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White RP, Lipson JEG. Why Volume and Dynamics Decouple in Nanocomposite Matrices: Space that Cannot Be Accessed is Not Free. Phys Rev Lett 2023; 131:018101. [PMID: 37478446 DOI: 10.1103/physrevlett.131.018101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2023] [Accepted: 05/31/2023] [Indexed: 07/23/2023]
Abstract
Polymer nanocomposites have important material applications and are an ongoing focus of many molecular level investigations, however, puzzling experimental results exist. For example, specific volumes for some polymer nanocomposite matrices are 2% to 4% higher than for the neat polymer; in a pure polymer melt this would correspond to a pressure change of 40 to 100 MPa, and a decrease in isothermal segmental relaxation times of 3 to 5 orders of magnitude. However, the nanocomposite segmental dynamics do not show any speed up. We can explain this apparent uncoupling of dynamics from specific volume, and the key is to consider the system expansivity, i.e., the temperature dependence of the volumetric data, together with the concept of limiting volume at close liquid packing. Using pressure, volume, temperature data as a path to both, we are able to predict the effect of nanoadditives on the accessible, i.e., free, space in the material, which is critical for facilitating molecular rearrangements in dense systems. Our analysis explains why an increase in specific volume in a material may not always lead to faster segmental dynamics.
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Affiliation(s)
- Ronald P White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
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Qiu J, Chen X, Le AN, López-Barrón CR, Rohde BJ, White RP, Lipson JEG, Krishnamoorti R, Robertson ML. Thermodynamic Interactions in Polydiene/Polyolefin Blends Containing Diverse Polydiene and Polyolefin Units. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c01866] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/09/2023]
Affiliation(s)
- Jialin Qiu
- William A. Brookshire Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas 77204, United States
| | - Xuejian Chen
- William A. Brookshire Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas 77204, United States
| | - Amy N. Le
- William A. Brookshire Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas 77204, United States
| | | | - Brian J. Rohde
- ExxonMobil Technology and Engineering Company, Baytown, Texas 77520, United States
| | - Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Ramanan Krishnamoorti
- William A. Brookshire Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas 77204, United States
| | - Megan L. Robertson
- William A. Brookshire Department of Chemical and Biomolecular Engineering, University of Houston, Houston, Texas 77204, United States
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White RP, Buculei D, Beale AMJM, Goovaerts I, Keddie JL, Lipson JEG. Spectroscopic ellipsometry as a route to thermodynamic characterization. Soft Matter 2022; 18:6660-6673. [PMID: 36004577 DOI: 10.1039/d2sm00959e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Strategies for synthesizing molecularly designed materials are expanding, but methods for their thermodynamic characterization are not. This shortfall presents a challenge to the goal of connecting local molecular structure with material properties and response. Fundamental thermodynamic quantities, including the thermal expansion coefficient, α, can serve as powerful inputs to models, yielding insight and predictive power for phenomena ranging from miscibility to dynamic relaxation. However, the usual routes for thermodynamic characterization often require a significant sample size (e.g. one gram), or challenging experimental set-ups (e.g. mercury as a confining fluid), or both. Here, we apply spectroscopic ellipsometry, which is an optical technique for thin film analysis, to obtain thermodynamic data. We clarify issues in the scientific literature concerning the connection between ellipsometric and volumetric thermal expansion coefficients for substances in both the glass and melt states. We analyze temperature-dependent data derived using both ellipsometry and macro-scale dilatometric techniques for ten different polymers. We find superb correlation between the α values obtained via the two techniques, after considering the effects of mechanical confinement by the substrate for a glassy thin film. We show how the ellipsometric α can serve as input to the locally correlated lattice theory to yield predictions for the percent free volume in each polymer as a function of temperature. We find that the ellipsometric α at the glass transition temperature, Tg, is not only material dependent, but it is linearly correlated with Tg itself. Spectroscopic ellipsometry, which requires only very small quantities of sample and is straightforward to perform, will significantly expand the range of systems for which thermodynamic properties can be characterized. It will thus advance our ability to use theory and modeling to predict the miscibility and dynamic relaxation of new materials. As such, ellipsometry will be able to underpin materials synthesis and property design.
