture of molecular structures with a variety of functionalities, which in turn impacts their physical properties. Discriminating between asphaltenes that are strongly and weakly interfacially active is providing a new direction to mitigate asphaltene-related problems. Whole asphaltenes (WA) were extracted from a South American heavy crude oil, further fractionated into interfacially active asphaltenes (IAA) and remaining asphaltenes (RA), and molecularly characterized by positive-ion (+) atmospheric pressure photoionization (APPI) using a 9.4 T Fourier transform ion cyclotron mass spectrometer (FT-ICR MS). The IAA fraction was found to contain a greater abundance of heteroatoms with >50% of IAA containing two or more heteroatoms as compared to ∼30% for RA. The IAA fraction was enriched in oxygen-containing species, more specifically higher-order Ox and OxSy groups that were predominantly of low DBE. Gas-phase fragmentation of RA and IAA precursor ions (m/z 650) by infrared multiphoton dissociation (IRMPD) revealed an abundance of multi-core motifs in IAA, while RA was found to be a mixture of single-core and multi-core structures. Analysis of the fragmented ions showed a prevalence of nitrogen-containing species of high DBE (aromatic molecular structures), while oxygen-containing species were most likely associated with aliphatic side chains. Extrography fractionation of RA and IAA verified the abundance of multi-core motifs in IAA, which were highly polar and of low DBE and carbon number. These “atypical” structures of IAA are classified as asphaltenes as a result of their functionality and polarity rather than high aromaticity.

Using the extended-SARA method to fractionate asphaltenes based on their interfacial activity, the current study reports the first results on the estimated size and shape of interfacially active asphaltene (IAA) and remaining asphaltene (RA) nanoaggregates. These fractions have been reported to exhibit distinctly different chemical architectures that influence the size of asphaltene clusters in good and poor solvents. However, little is known about the building blocks, commonly referred to as nanoaggregates, which form these clusters and how those subtle differences in chemical architecture impact aggregation of asphaltenes. The nanoaggregate size and shape of IAA and RA was measured using small-angle neutron scattering (SANS). The characteristic length and asymptotic power-law exponent of whole asphaltenes (WAs) extracted from heavy crude oil and dispersed in deuterated toluene were 28.0 ± 0.2 A and 2.86 ± 0.01, respectively, showing negligible variations with changing asphaltene concentration, source of asphaltenes (bitumen and heavy crude oil), and solvent aromaticity. For RA fractions, which account for 98.5 wt % of WA, the characteristic length and power-law exponent of 28.8 A and 2.86 were comparable to that of WA but in contrast to 59.7 A and 2.20 for IAA. A ∼100% increase in the characteristic length and reduced power-law exponent of the IAA fraction confirms that these two asphaltene subfractions form dissimilar nanoaggregate structures.

Funder: Infineum UK Ltd, A novel neutron and X-ray reflectometry sample environment is presented for the study of surface-active molecules at solid–liquid interfaces under shear. Neutron reflectometry was successfully used to characterise the iron oxide–dodecane interface at a shear rate of 7.0×102s-1 using a combination of conventional reflectometry theory coupled with the summation of reflected intensities to describe reflectivity from thicker films. Additionally, the structure adopted by glycerol monooleate (GMO), an Organic Friction Modifier, when adsorbed at the iron oxide–dodecane interface at a shear rate of 7.0×102s-1 was studied. It was found that GMO forms a surface layer that appears unaltered by the effect of shear, where the thickness of the GMO layer was found to be 24.3-10.2+9.9 Å under direct shear at 7.0×102s-1 and 25.8-5.2+4.4 Å when not directly under shear. Finally, a model to analyse X-ray reflectometry data collected with the sample environment is also described and applied to data collected at 3.0×103s-1.

The nucleation kinetics of the alpha form of p‐aminobenzoic acid from ethanolic and aqueous solutions is examined through a comparative examination of temperature‐jump and anti‐solvent drown‐out isothermal crystallization methodologies. Analysis of the data reveals the measured induction times, and the calculated effective interfacial tensions as a function of the supersaturation show broadly equivalent behavior for the aqueous‐ethanol mixed‐solvent drown‐out and temperature‐jump ethanol solution systems, confirming the comparability of the two methodologies. The results also demonstrate poorer agreement with the temperature‐jump pure aqueous system, highlighting the importance of the strength of solvation/desolvation as the key rate‐limiting process for the overall nucleation behavior.

