by Thamarasee Jeewandara , Physorg Blended homopolymer thin films
Macroscopic experimental dog bone–shaped specimen (pictured) loaded in TUTTUT for uniaxial extension
Molecular-level simulations depict chains sliding past one another to form openings in the film as it is strained
Blended systems are composed of long (dark blue) and short (light blue) chains where most load-bearing entanglements (orange dots), if not all, are among the long polymer chains
Photo credit: C
Bukowski, University of Massachusetts Amherst
Credit: Science Advances, 10
1126/sciadv
abg9763 The role of entanglements can determine the mechanical properties of glass polymer blends
In a new report now published on Science Advances, Cynthia Bukowski and a research team in polymer science and biomolecular engineering at the University of Massachusetts and the University of Pennsylvania, U
S
, developed a combined method of experiments and simulations to quantify the role of entanglements on polymer glasses
The team conducted uniaxial extension experiments on 100 nm thin films with a bidispersive mixture of polystyrene, for comparison with molecular dynamics simulations of a coarse-grained model of polymer glasses
The bidispersive blends allowed systematic tuning of the entanglement density present in both systems and the scientists measured the film strength experimentally and described the simulated film toughness using a model to account for load-bearing entanglements
Breaking glassy polymers Glassy polymers are important for a range of technologies from additive manufacturing to clean water filtration membranes
The stiffness and processability of the materials make them attractive for many applications for researchers to determine their lifetime and performance limits
The entanglements between polymer molecules in the glassy state play a significant role to determine strength
Glassy polymer materials are excessively brittle below a critical number of entanglements per molecule and can break at diminishing levels of stress
Polymer materials can dissipate energy above a critical entanglement density to enhance their strength and toughness
These processes are unique and give rise to wide-ranging technologies
Enlargements are important for strength but require volatile and costly solvents or excessive temperatures during processing
In this work, Bukowski et al
combined new experimental strategies with molecular dynamics simulations to reveal how all entanglements did not equally contribute to a polymer glass
The team developed and validated a scaling theory to describe the number of strengthening entanglements per polymer chain to provide a framework to maximize strength with minimal entanglements in a polymer glass
Stress-strain behavior of polymer blends
(A) Representative uniaxial deformation stress-strain response for each blend tested experimentally on TUTTUT
ϕ represents the volume fraction of long chains in the system
The top graph is blends with 13
7 kDa as the short chain diluent and the bottom with 59
5 kDa
(B) Uniaxial deformation stress-strain responses of N = 250 (⟨Z⟩ = 15
9) blended with N = 30 (top) and 60 (bottom) at a temperature of T/Tg = 0
71
⟨Z⟩ is 1
8 and 3
6 for each short chain, respectively
Low-strain response is included in the inset of each section
(C) The elastic modulus (E) for each experimentally measured blend
(D) The average maximum stress for each blend measured experimentally
Error bars are 1 SD of five to nine averaged films
Open symbols represent blends that were attempted but too brittle to manipulate in TUTTUT and stretch uniaxially
(E) The elastic modulus for each simulated blend
(F) The toughness value for each simulated blend
Credit: Science Advances, 10
1126/sciadv
abg9763 The interplay of forces The mechanical properties of the polymer glasses depended on the interplay of van der Waals forces and entanglements
Plastic deformation is often associated with shear deformation zones that precede crack growth
Entanglements play a significant role in shear deformation zones and their stability or resistance to form a crack is a function of entanglement density as well as temperature and strain rate
These deformations can be tracked experimentally with optical and transmission electron microscopy
Bukowski et al
overcame existing limits of the study by using a recently developed experimental method to measure the stress-strain response of ultrathin polymer films
Molecular dynamics (MD) simulations have provided valuable insights to the process of entanglements in polymer melts and glasses, where the simulations agreed very well with the experiments
In addition to the simulations, the scaling theories also contributed to define the role of entanglements in the mechanical properties of polymer glasses
The combined approach of experimental and MD approaches allowed the team to examine the macroscopic perspective of experimental films and the molecular view of local dynamics simulations, to understand polymer strength
Data plotted against the Mikos and Peppas model
Normalized experimental maximum stress, σMax/σ∞ (A), and normalized simulated toughness, Γ/Γ∞ (B), as a function of entanglements, ⟨Z⟩
Here, ⟨Z⟩ is the Mn obtained from gel permeation chromatography of each blend divided by the Me of polystyrene (18
1 kDa)
For simulations, ⟨Z⟩ is average chain length N for each blend divided by Ne (16)
