Open-access Rheo-optical characterization of polymer chain uncoil and disentanglement in shear flow

Abstract

Rheo-optical studies allow the monitoring of rheological properties by indirect measurements of optical properties. For pure polymeric fluids, flow birefringence can be used to quantify the molecular orientation level by the application of shear strain rates. In this work, flow birefringence experiments were carried out with a pure polystyrene under different shear rates, shear cycles, and temperature conditions, in a polarized light optical microscope under controlled shear. The level of orientation and its correlation with the dynamics of uncoil/recoil and disentanglement were analyzed. The expected increase in the orientation level as a function of the increase in the shear rate due to the chain uncoiling was confirmed. Following, the chain orientation level reduces over time, associated with chain disentanglement and its subsequent recoiling. Disentanglement behaves irreversibly, while uncoiling and recoiling are reversible processes. A model is proposed to represent these dynamics.

Keywords:
disentanglement; polymer chain orientation; flow birefringence; rheo-optical measurement; polystyrene

1. Introduction

Rheo-optics techniques jointly address the rheology of polymers and their optical properties, such as birefringence. Flow birefringence can be used to quantify chain orientation level, due to the anisotropy of polymer chains[1-5]. A relevant concept in polymer rheology is the dynamics of uncoiling/recoiling and disentanglement/reentanglement of chains during their orientation process under melt flow.

The first theories of molecular chain motions were developed by Rouse[6], Bueche[7], Zimm[8] and Peticolas[9] in the 1950s and 1960s, in which polymer chains are considered as a succession of equal submolecules, represented by a sequence of spheres connected by springs. This model is useful for polymer solutions with low concentration. For polymer flow in the melt state, the understanding of the entanglement concept is fundamental. This concept emerged in the 1930s[10] and has been an important topic ever since[11-18]. The de Gennes’[19] chain reptation model is one of the most adopted theories to correlate properties of polymeric fluids in the presence of entanglements. It assumes that the chain motion is restricted by entanglements, as if the chain was inside a tube, and the reptation mechanism allows the molecule to slip inside it.

There are several studies to develop methods to disentangle polymer chains, such as during the polymerization, under polymer solution, etc. Disentangling chains in the molten or softened state was first proposed by Ibar[20,21]. The development of grades with prior disentanglement treatment is interesting to achieve lower viscosities during processing and, thefore, better processability, especially for polymers with high molecular weight. It is known that high levels of disentanglemnt are possible to be obtained when applying shear rates for a long period, just as it is expected that the disentanglement rate decreases over time[20-23]. In 2018, Li and Matsuba[24] proposed that the higher level of entanglement is responsible for preserving molecular orientation in shear flow. Wattanabe et al.[25] and Noirez et al.[26] studies challenged the assumptions that flow shear thinning of entangled polymer chains is due to significant orientation of the segments between the entanglements under shear flow. In their studies, both concluded that the chains remained largely undeformed under steady-state shear flow conditions for which extensive shear thinning was present. These results also represent a challenge for the reptation model. Wang et al.[27] experimentally demonstrated that the chain retraction step of the tube model does not occur, which led to the conclusion that the current understanding of the flow and relaxation of entangled polymers based on the theoretical reptation model is limited.

The reentanglement effect is a much slower process. Roy and Roland[28] studied the process of reentangling polyisobutylene, it was more than an order of magnitude slower than expectations based on the linear relaxation time of the fully entangled material. Ibar[29] concluded that the recovery time of untangled PMMA treated by the so-called shear strengthening machine was 17 million times greater than its longest relaxation time (5 ms). Fu et al.[30] showed that higher shear rates induce higher levels of disentanglement, resulting in up to 93.7% lower viscosity, greater molar mass between entanglements, and longer reentanglement time.

The objective of this work is, by using flow birefringence optical measurement of a polystyrene (PS) during shearing flow, correlate it with the level of orientation of the chains, and propose a model for the dynamics of uncoiling, disentanglement and recoiling. The experiments are carried out in a shearing parallel plate system (CSS450) with temperature and shear rate control, fitted in a polarized light optical microscope, and a homemade optical detector for quantifying the cross polarized transmitted light intensity through the soften polymer to get the flow birefringence. The measurements were done under different shearing conditions, varing its maximum value, sequence and time of disentanglement shearing treatment, and temperature. With that, a model have been proposed for molecular chain disentanglement and recoiling.