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Affiliation(s)
- Ronald P White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire, 03755, USA.
| | - Dragos Buculei
- Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK.
| | - Alexia M J M Beale
- Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK.
| | - Ilias Goovaerts
- Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK.
| | - Joseph L Keddie
- Department of Physics, University of Surrey, Guildford, Surrey, GU2 7XH, UK.
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire, 03755, USA.
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Song Z, White RP, Lipson JEG, Napolitano S. Experimental and Modeling Comparison of the Dynamics of Capped and Freestanding Poly(2-chlorostyrene) Films. ACS Macro Lett 2022; 11:91-95. [PMID: 35574787 DOI: 10.1021/acsmacrolett.1c00674] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Proximity to a nonrepulsive wall is commonly considered to cause slower dynamics, which should lead to greater relaxation times for capped thin polymer films than for bulk melts. To the contrary, here we demonstrate that Al-capped films of poly(2-chlorostyrene) exhibit enhanced dynamics with respect to the bulk, similar to analogous freestanding films. To quantitatively resolve the impact of interfaces on whole film dynamics, we analyzed the experimental data via the Cooperative Free Volume rate model. We found that the interfacial region adjacent to a cap contains an excess of free volume (relative to the bulk) about half of that proximate to a free surface. Employing a useful analogy between confinement and pressure effects, we estimated that the effect of capping an 18 nm freestanding film would be equivalent to applying a pressure increase of 19 MPa.
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Affiliation(s)
- Zijian Song
- Polymer and Soft Matter Dynamics, Experimental Soft Matter and Thermal Physics (EST), Université libre de Bruxelles (ULB), 1050 Brussels, Belgium
| | - Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Simone Napolitano
- Polymer and Soft Matter Dynamics, Experimental Soft Matter and Thermal Physics (EST), Université libre de Bruxelles (ULB), 1050 Brussels, Belgium
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DeFelice J, Lipson JEG. Correction: The influence of additives on polymer matrix mobility and the glass transition. Soft Matter 2021; 17:9985. [PMID: 34709284 DOI: 10.1039/d1sm90195h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Correction for 'The influence of additives on polymer matrix mobility and the glass transition' by Jeffrey DeFelice et al., Soft Matter, 2021, 17, 376-387. DOI: 10.1039/D0SM01634A.
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Affiliation(s)
- Jeffrey DeFelice
- Department of Chemistry, Dartmouth College, Hanover, NH 03755, USA.
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, NH 03755, USA.
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White RP, Lipson JEG. The dynamics of freestanding films: predictions for poly(2-chlorostyrene) based on bulk pressure dependence and thoughtful sample averaging. Soft Matter 2021; 17:9755-9764. [PMID: 34647951 DOI: 10.1039/d1sm01175h] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
In this paper we model the segmental relaxation in poly(2-chlorostyrene) 18 nm freestanding films, using only data on bulk samples to characterize the system, and predict film relaxation times (τ) as a function of temperature that are in semi-quantitative agreement with film data. The ability to translate bulk characterization into film predictions is a direct result of our previous work connecting the effects of free surfaces in films with those of changing pressure in the bulk. Our approach combines the Locally Correlated Lattice (LCL) equation of state for prediction of free volume values (Vfree) at any given density (ρ), which are then used in the Cooperative Free Volume (CFV) rate model to predict τ(T, Vfree). A key feature of this work is that we calculate the locally averaged density profile as a function of distance from the surface, ρav(z), using the CFV-predicted lengthscale, Lcoop(z), over which rearranging molecular segments cooperate. As we have shown in the past, ρav(z) is significantly broader than the localized profile, ρ(z), which translates into a relaxation profile, τ(z), exhibiting a breadth that mirrors experimental and simulated results. In addition, we discuss the importance of averaging the log of position dependent relaxation times across a film sample (〈log τ(z)〉), as opposed to averaging the relaxation times, themselves, in order to best approximate a whole sample-averaged value that can be directly compared to experiment.
