Leszek Jarecki

Dynamic modelling of melt spinning

Abstract Dynamics of melt spinning is reconsidered to determine essential effects in modelling of the process. Basic dynamic equations are reformulated with heat production due to viscous friction in the melt, as well as for non-isochoric deformation. Viscoelastic effects are accounted for by applying co-rotational Maxwell fluid model. Different cooling (heating) zones are taken into account with different cross-blow velocity and temperature of the cooling medium. Crystallization is included in the set of basic equations, and specific effects of crystallization on spinning are calculated. Example computations of velocity, temperature and stress profiles are performed for melt spinning of PET fibres with extreme spinning conditions.

Theoretical analysis of oriented and non-isothermal crystallization III. Kinetics of crystal orientation

SummaryA general orientation equation for rigid particles embedded in a continuum has been derived. The equation includes hydrodynamic, thermodynamic, diffusional and kinetic terms, corresponding to physically different orientation mechanisms. Some special solutions of the general equation are presented, and discussed conditions under which the general equation reduces to more simple cases. Numerical examples of orientation in polyethylene subjected to uniaxial forces are discussed.

Ultra-high modulus polyethylene. 1 Effect of drawing temperature

Abstract Drawing behaviour and the properties of ultra-drawn high density polyethylene have been investigated as a function of the drawing temperature. An optimum temperature has been found for each type of polyethylene, at which the best drawing behaviour is found. It appears that the temperature range for effective drawing (leading to a high draw ratio and high Youngs modulus) depends on the molecular weight and its distribution. The temperature range of the effective drawing is shifted towards higher temperatures for polyethylene exhibiting broader molecular weight distribution and higher weightaverage molecular weight. Ultra-high modulus and transport samples have been obtained by drawing high density polyethylene with broad molecular weight distribution ( M w M n ∼ 20 and M w ∼ 200 000 ) at higher drawing temperatures. It has been found that in the range of drawing temperatures 80–105°C the modulus of this polyethylene is higher for samples drawn at higher temperatures. Transparent samples with draw ratios of 35–40 and with Youngs moduli of 600–650 kbar (at room temperature) have been obtained by drawing the polyethylene at 100°–105°C. We conclude that the high molecular fraction in the polyethylene, forming tie molecules in the drawn material, is responsible for the high modulus, while the low molecular weight fraction facilitates alignment of the long chains and retards the internal voiding (whitening) to a very high draw ratio during drawing at the higher temperatures.

Potential energy barriers in the kinetic theory of nucleation

The problem of partition of the transition free energy δf among the potential barriers for cluster growth (U+i−1) and dissociation (U−i) is discussed. The proposed simple solutions U+i−1=e+zδfi, U−i=e−(1−z)δfi, and z= 1/2 [1+sign(δfi)] satisfy all requirements imposed on the problem. Consequently, in the nucleation theory two different critical cluster sizes appear: i*0, which corresponds to the change of sign of δfi and transition in the potentials U+i−1, U−i, and i* (generally different from i*0 ), which accounts for nucleation rate.

Dynamics of hot-tube spinning from crystallizing polymer melts

Abstract Computer modeling is applied to discuss hot-tube effects in melt spinning from crystallizing polymers. The set of spinning equations used in the model accounts for stress-induced crystallization, crystallinity-dependent melt viscosity and heat of crystallization. Example computations are performed for polyethylene terephthalate assuming temperature-dependent Newtonian viscosity, strongly modified by crystallization. The consequence of coupling of stress-induced crystallization and crystallinity-controlled solidification is limited range of spinning speeds, and multiple solutions of the dynamic equations of spinning. The range of admissible spinning speeds and multiple (amorphous and crystalline) solutions is strongly affected by the hot-tube temperature. It is predicted that zone heating, with temperatures above glass transition (hot tube), results in considerable increase of amorphous orientation factor for moderate take-up speeds. In the high speed spinning range, the orientation effects saturate and does not exceed the values predicted for high-speed room-temperature spinning. Application of the hot tube is also predicted to reduce considerably take-up stress. Available experimental data on amorphous orientation in PET fibers spun by hot-tube technique are in qualitative agreement with the model predictions.