2. Materials and Methods

Pure GPPS N 2560 from Innova was used. It is a pure atactic homopolystyrene with high molar mass (Mw260.000g/mol, Mn 140.000g/mol). Polystyrene shows negative birefringence, high polarizability and intrinsic birefringence for completely oriented chains of Δn0.1=1,000×104[31].

The rheo-optical characterization of the polymer was carried out using a Leica DMRXP polarized light optical microscope (MOLP), with attachment of an Cambridge Shearing System CSS450 accessory from Linkam Scientific Instruments and an optical detector made of a light dependent resistor LDR, placed in the microscope optical tube, partially covered to reduce the sample measuring area and so unwanted changes in the shear rate. This sensor is set after the analyzer polarization filter. The cross polarized transmitted light intensity signal I, measured by the LDR, is normalized (0IN1) using Equation 1, converted into Optical Path Difference (OPD) using Equation 2, and finally converted into flow birefringence (Δn) using Equation 3, knowing the sample film thickness.

I N = I I C I P I C (1)
I N = 1 2 1 cos 2 π O P D / λ cosh ( β 2 π O P D / λ ) (2)
Δ n = O P D t (3)

being IC the transmitted light intensity with polarizers set crossed (minimum intensity), IP the transmitted light intensity with polarizers set parallels (maximum intensity), λ=550nm the average wavelength of the white light, β the damping coefficient, and t=400 μm the sample thickness. The data is collected at a frequency of 5 Hz by a software written in LabVIEW 8.6, developed inhouse[32], and edited as needed to better suit these measurements.

The normalized cross polarized transmitted light intensity IN, measured by the optical detector was calibrated using a Berek compensator B containing a tilting magnesium fluoride MgF2 plate[33], measurements taken every 0.1º tilting degree, in both directions (named black and red scales), up to 4 light interference orders. The two curves were shifted to minimize the uncertainty of the compensator screw drum at OPD=Zero nm. By tilting the crystal an angle i, a phase difference δ (nm) is introduced in the optical path, following Equation 4[33]:

δ = t n o 1 sin 2 i n e 2 1 sin 2 i n o 2 (4)

being, t the crystal thickness (1.525×106nm), no=1.37859 and ne=1.39043 the ordinary and extraordinary refractive indices of the MgF2 crystal respectively, given an intrinsic birefringence of Δn=neno=118.4×104, measured by a monochromatic light with λ=546.1nm (e line).

Two different shearing procedures were applied, using 0.27 g of the material in melt state. (1) Shearing scan: Shear the sample from 0.01s1γ˙180s1 (reaching the maximum shear rate of the equipment for the fixed sample thickness of 400 μm, set by the gap between the quartz plates), in a profile of 20 steps distributed on a log scale values, holding 60 seconds at each one to collect the signal and average it to get IN. Various isothermal scans in the range of 180 T230 were tested. (2) Disentanglement shearing treatment: The sample, starting at rest, is rapidly sheared time1min with increasing shear rates up to γ˙=180s1 at 180 . The rise in shear rate is done quickly to minimize the unwanted pre-disentanglement of the chains. Then the sample is kept at a constant γ˙=180s1 for a preset shearing time (2, 5 and 60 min, as indicated). The data is collected at 5 Hz and displayed.

2.1 Increase in the molecular chain orientation level during shearing scan

The sample was subjected to the shearing scan profile at 180 °C. This temperature was set under preliminary measurements at which a balance of high flow birefringence values and good melt flow stability is obtained for the PS used. The normalized intensity IN, optical path difference OPD and flow birefringence Δn as a function of the shear rate γ˙ were calculated and displayed.

2.2 Reduction in the molecular chain orientation level during disentanglement shearing treatment

The sample at 180 °C is rapidly sheared from rest up to γ˙=180 s1. The polymer chains are disentangled by keeping the shear rate γ˙=180 s1 constant during 60 min. The curve of IN as a function of time is obtained to monitor the changes in the level of chain orientation, revealed as flow birefringence.

2.3 Reduction in the molecular chain orientation level during sequential runs of disentanglement shearing treatments

The effect of cumulative chain disentanglement levels in the material was quantified by cycling up to three sequential shearing scans at 180 °C. Each cycle is done by the following steps: 1) fast shear rate increase up to γ˙=180 s1; 2) 60 min disentanglement shearing treatment at constant shear rate of γ˙=180 s1; 3) fast shear rate reduction down to rest; and 4) 1 min rest. After resting, a new cycle is applied. During each complete cycle, IN, OPD and Δn as a function of γ˙ were calculated.