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Affiliation(s)
- Ronald P White
- Department of Chemistry, Dartmouth College, Hanover, NH 03755, USA.
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, NH 03755, USA.
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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White RP, Lipson JEG. A Simple New Way To Account for Free Volume in Glassy Dynamics: Model-Free Estimation of the Close-Packed Volume from PVT Data. J Phys Chem B 2021; 125:4221-4231. [PMID: 33861608 DOI: 10.1021/acs.jpcb.1c01620] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
In this article we focus on the important role of well-defined free volume (Vfree) in dictating the structural relaxation times, τ, of glass-forming liquids and polymer melts. Our definition of Vfree = V - Vhc, where V is the total system volume, means the use of Vfree depends on determination of Vhc, the system's volume in the limiting closely packed state. Rejecting the historically compromised use of Vfree as a dynamics-dependent fitting function, we have successfully applied a clear thermodynamics-based route to Vhc using the locally correlated lattice (LCL) model equation of state (EOS). However, in this work we go further and show that Vhc can be defined without the use of an equation of state by direct linear extrapolation of a V(T) high-pressure isobar down to zero temperature (T). The results from this route, tested on a dozen experimental systems, yield ln τ vs 1/Vfree isotherms that are linear with T-dependent slopes, consistent with the general ln τ ∼ f(T) × (1/Vfree) form of behavior we have previously described. This functional form also results by implementing a simple mechanistic explanation via the cooperative free volume (CFV) rate model, which assumes that dynamic relaxation is both thermally activated and that it requires molecular segmental cooperativity. With the degree of the latter, and thus the activation energy, being determined by the availability of free volume, the new route we demonstrate here for determination of Vfree expands the potential for understanding and predicting local dynamic relaxation in glass-forming materials.
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Affiliation(s)
- Ronald P White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Abstract
In the region near an interface, the microscopic properties of a glass forming liquid may be perturbed from their equilibrium bulk values. In this work, we probe how the interfacial effects of additive particles dispersed in a matrix can influence the local mobility of the material and its glass transition temperature, Tg. Experimental measurements and simulation results indicate that additives, such as nanoparticles, gas molecules, and oligomers, can shift the mobility and Tg of a surrounding polymer matrix (even for relatively small concentrations of additive; e.g., 5-10% by volume) relative to the pure bulk matrix, thus leading to Tg enhancement or suppression. Additives thus provide a potential route for modifying the properties of a polymer material without significantly changing its chemical composition. Here we apply the Limited Mobility (LM) model to simulate a matrix containing additive species. We show that both additive concentration, as well as the strength of its very local influence on the surrounding matrix material, will determine whether the Tg of the system is raised or lowered, relative to the pure matrix. We demonstrate that incorporation of additives into the simple LM simulation method, which has successfully described the behavior of bulk and thin film glassy solids, leads to direct connections with available experimental and simulation results for a broad range of polymer/additive systems.
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Affiliation(s)
- Jeffrey DeFelice
- Department of Chemistry, Dartmouth College, Hanover, NH 03755, USA.
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, NH 03755, USA.
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White RP, Aoki Y, Higgins JS, Keddie JL, Lipson JEG, Cabral JT. Thermodynamics of Model PαMSAN/dPMMA Blend: A Combined Study by SANS, Ellipsometry, and Locally Correlated Lattice (LCL) Theory. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c00706] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Yutaka Aoki
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K
| | - Julia S. Higgins
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K
| | - Joseph L. Keddie
- Department of Physics, University of Surrey, Guildford, Surrey GU2 7XH, U.K
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - João T. Cabral
- Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K
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White RP, Lipson JEG. To Understand Film Dynamics Look to the Bulk. Phys Rev Lett 2020; 125:058002. [PMID: 32794834 DOI: 10.1103/physrevlett.125.058002] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2020] [Revised: 06/27/2020] [Accepted: 07/08/2020] [Indexed: 06/11/2023]
Abstract
We show that shifts in dynamics of confined systems relative to that of the bulk material originate in the properties of bulk alone, and exhibit the same form of behavior as when different bulk isobars are compared. For bulk material, pressure-dependent structural relaxation times follow τ(T,V)∝exp[f(T)×g(V)]. When two states (isobars) of the material, "1" and "2", are compared at the same temperature this leads to a form τ_{2}∝τ_{1}^{c}, where c=g[V_{2}(T)]/g[V_{1}(T)]. Using equation of state analysis and two models for P-dependent dynamics, we show that c is approximately T independent, and that it can be very simply expressed in terms of either the (free) volume above the close packed state (V_{free}) or the activation energy for cooperative motion. The effect of changing state through a shift in pressure (P_{1} to P_{2}) is thus mechanistically traceable to cooperativity changing with density, through V_{free}. The connection with confined dynamics follows when 1 and 2 are taken as bulk and film at ambient P, differing in density only due to the film surface. The general form for τ(T,V) also illuminates why samples in different states (film vs bulk, high P vs low) trend toward the same relaxation behavior at high T.
