Continuum formulation of the Scheutjens-Fleer lattice statistical theory for homopolymer adsorption from solution

Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n(1,e) and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction phi; both n(1,e) and phi enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z < or = 2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z = 2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z < or = 2l, continuum for distances z > 2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.     

MICELLIZATION STUDIES OF DODECYL BENZENESULFONIC ACID AND ITS INTERACTION WITH POLYVINYLPYRROLIDONE

Dodecyl benzenesulfonic acid (DBSA) surfactant was used in the present study to find the effect of concentration on its electrical conductance in solution from 293-323K above and below the critical micelle concentration (CMC). The micellization parameters i.e. degree of counter ion binding (β), aggregation number (n) and number of counter ion micelle(m) were measured. The interaction of DBSA with polyvinylpyrrolidone (PVP) was also studied at 293K throughconductance and surface tension measure ments. A number of important parameters i.e. critical aggregation concentration (CAC), Gibb‘s free energy (△G) and binding ratio (R) were determined and the effect of NaCl on the CAC and polymer saturation point (PSP) was also investigated.     

Static and dynamic properties of tethered chains at adsorbing surfaces: a Monte Carlo study

We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain's extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength epsilon(c) one has M(c) approximately N(phi), and we find (using the above results) as best candidate phi to equal 0.59. However, slight changes in the estimation of epsilon(c) lead to large deviations in the resulting phi; this might be a possible reason for the difference in the phi values reported in the literature. We also investigate the dynamical scaling behavior at epsilon(c), by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at epsilon(c) the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum.     

The critical adsorption point of self-avoiding walks: a finite-size scaling approach

The critical adsorption of self-avoiding polymer chain in a simple cubic lattice onto a flat surface is studied with Monte Carlo simulations. The dependence of number of surface contacts M on chain length N and polymer-surface interaction epsilon is investigated by a finite-size scaling approach. We estimate the critical adsorption point epsilon(c)=0.291+/-0.002 and the exponent phi=0.54+/-0.01. The asymptotic behaviors M proportional variant N for epsilon>epsilon(c) and M proportional variant N(0) for epsilon相似文献   

Effect of surface grafted polymers on the adsorption of different model proteins

Adsorption of a model protein to a surface with end-grafted polymers was studied by Monte Carlo simulations. In the model the effect on protein adsorption in the presence of end-grafted polymers was evaluated by calculating the change in free energy between an end-grafted surface and a surface without polymers. The change in free energy was calculated using statistical mechanical perturbation theory. Apart from ordinary athermal polymer-polymer and protein-polymer interactions we also study a broad selection of systems by varying the interaction between proteins and polymers and effective polymer-solvent interactions. The interactions between the molecules span an interval from -0.5 to +0.5 kT. Consequently, general features of protein adsorption to end-grafted surfaces is investigated by systematically changing properties like hydrophilicity/hydrophobicity of the polymer, protein and surface as well as grafting density, degree of polymerization and protein size. Increasing grafting density as well as degree of polymerization decreases the adsorption of protein except in systems with attractive polymer-protein interactions, where adsorption increases with increasing chain length and higher grafting density. At a critical polymer-protein interaction neither chain length nor grafting density affects the free energy of adsorption. Hydrophilic polymers were found to prevent adsorption better than hydrophobic polymers. Very small particles with radii comparable to the size of a polymer segment were, however, better excluded from the surface when using hydrophobic than hydrophilic polymers. For systems with attractive polymer-protein interaction not only the volume of the protein was shown to be of importance but also the size of the exposed surface.     

