Theory of adsorption of macromolecules in cylindrical pores and at surfaces of cylindrical shape

A rigorous theory of adsorption of a Gaussian chain of infinite length into cylindrically shaped pores and onto cylindrical surfaces of arbitrary diameter, D, has been developed for any energy of interaction ??. The change in the conformational free energy of a chain arriving inside the pores from an unrestricted volume is proportional to $\text{(D1)}{}^{\mathrm{?2}}$ ($\text{D1}$ is the effective pore width) over the entire molecular-sieve range (?? < ??_c). In the exclusion range (?? < 0), when the interaction of chain units with the adsorbent exhibits repulsive type forces, $\text{D1}$ is approximately equal to D. As the adsorption forces of attraction increase (0 < ?? < ??_c) the value of $\text{D1}$ increases and becomes infinite at the critical point. This makes it possible to use a single adsorbent for effective chromatographic separation of polymers over a wide range of molecular weights. In the adsorption range, where ?? > ??_c, the conformational free energy of the chain is virtually independent of the width and shape of the pores and is determined mainly by the value of ??. At the critical point, ?? = ??_c, the probability of the arrival of a polymer chain in the pore is independent of both the width and shape of the pore and is determined only by the ratio of geometrical volumes of the free volume to the pore volume. For cylindrical pores, a weak dependence of ??_c on D is observed only for narrow pores. This dependence virtually disappears on passing to adsorbents with wide pores. Consideration of the adsorption of the macromolecule on the outer surface of the cylinder showed that at any finite value of the diameter of the cylinder, D, adsorption occurs as an ‘infinite-order’ phase transition. The maximum value of the specific heat

$\text{(C}{}_{\mathrm{p}}\text{max}\text{k}\text{=}\text{25}\text{3}\text{=?}{}^2{}_{\mathrm{c}}$

does not depend on D. The degree of bonding of the macromolecule to the adsorbent increases with decreasing curvature of the surface, rapidly attaining values characteristic of chain adsorption on a plane.     

Potentiometric study of poly(l-glutamic acid) in water-dioxane mixtures

The potentiometric behaviour of poly(l-glutamic acid) (PLGA) has been studied in several water-dioxane mixtures and 0.2 M NaCl/dioxane mixtures. The intrinsic ionization constant pK₀ was found to increase with dioxane content and decreasing temperature. This variation of pK₀ with dioxane content can be explained by the variation of the dielectric constant, ? of the solvent. The free energy change ΔF° associated with the helix-coil transition for the uncharged conformers has been determined. At 25°C, the absolute value of ΔF° increases when decreasing the dielectric constant (i.e. when increasing the dioxane content) but the comparison with the experimental results of other authors show that a change in ? is not sufficient to explain the variations of ΔF° in all solvent mixtures. The temperature dependence of ΔF° in different 0.2 M NaCl/dioxane mixtures was determined between 3° and 55°C. The experimental results show that the stabilization of the α helix by dioxane has an entropic origin as it was already found for a 0.1 M KCl/ethanol/PLGA system. In the absence of salt, a sharp change in the variation of ΔF° is observed for the solvent composition at which a solvent induced conformational transition occurs, along with a change in the absolute adsorption of dioxane on the PLGA molecule. The free energy change involved in the adsorption of a molecule of dioxane on a PLGA residue has been evaluated.     

Octadecyl grafted MCM-41 silica spheres using trifunctionalsilane precursors – preparation and characterization

MCM-41 silica spheres were prepared via the pseudomorphic route. Subsequent surface modification of the mesoporous silica spheres was achieved by two silylating agents, n-octadecyltrihydridosilane and n-octadecyltrimethoxysilane, which provided different surface coverages. The MCM-41 pore structure, surface properties and morphological features were examined by small angle X-ray scattering, nitrogen adsorption–desorption and scanning electron microscopy. The investigations revealed an influence of the silica source on the mesoporous structure, as reflected by a higher long-range order for the pores in MCM-41 spheres prepared from Kromasil silica. Surface modification is accompanied by a reduction of the surface area, pore diameter and pore volume of the MCM-41 materials, whereas the spherical morphology of the spheres is retained. The degree of grafting and cross-linking of the alkylsilanes was determined by ²⁹Si NMR spectroscopy. A higher degree of alkyl chain grafting was observed for the solvent extracted MCM-41 spheres and for samples prepared via surface polymerization.FTIR and ¹³C NMR spectroscopies were employed to study the conformational behaviour and mobility of the grafted octadecyl chains. The conformational order was found to strongly depend on the history of the MCM-41 supports (calcination, solvent extraction) and on the actual surface modification procedure. In general, a lower conformational order was observed for the present mesoporous alkyl modified silica spheres as compared to conventional C₁₈ modified silica gels which is mainly attributed to the lower surface coverage.     

