Molecular dynamics simulation of solvent-polymer interdiffusion: Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t(1/2), which is expected for Fickian diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self-diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.     

Diffusion behavior in polymer–clay nanocomposites

This paper reviews our previous studies on the diffusion behavior in polymers clay nanocomposites. A geometric model for predicting the effective diffusivity through this type of systems as a function of clay sheets orientation, volume fraction, polymer clay interaction, and aspect ratio is proposed. Model predictions are compared to the effective diffusivity generated using random walk simulations as well as with predictions obtained from already existing theoretical models. Fair agreement is found between the model prediction and the results of numerical simulations. With respect to the already existing theoretical models, the present mathematical derivation seems more adequate to describe diffusion behavior in conventional nanocomposites systems (i.e. when fillers present very low values of volume to surface ratio). Experimental diffusion tests are discussed and interpreted with the aid of the proposed model. In addition to the aspect ratio and clay concentration, the polymer clay interactions as well as the sheets orientation are the factors controlling the barrier properties of polymer‐layered silicate nanocomposites. Good agreement was found in the case of samples containing exfoliated clay, whereas the model fails in the case of micro‐composites, in which the inorganic lamellae are agglomerated in clusters. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 265–274, 2006     

Process of drying a polymeric paint by diffusion-evaporation and shrinkage. Determination of the concentration-dependent diffusivity

The process of drying a paint made of a dispersion of a polymer in a solvent is experimentally and theoretically studied at various constant temperatures. The diffusion of the solvent through the paint and evaporation from the surface is considered, as well as the subsequent shrinkage. From measurements made at the beginning and at the end of the drying operation on the kinetics of drying, the diffusivity is found to largely depend on the solvent concentration. An exponential relationship of the diffusivity versus the concentration is thus found and successfully tested for the whole process of drying, the diffusivity increasing with the solvent concentration.     

Disentanglement and reptation during dissolution of rubbery polymers

The dissolution mechanism of rubbery polymers was analyzed by dividing the penetrant concentration field into three regimes that delineate three distinctly different transport processes. The solvent penetration into the rubbery polymer was assumed to be Fickian. The mode of mobility of the polymer chains was shown to undergo a change at a critical penetrant concentration expressed as a change in the diffusion coefficient of the polymer. It was assumed that beyond the critical penetrant concentration, reptation was the dominant mode of diffusion. Molecular arguments were invoked to derive expressions for the radius of gyration, the plateau modulus, and the reptation time, thus leading to an expression for the reptation diffusivity. The disentanglement rate was defined as the ratio between the radius of gyration of the polymer and the reptation time. Transport in the second penetrant concentration regime was modeled to occur in a diffusion boundary layer adjacent to the polymer-solvent interface, where a Smoluchowski type diffusion equation was obtained. The model equations were numerically solved using a fully implicit finite difference technique. The results of the simulation were analyzed to ascertain the effect of the polymer molecular weight and its diffusivity on the dissolution process. The results show that the dissolution can be either disentanglement or diffusion controlled depending on the polymer molecular weight and the thickness of the diffusion boundary layer. © 1996 John Wiley & Sons, Inc.     

Solubility,diffusivity, and mobility of n-pentane and ethanol in poly(1-trimethylsilyl-1-propyne)

The diffusion coefficient of ethanol and of n-pentane in PTMSP, at 27°C, was measured as a function of concentration up to a penetrant content of about 12% by weight, for polymer samples obtained through different processes; differential sorptions and desorptions with vapor phases were considered. In the case of ethanol a nonmonotonous behavior was observed for the diffusivity, while in the case of n-pentane the same property was found to monotonously decrease with increasing the penetrant content. The sorption isotherms were also reported, indicating that n-pentane exhibits a typical dual mode behavior, while ethanol follows an unusual s-shape curve. The chemical potential of the dissolved penetrants, calculated directly from the isotherms, shows the very different importance of the energetic interactions of the two penetrants with the polymer units. In spite of the remarkably different concentration dependencies observed for both solubility and diffusivity of the two penetrants, the mobility factors are in both cases monotonously decreasing with the penetrant concentration, and follow very similar trends. The significant differences observed for the concentration dependence of the diffusion coefficients are, thus, associated to the thermodynamic contributions, which are very different for n-pentane and ethanol. Different polymeric films, obtained through different solvent evaporation processes, show quite different solubility, diffusivity and mobility for both ethanol and n-pentane. On the other hand, the ratio between the mobility of the two penetrants as well as the slope of mobility as function of the concentration remains the same for all the different samples inspected. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2245–2258, 1997     