Colloidal aggregation in polymer blends

We consider here a low-density assembly of colloidal particles immersed in a critical polymer mixture of two chemically incompatible polymers. We assume that, close to the critical point of the free mixture, the colloids prefer to be surrounded by one polymer (critical adsorption). As result, one is assisted to a reversible colloidal aggregation in the nonpreferred phase, due the existence of a long-range attractive Casimir force between particles. This aggregation is a phase transition driving the colloidal system from dilute to dense phases, as the usual gas-liquid transition. We are interested in a quantitative investigation of the phase diagram of the immersed colloids. We suppose that the positions of particles are disordered, and the disorder is quenched and follows a Gaussian distribution. To apprehend the problem, use is made of the standard phi(4) theory, where the field phi represents the composition fluctuation (order parameter), combined with the standard cumulant method. First, we derive the expression of the effective free energy of colloids and show that this is of Flory-Huggins type. Second, we find that the interaction parameter u between colloids is simply a linear combination of the isotherm compressibility and specific heat of the free mixture. Third, with the help of the derived effective free energy, we determine the complete shape of the phase diagram (binodal and spinodal) in the (Psi,u) plane, with Psi as the volume fraction of immersed colloids. The continuous "gas-liquid" transition occurs at some critical point K of coordinates (Psi(c) = 0.5,u(c) = 2). Finally, we emphasize that the present work is a natural extension of that, relative to simple liquid mixtures incorporating colloids.     

微接触印刷法制造聚合物多层次准三维立体微结构

Microstructures of various polymers, such as polystyrene and polymethyl methacrylate, were fabricated with microcontact printing, directly using the corresponding dilute polymeric solutions as “inks”, whose concentrations were about 10 g/L. By repeatedly cross-stamping with the inks, multilayer quasi-three-dimensional polymeric microstructures could be obtained. Both optical photographs and SEM photos showed clear microstructures, which were nearly accurate replication of the original patterns in the PDMS stamps. Microlines of poly-bis-(p-toluene sulfonate)-2,4-hexadiyne-1,6-diol) (PTS) were also fabricated by first processed microcontact printing with solution of the corresponding monomer TS/acetone as ink, then followed with UV polymerization of the monomer micropatterns at solid state. Unlike small molecule processes, the molecules of polymeric inks did not self assembly on the surface of substrates. The formation of polymeric microstructures could be ascribed to the fact that, after volatilization of solvents, polymers tend to stick to the surface of glass substrate which has higher surface free energy (about 72 mN/m), but not to the surface of PDMS stamp which has lower surface free energy (about 20 mN/m). Also the microcontact printing process was studied with optical microscopy, and the main factor--volatilization time of solvent was discussed. The results showed that the volatilization time of solvent is very crucial to the process of polymeric microcontact printing, and with too longer or too shorter volatilization time, the obtained microstructures would become discontinuous or distorted, respectively. For example, with a polystyrene/chloroform solution as ink, the optimal volatilization time was about 15~20 s.     

Modelling aqueous solutions near the critical point of water

We review the thermodynamic properties of dilute solution near the critical point of the solvent. Two examples are discussed, a solution of a non-electrolyte and a solution of an electrolyte. The limiting behavior of the electrolyte solutions is modelled with a Debye-Huckel term in the Helmholtz free energy. The partial molar properties, in particular the volume and isobaric thermal expansion are examined in detail. The derivation of these properties is introduced by considering the geometry of the thermodynamic surfaces near to and far from the critical point of the solvent. We conclude that the properties of solutions near the solvent critical point are dominated by that feature; solution properties cannot be adequately modelled without including the functional forms associated with the critical point.     

TEMPERATURE DEPENDENCE OF THE FLUORESCENCE SPECTRA OF LADDERLIKE POLYPHENYLSILSESQUIOXANE AND LADDERLIKE 1,4-PHENYLENE-BRIDGED POLYVINYLSILOXANE