Effect of ligand chain length on hydrophobic charge induction chromatography revealed by molecular dynamics simulations

Hydrophobic charge induction chromatography (HCIC) is a mixed-mode chromatography which is advantageous for high adsorption capacity and facile elution. The effect of the ligand chain length on protein behavior in HCIC was studied. A coarse-grain adsorbent pore model established in an earlier work was modified to construct adsorbents with different chain lengths, including one with shorter ligands (CL2) and one with longer ligands (CL4). The adsorption, desorption, and conformational transition of the proteins with CL2 and CL4 were examined using molecular dynamics simulations. The ligand chain length has a significant effect on both the probability and the irreversibility of the adsorption/desorption. Longer ligands reduced the energy barrier of adsorption, leading to stronger and more irreversible adsorption, as well as a little more unfolding of the protein. The simulation results elucidated the effect of the ligand chain length, which is beneficial for the rational design of adsorbents and parameter optimization for high-performance HCIC.     

Polydisperse Brush with the Linear Density Profile

Macromolecules densely end-grafted to a planar solid surface form a polymer monolayer (brush). It is known that, in a good solvent, the density profile of monodisperse brushes parabolically decays on moving away from the plane. Using the analytical theory and computer simulation methods, we studied the structure of a polydisperse brush from homopolymers, for which molecular-mass distribution is set by the Schulz–Zimm distribution. It is found that, at a polydispersity index of 1.143, the polymer brush in a good solvent has a linear density profile. In this brush, the average distance of chain ends to the grafting plane is proportional to the square of their contour length. If any chain of the brush is chemically modified so that it will be able to adsorb on the grafting surface, then the adsorption of this chain inside the brush will proceed via a discontinuous first-order phase transition with the bimodal distribution of the order parameter (free end height). This transition has unusual features: the energy of adsorption corresponding to the midpoint of the transition is proportional to the contour length of the adsorbing chain N, the sharpness of the transition is proportional to N², and the height of the barrier separating adsorbed and desorbed states is proportional to N³. The predicted dependences are verified by computer simulation.     

Transition of the bounded polymer layer to a rigid amorphous phase: A computational and DSC study

The study focuses on the transition of the bounded to solid surfaces polymer layer to a rigid amorphous phase (RAP). Based on previous Monte Carlo (MC) simulation studies on bulk polyethylene (PE), we refine our numerical variable density Self Consistent Field (nSCF) method in order the calculated density in bulk to follow the predictions of the MC simulation. The proposed modification of the Sanchez–Lacombe equation of state allows us to examine thermodynamic aspects of the glass transition. By imposing a glass transition (T_g = 220 K) in the bulk we predict an earlier (during cooling), stronger transition of the bounded layer to a RAP, at ∼350 K. Also at short separation distances we record the appearance of undisturbed polymer bridges. Differential scanning calorimetry (DSC) experiments on polydimethylsiloxane (PDMS) and polyamide 6 (PA6) nanocomposites suggest that although the crystallization can be significantly suppressed by the addition of nanoparticles, the RAP layer may locally equilibrate, above T_g, for long experimental times with the melt phase. Our results support the idea that a significant free energy barrier of entropic origin appears due to the RAP formation, below the melting temperature (T_m) and above the T_g.     

The phase behaviors of adsorbed polymethylene chains

The phase behaviors of a single adsorbed polymethylene chain are investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, i.e., the coil-to-globule transition, and finite chain length effects are considered since the critical region may depend on the chain length. When the chain is adsorbed on an attractive surface, however, the equilibrium properties may not only depend on chain length but also depend on the adsorption energy. For short chain of N = 40 monomers, a coil-to-globule transition is found for weak adsorption energy of w = 2.5 kcal/mol, but the critical temperature is lower than the free chain, and for strong adsorptions of w = 3.5 and 4.5 kcal/mol, the structures at low temperatures are adsorbed hairpin like, so we may call the transition process coil-to-hairpin transition. For long chains of N = 80 monomers and N = 120 monomers, the critical regions are the same for the free chains both at T = 265 K, and for the adsorption energies of w = 2.5, 3.5, and 4.5 kcal/mol, the curves of the heat capacities are smooth when T > 200 K, and while T < 200 K, the values of the heat capacities decrease as the temperatures decreasing, so the transition may be from loose globular structures to compact globular structures, and for more stronger adsorption energy of w = 6.5 and 8.5 kcal/mol, the critical regions are obvious and they are coil-to-crystal like transitions.     