Surface diffusion of metal atoms on polymer substrates during physical vapour deposition

 The surface diffusion of physical-vapour-deposited metal atoms on thermoplastic polymer substrates was investigated. In accordance with the hypothesis of the “classical” atomistic diffusion model, diffusion coefficients are derived from a Monte Carlo simulation. Because the “classical” atomistic diffusion model neglects the desorption of the metal atoms, the absolute diffusion data obtained in our investigations should only be considered as rough estimates. It is more the intention of our work to present relative values in order to correlate the metal surface diffusion on polymer substrates with their physical states (morphologies and surface dynamics). As expected, the diffusivity of metal atoms is strongly influenced by the chemical affinity (“reactivity”) between the metal atoms and the polymer substrate. Furthermore, the diffusivity strongly depends on the physical state of the polymer substrate. On polymer surfaces above the glass-transition temperature the surface diffusivity of metal atoms is 1 order of magnitude higher than the diffusivity below the glass-transition temperature. Received: 9 April 1999/Accepted in revised form: 21 October 1999     

Differential sorption in viscoelastic fluids

The diffusion of organic solvents in concentrated polymer solutions often deviates from the predictions of Fick's second law, especially when the solution is in the glassy state; such behavior is called anomalous or non-Fickian. This paper analyzes the one-dimensional sorption of a solvent into a concentrated polymer solution under a small driving force. The treatment includes the effect of an entanglement network on the process as postulated by Thomas and Windle. The deformation of the entanglement network during sorption creates a normal stress on the solvent equivalent to an osmotic pressure. Including the osmotic pressure gradient in the driving force for solvent diffusion leads to a linear, third-order partial differential equation for solvent concentration distributions. By evaluating the physical constants in the theory for the system methyl acetate/poly(methyl methacrylate) at 30°C the treatment is shown to predict the anomalous characteristics found experimentally.     

Termination rate constant in free-radical polymerization

The specific rate constant for the termination reaction between two flexible polymer molecules with active chain ends has been considered in relation to the segmental diffusion of chain ends in solution. The probability of reaction between two chain ends per unit time when the centers of gravity of two polymer molecules are at a distance of separation has been calculated by using the Smoluchowski equation and a Gaussian distribution of chain ends. The time during which two polymer molecules are in contact has also been calculated by using the diffusion equation and the potential energy function for intermolecular interaction. The rate constant may then be completely expressed as a complex function of the intramolecular linear expansion factor, molecular weight, and the frictional properties of the reacting polymers' segment. This expression predicts that the rate constant is inversely proportional to solvent viscosity, decreasing with increasing molecular weight to some extent, and is affected by the excluded volume effect and chain flexibility. The complete expression for the rate constant has been simplified and the result compared with experimental data. Close agreement is found between the calculated rate constants and those experimentally obtained.     

Prediction and estimation of solvent diffusivities in polyacrylate and polymethacrylates

The relationship between polymer side‐chain length and the hole free volume that is effective for solvent diffusion was investigated for polyacrylates and polymethacrylates on the basis of free‐volume theory. Measurements of a polymer's viscoelasticity and solvent diffusivity provided experimental evidence for polymer segment mobility, and the results indicated that hole free volume in a linear polymer increases with hydrocarbon side‐chain length. Because the molecular mechanisms of polymer viscoelasticity and diffusivity are identical, the free‐volume parameters obtained for polyacrylates and polymethacrylates by measuring the polymer viscoelastic‐temperature dependence can reliably be used in predicting the solvent diffusion coefficient. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1393–1400, 2003     