The data presented in this article relates to the crystallisation of hexadecane (C16H34) and octadecane (C18H38), being the predominant alkanes present in hydrotreated vegetable oil (HVO), from solvents representative of fuel (dodecane, toluene and kerosene). Data was collected for eleven C16H34/C18H38 compositions for each solvent used. Raw crystallisation and dissolution data is provided over a range of solution concentrations and cooling rates used under a poly-thermal crystallisation methodology. Equilibrium saturation temperature data is also presented for each composition, concentration and solvent system, indicating the trend in solubility for each solution.

The crystallisation of methyl stearate under a range of crystallisation conditions has been studied and three new polymorphs have been identified and structurally characterised. Form III (monoclinic, space group Cc, Z = 8) was obtained at room temperature by slow evaporation of a saturated solution in CS2. Form IV (monoclinic, space group C2/c, Z = 4) was obtained by slow cooling of the melt. Both structures were characterised by single crystal X-ray diffraction. Form V (monoclinic, space group Cc, Z = 4) was obtained from the melt by rapid cooling. X-ray and neutron powder diffraction methods were employed in the determination of this structure. Form V shows highly anisotropic thermal expansion, with expansion along the crystallographic b-axis being substantially greater than along the other two axes.

A route to the accelerated nucleation of α-para-aminobenzoic acid in ethanol/water (EtOH/H2O) mixed solvent solutions, using antisolvent crystallization, is presented. An isothermal by design approach is adopted, whereby the exothermic enthalpy of mixing associated with antisolvent addition is offset by the control of the temperature of the antisolvent added. Induction times (τ) are found to be reduced by 4 orders of magnitude using this methodology, consistent with the use of this approach as a nucleation acceleration technique. Calculation of the nucleation kinetic parameters for a range of solution concentrations, compositions, and supersaturations (S) reveal that effective interfacial tensions (γeff) vary from 8.4 to 2.3 mJ m–2 from solutions in H2O solvent and EtOH solvent, respectively, in line with the trend in solubility. The critical nucleus radius (r*) decreases from 1.98 to 0.40 nm associated with a decrease in the number of molecules in the critical nucleus (i*) from 196 to 2 molecules. A change in nucleation mechanism from heterogeneous nucleation to homogeneous nucleation is observed to take place at S ≈ 1.5. Limitations, particularly with focus toward larger-scale operation, are highlighted together with potential solutions to overcome such aspects.

The structure and frictional properties of glycerol monooleate (GMO) in organic solvents, with and without water impurity, confined and sheared between two mica surfaces are examined using molecular dynamics simulations. The structure of the fluid is characterized in various ways, and the differences between systems with nonaggregated GMO and with preformed GMO reverse micelles are examined. Preformed reverse micelles are metastable under static conditions in all systems. In n-heptane under shear conditions, with or without water, preformed GMO reverse micelles remain intact and adsorb onto one surface or another, becoming surface micelles. In dry toluene, preformed reverse micelles break apart under shear, while in the presence of water, the reverse micelles survive and become surface micelles. In all systems under static and shear conditions, nonaggregated GMO adsorbs onto both surfaces with roughly equal probability. Added water is strongly associated with the GMO, irrespective of shear or the form of the added GMO. In all cases, with increasing shear rate, the GMO molecules flatten on the surface, and the kinetic friction coefficient increases. Under low-shear conditions, the friction is insensitive to the form of the GMO added, whereas the presence of water is found to lead to a small reduction in friction. Under high-shear conditions, the presence of reverse micelles leads to a significant reduction in friction, whereas the presence of water increases the friction in n-heptane and decreases the friction in toluene.

The solubility and crystallisability of a range of binary mixtures of n-hexadecane (C16H34) and n-octadecane (C18H38), as the predominant alkanes present in hydrotreated vegetable oil (HVO), from three representative fuel solutions (dodecane, toluene and kerosene) is presented. The dissolution (saturation) and crystallisation (supersaturation) points of the solutions are measured using poly-thermal methods utilising turbidometric detection over four concentrations from (192 g/l to 400 g/l). The data reveals the existence of more soluble, less stable crystal structures that form from the alkane mixtures, when compared to the stable triclinic crystal structures formed from the single solute component solutions. An increased carbon chain length results in lower solubility for all three solvents and the solvent type is not found to have any significant effect on the solid forms produced from the mixtures. van’t Hoff analysis reveals the solvent type to influence the solute solubility with the closest to ideal behaviour being dodecane followed by kerosene and toluene, respectively. This finding is further supported by the calculated dissolution enthalpies and activity coefficients, which are the lowest in dodecane followed by kerosene and toluene. Larger values of activity coefficients are observed for compositions with molar fraction (y) = 0.1, 0.5–0.7 C18H38 which reflect the complex multi-phase formation in the solutions when compared with the more simple binary melt crystallisation system.