Computer simulations of the conformations of strongly adsorbed chains at the solid-liquid interface

We have utilized molecular dynamics simulations to critically study the conformation of isolated polymer chains adsorbed on surfaces in the presence of explicit solvent. The changes in conformations of the polymer chain in good solvent as it adsorbs onto a substrate is mapped. The quasi two-dimensional pancake conformation of a well adsorbed polymer chain is confirmed. The effect of wetting characteristics of the solvent on the adsorption transition of polymer chain is also studied. We found that a non-wetting solvent aids adsorption of the polymer chain even at low sticking energies compared to wetting solvent.     

Characterization of asymmetric hollow fibre membranes with graded-density skins

Asymmetric hollow fibre membranes can be prepared from polysulphone, polyethersulphone, and polyphenylsulphone by phase inversion from Lewis acid:base complex solvent systems. Formation of a complex from the non-solvent (Lewis acid) and the solvent (Lewis base) permits higher concentrations of non-solvent to be included in the spinning dope than can be added with traditional solvent/non-solvent mixtures. These membranes exhibit gas permeation rates which are a multiple of those obtained with membranes fabricated from traditional solvent/non-solvent mixtures as well as maintenance of selectivity. This enhancement in permeation performance results primarily from the creation of a skin structure with a much thinner effective separating layer than can be obtained from spinning processes utilizing solvent/non-solvent mixtures. However, it is also believed that these membranes possess enhanced free volume which is derived from the kinetics of the sol-to-gel transition. The rapid dissociation of the Lewis acid:base complex by contact with water accelerates the coagulation process, which limits conformational rearrangement. The dissociation of the Lewis acid:base complex into smaller moieties facilitates their removal from the nascent hollow fibre membranes. The acceleration of the coagulation process increases the free volume in the resultant membrane, which is reflected by an increase in the glass transition temperature that disappears upon annealing. This increase is readily seen during the first heat in a DSC scan, and it is believed that this increase is not a result of superheating, which yields the ‘T_g overshoot’ commonly observed in glassy polymers annealed below their glass transition temperatures.     

Free volume behavior in spincast thin film of polystyrene by energy variable positron annihilation lifetime spectroscopy

Free volume behavior in polystyrene thin films with thickness ranging from 22 to 1200 nm on silicon substrates was studied by energy variable positron annihilation lifetime spectroscopy (EVPALS). The films were prepared by spincasting from toluene solutions of 0.5-5.0 wt% polystyrene with M_w = 1?090?000 g/mol. Distinct deviations from bulk polystyrene in thermal expansion of the free volume holes and the glass transition temperature associated with free volume behavior were observed for the thinnest film with 22 nm thickness, indicating its exclusively high chain mobility. Comparison of the polystyrene concentration in the precursor solution around the overlap concentration suggests that the high chain mobility is due to less entangled chains caused by rapid removal of the solvent from the diluted solution in order to prepare very thin film.     

Monte Carlo模拟对称型三嵌段共聚高分子的吸附

The adsorption behavior of symmetric triblock copolymers, Am/2BnAm/2, from a nonselective solvent at solid-liquid interface has been studied by Monte Carlo simulations on a simple lattice model. Either segment A or segment B is attractive, while the other is non-attractive to the surface. Influences of the adsorption energy,bulk concentration, chain composition and chain length on the microstructure of adsorbed layers are presented.The results show that the total surface coverage and the adsorption amount increases monotonically as the bulk concentration increases. The larger the adsorption energy and the higher the fraction of adsorbing segments, the higher the total surface coverage is exhibited. The product of surface coverage and the proportion of non-attractive segments are nearly independent of the chain length, and the logarithm of the adsorption amount is a linear function of the reciprocal of the reduced temperature. When the adsorption energy is larger, the adsorption amount exhibits a maximum as the fraction of adsorbing segment increases. The adsorption isotherms of copolymers with different length of non-attractive segments can be mapped onto a single curve under given adsorption energy. The adsorption layer thickness decreases as the adsorption energy and the fraction of adsorbing segments increases, but it increhses as the length of non-attractive segments increases. The tails mainly govern the adsorption layer thickness.     