DYNAMIC LIGHT SCATTERING STUDY ON TRANSLATION DIFFUSION OF 8-ARM STAR POLYSTYRENE IN GOOD AND THETA SOLVENTS

The technique of dynamic light scattering has been used to investigate the translation diffusion behavior of 8-arm star polystyrene (SPS)in a good solvent, tetrahydrofuran (THF) or benzene (BZ) and a theta solvent, cyclohexane (CH), by homodyne photon correlation spectroscopy .The intensityintensity autocorrelation function was analyzed by the method of cumulant. The translation diffusion coefficients have been obtained as a function of temperature and concentration. Under theta condition ,the non-concentration dependence of diffusion coefficient showed the unperturbed Gaussian state o the SPS molecular chain. The different hydrodynamic radii estimated from Stokes- Einstein equation reflected the stretch extent of the arm chain for regular star polymer. The data of diffusion activation energy of SPS in THF, BZ and CH were also obtained respectively.     

Diffusivity of solvent in a polymer solution—expansive free volume effect

The concentration dependency of the diffusivity of a solvent in a polymer solution is derived on the basis of a free volume theory. Applying a molecular kinetics approach, the Fujita-Doolittle equation is modified. The result of numerical simulation reveals that the diffusivity of solvent in a polymer solution depends largely on both the polymer chain structure and its concentration. The applicability of the analytical expression derived is justified by fitting the experimental data for n-alkyl acetate-(poly-methyl acrylate) polymer solutions in the literature.     

Comparison of theory and experiment for diffusion in dilute polymer solutions

Results from a number of theories for the concentration dependence of the mutual diffusion coefficient in dilute polymer solutions are examined, and clarifications are made as to what forms of the equations for these theories should be used in comparisons with experimental diffusivity data. An evaluation of the available theories for the concentration dependence of the diffusivity under theta conditions is carried out using experimental diffusivity data taken using sharp fractions of polystyrene. It is concluded that the Pyun—Fixman theory appears to provide the most promising method for estimating the concentration dependence of the mutual diffusion coefficient in dilute polymer solutions at the present time.     

The evolution of steep fronts in non-fickian polymer-penetrant systems

We adapt a recently proposed model for non-Fickian diffusion of penetrants into polymers and use it to study a drug-delivery problem. The model modified Fick's diffusion equation by the addition of stress-induced flux. A stress evolution equation incorporating aspects of the Maxwell and Kelvin-Voigt viscoelastic stress models completes the model. The relaxation time in the polymer is taken as a function of the penetrant concentration. The system is studied under the assumption that the diffusivity is large. Singular perturbation techniques are used to show that the concentration and stress evolve diffusively for small time, but exhibit steep fronts in a narrow region within the domain for larger time. These predictions are verified numerically for specified parameter values. Finally, the equations are studied in the steady state and are found to predict the evolution of shocks.     

Mean‐field‐theory for polymers in mixed solvents. Thermodynamic and structural properties

Theoretical aspects of polymers in mixed solvents are considered using the Edwards Hamiltonian formalism. Thermodynamic and structural properties are investigated and some predictions are made when the mixed solvent approaches criticality. Both the single and the many chain problems are examined. When the mixed solvent is near criticality without solute, addition of a small amount of polymers shifts the criticality towards either enhanced compatibility or induced phase separation depending upon the value of the parameter describing the interaction asymmetry of the solvents with respect to the polymer. The polymer‐solvent effective interaction parameter increases strongly when the solvent mixture approaches criticality. Accordingly, the apparent excluded volume parameter decreases and may vanish or even become negative. Consequently, the polymer undergoes phase transition from a swollen state to an unperturbed state or even takes a collapsed configuration. The effective potential acting on a test chain in strong solutions is calculated and the concept of Edwards screening discussed. Structural properties of ternary mixtures of polymers in mixed solvents are investigated within the Edwards Hamiltonian model. It is shown that the effective potential on a test chain in strong solutions could be written as an infinite series expansion of terms describing interactions via one chain, two chains etc. This summation can be performed following a similar scheme as in the Ornstein‐Zernike series expansion.     

Influence of the glass transition on solvent self-diffusion in amorphous polymers

The free-volume theory of diffusion is used to analyze the temperature dependence of solvent self-diffusion coefficients both above and below the glass transition temperature at concentrations removed from the pure polymer limit. The glass transition can have a pronounced effect on the temperature dependence of solvent self-diffusion coefficients at small solvent concentrations, but the theory predicts a decreased effect of the transition on the diffusion process with increasing solvent concentration.     