Atomistic molecular dynamics simulations are used to study the self-assembly and friction of glycerol monooleate mixed with with oleic acid, glycerol, calcium oleate, or water in n-heptane and toluene solvents. The aim is to determine how chemical degradation products of glycerol monooleate could lead to changes in structural and frictional properties. In bulk solution, almost all mixtures studied contain self-assembled reverse micelles. Under confinement between shearedmica surfaces, the reverse micelles disintegrate, but the distribution of molecules between the surfaces and the centre of the fluid layer depends sensitively on the chemical composition, with more polar mixtures showing stronger adsorption. The measured kinetic friction coefficient is correlated with the extent of surface adsorption: while degradation products lead to increases inthe friction coefficient in most cases, all changes are more pronounced when there is less surface adsorption.

The formation of glycerol monooleate reverse micelles in n-heptane and toluene at room temperature is studied using molecular-dynamics simulations and small-angle neutron scattering. The glycerol monooleate concentrations under consideration are in the range of 5-20 wt %. Under these conditions, spontaneous reverse-micelle formation is observed on the simulation timescale (up to 30 ns). From simulations, the typical dimensions (semiaxes) of the equivalent ellipsoids with the same masses and moments of inertia are in the range of 15-23 Å, with instantaneous shapes that are slightly nonspherical. By analyzing the scattering form factors from simulation and experiment, the radii of gyration of the reverse micelles are determined to be approximately 15 Å. The number of glycerol monooleate molecules in a reverse micelle is smaller in toluene (∼20) than in n-heptane (∼30), but the overall dimensions are similar due to greater penetration of the toluene in to the reverse micelle. The effects of low concentrations (1 wt %) of water, acetic acid, and ethanol on the reverse-micelle dimensions are determined. The overall structural effects are small, but the distributions of the molecules within the reverse micelles are shown to be sensitive to the molecular polarity.

The effect of hydrotropes on the geometry of reverse water-in-oil AOT-microemulsions is investigated as a function of water content, and hydrotrope additive architecture. SANS reveals that hydrotropes induce cylindrical morphologies which transition to ellipsoidal and then spherical geometries with increasing water content (w). The length of the elongated particles appeared to show some dependence on the hydrotrope-AOT tail compatibility, which is also reflected in the phase behaviour of these systems. This is the first report of hydrotrope-induced axial elongation of water microemulsions in the oil phase.

Dynamic light scattering (DLS) was used to map the stability of an aqueous silica colloid in the presence of differing concentrations of sodium polystyrene sulphonate (PSS) and sodium chloride (NaCl). Additionally, values of PSS size with salt and PSS osmotic pressure were measured as a function of PSS concentration. Six theoretical maps based on DLVO and simple depletion theory were then constructed as a comparison to the experimental map using the measured values as well as two theoretical values of PSS size and osmotic pressure. It was found that DLVO overestimates the effect of salt screening and of the various comparisons those calculated using size and osmotic pressure derived from a PSS chain with 1 charge between 5 monomers showed the greatest similarities to the experimental work.

The focused beam reflectance (FBRM) method is a relatively new method, developed to perform particle size measurements in the range 0.8–1000 μm. The particle size determined is given in terms of a chord length. The relationship between chord length and particle size obtained using other methods (image analysis and Malvern Mastersizer) has been investigated. The advantage of the FBRM method is the ability to perform in-situ particle size analysis in real time, without the need for sampling or dilution. In this work, we study the effects of various experimental factors (e.g. agitation rate and particle concentration) on FBRM measurements, and compare the size distributions with those obtained by other sizing methods. FBRM has also been used for studying the formation of (oil-in-water) emulsion droplets (with a droplet size >100 μm) with time under shear, where both sampling and dilution may affect the droplet size distribution.