2.4 Molecular chain orientation level after sequential disentanglement shearing treatment runs

Four shearing scans followed by disentanglement shearing treatment were applied sequentially at 180 °C. The sequence was performed twice, for 2 and 5 min disentanglement shearing treatment times. Flow birefringence Δn as a function of shear rate γ˙ was calculated and displayed.

2.5 Molecular chain orientation level as a function of melt shearing temperature

Shear scans were applied for melt temperatures of 180, 190, 200, 210, 220 and 230 °C, either without applying previous disentanglement or after applying 60 min shearing disentanglement treatment, by using different samples. IN, OPD and Δn as a function of γ˙ were calculated. By fitting straight lines in the initial portion of the Δn vs γ˙ curves (1×104<Δn<4×104), their extrapolation to Δn=0 leads to the polymer average relaxation time λr as Equation 5.

λ r = 1 / γ ˙ Δ n 0 (5)

3. Results and Discussions

3.1 Optical detector calibration

Figure 1 shows the normalized cross polarized transmitted light intensity IN experimental points (black and red) measured by inserting the Berek compensator B in the light path and the best fitting theoretical curve (continuous green line), which by applying Equation 2, one gets coefficient β=0.12. The experimental data follows closely the expected theoretical curve, confirming the efficiency of the optical arrangement for quantitative measurements.

Figure 1
Calibration curve of normalized cross polarized transmitted light intensity IN as a function of optical path difference OPD, done by using a Berek compensator B.

3.2 Increase in the molecular chain orientation level during shearing scan

Figure 2 shows the curve of normalized cross-polarized transmitted light intensity IN as a function of shear rate γ˙ applied to the PS sample at 180 °C. The maximum IN value (0.95) is obtained at γ˙ = 8.8 s1, revealing the half of the first light interference order, i.e. an OPD = 275 nm. The end of the first order occurs approximately at 20 to 30 s1 for a IN close to 0.30 to 0.40, for an OPD = 550 nm. Half of the second order occurs at approximately 60 to 100 s1 and IN close to 0.80 to 0.90, for an OPD = 825 nm. At the maximum measurable shear rate delivered by the equipment γ˙=180 s1, the IN obtained is 0.58, lying between the middle and the end of the second order.

Figure 2
The normalized cross-polarized transmitted light intensity IN of polystyrene as a function of shear rate γ˙ at 180 °C.

The curve of birefringence ∆n as a function of shear rate γ˙ applied is shown in Figure 3. It establishes a more direct correlation with the orientation level. At shear rates high enough to overcome the effect of molecular chain relaxation, the chains uncoil themselves and orient along the direction of stress, resulting in -Δn > 0. Increasing further γ˙ leads to higher -Δn values, that is, higher molecular chain orientation levels, as expected. The results are similar to those got by Vasconcelos’[34], which were obtained for the same material and equipment, but at 210 °C.

Figure 3
Flow birefringence -Δn of polystyrene as a function of shear rate γ˙ at 180 °C. Δn reaches 23.3×104 at 180 s1.

3.3 Reduction in the molecular chain orientation level during disentanglement shearing treatment

IN as a function of disentanglement shearing treatment time at 180 s1 and 180 °C for up to 60 minutes is presented in Figure 4. In the same figure, there is a miniature representation of Figure 2 at the top right, to support the interpretation. The initial IN value is 0.64 , given a Δn=23.3×104 , i.e. ~43 times lower than the intrinsic birefringence of polystyrene (Δn=1,000×104) and ~75 times lower than the calcite crystal (Δn=1,720*104). The value is close to that obtained in Figure 2 at 180 s1, as expected. During the 60 min treatment, IN reduces towards values that would be obtained at lower γ˙ values, which can be easily interpreted by following the curve presented in the miniature insert. Therefore, the molecular chain orientation level reduces over time. At the end of the experiment, IN = 0.57, setting its OPD in between the half and end of the first light interference order and, reaching a Δn=3.7×104, ~84% lower than the initial value.

Figure 4
Changes in the normalized cross-polarized transmitted light intensity IN as a function of time during polystyrene disentanglement shearing treatment at 180 °C and 180 s1. After 60 min the flow birefringence of polystyrene reduces to Δn=3.7×104.

Maintaining a constant shear rate γ˙, the reptation motion allows entangled chain segments that are closer to their chain ends to disentangle more easily. Gradually lower levels of entanglement are expected, as observed by Buchdahl[13] and Ibar[20,21]. The disentanglement leads to an increase in the conformational freedom of the chain, facilitating its partial recoiling, resulting in a gradual reduction in the orientation level over time. This dependence of the orientation on the entanglement level was also observed by Li and Matsuba[24]. The lower orientation level of the chain segments reduces the ability of the chains to disentangle, as they are in a more relaxed state. Therefore, the molecular chain disentanglement rate decreases over time, leading eventually to its stabilization.