Maximum stress and toughness are normalized by the maximum stress of polystyrene chains Mn = 1
928 MDa and the toughness of chains N = 250, respectively
Credit: Science Advances, 10
1126/sciadv
abg9763 Mechanical properties of polymer blends and counting entanglements Bukowski et al
regulated the number of entanglements in the system by mixing monodisperse polymers of the same chemical structure
This method allowed them to sample a wide range of entanglements per chain
Both experiments and simulations provided qualitative insights to understand how the entanglement network contributed to the mechanical properties of glassy polymer materials
During the experiments, when the concentration of the longest chains decreased, the maximum stress and failure strain also began to decrease
The team noted different failure mechanisms by varying the degree of dilution and dictated the elastic modulus of the glassy state of the polymer by local intersegment interactions dominated by van der Waals forces
As Bukowski et al
integrated long chain polymers, the toughness measured in the simulations revealed a monotonic increase
Force distribution on entanglements
(A) Simulation snapshots at various levels of strain
A single chain, highlighted in red in the top row, is shown in the row below at each of the indicated strains
The single chains are colored to show varying levels of average bond stress on each primitive path (PP) along the chain
(B) The average bond stress as a function of strain on each PP in a blend of N = 250 and 30 at ϕ = 0
50
The schematic next to the graph outlines where each mentioned PP is located
PPs are color coded to match the plotted points
Entanglements occur at each orange dot
Hollow orange dots represent non–load-bearing entanglements at the end of chains
(C and D) Solid symbols represent calculations that consider all entanglements in the blend systems, and hollow symbols only consider load-bearing entanglements
(C) The density of entanglements, ρ, in each simulated system as a function of dilution, calculated as the total number of entanglements divided by the system volume
Note that there is a solid blue star at point (0,0)
(D) The average number of entanglements per chain, ⟨Z⟩, as a function of dilution
The dashed line corresponds to N = 60, and the dotted line corresponds to N = 30 as the diluent chain
Credit: Science Advances, 10
1126/sciadv
abg9763 Experiments and simulations The experimental maximum stress and simulated toughness values appeared to scale differently for different experimental models
The findings matched well with a physics model introduced by Mikos and Peppas
According to the simulations, not all entanglements in a system were load bearing
Later, the team noted the simulated strains to be much larger than those observed experimentally
To precisely account for changes in load-bearing entanglements, the team considered the average number of entanglements per chain
Bukowski et al
next developed a model and successfully applied the method to both experiments and simulations to study the relationship between entanglements and the maximum stress or toughness
When considering the load-bearing fraction of entanglements in the system, the experiments and simulations scaled similarly at the molecular level
By comparing the experiment and simulations of thin glassy polymer films thereafter, the data indicated a quantitative link between the maximum stress and toughness
Strength and toughness of materials as a function of load-bearing entanglements
Normalization is carried out by the undiluted maximum stress of polystyrene at Mn = 1
928 MDa and the undiluted toughness of N = 250 for the experimental and simulation results, respectively
Experimental data are represented by solid symbols, and simulation data are represented by hollow symbols
The lines represent the modified Mikos and Peppas model calculated for both the experiment (solid line) and simulation (dashed line) including only load-bearing entanglements
Each shaded region represents 1 SD of error in each line
The schematic on the right shows a system of entanglements with long chains (dark blue) and short chains (light blue)
Solid orange dots represent load-bearing entanglements
Orange hollow dots represent entanglements that cannot bear load because they contain a first PP
Green hollow dots represent non–load-bearing entanglements that are made with a short species of chain
Ends of long chains are highlighted in red
Credit: Science Advances, 10
1126/sciadv
abg9763 Outlook In this way, Cynthia Bukowski and colleagues used a combination of experiments and simulations to show the importance of using load-bearing entanglements to improve the toughness of materials
To accomplish this, they systematically tuned the entanglement density using bidisperse and chemically identical blends
When they added a short chain diluent to the blends, the tensile tests of the polymer showed a decreased maximum stress
Similarly, the molecular dynamics of solutions also showed a decrease in the toughness with added diluent
The combined experiments and simulations provided an enhanced understanding of polymers and a novel framework to tune the mechanical properties based on their molecular makeup
The work has many practical implications beyond providing fundamental insights into the origin and toughness in polymer glasses, including additive manufacturing strategies
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