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Affiliation(s)
- Ronald P White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
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Panagopoulou A, Rodríguez-Tinoco C, White RP, Lipson JEG, Napolitano S. Substrate Roughness Speeds Up Segmental Dynamics of Thin Polymer Films. Phys Rev Lett 2020; 124:027802. [PMID: 32004047 DOI: 10.1103/physrevlett.124.027802] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2019] [Indexed: 06/10/2023]
Abstract
We show that the segmental mobility of thin films of poly(4-chlorostyrene) prepared under nonequilibrium conditions gets enhanced in the proximity of rough substrates. This trend is in contrast to existing treatments of roughness which conclude it is a source of slower dynamics, and to measurements of thin films of poly(2-vinylpiridine), whose dynamics is roughness invariant. Our experimental evidence indicates the faster interfacial dynamics originate from a reduction in interfacial density, due to the noncomplete filling of substrate asperities. Importantly, our results agree with the same scaling that describes the density dependence of bulk materials, correlating segmental mobility to a term exponential in the specific volume, and with empirical relations linking an increase in glass transition temperature to larger interfacial energy.
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Affiliation(s)
- Anna Panagopoulou
- Laboratory of Polymer and Soft Matter Dynamics, Experimental Soft Matter and Thermal Physics (EST), Faculté des Sciences, Université libre de Bruxelles (ULB), Boulevard du Triomphe, Bruxelles 1050, Belgium
| | - Cristian Rodríguez-Tinoco
- Laboratory of Polymer and Soft Matter Dynamics, Experimental Soft Matter and Thermal Physics (EST), Faculté des Sciences, Université libre de Bruxelles (ULB), Boulevard du Triomphe, Bruxelles 1050, Belgium
| | - Ronald P White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Simone Napolitano
- Laboratory of Polymer and Soft Matter Dynamics, Experimental Soft Matter and Thermal Physics (EST), Faculté des Sciences, Université libre de Bruxelles (ULB), Boulevard du Triomphe, Bruxelles 1050, Belgium
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White RP, Lipson JEG. COOPERATIVE FREE VOLUME RATE MODEL APPLIED TO THE PRESSURE-DEPENDENT SEGMENTAL DYNAMICS OF NATURAL RUBBER AND POLYUREA. Rubber Chemistry and Technology 2019. [DOI: 10.5254/rct.19.80394] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
ABSTRACT
We apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts, focusing on two new applications of the model, to natural rubber and to polyurea. In CFV, segmental relaxation times, τ, are analyzed as a function of temperature (T) and free volume (Vfree), where the latter provides an insightful route to expressing dynamics relative to using the system's overall total volume (V). Vfree is defined as the difference between the total volume and the volume at close packing and is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice equation-of-state analysis of characteristic thermodynamic data. The new results for natural rubber and polyurea are discussed in the context of results on a set of polymeric and small-molecule glass formers that had previously been modeled with CFV. We also discuss the results in the context of recent connections that we have made with the density-scaling approach.