3.4 Reduction in the molecular chain orientation level during sequential runs of disentanglement shearing treatments

The effect of multiple disentanglement shearing treatments can be followed by measuring IN as a function of time for three consecutive applied runs at 180 °C, which is shown in Figure 5. The increasing orientation with increasing shear rate γ˙ is seen up to the initial 15 minutes of shearing, when γ˙=180s1 is reached. After that, the shear rate is kept constant at this value and the disentanglement shearing treatment takes place. At its start, IN=0.65, given a flow birefringence of Δn=23.2×104. The disentanglement rate reduces over time and after 60 min of disentanglement shearing treatment, the OPD have passed by the first half of the second order and the end of the first order, reaching a IN=0.57 i.e. a flow birefringence of Δn=3.8×104. After the first disentanglement shearing treatment, the shear rate is reduced down to zero, while the molecular chain orientation also reduces by chain recoiling. By applying a second run, the IN value starts at IN=0.40 and then follows the previous behavior. During this second run, the molecular chain orientation level reduces at a much lower rate. Upon applying a third run, the whole IN curve shape is kept very similar to that of the second run, revealing that the reduction in molecular chain orientation during disentanglement shearing treatment had already occurred mainly in the first run. After that, the molecular chain entanglement level remains constant, independent of increasing further the time of treatment, at the same shear level. The disentanglement rate is high at the beginning of the first run and stabilizes by the end of the treatment. Thus the final molecular chain relaxation is the combination of a reversible behavior due to the molecular chain uncoiling/recoiling effect, and an irreversible contribution of the molecular chain disentanglement effect.

Figure 5
Changes in the normalized cross-polarized transmitted light intensity IN as a function of time t for three sequentially applied runs of disentanglement shearing treatment of 60 min at 180 °C and 180 s1.

3.5 Molecular chain orientation level after sequential disentanglement shearing treatment runs

The flow birefringence -Δn as a function of shear rates γ˙ after the sample had been subjected to consecutive disentanglement shearing treatment runs at 180 s1 and 180 for 2 min and 5 min treatments are presented in Figure 6. Run 0 represents the first curve obtained while the shear rate profile is applied for the first time. The subsequent runs count the number of disentanglement shearing treatments that the sample was subjected to. In general, at low γ˙ levels, -Δn reduces slightly, suggesting a irrelevant reduction in the chains average relaxation time λR. At high γ˙, the shift is much more significant, indicating that the level of molecular chain orientation is more affected by disentanglement when the polymer melt is at high γ˙s. The flow birefringence curve shown during Run 1, which is done after 2 min of shearing treatment time, shifts to the right, indicating a reduction in the accumulative level of chain orientation. In the subsequent runs, there is an irreversible accumulation of disentanglement, which is also shown during runs after 5 min shearing treatment times. However, after 10 min cumulative treatment time (i.e. from Run 2 onwards), the curves overlap, indicating the stabilization of the orientation level reached by the partially disentangled chains.

Figure 6
Flow birefringence -Δn as a function of shear rate γ˙ at 180 °C for runs after disentanglement shearing treatment times of (a) 2 min and (b) 5 min.

The values of -Δn at 180 °C and 180 s1 as a function of the accumulated disentanglement shearing treatment time after each run shown in Figure 6 were consolidated in Figure 7. There is a fast reduction of -Δn up to approximately 10 min of accumulated treatment time, subsequently leading to stability. The level of entanglement reduces with shearing treatment time, leveling after ~10 min of cumulative treatment, due to the reduction in the capacity of more disentagled chains to orient themselves.

Figure 7
Flow birefringence values -Δn at 180 °C and 180 s1 for consecutive runs with 2 and 5 min disentanglement shearing treatment time as a function of the cumulative treatment time.

3.6 Molecular chain orientation level as a function of melt shearing temperature

Figure 8 presents -Δn as a function of γ˙ at different melt shearing temperatures without (a); and after 60 min disentanglement shearing treatment at 180 s1 and 180 °C (b). In both (a) and (b) cases, ∆n decreases with increasing temperature, due to reducing λR as the chains present greater mobility and, therefore, the γ˙ necessary for the orientation to overcome the relaxation effect is greater. There is a shift to the right of (b) in relation to (a), which demonstrates the disentanglement effect. ∆n are smaller after the treatment and the same previous conclusions are valid at different temperatures.