聚乳酸的非等温结晶行为

用差示扫描量热法(DSC)研究聚乳酸(PLA)从熔体及玻璃态为初始条件下的非等温结晶行为,采用Ozawa方程、Mo法、Khanna法和Kissinger法对结晶动力学参数进行计算处理。 实验结果表明,这几种方法均适合处理PLA的非等温结晶过程,而Khanna法提出的结晶速率系数(CRC)能够方便地评价PLA相对结晶速率的大小。 PLA从玻璃态升温结晶比从熔体降温结晶容易得多,升温过程有利于晶核生成,而降温有利于晶体生长。 升温结晶时,升温速率2.0 ℃/min时,结晶焓(ΔH_c)达到最大为27.1 J/g。 从熔体等速降温过程中,随着冷却速率的降低ΔH_c单调增加,冷却速率为0.25 ℃/min时ΔH_c增加到28.3 J/g。 在较低温度下从玻璃态结晶,主要表现为异相成核的二维生长方式。 在较高的温度下从玻璃态升温结晶及从熔体冷却结晶时,以均相成核的三维生长方式结晶为主。 与升温过程相比,冷却不利于晶核的生成,所以导致冷却过程总体ΔH_c偏低,扩散活化能偏大。     

Transfer of liquids between plasticized PVC and acetic acid. Model and experiment

When plasticized PVC is in contact with acetic acid, there is simultaneous diffusion of the liquid into, and the plasticizer out of the polymer. These transfers are controlled by diffusion in the unsteady state, with concentration-dependent diffusivity for both liquids. The transfer process is complicated for acetic acid, because the amount transferred rises quickly to a maximum with a resulting swelling of polymer, and then decreases to the equilibrium value. A model is used for calculating the amount of the liquids transferred at various times, as well as the profiles of concentration developed through the PVC. Short tests help to give information on the kinetics of these transports.     

A mathematical model for stress-driven diffusion in polymers

A model for case II diffusion into polymers is presented. The addition of stress terms to the Fickian flux is used to produce the characteristics progressive front. The stress in turn obeys a concentration-dependent evolution equation. The model equations are analyzed in the limit of small diffusivity for the problem of penetration into a semiinfinite medium. Provided that the coefficient functions obey two monotonicity conditions, the solvent concentration profile is shown to have a steep front that progresses into the medium. The formulas governing the progression of the front are developed. After the front decays away, the long time behavior of the solution is shown to be a similarity solution as in Fickian diffusion. Two techniques for approximating the solvent concentration and the front position are presented. The first approximation method is a series expansion; formulas are given for the initial speed and deceleration of the front. The second approximation method uses a portion of the long time similarity solution to represent the short time solution behind the front.     

Self‐diffusion of small molecules into rubbery polymers: A lattice free‐volume theory

In the framework of the free‐volume (FV) theory, a new equation was derived for the evaluation of self‐diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas–Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self‐diffusion coefficients for several solvent/polymer binary systems confirmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 529–540, 2010     

Diffusion of small molecules in a chitosan/water gel determined by proton localized NMR spectroscopy

Proton localized NMR spectroscopy (MRS) has been applied to study the diffusion of three small molecules, caffeine, theophylline and caprolactam, in chitosan gels with different concentration of water. This technique allows the non-destructive monitorization of diffusant concentration as a function of time and location. Concentration profiles were compared with theoretical curves based on solutions of Fick's diffusion equation for the best fitting, with the appropriate boundary conditions. The measured concentration profiles show a good agreement with the Fickian law. Values of the diffusion coefficients D ranging from 6.1×10(-6) to 3.4×10(-6)cm(2)s(-1) depending on chitosan concentration and type of diffusant molecule were determined. In addition, measurements of diffusion coefficients at equilibrium conditions with proton pulsed field gradient NMR methods supported the observed Fickian behavior and showed values of D in excellent agreement with those determined by proton MRS. All these facts demonstrate that proton MRS is an appropriate method for investigating diffusion process in complex systems, such as polymer gels.