Analysis of the Adsorption of Alkanes on High Surface Area Cellulose by Inverse Gas Chromatography

The adsorption characteristics of alkanes on high surface area cellulose were investigated by inverse gas chromatography.

The enthalpy and entropy of adsorption of alkanes on the solvent exchanged cellulose were greater than the values on non-porous cellulose. The difference in the heats of adsorption of alkanes between the non-porous and the solvent exchanged cellulose was greater for larger molecules indicating stronger interaction for the higher alkanes in the pore structure. For n-hexane the differences in enthalpy and entropy of adsorption were 17 kJ/mole and 52 J/mole K, respectively. The London component of the surface free energy of adsorption was 116 mN/m for the solvent exchanged cellulose.     

Conformational transition characterization of glass transition behavior of polymers

The conformational transition behavior of polymer in the amorphous state has been investigated through molecular dynamics simulations across the glass transition temperature (T_g). We find that the conformational transition, a localized and short time dynamics feature, crosses over different barrier heights when the system transforms from the molten state into the glass state and the barrier height in the glass state is markedly lower than that above T_g. In addition to the overall transition behavior, the specific transitions between the rotational isomeric states (RIS) g⁺, t⁻, t⁺ and g⁻ are also investigated in detail. The populations of these specific transitions undergo considerable changes when the temperature decreases; meanwhile, the larger transition rates of the ending torsions get diminished. Besides the rate, the rotation degrees of the dihedrals during the transitions also change their distributions tremendously through T_g, below which most of the larger transition angles (50-100°) were inhibited remaining those sharply around 30°. This possibly explains why below T_g the conformational transition process has a lower effective barrier.     

Glass transition dynamics and structural relaxation of PLLA studied by DSC: Influence of crystallinity

Poly(l-lactic acid), PLLA, in amorphous and semi-crystalline forms were studied by DSC, in order to investigate both molecular dynamics and structural relaxation features, and to understand the influence of the crystalline confinement on the segmental mobility of the intra-spherulitic amorphous phase. Experimental data were generated after submitting the materials to different thermal histories below T_g and were treated with a model based on the configurational entropy concept, allowing to extract a series of physical-meaningful parameters and to obtain the temperature dependence of the relaxation times. The main features of the relaxation process in the glassy state (activation energy of the glassy state and x) and the fragility index were found to be apparently insensitive to crystallinity. Significant differences between the two materials were detected in both the position of the glass transition temperature and the width of the distribution of relaxation times. In the framework of the Adam and Gibbs theory, it is suggested that for the semi-cristalline PLLA the mobility of the amorphous chains is more or less restricted, depending on their distance to the rigid lamellar walls or on the intra-lamellar thickness; this will imply that their conformational motions will take place at different temperatures, typically above the glass transition temperature of the (unconfined) bulk amorphous phase.     

Molecular dynamics simulation of cis-1,4-polybutadiene. 2. Chain motion and origin of the fast process

Molecular dynamics (MD) simulations of cis-1,4-polybutadiene in bulk amorphous state were performed to elucidate the origin of a fast relaxation process observed by quasielastic neutron scattering (QENS) measurements. The details of the torsional motion for each dihedral angle were investigated with the torsional auto- and cross-correlation functions for several temperatures in this study. Temperature dependence of the correlation between the torsional autocorrelation and cross-correlation functions is also evaluated. The origin of the fast process of cis-1,4-polybutadiene is found to be mainly the cooperative conformational transitions of two dihedral angles located at both sides of the CH₂-CH₂ bond when the bond is in the trans conformation. The cooperative conformational transitions exhibit even below the glass transition temperature of cis-1,4-polybutadiene. The cooperative motion appears at about 50 K below the glass transition temperature, corresponding to the Vogel-Fulcher temperature.     