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, NH 03755
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White RP, Lipson JEG. The cooperative free volume rate model for segmental dynamics: Application to glass-forming liquids and connections with the density scaling approach ⋆. Eur Phys J E Soft Matter 2019; 42:100. [PMID: 31396721 DOI: 10.1140/epje/i2019-11862-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Accepted: 06/28/2019] [Indexed: 06/10/2023]
Abstract
In this paper, we apply the cooperative free volume (CFV) rate model for pressure-dependent dynamics of glass-forming liquids and polymer melts. We analyze segmental relaxation times, [Formula: see text] , as a function of temperature (T and free volume ( [Formula: see text] , and make substantive comparisons with the density scaling approach. [Formula: see text] , the difference between the total volume (V and the volume at close-packing, is predicted independently of the dynamics for any temperature and pressure using the locally correlated lattice (LCL) equation-of-state (EOS) analysis of characteristic thermodynamic data. We discuss the underlying physical motivation in the CFV and density scaling models, and show that their key, respective, material parameters are connected, where the CFV b parameter and the density scaling [Formula: see text] parameter each characterize the relative sensitivity of dynamics to changes in T , vs. changes in V . We find [Formula: see text] , where [Formula: see text] is the value predicted by the LCL EOS at the ambient [Formula: see text] . In comparing the predictive power of the two models we highlight the CFV advantage in yielding a universal linear collapse of relaxation data using a minimal set of parameters, compared to the same parameter space yielding a changing functional form in the density scaling approach. Further, we demonstrate that in the low data limit, where there is not enough data to characterize the density scaling model, the CFV model may still be successfully applied, and we even use it to predict the correct [Formula: see text] parameter.
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Affiliation(s)
- Ronald P White
- Department of Chemistry, Dartmouth College, 03755, Hanover, NH, USA
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, 03755, Hanover, NH, USA.
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Abstract
Data continue to accrue indicating that experimental techniques may differ in their sensitivity to mobility and glassiness. In this work the Limited Mobility (LM) kinetic model is used to show that two metrics for tracking sample mobility yield quantitatively different results for the glass transition and mobile layer thickness in systems where free surfaces are present. Both LM metrics track the fraction of material that embodies mobile free volume; in one it is relative to that portion of the sample containing any kind (mobile and dormant) of free volume, and in the other it is relative to the overall sample. Without any kind of optimization, use of the latter metric leads to semi-quantitative agreement with experimental film results, both for the mobile layer thickness and the dependence of sample glass transition temperature on film thickness. Connecting the LM predictions with experiment also produces a semi-quantitative mapping between LM model length and temperature scales, and those of real systems.
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Affiliation(s)
- Jeffrey DeFelice
- Department of Chemistry, Dartmouth College, Hanover, NH 03755, USA.
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Debot A, White RP, Lipson JEG, Napolitano S. Experimental Test of the Cooperative Free Volume Rate Model under 1D Confinement: The Interplay of Free Volume, Temperature, and Polymer Film Thickness in Driving Segmental Mobility. ACS Macro Lett 2019; 8:41-45. [PMID: 35619409 DOI: 10.1021/acsmacrolett.8b00844] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
We show that the Cooperative Free Volume (CFV) rate model, successful at modeling pressure-dependent dynamics, can be employed to describe the temperature and thickness dependence of the segmental time of polymers confined in thin films (1D confinement). The CFV model is based on an activation free energy that increases with the number of cooperating segments, which is determined by the system's free volume. Here, we apply the CFV model to new experimental results on the segmental relaxation of 1D confined poly(4-chlorostyrene), P4ClS, and find remarkable agreement over the whole temperature and thickness ranges investigated. This work further validates the robustness of the CFV model, which relates the effects of confinement on dynamics to pressure changes in the bulk, and supports the idea that confinement effects originate from local perturbations in density.