Figure 8
Flow birefringence -Δn as a function of shear rate γ˙ at different temperatures (a) without; and (b) after applying 60 min disentanglement shearing treatment at 180 °C and 180 s1.

The PS chains average relaxation times λR at varying melt shearing temperatures from 180 °C up to 230 °C were obtained by extrapolation the best fitting curve in the flow birefringence -∆n to zero, and calculated following Equation 5. Figure 9 shows λR as a function of 1/T. There is a reduction of λR with increasing temperature (reducing 1/T) analogous to the results obtained by Bernardo[35]. After disentanglement shearing treatment, λR is shifted to lower values, this effect being more pronounced at lower temperatures.

Figure 9
PS chain average relaxation times λR as a function of the reciprocal of the melt flow temperature 1/T, without and after applying 60 min of disentanglement shearing treatment at 180 °C.

3.7 Disentanglement and recoiling model

The rheo-optical data obtained for shear melt flow of polystyrene can be represented in a model of the disentanglement and recoiling dynamics of the polymer chain in Figure 10. Polymer chains in the molten or softened state at rest are in a coiled and entangled equilibrium conformation. When subjected to shear rates high enough to overcome molecular relaxation, they uncoil and orient along the direction of stress. Simultaneously, there is a reduction in the entanglement level through reptation mechanisms, in agreement with recent model proposals[36-39]. An increase in the applied shear rate leads to an increase in the level of chain uncoiling and orientation. Maintaining a constant shear rate, the reptation allows entangled segments that are closer to chain ends to disentangle easier. Gradually lower levels of entanglements lead to an increase in the conformational freedom degree of the chain segment, facilitating its partial recoiling, with a gradual reduction in the level of orientation over time, analogous to the conclusions of Watanabe et al.[25] and Noirez et al.[26]. The lower orientation level reduces the ability of the chains to disentangle, as they are in a more relaxed state. Therefore, the disentanglement rate decreases over time, leading to stabilization. The disentanglement rate increases when applying higher shear rates, as the reptation speed and orientation will be greater, in agreement with Fu et al.[30] and Liu et al.[40]. Higher temperatures reduce the disentanglement rate, as the orientation levels will be lower, due to the shorter average relaxation time. With a rapid suppression of shear, the chains recoil quickly and reversibly. However, reentanglement occurs much more slowly, as also observed by Roy and Roland[28], Ibar[29], and Litvinov et al.[41], and an irreversible effect can be assumed, within the time scale of this work.

Figure 10
Dynamics of polymer chain disentanglement, recoiling and the following reduction in the molecular chain orientation level during the shearing polymer flow.

4. Conclusions

Rheo-optical measurements quantifying polymer melt flow birefringence under controlled melt shearing conditions were carried out for a pure polystyrene of high molar mass with a Cambridge Shearing System CSS450 fitted in a polarized light optical microscope, and an optical detector to monitor the cross-polarized transmitted light intensity. With this rheo-optical setting, the level of the polymer chain orientation and its correlation with the dynamics of uncoiling/recoiling and disentanglement of the chains were studied. The expected increase in the average polymer chain orientation level with the increase in the applied shear rate due to chain uncoiling was confirmed. Under continuous shearing the average chain orientation level reduces over time, associated with the chain disentanglement, happening mainly by loosen the chain entanglements closest to the chain ends, leaving the terminal chain segments free to recoil. Under shearing, the disentanglement is irreversible, assuming that reentanglement is insignificant, while uncoiling and recoiling are reversible, depending on the level of the applied shear rate and flow temperature. A molecular model is proposed to represent these dynamics.

6. Acknowledgements

This study was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for a PQ scholarship 310441/2020-0 to S.V. Canevarolo, and the Programa de Pós-Graduação em Ciência e Engenharia de Materiais (PPG-CEM) of Federal University of São Carlos (UFSCar).

  • How to cite:
    Tambolim, M., & Canevarolo, S. V. (2024). Rheo-optical characterization of polymer chain uncoil and disentanglement in shear flow. Polímeros: Ciência e Tecnologia, 34(4), e20240038. https://doi.org/10.1590/0104-1428.202400636

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Publication Dates

  • Publication in this collection
    29 Nov 2024
  • Date of issue
    2024

History

  • Received
    14 June 2024
  • Reviewed
    25 Aug 2024
  • Accepted
    12 Sept 2024
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