On the form of adsorption isotherms for substitutional adsorption of molecules of different sizes

Adsorption from solution occurs by solvent displacement in the interphase. When the adsorbate differs appreciably in size from the previously adsorbed solvent, the relative size factor (x) of adsorbate and solvent determines (a) the form of the relation for free energy of adsorption and (b) the form of the configurational function in terms of fractional coverage θ or site fraction X. Various types of isotherms that have been proposed for this situation are critically compared in relation to the statistics of the solvent-lattice replacement process that occurs in adsorption, eg, of organic substances at electrodes. It is concluded that the correct configurational term to be used when x > 1 is θ/e^x?1 (1 ?θ)^x. Using this term in an equilibrium adsorption isotherm then allows standard free energies of adsorption and derived quantities to be properly calculated from experimental coverage or surface excess measurements.It is shown that it is strictly incorrect to refer to an isotherm containing the configurational term θ/x(1 ?θ)^x as the “Flory—Huggins isotherm,” since Flory—Huggins statistics leads to an isotherm having a different form for the configurational term, viz that containing e^x?1, as above.For adsorption of molecules for which x > 1, failure to include the size factor term in the isotherm leads to errors in the evaluation of any interaction effects in the adsorption behaviour.     

Elastic behavior of adsorbed single compact chains

Elastic behaviors of short single two-dimensional compact chains adsorbed on the attractive surface are investigated in this paper by using the enumeration calculation method. In our model a single compact chain is fixed with one of its end at a position above the impenetrable surface, and then it is pulled away from the attractive surface slowly through elastic force acting. We investigate the chain size and shape of adsorbed compact chains, such as mean-square end-to-end distance per bond 〈R²〉/N mean-square radii of gyration per bond 〈S²〉_x/N and 〈S²〉_y/N, shape factors 〈δ〉, and fraction of adsorbed monomers f_a in order to illuminate how the size and shape of adsorbed compact chains change during the process of tensile elongation. Especially for strong attraction interaction there are some special behaviors in the chain size and shape during this process. If there exits adsorption interaction, single compact chain is first almost pulled down to the adsorption surface and then moves in the direction of force until to leave the adsorption surface. These changes become more obvious with strong adsorption interaction. Our calculation can show this elastic process of adsorbed compact chains visually and simply. On the other hand, some thermodynamics properties are also studied here. We use average energy per bond, average Helmholtz free energy per bond, elastic force f and energy contribution to elastic force f_u to study the elastic behavior of adsorbed single compact chains in the process of tensile elongation. Elastic force f has a long plateau during the tensile elongation for strong adsorption interaction, which agrees well with experimental and theoretical ones. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

The rotational and translational dynamics of molecular hydrogen physisorbed in activated carbon: A direct probe of microporosity and hydrogen storage performance

We have measured Incoherent Inelastic Neutron Scattering (IINS) spectra of H₂ physisorbed in high purity chemically activated carbon (AC) at different surface coverage and at temperatures near the triple point of bulk hydrogen. Our experimental results and DFT calculations show that at low surface coverage, due to the very low corrugation of the adsorption potential, and in the absence of H₂-H₂ lateral interactions, the adsorbed molecules are practically free to translate in the 2D plane parallel to the surface. Model calculations show that a complete mixing between the sub-states of the J = 1 manifold occurs on the free surface. The J = 0-to-1 rotational transition should split if the H₂ molecule is adsorbed in a slit type pore. Rotational splitting of up to 13 meV is found in the narrowest pores of around 6 Å investigated. The calculated isosteric heat of adsorption for molecules adsorbed on the free surface, at different sites and molecule orientations, range between −39 and −42 meV/H₂ at 77 K. In the optimum size slit pores, these numbers double up. Micropore volume of 0.34-0.45 ml/g carbon, and an upper limit of 4 wt% hydrogen storage is anticipated for the investigated material.     

Effect of temperature and solvent composition on the unperturbed dimensions of polystyrene

Several procedures have been used to establish and verify the unperturbed state of polystyrene in 1-chlorodecane (θ = 6.2° C) and 3-methyl cyclohexanol (θ = 98.4° C) as well as in other single solvents having 6.2° < θ < 98.4°. At each θ-temperature for a single solvent, the unperturbed state for a binary solvent was established in mixtures of 1-chlorodecane and 3-methyl cyclohexanol of varying composition. Viscometric measurements showed that neither the nature of the solvent nor the temperature affects the unperturbed chain dimensions appreciably. On the other hand, the unperturbed mean square radius of gyration measured directly by light scattering exhibits a definite decrease with increase in temperature, which accords qualitatively with the conformational energy calculations of Flory and co-workers.