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Affiliation(s)
- Alice Debot
- Polymer and Soft Matter Dynamics, Faculté des Sciences, Université libre de Bruxelles (ULB), Brussels, Belgium
| | - Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Simone Napolitano
- Polymer and Soft Matter Dynamics, Faculté des Sciences, Université libre de Bruxelles (ULB), Brussels, Belgium
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White RP, Lipson JEG. Connecting Pressure-Dependent Dynamics to Dynamics under Confinement: The Cooperative Free Volume Model Applied to Poly(4-chlorostyrene) Bulk and Thin Films. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01392] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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White RP, Lipson JEG. Pressure-Dependent Dynamics of Polymer Melts from Arrhenius to Non-Arrhenius: The Cooperative Free Volume Rate Equation Tested against Simulation Data. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b00591] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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White RP, Lipson JEG. Explaining the T,V-dependent dynamics of glass forming liquids: The cooperative free volume model tested against new simulation results. J Chem Phys 2018; 147:184503. [PMID: 29141440 DOI: 10.1063/1.5001714] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this article, we derive a rate model, the "cooperative free volume" (CFV) model, to explain relaxation dynamics in terms of a system's free volume, Vfree, and its temperature, T, over widely varied pressure dependent conditions. In the CFV model, the rate a molecule moves a distance on the order of its own size is dependent on the cooperation of surrounding molecules to open up enough free space. To test CFV, we have generated extensive T,V dependent simulation data for structural relaxation times, τ, on a Kob and Andersen type Lennard-Jones (KA-LJ) fluid. The Vfree = V - Vhc values are obtained by estimating the limiting hard core volume, Vhc, through analysis of the KA-LJ PVT data. We provide the first simulation evidence that shows ln τ to be linearly proportional to 1/Vfree on isotherms, with T-dependent slopes, thus confirming our recent analysis of experimental systems. The linear relationship exhibited by the simulation data is further shown to occur at temperatures both above and below the transition to Arrhenius behavior. We also show that the gas kinetic T-dependent contribution is important in simulation results and that there can be a significant entropic contribution from lingering molecular hard-cores at high T. A key result is that non-Arrhenius relaxation behavior is always exhibited on isobars of the KA-LJ fluid, even at high T. The CFV model predicts all of this behavior over a surprisingly wide range of the KA-LJ T,V space, fitting it with just a single set of three parameters. The CFV approach leads to a framework wherein the number of cooperating particles, and thus, the process free energy of activation, is inversely proportional to Vfree, and this is the foundation for the form of the model's volume contribution, a form that we find to hold for all systems and at all temperatures.
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Affiliation(s)
- Ronald P White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
| | - Jane E G Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
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Abstract
In this article we show that inverse free volume is a natural variable for analyzing relaxation data on glass-forming liquids, and that systems obey the general form, log(τ/τref) = (1/Vfree) × f(T), where f(T) is a function of temperature. We demonstrate for eight glass-forming liquids that when experimental relaxation times (log τ), captured over a broad pressure-volume-temperature (PVT) space, are plotted as a function of inverse free volume (1/Vfree), a fan-like set of straight line isotherms with T-dependent slopes ensues. The free volume is predicted independently of the dynamic results for each state point using PVT data and the Locally Correlated Lattice (LCL) equation of state. Taking f(T) ∝ 1/Tb, we show that, for each of the systems studied, only the single, system-dependent parameter, b, is required to collapse the fan of linear isotherms into a straight line. We conclude that log τ is a function of the combined variable, 1/(VfreeTb), and because it is linear, it allows us to write an explicit analytic expression for log τ that covers a broad PVT space.
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Affiliation(s)
- Jeffrey DeFelice
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Tito NB, Milner ST, Lipson JEG. Enhanced diffusion and mobile fronts in a simple lattice model of glass-forming liquids. Soft Matter 2015; 11:7792-7801. [PMID: 26313541 DOI: 10.1039/c5sm01701g] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The diffusion of mobility in bulk and thin film fluids near their glass transition is examined with a kinetic lattice model, and compared to recent experiments on bulk liquids and vapor-deposited thin film glasses. The "limited mobility" (LM) lattice model exhibits dynamic heterogeneity of mobility when the fluid is near its kinetic arrest transition; a finite-parameter second-order critical point in the LM model bearing strong resemblance to the glass transition in real fluids. The spatial heterogeneity of mobility near kinetic arrest leads to dynamics that violate the Stokes-Einstein relation. To make connections with experiment, LM model simulations of self-diffusion constants in fluids near kinetic arrest are compared to those in two organic glass-formers. In addition, simulations of mobility in films that have been temperature-jumped above kinetic arrest (starting from an arrested state) are carried out. The films develop a "front" of mobility at their free surface that progresses into the film interior at a constant rate, thereby mobilising the entire film to fluidity. The velocity of the front scales with the self-diffusion constant for analogous bulk systems-an observation consistent with experiments on vapor-deposited molecular thin films.