Fluorescence spectra of ladderlike polyphenylsilsesquioxane (LPPS) and ladderlike 1,4-phenylene-bridgedpolyvinylsiloxane (LPPVS) have been measured as a function of temperature (4-55℃), in dilute tetrahydrofuran solution.The excimer (I_E) to monomer (I_M) intensity ratio (I_E/I_M) of LPPS dilute solution shows a double linear Arrhenius plot with abreak point ascribable to a transition temperature T_t This behavior has not been found for single chain polyorganosiloxanes.When InI_E of LPPS was plotted against I/T it also gave a double linear plot with one break point, which was found in singlechain polyorganosiloxanes. The different behaviors between LPPS and single chain polyorganosiloxanes may be mainlyattributed to the relatively rigid double-chain macromolecular backbone of LPPS. However, the In(I_E/I_M) of dilute LPPVSsolution versus I/T shows a simple linear variation with a positive slope which confirms our proposition. The differencebetween the fluorescence results of LPPS and those of LPPVS may possibly derive from their structure differences andcooperative motion in backbone chain bonds.     

Adsorption of hydrophobically modified polyelectrolytes at the n-octane/water interface

The interfacial activity of polyelectrolytes carrying alkyl side chains of different length has been studied. Potassium salts of poly(maleic acid-co-1-olefins), PA-n K2 with n=12 , 14, 16, 18, were synthesized, and the interfacial tension at the aqueous solution/n -octane interface was measured as a function of the length of the alkyl side chain. The results show that the interfacial tension lowering, the limiting excess concentration Gamma (m), and the efficiency of adsorption pC (20) depend on the number of methylene groups in the alkyl side chain. According to Rosen the last two parameters define two different contributions to the standard free energy of adsorption: one arises from the distribution of the polymer between the bulk of the solution and the interface Delta G (dist )(0), and another comes from the configuration adopted at the interface Delta G (int )(0). These free energies were plotted as a function of the number of carbon atoms in the alkyl side chain and a linear relation was found for both of them. From these plots contributions of 0.83 and -0.58 per methylene group were determined for Delta G (0)(dist ) and Delta G (0)(int ), respectively. The positive value for the incremental free energy of distribution is attributed to the formation of a polymer micelle which is stabilized by longer alkyl side chains. On the other hand, the negative value for Delta G (0)(int ) indicates that at the interface the polymer adopts a configuration where the hydrocarbon tail is interacting with the octane molecules.     

Transition from Incomplete to Complete Wetting of Solid Surface in Polymer–Solvent System: 2. The Regime of Strong Adsorption

The transition from incomplete to complete wetting of the solid surface by a semidilute polymer solution coexisting at equilibrium with the very-dilute polymer solution was studied using the Canh–de Gennes theory under the conditions corresponding to the tricritical state of semidilute solution and strong adsorption of the chain units on a substrate. It was established that the wetting transition can occur as the first- or second-order phase transition or as the transition of tricritical wetting depending on the repulsion energy of segments that are on the substrate surface. Near the temperatures of these transitions, the character of the variations in the differences of surface concentrations that are established at the boundaries of the substrate with semidilute and dilute polymer solutions, as well as in the differences of interfacial tensions and the cosine of contact angle were determined. It was shown that the temperature of each of these phase transitions varies in proportion to the surface potential of the substrate and does not depend on the polymer molecular mass. The observed behavior differs essentially from that established near the critical point of a polymer–solvent system.     

Effects of gemini surfactants on egg phosphatidylcholine bilayers in the fluid lamellar phase

The influence of 1,4-butanediamonium-N,N'-dialkyl-N,N,N',N'-tetramethyl dibromides (CmA, m = 7-16 is the number of alkyl carbons) on the egg yolk phosphatidylcholine (EYPC) bilayer thickness and lipid surface area at the bilayer-aqueous phase interface is studied using X-ray diffraction on fluid lamellar CmA + EYPC + H2O phases as a function of CmA:EYPC and H2O:EYPC molar ratios and the alkyl chain length m. At the constant CmA:EYPC = 0.4 and H2O:EYPC = 18 molar ratios, the CmA induced bilayer thickness decrease shows a minimum and the lipid surface area increase a maximum at the alkyl chain length m = 9. The obtained results are discussed in the context of a structural perturbation model of the cut-off effect in biological potencies of surfactants which occurs when increasing the alkyl substituent chain length above the critical value.     