Development of molecular orientation and stress in biaxially deformed polymers. I. Affine deformation in a solid state

Abstract Biaxial deformation of freely jointed chain molecules in a solid state is considered. Biaxial molecular orientation is directly related to the applied deformation. Segmental orientation and stress are considered using non-Gaussian inverse Langevin statistics of the chain end-to-end vectors. Pade approximation and series expansion of the inverse Langevin function are used. Global orientation of chain segments and stress are analyzed for affine biaxial deformation of non-Gaussian chains. Molecular anisotropy is characterized by the norm of the average orientation tensor, ‖ D ‖, and the global anisotropy of the stress tensor is characterized by the norm ‖ P ‖. Non-linear behavior of the orientation vs. stress characteristics for isochoric uniaxial deformation, calendering (λ1=1) and biaxial deformation are discussed.

The theory of non-linear molecular orientation and stress in polymer fluids

Non-linear stress, and orientation characteristics for polymer fluids (melts, solutions) composed of chain macromolecules of finite length have been derived. Freelyjointed chains with inverse Langevin statistics have been assumed, and their behaviour in potential hydrodynamic fields analyzed. Numerical calculations have been performed for uniaxial extensional flow in a wide range of flow rates (and stresses). In the range of small stresses, orientation is a linear function of stress. At higher stresses, orientation factor levels off, asymptotically approaching unity.Flow orientation characteristics significantly differ from those derived from affine deformation of polymer networks. This difference is a natural consequence of constraints imposed by network junctions on chain deformation.

Cross sections for molecular aggregation with positional and orientational restrictions

Effects of molecular symmetry and intermolecular interactions on the cross section for association–dissociation reactions are discussed. The cross section controls thermodynamic equilibrium, kinetics of aggregation, and sensitivity to external orienting fields. Example calculations indicate variation of the cross section for aggregation by several orders of magnitude and substantial changes in crystallization temperature of asymmetric rigid molecules.

Thermodynamically controlled crystal orientation in stressed polymers: 1. Effects of strain energy of crystals embedded in an uncrosslinked amorphous matrix and hydrodynamic potential

Abstract Thermodynamics is one of the factors which control the orientation distribution of polymer crystals. The present paper deals with crystal orientation in uncrosslinked polymer systems, in which small, isolated crystals are embedded in a viscous matrix. With transient effects neglected, and in the absence of the production of new crystals, orientation is controlled by the orientation-dependent free energy of an anisotropic crystal, F( ), and a hydrodynamic potential of the velocity field, Φ ( ). Example distributions for uniaxially stressed polyethylene are discussed. It has been shown that different mechanisms control crystal orientation depending on the stress difference Δϱ = ϱ 33 − ϱ 11 applied, and the crystal shape factor, o. At low stresses, Δϱ and high assymetry factors, o, crystal orientation is practically controlled by the hydrodynamic potential. At high stresses and/or low asymmetry ratios it is the strain energy of anisotropic crystals, F( ) , which is responsible for orientation distribution. In the intermediate range both mechanisms have to be considered.

Molecular orientation and stress in biaxially deformed polymers. II. Steady potential flow

Abstract The development of biaxial segmental orientation and stress in a flexible-chain polymer fluid subjected to steady biaxial extensional flow is analyzed. Closed-formula model based on the Pade approximation of the inverse Langevin function in the non-Gaussian distribution of the chain end-to-end vectors is considered. The approach is free from the limitations related to finite chain extensibility and slow convergence of the series expansion formulations at higher chain deformations. Segmental orientation is characterized by the average orientation tensor, related axial orientation factors and global orientation anisotropy. Orientational behavior and corresponding stresses in the biaxial elongational potential flow are discussed in a wide range of elongation rates. Orientation characteristics calculated for the biaxial flow deformation are much higher than those predicted for the affine biaxial stretch deformation in polymer solids.