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Affiliation(s)
- Nicholas B Tito
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Christopher C. Price
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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White RP, Lipson JEG. Free Volume in the Melt and How It Correlates with Experimental Glass Transition Temperatures: Results for a Large Set of Polymers. ACS Macro Lett 2015; 4:588-592. [PMID: 35596302 DOI: 10.1021/acsmacrolett.5b00217] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
There is a continuing, strong interest in making connections between the polymeric glass transition (Tg) and bulk properties. In this Letter we apply the Locally Correlated Lattice (LCL) model to study a group of 51 polymers and demonstrate two broad correlations. In the first, we show that the theoretically determined polymeric free volume in the melt, all at a single common T, P (425 K, 1 atm), correlates noticeably with the experimentally determined Tg values, and that this trend sharpens considerably when families of polymers are examined. Further, we show a strikingly linear correlation between the experimental Tg and the LCL model calculation for the percent free volume expected at the polymeric Tg. We suggest that this trend has a predictive value, acting as a boundary of T-dependent minimum-required free volume separating the melt and glassy regimes. Our theoretical estimates of free volume values at a polymer's Tg range between 4 and 16%, and their evident temperature dependence indicates an important role for temperature in glassification.
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Affiliation(s)
- Jeffrey DeFelice
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United
States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United
States
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United
States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United
States
| | - Julia S. Higgins
- Department of Chemical Engineering and Chemical Technology, Imperial College, London, SW7 2AZ, U.K
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Affiliation(s)
- Nicholas B. Tito
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Scott T. Milner
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United
States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United
States
| | - Julia S. Higgins
- Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7 2AZ, U.K
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White RP, Lipson JEG. Thermodynamic treatment of polymer thin-film glasses. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 84:041801. [PMID: 22181159 DOI: 10.1103/physreve.84.041801] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2011] [Indexed: 05/31/2023]
Abstract
We propose a new, simple, thermodynamically based model in order to study the effect of film thickness on the glass transition of a polymer. The model equation of state incorporates the effect of a free surface by accounting for missing interactions, and is parametrized using experimental data for bulk samples, leaving no freely adjustable parameters. To this end we focus on connecting model agreement in the bulk limit with two key physical properties: pressure-volume-temperature data and surface tension data. For the case of polystyrene we show that accounting for these effects, alone, yields results in surprisingly good agreement with experiment for the shift in glass transition in going from bulk to freestanding film. Insight from this simple model indicates that only a small increase in the specific volume of a thin film (compared to bulk) may drive the shift in the glass transition temperature. Herein we focus on a molecular weight independent regime. Looking ahead we consider the possible contributions of chain confinement to the thermodynamic properties of the film.
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Affiliation(s)
- Ronald P White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
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Affiliation(s)
- Nicholas B. Tito
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Scott T. Milner
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Affiliation(s)
- Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
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Affiliation(s)
- Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, United States
| | - Scott T. Milner
- Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
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Affiliation(s)
- Ronald P. White
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755
| | - Jane E. G. Lipson
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755
| | - Julia S. Higgins
- Department of Chemical Engineering and Chemical Technology, Imperial College, London SW7 2AZ, U.K
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Abstract
Polymeric mixtures are important materials, but the control and understanding of mixing behaviour poses problems. The original Flory-Huggins theoretical approach, using a lattice model to compute the statistical thermodynamics, provides the basic understanding of the thermodynamic processes involved but is deficient in describing most real systems, and has little or no predictive capability. We have developed an approach using a lattice integral equation theory, and in this paper we demonstrate that this not only describes well the literature data on polymer mixtures but allows new insights into the behaviour of polymers and their mixtures. The characteristic parameters obtained by fitting the data have been successfully shown to be transferable from one dataset to another, to be able to correctly predict behaviour outside the experimental range of the original data and to allow meaningful comparisons to be made between different polymer mixtures.