Size‐, Shape‐ and Composition‐Dependent Alloying Ability of Bimetallic Nanoparticles

Based on the surface‐area‐difference model, the formation enthalpies and the formation Gibbs free energies of bimetallic nanoparticles are calculated by considering size and shape effects. Composition–critical size diagrams were graphed for bulk immiscible bimetallic nanoparticles with the developed model. The results reveal that both the formation enthalpy and formation Gibbs free energy decrease with the decrease of particle size. The effect of rising temperature is similar to the diminishing of particle size on reducing the formation Gibbs free energy. Contrary to the positive formation enthalpy of the bulk immiscible system, a negative formation enthalpy is obtained when the particles are smaller than a critical size. With the decrease of size, the alloying process first takes place in the dilute solute regions, then broadens to the dense solute regions and finally, particles with all compositions can be alloyed. The composition–critical size diagram is classified into three regions by the critical size curves with shape factors of 1 and 1.49, that is, the non‐alloying region, alloying region and possible alloying region. The model predictions correspond well with experimental evidences and computer simulation results for Cu–Ag, Au–Ni, Ag–Pt and Au–Pt systems.     

自溶液中的吸附 VII: 硅胶自环己烷中吸附醇,酮和酯

The adsorption isotherms of some monofunctional alcohols, ketones and esters from cyclohexane onto silica gel have been determined at 30`C and 10`C. The silica gel used bad a BET area of 417 m2/g and an average pore radius of 45A. The concentrations of free and associated hydroxyls on the silica gel were 1.4 and 4.1/100A^2 respectively. The adsorption order is cyclohexanol>n-octyl alcohol>cyclohexanone>methyl isobutyl ketone>n-propyl acetate=n-amyl acetate. The adsorption decreases with increasing temperature as normal. Except at very low concentrations, the isotherms can be represented by the Langmuir equation. The limiting adsorption, nms, on the silica gel does not accord with the stoichiometric ratio (1:1) between the free surface hydroxyl groups of the adsorbent and the adsorbate. In addition to surface conditions and the functional group of the adsorbate, it seems that the limiting adsorption is also controlled by the other factors, including temperature, solvent, and, sometimes the chain length of the adsorbate. The standard free energy (ΔG0) and standard enthalpy (ΔH0) of the adsorbates in adsorptien processes have been determined from the Langmuir parameters. The results indicate that the absolute value of ΔH0 is higher than that of ΔG0 (in other words, standard entropy ΔS0 is negative), as in the case of the adsorption of gases. Since there is practically no difference in ΔG0 or ΔH0 of adsorption between alcohols or esters, it is suggested that in dilute solution only the polar groups take part in adsorption, and the hydrocarben chains remain in solution during the adsorption process. For ketones, the absolute values of ΔG0 and ΔH0 are somewhat lower for methyl isobutyl ketone than that for cyclohexanone. A possible explanation is that in the adsorbed state the isobutyl chain of the methyl isobutyl ketone may somewhat close to the surface and thus decreases the adsorption and changes the ΔG0 and ΔH0.     

Photophysical properties of discogenic triaryl pyrylium salts Excimer migration in columnar liquid crystals

The photophysical properties of a homologous series of 2, 4-6-triaryl pyrylium tetrafluoroborates substituted by six alkoxy chains (C_nH_2n+1O, n = 2, 3, 4, 5, 8, 12) are reported. in dilute solution, the electronic absorption and fluorescence spectra do not depend on the length of the alkoxy chains while both fluorescence lifetimes and fluorescence quantum yields increase when the chain length increases. Monomer and excimer fluorescence is observed with the pure compounds; the steady state and time resolved emission spectra and the decay kinetics which do not depend on the chain length suggest that the columnar structure exist with very short lateral chains. Excimer lifetimes determined in the liquid-crystalline phases follow an exponential law as a function of the reciprocal temperature: τ ∝ exp (E_M/RT). The activation energy for excimer migration is 0.046 eV, 0.061 eV and 0.087 eV respectively for n = 5, 8 and 12.     