The work described focuses on a two-stage process for the production of large porous suspension polymer beads of defined particle size and narrow size distribution. Emulsification has been performed using purpose built cross-flow membrane equipment, which allows controlled production of large emulsion droplets with a much narrower size distribution. The work described compares the production of large emulsion droplets of monomer prepared both by agitation and using a cross-flow membrane. The effects of variations in the pore size of the membrane and flow-rates on the size of the emulsion droplets produced are also investigated. The second stage of the process is polymerisation of performed monomer emulsion droplets using a continuous tubular reactor. Samples polymerised using such a method show a narrower size distribution than similar systems polymerised as a batch.

The conventional method employed for the production of large beaded particles is suspension polymerisation. A review of suspension polymerisation is presented, with particular reference to variations in chemical composition of the component phases. Both oil-in-water and water-in-oil systems are considered, as are the relevant methods of droplet stabilisation for such systems. Factors governing droplet stability and particle size and morphology are discussed. New developments including the use of continuous type reactors are also included.

Large, cross-linked polymer beads have been produced by suspension polymerization. The surface area of the beads can be increased by making the structure porous by the addition of an inert solvent to the droplet phase. Kinetic measurements have been performed with systematic changes in monomer ratio (styrene–glycidyl methacrylate), with an increase in glycidyl methacrylate concentration leading to an increase in reaction rate. The effects of changing the initiator type have also been studied, the use of azobisisobutyronitrile, as opposed to benzoyl peroxide, results in higher reaction rates and higher yields. The effects of these variations on both the emulsion and bead droplet size distributions have also been studied. An increase in styrene concentration has no significant effect on the average size of the emulsion droplets, but increases the final bead size. The average pore size and specific surface areas of the polymer beads (determined from BET isotherms) have also been investigated.

HypothesisInitial studies (Hopkins Hatzopoulos et al. (2013)) have shown that ionic hydrotropic additives can drive a sphere-to-cylinder (ellipsoid) transition in water-in-oil (w/o) microemulsions stabilized by the anionic surfactant Aerosol-OT; however the origins of this behaviour remained unclear. Here systematic effects of chemical structure are explored with a new set of hydrotropes, in terms of an aromatic versus a saturated cyclic hydrophobic group, and linear chain length of alkyl carboxylates. It is proposed that hydrotrope-induced microemulsion sphere-to-cylinder (ellipsoid) transitions are linked to additive hydrophobicity, and so a correlation between the bulk aqueous phase critical aggregation concentration (cac) and perturbation of microemulsion structure is expected.ExperimentsWater-in-oil microemulsions were formulated as a function of water content w (= [water]/[AOT]) and concentration of different hydrotropes, being either cyclic (sodium benzoate or sodium cyclohexanoate), or linear chain systems (sodium hexanoate, sodium heptanoate and sodium octanoate). Phase behaviour studies were performed as a function of w, additive type and temperature at total surfactant concentration [ST] = 0.10 M and constant mole fraction x = 0.10 (x = [hydrotrope]/[ST]). Microemulsion domain structures were investigated by small-angle neutron scattering (SANS), and these data were fitted by structural models to yield information on the shapes (spheres, ellipsoids or cylinders) and sizes of the nanodroplets.FindingsUnder the conditions of study hydrotrope chemical structure has a significant effect on microemulsion structure: sodium cyclohexanoate does not induce the formation of cylindrical/ellipsoidal nanodroplets, whereas the aromatic analogue sodium benzoate does. Furthermore, the short chain sodium hexanoate does not cause anisotropic microemulsions, but the more hydrophobic longer chain heptanoate and octanoate analogues do induce sphere-to-ellipsoid transitions. This study shows that underlying microemulsion structures can be tuned by hydrotropes, and that the strength of the effect can be identified with hydrotrope hydrophobicity in terms of the bulk aqueous phase cac.