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Affiliation(s)
- Julia S Higgins
- Department of Chemical Engineering and Chemical Technology, Imperial College, University of London, , London SW7 2BY, UK.
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White RP, Lipson JEG. Chain fluids: Contrasts of theoretical and simulation approaches, and comparison with experimental alkane properties. J Chem Phys 2009; 131:074109. [DOI: 10.1063/1.3200925] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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White RP, Lipson JEG. Fluid mixtures: Contrasts of theoretical and simulation approaches, and comparison with experimental alkane properties. J Chem Phys 2009; 131:074110. [DOI: 10.1063/1.3200926] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gitsas A, Floudas G, White RP, Lipson JEG. Effect of Pressure on the Phase Behavior and Segmental Dynamics in Blends of Polystyrene with Poly(methylphenyl siloxane). Macromolecules 2009. [DOI: 10.1021/ma900831h] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Colby RH, Lipson JEG. Modeling the Segmental Relaxation Time Distribution of Miscible Polymer Blends: Polyisoprene/Poly(vinylethylene). Macromolecules 2005. [DOI: 10.1021/ma0500741] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ralph H. Colby
- Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, and Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755
| | - Jane E. G. Lipson
- Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania 16802, and Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755
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Abstract
We incorporate density dependence into continuum Born-Green-Yvon (BGY) theory through calculation of the end-to-end intramolecular correlation function. Whereas in previous studies we had only performed this calculation for the case of an isolated (zero-density) square-well chain of m segments (3</=m</=7), here we consider this single chain to have been placed in a square-well monomeric fluid of variable density. We find that the results obtained by this more sophisticated approach are in good agreement with the predictions of both other theories and simulation concerning the structural properties of short chains. Using a homologous series of n-alkanes as a test case, we also conclude that BGY theory, with the current modifications, is capable of describing fluid properties for heptane (n-C7) through nonadecane (n-C19).
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Affiliation(s)
- J A Porter
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
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Affiliation(s)
- Michael Tambasco
- Department of Chemistry, Burke Laboratories, Dartmouth College, Hanover, New Hampshire 03755
| | - Jane E. G. Lipson
- Department of Chemistry, Burke Laboratories, Dartmouth College, Hanover, New Hampshire 03755
| | - Julia S. Higgins
- Department of Chemical Engineering and Chemical Technology, Imperial College, University of London
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Abstract
Using a homologous series of n-alkanes as a model system, we compare the predictions of a lattice Born-Green-Yvon (BGY) theory and a continuum BGY theory with experimental results. We find that both theories are capable of describing the fluid properties and critical points of alkanes ranging from heptamers (n-C7) to nonadecamers (n-C19). We probe the connection between the lattice and continuum BGY models and extend our discussion to include a sampling of other lattice and continuum treatments.
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Affiliation(s)
- J A Porter
- Department of Chemistry, Dartmouth College, Hanover, New Hampshire 03755, USA
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Lipson JEG, Tambasco M, Willets KA, Higgins JS. Correlations between the Effects of Pressure and Molecular Weight on Polymer Blend Miscibility. Macromolecules 2003. [DOI: 10.1021/ma0257301] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jane E. G. Lipson
- Department of Chemistry, Burke Laboratories, Dartmouth College, Hanover, New Hampshire 03755
| | - Michael Tambasco
- Department of Chemistry, Burke Laboratories, Dartmouth College, Hanover, New Hampshire 03755
| | - Katherine A. Willets
- Department of Chemistry, Burke Laboratories, Dartmouth College, Hanover, New Hampshire 03755
| | - Julia S. Higgins
- Department of Chemical Engineering and Chemical Technology, Imperial College, London, SW7 2BY, U.K
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