Polymer modifies the critical region of the coexisting liquid phases

Several recent conceptual advances, which take advantage of the polymer conformation in the near critical point of coexisting liquid phases and practical techniques of some unique molecular interactions between polymer chain and the solvent molecules, have been made to allow the investigation of the effect of the well-defined polymer in phase separation of binary mixtures. The behavior of a flexible linear or branched chain polymer (polyethylene oxide, PEO, MW = 9 x 10(5), as an impurity) in the critical binary mixture of isobutyric acid (I) + water (W) was studied by the refractive index (n) measurements using a very accurate and sensitive refractometer. The refractive index in each phase of IW as well as three different PEO concentrations (C = 0.395, 0.796, and 1.605 mg/cm(3)) in the near critical composition of IW have been measured at temperatures below the system's upper critical point. We observed that the polymer was significantly affected in the critical region of IW and these various concentrations of PEO show an important behavior on the critical exponents (beta), the critical temperatures (T(c)), and critical composition (phi(c)), which are depicting the shape of the coexistence curve. The phase-transition region of coexisting phases of IW shifts down with the addition of PEO and T(c) decreases linearly with increasing PEO concentrations. This may indicate that the polymer chain entangles with each phase, thereby the polymer monomers strongly interact with neighbor solvent particles and also intrachain interaction between the polymer segments. At such conditions, the collapse of polymer chain is possible in the vicinity of the critical point. At temperatures T close enough to T(c), the critical exponent beta (defined by the relation (n(1) - n(2)) proportional, variant (T(c) - T)(beta), with n(1) and n(2) being the refractive indices of the coexisting phases) was found to decrease from 0.382 to 0.360 when the PEO concentration changes from 0.395 to 1.605 mg/cm(3). These values are higher than that of 0.326 +/- 0.005 of pure IW, which is compatible with the three-dimensional Ising value beta = 0.325. The observed critical exponents for the PEO in IW are fully renormalized Ising critical exponents. Besides, the phi(c) values decrease with increasing the C values in the mixture of IW. It appears that the shape of the PEO in IW coexistence curves is similar from that of pure IW.     

Adsorption kinetics of 1-alkanethiols on hydrogenated Ge(111)

We have investigated the liquid-phase self-assembly of 1-alkanethiols (HS(CH2)n-1CH3, n = 8, 16, and 18) on hydrogenated Ge(111), using attenuated total reflection Fourier transform infrared spectroscopy as well as water contact angle measurements. The infrared absorbance of C-H stretching modes of alkanethiolates on Ge, in conjunction with water contact angle measurements, demonstrates that the final packing density is a function of alkanethiol concentration in 2-propanol and its chain length. High concentration and long alkyl chain increase the steady-state surface coverage of alkanethiolates. A critical chain length exists between n = 8 and 16, above which the adsorption kinetics is comparable for all long alkyl chain 1-alkanethiols. The steady-state coverage of hexadecanethiolates, representing long-chain alkanethiolates, reaches a maximum at approximately 5.9 x 10(14) hexadecanethiolates/cm2 in 1 M solution. The characteristic time constant to reach a steady state also decreases with increasing chain length. This chain length dependence is attributed to the attractive chain-to-chain interaction in long-alkyl-chain self-assembled monolayers, which reduces the desorption-to-adsorption rate ratio (kd/ka). We also report the adsorption and desorption rate constants (ka and kd) of 1-hexadecanethiol on hydrogenated Ge(111) at room temperature. The alkanethiol adsorption is a two-step process following a first-order Langmuir isotherm: (1) fast adsorption with ka = 2.4 +/- 0.2 cm3/(mol s) and kd = (8.2 +/- 0.5) x 10(-6)(s-1); (2) slow adsorption with ka = 0.8 +/- 0.5 cm3/(mol s) and kd = (3 +/- 2) x 10(-6) s(-1).     

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.