The physicochemical behavior of the phenyl-n-alkanoate (PhenCx) and cyclohexyl-n-alkanoate (CyclohexCx) series has been investigated, supporting previous work on the understanding of hydrotropes (Hopkins Hatzopoulos, M.; Eastoe, J.; Dowding, P.J.; Rogers, S. E.; Heenan, R.; Dyer, R. Langmuir2011, 27, 12346-12353). Electrical conductivity, surface tension, 1H NMR, and small-angle neutron scattering (SANS) were used to study adsorption and aggregation in terms of critical aggregation concentration (cac). The PhenCx series exhibited very similar d log(cac)/dn to n-alkylbenzoates (CnBenz), exhibiting two branches of behavior, with a common inflection point at four linear carbons, whereas the CyclohexCx series showed no break point. Electrical conductivity and 1H NMR concentration scans indicate a difference in physicochemical behavior between higher and lower homologues in both the PhenCx and CyclohexCx series. Surface tension measurements with compounds belonging to either group gave typical Gibbs adsorption profiles, having d log(cac)/dn curves consistent with limiting headgroup areas in the region of (35-55 Å 2) indicating monolayer formation. SANS profiles showed no evidence for aggregates below the electrical conductivity determined cac values, inferring an "on-off" mode of aggregation. Analyses of SANS profiles was consistent with charged ellipsoidal aggregates, persisting from lower through to higher homologues in both the PhenCx and CyclohexCx series.

Mixed 'hard-soft' colloidal systems have been generated in which the 'hard' components (80 nm diameter silica nanoparticles) coexist with a population of 'soft' microemulsion droplets, both structures stabilised by the anionic surfactant sodium bis(ethylhexyl)sulfosuccinate (AOT) with toluene as solvent. The addition of water to swell the inverse micelles to form microemulsion droplets appears to increase attractive interactions between the silica particles (determined by DLS), possibly due to adsorption of some water at the silica-toluene interface; however, long-term stability of the dispersions is maintained. Small-angle neutron scattering was used to examine the structures present in these new colloidal systems.

The synthesis and study of oil-soluble metal carbonate colloids are of interest in the area of lubricant additives. These surfactant-stabilised nanoparticles are important components in marine and automotive engine oils. Recently introduced, environmentally driven legislation has focused on lowering of gaseous emissions by placing limits on the levels of phosphorous sulphur and ash allowed in engine oil systems. These chemical limits, coupled with improved engine performance and extended oil drainage intervals, have lead to renewed interest in the production of stable, efficient nanodetergent systems. To date, this has resulted in modification of existing surfactant structures and development of new generations of surfactants. This review covers the current state of research in the area of nanodetergents.

The characterization of temperature- and pH-sensitive poly-N-isopropylacrylamide (poly-NIPAM) microgel particles, produced by surfactant-free emulsion polymerization, has been extensively reported. In the work described here poly(NIPAM) gel particles, cross-linked with N-N'-methylenebisacrylamide (BA), have been produced using inverse suspension polymerization. These particles have been termed "minigels" here since they are somewhat larger than conventional microgels. Results suggest that minigel particles are formed as a dilute suspension, within the aqueous dispersed (droplet) phase. The hydrodynamic diameter of the minigel particles produced in this work is/=2.5 µm, at 25 degrees C. The effects of temperature and pH changes, variation in cross-linker concentration, and incorporation of a charged comonomer (methacrylic acid, MAA) have been investigated. Both poly(NIPAM-BA) and poly(NIPAM-BA-MAA) minigel particles are temperature sensitive with swelling behavior consistent with comparable microgels. Variations in pH were found to effect the size of minigels containing ionizable groups (such as a carboxylate) by a mechanism of increased electrostatic repulsion of charged groups with increasing pH. Overall, the production of temperature- and/or pH-sensitive polymers by inverse suspension polymerization results in particles with swelling characteristics similar to those produced by emulsion polymerization, albeit with differing particle sizes. Copyright 2000 Academic Press.

The adsorption of surfactants from dilute oil solutions on to solid surfaces is studied as a function of surface curvature and surface coverage. Coarse-grained molecular models, computer simulations, and umbrella sampling are used to compute the dependence of the free energy of adsorption on to a spherical colloid surface with radius R. It is shown that for fixed surface coverage, and with all other things being equal, the free energy of adsorption decreases with decreasing R. For fixed surface curvature, the free energy of adsorption increases with increasing surface coverage. These trends arise from the excluded-volume interactions between the surfactant tails. The dependence on surface curvature is due to the geometrical effect of there being more free volume for the surfactant tails with a smaller colloid radius. The consequences of these effects on equilibrium partitioning are examined. It is shown that for surfactants adsorbed on small-colloid and large-colloid surfaces in mutual equilibrium with a dilute solution, the surface coverage of the small particles is significantly greater. The implications for industrial applications are discussed and could be significant.